TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 65
5
1
~ 655
9
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.624
4
6551
Re
cei
v
ed Ma
y 11, 201
4; Revi
sed
Jul
y
1, 2014; Accept
ed Jul
y
18, 2
014
SSR Alleviation using BVLC Supplementary Controlled
SVS of
Series Compensated Power
System
Nare
ndra Ku
m
a
r
*
,
S
a
nj
iv
Kum
a
r
Dep
a
rtment of Electrical E
ngi
neer
ing, De
lh
i T
e
c
hnolog
ica
l
Univers
i
t
y
, Ba
w
a
n
a
Roa
d
, Delhi, Ind
i
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: dnk_1
96
3@
yaho
o.com
A
b
st
r
a
ct
The sub sy
nchronous reso
nance (SSR) is
a substantial pr
oblem
in
power system
having a stea
m
turbin
e g
ener
a
t
or conn
ected
to a seri
es co
mp
ens
ated tra
n
smissio
n
syst
em. Fl
exib
le A
C
trans
missi
o
n
system
s (FACTS) controllers
are wide
ly
applied to
mitigate SSR. In
this
paper, a
bus
voltage and
lin
e
current (BV
L
C
)
sup
p
le
menta
r
y subsy
n
chro
nous
d
a
mpi
n
g
contro
ller
(S
SDC) is
pr
op
osed
to
all
e
vi
at
e
subsync
h
ronous resonanc
e (
SSR) and dam
ping power
system
oscillat
ions in a
power
system
.
Both
eig
enva
l
u
e
inv
e
stigati
on a
nd
time-
d
o
m
ain si
mu
lati
on
resu
lts verify that th
e prop
osed
method ca
n da
mp
torsional oscillations of the
powe
r system
with SVS bus voltage and li
ne current (BVLC) supplem
e
nt
ary
control
l
er.T
he r
e
sults de
monst
r
ate t
hat the pr
opos
ed co
ntroll
er has a succ
e
ssful perfor
m
a
n
ce in
mi
ni
mi
z
i
ng
the SSR.It is s
hown that the controll
er is able to stabili
z
e
all unst
able modes. The study is performed
on
the system a
dapte
d
fro
m
the IEEE first bench
m
ark
mo
de
l. All the
simu
lati
ons
are carri
ed o
u
t in
MAT
L
AB/SIMULINK envir
on
ment.
Ke
y
w
ords
:
bu
s voltage a
n
d
line curr
ent (BVLC), series
comp
ens
atio
n
,
sub synchro
nous res
o
n
a
n
c
e
(SSR), suppl
e
m
e
n
tary contro
lle
r, ei
genv
al
ue
investig
atio
n
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
In elect
r
ic p
o
w
er
syst
em serie
s
comp
en
sation i
n
an
AC tran
smi
s
sion line i
s
a
n
effective
mean
s to e
n
han
ce p
o
wer
transfe
r
cap
a
c
ity and im
pr
ove tran
sient
stability. Ho
wever, on
e of the
importa
nt pro
b
lems in
po
wer
syst
em
s
e
m
ploying
se
ri
es
ca
pa
citors in AC tran
smissi
on li
ne
s is
the
intera
ctio
n
between mech
ani
cal system co
m
p
risi
ng va
rio
u
s
stage
s of
steam tu
rbi
nes,
gene
rato
r rot
o
r an
d the serie
s
compe
n
sate
d ele
c
trical net
work.
If any natural freque
ncy
of
oscillation
of the co
mbin
ed torsion
a
l
system m
a
tches
with the
com
p
leme
nt of the re
so
nant
freque
ncy o
f
the line inducta
nce
and se
rie
s
ca
pa
citan
c
e, growin
g
oscill
ation
s
o
f
sub
s
yn
chron
ous frequ
en
cie
s
re
sult i
n
the po
we
r syste
m
. This ph
eno
m
enon i
s
call
ed
sub
s
yn
chron
ous
re
son
a
n
c
e. Two in
cid
e
n
ts of shaft failure
occu
rre
d
in 197
0 an
d 197
1.The S
S
R
phen
omen
on
wa
s discove
r
ed duri
ng the
extensive an
alysis
work fo
llowing th
ese
events [1-2].
After these i
n
cidents,
great e
ffort was directed
f
r
om
the utilities t
o
avoi
d the
ri
sk of SSR
durin
g syste
m
operation.
