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DST
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[
1
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Un
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d
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UP
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[
2
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[
2
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4
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h
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a
p
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p
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as
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etailed
in
[
5
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7
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.
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n
u
m
er
o
u
s
m
et
h
o
d
s
as d
etailed
in
[
8
-
12
].
B
o
u
teb
el
et
al.
[
8
]
h
as
u
s
ed
th
e
h
y
b
r
id
o
p
tim
izat
io
n
tech
n
iq
u
e
co
m
b
in
i
n
g
d
if
f
er
en
tial
e
v
o
lu
tio
n
a
n
d
P
SO
f
o
r
d
eter
m
i
n
i
n
g
t
h
e
o
p
ti
m
al
s
izi
n
g
a
n
d
lo
ca
tio
n
o
f
t
h
e
UP
QC
d
ev
ice
i
n
r
ad
ial
d
i
s
tr
ib
u
tio
n
s
y
s
te
m
s
.
Gan
g
u
l
y
et
a
l.
[
9
]
h
as
i
n
tr
o
d
u
ce
d
th
e
p
h
ase
an
g
le
co
n
tr
o
l
m
o
d
el
o
f
UP
QC
k
n
o
w
n
as
UP
Q
C
–
P
A
C
to
v
alid
ate
th
e
co
n
ce
p
t
o
f
m
ax
i
m
a
l
u
tili
z
atio
n
o
f
s
er
ies
in
v
er
ter
.
T
h
e
s
er
ies
in
v
er
ter
also
s
h
ar
e
s
th
e
l
o
ad
r
ea
ctiv
e
p
o
w
er
alo
n
g
w
it
h
t
h
e
s
h
u
n
t
i
n
v
er
ter
in
s
tead
y
s
tate
co
n
d
itio
n
s
,
lea
d
in
g
to
a
d
ec
r
ea
s
e
in
th
e
r
ati
n
g
o
f
s
h
u
n
t
i
n
v
er
ter
.
A
t
m
a
R
a
m
G
u
p
ta
et
al.
[
1
0
]
h
as
m
o
d
eled
th
e
s
h
u
n
t
co
m
p
e
n
s
ato
r
as
th
e
s
o
u
r
ce
o
f
1
MV
A
r
r
ea
ctiv
e
p
o
w
er
an
d
b
y
a
s
s
u
m
i
n
g
th
e
v
o
lta
g
e
at
t
h
e
ca
n
d
id
ate
b
u
s
a
s
1
p
.
u
.
T
h
e
v
al
u
e
o
f
s
er
ies
r
ea
cti
v
e
p
o
w
er
co
m
p
e
n
s
atio
n
i
s
ca
lcu
lated
in
t
h
e
s
tead
y
s
ta
te.
T
h
e
to
tal
p
o
w
er
lo
s
s
e
s
ar
e
ca
lcu
lated
b
y
p
lacin
g
t
h
e
ac
q
u
ir
e
d
s
ize
o
f
UP
QC
at
th
e
r
esp
ec
tiv
e
b
u
s
es.
T
h
e
b
u
s
h
av
i
n
g
t
h
e
m
in
i
m
u
m
v
al
u
e
o
f
lo
s
s
es
is
s
elec
ted
as
ca
n
d
i
d
ate
b
u
s
f
o
r
UP
QC
in
s
ta
llatio
n
.
M.
Ho
s
s
ei
n
i
et.
a
l
[
1
1
]
h
as
d
e
m
o
n
s
tr
ated
t
h
e
ef
f
ec
tiv
e
n
e
s
s
o
f
UP
QC
to
i
m
p
r
o
v
e
s
tead
y
s
tate
v
o
ltag
e.
S.
A
.
T
ah
er
et.
al
[
1
2
]
h
as
u
s
ed
Di
f
f
er
en
tial
E
v
o
lu
ti
o
n
(
DE
)
alg
o
r
ith
m
to
d
ec
id
e
th
e
o
p
ti
m
al
lo
ca
tio
n
o
f
u
n
if
ied
p
o
w
er
q
u
alit
y
co
n
d
itio
n
er
f
o
r
d
if
f
er
e
n
t
lo
ad
in
g
co
n
d
itio
n
s
a
n
d
al
s
o
th
e
s
a
v
i
n
g
s
w
it
h
UP
QC
ar
e
o
b
tain
ed
.
DE
r
esu
lts
ar
e
co
m
p
ar
ed
w
ith
Ge
n
etic
Alg
o
r
it
h
m
(
GA
)
a
n
d
I
m
m
u
n
e
A
l
g
o
r
ith
m
(
I
A
)
.
