TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3649 ~ 36
6
1
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.4423
3649
Re
cei
v
ed Se
ptem
ber 19, 2013; Revi
se
d De
ce
m
ber
15, 2013; Accepted Janu
ary 4, 2014
Optimal Location of Thyristor-controlled-series-
capacitor using Min Cut Algorithm
ThanhLo
ng Duong
*
1,2
, Yao JianGa
ng
1
, Tong Kang
1
1
Departme
n
t of Electrical En
gi
neer
ing, Hu
na
n Univ
ersit
y
, C
han
gsh
a
, Huna
n, Chin
a
2
Departme
n
t of Electrical En
gi
neer
ing, Ind
u
stri
al Un
iversit
y
of Hochim
inh
Cit
y
,
Viet
nam
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: thanhl
on
g80
200
3@
ya
ho
o.com, y
a
oji
ang
an
g@1
26.com,
kangto
n
g
126
@
126.com
A
b
st
r
a
ct
Existence
of many differ
ent Oper
ators i
n
the
new
electricity
has bro
u
g
h
t ma
ny cha
l
l
eng
es in t
h
e
system op
erati
on an
d control
to obtai
n
mi
ni
mum g
e
n
e
ratio
n
cost and secur
i
ty. With
the grow
ing de
ma
nd o
f
electricity
in t
he co
mpetitiv
e
elec
tric
ity ma
rket envir
on
ment, on
e or
more trans
missi
on l
i
n
e
s co
uld
b
e
overl
oad
ed, th
erefore c
aus
in
g con
gesti
on.
T
he con
ges
ti
o
n
can
be
el
i
m
i
nate
d
/all
evi
a
ted by
i
m
prov
i
ng
transfer ca
pa
b
ility of th
e
net
w
o
rk. Thyristor contro
lle
d
ser
i
es co
mpe
n
sat
o
rs (TCSC), w
i
th its a
b
i
lity t
o
directly c
ontrol
the pow
er fl
ow
can b
e
very
effective
to i
m
pro
v
e the o
per
atio
n of trans
miss
i
on n
e
tw
ork. T
h
is
pap
er descr
ibe
s
an ap
proac
h
for determin
i
n
g
the most
sui
t
able l
o
cati
ons
for installi
ng
T
C
SC devic
es
in
order
to eli
m
in
ate
l
i
ne
ov
erlo
ads an
d mi
ni
mi
z
e
gen
er
ati
o
n
costs. T
he
pro
pose
d
appr
oac
h is
bas
ed
o
n
t
h
e
mi
ni
mu
m cut
meth
od
olo
g
y that reduc
es the search sp
ac
e and us
ing b
enefit in
dex to
decid
e on the
best
locations for t
h
e TCSC. The
5-bus, IEEE
14-bus
and
30-
bus test system
s
are
used to demonstrate the
prop
osed
a
ppr
oach. R
e
su
lts
show
t
hat the
prop
osed
met
hod
is ca
pa
ble
of find
in
g the
best l
o
cati
on
for
TCSC installation to mi
nimi
z
e
total
costs.
Ke
y
w
ords
: co
ngesti
on, F
A
CT
S, T
C
SC, min cut, benefit ind
e
x
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
The re
structu
r
ing of the el
ectri
c
ity indu
stry
ha
s brou
ght many so
cial welfare benefits.
Ho
wever, it is also faci
ng
many chall
e
nge
s re
l
a
ted
to powe
r
sy
stem se
curity.
Variou
s fact
ors
su
ch a
s
environmental
and
econ
omi
c
co
nstrai
nts
h
a
ve limited the
expan
sion of
the tran
smission
netwo
rks. M
ean
while, the
creatio
n of electri
c
ity
ma
rket
s ha
s led
to the trading of significant
amount
s of
electri
c
al
en
ergy over l
o
ng di
sta
n
ces, and the n
u
mbe
r
of un
plann
ed po
wer
excha
nge
s i
n
cre
a
ses du
e
to the
com
p
e
t
ition am
o
ng
utilities a
nd
contra
cts con
c
luded
directly
betwe
en prod
uce
r
s a
nd co
nsum
ers ha
s made the leve
l of secu
rity of powe
r
syst
ems wea
k
en
ed.
In these m
a
rkets,
se
curity
is mea
s
u
r
e
d
thro
u
gh “system co
nge
stion” l
e
vels
[1]. Conge
sti
on
occurs wh
en
the tra
n
smitte
d po
we
r ex
ce
eds the
ca
pa
ci
ty or tran
sfe
r
limit of th
e transmi
ssion
li
ne
[2, 3]. Cong
e
s
tion le
ad
s to
inefficient
use of the
syst
em, incre
a
sin
g
total ge
ne
ration
co
sts a
n
d
effecting di
re
ct on m
a
rket
transactio
n
s
and el
ectri
c
it
y prices
(p
rices in
so
me a
r
ea
s
will increase
and in
others de
crea
se
). Con
g
e
s
ti
on
therefo
r
e di
stort
s
the m
a
rket [4]. He
nce,
con
g
e
s
tion
manag
eme
n
t is a
challe
n
g
ing ta
sk for Indep
ende
nt System O
p
erato
r
(ISO
)
for mai
n
taini
ng
stability, secu
rity and relia
b
ility [5].
In order to eli
m
inate/allevia
t
e conge
stion
,
managing di
spat
ch (g
ene
ration re-dispa
tching
[6] and load
shed
ding [7
]) are ea
sy to implement
and maybe
still nece
s
sary in the worst
situation
but
may not be
accepta
b
le
by bot
h po
wer p
r
ovide
r
s
and
cu
stome
r
s
due to th
eir
signifi
cant eff
e
ct on th
e e
x
isting po
we
r transacti
o
n
contract
s. He
nce, the
use
of controllab
l
e
flexible AC transmi
ssio
n system (FA
C
T
S
) [8] to improve tr
ansfer capability of
existing
power
system
s and
eliminate/alle
viate c
onge
st
ion, while still
be able to obtain minimal
cost, is one
of
main intere
st
s in cu
rre
nt issue
s
. TCS
C
can p
r
ovi
de benefits i
n
increa
si
ng
system tran
sfer
cap
ability and
power flo
w
control flexibilit
y and r
apidity
, howeve
r
, th
e cu
rrent chal
lenge i
s
n
o
w
to
obtain the opt
imal installati
on of (FACTS
) device
s
.
