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Vo
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.
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A
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20
25
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p
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8
I
SS
N:
2088
-
8
7
0
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,
DOI
: 1
0
.
1
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9
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v
15
i
4
.
pp
3
6
3
2
-
3
6
4
8
3632
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Saf
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Dep
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Facu
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c
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1.
I
NT
RO
D
UCT
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O
N
C
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m
an
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is
n
o
w
g
r
ap
p
lin
g
with
[
1
]
.
Un
d
o
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b
te
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ly
,
th
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o
ta
b
le
in
cr
ea
s
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in
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wid
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tem
p
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as
s
h
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b
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th
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Had
C
R
UT
4
g
lo
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ata,
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f
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ated
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f
clim
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ch
an
g
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in
t
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s
tr
ateg
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[
2
]
.
T
h
e
m
ai
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ca
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s
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in
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estatio
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r
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v
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2
4
%
[
3
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,
to
th
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x
ten
t
th
at
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Af
r
ica,
f
o
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ex
am
p
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ch
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in
to
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s
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ch
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p
r
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r
am
s
[
4
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,
a
s
tr
ateg
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th
at
co
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ld
h
elp
p
r
o
m
o
te
clim
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-
r
esil
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s
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s
ta
in
ab
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esear
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etr
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eq
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b
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s
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an
d
u
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s
co
r
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th
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c
r
itical
s
ig
n
if
ican
ce
o
f
tr
an
s
itio
n
in
g
to
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e
n
ewa
b
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en
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g
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s
o
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ce
s
to
allev
iate
th
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f
ec
ts
.
I
t
p
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d
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tan
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s
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in
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s
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x
p
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s
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th
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g
lo
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o
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y
[
5
]
,
[
6
]
.
İ
n
al
et
a
l.
[
7
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h
as
d
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o
n
s
tr
ated
a
v
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r
elatio
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C
O
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wth
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Af
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p
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to
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p
ar
am
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tim
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.
On
th
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th
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h
a
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d
,
r
ec
en
t
liter
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r
e
[
8
]
h
as
clea
r
ly
p
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th
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im
p
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f
g
lo
b
aliza
tio
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tech
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wth
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air
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in
6
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1
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m
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I
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I
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N:
2088
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8
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R
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3633
T
h
e
tr
an
s
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to
r
en
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b
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en
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g
ies,
d
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b
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[
9
]
.
I
n
a
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d
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,
th
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in
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n
m
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p
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clim
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ch
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Mo
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ch
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tech
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E
d
d
ah
ab
,
wh
ich
p
lay
a
s
tr
ateg
ic
r
o
le
in
th
is
tr
an
s
f
o
r
m
atio
n
[
1
1
]
,
[
1
2
]
.
I
n
teg
r
atin
g
in
ter
m
itten
t
r
e
n
e
wab
le
en
er
g
y
s
o
u
r
ce
s
in
to
p
o
wer
g
r
id
s
p
r
esen
ts
s
ig
n
if
ican
t
tech
n
ical
ch
allen
g
es,
n
ec
ess
itatin
g
ex
te
n
s
iv
e
r
esear
ch
t
o
g
u
ar
an
tee
th
e
r
eliab
ilit
y
an
d
s
tab
ilit
y
o
f
th
e
s
y
s
tem
,
esp
ec
ially
wh
en
d
ea
lin
g
with
in
ter
m
itten
cy
r
ates
o
f
u
p
to
1
0
0
%
[
1
3
]
.
T
h
e
g
eo
g
r
a
p
h
ical
d
is
tr
ib
u
tio
n
o
f
r
en
ewa
b
le
en
er
g
y
f
ac
ilit
ies
h
elp
s
to
al
lev
iate
th
e
is
s
u
e
o
f
in
ter
m
itten
t
p
o
wer
g
en
er
atio
n
b
y
m
i
n
im
izin
g
th
e
i
n
f
lu
en
ce
o
f
clim
atic
co
n
d
itio
n
s
o
n
th
eir
g
en
er
atio
n
.
Ad
d
itio
n
ally
,
th
e
u
tili
za
ti
o
n
o
f
d
iv
er
s
e
tech
n
o
lo
g
ies
h
elp
s
to
lo
wer
th
e
ex
p
en
s
es
ass
o
ciate
d
with
in
teg
r
atin
g
th
ese
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
[
1
4
]
.
T
h
e
v
ar
iatio
n
o
f
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
s
u
ch
as
win
d
o
r
s
o
lar
,
p
o
s
es
o
b
s
tacle
s
to
th
eir
o
p
ti
m
al
in
teg
r
atio
n
in
to
t
h
e
p
o
wer
g
r
id
.
Var
iatio
n
s
in
win
d
s
p
ee
d
an
d
s
o
lar
ir
r
ad
ia
n
ce
cr
ea
te
r
eliab
ilit
y
an
d
s
tab
ili
ty
is
s
u
es,
lead
in
g
to
o
v
e
r
v
o
lta
g
es
an
d
im
b
alan
ce
s
in
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
[
1
5
]
,
[
1
6
]
.
T
h
e
m
ain
g
o
al
o
f
a
p
o
wer
s
y
s
tem
o
p
er
ato
r
is
to
en
s
u
r
e
th
e
d
ep
en
d
a
b
le
b
alan
ce
b
etwe
en
p
o
we
r
g
e
n
er
atio
n
an
d
d
em
an
d
,
wh
ile
m
in
im
izin
g
c
o
s
ts
an
d
lo
s
s
es.
No
n
eth
eless
,
th
e
in
escap
ab
le
in
f
lu
e
n
ce
o
f
th
e
i
r
r
eg
u
lar
ity
o
f
win
d
a
n
d
s
o
lar
p
o
wer
o
n
th
e
elec
tr
ical
s
y
s
tem
r
elies
o
n
t
h
e
s
ca
le
an
d
in
h
er
en
t
ad
ap
tab
ilit
y
o
f
th
e
g
r
id
,
as
well
as
th
e
ex
ten
t
t
o
wh
ich
in
te
r
m
itten
t
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
ar
e
in
clu
d
ed
in
to
t
h
e
g
r
id
[
1
7
]
.
Ug
wu
an
y
i
et
a
l
.
[
1
8
]
s
u
g
g
ested
t
h
at
u
s
in
g
f
lex
ib
le
alter
n
atin
g
c
u
r
r
en
t tr
an
s
m
is
s
io
n
s
y
s
tem
(
FAC
T
S)
d
ev
ices
ca
n
in
cr
ea
s
e
r
en
ewa
b
le
en
er
g
y
p
en
etr
atio
n
in
Nig
er
ia
b
y
4
0
%,
allo
win
g
f
o
r
t
h
e
in
teg
r
atio
n
o
f
a
n
a
d
d
itio
n
al
1
5
2
MW
o
f
win
d
en
er
g
y
with
o
u
t
co
m
p
r
o
m
is
in
g
s
y
s
tem
s
tab
ilit
y
.
T
h
e
p
ap
er
[
1
9
]
ex
am
in
es
h
y
b
r
id
win
d
an
d
p
h
o
to
v
o
ltaic
(
PV)
i
n
teg
r
atio
n
in
u
r
b
a
n
ar
ea
s
,
f
o
cu
s
in
g
o
n
co
n
s
is
ten
t
DC
b
u
s
-
b
ar
v
o
ltag
e
an
d
b
atter
y
c
o
n
n
e
ctio
n
s
.
A
MA
T
L
AB
m
o
d
el
is
d
ev
elo
p
ed
to
s
im
u
late
g
r
id
p
e
r
f
o
r
m
an
ce
,
h
ig
h
lig
h
tin
g
th
e
ef
f
icac
y
o
f
h
y
b
r
id
win
d
a
n
d
PV
in
m
ee
tin
g
s
u
s
tain
ab
le
en
er
g
y
g
o
als,
co
n
t
r
ib
u
tin
g
to
p
o
licy
m
ak
in
g
an
d
r
esear
ch
.
