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as
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o
s
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w
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el
y
u
s
e
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as
m
o
s
t
r
en
e
w
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le
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g
y
co
m
e
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d
ir
ec
tl
y
o
r
in
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r
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r
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m
s
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at
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v
ar
iet
y
o
f
co
m
m
er
cial
p
u
r
p
o
s
e
s
[
1
]
.
T
h
e
g
r
id
co
n
n
ec
tio
n
allo
w
s
in
j
ec
tin
g
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n
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ated
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r
o
m
th
e
P
V
s
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s
te
m
i
n
to
th
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g
r
id
[2
]
.
I
n
o
r
d
er
to
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teg
r
ate
P
V
s
y
s
te
m
w
it
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g
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id
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e
P
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i
s
co
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m
o
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d
iv
id
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in
to
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ee
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ta
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t
h
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MP
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p
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d
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lter
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n
th
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v
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tio
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ted
P
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s
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w
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eq
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s
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o
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m
er
(
L
FT
)
to
c
o
n
n
ec
t
to
th
e
g
r
id
[
3
]
,
[
4
]
.
A
ls
o
,
th
is
L
FT
p
r
o
v
id
e
g
alv
an
ic
is
o
lati
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o
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g
leak
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g
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cu
r
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en
t
b
et
w
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P
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a
n
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g
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o
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.
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t
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ai
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p
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o
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lk
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d
ex
p
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F
u
r
t
h
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m
o
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h
ea
ti
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g
is
o
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s
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v
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in
th
e
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y
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te
m
w
h
ich
in
cr
ea
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e
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t
h
e
lo
s
s
e
s
,
a
f
f
ec
tin
g
t
h
e
o
v
er
all
e
f
f
icie
n
c
y
o
f
th
e
s
y
s
te
m
.
Mo
r
eo
v
er
,
th
e
e
f
f
icien
c
y
i
s
also
a
f
f
ec
t
ed
d
u
e
to
th
e
i
n
cl
u
s
io
n
o
f
ad
d
itio
n
al
p
o
w
er
s
t
a
g
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in
to
th
e
s
y
s
te
m
.
So
,
a
co
n
v
e
n
tio
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al
ap
p
r
o
ac
h
to
w
ar
d
s
tr
an
s
f
o
r
m
er
-
les
s
to
p
o
lo
g
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is
p
r
o
v
id
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to
d
ev
elo
p
a
m
o
r
e
ef
f
icie
n
t
s
y
s
te
m
[
5
]
.
B
u
t
th
e
ab
s
e
n
ce
o
f
g
al
v
an
ic
is
o
latio
n
r
es
u
lt
s
in
g
e
n
er
atio
n
o
f
lea
k
ag
e
c
u
r
r
en
t
f
lo
w
t
h
r
o
u
g
h
th
e
ca
p
ac
it
o
r
b
et
w
ee
n
th
e
p
h
o
to
v
o
ltaic
ar
r
ay
a
n
d
ea
r
th
th
at
m
a
y
lead
to
elec
tr
o
m
ag
n
etic
e
m
is
s
io
n
s
t
h
at
ca
n
d
am
a
g
e
th
e
cir
cu
it.
He
n
ce
an
e
f
f
icie
n
t
tr
a
n
s
f
o
r
m
er
-
les
s
to
p
o
lo
g
y
[
6
]
h
a
s
b
ee
n
s
elec
ted
w
h
ic
h
p
r
o
v
id
e
s
v
er
y
les
s
lea
k
ag
e
cu
r
r
en
t a
n
d
co
n
s
ta
n
t c
o
m
m
o
n
m
o
d
e
v
o
ltag
e
[
C
MV
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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e
Un
ip
o
lar
s
w
itc
h
i
n
g
u
s
in
g
H
-
b
r
id
g
e,
HE
R
I
C
to
p
o
lo
g
y
a
n
d
HB
Z
V
R
to
p
o
lo
g
y
.
Un
ip
o
lar
s
w
itc
h
in
g
u
s
i
n
g
H
-
b
r
id
g
e
[
8
]
en
s
u
r
es
h
i
g
h
ef
f
icie
n
c
y
b
u
t
r
esu
lt
s
in
lar
g
e
leak
a
g
e
cu
r
r
en
t
d
u
e
to
v
ar
iatio
n
i
n
t
h
e
C
MV
.
