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I
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Vo
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6
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Dec
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2
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1
7
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3
2
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2
5
3218
d
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n
h
ar
m
o
n
y
s
ea
r
ch
o
p
ti
m
izatio
n
(
HS)
tech
n
iq
u
e
f
o
r
p
ar
allel
t
w
o
-
ar
ea
p
o
w
er
s
y
s
te
m
.
T
h
e
t
w
o
-
ar
ea
p
o
w
er
s
y
s
te
m
an
d
L
F
C
lo
o
p
in
clu
d
in
g
t
h
e
p
r
o
p
o
s
ed
HS
-
P
I
c
o
n
tr
o
ller
ar
e
m
o
d
elled
u
s
i
n
g
Ma
tlab
en
v
ir
o
n
m
e
n
t.
T
h
e
in
te
g
r
al
ab
s
o
lu
te
er
r
o
r
(
I
A
E
)
f
u
n
c
tio
n
is
u
s
ed
to
d
eter
m
i
n
e
its
m
i
n
i
m
u
m
v
al
u
e
f
o
r
a
s
tep
lo
ad
ch
an
g
e.
Fo
r
a
g
o
o
d
d
y
n
a
m
ic
p
er
f
o
r
m
a
n
ce
,
th
e
r
o
b
u
s
t
n
ess
o
f
t
h
e
p
r
o
p
o
s
ed
HS
-
P
I
co
n
tr
o
l
alg
o
r
ith
m
is
co
m
p
ar
ed
w
it
h
th
e
P
I
co
n
tr
o
ller
b
ased
p
ar
ticle
s
w
a
r
m
o
p
ti
m
izatio
n
(
P
SO)
n
a
m
e
d
P
SO
-
P
I
co
n
tr
o
ller
in
ter
m
s
o
f
ti
m
e
s
ettli
n
g
,
m
ax
i
m
u
m
d
ev
iat
io
n
,
an
d
p
ea
k
ti
m
e.
2.
L
F
C
SI
M
UL
I
NK
M
O
DE
L
WI
T
H
P
RO
P
O
S
E
D
CO
NT
RO
L
L
E
R
T
h
e
o
v
er
all
p
o
w
er
s
y
s
te
m
o
f
t
w
o
-
ar
ea
p
o
w
er
s
y
s
te
m
s
in
c
lu
d
in
g
th
e
L
FC
m
o
d
el
an
d
t
h
e
P
I
co
n
tr
o
ll
er
is
in
v
est
ig
ated
as
s
h
o
w
n
in
F
i
g
u
r
e
1
.
E
ac
h
p
o
w
er
s
y
s
te
m
h
as
p
r
i
m
ar
y
an
d
s
ec
o
n
d
ar
y
lo
o
p
s
r
esp
ec
tiv
el
y
a
n
d
f
ee
d
b
ac
k
co
n
tr
o
ller
.
1
an
d
2
ar
e
th
e
co
n
tr
o
l
o
u
tp
u
ts
o
f
th
e
p
r
o
p
o
s
ed
P
I
c
o
n
tr
o
ller
s
r
esp
e
ctiv
el
y
;
1
an
d
2
ar
e
th
e
d
i
s
t
u
r
b
an
ce
lo
ad
ch
an
g
e
s
;
1
an
d
2
ar
e
r
e
p
r
esen
te
d
th
e
f
r
eq
u
en
c
y
c
h
an
g
es
i
n
ea
ch
p
o
w
er
s
y
s
te
m
.
T
h
e
n
o
m
i
n
al
p
ar
a
m
eter
s
o
f
t
h
e
o
v
er
all
p
o
w
er
s
y
s
te
m
ar
e
g
iv
e
n
in
[
1
9
]
.
An
ar
ea
co
n
tr
o
l
er
r
o
r
(
A
C
E
)
is
u
s
ed
f
o
r
ea
ch
ar
ea
to
r
ed
u
ce
its
o
w
n
v
al
u
e
to
b
e
ze
r
o
[
2
0
]
,
w
h
ic
h
is
d
e
f
in
ed
as:
1
=
1
∆
1
+
∆
12
(
1
)
2
=
2
∆
2
−
∆
12
(
2
)
w
h
er
e
∆
12
r
ep
r
esen
ts
t
h
e
ch
a
n
g
e
in
th
e
ti
e
li
n
e
p
o
w
er
p
lan
t
,
1
an
d
2
ar
e
th
e
b
ias
f
r
eq
u
e
n
cies
f
o
r
ea
ch
ar
ea
,
∆
1
an
d
∆
2
r
ep
r
esen
t th
e
f
r
eq
u
e
n
c
y
d
ev
iatio
n
f
o
r
ea
ch
ar
ea
.
K
ps
1
-------------
(
1
+
S
K
ps
1
)
Δω
1
K
ps
2
-------------
(
1
+
S
K
ps
2
)
1
-------------
(
1
+
S
T
g
1
)
1
------------
(
1
+
S
T
g
2
)
1
------------
(
1
+
S
T
t
1
)
1
------------
(
1
+
S
T
t
2
)
1
---
R
1
1
----
R
2
B
1
B
2
Δω
2
O
pt
i
m
a
l
V
a
l
ue
s
O
pt
i
m
a
l
V
a
l
ue
s
Ps
1
----
s
DP
12
A
CE
1
A
re
a
1
A
re
a
2
P
ri
m
a
ry L
oop
1
P
ri
m
a
ry L
oop
2
S
e
c
ond
a
ry L
oop
1
S
e
c
onda
ry L
oop
2
Ki
K
p
+
----
s
HS
_
A
l
gor
i
th
m
Ki
K
p
+
----
s
HS
_
A
l
gor
i
th
m
Kp
Ki
A
CE
2
Δ
PL
2
Δ
PL
1
O
U
T
1
O
U
T
2
Fig
u
r
e
1
.
