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lect
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I
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Vo
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15
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.
5
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Octo
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er
20
25
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p
p
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4
7
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I
SS
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Enha
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it
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im
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l
iab
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th
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C
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K
ey
w
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s
:
Activ
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p
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lo
s
s
es
El
Ab
io
d
h
Sid
i Ch
eik
h
E
lectr
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g
r
id
Gr
id
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eliab
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Ph
o
to
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Po
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f
lo
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aly
s
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T
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rticle
u
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CC B
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SA
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p
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A
uth
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az
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T
a
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SET
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ab
o
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titu
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tad
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1.
I
NT
RO
D
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O
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On
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tial
p
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f
in
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r
astru
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ak
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tr
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u
tio
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elec
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n
etwo
r
k
[
1
]
,
[
2
]
.
N
ev
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th
eless
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m
an
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o
f
th
e
d
is
tr
ib
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tio
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p
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atin
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e
n
v
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m
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ts
[
3
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–
[
5
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.
T
h
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ch
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es
o
f
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p
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atin
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to
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s
[
6
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,
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7
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a
r
e
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h
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wn
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3
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k
V
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8
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[
9
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ip
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[
1
1
]
,
[
1
2
]
.
Fig
u
r
e
1.
El
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A
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h
Sid
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E
SC
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m
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2
.
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is
tr
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p
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allen
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th
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Hig
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tech
n
ical
[
1
3
]
,
[
1
4
]
.
T
h
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tan
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ater
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u
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a
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o
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f
r
ag
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to
t
h
e
n
etwo
r
k
[
1
5
]
,
[
1
6
]
.
I
n
clu
d
in
g
a
2
4
MWc
s
o
lar
(
P
V)
p
lan
t
in
th
e
s
y
s
tem
h
as
cle
ar
ly
co
m
p
licated
th
in
g
s
.
T
h
is
r
en
ewa
b
le
en
er
g
y
p
r
o
ject
p
r
esen
ts
d
if
f
icu
lties
m
ain
tain
in
g
v
o
ltag
e
s
tab
ilit
y
an
d
g
u
ar
a
n
teein
g
g
en
er
al
n
etwo
r
k
d
ep
en
d
a
b
ilit
y
ev
en
if
it
ex
ac
tly
co
r
r
esp
o
n
d
s
with
th
e
o
b
jectiv
es
o
f
th
e
ar
ea
f
o
r
an
en
er
g
y
t
r
an
s
itio
n
.
W
ith
an
esti
m
ated
1
8
8
5
.
3
k
W
h
/k
W
p
s
h
o
wn
in
Fig
u
r
e
3
,
th
e
E
SC
r
eg
io
n
r
ea
lly
h
as
am
az
i
n
g
s
o
lar
p
o
ten
tial
an
d
is
o
b
v
io
u
s
ly
s
tr
ateg
ically
im
p
o
r
t
an
t
f
o
r
s
o
lar
e
n
er
g
y
h
ar
n
ess
in
g
.
B
u
t
p
o
wer
f
r
o
m
t
h
ese
d
is
tr
ib
u
ted
PV
(
s
o
u
r
ce
s
esp
ec
ially
d
u
r
in
g
lo
w
d
em
a
n
d
an
d
p
ea
k
s
u
n
s
h
in
e
)
m
a
y
g
en
er
ate
lo
ca
lized
o
v
e
r
v
o
ltag
e
is
s
u
es.
T
h
e
in
itial
d
esig
n
o
f
th
e
in
f
r
astru
ctu
r
e
f
o
r
a
m
o
r
e
ce
n
tr
alize
d
p
o
wer
s
y
s
tem
m
ak
es
g
r
id
m
an
a
g
em
en
t
co
n
s
id
er
ab
l
y
m
o
r
e
d
if
f
icu
lt.
B
esid
es
th
at,
th
e
ar
ea
h
as
u
n
r
ea
lized
win
d
en
er
g
y
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o
ten
ti
al
in
Fig
u
r
e
4
.
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n
te
g
r
atin
g
win
d
en
e
r
g
y
m
ig
h
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r
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r
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en
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ix
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er
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e
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s
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ee
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at
5
0
m
eter
s
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0
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.
