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r
n
o
f
Un
i
te
d
S
t
a
te
s
,
an
d
th
e
C
an
a
d
ia
n
p
r
o
v
in
c
e
o
f
On
ta
r
i
o
.
T
h
e
h
ig
h
r
e
a
c
t
iv
e
o
u
t
p
u
t
p
o
w
e
r
,
d
u
e
t
o
t
h
e
c
o
n
t
ac
t
w
it
h
t
r
e
e
s
,
c
a
u
s
e
d
th
e
in
i
ti
a
l
d
is
tu
r
b
a
n
c
e
s
[
6
]
.
T
h
e
d
i
s
t
u
r
b
an
c
e
t
h
at
af
f
e
c
te
d
th
e
e
le
c
t
r
ic
a
l
p
o
w
e
r
n
e
tw
o
r
k
o
f
I
t
aly
s
y
s
t
em
in
S
e
p
t
em
b
e
r
2
8
,
2
0
0
3
[
7
]
.
T
h
e
M
o
s
c
o
w
’
s
s
y
s
tem
d
i
s
tu
r
b
an
c
e
o
f
2
5
M
ay
2
0
0
5
,
t
h
e
B
r
a
z
i
l’
s
s
y
s
t
em
d
is
tu
r
b
an
c
e
o
f
N
o
v
em
b
e
r
1
0
,
2
0
0
9
,
t
h
e
T
o
k
y
o
s
y
s
t
e
m
d
i
s
tu
r
b
an
c
e
o
f
M
a
r
ch
1
1
,
2
0
1
1
,
a
n
d
th
e
I
n
d
i
a’
s
s
y
s
t
em
d
is
tu
r
b
a
n
c
e
o
f
J
u
ly
3
1
,
2
0
1
2
[
8
]
a
r
e
f
ew
e
x
am
p
l
e
s
.
Ne
w
m
o
n
ito
r
in
g
tec
h
n
iq
u
e
s
m
a
k
e
it
p
o
s
s
ib
le
to
i
m
p
r
o
v
e
t
h
e
co
n
tr
o
l
o
f
tr
an
s
it
s
o
n
e
x
is
ti
n
g
tr
an
s
m
is
s
io
n
lin
e
s
a
n
d
in
cr
ea
s
e
n
et
w
o
r
k
tr
a
n
s
p
o
r
t
ca
p
ac
ities
(
lo
ad
ab
ilit
y
)
.
T
h
ese
tec
h
n
o
lo
g
ical
s
o
l
u
tio
n
s
ar
e
b
ased
o
n
p
o
w
er
elec
tr
o
n
ics
ar
e
g
en
er
all
y
ca
lled
F
A
C
T
S,
an
ac
r
o
n
y
m
o
f
"
Flex
ib
le
Alter
n
ati
v
e
C
u
r
r
e
n
t
T
r
an
s
m
is
s
io
n
S
y
s
te
m
s
"
.
T
h
e
FAC
T
S
w
a
s
b
o
r
n
in
th
e
1
9
7
0
s
,
an
d
ce
r
tain
tec
h
n
o
lo
g
ies
ar
e
c
u
r
r
en
tl
y
i
n
s
tal
led
o
n
th
e
elec
tr
ical
n
et
w
o
r
k
.
T
h
u
s
,
th
e
SV
C
(
s
ta
tic
v
ar
co
m
p
e
n
s
ato
r
)
an
d
th
eir
i
m
p
r
o
v
e
m
en
t
s
,
th
e
ST
A
T
C
OM
s
(
k
n
o
w
n
as
s
tatic
s
y
n
ch
r
o
n
o
u
s
co
m
p
e
n
s
ato
r
)
ar
e
th
e
m
o
s
t
m
a
tu
r
e
tech
n
o
lo
g
ie
s
.
T
h
e
g
o
al
o
f
th
eir
d
ev
elo
p
m
e
n
t
is
to
allo
w
b
etter
v
o
lta
g
e
co
n
tr
o
l in
n
o
r
m
al
o
p
er
atio
n
an
d
in
ca
s
e
o
f
f
au
l
ts
.
T
h
e
o
p
ti
m
al
p
o
s
itio
n
i
n
g
o
f
F
AC
T
S
d
ev
ices
in
a
n
et
w
o
r
k
is
a
co
m
b
in
ato
r
ial
p
r
o
b
lem
.
T
o
th
is
d
a
y
,
th
er
e
is
n
o
a
n
al
y
t
ical
m
et
h
o
d
th
at
ca
n
s
o
lv
e
t
h
i
s
k
in
d
o
f
p
r
o
b
le
m
a
n
d
g
iv
e
th
e
o
v
er
all
o
p
ti
m
u
m
.
T
h
er
ef
o
r
e,
t
o
o
ls
s
u
c
h
a
s
t
h
e
m
eta
h
eu
r
i
s
tic
alg
o
r
ith
m
h
a
v
e
b
ee
n
u
s
ed
.
E
v
o
lu
t
io
n
ar
y
al
g
o
r
ith
m
s
(
E
A
)
,
s
u
ch
as
t
h
e
p
ar
ticle
s
w
a
r
m
,
g
en
et
ic
alg
o
r
ith
m
,
an
d
d
if
f
er
en
tia
l
ev
o
lu
tio
n
,
h
av
e
b
ee
n
co
m
m
o
n
l
y
u
s
ed
i
n
th
e
p
o
w
er
s
y
s
te
m
.
T
h
ese
alg
o
r
ith
m
s
w
er
e
o
r
ig
in
al
l
y
u
s
ed
f
o
r
o
p
ti
m
izin
g
s
in
g
le
-
o
b
j
ec
tiv
e
p
r
o
b
lem
s
.
I
n
ad
d
itio
n
,
ev
o
l
u
tio
n
ar
y
m
eth
o
d
s
p
r
o
v
id
e
m
o
r
e
f
lex
i
b
ilit
y
i
n
h
an
d
li
n
g
th
e
co
m
p
le
x
itie
s
i
n
o
b
j
ec
tiv
e
f
u
n
ct
io
n
s
an
d
co
n
s
tr
ai
n
ts
.
P
o
o
r
ly
k
n
o
w
n
j
u
s
t
a
f
e
w
y
ea
r
s
a
g
o
,
o
p
tim
a
l
p
o
s
itio
n
in
g
an
d
s
izi
n
g
o
f
F
AC
T
S
d
ev
ice
s
is
co
n
s
id
er
ed
to
i
m
p
r
o
v
e
el
ec
tr
ical
n
et
w
o
r
k
lo
ad
ab
ilit
y
.
E
n
h
a
n
ci
n
g
n
et
w
o
r
k
lo
ad
ab
ilit
y
is
cr
u
cial
in
m
o
d
er
n
elec
tr
ical
g
r
id
s
.
F
A
C
T
S
d
ev
i
ce
s
ar
e
u
s
ed
to
r
ed
u
ce
s
h
o
r
t
cir
cu
it
c
u
r
r
en
t
s
a
n
d
to
en
h
a
n
ce
b
o
th
tr
an
s
ie
n
t
an
d
s
t
ea
d
y
-
s
tate
s
tab
ilit
y
.