It is indi
cate
d that the e
ffectiveness
of
the controls fo
r different pu
rpo
s
e
s
mainly
depe
nd
s on t
he lo
cation of
control devi
c
e [9]. The pro
per lo
catio
n
o
f
FACTS devi
c
e
s
is a
key t
o
obtain minim
u
m gen
eratio
n co
st. There
f
ore, Ope
r
ato
r
s a
r
e fa
cing
the pro
b
lem
of whe
r
e T
C
SC
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3649 – 36
61
3650
sho
u
ld be in
stalled in ord
e
r
to achieve require goal
? This is o
ne o
f
difficult problems d
ue to
a
large
si
ze of
sea
r
ch spa
c
e
for a p
r
acti
cal sy
stem.
Howeve
r, it ca
n be
solved i
f
bottleneck
of
power
syste
m
is d
e
termi
ned. Determi
n
ing the
sy
st
em bottlene
ck play
s key role in
re
du
cing
sea
r
ch sp
ace
and numb
e
r of FACTS device
s
need
to be installe
d. The bottleneck is lo
cati
on
that demon
strates m
a
ximu
m possible p
o
we
r flow
f
r
o
m
sou
r
c
e
(
s
) t
o
sin
k
(
s
).
W
h
en t
he sy
st
e
m
load i
s
in
crea
sed, the
bottl
ene
ck i
s
the
first lo
ca
tio
n
where
conge
sti
on o
c
curs [10
]. Furthermore,
the existen
c
e
of bottlenecks i
n
the tra
n
smi
ssi
on lin
e
affects th
e
total supply
co
st, limiting the
che
ape
st pla
n
ts an
d forci
ng the
dispat
chin
g of
mo
re expen
sive
gene
rato
rs [1
1]. Therefore
,
it
need
s to b
e
e
liminated by
placi
ng T
C
S
C
devi
c
e
s
on
suitabl
e lo
cati
on in the
tran
smissio
n
syst
em
to redist
ribute
real po
we
r flows.
In fact, the distributio
n of p
o
we
r flow i
s
indep
ende
nt from capa
city loadi
n
g
of line but it is
rely on impe
dan
ce. This l
ead
s to the result
that the
bottleneck can be ove
r
lo
aded tho
ugh
the
cap
a
city load
ing of bottle
neck is
high
er t
han the
power d
e
ma
nd. Hen
c
e, t
he pla
c
em
en
t of
FACTS on t
he bra
n
ch b
o
ttleneck to modify the line imped
an
ce is a meth
od whi
c
h
ra
pidly
rebal
an
ce
s the power by re
dire
cti
ng the
power flow a
c
ross thi
s
bra
n
c
h to eliminat
e overloa
d
.
Variou
s meth
ods h
a
ve be
en pro
p
o
s
ed
to achieve
th
ese
different obje
c
tives via
optimal
loc
a
tion of FACTS devices
. But
mos
t
ly, thes
e wo
rks are com
m
o
n
ly focused
on the following
method
s and
techni
que
s.
Population
b
a
se
d intelli
g
ent techniq
u
e
s to
find
o
p
timal
soluti
ons,
su
ch
a
s
Geneti
c
Algorithm [12
], Evolutionary Programmi
ng [13], and
Particle Swarm Optimizatio
n
[14], combi
nes
PSO and
GA
[15], TS/SA method [1
6], and G
r
avita
t
ional Sea
r
ch
Algorithm
(GSA) [17] h
a
v
e
been u
s
e
d
to determi
ne
the optimal
setting of FACTS pa
ra
meters, mini
mizing th
e total
gene
rato
r fue
l
cost withi
n
p
o
we
r flowe
r
secu
rity limits.
Sensitivity based a
pproa
ch wa
s used to find
t
he optimal locatio
n
of FACTS
de
vices
in
power n
e
two
r
k. Th
e sen
s
itivity index is use
d
to
ra
n
k
the
system
bran
ch
es
according to th
eir
suitability for installing a TCSC. Once t
he locati
ons are determined, an opt
imi
z
ation probl
em of
finding the
be
st setting
s fo
r the install
ed
TCSC
i
s
form
ulated a
nd
so
lved [18]. Such an a
pproa
ch
is used in [19], where LM
P difference and co
nge
st
i
on rent contri
bution are utilized for o
p
timal
locatio
n
of TCSC to red
u
c
e the cong
estion
co
s
t. An overload
sen
s
itivity fa
ctor (po
w
er f
l
ow
index) i
s
u
s
e
d
for o
p
timal
locatio
n
of se
ries
FACTS
device
s
fo
r st
atic cong
esti
on ma
nage
m
ent
[20]. In [21],
optimal pla
c
e
m
ent of TCSC for
red
u
ci
n
g
cong
estio
n
cost ha
s be
en pre
s
e
n
ted
by
usin
g a pe
rfo
r
man
c
e in
dex
, which i
n
corporate
s
two
factors. On
e is the sen
s
itivity matrix of the
TCSC
with re
spe
c
t to the conge
sted line
and the othe
r is the sh
ado
w pri
c
e corre
s
po
ndin
g
to the
con
g
e
s
ted lin
e. A method based on the
sen
s
itivity
of the redu
ctio
n of total system VAR power
loss a
nd
re
al po
we
r p
e
r
forma
n
ce in
dex to dete
r
mine the
op
timal locatio
n
of T
C
SC
for
con
g
e
s
tion m
anag
ement is presented in
[22].
