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i
n
1.
I
NT
RO
D
UCT
I
O
N
P
h
o
to
v
o
ltaic
p
o
w
er
g
en
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t
ca
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s
e
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y
f
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e
l
co
s
t
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w
h
en
co
m
p
ar
ed
w
it
h
o
th
er
r
en
e
w
ab
le
en
er
g
y
r
eso
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r
ce
s
.
P
h
o
to
v
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ltaic
(
P
V)
s
y
s
te
m
s
n
ee
d
in
v
er
ter
to
ac
t
as
p
o
w
er
co
n
d
itio
n
i
n
g
u
n
i
t
b
et
w
ee
n
t
h
e
s
o
u
r
ce
an
d
lo
a
d
.
T
h
ese
in
v
er
ter
s
h
a
v
e
to
h
a
n
d
le
v
ar
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u
s
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w
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q
u
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y
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s
u
es
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u
e
to
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V
s
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r
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e
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l
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ct
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s
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w
h
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m
p
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s
e
s
tr
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g
e
n
t
r
eq
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m
e
n
t
s
f
o
r
in
v
e
r
ter
to
p
o
lo
g
ies
an
d
th
eir
co
n
tr
o
ls
.
[1
]
–
[3
]
Z
So
u
r
ce
I
n
v
er
ter
(
Z
SI)
e
m
p
l
o
y
i
n
g
an
i
m
p
e
d
an
ce
n
et
w
o
r
k
co
n
s
is
ti
n
g
o
f
i
n
d
u
cto
r
s
an
d
ca
p
ac
ito
r
s
,
co
u
p
led
w
i
th
in
v
er
ter
m
ain
cir
cu
it
to
t
h
e
v
ar
iab
le
D
C
s
o
u
r
ce
,
w
h
ic
h
o
v
er
co
m
es
t
h
e
v
o
lta
g
e
f
lu
c
tu
atio
n
p
r
o
b
lem
s
ca
u
s
ed
b
y
in
h
er
e
n
t
c
h
ar
ac
ter
is
tic
s
o
f
t
h
e
p
h
o
to
v
o
lt
aic
s
y
s
te
m
s
.
Z
SI
f
ea
t
u
r
es
a
w
i
d
e
r
an
g
e
o
f
v
o
lta
g
e
g
ain
w
h
i
c
h
i
s
s
u
i
tab
le
f
o
r
m
a
n
y
ap
p
licatio
n
s
.
[4
]
–
[
7
]
Z
SI
ca
n
b
e
u
s
ed
to
r
ea
lize
b
o
th
D
C
v
o
ltag
e
b
o
o
s
t
an
d
DC
–
A
C
i
n
v
er
s
io
n
i
n
a
s
i
n
g
le
s
tag
e,
an
ec
o
n
o
m
ical
ap
p
r
o
ac
h
f
o
r
p
h
o
to
v
o
ltaic
ap
p
licatio
n
s
.
[
8
,
9
]
T
h
e
w
o
r
k
r
ep
o
r
ted
in
t
h
i
s
p
ap
er
is
o
r
g
a
n
ized
as
:
Ma
t
h
e
m
atica
l
m
o
d
el
o
f
p
h
o
to
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o
ltai
c
p
an
el
in
s
ec
tio
n
2
,
T
o
p
o
lo
g
y
d
escr
ip
tio
n
o
f
s
in
g
le
p
h
ase
Z
s
o
u
r
ce
in
v
er
ter
alo
n
g
w
i
th
co
n
tr
o
l
s
tr
ateg
y
in
s
ec
t
io
n
3
.
Si
m
u
latio
n
a
n
d
ex
p
er
i
m
e
n
ta
l r
esu
lt
s
ar
e
p
r
esen
ted
in
s
ec
t
i
o
n
4
.
Fin
all
y
,
co
n
clu
s
io
n
i
s
r
ep
o
r
ted
in
s
ec
tio
n
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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699
2.
M
AT
H
E
M
AT
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CAL M
O
DE
L
O
F
P
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P
ANEL
P
V
p
an
el
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ts
th
e
p
h
o
to
en
er
g
y
o
f
s
u
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li
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h
t
to
DC
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ar
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le
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e.
T
h
e
am
o
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n
t
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f
p
o
w
er
ex
tr
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ted
b
y
a
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p
an
el
d
ep
en
d
s
o
n
its
o
p
er
atin
g
DC
v
o
ltag
e
.
