Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol.
5, No. 6, Decem
ber
2015, pp. 1319~
1
327
I
S
SN
: 208
8-8
7
0
8
1
319
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
The Transient Stability Study of a Synchronous Generator
Based on the Rotor Angle Stability
Fetissi Selwa,
Labed
Djam
el, Lab
e
d Im
en
Laborator
y
of
Electr
i
cal
Engineer
ing of Constant
ine,
D
e
partment of
Electr
i
cal Eng
i
neer
ing,
Frère Mentour
i
Constantine 1 U
n
iversity
, Constantine, Alg
e
ria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 2, 2015
Rev
i
sed
Ju
l 20
,
20
15
Accepte
d Aug 5, 2015
Trans
i
en
t s
t
abil
it
y is
an im
portan
t
as
pect in th
e operat
i
on of ele
c
t
r
ica
l
power
s
y
s
t
em
. In
cas
e
of faul
t oc
curs
in
the
s
y
stem
,
the
determ
ining
of f
a
ult
cl
earing
tim
e of circu
it b
r
eaker
is
cons
ide
r
ed one of the m
a
in fa
ctors
to en
s
u
re power
trans
f
er of th
e s
y
s
t
em
. Th
is
pap
e
r is
aim
to s
t
ud
y
th
e trans
i
ent
s
t
abili
t
y
o
f
si
ngl
e
ma
c
h
i
n
e
infi
ni
t
e
bus sy
st
em (S
MIB),
ba
se
d on t
h
e
rot
o
r a
ngl
e
st
a
b
i
lity
.
The s
t
ud
y is
pe
rform
ed to dete
rm
ine the inf
l
ue
nce of th
e cri
t
i
c
al c
l
ear
ing
tim
e of the c
i
rcu
it break
ers on th
e rotor angl
e sta
b
ilit
y of th
e gen
e
rator in
the
cas
e of thr
ee p
h
as
e faul
t. F
o
r
obtai
ning
and d
e
termining num
erically
the
nature of th
e ro
tor angle of
machine,
we
applied
the Step
-b
y
-
step method for
differen
t
va
lues
of fault
cl
earing
tim
e. Th
e resul
t
s of sim
u
lation in
dica
te th
a
t
determine of critical cl
earing time is a
major eval
uation in stab
ility
studies.
The s
y
s
t
em
m
odel
is
cr
eat
ed
in
M
A
TLAB/ S
I
M
U
LINK s
o
ftware
.
Keyword:
Critical clearing tim
e
Ro
to
r ang
l
e stab
ility
Syn
c
hro
nou
s gen
e
r
a
t
o
r
Transien
t stab
ility
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Fetissi Selwa,
Lab
o
rato
ry
of Electrical
E
n
g
i
n
eer
i
n
g of
C
o
nstan
tin
e,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Frère
M
e
nt
ou
ri
C
o
nst
a
nt
i
n
e
1
U
ni
versi
t
y
,
Ro
ad d’
A
i
n
El
Bey, Co
nstan
tin
e
2
500
0,
A
l
g
e
r
i
a.
Em
a
il: Selwa.f@ho
tm
ai
l.co
m
1.
INTRODUCTION
Stu
d
i
es
o
f
th
e tran
sien
t stabilit
y h
a
v
e
b
e
en
recog
n
i
zed
as an
essen
tial p
a
rt in
t
h
e
p
l
ann
i
ng
o
f
el
ect
ri
cal
sy
st
em
s, i
n
orde
r t
o
ensu
re t
h
e sy
st
em
operat
i
on
i
n
go
o
d
co
ndi
t
i
on an
d ret
u
r
n
t
o
no
rm
al
or stabl
e
state after h
a
v
i
n
g
b
e
en
su
bj
ected
to
so
m
e
fo
rm
o
f
d
i
stu
r
ban
ce.
Power
syste
m
stab
ili
ty
is th
e ab
ility o
f
t
h
e
syste
m
to
rem
a
in
in
op
erating
eq
u
ilibriu
m
o
r
syn
c
hron
ism
,
wh
ile
d
i
stu
r
b
a
n
ce
o
ccur
on
the syste
m
[1
]-[4].
Transien
t stab
i
lity is th
e ab
ilit
y o
f
t
h
e
p
o
wer
syste
m
to
m
a
in
tain
syn
c
h
r
o
n
i
sm
wh
en
it is sub
j
ected
t
o
a sev
e
re tran
si
en
t p
e
rturb
a
ti
on
[2
],
[5
]-[7
], lik
e th
e
case
of
s
e
parat
i
o
n
of
l
i
n
es
or electrical
gene
rators.
Th
e tran
sien
t stab
ility d
e
p
e
nd
s
n
o
t
on
ly on
th
e am
p
litu
d
e
o
f
t
h
e
d
i
stu
r
b
a
n
ce and
t
h
e starting
poin
t
of
o
p
e
ration
bu
t also
it d
e
p
e
nd
s
o
n
th
e
d
y
n
a
m
i
c ch
aracteristics o
f
th
e system [7
]. It
m
a
n
i
fests in
th
e short ter
m
as a
wid
e
n
i
ng
g
a
p a
p
e
riod
ically certain
ang
l
es
o
f
th
e ro
to
r [8
].
In
th
is p
a
p
e
r,
we are i
n
terested in
t
h
e stab
ility
st
udy
of
t
h
e r
o
t
o
r
an
gl
e.
Ro
to
r ang
l
e st
ab
ility is th
e syn
c
hrono
u
s
mach
in
es
cap
aci
ty o
f
an
i
n
terco
n
n
ected
p
o
wer system
to
rem
a
i
n
i
n
sy
nc
hr
o
n
i
s
m
aft
e
r a di
st
u
r
ba
nce
.
The
rot
o
r
an
gl
e o
f
t
h
e
ge
ne
ra
t
o
r
de
pen
d
s
o
n
t
h
e
bal
a
nce
be
t
w
een
the electrom
a
gnetic torque
and m
echan
i
c
al
t
o
rq
ue. I
n
ot
he
r w
o
r
d
s, t
h
e sy
st
em
i
s
unst
a
bl
e i
f
t
h
e angl
e
d
i
fferen
ce b
e
t
w
een
two
in
terco
n
n
ected
g
e
nerato
rs in
creas
es in
d
e
fi
n
itely
o
r
tran
sien
t oscillatio
n
cau
sed
b
y
a
di
st
ur
ba
nce, i
s
not
su
ffi
ci
ent
l
y
dam
p
ed i
n
t
h
e
eval
uat
i
on
t
i
m
e
[
9
]
.
