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2
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In
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[
2
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.
[
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4
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to
b
e
ad
d
r
ess
ed
u
s
in
g
i
n
telli
g
e
n
t
m
eth
o
d
s
s
u
c
h
as
s
i
m
u
la
te
d
an
n
u
lli
n
g
[
1
2
]
.
I
n
[
1
3
]
,
an
in
n
o
v
ativ
e
m
eth
o
d
ca
lled
th
e
B
ac
k
tr
ac
k
i
n
g
Sear
ch
Me
t
h
o
d
f
o
r
t
h
e
r
e
-
p
h
asi
n
g
p
r
o
b
le
m
i
s
u
s
ed
to
b
ala
n
ce
t
h
e
d
i
s
tr
ib
u
tio
n
n
e
t
w
o
r
k
.
T
h
e
au
th
o
r
s
i
n
[
1
4
]
d
esig
n
e
d
an
ex
p
er
t
s
y
s
te
m
to
ap
p
l
y
th
e
r
e
-
p
h
asi
n
g
m
et
h
o
d
f
o
r
b
alan
cin
g
p
h
a
s
es
i
n
d
is
tr
ib
u
tio
n
s
y
s
te
m
s
.
I
n
[
1
5
]
,
th
e
a
u
t
h
o
r
s
co
m
p
ar
ed
s
e
v
er
al
in
tel
lig
e
n
t
alg
o
r
it
h
m
s
f
o
r
t
h
e
p
h
a
s
e
b
alan
ci
n
g
p
r
o
b
lem
an
d
co
n
c
lu
d
ed
th
at
th
e
d
y
n
a
m
ic
p
r
o
g
r
a
m
m
i
n
g
alg
o
r
ith
m
p
er
f
o
r
m
s
b
etter
.
I
n
[
1
6
]
,
th
e
p
h
as
e
d
is
p
lace
m
e
n
t
m
eth
o
d
i
n
r
ad
ial
an
d
m
e
s
h
ed
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
s
is
ap
p
l
ied
u
s
i
n
g
t
h
e
B
F
-
P
SO
al
g
o
r
ith
m
.
I
n
r
ef
er
e
n
ce
[
1
7
]
,
th
e
i
m
m
u
n
e
alg
o
r
it
h
m
is
also
p
r
o
p
o
s
ed
to
b
alan
ce
t
h
e
p
h
ase
s
,
ta
k
i
n
g
i
n
to
ac
co
u
n
t
th
e
cu
r
r
en
t i
m
b
a
lan
ce
s
.
Usu
al
l
y
,
in
th
e
s
e
p
ap
er
s
,
co
n
s
tan
t
p
o
w
er
,
co
n
s
ta
n
t
cu
r
r
en
t,
o
r
co
n
s
tan
t
i
m
p
ed
a
n
ce
m
o
d
el
s
ar
e
u
s
ed
f
o
r
m
o
d
ellin
g
o
f
lo
ad
s
in
p
h
a
s
e
b
alan
cin
g
s
t
u
d
ies.
Gi
v
e
n
t
h
e
v
ar
iab
le
an
d
n
o
n
-
lin
ea
r
b
eh
av
io
u
r
s
o
f
to
d
a
y
's
lo
ad
s
,
th
ese
m
o
d
els
f
o
r
lo
ad
in
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
s
t
u
d
ies
ca
n
n
o
t
s
h
o
w
r
e
s
u
l
ts
i
n
ac
co
r
d
an
ce
w
it
h
r
ea
lit
y
.
A
lt
h
o
u
g
h
t
h
ese
r
e
s
u
l
t
s
ar
e
ac
c
ep
tab
le,
th
e
y
ar
e
n
o
t o
p
ti
m
al.
On
t
h
e
o
th
er
h
a
n
d
,
o
b
tain
i
n
g
a
p
r
ec
is
e
lo
ad
m
o
d
el
in
t
h
e
g
r
id
i
s
a
v
er
y
ti
m
e
co
n
s
u
m
in
g
,
co
m
p
licated
a
n
d
co
s
tl
y
o
n
e.