I
n
p
ap
er
[
2
0
]
r
en
ew
ab
le
en
er
g
y
s
o
u
r
ce
s
lik
e
s
o
lar
an
d
win
d
ar
e
in
cr
ea
s
in
g
ly
b
ein
g
u
s
ed
to
m
ee
t
g
lo
b
al
en
er
g
y
d
em
an
d
s
wh
ile
r
ed
u
cin
g
g
r
ee
n
h
o
u
s
e
g
as
em
is
s
io
n
s
.
Ho
wev
er
,
th
eir
u
n
p
r
ed
i
ctab
le
n
atu
r
e
p
o
s
es
ch
allen
g
es f
o
r
g
r
id
o
p
er
ato
r
s
.
T
h
e
co
m
b
i
n
ed
u
s
e
o
f
th
ese
s
o
u
r
ce
s
co
u
ld
im
p
r
o
v
e
g
r
i
d
o
p
e
r
ab
ilit
y
an
d
s
af
ety
.
T
h
is
s
tu
d
y
f
o
cu
s
es
o
n
t
h
e
M
o
r
o
cc
an
5
-
b
u
s
p
o
we
r
g
r
id
,
a
n
aly
zin
g
its
b
e
h
av
io
r
an
d
p
e
r
f
o
r
m
a
n
ce
u
n
d
er
v
a
r
y
in
g
s
ce
n
ar
io
s
o
f
s
o
lar
an
d
win
d
en
er
g
y
in
teg
r
a
tio
n
.
Usi
n
g
th
e
New
to
n
-
R
ap
h
s
o
n
m
eth
o
d
in
th
e
MA
T
L
AB
/
S
im
u
lin
k
en
v
ir
o
n
m
en
t,
th
e
r
esear
ch
ex
a
m
in
es
v
o
ltag
e
lev
els
an
d
ac
tiv
e
p
o
wer
f
lo
ws
ac
r
o
s
s
d
if
f
er
en
t
n
o
d
es
in
th
e
n
etw
o
r
k
.
Fo
u
r
d
is
tin
ct
s
ce
n
ar
io
s
o
f
r
e
n
ewa
b
le
en
e
r
g
y
p
en
etr
a
tio
n
ar
e
e
x
p
lo
r
ed
,
h
ig
h
lig
h
tin
g
th
e
g
r
i
d
'
s
r
esp
o
n
s
e
to
v
ar
iab
ilit
y
in
r
e
n
ewa
b
le
e
n
er
g
y
g
en
er
atio
n
.
T
h
e
a
n
aly
s
is
p
r
o
v
id
es
v
alu
a
b
le
in
s
ig
h
ts
in
to
th
e
im
p
ac
t
o
f
r
e
n
ewa
b
le
in
teg
r
ati
o
n
o
n
v
o
ltag
e
s
tab
ilit
y
,
ac
tiv
e
p
o
wer
d
is
tr
ib
u
tio
n
,
an
d
p
o
wer
lo
s
s
es,
id
en
tify
in
g
tech
n
ical
c
h
allen
g
es
an
d
ar
ea
s
f
o
r
o
p
tim
izatio
n
.
B
ased
o
n
th
ese
f
in
d
in
g
s
,
th
e
s
tu
d
y
o
f
f
e
r
s
r
ec
o
m
m
en
d
atio
n
s
to
en
h
an
c
e
g
r
id
s
tab
ilit
y
,
m
an
a
g
e
v
o
ltag
e
f
lu
ctu
atio
n
s
,
a
n
d
m
in
i
m
ize
p
o
wer
lo
s
s
es,
s
u
p
p
o
r
tin
g
ef
f
icien
t in
te
g
r
atio
n
o
f
r
e
n
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
s
.
T
h
e
p
ap
er
is
s
tr
u
ctu
r
ed
as
f
o
llo
ws:
in
s
ec
t
io
n
2
o
u
tlin
es
th
e
th
eo
r
etica
l
f
o
u
n
d
atio
n
s
o
f
lo
ad
f
lo
w
an
aly
s
is
,
d
etailin
g
its
o
b
jecti
v
es,
th
e
class
if
icatio
n
o
f
n
o
d
es
with
in
th
e
p
o
wer
g
r
id
,
an
d
th
e
r
eso
lu
tio
n
m
eth
o
d
s
,
s
p
ec
if
ically
th
e
ap
p
l
icatio
n
o
f
th
e
New
to
n
-
R
ap
h
s
o
n
m
eth
o
d
f
o
r
p
o
wer
f
lo
w
ca
lc
u
latio
n
s
.
I
n
s
ec
tio
n
3
,
we
p
r
esen
t
t
h
e
d
esig
n
o
f
t
h
e
Mo
r
o
cc
a
n
5
-
bu
s
n
etwo
r
k
m
o
d
el,
in
clu
d
in
g
d
ata
p
a
r
am
eter
s
f
o
r
b
u
s
es
an
d
lin
es,
an
d
d
escr
ib
e
v
ar
io
u
s
s
ce
n
ar
io
s
f
o
r
r
e
n
ewa
b
le
en
er
g
y
in
teg
r
atio
n
in
to
th
e
g
r
id
.
Sect
io
n
4
p
r
o
v
id
es
th
e
r
esu
lts
o
f
th
e
lo
ad
f
lo
w
an
a
ly
s
is
f
o
r
f
o
u
r
d
if
f
er
en
t
s
ce
n
ar
io
s
,
an
aly
zin
g
v
o
ltag
e
p
r
o
f
iles
,
ac
tiv
e
p
o
wer
g
en
er
atio
n
,
an
d
p
o
we
r
lo
s
s
es,
f
o
llo
wed
b
y
a
co
m
p
ar
ativ
e
d
is
cu
s
s
io
n
to
id
en
tify
t
h
e
o
p
tim
al
ca
s
e.
Als
o
,
we
ex
am
in
e
h
o
w
v
ar
iatio
n
s
in
s
o
lar
en
er
g
y
p
e
n
etr
atio
n
im
p
ac
t
th
e
n
etwo
r
k
'
s
v
o
ltag
e
p
r
o
f
ile,
p
o
wer
g
en
er
atio
n
,
an
d
lo
s
s
es.
Fin
ally
,
s
ec
tio
n
5
s
u
m
m
ar
izes
th
e
f
in
d
in
g
s
,
e
m
p
h
asizes
th
e
im
p
licatio
n
s
f
o
r
f
u
tu
r
e
r
en
ewa
b
le
en
er
g
y
in
teg
r
atio
n
,
an
d
p
r
o
v
i
d
es
r
ec
o
m
m
en
d
atio
n
s
f
o
r
im
p
r
o
v
in
g
g
r
id
s
tab
ilit
y
an
d
ef
f
icien
cy
in
Mo
r
o
cc
o
'
s
p
o
wer
s
y
s
tem
.
L
o
ad
f
lo
w
a
n
aly
s
is
is
an
in
n
o
v
ativ
e
tech
n
iq
u
e
u
s
ed
to
p
r
ed
i
ct
an
d
m
an
a
g
e
th
e
d
e
cr
ea
s
e
in
v
o
ltag
e
r
esu
ltin
g
f
r
o
m
th
e
in
teg
r
atio
n
o
f
r
en
ewa
b
le
en
er
g
ies
in
to
th
e
p
o
wer
g
r
i
d
[
2
1
]
.
T
h
e
s
tu
d
y
also
d
eter
m
in
es
p
o
wer
lo
s
s
es,
b
u
s
v
o
ltag
es,
g
en
er
ato
r
ac
tiv
e
p
o
wer
,
a
n
d
lo
ad
ac
tiv
e
p
o
wer
d
u
r
i
n
g
a
c
o
m
p
lete
d
ay
in
a
test
s
y
s
tem
b
y
em
p
lo
y
in
g
lo
ad
f
lo
w
an
aly
s
is
[
2
2
]
.
