I
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39
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pp
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ttp
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//ij
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cs
.
ia
esco
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co
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An
impro
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WO
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of
PI
co
ntrol
for
thre
e
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PW
M
rect
i
fier
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wet
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urus
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m
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ticle
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y:
R
ec
eiv
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J
u
l
12
,
2
0
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4
R
ev
is
ed
Oct
3
,
202
4
Acc
ep
ted
No
v
10
,
2
0
2
4
In
t
h
e
e
m
p
ire
of
e
lec
tri
c
v
e
h
icle
(EV)
p
ro
p
u
lsio
n
sy
ste
m
s,
e
fficie
n
t
e
n
e
rg
y
c
o
n
v
e
rsio
n
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a
ra
m
o
u
n
t
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o
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e
x
te
n
d
i
n
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d
riv
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n
g
ra
n
g
e
a
n
d
e
n
h
a
n
c
i
n
g
o
v
e
ra
ll
p
e
rfo
rm
a
n
c
e
.
Re
c
ti
fiers
p
la
y
a
c
r
u
c
ial
ro
le
in
c
o
n
v
e
rti
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g
AC
fro
m
th
e
g
ri
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to
DC
f
o
r
b
a
tt
e
ry
c
h
a
rg
in
g
a
n
d
m
o
t
o
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o
p
e
ra
ti
o
n
.
Ho
w
e
v
e
r,
th
e
p
e
rfo
rm
a
n
c
e
of
re
c
ti
fiers
is
h
e
a
v
il
y
in
fl
u
e
n
c
e
d
by
th
e
c
o
n
tr
o
l
a
lg
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rit
h
m
s
e
m
p
lo
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e
d
.
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w
o
rk
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re
se
n
ts
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o
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ti
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ize
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p
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ra
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o
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sig
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re
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ti
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a
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li
c
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ti
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s.
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e
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ro
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se
d
c
o
n
tro
ll
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a
ims
to
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c
h
iev
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ig
h
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c
y
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f
a
st
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se
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n
d
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stn
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riatio
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s
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lo
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d
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n
d
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t
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g
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h
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iza
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ro
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in
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o
rp
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th
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k
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ti
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z
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d
wh
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le
o
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ti
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iza
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o
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t
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n
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n
g
t
h
e
PI
c
o
n
tr
o
ll
e
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p
a
ra
m
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ters
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e
o
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jec
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v
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is
to
m
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imiz
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o
st
f
u
n
c
ti
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th
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t
re
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se
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ts
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e
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iatio
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of
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fier
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u
tp
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d
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sire
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ra
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teristics
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ter
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n
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it
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l
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o
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l
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h
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e
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M
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x
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m
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tal
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li
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ti
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n
v
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rifi
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th
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p
ro
p
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se
d
c
o
n
tro
ll
e
r'
s
re
li
a
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il
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y
a
n
d
e
fficie
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y
in
p
ra
c
ti
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a
l
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a
p
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a
ti
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n
s.
T
h
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o
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ti
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ize
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PI
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o
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tr
o
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c
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h
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ll
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li
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b
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li
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of
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lec
tri
c
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h
icle
p
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m
s.
K
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d
s
:
B
u
b
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le
s
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tech
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iq
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ller
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PW
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ith
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CC
BY
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C
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p
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A
uth
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r
:
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weth
a
G
Dep
ar
tm
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of
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lectr
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an
d
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UVCE,
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ail:
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.
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9
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1.
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NT
RO
D
UCT
I
O
N
In
th
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f
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Dif
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T
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p
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elativ
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u
tp
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t
r
ip
p
le
[1
]
-
[
5
]
.
C
o
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v
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s
ely
,
1ϕ
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u
ll
wav
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r
ec
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Dif
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n
t
ty
p
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s
ed
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if
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in
co
r
p
o
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ate
p
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ls
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wid
th
m
o
d
u
latio
n
(
PW
M)
tech
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iq
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es
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o
m
m
o
n
l
y
u
s
ed
in
m
an
y
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p
p
l
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icle
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ar
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ec
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s
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am
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[6
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-
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1
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l
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'
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u
tp
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t
v
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lta
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Op
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lo
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p
co
n
tr
o
l
is
r
esu
ltin
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in
in
ac
cu
r
ate.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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5
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52
In
d
o
n
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J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
8
,
No
.
1
,
Ap
r
il
20
2
5
:
39
-
49
40
In
th
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r
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(
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[
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a
i
n
t
ai
n
i
n
g
m
i
n
i
m
a
l
h
a
r
m
o
n
i
c
d
i
s
t
o
r
t
i
o
n
(
T
H
D
)
[
2
2
]
.
H
e
n
c
e
to
a
c
h
i
e
v
e
t
h
e
s
t
a
b
il
i
t
y
a
n
d
s
y
s
te
m
r
e
l
i
a
b
l
e
n
ess
,
r
es
e
a
r
c
h
e
r
s
c
o
n
d
u
c
t
e
d
t
h
e
o
r
e
t
i
c
al
i
n
v
e
s
t
i
g
at
i
o
n
s
a
n
d
e
s
t
a
b
l
is
h
e
d
a
c
o
r
r
e
s
p
o
n
d
i
n
g
d
i
a
g
n
o
s
t
i
c
s
ch
e
m
e
in
d
e
a
l
i
n
g
w
i
t
h
t
h
e
p
r
o
b
l
e
m
of
1ϕ
o
p
e
n
l
i
n
e
f
a
u
l
t
s
in
a
3ϕ
PW
M
r
e
c
ti
f
i
e
r
[
2
3
]
.