D
u
e
to
t
h
e
f
ac
t
t
h
at
d
is
t
r
ib
u
tio
n
co
m
p
a
n
ie
s
ar
e
r
eq
u
ir
ed
t
o
u
s
e
a
p
r
ec
is
e
m
o
d
el
f
o
r
lo
ad
m
o
d
ellin
g
t
o
co
n
d
u
ct
s
tu
d
ies
o
n
th
e
o
p
ti
m
al
u
s
e
o
f
p
o
w
er
s
y
s
te
m
s
,
in
cl
u
d
i
n
g
p
h
a
s
e
b
alan
cin
g
s
t
u
d
ies,
t
h
is
p
ap
er
s
tu
d
ies
th
e
ef
f
ec
t
o
f
d
i
f
f
er
e
n
t
lo
ad
m
o
d
elli
n
g
o
n
t
h
e
r
esu
lt
s
o
f
p
h
ase
b
alan
cin
g
.
An
u
n
b
ala
n
ce
d
2
5
-
b
ass
et
n
et
wo
r
k
w
as
u
s
ed
to
co
n
d
u
ct
th
is
s
tu
d
y
.
Si
m
u
la
tio
n
s
ca
r
r
ied
o
u
t
w
ell
ill
u
s
tr
ate
a
n
d
co
m
p
ar
e
t
h
e
e
f
f
ec
t
s
o
f
lo
ad
m
o
d
ellin
g
o
n
p
h
ase
b
ala
n
ci
n
g
s
tu
d
ies.
First
o
f
al
l,
a
v
ar
iet
y
o
f
lo
ad
m
o
d
els
ar
e
in
tr
o
d
u
ce
d
in
Sectio
n
2
.
Sectio
n
3
d
ea
ls
w
i
th
t
h
e
p
r
o
ce
s
s
o
f
b
alan
cin
g
u
s
in
g
th
e
re
-
p
h
asi
n
g
m
et
h
o
d
.
T
h
e
lo
a
d
d
is
tr
ib
u
tio
n
m
et
h
o
d
in
u
n
b
alan
ce
d
n
et
w
o
r
k
s
an
d
th
e
Har
m
o
n
y
Sear
c
h
Op
ti
m
izatio
n
Me
t
h
o
d
ar
e
p
r
esen
ted
i
n
Sec
tio
n
s
4
an
d
5
,
r
esp
ec
tiv
el
y
.
Sectio
n
6
p
r
esen
ts
th
e
r
e
s
u
l
ts
a
n
d
s
i
m
u
lat
io
n
s
,
a
n
d
f
i
n
all
y
,
co
n
cl
u
s
io
n
s
ar
e
g
i
v
e
n
in
Sec
tio
n
7
.
2.
E
XAM
I
NIN
G
DIFF
E
RE
N
T
L
O
AD
M
O
DE
L
S
T
h
er
e
ar
e
tw
o
g
en
er
al
m
o
d
els
f
o
r
esti
m
ati
n
g
lo
ad
p
ar
a
m
eter
s
,
th
e
f
ir
s
t
m
o
d
el
is
a
s
tatic
lo
ad
m
o
d
el,
w
h
ic
h
is
m
o
s
t
co
m
m
o
n
l
y
u
s
e
d
f
o
r
lo
a
d
f
lo
w
p
r
o
b
lem
s
a
n
d
ca
lcu
lati
n
g
th
e
lo
s
s
e
s
o
f
lin
es
an
d
o
th
er
n
et
w
o
r
k
s
in
t
h
e
s
tead
y
s
tate.
T
h
e
s
ec
o
n
d
m
o
d
el
is
k
n
o
w
n
as
t
h
e
D
y
n
a
m
ic
L
o
ad
Mo
d
el,
w
h
ic
h
is
u
s
u
all
y
u
s
ed
to
s
t
u
d
y
th
e
d
y
n
a
m
ic
s
a
n
d
s
tab
ilit
y
o
f
th
e
n
e
t
w
o
r
k
,
a
n
d
to
r
e
g
u
late
th
e
r
ela
y
s
,
a
n
d
all
t
h
e
ca
s
e
s
th
at
d
ep
en
d
o
n
th
e
n
et
w
o
r
k
a
n
d
lo
ad
d
y
n
a
m
ic
s
in
t
h
e
tr
an
s
ie
n
t
s
ta
te.
I
n
t
h
e
lo
n
g
r
u
n
,
d
u
e
to
th
e
f
ac
t
th
a
t
s
t
u
d
ies
o
n
p
h
ase
b
alan
cin
g
ar
e
ca
r
r
ied
o
u
t in
s
t
ea
d
y
s
tate,
w
e
in
tr
o
d
u
ce
th
e
s
t
atic
m
o
d
el
o
f
lo
ad
an
d
its
t
y
p
e
s
.
2
.
1
.
