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l J
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urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
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E
ng
ineering
(
I
J
E
CE
)
Vo
l.
14
,
No
.
6
,
Dec
em
b
er
20
24
,
p
p
.
6
1
1
1
~
6
1
2
1
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
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1
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v
14
i
6
.
pp
6
1
1
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-
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2
1
6111
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A comp
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CC B
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C
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p
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A
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R
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Dep
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PES
Un
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R
R
C
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p
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B
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5
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5
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am
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co
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1.
I
NT
RO
D
UCT
I
O
N
E
n
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g
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s
u
p
p
lied
b
y
th
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tili
ty
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wh
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m
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ely
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ased
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Hen
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u
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to
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ce
d
en
v
ir
o
n
m
en
tal
im
p
ac
t
[
1
]
–
[
3
]
.
T
h
is
h
as
led
to
a
m
o
r
e
d
e
ce
n
tr
alize
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,
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u
lated
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ar
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lo
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s
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b
etwe
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s
elv
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I
n
teg
r
atio
n
o
f
p
lu
g
in
elec
tr
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v
eh
icle
(
PEV)
is
in
cr
ea
s
in
g
as
it
r
e
d
u
ce
s
f
u
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c
o
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s
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u
r
ce
d
f
r
o
m
r
e
n
ewa
b
les
[
4
]
,
[
5
]
.
T
h
e
n
u
m
b
er
o
f
elec
tr
ic
v
eh
icles
(
E
Vs)
o
n
-
r
o
a
d
wo
r
ld
wid
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s
u
r
p
ass
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1
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illi
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in
2
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2
2
.
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n
er
g
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n
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m
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tio
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PEV
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o
r
d
r
iv
in
g
is
ar
o
u
n
d
0
.
2
k
W
h
/k
m
[
6
]
.
Ass
u
m
in
g
h
alf
o
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t
h
e
E
Vs
ar
e
o
n
-
r
o
ad
d
r
i
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in
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ce
o
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4
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k
m
p
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aily
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s
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4
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.
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u
t
d
eliv
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4
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G
W
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in
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w
v
o
ltag
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d
is
tr
ib
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tio
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etwo
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k
s
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b
ig
ch
allen
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th
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ch
ar
g
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n
g
is
n
o
t
co
o
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d
in
ated
,
c
o
n
s
id
er
in
g
th
e
s
h
o
r
tf
all
o
f
p
o
wer
[
7
]
.
T
h
e
g
r
o
win
g
n
u
m
b
er
o
f
E
Vs
will
lead
to
a
s
ig
n
if
ican
t
in
cr
ea
s
e
in
p
o
wer
d
e
m
an
d
t
h
at
ca
n
o
v
er
lo
a
d
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
1
1
1
-
6
1
2
1
6112
cu
r
r
en
t
g
r
i
d
in
f
r
astru
ctu
r
e
d
u
r
in
g
p
ea
k
h
o
u
r
s
[
8
]
.
T
h
is
u
n
u
s
u
al
s
u
r
g
e
in
p
o
we
r
d
e
m
an
d
h
ig
h
li
g
h
ts
th
e
im
p
o
r
tan
ce
o
f
e
x
p
lo
r
i
n
g
m
o
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s
u
s
tain
ab
le
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g
y
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r
ce
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an
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an
cin
g
th
e
g
r
id
in
f
r
astru
ctu
r
e
to
ac
co
m
m
o
d
ate
it
[
9
]
.
T
h
e
r
is
e
in
PEV
ad
o
p
tio
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will
lead
t
o
a
s
h
if
t
in
th
e
p
o
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s
y
s
tem
'
s
ch
ar
ac
ter
is
tics
,
tr
an
s
itio
n
in
g
f
r
o
m
co
n
s
tan
t
im
p
ed
an
ce
lo
ad
s
(
C
I
L
)
to
co
n
s
ta
n
t
p
o
wer
lo
ad
s
(
C
PL)
[
1
0
]
.
T
h
ese
n
ew
lo
ad
s
ar
e
in
h
er
en
tly
u
n
s
tab
le
an
d
ca
n
p
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r
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k
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if
n
o
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r
o
p
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l
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m
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d
[
1
1
]
.
I
n
ad
d
itio
n
,
m
o
s
t
o
f
to
d
ay
’
s
ap
p
lian
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h
av
e
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ased
co
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ter
s
wh
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ar
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ti
g
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tly
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u
lated
in
o
r
d
er
to
d
eliv
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co
n
s
tan
t
p
o
wer
[
1
2
]
.
Hen
ce
,
m
o
r
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o
f
th
e
lo
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d
s
to
d
ay
ar
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co
n
s
tan
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As
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tem
s
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tr
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ar
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est
wh
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w
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y
s
tem
[
1
3
]
,
[
1
4
]
.
B
y
ad
d
in
g
d
is
tr
ib
u
te
d
g
en
er
atin
g
s
o
u
r
ce
s
,
v
o
ltag
e
p
r
o
f
ile
is
im
p
r
o
v
ed
,
an
d
tr
an
s
m
is
s
io
n
lo
s
s
e
s
ar
e
r
ed
u
c
ed
[
1
5
]
–
[
1
7
]
.
T
h
e
d
ec
en
tr
alize
d
c
o
o
r
d
in
atio
n
o
f
en
er
g
y
p
r
o
d
u
ce
r
s
a
n
d
co
n
s
u
m
er
s
at
th
e
lo
ca
l
lev
el,
o
p
er
a
tin
g
in
d
e
p
en
d
e
n
tly
with
o
u
t
th
e
n
ee
d
f
o
r
ce
n
tr
aliz
ed
o
p
er
ato
r
s
is
ter
m
ed
p
ee
r
-
to
-
p
ee
r
en
er
g
y
s
h
a
r
in
g
.
T
h
is
s
y
s
tem
p
r
o
v
i
d
es
two
-
way
co
m
m
u
n
icatio
n
a
n
d
en
er
g
y
f
lo
w
b
etwe
en
lo
ca
l
p
r
o
s
u
m
er
s
[
2
]
.