Ro
to
r ang
l
e stab
ility is fu
rt
h
e
r classified
i
n
to sm
al
l d
i
stu
r
b
a
n
ce an
g
l
e stab
i
lity an
d
larg
e
d
i
stu
r
b
a
n
c
e
an
g
l
e stab
ility. Wh
en
a fau
lt o
ccu
rs at th
e
termin
als o
f
a syn
c
h
r
on
ou
s
g
e
n
e
rator, th
e
p
o
wer o
u
t
p
u
t
o
f
th
e
mach
in
e is greatly red
u
c
ed
: th
e ro
tatio
nal sp
eed of th
e
g
e
n
e
rat
o
r, its ang
u
l
ar po
sition
an
d th
e tran
smit
ted
po
we
r are e
x
p
o
se
d t
o
rapi
d c
h
an
ges
.
H
o
we
ver
,
t
h
e i
n
p
u
t
po
we
r t
o
t
h
e
g
e
nerat
o
r
fr
om
the t
u
rbi
n
e
has
no t
i
m
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1319 –
1327
1
320
to
ch
ang
e
durin
g
th
e sho
r
t period
o
f
th
e
fau
lt, th
e ro
t
o
r e
ndea
v
ors to
ga
in spee
d to store the excess e
n
ergy
[1
0]
.
If the fau
lt p
e
rsists lo
ng
enou
gh
, t
h
e ro
t
o
r
an
g
l
e
will in
crease un
til th
e ro
t
o
r l
o
sses all
th
e k
i
n
e
tic
en
erg
y
it gained
d
u
ring
t
h
e
fau
lt
p
e
ri
o
d
is exh
a
u
s
te
d
.
So-called
p
h
e
nomen
o
n
o
f
t
h
e
tran
sien
t
stab
ility, th
at
occurs on
the nearest ge
nerat
o
r
t
o
th
e
l
o
cat
i
o
n
o
f
di
st
ur
ba
nce.
If
t
h
e
ope
rat
i
ng t
i
m
e of t
h
e ci
rc
ui
t
b
r
ea
kers
i
s
very
i
m
port
a
nt
, t
h
r
o
ug
h
bet
t
e
r com
m
uni
cat
i
o
n
an
d
fast
act
i
ng
rel
a
y
s
a ra
pi
d e
ffect
,
t
h
e
ci
rcui
t
b
r
eake
r
o
p
en
s
whe
n
t
h
e fa
ult
is detected a
nd autom
a
tically
recloses a
f
ter a
specifie
d
peri
o
d
. If the fau
lt p
e
rsists, th
e ci
rcu
i
t
b
r
eak
e
r
reop
ens an
d
th
en
recl
o
s
es as b
e
fore. Th
is is rep
eated
on
ce m
o
re, wh
en
if th
e fau
lt still
p
e
rsists, th
e
brea
ker
rem
a
i
n
s ope
n [
10]
. T
h
e cri
t
i
cal
cl
eari
n
g
t
i
m
e
can
be de
fi
ne
d as a
m
a
xim
u
m
dur
at
i
on t
h
at
can r
e
m
a
i
n
a fau
lt in
th
e electrical syste
m
witho
u
t
l
o
sing th
eir stab
ility [5
].
Th
is p
a
p
e
r stud
ies th
e tran
sien
t stab
ility o
f
po
wer sy
stem
b
a
sed
on
th
e stab
ility o
f
th
e ro
to
r an
g
l
e and
foc
u
ses
o
n
t
h
e
m
o
st
severe
a
m
ong al
l
t
y
pes
fa
ul
t
w
h
i
c
h
i
s
t
h
e t
h
ree
-
p
h
as
e fa
ul
t
,
i
n
o
r
d
e
r t
o
d
e
t
e
rm
i
n
e t
h
e
influe
nce
of the critical clear
ing tim
e
of t
h
e ci
rcui
t
brea
k
e
rs f
o
r
di
ffe
re
nt
val
u
es
o
f
fa
ul
t
cl
eari
ng t
i
m
e
, t
o
en
su
re
stab
ility
of system
.
We studied t
h
e
case of
single
m
ach
in
e connected
to
infin
ite b
u
s system
li
k
e
[10
]
-[1
3
]
.
We tak
e
t
h
e
sam
e
syste
m
used i
n
[13].
Fo
r th
e
nu
m
e
rical so
lu
tion
of tran
sien
t stab
ility an
alysis o
f
sing
le m
a
c
h
in
es
conn
ected
to in
fi
n
ite
bus
,
we use
d
t
h
e st
ep
by
st
ep
m
e
t
hod
fo
r
di
f
f
ere
n
t
val
u
es o
f
fa
ul
t
cl
eari
n
g
t
i
m
e
. Thi
s
m
e
tho
d
pr
o
pose
d
i
n
[
1
1]
[1
2]
an
d [
1
4]
.
We a
ppl
i
e
d t
h
i
s
m
e
t
hod
o
n
o
u
r
pr
o
p
o
s
ed
sy
st
em
. It
i
s
a co
nve
nt
i
o
nal
an
d
app
r
oxi
m
a
t
e
m
e
t
hod
b
u
t
a well tried and
p
r
ov
en one.
We
also
relied
on
t
h
e resu
lt of
[10
]
, [12
]
-[15
], b
a
se
d
o
n
the ro
tor an
g
l
e stab
ility th
at is ju
dg
ed
fro
m
th
e n
a
t
u
re of swing
cu
rv
e
for
co
m
p
are and
ev
alu
a
te t
h
e stab
ility o
f
o
u
r sy
ste
m
.
2.
ROTO
R
AN
G
LE STABILI
T
Y ST
UD
Y
2.
1.
Single m
a
chin
e infinite
bus
(SMIB)
For a
n
alyze the rotor angle stability
of powe
r syste
m
according m
a
j
o
r
dist
urba
nces,
we will take the
case of single machine infini
te bus (SM
I
B). The sync
hronous m
achine can be re
pr
ese
n
ted by the cl
assical
m
odel, i.e. a c
onsta
nt voltage sour
ce in series with a constant reactan
c
e
supplying powe
r to infi
nite bus
through a trans
f
orm
e
r of a rea
c
tance Xt
and l
i
ne of a
reacta
n
ce Xl as s
h
own
in Fi
gure 1.
Thus the
gene
rator is
rep
r
ese
n
t
e
d
by
E an
d t
h
e i
n
fi
n
i
t
e
bus
i
s
re
pre
s
ent
e
d
by
U.
Fig
u
re
1
.