M.A. Khaburi
has
bee
n u
s
ed th
e pa
rtition metho
d
to
limit the se
arch spa
c
e [
23]. The
power
syste
m
wa
s divide
d into two
different a
r
ea
s.
The a
r
ea,
where
a lot of
gene
rato
rs
are
focu
sed, is called so
urce
area
while th
e area, wh
ere a lot of loa
d
s are focu
sed, is calle
d sin
k
area. Th
ese
area
s are conne
cted by
the li
nes. Comp
en
sate
d equipm
ent
s are
in
stalle
d on
the
bran
ch
es betwee
n
the two are
a
s to find t
he
optimal sol
u
tion
acco
rdin
g
to the
objective
function.
In this pape
r,
utilization of the TCSC to
eliminate con
gestio
n
and
minimum ge
n
e
ration
co
st is investigated. In orde
r to com
p
lete
ly elimin
ate con
g
e
s
tion but no n
eed gen
eration
resch
eduli
ng,
System
Ope
r
ator can
u
s
e
one,
two
or
many T
C
SC
device
s
.
Ho
wever, it n
eed
s to
be con
s
ide
r
e
d
pe
rform
a
n
c
e gain
ed fro
m
investme
nt in TCS
C
d
e
v
ices
so
that
can
choo
se
an
effective solution. In order to
evaluate the suitability of a giv
en branch for placi
ng a TCS
C
, an
index
calle
d t
he b
enefit in
d
e
x (BI) i
s
i
n
trodu
ced
fo
r e
a
ch
b
r
an
ch.
This index
is
obtaine
d fro
m
the
differen
c
e
bet
wee
n
the
min
i
mum g
ene
rat
i
on
co
st with
and
witho
u
t T
C
SC. Ba
se
o
n
the
index, t
he
best lo
cation
for the TCS
C
device
s
is d
e
c
ide
d
.
This pa
pe
r has ap
plied th
e minimum cut methodolo
g
y for determining bottle
neck of
power sy
ste
m
to redu
ce sea
r
ch sp
ace
as well a
s
u
s
ing b
enefit index for dete
r
minin
g
the most
suitabl
e lo
cati
ons for in
stall
i
ng T
C
SC de
vices.
The
ba
sic ide
a
of
th
e alg
o
rithm
is to find
the
cut
that has the minimum cut value over all possible
cuts in the ne
twork. That is the cut whi
c
h
contai
ns bottlene
ck bra
n
ches with
su
m
of
cap
a
ci
t
y
through it’
s
sm
alle
st. Therefore, if
the
minimum
cut
is ide
n
tified, the b
r
an
ch
th
at ha
s
the
ab
ility to contri
b
u
te to adj
ust
impeda
nce
will
be
re
cogni
ze
d an
d o
n
ly that b
r
an
ch
i
s
a
b
le to
in
stall TCS
C
to
help
the
co
nge
sted
bra
n
c
h.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Optim
a
l Loca
t
ion of Thyri
s
t
o
r-co
ntrolle
d-seri
es
-cap
aci
t
or usin
g Min
Cut… (T
han
h
Long
Duo
ng)
3651
Hence, searching space
will be
reduced from
n br
anch to m
branch.
(m
is the branches that
minimum cut passe
s thro
u
gh).
The s
t
udy res
u
lts
on 5-bus
,
IEEE 14-bus
and IEEE 30-bus
power s
y
s
t
em have proved
the effectiven
ess of the pro
posed metho
d
.
2. Problem Formulation
2.1. Static M
odeling of T
C
SC
The effect of
TCSC
on the
netwo
rk
ca
n be s
een a
s
a
controllabl
e reacta
nce inserted i
n
the rel
a
ted t
r
an
smi
ssi
on
line [16]. Se
ries capa
c
i
tive
co
mp
en
sa
tio
n
w
o
rks
by r
e
d
u
c
i
ng
th
e
effective seri
es i
m
ped
an
ce of the
tra
n
smissi
on
li
ne
b
y
can
c
eli
ng
p
a
rt of th
e in
d
u
ctive
rea
c
ta
nce.
Hen
c
e th
e p
o
we
r tra
n
sfe
r
red i
s
in
cre
a
s
ed. Th
e mo
del of the ne
twork with
T
C
SC i
s
sho
w
n in
Figure 1.
jx
r
ij
ij
jB
sh
jB
sh
jx
TC
SC
Figure 1. Model of Tran
sm
issi
on Lin
e
wi
th TCSC
The maximu
m comp
en
sa
tion by TCSC is limited t
o
70% of the rea
c
tan
c
e of
the un-
comp
en
sated
line whe
r
e T
C
SC is lo
cate
d. A new line rea
c
tan
c
e (X
ne
w
) is given as follows:
X
Ne
w
= X
ij
–
X
T
C
S
C
(1)
X
Ne
w
= (1- k)X
ij
(
2
)
Whe
r
e
k = X
TC
S
C
/X
ij
is the degre
e
of se
ries
com
pen
sation and X
ij
is the line re
a
c
tan
c
e
betwe
en bu
s-i and bu
s-j.
The po
we
r flow equ
ation
s
of the line with
a new rea
c
tance ca
n be
derived a
s
fol
l
ows:
)
sin
B
ij
cos
G
ij
(
V
V
G
ij
V
P
ij
ij
ij
j
i
2
i
(3)
)
cos
B
ij
sin
G
ij
(
V
V
B
ij
V
Q
ij
ij
ij
j
i
2
i
(
4
)
)
sin
B
ij
cos
G
ij
(
V
V
G
ij
V
P
ji
ij
ij
j
i
2
j
(
5
)
)
cos
B
ij
sin
G
ij
(
V
V
B
ij
V
Q
ji
ij
ij
j
i
2
j
(6)
Whe
r
e
ij
is the voltage an
gle differen
c
e
betwee
n
bu
s i and bus j.