HE
R
I
C
to
p
o
lo
g
y
o
n
th
e
o
th
er
h
an
d
r
e
s
u
lt
s
in
n
o
C
MV
th
at
lead
s
to
h
ig
h
ef
f
icien
c
y
.
B
u
t
t
h
is
r
es
u
lts
i
n
lar
g
e
s
w
itc
h
i
n
g
lo
s
s
e
s
d
u
e
to
th
e
p
r
esen
ce
o
f
s
ix
s
w
i
tch
e
s
[
9
]
.
T
o
r
ed
u
ce
th
e
s
w
itc
h
in
g
lo
s
s
e
s
a
n
d
lea
k
ag
e
cu
r
r
en
t,
a
n
e
w
to
p
o
lo
g
y
h
as
b
ee
n
ad
o
p
ted
i.e
.
HB
Z
V
R
t
h
at
r
esu
l
ts
in
co
n
s
tan
t
C
MV
an
d
r
ed
u
ce
d
leak
a
g
e
cu
r
r
en
t.
I
n
t
h
is
p
ap
er
,
th
e
e
f
f
icie
n
c
y
,
l
ea
k
ag
e
cu
r
r
e
n
t
a
n
d
T
HD
o
f
o
u
tp
u
t
cu
r
r
e
n
t
ar
e
co
m
p
ar
ed
f
o
r
d
if
f
er
e
n
t
tr
an
s
f
o
r
m
er
-
les
s
to
p
o
lo
g
ies
lik
e
Un
ip
o
lar
s
w
itc
h
i
n
g
w
ith
H
-
B
r
id
g
e,
HE
R
I
C
an
d
HB
-
Z
V
R
to
p
o
lo
g
y
.
B
ased
o
n
th
e
s
i
m
u
la
tio
n
r
es
u
lt
s
o
b
tai
n
e
d
HB
-
Z
VR
is
co
n
s
id
er
ed
as
t
h
e
m
o
s
t
e
f
f
ici
e
n
t
w
i
th
m
in
i
m
u
m
lea
k
ag
e
cu
r
r
en
t.
B
u
t
t
h
is
to
p
o
lo
g
y
s
u
f
f
er
s
f
r
o
m
v
ar
y
i
n
g
C
MV
.
He
n
ce
to
o
v
er
co
m
e
t
h
i
s
d
is
ad
v
a
n
ta
g
e
s
o
m
e
m
o
d
if
icat
io
n
i
s
d
o
n
e
in
th
e
co
n
v
e
n
tio
n
al
HB
-
Z
V
R
to
p
o
lo
g
y
.
T
h
e
MP
PT
tech
n
iq
u
e
i
s
u
s
ed
to
ex
tr
ac
t
m
a
x
i
m
u
m
p
o
w
er
f
r
o
m
P
V
ar
r
ay
at
an
y
o
p
er
at
in
g
te
m
p
er
at
u
r
e
an
d
ir
r
ad
ian
ce
co
n
d
itio
n
.
T
h
e
h
ar
d
w
ar
e
cir
cu
it
i
s
i
m
p
le
m
e
n
ted
f
o
r
m
o
d
i
f
ied
HB
-
Z
V
R
to
p
o
lo
g
y
.
2.
T
RANSF
O
RM
E
R
-
L
E
SS
T
O
P
O
L
O
G
I
E
S
T
h
e
co
m
m
o
n
m
o
d
e
v
o
lta
g
e
m
ea
s
u
r
ed
i
n
f
lu
e
n
ce
s
th
e
leak
a
g
e
cu
r
r
en
t
th
a
t
f
lo
w
s
t
h
r
o
u
g
h
t
h
e
p
ar
asit
ic
ca
p
ac
ito
r
o
f
th
e
P
V
p
an
els.