A
f
ee
d
b
ac
k
co
n
tr
o
l
m
eth
o
d
b
ased
on
ca
p
ac
itiv
e
en
e
r
g
y
s
to
r
ag
e
was
d
e
v
elo
p
ed
;
it
co
m
p
r
is
ed
of
an
o
u
ts
id
e
lo
o
p
(
ca
p
ac
itiv
e
en
e
r
g
y
s
to
r
ag
e)
a
n
d
an
in
n
er
l
o
o
p
(
cu
r
r
en
t)
.
T
h
r
o
u
g
h
em
p
lo
y
in
g
th
is
ap
p
r
o
ac
h
,
th
e
s
y
s
tem
'
s
d
y
n
am
ic
p
r
o
p
er
ties
b
ec
o
m
e
g
r
ad
u
ally
im
p
r
o
v
ed
a
n
d
d
elay
e
d
o
u
tp
u
t
v
o
ltag
e
r
eg
u
latio
n
d
u
r
in
g
l
o
ad
ch
an
g
es
ar
e
p
r
e
v
en
ted
[
2
4
]
.
In
a
s
im
ilar
s
tr
ea
m
,
an
in
n
er
l
o
o
p
c
o
n
s
is
tin
g
of
cu
r
r
en
t
a
n
d
an
o
u
ter
lo
o
p
with
v
o
ltag
e
d
o
u
b
led
s
itu
atio
n
is
d
e
v
elo
p
ed
to
m
ax
im
ize
th
e
r
ec
tif
ier
'
s
ef
f
ic
ien
cy
[
2
5
]
.
W
h
ile,
in
teg
r
al
win
d
u
p
is
a
m
ajo
r
lim
itatio
n
of
a
PI
co
n
tr
o
ll
er
.
T
h
is
p
ar
t
d
ev
elo
p
s
wh
en
th
e
in
teg
r
al
ter
m
co
n
tin
u
es
to
p
r
o
d
u
ce
er
r
o
r
s
ev
en
wh
en
th
e
s
y
s
tem
is
s
atu
r
ated
or
in
ca
p
ab
le
of
r
ea
ctin
g
due
to
co
n
s
tr
ain
ts
or
p
h
y
s
ical
r
estrictio
n
s
.
W
h
en
th
e
co
n
tr
o
l
s
ig
n
al
s
atu
r
ates,
th
e
in
teg
r
al
ter
m
k
ee
p
s
in
t
eg
r
atin
g
th
e
e
r
r
o
r
,
lead
in
g
to
o
v
er
s
h
o
o
t
or
o
s
cillatio
n
s
wh
en
th
e
s
y
s
tem
b
ec
o
m
es
ac
tiv
e
ag
ain
.
T
h
is
p
h
en
o
m
en
o
n
can
d
e
g
r
ad
e
co
n
tr
o
l
p
er
f
o
r
m
an
ce
,
esp
ec
ially
in
s
y
s
tem
s
with
lar
g
e
s
et
p
o
in
t
ch
an
g
es
or
d
is
tu
r
b
an
ce
s
.
T
h
u
s
,
to
o
v
er
c
o
m
e
th
is
p
r
o
b
lem
,
an
o
p
tim
izatio
n
of
PI
co
n
tr
o
ller
p
ar
am
ete
r
s
h
av
e
be
ad
o
p
ted
.
Kee
p
i
n
g
th
is
in
v
iew,
th
is
wo
r
k
f
o
r
m
u
lated
a
n
o
v
el
o
p
tim
ized
to
p
o
lo
g
y
ca
lled
wh
ale
o
p
tim
izatio
n
to
o
p
tim
ize
th
e
PI
co
n
tr
o
ller
ad
o
p
ted
in
th
e
R
ec
tifie
r
cir
cu
it
.
2.
ANALY
SI
S
A
ND
M
O
D
E
L
I
NG
OF
T
H
RE
E
-
P
H
AS
E
T
O
P
O
L
G
Y
T
h
e
p
r
im
a
r
y
ci
r
cu
it
of
th
e
th
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
PW
M
r
ec
tifie
r
cir
cu
it
is
s
h
o
wn
in
Fig
u
r
e
1,
h
er
e
I
a,
I
b
,
a
n
d
Ic
d
eter
m
i
n
e
th
e
in
p
u
t
s
o
u
r
ce
cu
r
r
en
t
of
g
r
id
-
s
id
e
an
d
Ua,
Ub
,
an
d
Uc
in
d
i
ca
tes
p
o
wer
-
s
u
p
p
ly
v
o
ltag
e
of
each
p
h
ase.
T
h
e
f
il
ter
in
d
u
ctan
ce
is
r
ep
r
esen
ted
by
L
s
,
l
o
ad
r
esis
tan
ce
is
d
en
o
t
ed
by
R
L
,
DC
-
s
id
e
o
u
tp
u
t
v
o
ltag
e
is
in
d
icate
d
by
Ud
c,
o
u
tp
u
t
cu
r
r
en
t
is
d
ep
icted
by
I
d
c,
th
e
f
ilter
-
in
d
u
ctan
ce
eq
u
iv
ale
n
t
r
esis
tan
ce
is
s
u
g
g
ested
as
R
s
,
a
n
d
I
GB
T
with
f
r
ee
wh
ee
lin
g
d
i
o
d
es
is
s
tated
as
s
witch
1
-
6.
