Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
4
,
No
. 5, Oct
o
ber
2
0
1
4
,
pp
. 69
7~
70
2
I
S
SN
: 208
8-8
7
0
8
6
97
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
Implementation of Phase Imba
lance Scheme for Stabilizing
Torsional Oscillations
Rac
h
a
n
a
n
j
a
l
i
K*,
Su
man
S *, R
a
mb
abu
M **
, Ash
o
k Kum
a
r
K
*
*
* Department of
Electrical and
El
ectron
i
cs Eng
i
neering, Vignan
University
, Guntu
r
, Andhra Prades
h, India
** Departmen
t
o
f
Electr
i
cal
and
Electronics Eng
i
neering
,
VNIT
Nagpur, Nagpur
, Maharashtr
a, In
dia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 20, 2014
Rev
i
sed
Ju
l 9
,
2
014
Accepte
d
J
u
l 20, 2014
This
paper
im
plem
ents
the ph
as
e im
ba
lan
ce sch
e
m
e
for dam
p
in
g torsiona
l
oscilla
tions of
a series
cap
aci
t
o
r com
p
ensated
power s
y
st
em
. The I
E
E
E
Second Benchm
ark Model, s
y
stem-1, wh
erein
two turbine gen
e
rator model
and two s
y
stem model connect
ed to an
infinite b
u
s is emplo
y
ed
as a standar
d
s
y
stem model to stud
y
the con
c
ept of
subsy
n
chro
nous resonance.
The turbin
e
generator models have
a common
torsional mode
. The Electromagnetic
Trans
i
en
ts
P
r
ogram
(EM
T
P
)
is em
plo
y
ed to si
m
u
late the dam
p
ing effec
t
s
provided b
y
th
e phase
imbalan
c
e scheme
. Th
e s
i
m
u
lation
results
also show
that p
a
ra
lle
l pha
se im
balan
ce sch
e
m
e
gives
the b
e
tter d
a
m
p
ing ch
a
r
act
eristi
cs
when com
p
ared
to th
at of
s
e
ri
es
phas
e
im
bal
a
nc
e
s
c
hem
e
.
Keyword:
Phase
im
balance schem
e
Tor
s
i
o
nal
osci
l
l
at
i
ons
Copyright ©
201
4 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
:
Rachana
n
jali K,
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
Vi
g
n
an
U
n
i
v
e
r
si
t
y
Vadl
am
udi
, G
unt
ur
, An
d
h
ra Pra
d
esh
,
In
di
a
Em
a
il: rach
an
an
j
a
li@g
m
ail.c
o
m
1.
INTRODUCTION
A
num
ber
of c
ont
rol
devi
ces
un
de
r t
h
e t
e
rm
Fl
exi
b
l
e
AC
T
r
ansm
i
ssi
on Sy
st
em
(FAC
TS
)
ha
ve b
een
p
r
op
o
s
ed
and
im
p
l
e
m
en
ted
to i
m
p
r
ov
e th
e
stab
ility o
f
transmissio
n
system
. Th
e FA
CTS d
e
v
i
ces can
b
e
used
fo
r p
o
we
r fl
o
w
co
nt
r
o
l
,
l
o
o
p
fl
o
w
co
nt
r
o
l
,
l
o
ad s
h
ari
n
g
am
ong
paral
l
el
corri
do
rs,
v
o
l
t
a
ge re
gul
at
i
o
n
,
an
d
en
h
a
n
cem
en
t of tran
sien
t stabilit
y an
d
m
itig
atio
n
o
f
system
o
s
cilla
tio
n
s
. Dep
e
nd
ing
on th
e
d
e
v
i
ce
u
s
ed
it is
k
now
n as ser
i
es co
m
p
en
sation
an
d sh
un
t com
p
en
satio
n
.