St
a
t
ic
lo
a
d m
o
del
A
m
o
d
el
th
a
t
ex
p
r
es
s
es
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
at
an
y
g
i
v
en
ti
m
e
as
a
f
u
n
ct
io
n
o
f
th
e
a
m
p
lit
u
d
e
an
d
f
r
eq
u
e
n
c
y
o
f
t
h
e
v
o
lta
g
e
a
t th
e
s
a
m
e
t
i
m
e.
Static lo
ad
m
o
d
els ar
e
u
s
ed
f
o
r
s
tatic
lo
ad
co
m
p
o
n
en
t
s
,
s
u
ch
a
s
lig
h
t
an
d
r
esi
s
tan
ce
lo
ad
s
,
a
n
d
also
ap
p
r
o
x
i
m
atio
n
s
f
o
r
d
y
n
a
m
ic
lo
ad
co
m
p
o
n
e
n
t
s
s
u
ch
as
m
o
to
r
lo
ad
s
[
1
8
]
.
T
h
ese
m
o
d
els ar
e
d
iv
id
ed
in
to
th
e
f
o
llo
w
i
n
g
t
y
p
es.
2
.
1
.
1.
Co
ns
t
a
nt
po
w
er
lo
a
d
m
o
de
l
A
s
ta
tic
lo
ad
m
o
d
el
d
o
es
n
o
t
ch
an
g
e
th
e
lo
ad
p
o
w
er
b
y
c
h
a
n
g
i
n
g
th
e
v
o
ltag
e
r
an
g
e.
L
o
ad
s
th
at
h
a
v
e
s
u
c
h
f
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tu
r
e
s
ar
e
k
n
o
w
n
a
s
c
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n
t
p
o
w
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ad
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f
o
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P
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s
.
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h
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h
ar
ac
ter
is
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ic
o
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th
e
s
e
lo
ad
s
is
as f
o
llo
w
s
:
00
P
=
P
Q
=
Q
(
1
)
2
.
1
.
2
.
Co
ns
t
a
nt
curr
ent
lo
a
d
m
o
d
le
A
s
ta
tic
lo
ad
m
o
d
el
in
w
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h
th
e
p
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n
ea
r
l
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an
d
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tl
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elate
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ltag
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L
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T
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(
2
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3
.
Co
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nt
i
m
pe
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lo
a
d
m
o
dle
A
s
tatic
lo
ad
m
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ad
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ter
is
tic
o
f
th
e
s
e
lo
a
d
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is
as f
o
llo
w
s
:
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.
T
h
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Valu
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o
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n
p
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n
q
f
o
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Di
f
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t
L
o
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Mo
d
els
[
1
8
]
L
o
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y
p
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R
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si
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t
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4
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B
AL
ANCI
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RO
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E
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h
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e
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n
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u
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n
tr
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h
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m
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p
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n
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er
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h
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t
h
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ap
p
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r
esen
ted
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Fi
g
u
r
e
1
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T
h
er
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ar
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ix
m
o
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es f
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r
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ch
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1
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v
en
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n
T
ab
le
2
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T
ab
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.
Mo
d
e
Nu
m
b
er
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Statu
s
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d
P
h
ase
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h
if
t M
atr
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1
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A
C
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A
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3
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B
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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u
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1464
Fig
u
r
e
1
.
Six
p
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s
s
ib
le
m
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d
es
f
o
r
r
e
-
p
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ase
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r
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et
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o
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r
S =
[
S1
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S2
,
.
.
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Sn
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is
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ef
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ed
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e
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eter
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r
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h
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m
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1
to
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Fo
r
ex
a
m
p
le:
S
=
[
3
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1
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2
4
1
2
3
4
5
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2
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1
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.
C
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ase
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ase
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icate
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lled
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ase
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r
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f
r
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(
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et
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n
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g
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:
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3
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a
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22
02
1
|
|
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||
II
R
M
S
I
I
(
4
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n
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elatio
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et
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ala
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ce
d
[
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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lec
&
C
o
m
p
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I
SS
N:
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Th
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1465
4.
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AL
ANC
E
NE
T
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RK
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F
L
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n
t
h
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p
ap
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s
o
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lled
b
ac
k
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r
w
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p
m
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th
o
d
[
1
9
]
is
u
s
ed
to
ca
r
r
y
o
u
t
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u
n
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ala
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h
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ip
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h
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s
tep
s
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as f
o
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w
s
:
a.
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late
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s
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r
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en
t
()
()
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(
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(
/
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k
k
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a
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ia
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b
i
b
i
b
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i
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I
I
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(
8
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i
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e
in
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n
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l
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f
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p
)
()
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a
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c
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V
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W
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aa
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bb
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f
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ca
ar
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m
u
tu
a
l
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m
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ed
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f
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e
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n
e
s
.
