TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 10, Octobe
r 20
14, pp. 7123
~ 713
0
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.642
1
7123
Re
cei
v
ed
Jun
e
20, 2014; Revi
sed
Jul
y
2
0
, 2014; Acce
pted Augu
st 6, 2014
Weakest Buses Identification and Ranking in Large
Power Transmission Network by Optimal Location of
Reactive Power Supports
M. Amroune
*, A. Bourza
mi, T. Boukti
r
Dep
a
rtment of Electrical E
ngi
neer
ing, Un
iver
sit
y
of Setif 1,
Setif, 1900
0, Algeri
a
*Corres
p
onding author, e-mail:
amrounemohammed@y
ahoo.fr, aref_pg
04@y
a
hoo.fr, t.b
ouktir@y
a
hoo.fr
A
b
st
r
a
ct
T
he d
e
tectio
n
of volta
ge c
o
lla
pse
is ess
ent
ia
l to av
oi
d poss
i
bl
e vo
l
t
age co
ll
apse
for th
e
preve
n
tive co
ntrol actio
n
s an
d voltag
e securit
y
asse
ssment. One effective
w
a
y to know
th
e locati
ons w
h
er
e
voltag
e c
o
ll
aps
es co
uld
b
e
ap
pear
is t
o
i
d
e
n
tify w
eakest
bu
ses i
n
th
e syst
ems.
The w
e
ak
est bus
is
the
fi
rst
poi
nt w
here voltag
e coll
aps
es app
ear in
a severe co
nti
nge
ncy. T
h
is pap
er prop
ose
s
a techniq
u
e
to
evaluate the weakest bus in large
sc
ale
power system
based on the
opt
im
al position of reactive power
supp
orts. T
o
solve the o
p
ti
mi
z
a
ti
on pr
obl
e
m
, Differentia
l E
v
oluti
onary (D
E) techniq
ue is
used. T
he fitnes
s
function co
nsi
s
ts of cost, p
o
w
e
r
losses and L
oad vo
ltage stab
ility i
ndex (L
mn
) which satisfying all
oper
ation
a
l c
o
nstraints. L
mn
is used
as th
e ind
i
cator for
voltag
e stabi
lity margi
n
an
d w
eakest bu
s
identification. The
m
e
thod is
appl
ied
on standard IEEE 30
bus, 57
bus
an
d 118 bus test system
s to s
h
ow
their co
mp
arati
v
e computi
ng e
ffectiveness.
Ke
y
w
ords
: w
eakest bus, volt
age co
lla
pse, r
eactive p
o
w
e
r s
upp
ort, voltag
e stabil
i
ty, differentia
l evol
utio
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
A system ex
perie
nces
a state of voltage in
stabilit
y when the
r
e is a p
r
og
ressive or
uncontroll
abl
e d
r
op
in vo
ltage ma
gnit
ude
after
a disturban
ce, increa
se
i
n
l
oad dema
n
d
or
cha
nge i
n
o
peratin
g con
d
ition. The
main fa
ctor,
whi
c
h
cau
s
e
s
the
s
e u
n
a
c
ceptabl
e vol
t
age
profiles, is the inability of
t
he power sy
stem to m
e
et the dem
and for
reactive power. Under
norm
a
l ope
ra
ting conditio
n
s
, the bus voltage magnitu
de increa
se
s as re
active p
o
we
r inje
cted
at
the sam
e
bu
s is increa
sed.
However
wh
en volt
age m
agnitud
e
of any one of the system’
s
bu
ses
decrea
s
e
s
wi
th the i
n
crea
se i
n
rea
c
tive po
we
r fo
r
t
hat
sa
me
b
u
s,
t
h
e
sy
st
e
m
is
s
a
id
t
o
be
unsta
ble. Alth
ough th
e volt
age in
stability
is a
lo
caliz
ed
pro
b
lem, its i
m
pact
on th
e
system
ca
n be
wide
sp
rea
d
as it d
epe
n
d
s o
n
the
re
lationshi
p b
e
t
ween t
r
an
smitted active
power, inj
e
cted
rea
c
tive p
o
wer
and
receiv
ing e
nd volta
ge [1]. Th
e
main
ch
allen
ge of
this p
r
o
b
lem i
s
to
id
entify
the locations where volt
age instability could be ini
t
iated an
d to understand
t
he
ori
g
in of the
probl
em. On
e
effective way
to kno
w
n the
voltage insta
b
ility origin i
s
to identify we
ake
s
t bu
se
s i
n
the system
s.