L
F
C
Si
m
u
lin
k
m
o
d
e
l
w
it
h
p
r
o
p
o
s
ed
co
n
tr
o
ller
P
I
co
n
tr
o
ller
is
o
n
e
o
f
t
h
e
p
o
p
u
lar
f
ee
d
b
ac
k
co
n
tr
o
ller
u
s
ed
w
it
h
th
e
lo
ad
f
r
eq
u
e
n
c
y
c
o
n
tr
o
l
f
o
r
p
r
o
v
id
in
g
a
n
e
x
ce
lle
n
t
co
n
tr
o
l
p
er
f
o
r
m
an
ce
an
d
h
i
g
h
er
s
ta
b
ilit
y
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
t
h
e
P
I
co
n
s
i
s
ts
o
f
t
w
o
b
asic
p
ar
a
m
eter
s
;
P
r
o
p
o
r
tio
n
al
(
P
)
an
d
I
n
teg
r
al
(
I
)
.
Acc
o
r
d
in
g
to
[
2
1
]
an
d
[
2
2
]
,
t
h
e
t
y
p
ica
l
tr
an
s
f
er
f
u
n
ctio
n
o
f
t
h
e
class
ical
P
I
co
n
tr
o
ller
in
ter
m
s
o
f
L
ap
lace
d
o
m
ai
n
is
d
escr
ib
ed
b
elo
w
:
(
)
=
(
)
(
)
=
+
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
A
n
Op
tima
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in
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s
in
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a
Meta
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h
eu
r
is
tic
Op
timiz
a
tio
n
....
(
Mu
s
h
ta
q
N
a
jeeb
)
3219
w
h
er
e,
(
)
an
d
(
)
ar
e
th
e
co
n
tr
o
l
s
i
g
n
al
a
n
d
th
e
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r
o
r
s
ig
n
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w
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h
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t
h
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d
if
f
er
en
ce
b
et
w
ee
n
t
h
e
in
p
u
t
a
n
d
th
e
f
ee
d
b
ac
k
co
r
r
esp
o
n
d
in
g
l
y
.
is
th
e
p
r
o
p
o
r
tio
n
al
g
ain
an
d
is
t
h
e
i
n
teg
r
atio
n
g
ai
n
.
Mo
r
eo
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er
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th
e
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tp
u
t
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alu
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f
th
e
p
r
o
p
o
s
ed
P
I
D
co
n
tr
o
ller
is
g
i
v
en
b
elo
w
w
h
ich
g
en
er
ates
t
h
e
p
r
o
p
er
co
n
tr
o
l
s
ig
n
al
to
k
ee
p
th
e
s
y
s
te
m
p
ar
a
m
eter
s
w
it
h
i
n
th
e
n
o
m
i
n
al
v
alu
e
s
;
(
)
=
(
)
+
∫
(
)
0
(
4
)
w
h
er
e
(
)
an
d
(
)
ar
e
th
e
co
n
tr
o
l a
n
d
tr
ac
k
in
g
er
r
o
r
s
ig
n
a
l
w
h
ic
h
is
i
n
th
e
f
o
r
m
o
f
t
i
m
e
d
o
m
a
in
.
Fo
r
ar
ea
1
:
1
(
)
=
1
1
(
)
+
1
∫
1
(
)
0
(
5
)
Fo
r
ar
ea
2
:
2
(
)
=
2
2
(
)
+
2
∫
2
(
)
0
(
6
)
3.
H
S AL
G
O
RI
T
H
M
CO
NCEPT
H
ar
m
o
n
y
s
ea
r
c
h
(
HS)
is
a
w
el
l
-
k
n
o
w
n
m
eta
-
h
e
u
r
is
tic
o
p
ti
m
i
za
tio
n
alg
o
r
it
h
m
in
s
p
ir
ed
b
y
t
h
e
m
o
d
er
n
n
atu
r
al
p
h
e
n
o
m
en
a,
w
h
ich
was
p
r
o
p
o
s
ed
b
y
[
2
3
]
.
T
h
e
b
as
ic
p
r
o
ce
s
s
o
f
th
is
al
g
o
r
ith
m
i
s
to
p
r
o
d
u
ce
m
u
s
ic
tu
n
e
s
t
h
r
o
u
g
h
p
itc
h
i
n
g
th
e
m
u
s
ical
i
n
s
tr
u
m
e
n
ts
i
n
o
r
d
er
t
o
s
ea
r
ch
f
o
r
a
h
ar
m
o
n
y
.
Fo
r
th
e
h
ar
m
o
n
y
i
m
p
r
o
v
is
at
io
n
,
m
u
s
ic
ian
s
tr
y
v
ar
io
u
s
m
u
s
ical
co
m
b
i
n
atio
n
s
s
to
r
ed
in
th
eir
m
e
m
o
r
y
to
g
et
an
ex
ce
lle
n
t
q
u
alit
y
.
Me
an
w
h
ile,
it
i
s
s
i
m
ilar
to
t
h
e
o
p
ti
m
izatio
n
p
r
o
ce
s
s
b
y
cr
ea
t
in
g
a
n
e
w
s
o
lu
tio
n
u
s
i
n
g
an
o
b
j
ec
tiv
e
f
u
n
ctio
n
in
o
r
d
er
to
im
p
r
o
v
e
th
e
q
u
alit
y
o
f
th
e
g
e
n
er
ated
s
o
lu
tio
n
s
.
