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M
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also
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5
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T
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ter
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W
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ilit
y
an
d
e
f
f
ic
ien
c
y
o
f
th
e
s
y
s
te
m
[
8
]
.
T
h
e
tr
an
s
f
o
r
m
er
cr
ea
tes
t
h
e
p
ath
f
o
r
th
e
leak
a
g
e
cu
r
r
en
t
b
et
w
ee
n
t
h
e
P
V
ar
r
ay
a
n
d
th
e
g
r
id
[
9
]
.
T
h
er
ef
o
r
e,
DC
-
T
L
I
is
u
s
ed
to
p
r
ev
en
t
t
h
e
leak
a
g
e
cu
r
r
en
t.
T
h
e
p
r
o
p
o
s
ed
s
y
s
t
e
m
u
s
es
h
y
s
ter
esi
s
s
p
ac
e
v
ec
to
r
m
o
d
u
lat
io
n
(
HSVM)
as
th
e
co
n
tr
o
l
tech
n
i
q
u
e.
HSVM
co
n
tr
o
l
s
th
e
cu
r
r
en
t
in
a
c
ir
cu
lar
h
y
s
ter
esi
s
ar
ea
to
p
er
f
o
r
m
t
h
e
b
alan
cin
g
o
f
d
c
v
o
lta
g
e
[
1
0
]
.
T
h
is
p
r
o
p
o
s
ed
s
y
s
te
m
m
ak
e
s
u
s
e
o
f
co
u
p
led
in
d
u
cto
r
z
s
o
u
r
ce
d
io
d
e
clam
p
ed
th
r
ee
le
v
el
in
v
er
ter
(
C
I
-
Z
-
D
C
-
T
L
I
)
w
it
h
t
h
e
P
V
ar
r
ay
a
s
t
h
e
i
n
p
u
t
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
te
m
;
co
u
p
led
i
n
d
u
cto
r
s
ar
e
u
s
ed
to
r
ed
u
ce
th
e
co
s
t
an
d
lo
s
s
es.
T
h
e
z
s
o
u
r
ce
n
et
w
o
r
k
b
o
o
s
ts
t
h
e
o
u
tp
u
t
v
o
ltag
e
an
d
f
u
r
th
er
i
m
p
r
o
v
e
s
t
h
e
r
eliab
ilit
y
o
f
t
h
e
s
y
s
te
m
b
y
p
r
ev
en
t
in
g
t
h
e
s
h
o
o
t
-
t
h
r
o
u
g
h
p
r
o
b
le
m
.
2.
P
V
ARRA
Y
AND
M
P
P
T
AL
G
O
R
I
T
H
M
P
h
o
to
v
o
ltaic
ar
r
ay
en
er
g
y
ca
n
b
e
d
i
r
ec
tly
r
eh
ab
il
itated
in
to
elec
tr
ic
en
er
g
y
u
s
i
n
g
a
d
ev
ice
k
n
o
w
n
a
s
P
h
o
to
v
o
ltaic
ce
ll.
L
ig
h
t
e
n
er
g
y
i
s
co
n
v
er
ted
in
to
elec
tr
i
ca
l
en
er
g
y
u
s
in
g
a
p
r
o
ce
s
s
ca
lled
as
th
e
“
p
h
o
to
v
o
ltaic
ef
f
ec
t”.
P
V
ce
lls
ar
e
m
ad
e
u
p
o
f
p
r
im
ar
il
y
t
w
o
s
e
m
i
-
co
n
d
u
cto
r
lay
er
s
,
v
iz;
a
P
-
la
y
er
w
h
ich
co
n
s
i
s
ts
o
f
th
e
p
o
s
itiv
e
c
h
ar
g
e
a
n
d
a
n
n
-
la
y
er
w
h
ic
h
co
n
s
i
s
t
o
f
n
e
g
ati
v
e
c
h
a
r
g
e.
T
h
e
P
V
ce
ll’s
o
u
tp
u
t
v
o
lt
ag
e
d
ep
en
d
s
o
n
t
h
e
s
u
n
li
g
h
t
i
n
ten
s
it
y
,
te
m
p
er
at
u
r
e,
ef
f
icien
c
y
a
n
d
s
ize
o
f
t
h
e
p
an
el.
