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I
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2088
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8
7
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v
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5
6
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3556
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R
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1
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,
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T
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[
1]
.
Ma
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[
2
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=
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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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N:
2088
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ey
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ath
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atica
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less
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m
p
lex
[
3
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.
Ho
we
v
er
,
t
h
ese
tech
n
iq
u
e
s
ar
e
m
o
r
e
tim
e
-
co
n
s
u
m
in
g
[
4
]
.
T
h
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s
en
s
itiv
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b
ased
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co
m
p
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tatio
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et
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s
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DC
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s
f
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d
is
tr
ib
u
tio
n
f
ac
t
o
r
s
(
PTDFs)
[
5
]
h
av
e
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u
s
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o
r
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g
AT
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b
y
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d
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u
te
AT
C
d
u
r
in
g
o
u
tag
es
b
y
co
m
p
u
tin
g
lin
e
o
u
tag
e
an
d
g
en
er
ato
r
o
u
tag
e
d
is
tr
ib
u
tio
n
f
ac
to
r
s
(
L
ODF,
GOD
F).
T
h
ese
m
eth
o
d
s
ar
e
f
aster
co
m
p
ar
ed
to
th
e
co
n
tin
u
o
u
s
p
o
wer
f
lo
w
(
C
PF
)
m
eth
o
d
an
d
r
e
p
ea
ted
p
o
wer
f
lo
w
(
R
PF
)
m
eth
o
d
[
6
]
;
h
o
we
v
er
,
t
h
ese
a
r
e
b
ased
o
n
ass
u
m
p
tio
n
s
.
So
m
e
r
esear
ch
er
s
h
av
e
f
o
r
m
u
lat
ed
th
e
ev
alu
atio
n
o
f
AT
C
as
an
o
p
tim
izatio
n
p
r
o
b
lem
an
d
t
h
en
d
if
f
er
e
n
t
o
p
tim
izatio
n
tech
n
iq
u
es
ar
e
u
s
ed
to
ev
alu
ate
th
e
s
am
e.
T
h
e
h
y
b
r
id
g
r
e
y
wo
lf
f
lo
wer
p
o
llin
atio
n
alg
o
r
ith
m
(
HGWF
PA)
m
eth
o
d
ca
n
b
e
u
s
ed
t
o
o
p
tim
ize
th
e
AT
C
in
th
e
tr
an
s
m
is
s
io
n
s
y
s
tem
wh
ic
h
is
th
e
h
y
b
r
id
izatio
n
o
f
g
r
e
y
wo
lf
o
p
tim
izatio
n
(
GW
O)
an
d
f
lo
wer
p
o
llin
atio
n
alg
o
r
ith
m
(
FP
A)
.
T
h
e
HGWF
PA m
eth
o
d
g
iv
es b
etter
r
esu
lts
f
o
r
AT
C
th
an
th
e
GW
O
an
d
FP
A
m
eth
o
d
[
7
]
.
AT
C
o
f
a
s
y
s
tem
ca
n
b
e
en
h
an
ce
d
u
s
in
g
f
lex
ib
le
AC
tr
an
s
m
is
s
io
n
s
y
s
tem
(
FA
C
T
S
)
d
ev
ices.
R
esear
ch
er
s
em
p
lo
y
v
ar
io
u
s
te
ch
n
iq
u
es to
ascer
tain
th
e
o
p
ti
m
al
v
alu
e
an
d
p
lace
m
e
n
t o
f
F
AC
T
S d
ev
ices,
s
u
ch
as
th
e
s
tatic
v
ar
co
m
p
en
s
ato
r
(
SVC
)
an
d
th
y
r
is
to
r
-
co
n
tr
o
lle
d
s
er
ies
co
m
p
en
s
ato
r
(
T
C
SC
)
.
T
h
e
ad
ap
tiv
e
Mo
th
Flam
e
o
p
tim
izatio
n
tech
n
iq
u
e
wh
ich
is
th
e
ad
o
p
tiv
e
v
er
s
io
n
o
f
th
e
m
o
th
f
lam
e
alg
o
r
ith
m
ca
n
b
e
u
s
ed
to
ev
alu
ate
an
d
e
n
h
an
ce
AT
C
in
th
e
p
r
esen
ce
o
f
T
C
S
C
.
T
h
is
alg
o
r
ith
m
r
esu
lted
in
a
b
etter
r
esp
o
n
s
e
r
eg
ar
d
in
g
th
e
en
h
an
ce
m
en
t
o
f
AT
C
ag
a
in
s
t
th
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
an
d
b
ac
ter
ial
s
war
m
o
p
tim
izatio
n
(
B
SO)
[
8
]
tech
n
iq
u
e
s
.
Du
r
k
o
v
ić
an
d
Sav
ić
[
9
]
p
r
esen
ted
th
e
m
eth
o
d
f
o
r
AT
C
en
h
an
ce
m
en
t
u
s
in
g
th
e
T
C
SC
d
ev
ice
in
ca
s
e
o
n
e
o
u
t o
f
two
an
n
o
u
n
ce
d
tr
an
s
ac
tio
n
s
is
ca
n
ce
led
.
T
h
is
r
esear
ch
e
v
alu
ates A
T
C
b
y
tak
in
g
i
n
to
ac
co
u
n
t
c
o
m
m
o
n
u
n
ce
r
tain
tie
s
th
at
ar
e
r
e
q
u
ir
ed
wh
ile
p
lan
n
in
g
a
p
o
wer
s
y
s
tem
o
v
er
a
lo
n
g
er
p
er
io
d
o
f
tim
e.
I
n
th
e
p
a
p
er
[
1
0
]
,
t
h
e
en
h
a
n
ce
m
en
t o
f
AT
C
o
f
a
d
er
eg
u
lated
p
o
wer
n
etwo
r
k
is
o
b
tain
ed
b
y
in
co
r
p
o
r
atin
g
SVC
an
d
T
C
SC
m
o
d
els
in
New
to
n
R
ap
h
s
o
n
lo
ad
f
lo
w
e
q
u
atio
n
s
.
I
n
t
h
is
p
ap
er
,
m
in
im
izatio
n
o
f
r
ea
l
p
o
wer
lo
s
s
es
an
d
im
p
r
o
v
em
e
n
t in
v
o
ltag
e
p
r
o
f
i
les at
all
b
u
s
es a
r
e
co
n
s
id
e
r
ed
as o
b
jectiv
es f
o
r
AT
C
ev
alu
atio
n
.
AT
C
o
f
a
s
y
s
tem
ca
n
also
b
e
e
n
h
an
ce
d
b
y
u
s
in
g
r
en
ewa
b
le
g
en
er
atio
n
.
I
n
th
e
p
a
p
er
[
1
1
]
,
a
s
en
s
itiv
e
-
b
ased
f
o
r
m
u
la
is
u
s
ed
to
f
i
n
d
th
e
o
p
tim
al
b
u
s
es
f
o
r
t
h
e
lo
ca
tio
n
o
f
win
d
g
e
n
er
ato
r
s
.
T
h
e
tr
an
s
m
is
s
io
n
co
n
g
esti
o
n
d
is
tr
ib
u
tio
n
f
ac
to
r
(
T
C
DF)
is
u
s
ed
to
cr
ea
te
th
e
z
o
n
es f
o
r
ass
ess
in
g
AT
C
.
