I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
,
p
p
.
6
2
6
8
~6
2
7
5
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v
1
0
i
6
.
p
p
6
2
6
8
-
6
2
7
5
6268
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m/in
d
ex
.
p
h
p
/I
JE
C
E
M
PP
T
o
scilla
tion
s
m
i
ni
m
i
z
a
tion
in
PV
sy
ste
m
by
con
trolling
n
on
-
l
inea
r dyna
mics
in
SE
PIC D
C
-
DC
co
nv
ert
er
M.
Va
ig
un
da
m
o
o
rt
hi
1
,
R.
R
a
m
e
s
h
2
,
V.
Va
s
a
n P
ra
bh
u
3
,
K.
Arul
K
u
m
a
r
4
1
,4
De
p
a
rtm
e
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
,
M
a
d
a
n
a
p
a
ll
e
In
stit
u
te o
f
T
e
c
h
n
o
lo
g
y
&
S
c
ie
n
c
e
,
In
d
ia
2
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
i
n
e
e
rin
g
,
CEG
,
A
n
n
a
Un
iv
e
rsity
,
In
d
ia
3
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
i
n
e
e
rin
g
,
S
t.
Jo
se
p
h
’s
C
o
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
In
d
ia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Feb
27
,
2
0
1
9
R
ev
i
s
ed
Ma
y
2
,
2020
A
cc
ep
ted
J
u
n
1
7
,
2
0
2
0
S
o
lar
P
V
p
o
w
e
r
g
e
n
e
ra
ti
o
n
h
a
s
a
c
h
iev
e
d
ra
p
i
d
g
ro
w
th
i
n
d
e
v
e
lo
p
i
n
g
c
o
u
n
tr
ies
w
h
ich
h
a
s
m
a
n
y
m
e
rit
s
su
c
h
a
s
a
b
se
n
c
e
o
f
n
o
ise
,
lo
n
g
e
r
li
f
e
,
n
o
p
o
ll
u
ti
o
n
,
les
s
ti
m
e
f
o
r
in
sta
ll
a
ti
o
n
,
a
n
d
e
a
se
o
f
g
rid
in
terf
a
c
e
.
A
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
c
ircu
it
(M
P
P
T
)
c
o
n
sists
o
f
DC
-
DC
p
o
w
e
r
e
lec
tro
n
ics
c
o
n
v
e
rters
th
a
t
a
re
u
se
d
to
im
p
ro
v
e
th
e
e
n
e
rg
y
a
tt
a
in
m
e
n
t
f
ro
m
so
lar
P
V
a
rra
y
.
T
h
is
p
a
p
e
r
p
re
se
n
ts
a
d
e
tailed
a
n
a
ly
sis
to
c
o
n
tro
l
o
f
c
h
a
o
s
,
a
n
o
n
-
l
in
e
a
r
d
y
n
a
m
i
c
in
S
E
P
IC
DC
-
DC
c
o
n
v
e
rter
i
n
terf
a
c
e
d
so
lar
P
V
sy
ste
m
,
to
m
in
im
i
z
e
th
e
o
sc
il
la
ti
o
n
s
n
e
a
r
to
M
P
P
.
In
S
E
P
IC
DC
-
DC
c
o
n
v
e
rter,
th
e
in
p
u
t
in
d
u
c
t
o
r
c
u
rre
n
t
is
c
o
n
ti
n
u
o
u
s
a
n
d
c
a
p
a
b
le
o
f
sw
e
e
p
in
g
th
e
w
h
o
l
e
I
-
V
c
u
rv
e
o
f
a
P
V
m
o
d
u
le
f
ro
m
o
p
e
n
c
ircu
i
t
v
o
lt
a
g
e
(V
oc
)
to
sh
o
r
t
c
ircu
it
c
u
rr
e
n
t
(I
sc
)
o
p
e
ra
ti
n
g
p
o
in
ts.
T
o
trac
e
th
e
tru
e
m
a
x
i
m
u
m
p
o
we
r
p
o
in
t
a
n
d
to
n
u
ll
if
y
th
e
o
sc
il
latio
n
s
n
e
a
r
to
M
P
P
,
th
e
y
ield
o
u
t
p
u
t
v
o
lt
a
g
e
n
e
e
d
s to
e
n
su
re
p
e
rio
d
-
1
o
p
e
ra
ti
o
n
.
K
ey
w
o
r
d
s
:
A
d
ap
tiv
e
co
n
tr
o
ller
C
h
ao
s
MP
PT
SEP
I
C
co
n
v
er
ter
So
lar
P
V
m
o
d
u
le
Co
p
y
rig
h
t
©
2
0
2
0
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
M.
Vaig
u
n
d
a
m
o
o
r
t
h
i,
Dep
ar
t
m
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
i
n
ee
r
in
g
,
Ma
d
an
ap
alle
I
n
s
t
i
tu
te
o
f
T
ec
h
n
o
lo
g
y
&
Scie
n
ce
,
Ma
d
an
ap
alle
,
An
d
h
r
a
P
r
ad
esh
-
5
1
7
3
2
5
,
I
n
d
ia
.
E
m
ail
:
b
ac
y
a
v
ai
g
o
2
0
0
0
@
g
m
a
il.c
o
m
;
d
r
v
ai
g
u
n
d
a
m
o
o
r
th
i
m
@
m
its
.
ac
.
i
n
1.
I
NT
RO
D
UCT
I
O
N
So
lar
p
o
w
er
is
a
Gr
ee
n
en
er
g
y
s
o
u
r
ce
s
th
at
e
m
p
lo
y
s
DC
-
D
C
co
n
v
er
ter
to
h
ar
v
est
m
a
x
i
m
u
m
p
o
w
er
.
T
h
e
ef
f
icie
n
c
y
o
f
th
e
e
n
er
g
y
co
n
v
er
s
io
n
p
r
o
ce
s
s
is
d
ec
li
n
ed
d
u
e
to
cli
m
ate
v
ar
iab
le
te
m
p
er
at
u
r
e,
p
ar
tial
s
h
ad
in
g
,
an
d
at
m
o
s
p
h
er
ic
ir
r
ad
iatio
n
c
h
an
g
e
an
d
lo
ad
co
n
d
itio
n
s
.
T
h
e
P
V
cu
r
r
en
t
ch
an
g
es
w
it
h
ir
r
ad
iatio
n
g
r
ea
tl
y
a
n
d
th
e
at
m
o
s
p
h
er
ic
te
m
p
er
at
u
r
e
af
f
ec
ts
P
V
v
o
lta
g
e
[
1
-
4
]
.
T
h
e
MP
P
is
d
etec
ted
b
y
A
d
ap
tiv
e
p
er
tu
r
b
an
d
o
b
s
er
v
er
MP
PT
alg
o
r
ith
m
w
h
ic
h
i
s
e
m
b
ed
d
ed
in
Mic
r
o
co
n
tr
o
ller
,
g
en
er
ate
g
a
te
p
u
l
s
e
w
h
ich
is
ap
p
lied
to
th
e
D
C
-
DC
co
n
v
er
ter
s
w
itc
h
es [
5
-
8
]
.