Se
v
er
al
ap
p
r
o
ac
h
es
h
av
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
th
e
o
p
ti
m
al
p
lace
m
en
t
of
th
e
F
A
C
T
S`s d
ev
ices
u
s
i
n
g
d
if
f
er
en
t
co
n
v
e
n
ti
o
n
al
an
d
m
eta
h
e
u
r
is
tic
o
p
ti
m
i
za
tio
n
m
et
h
o
d
s
.
T
h
e
au
th
o
r
s
in
[
1
0
]
p
r
o
p
o
s
ed
t
w
o
ap
p
r
o
ac
h
es
to
id
en
tify
t
h
e
p
lace
m
e
n
t
o
f
t
h
e
F
AC
T
S
co
n
tr
o
ller
o
f
th
e
s
u
itab
le
n
o
d
es
to
e
n
s
u
r
e
v
o
ltag
e
s
tab
ilit
y
.
T
h
e
f
ir
s
t
tec
h
n
i
q
u
e
is
b
ased
o
n
t
h
e
to
p
o
lo
g
ical
s
tr
u
ct
u
r
e
o
f
p
o
w
er
n
et
w
o
r
k
s
,
w
h
ile
t
h
e
s
eo
n
d
tec
h
n
iq
u
e
i
s
b
ased
o
n
t
h
e
co
n
v
e
n
tio
n
al
p
o
w
er
f
lo
w
[
1
0
]
.
I
n
[
1
1
]
,
a
m
u
lti
-
o
b
j
ec
tiv
e
allo
ca
tio
n
p
r
o
b
lem
o
f
F
A
C
T
S
d
ev
ices
is
s
o
l
v
ed
b
y
t
w
o
-
h
y
b
r
id
a
p
p
r
o
ac
h
es;
1
)
n
o
n
-
d
o
m
in
ated
s
o
r
tin
g
p
ar
ticle
s
w
ar
m
o
p
ti
m
izer
(
NSP
SO)
co
m
b
i
n
ed
w
i
th
th
e
f
u
zz
y
lo
g
i
c,
2
)
n
o
n
d
o
m
in
a
ted
s
o
r
tin
g
g
en
etic
alg
o
r
it
h
m
II
(
r
ef
er
r
ed
as
NSG
A
-
I
I
)
co
m
b
in
ed
w
it
h
t
h
e
f
u
zz
y
lo
g
ic.
I
n
t
h
is
w
o
r
k
,
p
o
w
er
lo
s
s
,
in
d
ex
v
o
l
tag
e
s
tab
ilit
y
,
an
d
v
o
ltag
e
d
ev
ia
tio
n
ar
e
o
p
ti
m
iz
ed
s
i
m
u
ltan
eo
u
s
l
y
.
T
h
e
g
o
al
o
f
[
1
2
]
is
to
f
in
d
th
e
o
p
ti
m
al
lo
ca
tio
n
an
d
s
etti
n
g
p
ar
am
eter
s
o
f
SV
C
an
d
t
h
y
r
is
t
o
r
co
n
tr
o
lled
s
er
ies
ca
p
ac
ito
r
(
T
C
SC
)
d
ev
ices,
u
s
in
g
P
SO
to
m
iti
g
ate
s
m
all
s
ig
n
a
l
o
s
cillatio
n
s
i
n
m
u
lti
-
m
ac
h
i
n
e
p
o
w
er
s
y
s
te
m
s
.
T
h
e
a
u
t
h
o
r
s
i
n
[
1
3
]
p
r
esen
t
t
h
e
ap
p
licatio
n
o
f
p
ar
ticle
s
w
ar
m
o
p
tim
izatio
n
to
d
eter
m
i
n
e
t
h
e
o
p
tim
a
l p
o
s
itio
n
o
f
t
h
e
F
AC
T
S d
ev
ices i
n
th
e
m
o
s
t c
o
s
t
-
e
f
f
e
ctiv
e
m
an
n
er
.
T
h
e
o
p
ti
m
al
p
lace
m
en
t
o
f
STA
T
C
OM
s
is
s
u
g
g
e
s
ted
in
[
1
4
]
.
T
h
r
o
u
g
h
th
e
s
i
m
u
lta
n
eo
u
s
a
p
p
licatio
n
o
f
P
SO
an
d
C
P
F
i
n
o
r
d
er
to
i
m
p
r
o
v
e
th
e
v
o
lta
g
e
p
r
o
f
ile
to
e
f
f
icien
tl
y
m
i
n
i
m
ize
p
o
w
er
lo
s
s
e
s
an
d
to
m
a
x
i
m
ize
s
y
s
te
m
lo
ad
ab
ilit
y
.
T
h
e
co
n
tin
u
atio
n
p
o
w
er
f
lo
w
(
C
P
F)
m
et
h
o
d
allo
w
s
ca
lcu
la
tin
g
th
e
s
tat
ic
v
o
ltag
e
s
tab
ilit
y
m
ar
g
i
n
w
h
e
n
o
n
l
y
t
h
e
ST
A
T
C
OM
s
s
ize
is
co
n
s
id
er
ed
.
T
h
e
P
SO
an
d
th
e
g
en
er
al
alg
eb
r
aic
m
o
d
eli
n
g
s
y
s
te
m
(
GA
M
S)
w
er
e
also
ad
o
p
ted
to
o
b
tain
lo
ca
tio
n
an
d
r
ati
n
g
o
f
D
-
ST
A
T
C
OM
f
o
r
v
o
ltag
e
s
tab
ilit
y
m
ar
g
i
n
en
h
a
n
ce
m
en
t
[
1
5
]
.
I
n
th
e
liter
atu
r
e,
C
P
F
h
as
b
ee
n
u
s
ed
to
s
o
l
v
e
th
e
p
r
o
b
le
m
o
f
t
h
e
s
i
n
g
u
lar
i
t
y
n
ea
r
t
h
e
s
tab
ilit
y
li
m
it
o
f
t
h
e
co
n
v
e
n
tio
n
al
p
o
w
e
r
f
lo
w
a
lg
o
r
it
h
m
s
.
T
h
e
au
t
h
o
r
s
in
[
1
6
]
in
v
es
tig
a
te
th
e
v
o
lta
g
e
s
tab
ilit
y
a
s
s
e
s
s
m
e
n
t
u
s
i
n
g
s
tatic
V
A
R
co
m
p
e
n
s
atio
n
(
SVC
)
an
d
th
y
r
i
s
to
r
co
n
tr
o
lled
s
er
ies
ca
p
ac
ito
r
(
T
C
SC
)
co
n
tr
o
ller
s
.
T
h
e
ef
f
ec
t
o
f
SVC
a
n
d
T
C
SC
s
izi
n
g
in
t
h
e
lo
ad
in
g
m
ar
g
i
n
w
as a
l
s
o
ev
a
lu
ated
[
1
7
]
.
T
h
e
aim
o
f
th
is
p
ap
er
is
to
d
eter
m
i
n
e
th
e
o
p
ti
m
al
p
lace
m
e
n
t
o
f
t
h
e
m
o
s
t
p
o
p
u
lar
F
A
C
T
S
d
ev
ices,
n
a
m
e
l
y
t
h
e
S
VC
.