T
h
e
ab
o
v
e
s
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ill co
n
ti
n
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n
t
il th
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itio
n
is
r
ea
ch
ed
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(
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−
(
−
1
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(
1
1
)
5.
H
ARM
O
NY
SE
ARCH
(
H
S)
AL
G
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R
I
T
H
M
T
h
e
Har
m
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Sear
ch
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l
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ith
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it
h
m
d
ev
e
lo
p
ed
in
2
0
0
1
[
2
0
]
.
I
n
th
i
s
w
a
y
,
s
o
lv
i
n
g
o
p
ti
m
izatio
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p
r
o
b
lem
s
is
i
n
s
p
ir
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f
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th
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m
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ltan
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ch
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s
.
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u
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p
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tatio
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izatio
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Ha
r
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Sear
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izat
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n
a
lg
o
r
ith
m
s
in
r
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r
s
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n
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ar
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u
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T
h
is
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g
o
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ith
m
c
a
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e
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s
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to
s
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g
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ee
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p
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s
d
u
e
to
les
s
m
at
h
e
m
a
tical
r
eq
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ir
e
m
e
n
ts
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h
an
o
t
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e
r
m
eta
-
h
eu
r
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s
tic
m
et
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o
d
s
[
2
1
-
2
2
]
.
T
h
e
p
ar
am
e
ter
s
o
f
th
e
Har
m
o
n
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Sear
ch
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ith
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Me
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y
Size
(
HM
S),
Har
m
o
n
y
Me
m
o
r
y
C
o
n
s
id
er
at
io
n
R
ate
(
HM
C
R
)
,
P
i
tch
A
d
j
u
s
t
m
e
n
t
R
ate
(
P
AR
)
an
d
B
an
d
w
id
t
h
(
B
W
)
.
E
ac
h
Har
m
o
n
y
is
,
in
f
ac
t,
a
p
o
s
s
ib
l
e
an
s
w
er
to
t
h
e
p
r
o
b
le
m
o
f
o
p
ti
m
izatio
n
.
T
h
e
d
if
f
er
en
t
s
te
p
s
o
f
t
h
is
al
g
o
r
it
h
m
ar
e
as f
o
llo
w
s
:
a.
Def
i
n
itio
n
o
f
o
p
ti
m
izat
io
n
p
r
o
b
le
m
an
d
in
itializat
io
n
P
ar
a
m
e
ter
s
:
Min
i
m
ize
f
(
x
)
Su
b
j
ec
t to
g
(
x)
≥
0
I
n
th
e
s
e
r
elatio
n
s
,
f
(
x
)
is
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
a
n
d
g
(
x)
is
th
e
p
r
o
b
le
m
co
n
s
tr
ain
t.
T
h
e
p
ar
am
eter
s
o
f
HM
S
(
Har
m
o
n
y
Me
m
o
r
y
Size)
,
HM
C
R
(
Har
m
o
n
y
Me
m
o
r
y
C
o
n
s
id
er
atio
n
R
a
te)
,
PAR
(
P
itch
A
d
j
u
s
t
m
e
n
t
R
ate)
an
d
B
W
(
B
an
d
w
id
th
)
ar
e
s
et
at
th
i
s
s
ta
g
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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n
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h
ar
m
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n
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m
e
m
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t t
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s
p
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in
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ar
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e
m
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et
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ize
o
f
t
h
e
h
ar
m
o
n
y
m
e
m
o
r
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o
r
t
h
e
n
u
m
b
er
o
f
h
ar
m
o
n
y
in
m
e
m
o
r
y
,
a
n
d
N
i
s
t
h
e
n
u
m
b
er
o
f
v
ar
iab
les
f
o
r
ea
ch
h
ar
m
o
n
y
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c.
C
r
ea
te
an
i
m
p
r
o
v
ed
n
e
w
h
ar
m
o
n
y
:
First,
r
1
,
r
2
a
n
d
r
3
ar
e
as
s
u
m
ed
to
b
e
r
an
d
o
m
n
u
m
b
er
s
b
et
w
ee
n
ze
r
o
a
n
d
o
n
e.
