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an
d
th
e
ap
p
licatio
n
o
f
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
m
eth
o
d
b
ec
o
m
es
c
r
u
cial
[
1
6
]
,
[
1
7
]
.
T
h
is
alg
o
r
ith
m
en
h
a
n
c
es
t
h
e
PV
s
y
s
tem
'
s
tr
ac
k
in
g
e
f
f
icien
cy
g
u
ar
an
tee
s
s
tead
y
lo
ad
v
o
ltag
e
m
ain
t
en
an
c
e
in
s
p
ite
o
f
tem
p
er
at
u
r
e
an
d
ir
r
ad
ian
ce
f
lu
ctu
atio
n
s
[
1
8
]
.
An
i
n
v
er
ter
is
th
en
u
s
ed
to
co
n
v
er
t t
h
e
PV sy
s
tem
'
s
D
C
o
u
tp
u
t to
AC
,
as seen
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
PV c
ell
eq
u
i
v
alen
t c
i
r
cu
it
2
.
1
.
P
ho
t
o
v
o
lt
a
ic
(
P
V)
pa
nel
Ph
o
to
v
o
ltaic
(
PV)
d
io
d
es
m
ak
e
u
p
a
s
o
lar
ce
ll
p
an
el,
wh
ich
u
s
es
th
e
p
h
o
to
v
o
ltaic
ef
f
ec
t
to
f
u
n
ctio
n
.
T
h
e
PV
ce
ll
p
r
o
d
u
ce
s
elec
tr
icity
wh
en
it
is
ex
p
o
s
ed
to
s
u
n
lig
h
t.
T
h
e
v
o
ltag
e
th
at
th
e
PV
ce
ll
n
o
r
m
ally
g
en
er
ates
r
an
g
es
f
r
o
m
0
.
3
to
0
.
6
V,
d
ep
en
d
in
g
o
n
th
e
tech
n
o
lo
g
y
.
Fig
u
r
e
1
d
ep
icts
th
e
PV
ce
ll
'
s
co
m
p
ar
ab
le
cir
cu
it.
Mo
d
elin
g
th
e
s
o
lar
p
a
n
el
is
d
o
n
e
u
s
in
g
(
1
)
an
d
(
2
)
.
=
1
−
1
(
(
(
−
)
/
)
−
1
)
−
(
−
)
/
ℎ
(
1
)
=
(
1
/
1000
)
[
+
.
(
−
25
)
]
(
2
)
I
n
th
e
g
iv
e
n
co
n
te
x
t,
r
ep
r
esen
ts
th
e
cu
r
r
en
t
in
a
s
h
o
r
t
cir
cu
it,
s
ig
n
if
ies
th
e
g
en
er
ated
cu
r
r
en
t
o
f
th
e
p
h
o
to
v
o
ltaic
ar
r
a
y
,
s
tan
d
s
f
o
r
th
e
p
h
o
t
o
cu
r
r
e
n
t,
1
d
en
o
te
s
th
e
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t,
r
ep
r
esen
ts
th
e
v
o
ltag
e
p
r
o
d
u
ce
d
b
y
th
e
s
o
lar
ce
ll.
T
h
e
B
o
ltzm
an
n
c
o
n
s
tan
t
is
d
en
o
ted
b
y
.
,
s
ig
n
if
ies
th
e
Kelv
in
tem
p
er
atu
r
e,
r
ep
r
esen
ts
th
e
el
ec
tr
o
n
c
h
ar
g
e,
λ
1
r
ep
r
esen
ts
th
e
ir
r
ad
ian
ce
,
a
n
d
is
th
e
d
io
d
e'
s
q
u
ality
f
ac
to
r
.
T
em
p
er
atu
r
e
a
n
d
illu
m
in
ati
o
n
p
lay
a
c
r
u
cial
r
o
le
in
d
ete
r
m
in
in
g
p
o
wer
g
e
n
er
atio
n
in
th
e
ce
ll,
with
th
is
g
en
er
atio
n
b
ein
g
c
o
n
n
ec
te
d
d
i
r
ec
tly
to
ir
r
ad
ia
n
ce
an
d
in
v
er
s
ely
to
tem
p
er
atu
r
e
[
1
9
]
-
[
2
2
]
.