T
h
e
P
SO
o
b
jectiv
e
f
u
n
ctio
n
w
h
ich
co
n
tai
n
s
a
ter
m
th
a
t
n
ee
d
s
to
b
e
m
a
x
i
m
ized
is
th
e
lo
ad
in
g
f
ac
to
r
.
T
h
e
o
p
tim
izatio
n
p
r
o
c
ed
u
r
e
w
as
ex
ec
u
ted
u
n
d
er
o
n
e
an
d
th
r
ee
SVC
co
n
s
tr
ain
t
s
.
I
n
th
e
f
ir
s
t
s
tep
,
w
e
co
n
s
id
er
o
n
l
y
th
e
r
e
f
er
en
ce
v
o
ltag
e
co
n
s
tr
ain
t
an
d
i
n
t
h
e
s
ec
o
n
d
s
tep
,
th
r
ee
co
n
s
tr
ain
t
s
ar
e
tak
en
in
to
ac
co
u
n
t,
th
e
r
ef
er
e
n
ce
v
o
lta
g
e,
t
h
e
r
ea
ct
an
ce
an
d
t
h
e
SV
C
r
ea
cti
v
e
p
o
w
er
i
n
t
h
e
p
u
r
p
o
s
e
to
m
a
x
i
m
iz
e
th
e
lo
ad
lev
el
a
n
d
m
i
n
i
m
ize
t
h
e
to
tal
lo
s
s
es
p
o
wer
s
y
s
te
m
an
d
f
latte
n
i
n
g
th
e
v
o
ltag
e
o
f
t
h
e
b
u
s
es.
T
o
th
e
b
es
t
o
f
o
u
r
k
n
o
w
led
g
e,
th
is
i
s
th
e
f
ir
s
t
s
tu
d
y
th
a
t
ad
d
r
e
s
s
es
t
h
e
p
r
o
b
lem
o
f
f
i
n
d
in
g
a
n
o
p
tim
a
l
lo
ca
tio
n
o
f
t
h
e
SV
C
`
s
d
ev
ice
u
n
d
er
th
o
s
e
o
p
tim
izatio
n
co
n
s
tr
ai
n
t
s
.
T
h
e
r
e
m
ain
d
er
o
f
th
is
p
ap
er
is
o
r
g
a
n
ized
as
f
o
llo
w
s
:
s
ec
tio
n
2
i
n
tr
o
d
u
ce
s
th
e
v
o
lta
g
e
s
tab
ilit
y
a
n
al
y
s
i
s
.
P
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
is
p
r
esen
ted
in
th
e
s
ec
tio
n
3
.
T
h
e
p
r
o
b
le
m
i
s
f
o
r
m
u
lated
in
s
ec
tio
n
4
.
T
h
e
s
i
m
u
la
tio
n
r
es
u
lts
ar
e
an
al
y
ze
d
an
d
d
is
cu
s
s
ed
in
s
ec
tio
n
5
.
Fin
all
y
,
o
u
r
co
n
tr
ib
u
tio
n
s
a
n
d
co
n
clu
s
io
n
s
ar
e
g
iv
e
n
i
n
s
ec
tio
n
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
S
V
C
d
ev
ice
o
p
tima
l lo
ca
tio
n
f
o
r
vo
lta
g
e
s
ta
b
ilit
y
en
h
a
n
ce
m
en
t b
a
s
ed
…
(
Ou
m
E
l F
a
d
h
el
Lo
u
b
eb
a
B
.
)
2103
2.
VO
L
T
A
G
E
S
T
AB
I
L
I
T
Y
A
NALYS
I
S
2
.
1
.
B
if
urca
t
io
n pa
r
a
m
et
er
B
if
u
r
ca
tio
n
t
h
eo
r
y
i
s
co
n
ce
r
n
e
d
w
it
h
th
e
s
t
u
d
y
o
f
to
p
o
lo
g
ical
t
y
p
e
c
h
an
g
es
i
n
t
h
e
tr
aj
ec
to
r
ies
s
o
l
u
tio
n
o
f
a
n
o
n
-
lin
ea
r
d
y
n
a
m
ic
s
y
s
te
m
w
h
e
n
t
h
e
co
n
tr
o
l
p
ar
am
eter
s
v
ar
y
.
I
t
f
o
cu
s
es
m
a
in
l
y
o
n
th
e
ev
o
lu
t
io
n
o
f
eq
u
ilib
r
iu
m
p
er
io
d
ic
o
r
b
it
s
(
w
h
ic
h
co
n
s
tit
u
te
as
y
m
p
to
t
ic
s
tates),
th
e
ir
m
u
ltip
lici
t
y
an
d
th
eir
s
tab
il
it
y
p
r
o
p
er
ties
[
1
6
-
1
8
]
.
P
ar
am
eter
esti
m
atio
n
is
a
co
m
p
le
m
e
n
tar
y
f
u
n
ctio
n
o
f
th
e
s
tate
est
i
m
a
to
r
n
ec
es
s
ar
y
to
en
s
u
r
e
its
r
o
b
u
s
t
n
es
s
an
d
r
eliab
ilit
y
.
T
h
ese
p
ar
a
m
eter
s
ar
e
u
s
ed
i
n
s
e
v
er
al
ad
v
a
n
ce
d
f
u
n
ct
io
n
s
o
f
n
e
t
w
o
r
k
co
n
tr
o
l,
s
u
c
h
as
f
o
r
ex
a
m
p
le:
co
n
tin
g
e
n
c
y
an
al
y
s
is
,
m
o
n
ito
r
in
g
o
f
s
af
e
t
y
li
m
it
s
,
o
p
ti
m
al
p
o
w
er
f
lo
w
,
etc.
I
n
th
i
s
t
h
eo
r
y
,
th
e
s
y
s
te
m
eq
u
at
io
n
s
d
ep
en
d
o
n
th
e
s
e
p
ar
a
m
eter
s
,
as
(
1
)
.
(
,
)
=
0
(
1
)
T
h
e
p
ar
am
eter
(
λ
)
is
u
s
ed
to
r
ep
r
o
d
u
ce
th
e
lo
ad
ch
an
g
e
s
t
h
at
d
r
iv
e
t
h
e
p
o
w
er
s
y
s
te
m
s
t
o
v
o
ltag
e
co
llap
s
e.
T
h
e
lo
ad
p
o
w
er
is
m
o
d
if
ied
as
:
=
0
(
1
+
)
(
2
)
=
0
(
1
+
)
(
3
)
r
ep
r
esen
ts
t
h
e
p
o
w
er
f
lo
w
eq
u
atio
n
s
,
is
d
ep
en
d
en
t
v
a
r
iab
les,
(
λ
)
is
th
e
lo
ad
in
g
p
ar
am
eter
,
0
an
d
0
r
ep
r
esen
t
th
e
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
s
at
t
h
e
b
as
i
c
o
p
er
atin
g
p
o
in
t
r
esp
ec
tiv
e
l
y
.
in
ter
p
r
e
t
th
e
ch
a
n
g
in
g
o
f
ac
t
iv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
at
b
u
s
i
as (
λ
)
v
ar
i
ed
.