L
C
I
c
+
-
Ua
Uc
Ub
R
I
a
I
b
R
L
u
o
O
+
+
+
L
L
R
R
S
1
S
2
S
3
S
4
S
5
S
6
v
a
v
b
v
c
N
U
dc
I
c
P
i
Q
i
P
o
Q
o
Fig
u
r
e
1.
T
o
p
o
lo
g
y
of
th
e
m
ain
cir
cu
it
of
th
e
th
r
ee
-
p
h
ase
b
r
id
g
e
r
ec
tifie
r
To
u
n
d
e
r
s
tan
d
wo
r
k
i
n
g
p
r
in
ci
p
le
an
d
s
y
s
tem
co
n
tr
o
l,
t
h
e
th
r
ee
-
p
h
ase
PW
M
r
ec
tifie
r
's
in
p
u
t
s
id
e
an
d
o
u
tp
u
t
m
ath
em
atica
l
m
o
d
el
s
h
o
u
ld
be
d
ev
elo
p
ed
.
In
th
e
b
eg
i
n
n
in
g
,
t
h
e
cir
cu
it
p
a
r
am
eter
s
a
r
e
m
ea
s
u
r
ed
u
s
in
g
th
e
KVL
an
d
KC
L
eq
u
atio
n
s
to
o
b
tain
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
A
n
imp
r
o
ve
d
WOA
o
f P
I
c
o
n
tr
o
l fo
r
th
r
ee
p
h
a
s
e
P
WM
r
ec
tifi
er
(
S
h
w
eth
a
G
)
41
−
+
+
+
=
0
−
+
+
+
=
0
−
+
+
+
=
0
+
=
(
1
)
T
h
e
o
u
tco
m
es
th
at
f
o
llo
w
p
r
o
p
er
ties
of
a
p
o
wer
s
u
p
p
ly
f
r
o
m
th
r
ee
-
p
h
ase
can
be
o
b
tain
ed
.
if
th
e
s
witch
in
g
v
alu
e
Sj
(
j=
a,
b
,
c)
is
ap
p
lied
in
p
lace
of
u
jo
(
j
=a
,
b
,
c)
w
h
er
e
f
o
r
m
u
la
(
Sj=1
p
r
ef
er
r
e
d
as
u
p
p
er
b
r
id
g
e
a
r
m
co
n
d
u
ctio
n
in
j
p
h
ase;
Sj
=
0
im
p
lies
lo
wer
b
r
id
g
e
p
ar
t
o
p
er
atio
n
)
:
+
+
=
0
.
=
−
−
−
1
3
[
+
+
]
=
−
−
−
1
3
[
+
+
]
=
−
−
−
1
3
[
+
+
]
=
+
+
−
T
h
e
m
ath
em
atica
l
m
o
d
el
ex
p
r
ess
io
n
s
f
r
o
m
3ϕ
co
n
s
tan
t
co
o
r
d
in
ate
ar
r
an
g
e
m
en
t
of
PW
M
r
ec
tifie
r
an
d
with
f
o
u
r
f
o
r
m
u
las
in
th
e
eq
u
atio
n
,
d
esig
n
i
n
g
a
co
n
t
r
o
l
s
y
s
tem
b
ec
o
m
es
u
n
n
ec
es
s
ar
ily
co
m
p
licated
.
Ma
th
em
atica
l
m
o
d
if
icatio
n
is
th
er
ef
o
r
e
s
till
r
eq
u
ir
ed
.
T
h
e
tr
an
s
itio
n
b
etwe
en
th
e
dq
r
o
tati
n
g
r
ef
er
e
n
ce
f
r
am
e
an
d
ab
c
th
r
ee
-
p
h
ase
s
tatio
n
a
r
y
-
co
o
r
d
in
ate
s
y
s
tem
ar
e
c
o
n
s
id
er
ed
as
s
o
lu
tio
n
.
A
PW
M
r
ec
tifie
r
'
s
co
n
tr
o
l
b
ec
o
m
es
s
u
b
s
tan
tially
more
co
m
p
lex
b
ec
au
s
e
th
e
v
a
r
iab
l
es
on
th
e
alter
n
atin
g
s
id
e
ar
e
tim
e
-
ch
an
g
i
n
g
.
To
s
o
lv
e
th
is
is
s
u
e,
a
c
o
o
r
d
in
at
ed
tr
an
s
f
o
r
m
atio
n
in
to
a
s
y
n
ch
r
o
n
o
u
s
r
o
tatio
n
co
r
r
elate
p
r
o
ce
d
u
r
e
(
d
q
)
is
s
u
g
g
ested
as
a
m
eth
o
d
to
s
im
p
lify
co
n
tr
o
l
r
eq
u
i
r
em
en
ts
.
-
C
o
n
tr
o
ller
d
esig
n
T
he
PI
co
n
tr
o
ller
is
u
s
ed
f
o
r
c
o
n
tr
o
l,
with
ud,
uq
as
th
e
o
u
tp
u
t
an
d
id
,
iq
f
o
r
in
p
u
t
r
esp
o
n
s
e.
It
can
be
d
er
iv
ed
in
s
u
ch
a
way
th
at
in
c
o
r
p
o
r
ates
f
ee
d
f
o
r
war
d
d
ec
o
u
p
l
in
g
in
to
ac
c
o
u
n
t:
=
(
−
∗
)
(
+
)
+
+
=
(
−
∗
)
(
+
)
+
+
(
3
)
w
h
er
e
Kp
an
d
Ki
r
ep
r
esen
t
th
e
co
ef
f
icien
t
of
p
r
o
p
o
r
tio
n
an
d
in
teg
r
atio
n
f
o
r
th
e
PI
co
n
tr
o
ller
r
esp
ec
tiv
ely
.