T
h
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
tr
ac
k
in
g
(
MP
PT
)
is
ca
p
ab
le
o
f
ex
tr
ac
tin
g
m
a
x
i
m
u
m
p
o
w
er
f
r
o
m
t
h
e
P
V
p
an
el
w
h
ic
h
is
in
f
l
u
e
n
ce
d
b
y
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h
e
s
o
lar
in
s
o
latio
n
le
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el
an
d
at
m
o
s
p
h
er
ic
te
m
p
er
at
u
r
e
wh
ic
h
ar
e
d
escr
ib
ed
in
[
1
0
]
–
[
1
3
]
A
P
V
p
an
el
is
f
o
r
m
ed
b
y
s
er
ies
–
p
ar
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in
ter
co
n
n
ec
ted
id
en
tical
P
V
ce
lls
.
P
V
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ll
is
r
ep
r
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ted
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s
in
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le
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io
d
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m
o
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1
in
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a
cu
r
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k
ep
t
i
n
p
ar
allel
w
it
h
a
d
io
d
e
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d
a
s
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ies r
es
is
tan
ce
.
Fig
u
r
e
1
.
Sin
g
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d
io
d
e
m
o
d
el
o
f
P
V
ce
ll
T
h
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b
asic c
u
r
r
en
t e
q
u
atio
n
o
f
t
h
e
P
V
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ll is
g
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v
e
n
b
y
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x
p
-
1
p
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I
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A
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(
1
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t c
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r
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pv
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t
g
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ated
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r
r
en
t,
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sat
is
th
e
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atio
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r
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ch
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n
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tr
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is
B
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a
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n
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s
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n
s
ta
n
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A
i
s
t
h
e
id
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lit
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ac
to
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o
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th
e
p
-
n
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n
c
tio
n
,
an
d
T
is
th
e
P
V
ce
ll te
m
p
er
atu
r
e
(
d
eg
r
ee
s
Kel
v
i
n
)
.
Fro
m
E
q
n
.
(
1
)
,
+
-
l
n
pv
s
a
t
s
a
t
A
K
T
I
I
I
V
qI
(
2
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T
h
e
o
u
tp
u
t p
o
w
er
o
f
th
e
P
V
c
ell,
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is
ex
p
r
ess
ed
as
e
x
p
-
1
p
v
s
a
t
qV
P
V
I
I
A
K
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(
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Si
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latio
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s
ar
e
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r
r
ied
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t
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r
m
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p
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3
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p
as
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ts
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s
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te
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m
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1
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p
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m
s
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h
e
o
p
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n
o
f
Z
SI
h
as
t
w
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p
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g
m
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d
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o
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–
s
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n
n
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t
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m
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SI
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s
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x
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s
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ac
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r
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s
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p
p
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w
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tch
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s
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t t
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u
p
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s
w
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h
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d
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v
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o
f
an
y
p
h
ase
leg
o
f
th
e
in
v
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ter
co
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d
u
cts.
W
h
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e
in
p
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v
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is
h
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g
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s
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t
ate
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t
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s
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a
n
d
Z
SI
p
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f
o
r
m
s
b
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co
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v
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s
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n
,
th
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s
a
m
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w
a
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as
v
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lta
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-
s
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in
v
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ter
.
W
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t
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p
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is
lo
w
,
s
h
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t
th
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o
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tate
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s
ed
to
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th
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t
h
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r
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Z
SI
p
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f
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r
m
s
as
a
b
u
c
k
–
b
o
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s
t
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v
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ter
.
T
h
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v
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e
b
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ca
p
ab
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y
o
f
Z
SI
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s
d
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to
en
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g
y
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an
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c
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th
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tate.
As
th
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ar
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t
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p
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a
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[
1
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l th
e
Z
SI.
Si
m
p
l
e
b
o
o
s
tin
g
s
w
itc
h
i
n
g
s
ch
e
m
e
i
s
e
m
p
lo
y
ed
f
o
r
s
w
itc
h
in
g
ac
tio
n
o
f
th
is
Z
SI
d
u
e
p
r
o
d
u
ce
v
o
lta
g
e
b
o
o
s
ti
n
g
ac
tio
n
s
.
Fig
.
