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20
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6
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703
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SS
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2252
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DOI
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i
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.
pp
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711
703
J
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p
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Dec
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M
a
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sy
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th
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ATLAB/S
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c
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d
g
rid
sta
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.
K
ey
w
o
r
d
s
:
Gr
id
Ma
x
im
u
m
p
o
wer
p
o
i
n
t tr
ac
k
in
g
Mo
th
f
lam
e
o
p
tim
izatio
n
Ph
o
to
v
o
ltaic
s
y
s
tem
s
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
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T
h
is i
s
a
n
o
p
e
n
a
c
c
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ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ujwala
Gaju
la
G.
Nar
ay
an
am
m
a
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
an
d
Scien
ce
Hy
d
er
ab
ad
,
T
elan
g
a
n
a
5
0
0
1
0
4
,
I
n
d
ia
E
m
ail:
u
jwalag
aju
la@
g
n
its
.
ac
.
in
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
ec
e
n
t
y
ea
r
s
,
en
h
a
n
cin
g
th
e
r
eliab
ilit
y
an
d
ef
f
icien
cy
o
f
g
r
id
-
co
n
n
ec
te
d
p
h
o
to
v
o
ltaic
(
P
V)
s
y
s
tem
s
h
as
b
ee
n
a
m
ajo
r
f
o
c
u
s
o
f
r
ese
ar
ch
,
esp
ec
ially
u
n
d
e
r
r
a
p
id
ly
ch
an
g
in
g
en
v
ir
o
n
m
en
tal
co
n
d
i
tio
n
s
.
W
h
ile
Su
p
er
-
twis
tin
g
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
ST
-
SMC
)
h
as
s
h
o
wn
s
tr
o
n
g
p
o
ten
tial
f
o
r
r
ed
u
cin
g
ch
atter
in
g
an
d
im
p
r
o
v
i
n
g
tr
an
s
ien
t
r
esp
o
n
s
e,
an
d
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
lik
e
m
o
th
-
f
lam
e
o
p
tim
izatio
n
(
MFO)
h
a
v
e
p
r
o
v
en
ef
f
ec
tiv
e
f
o
r
m
ax
im
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
in
g
(
MPPT)
u
n
d
er
p
a
r
tial
s
h
ad
in
g
,
m
o
s
t
ex
is
tin
g
wo
r
k
s
t
r
ea
t
th
e
s
e
s
o
lu
tio
n
s
s
ep
ar
ately
.
T
h
is
p
ap
er
ad
d
r
ess
es
th
e
cr
itical
g
ap
in
in
teg
r
atin
g
n
o
n
lin
ea
r
co
n
t
r
o
l
with
in
tellig
en
t
o
p
tim
izatio
n
b
y
p
r
o
p
o
s
in
g
a
h
y
b
r
id
MPPT
co
n
tr
o
ller
th
at
co
m
b
in
es
ST
-
SMC
with
MFO.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
lev
er
ag
es
th
e
r
o
b
u
s
tn
ess
o
f
ST
-
SMC
an
d
th
e
ad
ap
tiv
e
tu
n
in
g
ca
p
a
b
ilit
y
o
f
MFO
to
ac
h
iev
e
f
aster
co
n
v
er
g
en
ce
,
b
etter
d
is
tu
r
b
an
ce
r
ejec
tio
n
,
an
d
en
h
an
ce
d
p
o
wer
q
u
ality
in
g
r
id
-
c
o
n
n
ec
ted
PV
s
y
s
tem
s
.
Un
lik
e
p
r
io
r
s
tu
d
ies,
th
is
wo
r
k
p
r
esen
ts
a
u
n
if
ied
co
n
tr
o
l
f
r
am
ew
o
r
k
th
at
d
y
n
am
icall
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ad
ju
s
ts
co
n
tr
o
ll
er
p
ar
am
ete
r
s
in
r
ea
l
-
tim
e
f
o
r
im
p
r
o
v
e
d
p
er
f
o
r
m
a
n
ce
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
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E
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,
Vo
l.
1
5
,
No
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2
,
J
u
n
e
20
2
6
:
703
-
711
704
Simu
latio
n
r
esu
lts
co
n
f
ir
m
th
at
th
e
h
y
b
r
id
ap
p
r
o
ac
h
o
u
tp
er
f
o
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m
s
c
o
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co
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tr
o
ller
s
b
y
ac
h
iev
in
g
h
i
g
h
er
tr
ac
k
in
g
e
f
f
ic
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cy
,
lo
wer
to
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h
ar
m
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is
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tio
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T
HD)
,
a
n
d
b
etter
p
o
w
er
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eg
u
latio
n
u
n
d
er
v
ar
y
in
g
ir
r
ad
ian
ce
an
d
g
r
id
c
o
n
d
itio
n
s
.
Sam
i
et
a
l
.
[
1
]
an
d
Mo
h
ap
atr
a
et
a
l
.
[
2
]
p
r
o
p
o
s
ed
ST
-
SMC
tech
n
iq
u
es
f
o
r
g
r
id
-
co
n
n
ec
ted
PV
s
y
s
tem
s
,
d
em
o
n
s
tr
atin
g
s
u
p
er
io
r
s
tab
ilit
y
an
d
d
is
tu
r
b
an
ce
r
ejec
tio
n
.
