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P
er
tu
r
b
an
d
o
b
s
er
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e
(
P
&
O)
a
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
tec
h
n
iq
u
e
(
MPPT
)
h
as
b
ee
n
u
s
ed
[
1
3
]
.
Fig
u
r
e
2
.
P
V
ce
ll e
q
u
iv
alen
t c
i
r
cu
its
3.
B
O
O
ST
CO
NVER
T
E
R
T
h
e
MM
L
I
to
p
o
lo
g
y
u
s
es
th
e
P
V
tied
b
o
o
s
t
co
n
v
er
ter
.
T
h
e
o
u
tp
u
t
o
f
th
e
P
V
p
an
els
is
g
i
v
en
to
th
e
b
o
o
s
t
co
n
v
er
ter
.
T
h
e
b
o
o
s
t
co
n
v
er
ter
co
n
s
is
t
s
o
f
a
s
m
o
o
th
i
n
g
i
n
d
u
c
to
r
,
MO
SF
E
T
(
an
d
d
io
d
e
(
.
T
h
e
d
esig
n
o
f
an
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n
d
u
c
to
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an
d
th
e
D
C
b
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s
ca
p
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ito
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p
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s
a
n
i
m
p
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ta
n
t
r
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le
an
d
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ig
h
er
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r
eq
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en
c
y
is
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h
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s
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n
f
o
r
d
esig
n
i
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g
t
h
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n
d
u
cto
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,
i
n
w
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v
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m
e
o
f
t
h
e
in
d
u
c
to
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ca
n
b
e
r
ed
u
ce
d
.
F
u
r
th
er
m
o
r
e,
in
ter
f
er
e
n
ce
ca
n
b
e
m
in
i
m
ized
t
h
r
o
u
g
h
t
h
e
s
e
lectio
n
o
f
h
i
g
h
er
f
r
eq
u
en
c
y
r
an
g
e
s
.
T
h
e
DC
-
DC
b
o
o
s
t
c
o
n
v
er
ter
is
u
s
ed
to
in
cr
ea
s
e
r
eq
u
ir
ed
t
h
e
v
o
lta
g
e
lev
el.
T
h
is
i
s
d
o
n
e
b
y
c
h
an
g
i
n
g
th
e
d
u
t
y
c
y
cle
o
f
a
MO
S
F
E
T
.
T
h
e
eq
u
iv
alen
t
cir
cu
it o
f
t
h
e
b
o
o
s
t c
o
n
v
er
ter
i
s
s
h
o
w
n
i
n
th
e
F
ig
u
r
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2088
-
8
694
Tr
a
n
s
ien
t a
n
d
S
tea
d
y
S
ta
te
A
n
a
lysi
s
o
f Mo
d
ified
Th
r
ee
P
h
a
s
e
Mu
ltil
ev
el
I
n
ve
r
ter fo
r
.
.
.
.
(
M.
V
en
ka
tesa
n
)
33
Fig
u
r
e
3
.
E
q
u
iv
ale
n
t c
ir
cu
it o
f
b
o
o
s
t c
o
n
v
er
ter
4.
M
O
DIFIE
D
T
H
RE
E
P
H
AS
E
M
UL
T
I
L
E
V
E
L
I
NV
E
RT
E
R
T
O
P
O
L
O
G
Y
T
h
e
p
o
w
er
c
ir
cu
it
d
iag
r
a
m
o
f
P
I
/
F
L
C
b
ased
th
r
ee
p
h
ase
f
i
v
e
le
v
el
P
V
i
n
v
er
ter
alo
n
g
w
it
h
th
e
co
m
m
o
n
DC
s
o
u
r
ce
s
y
s
te
m
is
p
r
esen
ted
in
[
1
4
]
an
d
it is
illu
s
tr
ated
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
P
o
w
er
cir
cu
it o
f
M
ML
I
f
ed
f
r
o
m
s
i
n
g
le
DC
s
o
u
r
c
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
201
7
:
31
–
39
34
I
t
co
m
p
r
is
es
o
f
a
P
I
/FLC
b
a
s
ed
co
n
tr
o
l
s
y
s
te
m
;
P
V
tied
b
o
o
s
t
co
n
v
er
ter
,
t
h
r
ee
p
h
ase
f
i
v
e
le
v
el
in
v
er
ter
,
a
s
i
n
g
le
DC
in
p
u
t,
t
h
r
ee
p
h
a
s
e
tr
a
n
s
f
o
r
m
er
.