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d
d
in
g
win
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wer
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u
ld
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ir
e
m
aj
o
r
tech
n
ical
a
d
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s
tm
en
ts
to
g
u
ar
an
tee
it
r
u
n
s
well
with
th
e
cu
r
r
e
n
t in
f
r
astru
ctu
r
e
an
d
d
o
es n
o
t f
u
r
th
er
a
g
g
r
a
v
ate
alr
ea
d
y
ex
is
tin
g
is
s
u
es.
Fig
u
r
e
3
.
E
SC
PV p
o
ten
tial: 1
8
8
5
.
3
k
W
h
/k
W
p
Fig
u
r
e
4
.
E
SC
av
er
ag
e
win
d
:
1
2
0
0
W
/m
²
at
5
0
m
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.
15
,
No
.
5
,
Octo
b
e
r
20
25
:
4
7
7
4
-
4
7
8
4
4776
T
h
ese
all
p
o
in
t
clea
r
ly
to
th
e
m
u
lti
-
lay
er
e
d
ch
allen
g
es
in
v
ad
in
g
th
e
E
SC
n
etwo
r
k
:
T
ec
h
n
ical
ch
allen
g
es
in
clu
d
e
ad
d
r
ess
in
g
v
o
ltag
e
p
r
o
b
lem
s
(
b
o
th
d
r
o
p
s
an
d
s
u
r
g
es),
o
p
tim
izin
g
cu
r
r
en
t
f
r
o
m
ex
is
tin
g
in
f
r
astru
ctu
r
e,
a
n
d
m
a
n
ag
in
g
t
h
e
im
p
ac
t
o
f
clim
ate
o
n
e
n
er
g
y
s
y
s
tem
s
[
1
4
]
,
[
1
7
]
,
[
1
8
]
.
R
elate
d
to
en
er
g
y
:
I
t
is
ab
o
u
t
m
in
im
izin
g
tech
n
ical
l
o
s
s
es,
im
p
r
o
v
in
g
n
etwo
r
k
ef
f
icien
cy
,
an
d
s
ea
m
less
ly
in
tr
o
d
u
cin
g
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
[
2
]
,
[
7
]
,
[
1
9
]
.
T
h
is
ef
f
o
r
t
f
o
c
u
s
es
esp
ec
ially
o
n
th
e
E
SC
3
0
k
V
n
etwo
r
k
a
n
d
is
all
ab
o
u
t
ca
r
ef
u
ll
y
ass
es
s
in
g
th
ese
p
r
o
b
lem
s
.
W
e
in
ten
d
to
d
o
h
er
e:
Par
ticu
lar
ly
f
o
r
th
o
s
e
f
ar
-
o
f
f
lo
ad
s
lik
e
E
l
-
B
n
o
u
d
,
p
in
p
o
in
t v
o
ltag
e
v
io
latio
n
s
p
r
esen
t
ch
allen
g
es,
f
in
d
p
r
e
cisely
h
o
w
lo
ca
l
clim
ate
v
ar
iab
les
in
f
lu
en
ce
o
v
er
h
ea
d
lin
e
p
er
f
o
r
m
a
n
ce
,
co
n
s
id
er
in
g
t
h
e
n
ew
PV
s
y
s
tem
s
,
co
m
p
ar
e
t
h
e
to
tal
en
e
r
g
y
lo
s
s
es
o
f
th
e
n
etwo
r
k
t
o
its
p
r
o
d
u
ctio
n
,
an
d
p
r
o
v
id
e
d
o
a
b
le
tech
n
o
lo
g
ical
f
ix
es
th
at
in
cr
ea
s
e
th
e
d
ep
e
n
d
ab
ilit
y
,
r
o
b
u
s
tn
ess
,
an
d
en
er
g
y
ef
f
icien
cy
o
f
th
e
n
etwo
r
k
.
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
s
h
o
u
ld
tr
u
l
y
h
elp
m
ax
im
ize
th
e
p
er
f
o
r
m
an
ce
o
f
t
h
e
cu
r
r
en
t
n
etwo
r
k
an
d
p
r
o
v
id
e
s
p
ec
if
ic
ad
v
ice
o
n
im
p
r
o
v
e
d
in
teg
r
atio
n
o
f
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
.
E
m
p
h
asizin
g
s
u
s
tain
ab
le
an
d
f
in
an
cially
wis
e
s
o
lu
tio
n
s
,
th
is
wo
r
k
s
h
o
u
ld
also
co
n
tr
ib
u
te
to
a
b
etter
u
n
d
er
s
tan
d
i
n
g
o
f
h
o
w
to
m
o
d
e
r
n
ize
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
u
n
d
er
s
u
ch
co
n
d
itio
n
s
.