T
h
e
v
ar
i
o
u
s
ty
p
e
s
o
f
DC
-
D
C
co
n
v
er
ter
s
[
9
-
1
2
]
s
u
ch
as
b
u
ck
,
b
o
o
s
t,
b
u
ck
b
o
o
s
t,
C
u
k
an
d
SEP
I
C
a
r
e
i
m
p
le
m
en
ted
i
n
P
V
s
y
s
te
m
b
y
co
n
s
id
er
in
g
s
u
itab
ilit
y
f
ac
to
r
s
s
u
ch
a
s
co
s
t,
ef
f
icie
n
c
y
,
m
ax
i
m
u
m
p
o
w
er
f
lo
w
,
ea
s
e
o
f
d
r
iv
e
s
y
s
te
m
,
P
o
s
itiv
e
o
u
tp
u
t
v
o
lta
g
e,
s
y
s
te
m
s
tab
il
it
y
a
n
d
co
n
cl
u
d
ed
th
at
SEP
I
C
co
n
v
er
ter
is
co
m
m
o
n
l
y
u
s
ed
in
P
V
s
y
s
te
m
to
tr
ac
k
m
ax
i
m
u
m
p
o
w
er
f
r
o
m
P
V
p
an
el
.
Hig
h
er
o
r
d
er
c
o
n
v
er
ter
s
u
c
h
as
SEP
I
C
an
d
C
u
k
ar
e
w
id
el
y
u
s
ed
f
o
r
MP
PT
ch
ar
g
e
co
n
tr
o
ller
b
ec
au
s
e
o
f
th
eir
ex
ce
lle
n
t
s
tead
y
s
tate
p
er
f
o
r
m
an
ce
,
is
o
latio
n
,
o
v
er
cu
r
r
en
t
l
i
m
i
t
p
r
o
tectio
n
[
1
3
-
2
1
]
.
Qu
a
m
r
u
zz
a
m
a
n
[
1
7
]
h
as
ar
g
u
ed
t
h
at
t
h
e
P
V
c
u
r
r
en
t
with
le
s
s
r
ip
p
le
a
n
d
i
m
p
r
o
v
ed
d
y
n
a
m
ic
r
esp
o
n
s
e
c
an
b
e
ac
h
iev
ed
b
y
SEP
I
C
co
n
v
er
ter
also
p
r
o
v
ed
th
a
t
h
ig
h
i
n
p
u
t
c
u
r
r
en
t
r
ip
p
le
co
n
ten
t o
f
th
e
co
n
v
er
ter
r
ed
u
c
es th
e
a
v
er
ag
e
v
a
lu
e
o
f
cu
r
r
en
t
w
h
ic
h
m
a
y
lead
s
to
w
r
o
n
g
tr
u
e
MP
P tr
ac
k
in
g
.
No
n
-
l
in
ea
r
d
y
n
a
m
ic
s
i
n
p
o
w
er
elec
tr
o
n
ics
cir
c
u
it
s
w
as
p
u
t
f
o
r
w
ar
d
i
n
[
2
2
-
2
4
]
u
n
d
er
g
o
s
u
b
-
h
ar
m
o
n
ics,
q
u
asi
-
p
er
io
d
ic
o
s
cillatio
n
s
,
a
n
d
ch
ao
tic
m
o
d
e
o
f
o
p
er
atio
n
.
T
h
e
ch
ao
s
i
s
ex
p
er
ie
n
ce
d
in
D
C
-
D
C
co
n
v
er
ter
s
an
d
its
co
n
tr
o
l
m
eth
o
d
s
ar
e
co
n
d
u
cted
in
p
o
w
er
elec
tr
o
n
ics
cir
cu
it
s
.
T
h
is
ab
n
o
r
m
al
o
p
er
atio
n
w
o
u
ld
af
f
ec
t
co
n
v
er
te
r
tr
ac
k
in
g
ef
f
icie
n
c
y
s
i
n
ce
th
e
p
er
io
d
-
1
o
p
er
ati
o
n
n
ee
d
to
b
e
en
s
u
r
ed
f
o
r
MP
P
tr
ac
k
in
g
i
n
o
r
d
er
t
o
m
i
n
i
m
ize
o
s
cillatio
n
s
n
ea
r
to
MP
P
.
Sev
er
al
s
tu
d
ies
[
2
5
-
27]
h
a
v
e
s
u
g
g
ested
m
a
n
y
co
n
tr
o
l
m
et
h
o
d
s
t
h
at
ar
e
m
i
tig
a
ted
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Oscill
a
tio
n
s
min
imi
z
a
tio
n
a
t
MPP
b
y
co
n
tr
o
llin
g
n
o
n
-
lin
e
a
r
d
yn
a
mics in
..
.
(
M.
V
a
ig
u
n
d
a
mo
o
r
th
i)
6269
s
u
p
r
ess
c
h
ao
s
.
A
ls
o
,
T
h
e
P
I
D
co
n
tr
o
ller
an
d
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
s
ar
e
also
ex
p
er
i
m
e
n
ted
to
n
u
lli
f
y
t
h
e
ef
f
ec
t
o
f
ch
ao
s
i
n
DC
-
D
C
co
n
v
er
ter
s
.
T
h
is
p
ap
er
ex
p
lo
r
es
th
at
SEP
I
C
D
C
-
DC
co
n
v
er
ter
in
te
r
f
ac
ed
s
o
lar
P
V
s
y
s
te
m
m
a
y
e
n
ter
i
n
t
o
ch
ao
tic
-
ap
er
io
d
ic
m
o
d
e
d
u
r
in
g
m
ax
i
m
u
m
p
o
w
er
tr
ac
k
i
n
g
p
r
o
ce
s
s
.
T
h
e
an
al
y
s
i
s
an
d
s
u
p
p
r
ess
io
n
o
f
ch
ao
s
in
a
v
o
lta
g
e
m
o
d
e
-
co
n
tr
o
lled
SEP
I
C
co
n
v
er
ter
-
b
ased
s
o
lar
P
V
s
y
s
te
m
h
as
b
ee
n
m
iti
g
ated
an
d
th
e
u
s
e
o
f
ad
ap
tiv
e
s
lid
in
g
co
n
tr
o
l
m
et
h
o
d
is
ex
p
er
i
m
e
n
t
ed
to
n
u
lli
f
y
t
h
e
ch
ao
s
ef
f
ec
t
an
d
th
at
co
n
tr
o
l
h
as
b
ee
n
e
x
a
m
i
n
ed
to
m
in
i
m
ize
th
e
o
s
cillat
io
n
s
n
ea
r
to
MP
P
.
2.
SE
P
I
C
CO
N
VE
R
T
E
R
B
AS
E
D
SO
L
AR
P
V
SYS
T
E
M
2
.
1
.
Sy
s
t
em
d
e
s
cr
iptio
n
Fig
u
r
e
1
an
d
Fig
u
r
e
2
s
h
o
w
t
h
e
b
lo
ck
d
iag
r
am
a
n
d
h
ar
d
w
ar
e
s
etu
p
o
f
s
lid
in
g
m
o
d
e
co
n
tr
o
ll
ed
SEP
I
C
DC
-
DC
co
n
v
er
ter
in
ter
f
ac
ed
s
o
lar
P
V
s
y
s
te
m
.
T
h
e
p
o
w
er
cir
cu
it
h
a
s
an
in
d
u
c
to
r
s
L
1
,
L
2
,
ca
p
ac
ito
r
s
C
1
,
C
2
,
a
P
o
w
er
s
w
i
tch
S,
a
lo
ad
r
esis
t
an
ce
,
a
s
o
lar
P
V
m
o
d
u
le
(
L
1
2
3
5
-
3
7
W
p
)
s
h
o
w
n
i
n
Fi
g
u
r
e
3
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
a
m
Fig
u
r
e
2
.
E
x
p
er
i
m
en
tal
s
et
u
p
Fig
u
r
e
3
.
SEP
I
C
DC
-
D
C
co
n
v
er
ter
2
.
2
.