Sing
l
e
m
ach
in
e in
fi
n
ite bu
s
In th
is sim
p
le case,
X
s
= X
d
+X
t
+X
l
I
jX
U
E
S
(1)
Whe
r
e:
S
jX
U
E
I
(
2
)
The
el
ect
ri
cal
po
we
r of ge
ner
a
t
o
r
i
s
gi
ve
n b
y
t
h
e
f
o
l
l
o
wi
n
g
Eq
uat
i
o
n
(
3
), (
4
)
an
d (5
) [3]
:
)
Re(
I
E
P
e
)
Re(
s
jX
U
E
E
(
3
)
)
90
0
Re(
s
X
U
E
E
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Th
e Tran
sien
t S
t
ab
ility
S
t
ud
y o
f
a
S
y
n
c
h
r
o
nou
s Genera
t
o
r Ba
sed
o
n
th
e Ro
to
r
Ang
l
e S
t
ab
ility
(Fetissi
S
e
lwa
)
1
321
))
90
(
90
Re(
2
s
s
X
EU
X
E
)
90
cos(
s
X
EU
sin
s
e
X
EU
P
(5)
δ
: an
g
l
e
o
f
th
e
ro
t
o
r, it is th
e
p
h
a
se d
i
fferen
ce b
e
tween
th
e i
n
tern
al vo
ltag
e
E o
f
th
e
g
e
n
e
rato
r and
th
e
vol
t
a
ge
o
f
i
n
fi
ni
t
e
ba
r
U.
Th
is equ
a
tion
sh
ows th
at any ch
an
g
e
s affectin
g
th
e transmissio
n
p
o
wer will cau
se a
v
a
riation
of
rot
o
r a
n
gle
δ
. The
c
u
rve P ve
rsus
δ
i
s
k
n
o
w
n
as
t
h
e
p
o
we
r
angl
e c
u
rve
an
d i
s
pl
ot
t
e
d
i
n
Fi
gu
re
2.
Fi
gu
re
2.
P
o
we
r a
ngl
e c
u
r
v
e
We
have
f
o
r
t
h
e case
of
ge
ner
a
t
o
r:
a
m
e
P
P
P
(
6
)
Pe:
Electrical po
wer tran
sm
itt
ed
in th
e li
n
e
.
Pm: Mechanic
al powe
r
obtai
ned
f
r
om
t
h
e g
e
nerat
o
r.
Pa: The
acceleration Powe
r.
In
norm
al operation, the electrical
power is equal to the m
echan
ical power, i.e. there is
no
acceleration.
If the a
n
gle
δ
su
bj
ect a po
sitive ch
ang
e
Δδ
, th
e power
will b
e
also
sub
j
ect
ed
a ch
ang
e
Δ
P and such a
s
P
m
does not
de
pen
d
o
n
t
h
e
δ
,
t
h
e new re
gi
m
e
woul
d
be
P
e
> P
m
. i.e. th
e ro
tor will b
e
su
bj
ected
to
a b
r
ak
ing
torque
. This re
gim
e
continues until restor
ation
of the i
n
itial equilibrium
point “a”.
In t
h
e sam
e
reasoning, if t
h
e
angle
δ
s
u
b
j
ect
s a ne
gat
i
v
e
va
ri
at
i
on
Δδ
, th
e
ro
t
o
r
will b
e
su
bj
ected to
an acceleration torque.
Fo
r th
e op
eratin
g
po
in
t “b
”, we
h
a
v
e
for
a po
sitiv
e
d
e
v
i
atio
n
Δδ
b'
: P
b'
< P
m
an
d
th
e ro
t
o
r will be
subjecte
d
to a
n
acceleration torque.
Un
de
r the action of this
couple, the
de
l
t
a angle continues to inc
r
ease
from
(b'
t
o
b'
'
)
causi
ng
p
r
og
ressi
ve
decrease
in
power and m
a
king th
e
m
ach
in
e o
u
t
of
syn
c
hr
on
ism
.
For point “c”
and
for a
varia
tion
Δδ
>0
th
e
mach
in
e falls to
ward
s th
e instab
ility an
d
for a v
a
riation
Δδ
<0 t
h
e m
achine
returns to the i
n
itial stat
e (poi
nt “c”).
So
we ca
n say that
on the
branch
δ
(0
° to
9
0
°)
of
characte
r
istic P=f(
δ
) th
e estab
lish
e
d
reg
i
m
e
s are stab
le and
for th
e corresp
ond
ing
reg
i
mes
δ
(
9
0
°
t
o
18
0°
) a
r
e
unst
a
bl
e.
2.
2.
Stud
y
of Swin
g Equ
a
tion
For t
h
e case
of sync
hronous
m
ach
i
n
e co
n
n
ect
ed t
o
i
n
fi
n
i
t
e
bus, t
h
e
s
w
i
n
g eq
uat
i
o
n
i
s
gi
ven
by
Equ
a
tio
n (7
) an
d (8
)
:
a
e
m
P
P
P
dt
d
f
H
2
2
(7
)
H: th
e con
s
tan
t
in
ertia.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1319 –
1327
1
322
Whe
r
e:
sin
max
P
P
e
Or:
sin
max
2
2
P
P
dt
d
f
H
m
(
8
)
)
sin
(
max
2
2
P
P
H
f
d
t
d
m
A pl
ot
of
δ
ve
r
s
us t
cal
l
e
d
t
h
e
swi
n
g
cu
rve
s
h
o
w
n i
n
Fi
g
u
r
e
3 a
n
d t
w
o ca
s
e
s are
p
o
ssi
bl
e:
If
δ
star to
dec
r
ease after reac
hing a m
a
xim
u
m
value, the m
achine
re
m
a
in
s stab
le, and
if
δ
con
tinu
e
s
to
in
crease i
n
defin
itely, th
e mach
in
e l
o
ses
sy
nch
r
oni
sm
and
bec
o
m
e
unst
a
bl
e.
So
, th
e
syste
m
is stab
le if
d
δ
/d
t =0
The sy
st
em
i
s
unst
a
bl
e i
f
d
δ
/d
t
>
0
Fi
gu
re
3.
swi
n
g c
u
r
v
e
3.
STEP-BY-ST
EP SOL
U
SIO
N
OF THE
SWING EQUATION
There a
r
e se
ve
ral
m
e
t
hods a
v
ai
l
a
bl
e for t
h
e
sol
u
t
i
o
n o
f
t
h
e
swi
n
g eq
uat
i
o
n. I
n
t
h
e case
of a si
n
g
l
e
m
achine connected to infini
te bus ba
r, we
shall treat th
e step-by
-
step
m
e
thod for the soluti
on of critical
clearing tim
e
associated
with criti
cal clearing a
ngle and
determ
ine
δ
whi
c
h m
a
y
be pl
ot
t
e
d ver
s
us t
for a
mach
in
e to
ob
t
a
in
th
e swi
n
g
curve of that
machin
e. T
h
e
step-by-step
m
e
th
od
is a conv
en
tion
a
l, ap
pro
x
i
m
a
t
e
m
e
t
hod l
i
k
e
al
l
n
u
m
e
ri
cal
m
e
tho
d
s
b
u
t
a
wel
l
t
r
i
e
d a
n
d
p
r
ov
en
one
. T
h
e a
n
gl
e del
t
a
i
s
cal
cul
a
t
e
d as
a f
u
nct
i
o
n
of ti
m
e
over
a period long enough
t
o
determine whether delta,
will
increase
without lim
it or reach a
m
a
xim
u
m
and
st
art
t
o
decrea
s
e
. [
1
1]
-[
12]
,
[
1
4]
, [
1
6]
.