2
.
2
.
I
nte
g
ra
t
ed
P
V
-
t
herma
l
-
h
y
dro
po
wer
s
y
s
t
em
A
th
r
ee
-
ar
ea
in
ter
co
n
n
ec
ted
s
y
s
tem
's
b
lo
ck
d
iag
r
am
is
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
th
r
ee
a
r
ea
s
'
f
r
eq
u
en
cy
d
ev
iatio
n
s
(
∆f
1
-
∆f
3
)
ar
e
d
is
p
l
ay
ed
[
2
3
]
,
[
2
4
]
.
T
o
ex
am
in
e
th
e
d
if
f
er
en
ce
s
in
f
r
eq
u
e
n
cy
an
d
tie
-
lin
e
p
o
wer
,
eq
u
al
lo
ad
d
is
tu
r
b
an
ce
s
ar
e
in
t
r
o
d
u
ce
d
to
ea
ch
o
f
th
e
th
r
ee
s
y
s
tem
s
.
T
h
e
s
y
s
tem
's p
er
f
o
r
m
an
ce
is
ev
alu
ated
b
y
ev
alu
atin
g
d
if
f
er
e
n
t
lo
a
d
p
e
r
tu
r
b
atio
n
s
.
T
h
is
s
y
s
tem
'
s
m
ain
g
o
al
is
th
e
s
am
e
as
a
th
r
ee
-
ar
ea
th
er
m
al
s
y
s
tem
'
s
[
2
5
]
.
Ma
n
u
al
r
e
g
u
latio
n
is
r
ep
lace
d
b
y
a
clo
s
ed
-
lo
o
p
c
o
n
tr
o
l
m
eth
o
d
ca
lled
lo
a
d
f
r
eq
u
e
n
cy
co
n
tr
o
l,
o
r
L
FC
.
E
lim
in
atin
g
f
r
eq
u
en
cy
v
ar
iatio
n
s
b
r
o
u
g
h
t
o
n
b
y
lo
ad
d
is
tu
r
b
an
ce
s
in
th
e
tie
lin
es
an
d
th
r
o
u
g
h
o
u
t
th
e
th
r
ee
zo
n
es
is
th
e
p
r
im
ar
y
g
o
a
l
o
f
L
FC
.
E
v
er
y
s
y
s
tem
co
n
tr
o
ls
its
o
wn
o
s
cillatio
n
s
an
d
m
ak
es
u
p
f
o
r
th
o
s
e
in
r
eg
io
n
s
wh
er
e
d
ev
iatio
n
s
ar
e
u
n
co
n
tr
o
llab
le
[
2
6
]
.
T
h
e
t
h
r
ee
-
ar
ea
b
lo
c
k
s
ch
em
atic
o
f
a
n
e
two
r
k
ed
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
1
1
6
-
1123
1118
Fig
u
r
e
2
.
Diag
r
a
m
m
atic
r
ep
r
esen
tatio
n
o
f
a
n
in
teg
r
ated
th
r
ee
-
zo
n
e
s
y
s
tem
3.
ARTI
F
I
CI
AL
RA
I
NDRO
P
AL
G
O
RI
T
H
M
(
ARDA
)
A
s
ig
n
al
p
r
o
d
u
ce
d
b
y
th
e
L
F
C
r
eg
u
lates
f
r
eq
u
en
c
y
an
d
estab
lis
h
es
g
en
er
atio
n
.
T
h
e
L
F
C
'
s
A
R
DA
m
o
d
if
ies
th
e
PI
co
n
tr
o
ller
'
s
g
ain
s
.
T
h
is
is
th
e
d
ef
in
itio
n
o
f
th
e
g
en
er
al
o
p
tim
izatio
n
p
r
o
b
le
m
,
wh
er
e
x
is
an
n
-
d
im
en
s
io
n
al
v
ec
to
r
an
d
S
is
a
s
et
o
f
f
in
ite
m
ea
s
u
r
e.