T
h
e
DC
b
u
s
f
o
r
m
ed
b
y
co
n
n
ec
t
in
g
t
w
o
ca
p
ac
ito
r
s
i
s
co
n
n
ec
ted
i
n
s
er
ies
a
n
d
b
o
th
ar
e
eq
u
al
v
a
lu
e
s
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
ea
c
h
s
in
g
le
in
v
er
te
r
m
ai
n
l
y
d
ep
en
d
s
o
n
th
e
v
o
lta
g
e
r
an
g
e
o
f
D
C
b
u
s
.
Usu
al
l
y
,
D
C
b
u
s
v
o
ltag
e
s
h
o
u
ld
b
e
f
ix
ed
h
i
g
h
er
t
h
a
n
th
e
o
u
tp
u
t
v
o
lta
g
e
o
f
t
h
e
in
v
er
ter
.
E
ac
h
s
i
n
g
le
p
h
ase
in
v
er
ter
is
co
n
s
tr
u
cted
w
it
h
n
o
r
m
al
H
-
B
r
id
g
e
in
v
er
ter
al
o
n
g
w
it
h
au
x
iliar
y
in
v
er
ter
.
Her
e
a
u
x
iliar
y
co
n
s
i
s
ts
o
f
s
in
g
le
p
o
w
er
s
w
itc
h
al
o
n
g
w
i
th
f
o
u
r
p
o
w
er
d
io
d
e
[
1
0
]
.
T
h
e
au
x
iliar
y
in
v
er
ter
a
n
d
o
n
e
le
g
o
f
H
-
b
r
id
g
e
i
n
v
er
ter
o
p
er
ate
at
ca
r
r
ie
r
f
r
eq
u
e
n
c
y
r
an
g
e
a
n
d
an
o
t
h
e
r
leg
o
f
H
-
B
r
id
g
e
in
v
er
ter
is
o
p
er
atin
g
f
u
n
d
a
m
en
tal
f
r
eq
u
e
n
cies.
E
ac
h
s
i
n
g
le
p
h
ase
in
v
er
ter
ca
n
g
en
er
at
e
f
i
v
e
le
v
el
o
u
tp
u
t
v
o
ltag
e
f
r
o
m
co
m
m
o
n
D
C
b
u
s
.
T
h
e
o
u
tp
u
ts
o
f
th
e
in
v
er
t
er
s
ar
e
g
i
v
en
to
t
h
e
1
:1
t
h
r
ee
p
h
ase
1
2
ter
m
i
n
al
tr
an
s
f
o
r
m
er
s
a
n
d
th
e
n
f
ed
to
t
h
e
th
r
ee
p
h
a
s
e
g
r
id
.
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
T
h
e
p
r
esen
ted
P
I
/FL
C
b
ased
MM
L
I
f
o
r
P
V
ap
p
licatio
n
w
it
h
s
i
n
g
le
DC
i
n
p
u
t
is
s
i
m
u
lated
i
n
a
MA
T
L
A
B
/
S
i
m
u
li
n
k
.
T
h
e
M
ML
I
i
s
co
n
tr
o
lled
b
y
u
s
i
n
g
P
I
/FL
C
a
n
d
p
er
f
o
r
m
an
ce
s
o
f
MM
L
I
h
a
v
e
b
ee
n
ev
alu
a
ted
th
r
o
u
g
h
F
L
C
.
Mo
r
eo
v
er
,
p
er
f
o
r
m
a
n
ce
s
o
f
F
L
C
a
r
e
v
alid
ated
an
d
co
m
p
ar
ed
w
i
th
co
n
v
en
tio
n
al
P
I
co
n
tr
o
ller
.