T
h
e
u
tili
za
tio
n
o
f
l
o
ad
f
lo
w
an
aly
s
is
m
eth
o
d
o
lo
g
y
p
r
o
v
id
es
a
co
m
p
r
eh
e
n
s
iv
e
ass
ess
m
en
t
o
f
v
o
lta
g
e
im
b
alan
ce
,
e
n
ab
lin
g
o
p
er
ato
r
s
to
id
en
tif
y
k
ey
n
o
d
es
an
d
s
ce
n
ar
io
s
in
th
e
p
o
wer
g
r
id
[
2
3
]
.
A
n
o
v
el
i
ter
ativ
e
ap
p
r
o
ac
h
is
s
u
g
g
ested
f
o
r
c
o
m
p
u
tin
g
p
o
wer
f
lo
w
i
n
r
ad
ial
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
,
co
n
s
id
er
in
g
a
b
r
o
a
d
s
p
ec
tr
u
m
o
f
r
esis
tan
ce
an
d
r
ea
ctan
ce
,
as
well
as
th
e
attr
ib
u
tes
o
f
s
o
lar
(
SO)
p
r
o
d
u
ce
r
s
.
T
h
e
ef
f
ec
tiv
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e
e
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p
h
a
s
e
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a
d
f
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mo
d
e
l
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si
n
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a
mo
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e
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s
e
t
w
o
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p
o
r
t
n
e
t
w
o
r
k
m
o
d
e
l
.
Tw
o
-
p
o
r
t
n
e
t
w
o
r
k
mo
d
e
l
[
3
1
]
A
n
a
l
y
z
e
s I
EEE
5
-
B
u
s
a
n
d
1
4
-
B
u
s s
y
s
t
e
ms f
o
r
f
a
u
l
t
s
a
n
d
l
o
a
d
p
r
o
f
i
l
e
s
u
s
i
n
g
N
e
w
t
o
n
-
R
a
p
h
s
o
n
a
n
d
ETA
P
s
h
o
r
t
-
c
i
r
c
u
i
t
a
n
a
l
y
s
i
s.
ETA
P
so
f
t
w
a
r
e
a
n
d
N
e
w
t
o
n
-
R
a
p
h
s
o
n
m
e
t
h
o
d
[
3
2
]
D
e
v
e
l
o
p
s
a
n
e
w
st
e
a
d
y
-
s
t
a
t
e
m
o
d
e
l
f
o
r
D
F
I
G
-
b
a
se
d
W
i
n
d
P
o
w
e
r
P
l
a
n
t
s
(
W
P
P
s)
c
o
n
si
d
e
r
i
n
g
s
u
b
-
/
s
u
p
e
r
-
sy
n
c
h
r
o
n
o
u
s c
o
n
d
i
t
i
o
n
s
a
n
d
c
o
n
s
t
a
n
t
p
o
w
e
r
f
a
c
t
o
r
s.
S
t
e
a
d
y
-
st
a
t
e
mo
d
e
l
i
n
g
[
3
3
]
P
e
r
f
o
r
ms l
o
a
d
f
l
o
w
a
n
a
l
y
s
i
s
o
n
I
EEE
1
4
-
B
u
s
sy
s
t
e
ms t
o
e
v
a
l
u
a
t
e
st
e
a
d
y
-
s
t
a
t
e
e
l
e
c
t
r
i
c
a
l
p
e
r
f
o
r
m
a
n
c
e
a
n
d
p
o
w
e
r
f
l
o
w
s u
si
n
g
M
A
TLA
B
.
N
e
w
t
o
n
-
R
a
p
h
s
o
n
me
t
h
o
d
[
3
4
]
R
e
v
i
e
w
s
u
n
c
e
r
t
a
i
n
t
y
m
o
d
e
l
i
n
g
t
e
c
h
n
i
q
u
e
s
i
n
p
r
o
b
a
b
i
l
i
st
i
c
l
o
a
d
f
l
o
w
(
P
LF)
,
i
n
c
l
u
d
i
n
g
st
o
c
h
a
s
t
i
c
a
n
d
p
r
o
b
a
b
i
l
i
s
t
i
c
met
h
o
d
s.
P
r
o
b
a
b
i
l
i
st
i
c
l
o
a
d
f
l
o
w
a
n
a
l
y
si
s
[
3
5
]
I
n
t
r
o
d
u
c
e
s a
d
a
p
t
i
v
e
b
a
n
d
w
i
d
t
h
k
e
r
n
e
l
d
e
n
si
t
y
e
s
t
i
m
a
t
i
o
n
w
i
t
h
L
a
t
i
n
h
y
p
e
r
c
u
b
e
samp
l
i
n
g
f
o
r
a
c
c
u
r
a
t
e
P
LF
a
n
a
l
y
si
s
o
f
so
l
a
r
a
n
d
w
i
n
d
p
o
w
e
r
i
n
j
e
c
t
i
o
n
s.
P
r
o
b
a
b
i
l
i
st
i
c
l
o
a
d
f
l
o
w
w
i
t
h
k
e
r
n
e
l
d
e
n
si
t
y
[
3
6
]
D
e
mo
n
st
r
a
t
e
s
t
h
e
b
e
n
e
f
i
t
s
o
f
t
r
a
n
sf
o
r
mer
-
l
e
ss
i
n
v
e
r
t
e
r
s
i
n
p
h
o
t
o
v
o
l
t
a
i
c
(
P
V
)
sy
st
e
ms,
r
e
d
u
c
i
n
g
c
o
st
s
a
n
d
i
m
p
r
o
v
i
n
g
e
f
f
i
c
i
e
n
c
y
f
o
r
g
r
i
d
c
o
n
n
e
c
t
i
o
n
s.
A
n
a
l
y
s
i
s
o
f
P
V
g
r
i
d
i
n
t
e
g
r
a
t
i
o
n
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
R
en
ewa
b
le
en
erg
y
imp
a
ct
i
n
teg
r
a
tio
n
in
mo
r
o
cc
a
n
g
r
id
-
lo
a
d
flo
w
a
n
a
lysi
s
(
S
a
fa
a
E
s
s
a
id
)
3635
2.
M
E
T
H
O
DO
L
O
G
Y
2
.
1
.
T
heo
re
t
ica
l st
ud
y
2
.
1
.
1
.
T
he
o
bje
ct
iv
es o
f
lo
a
d f
lo
w
a
na
ly
s
is
L
o
ad
f
lo
w
an
aly
s
is
is
a
ter
m
in
o
lo
g
y
th
at
r
e
p
r
esen
ts
a
s
et
o
f
n
u
m
er
ical
an
aly
s
es
an
d
p
r
o
ce
d
u
r
es
p
er
f
o
r
m
ed
o
n
a
co
m
p
u
ter
to
d
eter
m
in
e
th
e
p
o
wer
d
is
tr
ib
u
tio
n
in
a
g
iv
en
s
y
s
tem
in
o
r
d
er
to
co
n
tr
o
l
th
is
p
o
wer
d
is
tr
ib
u
tio
n
.
T
h
e
d
eter
m
in
atio
n
o
f
r
ea
ctiv
e
an
d
ac
ti
v
e
p
o
we
r
in
th
e
tr
an
s
m
is
s
io
n
lin
e
is
b
ased
o
n
p
r
ed
e
f
in
ed
co
n
s
id
er
atio
n
s
r
elate
d
t
o
th
e
r
ec
eiv
er
o
r
g
en
e
r
ato
r
.
T
h
is
in
cl
u
d
es
ca
lcu
latin
g
th
e
p
o
ten
tial
d
if
f
er
en
ce
s
at
ea
c
h
n
o
d
e
o
r
s
et
o
f
b
u
s
es
an
d
e
n
s
u
r
in
g
th
at
n
o
lin
e
is
o
v
e
r
lo
ad
ed
.