Similar
ly
,
Du
n
n
a
et
al
.
[
3
]
an
d
Dar
d
o
u
r
i
et
a
l
.
[
4
]
d
ev
elo
p
e
d
s
u
p
er
-
twis
tin
g
-
b
ase
d
MPPT
co
n
tr
o
ller
s
th
at
en
h
an
ce
p
o
wer
tr
ac
k
in
g
an
d
ef
f
icien
cy
u
n
d
e
r
v
ar
y
i
n
g
e
n
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
Fu
r
th
er
r
ef
in
em
e
n
ts
in
ST
-
SMC
s
t
r
ateg
ies we
r
e
m
ad
e
by
[
5
]
-
[
7
]
,
wh
o
im
p
lem
e
n
ted
ST
-
SMC
in
m
u
ltifu
n
ctio
n
al
P
V
in
v
er
ter
s
,
ac
h
ie
v
in
g
im
p
r
o
v
ed
tr
an
s
ien
t
r
esp
o
n
s
e
an
d
r
o
b
u
s
tn
ess
.
I
n
ad
d
itio
n
,
th
e
s
tu
d
y
i
n
[
8
]
,
[
9
]
in
v
esti
g
ated
o
p
tim
ally
tu
n
e
d
ST
-
SMC
c
o
n
tr
o
ller
s
f
o
r
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
r
e
g
u
latio
n
in
g
r
id
-
c
o
n
n
ec
te
d
PV sy
s
tem
s
,
en
s
u
r
in
g
e
n
h
an
ce
d
p
o
wer
q
u
a
lity
.
Simu
ltan
eo
u
s
ly
,
o
p
tim
izatio
n
-
b
ased
MPPT
tech
n
iq
u
es,
p
ar
t
icu
lar
ly
MFO,
h
av
e
g
ain
e
d
s
ig
n
if
ican
t
atten
tio
n
d
u
e
to
th
eir
ca
p
ab
ilit
y
to
h
an
d
le
n
o
n
lin
ea
r
ities
an
d
p
ar
tial sh
ad
in
g
co
n
d
itio
n
s
.
T
h
e
s
tu
d
y
in
[
1
0
]
,
[
1
1
]
in
tr
o
d
u
ce
d
h
y
b
r
i
d
MPPT
co
n
t
r
o
ller
s
in
teg
r
atin
g
MFO
with
ch
ao
s
q
u
an
tu
m
p
ar
ticle
s
war
m
o
p
tim
izatio
n
an
d
o
th
er
b
io
-
in
s
p
ir
ed
tech
n
i
q
u
es,
im
p
r
o
v
in
g
tr
ac
k
in
g
ef
f
icien
c
y
an
d
co
n
v
er
g
en
ce
s
p
ee
d
.
T
h
e
s
tu
d
y
i
n
[
1
2
]
,
[
1
3
]
f
u
r
th
er
e
x
p
lo
r
e
d
MFO
-
b
ased
MPPT
s
ch
em
es
f
o
r
o
p
tim
al
p
o
wer
f
lo
w
an
d
p
o
wer
d
is
p
atch
in
g
,
en
s
u
r
in
g
m
in
im
al
p
o
wer
lo
s
s
.
T
h
e
e
f
f
ec
tiv
en
ess
o
f
MFO
in
r
en
ewa
b
le
en
e
r
g
y
ap
p
licatio
n
s
was
also
d
em
o
n
s
t
r
ated
b
y
[
1
4
]
,
[
1
5
]
,
wh
o
ap
p
lied
m
o
d
if
ied
MFO
a
lg
o
r
ith
m
s
in
c
o
r
p
o
r
atin
g
ch
ao
t
ic
m
ap
s
an
d
Gau
s
s
ian
m
u
tatio
n
to
o
p
tim
ize
g
r
i
d
p
o
wer
m
an
ag
e
m
en
t.
Mo
r
e
o
v
er
,
Hu
s
s
ien
et
a
l
.
[
1
6
]
ex
ten
d
ed
t
h
e
ap
p
licatio
n
o
f
MFO
to
win
d
en
er
g
y
co
n
v
er
s
io
n
s
y
s
tem
s
,
v
alid
atin
g
its
p
er
f
o
r
m
an
ce
in
d
if
f
er
e
n
t
r
e
n
ewa
b
le
e
n
er
g
y
s
ce
n
a
r
io
s
.
T
h
e
co
m
b
in
ati
o
n
o
f
ST
-
SMC
with
m
etah
eu
r
is
tic
o
p
tim
izatio
n
alg
o
r
ith
m
s
h
as b
ee
n
a
n
o
th
e
r
ar
ea
o
f
f
o
c
u
s
.