T
h
is
p
ap
er
also
ex
p
lo
r
es
th
e
ca
p
ab
ilit
y
o
f
s
er
ies
a
n
d
s
h
u
n
t
co
m
p
en
s
a
to
r
o
f
UP
QC
to
p
a
r
ticip
ate
in
lo
ad
r
ea
ctiv
e
p
o
w
er
co
m
p
e
n
s
atio
n
i
n
s
te
ad
y
s
tate
b
y
a
n
e
w
Op
ti
m
iza
tio
n
m
et
h
o
d
k
n
o
w
n
as
a
Mo
th
Fla
m
e
Op
ti
m
izatio
n
m
e
th
o
d
.
T
h
e
lo
s
s
es
a
n
d
v
o
lta
g
es
f
o
r
th
e
n
et
w
o
r
k
ar
e
o
b
tain
ed
w
it
h
th
e
l
o
ad
f
lo
w
m
eth
o
d
d
escr
ib
ed
in
th
e
f
o
llo
w
i
n
g
s
ec
t
io
n
2.
RADIA
L
DI
ST
R
I
B
UT
I
O
N
SYST
E
M
L
O
AD
F
L
O
W
L
o
ad
f
lo
w
is
a
n
i
m
p
o
r
ta
n
t
to
o
l
to
ass
ess
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
S.
D.
C
h
ia
n
g
et.
al
[
1
3
]
h
as d
ev
elo
p
ed
d
ec
o
u
p
led
an
d
f
ast
d
ec
o
u
p
led
lo
ad
f
lo
w
m
et
h
o
d
.
S.
Gh
o
s
h
et
a
l.
[
1
4
]
h
as d
ev
elo
p
ed
a
lo
ad
f
lo
w
m
et
h
o
d
b
ased
o
n
e
s
ti
m
atio
n
o
f
e
f
f
ec
t
iv
e
r
ea
l
a
n
d
r
ea
cti
v
e
p
o
w
er
lo
ad
s
.
J
.
H.
T
en
g
et.
al
[
1
5
]
h
as
p
r
o
p
o
s
ed
t
w
o
m
atr
ices
B
u
s
I
n
j
ec
tio
n
to
B
r
an
ch
C
u
r
r
en
t
(
B
I
B
C
)
an
d
B
r
an
ch
C
u
r
r
en
t
to
B
u
s
Vo
lta
g
e
(
B
C
B
V)
to
s
o
lv
e
th
e
lo
ad
f
lo
w
eq
u
at
io
n
s
.
Her
e
th
e
ac
ti
v
e
p
o
w
er
lo
ad
an
d
r
ea
ctiv
e
p
o
w
er
lo
ad
at
t
h
e
m
t
h
b
u
s
is
d
e
n
o
ted
b
y
(
)
an
d
(
)
r
esp
ec
tiv
el
y
.
(
)
: V
o
ltag
e
at
th
e
m
t
h
b
u
s
: B
r
an
ch
cu
r
r
en
t a
n
d
:
L
o
ad
cu
r
r
en
t
(
)
,
(
)
ar
e
th
e
r
ec
eiv
in
g
en
d
n
o
d
e
v
o
ltag
e
an
d
s
e
n
d
in
g
en
d
n
o
d
e
v
o
ltag
e
r
esp
ec
tiv
el
y
.
(
)
,
(
)
an
d
(
)
ar
e
th
e
i
m
p
ed
an
ce
,
r
esis
tan
ce
an
d
r
ea
ctan
ce
f
o
r
th
e
it
h
b
r
an
ch
r
esp
ec
tiv
e
l
y
.
C
alcu
latio
n
o
f
lo
ad
cu
r
r
en
ts
:
(
)
(
(
)
(
)
(
)
)
(
1
)
Fo
r
m
atio
n
o
f
B
I
B
C
m
a
tr
ix
:
B
y
ap
p
l
y
in
g
t
h
e
Kir
ch
h
o
f
f
’
s
C
u
r
r
en
t
L
a
w
to
t
h
e
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
,
B
I
B
C
m
atr
ix
ca
n
b
e
f
o
r
m
ed
.
C
o
n
s
id
er
a
s
ix
b
u
s
n
et
w
o
r
k
wh
ich
i
s
s
h
o
w
n
i
n
Fi
g
u
r
e
1.
Fig
u
r
e
1
.
Six
b
u
s
s
y
s
te
m
n
e
t
wo
r
k
co
n
f
i
g
u
r
atio
n
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.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
5
3
0
–
5
3
7
532
T
h
e
B
I
B
C
m
atr
ix
,
w
h
ic
h
g
i
v
e
s
th
e
r
elatio
n
b
et
w
ee
n
lo
ad
an
d
b
r
an
ch
cu
r
r
en
t
s
,
f
o
r
Fig
u
r
e
1
is
g
iv
e
n
as
[
]
[
]
[
]
[
]
[
]
[
]
(
2
)
B
us
vol
ta
ge
is
ob
ta
i
n
e
d
b
y
E
q
ua
tion
(
4
)
(
)
(
)
(
)
(
3
)
(
)
(
)
(
)
(
4
)
T
h
e
er
r
o
r
in
v
o
ltag
e
i
s
ca
lcu
lat
ed
.