5
ill
u
s
tr
ate
t
h
e
Ma
tlab
/Si
m
u
l
in
k
b
lo
ck
m
o
d
el
o
f
s
i
m
p
le
b
o
o
s
t s
w
i
tch
i
n
g
s
c
h
e
m
e
w
h
ich
i
s
ap
p
lied
f
o
r
th
e
i
n
v
er
ter
.
Fig
u
r
e
5
.
S
w
i
tch
i
n
g
s
eq
u
e
n
ce
b
lo
ck
d
iag
r
a
m
4.
CIRCU
I
T
AN
AL
Y
SI
S O
F
S
I
NG
L
E
P
H
ASE
Z
SO
URC
E
I
NVER
E
T
E
R
4
.
1
.
Si
m
ula
t
io
n r
esu
lt
s
T
h
e
o
p
er
atio
n
o
f
Z
SI
ar
e
an
al
y
ze
d
in
s
tead
y
s
tate
a
n
d
its
p
e
r
f
o
r
m
an
ce
s
ar
e
v
al
id
ated
u
s
i
n
g
s
i
m
u
lated
r
esu
lt
s
o
b
tain
ed
in
M
A
T
L
A
B
/
Si
m
u
li
n
k
,
w
h
er
e
t
h
e
s
o
lv
er
is
ch
o
s
en
as
v
ar
iab
le
s
tep
d
i
s
cr
ete
w
it
h
s
tep
o
f
1
.
0
µs
w
it
h
t
h
e
f
o
llo
w
i
n
g
s
y
s
te
m
p
ar
am
eter
s
:
V
dc
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1
2
V;
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1
a
n
d
L
2
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1
.
5
m
H
C
1
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d
C
2
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7
0
0
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an
d
th
e
s
w
itc
h
in
g
f
r
eq
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en
c
y
,
f
s
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0
k
Hz
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d
r
esis
ti
v
e
lo
ad
o
f
R
L
=5
0
0
Ω.
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h
e
MO
SF
E
T
m
o
d
els
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h
o
s
e
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ter
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al
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esis
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n
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er
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esis
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s
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ed
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o
r
t
h
e
s
w
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n
g
d
ev
ic
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Fi
g
u
r
e
6
s
h
o
w
s
th
e
ca
p
ac
ito
r
v
o
ltag
e
w
a
v
e
f
o
r
m
s
o
f
ca
p
ac
ito
r
s
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1
a
n
d
C
2
h
av
in
g
t
h
e
eq
u
al
v
al
u
es
o
f
2
5
V
ea
ch
.
T
h
e
o
u
tp
u
t
p
h
ase
v
o
lta
g
e
o
f
v
al
u
e
4
6
V
is
o
b
tain
ed
th
r
o
u
g
h
s
i
m
u
lat
io
n
ac
r
o
s
s
th
e
lo
ad
w
ith
o
u
t
f
i
lter
as
g
iv
e
n
in
Fi
g
u
r
e
7.
T
h
e
o
b
tain
ed
r
esu
lts
v
er
i
f
y
t
h
at
th
e
Z
SI
p
r
o
d
u
ce
s
b
etter
v
o
lt
ag
e
b
o
o
s
tin
g
an
d
i
n
v
er
s
io
n
ab
ilit
y
f
o
r
th
e
p
ass
iv
e
co
m
p
o
n
e
n
t
s
u
s
ed
in
t
h
e
Z
n
et
w
o
r
k
.
Fig
u
r
e
6
.
Si
m
u
lated
ca
p
ac
ito
r
v
o
ltag
e
w
a
v
e
f
o
r
m
s
(
C
1
an
d
C
2
)
Fig
u
r
e
7
.
Si
m
u
lated
o
u
tp
u
t v
o
l
tag
e
w
av
e
f
o
r
m
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
1
.
6
1
.
8
2
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20
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a
p
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c
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r
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o
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g
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o
l
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2
0
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0
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6
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8
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1
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2
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T
i
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e
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e
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r
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o
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C
2
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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
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
2
,
J
u
n
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2
0
1
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:
698
–
703
702
4
.
2
.
E
x
peri
m
ent
a
l
re
s
u
lt
s
T
o
d
em
o
n
s
tr
ate
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
Z
SI,
a
n
e
x
p
er
i
m
e
n
tal
p
r
o
to
ty
p
e
w
as
b
u
ilt
in
lab
o
r
ato
r
y
w
it
h
t
h
e
s
a
m
e
p
ar
a
m
e
ter
s
as
u
s
ed
i
n
t
h
e
s
i
m
u
lat
io
n
.