W
ith
p
r
o
p
er
en
er
g
y
tr
ad
in
g
m
ec
h
a
n
is
m
s
th
er
e
will b
e
b
etter
lo
ca
l
p
o
we
r
an
d
e
n
er
g
y
b
alan
ce
.
An
alter
n
ativ
e
f
o
r
la
r
g
e
s
ca
le
ch
an
g
es
in
d
is
tr
ib
u
ted
n
etwo
r
k
an
d
th
e
e
n
v
ir
o
n
m
en
tal
e
f
f
ec
t
s
wo
u
ld
b
e
to
h
av
e
co
n
s
u
m
er
s
g
en
er
ate
t
h
eir
o
wn
en
er
g
y
f
o
r
c
h
ar
g
in
g
PEVs
an
d
an
y
e
x
ce
s
s
/d
ef
icit
ca
n
b
e
m
an
ag
e
d
b
y
ad
o
p
tin
g
th
e
p
r
o
s
u
m
e
r
m
o
d
el
(
ce
r
tain
co
n
s
u
m
er
b
ec
o
m
in
g
en
er
g
y
p
r
o
d
u
ce
r
)
[
1
8
]
,
[
1
9
]
.
Her
e,
th
e
c
u
s
to
m
er
s
ac
tiv
ely
p
u
r
ch
ase
an
d
s
ell
en
er
g
y
at
p
r
ices
d
eter
m
in
ed
b
y
th
e
m
ar
k
et.
E
n
er
g
y
b
id
d
in
g
m
ar
k
etp
lace
s
,
wh
er
e
p
ar
ticip
an
ts
s
tr
ateg
ically
s
u
b
m
it o
f
f
er
s
to
b
u
y
o
r
s
ell
en
er
g
y
,
ar
e
th
e
h
ea
r
t o
f
th
is
p
r
o
ce
s
s
[
1
9
]
,
[
2
0
]
.
B
y
m
ea
n
s
o
f
th
is
m
eth
o
d
,
cu
s
to
m
e
r
s
ca
n
d
ir
ec
tly
in
f
lu
en
ce
an
d
r
esp
o
n
d
to
th
e
cu
r
r
e
n
t
m
ar
k
et
co
n
d
itio
n
s
,
tailo
r
in
g
th
ei
r
en
er
g
y
b
u
y
in
g
s
tr
ateg
y
to
ac
c
o
m
m
o
d
ate
th
eir
o
wn
n
ee
d
s
.
A
n
o
th
er
im
p
o
r
tan
t
c
o
m
p
o
n
en
t
o
f
en
er
g
y
s
h
ar
in
g
is
b
ilater
al
co
n
tr
ac
ts
,
wh
ich
g
iv
e
cu
s
to
m
er
s
a
m
o
r
e
d
ir
ec
t
a
n
d
in
d
iv
i
d
u
alize
d
way
to
m
a
n
ag
e
th
eir
en
e
r
g
y
tr
an
s
ac
tio
n
s
.
T
h
ese
co
n
tr
ac
ts
cr
ea
te
a
f
r
am
ewo
r
k
th
at
is
tailo
r
ed
to
th
e
p
ar
ticu
lar
n
ee
d
s
an
d
p
r
ef
er
en
ce
s
o
f
th
e
en
titi
es
in
v
o
lv
ed
b
y
allo
win
g
th
em
to
m
u
t
u
ally
ag
r
ee
o
n
ter
m
s
f
o
r
th
e
p
u
r
c
h
ase
o
r
s
ale
o
f
en
er
g
y
.
T
h
is
d
ir
ec
t
en
g
ag
em
e
n
t
b
etwe
en
co
n
s
u
m
er
s
f
ac
ilit
ates
a
m
o
r
e
f
lex
ib
le
an
d
d
y
n
am
ic
en
er
g
y
m
a
r
k
et,
f
o
s
ter
in
g
ef
f
icien
cy
an
d
r
esp
o
n
s
iv
e
n
ess
to
ch
an
g
in
g
d
em
an
d
s
.
T
h
ese
m
o
d
els
ex
h
ib
it
r
ed
u
ce
d
tr
a
n
s
m
is
s
io
n
lo
s
s
es
an
d
ar
e
r
esis
tan
t
to
d
is
r
u
p
tio
n
s
.
Hav
i
n
g
g
e
n
er
at
in
g
s
o
u
r
ce
s
s
u
ch
as
s
o
lar
p
h
o
t
o
v
o
ltaic
p
an
el,
win
d
r
eso
u
r
ce
alo
n
g
with
s
to
r
ag
e
d
ev
ices
ca
n
h
elp
m
ain
tain
v
o
l
tag
e
p
r
o
f
ile
a
n
d
r
ed
u
ce
tr
an
s
m
is
s
io
n
lo
s
s
e
s
.
B
u
t
ea
ch
en
er
g
y
tr
an
s
ac
tio
n
m
u
s
t
b
e
r
ec
o
r
d
ed
to
allo
ca
te
th
e
lo
s
s
es
co
n
tr
ib
u
ted
b
y
ea
ch
lo
ad
[
4
]
.
T
o
a
v
o
id
o
v
er
esti
m
atio
n
o
f
lo
s
s
es,
a
m
et
h
o
d
wh
er
e
lo
s
s
es
ar
e
n
o
r
m
alize
d
an
d
r
ef
lects
th
e
ef
f
ec
t
o
f
n
etwo
r
k
p
ar
am
ete
r
s
,
p
en
alty
/co
m
p
en
s
atio
n
f
o
r
en
er
g
y
im
b
alan
ce
d
u
e
to
d
i
f
f
er
en
ce
in
s
ch
ed
u
led
e
n
er
g
y
an
d
ac
t
u
al
en
er
g
y
tr
an
s
ac
tio
n
m
u
s
t
b
e
co
n
s
id
er
e
d
.