C
o
n
tin
u
o
u
s
m
o
n
ito
r
in
g
is
also
r
eq
u
ir
ed
,
esp
ec
ially
in
th
e
ev
en
t
o
f
r
ec
l
o
s
in
g
.
Ad
d
itio
n
ally
,
th
e
s
p
ec
i
f
ic
p
o
wer
f
l
o
w
is
d
eter
m
in
ed
to
ac
h
iev
e
o
p
tim
al
d
is
p
atch
b
y
ca
lcu
latin
g
t
h
e
n
etwo
r
k
'
s
s
ta
te
(
P,
Q,
V,
an
d
)
u
n
d
e
r
s
p
ec
if
ied
p
r
o
d
u
ctio
n
an
d
co
n
s
u
m
p
tio
n
ass
u
m
p
tio
n
s
.
E
v
er
y
s
et
o
f
b
ar
s
(
n
o
d
e)
is
ass
o
ciate
d
with
4
d
ef
in
ed
p
ar
am
eter
s
:
th
e
ac
tiv
e
p
o
wer
i
n
jecte
d
o
r
ex
tr
ac
ted
(
P),
th
e
r
ea
ctiv
e
p
o
w
er
in
jecte
d
o
r
ex
tr
ac
ted
(
Q)
,
th
e
v
o
ltag
e
m
o
d
u
le
(
V
)
,
v
o
ltag
e
p
h
ase
s
h
if
t
(
)
.
L
o
ad
f
l
o
w
is
th
er
ef
o
r
e
th
e
r
eso
lu
tio
n
o
f
a
s
y
s
tem
o
f
n
o
n
-
lin
ea
r
eq
u
atio
n
s
,
wh
ich
elim
in
ates
th
e
p
o
s
s
ib
ilit
y
o
f
an
an
aly
tical
s
o
lu
tio
n
in
m
o
s
t
ca
s
es.
Nu
m
er
ical
s
o
lu
tio
n
s
ar
e
co
m
p
u
ter
-
aid
ed
.
L
o
ad
Flo
w
an
aly
s
is
o
f
a
d
is
tr
ib
u
tio
n
n
et
wo
r
k
co
n
tain
in
g
a
h
u
n
d
r
ed
b
u
s
b
ar
s
an
d
tr
an
s
m
is
s
io
n
lin
es
ap
p
ea
r
s
to
b
e
a
co
m
p
lex
p
r
o
ce
s
s
.
Fo
r
a
h
ig
h
l
y
s
im
p
lifie
d
n
etwo
r
k
,
Fig
u
r
e
1
s
h
o
ws
a
s
im
p
ler
n
etwo
r
k
with
two
b
u
s
b
ar
s
.
T
h
e
tr
an
s
m
is
s
io
n
lin
e
will b
e
co
n
s
id
er
ed
lo
s
s
less
; th
e
lin
ea
r
r
esis
t
an
ce
is
n
eg
lig
ib
le
an
d
th
e
a
d
m
ittan
ce
:
=
.
Fig
u
r
e
1
.
A
s
im
p
ler
n
etwo
r
k
with
two
b
u
s
es
2
.
1
.
2
.
Det
er
m
ina
t
i
o
n o
f
g
ene
ra
t
o
r
a
nd
re
ce
pto
r
a
ct
iv
e
a
nd
re
a
ct
iv
e
po
wer
Ph
ase
s
h
if
t
b
etwe
en
1
an
d
2
s
u
ch
th
at:
=
2
−
1
(
1
)
T
h
e
co
m
p
le
x
p
o
we
r
at
th
e
g
e
n
er
ato
r
an
d
r
ec
eiv
er
will b
e:
{
1
=
1
+
1
=
1
∗
2
=
2
+
2
=
2
∗
(
2
)
2
is
tak
en
as th
e
p
h
ase
o
r
ig
in
.
T
h
e
cu
r
r
e
n
t in
th
e
lin
e:
=
1
−
2
(
3
)
1
is
th
e
co
m
p
lex
a
p
p
ar
e
n
t p
o
we
r
at
b
u
s
1
1
=
1
∗
=
1
[
(
1
∗
−
2
∗
)
∗
]
=
(
1
2
−
1
2
)
(
−
)
(
4
)
T
h
en
:
1
=
(
1
2
)
s
in
(
)
(
5
)
1
=
(
1
2
−
1
2
co
s
)
(
)
(
6
)
Fo
r
b
u
s
2
:
2
=
2
∗
=
2
[
1
∗
−
2
∗
∗
]
=
(
1
2
−
2
2
)
(
−
)
(
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
.
4
,
Au
g
u
s
t
20
25
:
3
6
3
2
-
3648
3636
So
:
2
=
(
1
2
)
s
in
(
)
(
8
)
2
=
(
1
2
co
s
−
2
2
)
(
)
(
9
)
Ass
u
m
in
g
th
is
lin
e
h
as o
n
e
r
es
is
tan
ce
R
p
er
p
h
ase,
th
e
J
o
u
le
E
f
f
ec
t
lo
s
s
es a
r
e:
=
|
|
2
(
)
(
1
0
)
=
+
=
∗
(
1
1
)
T
h
en
:
∗
=
|
|
2
=
(
2
+
2
)
|
|
2
(
1
2
)
So
=
(
2
+
2
|
|
2
)
(
)
(
1
3
)
I
n
r
ea
l
s
y
s
tem
s
,
an
ex
p
licit
an
aly
tical
ex
p
r
ess
io
n
will
b
e
u
n
f
ea
s
ib
le
d
u
e
to
f
lu
ctu
atin
g
b
u
s
b
ar
lo
ad
s
o
n
th
e
o
n
e
h
an
d
,
an
d
th
e
in
ab
ilit
y
to
p
r
ed
eter
m
in
e
th
e
v
o
ltag
e
at
th
e
r
ec
eiv
er
o
n
th
e
o
th
er
.
I
n
t
h
is
ca
s
e,
n
u
m
er
ical
m
eth
o
d
s
m
u
s
t b
e
u
s
ed
to
d
ete
r
m
in
e
th
e
u
n
k
n
o
wn
s
,
g
en
er
ally
th
r
o
u
g
h
iter
ativ
e
p
r
o
ce
d
u
r
es.
T
h
e
cu
r
r
e
n
t e
n
ter
in
g
n
o
d
e
K
is
g
iv
en
b
y
:
=
(
2
+
2
|
|
2
)
(
)
(
1
4
)
W
ith
,
tr
an
s
f
er
ad
m
ittan
ce
ass
o
ciate
d
with
n
o
d
es
'
'
an
d
'
',
,
v
o
ltag
e
at
n
o
d
e
'
'
an
d
,
to
tal
n
u
m
b
er
o
f
n
o
d
es.
W
h
ich
ca
n
b
e
r
ewr
itten
as
(
1
5
)
:
=
+
∑
=
1
≠
(
1
5
)
,
W
e
o
b
tain
:
=
=
1
∑
=
1
≠
(
1
6
)
=
∗
:
∗
=
∗
(
1
7
)
∗
=
∗
=
−
(
1
8
)
Hen
ce
:
=
−
∗
(
1
9
)
=
1
(
−
∗
−
∑
=
1
≠
)
=
1
,
2
,
…
,
(
20
)
T
h
e
s
et
o
f
in
(
2
0
)
co
n
s
titu
tes
th
e
lo
ad
f
l
o
w
eq
u
atio
n
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
R
en
ewa
b
le
en
erg
y
imp
a
ct
i
n
teg
r
a
tio
n
in
mo
r
o
cc
a
n
g
r
id
-
lo
a
d
flo
w
a
n
a
lysi
s
(
S
a
fa
a
E
s
s
a
id
)
3637
2
.
1
.
3
.