Fi
g
.
8
s
h
o
w
s
t
h
e
ex
p
er
i
m
e
n
tal
s
e
tu
p
o
f
th
e
p
r
o
p
o
s
ed
in
v
er
ter
s
et
u
p
w
h
ic
h
i
n
clu
d
e
s
p
o
w
er
MO
S
FET
S,
d
r
iv
er
b
o
ar
d
s
,
i
m
p
ed
an
ce
s
o
u
r
ce
n
et
w
o
r
k
s
,
A
/
D
co
n
v
er
s
io
n
,
s
er
ial
co
m
m
u
n
icatio
n
a
n
d
h
ig
h
p
er
f
o
r
m
a
n
ce
FP
G
A
u
n
it.
Si
m
p
le
b
o
o
s
t
P
W
M
p
u
ls
es
ar
e
s
en
t
to
th
e
g
a
te
d
r
iv
er
cir
cu
it.
Fo
r
th
e
lab
o
r
ato
r
y
p
r
o
to
t
y
p
e,
1
2
V
is
g
i
v
e
n
a
s
i
n
p
u
t
to
t
h
e
Z
s
o
u
r
ce
n
et
w
o
r
k
f
r
o
m
P
V
p
a
n
el
.
Po
w
er
s
u
p
p
l
y
u
n
it
i
s
e
m
p
lo
y
ed
s
ep
ar
atel
y
f
r
o
m
lab
o
r
ato
r
y
co
n
d
itio
n
s
f
o
r
th
e
o
p
er
atio
n
o
f
co
n
tr
o
l/fu
n
ct
io
n
al
u
n
its
o
f
th
e
i
n
v
er
ter
.
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h
e
b
r
id
g
e
r
ec
tifi
er
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N4
0
0
7
in
th
e
p
o
w
er
s
u
p
p
l
y
u
n
i
t
is
u
s
ed
to
co
n
v
er
t
AC
v
o
lta
g
e
i
n
to
D
C
v
o
ltag
e.
A
L
M
7
8
0
5
r
eg
u
lat
o
r
is
u
s
ed
to
f
ed
a
5
V
s
u
p
p
l
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to
Field
P
r
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g
r
a
m
m
ab
le
G
ate
A
r
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y
(
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d
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7
8
1
2
r
eg
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la
to
r
r
eg
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lates t
h
e
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n
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er
ter
d
r
iv
e
r
cir
cu
it o
p
er
atin
g
v
o
ltag
e
s
.
Fig
u
r
e
8
E
x
p
er
i
m
e
n
tal
s
et
u
p
SP
A
R
T
A
N
3
E
FP
GA
p
r
o
ce
s
s
o
r
is
u
s
ed
f
o
r
g
e
n
e
r
atin
g
P
W
M
p
u
ls
es
a
n
d
f
ed
to
MO
SF
E
T
I
R
F
8
4
0
s
w
itc
h
es.
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h
e
p
u
l
s
e
w
id
t
h
ca
n
b
e
in
cr
e
m
e
n
ted
o
r
d
ec
r
e
m
en
t
ed
b
ased
o
n
th
e
v
ar
iatio
n
in
t
h
e
d
u
t
y
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cle
g
i
v
en
to
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e
o
p
to
co
u
p
ler
6
N1
3
7
.
PW
M
p
u
ls
es
f
r
o
m
t
h
e
FP
G
A
ar
e
f
ed
to
th
e
o
p
to
c
o
u
p
ler
f
o
r
i
s
o
latio
n
o
f
co
n
tr
o
l
/
p
o
w
er
cir
cu
it
to
av
o
id
t
h
e
o
v
e
r
cu
r
r
en
t
co
n
d
itio
n
s
.
Op
to
co
u
p
ler
o
u
tp
u
t
s
i
g
n
a
l
is
i
n
v
er
ted
f
r
o
m
o
r
ig
in
al
P
W
M
in
p
u
t
s
i
g
n
a
l
b
y
t
h
e
u
s
e
o
f
N
OT
g
ate
4
5
8
4
.
I
R
2
1
1
0
is
u
s
ed
to
d
r
iv
e
th
e
MO
SF
E
T
s
w
itc
h
es.