T
h
e
MM
L
I
is
d
esi
g
n
ed
w
i
th
4
0
0
V
r
m
s
a
n
d
5
.
5
A
r
m
s
.
T
h
e
s
o
lar
p
an
el
is
u
s
ed
as
a
i
n
p
u
t
s
o
u
r
ce
an
d
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
w
it
h
P
&
O
alg
o
r
it
h
m
i
s
u
s
e
d
to
tr
ac
k
th
e
MPP
f
r
o
m
P
V
p
an
el
at
d
if
f
er
en
t
cli
m
atic
co
n
d
tio
n
d
s
.
I
n
o
d
er
to
g
en
er
ate
P
W
M
p
u
ls
es
to
th
e
in
v
e
r
ter
s
w
itc
h
es,
b
y
co
m
p
ar
in
g
to
r
ef
er
en
ce
s
ig
n
al
s
(
SVP
W
M)
an
d
h
ig
h
f
r
q
u
e
n
c
y
ca
r
r
ier
s
i
g
n
al
[
1
5
]
is
s
h
o
w
n
i
n
t
h
e
Fi
g
u
r
e
5
.
T
h
e
p
er
f
o
r
m
a
n
ce
s
o
f
MM
L
I
is
e
x
a
m
in
ed
t
h
r
o
u
g
h
b
o
th
tr
an
s
ie
n
t a
n
d
s
tead
y
s
tate
c
o
n
d
itio
n
s
.
Fig
u
r
e
5
.
P
W
M
P
u
ls
e
Gen
er
at
io
n
s
5
.
1
.
Sta
dy
s
t
a
t
e
a
nly
s
is
T
h
e
s
tead
y
-
s
tate
an
al
y
s
is
o
f
t
h
e
p
r
o
p
o
s
ed
MM
L
I
is
d
is
cu
s
s
e
d
in
th
is
s
ec
tio
n
.
T
h
e
ap
p
r
o
p
r
iate
cu
r
r
en
t
co
n
tr
o
ller
an
d
co
n
tr
o
l
lo
o
p
is
n
ee
d
ed
f
o
r
p
r
o
p
er
s
y
n
c
h
r
o
n
iz
atio
n
o
f
th
r
ee
p
h
ase
g
r
id
.
I
n
cu
r
r
en
t
co
n
tr
o
l
lo
o
p
th
e
r
e
f
er
en
ce
(
)
is
tr
ac
k
ed
f
r
o
m
MP
P
T
alg
o
r
ith
m
a
n
d
(
)
is
s
et
to
ze
r
o
.
T
h
e
ac
tu
al
(
)
an
d
(
)
is
g
en
er
ated
f
r
o
m
th
e
in
v
er
ter
cu
r
r
en
t
u
s
in
g
p
ar
k
tr
an
s
f
o
r
m
a
tio
n
.
No
w
th
e
ac
tu
al
an
d
r
ef
er
en
ce
d
ir
ec
t
c
u
r
r
en
ts
(
)
an
d
(
)
is
co
m
p
ar
ed
an
d
th
e
er
r
o
r
o
f
d
ir
ec
t
cu
r
r
en
t
(
)
is
g
iv
e
n
as
i
n
p
u
t
to
th
e
P
I
/F
L
C
.
Si
m
i
lar
l
y
th
e
q
u
ad
r
atu
r
e
cu
r
r
en
t e
r
r
o
r
is
g
i
v
e
n
to
th
e
i
n
p
u
t o
f
P
I
/FLC
.
T
h
e
d
ir
ec
t a
n
d
q
u
ad
r
atu
r
e
cu
r
r
en
t e
r
r
o
r
s
(
)
ar
e
s
h
o
wn
in
Fi
g
u
r
e
6
.
Fig
u
r
e
6
.
Dir
ec
t
an
d
q
u
ad
r
atu
r
e
cu
r
r
en
t e
r
r
o
r
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2088
-
8
694
Tr
a
n
s
ien
t a
n
d
S
tea
d
y
S
ta
te
A
n
a
lysi
s
o
f Mo
d
ified
Th
r
ee
P
h
a
s
e
Mu
ltil
ev
el
I
n
ve
r
ter fo
r
.