T
o
g
en
er
ate
a
n
e
w
h
ar
m
o
n
ic
v
ec
to
r
,
if
r
1
is
s
m
al
l
er
th
an
t
h
e
HM
C
R
v
alu
e
a
n
d
th
e
r
an
d
o
m
v
alu
e
r
2
is
g
r
ea
ter
th
an
P
A
R
,
t
h
en
:
X
ne
w
(
i
)
= X
old
(
i
)
(
1
3
)
I
f
r
1
is
s
m
a
ller
th
a
n
HM
C
R
an
d
r
2
is
s
m
aller
th
a
n
P
AR
,
th
e
n
:
X
ne
w
(
i
)
=X
old
(
i
)
+
r
3
×B
W
(
6
)
I
f
r
1
is
lar
g
er
th
a
n
HM
C
R
,
th
e
n
f
o
r
X
n
ew (
i
)
,
a
r
an
d
o
m
v
al
u
e
is
co
n
s
id
er
ed
w
i
th
i
n
it
s
p
er
m
i
tted
r
an
g
e.
d.
Up
d
atin
g
Har
m
o
n
y
Me
m
o
r
y
:
I
n
th
e
p
r
o
ce
s
s
o
f
u
p
d
atin
g
t
h
e
h
ar
m
o
n
ic
m
e
m
o
r
y
,
i
f
t
h
e
h
ar
m
o
n
ics
o
r
n
e
w
h
ar
m
o
n
ic
s
ar
e
m
o
r
e
co
m
p
ete
n
t t
h
an
t
h
e
w
o
r
s
t
h
ar
m
o
n
ic
s
in
t
h
e
m
e
m
o
r
y
,
t
h
e
y
r
ep
lace
it,
o
th
er
w
i
s
e
th
e
y
w
ill b
e
s
et
asid
e.
e.
R
ep
ea
t step
s
3
an
d
4
u
n
t
il th
e
f
i
n
al
co
n
d
itio
n
i
s
s
ati
s
f
ied
o
r
r
ep
etitio
n
s
e
n
d
.
6.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
T
o
p
er
f
o
r
m
th
e
b
ala
n
ci
n
g
p
r
o
ce
s
s
,
a
2
5
-
b
u
s
test
s
y
s
te
m
i
s
u
s
ed
,
w
h
o
s
e
in
f
o
r
m
at
io
n
is
p
r
esen
ted
in
[
6
]
.
T
h
e
s
i
n
g
le
-
li
n
e
d
ia
g
r
a
m
o
f
t
h
is
n
e
t
w
o
r
k
i
s
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
T
h
e
m
ai
n
b
u
s
v
o
ltag
e
i
s
co
n
s
id
er
ed
to
b
e
1
.
0
5
p
u
.
B
ase
ap
p
ar
en
t p
o
w
er
an
d
b
ase
v
o
lta
g
e
ar
e
1
0
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k
V
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an
d
2
.
4
k
V
r
esp
ec
ti
v
el
y
.
T
h
e
p
r
o
ce
s
s
o
f
n
et
w
o
r
k
b
alan
cin
g
is
d
o
n
e
f
o
r
d
if
f
er
en
t
lo
ad
m
o
d
els.
T
h
e
v
al
u
es
o
f
n
p
a
n
d
n
q
f
o
r
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x
p
o
n
e
n
tia
l
m
o
d
el
ar
e
g
iv
e
n
in
T
ab
le
3
an
d
V
0
is
1
p
u
.
Fig
u
r
e
2
.
Un
b
alan
ce
d
2
5
-
b
u
s
n
et
w
o
r
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
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C
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p
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I
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N:
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Th
e
effec
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a
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1467
T
ab
le
3
.
T
h
e
Valu
es
o
f
n
p
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d
n
q
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x
p
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tial
Mo
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el
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u
s
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o
n
p
a
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.
1
.
Net
wo
rk
lo
a
d ba
la
ncing
I
n
th
i
s
n
e
t
w
o
r
k
,
th
e
n
o
m
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ca
p
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it
y
o
f
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b
u
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a
n
s
f
o
r
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1
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0
0
k
V
A
f
o
r
ea
ch
p
h
ase.
S
a
r
ep
r
esen
ts
t
h
e
ap
p
ar
en
t
p
o
w
er
o
u
tp
u
t
o
f
ea
c
h
p
h
ase
o
f
t
h
e
m
ai
n
b
u
s
tr
a
n
s
f
o
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er
.
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ec
a
u
s
e
o
f
t
h
e
i
m
b
ala
n
ce
o
f
th
e
p
h
ases
,
t
h
e
lo
ad
o
f
t
h
e
m
ai
n
b
u
s
tr
an
s
f
o
r
m
er
b
et
w
ee
n
th
e
p
h
ase
s
is
n
o
t
t
h
e
s
a
m
e.