Hi
g
h
f
r
eq
u
en
c
y
d
io
d
e
B
YQ2
8
is
u
s
ed
a
n
d
b
o
th
t
h
e
an
o
d
e
i
n
th
e
m
ar
e
s
h
o
r
ted
to
s
p
lit
th
e
c
u
r
r
en
t
f
o
r
r
ed
u
cin
g
t
h
e
i
n
h
er
e
n
t
f
au
lt.
Fi
g
u
r
e
9
an
d
F
ig
u
r
e
1
0
s
h
o
w
th
e
e
x
p
er
i
m
e
n
tal
r
es
u
lt
s
o
b
tain
ed
f
r
o
m
Z
SI.
Fo
r
1
2
V
in
p
u
t D
C
v
o
lta
g
e,
Z
n
et
w
o
r
k
b
o
o
s
ts
t
h
e
v
o
lta
g
e
le
v
el
u
p
to
4
6
V
an
d
m
ad
e
av
ai
lab
le
at
DC
li
n
k
v
o
ltag
e,
w
h
ic
h
is
to
b
e
f
ed
to
th
e
in
v
er
ter
.
Af
ter
in
v
er
ti
n
g
ac
t
i
o
n
b
y
Z
SI,
th
e
p
ea
k
to
p
ea
k
v
o
ltag
e
ac
r
o
s
s
th
e
lo
ad
is
o
b
tain
ed
as
9
3
V
f
o
r
th
e
r
esis
ti
v
e
lo
ad
o
f
5
0
0
o
h
m
s
.
Fig
u
r
e
9
.
DC
in
p
u
t v
o
lta
g
e
w
a
v
ef
o
r
m
Fig
u
r
e
1
0
.
P
ea
k
to
p
ea
k
o
u
tp
u
t v
o
ltag
e
w
a
v
e
f
o
r
m
T
h
e
Z
SI
i
n
v
er
t
s
th
e
b
o
o
s
ted
DC
v
o
ltag
e
a
n
d
o
u
tp
u
t
AC
v
o
ltag
e
o
f
4
6
.
6
V
is
m
ad
e
av
ai
lab
le
ac
r
o
s
s
th
e
lo
ad
,
w
h
e
n
it
is
m
ea
s
u
r
ed
w
it
h
o
u
t
f
ilter
as
s
h
o
w
n
i
n
Fi
g
.
1
0
.
T
h
ese
r
esu
lts
co
r
r
esp
o
n
d
to
th
e
t
h
eo
r
etica
l
an
al
y
s
is
a
n
d
s
i
m
u
latio
n
r
esu
lt
s
.
T
h
e
p
r
o
p
o
s
ed
Z
SI
ac
h
eiv
es
h
ig
h
b
o
o
s
t
in
v
er
s
io
n
,
u
p
to
th
e
o
r
d
er
o
f
4.
T
h
e
p
r
o
p
o
s
ed
Z
SI
b
ased
P
V
p
o
w
er
g
en
er
atio
n
s
y
s
te
m
ca
n
b
e
s
ca
led
u
p
f
o
r
g
r
id
co
n
n
ec
ted
s
y
s
te
m
,
b
ec
au
s
e
it
tr
an
s
f
er
s
t
h
e
m
a
x
i
m
u
m
p
o
w
er
f
r
o
m
t
h
e
P
V
p
an
el
to
g
r
id
w
it
h
o
u
t a
n
y
ad
d
itio
n
al
MP
PT
alg
o
r
ith
m
.
5.
CO
NCLU
SI
O
N
T
h
e
o
p
er
atio
n
o
f
Z
s
o
u
r
ce
in
v
er
ter
is
ca
r
r
ied
o
u
t
in
s
tead
y
s
tate
co
n
d
itio
n
to
a
n
al
y
ze
b
o
o
s
tin
g
a
n
d
in
v
er
s
io
n
ca
p
ab
ilit
y
th
r
o
u
g
h
s
i
m
u
lat
io
n
an
d
e
x
p
er
i
m
e
n
tal
r
esu
lt
s
.
T
h
e
o
b
tain
ed
ex
p
er
im
en
tal
r
esu
lts
v
er
if
y
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
E
xp
erimen
ta
l V
erif
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tio
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f S
in
g
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to
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p
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lica
tio
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s
(
V
.