Series capacitor com
p
ensation of m
e
diu
m
a
nd l
o
ng
A
C
tr
an
s
m
is
s
i
o
n
lin
e
s
h
a
s
b
e
en
r
e
co
gn
iz
e
d
a
s
a
po
we
rf
ul
t
ool
f
o
r
o
p
t
i
m
u
m
and eco
n
o
m
i
cal
u
s
e of t
r
ansm
i
ssi
on l
i
n
es
. T
h
e
pot
e
n
t
i
a
l
i
nher
e
nt
p
r
o
b
l
e
m
i
n
seri
es
com
p
ensat
e
d t
r
ansm
i
ssi
on l
i
n
es con
n
ect
e
d
t
o
t
u
r
b
o ge
ne
rat
o
rs i
s
s
u
b
s
y
n
c
h
r
o
no
us re
so
na
nce (S
SR
) l
ead
i
ng t
o
ad
v
e
rse to
rsion
a
l in
teracti
o
ns [3
]-[6
]
wh
ich
resu
lts i
n
s
h
aft failure
of
mechani
cal syste
m
. Sub sy
nchronous
reso
na
nce (
S
S
R
) pr
o
b
l
e
m
s
have bee
n
br
o
u
ght
t
o
ge
neral
at
t
e
nt
i
on i
n
pa
rt
i
c
ul
ar i
n
c
o
n
n
ect
i
on
wi
t
h
t
h
e sh
aft
dam
a
ge
eve
n
ts
since
t
h
e first shaft failure due
to SSR
occu
r
r
ed
at
t
h
e
M
o
h
a
ve
ge
nerat
i
n
g
st
at
i
on i
n
Dec
e
m
ber
19
7
0
an
d Oct
o
ber
19
7
1
. A
f
t
e
r t
h
e sha
f
t
fai
l
u
re at
M
oha
ve
gene
rat
i
ng st
a
t
i
on t
h
e fi
rst
b
e
nchm
ark m
odel
fo
r
com
put
er si
m
u
l
a
t
i
on o
f
S
S
R
was
pu
bl
i
s
he
d
i
n
1
9
7
7
.
T
h
i
s
pr
o
v
i
d
e
d
t
h
e
si
m
p
l
e
st
possi
bl
e m
odel
wi
t
h
a
si
ngl
e
turbine-ge
nerat
o
r connected to a singl
e radi
a
l
seri
es co
m
p
ensat
e
d t
r
a
n
sm
issi
on l
i
n
e. T
h
e
m
odel
has bee
n
use
d
ext
e
nsi
v
el
y
for
com
p
ari
ng st
udy
t
ech
ni
q
u
es
and i
n
vest
i
g
at
i
ng di
ffe
rent
t
y
pes of S
S
R
cou
n
t
e
rm
easure
s
. Th
e
si
m
p
le typ
e
of
syste
m
was emp
l
o
y
ed in th
e
First Ben
c
hm
ark M
odel
.
B
u
t
t
h
at
w
o
ul
d
be
r
a
rel
y
enc
o
u
n
t
e
red
i
n
actual operation
of a
power
s
y
ste
m
. Therefore
,
a m
o
re
commo
n
typ
e
of
syste
m
is p
r
esen
ted
i
n
th
is Seco
nd
B
e
nchm
ark M
odel
w
h
i
c
h
de
al
s wi
t
h
t
h
e s
o
-cal
l
e
d
"pa
r
al
lel resona
nce"
and i
n
teraction bet
w
ee
n turbi
n
e-
gene
rat
o
rs wi
t
h
a com
m
on m
ode [2]
.
S
o
as t
o
av
oi
d t
h
e
shaft
fai
l
u
re
vari
ous c
o
unt
e
r
m
easures ha
v
e
been
pr
o
pose
d
. P
h
a
s
e im
bal
a
nce schem
e
bei
ng o
n
e o
f
t
h
em
. Apart
f
r
om
im
plem
ent
a
t
i
on of
t
h
e pha
se im
bal
a
nce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
697
–
7
02
69
8
schem
e
, co
m
p
ari
s
o
n
o
f
t
h
e
schem
e
i
s
al
so d
o
n
e i
n
t
h
i
s
pape
r.