T
h
e
s
tu
d
y
in
[
1
7
]
,
[
1
8
]
ex
p
lo
r
e
d
h
y
b
r
id
co
n
tr
o
l
s
tr
ateg
ies
in
co
r
p
o
r
atin
g
g
en
etic
alg
o
r
ith
m
s
an
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
in
t
o
ST
-
S
MC
-
b
ased
MPPT
co
n
tr
o
ller
s
,
en
h
an
cin
g
th
e
c
o
n
v
e
r
g
en
ce
r
a
te
an
d
s
tead
y
-
s
tate
ac
cu
r
ac
y
o
f
PV
p
o
wer
tr
ac
k
i
n
g
.
Similar
ly
,
Ah
m
ed
[
1
9
]
in
t
eg
r
ated
ar
tific
ial
n
eu
r
al
n
etw
o
r
k
s
with
ST
-
SMC
-
b
ased
n
o
n
lin
ea
r
MPPT
co
n
tr
o
ller
s
,
s
ig
n
if
ican
tly
im
p
r
o
v
in
g
t
h
e
ad
ap
ta
b
ilit
y
o
f
PV
s
y
s
tem
s
to
r
ap
i
d
ir
r
a
d
ian
ce
ch
an
g
es.
T
h
e
s
tu
d
y
in
[
2
0
]
,
[
2
1
]
d
esig
n
ed
ad
v
a
n
ce
d
ST
-
SMC
co
n
tr
o
ller
s
in
c
o
r
p
o
r
atin
g
d
if
f
er
en
tial
f
latn
ess
-
o
r
ien
ted
o
b
s
er
v
er
tech
n
iq
u
es
an
d
im
p
r
o
v
ed
s
lid
in
g
m
o
d
e
co
n
tr
o
l,
lead
i
n
g
to
b
etter
f
au
lt
to
ler
an
ce
an
d
d
is
tu
r
b
an
ce
r
ejec
tio
n
.
Fu
r
th
er
m
o
r
e,
r
ec
en
t
s
tu
d
ies
h
av
e
f
o
c
u
s
ed
o
n
r
ea
l
-
tim
e
en
er
g
y
m
a
n
ag
em
en
t
an
d
g
r
id
in
ter
ac
tio
n
o
f
PV
-
b
atter
y
h
y
b
r
id
s
y
s
tem
s
.
T
h
e
s
tu
d
y
i
n
[
2
0
]
,
[
2
1
]
d
esig
n
ed
[
2
2
]
in
v
e
s
tig
ated
ec
o
n
o
m
ical
o
p
er
atio
n
m
o
d
elin
g
an
d
s
u
p
er
-
twis
tin
g
MPPT
co
n
tr
o
l
f
o
r
g
r
id
-
co
n
n
ec
te
d
PV/b
atter
y
s
y
s
tem
s
,
d
em
o
n
s
tr
atin
g
ef
f
icien
t
en
er
g
y
u
tili
za
tio
n
an
d
co
s
t
o
p
tim
izatio
n
.
Ad
d
itio
n
ally
,
C
ar
m
o
n
a
et
a
l
.
[
2
3
]
an
d
Kan
tas
et
a
l
.
[
2
4
]
p
r
o
p
o
s
ed
n
o
v
el
s
lid
in
g
m
o
d
e
-
b
ased
MPPT
s
tr
ateg
ies
th
at
en
s
u
r
e
h
ig
h
-
s
p
ee
d
co
n
v
er
g
e
n
ce
a
n
d
m
ax
im
u
m
p
o
wer
ex
tr
ac
tio
n
u
n
d
er
d
y
n
am
ic
c
o
n
d
itio
n
s
.
Ov
er
all,
th
e
in
teg
r
ati
o
n
o
f
ST
-
SMC
an
d
MFO
-
b
ased
MPPT
tech
n
iq
u
es
h
as
s
ig
n
if
ican
tly
im
p
r
o
v
ed
th
e
r
eliab
ilit
y
an
d
e
f
f
icien
cy
o
f
P
V
s
y
s
tem
s
.
T
h
e
liter
atu
r
e
d
em
o
n
s
tr
ates
th
at
h
y
b
r
id
co
n
tr
o
l
ap
p
r
o
ac
h
es,
co
m
b
i
n
in
g
n
o
n
li
n
ea
r
co
n
tr
o
l
with
in
te
llig
en
t
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
o
f
f
er
p
r
o
m
is
in
g
s
o
lu
tio
n
s
f
o
r
ad
d
r
ess
in
g
th
e
ch
allen
g
es
o
f
g
r
i
d
in
teg
r
atio
n
,
p
o
wer
s
tab
ilit
y
,
an
d
en
er
g
y
m
a
n
a
g
em
en
t
in
m
o
d
er
n
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
.
2.
M
E
T
H
O
D
On
-
g
r
id
1
0
0
k
W
PV sy
s
tem
s
u
tili
ze
m
u
ltip
le
co
m
m
er
cial
PV m
o
d
u
les,
as illu
s
tr
ated
in
Fi
g
u
r
e
1
.