Desig
n o
f
SE
P
I
C
c
o
nv
er
t
er
T
h
e
SEP
I
C
DC
-
DC
co
n
v
er
ter
h
as
ad
v
a
n
ta
g
es
s
u
ch
as
n
o
n
-
p
u
ls
ati
n
g
n
atu
r
e
o
f
lo
ad
cu
r
r
en
t
a
n
d
p
o
s
itiv
e
lo
ad
v
o
ltag
e
an
d
h
as h
i
g
h
e
f
f
ic
ien
c
y
th
a
n
B
u
c
k
-
B
o
o
s
t
co
n
v
er
ter
.
T
h
e
p
o
s
itiv
e
o
u
tp
u
t v
o
ltag
e
is
o
b
tain
ed
b
ased
o
n
th
e
f
o
llo
w
in
g
t
w
o
m
o
d
es
o
f
o
p
er
atio
n
in
o
n
e
s
w
itch
in
g
p
er
io
d
.
1
)
MO
SF
E
T
is
ON
a
n
d
th
e
d
io
d
e
is
n
o
t
o
p
er
ated
.
T
h
e
in
p
u
t
i
n
d
u
cto
r
,
L
1
,
is
c
h
ar
g
ed
f
r
o
m
t
h
e
P
V
in
p
u
t
v
o
lta
g
e.
T
h
e
o
u
tp
u
t
in
d
u
c
to
r
L
2
f
i
n
d
s
en
er
g
y
f
r
o
m
th
e
f
ir
s
t
ca
p
ac
ito
r
,
an
d
th
e
o
u
tp
u
t
ca
p
ac
ito
r
C
2
is
lef
t
to
p
r
o
v
id
e
th
e
lo
ad
cu
r
r
en
t.
T
h
e
f
ac
t
is
th
at
b
o
th
L
1
an
d
L
2
ar
e
d
is
co
n
n
ec
ted
f
r
o
m
t
h
e
lo
ad
w
h
en
th
e
s
w
itc
h
S,
is
t
u
r
n
ed
o
n
.
I
n
m
o
d
e
2
)
,
T
h
e
MO
SF
E
T
is
tu
r
n
ed
o
f
f
an
d
d
io
d
e
is
o
p
e
r
ated
,
th
e
in
p
u
t
in
d
u
c
to
r
L
1
ch
ar
g
es
t
h
e
ca
p
ac
ito
r
C
1
an
d
als
o
p
r
o
v
id
es
cu
r
r
en
t
to
th
e
lo
ad
.
T
h
e
s
ec
o
n
d
in
d
u
cto
r
is
al
s
o
co
n
n
ec
ted
to
th
e
lo
ad
d
u
r
in
g
t
h
i
s
ti
m
e.
T
h
e
s
tead
y
s
tate
o
u
tp
u
t
v
o
ltag
e
eq
u
atio
n
is
g
iv
e
n
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
2
6
8
-
6
2
7
5
6270
V
O
V
IN
=
D
(
1
−
D
)
(
1
)
A
l
s
o
,
th
e
s
tead
y
s
tate
c
u
r
r
en
t e
q
u
atio
n
is
I
IN
I
0
=
D
(
1
−
D
)
(
2
)
T
h
e
(
3
)
s
h
o
w
s
th
e
d
es
ig
n
ed
v
a
lu
e
o
f
i
n
d
u
cto
r
s
L
1
=L
2
=
L
=
V
IN
(
MI
N
)
∗
D
MA
X
∆
I
L
∗
f
S
(
3
)
T
h
e
v
o
ltag
e
s
p
ec
i
f
icatio
n
s
o
f
ca
p
ac
ito
r
C
1
is
s
elec
ted
as
h
ig
h
as
i
n
p
u
t
v
o
ltag
e.
T
h
e
r
ip
p
le
v
o
ltag
e
o
f
C
1
is
g
i
v
e
n
b
y
∆V
c1
=
I
(
OUT
)
∗
D
MA
X
C
1
∗
f
S
(
4
)
T
h
e
SEP
I
C
DC
-
DC
co
n
v
er
ter
is
d
esig
n
ed
w
it
h
in
d
u
c
to
r
s
L
1
=L
2
=5
0
0
µH
,
C
ap
ac
ito
r
s
C
1
=C
2
=
2
2
0
µF
,
s
w
i
tch
i
n
g
f
r
eq
u
en
c
y
=
25
KHz
,
MO
SF
E
T
-
I
R
F5
1
0
,
an
d
d
io
d
e
-
MU
R
4
5
0
ar
e
s
elec
ted
f
o
r
h
ar
d
w
ar
e
i
m
p
l
e
m
en
tatio
n
.
2
.
3
.
L
1
2
3
5
-
3
7
Wp
So
la
r
P
V
m
o
d
ule
T
h
e
s
o
lar
P
V
o
u
tp
u
t
p
o
w
er
d
ep
en
d
s
o
n
in
s
o
latio
n
,
at
m
o
s
p
h
er
ic
te
m
p
er
atu
r
e
an
d
t
y
p
e
o
f
lo
ad
ch
ar
ac
ter
is
tic.
Fro
m
th
e
eq
u
i
v
alen
t
cir
c
u
it
s
h
o
w
n
in
Fig
u
r
e
4
(
a)
,
th
e
cu
r
r
en
t
an
d
v
o
ltag
e
eq
u
atio
n
s
ar
e
g
i
v
en
b
y
(
5
)
an
d
(
6
)
r
esp
ec
tiv
el
y
.
I
sc
=
I
D
+I
pv
+
(
V
D
/ R
p
)
(
5
)
V
pv
=V
D
-
(I
pv
*R
s
)
(
6
)
W
h
er
e
d
io
d
e
cu
r
r
en
t
is
,
I
D
=
I
o
+
(
e
(V
D
/
V
T
)
-
1
)
,
I
sc
is
th
e
s
h
o
r
t
cir
cu
it
cu
r
r
en
t,
V
t
=
N
s
KT
/
q
is
th
e
th
er
m
al
v
o
lta
g
e
w
it
h
N
s
ce
lls
co
n
n
ec
ted
in
a
s
er
ies
(
K
is
th
e
B
o
ltz
m
a
n
n
co
n
s
tan
t,
q
is
th
e
elec
tr
o
n
ch
ar
g
e
an
d
T
is
t
h
e
te
m
p
er
at
u
r
e
o
f
t
h
e
P
V
ce
ll
s
)
.
Usi
n
g
t
h
e
eq
u
atio
n
s
5
a
n
d
6
,
s
o
lar
P
V
is
m
o
d
ell
ed
an
d
s
i
m
u
lated
i
n
MA
T
L
A
B
,
h
as
V
-
I
ch
ar
ec
te
r
is
tics
w
h
ic
h
is
s
h
o
w
n
in
F
ig
u
r
e
4
(
b
)
,
T
h
e
V
-
I
ch
ar
ac
t
er
is
tics
d
ep
en
d
o
n
th
e
co
n
d
u
cta
n
ce
o
f
th
e
lo
ad
.
I
f
th
e
co
n
d
u
cta
n
ce
v
alu
e
is
h
i
g
h
,
T
h
e
P
V
ce
ll
b
eh
av
es
lik
e
a
c
o
n
s
tan
t
c
u
r
r
en
t
s
o
u
r
ce
r
eg
io
n
.
I
f
co
n
d
u
cta
n
ce
v
alu
e
is
lo
w
,
th
e
P
V
ce
ll
ac
ts
as
a
co
n
s
tan
t
v
o
lat
g
e
s
o
u
r
ce
.