Fo
r
ex
a
m
p
le,
p
h
a
s
e
h
as
b
ee
n
lo
ad
ed
m
o
r
e
th
an
e
x
i
s
tin
g
ca
p
ac
it
y
an
d
o
th
er
p
h
ase
s
less
th
a
n
th
e
a
v
ailab
le
ca
p
ac
it
y
.
T
h
e
p
r
o
ce
s
s
o
f
b
alan
cin
g
p
h
ase
s
i
s
p
er
f
o
r
m
e
d
in
d
i
f
f
er
en
t
lo
ad
m
o
d
els.
T
h
ese
m
o
d
els
in
c
lu
d
e
co
n
s
ta
n
t
p
o
w
er
,
co
n
s
tan
t
cu
r
r
en
t,
co
n
s
ta
n
t
i
m
p
ed
a
n
ce
an
d
m
ix
ed
(
in
d
u
s
tr
ial,
co
m
m
er
cial,
h
o
u
s
eh
o
ld
)
m
o
d
el.
Af
ter
b
alan
cin
g
,
it
is
o
b
s
er
v
ed
th
at
t
h
e
m
ai
n
b
u
s
tr
a
n
s
f
o
r
m
er
ca
p
ac
ities
o
f
t
h
e
p
h
a
s
es
ar
e
m
o
r
e
b
ala
n
ce
d
.
S
margin
is
t
h
e
d
if
f
er
en
ce
in
n
o
m
i
n
al
ca
p
ac
it
y
o
f
ea
ch
p
h
ase
o
f
th
e
tr
an
s
f
o
r
m
er
a
n
d
th
e
ap
p
ar
en
t
p
o
w
er
o
u
t
p
u
t
o
f
ea
c
h
p
h
a
s
e
(
S
margin
=1
1
0
0
-
S
a
)
.
A
cc
o
r
d
in
g
to
t
h
e
r
es
u
lt
s
o
f
T
ab
le
4
,
b
e
f
o
r
e
b
alan
ci
n
g
,
th
i
s
v
al
u
e
is
n
eg
at
iv
e
f
o
r
t
h
e
A
p
h
ase,
w
h
ic
h
in
d
icate
s
th
at
p
h
ase
A
is
lo
ad
ed
m
o
r
e
th
a
n
th
e
li
m
it.
Fo
r
o
th
er
p
h
ases
,
th
i
s
v
al
u
e
is
p
o
s
itiv
e,
w
h
ic
h
i
n
d
icate
s
t
h
at
t
h
e
m
a
x
i
m
u
m
ca
p
ac
it
y
o
f
th
o
s
e
p
h
ases
is
n
o
t
u
s
ed
.
Af
ter
th
e
b
ala
n
c
i
n
g
p
r
o
ce
s
s
,
as s
h
o
wn
in
T
ab
le
4
,
th
e
v
al
u
es
o
f
S
a
ar
e
f
air
l
y
eq
u
al
in
ea
ch
p
h
as
e.
As
a
r
e
s
u
lt,
S
margin
i
s
f
air
l
y
eq
u
al
i
n
d
if
f
er
e
n
t
p
h
ases
.
T
h
ese
v
al
u
es
ar
e
g
i
v
e
n
f
o
r
v
ar
io
u
s
m
o
d
els
i
n
T
ab
le
4
.
Fo
r
ex
a
m
p
le,
in
t
h
e
ca
s
e
w
h
er
e
th
e
lo
ad
s
ar
e
mo
d
elled
as
co
n
s
ta
n
t
p
o
w
er
,
th
e
S
a
is
9
7
2
k
V,
f
o
r
co
n
s
tan
t
cu
r
r
en
t
lo
ad
m
o
d
el
is
9
8
7
k
V,
f
o
r
co
n
s
tan
t
i
m
p
ed
an
ce
lo
ad
m
o
d
el
is
1
0
0
2
k
V,
an
d
f
o
r
m
ix
ed
m
o
d
el
(
s
o
ca
lled
E
x
p
o
n
en
tial
m
o
d
el)
is
1
0
0
4
k
V.
T
ab
le
4
.
T
h
e
C
ap
ac
ity
o
f
E
ac
h
T
r
an
s
f
o
r
m
er
P
h
ase
b
ef
o
r
e
an
d
A
f
ter
B
alan
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g
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r
Dif
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t L
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P
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p
h
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p
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C
p
h
a
se
A
p
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a
se
B
p
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p
h
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se
B
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f
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b
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A
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3
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0
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1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
8
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3
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2
.