T
h
e
P
V
ar
r
ay
i
s
s
i
m
p
l
y
a
co
m
b
i
n
ati
o
n
o
f
m
an
y
P
V
ce
lls
i
n
s
er
ies o
r
p
ar
allel
co
n
n
ec
t
io
n
to
p
r
o
d
u
ce
an
o
u
tp
u
t v
o
lta
g
e
an
d
c
u
r
r
en
t [
1
1
].
=
−
Q
R
(
1
)
Q
r
=
Q
0
(
e
q
V
p
hT
−
1
)
1)
(
2
)
W
h
er
e
h
is
t
h
e
B
o
ltz
m
a
n
n
’
s
co
n
s
ta
n
t,
ɸs
i
s
s
h
o
r
t
cir
cu
it
c
u
r
r
en
t,
q
is
t
h
e
elec
tr
o
n
c
h
ar
g
e,
ɸo
is
th
e
r
eser
v
e
s
atu
r
atio
n
cu
r
r
en
t,
T
is
th
e
ju
n
ct
io
n
te
m
p
er
at
u
r
e,
Vp
is
th
e
v
o
lta
g
e
ac
r
o
s
s
th
e
d
io
d
e
an
d
ɸr
is
th
e
d
io
d
e
cu
r
r
en
t.
T
h
er
ef
o
r
e
s
u
b
s
ti
tu
t
in
g
eq
u
atio
n
(
1
)
in
(
2
)
,
w
e
h
av
e,
ɸ
=
ɸ
S
−
ɸ
O
(
e
q
V
p
hT
−
1
)
−
1)
(
3
)
Sin
ce
th
e
s
o
u
r
ce
is
n
o
n
-
lin
ea
r
,
P
V
p
an
el’
s
ef
f
icie
n
c
y
is
ex
tr
e
m
el
y
lo
w
a
n
d
h
en
ce
to
in
cr
ea
s
e
th
e
ef
f
icie
n
c
y
o
p
er
atin
g
p
o
in
t
o
f
t
h
e
p
an
el
is
s
h
i
f
ted
to
t
h
e
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
(
MP
P
)
[
1
2
]
.
Ma
x
i
m
u
m
p
o
w
er
p
o
in
t tr
ac
k
er
(
MP
PT
)
is
u
s
ed
t
o
tr
ac
k
th
e
m
a
x
i
m
u
m
p
o
w
er
f
r
o
m
t
h
e
P
V
p
an
el.
(
a)
(
b
)
Fig
u
r
e
1
.
(
a)
P
V
Mo
d
el
an
d
(
b
)
I
-
V
C
h
ar
ac
ter
i
s
tics
2.
1.
M
P
P
T
Alg
o
rit
h
m
T
h
e
co
m
p
ete
n
ce
o
f
t
h
e
s
o
lar
p
an
el
ca
n
b
e
en
h
an
ce
d
w
h
e
n
M
P
PT
is
u
s
ed
to
ex
tr
ac
t
m
a
x
i
m
u
m
p
o
w
er
co
m
in
g
f
r
o
m
t
h
e
P
V
p
an
el.
T
h
e
P
V
o
u
tp
u
t
d
ep
en
d
s
o
n
th
e
en
v
ir
o
n
m
e
n
tal
f
ac
to
r
s
w
h
ic
h
v
ar
y
f
r
o
m
s
u
n
r
is
e
to
s
u
n
s
et.
T
o
ac
h
iev
e
m
a
x
i
m
u
m
ef
f
icie
n
c
y
o
f
th
e
p
an
e
l
w
e
m
a
k
e
th
e
g
r
o
u
p
to
o
p
er
atio
n
at
M
P
P
[
1
3
]
,
[
1
4
]
.