T
o
g
et
all
th
i
s
,
th
e
wo
r
k
em
p
lo
y
s
th
r
ee
well
-
k
n
o
wn
n
u
m
er
ical
ca
lcu
latio
n
tech
n
iq
u
es
s
elec
te
d
f
o
r
th
ei
r
ac
cu
r
ac
y
an
d
e
f
f
ic
ien
cy
in
p
o
we
r
f
lo
w
an
aly
s
is
:
New
to
n
-
R
ap
h
s
o
n
(
NR
)
,
a
d
ap
tiv
e
New
to
n
-
R
ap
h
s
o
n
(
ANR),
an
d
f
ast d
ec
o
u
p
led
(
FD)
.
2.
M
AT
H
E
M
AT
I
CA
L
F
O
RM
UL
A
T
I
O
N
W
e
tr
u
ly
d
ep
en
d
o
n
s
o
p
h
is
ticated
m
o
d
ellin
g
to
o
ls
to
tack
le
th
o
s
e
ch
allen
g
in
g
,
c
o
m
p
licated
eq
u
atio
n
s
an
d
lar
g
e
s
y
s
tem
co
m
p
u
tatio
n
s
.
T
h
ey
ar
e
n
ec
ess
ar
y
f
o
r
en
s
u
r
in
g
o
u
r
an
al
y
s
is
is
ac
cu
r
ate
an
d
s
p
o
t
-
o
n
.
T
h
ese
ad
v
an
ce
d
c
o
m
p
u
ter
to
o
ls
wer
e
cr
u
cial
f
o
r
o
u
r
wo
r
k
.
T
h
e
y
g
u
id
ed
u
s
in
ex
p
lo
r
in
g
th
e
s
ev
er
a
l c
o
n
f
ig
u
r
ati
o
n
s
o
f
th
e
E
SC
d
is
tr
ib
u
tio
n
n
etwo
r
k
an
d
d
eter
m
in
in
g
th
e
o
p
ti
m
al
ap
p
r
o
ac
h
es
to
im
p
r
o
v
e
its
p
er
f
o
r
m
an
ce
in
Fig
u
r
e
5
.
C
o
n
s
id
er
t
h
e
s
in
g
le
-
lin
e
f
ig
u
r
e
as
o
u
r
g
r
id
m
a
p
.
I
t
lets
u
s
ex
am
in
e
h
o
w
e
n
er
g
y
m
o
v
es,
h
o
w
to
r
ed
u
ce
lo
s
s
es,
an
d
h
o
w
to
m
ai
n
tain
v
o
ltag
e
s
tab
ilit
y
b
y
p
r
ec
is
ely
s
h
o
win
g
u
s
h
o
w
ev
er
y
th
in
g
is
lin
k
ed
.
L
o
o
k
at
th
e
s
in
g
le
-
lin
e
d
iag
r
am
f
o
r
t
h
e
f
ir
s
t z
o
n
e
o
f
th
e
E
SC
d
is
tr
ib
u
tio
n
n
etwo
r
k
in
Fig
u
r
e
6
.
Her
e
ar
e
s
o
m
e
s
alien
t
f
ea
tu
r
es
it
em
p
h
asizes:
s
im
p
ly
s
ai
d
,
r
ad
ial
ar
r
a
n
g
em
e
n
t
is
th
e
way
th
e
m
ed
iu
m
-
v
o
ltag
e
wir
es
b
r
an
c
h
f
r
o
m
th
e
m
ain
s
u
b
s
tatio
n
to
ev
er
y
o
th
e
r
d
is
tr
ib
u
tio
n
p
o
in
t
,
co
m
p
o
n
en
ts
o
f
a
n
etwo
r
k
: I
t sh
o
ws v
is
u
ally
all
th
e
im
p
o
r
tan
t
p
ar
ts
: tr
an
s
f
o
r
m
er
s
,
tr
an
s
m
is
s
io
n
lin
es,
an
d
wh
er
e
all
th
e
p
o
wer
is
b
ein
g
co
n
s
u
m
e
d
,
an
d
p
ar
ticu
lar
ly
in
h
ea
v
y
d
em
an
d
,
we
ca
n
q
u
ick
ly
id
en
tify
p
lace
s
ex
p
er
ien
cin
g
v
o
ltag
e
d
r
o
p
s
o
r
lo
s
s
o
f
elec
tr
icity
.