Vo
l
t
a
g
e
ba
l
a
ncing
T
h
e
u
n
b
alan
ci
n
g
in
v
o
lta
g
e
at
ea
ch
b
u
s
i
s
d
ef
i
n
ed
as:
m
a
x
,
,
,
,
m
a
x
(
|
|
)
m
i
n
(
|
|
)
a
b
c
a
b
c
V
V
V
(
1
5
)
Stu
d
ies
s
h
o
w
t
h
at
δV
max
is
h
ig
h
f
o
r
all
b
u
s
es
f
o
r
all
f
o
u
r
l
o
ad
m
o
d
els.
I
n
all
lo
a
d
m
o
d
els,
th
e
m
a
x
i
m
u
m
u
n
b
alan
ci
n
g
in
v
o
ltag
e
(
m
a
x
(
δV
max
)
)
is
s
ig
n
i
f
ican
t
b
ef
o
r
e
b
alan
cin
g
.
Af
ter
b
alan
cin
g
,
th
i
s
u
n
b
ala
n
ci
n
g
i
n
v
o
ltag
e
is
n
o
ticea
b
ly
r
ed
u
ce
d
.
Fo
r
th
e
co
n
s
ta
n
t
p
o
w
er
m
o
d
el,
as
s
h
o
w
n
i
n
T
ab
le
4
,
th
e
m
a
x
i
m
u
m
u
n
b
ala
n
ci
n
g
i
n
v
o
lta
g
e
is
eq
u
al
to
0
.
0
2
6
6
,
w
h
ic
h
is
r
ed
u
ce
d
to
0
.
0
0
6
8
af
ter
b
alan
cin
g
.
Si
m
i
lar
l
y
,
i
n
o
th
er
m
o
d
els,
t
h
e
m
ax
i
m
u
m
u
n
b
alan
c
in
g
i
n
v
o
lt
ag
e
af
ter
t
h
e
b
alan
ci
n
g
is
s
i
g
n
i
f
ica
n
tl
y
r
ed
u
ce
d
.
A
cc
o
r
d
in
g
to
T
ab
le
5
,
th
e
m
a
x
i
m
u
m
u
n
b
ala
n
ci
n
g
i
n
v
o
ltag
e
h
as
d
r
o
p
p
ed
f
r
o
m
0
.
0
2
5
6
to
0
.
0
0
8
3
f
o
r
co
n
s
ta
n
t
c
u
r
r
en
t
lo
ad
m
o
d
el
a
n
d
f
r
o
m
0
.
0
2
4
6
to
0
.
0
0
9
6
f
o
r
co
n
s
ta
n
t
i
m
p
ed
an
ce
lo
ad
m
o
d
el.
T
h
is
a
m
o
u
n
t
h
as
d
ec
r
ea
s
ed
f
o
r
th
e
m
i
x
ed
m
o
d
el
(
in
d
u
s
tr
ia
l,
co
m
m
er
cial,
r
esi
d
en
tial)
f
r
o
m
0
.
0
2
4
3
to
0
.
0
0
7
4
.
T
ab
le
5
.
Un
b
alan
cin
g
in
Vo
lta
g
e
f
o
r
Di
f
f
er
e
n
t
L
o
ad
Mo
d
els B
ef
o
r
e
an
d
Af
ter
B
alan
ci
n
g
L
o
a
d
mo
d
e
l
B
e
f
o
r
e
b
a
l
a
n
c
i
n
g
A
f
t
e
r
b
a
l
a
n
c
i
n
g
max
(
δ
V
m
a
x
)
max
(
δ
V
m
a
x
)
C
o
n
st
a
n
t
p
o
w
e
r
0
.
0
2
6
6
0
.
0
0
6
8
C
o
n
st
a
n
t
c
u
r
r
e
n
t
0
.
0
2
5
6
0
.
0
0
8
3
C
o
n
st
a
n
t
i
m
p
e
d
a
n
c
e
0
.
0
2
4
6
0
.
0
0
9
6
M
i
x
e
d
0
.
0
2
4
3
0
.
0
0
7
4
6
.
3
.