Subsynchro
nou
s oscilla
t
i
ons d
ue to the interact
ions of seri
es
cap
a
cito
rs
with turbine
-
g
e
n
e
rato
r mecha
n
ical
shaft sy
stem lead to
the failure of the entire sh
aft
system,
cau
s
ing
ele
c
trical insta
b
ility in a
freq
uen
cy ra
nge lo
wer t
han th
e normal
syste
m
freque
ncy. Fl
exible AC Transmi
ssion S
y
stem (F
ACT
S
) is a techn
o
logy-b
ased
con
c
e
p
t that can
provide
a full
dynami
c
co
ntrol ove
r
a
c
tive
and
rea
c
tive powe
r
fl
ow
on tran
smissi
on
syst
ems
based o
n
th
e key
cont
rol
variable
s
su
ch a
s
tran
smissi
on lin
e
impeda
nce, pha
se a
ngle
and
voltage. It also p
r
ovide
s
the nee
ded
correctio
n
s of
transmissio
n function
ality in ord
e
r to ful
l
y
utilize existin
g
tran
smi
ssio
n
system
and
theref
o
r
e, mi
nimizin
g
the
gap bet
wee
n
the stability a
nd
thermal l
e
vel
s
. The
co
ncept of FACT
S and FA
CT
S controllers are
high
po
wer ele
c
tro
n
i
cs
device
s
u
s
ed
to control th
e power flo
w
and enh
an
ce stability, have beco
m
e, not only com
m
on
words i
n
the
power in
du
stry, but
they have starte
d repla
c
ing m
a
n
y
mecha
n
ical
control devi
c
es.
They
a
r
e ce
rtainly
playing
an
imp
o
rta
n
t and a
maj
o
r
role in
the o
p
e
r
ation
and
co
ntrol of
mod
e
r
n
pow
er sy
st
e
m
s [
3
-6]
.
Successful a
pplication of Flexible AC
Tr
an
smi
ssi
on
Systems (F
ACTS) Controllers ha
s
been
re
porte
d in p
a
st to
mitigate sub
synchrono
us
reso
nan
ce [3]
.
One of th
e
widely
refe
rred
example
s
of
su
ch
appli
c
at
ions is [7]
where
thyri
s
tor co
ntrolle
d V
A
R comp
en
sator i
s
u
s
e
d
for
damping subsynchronous oscillations.
They us
ed a thyristor
controlled V
A
R compensator
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
51 – 655
9
6552
connected i
n
shunt at the sy
nchronous generator
bus to da
mp subsyn
chronous oscillati
ons
besi
d
e
s
cont
rolling t
he
system voltag
e
.
A pra
c
tical
installatio
n
of
SVC for SS
R mitigatio
n
is
repo
rted in [8
-16].
The IEEE Firs
t Benc
hmark
(FBM) model is
c
o
ns
idered for the analys
i
s of SS
R [17] and
the complet
e
sim
u
lation
of the
po
wer sy
stem
is
perfo
rm
ed in
the
MATLAB/Simulink
environ
ment.
The study i
s
carried o
u
t b
a
se
d on
da
m
p
ing torque a
nalysi
s
, eige
nvalue an
alysis,
and tran
sie
n
t simulation.
The re
sult
s sho
w
that
the sug
g
e
s
ted
controll
er is satisfa
c
tory
for
dampin
g
SS
R. Thi
s
pap
e
r
i
s
stru
cture
d
a
s
fo
llo
ws.
Section
2
de
scribe
s the m
odelin
g of
po
wer
system. Section 3 introd
uce
s
the de
velopment
o
f
supplem
en
tary controll
ers. Se
ction
4
introdu
ce
s th
e eigenval
ue
s and time
d
o
main
simula
tions. The m
a
jor
con
c
lu
si
ons of the p
aper
are given in
section 5.
2.
Stud
y
S
y
stem Model
The study system, as shown in Fig
u
re
1, co
nsi
s
ts of a st
eam turbi
n
e
driven
synchro
nou
s
gene
rato
r su
pplying bul
k
power to an
infinite bus
o
v
er a long t
r
ansmi
ssion li
ne
(IEEE firs
t benc
hmark
model) [17]. An SVS of s
w
it
c
hed c
a
pac
itor and thyr
is
tor contro
lled reactor
type is
co
nsi
dere
d
lo
cate
d at the
ce
nt
ral of th
e tra
n
smi
ssi
on li
n
e
which
p
r
ovi
des continuo
usly
controllabl
e reactive p
o
we
r at its te
rmin
als in
re
sp
on
se to b
u
s vol
t
age an
d line
cu
rre
nt (BVL
C)
sup
p
leme
ntary controller. T
he serie
s
co
mpen
sati
on i
s
ap
plied
at the sendi
ng e
nd of the lin
e
[18-
20].