T
h
is
o
p
ti
m
izatio
n
p
r
o
b
lem
is
in
ten
d
e
d
t
o
b
e
s
o
lv
ed
b
y
t
h
e
r
ain
d
r
o
p
alg
o
r
ith
m
.
At
f
ir
s
t,
N
r
ain
d
r
o
p
s
f
all
o
n
th
e
"g
r
o
u
n
d
,
"
wh
e
r
e
S
s
tan
d
s
f
o
r
th
e
"g
r
o
u
n
d
".
T
h
e
n
o
tatio
n
"
∈
x
i
∈
S"
in
d
icate
s
th
e
lo
ca
tio
n
o
f
th
e
i
-
th
r
ain
d
r
o
p
.
T
h
e
r
ain
d
r
o
p
will
m
ig
r
ate
d
u
r
i
n
g
ea
c
h
p
e
r
io
d
af
ter
it
h
as
f
allen
.
T
h
e
id
ea
l
v
alu
es
f
o
r
th
e
PI
co
n
tr
o
ller
ar
e
ascer
tain
ed
b
y
m
ea
n
s
o
f
th
e
s
ix
p
h
ases
o
f
AR
DA:
r
ain
d
r
o
p
p
r
o
d
u
ctio
n
,
r
ain
d
r
o
p
d
escen
t,
r
ain
d
r
o
p
co
llis
io
n
,
r
ai
n
d
r
o
p
f
l
o
w,
R
P
u
p
d
atin
g
,
an
d
v
ap
o
r
u
p
d
atin
g
.
I
f
t
h
er
e'
s
s
till
d
u
p
licate
v
ap
o
r
in
F
ig
u
r
e
3
,
wh
ich
s
h
o
ws th
e
p
r
o
ce
s
s
d
i
ag
r
am
o
f
th
e
ar
tific
ial
r
ain
d
r
o
p
alg
o
r
ith
m
.
Fig
u
r
e
3
.
Dis
p
lay
s
th
e
f
lo
w
d
i
ag
r
a
m
o
f
th
e
ar
tific
ial
r
ain
d
r
o
p
alg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i
Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
r
tifi
cia
l ra
in
d
r
o
p
a
lg
o
r
ith
m
fo
r
co
n
tr
o
l o
f freq
u
en
cy
i
n
a
n
e
tw
o
r
ke
d
…
(
La
ksh
mi
Dh
a
n
d
a
p
a
n
i
)
1119
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
T
h
e
m
o
m
e
n
tar
y
r
ea
ctio
n
ev
a
lu
atio
n
with
r
ef
er
e
n
ce
to
th
e
is
lan
d
ed
m
icr
o
g
r
id
(
MG
)
s
y
s
tem
was
co
n
d
u
cte
d
with
th
e
aid
o
f
MA
T
L
AB
/
Simu
lin
k
2
0
1
8
a.
T
o
en
s
u
r
e
a
f
air
an
d
co
m
p
r
eh
en
s
iv
e
ass
e
s
s
m
en
t
o
f
o
p
tim
izatio
n
o
f
p
ar
ticle
s
war
m
s
(
PS
O)
,
th
e
g
r
ey
w
o
lf
alg
o
r
ith
m
f
o
r
o
p
tim
izatio
n
(
GOA)
,
an
d
ar
tific
ial
r
ai
n
d
r
o
p
al
g
o
r
ith
m
(
AR
DA)
,
id
en
t
ical
s
y
s
tem
p
ar
am
eter
s
wer
e
em
p
lo
y
ed
in
b
o
th
s
im
u
latio
n
s
.
4
.
1
.
Co
ntr
o
llin
g
v
o
lt
a
g
e
a
nd
f
re
qu
ency
du
ring
lo
a
d v
a
ria
t
io
n a
nd
DG
inte
g
ra
t
io
n
I
n
an
is
lan
d
ed
m
icr
o
g
r
id
,
f
r
e
q
u
en
cy
,
v
o
ltag
e,
an
d
r
eg
u
latio
n
ar
e
cr
itical
d
u
e
to
th
e
lack
o
f
m
ain
g
r
id
s
u
p
p
o
r
t.