Cla
s
s
if
ica
t
io
n o
f
no
des
No
d
es
ca
n
b
e
class
if
ied
in
to
t
h
r
ee
ca
teg
o
r
ies:
C
o
n
s
u
m
er
n
o
d
e
(
lo
ad
b
u
s
)
:
it
i
s
a
s
et
o
f
b
ar
s
f
o
r
wh
ich
P
an
d
Q
ar
e
k
n
o
wn
,
wh
ile
V
an
d
ar
e
to
b
e
d
eter
m
in
ed
.
Pro
d
u
ce
r
n
o
d
e
(
g
en
er
at
o
r
b
u
s
)
:
th
is
is
a
s
et
o
f
b
ar
s
f
o
r
wh
ich
th
e
a
m
p
litu
d
e
o
f
th
e
g
en
er
ated
v
o
ltag
e
V
an
d
t
h
e
c
o
r
r
esp
o
n
d
in
g
p
o
wer
P a
r
e
k
n
o
wn
,
wh
ile
Q
an
d
ar
e
to
b
e
d
ete
r
m
in
ed
.
B
alan
ce
n
o
d
e
(
Swin
g
b
u
s
)
:
it
i
s
a
g
e
n
er
ato
r
b
ar
f
o
r
wh
ich
V
an
d
ar
e
s
p
ec
if
ied
,
P
an
d
Q
ar
e
to
b
e
d
eter
m
in
ed
.
T
h
is
is
u
s
u
ally
th
e
m
o
s
t p
o
wer
f
u
l g
en
er
ato
r
n
o
d
e.
I
t is tak
en
as a
r
ef
er
en
ce
.
Giv
en
th
e
lar
g
e
n
u
m
b
er
o
f
v
o
ltag
e
lev
e
ls
o
n
a
m
esh
ed
n
etwo
r
k
,
L
o
a
d
Flo
w
p
r
o
b
lem
s
will
b
e
s
o
l
v
ed
u
s
in
g
r
ed
u
ce
d
q
u
an
titi
es:
∠
=
1
∠
0
°
p
er
u
n
it.
2
.
1
.
4
.
Reso
lutio
n m
et
ho
ds
Nu
m
er
o
u
s
m
eth
o
d
s
h
av
e
b
e
en
u
s
ed
(
Gau
s
s
,
Gau
s
s
Sei
d
el,
New
to
n
-
R
ap
h
s
o
n
,
R
elax
atio
n
,
a
n
d
R
esid
u
als)
o
f
wh
ich
th
e
b
est
k
n
o
wn
a
r
e
th
e
f
o
llo
win
g
[
3
7
]
,
[
3
8
]
:
Gau
s
s
-
Seid
el
an
d
New
to
n
-
R
ap
h
s
o
n
.
T
h
e
m
o
s
t
co
m
m
o
n
ly
u
s
ed
m
eth
o
d
s
to
d
ay
ar
e
v
a
r
ian
ts
o
f
th
e
New
to
n
-
R
ap
h
s
o
n
(
NR
)
m
eth
o
d
,
to
ap
p
ly
it
to
a
L
o
ad
Flo
w
p
r
o
b
lem
,
f
o
r
n
o
d
e
K:
{
K
K
K
VV
=
n
n
n
VV
=
K
n
K
n
K
n
YY
=
(
2
1
)
T
h
e
u
tili
za
tio
n
o
f
th
e
New
to
n
-
R
ap
h
s
o
n
ap
p
r
o
ac
h
p
r
esen
ts
n
u
m
er
o
u
s
n
o
tab
le
b
en
ef
its
wh
e
n
ap
p
lied
to
th
e
an
aly
s
is
o
f
elec
tr
ical
s
y
s
tem
s
.
I
t
is
n
o
tab
le
f
o
r
its
ca
p
ac
ity
to
r
ea
ch
a
s
o
lu
tio
n
with
a
r
ed
u
ce
d
n
u
m
b
e
r
o
f
iter
atio
n
s
,
lead
in
g
to
a
m
o
r
e
e
f
f
icien
t
co
m
p
u
tin
g
tim
e.
I
n
a
d
d
itio
n
,
its
im
p
r
o
v
ed
p
r
ec
is
io
n
m
ak
es
it
a
s
tr
o
n
g
ch
o
ice,
less
af
f
ec
ted
b
y
f
ac
to
r
s
lik
e
th
e
s
elec
tio
n
o
f
th
e
Slac
k
b
u
s
o
r
twea
k
s
to
tr
an
s
f
o
r
m
e
r
m
an
ag
em
e
n
t.
An
esp
ec
ially
r
em
ar
k
ab
le
f
ea
tu
r
e
o
f
th
is
m
eth
o
d
is
th
at
th
e
n
u
m
b
er
o
f
iter
atio
n
s
n
ee
d
ed
r
e
m
ain
s
n
ea
r
ly
co
n
s
tan
t,
r
eg
ar
d
less
o
f
th
e
co
m
p
le
x
ity
o
f
th
e
s
y
s
tem
b
ein
g
an
aly
ze
d
.
T
h
is
h
ig
h
lig
h
ts
its
r
eliab
ilit
y
an
d
ap
p
licab
ilit
y
in
d
iv
er
s
e
an
d
c
o
m
p
lex
s
itu
atio
n
s
.
Fro
m
(
2
1
)
:
−
=
∑
|
|
=
1
(
+
−
)
(2
2
)
T
h
is
lead
s
u
s
to
d
ed
u
ce
:
=
∑
|
|
=
1
c
os
(
+
−
)
(2
3
)
=
∑
|
|
=
1
s
in
(
+
−
)
(
2
4
)
2
.
2
.
Sim
ula
t
i
o
n m
o
dels
T
h
e
s
in
g
le
-
lin
e
s
im
p
lifie
d
d
ia
g
r
am
o
f
Mo
r
o
cc
o
'
s
2
2
5
k
V,
5
-
b
u
s
p
o
wer
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
2
,
an
d
co
m
p
r
is
es
two
s
ta
tio
n
s
,
a
s
o
lar
p
lan
t
in
T
in
g
h
ir
I
I
(
f
r
o
m
th
e
No
o
r
Ou
ar
za
za
te
s
tatio
n
)
an
d
a
win
d
p
ar
k
(
W
P)
in
Mid
elt
(
Par
c
E
o
lien
Mid
elt)
,
an
d
4
lo
ad
s
.
E
a
ch
lin
e
h
as
a
s
er
ies
im
p
ed
a
n
ce
R
L
.
Mo
d
elin
g
p
ar
am
eter
s
ar
e
p
r
esen
ted
in
T
ab
les 2
an
d
3
.
I
n
th
is
s
tu
d
y
,
we
estab
lis
h
ed
s
ev
er
al
s
ce
n
ar
io
s
to
s
im
u
late
th
e
p
r
o
d
u
ctio
n
an
d
in
teg
r
atio
n
o
f
s
o
lar
an
d
win
d
en
er
g
y
i
n
to
th
e
elec
tr
i
ca
l
g
r
id
.
E
ac
h
s
ce
n
ar
io
m
o
d
els
en
er
g
y
o
u
tp
u
t
b
ased
o
n
v
ar
iatio
n
s
in
s
o
lar
ir
r
ad
iatio
n
an
d
win
d
s
p
ee
d
th
at
d
ir
ec
tly
im
p
ac
t
elec
tr
icity
g
en
er
atio
n
f
r
o
m
r
en
ewa
b
le
s
o
u
r
ce
s
.
B
y
a
d
ju
s
tin
g
th
ese
p
ar
am
eter
s
,
we
ca
n
s
im
u
late
h
o
w
r
en
ewa
b
le
e
n
er
g
y
s
y
s
tem
s
r
esp
o
n
d
to
d
if
f
e
r
en
t
en
v
i
r
o
n
m
e
n
tal
co
n
d
itio
n
s
.
Fo
r
s
o
lar
en
er
g
y
,
s
ce
n
ar
io
s
co
n
s
id
er
f
lu
ctu
atio
n
s
in
s
o
lar
ir
r
ad
iatio
n
d
u
e
to
f
ac
to
r
s
lik
e
tim
e
o
f
d
ay
,
wea
th
er
co
n
d
itio
n
s
,
a
n
d
s
ea
s
o
n
al
ch
an
g
es.
