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,
Sep
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20
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[
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[
6
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-
[
8
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Nu
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Vo
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,
No
.
3
,
Sep
tem
b
er
20
26
:
9
7
5
-
984
976
FAC
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S
co
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p
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tech
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th
r
ee
-
p
h
ase
s
h
o
r
t
-
cir
cu
it
e
v
en
ts
.
T
h
e
p
r
im
ar
y
aim
s
o
f
th
is
wo
r
k
ar
e:
i)
to
ev
alu
ate
th
e
ef
f
ec
ts
o
f
SVC
d
ep
lo
y
m
e
n
t
o
n
v
o
ltag
e
p
r
o
f
il
es
to
g
eth
er
with
p
o
wer
-
f
lo
w
d
is
tr
ib
u
tio
n
d
u
r
in
g
co
n
tin
g
en
c
y
c
o
n
d
itio
n
s
;
ii)
to
q
u
an
tify
im
p
r
o
v
em
e
n
ts
in
tr
a
n
s
ien
t
p
er
f
o
r
m
an
ce
th
r
o
u
g
h
C
C
T
ev
alu
atio
n
;
a
n
d
iii)
to
ex
am
in
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
SVC
co
m
p
en
s
atio
n
f
o
r
d
if
f
er
en
t
I
E
E
E
b
en
c
h
m
ar
k
n
et
wo
r
k
s
im
p
lem
en
ted
in
th
e
MA
T
L
AB
/PS
AT
p
latf
o
r
m
.
2.
M
E
T
H
O
D
2
.
1
.
T
ra
ns
ient
s
t
a
bil
it
y
is
s
ue
s
in po
wer
net
wo
rk
s
T
r
an
s
ien
t
s
tab
ilit
y
ass
ess
es
a
s
y
s
tem
d
y
n
am
ic
p
er
f
o
r
m
a
n
ce
to
m
ain
tain
g
en
e
r
ato
r
s
y
n
ch
r
o
n
is
m
af
ter
a
m
ajo
r
d
is
tu
r
b
an
ce
,
s
u
ch
as
a
th
r
ee
-
p
h
ase
f
au
lt.
T
h
e
class
ical
m
o
d
el
d
escr
ib
es
g
en
er
ato
r
d
y
n
am
ics
u
s
in
g
th
e
s
win
g
eq
u
atio
n
,
d
er
iv
ed
f
r
o
m
New
to
n
’
s
s
ec
o
n
d
law
[
1
2
]
,
[
1
3
]
.
I
t
r
elies
o
n
k
ey
ass
u
m
p
tio
n
s
[
1
4
]
-
[
1
6
]
:
co
n
s
tan
t
m
ec
h
an
ical
in
p
u
t
p
o
wer
,
n
o
d
am
p
in
g
,
co
n
s
tan
t
in
ter
n
al
v
o
ltag
e
b
eh
in
d
tr
an
s
ien
t
r
ea
ctan
ce
,
b
alan
ce
d
o
p
er
atio
n
(
p
o
s
itiv
e
-
s
eq
u
en
ce
o
n
ly
)
,
co
n
s
tan
t
-
im
p
ed
an
ce
lo
a
d
s
,
an
d
n
eg
lect
o
f
s
atu
r
atio
n
,
s
alien
cy
,
an
d
lo
s
s
es.
Desp
ite
th
ese
s
im
p
lific
atio
n
s
,
th
e
m
o
d
el
r
em
ain
s
p
o
p
u
lar
f
o
r
its
co
m
p
u
tatio
n
al
ef
f
icien
c
y
an
d
ab
ilit
y
t
o
o
f
f
er
q
u
alitativ
e
in
s
ig
h
ts
in
to
s
y
s
tem
d
y
n
a
m
ics [
1
7
]
.
2
.
1
.
1
.
Swin
g
equa
t
io
n
Gen
er
ato
r
elec
tr
o
m
e
ch
an
ical
b
eh
av
io
r
d
u
r
in
g
d
is
tu
r
b
a
n
ce
s
is
co
m
m
o
n
l
y
r
ep
r
esen
ted
u
s
in
g
t
h
e
s
win
g
eq
u
atio
n
.
T
h
e
s
win
g
eq
u
atio
n
is
ex
p
r
ess
ed
as
(
1
)
.