T
h
e
p
ar
am
eter
s
o
f
L
1
2
3
5
-
3
7
W
s
o
lar
P
V
m
o
d
u
le
w
h
ic
h
is
u
s
ed
f
o
r
ex
p
er
i
m
en
tal
v
alid
atio
n
ar
e
o
p
en
cir
c
u
it
v
o
ltag
e
(V
oc
)
=
21
,
Vo
ltag
e
at
MP
P
(
V
m
)
=
1
6
.
4
,
Sh
o
r
t
cir
cu
it
cu
r
r
en
t
(I
sc
)
=
2
.
5
A
,
C
u
r
r
en
t
at
MP
P
(I
m
)
=
2
.
2
5
A
,
R
ated
p
o
w
er
=
3
7
W
p
.
Fig
u
r
e
4
.
(
a)
E
q
u
iv
alen
t c
ir
c
u
i
t o
f
s
o
lar
P
V
Fig
u
r
e
4
.
(
b
)
No
n
-
lin
ea
r
V
-
I
ch
ar
ac
ter
is
tic
s
o
f
L
1
2
3
5
-
3
7
W
p
s
o
lar
m
o
d
u
le
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Oscill
a
tio
n
s
min
imi
z
a
tio
n
a
t
MPP
b
y
co
n
tr
o
llin
g
n
o
n
-
lin
e
a
r
d
yn
a
mics in
..
.
(
M.
V
a
ig
u
n
d
a
mo
o
r
th
i)
6271
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
h
e
SEP
I
C
DC
-
DC
co
n
v
er
ter
in
ter
f
ac
ed
s
o
lar
P
V
s
y
s
te
m
is
s
i
m
u
lated
i
n
M
A
T
L
A
B
/Si
m
u
l
in
k
s
h
o
wn
in
Fi
g
u
r
e
5
,
w
h
ic
h
co
m
p
r
is
e
s
P
V
elec
tr
ic
cir
cu
it
s
u
b
s
y
s
te
m
(
MA
T
L
A
B
m
o
d
el)
,
SEP
I
C
DC
-
DC
co
n
v
er
ter
an
d
a
r
esis
ti
v
e
lo
ad
.
Fig
u
r
e
5
.
SEP
I
C
c
o
n
v
er
ter
b
ased
a
d
ap
tiv
e
p
er
tu
r
b
an
d
o
b
s
er
v
er
MP
PT
T
h
e
atm
o
s
p
h
er
ic
co
n
s
ta
n
t
te
m
p
er
at
u
r
e
is
co
n
s
i
d
er
ed
at
2
5
°C
an
d
th
e
ir
r
ad
iatio
n
le
v
el
is
s
et
as
1
0
0
0
W
/m
^2
an
d
af
ter
0
.
0
1
s
ec
,
th
e
ir
r
ad
iatio
n
(
G)
is
s
u
d
d
en
ly
c
h
a
n
g
ed
to
5
0
0
W
/m
2
in
co
m
p
u
ter
s
i
m
u
latio
n
to
test
th
e
e
f
f
ec
t
iv
e
n
es
s
o
f
th
e
ad
ap
tiv
e
P
er
tu
r
b
an
d
Ob
s
er
v
er
al
g
o
r
ith
m
an
d
it
w
as
i
m
p
le
m
e
n
t
ed
in
A
T
ME
GA
1
6
m
icr
o
co
n
tr
o
ller
.
T
h
e
s
tep
s
ize
o
f
MP
PT
alg
o
r
ith
m
i
s
ad
j
u
s
ted
w
h
ich
i
n
tu
r
n
to
v
ar
y
th
e
d
u
t
y
c
y
cle
o
f
th
e
s
w
itc
h
in
o
r
d
er
to
h
ar
v
est
m
a
x
i
m
u
m
p
o
w
er
w
h
ic
h
ar
e
s
h
o
w
n
in
F
ig
u
r
e
6
an
d
Fig
u
r
e
7
.
T
h
e
o
u
tp
u
t
p
o
w
er
is
ex
tr
ac
ted
f
r
o
m
s
o
lar
P
V
m
o
d
u
le
at
ir
r
ad
iati
o
n
o
f
1
0
0
0
W
/m
2
a
n
d
5
0
0
W
/
m
2
ar
e
3
6
.
7
4
W
an
d
1
7
W
r
e
s
p
ec
tiv
el
y
.
Fig
u
r
e
6
.
C
h
a
n
g
e
i
n
d
u
t
y
c
y
c
l
e
f
o
r
v
ar
io
u
s
ir
r
ad
iatio
n
le
v
el
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
2
6
8
-
6
2
7
5
6272
Fig
u
r
e
7
.
E
x
tr
ac
ted
p
o
w
er
f
o
r
v
ar
io
u
s
ir
r
ad
iatio
n
le
v
el
3
.
1
.
B
if
urca
t
io
n a
na
l
y
s
is
o
f
a
da
ptiv
e
co
ntr
o
lled SE
P
I
C
c
o
nv
er
t
er
ba
s
ed
M
P
P
T
Un
d
er
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
tr
ac
k
ed
co
n
d
itio
n
,
to
m
in
i
m
iz
e
o
s
cillatio
n
s
n
ea
r
to
MPP
th
e
n
o
n
-
li
n
ea
r
d
y
n
a
m
ic
b
eh
a
v
io
r
o
f
SEP
I
C
DC
-
DC
co
n
v
er
ter
s
y
s
te
m
i
s
m
i
tig
a
ted
b
y
ad
j
u
s
ti
n
g
r
e
f
er
en
ce
v
o
lta
g
e
V
ref.
T
h
e
in
p
u
t
v
o
ltag
e
o
f
th
e
P
V
f
ed
SEPI
C
co
n
v
er
ter
is
1
6
.
4
V
.
T
h
e
r
ip
p
les
o
f
th
e
tr
ac
k
ed
v
o
ltag
e
ar
e
ex
a
m
i
n
ed
an
d
f
o
u
n
d
th
at
t
h
e
f
u
n
d
a
m
e
n
ta
l
p
er
io
d
1
-
w
a
v
e
f
o
r
m
is
r
ep
ea
te
d
w
it
h
V
ref
=5
.
6
8
V.
A
t
th
is
co
n
d
itio
n
,
SEP
I
C
DC
-
DC
co
n
v
er
ter
s
y
s
te
m
h
as
s
tab
l
e
p
er
io
d
ic
o
p
er
atin
g
b
eh
a
v
io
r
.
T
h
e
in
p
u
t
v
o
ltag
e
r
ip
p
le
o
f
t
h
e
p
er
io
d
-
1
o
p
e
r
atio
n
u
n
d
er
th
is
co
n
d
itio
n
is
g
iv
e
n
i
n
Fi
g
u
r
e
8
.
W
h
en
t
h
e
r
e
f
er
en
ce
v
o
lta
g
e
(
V
ref
)
is
ad
j
u
s
ted
a
n
d
s
e
t
as
5
.
2
V
an
d
t
h
e
r
ip
p
les
o
f
i
n
p
u
t
is
ex
a
m
i
n
ed
.
No
w
,
SEP
I
C
D
C
-
DC
co
n
v
er
t
er
u
n
d
er
g
o
an
u
n
s
tab
le
p
er
io
d
ic
b
eh
av
io
u
r
.
T
h
e
1
-
p
er
io
d
ic
o
r
b
it
lo
s
es
its
s
tab
le
o
p
er
atio
n
,
v
ia
f
l
ip
b
if
u
r
ca
tio
n
it
e
x
p
er
ien
ce
d
a
2
-
p
er
io
d
ic
w
a
v
e
f
o
r
m
.
T
h
e
v
o
lta
g
e
r
ip
p
le
o
f
t
h
e
p
er
io
d
-
2
o
p
er
atio
n
is
s
h
o
w
n
in
F
ig
u
r
e
9
.