.
.
.
(
M.
V
en
ka
tesa
n
)
35
T
h
e
co
n
tr
o
lled
er
r
o
r
o
f
P
I
/FL
C
is
s
h
o
w
n
i
n
F
ig
u
r
e
7
.
A
s
s
h
o
w
n
f
r
o
m
t
h
e
f
i
g
u
r
e
t
h
e
FLC
b
ased
tu
n
i
n
g
ap
p
r
o
ch
is
ef
f
ec
tiv
e
l
y
o
p
ti
m
ize
t
h
e
er
r
o
r
w
it
h
m
i
n
i
m
al
s
tead
y
s
tate
er
r
o
r
co
m
p
ar
ed
w
i
th
P
I
co
n
tr
o
ller
b
ased
tu
n
i
n
g
ap
p
r
o
ac
h
.
T
h
e
co
n
tr
o
lled
o
u
tp
u
t
(
)
i.e
.
t
w
o
p
h
ase
q
u
an
tit
y
is
s
u
p
er
i
m
p
o
s
ed
w
it
h
g
r
id
co
m
p
o
n
e
n
ts
a
n
d
f
u
r
t
h
er
tr
an
s
f
o
r
m
ed
i
n
to
t
h
r
ee
p
h
a
s
e
q
u
an
tit
y
u
s
i
n
g
i
n
v
er
s
e
p
ar
k
tr
an
s
f
o
r
m
atio
n
.
A
s
s
h
o
w
n
f
r
o
m
th
e
Fi
g
u
r
e
8
th
e
DC
b
u
s
v
o
lta
g
e
o
f
MM
L
I
i
s
ti
g
h
t
l
y
r
e
g
u
lated
u
s
in
g
F
L
C
w
it
h
m
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er
s
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n
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ed
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r
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t
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n
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d
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n
s
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o
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ith
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ased
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e
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ase
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e
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ated
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r
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m
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e
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r
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n
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ed
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ical
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er
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cr
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te
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e
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i
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le
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el
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t
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u
r
e
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a)
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h
r
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ase
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o
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cu
r
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en
t
5
.
3
.
C
o
m
pa
riso
n o
f
s
e
m
ico
nd
uct
o
r
dev
ices a
nd
co
m
po
nents
T
ab
le
1
s
h
o
w
s
t
h
e
co
m
p
ar
i
s
o
n
o
f
a
n
u
m
b
er
o
f
p
o
w
er
d
ev
ices
u
s
ed
i
n
t
h
i
s
to
p
o
lo
g
y
w
it
h
t
h
r
ee
to
p
o
lo
g
ies
ex
i
s
ti
n
g
to
p
o
lo
g
ie
s
as
r
e
f
er
r
ed
in
[
7
]
-
[
9
]
.
T
h
e
d
ev
ice
co
m
p
ar
is
o
n
m
ai
n
l
y
i
n
clu
d
e
s
t
h
e
p
o
w
er
s
e
m
ico
n
d
u
cto
r
s
w
itc
h
es,
n
u
m
b
er
o
f
in
p
u
t
DC
s
o
u
r
ce
,
an
d
tr
an
s
f
o
r
m
er
u
s
ed
.
T
h
is
to
p
o
lo
g
y
u
s
es
o
n
l
y
1
5
s
w
itc
h
es (
E
x
cu
ld
i
n
g
b
o
o
s
t c
o
n
v
er
ter
)
,
o
n
e
tr
an
s
f
o
r
m
er
,
a
s
in
g
le
i
n
p
u
t
D
C
s
o
u
r
ce
,
an
d
t
w
o
DC
li
n
k
ca
p
ac
ito
r
s
.
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,
to
tall
y
1
9
n
u
m
b
er
s
o
f
d
e
v
i
ce
s
an
d
co
m
p
o
n
en
t
s
ar
e
u
s
ed
.
Fro
m
t
h
e
T
ab
le.