It
is
p
o
s
s
ib
le
to
cr
ea
te
a
c
o
n
tr
o
ller
with
an
in
te
r
n
al
-
cu
r
r
e
n
t
lo
o
p
by
u
s
in
g
(
3
)
.
t
h
e
s
y
s
tem
-
b
lo
ck
d
iag
r
am
is
s
h
o
wn
in
d
etail
in
Fig
u
r
e
2.
T
h
e
cu
r
r
en
t
co
n
f
ig
u
r
atio
n
,
as
s
h
o
wn
in
th
e
d
iag
r
am
,
d
em
o
n
s
tr
ates
a
clo
s
ed
lo
o
p
u
s
in
g
th
e
s
y
s
tem
'
s
cu
r
r
e
n
t
id
an
d
iq
.
th
e
p
o
wer
t
ec
h
n
iq
u
e
f
ails
to
r
esp
o
n
d
with
th
e
DC
v
o
ltag
e
of
lo
ad
s
id
e.
in
s
tead
,
cu
r
r
en
t
-
cl
o
s
ed
lo
o
p
is
p
r
esen
t
in
th
e
p
r
im
ar
y
c
o
n
tr
o
l
lo
o
p
,
wh
ic
h
is
also
r
ef
er
r
ed
as
v
o
ltag
e
-
clo
s
ed
lo
o
p
.
h
en
ce
r
e
f
er
r
ed
as
th
e
o
u
ter
lo
o
p
of
v
o
ltag
e,
an
d
in
s
id
e
co
n
tr
o
l
p
r
o
c
ess
,
wh
ich
co
n
tr
o
ls
cu
r
r
en
t,
is
ca
lled
th
e
i
n
n
er
-
cu
r
r
en
t
lo
o
p
.
Fig
u
r
e
2
.
Desig
n
o
f
th
e
c
o
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
8
,
No
.
1
,
Ap
r
il
20
2
5
:
39
-
49
42
T
h
e
v
o
ltag
e
-
clo
s
ed
lo
o
p
co
n
t
r
o
l
p
r
o
ce
s
s
can
be
d
escr
ib
ed
by
f
o
llo
win
g
(
4
)
:
∗
=
(
∗
−
)
+
∫
(
∗
−
)
(
4
)
W
h
er
e:
udc
∗
:
r
ef
er
e
n
ce
v
o
ltag
e
udc
:
ac
tu
al
v
o
ltag
e
Kp
:
p
r
o
p
o
r
tio
n
al
g
ain
Ki
:
in
teg
r
al
p
ar
t
T
h
e
ab
o
v
e
u
tili
ze
d
co
n
t
r
o
ller
r
ec
eiv
es
er
r
o
r
s
ig
n
al
(
u
d
c
∗
−u
d
c)
in
th
is
co
n
tr
o
l
s
ch
em
e
a
n
d
d
eter
m
in
es
th
e
co
n
tr
o
l
s
ig
n
al
id
to
m
o
d
if
y
DC
s
id
e
v
o
ltag
e.
W
h
ile
th
e
in
teg
r
al
ter
m
h
elp
s
in
r
em
o
v
i
n
g
an
y
s
tead
y
-
s
tate
er
r
o
r
,
th
e
p
r
o
p
o
r
tio
n
al
ter
m
m
o
d
if
ies
o
u
tp
u
t
in
ac
c
o
r
d
a
n
ce
with
th
e
p
r
esen
t
er
r
o
r
.
T
h
e
cu
r
r
en
t
in
s
y
s
tem
'
s
d
-
ax
is
is
th
en
co
n
tr
o
lled
by
PI
co
n
tr
o
ller
'
s
o
u
tp
u
t,
id
,
allo
ws
m
o
d
if
icatio
n
s
to
th
e
v
o
ltag
e
on
o
u
tp
u
t
lo
a
d
s
id
e.
T
h
e
co
n
tr
o
l
s
eg
m
en
t
can
in
ter
ac
t
with
th
e
DC
s
id
e
v
o
ltag
e
f
lu
ctu
atio
n
s
an
d
r
eg
u
late
th
em
in
ac
co
r
d
an
ce
with
r
ef
er
en
ce
v
o
ltag
e
Ud
c
th
ese
ar
e
ad
v
a
n
tag
es
of
v
o
ltag
e
-
clo
s
ed
lo
o
p
co
n
tr
o
l
m
ec
h
a
n
is
m
.
L
ik
ewise,
th
e
d
ef
in
itio
n
of
a
cu
r
r
en
t
c
o
n
tr
o
ll
er
is
as
:
=
(
′
+
′
)
(
∗
−
)
(
5
)
T
h
e
3ϕ
PW
M
r
ec
tifie
r
'
s
en
tire
b
lo
ck
d
iag
r
am
is
s
h
o
wn
in
Fi
g
u
r
e
3.
T
h
e
r
ec
tifie
r
'
s
DC
-
s
id
e
v
o
ltag
e
is
s
tab
ilized
an
d
k
ep
t
co
n
s
tan
t
by
th
e
o
u
ts
id
e
v
o
ltag
e
lo
o
p
.