The st
e
p
-
b
y
-
st
ep m
e
t
hod i
s
b
a
sed
o
n
t
h
e
f
o
l
l
o
wi
ng
E
quat
i
o
n
(9
),
(
1
0
)
a
n
d
(1
1):
n
n
n
1
(9)
)
(
2
)
1
(
1
t
M
P
n
a
n
n
(10)
The accele
r
ation
powe
r is:
)
1
(
)
1
(
n
e
m
n
a
P
P
P
(11)
Whe
r
e:
δ
(n-1)
has b
e
en
p
r
ev
iou
s
ly calcu
lated.
I
t
is no
ted that d
u
r
i
ng
sudd
en ch
ang
e
s
o
f
situ
atio
n, i
t
is n
ecessary to
calcu
late
th
e av
erag
e
acceleration
power for the
variation of t
h
e a
n
gle
δ
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Th
e Tran
sien
t S
t
ab
ility
S
t
ud
y o
f
a
S
y
n
c
h
r
o
nou
s Genera
t
o
r Ba
sed
o
n
th
e Ro
to
r
Ang
l
e S
t
ab
ility
(Fetissi
S
e
lwa
)
1
323
4.
SIMULATION AND RESULTS
4,
1, T
e
s
t
Netw
ork
Fi
gu
re
4 s
h
ows
si
ngl
e m
achi
n
e i
n
fi
ni
t
e
b
u
s s
y
st
em
(SM
I
B
)
use
d
i
n
t
h
e si
m
u
l
a
t
i
on a
n
al
y
s
i
s
an
d Ta
bl
e
1
presen
t th
e
param
e
ter ele
m
e
n
t o
f
th
e system
.
A g
r
o
u
p
o
f
p
l
an
ts 900
0
M
W
is
d
e
liv
eri
n
g
po
wer to
infin
ite b
a
r
th
ro
ugh
a t
w
o
tr
an
sf
or
m
e
r
s
an
d f
e
ed
s
fo
ur
t
r
an
sm
issio
n
lines of
9
6
5
k
m
at a vo
ltag
e
o
f
1
200
k
V
to
carr
y th
e
9
000
M
W
t
h
at w
e
pro
p
o
s
ed
to
car
r
y
.
W
e
can
r
e
du
ce th
e
mach
in
e gr
oup syste
m
b
y
sys
t
e
m
eq
u
i
v
a
len
t
to
a
single m
achine
.
Fi
gu
re
4.
P
o
we
r Sy
st
em
M
ode
l
Table
1.
Param
e
ter elem
ents of the
system
Electrical system
para
m
e
ters
GS
X
d
’ (p
u
)
H (
M
J/MV
A)
P (M
W)
0.
25
3
9000
TR1
X
T1
(
p
u)
0.
12
TR2
X
T2
(
p
u)
0.
15
Line
X
l
(
pu)
Y/2 (
pu)
R
C
(
Ω
)
1.
875
0.
382
250
Pow
e
r
Base: 90
00
MVA
(6
0
H
z
)
Vo
ltag
e
Base: 1
200
KV
Im
pedance B
a
s
e
:
16
0
Ω
We are
n
o
w
ab
le to
pro
ceed w
ith
th
e study o
f
th
e stab
ility fo
r a symmetrical th
ree-ph
ase fau
lt in
o
r
d
e
r to
d
e
termin
e critical c
l
earing
ti
m
e
o
f
th
e circu
it b
r
ea
kers
for differe
n
t values
of
fa
ult clearing time, to
b
u
ild and
en
sure th
e stab
ility o
f
ou
r n
e
t
w
ork.
In
t
h
i
s
pape
r,
we rel
i
e
d on
[
1
0]
-[
1
5
]
.
In [1
0
]
, a m
o
d
e
l fo
r assessmen
t
o
f
tran
sien
t st
ab
ility of electrical power system
was presen
ted,
whe
r
e this last
studie
d
two c
a
ses for t
h
e sy
ste
m
: singl
e machine system
and 2- m
achine syste
m
, in order t
o
ev
alu
a
te th
e tran
sien
t stab
ility fro
m
th
e n
a
tu
re
o
f
th
e swin
g
curv
es
wh
ich is a p
l
o
t
o
f
the ro
tor ang
l
es ag
ain
s
t
ti
m
e
an
d
th
e co
m
p
lete syste
m
h
a
s b
een ad
op
ted on
a
prog
ram
th
at is written
in
M
A
TLAB
p
r
o
g
ra
mmin
g
lan
g
u
a
g
e
.
Wh
ile we stud
ied
in th
is work, th
e
case o
f
si
ngle
machine conne
cted to in
fi
ni
t
e
bus sy
st
em
(SM
I
B
)
as ap
pr
ove
s o
u
r
p
r
o
p
o
sal
sy
st
em
and t
h
e c
o
m
p
l
e
t
e
sy
st
em
has
been
rep
r
e
s
ent
e
d i
n
t
e
rm
s of
Si
m
u
l
i
nk bl
oc
ks
i
n
a si
ngl
e m
o
d
e
l
Fi
gu
re
5.
R
e
fere
nce [
1
1
]
, [1
2]
an
d
[
1
4]
p
r
esente
d t
h
e
num
erical solution m
e
thod
step
-by
-
step f
o
r
vario
u
s
cri
t
i
cal
cl
eari
ng t
i
m
e
. W
e
ap
pl
i
e
d t
h
i
s
m
e
t
hod
on o
u
r
sy
st
em
t
o
det
e
r
m
ine n
u
m
e
ri
cal
ly t
h
e vari
at
i
on
and t
h
e
nat
u
re
of t
h
e s
w
i
n
g c
u
r
v
e.