Fro
m
th
e
m
a
x
i
m
u
m
tr
an
s
f
er
th
eo
r
em
;
in
a
cir
cu
it,
th
e
o
u
tp
u
t
p
o
w
er
is
m
a
x
i
m
u
m
w
h
e
n
th
e
s
o
u
r
ce
s
id
e
i
m
p
ed
an
ce
m
atc
h
es
th
e
lo
ad
s
id
e
im
p
ed
a
n
ce
[
1
5
]
.
T
h
e
s
im
p
lest
a
n
d
m
o
s
t
u
s
ed
m
eth
o
d
to
en
s
u
r
e
th
at
th
e
P
V
p
an
el
is
o
p
er
atin
g
at
MP
P
is
p
er
tu
r
b
a
n
d
o
b
s
er
v
e
(
P
&
0
)
alg
o
r
it
h
m
.
A
p
er
t
u
r
b
atio
n
w
as
m
ad
e
f
r
o
m
t
h
e
P
V
p
an
el
t
h
e
v
o
ltag
e
a
n
d
cu
r
r
en
t
ar
e
o
b
tain
ed
to
ca
lcu
late
th
e
o
u
tp
u
t
p
o
wer
[
1
6
]
.
T
h
e
p
r
ev
io
u
s
p
o
w
er
an
d
Δ
P
is
co
m
p
ar
ed
w
it
h
ca
lc
u
lated
p
o
w
er
.
I
f
th
e
d
if
f
er
en
ce
Δ
P
˃
0
,
th
e
n
t
h
e
p
er
tu
r
b
atio
n
is
co
n
ti
n
u
ed
in
th
e
d
ir
ec
tio
n
b
u
t
w
h
e
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
:1
1
8
1
–
1
1
9
2
1183
Δ
P
˂
0
th
en
th
e
d
ir
ec
tio
n
i
s
r
ev
er
s
ed
.
Fig
u
r
e
2
.
Flo
w
C
h
ar
t o
f
P
er
tu
r
b
&
Ob
s
er
v
e
A
l
g
o
r
ith
m
3.
DIOD
E
C
L
AM
P
E
D
T
H
RE
E
L
E
VE
L
I
N
VE
R
T
E
R
Dio
d
e
-
cla
m
p
ed
th
r
ee
le
v
el
(
D
C
-
T
L
I
)
in
v
er
ter
h
a
s
g
a
in
ed
m
u
ch
i
n
ter
es
t
in
r
ec
e
n
t
y
ea
r
s
an
d
is
w
id
el
y
ac
ce
p
ted
b
y
r
esear
c
h
er
s
to
d
a
y
[
1
7
]
.
A
ls
o
k
n
o
w
n
a
s
NP
C
t
h
r
e
e
lev
el
i
n
v
er
ter
is
s
h
o
w
n
i
n
F
ig
u
r
e
3
.
B
ec
au
s
e
o
f
its
to
p
o
lo
g
ical
ad
v
an
ta
g
es
s
u
c
h
as
o
v
er
co
m
i
n
g
t
h
e
p
r
o
b
lem
o
f
leak
ag
e
c
u
r
r
en
t
an
d
p
r
ev
en
t
in
g
t
h
e
in
s
er
tio
n
o
f
DC
c
u
r
r
en
ts
in
to
th
e
g
r
id
,
d
io
d
e
cla
m
p
ed
th
r
ee
le
v
el
i
n
v
er
te
r
is
b
r
o
ad
ly
ac
ce
p
ted
in
a
tr
an
s
f
o
r
m
er
le
s
s
s
y
s
te
m
w
it
h
P
V
co
n
n
ec
ted
to
th
e
g
r
id
n
et
w
o
r
k
[
1
8
]
,
[1
9
]
.
Fig
u
r
e
3
.
T
h
r
ee
L
ev
el
Dio
d
e
-
C
la
m
p
ed
I
n
v
er
ter
Fig
u
r
e
4
.
C
o
u
p
led
I
n
d
u
cto
r
B
ased
Dio
d
e
C
la
m
p
ed
Dio
d
e
-
cla
m
p
ed
in
v
er
ter
g
e
n
e
r
ates
s
tair
ca
s
e
v
o
lta
g
e
at
it
s
o
u
tp
u
t
w
it
h
v
ar
io
u
s
D
C
v
o
lt
ag
e
lev
el
s
d
ev
elo
p
ed
b
y
D
C
s
p
lit
ca
p
ac
i
to
r
s
.