T
o
ad
d
r
ess
th
e
s
tab
ilit
y
an
d
ef
f
icien
cy
p
r
o
b
lem
s
in
t
h
e
E
SC
d
is
tr
ib
u
tio
n
n
etwo
r
k
,
o
u
r
r
esear
c
h
f
o
llo
wed
a
q
u
ite
r
eg
im
en
te
d
r
o
u
te.
Her
e
is
o
u
r
a
p
p
r
o
ac
h
:
W
e
co
m
p
iled
co
m
p
r
eh
en
s
iv
e
d
at
a
o
n
th
e
f
ea
t
u
r
es
o
f
th
e
n
etwo
r
k
,
n
o
r
m
al
u
s
ag
e
p
at
ter
n
s
,
an
d
p
o
ten
tial
g
e
n
er
atin
g
ca
p
ac
ity
.
T
h
is
clar
i
f
ied
j
u
s
t
wh
at
was
im
p
ed
i
n
g
its
f
u
n
ctio
n
in
g
[
2
0
]
,
[
2
1
]
.
C
o
n
s
tr
u
ctin
g
m
o
d
els
an
d
r
u
n
n
i
n
g
s
im
u
latio
n
s
:
W
e
d
ev
elo
p
e
d
m
o
d
els
o
f
e
v
er
y
n
etwo
r
k
c
o
m
p
o
n
en
t
with
ac
c
ep
ted
tech
n
iq
u
es
in
clu
d
in
g
FD,
ANR,
an
d
NR
.
Key
in
d
eter
m
in
in
g
v
o
ltag
e
is
s
u
es,
p
o
wer
lo
s
s
,
an
d
n
etwo
r
k
g
en
er
al
h
ea
lth
was th
ese
s
im
u
latio
n
s
.
Fin
d
in
g
s
o
lu
tio
n
s
:
W
e
f
o
cu
s
ed
esp
ec
ially
o
n
p
lace
s
with
d
u
b
io
u
s
v
o
ltag
e
lev
els
an
d
im
p
o
r
tan
t
elec
tr
icity
d
is
tr
ib
u
tio
n
p
o
in
ts
.
W
e
p
r
o
p
o
s
ed
an
d
im
p
lem
e
n
t
ed
m
eth
o
d
s
to
o
f
f
s
et
r
ea
ctiv
e
p
o
wer
i
n
o
r
d
er
to
r
eso
lv
e
v
o
ltag
e
p
r
o
b
lem
s
an
d
g
et
th
e
n
etwo
r
k
wo
r
k
in
g
as
in
ten
d
ed
.
T
h
is
m
eth
o
d
ical
m
eth
o
d
o
lo
g
y
g
u
a
r
an
tees
n
o
t
o
n
ly
i
d
en
tific
atio
n
o
f
ac
tu
al
is
s
u
es
b
u
t
also
g
en
er
ates
u
s
ef
u
l,
d
o
a
b
le
s
u
g
g
esti
o
n
s
to
g
u
ar
an
tee
ev
er
y
o
n
e'
s
d
ep
en
d
a
b
ilit
y
an
d
e
f
f
icien
cy
o
f
th
e
E
SC
d
is
tr
ib
u
tio
n
n
etwo
r
k
.
Par
ticu
lar
ly
f
o
r
t
h
e
b
e
h
av
io
r
o
f
lo
ad
s
,
d
y
n
am
ic
lo
a
d
m
o
d
els
(
th
at
wh
ich
tak
e
f
r
eq
u
en
cy
ch
an
g
es)
ar
e
v
er
y
v
ital
wh
en
we
r
eq
u
ir
e
a
n
ac
cu
r
ate
an
al
y
s
is
.
T
h
ese
m
o
d
els
en
ab
le
u
s
to
p
r
ec
is
ely
s
ee
h
o
w
f
r
eq
u
e
n
cy
ch
an
g
es
th
e
co
n
s
u
m
p
tio
n
o
f
e
lectr
icity
.
T
h
is
p
r
o
v
id
es
u
s
wi
th
a
f
ar
m
o
r
e
r
ea
lis
tic
v
iew
o
f
h
o
w
lo
ad
s
in
te
r
ac
t
with
th
e
c
o
m
p
lete
s
y
s
tem
an
d
th
eir
g
e
n
er
al
e
f
f
ec
t
o
n
p
er
f
o
r
m
an
ce
.
