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1
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3
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4
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[
5
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As
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8
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a
m
ic
r
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e.
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n
th
is
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ase,
ze
r
o
v
o
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g
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ec
to
r
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n
n
o
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ated
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s
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h
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n
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ar
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A
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n
tr
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ller
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s
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a
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tr
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m
p
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ate
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ith
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ates
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h
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a
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[
1
0
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d
d
itio
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t
h
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n
er
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r
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co
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tr
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g
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ter
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ac
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h
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alu
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o
f
v
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r
P
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m
o
d
u
le.
T
h
is
p
o
w
er
co
n
tr
o
l
s
tr
ateg
y
is
es
s
e
n
tial
to
f
u
lf
i
ll
r
eq
u
ir
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m
e
n
ts
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f
p
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s
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e
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co
n
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id
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1
1
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T
h
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f
o
cu
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th
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t
u
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3
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n
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r
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n
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1
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1
6
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1
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w
h
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co
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p
r
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o
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t
h
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y
s
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lack
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n
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ar
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atic
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ize
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p
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u
r
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u
d
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en
p
r
o
b
le
m
s
[
8
,
1
8
,
1
9
]
.
T
h
e
f
iv
e
co
n
s
ec
u
ti
v
e
p
o
r
tio
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s
o
f
t
h
e
p
ap
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ar
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d
iv
id
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as;
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at
h
e
m
a
tical
f
o
u
n
d
atio
n
o
f
g
r
i
d
co
n
n
ec
ted
VSI
is
p
r
ese
n
ted
in
Sectio
n
2
.
T
h
e
p
o
w
er
q
u
alit
y
r
eq
u
ir
e
m
en
ts
f
o
r
an
MG
ar
e
d
is
cu
s
s
ed
in
Sec
tio
n
3
.
T
h
e
d
etailed
ex
p
lan
at
io
n
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f
t
h
e
co
n
tr
o
l
s
y
s
te
m
is
p
r
esen
ted
in
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n
4
.
I
n
Sectio
n
5
,
th
e
o
u
tco
m
e
f
r
o
m
s
i
m
u
lat
io
n
r
es
u
lts
ar
e
c
h
ec
k
ed
an
d
co
m
p
ar
ed
to
v
alid
at
e
th
e
o
b
j
ec
tiv
es
o
f
s
t
u
d
y
.
L
astl
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,
i
n
Sect
io
n
6
co
n
clu
s
io
n
s
d
r
a
w
n
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r
o
m
t
h
i
s
s
t
u
d
y
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e
s
u
m
m
ar
ized
.
2.
RE
S
E
ARCH
M
E
T
H
O
DO
L
O
G
Y
2
.
1
.
M
a
t
he
m
a
t
ica
l
m
o
dellin
g
o
f
g
rid c
o
nn
ec
t
ed
VS
I
Fig
u
r
e
2
il
lu
s
tr
ates
th
e
VSI
b
ased
th
r
ee
p
h
ase
g
r
id
m
o
d
el
a
lo
n
g
w
it
h
a
n
L
C
f
ilter
co
n
s
id
er
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in
t
h
i
s
s
tu
d
y
.
I
t
m
a
y
b
e
n
o
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th
at
co
r
r
esp
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d
in
g
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ta
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n
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b
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R
s
,
L
s
a
n
d
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w
h
ile
th
e
g
r
id
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s
e
n
s
ed
b
y
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n
v
er
ter
its
el
f
.
W
h
er
e
Vs is
t
h
e
g
r
id
v
o
lta
g
e.
Fig
u
r
e
2
.
VSI
co
n
n
ec
ted
th
r
ee
p
h
ase
g
r
id
T
h
e
s
y
s
te
m
eq
u
i
v
ale
n
t state
-
s
p
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atio
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in
t
h
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th
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ee
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ph
a
s
e
ab
c
f
r
a
m
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ar
e
g
i
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n
by
[
2
0
]
ar
e
as u
n
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er
:
=
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u
tili
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s
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o
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m
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(
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ca
n
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e
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tated
in
d
q
r
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er
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f
r
a
m
e
as:
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]
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[
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w
h
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.