It
i
s
em
pl
oy
ed by
usi
n
g t
i
m
e
dom
ain
si
m
u
latio
n
s
.
The i
d
ea o
f
c
r
eat
i
ng
pha
se i
m
bal
a
nce sche
m
e
i
n
co
nj
u
n
c
t
i
on
wi
t
h
t
h
e
s
e
ri
es capaci
t
o
r
ba
nks
wa
s
prese
n
ted by
Edris
[10]. T
h
e basic idea
of phase im
ba
lance sc
hem
e
is to re
duce the energy exc
h
ange
of
tu
rb
in
e g
e
n
e
rato
r sets at sub
s
yn
chrono
u
s
o
s
cillatio
n
s
b
y
weak
en
i
n
g
t
h
e co
up
ling
b
e
t
w
een
th
e electrical sid
e
an
d th
e m
ech
an
ical sid
e
of t
h
e system
. Such
p
h
ase im
b
a
lan
ce
d
i
min
i
sh
es th
e cap
a
b
ility o
f
t
h
e t
h
ree ph
ase
cu
rren
ts,
wh
ich
d
e
v
e
l
o
p in
teractin
g
electromag
n
e
tic to
rques.
In t
h
is pa
per, the phase im
balance sc
hem
e
on
dam
p
ing
SS
R of the
IEEE
Second Be
nc
hm
ark Model
has bee
n
i
m
pl
em
ent
e
d an
d an
al
y
zed. Sect
i
o
n
II i
n
t
r
od
uces t
h
e st
u
d
i
e
d sy
st
em
and co
nfi
g
urat
i
o
ns
of t
h
e
pha
se
im
balance sc
he
m
e
. Section III c
o
m
p
ares t
h
e dam
p
ing
characteristics
c
ont
ributed by the phase
im
balance
schem
e
and
fi
n
a
l
l
y
sect
i
on I
V
dra
w
s c
o
ncl
u
si
ons
f
o
r
t
h
i
s
pa
per
.
2.
SYSTE
M
MO
DEL AND PH
AS
E IMBAL
A
NCE SCHE
ME
A.
The System
Description
The fi
rst
be
nc
hm
ark
m
odel
for com
put
er si
m
u
l
a
t
i
on of S
S
R
was p
ubl
i
s
hed i
n
19
7
7
. T
h
i
s
pr
o
v
i
d
e
d
th
e si
m
p
lest p
o
ssib
l
e m
o
d
e
l with
a sin
g
l
e tu
rb
in
e -g
en
er
at
or c
o
nnected t
o
a single ra
di
al series com
p
ensated
transm
ission line. T
h
e one line diagra
m
of the IEEE Sec
ond Benc
hm
ark Mode
l, system
-1 is shown in
Figure
1. T
h
e m
odel
c
o
m
p
ri
ses o
f
f
o
ur m
a
sses, i
.
e.
t
h
e hi
gh
p
r
ess
u
re turbi
n
e (HP), the l
o
w
p
r
ess
u
re t
u
r
b
ine
(L
P
)
, the
gene
rato
r (
G
E
N
), a
n
d the e
x
citer (EXC
),
w
h
ich a
r
e m
echan
ically co
up
led
on
th
e
sh
aft.
Fo
r t
h
is system th
ere
are t
h
ree t
o
rsi
onal
m
odes (
m
ode 1, 2 a
n
d
m
ode 3
)
an
d
one el
ect
r
o
m
e
chani
cal
m
ode (m
ode 0)
. Th
ese f
o
u
r
m
odes are cal
l
e
d SSR
m
odes
or t
o
rsi
o
nal
m
ode
s si
nce t
h
ei
r nat
u
ral
f
r
eq
u
e
nci
e
s are al
l
l
e
ss t
h
an sy
nch
r
o
n
ous
fre
que
ncy
or
p
o
we
r fre
q
u
enc
y
(6
0H
z).
Fi
gu
re
1.