I
f
th
e
er
r
o
r
is
less
th
a
n
to
le
r
an
ce
th
e
n
th
e
lo
ad
f
lo
w
co
n
v
er
g
es.
T
h
e
p
o
w
er
lo
s
s
e
s
in
a
d
is
tr
ib
u
t
io
n
s
y
s
te
m
ar
e
g
i
v
en
b
y
(
5
)
an
d
(
6
)
∑
(
(
)
)
(
)
(
5
)
∑
(
(
)
)
(
)
(
6
)
Her
e
n
is
t
h
e
to
tal
n
u
m
b
er
o
f
b
r
an
ch
es.
3.
UP
Q
C
S
T
RUC
T
UR
E
A
UP
QC
a
s
th
e
co
m
b
i
n
atio
n
o
f
s
er
ies a
n
d
s
h
u
n
t c
o
m
p
e
n
s
ato
r
is
d
is
p
la
y
ed
in
Fi
g
u
r
e
2
[
3
]
.
Fig
u
r
e
2
.
E
q
u
iv
ale
n
t c
ir
cu
it o
f
UP
QC
Her
e
is
th
e
s
en
d
in
g
en
d
v
o
ltag
e,
is
th
e
s
o
u
r
ce
i
m
p
ed
an
ce
,
P
C
C
is
th
e
p
o
n
t
o
f
co
m
m
o
n
co
u
p
lin
g
,
is
th
e
v
o
ltag
e
in
j
ec
ted
b
y
s
er
ies
co
m
p
en
s
ato
r
,
is
th
e
s
h
u
n
t
co
m
p
e
n
s
ati
n
g
cu
r
r
en
t
an
d
i
s
th
e
lo
ad
b
u
s
v
o
lta
g
e.
T
h
e
s
er
ies
co
m
p
e
n
s
ato
r
g
e
n
er
ates
a
v
o
ltag
e
a
n
d
in
j
ec
ts
it
in
s
er
ies
w
it
h
th
e
li
n
e
n
ea
r
to
th
e
r
ec
eiv
in
g
en
d
s
u
c
h
t
h
at
th
e
v
o
lta
g
e
at
th
e
l
o
ad
s
id
e
is
al
w
a
y
s
m
ai
n
tai
n
ed
at
d
esire
d
v
o
ltag
e
m
a
g
n
i
tu
d
e.
T
h
e
n
e
w
lo
ad
b
u
s
v
o
ltag
e
,
af
ter
in
j
ec
tin
g
v
o
lta
g
e
b
y
t
h
e
s
er
ies
co
m
p
en
s
ato
r
is
ca
lcu
lated
as
g
iv
e
n
i
n
E
q
u
atio
n
(
7
)
(
7
)
T
h
e
co
m
p
lex
p
o
w
er
o
b
tain
ed
b
y
t
h
e
s
er
ie
s
co
m
p
en
s
ato
r
is
o
b
tain
ed
as f
o
llo
w
s
:
(
8
)
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
Mo
th
F
la
me
Op
timiz
a
tio
n
Meth
o
d
fo
r
Un
ified
P
o
w
er
Qu
a
lity Co
n
d
itio
n
er
…
(
M.
La
xmid
ev
i
R
a
ma
n
a
i
a
h
)
533
Her
e
is
th
e
b
r
an
ch
c
u
r
r
en
t i
n
w
h
ic
h
s
er
ies co
m
p
e
n
s
ato
r
is
i
n
clu
d
ed
.
T
h
e
f
u
n
c
tio
n
o
f
s
h
u
n
t c
o
m
p
en
s
ato
r
is
to
p
r
o
v
id
e
lo
ad
VA
r
s
u
p
p
o
r
t.
Fig
u
r
e
3
s
h
o
w
s
t
h
e
p
h
a
s
o
r
d
iag
r
a
m
f
o
r
s
er
ies v
o
lta
g
e
i
n
j
ec
tio
n
.
Fig
u
r
e
3
.
P
h
aso
r
d
iag
r
a
m
f
o
r
s
er
ies v
o
ltag
e
i
n
j
ec
tio
n
T
h
e
UP
QC
s
er
ies
co
m
p
en
s
a
t
o
r
is
m
o
d
eled
as
a
s
o
u
r
ce
o
f
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
w
h
e
r
ea
s
s
h
u
n
t
co
m
p
e
n
s
ato
r
is
m
o
d
eled
as
th
e
s
o
u
r
ce
o
f
r
ea
ctiv
e
p
o
w
er
.
W
ith
th
e
i
n
j
ec
tio
n
o
f
v
o
ltag
e
b
y
t
h
e
s
er
ies
co
m
p
e
n
s
ato
r
,
th
e
r
ec
eiv
in
g
en
d
v
o
lta
g
e
is
ch
a
n
g
ed
to
.