So
,
en
er
g
y
s
h
ar
in
g
b
etwe
en
p
r
o
s
u
m
er
s
wh
o
h
a
v
e
lo
c
al
g
e
n
er
a
tio
n
will
b
e
th
e
o
p
tim
al
way
to
e
n
h
an
ce
p
o
wer
q
u
ality
,
im
p
r
o
v
e
o
v
e
r
all
ef
f
icien
cy
an
d
r
e
d
u
ce
th
e
n
ee
d
f
o
r
lar
g
e
s
ca
le
r
estru
ctu
r
in
g
o
f
th
e
p
o
wer
s
y
s
tem
to
m
ee
t
in
cr
ea
s
ed
d
em
an
d
d
u
e
t
o
in
cr
ea
s
ed
PEV
p
e
n
etr
atio
n
b
esid
es
b
ein
g
ec
o
n
o
m
ical
to
th
e
c
o
n
s
u
m
er
s
o
f
d
is
tr
ib
u
tio
n
s
y
s
tem
[
2
1
]
,
[
2
2
]
.
Dy
n
am
ic
m
o
d
els
ar
e
u
s
ed
f
o
r
th
eir
ab
ilit
y
to
m
o
d
el
b
o
th
tr
an
s
ien
t
an
d
s
tead
y
s
tate
co
n
d
i
tio
n
s
.
An
o
v
er
v
iew
o
f
th
e
co
m
p
e
n
s
atin
g
tech
n
iq
u
es
u
tili
ze
d
to
m
ain
tain
s
tab
ilit
y
was
p
r
esen
ted
i
n
[
2
3
]
,
w
h
ich
d
ev
elo
p
s
n
o
n
lin
ea
r
s
tate
s
p
ac
e
m
o
d
el
o
f
DC
an
d
AC
m
icr
o
g
r
i
d
s
with
co
n
s
tan
t
p
o
wer
an
d
co
n
s
tan
t
v
o
ltag
e
lo
ad
s
.
T
h
is
p
ap
er
co
m
p
a
r
es
th
e
d
y
n
am
ic
b
eh
av
io
r
o
f
co
n
s
tan
t
p
o
wer
lo
ad
s
an
d
co
n
s
tan
t
im
p
ed
an
ce
lo
ad
s
o
n
a
tes
t
s
y
s
tem
,
b
y
d
ev
elo
p
in
g
a
n
o
v
el
co
n
tr
o
l
m
o
d
el
o
f
a
co
n
s
tan
t
p
o
wer
lo
ad
co
n
s
id
er
in
g
tr
an
s
m
is
s
io
n
lin
e
r
esis
tan
ce
an
d
i
n
d
u
ctan
ce
.
T
h
e
co
m
p
ar
is
o
n
is
th
en
ex
ten
d
ed
u
s
in
g
s
tead
y
s
tate
a
n
aly
s
is
f
o
r
th
e
two
class
es
o
f
lo
ad
s
,
o
n
a
lar
g
er
I
E
E
E
test
s
y
s
tem
.
Var
iatio
n
s
in
tr
an
s
m
is
s
io
n
lo
s
s
es,
v
o
ltag
e
p
r
o
f
ile
an
d
lin
e
cu
r
r
e
n
ts
in
th
e
tr
an
s
m
is
s
io
n
lin
e
ar
e
an
aly
ze
d
.
Simu
latio
n
s
s
h
o
w
th
e
g
r
ea
te
r
in
f
lu
en
ce
o
f
co
n
s
tan
t p
o
wer
l
o
ad
s
o
n
lin
e
lo
s
s
es
.
Fin
ally
,
B
ialek
’
s
elec
tr
icity
tr
ac
in
g
m
eth
o
d
is
ap
p
lied
to
tr
ac
e
th
e
f
lo
w
o
f
p
o
wer
s
o
th
at
co
n
s
u
m
er
s
an
d
/o
r
g
en
er
ato
r
s
ar
e
ch
ar
g
e
d
with
r
e
s
p
ec
t to
th
eir
tr
an
s
m
is
s
io
n
lo
s
s
allo
ca
tio
n
.
2.
T
RANS
M
I
SS
I
O
N
L
I
NE
M
O
DE
L
A
r
ad
ial
s
h
o
r
t
tr
an
s
m
is
s
io
n
lin
e
m
o
d
el
is
co
n
s
id
er
ed
s
in
ce
th
e
len
g
th
o
f
th
e
li
n
e
is
lim
ited
.
T
h
e
s
h
u
n
t
r
ea
ctan
ce
is
n
eg
lecte
d
d
u
e
to
its
lo
w
leak
ag
e
cu
r
r
en
t
in
s
u
ch
a
lin
e.
T
h
e
eq
u
iv
alen
t
o
f
a
f
in
ite
len
g
th
tr
an
s
m
is
s
io
n
lin
e
with
n
n
u
m
b
er
o
f
co
n
s
u
m
e
r
s
/n
o
d
es
in
a
d
is
tr
ib
u
tio
n
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
1
.
E
ac
h
lin
e
h
as
a
r
esis
tan
ce
R
an
d
in
d
u
cta
n
ce
o
f
.
Par
am
eter
s
f
o
r
all
th
e
lin
es
ar
e
co
n
s
id
er
ed
th
e
s
am
e
f
o
r
co
n
v
e
n
ien
ce
.
is
th
e
s
en
d
in
g
en
d
v
o
ltag
e,
is
th
e
r
ec
eiv
in
g
en
d
v
o
ltag
e,
1
,
2
,
…
ar
e
th
e
n
o
d
e
v
o
ltag
es.
Mo
v
in
g
awa
y
f
r
o
m
t
h
e
s
o
u
r
ce
,
th
e
l
o
a
d
v
o
ltag
e
d
ec
r
ea
s
es
d
u
e
to
v
o
ltag
e
d
r
o
p
in
ea
c
h
lin
e
.
Hen
ce
th
e
v
o
ltag
e
in
th
e
last
n
o
d
e
will
b
e
th
e
least.
L
in
e
cu
r
r
en
t
in
th
e
n
o
d
e
d
ec
r
ea
s
e
s
m
o
v
in
g
awa
y
f
r
o
m
th
e
s
o
u
r
ce
as
th
e
lo
ad
in
g
in
th
e
n
o
d
e
k
ee
p
s
r
e
d
u
cin
g
.
T
h
is
v
ar
iatio
n
is
s
h
o
wn
in
Fig
u
r
e
2
.