R
ea
ctiv
e
co
m
p
o
n
en
t
(
iq
)
is
s
et
f
o
r
ze
r
o
in
o
r
d
er
to
p
r
eser
v
e
u
n
ity
PF
co
n
ten
t.
Su
b
s
eq
u
en
tly
,
f
ee
d
b
ac
k
v
alu
es
c
o
r
r
esp
o
n
d
in
g
to
th
e
cu
r
r
en
t
ele
m
en
t
on
dq
-
ax
is
ar
e
co
m
p
ar
ed
with
ac
tiv
e
cu
r
r
e
n
t
(
id
)
an
d
r
ea
ctiv
e
cu
r
r
en
t
(
iq
)
s
ep
ar
ately
.
T
h
ese
ar
e
th
e
co
m
p
ar
is
o
n
s
th
at
f
o
llo
w
th
e
PI
r
eg
u
lato
r
.
T
h
e
r
ec
tifie
r
'
s
s
witch
in
g
s
tates
ar
e
th
en
c
o
n
tr
o
lled
by
a
s
p
ac
e
-
v
ec
to
r
m
o
d
u
lato
r
wh
ile
th
e
o
u
tp
u
t
h
as
u
n
d
er
g
o
n
e
v
ec
t
o
r
t
r
an
s
latio
n
.
T
h
is
p
r
o
ce
d
u
r
e
ca
u
s
es
th
e
r
ec
tifie
r
'
s
AC
-
s
id
e
cu
r
r
en
t
wav
ef
o
r
m
to
b
ec
o
m
e
s
in
u
s
o
id
al,
w
h
ich
m
a
k
es
it
ea
s
ier
to
m
an
ag
e
an
d
r
ea
ch
u
n
ity
PF.
Fig
u
r
e
3
.
C
o
n
tr
o
l sch
em
e
-
s
tr
u
ctu
r
al
d
iag
r
am
o
f
p
r
o
p
o
s
ed
r
ec
tifie
r
Ma
n
y
ad
v
an
ta
g
es
co
m
e
with
th
is
co
n
tr
o
l
m
eth
o
d
,
s
u
ch
as
its
g
r
ea
t
s
tead
y
-
s
tate
p
er
f
o
r
m
a
n
ce
,
q
u
ick
d
y
n
am
ic
r
ea
ctio
n
,
an
d
in
-
b
u
ilt
p
r
o
tectio
n
f
o
r
c
u
r
r
en
t
-
lim
it.
Ad
d
itio
n
ally
,
it
ac
h
iev
es
u
n
ity
PF
an
d
s
u
cc
ess
f
u
lly
r
em
o
v
es
c
u
r
r
en
t
-
s
tead
y
-
s
tate
f
au
lts
,
m
ak
in
g
it
more
ap
p
r
o
p
r
iate
f
o
r
a
v
ar
iety
of
ap
p
licatio
n
s
.
In
ad
d
itio
n
,
th
is
s
tu
d
y
h
as
d
ev
is
ed
a
n
o
v
el
s
tep
p
ed
v
o
ltag
e
s
ettin
g
ap
p
r
o
ac
h
to
im
p
r
o
v
e
c
o
n
tr
o
l
e
f
f
icac
y
.
T
h
er
e
f
o
r
e,
o
p
tim
izatio
n
to
p
o
lo
g
y
h
as
b
ee
n
ex
am
in
e
d
in
o
r
d
er
to
f
u
r
th
er
in
cr
ea
s
e
th
e
PI
co
n
tr
o
ller
'
s
ef
f
icien
cy
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
A
n
imp
r
o
ve
d
WOA
o
f P
I
c
o
n
tr
o
l fo
r
th
r
ee
p
h
a
s
e
P
WM
r
ec
tifi
er
(
S
h
w
eth
a
G
)
43
3.
WH
AL
E
O
P
T
I
M
I
Z
A
T
I
O
N
AL
G
O
RI
T
H
M
F
O
R
PI
T
U
NING
T
h
e
co
n
ce
p
t
of
W
OA
o
r
ig
in
at
es
f
r
o
m
th
e
B
u
b
b
le
-
n
et
attac
k
i
n
g
s
tr
ateg
y
,
wh
e
r
e
wh
ales
c
o
r
r
al
f
is
h
by
cr
ea
tin
g
s
p
ir
al
-
s
h
ap
ed
air
p
o
c
k
ets
ar
o
u
n
d
th
em
up
to
12
m
e
ter
s
b
elo
w
th
e
wate
r
'
s
s
u
r
f
ac
e,
th
en
ascen
d
in
g
to
tr
ap
an
d
ca
p
tu
r
e
th
eir
tar
g
et
ed
p
r
ey
s
h
o
r
tly
af
ter
.
In
ter
m
s
of
wh
ale
o
b
s
er
v
atio
n
s
,
t
h
e
m
eth
o
d
o
lo
g
ical
ap
p
r
o
ac
h
is
r
ef
lecte
d
in
th
is
al
g
o
r
ith
m
th
r
o
u
g
h
th
e
co
m
p
le
x
s
ea
r
ch
f
o
r
f
o
o
d
,
wh
ich
s
tay
s
cien
tific
ally
clar
if
ied
by
r
esu
r
r
ec
tin
g
p
ast
p
atter
n
s
r
ath
er
th
an
ar
b
itra
r
ily
s
elec
tin
g
alter
n
ativ
e
co
u
r
s
es
of
ac
tio
n
wh
ich
is
s
h
o
wn
i
n
Fig
u
r
e
4.