T
h
e
r
ea
ctiv
e
p
o
w
er
to
b
e
in
j
e
cted
is
ca
lcu
lated
as
g
iv
e
n
i
n
E
q
u
atio
n
(
9
)
.
(
9
)
co
m
p
e
n
s
ati
n
g
cu
r
r
en
t a
f
ter
s
e
r
ies co
m
p
en
s
a
tio
n
w
h
ic
h
is
ca
l
cu
lated
as g
iv
e
n
i
n
[
1
6
]
.
4.
M
O
T
H
F
L
AM
E
O
P
T
I
M
I
Z
AT
I
O
N
T
h
e
in
s
p
ir
atio
n
o
f
t
h
is
al
g
o
r
ith
m
[
1
7
]
is
th
e
n
av
ig
at
io
n
m
et
h
o
d
o
f
m
o
th
s
k
n
o
w
n
as
tr
an
s
v
er
s
e
o
r
ien
tatio
n
.
Mo
t
h
s
f
l
y
at
n
i
g
h
t
u
s
i
n
g
t
h
e
m
o
o
n
li
g
h
t.
B
y
k
ee
p
in
g
a
c
o
n
s
tan
t
an
g
le
co
n
ce
r
n
i
n
g
t
h
e
m
o
o
n
,
m
o
t
h
s
f
l
y
in
s
tr
aig
h
t
li
n
e
to
ac
h
ie
v
e
th
e
g
o
al.
T
h
e
co
n
v
er
g
e
n
ce
o
f
m
o
t
h
s
i
s
to
w
ar
d
s
th
e
li
g
h
t.
Si
m
i
lar
to
m
o
th
s
,
f
la
m
es
ar
e
th
e
k
e
y
ele
m
e
n
ts
o
f
th
is
o
p
ti
m
izat
io
n
b
ased
o
n
wh
ich
t
h
e
m
o
t
h
s
u
p
d
ate
th
eir
p
o
s
itio
n
s
.
Fla
m
es
ar
e
th
e
b
est
s
o
lu
tio
n
s
.
I
n
ea
ch
ite
r
atio
n
th
e
f
la
m
e
s
ar
e
s
o
r
ted
b
ased
o
n
f
it
n
ess
.
T
h
e
m
o
t
h
s
u
p
d
ate
th
eir
p
o
s
itio
n
s
w
it
h
r
esp
ec
t
to
th
eir
co
r
r
esp
o
n
d
in
g
f
la
m
e
s
.
T
h
e
p
r
in
cip
al
m
o
th
d
ep
en
d
ab
l
y
u
p
d
ates
its
p
o
s
itio
n
co
n
ce
r
n
i
n
g
th
e
b
est f
la
m
e.
T
h
e
n
u
m
b
er
o
f
f
la
m
es d
ec
r
ea
s
es a
d
ap
tiv
el
y
o
v
er
th
e
co
u
r
s
e
o
f
iter
atio
n
s
.
4.
1.
A
l
gori
t
h
m
f
o
r
f
i
nd
i
ng
t
he
L
ocat
i
on an
d S
e
ri
es
C
o
m
pensat
o
r V
ol
t
age
o
f
U
PQ
C
Ste
p
1
:
I
n
itialize
th
e
m
o
t
h
p
o
p
u
latio
n
s
ize,
m
ax
i
m
u
m
iter
at
io
n
s
,
d
i
m
e
n
s
io
n
s
o
f
t
h
e
s
ea
r
ch
s
p
ac
e,
m
in
i
m
u
m
an
d
m
a
x
i
m
u
m
li
m
it
s
o
f
t
h
e
m
o
th
p
o
s
itio
n
s
.
Ste
p 2
:
R
u
n
t
h
e
lo
ad
f
lo
w
a
n
d
f
in
d
t
h
e
r
ea
l p
o
w
er
lo
s
s
b
ef
o
r
e
o
p
tim
iza
tio
n
.
Ste
p
3
:
Gen
er
ate
r
an
d
o
m
l
y
th
e
m
o
th
p
o
s
it
io
n
s
o
f
t
h
e
o
r
d
er
[
]
w
it
h
i
n
th
e
l
i
m
i
ts
,
w
h
er
e
m
d
en
o
tes
t
h
e
m
o
th
p
o
p
u
latio
n
s
ize
a
n
d
n
d
en
o
tes
t
h
e
d
i
m
e
n
s
io
n
.
T
h
e
d
im
en
s
io
n
s
ar
e
lo
ca
tio
n
,
r
ea
l
an
d
i
m
a
g
in
ar
y
p
ar
t
o
f
s
er
ies in
j
ec
ted
v
o
lta
g
e,
f
o
r
o
n
e
UP
QC
.
Hen
ce
,
n
i
s
ass
u
m
ed
as 3
.
Ste
p 4
:
Set th
e
iter
at
io
n
co
u
n
t to
1
.