Ma
in
tain
i
n
g
a
d
ep
en
d
ab
ilit
y
,
s
tab
ilit
y
,
an
d
s
ea
m
less
o
p
er
atio
n
o
f
th
e
n
et
wo
r
k
d
e
p
en
d
s
o
n
th
is
d
eg
r
ee
o
f
d
etail
[
2
2
]
,
[
2
3
]
.
C
o
m
m
o
n
an
d
ef
f
icien
t
f
o
r
b
o
t
h
s
tatic
an
d
d
y
n
am
ic
lo
ad
b
eh
av
io
r
r
e
p
r
esen
tatio
n
is
th
e
Z
I
P
m
o
d
el:
{
∗
(
)
=
(
)
−
(
)
=
∗
∗
(
t
)
=
i0
[
(
0
)
2
+
(
0
)
+
]
Q
i
(
t
)
=
i0
[
(
0
)
2
+
(
0
)
+
]
(
1
)
I
n
th
ese
eq
u
atio
n
s
,
an
d
Q
i
r
ep
r
esen
t
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
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o
f
t
h
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lo
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d
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th
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o
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er
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o
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wh
ile
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o
we
r
o
f
th
e
lo
ad
at
th
e
n
o
m
in
al
v
o
ltag
e.
T
h
e
co
ef
f
icien
ts
o
f
th
e
Z
I
P m
o
d
el
ar
e
,
,
,
,
,
an
d
in
p
e
r
u
n
it
(
P.u
.
)
.
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
E
n
h
a
n
cin
g
n
etw
o
r
k
r
esil
ien
ce
a
n
d
e
n
erg
y
efficien
cy
in
th
e
…
(
A
li A
b
d
err
a
z
a
k
Ta
d
jed
d
i
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)
4777
E
m
p
h
asizin
g
h
o
w
clo
s
ely
g
e
n
er
atio
n
,
t
r
an
s
m
is
s
io
n
,
an
d
c
o
n
s
u
m
p
tio
n
ar
e
all
in
te
r
co
n
n
e
cted
in
s
id
e
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
,
th
is
m
o
d
el
r
ea
lly
h
ig
h
lig
h
ts
th
e
d
y
n
am
ic
ch
a
r
ac
ter
o
f
en
e
r
g
y
f
lo
w.
Fin
d
in
g
th
e
in
tr
icate
n
o
d
al
v
o
ltag
es
is
th
e
p
r
im
ar
y
o
b
jectiv
e
o
f
t
h
is
wh
o
l
e
m
eth
o
d
.
On
ce
we
h
av
e
th
o
s
e
,
we
ca
n
f
ig
u
r
e
o
u
t
ev
er
y
th
in
g
else
in
clu
d
in
g
lin
e
p
o
wer
f
lo
w,
cu
r
r
en
ts
,
an
d
e
v
en
en
er
g
y
lo
s
s
es.
Simp
ly
s
aid
,
it
all
co
m
es
d
o
wn
to
s
o
lv
in
g
a
s
er
ies
o
f
ch
alle
n
g
in
g
eq
u
atio
n
s
in
wh
ich
o
u
r
m
ajo
r
u
n
k
n
o
wn
s
ar
e
th
e
r
ea
l
an
d
im
ag
in
ar
y
co
m
p
o
n
en
ts
o
f
th
o
s
e
n
o
d
al
v
o
l
tag
es.
Fig
u
r
e
5
.
B
u
s
with
p
r
o
d
u
ctio
n
,
tr
an
s
m
is
s
io
n
,
an
d
lo
ad
in
b
u
s
Fig
u
r
e
6
.
E
SC
Sin
g
le
-
lin
e
d
iag
r
am
(
Ar
ea
2
)
2
.
1
.
P
o
wer
f
lo
w
a
na
l
y
s
is
Po
wer
f
lo
w
an
aly
s
is
p
r
o
v
id
es
o
p
er
ato
r
s
an
d
p
lan
n
er
s
with
c
r
itical
in
f
o
r
m
atio
n
,
in
clu
d
i
n
g
l
in
e
lo
ad
s
,
b
u
s
v
o
ltag
es,
g
en
e
r
ated
p
o
w
er
,
lo
s
s
es
an
d
p
o
wer
s
o
p
tim
izatio
n
s
[
2
4
]
,
[
2
5
]
.