As
th
e
u
til
it
y
g
r
id
s
y
s
te
m
is
n
o
t
in
f
l
u
e
n
ce
d
b
y
th
e
co
m
m
o
n
m
o
d
e
b
eh
av
io
r
o
f
th
e
s
y
s
te
m
,
s
o
co
m
m
o
n
m
o
d
e
v
o
l
tag
e
o
f
a
n
i
n
v
er
ter
to
p
o
lo
g
y
c
an
b
e
s
h
o
w
n
t
h
r
o
u
g
h
a
r
esi
s
ti
v
e
lo
ad
.
Hen
ce
f
o
r
th
e
s
i
m
u
latio
n
s
a
n
d
h
ar
d
w
ar
e
i
m
p
le
m
en
tat
io
n
a
r
esi
s
ti
v
e
l
o
ad
is
tak
en
a
n
d
C
MV
i
s
m
e
asu
r
ed
b
et
w
ee
n
t
h
e
p
o
s
itiv
e
ter
m
in
al
o
f
th
e
D
C
s
o
u
r
ce
an
d
th
e
m
id
-
p
o
i
n
t b
et
w
ee
n
th
e
r
esi
s
to
r
s
w
h
ich
i
s
g
r
o
u
n
d
ed
.
2
.
1
.
Unip
o
la
r
Sw
it
ching
U
s
ing
H
-
B
ridg
e
Sin
g
le
p
h
ase
H
-
B
r
id
g
e
i
n
v
er
ter
s
p
r
ef
er
u
n
ip
o
lar
s
w
itc
h
i
n
g
to
p
o
lo
g
y
w
it
h
a
v
ie
w
to
g
et
b
etter
in
j
ec
ted
cu
r
r
en
t
q
u
alit
y
o
f
t
h
e
in
v
er
ter
s
.
I
n
th
is
m
et
h
o
d
,
t
w
o
s
in
e
w
a
v
es
o
f
s
a
m
e
f
r
eq
u
e
n
c
y
an
d
m
a
g
n
it
u
d
e
b
u
t
1
8
0
d
eg
r
ee
s
o
u
t
o
f
p
h
ase,
V
m
an
d
V
m
-
ar
e
co
m
p
ar
ed
w
it
h
a
tr
ian
g
u
lar
w
av
e
,
g
e
n
er
atin
g
t
w
o
g
ate
s
i
g
n
al
s
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
1
f
o
r
th
e
s
witch
es
S
1
a
n
d
S
3
o
f
t
h
e
u
n
ip
o
lar
cir
cu
it
as
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
I
n
th
is
ca
s
e
,
t
h
e
in
v
er
ter
o
u
tp
u
t
v
o
lta
g
e
eit
h
er
s
w
itch
es
b
et
w
ee
n
0
to
+V
d
u
r
in
g
p
o
s
itiv
e
h
al
f
o
r
b
etw
e
en
0
to
–
V
in
th
e
n
eg
at
iv
e
h
al
f
c
y
cle.
I
t
o
f
f
er
s
r
ed
u
ce
d
s
w
i
tch
i
n
g
lo
s
s
e
s
an
d
h
as
h
ig
h
er
ef
f
icie
n
c
y
t
h
a
n
B
ip
o
lar
P
W
M
b
u
t
th
e
C
MV
m
ea
s
u
r
ed
in
th
i
s
to
p
o
lo
g
y
i
s
v
ar
y
in
g
a
n
d
h
en
ce
lead
s
to
lar
g
e
leak
ag
e
c
u
r
r
en
t
i.e
.
u
n
s
a
f
e
f
o
r
o
p
er
atio
n
o
f
in
v
er
ter
[
1
0
,
1
4
,
1
6
].
Fig
u
r
e
1
.
W
av
ef
o
r
m
o
f
U
n
ip
o
l
ar
Mo
d
u
latio
n
Sch
e
m
e
Fig
u
r
e
2
.
Un
ip
o
lar
T
o
p
o
lo
g
y
2
.
2
H
E
RIC T
o
po
lo
g
y
HE
R
I
C
s
ta
n
d
s
f
o
r
h
ig
h
l
y
e
f
f
ic
ien
t
a
n
d
r
eliab
le
in
v
er
ter
co
n
c
ep
t.
HE
R
I
C
to
p
o
lo
g
y
ad
d
s
u
p
th
e
m
er
it
s
o
f
b
o
th
u
n
ip
o
lar
a
n
d
b
ip
o
lar
to
p
o
lo
g
y
.