T
h
e
s
u
itab
le
lo
ca
tio
n
f
o
r
th
e
s
y
s
tem
to
in
teg
r
ate
win
d
DG
to
im
p
r
o
v
e
AT
C
is
d
eter
m
in
ed
b
y
t
h
e
av
e
r
ag
e
tr
a
n
s
m
is
s
io
n
co
n
g
esti
o
n
d
is
tr
ib
u
tio
n
f
ac
to
r
(
AT
C
DF)
.
T
h
e
p
ap
er
[
1
2
]
d
em
o
n
s
tr
ates
th
e
p
er
f
o
r
m
an
ce
o
f
T
C
SC
in
en
h
an
cin
g
th
e
AT
C
b
ased
o
n
d
if
f
er
en
t
m
eth
o
d
s
o
f
p
lace
m
en
ts
.
R
ea
l
p
o
wer
p
er
f
o
r
m
an
ce
in
d
e
x
,
r
ea
l
p
o
wer
l
o
s
s
s
en
s
it
iv
ity
with
r
esp
ec
t
to
th
e
lin
e
r
ea
cta
n
ce
wh
er
e
T
C
SC
is
p
lace
d
an
d
p
o
wer
tr
an
s
f
er
d
is
tr
ib
u
tio
n
f
ac
to
r
ar
e
co
n
s
id
er
ed
f
o
r
ch
o
o
s
in
g
th
e
o
p
tim
al
lo
ca
tio
n
o
f
T
C
SC
.
T
h
e
o
p
tim
al
lo
ca
ti
o
n
f
o
r
th
e
T
C
SC
is
f
o
u
n
d
b
y
u
s
in
g
ea
ch
o
f
th
ese
tech
n
iq
u
es
s
ep
ar
ately
,
an
d
th
e
ass
o
ciate
d
AT
C
v
alu
es
ar
e
c
alcu
lated
.
AT
C
im
p
r
o
v
em
en
t
v
ar
ies
f
r
o
m
2
%
to
8
5
%,
an
d
r
ea
l
p
o
wer
lo
s
s
m
in
im
izatio
n
ca
n
r
ea
ch
2
5
%
d
e
p
en
d
in
g
o
n
p
lace
m
e
n
t
tech
n
i
q
u
es
u
s
ed
.
Als
o
,
th
e
im
p
o
r
tan
ce
o
f
AT
C
ev
alu
atio
n
b
y
in
co
r
p
o
r
atin
g
r
e
n
ewa
b
le
en
er
g
y
g
en
er
ati
o
n
is
ad
d
r
e
s
s
ed
in
th
is
p
a
p
er
.
T
h
e
p
ap
er
[
1
3
]
p
r
o
p
o
s
es
an
alg
o
r
ith
m
to
f
in
d
th
e
s
u
itab
le
lo
ca
tio
n
an
d
s
ize
o
f
T
C
SC
d
ev
ice
b
y
m
ax
im
izin
g
AT
C
an
d
m
i
n
im
izin
g
p
o
wer
lo
s
s
es.
Als
o
,
th
e
alg
o
r
ith
m
r
ed
u
ce
s
th
e
i
n
s
talla
tio
n
co
s
t
o
f
th
e
T
C
S
C
d
ev
ice.
Pap
e
r
[
1
4
]
p
r
esen
ts
th
e
ap
p
licatio
n
o
f
T
C
SC
to
im
p
r
o
v
e
th
e
tr
an
s
f
er
ca
p
ab
ilit
y
o
f
a
p
o
wer
s
y
s
tem
b
y
co
n
s
id
er
in
g
th
e
r
ea
ctiv
e
p
o
we
r
f
l
o
ws
in
A
T
C
co
m
p
u
tatio
n
s
.
T
h
e
co
m
p
u
tatio
n
o
f
tr
an
s
f
e
r
ca
p
ab
ilit
y
al
s
o
d
ep
e
n
d
s
o
n
t
h
e
ty
p
e
o
f
th
e
lo
ad
.
T
h
e
im
p
ac
t
o
f
lo
ad
v
ar
iatio
n
ca
n
b
e
c
o
n
s
id
er
ed
f
o
r
th
e
ex
ac
t
ev
alu
atio
n
o
f
AT
C
.
Hen
ce
,
th
e
im
p
ac
t o
f
th
e
g
en
er
al
l
o
ad
m
o
d
el
is
co
n
s
id
er
ed
as Z
I
P lo
a
d
a
lo
n
g
with
co
n
s
tan
t p
o
wer
l
o
ad
s
in
[
1
5
]
.
Ma
n
y
r
esear
c
h
er
s
h
a
v
e
ad
d
r
ess
ed
th
e
im
p
o
r
tan
ce
o
f
e
v
al
u
atin
g
th
e
ex
ac
t
v
alu
e
o
f
A
T
C
in
th
e
p
r
esen
t
d
er
e
g
u
lated
s
y
s
tem
at
a
f
aster
r
ate
an
d
en
h
a
n
cin
g
u
s
in
g
FAC
T
S.
An
attem
p
t
is
m
ad
e
in
th
is
wo
r
k
t
o
co
m
p
u
te
t
h
e
ac
cu
r
ate
v
alu
e
o
f
AT
C
at
a
f
aster
r
ate
with
r
ed
u
ce
d
co
m
p
u
tatio
n
s
u
s
in
g
d
o
m
in
atin
g
PTDFs
an
d
th
e
r
esu
lts
ar
e
co
m
p
ar
ed
ag
ai
n
s
t
th
o
s
e
o
b
tain
ed
u
s
in
g
DC
p
o
wer
tr
an
s
f
er
d
is
tr
ib
u
tio
n
f
a
cto
r
(
DC
PTDF)
an
d
r
ep
ea
ted
p
o
wer
f
lo
w
(
R
PF)
m
eth
o
d
.
Als
o
,
a
s
en
s
itiv
ity
-
b
ased
f
o
r
m
u
la
is
u
s
ed
f
o
r
ch
o
o
s
in
g
t
h
e
s
u
itab
le
lo
ca
tio
n
o
f
DG
to
im
p
r
o
v
e
AT
C
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
l
o
g
y
is
im
p
lem
en
ted
o
n
th
e
I
E
E
E
3
0
b
u
s
s
y
s
tem
.
2.
AT
C
CA
L
CU
L
AT
I
O
N
M
E
T
H
O
DS
As
en
er
g
y
r
eg
u
lato
r
y
c
o
m
m
is
s
io
n
s
p
r
o
v
id
ed
o
p
e
n
ac
ce
s
s
to
th
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
,
lar
g
e
-
s
ca
le
p
o
wer
tr
an
s
ac
tio
n
s
b
etwe
en
u
tili
ties
h
av
e
in
cr
ea
s
ed
r
ap
id
ly
.
Als
o
,
th
e
tr
an
s
ac
tio
n
s
b
etwe
en
ar
ea
s
an
d
b
u
s
es
ar
e
co
n
tin
u
o
u
s
ly
in
cr
ea
s
in
g
a
s
th
e
p
o
wer
d
em
an
d
is
in
cr
ea
s
in
g
.