Figure 1. SMIB Study Power Sys
t
em wit
h
SVS [18]
2.1. Modeling of Gene
rator
In the detail
ed ma
chi
ne
model
used
in this
pap
er, the stato
r
i
s
rep
r
esente
d
by a
depe
ndent
current so
urce
parallel
with
the induct
a
n
c
e. The g
ene
rator m
odel i
n
clu
d
e
s
the field
windi
ng ‘f’ an
d a damp
e
r
windi
ng ‘h’ al
ong d
-
axis a
n
d
two dam
pe
r win
d
ing
s
‘g’
and ‘k’ al
ong
q
-
axis. The IEEE type-1 excitation system
i
s
used for the generator [21-23].
The roto
r flux linkag
e
s ‘
ψ
’
asso
ciated
wi
th different wi
nding
s are de
fined by:
q
h
g
k
q
k
g
g
d
h
f
h
d
f
h
f
f
I
b
a
a
I
b
a
a
I
b
a
a
I
b
V
b
a
a
6
8
7
.
5
6
5
.
3
4
3
.
2
1
2
1
.
(
1
)
Whe
r
e V
f
is th
e field
excitati
on voltag
e. Consta
nts
a
1
to a
8
an
d b
1
to b
6
are d
e
fine
d in [2
4]. i
d,
i
q
are
d, and q axis comp
onent
s of the machi
ne termin
al
current re
sp
ectively which a
r
e defin
ed wit
h
respe
c
t to m
a
chin
e referen
c
e f
r
ame.
To
have a
comm
on axi
s
of
rep
r
esentation
with the n
e
two
r
k
and SVS, these flux link
ages are transformed to
the synchr
onously rotating D-Q fram
e o
f
referen
c
e u
s
i
ng the followi
ng tran
sform
a
tion:
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TELKOM
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ISSN:
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046
SSR Alleviati
on usi
ng BVLC Supplem
entary
C
ontrolled SVS of Series…
(Narendra Kum
a
r)
6553
Q
D
q
d
l
l
l
l
cos
sin
sin
cos
(
2
)
Whe
r
e i
D,
i
Q
are the re
spe
c
tive machine
curre
n
t comp
onent
s along
D and Q axis.
δ
is the angle
by whi
c
h d
-
ax
is lea
d
s th
e D-axis.
Current
s I
d
and
I
q
, wh
ich a
r
e th
e co
mpone
nts of t
he de
pen
dent
curre
n
t sou
r
ce along d a
n
d
q axis re
spe
c
tively, are expre
s
sed a
s
:
I
d
= c
1
ψ
f
+ c
2
ψ
h
I
q
= c
3
ψ
g
+ c
4
ψ
k
(
3
)
Whe
r
e co
nst
ants c
1
- c
4
are defin
ed in
[20]. The
abo
ve nonlin
ea
r
differential
eq
uation
s
a
r
e
u
s
ed
in the power
system mo
de
ling.
2.2. Modeling of Mech
anical Sy
stem
In the m
e
cha
n
ical
mod
e
l d
e
tailed
sh
aft torqu
e
dyn
a
mi
cs [2] ha
s be
en
con
s
id
ere
d
for the
analysi
s
of to
rsio
nal
mod
e
s
d
u
e
to SSR. The
me
cha
n
ical
sy
stem i
s
d
e
scribe
d
b
y
the
six spri
ng-
mass model
as shown in
Figure 2. This sh
ows th
e electrome
c
hani
cal ma
ss-sp
r
in
g damp
e
r
system. It co
nsi
s
ts of Exci
ter (
EXC), G
enerator
(GE
N
), Lo
w Pres
sure of two
section
s
(LPA and
LPB), interm
e
d
iate pressu
re (IP) a
nd
Hi
gh Pre
s
su
re (HP) tu
rbine
section
s
. Every sectio
n ha
s its
own
ang
ular
momentum
(M) an
d da
m
p
ing
coeffici
e
n
t (D), an
d e
v
ery two
su
cce
ssive
ma
sses
have their o
w
n shaft stiffness con
s
tan
t
(K). A
ll masses a
r
e me
cha
n
ically co
nne
cted to e
a
ch
other by ela
s
tic shafts [2
5]. The data for elec
tri
c
al
and mecha
n
ical
system
are provid
e
d
in
appe
ndix.