Ste
p 5
:
Fin
d
th
e
n
u
m
b
er
o
f
f
la
m
es
u
s
i
n
g
E
q
u
atio
n
(
1
0
)
.
Nu
m
b
er
o
f
f
la
m
es
(
)
(
1
0
)
Her
e
N
is
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
f
la
m
es,
m
is
t
h
e
cu
r
r
en
t
iter
atio
n
n
u
m
b
er
an
d
T
is
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
.
Ste
p
6
:
R
u
n
t
h
e
lo
ad
f
lo
w
b
y
in
j
ec
tin
g
th
e
v
o
lta
g
e
at
th
e
co
r
r
esp
o
n
d
in
g
lo
ca
tio
n
as
g
i
v
en
i
n
E
q
u
atio
n
(
7
)
an
d
b
y
i
n
j
ec
tin
g
th
e
r
ea
cti
v
e
p
o
w
e
r
as g
iv
e
n
i
n
E
q
u
atio
n
(
9
)
.
Ste
p
7
:
E
v
alu
ate
t
h
e
f
itn
e
s
s
.
Dis
ca
r
d
th
e
m
o
th
s
w
h
ich
v
io
late
th
e
co
n
s
tr
ai
n
t
th
a
t
th
e
v
o
lta
g
e
a
t
th
e
co
r
r
esp
o
n
d
in
g
lo
ca
tio
n
s
h
o
u
ld
n
o
t e
x
ce
ed
1
p
.
u
.
So
r
t th
e
m
o
t
h
s
b
ased
o
n
f
itn
e
s
s
v
al
u
es.
Ste
p
8
:
I
n
it
ialize
t
h
ese
m
o
t
h
s
as
f
la
m
es
a
n
d
f
it
n
ess
v
al
u
e
s
as
f
la
m
e
f
i
tn
e
s
s
e
s
.
I
f
c
u
r
r
en
t
i
ter
atio
n
n
u
m
b
er
is
g
r
ea
ter
th
an
1
th
e
n
s
o
r
t
th
e
m
o
th
s
b
ased
o
n
f
it
n
es
s
v
al
u
e
s
o
f
th
e
m
o
t
h
s
i
n
th
e
p
r
ev
io
u
s
iter
atio
n
a
n
d
th
e
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
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n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
5
3
0
–
5
3
7
534
cu
r
r
en
t
iter
atio
n
an
d
a
s
s
i
g
n
t
h
ese
to
f
la
m
es.
Select
t
h
e
b
est
f
la
m
e
f
it
n
e
s
s
a
n
d
i
ts
co
r
r
esp
o
n
d
in
g
f
la
m
e
p
o
s
itio
n
k
n
o
w
n
as b
est
f
la
m
e
p
o
s
itio
n
.
Ste
p 9
:
I
n
itialize
g
iv
e
n
b
y
E
q
u
atio
n
(
1
1
)
(
)
(
)
(
1
1
)
Ste
p 1
0
:
C
alcu
late
t
h
e
d
is
ta
n
c
e
o
f
th
e
p
th
m
o
t
h
f
o
r
th
e
q
th
f
la
m
e
u
s
i
n
g
E
q
u
at
io
n
(
1
2
)
(
1
2
)
Ste
p 1
1
:
Up
d
ate
th
e
p
o
s
itio
n
o
f
th
e
m
o
t
h
u
s
in
g
E
q
u
atio
n
(
1
3
)
(
)
(
1
3
)
W
h
er
e
S=Sp
ir
al
f
u
n
ct
io
n
.
T
h
e
Sp
ir
al
Fu
n
ctio
n
i
s
g
i
v
e
n
in
E
q
u
atio
n
(
1
4
)
(
)
(
)
(
1
4
)
W
h
er
e
(
)
(
1
5
)
b
is
a
co
n
s
tan
t
w
h
ic
h
d
ef
in
e
s
t
h
e
s
h
ap
e
o
f
th
e
s
p
ir
al
f
u
n
ct
io
n
(
lo
g
ar
ith
m
ic
s
p
ir
al)
.
I
t
is
ass
u
m
ed
as
1
in
th
is
p
ap
er
.
Ste
p 1
2
:
I
n
cr
ea
s
e
th
e
iter
atio
n
n
u
m
b
er
.
Ste
p 1
3
:
R
ep
r
is
e
th
e
s
tep
s
f
r
o
m
5
-
1
2
u
n
til t
h
e
iter
atio
n
s
r
ea
ch
th
eir
m
a
x
i
m
u
m
li
m
it.
Ste
p
1
4
:
Dis
p
lay
t
h
e
b
est
f
la
m
e
f
i
tn
e
s
s
an
d
th
e
co
r
r
esp
o
n
d
in
g
b
est
f
la
m
e
p
o
s
itio
n
w
h
ich
g
iv
e
s
th
e
lo
ca
tio
n
o
f
UP
QC
an
d
v
o
ltag
e
i
n
j
ec
ted
b
y
t
h
e
s
er
ie
s
co
m
p
e
n
s
ato
r
.