2
New
2
ij
ij
ij
X
R
R
G
and
2
New
2
ij
New
ij
X
R
X
B
(
7
)
2.2. Objectiv
e Functio
n
The o
b
jective
function fo
r
determi
ning t
he lo
cation
s
and
cont
rol
settings of T
C
SC to
minimize the active po
wer
gene
ration
co
st is formul
ated as follo
ws:
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61
3652
TCSC
gi
N
i
i
C
)
P
(
Min
g
C
(
8
)
Whe
r
e
c
bP
aP
)
P
(
C
gi
2
gi
gi
i
is the bid curve of
i
th
generato
r
; a, b and c are cost coefficients for
the gene
rato
r.
Subject to:
a)
Power bal
ance equ
atio
n:
b
gi
di
i
N
,...,
1
i
0
P
P
)
,
V
(
P
(9)
b
gi
di
i
N
,...,
1
i
0
Q
Q
)
,
V
(
Q
(
1
0
)
b)
Power generation limit:
g
max
gi
gi
min
gi
N
,.....,
1
i
P
P
P
(
1
1
)
g
max
gi
gi
min
gi
N
,.....,
1
i
Q
Q
Q
(12)
c) Bus voltage limits:
b
max
i
i
min
i
N
,.....,
1
i
V
V
V
(
1
3
)
d) Appa
rent li
ne flow limit:
l
max
,
l
l
N
,.....,
1
l
S
S
(
1
4
)
TCSC
max
TCSCi
TCSCi
N
,.....,
1
i
X
X
0
(
1
5
)
Whe
r
e P
gi
, Q
gi
are th
e a
c
t
i
ve and
re
act
i
ve power ge
neratio
n at
b
u
s-i:
P
di
, Q
di
the a
c
tive a
nd
rea
c
tive power dem
and at
bus i: V
i
the
voltage magn
itude at bus i: V
i,min
and V
i,ma
x
the minimum
and m
a
ximu
m voltage li
mits; P
gi,min
and P
gi,max
are the minim
u
m and
maxi
mum limits
o
f
real
power g
ene
ration: N
b
the
total numbe
r
of buses, N
g
is the total
numbe
r of g
eneration b
u
s
e
s
:
N
TC
S
C
is the
set of TCS
C
indice
s: S
l
the app
are
n
t power flow i
n
transmi
ssion
line con
n
e
c
ting
node
s
i
and
j
,
and S
l
,max
is its maximum
limit.
2.3. Cost Fu
nction
The TCS
C
co
st in line-k is
given by [24]:
power
_
Base
.
P
.
X
.
C
C
2
L
k
c
k
TCSC
(
1
6
)
Whe
r
e
C i
s
t
he u
n
it invest
ment cost
of
TCSC, X
c
k
i
s
the
seri
es capa
citive re
a
c
tan
c
e
and P
L
is
the power flo
w
in line-k.
)
h
/
($
8760
C
.
C
k
TCSC
t
TCSC
and
1
r
)
r
1
(
)
r
1
(
n
n
(17
)
α
= the capita
l recove
ry factor (CRF
);
r
=
the interes
t
rate;
n
= the ca
pita
l recove
ry pla
n
.
It is assu
me
d that the investment cost of
the TCSC is 15
0$/kV
ar. Co
nsid
eri
ng the
intere
st rate
r
=
0.05
,
the
capital re
cove
ry period
n =1
0 years,
the
capital
re
cov
e
ry facto
r
ca
n b
e
comp
uted, i.e.,
α
= 0.1295.
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Optim
a
l Loca
t
ion of Thyri
s
t
o
r-co
ntrolle
d-seri
es
-cap
aci
t
or usin
g Min
Cut… (T
han
h
Long
Duo
ng)
3653
2.4. Bene
fit Index
The ben
efit index (BI) for the investment
in
FACTS de
vices
can b
e
cal
c
ulate
d
as
follow:
TCSC
of
investmen
t
Cost
TCSC
with
redispatch
after
cost
Generation
-
TCSC
without
redispatch
after
cost
Generation
BI
(18
)
This i
ndex i
s
cal
c
ulate
d
for each lo
catio
n
of
TCS
C
an
d used to eva
l
uate the
suit
ability of
a given b
r
an
ch for pla
c
in
g
a TCS
C
. The
bran
ch th
at gives a m
a
ximum be
nefit index is th
e m
a
in
prop
er lo
catio
n
of TCSC.
3. Proposed
Metho
d
3.1. Min Cut
Algorithm
The be
st lo
cation of T
C
SC play
s key role in
co
ntro
lling of the
system po
we
r flows to
eliminate
co
nge
stion. Th
e pro
b
lem
can be
solv
ed if minimum cut of power sy
stem
i
s
determi
ned. There are
se
veral method
s to find
minimum cut for
any netwo
rk
having a sin
g
le
origin n
ode a
nd sin
g
le de
stination nod
e. One of t
he u
s
ual a
pproa
ches to
solve this p
r
oble
m
is to
use its
clo
s
e relatio
n
ship to the ma
ximum
flow
probl
em. Th
e famou
s
M
a
x-Flo
w
/Min-Cut-
Theo
rem by
Ford a
nd Ful
k
erso
n (1
956
) [25] sh
o
w
e
d
the duality of the maximum flow an
d the
so-call
ed
mini
mum
s-t-cut.
There, s an
d
t are
two
ve
rti
c
e
s
that
are t
he
sou
r
ce
an
d the
sin
k
in t
he
flow problem
and have to
be se
pa
rated
by the cut, that
is, they h
a
ve to lie in different pa
rt
s of
the partition.
a.
Max-Flow
Max flow is t
he m
a
ximum
po
ssi
ble
flo
w
fr
om origi
n
to destinatio
n equal
s the minimum
c
u
t values
for all c
u
ts
in the network
.
b.