HP
IP
LP
A
LP
B
G
EN
EX
C
Tm1
Tm
2
Tm
3
Tm4
Te
1
2
3
4
5
6
D
12
D
23
D
34
D
45
D
56
K
12
K
23
K
34
K
45
K
56
D
11
D
22
D
33
D
44
D
55
D
66
Figure 1. Six
Mass Sprin
g
Mech
ani
cal S
y
stem (Typi
c
al SSR Studies) [18]
The leadi
ng e
quation
s
an
d the state and
output equ
ations a
r
e given
as follows:
i
=
i
i
=
1, 2, 3, 4, 5,
6
1
)
(
)
(
1
2
1
12
2
12
1
12
11
1
1
M
T
K
D
D
D
M
dt
d
2
1
2
12
3
23
2
23
22
12
1
12
2
2
)
(
)
(
1
M
T
K
D
D
D
D
D
M
dt
d
3
)
(
)
(
)
(
1
4
3
34
2
3
23
4
34
3
34
33
23
2
23
3
3
M
T
K
K
D
D
D
D
D
M
dt
d
4
)
(
)
(
)
(
1
5
4
45
3
4
34
5
45
4
45
44
34
3
34
4
4
M
T
K
K
D
D
D
D
D
M
dt
d
e
T
K
K
D
D
D
D
D
M
dt
d
)
(
)
(
)
(
1
6
5
56
4
5
45
6
56
5
56
55
45
4
45
5
5
)
(
)
(
1
5
6
56
6
66
56
5
56
6
6
K
D
D
D
M
dt
d
)
(
"
D
Q
Q
D
d
e
I
i
I
i
X
T
(
4
)
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
51 – 655
9
6554
Whe
r
e
1,
2,
3,
4,
5,
6,
are the angula
r
displa
ce
men
t
s and
ɷ
1
,
ɷ
2
,
ɷ
3
,
ɷ
4
,
ɷ
5
,
ɷ
6
are the a
ngu
lar
velocitie
s
of different shaft
segm
ents a
s
sho
w
n in Fig
u
re 2.
2.3. Modeling of Excita
tion Sy
stem
The IEEE typ
e
-1 excitation system [26]
is described by t
he following equations:
r
E
f
E
E
E
f
V
T
V
T
S
K
V
dt
d
1
)
(
r
F
E
F
S
E
f
F
E
E
E
F
S
V
T
T
K
V
T
V
T
T
S
K
K
V
dt
d
1
)
(
(
5
)
REF
A
A
A
A
r
A
S
A
A
r
V
T
K
Vg
T
K
V
T
V
T
K
V
dt
d
1
2.4. Modeling of T Ne
t
w
o
r
k
The ac transmissi
on line
in this study
sy
stem is adapted from the IEEE first SSR
ben
chma
rk
system [17]. T
he tran
smissi
on lin
e i
s
rep
r
ese
n
ted
by st
anda
rd l
u
mp
ed p
a
ra
meter T-
circuit. The n
e
twork h
a
s
b
een represen
ted by its
–a
xis equivale
nt circuit, whi
c
h
is identi
c
al with
the po
sitive seque
nce net
work. Th
e g
o
v
erning
equ
ations
of the
-a
xis
,
T
-
ne
tw
or
k
r
e
pr
es
en
tatio
n
is derived as
follows:
1
2
2
2
1
2
1
1
1
V
L
V
L
i
L
R
dt
di
4
1
"
1
1
1
1
4
1
1
V
dt
di
L
L
i
L
R
V
L
dt
di
d
(6)
1
2
2
1
1
1
i
C
i
c
i
C
dt
dV
n
n
n
i
C
dt
dV
se
1
4
Whe
r
e C
n
=
C
T
+
C
FC
,L
1
= L +
L
A,
L
2
= L + L
T2
,L
A
= L
T1
+ L”
n
an
d R
1
= R +
R
a
Similarly, the
equatio
ns ca
n be
de
rived
for the
- net
work. T
he
-
n
e
two
r
k e
quation
s
are then tran
sform
ed to D-Q frame of re
feren
c
e.
2.5. Modeling of Static V
a
r Sy
stem
The te
rminal
voltage pe
rtu
r
bation
∆
V and the SVS inc
r
emental
c
u
rrent
weighted by the
fac
t
or K
D
re
pre
s
entin
g
current d
r
oo
p
are
f
ed t
o
the refe
re
nce jun
c
tion. T
M
repre
s
ent
s the
measurement
time
con
s
ta
nt, whi
c
h
for
simpli
city is a
s
sumed
to
b
e
eq
ual fo
r
b
o
th voltage
a
n
d
curre
n
t mea
s
urem
ents. Th
e voltage re
gulator i
s
a
s
sume
d to be
a pro
portio
n
a
l- integ
r
al (PI)
controlle
r. Th
yristor
co
ntrol
action
is
rep
r
ese
n
ted by
a
n
average
de
ad time T
D
a
nd a firi
ng d
e
l
a
y
time T
s
.
∆
B is
the variation in TCR
su
sce
p
tance.
∆
V
F
repre
s
e
n
ts the
incre
m
ental
sup
p
leme
ntary
control co
ntro
ller [27].