P
r
in
t
th
e
r
e
s
u
l
ts
f
o
r
r
ea
l
a
n
d
r
ea
ctiv
e
i
n
j
ec
ted
b
y
t
h
e
s
er
ies co
m
p
en
s
ato
r
an
d
r
ea
ctiv
e
p
o
w
er
in
j
ec
ted
b
y
th
e
s
h
u
n
t
co
m
p
e
n
s
ato
r
.
5.
RE
SU
L
T
S
T
h
e
test
s
y
s
te
m
s
co
n
s
id
er
ed
f
o
r
ch
ec
k
in
g
t
h
e
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f
ec
t
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e
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es
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o
f
t
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e
p
r
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p
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et
h
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d
ar
e
1
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u
s
,
34
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b
u
s
a
n
d
3
3
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u
s
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y
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te
m
s
.
T
h
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lo
s
s
es,
v
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g
e
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r
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ile,
l
o
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tio
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d
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l
a
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d
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e
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o
w
er
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ted
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y
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QC
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e
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5
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1
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f
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10
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2
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p
e
n
s
ato
r
p
r
o
v
id
es
b
o
th
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
an
d
s
h
u
n
t
co
m
p
en
s
ato
r
p
r
o
v
id
es
th
e
r
eq
u
ir
ed
lo
ad
r
ea
ctiv
e
p
o
w
er
.
T
h
is
f
u
n
ctio
n
alit
y
o
f
UP
QC
allo
w
s
th
e
s
er
ies
co
m
p
e
n
s
ato
r
to
ta
k
e
p
ar
t
in
r
ea
cti
v
e
p
o
w
er
co
m
p
e
n
s
at
io
n
.
T
h
e
b
est lo
ca
tio
n
an
d
co
m
p
lex
v
o
lta
g
e
in
j
ec
t
ed
b
y
s
er
ies co
m
p
en
s
ato
r
o
f
U
P
QC
is
o
b
tain
ed
b
y
u
s
i
n
g
MFO.
MFO
h
as
s
tr
o
n
g
co
n
v
er
g
e
n
ce
c
h
ar
ac
ter
is
tics
f
o
r
s
o
lv
in
g
t
h
e
p
r
o
b
lem
o
f
UP
Q
C
p
lace
m
e
n
t.
T
h
e
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
Mo
th
F
la
me
Op
timiz
a
tio
n
Meth
o
d
fo
r
Un
ified
P
o
w
er
Qu
a
lity Co
n
d
itio
n
er
…
(
M.
La
xmid
ev
i
R
a
ma
n
a
i
a
h
)
537
r
esu
lt
s
p
r
o
v
e
th
e
ef
f
ec
ti
v
en
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
to
r
ed
u
ce
r
ea
l
p
o
w
er
lo
s
s
e
s
an
d
im
p
r
o
v
e
th
e
v
o
lta
g
e
p
r
o
f
ile.
C
o
m
p
ar
ativ
e
r
es
u
lt
s
d
e
m
o
n
s
tr
ate
th
e
e
f
f
ec
ti
v
en
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
m
e
th
o
d
.
RE
F
E
R
E
NC
E
S
[1
]
A
.
R.
G
u
p
ta
,
e
t
a
l.
,
“
Op
ti
ma
l
D
-
S
T
AT
COM
Pl
a
c
e
me
n
t
in
R
a
d
ia
l
Distrib
u
ti
o
n
S
y
ste
m
Ba
se
d
o
n
P
o
we
r
L
o
ss
In
d
e
x
Ap
p
ro
a
c
h
,
”
I
n
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
En
e
rg
y
,
P
o
w
e
r
a
n
d
En
v
i
ro
n
m
e
n
t:
T
o
w
a
rd
s
S
u
sta
in
a
b
le
G
ro
w
th
(ICE
P
E
)
2
0
1
5
,
p
p
.
1
-
5
.
d
o
i
:1
0
.
1
1
5
5
/2
0
1
2
/
8
3
8
6
2
9
[2
]
V
.
Kh
a
d
k
ik
a
r
,
e
t
a
l.
,
“
En
h
a
n
c
i
n
g
El
e
c
tri
c
P
o
w
e
r
Qu
a
li
t
y
Us
in
g
UP
QC:
A
Co
m
p
re
h
e
n
siv
e
O
v
e
rv
ie
w
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
i
c
s
,
v
o
l.
2
7
,
p
p
.
2
2
8
4
–
2
2
9
7
,
2
0
1
2
.
[3
]
V
.
Kh
a
d
k
ik
a
r
,
e
t
a
l.