(
3
)
w
h
er
e,
0
=
[
0
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,
=
[
]
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
C
o
m
p
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N:
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t
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h
at
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ai
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ess
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h
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f
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m
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d
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s
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f
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its
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n
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is
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t
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er
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o
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m
a
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ce
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u
r
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n
g
is
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d
i
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g
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ter
m
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d
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d
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ai
n
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ed
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r
th
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o
n
,
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n
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s
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ad
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t
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n
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o
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o
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e,
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ain
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en
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th
i
n
t
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e
th
r
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s
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o
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d
li
m
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en
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atin
g
i
n
t
w
o
d
i
f
f
er
e
n
t
m
o
d
es
[
1
7
]
.
T
h
e
an
ticip
ated
co
n
tr
o
ller
in
b
lo
ck
d
iag
r
a
m
il
lu
s
t
r
atio
n
is
s
h
o
w
n
i
n
Fig
u
r
e
3
.
I
t
is
p
er
tin
en
t
to
m
e
n
tio
n
t
h
at
v
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e
o
f
r
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er
en
ce
v
o
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d
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r
eq
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e
n
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y
ca
n
b
e
d
ef
i
n
ed
lo
ca
ll
y
o
r
b
y
th
e
m
icr
o
g
r
id
co
n
tr
o
l
ce
n
tr
e
(
MG
C
C
)
[
6
]
an
d
t
h
at
p
h
ase
-
lo
c
k
ed
-
lo
o
p
(
P
L
L
)
ca
n
b
e
u
s
ed
to
m
ea
s
u
r
e
f
r
eq
u
en
c
y
o
f
s
y
s
te
m
,
an
d
th
e
V_
r
m
s
is
g
i
v
en
b
y
[
1
4
]
:
=
√
2
+
2
(
6
)
Fig
u
r
e
3
.
P
r
o
p
o
s
ed
c
o
n
tr
o
ller
2
.
3
.
Su
g
g
este
d c
o
ntr
o
l st
ra
t
eg
y
T
h
e
s
u
g
g
e
s
ted
s
tr
ate
g
y
f
o
r
a
V
SI
b
ased
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r
id
co
n
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ted
s
y
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te
m
i
s
s
h
o
w
n
i
n
F
ig
u
r
e
4
.
I
t is
e
v
id
en
t
th
a
t
th
e
s
c
h
e
m
e
f
o
r
co
n
tr
o
ller
co
n
s
is
ts
m
ai
n
l
y
t
h
r
ee
b
lo
ck
s
w
h
ic
h
ar
e:
p
o
w
er
co
n
tr
o
ller
,
th
e
c
u
r
r
en
t
co
n
tr
o
ller
an
d
P
SO
s
et
o
f
r
u
le
s
f
o
r
a
u
to
m
a
ti
c
tu
n
i
n
g
o
f
p
o
w
er
co
n
tr
o
ller
p
ar
a
m
eter
s
.
T
h
e
d
etailed
d
es
cr
i
p
tio
n
o
f
ea
c
h
b
lo
ck
is
d
is
cu
s
s
ed
i
n
s
u
b
s
eq
u
e
n
t s
u
b
-
s
ec
tio
n
s
.
2.
3
.
1
.
P
o
w
er
co
ntr
o
l t
ec
hn
iqu
e
T
h
is
is
co
n
s
id
er
ed
as
o
u
ter
co
n
tr
o
l
lo
o
p
o
f
p
r
o
p
o
s
ed
s
y
s
te
m
w
h
ic
h
is
u
tili
ze
d
to
g
e
n
er
ate
r
ef
er
en
ce
cu
r
r
en
t
v
al
u
es
∗
an
d
∗
.