I
n
a
ty
p
ical
b
i
f
u
r
ca
tio
n
d
iag
r
a
m
s
,
th
e
v
o
ltag
e
s
ar
e
r
ep
r
esen
ted
as
f
u
n
c
tio
n
s
o
f
th
e
s
y
s
te
m
lo
ad
ab
ilit
y
m
e
asu
r
e
m
en
t
(
λ
)
.
T
h
is
r
ep
r
esen
tatio
n
is
ca
lled
P
-
V
o
r
n
o
s
e
cu
r
v
es,
as
s
h
o
w
n
i
n
(
2
)
,
an
d
th
e
y
ar
e
w
id
lel
y
u
s
ed
i
n
th
e
co
n
ti
n
u
a
tio
n
p
o
w
er
f
lo
w
(
C
P
F)
an
al
y
s
is
.
2
.
2
.
Co
ntinua
t
io
n po
w
er
f
lo
w
CP
F
P
o
w
er
s
y
s
te
m
s
P
-
V
c
u
r
v
e
s
an
d
th
e
m
a
x
i
m
u
m
lo
ad
in
g
p
ar
a
m
eter
ar
e
ca
lcu
lated
u
s
in
g
e
x
ten
s
iv
el
y
C
P
F
tech
n
iq
u
es.
T
h
u
s
,
an
iter
ati
v
e
p
r
o
ce
s
s
is
u
s
ed
.
T
h
is
p
r
o
ce
s
s
i
n
a
d
is
cr
ete
co
n
tex
t
co
m
p
r
i
s
es
2
s
ta
g
es,
th
e
p
r
e
d
i
c
ti
o
n
(
p
r
e
d
i
ct
o
r
s
t
e
p
)
a
n
d
th
e
u
p
d
a
t
e
(
c
o
r
r
e
c
t
o
r
s
t
e
p
)
.
T
h
e
i
d
e
a
i
s
t
o
o
b
t
a
in
a
b
e
t
t
e
r
e
s
t
im
at
e
f
o
r
e
a
ch
s
am
p
l
e
o
f
t
im
e
.
F
ig
u
r
e
1
i
ll
u
s
t
r
a
t
e
s
th
e
i
t
e
r
at
iv
e
p
r
o
c
es
s
;
f
r
o
m
a
k
n
o
w
n
in
it
i
a
l
p
o
s
it
i
o
n
A
,
a
ls
o
c
a
l
le
d
s
o
l
u
t
i
o
n
A
,
a
t
a
n
g
en
t
p
r
e
d
i
ct
o
r
i
s
u
s
e
d
t
o
es
t
im
at
e
a
n
e
w
s
o
lu
ti
o
n
f
o
r
a
s
p
e
c
if
i
e
d
p
a
t
t
e
r
n
o
f
l
o
a
d
i
n
c
r
e
a
s
e
(
c
a
l
l
e
d
s
o
lu
ti
o
n
B
)
.
W
h
ile
th
e
s
y
s
te
m
lo
ad
ass
u
m
ed
to
b
e
f
ix
ed
,
a
co
r
r
ec
to
r
s
tep
(
u
p
d
ate
iter
atio
n
)
is
u
s
ed
to
d
eter
m
in
ed
th
e
e
x
ac
t
s
o
l
u
tio
n
(
o
r
s
o
lu
tio
n
C
)
b
y
u
s
in
g
a
co
n
v
e
n
tio
n
al
p
o
w
er
f
lo
w
an
a
l
y
s
is
.
T
h
is
p
r
o
ce
s
s
i
s
iter
ated
u
n
t
il
th
e
d
esire
d
P
–
V
cu
r
v
e
is
o
b
tain
ed
.
I
n
o
r
d
er
to
o
p
tim
ize
t
h
e
ca
lcu
lated
lo
ad
in
g
p
ar
a
m
eter
,
w
e
h
av
e
d
ev
e
lo
p
ed
an
o
p
ti
m
izatio
n
alg
o
r
it
h
m
b
y
co
m
b
i
n
i
n
g
t
h
e
C
P
F a
n
d
P
SO,
w
h
ic
h
is
d
escr
ib
ed
in
t
h
e
f
o
llo
w
i
n
g
s
ec
tio
n
.
Fig
u
r
e
1
.
An
ill
u
s
tr
atio
n
o
f
th
e
C
P
F tec
h
n
iq
u
e
3.
P
ARTI
C
L
E
SWA
RM
O
P
T
I
M
I
Z
AT
I
O
N
S
w
ar
m
i
n
telli
g
en
ce
(
SI)
r
ef
er
s
to
a
d
is
tr
ib
u
ted
co
m
p
u
tin
g
p
ar
ad
ig
m
b
ased
o
n
co
llectiv
e
in
t
ellig
e
n
c
e
th
at
e
m
er
g
e
s
f
r
o
m
t
h
e
co
o
p
er
atio
n
o
f
m
u
ltip
le
a
u
to
n
o
m
o
u
s
a
g
en
t
s
.
T
h
e
SI
ap
p
lies
co
n
ce
p
t
s
b
ased
o
n
th
e
f
o
d
d
er
o
f
an
t
co
lo
n
ies
a
n
d
th
e
g
r
o
u
p
i
n
g
o
f
s
o
cial
an
i
m
al
s
s
u
c
h
as
b
ir
d
s
u
s
i
n
g
ag
e
n
t
-
b
ased
ca
lc
u
lati
o
n
s
.
T
h
e
th
r
ee
m
aj
o
r
p
ar
ad
ig
m
s
o
f
S
w
ar
m
I
n
te
llig
e
n
ce
ar
e
:
“An
t
C
o
lo
n
y
Op
ti
m
izat
io
n
”,
“
P
ar
ticle
S
w
ar
m
Op
ti
m
iz
atio
n
”
,
an
d
r
o
b
o
tic
s
w
ar
m
s
(
“S
w
ar
m
R
o
b
o
to
tics
“
o
r
SR
)
[
1
9
]
.
T
h
e
o
p
tim
izat
i
o
n
b
y
a
s
w
ar
m
o
f
p
ar
ticles
i
s
b
ased
o
n
a
s
et
o
f
in
d
iv
id
u
als
o
r
ig
in
al
l
y
ar
r
an
g
e
d
r
an
d
o
m
l
y
an
d
h
o
m
o
g
e
n
eo
u
s
l
y
,
w
h
ic
h
w
e
w
il
l
h
e
n
ce
f
o
r
t
h
ca
ll
p
ar
ticles,
w
h
ic
h
m
o
v
e
i
n
t
h
e
h
y
p
er
s
p
ac
e
o
f
r
esear
ch
an
d
co
n
s
tit
u
te,
ea
ch
a
p
o
ten
tial
s
o
lu
t
io
n
.
E
ac
h
p
ar
t
icle
h
as
a
m
e
m
o
r
y
co
n
ce
r
n
i
n
g
it
s
b
est
-
v
i
s
ited
s
o
lu
tio
n
as
w
el
l
as
th
e
ab
ilit
y
to
co
m
m
u
n
ica
te
w
ith
t
h
e
p
ar
ticles
co
n
s
tit
u
ti
n
g
it
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
18
,
No
.
