Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 2
,
A
p
r
il
201
5, p
p
.
18
9
~
19
7
I
S
SN
: 208
8-8
7
0
8
1
89
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
Voltage Stability Analysis and
Stability Improvement of Power
System
Pavithren
Th
annim
a
lai,
Raman
Raghu
Ram
a
n, Prata
p
N
a
ir,
K.
N
i
t
h
i
y
anant
h
a
n
Faculty
of
Engin
eering
and
Computer
Technolog
y
,
AIMST University
Bedong, Kedah,
Malay
s
ia
Em
ail:
prat
aps
a
m
r
at@gm
a
il.co
m
,
ram
a
n_ragur
am
an@aim
s
t
.ed
u
.m
y
,
nith
ii
eee
@
y
ahoo
.co
.
in
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 22, 2014
Rev
i
sed
Jan 26, 201
5
Accepted
Feb 10, 2015
The m
a
in objec
ti
ve of this researc
h
work
is to analysis the volt
a
ge
stabili
t
y
o
f
the power
s
y
stem network and
its im
provement in
the netw
ork voltage
s
t
abili
t
y
of a po
wer s
y
s
t
em
. A
s
y
s
t
em
ente
rs
a
s
t
ate of vol
tag
e
ins
t
abi
l
i
t
y
when a disturb
a
nce,
incr
ease
in
load dem
a
nd
, or
change
in s
y
s
t
e
m
condition
causes a progr
essive and an
uncontroll
able
drop in voltage or voltag
e
coll
aps
e
. Th
e co
ntinuing in
cre
a
s
e
in
demand for
electric power
has resulted
in an
increasing
l
y
complex, in
ter
c
onnect
ed
s
y
stem, forced
to
op
erate
closer
to the lim
its of the stabili
t
y
. T
h
is has necessit
a
ted th
e im
ple
m
entation of
techn
i
ques for analy
z
ing and detecting vol
tage
collapse in bus bar or lines
prior to
its o
c
c
u
rrence
.
Sim
p
le
Ne
wton Raphs
on algorithm based voltag
e
stabili
t
y
an
al
ysis
has been
c
a
rrie
d
out. Ma
tl
ab b
a
sed sim
u
lations
for al
l th
e
factors
that
c
a
uses voltag
e
instab
ilit
y
has be
en
im
plem
ented
and
a
n
al
yz
ed for
an IEEE 30 bus s
y
stem. Th
e pro
posed m
odel is able to
iden
tif
y t
h
e behav
i
or
of the pow
er s
y
s
t
ems, network u
nder va
r
i
ous voltage stabi
lit
y co
nditions
an
d
its possibilit
y
of recov
e
r
y
/sta
bilit
y
im
prove
m
e
nt of the
p
o
wer s
y
stem
network has
been discussed.
Keyword:
Co
n
tinu
a
tion
Po
wer flo
w
a
n
aly
s
is
Power system
Reactive powe
r
Vo
ltag
e
co
llapse
Vo
ltag
e
stab
ility
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Dr K.
Nith
iyanan
th
an
Faculty of Elec
trical an
d
C
o
m
put
e
r
E
ngi
neer
i
ng,
AIMST Un
iversity
Bed
ong
, K
e
d
a
h
e
m
ail: n
ith
iiee
e
@yaho
o
.co.in, n
ith
i
@
aim
s
t.e
d
u.m
y
1.
INTRODUCTION
The voltage sta
b
ility problem
is now a se
rious conce
r
n to the electric utility
industry. Ele
c
tric power
u
tilities to
d
a
y are faci
n
g
m
a
n
y
ch
allen
g
e
s
du
e to ev
er-i
n
c
reasin
g
co
m
p
lex
ity in
th
eir
operatio
n and
st
ru
cture.
In the
rece
nt years,
one
of t
h
e probl
em
s that receive wi
de
attention is
the
voltage i
n
stabilit
y. W
ith a
n
ope
n-
access m
a
rket, poorly sc
heduled gene
ration
for the
c
o
m
p
et
itive bidding i
s
one
of m
a
ny reasons
for
voltage
in
stab
ility p
r
ob
lem
in
th
e d
e
regu
lated
elect
ricity en
v
i
ro
nmen
t. Thu
s
, in o
r
d
e
r to
relieve o
r
at least min
i
m
i
ze
th
e syste
m
fro
m th
e v
o
ltag
e
in
stab
ility p
r
ob
lem
m
a
n
y
e
l
e
c
tric u
tilit
ies a
n
d
research
ers h
a
v
e
d
e
vo
ted
a g
r
eat
d
eal o
f
efforts in
syste
m
st
u
d
i
es related
t
o
static v
o
ltag
e
stab
ility.