,
“
Co
n
c
e
p
tu
a
l
S
tu
d
y
o
f
Un
if
ied
Po
we
r
Qu
a
l
it
y
Co
n
d
it
io
n
e
r
(
UPQC)
,”
2
0
0
6
IEE
E
In
tern
a
ti
o
n
a
l
S
y
m
p
o
siu
m
o
n
In
d
u
strial
El
e
c
tro
n
ics
,
M
o
n
trea
l,
Qu
e
b
e
c
,
2
0
0
6
[4
]
V
.
Kh
a
d
k
ik
a
r
,
e
t
a
l.
,
“
U
P
QC
-
S
:
A
n
o
v
e
l
c
o
n
c
e
p
t
o
f
sim
u
lt
a
n
e
o
u
s
v
o
lt
a
g
e
sa
g
/s
w
e
ll
a
n
d
lo
a
d
re
a
c
ti
v
e
p
o
we
r
c
o
m
p
e
n
sa
ti
o
n
s
u
ti
li
z
i
n
g
se
ries
in
v
e
rter
o
f
UP
QC,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
ics
,
v
o
l.
2
6
,
p
p
.
2
4
1
4
–
2
4
2
5
,
2
0
1
1
.
[5
]
K.Ra
m
a
li
n
g
e
s
w
a
r
a
Ra
o
,
e
t
a
l.
,
“
Im
p
ro
v
e
m
e
n
t
o
f
P
o
w
e
r
Qu
a
li
ty
u
sin
g
F
u
z
z
y
L
o
g
ic
Co
n
tro
ll
e
r
In
G
rid
Co
n
n
e
c
ted
P
h
o
t
o
v
o
lt
a
ic
Ce
ll
Us
in
g
UP
QC
,
”
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
m
(
IJ
PE
DS
)
,
v
o
l.
5
,
n
o
.
1
,
p
p
.
1
0
1
-
1
1
1
,
2
0
1
4
.
[6
]
K.
S
a
i
T
e
ja,
e
t
a
l.
,
“
P
o
w
e
r
Qu
a
li
ty
I
m
p
ro
v
e
m
e
n
t
Us
in
g
Cu
sto
m
P
o
w
e
r
D
e
v
ic
e
s
in
S
q
u
irrel
Ca
g
e
In
d
u
c
ti
o
n
G
e
n
e
r
a
to
r
W
in
d
F
a
rm
to
W
e
a
k
-
G
rid
Co
n
n
e
c
ti
o
n
b
y
u
sin
g
Ne
u
ro
-
f
u
z
z
y
Co
n
tro
l
”
,
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
m (
IJ
PE
DS
)
,
v
o
l
.
5
,
n
o
.
4
,
p
p
.
4
7
7
-
4
8
5
,
2
0
1
5
.
[7
]
R.
S
a
ra
v
a
n
a
n
,
e
t
a
l
.
,
“
Ne
u
ro
F
u
z
z
y
B
a
se
d
Un
if
ied
P
o
w
e
r
Qu
a
li
t
y
Co
n
d
it
io
n
e
r
f
o
r
P
o
w
e
r
Qu
a
li
t
y
I
m
p
ro
v
e
m
e
n
t
F
e
d
In
d
u
c
ti
o
n
M
o
to
r
Driv
e
,
”
IAE
S
I
n
t
e
rn
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Arti
fi
c
i
a
l
In
telli
g
e
n
c
e
(
IJ
-
AI)
,
v
o
l.
4
,
n
o
.
1
,
p
p
.
1
-
7
,
2
0
1
5
.
[8
]
M
.
Bo
u
teb
e
l
,
e
t
a
l
.
,
“
Op
ti
m
a
l
S
tea
d
y
S
tate
Op
e
ra
ti
o
n
o
f
Un
if
ied
P
o
w
e
r
Qu
a
li
t
y
Co
n
d
it
i
o
n
e
r
f
o
r
P
o
w
e
r
L
o
ss
e
s
Re
d
u
c
ti
o
n
a
n
d
V
o
l
tag
e
Re
g
u
latio
n
Im
p
ro
v
e
m
e
n
t,
”
J
o
u
rn
a
l
o
f
El
e
c
t
ric
a
l
En
g
in
e
e
rin
g
,
v
o
l
.
1
4
,
p
p
.
1
1
4
-
1
2
1
,
2
0
1
4
.
[9
]
S
.
G
a
n
g
u
ly
,
e
t
a
l.
,
“
Un
if
ied
p
o
w
e
r
q
u
a
li
ty
c
o
n
d
it
io
n
e
r
a
ll
o
c
a
ti
o
n
f
o
r
re
a
c
ti
v
e
p
o
w
e
r
c
o
m
p
e
n
s
a
ti
o
n
o
f
ra
d
ia
l
d
istri
b
u
ti
o
n
n
e
tw
o
rk
s,
”
IET
Ge
n
e
ra
ti
o
n
,
T
r
a
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
,
v
o
l
.