2
2
2
=
−
(
1
)
W
h
er
e
δ
is
th
e
r
o
to
r
an
g
le,
is
th
e
in
er
tia
co
n
s
tan
t,
is
th
e
m
ec
h
an
ical
in
p
u
t,
an
d
is
th
e
elec
tr
ical
o
u
tp
u
t
p
o
wer
[
2
]
,
[
1
5
]
.
W
ith
d
am
p
in
g
,
it b
ec
o
m
es
(
2
)
.
2
2
2
+
=
−
(
2
)
W
h
er
e
is
th
e
d
am
p
in
g
co
ef
f
ic
ien
t
[
16
]
.
T
h
is
s
im
p
lifie
d
m
o
d
el
r
em
ain
s
a
s
tan
d
ar
d
to
o
l
f
o
r
tr
an
s
ien
t
s
tab
ilit
y
an
aly
s
is
.
2
.
1
.
2
.
E
lect
rica
l po
wer
ex
press
io
n
T
h
e
elec
tr
ical
p
o
wer
o
u
t
p
u
t
o
f
a
g
en
er
ato
r
is
g
iv
en
b
y
th
e
n
o
n
lin
ea
r
p
o
wer
-
an
g
le
eq
u
atio
n
.
T
h
is
eq
u
atio
n
is
p
r
esen
ted
in
(
3
)
=
′
(
)
(
3
)
W
h
er
e
an
d
′
ar
e
th
e
ter
m
in
al
v
o
ltag
e
a
n
d
in
ter
n
al
E
MF,
a
n
d
is
th
e
eq
u
iv
alen
t
r
ea
ctan
c
e
[
1
4
]
,
[
15
]
.
T
h
is
r
elatio
n
s
h
ip
is
k
ey
to
ass
ess
in
g
tr
an
s
ien
t stab
ilit
y
an
d
s
y
s
tem
r
esp
o
n
s
e
d
u
r
in
g
d
is
tu
r
b
an
ce
s
[
1
7
]
,
[
18
].
2
.
1
.
3
.
M
ulti
-
m
a
chine m
o
del
I
n
m
u
lti
-
g
e
n
er
ato
r
p
o
wer
s
y
s
tem
s
,
r
o
to
r
d
y
n
am
ics ar
e
d
escr
i
b
ed
b
y
a
s
et
o
f
co
u
p
led
s
win
g
eq
u
atio
n
s
.
T
h
e
elec
tr
ical
p
o
wer
o
u
tp
u
t
o
f
ea
ch
g
en
er
ato
r
is
d
eter
m
in
ed
f
r
o
m
th
e
n
etwo
r
k
a
d
m
ittan
ce
m
atr
ix
,
as
ex
p
r
ess
ed
in
(
4
)
-
(
6
)
.
ᵢ
=
ᵢ
−
(
4
)
ᵢ
=
2
ᵢ
(
ᵢ
−
ᵢ
)
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
I
mp
a
ct
o
f a
n
S
V
C
d
ev
ice
o
n
v
o
lta
g
e
a
n
d
tr
a
n
s
ien
t sta
b
ilit
y
in
p
o
w
er sys
tems
(
Ma
kh
lo
u
f C
h
o
u
ki
)
977
ᵢ
=
ᵢ
2
ᵢᵢ
+
∑
ᵢ
ⱼ
ⱼ
=
1
ⱼ
≠
ᵢ
[
ᵢⱼ
s
in
(
ᵢ
−
ⱼ
)
+
ᵢⱼ
c
os
(
ᵢ
−
ⱼ
)]
(
6
)
Her
e,
ᵢ
,
ᵢⱼ
,
an
d
ᵢⱼ
ar
e
th
e
i
n
ter
n
al
v
o
ltag
es,
co
n
d
u
cta
n
ce
,
a
n
d
s
u
s
ce
p
tan
ce
,
r
esp
ec
tiv
ely
.
T
h
is
m
o
d
el
ca
p
tu
r
es d
y
n
am
ic
in
ter
ac
tio
n
s
an
d
s
u
p
p
o
r
ts
tr
an
s
ien
t stab
ilit
y
an
aly
s
is
[
1
3
]
-
[
15
]
,
[
18
].