T
h
is
allo
ws
u
s
to
ass
ess
th
e
v
ar
iab
ilit
y
in
s
o
lar
p
o
wer
g
en
er
atio
n
a
n
d
its
ef
f
ec
ts
o
n
g
r
id
s
tab
ilit
y
.
Fo
r
win
d
e
n
e
r
g
y
,
we
s
im
u
late
d
if
f
e
r
en
t
w
in
d
s
p
ee
d
p
r
o
f
iles
,
ac
co
u
n
tin
g
f
o
r
ch
a
n
g
es
ca
u
s
ed
b
y
wea
th
er
p
atter
n
s
an
d
g
eo
g
r
a
p
h
ical
in
f
lu
en
ce
s
.
T
h
e
s
e
p
r
o
f
iles
h
elp
u
s
u
n
d
er
s
tan
d
th
e
r
eliab
ilit
y
o
f
win
d
p
o
wer
u
n
d
e
r
v
ar
i
o
u
s
co
n
d
itio
n
s
.
B
y
in
teg
r
atin
g
th
ese
s
im
u
latio
n
s
,
we
ca
n
ev
alu
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
g
r
id
w
h
en
s
u
b
jecte
d
t
o
th
e
in
ter
m
itten
t
n
atu
r
e
o
f
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
.
T
h
e
s
ce
n
ar
io
s
h
elp
id
en
tify
p
o
ten
tial
ch
allen
g
es,
s
u
ch
as
p
er
io
d
s
o
f
lo
w
g
en
e
r
atio
n
d
u
r
i
n
g
ca
lm
o
r
clo
u
d
y
d
ay
s
,
an
d
allo
w
u
s
to
ex
p
l
o
r
e
s
o
lu
t
io
n
s
lik
e
en
er
g
y
s
to
r
a
g
e
o
r
d
em
an
d
r
esp
o
n
s
e
s
tr
ateg
ies.
T
h
e
d
ata
p
r
esen
ted
in
T
ab
le
3
is
s
o
u
r
ce
d
f
r
o
m
th
e
Natio
n
al
Of
f
ice
o
f
E
lectr
icity
an
d
Dr
in
k
i
n
g
W
ater
(
ONE
E
)
.
Fig
u
r
e
3
illu
s
tr
ates
th
e
b
lo
ck
d
iag
r
am
o
f
a
s
ec
tio
n
o
f
th
e
Mo
r
o
cc
an
n
atio
n
al
elec
tr
ical
n
etw
o
r
k
,
m
o
d
eled
i
n
MA
T
L
AB
/Si
m
u
lin
k
.
T
h
is
s
ec
tio
n
co
m
p
r
is
es
f
iv
e
k
ey
b
u
s
es:
th
e
n
ati
o
n
al
n
etwo
r
k
,
T
in
g
h
ir
I
I
,
E
r
r
ac
h
id
ia,
PE
Mid
elt,
an
d
Mib
lad
en
.
T
h
e
g
lo
b
al
d
iag
r
am
o
f
th
e
en
tire
Mo
r
o
cc
a
n
n
etwo
r
k
was
also
d
ev
elo
p
e
d
in
MA
T
L
AB
/Si
m
u
lin
k
to
p
r
o
v
id
e
a
co
m
p
r
eh
e
n
s
iv
e
r
ep
r
esen
tatio
n
o
f
its
s
tr
u
ctu
r
e
an
d
co
m
p
o
n
en
ts
.
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
.
4
,
Au
g
u
s
t
20
25
:
3
6
3
2
-
3648
3638
Fig
u
r
e
2
.
Simp
lifie
d
d
iag
r
am
o
f
Mo
r
o
cc
o
'
s
5
-
b
u
s
n
etwo
r
k
T
ab
le
2
.
L
in
e
DAT
A
o
f
5
-
b
u
s
Mo
r
o
cc
an
p
o
wer
s
y
s
tem
Li
n
e
f
r
o
m
Li
n
e
T
o
Li
n
e
I
mp
e
d
a
n
c
e
R
(
Ω
)
X
(
Ω
)
0
1
R
=
7
.
2
4
3
3
X
=
4
0
.
8
7
3
0
1
2
R
=
9
.
6
8
9
6
X
=
5
4
.
6
7
7
0
2
3
R
=
7
.
2
4
3
3
X
=
4
0
.
8
7
3
0
3
4
R
=
0
.
7
9
3
0
X
=
4
.
4
7
4
9
4
0
R
=
7
.
2
4
3
3
X
=
4
0
.
8
7
3
0
T
ab
le
3
.
B
u
s
DAT
A
o
f
5
-
b
u
s
Mo
r
o
cc
an
p
o
wer
s
y
s
tem
B
u
s
N°
N
a
me
B
u
s
c
o
d
e
V
o
l
t
a
g
e
(
p
.
u
)
G
e
n
e
r
a
t
i
o
n
Lo
a
d
MW
M
v
a
r
MW
M
v
a
r
0
N
a
t
i
o
n
a
l
N
e
t
w
o
r
k
S
w
i
n
g
1
.
0
5
+
0
j
0
0
0
0
1
Ti
n
g
h
i
r
I
I
PV
1
+
0
j
1
4
0
2
2
6
.
1
7
20
3
2
.
3
2
Er
r
a
c
h
i
d
i
a
PQ
1
+
0
j
0
0
68
1
1
0
3
P
E
M
i
d
e
l
t
PV
1
+
0
j
1
8
0
2
9
0
.
8
1
1
.
6
1
4
M
i
b
l
a
d
e
n
PQ
1
+
0
j
0
0
30
4
8
.
4
6
Fig
u
r
e
3
.
Simp
lifie
d
m
o
d
elin
g
o
f
th
e
5
-
b
u
s
Mo
r
o
cc
an
n
etwo
r
k
in
MA
T
L
AB
/
Simu
lin
k
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
R
en
ewa
b
le
en
erg
y
imp
a
ct
i
n
teg
r
a
tio
n
in
mo
r
o
cc
a
n
g
r
id
-
lo
a
d
flo
w
a
n
a
lysi
s
(
S
a
fa
a
E
s
s
a
id
)
3639
3.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
I
N
T
E
RP
R
E
T
AT
I
O
NS
3
.
1
.
Resul
t
s
o
f
lo
a
d f
l
o
w
a
na
ly
s
is
f
o
r
4
s
ce
na
rio
s
I
n
th
is
s
tu
d
y
,
a
Mo
r
o
cc
a
n
5
-
b
u
s
p
o
wer
g
r
id
in
clu
d
in
g
d
if
f
er
en
t
en
er
g
y
s
o
u
r
ce
s
,
s
u
ch
as
th
e
n
atio
n
al
g
r
id
,
s
o
lar
an
d
win
d
p
o
wer
,
is
u
s
ed
to
s
u
p
p
ly
a
co
n
s
u
m
er
ar
ea
.
Mo
s
t
o
f
th
e
elec
tr
icity
will
b
e
s
u
p
p
lied
b
y
t
h
e
n
atio
n
al
g
r
id
,
d
u
r
in
g
th
e
co
u
r
s
e
o
f
th
e
d
ay
,
s
o
lar
e
n
er
g
y
p
r
o
d
u
ctio
n
i
n
cr
ea
s
es
p
r
o
g
r
ess
iv
ely
,
wh
ile
win
d
en
er
g
y
b
e
g
in
s
to
o
p
er
ate
wh
en
th
e
r
eg
io
n
is
win
d
y
,
th
u
s
r
ed
u
cin
g
d
ep
en
d
en
ce
o
n
th
e
n
atio
n
al
g
r
id
.