S
a
r
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va
n
a
n
)
703
th
e
a
n
al
y
s
is
an
d
d
is
c
u
s
s
io
n
o
f
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
to
th
e
o
p
er
atio
n
o
f
Z
SI
f
o
r
p
h
o
to
v
o
ltaic
s
y
s
te
m
.
T
h
e
p
r
o
p
o
s
ed
in
v
er
ter
ca
n
r
ea
lize
b
u
ck
/b
o
o
s
t,
in
v
er
s
io
n
a
n
d
p
o
w
er
co
n
d
itio
n
in
g
in
a
s
i
n
g
le
s
tag
e
w
it
h
i
m
p
r
o
v
ed
r
eliab
ilit
y
an
d
it
ca
n
b
e
ap
p
lied
to
th
e
en
tire
s
p
ec
tr
u
m
o
f
p
o
w
er
co
n
v
er
s
io
n
.
W
h
e
n
Z
SI
co
n
n
ec
ted
to
th
e
g
r
id
s
u
p
p
l
y
,
it
r
eq
u
ir
es
to
th
e
ad
d
r
ess
t
h
e
co
n
ce
r
n
s
i
n
v
o
lv
i
n
g
p
o
w
er
r
e
g
u
latio
n
,
h
ar
m
o
n
ic
s
r
e
d
u
ctio
n
a
n
d
p
o
w
er
fa
cto
r
co
r
r
ec
tio
n
f
o
r
v
ar
io
u
s
a
p
p
licatio
n
s
w
h
ich
ar
e
le
f
t to
th
e
r
ea
d
er
s
.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
is
w
o
r
k
w
as
s
u
p
p
o
r
ted
b
y
W
in
d
E
n
er
g
y
D
iv
i
s
io
n
,
Mi
n
is
tr
y
o
f
Ne
w
&
R
en
e
w
ab
le
E
n
e
r
g
y
,
Go
v
er
n
m
e
n
t
o
f
I
n
d
ia
u
n
d
er
g
r
an
t
(
I
FD
D
y
.
No
.
1
4
2
9
d
ated
0
4
/
1
1
/2
0
1
6
,
Dem
an
d
No
.
6
1
/6
9
,
B
u
d
g
et
Hea
d
:
2
8
1
0
.
0
0
.
1
0
4
.
0
4
.
0
5
.
3
1
/3
5
)
.
RE
F
E
R
E
NC
E
S
[1
]
L
a
ri
No
u
sia
in
e
n
,
Jo
o
n
a
s
P
u
u
k
k
o
,
A
n
ss
iM
¨a
k
i
,
T
u
o
m
a
s M
e
s
so
,
Ju
h
a
Hu
u
sa
ri
,
Ju
h
a
Jo
k
ip
i
i
,
Ju
k
k
a
V
ii
n
a
m
¨a
k
i,
Die
g
o
T
o
rre
s
L
o
b
e
ra
,
S
e
p
p
o
V
a
lk
e
a
lah
ti
,
a
n
d
T
e
u
v
o
S
u
n
ti
o
,
“
P
h
o
to
v
o
lt
a
ic
G
e
n
e
ra
to
r
a
s
a
n
In
p
u
t
S
o
u
rc
e
f
o
r
P
o
w
e
r
El
e
c
tro
n
ic C
o
n
v
e
rters
”
,
IEE
E
T
r
a
n
sa
c
ti
o
n
s o
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l.
2
8
,
p
p
.
3
0
2
8
-
3
0
3
8
,
2
0
1
3
.
[2
]
Ya
o
su
o
X
u
e
,
L
iu
c
h
e
n
C
h
a
n
g
,
S
ø
re
n
Bæk
h
ø
j
Kjær
,
Jo
se
p
Bo
r
d
o
n
a
u
a
n
d
T
o
sh
ih
isa
S
h
im
izu
,
“
T
o
p
o
l
o
g
ies
o
f
S
in
g
le
P
h
a
se
In
v
e
rters
f
o
r
S
m
a
ll
Distrib
u
ted
P
o
w
e
r
G
e
n
e
ra
to
rs:
A
n
Ov
e
r
v
ie
w
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
1
9
,
p
p
.
1
3
0
5
–
1
3
1
4
,
2
0
0
4
.
[3
]
G
u
n
jan
V
a
rsh
n
e
y
,
D.
S
.
Ch
a
u
h
a
n
,
M
.
P
.