T
h
e
p
r
o
p
o
s
ed
s
y
s
tem
co
m
p
r
is
es
a
g
r
id
-
co
n
n
ec
ted
s
o
lar
PV
s
y
s
tem
in
teg
r
ated
with
a
b
atter
y
en
er
g
y
s
to
r
a
g
e
s
y
s
tem
(
B
E
SS
)
an
d
an
ad
v
a
n
ce
d
co
n
t
r
o
l
s
ch
em
e
t
o
en
h
an
ce
p
o
wer
q
u
ality
,
s
tab
ilit
y
,
a
n
d
e
n
er
g
y
ef
f
icien
cy
.
T
h
e
PV
ar
r
ay
g
en
er
ates
DC
p
o
wer
,
wh
ich
is
p
r
o
ce
s
s
ed
th
r
o
u
g
h
a
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
co
n
tr
o
lle
d
b
y
a
MFO
-
b
ased
MPPT
alg
o
r
ith
m
.
A
s
u
p
er
-
twi
s
tin
g
b
ased
co
n
tr
o
ller
(
STBC
)
f
u
r
th
e
r
r
ef
in
es
th
e
n
o
n
lin
ea
r
MPPT
co
n
tr
o
l
f
o
r
r
ap
id
c
o
n
v
er
g
en
ce
an
d
r
o
b
u
s
tn
ess
u
n
d
er
d
y
n
am
ic
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
T
h
e
r
eg
u
lated
DC
p
o
wer
is
f
ed
in
to
a
th
r
ee
-
p
h
ase
v
o
lta
g
e
s
o
u
r
ce
co
n
v
er
ter
(
VSC
)
,
wh
ich
in
j
ec
ts
co
n
tr
o
lled
AC
p
o
wer
in
to
th
e
g
r
id
v
ia
an
L
C
L
f
ilter
to
r
ed
u
ce
s
witch
in
g
h
ar
m
o
n
ics.
T
h
e
B
E
SS
is
co
n
n
ec
t
ed
to
th
e
DC
-
lin
k
th
r
o
u
g
h
a
b
i
d
ir
ec
tio
n
al
co
n
v
er
ter
an
d
m
a
n
ag
ed
u
s
in
g
a
s
u
p
er
tw
is
tin
g
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
(
STSMC),
wh
ich
en
s
u
r
es
s
tab
le
b
atter
y
ch
a
r
g
in
g
an
d
d
is
ch
ar
g
in
g
wh
ile
m
ain
tai
n
in
g
cu
r
r
en
t b
alan
ce
.
T
h
e
en
ti
r
e
s
y
s
tem
is
co
o
r
d
in
ated
to
en
s
u
r
e
o
p
tim
al
en
er
g
y
f
lo
w,
im
p
r
o
v
ed
d
y
n
am
ic
r
esp
o
n
s
e,
an
d
s
ig
n
if
ican
tly
r
ed
u
ce
d
T
H
D,
th
er
eb
y
e
n
s
u
r
in
g
e
f
f
ec
tiv
e
o
p
er
atio
n
in
g
r
id
-
co
n
n
ec
ted
c
o
n
d
itio
n
s
wh
ile
s
u
p
p
o
r
tin
g
lo
ad
v
ar
iatio
n
s
an
d
r
e
n
ewa
b
le
in
ter
m
itten
cy
.
2
.
1
.
Desig
n a
nd
im
plem
ent
a
t
io
n o
f
s
up
er
t
wis
t
ing
s
li
din
g
m
o
de
co
ntr
o
ller
I
n
SMC
,
th
e
s
y
s
tem
s
tates
ar
e
g
u
id
e
d
to
war
d
th
e
s
lid
in
g
s
u
r
f
ac
e
(
SS
)
.
A
g
r
a
p
h
ical
r
e
p
r
ese
n
tatio
n
o
f
SMC
is
s
h
o
wn
in
Fig
u
r
e
2
.
O
n
ce
th
e
s
tates
r
ea
ch
th
e
SS
,
S
MC
en
s
u
r
es
th
ey
r
em
ain
with
in
its
clo
s
e
v
icin
ity
.
T
h
e
d
esig
n
o
f
SMC
co
m
p
r
is
es two
k
ey
co
m
p
o
n
en
ts
: th
e
SS
an
d
th
e
c
o
n
tr
o
l la
w
.
T
h
e
SS
f
o
r
m
is
g
iv
en
b
y
(1
)
.
=
+
∑
−
1
=
0
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mo
th
fla
me
o
p
timiz
a
tio
n
b
a
s
e
d
s
u
p
er tw
is
tin
g
s
lid
in
g
mo
d
e
MPP
T c
o
n
tr
o
ller
fo
r
…
(
Ujw
a
la
Ga
ju
la
)
705
W
h
er
e
=
−
1
,
with
r
r
ep
r
esen
tin
g
t
h
e
r
elativ
e
d
eg
r
ee
b
etwe
en
u
an
d
y
.
T
h
e
co
n
s
tan
t
ca
n
b
e
c
h
o
s
en
as
an
y
p
o
s
itiv
e
v
alu
e.
T
h
e
p
ar
am
eter
m
u
s
t
b
e
s
elec
ted
s
u
ch
t
h
at
th
e
d
if
f
e
r
en
tial
eq
u
atio
n
r
e
m
ain
s
s
tab
le
wh
en
σ=0
.