The wea
k
e
s
t bu
s ha
s b
een ide
n
tified as th
e bu
s which lacks re
active p
o
we
r
sup
port
s
the most to defen
d again
s
t voltage collap
s
e.
The i
dentification of
we
a
k
e
s
t bu
se
s is a
n
im
porta
nt task fo
r t
he a
nalysi
s
of po
we
r
system
stabili
ty [2, 3]. To identify the weak
bu
se
s
se
veral meth
od
s ha
s
bee
n p
r
opo
se
d in th
e
literature, the
most
of the
s
e m
e
thod
s
are
ba
s
ed
o
n
Voltage St
ability Indice
s. In
Ref. [4
] the
voltage
colla
pse
p
r
oximity indi
cato
r (V
CPI) m
e
thod
for e
a
ch lo
ad
bu
s i
s
appli
ed to
identify the
wea
k
bu
se
s
of the
syste
m
. Ref. [5] p
r
opo
se
s th
e
use
of
Conti
nuation
Power Fl
ow (CP
F
) to
identify the weak
bu
se
s. The Ref. [6] uses lin
e
stabilit
y index desi
g
nated a
s
fa
st voltage sta
b
ility
index (FVSI) to determi
n
e
the maxim
u
m re
active l
oad-ability an
d the wea
k
e
s
t bu
se
s. A Ne
w
Voltage Stabi
lity Index (NV
S
I) is p
r
op
osed in
Re
f. [7]. A fuzzy logi
c ba
se
d fast
decoupl
ed lo
ad
flow metho
d
is co
nsi
dered
to estimate
the va
lue of NVSI. Ref. [8] presented t
he use of Li
ne
voltage stabil
i
ty index (L
mn
) for Wea
k
Bus Identification for FA
CT
S location. Ref. [9] propo
ses
the identificat
ion of the weakest bu
se
s over
24 hou
rs in order to
study and compen
sate t
h
e
detrime
ntal i
m
pact
s
of P
EV cha
r
gin
g
station
s
o
n
voltage p
r
ofile
s a
nd voltag
e sta
b
ility of sma
r
t
grid.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 712
3
– 7130
7124
The ide
n
tifica
tion of the weakest b
u
se
s
using above
mentione
d method
s
is b
a
se
d
on
grad
uation i
n
cre
a
si
ng of l
o
ad at
cho
s
en
load b
u
s
and
cal
c
ulatin
g of
the Voltage
Stability Indices
(VSI). The value of VSI close to 1.00 i
ndicates t
hat
the particul
a
r bus i
s
close to its instability
point. In the final step the maximum power loa
d
in
g or maximu
m load-a
b
ility limit (MLL) is
extracted fo
r every load bu
se
s and the smallest M
LL i
s
ran
k
e
d
the highe
st implying the wea
k
e
s
t
bus in th
e sy
stem. The m
a
jor
wea
k
n
e
ss of these m
e
thod
s is tha
t
requi
red a l
a
rge
cal
c
ul
ation
t
i
me part
i
cul
a
rly
f
o
r la
rge
sc
ale p
o
w
e
r
sy
st
em
s.