Fo
u
r
ca
s
es
will b
e
tr
ea
ted
:
-
C
ase
R
1
(
W
P=0
&
SO=0
)
:
At
an
y
tim
e
o
f
d
a
y
,
th
e
n
atio
n
al
n
etwo
r
k
is
ac
tiv
ated
if
n
eith
er
s
o
lar
n
o
r
win
d
en
er
g
y
is
av
ailab
le
t
o
s
u
p
p
ly
th
e
p
o
wer
g
r
id
.
-
C
ase
R
2
(
W
P=0
&
SO=1
)
:
W
h
en
th
e
s
u
n
is
s
h
in
in
g
b
r
ig
h
tly
,
elec
tr
icity
is
s
u
p
p
lied
s
o
lely
b
y
s
o
lar
p
o
wer
,
with
o
u
t r
ec
o
u
r
s
e
to
th
e
n
atio
n
al
g
r
id
.
-
C
ase
R
3
(
W
P=1
&
SO=0
)
:
I
n
th
e
p
r
esen
ce
o
f
f
av
o
r
ab
le
win
d
s
,
win
d
p
o
wer
o
p
er
ates
au
to
n
o
m
o
u
s
ly
to
s
u
p
p
ly
th
e
elec
tr
ical
g
r
id
,
in
d
e
p
en
d
en
tly
o
f
th
e
n
atio
n
al
g
r
id
.
-
C
ase
R
4
(
W
P=1
&
SO=1
)
:
W
h
en
th
e
s
u
n
is
s
h
in
in
g
an
d
th
e
win
d
is
b
lo
win
g
at
th
e
s
am
e
t
im
e,
b
o
th
s
o
lar
an
d
win
d
e
n
er
g
y
co
n
t
r
ib
u
te
to
th
e
p
o
wer
s
u
p
p
ly
with
o
u
t h
av
i
n
g
to
r
el
y
o
n
th
e
n
atio
n
al
g
r
id
.
3
.
2
.
Ca
s
e
R1
(
WP
=
0
& SO
=
0
)
I
n
th
is
h
y
p
o
th
esis
,
b
o
th
th
e
wi
n
d
p
ar
k
an
d
th
e
s
o
lar
p
ar
k
d
o
n
o
t
co
n
tr
i
b
u
te
to
p
o
wer
g
en
er
atio
n
,
an
d
o
n
ly
th
e
n
atio
n
al
g
r
id
is
r
esp
o
n
s
ib
le
f
o
r
p
r
o
d
u
cin
g
elec
tr
icity
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
p
r
o
p
o
r
tio
n
al
v
o
ltag
es
(
p
er
u
n
it)
at
d
if
f
er
en
t
b
u
s
es
i
n
th
e
n
etwo
r
k
,
in
d
icatin
g
a
litt
le
r
is
e
in
v
o
ltag
e
at
b
u
s
0
,
wh
ich
s
er
v
es
as
th
e
p
r
im
ar
y
p
o
wer
s
u
p
p
ly
.
B
u
s
es
1
,
3
,
an
d
4
ex
h
ib
it
a
litt
le
d
ec
lin
e
in
v
o
ltag
e,
wh
ic
h
m
ay
b
e
to
ler
ab
le
f
o
r
r
eg
u
la
r
n
etwo
r
k
o
p
er
atio
n
.
Ho
wev
er
,
th
e
v
o
ltag
e
o
n
b
u
s
2
is
m
u
ch
b
elo
w
its
d
esig
n
ated
v
alu
e,
r
e
s
u
ltin
g
in
im
m
in
en
t
s
tab
ilit
y
an
d
q
u
ality
is
s
u
es th
at
d
em
an
d
im
m
ed
iate
at
ten
tio
n
.
Fig
u
r
e
5
r
ep
r
esen
ts
th
e
ac
tiv
e
p
o
wer
g
en
er
ate
d
at
d
if
f
e
r
en
t
b
u
s
es
in
th
e
an
aly
ze
d
n
etwo
r
k
.
I
t
d
em
o
n
s
tr
ates
th
e
ass
u
m
p
tio
n
s
m
ad
e
in
th
is
ca
s
e
s
tu
d
y
,
wh
er
e
o
n
ly
th
e
n
atio
n
al
g
r
id
(
B
u
s
0
)
s
er
v
es
as
th
e
o
n
ly
p
o
wer
s
o
u
r
ce
.
I
t
is
cr
u
cial
to
tak
e
in
to
a
cc
o
u
n
t
th
e
p
ar
tic
u
lar
co
n
tex
t
o
f
th
e
p
o
wer
s
y
s
tem
,
s
in
ce
an
e
x
ce
s
s
iv
e
co
n
ce
n
tr
atio
n
o
f
ac
tiv
e
g
e
n
er
atio
n
o
n
a
s
in
g
le
b
u
s
co
u
ld
p
r
o
v
id
e
d
if
f
icu
lties
in
ter
m
s
o
f
n
etwo
r
k
b
alan
cin
g
an
d
s
tab
ilit
y
.
Po
wer
lo
s
s
es a
r
e
ca
lcu
lated
u
s
in
g
th
e
f
o
llo
win
g
eq
u
atio
n
:
=
(
∑
+
)
−
(
∑
)
I
n
th
is
ca
s
e,
p
o
wer
lo
s
s
es a
r
e
eq
u
al
to
6
.
2
9
4
9
MW.
Fig
u
r
e
4
.
Vo
ltag
e
p
r
o
f
ile
o
f
t
h
e
5
-
b
u
s
Mo
r
o
cc
an
n
etwo
r
k
s
y
s
tem
with
PE=
0
&
SO=0
o
n
th
e
b
u
s
es
Fig
u
r
e
5
.
Activ
e
p
o
wer
g
e
n
er
a
ted
o
f
th
e
5
-
b
u
s
Mo
r
o
cc
an
n
etwo
r
k
s
y
s
tem
wit
h
PE=
0
&
SO=0
o
n
th
e
b
u
s
es
3
.
3
.
Ca
s
e
R2
(
WP
=
0
& SO
=
1
)
I
n
th
is
h
y
p
o
th
esis
,
th
e
s
o
lar
p
ar
k
is
p
r
o
d
u
ctiv
e,
wh
ile
th
e
win
d
p
ar
k
is
o
u
t
o
f
s
er
v
ice.
Fig
u
r
e
6
illu
s
tr
ates
th
e
r
elativ
e
v
o
ltag
e
v
alu
es,
ex
p
r
ess
ed
in
p
e
r
u
n
it
(
p
.
u
.
)
,
at
v
ar
io
u
s
b
u
s
es
with
in
th
e
elec
tr
ical
n
etwo
r
k
.
At
B
u
s
0
,
th
e
v
o
lta
g
e
is
1
.
0
5
p
.
u
.
,
s
lig
h
tly
ab
o
v
e
th
e
n
o
m
i
n
al
v
alu
e,
i
n
d
icatin
g
a
m
in
o
r
v
o
ltag
e
ex
ce
s
s
th
at
m
ay
b
e
ac
ce
p
tab
le
d
ep
en
d
i
n
g
o
n
n
etwo
r
k
s
p
ec
if
icatio
n
s
.
B
asically
,
th
is
s
itu
atio
n
r
esu
lts
in
f
lu
ctu
atio
n
s
in
v
o
ltag
e
lev
els
at
v
ar
io
u
s
lo
ca
tio
n
s
with
in
th
e
n
etwo
r
k
.
I
t
s
ee
m
s
th
at
b
u
s
es
1
,
2
,
3
an
d
4
ar
e
ex
p
er
ien
cin
g
v
o
ltag
e
d
e
v
iatio
n
s
th
at
n
ee
d
to
b
e
an
aly
ze
d
an
d
p
o
ten
tially
ad
ju
s
ted
in
o
r
d
er
to
en
s
u
r
e
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.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
3
6
3
2
-
3648
3640
s
tab
ilit
y
o
f
th
e
p
o
we
r
s
y
s
tem
.