C
o
n
s
eq
u
en
tl
y
,
t
h
e
p
o
w
er
o
u
tp
u
t
o
f
in
v
er
ter
w
i
ll
b
e
o
f
h
ig
h
q
u
ali
t
y
i
f
ch
an
g
e
i
n
th
e
tr
aj
ec
to
r
y
o
f
r
ef
er
en
ce
cu
r
r
en
t
is
s
lo
w
[
2
1
]
.
O
w
in
g
to
li
m
i
tat
io
n
o
f
co
n
v
e
n
tio
n
a
l
P
I
co
n
tr
o
l
ler
,
th
e
g
ain
v
alu
e
s
ar
e
s
et
at
a
f
ix
ed
v
alu
e
(
b
y
tr
ia
l
an
d
er
r
o
r
m
e
th
o
d
)
,
h
en
ce
,
P
I
co
n
tr
o
ller
w
i
ll
n
o
t
b
e
ca
p
ab
le
to
r
eg
u
late
co
n
tr
o
l
o
b
j
ec
tiv
es
a
u
to
m
a
ticall
y
.
W
it
h
t
h
is
ar
r
a
n
g
e
m
e
n
t,
a
P
SO
b
as
ed
s
elf
-
t
u
n
in
g
m
et
h
o
d
is
ap
p
li
ed
to
ac
h
iev
e
b
etter
co
n
tr
o
l
o
b
j
ec
tiv
es.
I
n
Vf
co
n
tr
o
ller
,
v
o
ltag
e
a
n
d
f
r
eq
u
e
n
c
y
a
r
e
t
w
o
f
o
r
e
m
o
s
t
g
o
als
w
h
ic
h
n
ee
d
to
b
e
r
eg
u
lated
d
u
r
in
g
i
s
lan
d
i
n
g
m
o
d
e.
I
n
t
h
is
i
n
s
ta
n
ce
,
r
e
g
u
latio
n
o
f
f
r
e
q
u
en
c
y
a
n
d
v
o
ltag
e
d
ep
en
d
s
o
n
t
h
eir
r
e
f
er
en
ce
v
alu
e
s
(
f
r
ef
an
d
Vr
e
f
)
.
F
u
r
th
er
,
b
o
th
co
n
tr
o
ller
s
P
I
an
d
P
SO
-
P
I
s
ep
ar
atel
y
g
e
n
er
ate
co
n
tr
o
l
o
b
j
ec
tiv
es,
b
u
t
s
in
ce
th
e
P
SO
is
an
in
telli
g
en
t
p
r
o
ce
s
s
th
u
s
it
w
i
ll
p
r
o
v
id
e
o
p
ti
m
al
co
n
tr
o
l
p
ar
a
m
eter
s
to
y
ield
b
est
r
ef
er
e
n
ce
cu
r
r
en
t v
ec
to
r
s
.
Su
b
s
eq
u
en
t
l
y
,
th
e
cu
r
r
en
t r
e
f
er
en
ce
v
alu
e
s
c
an
b
e
ex
p
r
ess
ed
as:
∗
=
(
−
)
(
+
)
(
7
)
∗
=
(
−
)
(
+
)
(
8
)
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.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
1
0
6
8
-
1076
1072
2
.
3
.
2
.
Cu
r
r
e
n
t
c
o
n
tr
o
l
te
c
h
n
iq
u
e
T
h
e
r
ig
h
t
s
id
e
o
f
Fi
g
u
r
e
4
ill
u
s
tr
ates
a
n
in
n
er
lo
o
p
o
f
cu
r
r
en
t
co
n
tr
o
l,
co
n
s
id
er
ed
in
v
ie
w
o
f
SR
F.
I
n
o
r
d
er
to
tr
ac
k
ac
cu
r
atel
y
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th
e
s
h
o
r
t
tr
an
s
ie
n
t
s
i
n
in
v
er
ter
o
u
tp
u
t
c
u
r
r
en
t
i
s
o
f
t
h
e
s
ig
n
i
f
ica
n
t
i
m
p
o
r
tan
ce
i
n
t
h
is
tech
n
iq
u
e.