In
re
cent yea
r
s evolutio
nary/meta-heu
ristic
comp
uting
tech
niqu
es li
ke
Gen
e
tic
Algorithm
(G
A), Particl
e
Swarm
O
p
timization
(PS
O
),
evolutiona
ry prog
ram
m
ing
and oth
e
rs h
a
ve eme
r
g
e
d
as ve
ry po
werful g
ene
ral
purp
o
se
solut
i
on
tools. Ba
si
cal
l
y these
tool
s ar
e
sea
r
ch t
e
ch
niqu
es ca
pable
of
fi
ndi
ng the
optim
um
solutio
n
o
f
a
probl
em. The
most rema
rkable feature o
f
these tool
s i
s
that they do not impose a
n
y restri
ction
to
the nature of
the search
spa
c
e
an
d type of the variable
s
[10]. In this pape
r a techniq
ue to
evaluate th
e
we
akest
bu
s in
large
scale p
o
wer
systems ba
se
d on
the
opt
imal lo
cation
of
rea
c
tive po
wer
sup
port
s
i
s
pro
p
o
s
ed. Pl
annin
g
of
rea
c
tive po
we
r
suppo
rts
wo
ul
d give b
enefit
s to
the use
r
s of
the tran
smi
ssi
on sy
stem
s, in term
s
of loss re
du
ction, amo
n
g
other te
chni
cal
benefits,
su
ch as imp
r
ovin
g stea
dy stat
e and
dynami
c
sta
b
ility;
improve
system
voltage p
r
ofil
es
[11]. The rea
c
tive power p
l
annin
g
pro
b
l
e
m involves
optimal allo
ca
tion of rea
c
tive power
sou
r
ce
s
(Var
sou
r
ces) to improve t
he syste
m
voltage stab
ility
and redu
ce f
uel co
st an
d power lo
sse
s
. In
this pap
er the
optimizatio
n probl
em is
so
lved usin
g Dif
f
erential Evol
utionary (DE) techniq
ue. T
h
e
Load voltag
e
stability ind
e
x (L
mn
) is u
s
ed a
s
the i
ndicator for
voltage stabil
i
ty margin a
nd
weakest
bus
i
dentification and ranking. Simula
tions are performed
on IEEE 30, 57 and 118 bus
sy
st
em
s.
2. Formulation of Voltage Stabilit
y
In
dex
Voltage
stabi
lity is current
ly one
of the
mo
st
impo
rt
ant rese
arch
are
a
s in
the
field of
electri
c
al
po
wer
system. V
o
ltage in
stabi
lity problem
i
s
a
s
so
ciated
with the
incre
a
se
d loa
d
ing
of
system
(he
a
v
ily loaded),
and in
suffici
ent local rea
c
tive su
pply. The m
a
in
challen
ge of t
h
is
probl
em i
s
to
identify the lo
cation
s
wh
ere voltage
in
stability co
uld
b
e
initiated
an
d to u
nde
rsta
nd
the ori
g
in of t
he p
r
oble
m
. One effe
ctive way to
kn
o
w
n the voltage
instability o
r
i
g
in is to
ident
ify
wea
k
e
s
t buses in the systems. The weakest bu
s h
a
s be
en iden
tified as the bus
which la
cks
rea
c
tive power su
ppo
rts th
e most to def
end ag
ain
s
t voltage collap
s
e.
Identifying weak bu
se
s can give
correct info
rmati
on fo
r the
o
p
timal rea
c
tive po
we
r
planni
ng invo
lved that wou
l
d decid
e whi
c
h bu
se
s
are
the most se
vere and n
e
e
d
to have new
rea
c
tive po
wer
sou
r
ce
s in
stalled
and
di
stribute
d
g
e
n
e
rato
r to
enh
ance loa
d
-abi
lity of the system
[4, 12]. There are m
any method
s currently in
use t
o
help in the
voltage stab
ility analysis
and
wea
k
area id
entification.
Some of them are
PV and QV analy
s
is [13], Mod
a
l Analysis [
14],
Maximum Lo
ading M
a
rgin
Index (ML
M
) [15], load
p
r
oximity inde
x [16, 17], impeda
nce in
dex
[18], Fast Vo
ltage Stability Index (FVSI) [6], Line stability inde
x [19]. In thi
s
pa
per th
e
line
voltage sta
b
il
ity index (L
mn
) is
use
d
for
wea
k
e
s
t bu
ses id
entificati
on. The lin
e
voltage sta
b
il
ity
Index symb
o
lized
(L
mn
) p
r
opo
se
d by
Moghavvemi
[20] is formulated
ba
sed o
n
a
po
wer
transmission line. This index is
basi
c
ally used to determine the
max
i
mum load-ability in a power
system. T
h
e
voltage
sta
b
ility index
referred
to
a line
was
formulate
d
from the
2-b
u
s
rep
r
e
s
entatio
n of power
system. The val
ue of line in
d
e
x that is clo
s
ed to the
uni
ty indicates t
hat
the respective line is closed to its stability limit
. The representation of a
2-bus model is illust
rat
ed
in Figure 1.