I
n
b
r
ief
,
th
e
o
p
tim
izat
io
n
p
r
o
ce
s
s
o
f
th
e
h
ar
m
o
n
y
s
ea
r
ch
al
g
o
r
ith
m
is
s
h
o
w
n
in
F
ig
u
r
e
2
w
h
ic
h
ca
n
b
e
co
n
clu
d
ed
in
f
i
v
e
s
tep
s
[
2
4
]
,
[
2
5
]
:
(
1
)
th
e
HS
al
g
o
r
ith
m
p
ar
am
eter
s
ar
e
in
itial
ized
s
u
c
h
as
t
h
e
h
ar
m
o
n
y
m
e
m
o
r
y
s
i
ze
(
HM
S)
w
h
ic
h
is
u
s
ed
to
s
p
ec
if
y
t
h
e
s
o
l
u
tio
n
v
ec
to
r
s
n
u
m
b
er
,
h
ar
m
o
n
y
m
e
m
o
r
y
co
n
s
id
er
in
g
r
ate
(
H
MC
R
,
its
r
an
g
e
b
et
w
ee
n
[
0
,
1
]
)
w
h
ich
is
u
s
ed
f
o
r
t
h
e
s
o
lu
tio
n
v
ec
to
r
i
m
p
r
o
v
e
m
e
n
t
in
t
h
e
h
ar
m
o
n
y
m
e
m
o
r
y
as
w
ell
as
t
h
e
p
itch
ad
j
u
s
tin
g
r
a
te
(
P
A
R
,
it
s
r
an
g
e
b
et
w
ee
n
[
0
,
1
]
)
,
an
d
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
i
m
p
r
o
v
is
atio
n
(
Ma
x
I
)
is
u
s
ed
to
ch
ec
k
t
h
e
s
to
p
p
in
g
cr
iter
ia;
(
2
)
th
e
h
ar
m
o
n
y
m
e
m
o
r
y
(
HM
)
is
in
itial
ized
b
y
g
e
n
er
ati
n
g
a
r
an
d
o
m
s
et
o
f
s
o
l
u
tio
n
s
v
ec
to
r
s
w
h
ic
h
ar
e
id
en
tica
l
to
th
e
h
ar
m
o
n
y
m
e
m
o
r
y
s
ize
(
HM
S);
(
3
)
A
n
e
w
s
o
l
u
tio
n
(
h
a
r
m
o
n
y
)
i
s
p
r
o
d
u
ce
d
in
th
e
i
m
p
r
o
v
is
atio
n
p
r
o
ce
s
s
;
(
4
)
th
e
h
ar
m
o
n
y
m
e
m
o
r
y
is
u
p
d
ated
to
ch
ec
k
th
e
n
e
w
g
e
n
e
r
ated
s
o
lu
tio
n
e
ith
er
it
is
b
ette
r
o
r
w
o
r
s
e
th
a
n
t
h
e
p
r
ev
io
u
s
o
n
e;
(
5
)
th
e
s
to
p
p
in
g
cr
iter
ia
p
r
o
ce
s
s
is
test
ed
i
n
t
h
is
s
tep
to
ch
ec
k
w
h
et
h
er
t
h
e
m
ax
i
m
u
m
i
ter
atio
n
s
n
u
m
b
er
is
s
atis
f
ied
o
r
n
o
t.
I
f
y
es,
t
h
e
HS
p
r
o
ce
s
s
w
i
ll
s
to
p
an
d
th
e
b
est
s
elec
ted
s
o
l
u
tio
n
(
,
)
is
r
etu
r
n
ed
b
ac
k
.
Oth
er
w
i
s
e,
th
e
p
r
o
ce
d
u
r
es in
s
tep
s
3
an
d
4
ar
e
r
ep
ea
ted
r
esp
ec
tiv
ely
.
S
t
a
rt
Ini
t
i
a
l
i
z
a
t
i
on
t
he
H
S
pa
ra
m
e
t
e
rs
(
H
M
S
,
H
M
CR
,
P
A
R
,
M
a
xI
)
H
a
rm
ony
M
e
m
ory
(
HM
)
Ini
t
i
a
l
i
z
a
t
i
on
N
e
w
i
m
pr
ov
i
s
a
t
i
on
pr
oc
e
s
s
(
a
ne
w
ha
rm
ony
i
m
provi
s
e
d
)
U
pda
t
e
t
he
H
a
rm
ony
M
e
m
ory
E
nd
No
Y
e
s
Re
t
ur
n
t
he
b
e
s
t
s
ol
ut
i
on
f
ou
nd
S
a
t
i
s
fa
c
t
i
on o
f s
t
opp
i
ng c
ri
t
e
ri
a
Fig
u
r
e
2
.
Har
m
o
n
y
s
ea
r
ch
al
g
o
r
ith
m
f
lo
w
ch
ar
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
2
0
1
7
:
3
2
1
7
–
3
2
2
5
3220
4.
H
S IM
P
L
E
M
E
NT
AT
I
O
N
T
O
O
B
T
AIN O
P
T
I
M
AL
P
I
P
ARAM
E
T
E
R
S
I
n
an
y
o
p
ti
m
iza
tio
n
al
g
o
r
ith
m
,
th
e
in
p
u
t
v
ec
to
r
f
o
r
m
u
la
to
f
in
d
th
e
o
p
ti
m
al
s
o
l
u
tio
n
s
ca
n
b
e
d
ef
in
ed
as;
.
.
=
(
)
,
∈
;
(
=
1
,
2
,
…
…
.
.