R
e
fere
nce [
11]
prese
n
t
e
d a st
abi
l
i
zat
i
on of
m
u
lt
i
-
m
achi
n
e sy
st
em
conn
e
c
t
e
d t
o
i
n
fi
ni
t
e
bus
, w
h
ere
th
is last u
s
ed
two
m
ach
in
e intercon
n
ected
syste
m
fo
r
3-
ph
ase fa
ul
t
and
t
w
o
di
f
f
ere
n
t valu
es
of fau
lt
clearing
t
i
m
e
at
0.08
s
and
0
.
2
7
5
s.
We al
s
o
used
t
w
o
di
f
f
ere
n
t
val
u
es
o
f
f
a
ul
t
cl
eari
n
g t
i
m
e at
0.
0
8
s a
n
d
0.
1s, t
o
d
e
term
in
e th
e
n
a
ture
o
f
ro
tor ang
l
e
δ
c
u
rve
according t
o
ti
me and also we
we
re a
b
le to
obtain the
followi
ng
curves: the
ele
c
tric powe
r, t
h
e acceleration
powe
r a
n
d the
angu
lar spee
d
of the
ge
nerat
o
r.
In
[13
]
as is ev
id
en
t, we stud
ied
th
e tran
si
en
t stab
ility o
f
electrical syst
e
m
b
a
sed
on
th
e stab
ility o
f
th
e ro
tor an
g
l
e to
d
e
term
in
e th
e
n
u
m
b
e
r o
f
lin
e
for
on
e
v
a
lu
e
of critical clearin
g ti
m
e
0
.
1
s
and
two
h
ypo
th
esis: fou
r
lin
es and
fiv
e
s lin
es.
Wh
ile in
th
is
p
a
p
e
r, to
fu
rt
h
e
r im
p
r
ov
e system
efficien
cy we t
o
o
k
t
h
e
first h
ypo
th
esi
s
in
[1
3
]
fo
r fou
r
lin
es and
we tried
to
ev
aluate th
e o
p
e
rati
o
n
system fo
r
3
-
ph
ase fau
lt th
rou
g
h
th
e d
e
term
in
ati
o
n a
v
a
lu
e
of fau
lt clearing
time b
e
tween two
v
a
lu
es.
Th
e fau
lt is assu
m
e
d
to
th
e in
pu
t lin
e (Fi
g
.4
: po
in
t A).
We can
con
s
id
er in
th
e case o
f
th
ree-ph
ase
symm
e
t
rical fault steady state
and also
t
h
e vo
ltag
e
at th
e term
in
als o
f
th
e altern
ator is k
e
p
t
con
s
tan
t
b
e
cau
s
e
o
f
its ex
citation
system
. Th
is
fact allo
ws us t
o
co
nsid
er
th
e u
n
it v
o
ltage U for
calcu
lations
(X'd
=0).
We applied t
h
e
m
e
thod ste
p
by step on our
s
y
stem
(SMIB), to determ
ine num
e
rically the stability of
rot
o
r a
n
gle
δ
.
The cal
c
u
l
a
t
i
ons f
o
r t
h
i
s
m
e
tho
d
ha
ve bee
n
per
f
o
rm
ed by
a pr
o
g
ram
usi
n
g M
A
T
L
AB
.
Tabl
e
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1319 –
1327
1
324
and Ta
bl
e 2 p
r
esent
t
h
e st
ep-
b
y
-
st
ep m
e
t
hod fo
r fa
ul
t
cl
eared t
i
m
e respe
c
t
i
v
el
y
at 0.0
8
s
and 0
.
1s
.
W
i
t
h
Δ
t=
0.
05s
.
Tabl
e 2. St
ep
-b
y
-
St
ep
m
e
t
hod
for fault
cleare
d
at 0.08s
t (
s
ec)
Pe (
pu)
Pa (
pu)
[(
Δ
t
2
)/M]Pa
(d
eg
)
Δδ
n
(d
eg
)
δ
n
(d
eg
)
0
-
0
+
0
av
g
0.
05
0.
1
0.
15
0.
20
0.
25
0.
30
0.
35
0.
40
0.
45
0.
50
0.
55
1
0
0
0
1.
2315
1.
3173
1.
3475
1.
3511
1.
3490
1.
3501
1.
3509
1.
3359
1.
2788
….
0.
00
1.
00
0.
50
1.
00
-
0
.
2315
-
0
.
3173
-
0
.
3475
-
0
.
3511
-
0
.
3490
-
0
.
3501
-
0
.
3509
-
0
.
3359
-
0
.
2788
….
0.
00
9.
00
4.
5
9.
00
-
2
.
0832
-
2
.
8556
-
3
.
1278
-
3
.
1603
-
3
.
1414
-
3
.
1503
-
3
.
1584
-
3
.
0235
-
2
.
5089
….
0.
00
0.
00
4.
5
13.
504
2
11.
421
1
8.
5655
5.
4377
2.
2773
-
0
.
8641
-
4
.
0150
-
7
.
1734
-
10.
1970
-
12.
7059
….
47.
67
47.
67
47.
67
52.
174
2
65.
678
5
77.
099
5
85.
665
0
91.
102
7
93.
380
0
92.
515
8
88.
500
8
81.
327
4
71.
130
4
58.
424
5
Tabl
e 3. St
ep
-b
y
-
St
ep
m
e
t
hod
for fault
cleare
d
at 0.1s
t (
s
ec)
Pe (
pu)
Pa (
pu)
[(
Δ
t
2
)/M]Pa
(d
eg
)
Δδ
n
(d
eg
)
δ
n
(d
eg
)
0
-
0
+
0
av
g
0.
05
0.
1
-
0.
1
+
0.
1
0.
15
0.
20
0.
25
0.
30
0.
35
0.
40
0.
45
0.
50
0.
55
1.
00
0.
00
0.
00
0.
00
0.
00
1.
2315
0.
00
1.
3403
1.
3426
1.
2899
1.
2191
1.
1485
1.
0835
1.
0222
1.
0411
….
0.
00
1.
00
0.
50
1.
00
1.
00
-
0
.
2315
0.
3843
-
0
.
3403
-
0
.
3426
-
0
.
2899
-
0
.
2191
-
0
.
1485
-
0
.
0835
-
0
.
0222
0.
0411
….
0.
00
9.
00
4.
5042
9.
00
0.
00
0.
00
3.
4584
-
3
.
0624
-
3
.
0834
-
2
.
6087
-
1
.
9717
-
1
.
3366
-
0
.
7514
-
0
.
2000
0.
3697
….
0.
00
0.
00
4.
5042
13.
504
2
0.
00
0.
00
16.
962
6
13.
900
2
10.
816
8
8.
2081
6.
2364
4.
8998
4.
1484
3.
9484
4.
3181
….
47.
67
47.
67
47.
67
52.
174
2
65.
678
5
65.
678
5
65.
678
5
82.
641
1
96.
541
3
107.