Minimum Cut
The minim
u
m cut p
r
oble
m
is to find t
he cut acro
ss the n
e
two
r
k that ha
s th
e minimum
cut value ove
r
all possibl
e cuts.
3.2. Modeling Po
w
e
r Ne
tw
o
r
k Using Min Cut Alg
o
rithm
The po
we
r sy
stem is m
ode
led as
a dire
cted netwo
rk
G(N,A)
wh
ere
it is defined
by a set
N
of
n
nod
es and
a
set
A
of
m
directed
arcs. Ea
ch
arc
a
ij
∈
A
ha
s a capa
city
u
ij
that sh
ows t
he
maximum a
m
ount that
can flow
between n
ode i
a
nd j. The mi
n cut al
gorith
m
is a
dded t
w
o
node
s, the
virtual
sou
r
ce
and th
e virtu
a
l si
nk,
rep
r
e
s
entin
g the
combinatio
n of
the g
ene
rat
o
rs
and load
s, re
spe
c
tively. Each line o
u
t of the vi
rtual
sou
r
ce ha
s a maximum flow that matche
s
the gene
ratio
n
of the con
necte
d nod
e, and ea
ch lin
e into the virtual sin
k
re
prese
n
ts the lo
ad
deman
ded
b
y
the co
nne
cted no
de. Th
e mod
e
ling
o
f
an exam
ple
po
wer sy
ste
m
depi
cted
i
n
Figure 2 is sh
own in Fig
u
re
3.
Figure 2. Example Power
System with
Gene
rato
rs of
16 at 1, 48 at 2 and 24 at 3
and
Load
s of 40 a
nd 48
Figure 3. Power
Networ
k
Shown a
s
a
Dire
cted
Flow G
r
ap
h with Virtual Node
s s an
d t.
Edges
are La
bele
d
with (flow/
cap
a
city).
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Vol. 12, No. 5, May 2014: 3649 – 36
61
3654
The
algo
rith
m works by
succe
ssively
a
ssi
gnin
g
flo
w
f(a
ij
) to a
r
cs
along
a
dire
cted path
from
s to t
u
n
til no m
o
re
flow
can
be
adde
d. The
details for
de
terminin
g the
minimum
cu
t of
power sy
ste
m
is pre
s
e
n
te
d in Referen
c
e [10, 25].
a) The
step
s in the method
are:
1.
Find
any p
a
th from
the
o
r
igin n
ode
to
the de
stinatio
n no
de. If th
ere
are
no
m
o
re
su
ch path, ex
it.
2.
Detemine f, the maxim
u
m
flow al
ong this
path, whi
c
h
will be equal to the sm
allest
flow ca
pa
city on any arc in
the path ( the
bottleneck arc).
3.
Subtra
ct f fro
m
the re
maini
ng flow
ca
pa
city
acco
rdin
g
to the directio
n from the
ori
g
in
node to the d
e
stinatio
n no
de for ea
ch a
r
c in the path.
4.
Go to Step 1
b) The al
gorit
hm will be used to determi
ne the mi
nim
u
m cut of the 5-bus sy
stem
in Figure 2
1.
The a
r
cs alo
ng the path
s - 1
- 4 - t are lab
e
le
d usi
ng 12
u
n
its of flow.
The
bottlene
ck h
e
r
e is the a
r
c 1
– 4 as sh
own in Figure 4
2.
The a
r
cs alo
ng the path
s - 2
- 4 - t are lab
e
le
d usi
ng 16
u
n
its of flow.
The
bottlene
ck h
e
r
e is the a
r
c
2 – 4. Note that with the si
multaneo
us fl
ow on p
a
th s
- 1 -
4 - t, the total
flow on arc 4
– t is now 28
units of flow a
s
Figu
re 5
3.
The a
r
cs alo
ng the path
s - 2
- 5 - t are lab
e
le
d usi
ng 24
u
n
its of flow.
The
bottlene
ck o
n
this path is a
r
c 2 – 5 a
s
Fi
gure 6
4.
The a
r
cs alo
ng the path
s - 3
- 5 - t are lab
e
le
d usi
ng 20
u
n
its of flow.
The
bottlene
ck o
n
this path is a
r
c 3 – 5 a
s
Fi
gure 7
The
algo
rith
m termi
nate
s
after t
he l
a
st
path
is foun
d in
Figu
re
7
be
cau
s
e
the
r
e
are
n
o
more
availabl
e path
s
to
b
e
foun
d b
e
tween
s
and
t. This i
s
obvio
us
sin
c
e
all
paths mu
st p
a
ss
throug
h the set of arcs 1-4
,
2-4, 2-5 a
n
d
3-5,
and the
s
e a
r
cs have
all had thei
r flow capa
city in
the directio
n from
s to t
red
u
ce
d to
zero.
The final
grap
h is i
n
Fig
u
re
7. From
the F
i
gure
it ca
n b
e
see
n
that, su
m the units o
f
flow on bott
l
ene
ck a
r
cs
(12 + 1
6
+
24
+ 20
= 72
)
equal
s sum t
h
e
units of flo
w
on the a
r
cs
o
u
t of the so
urce
(12
+
40
+2
0=7
2
) o
r
into
the sin
k
(28
+
44
=7
2). Thi
s
i
s
maximum po
ssi
ble po
we
r
flow from
sou
r
ce
(s) to
sin
k
(s) e
qual
s the
minimum
cut
value for all t
he
cuts in the network. Some pos
sible
cuts are illustrated in Figur
e 8.