)
(
7
)
w
h
er
e
(
)
is
th
e
in
p
u
t
v
ec
to
r
to
th
e
o
p
ti
m
izatio
n
alg
o
r
it
h
m
,
is
th
e
d
ec
is
io
n
p
ar
a
m
eter
,
is
th
e
lo
w
e
r
an
d
u
p
p
er
v
alu
e
s
o
f
ea
c
h
d
ec
is
io
n
p
ar
a
m
eter
(
<
<
)
,
an
d
is
t
h
e
to
tal
n
u
m
b
er
o
f
d
ec
i
s
io
n
p
ar
am
eter
s
.
B
ased
o
n
eq
u
atio
n
(
7
)
,
t
w
o
d
ec
is
io
n
p
ar
a
m
eter
s
(
,
)
o
f
th
e
in
p
u
t
v
ec
to
r
(
)
ar
e
u
s
ed
in
th
i
s
r
esear
ch
to
p
r
o
v
id
e
th
e
o
p
tim
al
s
o
l
u
tio
n
s
f
r
o
m
t
h
e
HS
o
p
ti
m
izatio
n
alg
o
r
it
h
m
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
2
.
I
n
ad
d
itio
n
,
an
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
r
eq
u
ir
ed
to
ev
al
u
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
i
n
p
u
t
v
ec
t
o
r
(
)
.
T
h
er
ef
o
r
e,
th
e
in
teg
r
al
ab
s
o
l
u
te
er
r
o
r
(
I
A
E
)
s
h
o
w
n
b
elo
w
is
ap
p
lied
as a
n
o
p
ti
m
izatio
n
p
r
o
b
lem
at
t
h
e
Si
m
u
li
n
k
t
i
m
e.
(
.
)
=
∫
|
|
0
+
∫
|
1
+
2
|
0
(
8
)
A
m
o
r
e
e
x
p
lan
a
tio
n
o
f
t
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
f
o
r
th
e
h
ar
m
o
n
y
s
ea
r
c
h
al
g
o
r
it
h
m
b
ased
P
I
co
n
tr
o
ller
is
p
r
esen
ted
as f
o
llo
w
s
:
Co
ntr
o
l f
lo
w
o
f
H
a
rm
o
ny
Se
a
rc
h Alg
o
rit
h
m
ba
s
e
d P
I
Co
ntr
o
ller:
p
s
eu
d
o
co
d
e
Sta
rt
pro
g
ra
m
:
Def
in
itio
n
o
f
=
(
)
,
∈
;
(
=
1
,
2
,
…
…
.
.
)
;
Def
in
itio
n
o
f
HM
S,
H
MCR
,
P
AR
,
an
d
Ma
x
I
;
Def
in
itio
n
th
e
u
p
p
er
an
d
lo
w
er
b
o
u
n
d
ar
ies o
f
t
h
e
d
ec
is
io
n
p
ar
a
m
eter
s
(
,
)
;
Har
m
o
n
y
m
e
m
o
r
y
(
H
M)
in
itializat
io
n
;
≤
,
if
s
ati
s
f
ied
≤
de
c
ision
pa
r
a
me
te
r
s
,
if
s
ati
s
f
ied
HM
C
R
>
1
,
if
s
ati
s
f
ied
C
h
o
o
s
e
a
d
ec
is
io
n
p
ar
a
m
eter
f
r
o
m
t
h
e
HM
;
′
=
[
1
…
1
…
]
;
PAR
>
2
,
if
s
ati
s
f
ied
A
d
j
u
s
t th
e
d
ec
is
io
n
p
ar
a
m
eter
b
y
;
′
=
(
s
el
ect
ed
′
+
);
C
h
o
o
s
e
a
n
e
w
r
an
d
o
m
d
ec
i
s
io
n
p
ar
a
m
eter
b
y
;
′
=
∗
[
(
−
)
+
]
;
the
fit
n
e
s
s
va
l
ue
(
′
)
of
the
n
e
w
s
ol
ution
ve
c
tor
<
the
wo
r
s
t
fit
n
e
s
s
va
l
ue
s
tor
e
d
in
the
HM
,
A
cc
ep
t th
e
n
e
w
s
o
lu
tio
n
v
ec
to
r
an
d
r
ep
lace
d
b
y
t
h
e
o
ld
o
n
e,
th
en
ad
d
ed
it to
th
e
HM
;
R
etu
r
n
b
ac
k
th
e
b
est
s
o
lu
tio
n
f
o
u
n
d
(
,
)
;
E
nd
P
ro
g
ra
m
d
is
cu
s
s
io
n
)
.
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
o
b
j
ec
tiv
e
o
f
th
i
s
s
t
u
d
y
i
s
to
test
t
h
e
p
r
o
p
o
s
ed
HS
-
P
I
co
n
tr
o
l
alg
o
r
ith
m
f
o
r
L
F
C
i
n
t
w
o
-
ar
e
a
p
o
w
er
s
y
s
te
m
a
n
d
co
m
p
ar
ed
it
w
i
th
t
h
e
r
es
u
lts
o
b
tai
n
ed
b
y
P
SO
-
P
I
.
MA
T
L
A
B
p
r
o
g
r
am
h
a
s
b
ee
n
u
s
ed
to
m
o
d
el
t
h
e
o
v
er
all
s
y
s
te
m
s
h
o
w
n
in
F
i
g
u
r
e
1
.
T
o
ch
ec
k
th
e
ef
f
ec
ti
v
en
e
s
s
a
n
d
r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
alg
o
r
ith
m
,
th
e
s
tep
lo
ad
d
is
tu
r
b
an
ce
1
is
s
elec
ted
to
b
e
0
.
2
w
h
ile
2
is
0
.
3
f
o
r
b
o
t
h
ar
ea
1
an
d
ar
ea
2
r
esp
ec
tiv
ely
.