I
t
h
as
th
r
ee
le
v
el
s
o
f
v
o
ltag
e
o
u
tp
u
t,
h
i
g
h
er
ef
f
ici
en
c
y
a
n
d
h
as
v
er
y
less
lea
k
ag
e
c
u
r
r
en
t.
Her
e
Z
er
o
v
o
ltag
e
s
tate
ca
n
b
e
ac
h
i
ev
ed
b
y
i
n
tr
o
d
u
ci
n
g
a
b
i
-
d
ir
ec
tio
n
al
s
w
i
tch
t
h
at
co
n
s
is
ts
o
f
t
w
o
MO
S
FET
s
(
S
5
an
d
S
6
)
an
d
t
w
o
d
io
d
es
as
s
h
o
w
n
in
Fi
g
u
r
e
3
.
T
h
e
f
u
n
ctio
n
o
f
th
e
s
e
b
id
ir
ec
tio
n
al
s
w
i
tch
e
s
i
s
to
p
r
o
v
id
e
ze
r
o
v
o
lta
g
e
s
tag
e
s
d
u
r
in
g
t
h
e
p
o
s
iti
v
e
a
n
d
n
e
g
ativ
e
h
al
f
c
y
cles.
I
n
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
730
–
737
732
p
o
s
itiv
e
h
al
f
c
y
cle,
S
1
an
d
S
4
ar
e
in
ON
s
tate
a
n
d
f
r
ee
w
h
ee
li
n
g
p
er
io
d
o
cc
u
r
s
w
h
e
n
S
6
is
t
u
r
n
ed
ON.
Si
m
i
lar
l
y
,
in
n
e
g
ati
v
e
h
al
f
c
y
cle,
S
2
a
n
d
S
3
ar
e
t
u
r
n
ed
O
N
an
d
S
5
i
s
u
s
ed
d
u
r
i
n
g
t
h
e
f
r
ee
w
h
ee
li
n
g
p
er
io
d
.
A
lt
h
o
u
g
h
ef
f
icie
n
c
y
i
s
in
cr
ea
s
ed
h
er
e
an
d
s
y
s
te
m
g
e
n
er
ates
al
m
o
s
t
n
o
C
MV
b
u
t
in
t
h
is
t
y
p
e
o
f
to
p
o
l
o
g
y
th
e
n
u
m
b
er
o
f
s
e
m
ico
n
d
u
cto
r
s
u
s
ed
is
m
o
r
e
th
at
in
cr
ea
s
es
t
h
e
s
w
itc
h
i
n
g
lo
s
s
es
[
1
1
]
an
d
t
h
e
e
f
f
icie
n
c
y
g
o
es
d
o
w
n
.
Fig
u
r
e
3
.
HE
R
I
C
T
o
p
o
l
o
g
y
2
.
3
H
B
Z
VR
T
o
po
lo
g
y
I
n
t
h
is
m
et
h
o
d
,
ze
r
o
s
tate
ca
n
b
e
g
e
n
er
ated
b
y
u
s
in
g
b
i
-
d
ir
ec
tio
n
al
s
w
itc
h
w
h
ic
h
co
m
p
r
i
s
es
o
f
o
n
e
MO
SF
E
T
an
d
d
io
d
e
b
r
i
d
g
e.
T
h
e
b
i
-
d
ir
ec
tio
n
al
s
w
i
tch
i
s
co
n
n
ec
ted
to
th
e
m
id
p
o
in
t
o
f
t
h
e
DC
-
li
n
k
ca
p
ac
ito
r
s
th
r
o
u
g
h
a
d
io
d
e
as
s
h
o
w
n
in
Fig
u
r
e
4
,
i
n
o
r
d
er
to
m
ak
e
th
e
v
o
lta
g
e
co
n
s
ta
n
t
d
u
r
in
g
t
h
e
ze
r
o
s
tate
.
T
h
e
ze
r
o
v
o
ltag
e
is
ac
h
ie
v
ed
w
h
en
S
5
i
s
t
u
r
n
ed
ON
an
d
co
n
s
eq
u
e
n
tl
y
all
o
th
er
s
w
itc
h
es
S
1
,
S
2
,
S
3
an
d
S
4
ar
e
in
OF
F
s
tate
[
11
]
.