O
n
e l
i
ne di
a
g
ram
of
t
h
e IE
EE Se
co
nd
B
e
nc
hm
ark
m
odel
The i
nhe
re
nt
n
a
t
u
ral
fre
que
nc
y
fo
r m
ode
0 i
s
1
.
3
5
Hz,
m
ode
1 i
s
2
4
.
7
2
Hz, m
ode
2
i
s
32
.3
9
Hz
an
d
m
ode 3 i
s
5
1
.
1
2 Hz
res
p
ect
i
v
el
y
.
The SSR
m
ode i
,
i
=
0, 1
,
2,
3 st
an
ds
f
o
r t
h
e
num
ber
o
f
t
w
i
s
t
s
o
n
t
h
e
shaft
.
All tu
rb
in
e torq
u
e
s are pro
portio
n
a
l, with each
co
n
t
ri
b
u
t
i
n
g
a f
r
act
i
o
n. T
h
e fract
i
ons
f
o
r
bot
h
HP a
n
d L
P
are
equal
t
o
5
0
%.
On t
h
e ot
her
h
a
nd
, t
h
e el
ect
ri
cal
m
odel
of t
h
e st
udi
e
d
sy
st
em
co
m
p
ri
ses of G
E
N co
n
n
e
c
t
e
d t
o
an i
n
fi
ni
t
e
bus
t
h
ro
u
gh a st
e
p
u
p
t
r
an
sf
or
m
e
r and t
w
o
p
a
rallel tran
sm
issio
n
lin
es,
on
e of wh
ich
is series-
capacitor com
p
ensated. T
h
e
values
of
X
c
/X
l
o
f
th
e co
m
p
ensated
lin
e
d
e
fin
e
the series co
m
p
en
satio
n ratio
[7
]-
[9]. The capac
itive reactance X
c
can be va
ried and X
c
/X
l
ran
g
es f
r
o
m
1
0
-
9
0%. T
h
e m
ode
fre
que
nci
e
s are
calcu
lated
with th
e
h
e
lp
of in
ertia con
s
tan
t
s an
d
sp
ri
n
g
c
o
nst
a
nt
s
whi
c
h are
sho
w
n i
n
Ta
bl
e 1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Imp
l
emen
ta
tion
o
f
Ph
a
s
e Imba
lan
ce
S
c
h
e
me fo
r
S
t
ab
ilizin
g To
rsion
a
l
Oscilla
tio
n
s
(Ra
c
ha
nan
ja
li K)
69
9
Tabl
e
1.
Ine
r
t
i
a
co
nst
a
nt
s a
n
d
spri
ng
co
nst
a
nt
s f
o
r
IEE
E
Sec
o
n
d
be
nchm
ark m
odel
,
sy
st
e
m
1
Mass In
ertia(lb
m
-f
t
2
)
Shaft
Spr
i
ng constant (
l
bf-
f
t/r
ad)
E
x
citer 0.
0068
9
E
X
C-
GE
N
3.
7403
Gener
a
tor 0.
8788
2
GE
N-L
P
83.
472
L
P
1.
5497
L
P
-
H
P
42.
702
HP 0.
2489
Usi
n
g t
h
e a
b
ov
e sy
st
em
param
e
t
e
rs t
h
e m
ode
fre
q
u
encies
are calculate
d
with t
h
e
help of MATLAB
pr
o
g
ram
and t
h
e m
ode
fre
qu
enci
es are
f
o
u
n
d
t
o
be M
o
de
0:
1.
35
Hz
, M
ode
1:
2
4
.
6
5
H
z
, M
o
de
2:
32
.
3
9
Hz
an
d
Mod
e
3
:
51
.1
0
H
z
The m
ode s
h
a
p
es co
rres
p
on
di
ng
t
o
t
h
e m
ode
fre
q
u
ency
i
s
s
h
o
w
n i
n
Fi
g
u
r
e
2:
Fi
gu
re
2.