2
.
2
.
M
o
delin
g
o
f
SVC
T
h
e
p
r
o
p
o
s
ed
s
tu
d
y
f
o
c
u
s
es
o
n
s
h
u
n
t
-
co
n
n
ec
ted
FAC
T
S
d
ev
ices,
in
clu
d
in
g
SVC
,
T
C
R
,
an
d
T
SC
.
W
h
ile
th
eir
d
y
n
am
ic
r
esp
o
n
s
e
is
g
en
er
ally
in
f
er
i
o
r
t
o
th
at
o
f
STAT
C
OM
-
b
ased
s
o
lu
tio
n
s
,
th
ey
r
em
ai
n
ex
ten
s
iv
ely
in
v
esti
g
ated
f
o
r
m
ain
tain
in
g
ac
ce
p
ta
b
le
v
o
ltag
e
p
r
o
f
iles
u
n
d
er
s
tead
y
-
s
tate
o
p
er
atin
g
co
n
d
itio
n
s
[
1
9
]
,
[
2
0
]
.
2
.
2
.
1
.
M
o
delin
g
o
f
s
t
a
t
ic
re
a
c
t
iv
e
po
wer
co
m
pens
a
t
o
r
SV
C
SVC
i
s
m
o
d
eled
as a
v
ar
iab
le
s
h
u
n
t a
d
m
ittan
ce
=
j
,
ass
u
m
ed
lo
s
s
les
s
an
d
p
u
r
ely
im
a
g
in
ar
y
Fig
u
r
es
1
(a
)
a
n
d
1
(
b)
[2
1
]
.
T
h
e
s
u
s
ce
p
tan
ce
ca
n
b
e
ca
p
ac
itiv
e
o
r
in
d
u
ctiv
e,
in
jectin
g
o
r
ab
s
o
r
b
in
g
r
ea
ctiv
e
p
o
wer
Q
SVC
,
ac
co
r
d
in
g
ly
,
Fig
u
r
es
1
(
c
)
an
d
1
(
d
)
.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
B
SVC
an
d
th
e
r
a
ted
v
o
ltag
e
is
g
iv
en
by
(
7
)
an
d
(
8
)
.
=
−
2
=
−
2
[
2
(
−
)
+
s
i
n
2
]
−
(
7
)
=
−
(
)
2
(
8
)
T
h
e
n
eg
ativ
e
s
ig
n
in
d
icate
s
ca
p
ac
itiv
e
o
p
e
r
atio
n
(
p
o
we
r
in
jectio
n
)
o
r
in
d
u
ctiv
e
(
p
o
wer
ab
s
o
r
p
tio
n
)
.
Fig
u
r
e
1
(
d
)
illu
s
tr
ates
Q
SVC
as
a
f
u
n
ctio
n
o
f
n
o
d
al
v
o
ltag
e
[
2
]
,
[
2
2
]
,
[2
3
].
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
.
SVC
m
o
d
elin
g
an
d
r
ea
ctiv
e
p
o
wer
v
a
r
iatio
n
: (
a)
p
l
ac
em
en
t a
t b
u
s
j,
(
b
)
SVC
s
y
m
b
o
l,
(
c)
SVC
m
o
d
el,
an
d
(
d
)
r
ea
cti
v
e
p
o
wer
v
er
s
u
s
n
o
d
al
v
o
ltag
e
2
.
2
.
2
.
O
pera
t
io
na
l
c
o
ns
t
ra
ints a
nd
equa
t
io
n bo
un
ds
T
h
e
m
o
d
el
is
f
o
r
m
u
lated
with
in
a
r
estricte
d
o
p
e
r
atin
g
d
o
m
a
in
.
T
h
e
r
ea
ctiv
e
o
u
tp
u
t
o
f
th
e
s
tatic
v
ar
co
m
p
en
s
ato
r
is
b
o
u
n
d
e
d
b
y
its
ca
p
ab
ilit
y
lim
its
:
≤
≤
.
Vo
ltag
e
m
ag
n
itu
d
es
ar
e
lik
ewise
m
ain
tain
ed
with
in
ac
ce
p
tab
le
r
an
g
es
to
p
r
eser
v
e
s
ec
u
r
e
s
y
s
tem
o
p
er
atio
n
.