Ad
d
in
g
an
o
th
er
g
en
er
atin
g
s
o
u
r
ce
n
ea
r
th
e
last
lo
ad
will
im
p
r
o
v
e
th
e
v
o
ltag
e
p
r
o
f
ile
an
d
r
ed
u
ce
lin
e
c
u
r
r
en
t
s
as
s
h
o
wn
in
Fig
u
r
e
3
.
Hen
ce
to
tal
tr
an
s
m
is
s
io
n
lo
s
s
in
th
e
s
y
s
tem
i
s
r
ed
u
ce
d
.
T
h
is
m
o
d
el
co
n
s
id
er
s
a
d
is
t
r
ib
u
tio
n
s
y
s
tem
with
4
co
n
s
u
m
er
s
.
Dis
tr
ib
u
tio
n
tr
an
s
f
o
r
m
er
is
th
e
s
o
u
r
ce
at
th
e
s
en
d
in
g
en
d
.
T
h
e
lo
a
d
s
co
n
s
id
er
ed
h
er
e
ar
e
o
f
c
o
n
s
tan
t
im
p
ed
an
ce
lo
ad
ty
p
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:
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8
7
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8
A
co
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lysi
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ta
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t imp
ed
a
n
ce
a
n
d
co
n
s
ta
n
t p
o
w
er lo
a
d
s
in
…
(
R
a
my
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)
6113
h
av
in
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r
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tan
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1
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.
3
3
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(
A
s
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d
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f
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h
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f
i
r
s
t
g
e
n
e
r
a
ti
n
g
s
o
u
r
c
e
.
Fig
u
r
e
1
.
E
q
u
iv
alen
t c
ir
c
u
it o
f
d
is
tr
ib
u
tio
n
n
etwo
r
k
o
f
f
in
ite
len
g
th
with
‘
n
’
lo
ad
s
Fig
u
r
e
2
.
Var
iatio
n
o
f
v
o
ltag
e
p
r
o
f
ile
an
d
lin
e
cu
r
r
en
ts
at
d
if
f
e
r
en
t lo
a
d
p
o
i
n
ts
with
a
s
in
g
le
s
o
u
r
ce
Fig
u
r
e
3
.
Var
iatio
n
o
f
v
o
ltag
e
p
r
o
f
ile
an
d
lin
e
cu
r
r
en
ts
at
d
if
f
er
en
t lo
a
d
p
o
in
ts
with
two
s
o
u
r
ce
s
at
eith
er
en
d
3.
CO
NSUM
E
R
L
O
AD
M
O
D
E
L
A
ty
p
ical
r
esid
en
tial
lo
ad
co
n
s
is
ts
o
f
h
ea
tin
g
,
lig
h
tin
g
an
d
o
th
er
r
o
tar
y
a
p
p
lian
ce
s
.
T
h
ese
h
av
e
v
ar
iab
le
p
o
wer
co
n
s
u
m
p
tio
n
b
ased
o
n
ter
m
i
n
al
v
o
ltag
e
.
C
o
n
s
tan
t
p
o
wer
lo
ad
s
a
r
e
m
o
s
tly
u
s
ed
in
co
m
m
er
cial
ap
p
licatio
n
s
s
u
ch
as
in
d
u
s
tr
ial
m
an
u
f
ac
tu
r
in
g
,
test
in
g
u
n
its
,
s
tab
le
p
o
wer
s
u
p
p
lies
f
o
r
d
ata
ce
n
ter
s
an
d
PEV
ch
ar
g
in
g
s
tatio
n
s
an
d
ce
r
tain
d
o
m
esti
c
ap
p
lian
ce
s
[
2
4
]
.
I
n
th
is
p
ap
er
,
two
ty
p
es
o
f
lo
ad
s
ar
e
co
n
s
id
er
ed
:
co
n
s
tan
t
im
p
e
d
an
ce
l
o
ad
s
r
e
p
r
esen
tin
g
r
esid
en
tial
lo
a
d
s
an
d
co
n
s
tan
t
p
o
we
r
lo
a
d
s
r
ep
r
esen
tin
g
PEV
ch
a
r
g
in
g
s
tatio
n
s
in
r
esid
en
tial a
r
ea
s
.
3
.
1
.
Co
ns
t
a
nt
i
m
peda
nce
lo
a
ds
E
lectr
ical
lo
ad
s
th
at
m
ai
n
tain
co
n
s
tan
t
im
p
ed
a
n
ce
r
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g
ar
d
les
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o
f
th
e
v
ar
iatio
n
s
i
n
v
o
ltag
e
o
r
cu
r
r
en
t
ar
e
s
aid
to
b
e
c
o
n
s
tan
t im
p
ed
a
n
ce
lo
ad
s
.
I
ts
r
atio
o
f
lo
ad
v
o
lt
ag
e
to
cu
r
r
en
t r
em
ai
n
s
co
n
s
tan
t.
=
=
(
1
)
3
.
2
.
Co
ns
t
a
nt
po
wer
lo
a
ds
C
o
n
s
tan
t
p
o
wer
lo
ad
s
ar
e
th
o
s
e
th
at
co
n
s
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m
e
a
co
n
s
tan
t
am
o
u
n
t
o
f
elec
tr
ical
p
o
wer
r
e
g
ar
d
less
o
f
v
ar
iatio
n
s
in
s
u
p
p
ly
v
o
lta
g
e.
A
ty
p
ical
v
o
ltag
e
v
er
s
u
s
cu
r
r
en
t
g
r
a
p
h
o
f
a
co
n
s
tan
t
p
o
wer
lo
ad
is
s
h
o
wn
in
Fig
u
r
e
4
.
B
ec
au
s
e
lin
e
cu
r
r
en
t
n
ea
r
th
e
s
o
u
r
ce
is
th
e
to
tal
o
f
all
lo
ad
cu
r
r
en
ts
,
it
h
as
th
e
lar
g
est
v
alu
e
wh
ile
b
u
s
v
o
ltag
e
is
at
its
p
ea
k
n
ea
r
th
e
g
e
n
er
ato
r
an
d
d
ec
r
ea
s
es
m
o
v
in
g
awa
y
f
r
o
m
th
e
g
en
er
a
tio
n
.