M
o
d
e
sha
p
es
f
o
r
IE
EE Sec
o
n
d
B
e
nchm
ark m
ode
l
B.
Phase
Imb
a
lance Sche
me
The i
d
ea o
f
c
r
eat
i
ng
pha
se i
m
bal
a
nce sche
m
e
i
n
co
nj
u
n
c
t
i
on
wi
t
h
t
h
e
s
e
ri
es capaci
t
o
r
ba
nks
wa
s
prese
n
t
e
d
by
Edri
s
.
The
p
h
a
se im
bal
a
nce schem
e
i
s
cr
eat
ed by
i
n
t
r
o
duci
ng i
n
o
n
e
or m
o
re p
h
a
s
es LC
reso
na
nce ci
rc
ui
t
s
wi
t
h
a
res
o
nance
f
r
eq
ue
nc
y
equal
t
o
t
h
e
po
we
r f
r
eq
ue
n
c
y
(6
0 H
z
).
W
i
t
h
di
f
f
ere
n
t
val
u
es
of
L and C in eac
h
phase
, these
pha
se circ
uits will have
un
e
q
ual reacta
n
ce a
t
any freque
nc
y other tha
n
the powe
r
freq
u
e
n
c
y. Basically
th
ere are two
typ
e
s o
f
p
h
ase i
m
bal
a
nce schem
e
s:
seri
es reso
na
nce an
d pa
ral
l
e
l
reso
nanc
e
wh
ose c
o
nfi
g
u
r
at
i
ons
are s
h
o
w
n i
n
Fi
gu
re
3
(a) a
n
d (
b
) resp
ectiv
ely [1
]. Th
e
v
a
lu
es of L and
C in parallel
reso
na
nce
sche
m
e
are
deci
de
d
by
1
. Th
e d
e
gr
ee
of
asymme
tr
y,
w
h
ich u
s
es
p
a
r
a
llel
r
e
son
a
n
ce
bet
w
ee
n t
h
e t
h
ree
p
h
ases, c
a
n be
co
nt
r
o
l
l
e
d by
t
uni
ng
th
e two resonan
ce circu
its in
p
a
rallel with
th
ei
r
resp
ectiv
e part
s of th
e co
m
p
en
sating
cap
acito
rs.
Fig
u
re
3
.
Con
f
i
g
uration
s
o
f
phase im
b
a
lan
ce sch
e
m
e
(a) Series Co
m
p
en
satio
n (b
) Parallel co
m
p
en
satio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
697
–
7
02
70
0
C.
Sub Synchr
on
ous
r
e
sonance
Su
b sy
nch
r
on
ous
reso
na
nce
i
s
an el
ect
ri
cal
powe
r
sy
st
em
condi
t
i
on
whe
r
e, el
ect
ri
cal
net
w
o
r
k
excha
n
ges ene
r
gy
wi
t
h
t
u
r
b
i
n
e gene
rat
o
r at
one
or m
o
re
na
tural fre
quency
of the c
o
m
b
ined system
, below the
sy
nch
r
o
n
o
u
s
f
r
eq
ue
ncy
o
f
t
h
e sy
st
em
. Fo
r t
h
e
IEEE
fi
rst
be
nc
hm
ark m
odel
t
h
e m
ode
f
r
eq
ue
nci
e
s are
calcu
lated
with
th
e h
e
lp
o
f
a MATLAB
p
r
ogram
. At
these freque
n
cies all rotating m
achinery syste
m
ex
p
e
rien
ce to
rsio
n
a
l
o
s
cillatio
n
s
to so
m
e
d
e
gree during
co
n
t
in
uo
us
or
an
y d
i
stu
r
b
a
n
ce o
p
eratio
n
in
t
h
e po
wer
syste
m
. Wh
en
th
e stress ex
ceed
s th
e endu
ran
ce limit i.e. 4
5
*10
7
N/m
2
, th
e sh
aft will b
e
d
a
m
a
g
e
d
.