Fig
u
r
e
8
.
T
r
ac
k
ed
v
o
ltag
e
r
ip
p
les
-
p
er
io
d
-
1
w
av
e
f
o
r
m
w
h
e
n
V
ref
=5
.
6
2
V
Fig
u
r
e
9
.
T
r
ac
k
ed
v
o
ltag
e
r
ip
p
les
-
p
er
io
d
-
2
w
av
e
f
o
r
m
w
h
e
n
V
ref
=5
.
2
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Oscill
a
tio
n
s
min
imi
z
a
tio
n
a
t
MPP
b
y
co
n
tr
o
llin
g
n
o
n
-
lin
e
a
r
d
yn
a
mics in
..
.
(
M.
V
a
ig
u
n
d
a
mo
o
r
th
i)
6273
Fu
r
t
h
er
,
if
V
ref
is
v
ar
ied
,
th
e
co
n
v
er
ter
o
p
er
atio
n
ch
an
g
ed
f
r
o
m
a
s
tab
le
p
er
io
d
-
1
o
p
er
atio
n
to
an
u
n
s
tab
le
o
p
er
atio
n
.
T
h
e
in
p
u
t
v
o
lta
g
e
r
ip
p
les
o
f
SE
P
I
C
co
n
v
er
ter
-
h
as
u
n
s
tab
le
ap
er
io
d
ic
b
eh
av
io
r
.
C
h
ao
tic
w
a
v
ef
o
r
m
i
s
o
b
s
er
v
ed
f
o
r
th
e
V
ref
=
4
.
6
V
as
s
h
o
w
n
in
Fi
g
u
r
e
1
0
.
T
h
e
s
tate
ch
an
g
e
f
r
o
m
p
er
io
d
ic
to
ap
er
io
d
ic
w
h
e
n
Vr
ef
is
ad
j
u
s
ted
,
b
e
th
e
m
ai
n
ca
u
s
e
to
n
ea
r
to
MP
P
.
T
h
e
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
is
d
esi
g
n
ed
f
o
r
SEP
I
C
DC
-
DC
co
n
v
er
ter
b
y
s
e
n
s
i
n
g
o
u
tp
u
t
v
o
lta
g
e
an
d
in
p
u
t
in
d
u
cto
r
cu
r
r
en
t.
T
h
e
V
ref
is
v
ar
ied
f
r
o
m
4
.
0
0
V
to
5
.
6
V
an
d
I
r
ef
is
s
et
as
0
-
2
A
an
d
it
i
s
p
r
o
v
ed
f
r
o
m
Fi
g
u
r
e
1
1
th
at
th
e
SEP
I
C
DC
-
DC
co
n
v
er
ter
i
s
o
p
er
ated
in
p
er
io
d
-
1
s
tab
le
r
eg
io
n
f
o
r
p
ar
a
m
eter
v
ar
iatio
n
T
h
e
ch
ao
tic
f
r
ee
tr
ac
k
ed
in
p
u
t
v
o
ltag
e
f
r
o
m
s
o
lar
P
V
s
tr
in
g
is
s
h
o
w
n
in
Fi
g
u
r
e
1
2
.
T
h
e
o
s
cillatio
n
s
ar
e
n
u
l
li
f
ied
n
ea
r
to
MP
P
b
y
eli
m
i
n
ati
n
g
ap
er
io
d
ic
-
c
h
ao
s
in
s
o
lar
P
V
s
y
s
te
m
.
T
h
e
Fi
g
u
r
e
1
3
s
h
o
w
s
th
e
e
x
p
er
i
m
e
n
tal
h
ar
v
e
s
ted
n
o
n
o
s
ci
la
tin
g
p
o
w
e
r
o
f
3
6
.
5
w
f
r
o
m
s
o
lar
P
V
u
n
d
e
r
s
tan
d
ar
d
test
co
n
d
itio
n
s
.
Fig
u
r
e
1
0
.
T
r
ac
k
ed
v
o
ltag
e
r
ip
p
les
–
ap
er
io
d
ic
w
av
e
f
o
r
m
w
h
en
V
ref
=4
.
6
V
Fig
u
r
e
1
1
.
T
r
ac
k
ed
v
o
ltag
e
r
ip
p
les
-
p
e
r
i
o
d
-
1
w
a
v
e
f
o
r
m
f
o
r
3
V
<
V
r
e
f
<
5
.
7
6
V
Fig
u
r
e
1
2
.
T
r
ac
k
ed
I
n
p
u
t
v
o
lta
g
e
w
av
e
f
o
r
m
o
f
th
e
co
n
v
er
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
2
6
8
-
6
2
7
5
6274
Fig
u
r
e
1
3
.
E
x
p
er
im
e
n
tal
h
ar
v
e
s
ted
p
o
w
er
f
r
o
m
s
o
lar
P
V
4.
CO
NCLU
SI
O
N
T
h
e
ad
a
p
tiv
e
P
er
tu
r
b
an
d
Ob
s
er
v
er
alg
o
r
ith
m
i
s
i
m
p
le
m
e
n
te
d
an
d
h
ar
v
ested
m
a
x
i
m
u
m
p
o
w
er
f
r
o
m
s
o
lar
P
V
u
s
in
g
SEP
I
C
DC
-
D
C
co
n
v
er
ter
.
T
o
n
u
lli
f
y
t
h
e
o
s
cillatio
n
s
n
ea
r
to
MP
P
,
a
p
er
io
d
ic
ch
ao
tic
b
eh
av
io
r
o
f
DC
-
D
C
co
n
v
er
ter
is
e
x
e
m
p
ted
ex
p
er
i
m
en
tal
l
y
.
T
h
e
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
is
d
esi
g
n
ed
to
en
s
u
r
e
p
er
io
d
1
-
o
p
er
atio
n
o
f
th
e
i
n
p
u
t
v
o
ltag
e
o
f
SEP
I
C
DC
-
DC
co
n
v
er
ter
.
RE
F
E
R
E
NC
E
S
[1
]
Y
.
M
a
h
m
o
u
d
,
e
t
a
l
.,
“
A
si
m
p
le
a
p
p
r
o
a
c
h
to
m
o
d
e
li
n
g
a
n
d
sim
u
lati
o
n
o
f
p
h
o
to
v
o
lt
a
ic
m
o
d
u
les
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
on
S
u
st
a
in
a
b
le
En
e
rg
y
,
v
o
l.
3
,
n
o
.
1
,
p
p
.
1
8
5
-
18
6
,
2
0
1
2
.
[2
]
Y
.
H
.
L
im
a
n
d
D.
C.
Ha
m
il
,
“
S
im
p
le
M
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
T
ra
c
k
e
r
f
o
r
p
h
o
t
o
v
o
lt
a
ic
a
rra
y
s
,”
El
e
c
tro
n
ics
L
e
tt
e
rs
,
v
o
l.
36
,
n
o
.
11
,
p
p
.
9
9
7
-
99
9
,
2
0
0
0
.
[3
]
H.
P
a
tel
a
n
d
V
.
A
g
a
r
w
a
l,
“
M
ATLA
B
-
b
a
se
d
m
o
d
e
li
n
g
to
stu
d
y
th
e
e
ff
e
c
ts
o
f
p
a
rti
a
l
sh
a
d
in
g
o
n
P
V
a
rra
y
c
h
a
ra
c
t
e
risti
c
s
,
”
IEE
E
T
ra
n
s
a
c
t
io
n
s o
n
En
e
rg
y
C
o
n
v
e
rs
io
n
,
v
o
l
.
23
,
n
o
.
1
,
p
p
.