Desp
ite
th
is
im
p
ac
tf
u
l
b
eh
av
io
r
,
W
OA
d
is
tin
g
u
is
h
es
it
s
elf
f
r
o
m
o
th
er
im
p
r
o
v
em
en
t
s
tr
ateg
ies
b
ec
au
s
e
it
o
n
ly
n
ec
ess
itates
two
b
o
u
n
d
ar
y
ad
j
u
s
tm
en
ts
.
T
h
ese
b
o
u
n
d
ar
ies
f
ac
ilit
ate
s
m
o
o
th
tr
a
n
s
itio
n
s
b
etwe
en
ex
p
lo
itatio
n
an
d
e
x
p
l
o
r
atio
n
f
r
am
ewo
r
k
s
.
Fig
u
r
e
4.
Fin
d
i
n
g
attac
k
p
r
ey
t
ec
h
n
iq
u
e
T
h
e
s
eg
m
en
t
ah
ea
d
will
d
em
o
n
s
tr
ate
m
o
d
el
f
o
r
en
ci
r
clin
g
p
r
ey
,
s
ea
r
ch
in
g
f
o
r
p
r
ey
,
an
d
em
p
lo
y
in
g
th
e
air
-
f
illed
p
o
ck
et
n
et
of
s
ca
v
en
g
in
g
ac
tio
n
.
T
h
e
b
eh
a
v
io
r
of
h
u
m
p
b
ac
k
wh
ales
s
u
r
r
o
u
n
d
in
g
p
r
ey
a
n
d
u
p
d
atin
g
th
eir
s
itu
atio
n
to
o
p
tim
ize
th
eir
ch
ase
ca
n
be
q
u
an
tifie
d
as
f
o
llo
ws:
As
th
e
n
u
m
b
e
r
of
cy
cles
in
cr
ea
s
es
f
r
o
m
th
e
in
itial
s
tag
es
to
th
e
m
o
s
t
ex
tr
em
e
n
u
m
b
er
s
,
h
u
m
p
b
ac
k
wh
ales
en
g
a
g
e
in
a
co
o
r
d
in
ated
ef
f
o
r
t
to
e
n
cir
cle
th
e
p
r
e
y
.
Du
r
in
g
th
is
p
r
o
ce
s
s
,
th
ey
d
y
n
am
ically
ad
ju
s
t
th
eir
p
o
s
itio
n
s
an
d
tactics
to
m
ax
im
ize
th
eir
ef
f
icien
cy
in
c
h
asin
g
an
d
ca
p
tu
r
in
g
th
e
p
r
ey
.
On
th
e
o
f
f
ch
an
ce
th
at
(
p
<
0
.
5
an
d
m
o
d
(
U)
<
1
)
A
t
th
at
p
o
in
t,
th
e
s
itu
atio
n
of
co
m
p
etito
r
p
o
s
itio
n
X
(
t
+1
)
is
r
ef
r
esh
ed
by
th
e
ac
c
o
m
p
an
y
in
g
co
n
d
itio
n
s
:
D
=
mod
{
(
C
.
X
)
−
X
(
t
)
}
X
(
t
+
1
)
=
[
X
(
t
)
–
{
U
.
D
}
]
(
6
)
W
h
er
e
p
=
0
.
1
(
co
n
s
is
ten
t)
.
X
(
t+1
)
is
th
e
b
est
s
itu
atio
n
in
th
e
c
u
r
r
en
t
cir
cu
m
s
tan
ce
.
U
an
d
C
ar
e
d
eter
m
in
e
d
by
ac
c
o
m
p
an
y
in
g
co
n
d
itio
n
s
:
U=
mod
{2
.
a
.
r
-
a}
C
=2
.
r
W
h
er
e
a
is
d
ir
ec
tly
d
im
in
is
h
e
s
f
r
o
m
2
to
0
a
n
d
r
is
th
e
h
ap
h
az
ar
d
ly
ch
o
s
en
v
ec
to
r
.
Pre
y
Sear
ch
in
g
eq
u
atio
n
s
ar
e
g
iv
en
as
f
o
llo
ws:
D
=
mod
{
(
C
.
X
r
a
n
dom
)
−
X
(
t
)
}
X
(
t
+
1
)
=
[
X
r
a
n
dom
(
t
)
–
{
U
.
D
}
]
(
7
)
Du
r
in
g
th
e
in
q
u
ir
y
p
h
ase
of
wh
ale
ad
v
an
ce
m
e
n
t
co
m
p
u
tatio
n
,
th
e
s
u
r
r
o
u
n
d
in
g
an
d
win
d
in
g
r
ef
r
esh
in
g
of
p
r
ey
wer
e
c
o
m
p
l
eted
.
s
et
th
e
ze
r
o
v
alu
es
to
p
o
p
u
latio
n
n
u
m
b
er
,
d
esig
n
v
ar
ia
b
les,
an
d
m
ax
im
u
m
n
u
m
er
al
of
iter
atio
n
s
.
Fo
r
ea
c
h
d
esig
n
v
a
r
iab
le,
f
in
d
th
e
f
itn
ess
f
u
n
ctio
n
f
o
r
ea
c
h
s
ea
r
ch
a
g
en
t
.
T
h
e
o
th
er
o
n
e
s
h
o
u
ld
n
e
x
t
tr
y
to
m
o
d
if
y
th
e
ir
p
o
s
itio
n
s
to
m
atch
b
est
f
it,
or
o
p
tim
al
s
o
lu
tio
n
,
as
s
ee
n
in
Fig
u
r
e
5.