T
ab
le
1
s
h
o
w
s
t
h
e
o
p
ti
m
al
v
al
u
es
(
,
)
o
f
th
e
o
p
ti
m
izatio
n
p
r
o
ce
s
s
o
b
tain
e
d
b
y
b
o
th
al
g
o
r
ith
m
s
u
s
i
n
g
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
(
I
A
E
)
.
T
ab
les
2
,
3
,
an
d
4
g
iv
e
t
h
e
tr
an
s
ie
n
t
r
e
s
p
o
n
s
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2
0
8
8
-
8708
A
n
Op
tima
l LF
C
in
Tw
o
A
r
ea
P
o
w
er S
ystems
U
s
in
g
a
Meta
-
h
eu
r
is
tic
Op
timiz
a
tio
n
....
(
Mu
s
h
ta
q
N
a
jeeb
)
3221
s
p
ec
if
icatio
n
s
f
o
r
,
∆
,
an
d
∆
in
te
r
m
s
o
f
s
ettli
n
g
ti
m
e,
m
ax
i
m
u
m
d
e
v
iatio
n
,
an
d
p
ea
k
ti
m
e.
I
t
is
n
o
ted
th
at
t
h
e
HS
-
PI
co
n
tr
o
ller
p
r
o
d
u
ce
s
g
o
o
d
d
y
n
a
m
ic
p
er
f
o
r
m
a
n
ce
s
a
s
co
m
p
ar
ed
to
P
SO
-
P
I
.
Fig
u
r
es
3
an
d
4
r
ep
r
esen
t
t
h
e
s
i
m
u
latio
n
r
es
u
lts
f
o
r
AC
E
1
a
n
d
A
C
E
2
r
es
p
ec
tiv
el
y
f
o
r
b
o
th
al
g
o
r
ith
m
s
,
it
i
s
v
er
y
clea
r
th
a
t
th
e
d
y
n
a
m
ic
c
h
ar
ac
ter
is
tic
s
f
o
r
HS
-
P
I
ar
e
ab
le
to
m
ak
e
th
e
s
tea
d
y
s
tate
er
r
o
r
to
b
e
ze
r
o
f
aster
th
a
n
P
SO
-
P
I
an
d
th
e
o
v
er
s
h
o
o
t
is
m
i
n
i
m
ize
d
as
w
ell.
Fi
g
u
r
e
5
s
h
o
w
s
th
e
∆
12
r
esu
lt,
th
e
s
ett
lin
g
ti
m
e,
m
ax
i
m
u
m
d
ev
iat
io
n
an
d
p
ea
k
ti
m
e
ar
e
r
ed
u
ce
d
w
h
ich
m
a
k
e
th
e
s
y
s
te
m
r
elat
iv
e
l
y
m
o
r
e
s
tab
le.
Fi
g
u
r
e
s
6
an
d
7
d
em
o
n
s
tr
ate
t
h
e
r
esp
o
n
s
es
f
o
r
∆
1
an
d
∆
2
.
I
t
is
s
h
o
w
n
t
h
at
th
e
r
esp
o
n
s
e
o
f
t
h
e
m
ax
i
m
u
m
o
v
er
s
h
o
o
t
an
d
s
ettl
in
g
t
i
m
e
i
s
m
u
c
h
b
etter
th
a
n
t
h
at
o
n
e
’
s
o
b
tain
ed
b
y
P
SO
-
P
I
.
T
ab
le
1
.
Op
tim
al
v
alu
e
s
o
f
P
I
tu
n
in
g
u
s
i
n
g
H
S a
n
d
P
SO
P
I
P
a
r
a
me
t
e
r
s
H
S
_
I
A
E
P
S
O
_
I
A
E
A
r
e
a
1
K
p
1
0
.
4
3
4
2
.
6
2
9
0
K
i
1
1
.
5
0
4
2
.
8
9
1
0
A
r
e
a
2
K
p
2
1
.
0
9
2
3
.
8
8
4
9
K
i
2
1
.
1
4
4
4
.
2
1
0
6
M
i
n
_
I
A
E
0
.
0
1
6
6
0
.
0
3
2
El
a
p
se
d
T
i
me
(
se
c
)
2
2
.
6
7
6
2
9
.
1
1
2
T
ab
le
2
.
p
ar
am
eter
s
u
s
i
n
g
HS
an
d
P
SO b
ased
o
n
I
A
E
S
e
t
t
l
i
n
g
T
i
me
(
se
c
)
M
a
x
.
d
e
v
i
a
t
i
o
n
(
p
.
u
)
P
e
a
k
T
i
me
(
se
c
)
H
S
_
I
A
E
A
C
E1
6
.
4
5
0
.
0
2
8
9
1
.
4
4
5
A
C
E2
7
.
6
5
0
.
1
2
6
1
.
9
8
P
S
O
_
I
A
E
A
C
E1
8
.
7
5
0
.
0
8
0
6
2
.
0
5
A
C
E2
9
.
9
8
0
.
2
2
4
3
.
0
1
T
ab
le
3
.
∆
p
ar
am
eter
s
u
s
i
n
g
H
S a
n
d
P
SO b
ased
o
n
I
A
E
S
e
t
t
l
i
n
g
T
i
me
(
se
c
)
M
a
x
.
d
e
v
i
a
t
i
o
n
(
p
.
u
)
P
e
a
k
T
i
me
(
se
c
)
H
S
_
I
A
E
D
P
1
2
1
7
.
1
0
.
0
0
5
8
9
2
.
5
1
P
S
O
_
I
A
E
D
P
1
2
1
9
.
1
9
0
.
0
1
5
6
1
3
.