T
h
ese
co
n
s
tr
ain
ts
r
estrict
th
e
s
o
lu
tio
n
s
p
ac
e
an
d
p
r
ev
en
t
n
o
n
-
p
h
y
s
ical
r
esp
o
n
s
es,
th
er
eb
y
im
p
r
o
v
in
g
t
h
e
r
eliab
ilit
y
o
f
th
e
co
m
p
u
ted
r
esp
o
n
s
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
15
,
No
.
3
,
Sep
tem
b
er
20
26
:
9
7
5
-
984
978
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
SVC
m
o
d
el
is
d
ev
elo
p
ed
an
d
s
im
u
lated
u
s
in
g
th
e
PS
AT
p
latf
o
r
m
[
2
4
]
,
a
n
d
s
u
b
s
eq
u
e
n
tly
test
ed
o
n
ex
ten
s
iv
ely
in
v
esti
g
ated
I
E
E
E
b
en
ch
m
a
r
k
n
etwo
r
k
s
to
ev
alu
ate
its
in
f
lu
en
ce
o
n
v
o
ltag
e
r
eg
u
latio
n
,
p
o
wer
f
lo
w
allo
ca
tio
n
,
an
d
tr
a
n
s
ien
t
s
tab
ilit
y
.
T
h
e
I
E
E
E
1
4
-
b
u
s
s
y
s
tem
is
co
n
s
id
er
ed
to
ex
am
in
e
v
o
ltag
e
s
u
p
p
o
r
t
p
er
f
o
r
m
an
ce
,
wh
ile
th
e
I
E
E
E
5
-
b
u
s
co
n
f
ig
u
r
atio
n
is
u
s
ed
to
an
aly
ze
s
tead
y
-
s
tate
p
o
wer
f
l
o
w
ch
ar
ac
ter
is
tics
.
Fu
r
th
er
m
o
r
e
,
th
e
I
E
E
E
9
-
b
u
s
is
em
p
lo
y
ed
to
ass
e
s
s
th
e
cr
itical
clea
r
in
g
tim
e
(
C
C
T
)
u
n
d
er
f
au
lt
s
ce
n
ar
io
s
[
2
5
]
.
T
h
ese
an
aly
s
es
ar
e
ca
r
r
i
ed
o
u
t
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I
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2252
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8
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m
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d
e
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s
tr
ates
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s
t
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n
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r
tr
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s
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,
th
e
cr
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in
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tim
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o
f
th
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3
-
m
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alu
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d
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f
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s
to
ass
ess
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g
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d
th
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m
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e
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d
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g
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m
0
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1
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to
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2
9
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s
.
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h
is
v
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ef
lects th
e
in
f
lu
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o
f
f
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ca
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n
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e
tr
a
n
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e
an
d
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4.
CO
NCLU
SI
O
N
Dev
elo
p
ed
an
aly
s
is
p
r
o
v
id
es
a
s
y
s
tem
atic
ass
ess
m
en
t
o
f
th
e
im
p
ac
t
o
f
s
tatic
v
ar
co
m
p
e
n
s
ato
r
s
on
v
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ltag
e
r
eg
u
latio
n
an
d
r
o
t
o
r
-
a
n
g
le
s
tab
ilit
y
in
tr
an
s
m
is
s
io
n
n
etwo
r
k
s
u
s
in
g
s
tan
d
ar
d
I
E
E
E
b
en
ch
m
ar
k
s
y
s
tem
s
(
14
-
b
u
s
,
5
-
b
u
s
,
an
d
9
-
bus
)
.
T
im
e
-
d
o
m
ain
s
im
u
latio
n
s
co
n
s
is
ten
tly
d
em
o
n
s
tr
ate
th
a
t
SVC
in
teg
r
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ig
n
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ican
tly
en
h
a
n
ce
s
s
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s
tem
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n
d
er
a
b
r
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ad
s
p
e
ctr
u
m
o
f
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n
tin
g
en
cies.