Fo
r
v
a
r
io
u
s
v
alu
es
o
f
k
,
th
e
co
r
r
esp
o
n
d
in
g
s
tate
-
s
p
ac
e
(
SS
)
r
ep
r
esen
tatio
n
s
ar
e
g
iv
e
n
b
y
(
2
)
.
=
1
=
̇
+
(
2
)
=
1
=
̈
+
2
̇
+
2
T
h
e
d
e
v
el
o
p
m
e
n
t
o
f
SMC
in
v
o
lv
es
a
two
-
s
tep
p
r
o
ce
s
s
.
T
o
a
ch
iev
e
th
e
d
esire
d
p
er
f
o
r
m
an
c
e
in
a
DC
-
DC
co
n
v
er
ter
,
a
s
lid
in
g
s
u
r
f
ac
e
m
u
s
t
f
ir
s
t
b
e
d
esig
n
ed
f
o
r
th
e
s
y
s
tem
to
o
p
er
ate
o
n
.
T
h
e
n
ex
t
s
tep
is
to
f
o
r
m
u
late
a
co
n
tr
o
l
law
th
at
en
s
u
r
es
th
e
s
y
s
tem
r
em
ain
s
co
n
f
in
ed
to
th
e
s
lid
in
g
s
u
r
f
ac
e.
T
h
e
ch
o
s
en
s
lid
in
g
s
u
r
f
ac
e,
(
,
)
,
alo
n
g
with
its
in
itial d
er
iv
ati
v
e,
m
u
s
t b
o
t
h
b
e
e
q
u
al
to
ze
r
o
g
iv
en
b
y
(
3
)
.
(
,
)
=
0
,
̇
(
,
)
=
0
(3
)
W
e
ca
n
o
p
tim
ize
s
y
s
tem
p
e
r
f
o
r
m
an
ce
b
y
g
u
id
in
g
th
e
t
r
ajec
to
r
ies
to
war
d
an
d
m
ain
tain
i
n
g
th
em
o
n
th
e
s
lid
in
g
s
u
r
f
ac
e.
T
o
ac
co
m
p
lis
h
th
is
,
we
u
tili
ze
th
e
s
lid
in
g
s
u
r
f
ac
e
(
4
)
.
(
,
)
=
=
(
+
)
=
0
(4
)
2
.
2
.
M
o
t
h
-
f
l
a
m
e
o
ptim
izer
Mir
jalili
et
a
l.
[
2
5
]
d
ev
elo
p
ed
a
m
eta
-
h
eu
r
is
tic
o
p
tim
izatio
n
alg
o
r
ith
m
ca
lled
MFO
.
T
h
e
p
r
in
cip
le
o
f
MFO
o
r
ig
in
ates
f
r
o
m
th
e
way
m
o
th
s
u
s
e
tr
an
s
v
er
s
e
o
r
ien
tati
o
n
f
o
r
n
av
ig
atio
n
,
wh
ich
e
n
ab
l
es
th
em
to
n
av
ig
ate
in
d
ar
k
n
ess
.
T
h
ese
in
s
ec
ts
m
ai
n
tain
a
co
n
s
tan
t
an
g
le
o
f
f
lig
h
t
r
elativ
e
to
th
e
m
o
o
n
lig
h
t'
s
p
o
s
itio
n
,
g
u
id
in
g
th
eir
m
o
v
em
en
t.
W
h
en
th
e
lig
h
t
s
o
u
r
ce
,
o
r
“
f
lam
es,
”
is
d
is
tan
t,
m
o
th
s
will
tr
av
el
in
a
s
tr
aig
h
t
lin
e.
I
n
th
e
p
r
esen
ce
o
f
clo
s
ed
,
n
o
n
-
u
n
i
f
o
r
m
f
lam
e
s
o
r
lig
h
ts
,
m
o
th
s
f
o
llo
w
a
s
p
ec
if
ic
p
ath
to
n
a
v
ig
ate
a
n
d
ex
p
lo
it
th
e
g
lo
b
al
m
in
im
u
m
s
o
lu
tio
n
s
.
T
h
e
MFO
f
lo
wch
ar
t c
an
b
e
g
i
v
en
in
Fig
u
r
e
3
.
MFO
is
cla
s
s
if
ied
as
a
p
o
p
u
latio
n
-
b
ased
o
p
tim
izatio
n
t
ec
h
n
iq
u
e
th
at
d
ef
in
es
an
“
M”
m
atr
ix
r
ep
r
esen
tin
g
m
o
th
s
,
wh
er
e
“
n
”
d
en
o
tes
th
e
n
u
m
b
er
o
f
m
o
t
h
s
[
1
,
.
.
.
,
n
]
a
n
d
“
d
”
r
ep
r
esen
ts
th
e
s
ea
r
ch
-
s
p
ac
e
d
im
en
s
io
n
[
1
,
.
.
.
,
d
]
.
T
h
e
o
b
jec
tiv
e
f
u
n
ctio
n
s
o
f
th
e
m
o
th
s
,
d
e
n
o
ted
as
“OM
,
”
ar
e
ar
r
a
n
g
ed
i
n
an
OM
m
atr
i
x
[
1
,
.