I
f
t
h
e
n
u
m
b
er
o
f
r
eq
u
ir
e
d
lev
el
i
s
g
iv
e
n
as
k
,
t
h
e
n
u
m
b
er
o
f
ca
p
ac
ito
r
s
n
ee
d
ed
ac
r
o
s
s
th
e
DC
b
u
s
ar
e
(
k
-
1
)
,
p
o
w
er
elec
tr
o
n
ic
s
w
i
tc
h
es
p
er
p
h
ase
ca
n
b
e
ca
lcu
late
d
as
2
(
k
-
1
)
an
d
th
e
n
u
m
b
er
o
f
d
io
d
es
p
e
r
p
h
ase
w
ill
b
e
g
iv
en
as
2
(
k
-
2
)
.
T
h
is
f
o
r
m
u
la
is
m
o
s
tl
y
s
ta
n
d
ar
d
f
o
r
all
th
e
d
io
d
e
cl
am
p
ed
m
u
ltil
e
v
el
i
n
v
er
ter
s
.
Fro
m
th
e
d
esig
n
f
o
r
m
u
la,
t
h
r
ee
le
v
e
l
in
v
er
ter
r
eq
u
ir
es
2
ca
p
ac
it
o
r
s
,
t
h
en
4
p
o
w
er
s
w
itc
h
es
a
n
d
2
cla
m
p
in
g
d
io
d
es
p
er
p
h
ase
(
leg
)
.
E
ac
h
o
f
t
h
e
p
o
w
er
s
w
itc
h
es
h
a
s
co
m
p
li
m
en
tar
y
s
w
itch
p
air
,
w
h
e
n
a
s
w
itc
h
is
t
u
r
n
ed
ON
t
h
en
its
co
m
p
l
i
m
e
n
tar
y
s
w
itc
h
s
h
o
u
ld
b
e
OFF
.
3
.
1
.
Co
up
led In
du
ct
o
r
B
a
s
e
d Dio
de
Cla
m
ped
I
nv
er
t
er
I
n
g
r
id
-
co
n
n
e
cted
P
V
s
y
s
te
m
s
li
n
e
tr
a
n
s
f
o
r
m
er
s
ar
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I
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PEDS
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u
r
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a)
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1
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b
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1
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c)
0
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(
d
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11
5.
H
YST
E
RE
SI
S
SPAC
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T
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DULAT
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co
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ir
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cir
cle
w
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th
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s
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1
+
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2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
694
IJ
PEDS
Vo
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7
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h
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ased
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u
r
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r
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Fig
u
r
e
9
.
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t
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s
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g
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s
w
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h
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f
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eq
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lated
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o
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e
t
h
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d
ar
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-
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I
I
w
it
h
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ad
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=
(
r
>
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.
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r
ea
A
-
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r
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r
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t
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o
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e
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ec
t
o
r
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h
ic
h
is
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0
.
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r
ea
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I
i
s
s
u
b
d
iv
id
ed
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n
to
s
i
x
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ec
to
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s
:
S
1
,
S
4
,
S
7
,
S
1
0
,
S
1
3
,
an
d
S
1
6
.
I
n
Fi
g
u
r
e
9
,
t
w
o
s
eq
u
en
tial
s
ec
to
r
s
ar
e
s
ep
ar
ate
d
ap
ar
t
b
y
an
a
n
g
le
o
f
6
0
◦
.
=
ta
n
(
∆
∆
)
(
1
7
)
T
h
e
lo
ca
tio
n
o
f
th
e
v
ec
to
r
(
∆
)
h
ea
d
ca
n
b
e
f
o
u
n
d
w
it
h
i
n
o
n
e
am
o
n
g
th
e
s
ec
to
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s
w
h
ich
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n
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e
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ased
o
n
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e
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g
le
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n
d
ar
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h
er
e
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f
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I
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