T
h
e
r
eq
u
ir
ed
g
ate
s
ig
n
al
f
o
r
S
5
is
co
m
p
le
m
e
n
tar
y
to
th
at
o
f
S
1
,
S
4
i
n
p
o
s
iti
v
e
c
y
cle
an
d
S
2
,
S
3
i
n
n
eg
at
iv
e
c
y
cle
w
it
h
a
s
m
all
-
t
i
m
e
i
n
ter
v
a
l
s
o
t
h
at
s
h
o
r
t
cir
cu
it
o
f
in
p
u
t
ca
p
ac
ito
r
w
ill
n
o
t
h
ap
p
en
.
I
n
t
h
e
p
o
s
itiv
e
c
y
cle
S
1
an
d
S
4
ar
e
i
n
O
N
s
tate
t
h
at
g
e
n
er
ate
s
p
o
s
i
tiv
e
o
u
tp
u
t
v
o
ltag
e
an
d
S
5
is
c
o
n
tr
o
lled
u
s
in
g
th
e
co
m
p
le
m
e
n
tar
y
s
i
g
n
a
l.
Si
m
il
ar
l
y
,
in
th
e
n
e
g
ati
v
e
h
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I
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N:
2088
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8
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
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t J
P
o
w
E
lec
&
Dr
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S
y
s
t
,
Vo
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9
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2
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
A
n
a
lysi
s
a
n
d
Desi
g
n
o
f
S
i
n
g
le P
h
a
s
e Hig
h
E
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cy Tr
a
n
s
fo
r
m
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ess
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Fig
.
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an
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M
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.
8
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icts
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e
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r
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en
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HB
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Z
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to
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g
y
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l
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ak
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e
c
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r
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ies
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o
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ed
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r
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g
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(
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w
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ch
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n
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e
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ce
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.
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t V
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u
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e
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r
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ied
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
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8
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8
694
I
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P
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w
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lec
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Dr
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S
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9
,
No
.
2
,
J
u
n
e
2
0
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:
730
–
737
736
4.
H
ARDWA
R
E
RE
SUL
T
S
Si
m
u
latio
n
r
es
u
lts
h
a
v
e
b
ee
n
r
ep
o
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ted
t
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ar
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e
p
er
f
o
r
m
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ce
o
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th
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d
i
f
f
er
en
t
tr
an
s
f
o
r
m
er
-
les
s
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ter
to
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lo
g
ies
.
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m
t
h
e
s
e
s
i
m
u
lat
io
n
r
es
u
lts
it
is
r
e
v
e
aled
th
at
t
h
e
leak
a
g
e
cu
r
r
e
n
t
i
s
f
o
u
n
d
to
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e
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er
y
less
f
o
r
th
e
m
o
d
if
ied
HB
Z
VR
to
p
o
lo
g
y
w
it
h
h
i
g
h
er
ef
f
icien
c
y
an
d
lo
w
T
HD
o
f
lo
a
d
cu
r
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en
t.
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or
t
he
ha
r
d
w
a
r
e
i
m
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e
nt
at
i
o
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he
m
o
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i
f
ied
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Z
V
R
,
s
a
m
e
s
pe
c
i
f
ic
a
ti
on
s
a
s
i
n
t
he
c
a
s
e
of
s
i
m
ul
at
i
on
a
r
e
c
on
s
i
de
r
e
d
.
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he
ha
r
d
w
a
r
e
s
e
t
up
of
t
h
e
m
o
d
i
f
ied
HB
Z
V
R
to
p
o
lo
g
y
i
s
s
h
o
w
n
i
n
F
i
g
ur
e
9
.
A
r
d
u
i
n
o
UNO
is
u
s
ed
to
g
en
er
ate
th
e
P
W
M
s
i
g
n
al
t
h
at
i
s
g
iv
e
n
to
th
e
g
ate
o
f
MO
SF
E
T
s
p
r
esen
t
i
n
t
h
e
i
n
v
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r
ter
cir
cu
it
t
h
r
o
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g
h
th
e
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S
FET
d
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R
2
1
1
0
.