T
o
o
p
tim
ize
s
tab
ilit
y
af
ter
DG
in
s
er
tio
n
an
d
lo
a
d
ch
a
n
g
es,
th
r
ee
m
et
a
h
eu
r
is
tic
tech
n
iq
u
es
(
PS
O,
GOA,
AR
DA)
wer
e
em
p
lo
y
ed
to
f
in
e
-
tu
n
e
t
h
e
ca
p
ac
i
tan
c
e
o
f
th
e
DC
-
lin
k
a
n
d
PI
co
n
tr
o
ller
p
ar
am
eter
s
.
AR
DA
iter
ativ
ely
s
ea
r
ch
ed
f
o
r
o
p
tim
al
v
alu
es
b
y
m
in
im
iz
in
g
th
e
FF
p
ar
am
ete
r
d
u
r
in
g
s
im
u
latio
n
.
At
0
.
0
5
s
ec
o
n
d
s
,
p
h
o
t
o
v
o
ltaic
(
PV)
m
o
d
u
les p
o
wer
e
d
b
y
s
o
lar
wer
e
ac
tiv
ated
,
ca
u
s
in
g
v
o
ltag
e
o
v
e
r
s
h
o
o
ts
(
Fig
u
r
e
4
)
.
T
h
e
o
p
tim
ized
PI
g
ain
s
an
d
c
ap
ac
itan
ce
v
alu
es
o
b
tai
n
ed
th
r
o
u
g
h
th
ese
tech
n
iq
u
es
en
s
u
r
e
m
in
im
al
o
v
er
s
h
o
o
t
an
d
s
ettlin
g
tim
e,
en
s
u
r
in
g
o
p
tim
al
d
y
n
a
m
ic
b
eh
a
v
io
r
in
t
h
e
MG
m
o
d
el
b
e
h
av
io
r
.
Fig
u
r
e
4
illu
s
tr
ates
v
o
ltag
e
o
v
er
s
h
o
o
t
at
0
.
0
5
s
ec
o
n
d
s
in
th
e
DG
in
teg
r
atio
n
p
r
o
ce
s
s
,
in
f
lu
e
n
ce
d
b
y
DG
r
atin
g
an
d
co
n
tr
o
ller
p
ar
am
eter
s
.
T
o
en
s
u
r
e
a
f
air
co
m
p
ar
is
o
n
b
et
wee
n
PS
O,
GOA,
an
d
AR
DA,
th
e
s
am
e
s
y
s
tem
s
ettin
g
s
wer
e
m
ain
tain
ed
.
L
o
a
d
ch
a
n
g
e
s
at
0
.
2
5
s
(
ad
d
itio
n
)
an
d
0
.
5
5
s
(
d
is
co
n
n
ec
tio
n
)
ca
u
s
ed
co
r
r
esp
o
n
d
in
g
v
o
ltag
e
f
lu
ctu
ati
o
n
s
.
Fig
u
r
e
5
d
ep
icts
r
esp
o
n
s
es
d
u
r
in
g
DG
in
s
er
tio
n
,
lo
a
d
a
d
d
itio
n
,
a
n
d
d
is
co
n
n
ec
tio
n
o
f
lo
ad
[
2
0
]
-
[
2
2
]
.
Op
tim
al
p
ar
am
eter
s
f
r
o
m
A
R
DA
o
u
tp
er
f
o
r
m
PS
O
an
d
GOA
in
Fig
u
r
e
s
5
(
a)
an
d
5
(
b
)
,
ev
id
e
n
t
in
lo
wer
o
v
er
s
h
o
o
t
an
d
s
ettlin
g
tim
es
ac
r
o
s
s
co
n
d
itio
n
s
.
I
n
is
lan
d
e
d
MG
o
p
er
atio
n
s
,
ad
d
r
ess
in
g
s
y
s
tem
f
r
eq
u
en
cy
is
cr
u
cial.
Fig
u
r
e
5
(
c)
s
h
o
ws
AR
DA
'
s
s
u
p
er
io
r
f
r
eq
u
en
cy
r
eg
u
latio
n
co
m
p
a
r
ed
to
PS
O
an
d
GOA,
em
p
h
asizin
g
AR
DA
's
ef
f
ec
tiv
en
ess
in
en
h
a
n
cin
g
o
v
er
all
MG
s
y
s
tem
p
er
f
o
r
m
an
ce
.