1
,
it
is
clea
r
l
y
o
b
s
er
v
ed
th
at
t
h
e
p
r
o
p
o
s
ed
MM
L
I
u
s
e
s
less
er
d
ev
ice
u
tili
za
tio
n
co
m
p
ar
ed
to
o
th
er
s
.
T
h
is
in
tu
r
n
w
o
u
ld
r
esu
lt
i
n
le
s
s
er
co
m
p
le
x
it
y
an
d
co
s
t.
T
ab
le
1
.
Se
m
i
co
n
d
u
cto
r
d
ev
ices a
n
d
co
m
p
o
n
en
ts
co
m
p
ar
is
o
n
o
f
t
h
e
p
r
o
p
o
s
ed
MM
L
I
w
it
h
o
th
er
s
R
e
f
e
r
e
n
c
e
s
N
u
mb
e
r
o
f
P
o
w
e
r
D
e
v
i
c
e
s
S
w
i
t
c
h
e
s
T
r
a
n
sf
o
r
me
r
s
I
n
p
u
t
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C
so
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r
c
e
s
D
C
b
u
s
C
a
p
a
c
i
t
o
r
s
T
o
t
a
l
[
7
]
24
-
6
6
36
[
8
]
24
6
1
1
32
[
9
]
24
2
1
1
28
P
r
o
p
o
se
d
T
o
p
o
l
o
g
y
15
1
1
2
19
I
n
co
m
p
ar
is
o
n
w
it
h
th
e
o
th
er
t
o
p
o
lo
g
ies,
th
e
p
r
esen
ted
to
p
o
lo
g
y
h
as
co
m
p
ar
ati
v
el
y
le
s
s
er
n
u
m
b
er
o
f
co
m
p
o
n
e
n
t
s
an
d
th
e
least
n
u
m
b
er
o
f
co
n
d
u
ct
in
g
d
ev
ices
a
n
d
o
p
er
ated
in
f
aster
.
T
h
e
D
C
b
u
s
v
o
lta
g
e
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
te
m
is
e
f
f
ec
ti
v
e
l
y
u
tili
ze
d
b
ec
au
s
e
o
f
th
e
i
m
p
le
m
e
n
tat
io
n
o
f
SVP
W
M
tech
n
iq
u
e
a
n
d
th
e
p
r
o
p
o
s
ed
MM
L
I
w
as
co
n
tr
o
ll
ed
b
y
u
s
i
n
g
b
o
th
P
I
an
d
F
L
C
an
d
th
e
ir
r
esu
l
ts
w
er
e
co
m
p
a
r
ed
.
T
h
e
p
r
o
p
o
s
ed
MM
L
I
u
s
es
a
s
i
n
g
le
DC
s
o
u
r
ce
f
o
r
th
e
e
n
tire
P
V
in
v
er
ter
an
d
o
n
l
y
o
n
e
t
h
r
ee
p
h
ase
tr
a
n
s
f
o
r
m
er
.
He
n
ce
,
s
ize
an
d
co
s
t o
f
th
e
p
r
o
p
o
s
ed
MM
L
I
is
r
ed
u
ce
d
co
n
s
id
er
ab
l
y
.
6.
CO
NCLU
SI
O
N
I
n
th
i
s
p
ap
er
p
r
esen
ts
tr
an
s
ien
t
an
d
s
tead
y
s
tate
an
a
l
y
s
is
o
f
m
o
d
i
f
ied
t
h
r
ee
p
h
ase
m
u
ltil
e
v
el
in
v
er
ter
f
o
r
P
V
s
y
s
te
m
.
T
h
e
p
r
esen
te
d
PI/FL
C
co
n
tr
o
lled
MM
L
I
to
p
o
lo
g
y
h
a
s
b
ee
n
d
esig
n
ed
an
d
s
i
m
u
lated
u
s
in
g
MA
T
L
A
B
/S
i
m
u
li
n
k
.
Si
m
u
la
ti
o
n
r
esu
lt
s
p
r
o
v
e
th
at,
th
e
s
t
e
ad
y
a
n
d
tr
an
s
ie
n
t
s
ta
te
p
er
f
o
r
m
an
ce
s
o
f
MM
L
I
h
av
e
b
ee
n
e
v
alu
a
ted
w
it
h
P
I
/FLC
.