4
,
A
u
g
u
s
t 2
0
2
0
:
2
1
0
1
-
2
1
1
1
2104
s
u
r
r
o
u
n
d
in
g
s
.
Fro
m
th
i
s
in
f
o
r
m
atio
n
,
t
h
e
p
ar
ticle
w
ill
f
o
llo
w
a
ten
d
en
c
y
m
ad
e,
o
n
th
e
o
n
e
h
an
d
,
o
f
its
w
ill
to
r
etu
r
n
to
it
s
o
p
ti
m
al
s
o
lu
tio
n
,
an
d
o
n
t
h
e
o
th
er
h
a
n
d
,
o
f
it
s
m
i
m
icr
y
co
m
p
ar
ed
to
th
e
s
o
l
u
tio
n
s
f
o
u
n
d
in
it
s
v
ici
n
it
y
.
Fro
m
lo
ca
l
an
d
e
m
p
i
r
ical
o
p
tim
u
m
s
,
th
e
s
et
o
f
p
ar
ticles
w
ill
n
o
r
m
al
l
y
co
n
v
er
g
e
t
o
w
ar
d
s
th
e
o
p
ti
m
al
g
lo
b
al
s
o
lu
tio
n
o
f
t
h
e
p
r
o
b
le
m
tr
ea
ted
.
T
h
e
P
SO
is
a
s
u
b
s
tit
u
te
to
g
en
etic
alg
o
r
it
h
m
s
an
d
an
t
co
lo
n
ies
f
o
r
th
e
o
p
ti
m
izat
io
n
o
f
n
o
n
-
li
n
ea
r
f
u
n
ctio
n
s
[
2
0
]
.
B
in
ar
y
s
tr
in
g
co
d
in
g
i
s
a
m
o
d
i
f
icatio
n
o
f
th
e
P
SO
alg
o
r
ith
m
t
o
s
o
lv
e
p
r
o
b
lem
s
w
ith
s
o
l
u
tio
n
elem
e
n
t
s
w
it
h
b
i
n
ar
y
v
al
u
e
s
.
T
h
e
m
e
an
in
g
o
f
t
h
e
s
p
ee
d
v
ar
iab
le
h
as
b
ee
n
c
h
a
n
g
ed
to
i
n
d
ic
ate
th
e
p
r
o
b
ab
ilit
y
o
f
th
e
co
r
r
esp
o
n
d
in
g
s
o
lu
t
io
n
ele
m
e
n
t
w
i
th
a
v
al
u
e
o
f
0
o
r
1
.
T
h
e
s
p
ee
d
is
u
p
d
ated
in
t
h
e
s
a
m
e
w
a
y
a
s
f
o
r
th
e
cla
s
s
ic
P
SO.
No
co
ef
f
icie
n
t
o
f
i
n
er
tia
i
s
u
s
ed
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
ea
ch
p
ar
ticle
(
i.
e.
,
its
p
r
o
x
i
m
it
y
to
th
e
g
lo
b
al
o
p
ti
m
u
m
)
i
s
m
ea
s
u
r
ed
b
y
m
ea
n
s
o
f
a
n
o
b
j
ec
tiv
e
f
u
n
ctio
n
,
w
h
ic
h
v
ar
ies
w
i
th
t
h
e
o
p
ti
m
iza
tio
n
p
r
o
b
lem
[
2
0
]
.
A
s
w
i
th
o
th
er
s
w
ar
m
al
g
o
r
ith
m
s
,
ch
o
o
s
i
n
g
th
e
r
ig
h
t
p
ar
am
eter
s
is
i
m
p
o
r
tan
t
f
o
r
ef
f
icien
t
P
SO
ex
ec
u
t
io
n
.
C
o
n
s
id
er
ab
le
w
o
r
k
h
as
b
ee
n
d
o
n
e
to
s
elec
t
a
co
m
b
in
at
io
n
o
f
v
alu
e
s
th
a
t
w
o
r
k
w
ell
ac
r
o
s
s
a
w
id
e
r
an
g
e
o
f
is
s
u
es.
L
et
’
s
co
n
s
id
er
χ
a
n
d
υ
as
th
e
co
o
r
d
in
ates
an
d
v
elo
cit
y
o
f
t
h
e
p
ar
ticle
,
r
esp
ec
t
iv
el
y
.
T
h
e
p
ar
ticles
m
o
v
e
to
ta
k
e
in
to
ac
co
u
n
t
t
h
ei
r
b
est
p
o
s
itio
n
an
d
b
est
v
icin
it
y
(
p
an
u
r
g
ic
d
is
p
lace
m
en
t)
,
th
i
s
w
ill
r
ep
ea
ted
f
o
r
ea
ch
iter
atio
n
.
T
h
e
p
o
s
itio
n
o
f
ea
ch
p
ar
ticle
in
th
e
n
ex
t step
i
s
th
e
n
ev
al
u
ated
as th
e
s
u
m
o
f
its
cu
r
r
en
t p
o
s
itio
n
an
d
th
e
s
p
ee
d
is
r
ep
r
esen
ted
a
s
.
T
h
e
in
d
ex
o
f
th
e
b
es
t
p
ar
ticle
is
r
ep
r
esen
ted
as
;
th
en
t
h
e
s
war
m
ca
n
b
e
ca
r
r
ied
o
u
t
b
y
s
o
l
v
in
g
th
e
f
o
llo
w
i
n
g
u
p
d
ate
eq
u
atio
n
s
:
+
1
=
∙
+
1
∙
r
a
n
d
(
∙
)
∗
(
pBe
s
t
−
)
+
2
∙
r
a
n
d
(
∙
)
∗
(
gB
e
s
t
−
)
(
3
)
+
1
=
+
+
1
(
4
)
w
h
er
e
d
is
th
e
iter
atio
n
s
i
n
d
ex
,
is
th
e
c
u
r
r
en
t
p
ar
t
icle
p
o
s
itio
n
at
t
h
e
d
th
iter
atio
n
.
is
th
e
p
ar
ticle
v
elo
cit
y
at
t
h
e
d
th
iter
atio
n
.
r
ep
r
esen
ts
t
h
e
in
er
tia
w
ei
g
h
t
f
ac
to
r
,
1
an
d
2
ar
e
ac
ce
ler
atio
n
co
n
s
ta
n
t.
r
a
n
d
(
∙
)
is
u
n
i
f
o
r
m
l
y
d
is
tr
ib
u
ted
r
an
d
o
m
n
u
m
b
er
i
n
th
e
in
ter
v
al
[
0
,
1
]
,
r
ep
r
esen
ts
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
w
h
ile
ite
r
is
th
e
n
u
m
b
er
o
f
th
e
iter
atio
n
s
u
n
ti
l
th
e
cu
r
r
en
t
s
tag
e.
P
r
o
p
er
s
elec
tio
n
o
f
th
e
in
er
tia
w
ei
g
h
t
p
r
o
v
id
es
a
b
alan
ce
b
etw
ee
n
th
e
g
lo
b
al
an
d
th
e
lo
ca
l
ex
p
lo
r
atio
n
.