B
ec
au
s
e
o
f
th
is
th
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
is
h
ig
h
ly
co
n
g
ested
an
d
s
y
s
tem
l
im
its
ar
e
v
io
lated
wh
ich
r
esu
lts
in
th
e
i
n
s
ec
u
r
e
o
p
er
atio
n
o
f
th
e
p
o
wer
s
y
s
tem
.
T
h
e
ev
alu
atio
n
o
f
AT
C
p
lay
s
an
im
p
o
r
tan
t
r
o
le
in
g
u
id
i
n
g
d
er
e
g
u
lated
m
ar
k
et
p
ar
tic
ip
an
ts
to
ca
r
r
y
o
u
t
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
5
5
6
-
3565
3558
b
ilater
al
tr
an
s
ac
tio
n
s
with
o
u
t
af
f
ec
tin
g
s
y
s
tem
s
ec
u
r
ity
.
Var
io
u
s
m
eth
o
d
s
ar
e
p
r
o
p
o
s
ed
in
liter
atu
r
e
to
ca
lcu
late
AT
C
.
T
h
ese
m
eth
o
d
s
ar
e
ca
teg
o
r
ized
i
n
to
f
o
u
r
ty
p
es
:
i
)
r
ep
ea
ted
lo
ad
f
lo
w
(
R
PF
)
m
eth
o
d
,
ii
)
lin
ea
r
ap
p
r
o
x
im
atio
n
m
eth
o
d
,
iii
)
o
p
t
im
al
p
o
wer
f
lo
w
(
OPF)
m
eth
o
d
,
an
d
i
v
)
b
ased
o
n
a
p
r
o
b
ab
ili
s
tic
ap
p
r
o
ac
h
.
2
.
1
.
Repea
t
ed
po
wer
f
l
o
w
t
e
chniq
ue
(
RP
F
)
I
n
th
e
R
PF
m
eth
o
d
,
AT
C
is
ev
alu
ated
b
y
p
er
f
o
r
m
in
g
p
o
wer
f
lo
w
an
aly
s
is
r
ep
ea
ted
ly
[
1
6
]
u
n
til
s
y
s
tem
lim
its
ar
e
v
io
lated
.
I
n
th
is
m
eth
o
d
,
o
n
e
p
air
o
f
s
o
u
r
ce
s
an
d
s
in
k
b
u
s
es
ar
e
ch
o
s
en
th
en
r
ea
l
p
o
wer
in
jectio
n
at
th
e
s
o
u
r
ce
b
u
s
i
s
in
cr
ea
s
ed
an
d
th
e
eq
u
al
a
m
o
u
n
t
o
f
r
ea
l
p
o
wer
d
em
an
d
at
th
e
s
in
k
b
u
s
is
in
cr
ea
s
ed
in
r
e
g
u
lar
s
tep
s
.
T
h
e
lo
ad
f
lo
w
an
al
y
s
is
is
p
er
f
o
r
m
ed
an
d
b
u
s
v
o
ltag
es
an
d
lin
e
lo
a
d
in
g
s
ar
e
o
b
s
er
v
ed
in
ev
er
y
s
tep
.
T
h
e
p
r
o
ce
s
s
o
f
r
ep
ea
ted
ly
p
er
f
o
r
m
in
g
lo
ad
f
lo
w
is
co
n
tin
u
ed
u
n
til
an
y
o
n
e
lin
e
in
th
e
s
y
s
tem
r
ea
ch
es
its
m
ax
im
u
m
lo
ad
in
g
l
im
it.
On
r
ea
ch
in
g
t
h
e
lim
it,
th
e
p
o
wer
f
l
o
w
an
aly
s
is
is
s
to
p
p
ed
.
T
h
e
s
o
u
r
ce
b
u
s
’
s
p
o
wer
in
jectio
n
f
o
r
th
e
last
s
tep
is
n
o
ted
d
o
wn
.
I
f
P
lmax
r
ep
r
esen
ts
th
e
p
o
w
er
in
jectio
n
at
th
e
s
o
u
r
ce
b
u
s
wh
en
th
e
m
ax
im
u
m
lim
it
is
attain
ed
an
d
P
base
r
ep
r
esen
ts
r
ea
l
p
o
wer
at
th
e
s
am
e
b
u
s
f
o
r
th
e
b
ase
ca
s
e,
th
en
AT
C
is
ca
lcu
lated
u
s
in
g
(
2
)
.
=
−
(
2
)
2
.
2
.
L
inea
r
a
pp
ro
x
ima
t
io
n
m
et
ho
d
(
L
AM
)
I
n
L
AM
,
th
e
AT
C
o
f
a
h
ig
h
ly
in
ter
co
n
n
ec
ted
s
y
s
tem
is
o
b
tain
ed
b
y
ca
lcu
latin
g
s
en
s
itiv
ity
f
ac
to
r
s
f
o
r
th
e
g
iv
en
n
etwo
r
k
to
p
o
l
o
g
y
.
T
h
e
p
o
wer
tr
an
s
f
er
d
is
tr
ib
u
tio
n
f
ac
to
r
(
PTDF)
is
u
s
ed
to
f
in
d
th
e
in
cr
em
en
ta
l
d
is
tr
ib
u
tio
n
o
f
p
o
wer
f
l
o
ws
co
r
r
esp
o
n
d
in
g
to
tr
an
s
ac
tio
n
s
b
etwe
en
two
ar
ea
s
/b
u
s
s
e
s
/r
eg
io
n
s
[
1
7
]
.
T
wo
ty
p
es
o
f
PTDF
ar
e
u
s
ed
f
o
r
ev
alu
ati
o
n
o
f
th
e
AT
C
o
f
th
e
s
y
s
tem
v
iz.
AC
-
PTDF
an
d
DC
-
PTD
F.
I
n
th
e
AC
-
PTDF
m
eth
o
d
ac
tiv
e
alo
n
g
with
r
ea
ctiv
e
p
o
wer
f
lo
ws
ar
e
co
n
s
id
er
ed
in
t
h
e
co
m
p
u
tatio
n
o
f
A
T
C
wh
er
ea
s
in
DC
-
PTDF
o
n
ly
ac
tiv
e
p
o
wer
f
l
o
ws
ar
e
co
n
s
id
er
ed
.
E
v
e
n
th
o
u
g
h
AC
-
PTDF
g
iv
es
b
etter
r
esu
lts
in
co
m
p
ar
is
o
n
with
DC
-
PTDF,
it
i
s
co
m
p
lex
b
ec
au
s
e
o
f
m
o
r
e
c
o
m
p
u
tatio
n
s
an
d
also
tim
e
-
co
n
s
u
m
in
g
b
ec
au
s
e
o
f
th
e
im
p
lem
en
tatio
n
o
f
c
o
m
p
lete
AC
p
o
wer
f
lo
w
f
o
r
ea
ch
g
en
e
r
ato
r
o
u
tag
e
c
o
n
tin
g
e
n
cy
an
al
y
s
is
.
T
h
er
ef
o
r
e
DC
-
PTDF
m
eth
o
d
is
m
o
r
e
co
m
m
o
n
ly
u
s
ed
to
ca
lc
u
late
AT
C
.
2
.
2
.
1
.