Figure 1. Model of Simple Bran
ch for Vo
ltage Stability Research
R+j
X
V
i
0
V
j
δ
P
i
+j
Q
i
P
j
+j
Q
j
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Wea
k
e
s
t Buses Identification and
Ran
k
i
ng in
Large P
o
we
r Tra
n
sm
i
ssi
on… (M. Am
roune)
7125
The voltage stability index for a line is d
e
fi
ne
d as follo
ws:
2
4
1.0
si
n(
)
r
mn
s
XQ
L
V
(1)
Whe
r
e:
X: Line rea
c
tance;
Q
r
: Rea
c
tive power at the receivin
g end;
V
s
: Sending end voltage;
θ
: Line imped
ance angl
e;
δ
: Angle differen
c
e bet
wee
n
the sup
p
ly voltage and t
he re
ceiving
voltage.
The value of L
mn
ranges from 0 (no lo
ad) to 1 (voltage coll
ap
se), and it must be less
than 1 fo
r
stable
system
s. The Lm
n is use
d
to
find
the sta
b
ility index for
ea
ch line
con
n
e
c
ted
betwe
en t
w
o
bu
se
s in
an
intercon
ne
cted n
e
two
r
k, l
i
ne
with the
highe
st value
of L
mn
index i
s
con
s
id
ere
d
to be wea
k
co
mpared to a line with the lo
wer valu
e of L
mn
index.
3. Formulation of the
Op
timization Pr
oblem
This
se
ction
pre
s
ent
s a m
e
thodol
ogy to find t
he opti
m
al po
sition
s of Var so
urces o
n
an
existing po
wer network, these positio
n
s
or no
des
i
s
con
s
ide
r
ed
as the we
akest node
s in
th
e
system. Th
e obje
c
tive of optimal po
siti
ons of
Va
r source
s is to
optimize
a certain o
b
je
ctive
function
such as co
st, loss, and voltage stab
ilit
y index while satisfying
all operatio
nal
constrai
nts.
The optimization of voltage stability in
dex is i
n
cluded in the
obj
ective function to
improve
syst
em voltage st
ability. In this contex
t the general optimi
z
ation p
r
obl
e
m
can be
writ
te
n
in the following form:
11
NG
NB
iL
O
S
S
m
n
ii
M
in
f
f
P
L
(2)
Whe
r
e,
f
i
is the fuel co
st of the
i
th
generat
or.
The fuel co
st
curve i
s
mod
e
l
ed by qua
dratic functio
n
as:
2
ii
i
G
i
i
G
i
f
ab
P
c
P
(3)
In this equ
ation,
P
Gi
is the actu
al po
wer p
r
odu
ce
d i
n
the gen
erator
i
.
a
i
,
b
i
an
d
c
i
are
the invariant factors and
NG
is the nu
mber of gen
erato
r
s in the system.
The active po
wer lo
sse
s
are expre
s
sed fr
om the eq
ua
tion of active power bal
an
ce:
L
OS
S
g
i
l
j
iN
G
j
N
L
P
PP
(4)
L
mn
is the line voltage stabil
i
ty index and
NB
is the nu
mber of b
r
an
che
s
in the p
o
we
r syste
m
.
The e
quality
and i
nequ
ality con
s
trai
nts to be
satisfi
ed
while
se
a
r
chi
ng fo
r th
e
optimal
solutio
n
ca
n be written a
s
:
1
1
co
s
s
i
n
sin
c
os
NB
g
i
d
i
i
j
ij
ij
ij
ij
j
NB
g
id
i
i
j
i
j
i
j
i
j
i
j
j
PP
U
U
G
B
QQ
U
U
G
B
(5)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 712
3
– 7130
7126
The sy
stem inequ
ality ope
ration con
s
tra
i
nts incl
ude:
mi
n
m
a
x
g
i
gi
gi
PP
P
(6)
mi
n
m
a
x
gi
gi
gi
QQ
Q
(7)
mi
n
m
a
x
D
GD
G
D
G
QQ
Q
(8)
mi
n
m
ax
ii
i
VV
V
(9)
Whe
r
e,
NB
i
s
the numb
e
r
of buses;
P
gi
and
Q
gi
a
r
e t
he a
c
tive and
rea
c
tive po
wer ge
ne
ration
s at
i
th
bus;
P
li
and
Q
li
a
r
e the
active an
d re
active po
we
r
deman
ds at
i
th
bus;
P
i
and
Q
i
are the
act
i
ve
and re
active
power inje
ctio
ns at
i
th
bus;
δ
ij
is the deference betwee
n
voltage ang
les at bu
s
i
and
j
.