T
h
e
is
s
et
ac
co
r
d
in
g
to
(
5
)
.
A
d
d
itio
n
all
y
,
Fig
u
r
e
2
illu
s
tr
ates t
h
e
P
SO p
ar
ticles b
eh
av
io
r
.
W
i
=
W
i
m
ax
−
W
i
m
ax
−
W
i
m
in
It
er
m
ax
×
Ite
r
(
5
)
A
t
f
ir
s
t
g
lan
ce
,
it
s
ee
m
s
th
at
s
e
v
er
al
p
ar
am
e
ter
s
h
a
v
e
b
ee
n
co
n
s
id
er
ed
f
o
r
th
e
P
SO
alg
o
r
ith
m
.
Ho
w
ev
er
,
s
ev
er
al
o
f
t
h
o
s
e
p
ar
a
m
eter
s
ca
n
b
e
f
i
x
ed
in
ad
v
a
n
ce
;
o
th
er
s
,
o
n
th
e
co
n
tr
ar
y
,
ca
n
o
n
l
y
b
e
d
ef
i
n
ed
e
m
p
ir
icall
y
.
T
h
is
is
th
e
ca
s
e
w
it
h
th
e
s
w
ar
m
p
o
p
u
lat
io
n
s
ize
.
T
h
er
e
is
n
o
r
u
le
to
d
eter
m
i
n
e
th
is
p
ar
a
m
et
er
;
d
o
in
g
m
a
n
y
tes
ts
allo
w
s
y
o
u
to
g
ain
t
h
e
ex
p
er
ien
ce
n
ec
es
s
ar
y
to
u
n
d
er
s
tan
d
t
h
is
p
ar
a
m
eter
.
W
e
m
u
s
t
also
co
n
s
id
er
th
e
i
n
itia
lizatio
n
o
f
t
h
e
s
w
ar
m
;
it
i
s
g
en
er
all
y
d
o
n
e
r
a
n
d
o
m
l
y
ac
co
r
d
in
g
to
a
u
n
if
o
r
m
d
is
tr
ib
u
tio
n
o
n
[
0
,
1
]
.
I
n
th
e
ab
o
v
e
p
r
o
ce
d
u
r
e,
th
e
p
ar
ticle
v
elo
cit
y
is
li
m
i
ted
b
y
t
h
e
m
a
x
i
m
u
m
v
al
u
e
υ
m
ax
.
T
w
o
o
th
er
i
m
p
o
r
ta
n
t
p
ar
am
eter
s
ar
e
th
e
co
n
f
id
en
ce
co
ef
f
icie
n
ts
p
r
ev
io
u
s
l
y
n
a
m
e
d
1
an
d
2
(
also
ca
lled
ac
ce
ler
ati
o
n
co
n
s
tan
t)
.
T
h
ey
m
ak
e
it p
o
s
s
ib
le
to
b
alan
ce
th
e
ten
d
en
cie
s
o
f
p
ar
ticles to
f
o
llo
w
th
eir
co
n
s
er
v
atio
n
in
s
tin
ct.
Si
m
ilar
l
y
,
a
n
i
m
p
o
r
tan
t
p
ar
a
m
eter
to
ta
k
e
i
n
to
ac
co
u
n
t
i
s
th
e
co
e
f
f
icie
n
t
o
f
in
er
tia
(
)
in
th
e
f
o
r
m
u
la
s
ee
n
b
e
f
o
r
e.
I
t
d
ef
in
e
s
th
e
ex
p
lo
r
atio
n
ca
p
ac
it
y
o
f
e
a
ch
p
ar
ticle
in
o
r
d
er
to
im
p
r
o
v
e
th
e
co
n
v
er
g
e
n
ce
o
f
t
h
e
m
et
h
o
d
.
Settin
g
t
h
is
p
ar
am
eter
a
m
o
u
n
t
s
to
f
i
n
d
in
g
a
co
m
p
r
o
m
i
s
e
b
et
w
ee
n
a
g
l
o
b
al
ex
p
lo
r
atio
n
(
>1
)
an
d
a
l
o
ca
l
ex
p
lo
r
atio
n
(
<1
)
.
I
t
r
ep
r
esen
ts
th
e
ad
v
en
t
u
r
o
u
s
in
s
ti
n
ct
o
f
th
e
p
ar
ticle
[
2
1
-
2
3
]
.
Th
u
s
,
a
s
u
itab
le
s
elec
tio
n
o
f
th
e
in
er
tia
w
ei
g
h
t
u
s
in
g
(
5
)
allo
w
s
ac
h
ie
v
in
g
a
b
etter
ex
p
lo
r
atio
n
o
f
t
h
e
s
ea
r
ch
s
p
ac
e.
Fig
u
r
e
2
.
T
h
e
P
SO p
a
r
ticles b
eh
av
io
u
r
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
S
V
C
d
ev
ice
o
p
tima
l lo
ca
tio
n
f
o
r
vo
lta
g
e
s
ta
b
ilit
y
en
h
a
n
ce
m
en
t b
a
s
ed
…
(
Ou
m
E
l F
a
d
h
el
Lo
u
b
eb
a
B
.
)
2105
4.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
4
.
1
.
O
bje
ct
iv
e
f
un
ct
io
n
T
h
r
o
u
g
h
o
u
t
th
e
p
r
ev
io
u
s
s
ec
ti
o
n
,
w
e
h
a
v
e
s
ee
n
t
h
e
th
eo
r
etica
l
asp
ec
ts
o
f
s
w
ar
m
in
tel
lig
e
n
ce
,
an
d
m
o
r
e
s
p
ec
if
icall
y
,
P
SO.
T
h
e
u
s
u
al
a
p
p
licatio
n
o
f
P
SO
r
em
ai
n
s
o
p
ti
m
izatio
n
.
Fro
m
th
e
m
o
m
e
n
t
w
h
e
n
th
e
s
e
m
a
n
tic
s
o
f
th
e
p
r
o
b
lem
to
b
e
s
o
lv
ed
ca
n
b
e
ex
p
r
ess
ed
in
t
h
e
f
o
r
m
o
f
a
f
u
n
ctio
n
to
b
e
o
p
tim
ize
d
,
th
e
P
SO
ap
p
lies
.
I
n
th
is
p
ap
er
,
an
o
p
tim
izatio
n
p
r
o
ce
s
s
is
u
s
ed
is
to
o
b
tain
an
ef
f
icien
t u
tili
za
tio
n
o
f
th
e
ex
i
s
tin
g
p
o
w
er
n
et
w
o
r
k
w
it
h
S
VC
o
p
ti
m
a
l lo
ca
tio
n
.
I
n
th
is
s
co
p
e,
th
e
co
s
t f
u
n
ct
io
n
t
h
at
n
ee
d
to
b
e
m
ax
i
m
ize
d
ca
n
b
e
w
r
itte
n
as:
M
a
ximi
ze
(
λ
)
(
6
)
4
.
2
.
SVC
m
o
delin
g
T
h
e
ti
m
e
co
n
s
ta
n
t
r
eg
u
lato
r
is
ass
u
m
ed
to
b
e
k
n
o
w
n
u
s
in
g
t
h
e
m
o
d
el
d
escr
ib
ed
in
Fig
u
r
e
3
.