Fig
u
r
e
6
d
e
p
icts
MG
s
y
s
tem
f
r
eq
u
en
cy
r
esp
o
n
s
e
f
o
r
th
r
ee
o
p
tim
izatio
n
m
eth
o
d
s
,
i
n
d
icatin
g
s
tab
le
r
esp
o
n
s
es
with
in
±
1
%
d
e
v
iatio
n
.
No
tab
l
y
,
AR
DA
ex
h
ib
its
s
u
p
er
io
r
d
y
n
a
m
ic.
T
ab
le
1
p
r
esen
ts
a
co
m
p
ar
a
tiv
e
an
aly
s
is
o
f
co
n
t
r
o
l
o
f
f
r
eq
u
en
c
y
a
n
d
v
o
ltag
e
in
t
h
e
is
lan
d
ed
m
icr
o
g
r
id
s
etu
p
(
MG
)
u
n
d
e
r
s
tu
d
y
,
h
i
g
h
lig
h
tin
g
th
e
s
u
p
er
io
r
ef
f
ec
ti
v
en
ess
o
f
AR
DA
co
m
p
ar
e
d
to
its
co
m
p
etito
r
s
.
T
h
e
r
esu
lts
s
h
o
w
n
in
T
a
b
le
1
s
h
o
w
th
at
th
e
A
R
DA
co
n
tr
o
ller
wo
r
k
e
d
b
etter
th
an
b
o
th
PS
O
an
d
GOA.
T
h
is
m
ea
n
t
th
at
th
e
s
tu
d
ied
MG
s
y
s
tem
h
ad
b
etter
d
y
n
am
ic
r
esp
o
n
s
e
in
d
icato
r
s
an
d
s
tab
le
o
p
er
atio
n
.
I
t
m
ai
n
tain
ed
v
o
ltag
e
with
in
±
5
%
an
d
f
r
e
q
u
en
c
y
with
in
±
1
%
,
m
ee
tin
g
I
E
E
E
s
tan
d
a
r
d
s
.
N
o
tab
ly
,
th
e
s
ettlin
g
tim
e
f
o
r
f
r
eq
u
e
n
cy
wasn
'
t c
alcu
lated
d
u
e
t
o
th
e
cu
r
v
e
s
tay
in
g
with
in
±
2
% o
f
t
h
e
r
ated
v
alu
e
.
T
ab
le
1
. S
u
m
m
a
r
izes c
o
m
p
ar
a
tiv
e
an
aly
s
es f
o
r
co
n
tr
o
l o
f
f
r
e
q
u
e
n
cy
an
d
v
o
ltag
e
in
th
e
ex
a
m
in
ed
is
lan
d
ed
m
icr
o
g
r
id
em
p
h
asizin
g
AR
DA's e
f
f
icac
y
o
v
er
c
o
m
p
etito
r
s
Ex
a
m
i
n
e
d
sc
e
n
a
r
i
o
A
p
p
r
o
a
c
h
M
O
S
/
M
U
S
(
%)
P
e
a
k
p
e
r
i
o
d
(
mi
l
l
i
sec
o
n
d
s)
S
e
t
t
l
i
n
g
t
i
me
(
ms)
V
o
l
t
a
g
e
M
G
i
n
s
e
r
t
i
o
n
PSO
5
.
8
6
2
7
.
2
3
7
.
7
GOA
4
.
6
8
3
6
.
3
6
4
.
5
A
R
D
A
1
.
4
5
2
6
.
2
2
6
.
3
6
Lo
a
d
i
n
j
e
c
t
i
o
n
PSO
1
6
.
4
5
4
.
0
0
9
4
.
2
1
GOA
1
6
.
0
0
4
.
7
0
9
4
.
2
0
A
R
D
A
1
5
.
0
4
3
.
9
0
9
4
.
1
9
Lo
a
d
d
e
t
a
c
h
me
n
t
PSO
1
6
.
4
1
7
.
7
0
7
3
.