The
α
-
β
axes current
s ente
r
ing T
CR fro
m
the netwo
rk are exp
r
e
ssed as:
2
2
2
V
i
R
dt
di
L
s
s
2
2
2
V
i
R
dt
di
L
s
s
(
7
)
Whe
r
e R
S
, L
S
represent
TCR
re
si
stan
ce a
nd ind
u
ctanc
e
s
respe
c
tively. The other e
quatio
ns
descri
b
ing the SVS model are:
Z
1
=
V
ref
– Z
2
+
V
F
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
SSR Alleviati
on usi
ng BVLC Supplem
entary
C
ontrolled SVS of Series…
(Narendra Kum
a
r)
6555
2
)
2
2
2
.
1
(
1
Z
T
i
K
V
T
Z
M
D
M
(
8
)
F
p
ref
S
P
s
S
P
I
V
Ts
K
V
T
K
Z
T
Z
T
K
Z
T
K
Z
3
2
1
3
3
.
1
∆
B =
(Z
3
-
∆
B)/ T
D
W
h
er
e
∆
V2,
∆
i
2
are increm
ental m
agnitudes of SVS v
o
lt
age
and current, respectively, obtained
by lineari
z
ing.
2
2
2
2
2
2
Q
D
V
V
V
,
2
2
2
2
2
2
Q
D
i
i
i
3.
Design o
f
Subs
y
n
chronous Damping
Con
t
roller
The su
pplem
entary cont
ro
ller U
C
is im
p
l
emented
through
a fi
rst
orde
r
su
pple
m
entary
controlle
r tran
sfer fun
c
tion
G(s), whi
c
h i
s
assumed to
be:
C
C
C
C
C
U
B
X
A
X
.
C
C
C
C
C
U
D
X
C
Y
3.1. Bus Voltage (BV) Su
pplementar
y
Contr
o
ller
The SVS bus voltage can
be expressed as:
2
Q
2
2
D
2
2
2
V
V
V
(
9
)
Linearizi
ng (9)
give
s the
deviation in the SVS bus voltage
∆
V
2
,
whic
h is taken as
the
Supplem
enta
r
y control Co
ntrolle
r:
Q
Q
D
D
V
V
V
V
V
V
V
2
20
0
2
2
20
0
2
2
)
/
(
)
/
(
(
1
0
)
Whe
r
e ‘o’ rep
r
esents o
p
e
r
a
t
ing point or steady state value
s
.
3.2. Line Cur
r
ent (LC) Supplementar
y
Contr
o
ller
The line current entering to
SVS Bus from generator
end bus is giv
en by:
2
Q
2
2
D
2
2
2
i
i
i
+
=
(
1
1
)
Linea
rizi
ng (1
1) gives the d
e
viation in line curre
n
t:
Q
o
Qo
D
o
Do
i
i
i
i
i
i
i
(
1
2
)
Whe
r
e ‘o’ rep
r
esents o
p
e
r
a
t
ing point or steady state value
s
.
4. Resul
t
s
and
Analy
s
is
The stu
d
y po
wer
syste
m
consi
s
ts
of 11
10MVA syn
c
hron
ou
s ge
n
e
rato
r supplyi
ng po
we
r
to an infinite
bus
over a
40
0kV, 600
km. l
ong
seri
es co
mpen
sated si
ngle circuit
transmi
ssion
li
ne.
The
study
system i
s
as per the IEEE first benc
h m
a
rk model. T
he
system
data and torsi
onal
spri
ng mass
system data
are gi
ven in appendix. The SVS rating for the line has
been
chosen
to
be 10
0MVAR ind
u
ctive t
o
300
MVAR capa
citive. 40% serie
s
com
pen
sati
on is
used a
t
the
sen
d
ing e
nd
of the transmi
ssi
on line [28
-
29].
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
51 – 655
9
6556
4.1 Eigenv
alue
Inv
estigation
The eige
nval
ue investigati
on has b
een
carrie
d usin
g the lineari
z
e
d
system mod
e
ling of
power sy
ste
m
. The
natu
r
al sy
stem
da
mping
ha
s
be
en
c
o
ns
ide
r
ed
to
be
z
e
r
o
in
or
d
e
r
to s
i
mu
la
te
the wea
k
e
s
t system
con
d
i
t
ions. Tabl
e 1 sh
o
w
s the
eigenvalu
e
s without any
suppl
ement
ary
c
ontroller incorporated in t
he SVS. Mode 0 is
uns
t
able at 800MW.
Table
2 shows
the
s
y
s
t
em
eigenvalu
e
s
at P = 20
0,
500
and
80
0
M
W
with BV
LC su
pplem
e
n
tary controll
era
r
e stabl
e. Th
e
sup
p
leme
ntary controll
er
para
m
eters a
r
e sele
cted based
on an
extensiv
e ro
ot locu
s.All the
electri
c
al a
n
d
electrome
c
ha
nical mo
des a
r
e fo
und to be
stable wh
en the pro
posed
sup
p
leme
ntary controlle
ri
s applie
d.