.
.
,
n
]
,
wh
ic
h
h
el
p
s
g
en
er
ate
o
p
tim
al
s
o
lu
tio
n
s
.
Similar
ly
,
th
e
f
lam
es
“F”
ar
e
ev
al
u
ated
in
th
e
s
am
e
m
an
n
e
r
.
T
h
e
MFO
tech
n
iq
u
e
f
o
llo
ws
a
s
tep
-
by
-
s
tep
p
r
o
ce
s
s
in
v
o
l
v
in
g
a
n
in
itializatio
n
f
u
n
ctio
n
“I
,
”
t
h
r
ee
a
p
p
r
o
x
im
atio
n
f
u
n
ctio
n
s
,
a
p
o
p
u
latio
n
f
u
n
ctio
n
“P,
”
an
d
a
ter
m
in
atio
n
c
r
iter
io
n
“T
.
”
T
h
e
“I
”
f
u
n
ctio
n
i
n
itializes
a
r
an
d
o
m
p
o
p
u
latio
n
o
f
m
o
th
s
b
y
g
en
er
ati
n
g
“r
a
n
d
”
v
al
u
e
s
f
o
r
th
eir
co
r
r
esp
o
n
d
in
g
o
b
jectiv
e
f
u
n
ctio
n
s
wh
ile
co
n
s
id
er
in
g
th
e
u
p
p
er
(
“u
b
”)
a
n
d
l
o
wer
(
“l
b
”)
lim
i
ts
.
T
h
ese
f
u
n
ctio
n
s
ca
n
b
e
r
e
p
r
esen
ted
as f
o
llo
ws
g
iv
en
in
(
5
)
.
(
,
)
=
(
(
)
−
(
)
)
(
,
)
+
(
)
(
5
)
OM
=
f
itn
ess
f
u
n
ctio
n
(
M)
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
ST
SMC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
703
-
711
706
Fig
u
r
e
2
.
Gr
a
p
h
ical
r
ep
r
esen
tatio
n
o
f
SMC
Fig
u
r
e
3
.
T
h
e
ev
alu
atio
n
p
r
o
c
ess
o
f
MFO
Hen
ce
,
th
e
‘
P’
f
u
n
ctio
n
b
eg
in
s
af
ter
th
e
co
m
p
letio
n
o
f
‘
I
’
an
d
co
n
tin
u
es u
n
til
th
e
‘
T
’
cr
iter
ia
ar
e
m
et.
I
t
g
u
id
es
th
e
m
o
th
s
th
r
o
u
g
h
o
u
t
th
e
s
ea
r
ch
s
p
ac
e.
T
h
e
lo
g
ar
ith
m
ic
s
p
ir
al
f
u
n
ctio
n
s
er
v
es
as
th
e
p
r
im
ar
y
u
p
d
atin
g
m
ec
h
an
is
m
f
o
r
ea
c
h
m
o
th
’
s
p
o
s
itio
n
r
elativ
e
to
th
e
f
lam
e
.
T
h
e
lo
ca
tio
n
o
f
th
e
f
lam
e
i
s
u
p
d
ated
u
s
in
g
th
e
f
o
llo
win
g
ex
p
r
ess
io
n
g
iv
e
n
in
(
6
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mo
th
fla
me
o
p
timiz
a
tio
n
b
a
s
e
d
s
u
p
er tw
is
tin
g
s
lid
in
g
mo
d
e
MPP
T c
o
n
tr
o
ller
fo
r
…
(
Ujw
a
la
Ga
ju
la
)
707
=
(
,
)
(
6
)
T
h
e
MFO
o
p
tim
izer
u
tili
ze
s
th
e
f
o
llo
win
g
e
x
p
r
ess
io
n
to
d
ef
i
n
e
th
e
lo
g
a
r
ith
m
ic
h
elix
g
iv
en
in
(
7
)
.
(
,
)
=
.
.
2
+
(7
)
I
n
th
is
r
eg
ar
d
,
r
ep
r
esen
ts
th
e
"
i
-
th
m
o
n
th
,
"
wh
ile
d
en
o
tes th
e
"j
-
th
f
lam
e.
"
T
h
e
f
u
n
ctio
n
H
r
ep
r
esen
ts
th
e
h
elix
f
u
n
ctio
n
.
d
ef
in
es
th
e
d
is
tan
ce
b
etwe
en
th
e
"i
-
th
m
o
th
"
an
d
th
e
"j
-
t
h
f
lam
e.
"
T
h
e
p
a
r
am
eter
s
‘
b
’
a
n
d
‘
t
’
ar
e
d
e
f
in
ed
as
a
co
n
s
tan
t
a
n
d
a
r
a
n
d
o
m
v
alu
e,
r
esp
ec
tiv
e
ly
,
g
iv
en
b
y
(
8
)
.
T
h
er
ef
o
r
e,
ca
n
b
e
d
eter
m
in
ed
b
y
(
8
)
.