1
1
T
ab
le
4
.
∆
p
ar
am
eter
s
u
s
i
n
g
HS
an
d
P
SO b
ased
o
n
I
A
E
S
e
t
t
l
i
n
g
T
i
me
(
se
c
)
M
a
x
.
d
e
v
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ased
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izatio
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T
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
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6
,
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2
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1
7
:
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–
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5
3224
RE
F
E
R
E
NC
E
S
[1
]
J
.
V
e
n
k
a
tac
h
a
la
m
,
e
t
a
l.
,
“
A
P
a
r
ti
c
le
S
w
a
r
m
Op
ti
m
iz
a
ti
o
n
A
lg
o
rit
h
m
f
o
r
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u
to
m
a
ti
c
Ge
n
e
ra
ti
o
n
C
o
n
tr
o
l
o
f
Tw
o
A
re
a
In
terc
o
n
n
e
c
ted
P
o
w
e
r
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
En
g
i
n
e
e
rin
g
Res
e
a
rc
h
&
T
e
c
h
n
o
lo
g
y
,
v
o
l
/i
ss
u
e
:
2
(
6
)
,
2
0
1
3
.
[2
]
M
.
Na
jee
b
,
e
t
a
l.
,
“
P
ID
P
a
ra
m
e
ters
I
m
p
ro
v
e
m
e
n
t
f
o
r
AG
C
in
T
h
re
e
P
a
ra
ll
e
l
Co
n
n
e
c
ted
p
o
w
e
r
S
y
ste
m
s,”
T
h
e
Na
ti
o
n
a
l
Co
n
fer
e
n
c
e
fo
r P
o
stg
ra
d
u
a
te R
e
s
e
a
rc
h
,
Un
iv
e
rsiti
M
a
lay
sia
P
a
h
a
n
g
,
v
o
l.
P
0
7
5
.
p
p
.
5
4
4
-
5
5
1
,
2
0
1
6
.
[3
]
Ib
ra
h
e
e
m
,
e
t
a
l.
,
“
Re
c
e
n
t
p
h
il
o
so
p
h
ies
o
f
a
u
to
m
a
ti
c
g
e
n
e
ra
ti
o
n
c
o
n
tr
o
l
stra
teg
ies
in
p
o
w
e
r
s
y
ste
m
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l
/i
ss
u
e
:
20
(
1
)
,
p
p
.
3
4
6
–
3
5
7
,
2
0
0
5
.
[4
]
G
.
A
.
S
a
lma
n
,
“
A
u
to
m
a
ti
c
Ge
n
e
ra
ti
o
n
C
o
n
t
ro
l
in
M
u
l
ti
A
re
a
In
terc
o
n
n
e
c
ted
P
o
w
e
r
S
y
st
e
m
Us
in
g
P
ID
C
o
n
tro
ll
e
r
Ba
se
d
o
n
GA
a
n
d
P
S
O,”
S
e
c
o
n
d
En
g
i
n
e
e
rin
g
S
c
ien
ti
fi
c
Co
n
fer
e
n
c
e
,
Co
ll
e
g
e
o
f
E
n
g
i
n
e
e
rin
g
,
U
n
iv
e
rsity
o
f
Di
y
a
la,
p
p
.
2
9
7
-
3
1
0
,
2
0
1
5
.
[5
]
J
.
V
e
n
k
a
tac
h
a
la
m
,
e
t
a
l.
,
“
A
u
to
m
a
ti
c
g
e
n
e
ra
ti
o
n
c
o
n
tro
l
o
f
tw
o
a
re
a
in
terc
o
n
n
e
c
ted
p
o
w
e
r
s
y
ste
m
u
sin
g
p
a
rti
c
le
sw
a
r
m
o
p
ti
m
iza
ti
o
n
,
”
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
E
lec
tro
n
ics
E
n
g
i
n
e
e
rin
g
,
v
o
l
/
issu
e
:
6
(
1
)
,
p
p
.
2
8
-
3
6
,
2
0
1
3
.
[6
]
S
.
P
ra
k
a
sh
,
e
t
a
l.
,
“
L
o
a
d
f
re
q
u
e
n
c
y
c
o
n
tro
l
o
f
th
re
e
a
re
a
in
terc
o
n
n
e
c
ted
h
y
d
ro
-
th
e
rm
a
l
re
h
e
a
t
p
o
w
e
r
s
y
ste
m
u
sin
g
a
rti
f
icia
l
in
telli
g
e
n
c
e
a
n
d
P
I
c
o
n
tr
o
ll
e
rs,”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
En
g
i
n
e
e
rin
g
,
S
c
ie
n
c
e
a
n
d
T
e
c
h
n
o
lo
g
y
,
v
o
l
/i
ss
u
e
:
4
(
1
)
,
p
p
.
2
3
-
3
7
,
2
0
1
1
.
[7
]
J.
G
.
Zi
e
g
ler
a
n
d
N.
B.
Nic
h
o
ls,
“
Op
ti
m
u
m
se
tt
in
g
s
f
o
r
a
u
to
m
a
ti
c
c
o
n
tro
ll
e
rs,”
T
ra
n
s
a
c
ti
o
n
s
o
f
th
e
AS
M
E
,
v
o
l/
issu
e
:
64
(
8
)
,
p
p
.
7
5
9
/7
6
8
–
7
5
9
/7
6
8
,
1
9
4
2
.
[8
]
T
.
C.
Ya
n
g
,
e
t
a
l
.
,
“
De
c
e
n
tralize
d
P
o
w
e
r
S
y
ste
m
lo
a
d
f
re
q
u
e
n
c
y
c
o
n
tro
l
b
e
y
o
n
d
th
e
l
im
it
o
f
d
iag
o
n
a
l
d
o
m
in
a
n
c
e
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
, v
ol
/i
s
su
e
:
24
(
3
)
,
p
p
.