I
n
s
tan
tan
eo
u
s
im
p
ed
an
ce
(
)
o
f
th
e
co
n
s
tan
t
p
o
wer
l
o
ad
is
p
o
s
itiv
e.
W
h
er
ea
s
its
in
cr
em
en
tal
im
p
ed
a
n
ce
(
)
is
n
eg
ativ
e
wh
ich
m
ak
es
t
h
e
s
y
s
tem
u
n
s
tab
le
[
1
1
]
.
i.e
.
,
a
n
y
i
n
cr
ea
s
e
o
r
d
ec
r
ea
s
e
in
v
o
ltag
e
o
f
C
PL,
th
e
r
e
will
b
e
d
ec
r
ea
s
e
o
r
in
cr
ea
s
e
in
th
e
c
u
r
r
e
n
t
r
esp
ec
tiv
ely
.
T
h
is
h
as
a
d
estab
ilizin
g
ef
f
ec
t
in
th
e
s
y
s
tem
[
2
3
]
.
T
h
e
b
lo
c
k
d
iag
r
am
o
f
co
n
s
tan
t p
o
wer
lo
ad
m
o
d
el
alo
n
g
with
tr
an
s
m
is
s
io
n
lin
e
is
s
h
o
wn
in
Fig
u
r
e
5
.
*
is
th
e
r
ef
er
en
ce
p
o
wer
,
is
th
e
er
r
o
r
s
ig
n
al,
is
th
e
co
n
tr
o
l
o
u
tp
u
t
o
f
PI
co
n
tr
o
ller
,
_
is
th
e
r
ef
er
en
ce
lo
a
d
r
esis
tan
ce
,
is
th
e
lo
ad
r
esis
tan
ce
,
an
d
ar
e
tr
an
s
m
is
s
io
n
lin
e
r
esis
tan
ce
an
d
in
d
u
cta
n
ce
,
is
th
e
cu
r
r
en
t
f
lo
win
g
in
th
e
lo
ad
,
is
th
e
lin
e
cu
r
r
e
n
t,
is
th
e
v
o
ltag
e
ac
r
o
s
s
lo
ad
an
d
is
th
e
in
s
tan
tan
eo
u
s
p
o
wer
.
Su
b
s
cr
ip
t
,
−
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
1
1
1
-
6
1
2
1
6114
an
d
+
1
in
d
icate
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e
n
o
d
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c
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id
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ed
,
p
r
ev
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u
s
n
o
d
e
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d
n
e
x
t
n
o
d
e
r
esp
ec
tiv
ely
.
T
h
e
PI
c
o
n
tr
o
ller
r
ec
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th
e
er
r
o
r
s
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n
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r
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ltin
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f
r
o
m
th
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v
ar
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n
b
etwe
en
th
e
r
ef
er
en
ce
p
o
wer
an
d
th
e
d
er
iv
ed
p
o
wer
.
T
o
o
b
tain
th
e
co
n
t
r
o
l
s
ig
n
al
u
,
p
r
o
p
o
r
tio
n
al
an
d
in
teg
r
al
g
ain
s
(
an
d
)
ar
e
tu
n
e
d
.
R
atio
o
f
lo
ad
r
ef
e
r
e
n
ce
r
esis
tan
ce
(
_
)
to
u
g
iv
es
in
s
tan
tan
eo
u
s
c
u
r
r
en
t
f
r
o
m
wh
ic
h
p
o
wer
is
d
er
iv
ed
.
L
i
n
e
c
u
r
r
en
t
is
d
er
iv
e
d
b
y
ap
p
ly
in
g
Kir
ch
h
o
f
f
’
s
cu
r
r
e
n
t
l
aw;
n
o
d
e
v
o
ltag
e
is
d
er
iv
e
d
b
y
a
p
p
ly
in
g
Kir
ch
h
o
f
f
’
s
v
o
lta
g
e
law.
Fig
u
r
e
6
d
ep
icts
a
m
o
d
el
b
l
o
ck
o
f
C
PL
b
ased
o
n
th
e
m
o
d
el
d
is
p
lay
ed
in
Fig
u
r
e
5
.
Fig
u
r
e
4
.
Vo
ltag
e
v
er
s
u
s
cu
r
r
e
n
t g
r
ap
h
o
f
co
n
s
tan
t p
o
wer
l
o
ad
Fig
u
r
e
5
.
B
lo
ck
d
iag
r
am
r
ep
r
e
s
en
tatio
n
o
f
co
n
s
tan
t p
o
wer
l
o
ad
m
o
d
el
alo
n
g
with
tr
an
s
m
is
s
io
n
lin
e
Fig
u
r
e
6
.
Simu
lin
k
m
o
d
el
o
f
s
y
s
tem
with
4
C
PLs c
o
n
n
ec
ted
v
ia
tr
an
s
m
is
s
io
n
lin
es in
an
A
C
m
icr
o
g
r
id
4.
SI
M
UL
A
T
I
O
N
M
O
D
E
L
Simu
latio
n
is
ca
r
r
ied
o
u
t
in
MA
T
L
AB
/S
im
u
lin
k
s
o
f
twar
e
u
s
in
g
s
im
-
p
o
wer
s
y
s
tem
to
o
ls
.
Mu
ltip
le
lo
ad
s
ar
e
co
n
n
ec
ted
to
g
e
n
er
a
to
r
v
ia
d
is
tr
ib
u
tio
n
tr
a
n
s
f
o
r
m
er
.
Par
am
eter
s
u
s
ed
f
o
r
s
im
u
latio
n
ar
e
s
h
o
wn
i
n
T
ab
le
1
.
Simu
latio
n
is
r
u
n
an
d
s
tead
y
s
tate
an
aly
s
is
o
f
s
y
s
tem
is
s
tu
d
ied
.
T
ab
le
1
.
Par
am
eter
s
u
s
ed
i
n
s
im
u
latio
n
P
a
r
a
me
t
e
r
V
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l
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d
v
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3
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5
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i
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p
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T
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Po
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y
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c
h
lo
ad
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J E
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&
C
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m
p
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n
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I
SS
N:
2088
-
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A
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ed
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ce
a
n
d
co
n
s
ta
n
t p
o
w
er lo
a
d
s
in
…
(
R
a
my
a
)
6115
2
,
9
7
3
,
2
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3
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2
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2
.