F
L
C
o
f
f
er
s
i
g
n
i
f
ica
n
tl
y
i
m
p
r
o
v
ed
p
er
f
o
r
m
a
n
ce
i
n
ter
m
s
o
f
p
er
k
o
v
er
s
h
o
o
t,
p
ea
k
u
n
d
er
s
h
o
o
t
an
d
s
e
tti
n
g
ti
m
e.
Hen
ce
,
d
esi
g
n
ed
F
L
C
g
iv
e
s
b
etter
p
er
f
o
r
m
an
ce
co
m
p
ar
ed
w
ith
P
I
co
n
tr
o
lle
r.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
e
au
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I
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:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
201
7
:
31
–
39
38
RE
F
E
R
E
NC
E
S
[1
]
V
.
G
.
A
g
e
li
d
is
e
t
al
.
,
“
A
M
u
lt
il
e
v
e
l
PW
M
In
v
e
rte
r
T
o
p
o
l
o
g
y
fo
r
Ph
o
t
o
v
o
lt
a
ic
Ap
p
li
c
a
ti
o
n
s
,
”
P
ro
c
e
e
d
in
g
s
o
f
th
e
IEE
E
In
tern
a
ti
o
n
a
l
S
y
m
p
o
siu
m
o
n
In
d
u
strial
El
e
c
tro
n
ics
(IS
IE'
9
7
)
,
v
o
l.
2
,
p
p
.
5
8
9
-
5
9
4
,
1
9
9
7
.
[2
]
K.
S
.
S
rik
a
n
t
,
“
A
T
h
re
e
P
h
a
se
M
u
lt
i
L
e
v
e
l
Co
n
v
e
rter
f
o
r
g
rid
Co
n
n
e
c
ted
P
V
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
,
v
o
l.
5
,
p
p
.
7
1
-
7
5
,
2
0
1
4
.
[3
]
M
.
V
e
n
k
a
tes
a
n
,
e
t
a
l
.
,
“
Co
m
p
a
ra
ti
v
e
S
tu
d
y
o
f
T
h
re
e
P
h
a
se
G
rid
Co
n
n
e
c
ted
P
h
o
to
v
o
lt
a
ic
I
n
v
e
rter
Us
in
g
P
I
a
n
d
F
u
z
z
y
L
o
g
ic
Co
n
tro
ll
e
r
w
it
h
S
witch
in
g
L
o
ss
e
s
Ca
lcu
latio
n
,
”
In
te
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
Dr
ive
s
S
y
ste
ms
,
v
o
l.
7
,
p
p
.
5
4
3
-
5
5
0
,
2
0
1
6
.
[4
]
M.
Ka
li
a
m
o
o
rth
y
,
e
t
a
l
.
,
“
Ex
p
e
ri
m
e
n
tal
V
a
li
d
a
ti
o
n
o
f
a
Ca
sc
a
d
e
d
S
in
g
le
P
h
a
se
H
-
Brid
g
e
In
v
e
rter
with
a
S
im
p
li
f
i
e
d
S
w
it
c
h
in
g
A
lg
o
rit
h
m
,”
J
o
u
rn
a
l
o
f
Po
we
r E
lec
tro
n
ics
,
v
o
l.
1
0
,
p
p
.
5
0
7
-
5
1
8
,
2
0
1
4
.
[5
]
N.
De
v
e
ra
jan
a
n
d
A
.
Re
e
n
a
,
“
Re
d
u
c
ti
o
n
o
f
S
w
it
c
h
e
s
a
n
d
DC
S
o
u
r
c
e
s
in
Ca
sc
a
d
e
d
M
u
lt
il
e
v
e
l
In
v
e
rter
,
”
Bu
ll
e
ti
n
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
In
f
o
r
ma
ti
c
s,
v
o
l.
4
,
p
p
.
1
8
6
-
1
9
5
,
2
0
1
5
.