DC
P
T
DF
m
et
ho
d
PTDF
is
a
f
r
ac
tio
n
o
f
t
h
e
tr
a
n
s
ac
tio
n
f
r
o
m
s
eller
to
b
u
y
er
th
at
f
lo
ws
th
r
o
u
g
h
a
g
iv
e
n
tr
a
n
s
m
is
s
io
n
lin
e
[
1
8
]
.
Sy
m
b
o
lically
P
TDF
ij,
mn
is
a
f
r
ac
tio
n
o
f
a
tr
an
s
ac
tio
n
f
r
o
m
s
o
u
r
ce
b
u
s
‘
m
’
to
s
in
k
b
u
s
‘
n
’
t
h
at
f
lo
ws
th
r
o
u
g
h
a
tr
a
n
s
m
is
s
io
n
lin
e
f
r
o
m
b
u
s
‘
’
to
b
u
s
‘
’
.
T
h
e
f
o
r
m
u
l
a
f
o
r
ca
lcu
latin
g
PTDF
is
m
en
tio
n
ed
in
(
3
)
.
,
=
−
−
+
(
3
)
I
n
(
3
)
,
r
ep
r
esen
ts
th
e
r
ea
ctan
c
e
o
f
tr
a
n
s
m
is
s
io
n
lin
e
co
n
n
ec
t
in
g
th
e
b
u
s
es
i
an
d
j.
,
,
an
d
ar
e
th
e
elem
en
ts
o
f
th
e
b
u
s
s
en
s
itiv
ity
m
atr
ix
o
r
r
ea
cta
n
ce
m
atr
i
x
o
b
tain
ed
f
r
o
m
th
e
b
u
s
ad
m
it
tan
ce
m
atr
ix
.
On
ce
th
e
PTDFs ar
e
ca
lcu
lated
,
th
e
to
t
al
tr
an
s
f
er
ca
p
ab
ilit
y
(
T
T
C
)
o
f
a
lin
e
c
o
n
n
ec
tin
g
i
-
j is co
m
p
u
ted
u
s
in
g
(
4
)
,
,
=
{
−
0
,
;
,
>
0
−
−
0
,
;
,
<
0
∞
;
,
<
0
(
4
)
I
n
(
4
)
,
is
th
e
th
er
m
al
co
n
s
tr
ain
t
o
f
lin
e
co
n
n
ec
tin
g
b
u
s
an
d
,
0
is
th
e
b
ase
ca
s
e
p
o
wer
f
lo
w
th
r
o
u
g
h
a
lin
e
co
n
n
ec
tin
g
b
u
s
an
d
.
T
h
e
lin
e
with
m
in
im
u
m
tr
an
s
f
er
ca
p
a
b
ilit
y
is
ca
ll
ed
a
co
n
s
tr
ain
in
g
b
r
an
ch
w
h
ich
d
ec
id
es th
e
AT
C
o
f
th
e
s
y
s
tem
.
Fin
ally
,
th
e
A
T
C
o
f
th
e
s
y
s
tem
is
co
m
p
u
ted
b
y
u
s
in
g
(
5
)
.
=
{
,
}
(
5
)
2
.
2
.
2
.
P
ro
po
s
ed
a
pp
ro
a
ch
us
ing
d
o
m
ina
t
ing
P
T
DF
I
t
is
o
b
s
er
v
e
d
f
r
o
m
ex
is
tin
g
l
iter
atu
r
e
th
at
AC
-
PTDF
an
d
DC
-
PTDF
m
eth
o
d
s
ar
e
m
ath
em
atica
lly
co
m
p
lex
,
esp
ec
ially
f
o
r
lar
g
e
in
ter
co
n
n
ec
ted
s
y
s
tem
s
.
T
h
is
is
b
ec
au
s
e
th
ese
m
eth
o
d
s
r
eq
u
ir
e
co
m
p
u
tatio
n
o
f
tr
an
s
f
er
ca
p
ab
ilit
ies
f
o
r
all
th
e
lin
es
a
n
d
th
en
f
in
d
i
n
g
th
e
m
in
im
u
m
o
f
t
h
ese
as
AT
C
[
1
9
]
.
T
h
is
m
ak
es
th
e
p
r
o
ce
s
s
co
m
p
lex
a
n
d
tim
e
-
c
o
n
s
u
m
in
g
.
Als
o
,
wh
en
a
p
o
we
r
s
y
s
tem
o
p
er
ato
r
is
r
eq
u
ir
ed
to
d
ec
id
e
to
allo
w
p
ar
ticip
an
ts
in
th
e
d
er
eg
u
lat
ed
m
ar
k
et
to
s
ell
o
r
b
u
y
p
o
wer
q
u
ick
ly
,
it
wo
u
ld
b
e
d
if
f
icu
lt
r
esu
ltin
g
in
co
n
g
esti
o
n
i
n
tr
a
n
s
m
is
s
io
n
lin
es.
T
o
o
v
e
r
co
m
e
s
u
ch
p
r
o
b
lem
s
,
a
co
m
p
u
tatio
n
ally
ef
f
ici
en
t
ap
p
r
o
ac
h
u
s
in
g
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
S
en
s
itivity fa
cto
r
s
b
a
s
ed
co
mp
u
ta
tio
n
a
lly
efficien
t a
p
p
r
o
a
ch
fo
r
ev
a
lu
a
tio
n
…
(
Ma
n
ju
la
S
.
S
u
r
eb
a
n
)
3559
o
n
ly
d
o
m
in
atin
g
PTD
F
is
p
r
o
p
o
s
ed
f
o
r
t
h
e
co
m
p
u
tatio
n
o
f
AT
C
in
th
is
p
ap
er
.
I
n
th
is
ap
p
r
o
ac
h
PTDFs
ar
e
ca
lcu
lated
f
o
r
all
lin
es
f
o
r
all
r
eq
u
ir
ed
tr
a
n
s
ac
tio
n
s
(
s
eller
-
b
u
y
er
p
air
)
,
th
eir
a
b
s
o
lu
te
v
al
u
es
ar
e
co
n
s
id
er
ed
an
d
4
0
%
o
f
t
h
e
to
tal
lin
es
wit
h
h
ig
h
er
ab
s
o
lu
te
PTDF
ar
e
c
o
n
s
id
er
ed
f
o
r
c
o
m
p
u
tatio
n
o
f
AT
C
o
f
a
s
y
s
tem
.
T
h
is
is
tr
u
e
b
ec
au
s
e,
wh
en
li
n
es
with
th
e
lo
wer
v
alu
e
o
f
ab
s
o
lu
te
PTDFs
ar
e
u
s
ed
in
ev
alu
atin
g
tr
an
s
f
er
ca
p
ab
ilit
y
,
it
r
esu
lts
in
a
lar
g
e
v
alu
e
o
f
T
T
C
f
r
o
m
(
4
)
.
Su
ch
lin
es
wh
en
co
m
p
a
r
ed
with
o
th
er
s
to
ch
o
o
s
e
m
in
i
m
u
m
,
o
b
v
io
u
s
ly
th
ey
ar
e
d
is
ca
r
d
ed
.