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h
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o
u
tp
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t
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g
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o
f
th
e
m
o
d
if
ied
HB
Z
VR
i
n
v
er
ter
to
p
o
lo
g
y
i
s
d
ep
icted
in
Fi
g
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e
1
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d
h
as
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0
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n
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.
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g
u
r
e
11
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ep
icts
t
h
e
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ilter
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t
p
u
t
v
o
ltag
e
of
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o
d
if
ied
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Z
VR
to
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o
lo
g
y
w
h
ich
is
s
in
u
s
o
id
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in
n
at
u
r
e
an
d
g
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v
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to
lo
ad
.
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m
th
e
g
iv
e
n
h
ar
d
w
ar
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s
et
u
p
in
Fi
g
.
9
w
e
w
er
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ab
le
to
ac
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iev
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ig
h
e
f
f
icie
n
c
y
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5
.
4
%
w
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h
t
h
e
least
leak
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g
e
c
u
r
r
en
t
to
b
e
ar
o
u
n
d
2
.
3
%
w
h
ic
h
m
atch
e
s
to
th
e
s
i
m
u
la
tio
n
r
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lt
s
p
r
esen
ted
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o
v
e.
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n
c
o
m
p
ar
i
n
g
w
it
h
t
h
e
HB
-
Z
V
R
t
o
p
o
lo
g
y
w
i
th
o
u
r
p
r
o
p
o
s
ed
to
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lo
g
y
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e
w
er
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le
to
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h
ie
v
e
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ig
h
e
f
f
icie
n
c
y
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r
o
m
9
4
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to
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5
.
5
%
th
r
o
u
g
h
m
i
n
i
m
izi
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g
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lo
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tr
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er
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y
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m
iti
n
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itio
n
lo
s
s
es
b
et
w
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n
ac
ti
v
e
a
n
d
ze
r
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v
o
ltag
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s
tate.
Als
o
,
w
e
f
o
u
n
d
t
h
at
t
h
e
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k
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g
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h
ic
h
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s
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m
o
n
g
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ies
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y
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ak
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t
h
e
C
MV
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n
s
ta
n
t
t
h
r
o
u
g
h
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n
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r
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g
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io
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h
r
o
u
g
h
t
h
is
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e
w
er
e
ab
le
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h
iev
e
h
i
g
h
ef
f
ic
ien
c
y
a
n
d
lo
w
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k
a
g
e
cu
r
r
en
t
co
m
b
i
n
ed
to
ac
h
iev
e
h
ig
h
er
p
o
w
er
.
Fig
u
r
e
9
.
Har
d
w
ar
e
Setu
p
o
f
Mo
d
if
ied
HB
Z
VR
Fig
u
r
e
10
.
I
n
v
er
ter
Ou
tp
u
t V
o
ltag
e
o
f
Mo
d
if
ied
HB
Z
V
R
Fig
u
r
e
1
1
.
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n
v
er
ter
Ou
tp
u
t V
o
ltag
e
o
f
Mo
d
if
ied
HB
Z
VR
5.
CO
NCLU
SI
O
N
T
r
an
s
f
o
r
m
er
les
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n
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er
ter
s
h
as
m
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r
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e
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f
icien
c
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as
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m
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ar
ed
to
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o
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e
in
v
er
ter
s
th
at
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av
e
tr
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n
s
f
o
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er
.
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t
h
as
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ee
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o
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er
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at
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en
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e
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s
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o
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m
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e
C
M
V
o
f
th
e
i
n
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er
t
er
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a
s
a
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ig
n
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ica
n
t
i
m
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h
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r
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et
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ase
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v
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o
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m
o
d
if
ied
HB
-
Z
VR
to
p
o
l
o
g
y
i
s
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n
s
ta
n
t
a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
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w
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Dr
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SS
N:
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694
A
n
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Desi
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S
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a
n
s
fo
r
m
er
L
ess
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V
I
n
verter
To
p
o
lo
g
y
(
J
a
ya
la
ks
h
mi
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.
S
.
)
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h
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g
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h
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es
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e
o
b
tain
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.