[6
]
Ch
e
tan
y
a
,
e
t
a
l
,
“
Ha
r
m
o
n
ic
A
n
a
ly
sis
o
f
S
e
v
e
n
a
n
d
Nin
e
L
e
v
e
l
Ca
sc
a
d
e
M
u
lt
il
e
v
e
l
In
v
e
rter
u
sin
g
M
u
lt
i
-
Ca
rrier
P
W
M
T
e
c
h
n
iq
u
e
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
,
v
o
l.
5
,
p
p
.
7
6
-
8
2
,
2
0
1
4
.
[7
]
I.
Co
lak
,
e
t
a
l
.
,
“
Re
v
iew
o
f
m
u
lt
il
e
v
e
l
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rter
to
p
o
l
o
g
ies
a
n
d
c
o
n
tro
l
sc
h
e
m
e
s,”
En
e
rg
y
Co
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t
,
v
o
l.
5
2
,
p
p
.
1
1
1
4
-
1
1
2
8
,
2
0
1
1
.
[8
]
A
.
K.
P
a
n
d
a
a
n
d
Y.
S
u
re
sh
,
“
Re
se
a
rc
h
o
n
c
a
sc
a
d
e
m
u
lt
il
e
v
e
l
in
v
e
rter
w
it
h
sin
g
le
DC
so
u
rc
e
b
y
u
sin
g
th
re
e
-
p
h
a
se
t
ra
n
sf
o
r
m
e
rs,
”
El
e
c
trica
l
Po
we
r a
n
d
E
n
e
rg
y
S
y
ste
ms
,
v
o
l.
4
0
,
p
p
.
9
-
2
0
,
2
0
1
2
.
[9
]
S
.
G
.
S
o
n
g
,
e
t
a
l.
,
“
Ca
sc
a
d
e
m
u
lt
il
e
v
e
l
in
v
e
rter
e
m
p
lo
y
in
g
th
re
e
p
h
a
se
tra
n
sf
o
rm
e
r
a
n
d
sin
g
le
D
C
in
p
u
t
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tr
o
n
ics
,
v
o
l
.
5
6
,
p
p
.
2
0
0
5
-
5
0
1
4
,
2
0
0
9
.
[1
0
]
N.
A
.
Ra
h
i
m
a
n
d
J.
S
e
lv
a
r
a
j,
“
M
u
lt
istri
n
g
F
iv
e
-
Lev
e
l
In
v
e
rter
w
it
h
No
v
e
l
P
W
M
Co
n
tro
l
S
c
h
e
m
e
f
o
r
P
V
A
p
p
li
c
a
ti
o
n
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
I
n
d
u
strie
s E
lec
tro
n
ics
,
v
o
l.
5
7
,
p
p
.
2
1
1
1
-
2
1
2
3
,
2
0
1
0
.
[1
1
]
S
.
Ja
in
a
n
d
V
.
A
g
a
r
w
a
l
,
“
Co
m
p
a
riso
n
o
f
th
e
p
e
rf
o
rm
a
n
c
e
o
f
m
a
x
im
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
sc
h
e
m
e
s
a
p
p
li
e
d
t
o
sin
g
le sta
g
e
g
rid
-
c
o
n
n
e
c
ted
p
h
o
t
o
v
o
lt
a
ic s
y
ste
m
s
,
”
IET
El
e
c
tric P
o
we
r A
p
p
li
c
a
ti
o
n
s,
v
o
l.
1
,
p
p
.
7
5
3
-
7
6
2
,
2
0
0
7
.
[1
2
]
D.
V.
N
.
A
n
a
n
th
a
n
d
G
.
V
.
Na
g
e
sh
k
u
m
a
r,
“
De
sig
n
o
f
S
o
lar
P
V
C
e
ll
Ba
se
d
In
v
e
rter
f
o
r
Un
b
a
lan
c
e
d
a
n
d
Dist
o
rt
e
d
In
d
u
strial
L
o
a
d
s,
”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
In
f
o
rm
a
ti
c
s,
v
o
l.
3
,
p
p
7
0
-
7
7
,
2
0
1
5
.