5
0
GOA
1
5
.
5
9
7
.
5
0
7
8
.
5
0
A
R
D
A
1
4
.
7
7
7
.
8
0
7
7
.
4
0
F
r
e
q
u
e
n
c
y
M
G
i
n
j
e
c
t
i
o
n
PSO
0
.
4
4
2
.
0
5
-
GOA
0
.
5
4
5
.
5
8
-
A
R
D
A
0
.
4
6
2
.
3
0
-
Lo
a
d
i
n
j
e
c
t
i
o
n
PSO
0
.
6
6
3
5
.
2
-
GOA
0
.
5
0
3
4
.
8
-
A
R
D
A
0
.
4
6
3
5
.
0
-
Lo
a
d
d
e
t
a
c
h
me
n
t
PSO
0
.
5
0
3
6
.
4
-
GOA
0
.
4
8
3
6
.
7
-
A
R
D
A
0
.
4
6
3
6
.
8
-
4
.
2
.
E
v
a
lua
t
i
o
n o
f
t
he
a
na
ly
ze
d o
ptim
iza
t
io
n a
lg
o
rit
hm
s
ef
f
ec
t
iv
eness
T
h
is
s
eg
m
en
t
p
r
esen
ts
r
esu
lts
f
r
o
m
ev
alu
atin
g
th
r
ee
o
p
tim
izatio
n
alg
o
r
ith
m
s
(
PS
O,
GOA,
AR
DA)
u
n
d
er
id
en
tical
co
n
d
itio
n
s
.
All
alg
o
r
ith
m
s
u
n
d
er
we
n
t
5
0
iter
atio
n
s
with
5
0
s
ea
r
c
h
ag
e
n
ts
in
a
f
air
co
m
p
ar
is
o
n
.
Ov
er
2
0
s
im
u
latio
n
r
u
n
s
,
AR
DA
ac
h
iev
ed
th
e
m
i
n
im
u
m
f
itn
ess
f
u
n
cti
o
n
v
al
u
e
(
0
.
5
8
4
1
)
in
th
e
s
ev
en
teen
t
h
cy
cle,
o
u
tp
e
r
f
o
r
m
in
g
PS
O
(
0
.
9
2
1
1
5
8
6
at
2
1
s
t
iter
atio
n
)
a
n
d
GOA
(
0
.
8
7
4
8
7
7
4
at
2
5
th
iter
atio
n
)
.
AR
DA
ex
h
ib
ited
f
aster
co
n
v
er
g
en
ce
an
d
s
u
p
er
i
o
r
s
o
lu
tio
n
q
u
alit
y
.
Fig
u
r
e
7
s
h
o
ws
th
e
PS
O,
GOA
,
an
d
AR
DA
co
n
v
er
g
en
ce
cu
r
v
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
1
1
6
-
1123
1120
Fig
u
r
e
4
.
R
esp
o
n
s
e
o
f
th
e
s
y
s
tem
'
s
v
o
ltag
e
u
n
d
er
lo
a
d
v
ar
iat
io
n
an
d
DG
in
teg
r
atio
n
(
a)
(
b
)
(
c)
Fig
u
r
e
5
.
Pro
f
ile
o
f
v
o
ltag
e
at
(
a)
DG
in
teg
r
atio
n
,
(
b
)
ab
r
u
p
t
lo
ad
in
cr
ea
s
e,
an
d
(
c)
ab
r
u
p
t l
o
ad
d
r
o
p
Fig
u
r
e
6
.
T
h
e
m
icr
o
g
r
id
s
y
s
te
m
'
s
f
r
eq
u
en
cy
r
esp
o
n
s
e
f
o
r
t
h
e
ex
p
lo
r
e
d
o
p
tim
izatio
n
m
eth
o
d
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i
Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
r
tifi
cia
l ra
in
d
r
o
p
a
lg
o
r
ith
m
fo
r
co
n
tr
o
l o
f freq
u
en
cy
i
n
a
n
e
tw
o
r
ke
d
…
(
La
ksh
mi
Dh
a
n
d
a
p
a
n
i
)
1121
Fig
u
r
e
7
.