Fro
m
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v
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s
tab
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s
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e,
f
ast
-
r
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s
e
s
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n
t
r
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e
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o
m
p
e
n
s
atio
n
ef
f
ec
tiv
ely
m
itig
ates
v
o
ltag
e
d
e
p
r
ess
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n
s
an
d
ac
ce
ler
ates
p
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s
t
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d
is
tu
r
b
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ce
r
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o
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er
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th
er
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y
in
cr
ea
s
in
g
t
h
e
av
ailab
le
s
tab
ilit
y
m
ar
g
in
.
R
eg
ar
d
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g
tr
an
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t
s
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,
th
e
an
aly
s
is
o
f
th
e
9
-
b
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s
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tem
u
n
d
er
s
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f
au
lt c
o
n
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n
s
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ates
th
e
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r
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tim
e
f
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r
d
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lt
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s
.
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h
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h
o
w
th
at
th
e
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r
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k
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rtme
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g
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rin
g
,
U
n
iv
e
rsit
y
o
f
Jijel
,
Al
g
e
ria.
His
m
a
in
re
se
a
r
c
h
in
tere
sts
in
c
lu
d
e
p
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we
r
sy
ste
m
s
e
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g
,
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tro
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g
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e
ti
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c
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p
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ti
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il
it
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(EM
C),
p
o
we
r
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a
n
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re
n
e
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le
e
n
e
rg
y
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r
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m
2
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lec
t
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p
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rtme
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t
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a
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g
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n
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s
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ri
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e
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e
ria.
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in
c
e
2
0
2
0
,
h
e
h
a
s
b
e
e
n
with
t
h
e
Un
iv
e
rsit
y
o
f
Jijel,
Al
g
e
ria.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
c
h
o
u
k
i_
m
a
k
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lo
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f@u
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iv
-
j
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d
z
.
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icha
m
Z
a
im
e
n
wa
s
b
o
rn
in
Jijel,
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e
ria,
i
n
1
9
8
3
.
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re
c
e
iv
e
d
t
h
e
B.
S
c
.
a
n
d
M
.
S
c
.
d
e
g
re
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s
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tri
c
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l
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g
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e
rin
g
f
ro
m
t
h
e
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i
v
e
rsity
o
f
M
o
h
a
m
e
d
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e
d
d
i
k
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n
y
a
h
ia,
Jijel,
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e
ria,
in
2
0
0
7
a
n
d
2
0
1
0
,
re
sp
e
c
ti
v
e
ly
.
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is
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u
rre
n
tl
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a
n
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ss
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t
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ro
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t
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o
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k
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h
ra
s Un
iv
e
rsity
,
Al
g
e
ria.
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e
a
r
c
h
in
tere
sts
in
c
lu
d
e
fa
u
lt
d
iag
n
o
sis
a
n
d
fa
u
lt
-
to
lera
n
t
c
o
n
tro
l
in
AC
m
o
to
r
d
ri
v
e
s.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
h
ich
a
m
.
z
a
ime
n
@u
n
iv
-
s
o
u
k
a
h
ra
s.d
z
.
H
a
ss
e
n
Be
li
la
re
c
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e
d
th
e
M
.
S
c
.
d
e
g
re
e
i
n
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tri
c
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l
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g
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n
e
e
rin
g
fr
o
m
th
e
Un
iv
e
rsity
o
f
Jijel,
Al
g
e
ria,
in
2
0
0
5
,
a
n
d
th
e
P
h
.
D.
d
e
g
re
e
in
e
le
c
tri
c
a
l
e
n
g
in
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e
rin
g
fro
m
t
h
e
Un
iv
e
rsity
o
f
Ou
m
E
l
Bo
u
a
g
h
i,
Alg
e
ria,
in
2
0
2
1
.
He
is
c
u
rre
n
tl
y
a
n
a
ss
o
c
iate
p
ro
fe
ss
o
r
a
t
t
h
e
Un
iv
e
rsity
o
f
Ou
m
El
Bo
u
a
g
h
i,
A
lg
e
ria.
His
m
a
in
re
se
a
rc
h
in
tere
st
s
in
c
lu
d
e
p
o
we
r
q
u
a
li
ty
a
n
d
re
n
e
wa
b
le en
e
rg
y
.
H
e
c
a
n
b
e
c
o
n
t
a
c
ted
a
t
e
m
a
il
:
h
a
ss
e
n
b
e
li
la@
y
a
h
o
o
.
fr
.
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