RE
F
E
R
E
NC
E
S
[1
]
“
T
re
n
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s
in
p
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to
v
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a
ic
a
p
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ra
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VPS
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]
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[4
]
G
e
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rd
o
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V.
G
.
,
M
a
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R.
P
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J.
M
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u
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,
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Hig
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Eff
icie
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in
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ra
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s
f
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In
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r
P
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a
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p
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In
v
e
stig
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c
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T
e
c
n
o
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1
6
(
2
),
1
7
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,
2
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.
[5
]
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re
k
e
s,
T
a
m
a
s,
Re
m
u
s
T
e
o
d
o
r
e
sc
u
,
a
n
d
M
a
rc
o
L
ise
rr
e
.
"
Co
m
m
o
n
m
o
d
e
v
o
lt
a
g
e
in
c
a
se
o
f
tra
n
sf
o
rm
e
r
les
s
P
V
in
v
e
rters
c
o
n
n
e
c
ted
to
th
e
g
rid
.
"
In
d
u
stria
l
El
e
c
tro
n
ics
,
2
0
0
8
.
IS
I
E
2
0
0
8
.
IEE
E
In
ter
n
a
ti
o
n
a
l
S
y
mp
o
siu
m
o
n
.
IEE
E
,
2
0
0
8
.
[6
]
G
o
n
z
a
lez
,
Ro
b
e
rto
,
e
t
a
l.
"
Hig
h
-
e
ff
ici
e
n
c
y
tran
s
f
o
r
m
e
r
les
s
sin
g
le
-
p
h
a
se
p
h
o
to
v
o
l
taic
in
v
e
rter."
Po
we
r
El
e
c
tro
n
ics
a
n
d
M
o
ti
o
n
C
o
n
tr
o
l
C
o
n
fer
e
n
c
e
,
2
0
0
6
.
EP
E
-
PE
M
C
2
0
0
6
.
1
2
th
In
t
e
rn
a
ti
o
n
a
l
.
IEE
E,
2
0
0
6
.
[7
]
Ke
re
k
e
s,
Ta
m
a
s,
e
t
a
l.
"
A
n
e
w
h
ig
h
-
e
ff
icie
n
c
y
sin
g
le
-
p
h
a
se
tran
sf
o
r
m
e
r
le
ss
P
V
i
n
v
e
rter
to
p
o
lo
g
y
.
"
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
5
8
(
1
),
1
8
4
-
1
9
1
,
2
0
1
1
.
[8
]
S
o
o
m
ro
,
Ja
h
a
n
g
e
e
r,
T
a
y
a
b
D.
M
e
m
o
n
,
a
n
d
M
.
A
.
S
h
a
h
.
"
De
sig
n
a
n
d
a
n
a
ly
sis
o
f
sin
g
le
p
h
a
se
v
o
lt
a
g
e
so
u
rc
e
i
n
v
e
rter
u
sin
g
Un
ip
o
lar
a
n
d
Bi
p
o
lar
p
u
l
se
w
id
th
m
o
d
u
latio
n
tec
h
n
i
q
u
e
s
.
"
In
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
.
Ad
v
a
n
c
e
s
in
El
e
c
trica
l,
El
e
c
tro
n
ic a
n
d
S
y
ste
ms
En
g
i
n
e
e
rin
g
(
ICAE
ES
),
2
0
1
6
.
[9
]
Kja
e
r,
S
o
e
re
n
Ba
e
k
h
o
e
j,
Jo
h
n
K.
P
e
d
e
rse
n
,
a
n
d
F
re
d
e
Blaa
b
jerg
.
"
A
r
e
v
ie
w
o
f
sin
g
le
-
p
h
a
se
g
rid
-
c
o
n
n
e
c
ted
in
v
e
rters
f
o
r
p
h
o
t
o
v
o
lt
a
ic m
o
d
u
les
.
"
IEE
E
tra
n
sa
c
ti
o
n
s
o
n
in
d
u
stry
a
p
p
li
c
a
ti
o
n
s
4
1
(
5
),
1
2
9
2
-
1
3
0
6
,
2
0
0
5
.
[1
0
]
Na
m
b
o
o
d
ir
i,
A
n
u
ja,
a
n
d
Ha
rsh
a
l
S
.
W
a
n
i.