T
h
e
r
ef
o
r
e
,
in
th
is
p
r
o
p
o
s
ed
m
eth
o
d
f
o
r
a
g
iv
e
n
s
y
s
tem
to
p
o
lo
g
y
a
n
d
th
e
r
eq
u
ir
ed
p
air
o
f
tr
a
n
s
ac
tio
n
s
,
d
o
m
in
atin
g
PTDFs
ar
e
ca
lcu
lated
an
d
s
to
r
ed
as
s
tan
d
ar
d
d
ata.
Du
r
in
g
t
h
e
tim
e
o
f
ev
alu
atio
n
o
f
AT
C
,
th
e
p
o
wer
f
l
o
w
an
aly
s
is
is
ca
r
r
ied
o
u
t
a
n
d
tr
a
n
s
f
er
ca
p
a
b
ilit
y
is
ev
alu
ated
f
o
r
o
n
ly
th
o
s
e
lin
es h
av
in
g
d
o
m
in
atin
g
PTDF
an
d
co
r
r
esp
o
n
d
in
g
AT
C
is
n
o
ted
d
o
wn
.
Step
s
in
v
o
lv
ed
in
d
o
m
in
atin
g
-
PTDF
ap
p
r
o
ac
h
:
Step
1
:
Do
m
in
atin
g
PTDFs
ar
e
ca
lcu
lated
u
s
in
g
(
3
)
f
o
r
a
g
iv
en
s
y
s
tem
to
p
o
lo
g
y
,
also
f
o
r
p
o
s
s
ib
le
b
ilater
al
tr
an
s
ac
tio
n
s
,
an
d
ar
e
m
ad
e
a
v
a
ilab
le
f
o
r
f
u
r
th
er
u
s
e.
Step
2
:
Po
wer
f
lo
w
an
aly
s
is
is
ca
r
r
ied
o
u
t
f
o
r
th
e
s
y
s
tem
d
u
r
in
g
p
ar
ticu
lar
co
n
d
itio
n
s
an
d
c
h
ec
k
ed
ag
ain
s
t
th
e
s
y
s
tem
co
n
s
tr
ain
ts
.
Po
wer
f
lo
ws th
r
o
u
g
h
t
r
an
s
m
is
s
io
n
lin
e
s
ar
e
n
o
ted
.
Step
3
:
T
r
an
s
f
er
ca
p
a
b
ilit
ies
ar
e
ca
lcu
lated
u
s
in
g
(
4
)
f
o
r
o
n
ly
th
o
s
e
lin
es
h
av
in
g
h
i
g
h
PT
DF
as
o
b
tain
ed
in
s
tep
1
.
Step
4
:
AT
C
f
o
r
a
p
a
r
ticu
lar
c
o
n
d
itio
n
is
o
b
tain
ed
b
y
ch
o
o
s
in
g
th
e
m
i
n
im
u
m
v
alu
e
o
f
tr
an
s
f
er
ca
p
ab
ilit
y
.
3.
M
O
DE
L
I
NG
AN
D
O
P
T
I
M
AL
L
O
CA
T
I
O
N
O
F
DG
AT
C
o
f
a
g
iv
e
n
s
y
s
tem
ca
n
b
e
en
h
a
n
ce
d
with
d
is
tr
ib
u
te
d
e
n
er
g
y
g
e
n
er
atio
n
(
DG)
.
T
h
e
d
is
tr
ib
u
ted
g
en
er
atio
n
s
m
ain
l
y
in
clu
d
e
n
o
n
co
n
v
en
tio
n
al
e
n
er
g
y
r
eso
u
r
ce
s
lik
e
s
o
lar
,
win
d
,
b
io
m
ass
,
an
d
h
y
d
r
o
p
o
wer
.
T
h
ese
g
en
er
atio
n
p
lan
ts
ar
e
u
s
u
ally
in
s
talled
at
th
e
lo
ad
ce
n
ter
s
d
ep
en
d
in
g
u
p
o
n
th
e
a
v
ai
lab
ilit
y
o
f
r
eso
u
r
ce
s
an
d
u
tili
ze
d
f
o
r
lo
ca
l n
ee
d
s
.
DGs
ar
e
s
u
b
s
titu
tes
f
o
r
n
ew
tr
an
s
m
is
s
io
n
lin
es
to
m
ee
t
th
e
in
cr
ea
s
in
g
d
em
an
d
.
I
n
th
is
p
ap
er
,
th
e
u
s
e
o
f
s
o
lar
a
n
d
win
d
g
en
e
r
ato
r
s
to
en
h
an
ce
th
e
AT
C
is
d
em
o
n
s
tr
ated
.
3
.
1
.
M
o
delin
g
o
f
ph
o
t
o
v
o
lt
a
ic
DG
Ph
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
ar
e
eith
er
g
r
id
-
c
o
n
n
ec
ted
o
r
s
tan
d
-
alo
n
e
.
T
h
e
elec
tr
ic
c
u
r
r
en
t
r
esu
ltin
g
f
r
o
m
th
e
PV
ce
ll
is
d
ir
ec
t.
T
h
er
ef
o
r
e
,
p
o
wer
g
en
er
ate
d
b
y
PV
ce
lls
is
alwa
y
s
DC
p
o
w
er
an
d
n
ee
d
s
to
b
e
co
n
v
er
ted
in
to
AC
b
ef
o
r
e
co
n
n
ec
tin
g
t
o
th
e
g
r
id
.
Dif
f
er
e
n
t
to
p
o
lo
g
ies
o
f
i
n
v
er
ter
s
a
r
e
u
s
ed
to
c
o
n
v
e
r
t
DC
p
o
wer
f
r
o
m
th
e
PV
s
y
s
tem
in
to
AC
wh
ich
also
tak
es
in
to
ac
co
u
n
t
v
o
ltag
e
an
d
f
r
eq
u
en
cy
m
atch
.
I
n
t
h
is
s
tu
d
y
,
PV
-
DG
is
m
o
d
eled
as
a
r
ea
l
p
o
wer
g
en
e
r
ato
r
[
2
0
]
at
lo
ad
b
u
s
es
wh
o
s
e
o
u
tp
u
t
v
ar
ies
with
s
o
lar
ir
r
ad
ian
ce
.
T
h
e
o
u
tp
u
t p
o
we
r
f
r
o
m
th
e
P
V
s
y
s
tem
is
g
iv
en
b
y
(
6
)
.
=
{
×
(
0
)
0
≤
≤
0
0
≤
(
6
)
Her
e
P
p
v
r
is
th
e
r
ated
o
u
tp
u
t
p
o
wer
o
f
th
e
PV
s
y
s
tem
at
s
tan
d
ar
d
co
n
d
itio
n
s
(
s
o
lar
r
ad
iatio
n
=1
0
0
0
W
/
m
2
an
d
tem
p
er
atu
r
e=
25
°
C
)
.
Als
o
,
G
an
d
G
0
ar
e
th
e
s
o
lar
r
ad
iatio
n
(
W
/
m
2
)
f
o
r
t
h
e
s
elec
ted
lo
ca
tio
n
an
d
r
ate
d
r
ad
iatio
n
o
n
ea
r
th
’
s
s
u
r
f
ac
e
(
1000
W
/
m
2
)
r
esp
ec
tiv
ely
.
3
.
2
.