T
h
is
tech
n
iq
u
e
is
u
s
u
all
y
u
s
ed
to
m
i
n
i
m
ize
er
r
o
r
in
in
d
u
cto
r
i
m
p
u
ls
e
c
u
r
r
en
t
w
h
e
n
a
v
o
lta
g
e
is
ap
p
lied
to
in
d
u
ctiv
e
R
-
L
cir
cu
its
.
I
n
t
h
is
ca
s
e,
f
o
r
d
etec
tin
g
th
e
p
h
ase
a
n
g
le,
P
L
L
i
s
u
s
ed
in
o
r
d
er
t
o
i
m
p
l
e
m
en
t
P
ar
k
’
s
tr
an
s
f
o
r
m
a
tio
n
.
F
u
r
th
er
m
o
r
e,
t
w
o
P
I
co
n
tr
o
ller
s
ar
e
u
s
ed
in
t
h
e
s
y
s
te
m
to
r
ed
u
ce
t
h
e
cu
r
r
en
t
er
r
o
r
.
T
h
e
cu
r
r
en
t
lo
o
p
o
f
in
v
er
ter
a
n
d
f
ee
d
f
o
r
w
ar
d
v
o
ltag
e
lo
o
p
o
f
th
e
g
r
id
ar
e
u
tili
ze
d
to
en
h
a
n
ce
d
y
n
a
m
i
c
a
n
d
s
t
e
a
d
y
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t
a
t
e
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e
s
p
o
n
s
e
.
S
u
b
s
e
q
u
e
n
t
l
y
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o
n
t
r
o
l
l
e
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o
u
t
p
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t
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g
n
a
l
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s
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t
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h
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t
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t
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d
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f
r
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e
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t
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s
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h
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n
t
r
a
i
l
e
d
b
y
i
n
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e
r
s
e
P
a
r
k
’
s
t
r
a
n
s
f
o
r
m
a
t
i
o
n
a
n
d
C
l
a
r
k
e
’
s
tr
an
s
f
o
r
m
atio
n
,
all
to
g
et
h
er
t
h
at
co
n
tr
o
ller
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ie
ld
s
v
o
lta
g
e
r
ef
er
en
ce
s
i
g
n
al
i
n
α
β
ax
i
s
,
p
r
o
d
u
cin
g
SVP
W
M
s
ix
p
u
ls
e
to
tr
ig
g
er
I
GB
T
in
v
er
ter
.
B
esid
es,
SVP
W
M
tech
n
iq
u
e
also
co
n
f
ir
m
s
t
h
at
th
e
d
esire
d
v
alu
e
o
f
v
o
ltag
e
is
g
i
v
en
b
y
co
n
tr
o
ller
an
d
w
it
h
less
T
HD.
Fig
u
r
e
4
.
T
h
e
s
u
g
g
ested
p
o
w
e
r
co
n
tr
o
ller
Fro
m
(
2
)
,
th
e
v
o
ltag
e
r
e
f
er
en
c
e
v
alu
e
s
tated
in
s
y
n
ch
r
o
n
o
u
s
d
q
f
r
am
e
a
s
:
[
∗
∗
]
=
[
−
−
−
]
[
]
+
[
0
0
]
[
∗
∗
]
+
[
0
0
]
[
]
[
]
(
9
)
s
u
b
s
cr
ip
t
‘
*
’
d
esi
g
n
a
tes r
ef
er
e
n
ce
v
al
u
es,
=
∗
−
a
n
d
=
∗
−
Ash
s
h
o
w
n
i
n
(
9
)
ca
n
b
e
co
n
v
er
ted
to
ab
c
f
r
a
m
e
a
n
d
t
h
en
to
α
β
f
r
a
m
e
b
y
ap
p
l
y
in
g
in
v
e
r
s
e
P
ar
k
’
s
tr
an
s
f
o
r
m
atio
n
an
d
C
lar
k
e
’
s
tr
an
s
f
o
r
m
atio
n
r
esp
ec
tiv
e
l
y
,
[
]
=
[
∅
−
∅
1
c
os
(
∅
−
2
3
)
−
(
∅
−
2
3
)
1
c
os
(
∅
+
2
3
)
−
s
in
(
∅
+
2
3
)
1
]
(
1
0
)
[
0
]
=
2
3
[
]
[
1
−
0
.