"
Un
ip
o
lar
a
n
d
b
i
p
o
lar
P
W
M
in
v
e
rter."
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
f
o
r
In
n
o
v
a
ti
v
e
Res
e
a
rc
h
in
S
c
ien
c
e
&
T
e
c
h
n
o
lo
g
y
1
(
7
),
2
0
1
4
.
[1
1
]
J.
Nish
i,
M
.
R
o
sh
i
n
i,
G
.
K.
G
o
w
ri,
K.
Im
m
a
n
u
v
e
l
A
ro
k
ia
J
a
m
e
s”
Ex
p
e
rime
n
tal
A
n
a
l
y
sis
o
f
S
in
g
le
-
P
h
a
se
No
n
-
T
ra
n
s
f
o
r
m
e
r
P
h
o
t
o
v
o
lt
a
ic
In
v
e
rter
w
it
h
Op
ti
m
u
m
E
ff
icie
n
c
y
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Ad
v
a
n
c
e
d
Res
e
a
rc
h
in
El
e
c
trica
l,
El
e
c
tro
n
ics
a
n
d
I
n
stru
me
n
ta
ti
o
n
E
n
g
in
e
e
rin
g
,
3
(4
)
,
2
0
1
4
.
[1
2
]
M
e
rin
Ra
p
h
e
l,
G
.
Ra
jk
u
m
a
r
“
El
im
in
a
ti
o
n
o
f
L
e
a
k
a
g
e
Cu
rre
n
t
u
sin
g
HBZV
R
-
D
T
o
p
o
l
o
g
y
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ad
v
a
n
c
e
d
Res
e
a
rc
h
in
El
e
c
trica
l,
El
e
c
tro
n
ics
a
n
d
I
n
stru
me
n
t
a
ti
o
n
En
g
i
n
e
e
rin
g
,
4
(
6
),
2
0
1
5
.
[1
3
]
Ch
e
n
,
Ya
n
g
,
a
n
d
Ke
y
u
e
M
a
S
m
e
d
le
y
.
"
A
c
o
st
-
e
ff
e
c
ti
v
e
sin
g
le
-
sta
g
e
in
v
e
rter
w
it
h
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
.
"
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
ics
,
1
9
(5
),
1
2
8
9
-
1
2
9
4
,
2
0
0
4
.
[1
4
]
G
.
S
rid
h
a
r,
P
.
S
a
ti
sh
K
u
m
a
r,
M
.
S
u
sh
a
m
,
"
A
No
v
e
l
G
e
n
e
ra
li
z
e
d
T
o
p
o
lo
g
y
f
o
r
M
u
lt
i
-
lev
e
l
In
v
e
rte
r
w
it
h
S
w
it
c
h
e
d
S
e
ries
-
P
a
ra
ll
e
l
DC
S
o
u
rc
e
s.
"
In
d
o
n
e
sia
n
Jo
u
rn
a
l
o
f
El
e
c
t
rica
l
En
g
in
e
e
rin
g
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
Vo
l.
4
,
No
.
1
,
Oc
to
b
e
r
2
0
1
6
,
p
p
.
4
1
-
5
1
.
[1
5
]
Ro
k
a
n
A
li
A
h
m
e
d
,
S
M
e
k
h
il
e
f
,
He
w
W
o
o
i
P
i
n
g
.
"
Ne
w
M
u
lt
i
-
l
e
v
e
l
in
v
e
rter
to
p
o
lo
g
y
w
it
h
re
d
u
c
e
d
n
u
m
b
e
r
o
f
sw
it
c
h
e
s
"
.
M
EP
CON
’
1
0
,
Ca
ir
o
U
n
iv
e
rsity
.
Eg
y
p
t.
2
0
1
0
:
5
6
5
-
5
7
0
.
[1
6
]
M
o
h
a
n
,
Ne
d
,
a
n
d
T
o
re
M
.
Un
d
e
l
a
n
d
.
P
o
w
e
r
El
e
c
tro
n
ics
:
Co
n
v
e
rters
,
A
p
p
li
c
a
ti
o
n
s
a
n
d
De
sig
n
.
J
o
h
n
W
il
e
y
&
S
o
n
s,
2
0
0
7
.
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