4. Diffe
ren
t
ia
l Ev
o
l
ution Based Op
tima
l Location of Var Sources
Differential E
v
olution (DE
)
is a pop
ulatio
n
based alg
o
rithm prop
ose
d
by Strom and Price
(199
5) [2
1] whose mai
n
st
rategy is to
ge
nerate
a p
o
sit
i
on for
an in
di
vidual with th
e help
of vect
or
differen
c
e am
ong othe
r ra
n
domly sele
cte
d
membe
r
s of
the populatio
n.
The advanta
g
e
of DE can b
e
summ
ari
z
e
d
as follo
ws [
22, 23]:
DE is
an
effec
t
ive, fas
t, s
i
mple, robus
t,
inhe
re
ntly parall
e
l, a
nd ha
s fe
w cont
rol
para
m
eters
need little tu
ning. It ca
n
be u
s
ed
to
minimize no
n-continu
o
u
s
, non
-line
a
r,
non-
differentiabl
e
sp
ace fun
c
tions,
also it
can
work
with nois
y
, flat, multi-
dim
e
n
s
ion
a
l, and
time
depe
ndent o
b
j
ective functio
n
s an
d co
nstraint optimiz
ati
on in co
njun
ction with pen
alty functions.
The optimi
z
at
ion pro
c
e
s
s in DE is carrie
d out usin
g the followin
g
st
eps:
Step 1:
Initi
a
lizatio
n of power flow
data and DE c
ontrol pa
ramete
rs
su
ch as the si
ze of
popul
ation (NP), the m
a
ximum num
ber of ite
r
ati
on, the mut
a
tion facto
r
(F); the
cro
s
sove
r factor (CR)
and t
he numb
e
r of
variable
s
to be optimized
(D).
Step 2:
Initi
a
lizatio
n of popul
ation: T
he initial po
pulation i
s
g
enerated ran
domly usi
n
g
the
followin
g
equ
ation:
(0
)
0
,1
L
uL
ij
j
j
j
x
xr
a
n
d
x
x
Whe
r
e
x
ij
is t
he variabl
e that shoul
d b
e
optimize
d
(the exact location whe
r
e i
t
will b
e
installe
d the
Var sou
r
ce (
L
oad
Bus
e
s
)), and
u
j
x
,
L
j
x
are the
lowe
r an
d the
uppe
r b
ound
(the bu
se
s of powe
r
network ex
cept where t
he g
e
n
e
rato
rs a
r
e i
n
stalle
d). Th
e rand
om
numbe
r
ra
nd (0,
1)
is u
n
iformly distribute
d
in interval (0, 1).
Step 3:
evaluate the
fitness for ea
ch
individual
in
the p
opulati
on a
c
cording
to the o
b
je
ctive
function.
Step 4:
creat
e a new p
opu
lation by:
a)
Mutation
: Fo
r each target
vector
a mut
ant vecto
r
i
s
gene
rated
a
c
cording
to foll
owing
equatio
n:
12
3
1,
ir
r
r
vg
x
g
F
x
g
x
g
Whe
r
e
1
,
2
,
3
1
,
2
,
...
,
rr
r
N
P
intege
r, mutually different
and
F
> 0, th
e rand
omly ch
osen
integers
r
1
, r
2
and r
3 a
r
e
also
cho
s
en t
o
be different
from the run
n
ing index
i
.