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iatio
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Fig
u
r
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d
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s
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t.
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ce
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2
6
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Fig
u
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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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6116
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as
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v
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5
3
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tial
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9
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.
L
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1
3
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1
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5
k
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2
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th
e
th
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46
,
an
d
n
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e
5
3
)
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p
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if
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n
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.
Fig
u
r
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1
4
s
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s
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n
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r
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l
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o
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ty
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er
s
co
r
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cr
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t
o
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io
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itize
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ality
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th
e
n
u
m
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Vs in
cr
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1
6
1
1
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1
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1
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1
6
1
6
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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0
8
8
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8
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0
8
I
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l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
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1
1
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6118
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2
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L
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r
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1
4
.
Vo
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o
f
ile
with
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I
L
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C
PL
,
an
d
ad
d
itio
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o
f
s
o
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s
6.
AL
L
O
C
AT
I
O
N
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F
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RANS
M
I
S
SI
O
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L
O
SS
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B
ialek
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ac
in
g
with
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o
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lo
w
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o
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o
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ith
m
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ed
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to
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ca
te
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s
m
is
s
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n
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s
s
in
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g
e
n
er
ato
r
a
n
d
lo
a
d
s
[
2
8
]
.
Acc
o
r
d
in
g
to
B
ialek
[
2
8
]
,
Gr
o
s
s
n
o
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al
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e
ca
n
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e
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as
(
2
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(
6
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:
[
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∑
[
|
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|
]
[
]
[
]
=
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]
=
(
2
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[
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[
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[
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(
3
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[
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=
{
1
;
=
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[
|
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[
]
;
∈
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(
4
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[
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[
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[
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[
]
(
5
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[
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=
[
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(
6
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wh
er
e
|
−
|
is
th
e
lin
e
p
o
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f
lo
w
f
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o
m
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e
to
;
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d
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al
p
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f
l
o
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s
s
p
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r
f
lo
win
g
th
r
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g
h
n
o
d
e
;
is
th
e
g
en
er
ati
o
n
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n
o
d
e
;
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n
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m
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er
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f
n
o
d
es,
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th
e
s
et
o
f
n
o
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e
s
s
u
p
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lied
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ir
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tly
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r
o
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o
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e
;
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a
×
u
p
s
tr
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m
d
is
tr
ib
u
tio
n
m
atr
ix
;
is
th
e
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tu
al
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em
an
d
in
n
o
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e
;
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th
e
g
r
o
s
s
d
em
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d
in
n
o
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e
;
is
th
e
lo
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is
tr
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u
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m
atr
ix
wh
er
e
tr
an
s
m
is
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s
s
is
allo
ca
ted
to
in
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iv
id
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al
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s
.
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o
ad
f
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w
ca
r
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ied
o
u
t
to
th
e
s
y
s
tem
with
PE
V’
s
o
f
C
I
L
t
y
p
e
lead
to
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to
tal
tr
an
s
m
is
s
i
o
n
lo
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o
f
2
7
3
8
.
3
7
W
an
d
with
PEV’
s
o
f
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PL
ty
p
e
lead
to
a
to
tal
t
r
an
s
m
is
s
io
n
lo
s
s
o
f
.
1
W
.
Fig
u
r
e
1
5
s
h
o
ws
th
e
co
m
p
ar
is
o
n
o
f
lo
s
s
allo
ca
tio
n
with
C
I
L
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d
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PL
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ased
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n
B
ialek
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s
m
eth
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d
.
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t
is
o
b
s
er
v
ed
th
at
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ad
s
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r
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th
e
g
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n
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a
v
e
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tr
an
s
m
is
s
io
n
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s
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m
p
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ich
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e
f
ar
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f
r
o
m
g
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er
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n
.
T
h
is
b
ec
o
m
es
a
cr
itical
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o
in
t
wh
e
n
th
er
e
ar
e
m
u
ltip
le
tr
a
n
s
ac
tio
n
s
o
f
p
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we
r
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en
th
e
u
s
er
s
in
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
[
2
5
]
.
He
n
ce
a
n
o
r
m
al
izin
g
f
ac
to
r
o
f
l
o
s
s
es
m
u
s
t
b
e
i
n
clu
d
ed
to
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m
p
e
n
s
ate
f
o
r
th
e
o
v
er
esti
m
atio
n
o
f
elec
tr
icity
b
ill.
Fu
r
th
er
it
is
o
b
s
er
v
ed
th
at
tr
an
s
m
is
s
io
n
lo
s
s
in
th
e
s
y
s
tem
is
r
ed
u
ce
d
to
1
1
6
2
.
3
8
W
wh
e
n
g
en
er
atio
n
s
o
u
r
ce
s
ar
e
ad
d
e
d
in
b
etwe
en
th
e
s
y
s
tem
.
T
ab
le
3
g
iv
es
a
clea
r
p
ictu
r
e
o
f
h
o
w
lo
s
s
es
ar
e
af
f
ec
ted
with
g
en
er
atio
n
a
n
d
lo
a
d
s
.
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:
2088
-
8
7
0
8
A
co
mp
a
r
a
tive
a
n
a
lysi
s
o
f c
o
n
s
ta
n
t imp
ed
a
n
ce
a
n
d
co
n
s
ta
n
t p
o
w
er lo
a
d
s
in
…
(
R
a
my
a
)
6119
F
i
g
u
r
e
1
5
.
C
o
m
p
a
r
is
o
n
o
f
l
o
s
s
a
l
l
o
c
a
ti
o
n
w
i
t
h
l
o
a
d
s
o
f
C
I
L
t
y
p
e
,
P
E
V
o
f
C
P
L
t
y
p
e
a
n
d
wi
t
h
a
d
d
i
t
i
o
n
o
f
s
o
u
r
c
e
s
T
ab
le
3
.