Th
e
stress
is calculated as
∗
∗
w
h
er
e
δ
= twist ang
l
e
G =m
odul
us
of
ri
gi
di
t
y
R= Rad
i
u
s
of sh
aft
L= Length of s
h
aft
For t
h
e m
ode fre
que
nci
e
s t
h
e st
ress excee
ds t
h
e en
d
u
ra
n
ce l
i
m
i
t
of 45
*1
0
7
N/m
2
.
W
i
th
t
h
e
h
e
lp
o
f
SSSC the stres
s
at these
fre
quencies ca
n
be
reduce
d
below t
h
e e
n
durance
lim
it.
3.
RESULTS
U
NDE
R
DIST
U
R
BA
NCE
C
O
NDITI
ON
The
IEEE
fi
rst
benc
hm
ark m
odel
,
sy
st
em
1 h
a
s bee
n
i
m
pl
em
ent
e
d wi
t
h
t
h
e p
h
ase i
m
bal
a
nce sc
hem
e
b
o
t
h
series an
d p
a
rallel an
d the resu
lts are co
m
p
ared
fo
r d
i
fferen
t
d
i
sturb
a
nce con
d
ition
s
Three
ph
ase t
o
gr
oun
d
f
a
ul
t
I
t
is assu
m
e
d
th
at a t
h
r
e
e ph
ase to
gr
oun
d f
a
u
lt, st
art
i
n
g at
t
=
0.
1 sec
a
n
d
l
a
st
i
ng
fo
r
17
m
s
, occurs
at
t
h
e hi
g
h
v
o
l
t
a
ge si
de o
f
t
h
e
st
ep u
p
t
r
ans
f
o
r
m
e
r. Fi
gure
4
sho
w
s t
h
e
dy
nam
i
c respons
e of t
o
rsi
o
nal
t
o
r
q
ue
GEN
-
LP
fo
r the sy
stem
with n
o
da
m
p
i
ng
schem
e
, seri
es reso
nance sc
h
e
m
e
and paral
l
el
resona
nce s
c
hem
e
.
Fi
gu
re
5 s
h
o
w
s t
h
e dy
nam
i
c
resp
o
n
se
of t
o
r
s
i
onal
st
re
ss G
E
N-
LP f
o
r t
h
e
sy
st
em
wi
t
h
n
o
d
a
m
p
i
ng sc
h
e
m
e
,
seri
es res
o
nan
ce schem
e
and
paral
l
e
l reson
a
n
c
e sch
e
m
e
. It is fo
und
that th
e system
is u
n
s
tab
l
e when
no
cont
rol
sc
hem
e
s are i
n
se
rvi
ce. The
res
u
l
t
fr
om
t
h
e paral
l
e
l
resona
nce
of
pha
se i
m
bal
a
nce schem
e
cl
earl
y
in
d
i
cates th
at GEN-LP t
o
rque co
m
e
s to
sta
b
le po
siti
on in a
m
u
ch short
e
r spa
n
of time whe
n
com
p
a
r
ed to
seri
es. So
par
a
l
l
e
l
resonan
c
e schem
e
has bet
t
e
r dam
p
ing
pr
op
ert
i
e
s whe
n
com
p
ar
ed t
o
t
h
at
of
seri
es
reso
na
nce.
Fi
gu
re
4.
Dy
na
m
i
c respo
n
se
o
f
G
E
N
-
LP
T
o
r
que
wi
t
h
n
o
da
m
p
i
ng schem
e
, seri
es
res
ona
n
ce schem
e
and
paral
l
e
l
res
o
na
nce sc
hem
e
Fi
gu
re
5.