Da
v
e
,
“
Ev
a
lu
a
ti
o
n
o
f
p
o
we
r
q
u
a
li
ty
i
ss
u
e
s
in
g
rid
c
o
n
n
e
c
ted
P
V
s
y
ste
m
s
”
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l.
6
,
p
p
.
1
4
1
2
-
1
4
2
0
,
2
0
1
6
.
[4
]
Ya
m
P
.
S
iw
a
k
o
ti
,
F
a
n
g
Zh
e
n
g
P
e
n
g
,
F
re
d
e
Blaa
b
jerg
,
P
o
h
Ch
ian
g
L
o
h
,
a
n
d
G
ra
h
a
m
E.
T
o
w
n
,
“
I
m
p
e
d
a
n
c
e
so
u
rc
e
n
e
tw
o
rk
s
f
o
r
e
lec
tri
c
p
o
w
e
r
c
o
n
v
e
rsio
n
P
a
rt
I
:
A
to
p
o
l
o
g
ica
l
re
v
iew
”
,
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
ics
,
v
o
l.
3
0
,
p
p
.
6
9
9
–
7
1
6
,
2
0
1
5
.
[5
]
De
e
p
a
k
Ku
m
a
r,
Zak
ir
H
u
sa
in
,
“
A
c
o
m
p
a
ra
ti
v
e
stu
d
y
o
f
Z
so
u
rc
e
in
v
e
rter
f
e
d
th
re
e
p
h
a
s
e
IM
d
riv
e
w
it
h
CS
I
a
n
d
V
S
I
f
e
d
IM
”
,
I
n
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
m
,
v
o
l.
3
,
p
p
.
2
5
9
-
2
7
0
,
2
0
1
3
.
[6
]
S
.
S
h
a
n
m
u
g
a
su
n
d
a
ra
m
,
“
S
o
lar
b
a
se
d
Z
so
u
rc
e
in
v
e
rter
f
o
r
h
ig
h
p
o
w
e
r
a
p
p
li
c
a
ti
o
n
”
,
Bu
l
letin
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
I
n
fo
rm
a
ti
c
s
,
v
o
l.
6
,
p
p
.
3
4
3
-
3
4
7
,
2
0
1
7
.
[7
]
R.
M
a
lath
i,
M
.
Ra
th
in
a
k
u
m
a
r,
“
C
o
m
p
a
riso
n
o
f
sin
e
a
n
d
sp
a
c
e
v
e
c
to
r
m
o
d
u
late
d
e
m
b
e
d
d
e
d
Z
so
u
r
c
e
in
v
e
rter
f
e
d
th
re
e
p
h
a
se
in
d
u
c
ti
o
n
m
o
to
r
d
r
iv
e
s
y
ste
m
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
,
v
o
l.
7
,
p
p
.
1
2
4
0
-
1
2
5
1
,
2
0
1
6
.
[8
]
Ha
n
if
,
M
.
,
Ba
su
,
M
.
a
n
d
G
a
u
g
h
a
n
,
K,
“
Un
d
e
rsta
n
d
i
n
g
th
e
o
p
e
ra
ti
o
n
o
f
a
Z
so
u
rc
e
in
v
e
rter
fo
r
p
h
o
to
v
o
l
taic
a
p
p
li
c
a
ti
o
n
w
it
h
a
d
e
sig
n
Ex
a
m
p
le”
,
IET
Po
we
r E
lec
tro
n
ics
, v
o
l.
4
,
p
p
.
2
7
8
-
2
8
7
,
2
0
1
1
.
[9
]
C
.
Bh
a
ra
ti
ra
ja
e
t.
a
l,
“
A
n
a
ly
sis,
d
e
sig
n
a
n
d
in
v
e
stig
a
ti
o
n
o
n
a
n
e
w
sin
g
le
p
h
a
se
sw
it
c
h
e
d
q
u
a
si
Z
so
u
rc
e
in
v
e
rter
f
o
r
p
h
o
to
v
o
lt
a
ic a
p
p
li
c
a
ti
o
n
”
,
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
i
c
s a
n
d
Dr
ive
S
y
ste
m
, v
o
l.
8
,
p
p
.
8
5
3
-
8
6
0
,
2
0
1
7
.