B
u
s
0
s
ee
m
s
to
b
e
s
lig
h
tly
h
ig
h
er
th
an
u
s
u
al,
b
u
t
it
is
s
till
w
ith
in
an
ac
ce
p
tab
le
r
an
g
e.
Fig
u
r
e
7
d
ep
ictin
g
th
e
d
is
tr
ib
u
tio
n
o
f
ac
tiv
e
p
o
we
r
in
th
e
elec
tr
ical
n
etwo
r
k
s
h
o
w
ca
s
es
th
e
r
elatio
n
s
h
ip
b
etwe
en
ac
tiv
e
p
o
wer
an
d
b
u
s
es.
Simp
ly
p
u
t,
ac
tiv
e
p
o
wer
is
p
r
im
ar
ily
g
en
e
r
a
ted
b
y
b
u
s
1
,
wh
ile
bus
0
co
n
s
u
m
es
ac
tiv
e
p
o
we
r
.
I
t
s
ee
m
s
th
at
b
u
s
es
2
,
3
,
a
n
d
4
a
r
e
n
o
t
c
u
r
r
en
tly
p
lay
in
g
a
r
o
le
in
p
o
wer
g
en
er
atio
n
.
T
h
is
d
is
tr
ib
u
tio
n
o
f
ac
tiv
e
p
o
wer
s
u
g
g
ests
a
s
p
ec
if
ic
ar
r
an
g
em
en
t
o
f
th
e
elec
tr
ical
n
etwo
r
k
,
with
ac
tiv
e
s
o
u
r
ce
s
an
d
lo
ad
s
u
n
iq
u
e
to
ea
ch
b
u
s
.
Un
d
er
s
tan
d
in
g
th
e
u
n
iq
u
e
cir
c
u
m
s
tan
ce
s
s
u
r
r
o
u
n
d
in
g
ea
c
h
b
u
s
is
cr
u
cial.
C
o
n
s
id
er
in
g
th
e
s
p
ec
if
ic
co
n
tex
t
o
f
t
h
e
s
y
s
tem
is
cr
u
cial
wh
e
n
ev
al
u
atin
g
n
et
wo
r
k
b
ala
n
ce
an
d
s
tab
ilit
y
.
I
n
th
is
c
ase,
p
o
wer
lo
s
s
es a
r
e
eq
u
al
to
4
.
5
1
2
6
MW.
Fig
u
r
e
6
.
Vo
ltag
e
p
r
o
f
ile
o
f
t
h
e
5
-
b
u
s
Mo
r
o
cc
an
n
etwo
r
k
s
y
s
tem
with
PE=
0
&
SO=1
o
n
th
e
b
u
s
es
Fig
u
r
e
7
.
Activ
e
p
o
wer
g
e
n
er
a
ted
o
f
th
e
5
-
b
u
s
Mo
r
o
cc
an
n
etwo
r
k
s
y
s
tem
wit
h
PE=
0
&
SO=1
o
n
th
e
b
u
s
es
3
.
4
.
Ca
s
e
R3
(
WP
=
1
& SO
=
0
)
I
n
th
is
ca
s
e,
th
e
win
d
p
ar
k
is
p
r
o
d
u
ctiv
e,
wh
ile
th
e
s
o
lar
p
ar
k
is
o
u
t
o
f
s
er
v
ice,
Fig
u
r
e
8
s
h
o
ws
v
o
ltag
e
p
r
o
f
ile
o
f
th
e
5
-
b
u
s
Mo
r
o
cc
an
n
etwo
r
k
s
y
s
tem
o
n
th
e
b
u
s
es
.
B
u
s
e
s
0
,
1
an
d
2
ex
h
ib
it
a
v
o
ltag
e
th
at
is
s
lig
h
tly
ab
o
v
e
th
e
s
tan
d
ar
d
v
o
ltag
e
lev
el,
n
ec
ess
itatin
g
s
p
ec
if
ic
m
o
n
ito
r
in
g
.
B
u
s
3
an
d
4
ar
e
d
is
p
lay
in
g
elev
ated
v
o
ltag
es,
s
u
g
g
esti
n
g
t
h
e
p
o
s
s
ib
ilit
y
o
f
r
e
q
u
ir
in
g
r
eg
u
latio
n
to
en
s
u
r
e
s
tab
ilit
y
.
T
h
e
ac
tiv
e
p
o
wer
f
o
r
ea
ch
b
u
s
s
h
o
wn
in
Fig
u
r
e
9
illu
s
tr
ates th
e
d
is
tr
ib
u
tio
n
o
f
p
o
wer
in
th
e
elec
tr
ical
n
etwo
r
k
.
T
o
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o
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ate
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h
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ests
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ce
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o
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al
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r
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Activ
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e
b
u
s
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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atch
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ates
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ates
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ib
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ak
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ile
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atin
g
.
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n
th
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s
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wer
lo
s
s
es
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e
eq
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al
to
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.
0
5
0
1
MW.
Fig
u
r
e
1
0
.
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ltag
e
p
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ile
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f
t
h
e
5
-
b
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s
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r
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cc
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n
n
etwo
r
k
s
y
s
tem
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PE=
1
&
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n
th
e
b
u
s
es
Fig
u
r
e
1
1
.
Activ
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p
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ated
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k
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tem
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h
PE=
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DIS
CU
SS
I
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N
4
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1
.
Num
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t
a
t
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m
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ai
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am
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1
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2
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3
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a
n
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R
4
s
h
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Fig
u
r
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4
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ith
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w
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ase
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ly
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h
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ax
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m
en
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u
t
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n
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n
d
e
r
v
o
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s
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.
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ith
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im
al
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d
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ase
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ly
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f
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ed
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atin
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ee
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.
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th
e
o
th
er
h
a
n
d
,
C
ase
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4
(
s
o
lar
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in
d
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p
u
t
m
o
r
e
s
tr
ain
o
n
th
e
s
y
s
tem
d
u
e
to
th
e
lar
g
est
p
o
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lo
s
s
es
(
9
.
0
5
MW,
7
.
1
7
%)
an
d
o
v
er
v
o
ltag
es.
B
ec
au
s
e
o
f
th
is
,
R
2
an
d
R
3
ar
e
m
o
r
e
e
f
f
ec
tiv
e
in
th
e
ex
is
tin
g
g
r
id
en
v
ir
o
n
m
e
n
t,
wh
er
ea
s
R
4
wo
u
ld
n
ec
ess
itate
th
e
u
s
e
o
f
s
o
p
h
is
ticated
g
r
id
m
a
n
ag
e
m
en
t
tech
n
iq
u
es.
T
ab
le
4
p
r
esen
t
a
s
tatis
tical
co
m
p
ar
is
o
n
b
e
twee
n
ca
s
es
R
1
,
R
2
,
R
3
an
d
R
4
.
T
ab
le
4
.
Statis
tical
co
m
p
ar
is
o
n
b
etwe
en
th
e
4
ca
s
es
M
e
t
r
i
c
C
a
se
R
1
(
N
o
S
o
l
a
r
/
W
i
n
d
)
C
a
se
R
2
(
S
o
l
a
r
O
n
l
y
)
C
a
se
R
3
(
W
i
n
d
O
n
l
y
)
C
a
se
R
4
(
S
o
l
a
r
+
W
i
n
d
)
V
o
l
t
a
g
e
a
t
B
u
s
0
(
p
.
u
.
)
1
.
0
5
1
.
0
5
1
.
0
5
1
.
0
5
V
o
l
t
a
g
e
a
t
B
u
s
1
(
p
.
u
.
)
1
.
0
1
.
1
1
2
2
1
.
0
5
1
.
1
6
8
4
V
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l
t
a
g
e
a
t
B
u
s
2
(
p
.
u
.
)
0
.
9
2
2
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.
9
8
8
1
1
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5
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t
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t
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A
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t
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A
c
t
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l
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p
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(
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3
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7
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Evaluation Warning : The document was created with Spire.PDF for Python.