T
h
e
ab
s
o
lu
te
r
ea
ctan
ce
b
S
VC
i
s
w
ell
d
e
f
in
ed
.
T
h
e
f
o
llo
w
i
n
g
d
if
f
er
en
tia
l e
q
u
atio
n
ca
n
b
e
u
s
e
d
[
2
4
]
:
b
̇
=
(
(
+
−
)
−
)
(
7
)
T
h
e
to
tal
r
ea
ctiv
e
p
o
w
er
i
n
tr
o
d
u
ce
d
at
th
e
SV
C
d
ev
ice
is
e
x
p
r
ess
in
g
as
f
o
llo
w
s
[
2
4
-
2
5
]
:
=
b
2
(
8
)
w
h
er
e
V
is
b
u
s
v
o
lta
g
e
m
a
g
n
i
t
u
d
e,
V
is
t
h
e
s
i
g
n
a
l
o
u
tp
u
t
o
f
t
h
e
p
o
w
er
o
s
cillatio
n
d
a
m
p
er
,
is
r
ef
er
en
ce
v
o
ltag
e,
is
r
e
g
u
lato
r
g
ai
n
,
is
r
eg
u
lato
r
ti
m
e
co
n
s
ta
n
t,
b
m
ax
is
m
a
x
i
m
u
m
s
u
s
ce
p
ta
n
ce
,
b
m
in
is
m
i
n
i
m
u
m
s
u
s
ce
p
tan
ce
a
n
d
b
S
VC
i
s
to
tal
r
ea
ctan
ce
.
T
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
m
a
x
i
m
izes
(
λ
)
w
h
ile
s
ati
s
f
y
i
n
g
t
h
e
f
o
llo
w
in
g
in
eq
u
ali
t
y
co
n
s
tr
ai
n
t.
Fig
u
r
e
3
.
T
h
e
s
tr
u
ctu
r
e
o
f
t
h
e
SVC
4
.
3
.
E
qu
a
lity
co
ns
t
ra
ints
T
h
e
ty
p
ical
lo
ad
f
lo
w
eq
u
at
io
n
s
ca
n
b
e
g
i
v
en
b
y
:
−
−
∑
[
c
os
(
−
)
+
s
in
(
−
)
]
=
1
=
0
,
i
=
1
,
…
,
NB
(
9
)
Q
−
Q
−
∑
[
s
in
(
−
)
+
c
os
(
−
)
]
=
1
=
0
,
i
=
1
,
…
,
NB
(
1
0
)
w
h
er
e
an
d
ar
e
r
esp
ec
tiv
el
y
th
e
r
ea
l
an
d
r
ea
cti
v
e
p
o
w
e
r
g
en
er
ato
r
.
an
d
ar
e
r
esp
ec
tiv
el
y
th
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
lo
ad
.
an
d
ar
e
r
esp
ec
tiv
el
y
t
h
e
tr
an
s
f
er
co
n
d
u
cta
n
ce
an
d
s
u
s
ce
p
ta
n
ce
b
et
w
ee
n
b
u
s
an
d
b
u
s
w
h
ile
NB
r
ep
r
esen
ts
t
h
e
n
u
m
b
er
o
f
b
u
s
e
s
o
f
t
h
e
elec
tr
ic
n
et
w
o
r
k
.
4
.
4
.
I
nequ
a
lity
co
ns
t
ra
ints
An
o
p
ti
m
izatio
n
p
r
o
b
lem
w
it
h
co
n
s
tr
ain
t
s
is
a
co
m
b
in
ato
r
ial
p
r
o
b
lem
w
h
er
e
w
e
w
a
n
t to
m
a
x
i
m
ize
an
o
b
j
ec
tiv
e
f
u
n
c
tio
n
.
W
e,
th
er
ef
o
r
e,
f
in
d
o
u
r
s
elv
e
s
i
n
an
o
p
ti
m
izatio
n
co
n
te
x
t
w
h
er
e
it
i
s
n
o
t
o
n
l
y
a
q
u
e
s
tio
n
o
f
s
atis
f
y
in
g
a
s
et
o
f
co
n
s
tr
ain
ts
b
u
t
also
o
f
ac
h
iev
i
n
g
a
s
o
-
c
alled
o
p
tim
al
s
o
lu
t
io
n
.
T
h
ese
co
n
s
tr
ain
ts
u
s
ed
in
th
i
s
w
o
r
k
r
ep
r
esen
t th
e
s
y
s
te
m
o
p
er
atin
g
an
d
th
e
y
ar
e
r
ep
r
esen
ted
b
y
:
-
E
lectr
icit
y
g
en
er
atio
n
co
n
s
tr
ai
n
ts
:
th
e
v
o
lata
g
e
V
G
an
d
r
ea
cti
v
e
p
o
w
er
o
u
tp
u
ts
Q
G
ar
e
li
m
ite
d
b
y
t
h
eir
lo
w
er
b
o
u
n
d
s
,
an
d
u
p
p
er
b
o
u
n
d
s
,
,
r
esp
ec
tiv
el
y
,
w
h
er
e
NG
is
th
e
n
u
m
b
er
o
f
g
en
er
ato
r
s
.
an
d
th
e
y
ca
n
b
e
d
escr
ib
ed
as f
o
llo
w
s
:
≤
≤
,
=
1
,
…
,
(
1
1
)
≤
≤
,
=
1
,
…
,
(
1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
18
,
No
.
4
,
A
u
g
u
s
t 2
0
2
0
:
2
1
0
1
-
2
1
1
1
2106
-
T
r
an
s
f
o
r
m
er
co
n
s
tr
ai
n
ts
:
T
h
e
tr
an
s
f
o
r
m
er
r
atio
s
ar
e
d
is
cr
e
te
v
alu
e
s
alth
o
u
g
h
th
e
y
ar
e
h
er
e
m
o
d
eled
as
co
n
tin
u
o
u
s
v
ar
iab
les.
T
r
an
s
f
o
r
m
er
tap
T
s
ettin
g
s
,
w
h
ic
h
ar
e
b
ased
o
n
tr
an
s
f
o
r
m
er
r
atin
g
an
d
s
y
s
te
m
v
o
ltag
e
,
w
h
er
e
NT
is
th
e
n
u
m
b
er
o
f
tr
a
n
s
f
o
r
m
er
s
,
ar
e
b
o
u
n
d
ed
as f
o
ll
o
w
s
:
≤
≤
,
=
1
,
…
,
(
1
3
)
-
SVC
co
n
s
tr
ain
ts
: T
h
ese
i
n
clu
d
e
th
e
co
n
s
tr
ai
n
t
s
o
f
r
ef
er
e
n
ce
v
o
ltag
e
,
,
th
e
to
tal
r
ea
ctan
ce
an
d
th
e
r
ea
ctiv
e
p
o
w
er
,
w
h
er
e
NS
VC
is
t
h
e
n
u
m
b
er
o
f
SVC
s
as
f
o
llo
w
s
:
≤
≤
,
=
1
,
…
,
(
1
4
)
≤
≤
,
=
1
,
…
,
(
1
5
)
≤
≤
,
=
1
,
…
,
(
1
6
)
T
h
e
p
r
o
p
o
s
ed
P
SO
-
C
P
F a
lg
o
r
i
th
m
is
d
escr
ib
ed
in
t
h
e
f
lo
w
c
h
ar
t o
f
Fig
u
r
e
4
.