Flow chart for determinati
on
optimal location of TCSC i
n
con
g
e
s
tion
manag
eme
n
t is pre
s
e
n
ted i
n
Figure 9
Figure 4. The
Units of Flo
w
along s-1
-
4-t
Figure 5. The
Units of Flo
w
along s-2
-
4-t
Figure 6. The
Units of Flo
w
along s-2
-
5-t
Figure 7. The
Units of Flo
w
along s-3
-
5-t
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Optim
a
l Loca
t
ion of Thyri
s
t
o
r-co
ntrolle
d-seri
es
-cap
aci
t
or usin
g Min
Cut… (T
han
h
Long
Duo
ng)
3655
Figure 8. Some Possible
Cuts
Figure 9. Flow Ch
art for Determin
ation
Optimal Lo
ca
tion of TCSC
in Con
g
e
s
tion
Manage
ment
4. Results a
nd Discu
ssi
ons
The propo
se
d method for
the optimal lo
cation
of the TCSC for
con
gestio
n
mana
gement
has been implemented on 5-bu
s
,
IEEE 14-bus
and IEEE 30-bus
tes
t
s
y
s
t
ems
.
MATPOWER
[26], a toolbox of MATLAB, has bee
n used for the sim
u
lation
s.
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Vol. 12, No. 5, May 2014: 3649 – 36
61
3656
4.1. The 5-Bus Sy
stem
The network
and data of th
e 5-bu
s sy
ste
m
are given i
n
Appendix
In order to verify the pro
posed approach and illu
strate the impacts
of TCS
C
, three
ca
se
s f
o
r t
e
st
sy
st
em
s we
r
e
inv
e
st
igat
e
d
:
Ca
se 1: Gen
e
ration initial
sched
ule, minimum ge
neration co
st.
Ca
se 2: Gen
e
ration
redi
sp
atchin
g witho
u
t TCSC.
Ca
se 3: Gen
e
ration
redi
sp
atchin
g with
TCSC.
Table 1. Re
-d
ispat
ch with T
C
SC in line 2
-
5 Obje
ctive Functio
n
Mini
mum Gen
e
rat
i
on for the 5
bus System
Ge
P
scheduled
Re-
dispatch
w
i
thout
TCSC
Re-
dispatch
wi
t
h
TCSC
Total
absolute
redispatch
w
i
thout
TCSC
Total
absolute
redispatch
wi
t
h
TCSC
Gene
ration
cost before
redispatch
Gene
ration
cost after
re-di
s
patc
h
w
i
thout
TCSC
Gene
ration
cost after
re-di
s
patc
h
wi
t
h
T
C
S
C
1 48
85.3
48
74.1
0.0
2811.38
(
$
/h
r)
3033.86
(
$
/h
r)
2811.39
(
$
/h
r)
2 116.2
79.4
116.2
3
72
72
72
From T
able 1
(
Col
u
mn 2
)
, it wa
s ob
se
rve
d
t
hat gene
ra
tion power
of Gene
rato
r 2 i
s
mo
re
than compa
r
e with Ge
ne
rator 1 a
nd 3
due to Ge
ne
rator 2 i
s
the
che
ape
st Ge
nerato
r
. With
this
gene
ration
schedul
e, total
co
st of a
c
tive po
wer ge
neration
was obt
ained
optimal
281
1.38($/hr)
(Ca
s
e
1
)
a
s
Table
1
(Col
umn
7)
but n
o
t se
cu
re
d d
ue to
co
nge
stion o
c
curred
in lin
es 2
-
4
a
s
sho
w
n
in T
a
b
l
e 2
(Colum
n
3). Th
e n
e
twork
cann
ot b
e
op
erate
d
in
this
way
sin
c
e security of t
h
e
netwo
rk was
violated. Ho
wever, the
con
gestio
n
on th
e line 2
–4
wa
s elimi
nated
by gene
ration
re
-
disp
atchi
ng
b
u
t may n
o
t b
e
obtai
n mi
ni
mal
co
st. The
bran
ch
2-4 i
s
o
n
e
of b
r
an
ch
bottlene
ck of
power sy
ste
m
that preven
ts load
s to
be
served from
che
ape
st gen
erato
r
s.
To sati
sfy suf
f
icient the po
wer to th
e loa
d
s,
some
che
ap ge
nerators have to
red
u
ce th
ei
r
disp
atch
an
d
some
exp
e
n
s
ive gen
erato
r
s in
the
cong
ested
zone
h
a
ve to i
n
crea
se th
eir di
spa
t
ch
and con
s
eq
u
ently total co
st of active
power g
ene
ration wa
s in
cre
a
sed fro
m
2811.38
$/h
to
3033.8
6
$/h (Ca
s
e 2
)
as T
able 1 (col
u
m
n 8). T
he
p
o
ssibility of operatin
g the
power
syste
m
at
t
he minimal
co
st
while
sa
t
i
sf
y
i
ng sy
st
e
m
se
cu
rit
y
by placing T
C
SC at pro
per location
with
an
optimal settin
g
size of TCSC to incre
a
s
e the us
e of available ca
pacity of the
existing line
s
. In
orde
r to
archi
v
e req
u
ire g
o
a
l, the T
C
SC nee
d to
be i
n
stalle
d o
n
b
r
an
ch th
at th
e minim
u
m
cut
passe
s th
rou
gh an
d lie
s in
loop
whi
c
h
contain
s
b
r
an
ch overl
oad. F
r
om T
able
3, it can
been
see
that,
line
2-5,
1-4 and 3-5 are
li
nes
that
the minimu
m cut p
a
sse
s
throu
gh a
nd
are
also line
s
in
loop
s 1 (1-2
-4-1
), loop 2
(
2
-
5-4-2
)
a
nd l
oop 3
(
2
-
3-5-4-2
)
which co
ntains bra
n
ch
overloa
ded 2-4
respe
c
tively. Therefore,
to
eliminate/alleviat
e cong
e
s
tion, TCSC
can be in
stall
ed on one of
the
lines. O
n
ce th
e location
s a
r
e dete
r
mine
d, an optimi
z
ati
on p
r
oble
m
of
finding the
b
e
st settings for
the installe
d TCSC i
s
formulated an
d
solved. As
th
ere a
r
e a lot
of location
s that can in
stal
l on
TCSC to elim
inate cong
est
i
on, it nee
ds
base on
be
ne
fit gained f
r
o
m
investme
nt
in T
C
SC
so t
hat
can d
e
ci
de b
e
st location o
f
TCSC. The
bran
ch th
at gives the large
s
t benefit ind
e
x is the mai
n
loc
a
tion of TCSC.