Wind
g
ener
a
t
io
n mo
delin
g
T
h
e
win
d
g
en
er
at
o
r
(
W
G)
p
r
o
d
u
ce
s
AC
p
o
wer
an
d
ca
n
b
e
c
o
n
n
ec
ted
to
th
e
g
r
id
at
m
ed
iu
m
o
r
h
ig
h
v
o
ltag
e
lev
els.
I
n
th
is
s
tu
d
y
,
W
G
i
s
m
o
d
eled
as a
r
ea
l p
o
wer
g
en
er
ato
r
[
2
1
]
,
at
lo
ad
b
u
s
es wh
o
s
e
o
u
tp
u
t v
ar
ies
with
win
d
s
p
ee
d
.
T
h
e
o
u
tp
u
t p
o
wer
f
r
o
m
W
G
is
g
iv
en
b
y
(
7
)
.
=
{
0
0
≤
≤
−
−
≤
≤
≤
≤
0
≤
(
7
)
Her
e
is
th
e
win
d
s
p
ee
d
,
is
th
e
cu
t
-
in
s
p
ee
d
,
is
th
e
cu
t
-
o
u
t
s
p
ee
d
an
d
is
th
e
r
ated
s
p
ee
d
.
r
ep
r
esen
ts
th
e
r
ated
p
o
wer
o
u
t
p
u
t o
f
W
G.
3
.
3
.
O
pti
m
a
l lo
c
a
t
io
n o
f
DG
s
E
v
en
th
o
u
g
h
s
o
lar
p
h
o
to
v
o
ltaic
DG
an
d
win
d
DG
ar
e
av
aila
b
le
in
lar
g
er
ca
p
ac
ities
an
d
all
lo
ca
tio
n
s
,
th
eir
u
s
es
ar
e
lim
ited
b
y
s
o
m
e
im
p
o
r
tan
t
ch
allen
g
es.
So
lar
PV
DG
is
an
in
ter
m
itten
t
s
o
u
r
ce
av
ailab
le
o
n
s
u
n
n
y
d
ay
s
an
d
win
d
DG
is
av
ailab
le
o
n
ly
wh
en
win
d
s
p
ee
d
is
m
o
r
e
th
an
its
cu
t
-
in
s
p
ee
d
.
Als
o
,
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
5
5
6
-
3565
3560
co
n
n
ec
tio
n
o
f
m
u
ltip
le
DGs
o
f
in
ap
p
r
o
p
r
iate
s
ize
a
n
d
at
in
c
o
r
r
ec
t
lo
c
atio
n
s
lead
s
t
o
a
r
ev
er
s
e
f
lo
w
o
f
p
o
we
r
as
well
a
s
in
cr
ea
s
ed
s
y
s
tem
lo
s
s
es.
I
t
a
ls
o
r
esu
lt
s
in
th
e
u
n
ec
o
n
o
m
ical
o
p
e
r
atio
n
o
f
th
e
s
y
s
tem
.
T
h
is
is
s
u
e
o
f
f
in
d
in
g
th
e
c
o
r
r
ec
t
s
ize
o
f
DG
at
an
o
p
tim
al
lo
ca
tio
n
with
th
e
s
y
s
tem
lo
s
s
es
[
2
2
]
is
ad
d
r
es
s
ed
in
th
is
p
ap
er
b
y
f
in
d
in
g
t
h
e
r
ea
l p
o
wer
lo
s
s
r
ed
u
ctio
n
s
en
s
itiv
ity
f
ac
to
r
(
PLR
SF
)
g
iv
en
b
y
(
8
)
.
PL
R
SF
=
P
l
o
s
s
wit
h
DG
−
P
l
o
s
s
b
as
e
P
D
Gi
(
8
)
Her
e,
is
th
e
s
ize
o
f
th
e
DG
p
lace
d
at
lo
ad
b
u
s
i,
is
th
e
in
itial
p
o
wer
lo
s
s
in
th
e
s
y
s
tem
,
ℎ
is
th
e
p
o
wer
lo
s
s
af
ter
p
lacin
g
DG.
I
f
th
e
PLRS
F
v
alu
e
is
s
tr
ictly
n
eg
ativ
e
as
th
e
s
y
s
tem
lo
s
s
es
ar
e
r
ed
u
ce
d
af
ter
p
lace
m
en
t
o
f
DG,
else
th
e
DG
in
teg
r
atio
n
is
n
o
t
s
u
g
g
ested
.
T
h
e
r
ef
o
r
e,
th
e
b
u
s
h
a
v
in
g
a
lar
g
e
PLRS
F v
alu
e
is
s
elec
ted
as th
e
o
p
tim
al
lo
ca
t
io
n
f
o
r
DG
p
lace
m
en
t.
4.
CASE
S
T
UD
Y
I
n
th
is
s
tu
d
y
,
t
h
e
I
E
E
E
3
0
b
u
s
s
y
s
tem
[
2
3
]
is
co
n
s
id
er
ed
f
o
r
AT
C
ev
alu
atio
n
b
y
R
PF
,
PTD
F,
an
d
th
e
d
o
m
in
atin
g
PTDF
m
eth
o
d
.
T
h
is
s
y
s
tem
h
as
s
ix
g
en
er
ato
r
s
an
d
twen
ty
-
o
n
e
l
o
ad
s
with
f
o
u
r
tr
an
s
f
o
r
m
er
s
an
d
two
s
h
u
n
t
ca
p
ac
ito
r
s
.
Als
o
,
t
o
d
eter
m
in
e
th
e
AT
C
o
f
th
e
tes
t
s
y
s
tem
u
n
d
er
d
if
f
er
e
n
t
lo
ad
i
n
g
co
n
d
itio
n
s
o
v
er
2
4
h
o
u
r
s
,
a
s
a
m
p
le
lo
ad
d
u
r
atio
n
cu
r
v
e
s
h
o
wn
in
Fig
u
r
e
1
i
s
co
n
s
id
er
ed
.
E
v
en
th
o
u
g
h
th
e
b
ase
ca
s
e
lo
ad
is
2
8
3
.
4
MW,
o
v
er
2
4
h
o
u
r
s
th
e
lo
ad
o
n
th
e
s
y
s
tem
v
ar
ies f
r
o
m
2
5
6
t
o
3
1
2
MW.
4
.
1
.
DG
c
o
ns
idera
t
io
ns
I
n
th
is
p
r
o
p
o
s
ed
wo
r
k
,
th
e
r
at
ed
p
o
wer
o
f
s
o
lar
DG
co
n
s
id
er
ed
is
2
5
MW,
at
a
r
ated
ir
r
ad
ian
ce
o
f
1
0
0
0
W
/m
2
.
T
h
e
s
am
p
le
v
ar
iatio
n
o
f
s
o
lar
ir
r
ad
ian
ce
in
W
/m
2
o
v
er
2
4
h
o
u
r
s
is
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
p
o
wer
o
u
tp
u
t
f
r
o
m
s
o
lar
DG
f
o
r
2
4
h
o
u
r
s
is
ca
lcu
lated
an
d
tab
u
lated
in
T
ab
le
1
.
T
h
e
r
ated
p
o
wer
o
u
tp
u
t
o
f
win
d
DG
co
n
s
id
er
ed
is
3
0
MW,
at
a
r
ated
win
d
s
p
ee
d
o
f
3
5
k
m
/h
r
.