T
h
is
in
f
o
r
m
atio
n
h
ig
h
lig
h
ts
co
n
s
tr
ain
ts
an
d
h
el
p
s
id
en
tify
ar
ea
s
wh
er
e
lim
its
ar
e
ex
ce
ed
e
d
.
Mo
d
e
r
n
c
o
m
p
u
tatio
n
al
to
o
l
s
m
ak
e
p
o
wer
f
lo
w
ca
lcu
latio
n
s
f
ea
s
ib
le
f
o
r
n
etwo
r
k
s
o
f
v
ir
tu
ally
an
y
s
ize
[
2
6
]
,
[
2
7
]
.
E
ac
h
is
ch
ar
ac
ter
ized
b
y
s
ix
v
ar
iab
les:
,
,
,
,
,
an
d
.
Fo
r
a
s
y
s
tem
with
n
o
d
es,
th
is
r
esu
lts
in
6
v
ar
iab
les
[
2
8
]
.
T
o
e
n
s
u
r
e
th
e
s
y
s
tem
is
s
o
lv
ab
le,
2
u
n
k
n
o
wn
s
an
d
4
k
n
o
wn
p
ar
am
eter
s
m
u
s
t b
e
d
ef
in
e
d
.
a.
No
n
-
g
en
e
r
atin
g
b
u
s
s
es,
{
}
=
{
}
=
0
,
an
d
an
d
ar
e
u
n
k
n
o
wn
.
T
h
e
T
ab
le
1
p
r
esen
t
th
e
c
o
n
s
tr
ain
ts
with
f
o
r
m
u
latio
n
m
ath
em
atica
l
.
T
ab
le
1
.
C
o
n
s
tr
ain
ts
with
f
o
r
m
u
latio
n
m
ath
em
atica
l
C
o
n
st
r
a
i
n
t
s
M
a
t
h
e
ma
t
i
c
a
l
f
o
r
m
u
l
a
t
i
o
n
G
e
n
e
r
a
t
i
o
n
a
n
d
l
o
a
d
b
a
l
a
n
c
e
:
{
∑
=
1
−
(
∑
+
=
1
)
=
0
∑
=
1
−
(
∑
+
=
1
)
=
0
(
2
)
G
e
n
e
r
a
t
i
o
n
l
i
m
i
t
s
:
{
≤
≤
≤
≤
(
3
)
V
o
l
t
a
g
e
c
o
n
s
t
r
a
i
n
t
s
:
≤
≤
(
4
)
A
n
g
l
e
c
o
n
s
t
r
a
i
n
t
s:
≤
(
−
)
≤
(
5
)
b.
Gen
er
atin
g
b
u
s
s
es: f
o
r
g
en
er
at
in
g
n
o
d
es,
th
e
f
o
ll
o
win
g
r
elati
o
n
s
h
ip
s
ap
p
ly
:
{
=
∑
=
∗
=
∗
∗
(
∑
=
)
(
6
)
c.
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
in
jecte
d
at
a
n
o
d
e
ar
e
d
ef
in
ed
as:
{
=
(
∑
=
)
∗
(
−
+
)
=
(
∑
=
)
∗
(
−
+
)
(
7
)
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.
15
,
No
.
5
,
Octo
b
e
r
20
25
:
4
7
7
4
-
4
7
8
4
4778
2
.
2
.
P
o
wer
f
lo
w
in t
ra
ns
m
is
s
io
n lines
On
ce
th
e
iter
ativ
e
v
o
ltag
e
s
o
lu
tio
n
is
co
m
p
lete,
lin
e
f
lo
ws
ca
n
b
e
ca
lcu
lated
.
T
h
e
cu
r
r
e
n
t
b
etwe
en
n
o
d
es
ii
an
d
is
:
{
=
(
−
)
∗
+
∗
(
′
2
⁄
)
∗
=
−
=
∗
∗
(
−
)
∗
+
∗
(
′
2
)
(
8
)
W
h
er
e
is
lin
e
ad
m
ittan
ce
an
d
′
is
s
h
u
n
t
ad
m
ittan
ce
.
Sy
s
tem
l
o
s
s
es a
r
e
r
ep
r
esen
ted
as:
{
=
(
∑
=
0
)
−
(
∑
=
0
)
=
(
∑
=
0
)
−
(
∑
=
0
)
=
(
∑
=
0
)
−
(
∑
=
0
)
(
9
)
W
h
er
e
r
ep
r
esen
ts
to
tal
n
etwo
r
k
lo
s
s
es.