F
is a real
con
s
tant fact
or usually wit
h
in ran
ge of [0.4 1.0].
b)
Cro
s
so
ve
r
: In orde
r to i
n
cre
a
se the
di
versity of th
e
pertu
rb
ed
p
a
ram
e
ter ve
ctors,
cro
s
sove
r is i
n
trodu
ce
d. To this end,
th
e trial vector i
s
forme
d
, wh
ere:
1 i
f
0
,
1
o
r
1
ot
herzi
s
e
ij
r
a
n
d
ij
ij
vg
r
a
n
d
C
R
j
j
ug
xg
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Wea
k
e
s
t Buses Identification and
Ran
k
i
ng in
Large P
o
we
r Tra
n
sm
i
ssi
on… (M. Am
roune)
7127
Whe
r
e
ran
d
j
is a
ran
domly
ch
ose
n
ind
e
x to en
su
re tha
t
the trail ve
ctor
u
ij
do
es
not
dupli
c
ate
x
ij
.
CR
i
s
the
cro
s
sover
con
s
t
ant whi
c
h
ha
s to be dete
r
mi
ned by the
user in th
e
rang
e of [0 1].
c)
Selection
:
th
e trial
vecto
r
is compa
r
ed
to the
targe
t
vector an
d
the bette
r o
n
e
is
sele
cted into
the next gene
ration a
s
follo
ws:
'
1,
i
f
f
1
1
, o
t
h
e
r
z
i
s
e
ii
i
i
i
g
gf
g
xg
g
uu
x
x
Whe
r
e
'
i
x
is the offspring of
i
x
for the next generation.
Step 5:
en
d of the pro
c
e
s
s an
d save the be
st indivi
dual
(optimal
locatio
n
of Var sou
r
ce) if the
stoppi
ng crite
r
ion is
satisfie
d, else go b
a
ck to ste
p
4.
The DE co
ntrol paramete
r
s
are set a
s
fo
llo
w: th
e
num
ber of
popul
ation i
s
20; th
e
mutation fac
t
or
F
= 0.
8;
t
h
e
cro
s
sov
e
r f
a
ct
or
CR
= 0.8
and the iterati
on numb
e
r i
s
150.
5. Simulation Resul
t
s an
d Discus
s
io
n
The
solutio
n
s
results fo
r
optimal lo
cati
on of
rea
c
tive po
we
r
sou
r
ce
s to
mini
mize th
e
fitness fun
c
tio
n
mentione
d above in obje
c
tive to
fi
nd the weakest buses for IEEE 30, 57 and 118
power sy
ste
m
s are obtain
ed and di
scu
s
sed bel
ow.
T
he impo
rtan
t paramete
r
value
s
of IEEE 30,
57 and 1
18 te
st system
s are given in Ta
ble 1 and
the
detailed p
a
ra
meters are li
sted in [24].
Table 1. Important Data of IEEE Standard Test Systems
IEEE test
sy
st
em
s
Num
b
er o
f
genera
tors
Num
b
er o
f
lines
Num
b
er o
f
loads
Total
P
D
(MW
)
Total
P
Q
(MV
A
r
)
Num
b
er o
f
Transf
ormer
tapin
g
s
Num
b
er o
f
shun
t
capacit
a
nce
s
30 Bus
6 41
24
283.4
126.2
4
2
57 Bus
7 80
50
1251.8
3364
15
3
118 Bus
54 186 64
3678
1438
9
15
5.1. Dete
rmination of
We
ak Bus
es in 30-b
u
s Tes
t
Sy
stem
The IEEE 30-bus test syst
em co
nsi
s
ts
of six generat
o
rs
at
buses
1, 2, 5, 8, 11 and 13.
The
system
has 41 t
r
an
smissi
on li
ne
s and
24 l
oad
s. The
total
system loa
d
i
s
283.4
MW.
The
co
st
coef
fi
c
i
ents
for 30-bus s
y
s
t
em are tak
e
n from [25].