35
81
115.
56
62
121.
80
26
126.
70
24
130.
85
08
134.
79
93
139.
11
74
Accord
ing
to
t
h
e two
tab
l
es,
we fi
nd t
h
at th
e rot
o
r a
ngle
δ
reach a m
a
ximum
of and start
to dec
r
ease
for fau
lt cleared
at 0
.
8
s
,
Wh
ile it in
crease with
ou
t li
mit for fa
ult cleared at 0.1s
.
We can say t
h
at the
g
e
n
e
rator
rem
a
in
s its stab
ility at 0
.
8
s
bu
t it loses its stab
ility at 0
.
1
s
.
The com
p
l
e
t
e
sy
st
em
has been rep
r
ese
n
t
e
d i
n
t
e
rm
s of Sim
u
l
i
nk
bl
oc
ks i
n
a si
ngl
e
m
odel
Fi
g.5. T
h
e
si
m
u
latio
n
is d
o
n
e
for a
p
e
riod
of
2
s
.
We ob
serv
ed
thro
ugh
to
ch
an
gin
g
t
h
e fau
lt clearin
g
tim
es
ex
tent
stab
ility o
f
th
e
syste
m
fro
m
fig
u
res
b
e
low.
Fi
gu
re
5.
Si
m
u
l
a
t
i
on bl
oc
k
di
agram
of t
h
e s
y
st
em
i
n
M
A
T
L
AB
/
S
I
M
U
L
I
N
K
Before the
fa
ult, the electri
cal powe
r is
equal
t
o
the
mechanical power. T
h
e
generator is in
eq
u
ilibriu
m
sta
t
e an
d
its sp
eed
rem
a
in
s co
n
s
tan
t
. As th
e electrical p
o
w
er i
s
u
n
itary, it is p
o
s
sib
l
e to
d
e
t
e
rm
in
e
th
e in
itial ang
l
e v
a
lu
e of
δ
0
by
Pe=EU
/
X
s
sin
δ
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Th
e Tran
sien
t S
t
ab
ility
S
t
ud
y o
f
a
S
y
n
c
h
r
o
nou
s Genera
t
o
r Ba
sed
o
n
th
e Ro
to
r
Ang
l
e S
t
ab
ility
(Fetissi
S
e
lwa
)
1
325
A
t
th
e d
e
fau
l
t
p
h
a
se, th
e
p
o
w
e
r tran
sferred
fro
m
th
e g
e
n
e
rat
o
r (Pe)
will g
o
to
zero
.
A
s
tho
ugh
Pa=Pm
-
Pe an
d
Pm
i
s
consi
d
e
r
ed c
o
n
s
t
a
nt
a
n
d
uni
t
a
ry
,
Pa al
so
bec
o
m
e
s un
i
t
a
ry
.
After rem
o
v
a
l
th
e fau
lt, we
get in
to
th
e
same situ
atio
n
as before th
e
fau
lt Pe=EU/
X
s
sin
δ
, but
δ
has
not
t
h
e
sam
e
val
u
e
of
δ
0
. T
h
ere
f
ore the el
ectrical power and
ge
ne
rat
o
r
spee
d are
bec
o
m
i
ng vari
a
b
l
e
. T
h
e
g
e
n
e
rator go
ing
to
con
tinu
e
to
swi
n
g
u
n
til h
e
find
s an
equ
ilib
riu
m
p
o
i
n
t
, o
t
h
e
rwise it lo
ses its syn
c
hro
n
i
sm
and this
will be
accordi
n
g to t
h
e influe
nce
of the c
r
itical clearing tim
e of th
e circ
uit brea
ker on t
h
e
network.
(a) Electrical
p
o
we
r of
the ge
nerat
o
r
(b) Acceleration powe
r of
t
h
e gene
rator
(c)
The
an
g
u
lar s
p
eed
o
f
t
h
e
gene
rato
r
(d
).
The
r
o
to
r a
ngle
δ
of
t
h
e g
e
nerat
o
r
Fig
u
re
6
.
Sim
u
latio
n
resu
lts
of th
e system
fo
r fau
lt cleared
t
i
m
e
=0
.0
8s
0
0.2
0.
4
0.6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
t (
s
)
Pe
(
p
u
)
F
ault
c
l
eared
at
0.
0
8
s
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.4
1.6
1.8
2
-0
.
4
-0
.
2
0
0.2
0.4
0.6
0.8
1
t (s
)
Pa
(
pu)
F
a
u
l
t
c
l
ea
r
e
d a
t
0.
0
8
s
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
-6
-4
-2
0
2
4
6
t (s
)
w (
r
a
d
/
s
)
F
a
u
l
t
c
l
eare
d
at
0
.
08s
0
0.2
0.
4
0.6
0.
8
1
1.
2
1.
4
1.
6
1.
8
2
0
20
40
60
80
10
0
t (s
)
de
l
t
a
(de
g
)
F
a
u
l
t
c
l
ea
re
d at
0.
08
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE
Vol. 5, No. 6, D
ecem
ber
2015 :
1319 –
1327
1
326
(a) Electrical
p
o
we
r of
the ge
nerat
o
r
(b) Acceleration powe
r of
t
h
e gene
rator
(c)
The
an
g
u
lar s
p
eed
o
f
t
h
e
gene
rato
r
(d
) T
h
e
rot
o
r
a
ngle
δ
of
t
h
e g
e
nerat
o
r
Fig
u
re
7
.
Sim
u
latio
n
resu
lts
of th
e system
fo
r fau
lt cleared
t
i
m
e
=0
.1
s
Figure
6(a) and
(b) s
h
ow the el
ectric power a
n
d the
acc
eleration
p
o
w
e
r of
t
h
e ge
ner
a
t
o
r f
o
r
t
h
e
syste
m
with
fau
lt clearing
ti
me = 0
.
08
s, wh
ile Figu
re
6
(c
)
an
d (d
) sh
ow
th
e an
gu
la
r
s
p
e
e
d
an
d th
e
in
te
r
n
a
l
angl
e
δ
of th
e
g
e
n
e
rator. Th
e resu
lts
o
f
t
h
e
work ind
i
cate
t
h
at
fr
om
0 t
o
0.
08s
t
h
e
electrical powe
r equal t
o
zero, while the
acceleration powe
r go to
1 p.u. T
h
is shows
that at
this
time the acceler
ation powe
r equal to
mech
an
ic po
wer.
W
e
also
observ
e
th
at
d
e
lta tak
e
th
eir
in
itial v
a
lu
e o
f
47
.6
7° at 0
s
and in
crease to
59.14
° at
0.08s
, als
o
t
h
e
angular speed increase
fro
m
0rad/
s
at
0s
t
o
5
.