=
|
−
|
(
8
)
E
x
p
lo
r
atio
n
tak
es
p
lace
w
h
en
th
e
m
o
th
’
s
n
ex
t
p
o
s
itio
n
is
c
alcu
lated
at
th
e
o
u
ter
lim
it
o
f
th
e
r
eg
io
n
s
ep
ar
atin
g
it
f
r
o
m
th
e
f
lam
e
.
I
n
co
n
tr
ast,
ex
p
lo
itatio
n
h
ap
p
e
n
s
wh
en
th
e
n
ex
t
p
o
s
itio
n
is
s
elec
ted
with
in
th
at
r
eg
io
n
.
I
n
(
9
)
s
h
o
ws
th
at
th
e
n
u
m
b
er
o
f
f
lam
es
is
r
ed
u
ce
d
p
r
o
g
r
ess
iv
ely
as
th
e
iter
atio
n
s
p
r
o
ce
ed
,
h
elp
in
g
m
ain
tain
a
p
r
o
p
er
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
an
d
ex
p
l
o
itatio
n
.
C
o
n
s
eq
u
e
n
tly
,
to
wa
r
d
th
e
f
in
al
iter
atio
n
s
,
th
e
m
o
th
s
ad
ju
s
t th
eir
p
o
s
itio
n
s
with
r
esp
ec
t to
th
e
b
est
-
p
er
f
o
r
m
i
n
g
f
lam
e.
=
(
−
∗
−
1
)
(
9
)
W
h
er
e
is
th
e
f
lam
e
'
s
m
ax
im
u
m
n
u
m
b
e
r
at
th
e
iter
atio
n
‘
’
an
d
is
th
e
m
ax
im
u
m
iter
atio
n
n
u
m
b
er
.
As
m
en
tio
n
ed
ea
r
lier
,
th
e
“P”
f
u
n
ctio
n
is
ca
r
r
ie
d
o
u
t
af
ter
th
e
co
m
p
letio
n
o
f
th
e
“T
”
f
u
n
ctio
n
.
At
th
is
s
tag
e,
th
e
b
est
-
p
e
r
f
o
r
m
in
g
m
o
th
is
id
en
tifie
d
,
wh
ich
s
er
v
es
as
th
e
clo
s
est
esti
m
ate
o
f
t
h
e
o
p
tim
al
s
o
lu
tio
n
.
I
n
th
is
wo
r
k
,
th
e
d
u
ty
cy
cle
(
D
)
o
f
th
e
DC
–
DC
co
n
v
er
ter
is
tr
ea
ted
as
th
e
d
ec
is
io
n
v
ar
iab
le,
an
d
its
v
alu
es
co
r
r
esp
o
n
d
to
th
e
p
o
s
itio
n
s
o
f
th
e
m
o
th
s
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
s
im
u
latio
n
r
esu
lts
in
Fig
u
r
e
s
4
a
n
d
5
d
em
o
n
s
tr
ate
th
at
d
is
to
r
tio
n
s
ar
e
m
o
r
e
p
r
o
n
o
u
n
ce
d
wh
en
u
s
in
g
a
PI
co
n
tr
o
ller
co
m
p
ar
e
d
to
a
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
with
STSM
C
.
T
h
e
PI
co
n
tr
o
ller
,
wh
ile
s
im
p
le
an
d
wid
ely
u
s
ed
,
s
tr
u
g
g
les
to
h
a
n
d
le
n
o
n
lin
ea
r
ities
an
d
r
ap
id
d
y
n
am
ic
c
h
an
g
es
e
f
f
ec
tiv
ely
,
lead
in
g
to
h
ig
h
er
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
,
o
v
e
r
s
h
o
o
ts
,
an
d
o
s
cillatio
n
s
in
t
h
e
o
u
t
p
u
t.
T
h
is
is
p
r
im
a
r
ily
d
u
e
t
o
it
s
f
ix
ed
g
ain
s
,
wh
ic
h
lack
th
e
ad
ap
ta
b
ilit
y
r
eq
u
ir
e
d
f
o
r
v
ar
y
in
g
s
y
s
tem
co
n
d
itio
n
s
.
Fig
u
r
e
4
.
Vp
v
,
I
p
v
,
Pp
v
,
Vd
c
u
s
in
g
MFO
-
PI
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
703
-
711
708
Fig
u
r
e
5
.
Vp
v
,
I
p
v
,
Pp
v
,
Vd
c
u
s
in
g
MFO
-
STSMC
co
n
tr
o
ller
I
n
co
n
tr
ast,
th
e
STSMC
ex
ce
ls
in
r
ed
u
cin
g
d
is
to
r
tio
n
s
b
y
lev
er
ag
in
g
its
r
o
b
u
s
tn
ess
ag
ain
s
t
d
is
tu
r
b
an
ce
s
an
d
p
ar
a
m
eter
v
ar
iatio
n
s
.
I
ts
ab
ilit
y
to
m
an
ag
e
n
o
n
lin
ea
r
ities
an
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
m
o
r
e
ef
f
ec
tiv
ely
r
esu
lts
in
s
m
o
o
th
e
r
an
d
m
o
r
e
s
tab
le
co
n
tr
o
l,
a
s
ev
id
en
ce
d
b
y
th
e
lo
wer
d
is
to
r
tio
n
lev
els
in
th
e
s
im
u
latio
n
o
u
tp
u
t.