Dy
na
m
i
c respo
n
se
o
f
G
E
N
-
LP
st
re
ss wi
t
h
n
o
dam
p
i
n
g sc
hem
e
, seri
es res
o
nance
schem
e
and
paral
l
e
l
res
o
na
nce sc
hem
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Imp
l
emen
ta
tion
o
f
Ph
a
s
e Imba
lan
ce
S
c
h
e
me fo
r
S
t
ab
ilizin
g To
rsion
a
l
Oscilla
tio
n
s
(Ra
c
ha
nan
ja
li K)
70
1
Insertio
n of
cap
a
c
itor
Th
e system
is
o
r
i
g
in
ally o
p
e
rated
with
on
e
seg
m
en
t of se
ries capacitor i
n
service
whil
e the ot
her
capaci
t
o
r i
s
i
n
s
e
rt
ed at
t
=
0.
1 s
ec. Fi
g
u
re
6 s
h
ows t
h
e dy
na
m
i
c respo
n
ses
of t
o
rsi
o
nal
t
o
r
que
GE
N-L
P
f
o
r t
h
e
sy
st
em
wi
t
h
no dam
p
i
ng sc
h
e
m
e
s, prefi
r
i
n
g
NG
H schem
e
, seri
es reso
na
n
ce of p
h
ase i
m
bal
a
nce an
d pa
ral
l
e
l
reso
na
nce
of
p
h
ase i
m
bal
a
nce schem
e
. Fi
gu
re 7
sh
o
w
s t
h
e
dy
nam
i
c respo
n
ses
of
t
o
r
s
i
o
n
a
l
st
ress G
E
N
-
LP f
o
r
t
h
e sy
st
em
wi
t
h
no
dam
p
i
n
g sc
hem
e
s, p
r
efi
r
i
n
g
N
G
H
s
c
hem
e
, seri
es
reso
na
nce
of
pha
se i
m
bal
a
nce an
d
p
a
rallel reson
a
n
ce
o
f
ph
ase i
m
b
a
lan
ce sch
e
me.
W
ith
th
e in
sertion
of capacito
r th
e system
b
eco
m
e
s u
n
stab
le
i
n
t
h
e abse
nce
of any
c
ont
r
o
l
schem
e
. The resul
t
fr
om
t
h
e paral
l
e
l
reso
nance
of
pha
s
e
im
bal
a
nce schem
e
clearly indicates that GE
N-L
P
torque
co
m
e
s to
stab
le po
si
tio
n
in
a m
u
ch
sh
orter s
p
a
n
of tim
e
when com
p
ared
t
o
seri
es
. S
o
paral
l
e
l
res
o
na
nce sc
hem
e
h
a
s bet
t
e
r
da
m
p
ing
propertie
s whe
n
c
o
m
p
ared to t
h
at
of se
ries
reso
na
nce.
Fi
gu
re
6.
Dy
na
m
i
c respo
n
se
o
f
G
E
N
-
LP
t
o
rq
ue
wi
t
h
no
da
m
p
i
ng schem
e
, seri
es
res
ona
n
ce schem
e
and
paral
l
e
l
res
o
na
nce sc
hem
e
Fi
gu
re
7.
Dy
na
m
i
c respo
n
se
o
f
G
E
N
-
LP
st
re
sses wi
t
h
no
da
m
p
i
ng schem
e
, seri
es
res
ona
n
ce schem
e
and
paral
l
e
l
res
o
na
nce sc
hem
e
4.
CO
NCL
USI
O
N
Th
is p
a
p
e
r presen
ted
t
h
e simu
latio
n
resu
lts
o
f
a st
a
nda
rd s
e
ries capacitor
com
p
ensated
powe
r syste
m
whic
h use
s
pha
s
e i
m
balance schem
e
for stabilizing tors
iona
l oscillations.
This pa
pe
r studied the
IEEE
Second
b
e
n
c
h
m
ar
k
m
o
d
e
l, syste
m
1
w
h
e
n
su
bj
ected
to
d
i
ff
er
en
t d
i
stu
r
b
a
n
ce con
d
i
t
i
o
n
s
su
ch
as thr
ee ph
ase to
gro
und
fau
lt and
in
sertio
n
of cap
acito
r. Fro
m
th
e resu
lts it is fo
un
d
t
h
at th
e p
a
rallel reson
a
n
c
e sch
e
m
e
h
a
s b
e
tter
dam
p
ing cha
r
a
c
teristics whe
n
com
p
ared to
series. T
h
e
stress is also obt
a
ined
be
low the endurance li
mit of
4
5*1
0
7
N/m
2
.