Fig
u
r
e
4
.
Flo
w
c
h
ar
t o
f
t
h
e
p
r
o
p
o
s
ed
P
SO
-
C
P
F
5.
CASE
S
T
UD
I
E
S
I
n
th
is
f
o
r
m
u
latio
n
,
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
r
e
m
ai
n
s
q
u
ad
r
ati
c,
b
u
t
it
i
s
u
n
w
ei
g
h
ted
.
R
at
h
e
r
,
s
tan
d
ar
d
d
ev
iatio
n
s
ar
e
u
s
ed
as
v
ar
iab
les
th
at
ad
d
to
th
e
m
ea
s
u
r
es.
I
n
ad
d
itio
n
,
b
in
ar
y
v
ar
iab
les
ar
e
in
teg
r
ated
in
o
r
d
er
to
d
etec
t
er
r
o
n
eo
u
s
p
ar
a
m
eter
s
.
A
P
SO
-
C
P
F
alg
o
r
it
h
m
b
ase
d
o
n
th
e
i
m
p
r
o
v
e
m
en
t
o
f
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
s
p
r
o
p
o
s
ed
to
h
elp
s
o
lv
e
th
is
m
i
x
ed
v
ar
iab
le
p
r
o
b
lem
.
Fo
r
o
u
r
s
i
m
u
latio
n
r
esu
lt
s
,
w
e
w
i
ll
u
s
e
t
h
e
P
SO
-
C
P
F
alg
o
r
ith
m
t
h
at
w
e
d
e
v
elo
p
ed
.
T
o
im
p
r
o
v
e
th
e
v
o
lta
g
e
s
tab
ili
t
y
o
f
th
e
elec
tr
ic
n
et
w
o
r
k
,
an
o
p
tim
a
l
lo
ca
tio
n
o
f
th
e
SV
C
is
co
n
s
id
er
ed
.
Dif
f
er
en
t
s
ce
n
ar
io
s
w
ill
b
e
test
ed
f
o
r
th
e
I
E
E
E
-
3
0
n
o
d
e
n
et
w
o
r
k
.
O
u
r
s
i
m
u
la
tio
n
s
tep
s
w
il
l
g
o
t
h
r
o
u
g
h
2
ca
s
es,
i
n
t
h
e
f
ir
s
t
t
h
e
co
n
s
tr
ai
n
t
is
tak
e
n
o
n
l
y
t
h
e
v
o
lta
g
e
o
f
th
e
SVC
,
a
n
d
f
o
r
th
e
s
ec
o
n
d
ca
s
e,
th
e
v
o
lta
g
e
o
f
th
e
F
A
C
T
S
d
ev
ice
t
h
u
s
co
n
s
id
er
ed
its
r
ea
ctan
ce
an
d
it
s
r
ea
ctiv
e
p
o
w
er
i
n
th
e
o
b
j
ec
tiv
e
o
f
m
ax
i
m
izin
g
t
h
e
lo
ad
in
g
p
ar
a
m
eter
tak
en
as t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
.
5
.
1
.
Si
m
ula
t
io
n r
esu
lt
f
o
r
I
E
E
E
3
0
-
b
us
s
y
s
t
e
m
First,
t
h
e
f
o
r
m
u
la
tio
n
i
s
test
e
d
o
n
th
e
I
E
E
E
3
0
-
b
us
n
et
w
o
r
k
.
E
r
r
o
r
s
r
an
g
i
n
g
f
r
o
m
5
%
to
1
0
0
%
o
f
th
e
in
i
tial
p
ar
a
m
eter
v
al
u
es
ar
e
in
tr
o
d
u
ce
d
an
d
co
r
r
ec
tly
id
en
ti
f
ied
.
E
v
en
i
n
ca
s
es
w
h
er
e
th
e
s
u
s
ce
p
tan
ce
a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
S
V
C
d
ev
ice
o
p
tima
l lo
ca
tio
n
f
o
r
vo
lta
g
e
s
ta
b
ilit
y
en
h
a
n
ce
m
en
t b
a
s
ed
…
(
Ou
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l F
a
d
h
el
Lo
u
b
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a
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.
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2107
tr
an
s
f
o
r
m
er
r
atio
er
r
o
r
s
ar
e
a
d
j
ac
en
t,
th
e
p
ar
a
m
eter
s
ca
n
b
e
d
etec
ted
an
d
esti
m
ated
w
ith
ac
cu
r
ac
y
.
T
h
e
lo
ad
ca
s
es
(
o
r
o
p
er
atin
g
p
o
in
ts
)
ar
e
r
ep
r
esen
ted
b
y
th
e
r
ea
l
a
n
d
r
ea
ctiv
e
p
o
w
er
s
n
ec
ess
ar
y
f
o
r
ea
ch
b
u
s
i
n
th
e
n
et
w
o
r
k
.
So
m
e
b
ar
s
lin
k
ed
to
a
g
en
er
ato
r
g
en
er
ate
p
o
w
er
.
Oth
er
b
u
s
es
ar
e
co
n
n
ec
ted
to
s
u
b
n
et
s
an
d
r
eq
u
ir
e
a
ce
r
tain
o
u
t
g
o
i
n
g
p
o
w
er
lo
ad
.
T
h
e
p
o
w
er
f
lo
w
s
i
n
t
h
e
b
r
an
ch
es
ad
j
u
s
t
ac
co
r
d
in
g
to
th
e
g
e
n
er
atio
n
an
d
th
e
d
e
m
a
n
d
b
et
w
ee
n
th
e
b
u
s
[
2
6
]
.
Fig
u
r
e
5
illu
s
tr
ates
t
h
e
n
et
w
o
r
k
w
i
th
t
h
e
d
ata
co
n
s
id
er
ed
.
T
h
e
s
u
s
ce
p
ta
n
ce
er
r
o
r
v
ar
ies
f
r
o
m
1
%
to
1
0
0
%
o
f
its
in
i
tial
v
alu
e.
T
h
e
m
ea
s
u
r
e
m
e
n
t
o
f
r
ea
ctiv
e
p
o
w
er
f
lo
w
i
n
t
h
e
b
r
an
c
h
es
i
s
w
h
er
e
s
u
s
ce
p
tan
ce
h
as
th
e
m
o
s
t
i
m
p
ac
t.
T
h
e
r
ed
u
n
d
a
n
c
y
o
f
th
is
m
ea
s
u
r
e
m
en
t,
as
w
ell
as
i
ts
a
m
p
lit
u
d
e,
v
ar
ie
s
ac
co
r
d
in
g
to
th
e
lin
es.
T
a
b
le
1
p
r
esen
ts
th
e
ca
s
e
s
test
ed
an
d
P
SO
p
ar
am
eter
s
.
T
h
e
co
n
cl
u
s
io
n
s
w
h
ic
h
ca
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