C
o
m
p
a
r
is
o
n
o
f
tr
an
s
m
is
s
io
n
lo
s
s
es wi
th
g
en
er
atio
n
an
d
lo
a
d
C
a
ses
W
i
t
h
l
o
a
d
s
o
f
C
I
L
t
y
p
e
W
i
t
h
P
EV
o
f
C
P
L
t
y
p
e
W
i
t
h
a
d
d
i
t
i
o
n
a
l
so
u
r
c
e
s
P
o
w
e
r
c
o
n
su
me
d
(
W
a
t
t
s)
5
7
7
1
2
.
7
6
6
1
6
3
5
.
8
9
6
1
0
1
7
.
8
5
Lo
a
d
p
o
w
e
r
(
W
a
t
t
s)
5
4
9
7
4
.
3
9
5
8
3
4
3
.
7
6
5
9
8
5
5
.
4
7
%
o
f
l
o
ss
4
.
7
4
4
8
%
5
.
3
4
1
3
%
1
.
9
0
4
9
%
7.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Stead
y
s
tate
r
esu
lts
ar
e
co
m
p
a
r
ed
with
s
y
s
tem
h
a
v
in
g
co
n
s
ta
n
t
im
p
ed
a
n
ce
lo
ad
s
a
n
d
co
n
s
t
an
t
p
o
wer
lo
ad
s
.
W
h
en
th
e
s
y
s
tem
h
as
c
o
n
s
tan
t
im
p
ed
a
n
ce
lo
a
d
s
,
it
is
o
b
s
er
v
ed
th
at
v
o
ltag
e
at
th
e
lo
ad
p
o
i
n
ts
d
ec
r
ea
s
es
g
o
in
g
f
ar
awa
y
f
r
o
m
g
en
e
r
atin
g
s
o
u
r
ce
.
Hen
ce
th
e
v
o
ltag
e
at
th
e
r
ec
ei
v
in
g
en
d
o
f
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
will
b
e
th
e
least
wh
ich
af
f
ec
ts
th
e
p
o
wer
d
eliv
er
e
d
to
th
e
lo
a
d
s
at
th
e
r
ec
eiv
in
g
en
d
.
L
in
e
c
u
r
r
en
t
f
lo
win
g
in
t
h
e
tr
an
s
m
is
s
io
n
lin
e
n
ea
r
to
th
e
g
en
er
atio
n
is
h
ig
h
e
r
wh
en
c
o
m
p
ar
ed
to
th
e
lin
e
cu
r
r
en
ts
g
o
in
g
f
ar
awa
y
f
r
o
m
t
h
e
g
en
er
atio
n
.
T
h
e
s
am
e
s
y
s
tem
h
av
in
g
co
n
s
tan
t
p
o
wer
lo
a
d
s
will
h
av
e
m
u
c
h
h
ig
h
er
tr
a
n
s
m
is
s
io
n
lin
e
cu
r
r
e
n
t
an
d
v
o
ltag
e
d
r
o
p
a
n
d
wh
en
c
o
m
p
ar
ed
t
o
th
e
p
r
ev
i
o
u
s
ca
s
e.
No
d
e
v
o
ltag
e
d
r
o
p
p
ed
b
elo
w
s
tan
d
ar
d
v
o
ltag
e
lim
it
o
f
0
.
9
p
u
ca
n
b
e
o
b
s
er
v
e
d
in
Fig
u
r
e
1
4
.
Hen
ce
,
it
in
cr
e
ases
o
v
er
all
tr
an
s
m
is
s
io
n
lo
s
s
[
2
4
]
.
Ad
d
in
g
m
o
r
e
s
o
u
r
ce
o
f
p
o
wer
s
u
ch
as
r
en
e
wab
le
en
er
g
y
s
o
u
r
ce
o
r
p
o
we
r
co
n
v
er
te
r
f
ed
b
atter
y
p
o
wer
ed
co
n
v
e
r
ter
at
th
e
r
ec
eiv
in
g
e
n
d
,
r
ed
u
ce
v
o
ltag
e
d
r
o
p
ac
r
o
s
s
lo
ad
p
o
in
ts
with
o
v
er
all
r
ed
u
cti
o
n
in
tr
an
s
m
is
s
io
n
lo
s
s
es.
T
h
is
ca
n
b
e
o
b
s
er
v
ed
in
Fig
u
r
e
1
4
th
at
n
o
d
e
v
o
ltag
es
ar
e
with
in
th
e
s
tan
d
ar
d
v
o
ltag
e
lim
its
wh
en
ad
d
itio
n
al
s
o
u
r
ce
s
ar
e
ad
d
ed
.
L
in
e
c
u
r
r
en
ts
in
th
e
tr
an
s
m
is
s
io
n
lin
e
ar
e
also
m
u
ch
less
co
m
p
ar
ed
with
s
in
g
le
g
en
er
atio
n
.
B
ialek
’
s
p
o
wer
tr
ac
in
g
m
eth
o
d
is
u
s
ed
h
er
e
to
allo
ca
te
lo
s
s
es
co
n
tr
ib
u
ted
b
y
ea
c
h
lo
ad
w
ith
r
esp
ec
t
to
th
e
g
en
er
atio
n
.
T
h
e
c
o
n
tr
i
b
u
tio
n
o
f
a
lo
a
d
t
o
tr
an
s
m
is
s
io
n
lo
s
s
is
less
wh
en
th
e
lo
ad
is
clo
s
er
t
o
th
e
g
en
er
atio
n
(
r
e
f
er
Fig
u
r
e
1
5
)
.
T
h
is
is
an
im
p
o
r
tan
t
co
n
s
id
er
atio
n
if
en
er
g
y
is
to
b
e
s
h
ar
e
d
b
etwe
en
a
p
air
o
f
p
r
o
s
u
m
er
s
alth
o
u
g
h
in
co
n
v
e
n
tio
n
al
d
is
tr
ib
u
tio
n
,
l
o
s
s
es
ar
e
ap
p
o
r
tio
n
ed
eq
u
ally
ir
r
esp
ec
tiv
e
o
f
co
n
tr
ib
u
tio
n
o
f
a
lo
ad
to
o
v
er
all
lo
s
s
es.
8.
CO
NCLU
SI
O
N
Sin
g
le
-
p
h
ase
AC
s
y
s
tem
with
m
u
ltip
le
lo
ad
s
c
o
n
n
ec
te
d
v
ia
tr
an
s
m
is
s
io
n
lin
es
ar
e
an
aly
z
ed
in
th
is
p
ap
er
.