Figure 2 depi
cts the IEEE
30-bus test system
load curve (hourly l
oad curve),
where is
divided into t
w
o different
perio
ds, i.e.
pea
k pe
riod
and off-p
e
a
k
perio
d. Figu
re 3 and
Figu
re 4
sho
w
re
spe
c
t
i
vely the po
wer g
ene
ratio
n
and
sy
stem voltage
ma
gn
itudes
for pe
ak and
off-pe
ak
perio
ds. It i
s
ob
serve
d
th
at more the
n
allo
we
d le
vel of loa
d
i
n
crea
sing,
p
o
we
r g
ene
rat
i
on
increa
sed
an
d voltage
at
all bu
se
s dro
pped. Figu
re
5 sho
w
s
th
e
L
mn
ind
e
x in
the n
o
rm
al
and
heavy load condition
s (p
e
a
k pe
riod
). It can be
se
e
n
that the L
mn
incre
a
sed
whe
n
the system
operate in th
e heavy load
conditio
n
s, f
o
r this
rea
s
o
n
it is more pra
c
tical to fi
nd the wea
k
est
buses at he
a
vy load condit
i
ons.
Figure 2. IEEE 30-bu
s System Load Curve
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 712
3
– 7130
7128
Figure 3. Power
Gene
rati
on
Figure 4. Voltage Mag
n
itud
es
Figure 5. L
mn
Index in Normal and Hea
vy Load Con
d
itions
In this
su
bse
c
tion
DE o
p
timization
techniqu
e i
s
u
s
ed to
define
the b
e
st l
o
cation to
provide
de
sired re
active
power
sup
p
o
r
t unde
r h
e
a
vy load con
d
itions. Th
e
find bu
se
s a
r
e
con
s
id
ere
d
a
s
the
wea
k
e
s
t buses in th
e sy
stem
fro
m
the p
o
int o
f
view of volt
age
stability.
The
result of th
e
wea
k
e
s
t b
u
s
ran
k
ing
un
de
r heavy lo
ad
condition
s
obt
ained
is presented i
n
T
abl
e 2.
The b
u
ses a
r
e
ran
k
e
d
st
arting
with t
he mo
st
criti
c
al
bu
s which is the b
u
s 30. Th
e results
obtaine
d fro
m
the metho
d
pro
p
o
s
ed i
n
Ref. [26-2
8
] are u
s
e
d
for ma
king
a
comp
ari
s
o
n
with
those re
sults obtaine
d
from
the
propo
sed
method. F
r
o
m
Table
2,
we co
ncl
ude th
at the propo
sed
method
ca
n
efficiently ide
n
tify the we
a
k
e
s
t bu
se
s.
Figure 6
sho
w
the
wea
k
e
s
t area i
n
th
e
system, from
this figure
we
can ob
se
rve that this
area
has not in
clu
ded any ge
ne
rators an
d it is
remote
from
the g
ene
rato
r
buses. In
oth
e
rwi
s
e
the
bu
se
s 3
0
, 26
an
d 29
are all
a
t
the en
d of t
he
radial n
e
two
r
k, they are re
quirin
g
the re
active po
wer
comp
en
satio
n
.
Table 2.
Weak
es
t Bus
e
s
Rank
ing under
Heavy Loa
d Conditions
in IEEE 30-bus
Sys
t
em
Ref [26]
30, 26, 29, 25
, 2
7
Ref [27]
30, 26, 29, 14
, 2
3
Ref [28]
30, 26, 29, 19
, 2
0
Proposed metho
d
30, 26, 29, 21
, 2
4
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Wea
k
e
s
t Buses Identification and
Ran
k
i
ng in
Large P
o
we
r Tra
n
sm
i
ssi
on… (M. Am
roune)
7129
Figure 6. Weak
es
t Area in
IEEE 30-bus
Sys
t
em
5.2. Dete
rmination of
We
ak Bus
es in 57-b
u
s and 1
18-b
u
s Tes
t
Sy
stems
In this case,
the propos
ed method is applied on
the IEEE 57-bus and IEEE 118-bus
system
s [2
5]. Based o
n
DE optimizatio
n techniq
ue
t
he first five
weakest
bu
se
s are
p
r
e
s
ente
d
in
Table
3. For IEEE 57-bus
sys
tem the
weak
area is
recovered the following bus
e
s
:
37, 15, 31, 52
and
13. Th
e
se
co
nd te
st
syste
m
can
be
reg
a
rde
d
a
s
a
re
ali
s
tic t
r
an
smi
s
sion
level p
o
wer
netwo
rk in te
rms of
num
be
r of n
ode
s
an
d bran
ch
e
s
. It co
nsi
s
ts of 1
18 n
ode
s
and
186
bran
che
s
but usin
g the
propo
se
d m
e
thod the ide
n
tification an
d ran
k
ing of
wea
k
e
s
t bu
ses can only take a
few of minute
s
. For thi
s
te
st system th
e
follo
wing
bu
se
s 95, 63, 2
2
, 94 and
10
1 are
defined
as
the wea
k
e
s
t buses.