[1
0
]
M
a
rc
e
lo
G
r
a
d
e
ll
a
V
il
lalv
a
,
Jo
n
a
s
Ra
fa
e
l
G
a
z
o
li
a
n
d
Ern
e
sto
Ru
p
p
e
rt
F
il
h
o
,
“
Co
m
p
re
h
e
n
siv
e
a
p
p
ro
a
c
h
to
m
o
d
e
li
n
g
a
n
d
sim
u
latio
n
o
f
p
h
o
to
v
o
lt
a
i
c
a
rra
y
s”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
ics
, v
o
l.
2
4
,
p
p
.
1
1
9
8
-
1
2
0
8
,
2
0
0
9
.
[1
1
]
Him
a
n
sh
u
S
h
a
rm
a
,
Nitai
P
a
l,
P
ra
d
ip
Ku
m
a
r
S
a
d
h
u
,
“
M
o
d
e
li
n
g
a
n
d
sim
u
latio
n
o
f
o
ff
g
rid
p
o
w
e
r
g
e
n
e
ra
ti
o
n
sy
ste
m
u
sin
g
p
h
o
t
o
v
o
lt
a
ic”
,
T
E
L
KOM
NIKA
In
d
o
n
e
si
a
n
J
o
u
rn
a
l
o
f
E
lec
trica
l
En
g
in
e
e
rin
g
,
v
o
l
.
1
3
,
p
p
.
4
1
8
-
4
2
4
,
2
0
1
5
.
[1
2
]
S
o
b
h
a
n
Do
ra
h
a
k
i,
“
Ev
a
lu
a
ti
n
g
th
e
ra
d
iatio
n
a
n
d
tem
p
e
ra
tu
re
e
ff
e
c
t
o
n
p
h
o
t
o
v
o
lt
a
ic
s
y
ste
m
s
”
,
Bu
ll
e
ti
n
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
I
n
fo
rm
a
ti
c
s
,
v
o
l.
4
,
p
p
.
1
-
6
,
2
0
1
5
.
[1
3
]
M
.
A
ra
v
in
d
a
n
a
n
d
V
.
S
a
ra
v
a
n
a
n
,
“
P
e
rf
o
rm
a
n
c
e
a
n
a
l
y
sis
o
f
sin
g
le
p
h
a
se
in
v
e
rter
f
o
r
p
h
o
t
o
v
o
l
taic
s
y
ste
m
s
”,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
A
p
p
li
e
d
En
g
i
n
e
e
rin
g
Res
e
a
rc
h
,
v
o
l.
1
0
,
p
p
.
2
7
7
7
0
–
2
7
7
7
4
,
2
0
1
5
.
[1
4
]
Yu
T
a
n
g
,
S
h
a
o
ju
n
X
ie
a
n
d
Ch
a
o
h
u
a
Zh
a
n
g
,
“
S
i
n
g
le
p
h
a
se
Z
so
u
rc
e
i
n
v
e
rter”
,
IEE
E
T
ra
n
sa
c
t
io
n
s
o
n
Po
we
r
El
e
c
tro
n
ics
, v
o
l.
2
6
,
p
p
.
3
8
6
9
-
3
8
7
3
,
2
0
1
1
.
[1
5
]
Do
n
g
Ca
o
,
S
h
u
a
i
Jia
n
g,
X
ia
n
h
a
o
Yu
,
a
n
d
F
a
n
g
Zh
e
n
g
P
e
n
g
,
“
L
o
w
c
o
st
se
m
i
Z
so
u
rc
e
in
v
e
rter
f
o
r
sin
g
le
p
h
a
se
p
h
o
to
v
o
lt
a
ic
s
y
ste
m
s
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
2
6
,
p
p
.
3
5
1
4
–
3
5
2
3
,
2
0
1
1
.
[1
6
]
P
o
h
Ch
ia
n
g
L
o
h
,
F
e
n
g
G
a
o
a
n
d
F
re
d
e
Blaa
b
jerg
,
“
Em
b
e
d
d
e
d
EZ
so
u
rc
e
i
n
v
e
rters
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
In
d
u
str
y
Ap
p
li
c
a
ti
o
n
s
, v
o
l
.
4
6
,
p
p
.
2
5
6
–
2
6
7
,
2
0
1
0
.
[1
7
]
Ya
m
P
.
S
iw
a
k
o
ti
,
F
Z
P
e
n
g
,
F
re
d
e
Blaa
b
jerg
,
P
C
L
o
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