Net
wo
rk
un
ba
la
ncing
i
nd
ex
T
ab
le
6
s
h
o
w
s
t
h
e
v
al
u
es
o
f
t
h
e
ze
r
o
,
p
o
s
itiv
e
a
n
d
n
e
g
ati
v
e
co
m
p
o
n
en
t
s
o
f
th
e
c
u
r
r
en
t
a
s
w
ell
as
t
h
e
n
et
w
o
r
k
u
n
b
ala
n
ci
n
g
i
n
d
ex
(
R
MSI
)
f
o
r
d
if
f
er
en
t
lo
ad
m
o
d
els
b
ef
o
r
e
an
d
af
ter
b
alan
ci
n
g
.
B
ef
o
r
e
b
alan
cin
g
th
e
i
n
d
ex
o
f
n
et
w
o
r
k
u
n
b
ala
n
cin
g
,
as
w
ell
as
t
h
e
v
al
u
es
o
f
n
e
g
ati
v
e
an
d
ze
r
o
co
m
p
o
n
en
ts
o
f
th
e
c
u
r
r
en
t,
ar
e
h
ig
h
,
b
u
t
a
f
ter
b
alan
ci
n
g
th
ese
v
a
lu
e
s
h
av
e
b
ee
n
s
ig
n
i
f
ican
tl
y
r
ed
u
ce
d
.
Fo
r
co
n
s
t
an
t
p
o
w
er
m
o
d
el,
th
e
co
m
p
o
n
en
t
s
o
f
ze
r
o
an
d
n
eg
at
iv
e
b
ef
o
r
e
b
alan
ci
n
g
ar
e
eq
u
al
to
1
.
2
8
1
an
d
1
.
2
7
4
,
w
h
ich
ar
e
s
i
g
n
i
f
ican
t
va
lu
e
s
.
I
n
t
h
is
ca
s
e,
th
e
R
M
S
I
in
d
ex
is
0
.
1
9
4
7
.
A
f
ter
b
ala
n
cin
g
,
t
h
e
c
u
r
r
en
t
ze
r
o
a
n
d
n
e
g
ati
v
e
co
m
p
o
n
en
t
s
w
er
e
0
.
0
0
2
2
an
d
0
.
0
0
5
5
r
esp
e
ctiv
el
y
.
A
l
s
o
,
th
e
R
MSI
h
as
d
ec
r
ea
s
ed
to
0
.
0
0
0
6
.
R
esu
lt
s
f
o
r
o
th
er
m
o
d
els
ar
e
s
h
o
w
n
in
T
ab
le
6.
T
ab
le
6
.
C
u
r
r
en
t Co
m
p
o
n
e
n
t
s
an
d
R
MSI
f
o
r
Dif
f
er
en
t
L
o
ad
Mo
d
els B
ef
o
r
e
an
d
Af
ter
B
alan
cin
g
L
o
a
d
mo
d
e
l
B
e
f
o
r
e
b
a
l
a
n
c
i
n
g
A
f
t
e
r
b
a
l
a
n
c
i
n
g
I
0
I
1
I
2
R
M
S
I
I
0
I
1
I
2
R
M
S
I
C
o
n
st
a
n
t
p
o
w
e
r
1
.
2
8
9
.
2
7
1
.
2
7
0
.
1
9
4
0
.
0
0
2
2
9
.
2
6
0
.
0
0
5
5
0
.
0
0
0
6
C
o
n
st
a
n
t
c
u
r
r
e
n
t
1
.
2
4
9
.
4
0
1
.
2
4
0
.
1
8
7
0
.
0
0
2
0
9
.
4
0
0
.
0
1
1
0
.
0
0
1
2
C
o
n
st
a
n
t
i
m
p
e
d
a
n
c
e
1
.
2
1
9
.
5
3
1
.
2
1
0
.
1
8
0
0
.
0
1
3
9
9
.
5
4
0
.
0
0
5
5
0
.
0
0
1
5
M
i
x
e
d
1
.
2
5
9
.
5
5
1
.
1
8
0
.
1
8
0
0
.
0
1
2
3
9
.
5
6
0
.
0
0
6
3
0
.
0
0
1
4
6
.
4
.
Net
wo
rk
lo
s
s
e
s
T
ab
le
7
s
h
o
w
s
t
h
e
s
y
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ab
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9
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C
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m
p
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R
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Har
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R
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M
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RE
F
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NC
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[
1
]
.
N.
W
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J.
M
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Distrib
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Po
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3
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p
p
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1
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5
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0
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2
0
1
2
.
[
2
]
.
L
.
Yo
u
b
,
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Eff
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Un
b
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V
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In
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M
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to
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l
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En
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rg
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v
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l.
2
,
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o
.
1
,
2
0
1
4
.
[
3
]
.
M
.
Bi
n
a
a
n
d
A
.
Ka
sh
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