Table 1.Syste
m
Eigenvalue
s witho
u
t BVLC Supple
m
en
tary Controlle
r
Torsional ModeP
=200 MWP =500 MWP =800 MW
Mode # 5
Mode # 4
Mode # 3
Mode # 2
Mode # 1
Mode # 0
-0.0000±
298.1i
-0.22236
±202.88
i
-.010518
±160.52
i
-.005104
±126.97
i
-.026618
±98.757
i
-0.33922
±4.0339
i
-13.132±
833.01i
-532.8±3.
3619i
-12.767± 442.17i
-5.4252±
311.97i
-34.282±
189.06i
-3.2239±
187.16i
-57.127±
86.317i
-25.634±
24.258i
-39.674
-27.443
-2.5406
-0.5906±
0.74682
i
-0.0000±
298.1i
-0.27157
±202.84
i
-.047052
±160.53
i
-.010512
±126.96
i
-.030093
±98.665
i
-.098976
±4.2864
i
-13.133±
833i
-532.82±
4.4606i
-12.769±
442.15i
-5.4245±
311.97i
-35.515±
187.54i
-3.2602±
188.75i
-53.469±
85.459i
-25.689±
24.357i
-40.643
-31.073
-2.8919
-0.5662±
0.79191
i
-0.0000±
298.1i
-0.33712
±202.78
i
-.096185
±160.52
i
-.017161
±126.95
i
-.024943
±98.517
i
.078793±4.1
284i
-13.133±
833i
-532.83±
4.7221i
-12.769±
442.16i
-5.4245±
311.97i
-35.498±
187.12i
-3.4007±
189.12i
-52.804±
85.669i
-25.744±
24.309i
-40.979
-31.573
-2.9457
-.66527±
0.84667
i
Note: Bold values rep
r
e
s
en
t unstable mo
de.
Table 2. System Eigenvalu
e
s with BVL
C Suppleme
n
tary Cont
rolle
r
Torsional ModeP
=200 MWP =500 MWP =800 MW
Mode # 5
Mode # 4
Mode # 3
Mode # 2
Mode # 1
Mode # 0
-0.0000±
298.1i
-0.27644
±202.8i
-0.00078
±160.49
i
-0.00107
±126.97
i
-0.01376
±98.788
i
-0.32208
±4.0334
i
-13.631±
832.76i
-532.74±
22.156i
-11.957±
444.13i
-5.4375±
311.87i
-30.693±
201.3i
-7.0629±
196.4i
-123.69
-10.015±
32.411i
-27.866±
24.192i
-28.713
-8.6611
-3.2366
-2.5602
-0.46533
±0.7010
3i
-0.0000±
298.1i
-0.27889
±202.82
i
-0.01263
±160.48
i
-0.00318
±126.97
i
-0.02451
±98.724
i
-0.7±4.56
33i
-13.678±
833.14i
-532.4±2
7
.532i
-10.874±
443.12i
-5.4377±
311.84i
-33.749± 206.43i
-3.4775±
193.81i
-135.66
-5.7679±
35.243i
-26.712±
24.246i
-31.529
-7.3559
-3.0933±
0.03538
9i
-0.42708
±0.7345
1i
-0.0000±
298.1i
-0.32836
±202.78
i
-0.03685
±160.47
i
-0.00752
±126.96
i
-0.05356
±98.607
i
-1.2374±
5.1934i
-13.624±
833.27i
-532.33±
27.507i
-10.71±4
42.6i
-5.4344±
311.85i
-35.228±
206.2i
-1.9517±
192.73i
-130.69
-8.7622±
37.527i
-26.528±
24.247i
-31.749
-5.3472
-3.4477
-3.0834
-0.5233±
0.79835
i
4.2 Time Domain Simula
tions of SSR Stud
y
A digital com
puter
simulati
on stu
d
y, usi
ng a no
nline
a
r sy
stem m
odel, ha
s be
en carried
out to demonstrate the
effectiv
ene
ss of the BVL
C sup
p
lem
e
ntary cont
roll
er und
er large
disturban
ce
condition
s. Ap
plying a p
u
lsed torq
ue
of
30% for 0.1
se
c si
mulate
s a di
stu
r
ban
ce.