Fig
u
r
e
6
il
lu
s
tr
ates
th
e
T
HD
o
f
th
e
g
r
id
cu
r
r
en
t
f
o
r
b
o
th
th
e
MFO
-
S
T
SMC
an
d
MFO
-
PI
co
n
tr
o
ller
s
.
(
a)
(
b
)
Fig
u
r
e
6
.
T
HD
o
f
g
r
i
d
cu
r
r
en
t
with
(
a)
MFO
-
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MFO
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Evaluation Warning : The document was created with Spire.PDF for Python.
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DATA AV
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[
1
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I
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S
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s
fro
m
Ja
wa
h
a
rlal
Ne
h
ru
Tec
h
n
o
l
o
g
ica
l
Un
i
v
e
rsity
Hy
d
e
ra
b
a
d
(JN
TU
-
Hy
d
e
ra
b
a
d
)
,
Hy
d
e
ra
b
a
d
,
In
d
ia,
i
n
2
0
0
9
a
n
d
2
0
1
3
,
re
sp
e
c
ti
v
e
ly
.
Aw
a
rd
e
d
a
p
o
st
d
o
c
to
ra
te
a
t
An
n
a
m
a
lai
Un
iv
e
rsity
,
C
h
id
a
m
b
a
ra
m
,
In
d
ia,
in
2
0
2
5
.
S
h
e
is
c
u
rre
n
t
ly
a
n
a
ss
istan
t
p
ro
fe
ss
o
r
with
th
e
V
a
ll
u
ru
p
a
ll
i
Na
g
e
sw
a
ra
Ra
o
Vi
g
n
a
n
a
Jy
o
th
i
I
n
stit
u
te
o
f
En
g
i
n
e
e
rin
g
a
n
d
Tec
h
n
o
lo
g
y
,
a
n
a
u
t
o
n
o
m
o
u
s
e
n
g
in
e
e
rin
g
i
n
stit
u
te,
in
Hy
d
e
ra
b
a
d
.
S
h
e
i
s
wo
rk
i
n
g
i
n
th
e
re
se
a
rc
h
a
re
a
s
o
f
re
so
n
a
n
t
c
o
n
v
e
rters
,
DC
-
DC
c
o
n
v
e
rters
,
fa
st
c
h
a
rg
in
g
tec
h
n
o
l
o
g
ies
f
o
r
e
le
c
tri
c
v
e
h
icle
s
(EVs)
,
a
n
d
re
n
e
wa
b
le en
e
rg
y
sy
st
e
m
s.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
ge
sh
m
a
k
u
m
a
ri_
r@v
n
rv
j
iet.
i
n.
Ve
e
r
a
n
ja
n
e
y
u
lu
G
o
p
u
is an
a
ss
o
c
iate
p
ro
fe
ss
o
r
in
th
e
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
De
p
a
rtme
n
t
a
t
t
h
e
RVR&
JC
Co
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
G
u
n
tu
r,
In
d
ia.
He
re
c
e
iv
e
d
h
is
P
h
.
D.
d
e
g
re
e
fro
m
Visv
e
sv
a
ra
y
a
Tec
h
n
o
l
o
g
ica
l
Un
iv
e
rsit
y
(VT
U)
in
2
0
2
5
.
He
re
c
e
iv
e
d
h
is
B.
Tec
h
.
a
n
d
M
.
Tec
h
.
d
e
g
re
e
s in
e
lec
tri
c
a
l
a
n
d
e
lec
tro
n
ics
e
n
g
in
e
e
ri
n
g
fro
m
Ja
wa
h
a
rlal
Ne
h
r
u
Tec
h
n
o
l
o
g
ica
l
U
n
i
v
e
rsity
,
Hy
d
e
r
a
b
a
d
,
a
n
d
Ac
h
a
ry
a
Na
g
a
rj
u
n
a
Un
iv
e
rsit
y
,
G
u
n
tu
r,
in
2
0
0
7
a
n
d
2
0
0
9
,
re
sp
e
c
ti
v
e
ly
.
He
h
a
s
b
e
e
n
a
n
a
ss
istan
t
p
ro
fe
ss
o
r
i
n
RVR&
JC
Co
ll
e
g
e
o
f
E
n
g
i
n
e
e
rin
g
,
G
u
n
tu
r,
I
n
d
ia
,
sin
c
e
2
0
1
3
a
n
d
h
a
s
b
e
e
n
wo
r
k
in
g
a
s
a
n
a
ss
o
c
iate
p
r
o
f
e
ss
o
r
fro
m
2
0
2
5
o
n
wa
rd
s
.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
t
h
e
field
o
f
p
o
we
r
s
y
ste
m
s,
p
o
we
r
e
lec
tro
n
ics
,
m
o
t
o
r
d
r
iv
e
s,
re
n
e
wa
b
le en
e
rg
y
,
a
n
d
m
icr
o
g
ri
d
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
g
v
a
n
jan
e
y
u
l
u
@rv
r
jc.ac
.
in
.
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