1
7
3
-
1
8
4
,
2
0
0
2
.
[9
]
V
.
D
o
n
d
e
,
e
t
a
l.
,
“
S
im
u
latio
n
a
n
d
O
p
ti
m
iza
ti
o
n
i
n
a
n
AG
C
S
y
s
tem
a
f
t
e
r
De
re
g
u
latio
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
ste
ms
,
v
o
l
/i
ss
u
e
:
16
(
3
)
,
p
p
.
4
8
1
–
4
8
9
,
2
0
0
1
.
[1
0
]
C.
H.
L
ian
g
,
e
t
a
l.
,
“
S
tu
d
y
o
f
Diff
e
r
e
n
ti
a
l
Ev
o
lu
ti
o
n
f
o
r
Op
ti
m
a
l
Re
a
c
ti
v
e
P
o
w
e
r
Disp
a
tch
,
”
IET
Ge
n
e
ra
ti
o
n
T
ra
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
,
v
o
l
/i
ss
u
e
:
1
(
2
)
,
p
p
.
2
5
3
-
2
6
0
,
2
0
0
7
.
[1
1
]
L
.
X
.
L
o
n
g
,
e
t
a
l.
,
“
A
Ba
c
ter
ial
F
o
ra
g
in
g
G
lo
b
a
l
Op
ti
m
iza
ti
o
n
A
lg
o
rit
h
m
Ba
se
d
On
th
e
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
,
”
IEE
E
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
I
n
telli
g
e
n
t
C
o
m
p
u
ti
n
g
a
n
d
In
tell
ig
e
n
t
S
y
ste
ms
,
v
o
l.
2
,
p
p
.
2
2
-
2
7
,
2
0
1
0
.
[1
2
]
A
.
M
.
Ja
d
h
a
v
,
e
t
a
l.
,
“
P
e
rf
o
rm
a
n
c
e
V
e
rif
ica
ti
o
n
o
f
P
ID
Co
n
tr
o
l
ler
in
a
n
In
terc
o
n
n
e
c
ted
P
o
w
e
r
S
y
st
e
m
Us
in
g
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
,
”
2
nd
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Ad
v
a
n
c
e
s
in
E
n
e
rg
y
E
n
g
i
n
e
e
rin
g
(
ICAE
E),
E
n
e
rg
y
Pro
c
e
d
ia
,
v
o
l
.
1
4
,
p
p
.
2
0
7
5
-
2
0
8
0
,
2
0
1
2
.
[1
3
]
A
.
J
.
S
h
a
rm
il
i,
e
t
a
l.
,
“
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iz
a
ti
o
n
b
a
se
d
P
ID
c
o
n
tr
o
ll
e
r
f
o
r
tw
o
a
re
a
L
o
a
d
F
re
q
u
e
n
c
y
Co
n
tro
l
S
y
st
e
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
En
g
in
e
e
rin
g
Res
e
a
rc
h
a
n
d
Ge
n
e
ra
l
S
c
ie
n
c
e
,
v
o
l
/i
ss
u
e
:
3
(
2
)
,
p
p
.
7
7
2
-
7
7
8
,
2
0
1
5
.
[1
4
]
R
.
Ch
a
u
d
h
a
ry
,
e
t
a
l.
,
“
A
No
v
e
l
A
p
p
ro
a
c
h
to
P
ID
Co
n
tr
o
ll
e
r
De
sig
n
f
o
r
I
m
p
ro
v
e
m
e
n
t
o
f
T
ra
n
sie
n
t
S
tab
il
i
ty
a
n
d
V
o
l
tag
e
Re
g
u
latio
n
o
f
No
n
li
n
e
a
r
P
o
w
e
r
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
t
e
r
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l
/i
ss
u
e
:
6
(
5
)
,
p
p
.
2
2
2
5
-
2
2
3
8
,
2
0
1
6
.
[1
5
]
N.
R
.
Ra
ju
,
e
t
a
l.
,
“
Ro
b
u
stn
e
ss
S
tu
d
y
o
f
F
ra
c
ti
o
n
a
l
Ord
e
r
P
ID
Co
n
tr
o
ll
e
r
Op
ti
m
ize
d
b
y
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
in
A
V
R
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l
/i
ss
u
e
:
6
(
5
)
,
p
p
.
2
0
3
3
-
2
0
4
0
,
2
0
1
6
.
[1
6
]
M
.
Do
r
ig
o
,
e
t
a
l
.
,
“
A
n
t
Co
l
o
n
y
o
p
ti
m
iza
ti
o
n
:
a
rti
f
icia
l
a
n
ts
a
s
a
c
o
m
p
u
tatio
n
a
l
in
tell
ig
e
n
c
e
tec
h
n
i
q
u
e
,
”
I
EE
E
Co
mp
u
t
a
ti
o
n
a
l
I
n
telli
g
e
n
c
e
M
a
g
a
zin
e
,
v
o
l
/i
ss
u
e
:
1
(
4
)
,
p
p
.
2
8
-
3
9
,
2
0
0
7
.
[1
7
]
V
.
Ja
in
,
e
t
a
l.
,
“
M
o
d
e
li
n
g
a
n
d
sim
u
latio
n
o
f
L
o
a
d
F
re
q
u
e
n
c
y
Co
n
tr
o
l
in
A
u
to
m
a
ti
c
G
e
n
e
ra
ti
o
n
Co
n
tro
l
u
sin
g
G
e
n
e
ti
c
A
l
g
o
rit
h
m
s
T
e
c
h
n
iq
u
e
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
In
n
o
v
a
ti
v
e
S
c
ien
c
e
,
En
g
in
e
e
rin
g
&
T
e
c
h
n
o
lo
g
y
,
v
o
l
/i
ss
u
e
:
1
(
8
)
,
p
p
.