I
t
is
o
b
s
er
v
ed
th
at
co
n
s
tan
t
p
o
wer
lo
ad
s
lead
to
h
ig
h
e
r
v
o
ltag
e
d
r
o
p
s
an
d
lo
s
s
es
co
m
p
ar
ed
to
c
o
n
s
tan
t
im
p
ed
an
ce
l
o
ad
s
.
I
t
also
af
f
ec
t
s
th
e
s
y
s
tem
d
y
n
a
m
ics
an
d
co
u
ld
p
o
ten
tially
lead
t
h
e
s
y
s
tem
to
in
s
tab
ilit
y
.
T
h
e
d
y
n
am
ic
m
o
d
el
d
ev
elo
p
ed
ca
n
b
e
u
s
ed
to
s
tu
d
y
th
e
ef
f
ec
ts
o
f
lo
ad
d
y
n
am
ics
wh
ich
ca
n
b
e
alter
ed
to
m
ak
e
in
d
iv
id
u
al
lo
a
d
s
.
L
o
ad
f
l
o
w
a
n
aly
s
is
is
ca
r
r
ied
o
u
t
to
d
eter
m
in
e
lo
s
s
in
th
e
s
y
s
tem
.
E
n
er
g
y
s
h
ar
in
g
b
etwe
en
th
e
cu
s
to
m
er
s
h
elp
s
to
av
o
id
v
o
ltag
e
-
d
r
o
p
an
d
m
in
im
ize
tr
an
s
m
is
s
io
n
p
o
wer
lo
s
s
in
a
r
ad
ial
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
C
o
n
s
u
m
er
s
wh
o
h
a
v
e
r
en
ewa
b
le
en
er
g
y
o
r
b
atte
r
y
s
to
r
ag
e
m
ay
b
ec
o
m
e
p
r
o
d
u
ce
r
s
b
ased
o
n
th
eir
en
er
g
y
a
v
ailab
ilit
y
.
T
h
is
wo
u
l
d
also
g
r
ea
tly
e
n
h
an
ce
t
h
e
p
o
wer
h
an
d
lin
g
ca
p
ac
ity
o
f
th
e
n
etwo
r
k
.
I
n
ce
r
tain
lin
es,
en
er
g
y
s
h
a
r
in
g
r
esu
lts
in
g
r
ea
ter
en
e
r
g
y
tr
a
n
s
m
is
s
io
n
th
an
in
o
th
er
s
.
I
n
th
e
p
r
o
s
u
m
e
r
m
o
d
el,
co
m
p
u
tatio
n
an
d
allo
c
atio
n
o
f
l
o
s
s
es
is
im
p
o
r
tan
t
f
o
r
m
atch
in
g
en
er
g
y
an
d
b
illed
u
s
ag
e,
an
d
th
is
h
as
also
b
ee
n
an
aly
ze
d
in
th
e
p
ap
e
r
.
As a
r
esu
lt,
allo
ca
tin
g
th
e
lo
s
s
es b
ec
o
m
es c
r
u
cial
to
th
e
b
illi
n
g
p
r
o
ce
s
s
.
T
h
u
s
,
th
e
an
aly
s
is
ca
m
e
o
u
t in
t
h
is
p
ap
er
ca
n
b
e
ex
ten
d
ed
to
o
p
tim
ize
an
d
co
s
t e
n
er
g
y
tr
a
n
s
f
er
b
e
twee
n
p
ee
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
1
1
1
-
6
1
2
1
6120
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
au
th
o
r
R
am
y
a,
s
in
ce
r
ely
th
an
k
PES
Un
iv
er
s
ity
an
d
D
ep
ar
tm
en
t
o
f
E
lectr
ical
an
d
E
lectr
o
n
ics
E
n
g
in
ee
r
in
g
wh
er
e
t
h
e
p
r
esen
t
r
esear
ch
wo
r
k
was c
ar
r
ied
o
u
t
.
RE
F
E
R
E
NC
E
S
[
1
]
C
.
D
e
C
a
u
w
e
r
,
M
.
M
e
ssa
g
i
e
,
S
.
H
e
y
v
a
e
r
t
,
T
.
C
o
o
sema
n
s
,
a
n
d
J
.
v
a
n
M
i
e
r
l
o
,
“
El
e
c
t
r
i
c
v
e
h
i
c
l
e
u
s
e
a
n
d
e
n
e
r
g
y
c
o
n
su
mp
t
i
o
n
b
a
se
d
o
n
r
e
a
l
w
o
r
l
d
e
l
e
c
t
r
i
c
v
e
h
i
c
l
e
f
l
e
e
t
t
r
i
p
a
n
d
c
h
a
r
g
e
d
a
t
a
a
n
d
i
t
s
i
mp
a
c
t
o
n
e
x
i
st
i
n
g
EV
r
e
se
a
r
c
h
m
o
d
e
l
s
,
”
Wo
r
l
d
El
e
c
t
r
i
c
Ve
h
i
c
l
e
J
o
u
rn
a
l
,
v
o
l
.
7
,
n
o
.
3
,
p
p
.
4
3
6
–
4
4
6
,
S
e
p
.
2
0
1
5
,
d
o
i
:
1
0
.
3
3
9
0
/
w
e
v
j
7
0
3
0
4
3
6
.
[
2
]
K
.
K
u
s
a
k
a
n
a
,
“
O
p
t
i
m
a
l
p
e
e
r
-
to
-
p
e
e
r
e
n
e
r
g
y
s
h
a
r
i
n
g
b
e
t
w
e
e
n
p
r
o
su
m
e
r
s
u
si
n
g
h
y
d
r
o
k
i
n
e
t
i
c
,
d
i
e
sel
g
e
n
e
r
a
t
o
r
a
n
d
p
u
m
p
e
d
h
y
d
r
o
st
o
r
a
g
e
,
”
J
o
u
r
n
a
l
o
f
E
n
e
r
g
y
S
t
o
ra
g
e
,
v
o
l
.
2
6
,
D
e
c
.
2
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