0
2
ra
d/
s at
0.
0
8
s. In
0.08s the fa
ult is cleared,
we
obs
erve that t
h
e electrical power i
n
cr
ea
se to 1.16
p.u
while
the acceleratio
n
power dec
r
e
a
se to
-0.16
p.u. T
h
e
ang
u
l
a
r s
p
ee
d
begi
ns t
o
decre
a
se and t
h
e r
o
t
o
r a
ngl
e
δ
cont
inues t
o
increa
se until it reaches a m
a
xi
m
u
m value
of 97.55°
a
nd
t
h
en begi
ns
to decr
ease
.
The
electrical powe
r
and the acceler
ation power continue
to vary
with
th
e v
a
riatio
n of d
e
lta.
The
res
u
lts s
h
ow that
the
power system
is stab
le. T
h
e
electric power and
the acceleration
powe
r a
r
e
depreciated, t
h
e angular s
p
ee
d and the rot
o
r angle
δ
varies according to a
dam
p
ed
oscillatory pace
with ti
m
e
aro
u
n
d
an
e
qui
l
i
b
ri
um
poi
nt
.
We ca
n
say
t
h
a
t
t
h
e
ki
net
i
c
e
n
ergy
gai
n
e
d
d
u
r
i
n
g
faul
t
i
s
a
b
sor
b
e
d
by
t
h
e
s
y
st
em
an
d th
e
g
e
n
e
rat
o
r m
a
in
tain
s it
s stab
ility after fau
lt
clearan
ce and
is sy
n
c
hron
ized
with
t
h
e
n
e
two
r
k
.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
t (s
)
Pe
(
p
u
)
F
a
ul
t
c
l
e
a
re
d at
0
.
1s
0
0.2
0.4
0.
6
0.
8
1
1.2
1.4
1.
6
1.
8
2
-0
.
5
0
0.5
1
1.5
2
2.5
t (s
)
P
a
(pu)
F
a
u
l
t
c
l
ea
re
d
at
0
.
1s
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.6
1.8
2
0
20
40
60
80
10
0
t (s
)
w (r
a
d
/
s
)
F
a
ult
c
l
ea
red
at
0
.
1
s
0
0.
2
0.4
0.
6
0.8
1
1.2
1.4
1.
6
1.8
2
0
500
1
000
1
500
2
000
2
500
3
000
t (s
)
d
e
l
t
a (
d
eg
)
F
a
ul
t
c
l
ea
re
d a
t
0.
1
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Th
e Tran
sien
t S
t
ab
ility
S
t
ud
y o
f
a
S
y
n
c
h
r
o
nou
s Genera
t
o
r Ba
sed
o
n
th
e Ro
to
r
Ang
l
e S
t
ab
ility
(Fetissi
S
e
lwa
)
1
327
Figu
re 8
(
a), (
b
), (c) a
nd (
d
) s
h
o
w
the sy
stem
respo
n
se for fau
lt clearin
g
ti
m
e
=
0
.
1
s
. In
th
is ti
m
e
th
e
electrical powe
r inc
r
ease t
o
1.23 p.u
a
n
d
the
acceleration powe
r decrease to
-1
.23
p.u, t
h
en they
continue to
o
s
cillate rap
i
dly an
d
in
d
e
fi
n
ite way.
W
e
n
o
t
e also
the an
gu
lar sp
eed
and
th
e ro
tor ang
l
e increases
co
n
tinuo
usly with
ti
m
e
wit
h
ou
t p
a
ss th
rou
g
h
a m
a
x
i
m
u
m v
a
lu
e. Th
e
si
m
u
latio
n
resu
lts in
d
i
cate th
at th
e
sy
st
em
becom
e
unst
a
bl
e an
d
t
h
e ge
nerat
o
r
bet
w
ee
n i
n
ov
er spee
d a
f
t
e
r
el
im
i
n
at
i
on
of
t
h
e fa
ul
t
and l
o
si
n
g
syn
c
hron
ism
with
th
e
n
e
two
r
k.
We com
p
ared
t
h
e resul
t
s
o
b
t
a
i
n
ed wi
t
h
t
h
a
t
obt
ai
ne
d i
n
[
10]
, [
1
2]
, [1
4]
-[
15]
an
d we
cam
e
t
o
t
h
e
sam
e
resu
lts b
y
stu
d
y
in
g
th
e
tran
sit stab
ility
th
at th
e tran
sien
t stab
ility
is
j
udg
ed
fro
m
th
e n
a
tu
re
o
f
th
e
swi
ng
curves
it is also
o
b
serv
ed
by
det
e
rm
i
n
i
ng s
w
i
n
g c
u
r
v
es
f
o
r
vari
ous
cl
eari
n
g
t
i
m
es t
h
at
we
hav
e
been
abl
e
t
o
find
th
e ti
m
e
p
e
rm
i
tted
b
e
fo
re clearing
a
fa
u
lt to
reg
a
in th
e
stab
ility o
f
o
u
r
n
e
two
r
k
.
An
d by
com
p
a
r
i
n
g t
h
e res
u
l
t
s
obt
ai
ne
d wi
t
h
al
so i
n
[
13]
, i
t
can be
not
e
d
t
h
at
t
h
e sy
st
em
ope
rat
e
s i
n
th
e
m
o
st efficien
t an
d
less costly th
ro
ugh a
change in the fault clearing tim
e of circuit breake
r
com
p
ared with
a cha
nge
in t
h
e
num
b
er of line
s
.
5.
CO
NCL
USI
O
N
Th
is p
a
p
e
r is
b
a
sed
on
th
e stab
ility o
f
th
e ro
t
o
r
an
g
l
e stud
y;
m
o
re p
r
écisin
g
fro
m
a si
m
u
la
tio
n
of
po
we
r sy
stem
fo
r dif
f
e
r
ent
v
a
lues o
f
fa
ult clearing tim
es. In the case
of
a
defa
ult, the el
ectrical power
drops
t
o
zero as we e
xpl
ai
ne
d p
r
e
v
i
ousl
y
. I
n
t
h
i
s
t
i
m
e, t
h
e ci
rcui
t
brea
ker
ope
ne
d t
h
e ci
rcui
t
w
a
s t
h
en cl
ose
d
agai
n
to
clear th
e fault. Th
e stab
ilit
y an
alysis o
f
ou
r system
is p
e
rfo
r
m
e
d
for the case o
f
m
o
st
sev
e
re
3
-
ph
ase fau
lt,
using a
system
of
m
achine
connecte
d
to
in
fin
ite
b
u
s
, so
if t
h
e
fau
lt i
s
cleared with
i
n
a tim
e o
f
0
.