[1
3
]
A
.
S
o
e
ted
jo
,
e
t
a
l
.
,
“
M
o
d
e
li
n
g
o
f
M
a
x
i
m
u
m
P
o
w
e
r
P
o
i
n
t
T
ra
c
k
in
g
Co
n
tro
ll
e
r
f
o
r
S
o
lar
P
o
w
e
r
S
y
ste
m
,
”
T
EL
KOM
NIKA,
v
o
l.
1
0
,
p
p
.
4
1
9
-
4
3
0
,
2
0
1
2
.
[1
4
]
M.
V
e
n
k
a
tes
a
n
,
e
t
a
l.
,
“
Im
p
lem
e
n
tatio
n
o
f
a
m
o
d
if
ied
S
VP
W
M
-
b
a
se
d
th
re
e
-
p
h
a
se
in
v
e
rter
w
it
h
re
d
u
c
e
d
sw
it
c
h
e
s
u
sin
g
a
sin
g
le
DC
so
u
rc
e
f
o
r
a
g
rid
-
c
o
n
n
e
c
ted
P
V
sy
ste
m
,
”
T
u
rk
ish
J
o
u
rn
a
l
o
f
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
a
n
d
Co
mp
u
ter
S
c
ien
c
e
s
,
v
o
l.
2
4
,
p
p
.
3
0
2
3
-
3
0
3
5
,
2
0
1
6
.
[1
5
]
M
.
V
e
n
k
a
tes
a
n
,
e
t
a
l.
,
“
A
F
u
z
z
y
lo
g
ic
Ba
se
d
th
re
e
p
h
a
se
in
v
e
rter
w
it
h
sin
g
le
DC
so
u
rc
e
f
o
r
g
rid
c
o
n
n
e
c
ted
P
V
s
y
ste
m
e
m
p
lo
y
in
g
th
re
e
p
h
a
se
tra
n
sf
o
rm
e
r,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Ren
e
wa
b
le
En
e
rg
y
Res
e
a
rc
h
,
v
o
l.
5
,
p
p
.
7
3
9
-
7
4
5
,
2
0
1
5
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
V
e
n
k
a
t
e
sa
n
M
w
a
s
re
c
e
iv
e
d
h
is
B.
E.
,
i
n
E
lec
tro
n
ics
a
n
d
c
o
m
m
u
n
ica
ti
o
n
E
n
g
in
e
e
rin
g
f
ro
m
A
n
n
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i,
T
a
m
il
Na
d
u
,
In
d
ia,
in
2
0
0
8
,
a
n
d
h
is
M
.
E.
in
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
s
f
ro
m
G
o
v
e
rn
m
e
n
t
c
o
ll
e
g
e
o
f
Tec
h
n
o
lo
g
y
,
Co
im
b
a
to
re
,
Ta
m
i
l
Na
d
u
,
I
n
d
ia,
i
n
2
0
1
0
.
He
is
c
u
rre
n
tl
y
w
o
rk
in
g
to
w
a
rd
s
to
h
is
P
h
.
D
a
n
d
a
lso
w
o
rk
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g
a
s
a
n
A
ss
istan
t
P
r
o
f
e
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o
r
in
th
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
,
F
a
c
u
lt
y
o
f
En
g
in
e
e
rin
g
,
Ka
rp
a
g
a
m
Un
iv
e
rsit
y
,
Co
im
b
a
to
re
,
T
a
m
il
Na
d
u
,
In
d
ia.
His
c
u
rr
e
n
t
re
se
a
rc
h
in
tere
sts
in
c
l
u
d
e
P
o
w
e
r
e
lec
tro
n
ics
,
DC
-
DC
c
o
n
v
e
rter,
M
u
lt
il
e
v
e
l
in
v
e
rter,
P
V
b
a
se
d
sy
st
e
m
d
e
sig
n
.
He
is
A
s
so
c
iate
m
e
m
b
e
r
o
f
t
h
e
I
n
stit
u
ti
o
n
o
f
En
g
in
e
e
rs (In
d
ia).
Ra
je
sw
a
r
i
R
w
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