Ad
ju
s
t
each
s
ea
r
ch
a
g
en
t'
s
p
o
s
itio
n
by
d
o
in
g
th
e
f
o
llo
win
g
:
W
h
e
n
P
is
less
th
an
0
.
5
,
a
n
d
p
is
a
r
an
d
o
m
n
u
m
b
er
b
etwe
en
0
an
d
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
8
,
No
.
1
,
Ap
r
il
20
2
5
:
39
-
49
44
I
n
i
t
i
al
i
z
e
p
ar
am
e
t
e
r
s
G
e
n
e
r
at
e
a
r
and
om
I
n
i
t
i
al
p
op
u
l
at
i
on
E
val
u
at
e
t
h
e
f
i
t
n
e
s
s
of
e
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RE
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tili
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elate
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ar
iab
les
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ad
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lts
.
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h
e
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elev
an
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cir
cu
it
m
ea
s
u
r
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m
en
ts
ar
e
p
r
o
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T
a
b
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T
ab
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1.
C
ir
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it
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ar
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C
i
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i
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P
a
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e
r
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a
l
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g
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(V)
3
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40
1
C
a
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n
c
e
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C
ur
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2
C
ur
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e
n
t
45
T
h
e
ef
f
ec
tiv
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PW
M
r
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em
p
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ewly
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ested
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alu
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ct
o
p
er
atin
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ar
io
s
,
co
n
s
id
er
in
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m
etr
ics
lik
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r
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e
tim
e
(t
r
),
s
ettlin
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s
),
an
d
PF.
T
h
e
d
if
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er
en
t
o
p
er
atin
g
co
n
d
itio
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s
ar
e
g
iv
en
in
b
elo
w.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
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g
&
C
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m
p
Sci
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5
0
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-
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7
52
A
n
imp
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WOA
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45
4
.
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.
Under
c
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it
io
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1
T
h
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v
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ltag
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ac
r
o
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o
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t
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t
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r
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im
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F
ig
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t
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e
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0
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0
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s
ec
o
n
d
s
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d
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m
e
s
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le.
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h
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u
t
p
u
t
v
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e
h
as
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f
ec
t
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n
th
e
R
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ad
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d
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ly
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g
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2
5
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d
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ick
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in
0
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0
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ec
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d
s
.
Fig
u
r
e
7
d
e
p
icts
th
e
o
b
s
er
v
at
io
n
o
f
s
o
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r
ce
v
o
ltag
e
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d
cu
r
r
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t
wav
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m
s
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i
n
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t
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At
0
.
2
5
s
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o
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d
s
in
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im
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t
h
e
lo
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esis
tan
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s
u
d
d
en
ly
h
alv
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d
,
ef
f
ec
ts
as
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ev
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o
p
m
en
t
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r
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m
ag
n
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e.
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ite
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is
ch
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th
e
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s
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ely
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ased
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Fig
u
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6.
DC
-
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Fig
u
r
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tag
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r
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2
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u
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8
illu
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ates
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r
s
tr
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r
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r
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ch
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t
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h
en
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tifie
r
at
s
tead
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d
itio
n
,
th
e
u
n
b
al
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d
s
tate
in
AC
s
u
p
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ly
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ap
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=
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4
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s
.
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r
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k
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o
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e
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ar
ies
ar
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n
d
its
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ef
er
en
ce
v
alu
e
in
b
o
th
co
n
tr
o
ller
s
ce
n
ar
io
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
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J
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&
C
o
m
p
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,
Vo
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3
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,
No
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1
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Ap
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il
20
2
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:
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-
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46
Fig
u
r
e
8
.
Simu
latio
n
r
esu
lts
o
f
s
tep
ch
an
g
e
o
p
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atio
n
4
.
3
.
Co
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it
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3
Fig
u
r
e
9
d
e
p
icts
th
e
r
esp
o
n
s
e
of
th
e
s
y
s
tem
u
n
b
alan
ce
d
AC
s
u
p
p
ly
.
it
clea
r
ed
f
o
r
th
e
i
m
ag
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th
at
wh
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th
er
e
is
a
c
h
an
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e
s
u
d
d
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ch
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n
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es
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r
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m
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u
t
s
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e
is
two
c
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g
es
at
0
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3
9
a
n
d
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e
ch
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g
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o
m
0
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5
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to
0
.
6
5
.
Hen
ce
co
n
c
lu
d
e
th
at
s
u
p
p
l
y
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s
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d
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er
e
n
t
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ar
iatio
n
s
.
Fig
u
r
e
9.
Simu
latio
n
r
esu
lts
of
u
n
b
alan
ce
d
AC
s
u
p
p
ly
o
p
er
at
io
n
4
.
4
.
Co
nd
it
io
n
-
4
T
h
is
ca
s
e
s
tu
d
y
in
v
esti
g
ates
th
e
ef
f
ec
ts
of
lo
a
d
c
h
an
g
es
on
th
e
DC
s
id
e
of
a
r
ec
tifie
r
.
Sp
e
cif
ically
,
it
ex
am
in
es
th
e
im
p
ac
t
of
r
ed
u
cin
g
th
e
lo
ad
by
5
0
%.th
e
Fi
g
u
r
e
10
s
h
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ws
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f
ec
ts
.
Fro
m
all
th
e
ca
s
es,
it
is
ev
id
en
t
th
at
p
r
o
p
o
s
ed
co
n
tr
o
ll
er
m
ain
tain
s
a
co
n
s
tan
t
DC
li
n
k
v
o
ltag
e
ar
o
u
n
d
its
p
r
e
-
d
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i
n
ed
r
ef
er
en
ce
v
al
u
e.