3
5
6
-
3
6
2
,
2
0
1
4
.
[1
8
]
G
.
Ko
n
a
r,
e
t
a
l.
,
“
Tw
o
A
re
a
L
o
a
d
F
re
q
u
e
n
c
y
Co
n
tro
l
U
sin
g
GA
T
u
n
e
d
P
ID
Co
n
tro
ll
e
r
in
De
re
g
u
late
d
En
v
iro
n
m
e
n
t,
”
Pro
c
e
e
d
in
g
s o
f
t
h
e
In
ter
n
a
ti
o
n
a
l
M
u
lt
i
Co
n
fer
e
n
c
e
o
f
En
g
in
e
e
rs
a
n
d
C
o
mp
u
ter
S
c
ien
ti
sts
,
v
o
l.
2
,
p
p
.
1
-
6
,
2
0
1
4
.
[1
9
]
M
.
M
.
Ism
a
il
,
e
t
a
l.
,
“
L
o
a
d
F
re
q
u
e
n
c
y
Co
n
tro
l
A
d
a
p
tatio
n
Us
in
g
Artif
icia
l
In
telli
g
e
n
t
T
e
c
h
n
iq
u
e
s
f
o
r
On
e
a
n
d
Tw
o
Diff
e
r
e
n
t
A
re
a
s
P
o
w
e
r
S
y
ste
m
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Co
n
tro
l,
Au
to
m
a
ti
o
n
a
n
d
S
y
ste
ms
,
v
o
l
/i
ss
u
e
:
1
(
1
)
,
p
p
.
1
2
-
2
3
,
2
0
1
2
.
[2
0
]
G
a
n
e
sh
V
.
,
e
t
a
l.
,
“
L
QR
Ba
s
e
d
Lo
a
d
F
re
q
u
e
n
c
y
Co
n
tro
ll
e
r
f
o
r
T
wo
A
re
a
P
o
w
e
r
S
y
ste
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Ad
v
a
n
c
e
d
Res
e
a
rc
h
in
El
e
c
trica
l,
El
e
c
tro
n
ics
a
n
d
I
n
stru
me
n
t
a
ti
o
n
En
g
i
n
e
e
rin
g
,
v
o
l
/i
ss
u
e
:
1
(
4
)
,
p
p
.
2
6
2
-
2
6
9
,
2
0
1
2
.
[2
1
]
M
.
S
h
a
h
o
o
t
h
,
e
t
a
l.
,
“
A
n
o
p
ti
m
ize
d
P
ID
p
a
ra
m
e
ter
s
f
o
r
L
F
C
i
n
in
terc
o
n
n
e
c
ted
p
o
w
e
r
s
y
ste
m
s
u
sin
g
M
L
S
L
o
p
ti
m
iza
ti
o
n
a
lg
o
ri
th
m
,
”
AR
PN
J
o
u
rn
a
l
o
f
En
g
in
e
e
rin
g
a
n
d
A
p
p
li
e
d
S
c
ien
c
e
s
,
v
o
l
/i
ss
u
e
:
11
(
19
)
,
p
p
.
1
1
7
7
0
-
1
1
7
8
1
,
2
0
1
6
.
[2
2
]
M
.
Ho
jab
ri,
e
t
a
l.
,
“
A
n
O
v
e
r
v
ie
w
o
n
M
icro
g
rid
Co
n
tro
l
S
trate
g
ies
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
a
n
d
Ad
v
a
n
c
e
d
T
e
c
h
n
o
lo
g
y
,
v
ol
/
issu
e
:
4
(
5
)
,
p
p
.
9
3
-
9
8
,
2
0
1
5
.
[2
3
]
Z.
W
.
G
e
e
n
,
e
t
a
l.
,
“
A
Ne
w
H
e
u
risti
c
Op
ti
m
iz
a
ti
o
n
A
l
g
o
rit
h
m
:
Ha
rm
o
n
y
S
e
a
r
c
h
,
”
S
imu
la
ti
o
n
,
v
o
l.
7
6
,
p
p
.
60
-
6
9
,
2
0
0
1
.
[2
4
]
H
.
Da
n
iy
a
l,
e
t
a
l.
,
“
A
n
Ef
f
icie
n
t
Co
n
tro
l
Im
p
le
m
e
n
tatio
n
f
o
r
Vo
lt
a
g
e
S
o
u
rc
e
I
n
v
e
rter
b
a
se
d
H
a
r
m
o
n
y
S
e
a
rc
h
A
l
g
o
rit
h
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
ms
,
v
ol
/i
ss
u
e
:
8
(
1
)
,
p
p
.
2
7
9
-
2
8
9
,
2
0
1
7
.
[2
5
]
M
.
M
a
n
s
o
r,
e
t
a
l.
,
“
A
n
In
telli
g
e
n
t
Vo
lt
a
g
e
Co
n
tr
o
ll
e
r
f
o
r
a
P
V
In
v
e
rter
S
y
ste
m
u
sin
g
S
im
u
l
a
ted
A
n
n
e
a
li
n
g
A
l
g
o
rit
h
m
-
b
a
se
d
P
I
T
u
n
i
n
g
A
p
p
ro
a
c
h
,
”
J
o
u
r
n
a
l
o
f
En
g
i
n
e
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Qu
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.
Evaluation Warning : The document was created with Spire.PDF for Python.