3
0
2
-
3
10
,
2
0
0
8
.
[4
]
S
.
L
.
Bru
n
to
n
,
e
t
a
l
.,
“
M
a
x
im
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
f
o
r
p
h
o
t
o
v
o
lt
a
ic
o
p
t
im
iza
ti
o
n
u
sin
g
rip
p
le
-
b
a
se
d
e
x
tre
m
u
m
se
e
k
in
g
c
o
n
tro
l
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l.
25
,
n
o
.
10
,
p
p
.
2
5
3
1
-
25
40
,
2
0
1
0
.
[5
]
M.
V
a
ig
u
n
d
a
m
o
o
rth
i
a
n
d
R.
Ra
m
e
sh
,
“
Im
p
le
m
e
n
tatio
n
a
n
d
c
h
a
o
ti
c
P
W
M
c
o
n
tr
o
l
o
f
Cu
k
c
o
n
v
e
rter b
a
se
d
M
P
P
T
f
o
r
so
lar
P
V
sy
ste
m
,
”
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
g
,
v
o
l
.
1
7
,
no.
3
,
p
p
.
1
-
8
,
2
0
1
7
.
[6
]
M.
V
a
ig
u
n
d
a
m
o
o
rth
i
a
n
d
R.
Ra
m
e
sh
,
“
ZV
S
-
P
W
M
A
c
ti
v
e
c
l
a
m
p
in
g
m
o
d
if
ied
Cu
k
c
o
n
v
e
rter
b
a
se
d
M
P
P
T
f
o
r
so
lar
P
V
m
o
d
u
les
,
”
Eu
ro
p
e
a
n
J
o
u
rn
a
l
o
f
S
c
ien
ti
fi
c
Res
e
a
rc
h
,
v
o
l.
58
,
n
o.
3
,
p
p
.
3
0
5
-
3
1
5
,
2
0
1
1
.
[7
]
M.
V
a
ig
u
n
d
a
m
o
o
rth
i
a
n
d
R.
Ra
m
e
sh
,
“
Ha
rd
w
a
re
i
m
p
le
m
e
n
tatio
n
a
n
d
ste
a
d
y
sta
te
a
n
a
ly
sis
o
f
ZV
S
-
P
W
M
Cu
k
c
o
n
v
e
rter
b
a
se
d
M
P
P
trac
k
in
g
f
o
r
so
lar
P
V
m
o
d
u
le,
”
I
n
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Eme
rg
in
g
El
e
c
tric
Po
we
r
S
y
ste
ms
,
v
o
l.
1
3
,
n
o
.
4
,
p
p
.
1
-
20
,
2
0
1
2
.
[8
]
M.
V
a
ig
u
n
d
a
m
o
o
rth
i
a
n
d
R
.
Ra
m
e
sh
,
“
P
e
rf
o
rm
a
n
c
e
a
n
a
l
y
sis
o
f
so
f
t
c
o
n
tro
l
led
DC
-
DC
c
o
n
v
e
rter
-
b
a
se
d
M
P
P
T
c
ircu
it
s f
o
r
so
lar
P
V
m
o
d
u
le
,
”
I
n
t
e
rn
a
ti
o
n
a
l
Rev
iew o
n
M
o
d
e
ll
i
n
g
a
n
d
S
im
u
la
ti
o
n
,
v
ol
.
6
,
n
o
.
1
,
p
p
.
1
-
8
,
2
0
1
3
.
[9
]
K.
K.
T
se
,
e
t
a
l
.
,
“
A
Co
m
p
a
ra
ti
v
e
S
tu
d
y
o
f
M
a
x
i
m
u
m
-
P
o
w
e
r
-
P
o
in
t
T
ra
c
k
e
rs
f
o
r
P
h
o
t
o
v
o
lt
a
ic
P
a
n
e
ls
Us
i
n
g
S
w
it
c
h
in
g
-
F
re
q
u
e
n
c
y
M
o
d
u
lati
o
n
S
c
h
e
m
e
,
”
IEE
E
tra
n
sa
c
ti
o
n
s
o
n
i
n
d
u
stria
l
e
lec
tro
n
ics
,
v
o
l.
5
1
,
n
o
.
2
,
pp
.
4
1
0
-
418
,
2
0
0
4
.
[1
0
]
K.
K.
T
se
,
e
t
a
l.
,
“
A
No
v
e
l
M
a
x
i
m
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
e
r
f
o
r
P
V
P
a
n
e
ls Usin
g
S
w
it
c
h
in
g
F
re
q
u
e
n
c
y
M
o
d
u
lati
o
n
,
”
IEE
E
tra
n
sa
c
ti
o
n
s
o
n
p
o
we
r e
lec
t
ro
n
ics
, v
o
l.
1
7
,
n
o
.
6
,
pp
.
9
8
0
-
9
8
9
,
2
0
0
2
.
[1
1
]
H
.
S
.
H
.
Ch
u
n
g
,
e
t
a
l.
,
“
A
No
v
e
l
M
a
x
i
m
u
m
P
o
w
e
r
P
o
i
n
t
T
ra
c
k
in
g
T
e
c
h
n
iq
u
e
f
o
r
S
o
lar
P
a
n
e
ls
Us
i
n
g
a
S
E
P
IC
o
r
C
u
k
Co
n
v
e
rter
,
”
IEE
E
tr
a
n
sa
c
ti
o
n
s
o
n
p
o
we
r e
lec
tro
n
ics
,
v
o
l.
1
8
,
n
o
.
3
,
p
p
.
7
1
7
-
7
2
4
,
2
0
0
3
.
[1
2
]
M
.
V
e
e
ra
c
h
a
ry
,
“
P
o
w
e
r
T
ra
c
k
in
g
f
o
r
No
n
l
in
e
a
r
P
V
S
o
u
rc
e
s
w
it
h
C
o
u
p
led
In
d
u
c
t
o
r
S
E
P
IC
C
o
n
v
e
rter
,
”
IEE
E
tra
n
sa
c
ti
o
n
s
o
n
a
e
ro
sp
a
c
e
a
n
d
e
l
e
c
tro
n
ic sy
ste
ms
,
v
o
l.
4
1
,
n
o
.
3
,
p
p
.
1
0
1
9
-
1
0
2
8
,
2
0
0
5
.
[1
3
]
A
.
R.
Ka
sh
y
a
p
,
e
t
a
l.
,
“
In
p
u
t
v
o
lt
a
g
e
c
o
n
tro
l
o
f
S
E
P
IC
f
o
r
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
,
”
IEE
E
Po
we
r
a
n
d
En
e
rg
y
Co
n
fer
e
n
c
e
a
t
I
ll
in
o
is (
PE
CI)
,
pp.
30
-
3
5
,
2
0
1
3
.
[1
4
]
A
.
Tai
w
o
a
n
d
J.
Oric
h
a
,
“
M
o
d
e
li
n
g
,
S
tea
d
y
-
sta
te
A
n
a
l
y
sis
o
f
a
S
EP
I
C
DC
-
DC
c
o
n
v
e
rter
b
a
se
d
on
sw
it
c
h
in
g
F
u
n
c
ti
o
n
a
n
d
h
a
rm
o
n
ic
b
a
la
n
c
e
tec
h
n
iq
u
e
,
”
J
o
u
rn
a
l
o
f
P
o
we
r
a
n
d
E
n
e
rg
y
E
n
g
in
e
e
rin
g
,
v
o
l.
2
,
p
p
.
7
0
4
-
7
11
,
2
0
1
4
.
[1
5
]
I.