REFERE
NC
ES
[1]
Li Wang. “Comparative Studi
es of prefiring N
GH Scheme and phase
imbalan
ce scheme on
st
abili
zing to
rsiona
l
oscilla
tions”
.
I
E
EE Trans on Po
wer Systems
. 20
00; 15(1).
[2]
IEEE SSR working group.”Se
c
o
nd benchm
ark m
odel for
co
m
puter sim
u
lation of
subsy
n
chronous
resonance
”
.
IE
EE
Trans on Power
apparatus and systems
. 1985; 10
4: 1057-1066.
[3]
MC Hall and D
A
Hodges. “Experien
ce wi
th 500
kV subsy
n
ch
ron
ous resonance
and resulting
turb
ine gen
e
rator shaft
damage at Mohave gener
a
ting station
”
. in
Analys
is and control of subsynchr
onous resonance, 197
6, IEEE Publ 7
6
CH 1066-O-PWR. N
e
w
York: I
E
EE
Press
. 1976:
22-29.
[4]
CEG Bowler, DN Ewart, and C
Concordia
.
“
S
elf exci
ted to
rsio
nal frequ
enc
y
o
s
cilla
tions
with
series cap
aci
tors”
.
IEEE Trans. Po
wer App systems
. 1973; PAS-92:
1688-1695.
[5]
LA Kilgore
,
D
G
Ram
e
y, and
MC Hall. “
S
im
plified
tr
an
smission and g
e
ner
a
tion s
y
stem
an
alysis procedures f
o
r
subsy
n
chronous resonance
problems”.
IEEE Trans Power App
Sys
t
. 1977
; PAS-96: 1840-1846.
[6]
KR Padiy
a
r.
Ana
l
ysis of subs
ynch
ronous resonance in
power systems
. Boston, MA
: Kluwer. 1999
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
697
–
7
02
70
2
[7]
“A bibliography
for th
e stud
y
o
f
subsy
n
chronou
s re
sonance between rotating mach
in
es and power s
y
stems”.
IE
EE
Trans on Power
apparatus and systems, I
EEE
Co
mmittee Report
. 1976;
95.
[8]
“First Supplement to a bibliogr
aph
y
for th
e stu
d
y
of
subs
y
n
chr
onous resonance betw
een
rotatin
g machines and
power s
y
s
t
em
s
”
.
IEE
E
Trans on
Power apparatu
s
and
systems, I
EEE
Committee
Report
. 1979; 98
.
[9]
“Second Supplement to a bib
lio
graph
y
for the s
t
ud
y
of
subs
y
n
chronous resonance betw
een ro
tating machines an
d
power s
y
s
t
em
s
”
.
IEE
E
Trans on
Power apparatu
s
and
systems, I
EEE
Committee
Report
. 1985; 10
4.
[10]
AA Edris.
“Se
r
ie
s c
o
mpe
n
sa
tion sc
he
me
s re
ducing
the po
ten
tial of subs
y
n
ch
ron
ous resonance”.
IEEE Trans on
Powe
r Sy
ste
m
s
.
1990; 5: 210-21
6.
[11]
P Sunil Ku
mar. “Transient
s
t
abi
l
i
t
y
enhan
cem
ent
of pow
er sy
stem using TCSC”.
International Jo
urnal
of Electrical
and computer
en
gineering
. 2012; 2(3): 317-3
26.
[12]
S
M
M
a
haei
, M
Tarafdar Hag
h
, K Zare. “
M
odeling F
A
CTS
Devices
in P
o
wer S
y
s
t
em
Stat
e Es
tim
ation
”
.
International Jo
urnal of
Electr
ical
and computer engineering
. 201
2; 2(1): 55-67.
Evaluation Warning : The document was created with Spire.PDF for Python.