5
−
0
.
5
0
√
3
2
⁄
−
√
3
2
⁄
0
.
5
0
.
5
0
.
5
]
(
1
1
)
Mo
r
eo
v
er
,
lo
w
p
ass
f
i
lter
is
u
s
ed
to
o
b
tain
t
h
e
i
n
d
u
cto
r
cu
r
r
en
t
[
7
]
.
I
n
t
h
is
s
t
u
d
y
,
f
ir
s
t
o
r
d
er
tr
an
s
f
er
f
u
n
ctio
n
is
p
r
esen
ted
as L
P
F a
n
d
is
g
i
v
e
n
b
y
:
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
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f rea
l
-
time
P
S
O
tu
n
ed
P
I
co
n
tr
o
ller
fo
r
r
eg
u
la
tin
g
vo
lta
g
e
a
n
d
…
(
Umb
r
in
S
u
lta
n
a
)
1073
=
1
1
+
(
1
2
)
w
h
er
e
f
i
s
th
e
v
al
u
e
o
f
in
p
u
t
f
i
lter
,
f
l is t
h
e
f
i
lter
ed
v
alu
e,
a
n
d
T
i is th
e
ti
m
e
co
n
s
ta
n
t
.
2
.
4
.
Alg
o
rit
h
m
o
f
pa
rt
icle
s
w
a
r
m
o
pti
m
iza
t
io
n (
P
SO
)
I
n
th
is
p
ap
er
,
th
e
u
p
p
er
an
d
lo
w
er
b
an
d
o
f
s
ea
r
ch
s
co
p
e
ar
e
co
n
s
id
er
ed
as
,
1
=
2
=
1
,
=
0
.
4
an
d
=
0
.
9
.
Fu
r
th
er
,
th
e
s
tep
s
o
f
ap
p
l
y
i
n
g
P
SO
an
d
th
eir
p
ar
am
e
ter
s
ar
e
g
iv
en
i
n
T
ab
le
1
a
n
d
T
ab
le
2
as
u
n
d
er
.
1
-
Initialize random position and velocity of particles,
2
-
For K iterations,
3
-
Update w
eight of inertia by
(15),
4
-
For every i particle of the population,
-
At iteration K update positions and velocities of all particles by
(13) and (14),
respectively,
-
Calculate the fitness value of all particles,
-
If fitness
<local best position, then update
and local best position,
=
;
-
Local best position = fitness
,
-
If local best position < global best then update
and global best position,
=
;
-
Global best position= local best position,
5
-
New particle,
6
-
New iteration,
7
-
Solution is
T
ab
le
1
.
P
SO a
lg
o
r
ith
m
p
ar
a
m
eter
s
D
e
scri
p
t
i
o
n
o
f
p
a
r
a
me
t
e
r
s
V
o
l
t
a
g
e
C
o
n
t
r
o
l
P
a
r
a
me
t
e
r
s
F
r
e
q
u
e
n
c
y
C
o
n
t
r
o
l
P
a
r
a
me
t
e
r
s
K
p
v
K
i
v
K
p
f
K
i
f
A
c
c
e
p
t
e
d
v
i
o
l
a
t
i
o
n
(
p
.
u
)
±
0
.
0
1
±
0
.
0
1
±
0
.
1
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n
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s
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RE
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NC
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.
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b
jerg
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Z.
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B
.
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2
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l
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[7
]
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tu
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[8
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[9
]
B.
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d
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0
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1
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2
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3
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4
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W
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Qi,
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5
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.
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6
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Yo
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7
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B.
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