T
h
is
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e
p
er
f
o
r
m
an
ce
o
f
t
h
e
c
o
n
tr
o
ller
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n
d
er
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io
u
s
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n
d
iti
o
n
is
d
ep
icted
in
T
ab
le
2
.
Fig
u
r
e
10.
Simu
latio
n
r
esu
lts
of
lo
ad
c
h
an
g
e
o
p
e
r
atio
n
T
ab
le
2.
Per
f
o
r
m
an
ce
m
ea
s
u
r
e
s
C
r
i
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e
r
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a
t
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o
n
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o
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0
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9
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i
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9
8
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
A
n
imp
r
o
ve
d
WOA
o
f P
I
c
o
n
tr
o
l fo
r
th
r
ee
p
h
a
s
e
P
WM
r
ec
tifi
er
(
S
h
w
eth
a
G
)
47
4
.
5
.
I
m
ple
m
ent
a
t
io
n r
esu
lt
s
T
h
e
v
alid
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n
of
t
h
e
s
im
u
latio
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s
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y
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r
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ase
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ato
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In
th
e
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er
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in
ts
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e
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e
p
icted
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Fig
u
r
e
1
1
.
Fig
u
r
e
12
T
h
r
o
u
g
h
o
u
t
th
is
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am
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atio
n
,
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o
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ely
715
an
d
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e
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.
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h
e
r
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lts
in
d
icate
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m
ax
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m
in
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I
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52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
8
,
No
.
1
,
Ap
r
il
20
2
5
:
39
-
49
48
C
o
n
s
eq
u
en
tly
,
it
can
be
in
f
er
r
ed
th
at
th
e
s
u
g
g
ested
ap
p
r
o
ac
h
y
ield
s
a
s
tead
y
s
tate
er
r
o
r
clo
s
e
to
ze
r
o
.
Ad
d
itio
n
ally
,
wh
ich
also
d
e
p
icts
th
e
T
HD
d
u
r
in
g
f
u
ll
lo
a
d
o
p
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n
.
C
o
n
s
eq
u
en
tly
,
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e
v
o
ltag
e
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ip
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le
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n
d
e
r
th
e
m
o
s
t
d
em
an
d
i
n
g
co
n
d
iti
o
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s
(
f
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ll
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is
co
n
f
ir
m
e
d
to
be
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th
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%,
v
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atin
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tio
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r
f
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ce
of
th
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p
r
o
p
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t
r
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l
m
eth
o
d
.
5.
CO
NCLU
SI
O
N
T
h
er
e
ar
e
m
an
y
u
s
es
f
o
r
th
e
th
r
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p
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ase
v
o
ltag
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s
o
u
r
ce
PW
M
r
ec
tifie
r
in
p
o
wer
elec
tr
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cs
s
y
s
tem
s
,
an
d
r
esear
ch
er
s
ar
e
alwa
y
s
wo
r
k
in
g
to
im
p
r
o
v
e
its
co
n
tr
o
l
s
ch
em
es.
T
h
e
m
ath
em
atica
l
m
o
d
el
f
o
r
i
n
p
u
t
s
id
e
an
d
o
u
tp
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t
of
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p
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p
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r
is
d
er
iv
ed
in
th
is
s
tu
d
y
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T
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c
o
n
tr
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l
t
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h
n
iq
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p
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f
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m
s
ex
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ally
well
d
y
n
am
icall
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d
q
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v
ar
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s
in
lo
ad
by
r
esettin
g
to
a
p
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ed
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m
in
ed
v
alu
e
.
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r
eo
v
er
,
it
ef
f
icien
tly
cr
ea
t
es
a
s
in
u
s
o
id
al
wav
ef
o
r
m
out
of
th
e
n
etwo
r
k
-
s
id
e
cu
r
r
e
n
t,
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ed
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cin
g
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ar
m
o
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ic
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a
n
d
p
r
eser
v
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n
ity
PF
f
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ctio
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W
h
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co
m
p
ar
ed
to
co
n
v
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tio
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al
p
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ce
d
u
r
es,
th
is
tech
n
o
l
o
g
y
o
f
f
er
s
im
p
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v
e
d
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p
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a
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f
lex
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ilit
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.
T
h
e
m
ain
g
o
al
in
th
is
p
r
o
ject
is
to
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n
cr
ea
s
e
d
y
n
am
ically
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d
s
tatic
s
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f
o
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m
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n
ce
of
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al
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wo
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ld
ap
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licatio
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s
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te
n
d
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g
th
eir
ef
f
ec
tiv
e
v
o
ltag
e
-
co
n
tr
o
l
r
a
n
g
e.
RE
F
E
R
E
NC
E
S
[
1
]
Z.
L
i
,
Y
.
Li
,
P
.
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.
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Li
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.
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3
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A
.
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n
d
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.
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b
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e
sl
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[
4
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A
.
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.
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.
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h
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[
5
]
T.
N
a
,
X
.
Y
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a
n
,
J.
Ta
n
g
,
a
n
d
Q
.
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[
6
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J.
W
.
K
o
l
a
r
,
T.
F
r
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d
l
i
,
J.
R
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d
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,
a
n
d
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.
W
.
W
h
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,
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p
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7
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W
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.
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m,
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M
.
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,
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[
8
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Y
.
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g
,
Z.
W
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,
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Ji
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