The
simul
a
tio
n
stu
d
y ha
s
b
een
ca
rri
ed
o
u
t at P=800M
W. Th
e n
a
tural dam
ping
of
the me
ch
ani
cal
sub
s
ystem
is assum
ed to
be
ze
ro in
orde
r to
sim
u
late
the wo
rst system condition
s
a
n
d
to
demonstrate the dampi
ng effe
ctiveness
of the proposed
SVS
controll
er al
one wit
hout
con
s
id
erin
g the alre
ady existing
natu
r
al
system da
mp
ing [30-3
1
]. Figure 3 to Fig
u
re 7 sho
w
s t
he
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
SSR Alleviati
on usi
ng BVLC Supplem
entary
C
ontrolled SVS of Series…
(Narendra Kum
a
r)
6557
response curves of
the term
inal voltage, SVS bus voltage,
SVS susceptance,
power angl
e
and
angul
ar vel
o
city with BVLC su
pplem
enta
r
y controll
er
after the
di
sturba
nce. It
can b
e
see
n
t
hat
there is tendency toward
s stability
when BVLC supplementary
controller i
s
used in the S
V
S
control system. The torsi
onal oscillati
ons
are stabilized and the
BVLC SVS supplem
entary
controlle
r attains
a
signi
ficant imp
r
ov
ement in th
e tran
sie
n
t perfo
rman
ce
of the seri
e
s
comp
en
sat
e
d
powe
r
sy
st
e
m
.
The co
nt
r
o
l st
rat
e
gy
is
easily imple
m
ental as it util
ize
s
the local
l
y
derived
c
ont
rollers
from the SVS bus
.
Figure 3. Power An
gle Re
spo
n
se with
BVLC
Supplem
enta
r
y Controller
Figure 4. SVS Sus
c
e
ptanc
e
Respons
e
with
BVLC Supple
mentary Cont
rolle
r
Figure 5. Terminal Voltage
Respon
se
wi
th
BVLC Supple
m
entary Cont
rolle
r
Figure 6. SVS Bus Voltage Response with
BVLC Supple
mentary Cont
rolle
r
Figure 7. Angular Velo
city Re
spo
n
se wit
h
BVLC Supp
lementa
r
y Co
ntrolle
r
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
51 – 655
9
6558
5. Conclu
sion
A combine
d
bus voltage a
nd line cu
rre
n
t (BVLC) S
VS supplem
e
n
tary sub
s
yn
chrono
us
dampin
g
con
t
roller
(SSDC) h
a
s
bee
n
prop
osed
a
nd de
sign
ed
for improving the tra
n
sient
perfo
rman
ce
of
se
rie
s
com
pen
sated po
wer
sy
st
em.
The u
s
e
of supplem
enta
r
y su
bsyn
ch
ron
ous
dampin
g
co
ntrolle
r (SSDC) is to improve torsio
nal
c
h
ara
c
t
e
ri
st
ic
s.
This
lo
cation
of SSDC is a
n
electri
c
al
mid
d
le p
o
int of th
e tra
n
smi
s
sio
n
line.
Dam
p
i
ng of to
rsion
a
l mod
e
s is f
ound
sta
b
le
with
SSDC fo
r
40
% com
pen
sat
i
on level
is p
r
ese
n
ted i
n
T
able
1
and
T
able
2. It can
be
seen
that
the
pre
s
en
ce of t
he su
pplem
e
n
tary cont
roll
er line in
the
netwo
rk im
proves t
he da
m
p
ing of the lo
wer
freque
ncy torsion
a
l mode
s. Eigen value studie
s
and time domain
simulation
s de
monst
r
ate
s
that
the BVLC su
ppleme
n
tary
controlle
r im
prove
s
the
d
a
mping
of the torsi
onal
el
ectro
m
e
c
ha
ni
cal
oscillation
s d
ue to
sub
syn
c
hrono
us re
sonan
ce
(
SSR) in the
se
rie
s
com
pen
sate
d po
wer sy
stem.
The power angle ,terminal
voltage, SVS
bus
voltage,
SVS suscept
ance and dev
iation in angular
speed response
curves
s
hows poorly
damped
oscil
l
ations or
growing os
cillati
ons dies
out with
BVLC s
u
pplementary damping controller. It is
s
h
own
that the us
e
of SVS SSDC in the
s
e
lec
t
ed
locatio
n
effectively damps SSR succe
s
sfully in
addi
tion to control the line active powe
r
and
dampin
g
to
rsional
oscillati
ons. Ei
genva
l
ues inve
stig
ation a
s
well
as no
nline
a
r
time
dom
ai
n
simulatio
n
s in
a MATLAB/Simulink e
n
viro
nment are ca
rrie
d
out.