Kim
,
e
t
a
l
.,
“
A
n
a
l
y
sis
a
n
d
d
e
sig
n
o
f
so
f
ts
w
it
c
h
e
d
P
W
M
se
p
ic
DC
DC
c
o
n
v
e
rter
,
”
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
10
,
n
o
.
5
,
p
p
.
4
6
1
-
46
7
,
2
0
1
0
.
[1
6
]
J.
H
u
,
e
t
a
l
.,
“
Hig
h
f
re
q
u
e
n
c
y
re
so
n
a
n
t
S
E
P
IC
c
o
n
v
e
rter
w
it
h
w
id
e
in
p
u
t
a
n
d
o
u
tp
u
t
v
o
lt
a
g
e
ra
n
g
e
s
,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
i
c
s
,
v
o
l.
27
,
n
o
.
1
,
p
p
.
1
89
-
2
0
0
,
2
0
1
2
.
[1
7
]
M.
Qu
a
m
ru
z
z
a
m
a
n
,
e
t
a
l
.,
“
Hig
h
ly
e
ffi
c
ien
t
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
u
sin
g
DC
-
DC
c
o
u
p
led
i
n
d
u
c
t
o
r
sin
g
le
-
e
n
d
e
d
p
rim
a
r
y
in
d
u
c
tan
c
e
c
o
n
v
e
r
ter
f
o
r
p
h
o
to
v
o
l
taic
p
o
w
e
r
sy
ste
m
s
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
S
u
sta
in
a
b
le
E
n
e
rg
y
,
v
o
l.
35
,
n
o
.
9
,
p
p
.
9
1
4
-
9
3
2
,
2
0
1
6
.
[1
8
]
D
.
Hy
u
n
-
L
a
r
k
,
“
S
o
f
t
-
s
w
it
c
h
in
g
S
E
P
IC
c
o
n
v
e
rter
w
it
h
rip
p
le
-
f
re
e
in
p
u
t
c
u
rre
n
t
,
”
IEE
E
T
r
a
n
s
a
c
t
io
n
s
o
n
Po
we
r
El
e
c
tro
n
ics
,
v
o
l.
27
,
n
o
.
6
,
p
p
.
2
8
7
9
-
28
87
,
2
0
1
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Oscill
a
tio
n
s
min
imi
z
a
tio
n
a
t
MPP
b
y
co
n
tr
o
llin
g
n
o
n
-
lin
e
a
r
d
yn
a
mics in
..
.
(
M.
V
a
ig
u
n
d
a
mo
o
r
th
i)
6275
[1
9
]
M
.
A
.
Al
-
Sa
ff
a
r,
e
t
a
l
.,
“
A
n
imp
ro
v
e
d
to
p
o
l
o
g
y
o
f
S
EP
IC
c
o
n
v
e
rter
w
it
h
re
d
u
c
e
d
o
u
tp
u
t
v
o
lt
a
g
e
rip
p
le
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
i
c
s
,
v
o
l.
23
,
n
o
.
5
,
p
p
.
2
3
7
7
-
23
86
,
2
0
0
8
.
[2
0
]
G
.
Ro
g
e
r,
e
t
a
l.
,
“
A
m
o
d
ifi
e
d
S
EP
IC
c
o
n
v
e
rter
w
it
h
h
ig
h
sta
ti
c
g
a
in
f
o
r
re
n
e
w
a
b
le
e
n
e
rg
y
a
p
p
li
c
a
ti
o
n
s
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
o
n
P
o
we
r E
lec
tro
n
ic
s
,
v
o
l.
29
,
n
o
.
11
,
p
p
.
5
8
6
0
-
58
71
,
2
0
1
4
.
[2
1
]
N
.
M
o
h
a
m
m
a
d
,
e
t
a
l
.,
“
P
a
ra
siti
c
e
ff
e
c
ts
o
n
th
e
p
e
rf
o
rm
a
n
c
e
o
f
DC
-
DC
S
EP
IC
in
p
h
o
to
v
o
lt
a
ic
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
a
p
p
li
c
a
ti
o
n
s
,
”
S
ma
rt Gri
d
Ren
e
w
E
n
e
rg
y
,
v
o
l.
4
,
p
p
.
1
1
3
-
1
21
,
2
0
1
3
.
[2
2
]
M
.
d
i
Be
rn
a
rd
o
,
e
t
a
l.
,
“
S
w
it
c
h
in
g
s,
Bif
u
rc
a
ti
o
n
s,
a
n
d
Ch
a
o
s
in
DC/DC
Co
n
v
e
rters
,
”
IEE
E
tra
n
s
a
c
ti
o
n
s
o
n
c
irc
u
it
s
a
n
d
sy
ste
ms
-
I:
fu
n
d
a
me
n
t
a
l
t
h
e
o
r
y
a
n
d
a
p
p
l
ica
ti
o
n
s,
v
o
l
.
4
5
,
n
o
.
2
,
pp
.
1
3
3
-
1
4
1
,
1
9
9
8
.
[2
3
]
F.
A
n
g
u
lo
,
e
t
a
l.
,
“
No
n
li
n
e
a
r
a
n
d
n
o
n
sm
o
o
th
d
y
n
a
m
ics
in
a
DC
–
DC
b
u
c
k
c
o
n
v
e
rter:
tw
o
e
x
p
e
ri
m
e
n
tal
se
t
-
ups
,
”
No
n
li
n
e
a
r Dy
n
a
mic
s
,
v
o
l.
4
6
,
p
p
.
2
3
9
-
2
5
7
,
2
0
0
6
.
[2
4
]
P
.
Ko
w
a
lcz
y
k
,
e
t
a
l.
,
“
Tw
o
-
p
a
ra
m
e
ter
n
o
n
sm
o
o
th
b
if
u
rc
a
ti
o
n
s
o
f
li
m
it
c
y
c
les
:
c
h
a
ll
e
n
g
e
s
a
n
d
o
p
e
n
p
ro
b
lem
s
,
”
In
t
e
rn
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
B
if
u
rc
a
t
i
o
n
a
n
d
Ch
a
o
s
,
v
o
l.
1
6
,
n
o
.
3
,
p
p
.
6
0
1
-
6
2
9
,
2
0
0
6
.
[2
5
]
X
.
Z
h
o
u
,
e
t
a
l.
,
“
Ch
a
o
s
P
h
e
n
o
m
e
n
a
in
d
c
-
d
c
c
o
n
v
e
rter
a
n
d
c
h
a
o
s
c
o
n
tr
o
l
,
”
Pro
c
e
d
i
a
e
n
g
in
n
e
rin
g
,
v
o
l.
29,
pp.
4
7
0
-
473
,
2
0
1
2
.
[2
6
]
M
.
F
e
k
i,
“
A
d
a
p
ti
v
e
f
e
e
d
b
a
c
k
c
o
n
tr
o
l
o
f
li
n
e
a
riza
b
le
c
h
a
o
ti
c
sy
ste
m
s
,
”
Ch
a
o
s,
S
o
li
to
n
s
a
n
d
Fr
a
c
ta
ls
,
v
o
l.
15
,
pp.
8
8
3
-
890
,
2
0
0
3
.
[2
7
]
G
.
P
o
d
d
a
r,
e
t
a
l.
,
“
Co
n
t
ro
l
o
f
c
h
a
o
s
in
DC
-
DC
c
o
n
v
e
rter,
”
IEE
E
tra
n
sa
c
ti
o
n
s
o
n
c
irc
u
i
ts
a
n
d
sy
ste
ms
—
I:
fu
n
d
a
me
n
t
a
l
th
e
o
ry
a
n
d
a
p
p
li
c
a
ti
o
n
s
,
v
o
l.
4
5
,
n
o
.