0
8
s
, the
g
e
n
e
rator is stab
le with th
e n
e
twork. However if
fa
u
lt cleared
in 0.1s th
e gen
e
rat
o
r
will be un
stab
le.
Fro
m
a two v
a
lu
es of
fau
lt cl
earing
tim
es th
at we
h
a
v
e
chosen
,
we can
con
c
lud
e
th
at t
h
e stab
ility o
f
po
we
r sy
st
em
depe
n
d
s o
n
i
t
s
durat
i
o
n o
f
t
h
e cri
t
i
cal cl
earing t
i
m
e of t
h
e ci
rcui
t
brea
ker
,
t
o
avoi
d t
h
e ri
sk of
o
v
e
r sp
eed
i
n
case of sho
r
t circu
itin
g. Fi
n
a
lly, we can
say
th
at th
e resu
ltin
g
sim
u
lat
i
o
n
s are
con
s
istent wit
h
th
o
s
e fo
und
in
th
e literatu
re.
REFERE
NC
ES
[1]
S
y
ed
A. Nasar
,
“
E
lectri
c Power S
y
stem
,” McGraw-Hill, 1st
ed
itio
n, 1989
.
[2]
Prabha Kundur,
et al
.,
“Joint Task Force on Stability
Terms and
Defi
nitions
. Definition
and Classification of
Power
S
y
s
t
em
S
t
abi
lit
y,”
I
E
EE Transactions on
Power S
y
stems
, Vol. 19
,
No. 2, pp. 1387-
1401, 2004
.
[3]
Jignesh S. Patel
and Manish N. Si
nha,
“
P
ower S
y
s
t
em
Trans
i
en
t S
t
abil
it
y Ana
l
y
s
is
Us
ing ETAP
S
o
ftware,
”
Nati
onal
Conferenc
e
on
R
ecen
t Trends in
Engine
ering
&
Technolog
y,
2011
.
[4]
Koma
l S.
She
t
ye
,
Thoma
s
J.
O
v
e
r
by
e
,
a
n
d Ja
me
s F.
Gr
onquist. “Va
lida
t
ion of
Powe
r
S
y
ste
m
Tra
n
sie
n
t
Sta
b
ility
Results,”
Power
and Energy Con
f
erence
at Illinois (
PECI)
, 2012 I
EEE,
pp
. 1-8
.
[5]
Bables
h Kum
a
r
J
h
a, Ram
j
ee P
r
a
s
ad Gupta,
Upe
ndra P
r
as
ad
, “
C
om
bined
Operat
ion
of
S
V
C, P
S
S
and
Increas
ing
Inerti
a of M
achi
n
e for P
o
wer S
y
s
t
em
Tr
ans
i
ent
S
t
abili
t
y
Enhan
cem
ent,
”
International Journal
of Applied Pow
e
r
Engine
ering (
I
J
APE)
,
Vol. 3
,
N
o
. 1
,
pp
. 15-22
,
2014.
[6]
G. R. Mohapatr
a and A. Kal
a
m
,
“Dy
n
am
ic Stab
ilit
y
Anal
y
s
is of Renewabl
e Energ
y
Sources Interconnected to
th
e
Distribution
Networks,”
Australasian Univ
e
rsitie
s Powe
r
Engi
n
e
ering Conference (
A
UPEC'08)
,
p
p
. 1-4
,
2008
.
[7]
Sara Eftekharn
ejad,
et al.
, “
I
m
p
act of Incr
eas
ed
P
e
netra
tion of
Photovoltaic Gen
e
ration on Power S
y
stems,”
IEEE
Transactions on
Power Systems
,
Vol. 28
, No. 2, p
p
. 893-901
, 201
3.
[8]
H. Alkhatib
, Etu
d
e De La Stab
ili
té Aux Petit
es Perturba
ti
ons dan
s
les Grandes Réseaux E
l
ec
triqu
e
s
: Optim
isati
o
n
de la Régulation par une
Méthode Métaheuristique,
Th
èse de
Doctorat,
Univers
ité PAUL CEZANNE D’AIX
-
MARSEILLE (
A
IX- MARSEILLE III)
, 2008
.
[9]
C. APPRAEZ, Etude Comparative de Mé
thod
es de Simulation de La Stabilit
é Transitoir
e, école de technolo
g
ie
supérieure, Univ
ersité du Québ
ec, 2012
.
[10]
Ganiy
u
A. Ajenikoko and Anthon
y
A. Ol
aomi, “A Model for
Assessment of Tra
n
sient Stability
of Electrical Power
Sy
s
t
e
m
,
”
International Journal of
Electrical
and
Computer Eng
i
neering (
I
JEC
E
)
,
Vol. 4
,
No. 4, p
p
. 498-511
, 201
4.
[11]
D. P. Koth
ari, I
.
J. Nagrath, “Modern
Power S
y
s
t
em Analy
s
is,”
Tata Mc Graw-Hill
Educatio
n
,
Th
ird Edition, 2003.
[12]
Samita Padhi and Bishnu Prasad Mish
ra, “Numerical Method
Based Singl
e
Machine Analysis for Transien
t
St
a
b
i
l
ity
,”
Inter
national Journal of Emerging
Technology and Advanced
Engineering.
Vol. 4
,
No. 2, pp. 330-33
5
,
2014.
[13]
Fetissi Selwa an
d Labed
Djam
el
, “Transien
t
Stabilit
y
An
al
y
s
is
of S
y
nchronous
Generator
in E
l
ectr
i
cal Network
,
”
International Jo
urnal of S
c
ien
tific
&
Engineering Research
,
Vol.
5, No. 8, pp. 55-
59, 2014
.
[14]
Chandra S
h
ekha
r S
h
arm
a
, “
T
rans
ient S
t
abil
it
y
Anal
y
s
is
of S
i
ngle M
achin
e Infinite Bus
S
y
s
t
e
m
by
Num
e
rica
l
Methods,”
I
n
ter
national Journal
of Electr
ical an
d Electr
onics Research,
Vol. 2
,
No. 3, pp. 158-1
66, 2014
.
[15]
Kanika Gupta
and Ankit Pandey
,
“Stabili
zat
i
on Of
Multi Machine S
y
s
t
em
Connected To Infinit
e
Bus,”
International Jo
urnal of S
c
ie
n
tific &
Technology
Research,
Vol. 2
,
No. 8, pp. 82-8
5
, 2013
.
[16]
John J. Grainger and William
D. Stevenson Jr, “Power Sy
st
em
Anal
y
s
is
,” McG
r
aw-Hill Scien
c
e/Engin
eer
ing. 1
s
t
Edition
,
1994
.
Evaluation Warning : The document was created with Spire.PDF for Python.