T
h
e
cu
t
-
in
an
d
cu
t
-
o
u
t
s
p
ee
d
s
o
f
win
d
ar
e
2
0
k
m
/h
r
an
d
5
0
k
m
/h
r
r
esp
ec
tiv
ely
.
T
h
e
s
am
p
le
v
ar
iatio
n
o
f
win
d
s
p
ee
d
in
k
m
/h
r
o
v
er
2
4
h
o
u
r
s
is
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
o
u
tp
u
t p
o
we
r
f
r
o
m
win
d
DG
f
o
r
o
v
e
r
2
4
h
o
u
r
s
is
ca
lcu
lated
u
s
in
g
(
7
)
an
d
tab
u
lated
i
n
T
ab
le
2
.
Fig
u
r
e
1
.
Daily
lo
a
d
d
u
r
atio
n
cu
r
v
e
Fig
u
r
e
2
.
Sam
p
le
d
ata
o
f
s
o
lar
ir
r
ad
ian
ce
o
v
er
a
p
er
io
d
o
f
2
4
h
o
u
r
s
3
3
o
a
d
i
n
T
i
m
e
i
n
h
o
u
r
s
3
3
So
l
a
r
i
r
r
a
d
i
a
n
c
e
i
n
m
T
i
m
e
i
n
h
o
u
r
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
S
en
s
itivity fa
cto
r
s
b
a
s
ed
co
mp
u
ta
tio
n
a
lly
efficien
t a
p
p
r
o
a
ch
fo
r
ev
a
lu
a
tio
n
…
(
Ma
n
ju
la
S
.
S
u
r
eb
a
n
)
3561
T
ab
le
1
.
So
lar
DG
o
u
tp
u
t
o
v
er
2
4
h
o
u
r
s
Ti
me
i
n
h
o
u
r
s
S
o
l
a
r
i
r
r
a
d
i
a
n
c
e
W
/
m
2
P
o
w
e
r
o
u
t
p
u
t
i
n
M
W
0
0
0
4
0
0
8
1
0
0
2
.
5
12
8
0
0
20
16
7
0
0
1
7
.
5
20
1
0
0
2
.
5
24
0
0
Fig
u
r
e
3
.
Sam
p
le
d
ata
o
f
win
d
s
p
ee
d
o
v
er
a
d
u
r
atio
n
o
f
2
4
h
o
u
r
s
T
ab
le
2
.
Ou
tp
u
t p
o
we
r
f
r
o
m
w
in
d
DG
Ti
me
i
n
h
o
u
r
s
W
i
n
d
s
p
e
e
d
i
n
k
m/
h
r
P
o
w
e
r
o
u
t
p
u
t
i
n
M
W
0
22
4
4
21
2
8
28
16
12
26
12
16
35
30
20
30
20
24
25
10
5.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
5
.
1
.
AT
C
re
s
u
lt
s
in
co
m
pa
riso
n
us
ing
DC
-
P
T
DF
,
do
m
ina
t
ing
P
T
DF
a
nd
RP
F
m
et
ho
d
s
f
o
r
t
he
ba
s
e
ca
s
e
AT
C
v
alu
es
ar
e
o
b
tain
ed
f
o
r
t
h
e
I
E
E
E
3
0
b
u
s
s
y
s
tem
u
s
in
g
DC
-
PTDF
m
eth
o
d
u
s
in
g
MA
T
L
AB
an
d
h
er
e
PTDF
v
al
u
es
ar
e
ca
lcu
lat
ed
ev
e
r
y
tim
e
,
th
e
n
th
e
co
r
r
esp
o
n
d
in
g
t
r
an
s
f
er
ca
p
ab
ilit
ies
a
r
e
ev
alu
ate
d
f
o
r
all
lin
es
to
o
b
tain
a
m
i
n
im
u
m
o
n
e
as
AT
C
an
d
th
e
tim
e
tak
en
f
o
r
co
m
p
u
tatio
n
is
n
o
ted
.
Als
o
,
AT
C
v
alu
es
ar
e
o
b
tain
ed
f
o
r
th
e
s
y
s
tem
u
s
in
g
o
n
ly
d
o
m
i
n
atin
g
PTDFs
u
s
in
g
MA
T
L
AB
,
an
d
tim
e
tak
en
is
n
o
ted
.
Her
e
tim
e
f
o
r
co
m
p
u
tatio
n
is
n
o
ted
d
o
w
n
u
s
in
g
th
e
s
am
e
PC
with
p
ar
t
icu
lar
s
p
ec
if
icatio
n
s
an
d
tim
e
tak
en
in
b
o
th
ca
s
es
is
co
m
p
ar
ed
.
Fin
ally
,
th
e
AT
C
v
alu
es
o
b
tain
ed
b
y
th
ese
m
eth
o
d
s
ar
e
v
alid
ated
u
s
in
g
R
PF
m
eth
o
d
u
s
in
g
th
e
p
o
wer
wo
r
ld
s
im
u
lato
r
[
2
4
]
.
I
t
is
o
b
s
er
v
ed
f
r
o
m
T
ab
le
3
th
at
AT
C
v
alu
es
o
b
tain
ed
b
y
u
s
in
g
all
PTDF
an
d
u
s
in
g
o
n
ly
d
o
m
in
atin
g
PTDF
ar
e
th
e
s
am
e,
b
u
t
th
e
tim
e
tak
en
f
o
r
co
m
p
u
tati
o
n
is
m
o
r
e
if
all
PTDFs
ar
e
u
s
ed
.
Als
o
,
th
e
AT
C
v
alu
es
o
b
tain
ed
u
s
in
g
R
PF
m
eth
o
d
f
r
o
m
th
e
p
o
wer
wo
r
ld
s
im
u
la
to
r
ar
e
co
m
p
ar
ab
le
with
t
h
at
o
f
th
e
d
o
m
in
atin
g
PTDF
m
eth
o
d
.
T
h
e
r
ef
o
r
e,
in
th
is
p
ap
er
f
o
r
all
f
u
r
th
e
r
an
al
y
s
is
d
o
m
in
atin
g
PTDF
m
eth
o
d
is
u
s
ed
wh
ich
i
s
co
m
p
u
tatio
n
ally
ef
f
icien
t a
n
d
ac
cu
r
ate.
T
ab
le
3
.
AT
C
in
MW u
s
in
g
d
i
f
f
er
en
t m
eth
o
d
s
an
d
tim
e
tak
e
n
f
o
r
c
o
m
p
u
tatio
n
S
o
u
r
c
e
B
u
s
S
i
n
k
B
u
s
D
C
P
TD
F
M
e
t
h
o
d
D
o
mi
n
a
t
i
n
g
P
TD
F
R
P
F
me
t
h
o
d
A
T
C
i
n
M
W
A
TC
i
n
M
W
Ti
me
t
a
k
e
n
i
n
sec
o
n
d
s
i
s
0
.
0
2
0
S
a
y
T1
A
TC
i
n
M
W
Ti
me
t
a
k
e
n
i
n
sec
o
n
d
s
i
s
0
.
0
0
1
1
0
.
0
5
*
T
1
2
8
5
.
6
3
0
5
5
.
6
3
0
5
4
2
21
1
0
.
7
3
2
1
1
0
.
7
3
2
1
12
2
24
1
6
.