Table 2. Line
Loadi
ng
s fro
m
Load Flo
w
with Initial Schedul
ed and
Re-dispatch with TCS
C
in
Line 2-5
Line no
i - j
Loading %
w
i
th i
n
itial scheduled
Loading %
re-dis
patch w
i
th
TCSC
1
1 – 2
18.41
19.10
2
2 – 4
107.45
99.05
3
1 – 4
40.9
39.25
4
2 – 3
22.4
30.90
5
2 – 5
41.44
58.84
6
3 – 5
50.39
41.38
7
4 – 5
15.01
23.51
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Optim
a
l Loca
t
ion of Thyri
s
t
o
r-co
ntrolle
d-seri
es
-cap
aci
t
or usin
g Min
Cut… (T
han
h
Long
Duo
ng)
3657
Table 3.Th
e Minimum of the 5-b
u
s Syst
em
Line no
The minimum cut
1
2 - 5
2
2 - 4
3
1 – 4
4
3 – 5
Table 4. Ben
e
fit Index Computed for
Di
fferent
Bran
che
s
in the Minimum
Cut
Table 5. Ben
e
fit Index Computed for
Di
fferent
Location
s
of the TCS
C
Line no
i-j
Loop i
BI
1 1-4
1-2-4
-
1
7.79
3 2-5
2-5-4
-
2
9.22
4 3-5
2-3-5
-
4-2
3.90
Line no
i-j
BI
1 1-4
7.79
3 2-5
9.22
4 3-5
3.90
5 1-2
-56.2
6 2-3
-8.32
7 4-5
0.84
As
sho
w
n
in
Table
4, the
li
ne 2
-
5
is the
best l
o
cation
for pl
acement
TCS
C
sin
c
e
it gives
the la
rge
s
t b
e
nefit index. T
he valu
e
of control
pa
ram
e
ter of TCSC is taken as -0.064p
u. System
power flo
w
result after
pl
acin
g TCS
C
i
n
line 2
-
5 i
s
sho
w
n i
n
Ta
ble 2. It can
be ob
se
rved
from
Table
2 (Col
umn 4)
that con
g
e
s
tion h
a
s bee
n re
lie
ved. The
loa
d
ing
of the
li
nes 2
-
4
ha
s
now
redu
ce
d to 9
9
.05% from t
he initial
sche
duled
107.4
5
%
. Line 2
-
5 i
s
now loa
ded t
o
58.84%
whi
c
h
is mu
ch hig
h
e
r than i
n
initial sched
uled.
The TCS
C
redu
ced the
serie
s
impe
da
nce of the li
n
e
2-5
hen
ce po
we
r flow on the l
i
ne incre
a
ses. Acco
rding
t
o
the table 1,
the re-dispat
che
d
amo
unt
to
remove
cong
estion
in th
e
pre
s
en
ce
of t
he T
C
SC
on
l
i
ne 2
-
5
is 0.0
MW comp
ared to
74.1M
W i
n
the case
re
-d
ispat
ch
witho
u
t TCS
C
, g
e
neratio
n
co
st
is o
n
ly 28
11.
39 $/h
r
(Ca
s
e 3
)
compar
ed to
3033.8
6$/hr f
o
r the case re-di
s
pat
ch wi
thout
TCSC.
So, the annual savin
g
is 1.94(millio
n$
).
Table
5 i
s
co
nstru
c
ted
for
verification
p
u
rpo
s
e,
by pl
acin
g T
C
SC
on e
a
ch lin
e
one
at a
time
and
runni
ng
OPF
.
Acco
rdin
g t
o
Tabl
e 5, li
ne 2
-
5 i
s
th
e be
st location for
TCS
C
installatio
n
to
eliminate
con
gestio
n
an
d
minimize ge
n
e
ration
co
st f
o
llowed by lin
e 1-4 an
d 3
-
5
.
The othe
r li
nes
are give
s a benefit index
less than o
ne or ze
ro
.
Hen
c
e, it is not advisabl
e to make the
in
ve
s
t
me
n
t
s
i
n
c
e th
e s
a
ving
s
in
th
e ge
ne
r
a
tio
n
c
o
s
t
s
c
a
nn
o
t
pa
y for
th
e in
ves
t
me
n
t. F
r
om Tab
l
e
3 it
can
be
o
b
se
rved
that
the nu
mbe
r
o
f
bra
n
che
s
which
ne
ed to
be inve
stigat
ed to
dete
r
mi
ne
the locatio
n
o
f
TCSC ha
s redu
ced fro
m
7 bran
ch
es to
3 bran
che
s
i
n
the minimu
m cut.
4.2.
IEEE 14-Bus Test S
y
stem
There are 20
line sections in IEEE 14-bus
system. The network
and load data for IEEE
14-b
u
s a
r
e
sh
own in [19].
From Ta
ble 7 (Col
umn 3) it can be se
en t
hat, one part of the system is co
n
geste
d.
Gene
rato
r 1 i
s
the chea
pe
st gene
rato
r
and is
se
rv
e
d
by two tran
smissio
n
line
s
(1
-2 a
nd 1
-
5)
with a
total
capa
city of 11
0MW. T
h
e
two line
s
are n
o
t equ
ally loa
ded
due
to t
he diffe
ren
c
e
in
impeda
nce a
nd the re
sult is that line 1-2 is loade
d to 132.86% of its capa
city while line 1
-
5
is
only load
ed t
o
55.95%
of its ca
pa
city. Placin
g TC
S
C
at suitabl
e lo
cation via th
e
minimum
cut
of
power sy
ste
m
can elimi
n
ate the overlo
ad on line 1
-
2
.