T
h
ese
co
n
s
tr
ain
ts
en
s
u
r
e
th
at
th
e
s
y
s
tem
o
p
e
r
ates
s
af
ely
,
av
o
i
d
in
g
d
am
ag
e
,
in
s
t
ab
ilit
y
,
o
r
in
s
ec
u
r
ity
.
Fig
u
r
e
7
o
u
tlin
es
th
e
p
r
o
ce
s
s
o
f
ev
alu
atin
g
p
o
w
er
f
lo
w
r
esu
lts
,
wh
ich
ar
e
a
p
p
lied
in
in
v
estme
n
t
p
lan
n
in
g
a
n
d
o
p
e
r
atio
n
al.
T
h
e
Fig
u
r
e
7
illu
s
tr
ates
th
e
s
tep
-
by
-
s
tep
p
r
o
ce
s
s
f
o
r
ev
alu
atin
g
p
o
wer
f
lo
w
r
esu
lts
,
h
ig
h
lig
h
tin
g
th
e
s
eq
u
en
ce
o
f
d
ata
in
p
u
t,
co
m
p
u
tatio
n
,
an
d
an
aly
s
is
p
h
ases
.
I
t
is
a
cr
itical
to
o
l
f
o
r
u
n
d
er
s
tan
d
i
n
g
th
e
in
teg
r
ati
o
n
o
f
p
o
wer
f
l
o
w
co
m
p
u
tatio
n
s
in
to
s
y
s
tem
p
lan
n
in
g
,
in
cl
u
d
in
g
th
e
id
en
tific
atio
n
o
f
co
n
s
tr
ain
ts
,
o
p
tim
izatio
n
o
f
n
etwo
r
k
o
p
er
atio
n
s
,
an
d
ass
ess
m
en
t o
f
r
eliab
ilit
y
an
d
ef
f
icie
n
cy
.
Fig
u
r
e
1
.
Flo
wch
ar
t
o
f
p
o
wer
f
lo
w
r
esu
lt e
v
alu
atio
n
p
r
o
ce
s
s
T
h
e
lo
wer
at
0
.
9
p
.
u
.
a
n
d
u
p
p
er
at
1
.
1
p
.
u
.
v
o
ltag
e
lim
i
ts
ar
e
u
s
ed
in
o
u
r
s
tu
d
y
.
T
h
e
New
to
n
-
R
ap
h
s
o
n
(
NR
)
m
eth
o
d
is
wid
ely
u
s
ed
f
o
r
s
o
lv
in
g
n
o
n
lin
ea
r
p
o
wer
f
lo
w
p
r
o
b
lem
s
d
u
e
to
its
ef
f
icien
cy
an
d
f
ast co
n
v
er
g
e
n
ce
[
2
7
]
–
[
2
9
]
.
B
elo
w
is
a
d
etailed
ex
p
lan
atio
n
o
f
th
e
m
ath
e
m
atica
l p
r
o
ce
s
s
.
T
o
s
o
lv
e
a
n
o
n
lin
ea
r
eq
u
at
io
n
(
)
=
0
,
th
e
New
to
n
-
R
ap
h
s
o
n
m
eth
o
d
r
elies
o
n
s
u
cc
ess
iv
e
ap
p
r
o
x
im
atio
n
s
o
f
th
e
s
o
lu
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n
x
.
I
f
∆
0
is
th
e
co
r
r
ec
tio
n
ap
p
lied
to
th
e
in
itial
v
alu
e
0
,
th
e
s
o
lu
tio
n
is
ex
p
r
ess
ed
as:
=
0
+
∆
0
(
1
0
)
Usi
n
g
th
e
T
ay
lo
r
s
er
ies ex
p
an
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n
d
0
,
th
e
eq
u
atio
n
(
)
=
0
b
ec
o
m
es:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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I
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2
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8
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I
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r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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lec
&
C
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m
p
E
n
g
I
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N:
2088
-
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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7
0
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t
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Un
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m
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(LS
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fr
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m
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c
h
ir
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rsity
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f
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ter,
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ria.
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r
f
ield
s
o
f
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n
tere
st
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re
:
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a
l
p
ro
c
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tell
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m
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g
.
Sh
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c
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c
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tac
ted
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m
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:
s.d
jela
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a
@c
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lb
a
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d
z
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