6
,
p
p
.
6
7
2
-
6
7
6
,
1
9
9
8
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
Dr
.
M.
V
a
ig
u
n
d
a
m
o
o
r
t
h
i
,
w
o
rk
i
n
g
a
s
P
ro
f
e
ss
o
r
in
th
e
d
e
p
a
rtm
e
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
,
M
a
d
a
n
a
p
a
ll
e
In
sti
tu
te
o
f
T
e
c
h
n
o
l
o
g
y
a
n
d
sc
ien
c
e
,
M
a
d
a
n
a
p
a
ll
e
,
A
n
d
h
ra
P
ra
d
e
sh
,
In
d
ia.
He
re
c
e
iv
e
d
h
is
B.
E
d
e
g
re
e
in
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ic
s
En
g
in
e
e
rin
g
f
ro
m
M
a
d
u
ra
i
Ka
m
a
ra
j
Un
iv
e
rsit
y
,
T
a
m
il
n
a
d
u
,
I
n
d
ia
i
n
2
0
0
2
.
He
re
c
e
iv
e
d
h
is
M
a
ste
r
o
f
En
g
in
e
e
rin
g
d
e
g
re
e
a
n
d
P
h
.
D.
i
n
t
h
e
a
re
a
o
f
P
o
w
e
r
e
lec
tro
n
ics
a
n
d
Driv
e
s
f
ro
m
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
G
u
in
d
y
(Estab
li
sh
e
d
1
7
9
4
-
T
h
e
F
irst
e
n
g
in
e
e
rin
g
c
o
ll
e
g
e
i
n
I
n
d
ia),
A
n
n
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i,
I
n
d
ia
i
n
2
0
0
7
&
2
0
1
3
re
sp
e
c
ti
v
e
ly
.
He
is
h
a
v
in
g
1
6
y
e
a
rs
o
f
tea
c
h
in
g
e
x
p
e
rien
c
e
a
n
d
h
a
s
p
u
b
li
sh
e
d
7
re
se
a
rc
h
a
rti
c
les
in
re
p
u
te
d
i
n
tern
a
ti
o
n
a
l
j
o
u
r
n
a
ls.
His
a
re
a
o
f
i
n
tere
st
in
c
lu
d
e
P
o
w
e
r
El
e
c
tro
n
ic
s
f
o
r
Re
n
e
w
a
b
le
En
e
rg
y
S
y
ste
m
,
c
o
n
tr
o
ll
e
r
d
e
sig
n
,
N
o
n
li
n
e
a
r
d
y
n
a
m
ic
s
a
n
a
l
y
sis
a
n
a
l
y
sis
in
so
lar
P
V
sy
ste
m
.
Dr
.
R.
Ra
m
e
sh
wa
s
b
o
rn
i
n
T
a
m
il
Na
d
u
,
In
d
ia.
He
re
c
e
iv
e
d
h
is
B.
E
d
e
g
re
e
in
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
E
n
g
in
e
e
rin
g
f
ro
m
Un
iv
e
rsit
y
o
f
M
a
d
ra
s,
Ch
e
n
n
a
i,
In
d
ia
in
1
9
9
9
.
He
re
c
e
iv
e
d
h
is
M
.
E
d
e
g
re
e
in
P
o
w
e
r
S
y
ste
m
s
f
ro
m
An
n
a
m
a
lai
Un
iv
e
rsit
y
,
Ch
id
a
m
b
a
ra
m
,
In
d
ia
in
2
0
0
2
.
He
re
c
e
iv
e
d
P
h
.
D
f
ro
m
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
G
u
in
d
y
,
A
n
n
a
Un
iv
e
rsity
,
Ch
e
n
n
a
i,
In
d
ia
in
2
0
0
8
.
P
re
se
n
tl
y
h
e
is
w
o
rk
in
g
a
s
a
P
r
o
f
e
ss
o
r
in
th
e
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
E
lec
tro
n
ics
E
n
g
in
e
e
rin
g
,
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
G
u
in
d
y
,
A
n
n
a
Un
i
v
e
rsit
y
,
Ch
e
n
n
a
i,
In
d
ia.
His
re
se
a
rc
h
a
re
a
s
a
re
M
u
lt
i
-
a
re
a
P
o
w
e
r
S
y
st
e
m
s,
S
o
lar
P
V sy
ste
m
s,
P
o
w
e
r
El
e
c
tro
n
ic C
o
n
v
e
rters
,
W
e
b
a
n
d
Em
b
e
d
d
e
d
b
a
se
d
sy
ste
m
s.
Dr
.
V.
Va
s
a
n
Pra
b
h
u
,
a
ss
o
c
iate
p
ro
f
e
ss
o
r
in
th
e
d
e
p
a
rtm
e
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
in
S
t.
J
o
se
p
h
’s
C
o
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
Ch
e
n
n
a
i
h
a
s
1
1
y
e
a
rs
o
f
te
a
c
h
in
g
a
n
d
re
se
a
rc
h
e
x
p
e
rien
c
e
.
He
re
c
e
iv
e
d
h
is
BE
a
n
d
M
E
d
e
g
re
e
s
in
El
e
c
tri
c
a
l
&
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
d
e
p
a
rtm
e
n
t
f
ro
m
A
n
n
a
Un
iv
e
rs
it
y
Ch
e
n
n
a
i.
He
c
o
m
p
lete
d
h
is
re
se
a
rc
h
w
o
rk
in
S
w
it
c
h
e
d
Re
lu
c
tan
c
e
M
a
c
h
in
e
a
n
d
it
s
c
o
n
tro
l.
His
a
re
a
o
f
in
tere
st
li
e
s
in
sp
e
c
ial
e
lec
tri
c
a
l
m
a
c
h
in
e
s,
m
a
c
h
in
e
d
e
sig
n
,
d
r
iv
e
s a
n
d
c
o
n
tr
o
l
a
n
d
a
rti
f
icia
l
in
telli
g
e
n
c
e
.
Dr
.
K.
Ar
u
l
K
u
m
a
r
h
a
s
o
b
tain
e
d
B.
E.
,
(El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
)
d
e
g
re
e
f
ro
m
A
n
n
a
Un
iv
e
rsit
y
,
Ch
e
n
n
a
i
i
n
2
0
0
8
a
n
d
M
.
T
e
c
h
(P
o
w
e
r
El
e
c
tro
n
ics
)
d
e
g
re
e
f
ro
m
V
e
l
T
e
c
h
Dr.RR
&
Dr.S
R
T
e
c
h
n
ica
l
U
n
iv
e
rsit
y
,
Ch
e
n
n
a
i
in
2
0
1
1
a
n
d
P
h
.
D.
d
e
g
re
e
in
t
h
e
S
c
h
o
o
l
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
i
c
En
g
in
e
e
rin
g
,
V
IT
Un
iv
e
rsity
,
V
e
ll
o
re
in
2
0
1
7
.
His
c
u
rre
n
t
a
re
a
o
f
re
se
a
rc
h
in
tere
sts
a
r
e
P
o
w
e
r
e
lec
tro
n
ics
i
n
Re
n
e
w
a
b
le
En
e
rg
y
S
y
ste
m
s.
He
is
c
u
rre
n
tl
y
w
o
rk
i
n
g
a
s
A
ss
o
c
iate
P
r
o
f
e
ss
o
r
i
n
El
e
c
tri
c
a
l
d
e
p
a
rtm
e
n
t
in
M
a
d
a
n
a
p
a
ll
e
in
stit
u
te o
f
T
e
c
h
n
o
lo
g
y
&
S
c
i
e
n
ce
Evaluation Warning : The document was created with Spire.PDF for Python.