3
2
8
9
1
6
.
3
2
8
9
15
3
3
3
3
3
i
n
d
s
p
e
e
d
i
n
k
m
hr
T
i
m
e
i
n
h
o
u
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.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
3
5
5
6
-
3565
3562
5
.
2
.
AT
C
re
s
ults f
o
r
s
a
m
ple lo
a
d pro
f
ile
T
h
e
AT
C
v
alu
es
a
r
e
e
v
alu
ate
d
u
s
in
g
d
o
m
in
atin
g
PTDF
m
e
th
o
d
b
y
co
n
s
id
er
in
g
s
am
p
le
l
o
ad
p
r
o
f
ile
an
d
a
r
e
tab
u
lated
i
n
T
a
b
le
4
.
I
t
is
o
b
s
er
v
e
d
th
at
th
e
AT
C
at
0
:0
0
,
4
:0
0
,
8
:0
0
,
an
d
2
4
:0
0
h
o
u
r
is
m
o
r
e
th
an
th
e
b
ase
ca
s
e
th
er
ef
o
r
e
n
o
n
ee
d
to
en
h
an
ce
.
W
h
er
ea
s
at
2
0
:0
0
h
o
u
r
,
s
in
ce
th
e
l
o
ad
in
g
is
n
e
ar
ly
1
1
0
%,
AT
C
is
n
eg
ativ
e
in
d
icatin
g
t
h
at,
th
e
lin
es
ar
e
h
ig
h
ly
c
o
n
g
ested
wh
ich
is
a
r
ar
e
ca
s
e
in
p
o
wer
s
y
s
tem
o
p
er
atio
n
.
Ho
wev
er
,
AT
C
h
as
to
b
e
e
n
h
an
ce
d
at
1
2
:0
0
h
o
u
r
as
th
e
lo
a
d
in
g
is
n
ea
r
ly
1
0
4
%
at
th
is
tim
e
an
d
AT
C
is
less
th
an
th
e
b
ase
ca
s
e
AT
C
f
o
r
all
tr
an
s
ac
tio
n
s
.
T
ab
le
4
.
AT
C
in
MW f
o
r
d
if
f
e
r
en
t d
u
r
atio
n
s
in
a
d
a
y
f
r
o
m
0
0
to
2
4
h
o
u
r
s
S
o
u
r
c
e
B
u
s
S
i
n
k
B
u
s
0
:
0
0
4
:
0
0
8
:
0
0
1
2
:
0
0
1
6
:
0
0
2
0
:
0
0
2
4
:
0
0
9
1
%
9
0
%
9
3
%
1
0
4
%
1
0
2
%
1
1
0
%
9
2
%
2
8
1
0
.
9
1
9
0
1
2
.
0
8
8
2
8
.
0
7
8
4
2
.
3
4
3
.
4
8
4
9
-
4
.
3
8
3
6
1
0
.
9
2
0
3
2
21
1
8
.
1
8
2
2
2
0
.
1
7
7
6
1
4
.
5
8
9
0
6
.
2
8
3
1
7
.
6
5
5
8
-
9
8
.
3
8
4
1
8
.
2
0
6
6
2
24
1
9
.
7
4
2
1
2
0
.
2
1
7
4
1
9
.
9
7
0
7
1
3
.
2
5
3
0
1
5
.
6
8
1
6
-
4
9
.
5
1
1
9
.
7
3
9
3
5
.
3
.
AT
C
E
nh
a
ncem
ent
us
in
g
DG
5
.
3
.
1
.
Co
m
pu
t
a
t
i
o
n o
f
P
L
RSF
f
o
r
a
ll lo
a
d bus
es
As
th
e
AT
C
h
as
to
b
e
en
h
an
ce
d
at
1
2
:0
0
h
o
u
r
th
e
o
u
t
p
u
t
p
o
wer
o
f
th
e
s
o
lar
DG
at
th
is
tim
e
is
2
0
MW a
n
d
th
at
o
f
win
d
DG
is
1
2
MW f
r
o
m
T
ab
le
1
a
n
d
2
r
esp
ec
tiv
ely
.
T
o
f
in
d
th
e
o
p
tim
al
lo
ca
tio
n
o
f
th
ese
DGs,
th
e
r
ea
l
p
o
wer
lo
s
s
r
ed
u
ctio
n
s
en
s
itiv
ity
f
ac
to
r
(
PLRS
F)
is
co
m
p
u
ted
b
y
p
lacin
g
2
0
MW
an
d
1
2
MW
DG
at
all
lo
ad
b
u
s
es
an
d
is
tab
u
lated
in
T
a
b
le
5
.
I
t
is
o
b
s
er
v
ed
th
at
b
u
s
n
u
m
b
er
2
3
is
th
e
s
u
itab
le
lo
ca
tio
n
f
o
r
p
lace
m
en
t
o
f
s
o
lar
DG
an
d
b
u
s
n
u
m
b
er
3
0
is
f
o
r
win
d
DG
a
s
th
ey
r
esu
lt
in
th
e
least
p
o
we
r
lo
s
s
es
w
ith
lar
g
er
PLRS
F.
Fin
ally
,
th
e
AT
C
is
c
o
m
p
u
ted
at
p
ea
k
lo
a
d
with
an
d
with
o
u
t
DG
at
th
e
ch
o
s
en
l
o
ca
tio
n
an
d
tab
u
lated
in
T
ab
le
6
.
I
t
is
o
b
s
er
v
ed
th
at
th
e
AT
C
v
alu
es
ar
e
en
h
an
ce
d
in
th
e
p
r
esen
ce
o
f
DGs.
T
ab
le
7
s
h
o
ws
th
at
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
o
f
ev
alu
ati
n
g
AT
C
an
d
im
p
r
o
v
in
g
t
h
e
s
am
e
with
o
p
tim
ally
p
lace
d
DG
b
y
u
s
in
g
s
en
s
itiv
ity
f
ac
to
r
g
iv
es b
etter
r
e
s
u
lts
in
co
m
p
ar
is
o
n
with
o
th
er
m
et
h
o
d
s
in
th
e
ex
is
tin
g
liter
atu
r
e
.
T
ab
le
5
.
R
ea
l p
o
wer
l
o
s
s
r
ed
u
ctio
n
s
en
s
itiv
ity
f
ac
to
r
(
PLRS
F)
with
DG
at
lo
ad
b
u
s
es
Lo
a
d
B
u
s
n
u
m
b
e
r
W
i
t
h
2
0
M
W
D
G
a
t
a
l
l
l
o
a
d
b
u
ses
W
i
t
h
1
2
M
W
D
G
a
t
a
l
l
l
o
a
d
b
u
ses
P
o
w
e
r
l
o
ss
i
n
M
W
P
LR
SF
R
a
n
k
P
o
w
e
r
l
o
ss
i
n
M
W
P
LR
S
F
R
a
n
k
3
1
5
.
9
7
0
-
0
.
0
7
7
9
20
1
6
.
5
6
5
-
0
.
0
8
0
2
20
4
1
5
.
4
8
6
-
0
.
1
0
2
1
15
1
6
.
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7
3
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0
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9
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9
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0
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10
1
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8
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0
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I
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N
:
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I
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Vo
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15
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No
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4
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Au
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3565
3564
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