Table 6. Re-dis
pat
c
h
with TCSC in line 1-5 Ob
jec
t
ive Func
tion Minimum Generat
i
on for IEEE-14
Bus
Sys
t
em
Ge
P
scheduled
Re-
dispatch
w
i
thout
TCSC
Re-
dispatch
wi
t
h
TCSC
Total
absolute
redispatch
w
i
thout
TCSC
Total
absolute
redispatch
wi
t
h
TCSC
Gene
ration
cost before
redispatch
Gene
ration
cost after
re-di
s
patc
h
w
i
thout
TCSC
Gene
ration
cost after
re-di
s
patc
h
wi
t
h
T
C
S
C
1 100
76.71
97.09
46.58
7.56
5944.21
($/hr)
6448.28
($/hr)
6000.25
($/hr)
2
50 50
50
3
29.71
42.29
33.49
6
45 45
45
8
34.29
45
33.42
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ISSN: 23
02-4
046
TELKOM
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KA
Vol. 12, No. 5, May 2014: 3649 – 36
61
3658
Table 7. Line
Loadi
ng
s fro
m
Load Flo
w
with Initial Schedul
ed and
Re-dispatch with TCS
C
in
Line 1-5
Line
no
i - j
Loading %
w
i
th
initial scheduled
Loading %
re-dis
patch
wi
t
h
T
C
S
C
1
1 – 2
132.86
99.28
2
1 – 5
55.95
78.48
3
2 – 3
73.73
66.6
4
2 – 4
75.1
61.85
5
2 – 5
51.12
32.65
6
3 – 4
67.5
69.16
7
4 – 5
51.62
59.31
8
4 – 7
5.85
5.02
9
4 – 9
28.15
28.25
10
5 – 6
10.24
11.28
11
6 – 11
44.6
45.84
12
6 – 12
41.3
41.5
13
6 – 13
65.06
65.6
14
7 – 8
57.15
55.7
15
7 – 9
63.88
62.82
16
9 – 10
6.75
5.2
17
9 – 14
22.4
21.73
18
10 – 11
38.25
39.8
19
12 – 13
10.8
11
20
13 – 14
40.9
41.9
Table 8. The
Minimum of IEEE 14-bus
Sys
t
em
Table 9. Ben
e
fit Index Computed for
Di
fferent
Location
s
of the TCS
C
Line no
The minimum cut
1
2 - 5
2
2 - 4
Line no
i-j
BI
2 1-5
8.28
6 3-
4
3.62
3 2-3
-2.32
7 4-5
0.16
1 1-2
-10.38
10 5-6
0.14
4 2-4
-6.9
14 7-8
0.09
8 4-7
0.6
15 7-9
-0.25
From
Tabl
e 8
it ca
n b
e
o
b
s
erve
d that, li
ne 1
-
5 i
s
th
e
line that th
e
minimum
cut
passe
s
throug
h an
d is also line in l
oop (1-2
-5
-1
). Therefo
r
e, suitable po
sitio
n
of TCSC i
s
at line 1-5. T
h
e
value of co
ntrol paramete
r
of TCSC for
comp
uti
ng m
a
ximum ben
e
f
it index is taken a
s
-0.11
pu.
System po
we
r flow
re
sult a
fter pla
c
ing
T
C
SC i
n
line
1
-
5 i
s
sho
w
n i
n
Tabl
e 7
(Column
4). It can
be ob
serve
d
from this Tab
l
e, cong
estio
n
has
be
en relieved. The
loadin
g
of the lines 1
-
2 h
a
s
now
redu
ce
d
to 99.28%. Line 1-5 is no
w loaded to 7
8
.
48% whi
c
h i
s
mu
ch hig
h
e
r
than from th
e
initial sched
ul
ed. Accordi
n
g to the Tabl
e 6, the re-di
s
pat
che
d
am
ount to remo
ve cong
estio
n
in
the presen
ce
of the T
C
SC on
line
1-5 is
onl
y 7.5
6
MW
com
p
a
r
ed to
46.58
MW in th
e
case
without T
C
SC, gene
ratio
n
co
st is o
n
ly 6000.
25$/h
r
co
mpa
r
ed
to 6448.28
$/hr for the
ca
se
without TCS
C
. So, the annual saving is 3.92(million
$
). From Ta
b
l
e 9 it can se
e the line 1-5
is
the best lo
cat
i
on for pla
c
e
m
ent TCS
C
since it gives t
he larg
est be
nefit index.
Observation
of Tabl
e 9
sh
ows that th
e
prop
os
ed met
hod also capt
ure
s
th
e
b
e
st locatio
n
for the place
m
ent of TCSC in comp
ari
s
on with
the
result in [19]. Howeve
r, the number of
bran
ch
es
whi
c
h ne
ed to be
investigated
to deter
min
e
the location of TCSC ha
s re
duced from 2
0
bran
ch
es to
2
bran
ch
es i
n
the minimu
m
cut a
s
sho
w
n
in Table
8 wh
ich i
s
less tha
n
as
com
pare
d
with [19].
4.3. IEEE 30-Bus Test S
y
stem
IEEE 30-bus
system has 41 line sections.
The net
work and load data for IEEE
30-bus
s
h
own in [26]
, the c
o
s
t
c
oeffic
i
ents
for IEEE 30-bus
is
given in Appendix
The load flow of IEEE 30-bus
system i
s
sh
own in T
a
ble 11 (Colum
n 3 and 7). F
r
om the
load flo
w
, it
wa
s fou
nd th
at line 6
–8
a
nd line
21
–2
2 was
overl
o
aded. T
o
avo
i
d overl
oadi
n
g
, it
need
s to pl
ace TCS
C
at suitable lo
cati
on. It c
an b
e
observed f
r
o
m
Table
12 t
hat, the mini
mum
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