Ackn
o
w
l
e
dg
ements
The
wo
rk p
r
ese
n
ted i
n
t
h
is
re
se
arch
paper ha
s
been pe
rformed und
er the proj
ect
AICTE R&
D,
“Enha
nci
ng t
he po
we
r
system pe
rfor
m
a
nce
u
s
ing
FACTS d
e
vice
s” in the
Flexibl
e
AC Tra
n
smi
s
sion
Re
sea
r
ch Labo
rato
ry at Delhi Te
ch
nologi
cal Uni
v
ersity, Delhi
(India
)
.
Referen
ces
[1]
NG Hin
gor
ani
, L G
y
ug
yi.
Und
e
rstand
in
g
F
A
CT
S: Co
ncepts
and
T
e
chn
o
lo
gy
of F
l
exib
le A
C
Transmission System
s
. IEEE Press, Ne
w
Y
o
rk. 2000.
[2]
YH Song, AT
Johns, eds.
F
l
ex
ible A
C
T
r
ans
miss
ion Syste
m
s (F
ACT
S
)
. IEE Press, U.K., 1999.
[3]
IEEE SSR Workin
g Group.
Cou
n
ter
m
eas
ures to Su
bs
ynchro
nous
R
e
son
anc
e Pro
b
le
ms.
IEEE
T
r
ansactions o
n
Po
w
e
r Ap
par
atus and
S
y
ste
m
s. 1980; PAS-99(5): 18
10-1
816.
[4]
KR Padiy
a
r, RK Varma.
Static Var System Auxili
ary Contr
o
lle
r for Da
mp
ing Torsio
na
l Oscillatio
n
s.
Internatio
na
l Journ
a
l of Po
w
e
r and Ener
g
y
S
y
stems. 19
90; 12(4): 27
1-2
8
6
.
[5]
KR Padiy
a
r,
RK Varm
a.
Da
mpi
n
g
T
o
rq
ue A
nalys
is
of Static Var
System C
o
n
t
rollers
. IEEE
T
r
ansactions o
n
Po
w
e
r S
y
ste
m
s. 1991; 6(2):
458-4
65.
[6] KR
Padiy
a
r.
F
a
cts Controll
ers in Pow
e
r
T
r
ansmissio
n
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ron
ous
reso
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nce
.
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Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
SSR Alleviati
on usi
ng BVLC Supplem
entary
C
ontrolled SVS of Series…
(Narendra Kum
a
r)
6559
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e
lo
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m
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r S
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a
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h
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r Syste
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r
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w
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r A
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r
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r
S
y
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RS-1(4): 222–
22
7.
Appe
ndix
Table 3. Sup
p
lementa
r
y Controlle
r Para
meters
SVS Supplementary
K
B1
T
1
T
2
Controller
Bus Voltage (BV)
-0.845
0.008
0.5
K
B2
T
3
T
4
Line Curr
ent (L
C
)-0.039
0.390.2
The
data
for electrome
c
h
a
n
ical system con
c
e
r
nin
g
to IEEE FBM is given below.
All th
e
data are in p
e
r
unit (p.u.) o
n
1110 MVA base.
Generator data:
Powe
r rating
=11
10 MVA,V
LL
=22 kV,R
a
= 0.003
6, X
l
= 0.21 pu
Stability data:T
uo
’
=6.66 sec,
T
vo
’=0.44 se
c, T
uo
”
=
0.032 se
c, T
vo
”
=0.057 se
c
X
u
= 1.933
p
u
, X
v
= 1.743
pu, X
u
’
=
0
.467
p
u
,
X
v
’
= 1.
144 p
u
, X
u
”
= 0.31
2, X
v
”
= 0.312
pu
ɷ
0 =
314 rad/sec.
IEEE Type 1
Exc
i
tation s
ystem
:
T
R
=
0
, T
A
=0.02, T
E
=
1
.0, T
F
=1.
0
se
c,
K
A
=
4
00, K
E
=
1
.0; K
F
=0.06 pu
V
Fma
x
=
3
.9, V
Fm
i
n
=
0
, V
Rma
x
=
7
.3, V
R min
= -7.
3
Tran
sfo
r
mer data:
R
T
= 0,
X
T
=0.15 pu (Gene
rato
r ba
se)
Tran
smi
ssi
on
line data
:
Voltage=400
kV, Length
= 600
km, Resi
stan
ce R=0.034
Ω
/k
m, R
e
ac
ta
nc
e
X=
0
.
3
25
Ω
/km, Susce
p
tance, B
c
=3.
7
μ
mho/km
SVS Data (Six-Puls
e
Operation)
SVC rating:
Q
L
= 100 MV
Ar and Q
C
=
350 MVAr.
T
M
=
2
.4, T
S
=
5
, T
D
= 1.667
ms, K
I
= 950,
K
P
= 0.5, K
D
= 0.01.
Evaluation Warning : The document was created with Spire.PDF for Python.