Table 3. Weakest Buses Ranki
ng under
Hea
vy Load Conditions in IEEE 57-bus
and IEEE 118-
bus Te
st Systems
Test s
y
stem
Weakest buses
IEEE 57-bus
37, 15, 31, 52
, 1
3
IEEE 118-bus
95, 63, 22, 94
, 1
01
6. Conclusio
n
Differential
Evolution Ba
se
d Optimal
Lo
cation
of re
active powe
r
su
pport
s
(V
ar
source
s)
is proposed t
o
identify the
weak
est buses for different
IEEE standa
rd test
system
s. The weakes
t
buses id
entification p
r
obl
e
m
is model
ed
as optim
ization pro
b
lem
consi
deri
ng th
e voltage sta
b
ility
of po
wer sy
stem. The
scheme
optimi
z
e
s
the
cost,
the p
o
wer l
o
sse
s
a
nd t
he lo
ad volt
age
stability inde
x to find the
bu
se
s were
the Va
r sou
r
ce
s to
be
in
stalled,
and t
hese bu
se
s
are
c
o
ns
idered as
the
weakest bus
es
in the s
y
s
t
em. Simulations
were performed on IEEE 30,
57
and 1
18 b
u
s system
s. Th
e sim
u
lation
results
aut
he
nticate the
ef
fectivene
ss
o
f
the pro
p
o
s
ed
method.
Referen
ces
[1] Kund
ur
P.
Power System Sta
b
ility an
d Co
ntrol,
EPRI Po
w
e
r
S
y
stem Engi
n
eeri
ng Seri
es, McGra
w
-
Hil
l,
199
4. ISBN 0-07-0
359
58-
X.
[2] Liu
Z
h
uo.
The
i
m
p
e
d
ance
an
a
l
yses of h
eavy
loa
d
n
ode
in v
o
ltag
e stab
ility
studies
, Proc
e
edi
ngs
of th
e
CSEE. 2000; 2
0
: 35-39.
[3]
Coel
ho LS, Le
e CS.
Solvin
g econ
o
m
ic lo
ad
dispatch pr
obl
ems i
n
pow
er systems usi
n
g
chaotic a
n
d
Ga
u
ssi
an
pa
rticl
e
swa
r
m
op
tim
i
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on
ap
p
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e
a
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pow
er
pla
n
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i
ng
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e
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r
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on
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i
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par
u V,
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y C.
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he contin
uati
on p
o
w
e
r
fl
ow
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ol for
stea
dy st
ate vo
ltag
e sta
b
ility
an
alysis
.
IEEE
T
r
ans Pow
e
r S
y
st. 19
92
; 7(1): 416–
23.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 712
3
– 7130
7130
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I Musirin, T
KA Rahm
an.
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o
v
e
l F
a
st Vo
ltag
e Stabi
lity In
d
e
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VSI
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e Stab
ili
ty Analysis
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n
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e
r T
r
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ssion Syste
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n
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e
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r
ch
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e
ve
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h
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b
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o
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e Stabi
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ani
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ans
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a
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a
r
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e
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nti
nge
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eni
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w
e
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ems.
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n
u
w
att
a
naku
l
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a
m
m
ad AS
Maso
um.
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ati
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e
akest Bus
e
s i
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ba
lanc
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d
Multip
hase
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m
art Gri
d
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t
h Plu
g
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e
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ee. Id
enti
fi
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on
of
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d
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abil
i
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lim
it an
d
w
e
ak b
u
ses
usin
g sec
u
rit
y
c
onstrai
nt
gen
etic al
gorith
m
.
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e
r and En
er
gy Systems
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012; 36: 4
0–5
0
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BF
W
o
llen
berg
.
T
r
ansmission
s
y
stem re
activ
e
po
w
e
r com
p
ensati
on.
IEEE
Pow
e
r Engi
ne
erin
g Soci
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i
nter Meetin
g
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[12]
T
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