8
,
p
p
.
1
4
1
8
–
1
4
2
9
,
2
0
1
4
.
[1
0
]
A
.
R.
G
u
p
ta
,
e
t
a
l.
,
“
P
e
rf
o
r
m
a
n
c
e
A
n
a
l
y
sis
o
f
R
a
d
ial
Distrib
u
ti
o
n
S
y
ste
m
s
w
it
h
UP
QC
a
n
d
D
-
S
TAT
COM,
”
J
o
u
rn
a
l
o
f
In
sti
tu
ti
o
n
o
f
En
g
in
e
e
r
s,
In
d
i
a
S
e
r.
B
,
p
p
.
1
-
8
,
2
0
1
6
.
[1
1
]
M
.
Ho
ss
e
in
i
,
e
t
a
l.
,
“
M
o
d
e
li
n
g
o
f
u
n
if
ied
p
o
w
e
r
q
u
a
li
ty
c
o
n
d
it
io
n
e
r
(UP
QC)
i
n
d
istri
b
u
ti
o
n
sy
ste
m
s
lo
a
d
f
lo
w
,
”
En
e
rg
y
Co
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t
,
v
o
l.
5
0
,
p
p
.
1
5
7
8
–
1
5
8
5
,
2
0
0
9
.
[1
2
]
S
.
A
.
T
a
h
e
r
,
e
t
a
l.
,
“
Op
ti
m
a
l
L
o
c
a
ti
o
n
a
n
d
S
izin
g
o
f
UP
QC
in
Dis
tri
b
u
t
io
n
Ne
tw
o
rk
s
Us
in
g
Diff
e
r
e
n
ti
a
l
Ev
o
l
u
ti
o
n
A
l
g
o
rit
h
m
,
”
M
a
th
e
ma
ti
c
a
l
Pro
b
le
ms
in
e
n
g
in
e
e
rin
g
,
v
o
l.
2
0
1
2
,
p
p
.
1
-
2
0
,
2
0
1
2
.
[1
3
]
H.
D.
Ch
ian
g
,
e
t
a
l.
,
“
A
d
e
c
o
u
p
l
e
d
lo
a
d
f
lo
w
-
m
e
th
o
d
f
o
r
d
istr
ib
u
ti
o
n
p
o
w
e
r
n
e
tw
o
rk
s:
A
lg
o
rit
h
m
s,
a
n
a
ly
sis
a
n
d
c
o
n
v
e
rg
e
n
c
e
stu
d
y
,
”
El
e
c
tric P
o
w
e
r a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
1
3
,
p
p
.
1
3
0
–
1
3
8
,
1
9
9
1
.
[1
4
]
S
.
G
h
o
sh
,
e
t
a
l.
,
“
M
e
t
h
o
d
f
o
r
l
o
a
d
so
l
u
ti
o
n
o
f
ra
d
ial
d
istri
b
u
ti
o
n
n
e
tw
o
rk
s
,
”
IEE
Pro
c
e
e
d
i
n
g
s
o
n
Ge
n
e
ra
t
io
n
,
T
ra
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
,
v
o
l.
1
4
6
,
p
p
.
6
4
1
–
6
4
8
,
1
9
9
9
.
[1
5
]
J.
H.
T
e
n
g
,
e
t
a
l.
,
“
A
d
irec
t
a
p
p
r
o
a
c
h
f
o
r
d
istri
b
u
ti
o
n
sy
ste
m
lo
a
d
f
lo
w
so
lu
ti
o
n
s,”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Po
we
r
De
li
v
e
ry
,
v
o
l.
1
8
,
p
p
.
8
8
2
–
8
8
7
,
2
0
0
3
.
[1
6
]
M
.
H.Ha
q
u
e
,
e
t
a
l.
,
“
C
a
p
a
c
it
o
r
p
la
c
e
me
n
t
in
r
a
d
i
a
l
d
istri
b
u
ti
o
n
sy
ste
ms
fo
r
lo
ss
re
d
u
c
ti
o
n
,
”
IE
E
P
r
o
c
e
e
d
in
g
s
-
G
e
n
e
r
a
ti
o
n
T
ra
n
sm
issio
n
,
Distrib
u
ti
o
n
,
v
o
l
.
1
4
6
,
p
p
.
5
0
1
-
5
0
5
,
1
9
9
9
.
[1
7
]
S
.
M
irj
a
li
li
,
e
t
a
l.
,
“
M
o
t
h
-
f
la
m
e
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
:
A
n
o
v
e
l
n
a
tu
re
-
in
s
p
ired
h
e
u
r
isti
c
p
a
ra
d
ig
m
,
”
Kn
o
wled
g
e
-
Ba
se
d
S
y
ste
ms
,
v
o
l.
8
9
,
p
p
.
2
2
8
–
2
4
9
,
2
0
1
5
.
[1
8
]
M
.
Ch
is
,
e
t
a
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