T
h
e
c
o
n
v
er
g
e
n
ce
p
r
o
f
ile
f
o
r
GOA,
PS
O,
an
d
AR
DA
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
p
r
esen
ts
th
e
s
u
cc
e
s
s
f
u
l
d
ev
elo
p
m
e
n
t
o
f
an
o
p
ti
m
al
co
n
tr
o
ller
f
o
r
an
is
lan
d
ed
m
icr
o
g
r
id
(
MG
)
u
tili
zin
g
th
e
ad
ap
tiv
e
r
an
d
o
m
ized
d
if
f
e
r
en
tial
alg
o
r
ith
m
(
AR
DA)
.
T
h
e
d
esig
n
ed
c
o
n
tr
o
ller
e
f
f
ec
tiv
ely
r
eg
u
lates
v
o
ltag
e
an
d
f
r
eq
u
e
n
cy
d
u
r
in
g
lo
ad
v
a
r
iatio
n
a
n
d
m
icr
o
g
r
id
in
teg
r
atio
n
,
m
in
im
i
zin
g
o
v
er
s
h
o
o
t
an
d
s
ettlin
g
tim
e
s
ce
n
ar
io
s
.
C
o
m
p
ar
ativ
e
an
aly
s
is
o
f
o
p
tim
izatio
n
alg
o
r
ith
m
s
d
em
o
n
s
tr
ates
th
at
AR
DA
ex
h
ib
its
s
u
p
er
io
r
c
o
n
v
e
r
g
en
ce
b
eh
a
v
i
o
r
,
o
f
f
er
in
g
h
ig
h
er
q
u
ality
s
o
lu
tio
n
s
an
d
f
aster
o
p
tim
izatio
n
ca
p
a
b
ili
ties
co
m
p
ar
ed
to
alter
n
ativ
e
al
g
o
r
i
th
m
s
.
T
h
e
im
p
lem
en
te
d
co
n
t
r
o
ller
p
r
o
v
i
d
es
r
em
ar
k
a
b
le
p
o
wer
q
u
ality
b
y
en
s
u
r
i
n
g
v
i
r
tu
al
ly
p
er
f
ec
t
s
in
u
s
o
id
al
wav
ef
o
r
m
s
f
o
r
b
o
th
v
o
ltag
e
an
d
c
u
r
r
e
n
t,
ac
c
o
r
d
in
g
to
t
h
e
p
o
wer
q
u
ality
a
n
aly
s
is
.
Un
d
er
th
e
id
en
tical
o
p
e
r
atin
g
co
n
d
itio
n
s
an
d
s
y
s
tem
s
ettin
g
s
,
a
th
o
r
o
u
g
h
co
m
p
a
r
is
o
n
with
co
n
tr
o
ll
er
s
th
at
u
s
e
p
ar
ticle
s
war
m
o
p
tim
iz
atio
n
(
PS
O)
an
d
g
e
n
etic
o
p
tim
izatio
n
alg
o
r
ith
m
(
GOA)
h
i
g
h
lig
h
ts
th
e
AR
DA
-
b
ased
co
n
tr
o
ller
'
s
s
u
p
er
io
r
p
er
f
o
r
m
a
n
ce
.
T
h
e
r
esu
lts
s
h
o
w
th
at
in
ev
er
y
s
tu
d
ied
ca
s
e,
th
e
AR
DA
-
b
ased
p
ar
a
m
eter
s
elec
tio
n
p
r
o
d
u
ce
s
th
e
b
est
d
y
n
am
ic
r
esp
o
n
s
es,
o
u
tp
er
f
o
r
m
in
g
alter
n
ativ
e
ap
p
r
o
ac
h
es.
Fu
r
th
er
m
o
r
e,
th
er
e
m
ay
b
e
f
u
tu
r
e
u
s
es f
o
r
th
is
s
tr
ateg
y
th
at
tr
y
t
o
in
cr
ea
s
e
en
e
r
g
y
ef
f
icien
c
y
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
tate
n
o
f
u
n
d
in
g
i
n
v
o
l
v
ed
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
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25
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1123
1122
DATA AV
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Evaluation Warning : The document was created with Spire.PDF for Python.