In th
e static
v
o
ltag
e
stab
ility
stu
d
y
,
C
ont
i
n
uat
i
o
n
Po
wer
Fl
o
w
(
C
PF) a
n
d
o
p
t
i
m
i
zat
i
on
m
e
t
hods
are t
h
e m
a
i
n
anal
y
s
i
s
t
echni
que
s an
d t
h
ey
ar
e
u
s
ed
to
find
vo
ltag
e
stab
ility
m
a
rg
in
o
r
l
o
ad
ing
m
a
rg
in
(LM) of th
e sy
ste
m
. U
tilit
ies an
d researchers are
devel
opi
ng s
o
f
t
ware ba
sed
on
t
h
ese t
echni
qu
es, fo
r t
h
e st
ud
y
.
The C
PF t
e
c
hni
que i
n
v
o
l
v
e
s
i
n
sol
v
i
ng a s
e
ri
es
o
f
l
o
ad
flow calcu
l
atio
n
with p
r
ed
ictor and
co
rrector
steps
.
The
optim
i
za
tion tech
n
i
qu
e
in
vo
lv
es i
n
so
lv
ing
equat
i
o
ns
of
n
ecessary
co
ndi
t
i
ons ba
sed
on
an o
b
j
ect
i
v
e f
u
nct
i
on a
n
d co
n
s
t
r
ai
nt
s. M
a
ny
l
a
rge i
n
t
e
rc
o
n
n
ect
ed
po
we
r sy
st
em
s are ex
peri
e
n
ci
ng a
b
n
o
rm
all
y
hi
gh o
r
l
o
w v
o
l
t
a
ges a
n
d v
o
l
t
a
ge col
l
apse. T
h
ese
v
o
l
t
a
ge
problem
s
are associated
with
th
e in
creased
l
o
ad of tran
sm
i
ssio
n
lin
es
, in
su
fficien
t
lo
cal
reactiv
e su
pp
ly
, and
th
e sh
ipp
i
ng
of
p
o
wer acro
s
s lo
ng
d
i
stan
ces. Th
e
h
eart
of th
e
vo
ltag
e
st
ab
ility p
r
ob
lem
is th
e vo
ltag
e
d
r
op
th
at o
ccurs when
th
e po
wer syste
m
ex
p
e
rien
ces a h
eav
y
lo
ad, and
on
e seriou
s typ
e
o
f
v
o
ltag
e
instab
i
lity
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Vo
ltag
e
S
t
ab
ility Ana
l
ysis and S
t
ab
ility Imp
r
o
vem
en
t
o
f
Power S
y
stem
(D
r K. Nith
iyan
an
t
h
an
)
19
0
v
o
ltag
e
co
llapse.
Vo
ltag
e
collap
s
e is ch
aracterized
b
y
an in
itial slo
w
prog
ressiv
e
d
e
clin
e in
t
h
e
voltag
e
m
a
gni
t
ude
o
f
t
h
e p
o
w
er sy
st
em
buses a
nd
a fi
nal
ra
pi
d
d
ecl
i
n
e i
n
t
h
e v
o
l
t
a
ge m
a
gni
t
u
de. T
h
e t
r
i
p
pi
ng
of
fai
r
l
y
sm
all
g
e
nerat
o
rs
co
ul
d, i
f
t
h
ey
are
pl
ace
d i
n
p
o
s
i
t
i
ons t
h
at
ne
ed
vol
t
a
ge s
u
pp
o
r
t
(
vol
t
a
ge
wea
k
positions), cause a large inc
r
ease of
reactive power l
o
sses in the transm
ission
ne
twork. This causes large
v
o
ltag
e
drop
s
wh
ich
can g
e
nerate stab
ility
p
r
ob
lem
s
.
Two ex
am
p
l
es are th
e 197
0 New
York d
i
sturb
a
nce and
the disturbanc
e at Zealand i
n
De
nm
ark 1979. In the
Ne
w Y
o
r
k
di
st
u
r
bance
,
an
i
n
cr
eased l
o
a
d
i
n
g
on t
h
e
t
r
ansm
i
ssi
on sy
st
em
and a t
r
i
ppi
ng
of a
3
5
M
W
ge
nerat
o
r
resul
t
e
d i
n
a p
o
st
-c
ont
i
n
ge
nc
y
vol
t
a
ge
decl
i
n
e.
At
Zealan
d, a tr
ipp
i
ng
o
f
th
e only u
n
it in th
e
so
u
t
h
e
rn
p
a
r
t
o
f
th
e islan
d
p
r
od
u
c
i
n
g 270 M
W
cau
s
ed
a slow
vol
t
a
ge
decl
i
n
e i
n
t
h
at
pa
r
t
. Aft
e
r
1
5
m
i
nut
es t
h
e
vol
t
a
ge
s ha
d
decl
i
n
ed
t
o
0
.
7
5
p
u
, m
a
ki
ng t
h
e
sy
nch
r
o
n
i
zat
i
o
n
of
a
70
M
W
gas t
u
r
b
i
n
e
i
m
pos
si
bl
e. B
o
t
h
sy
st
em
s were s
a
ved
by
m
a
nual
l
o
ad
she
d
di
n
g
.
The
col
l
a
pse i
n
C
a
nada
, i
n
B
.
C
Hy
dr
os
n
o
rt
h c
o
ast
re
gi
o
n
i
n
J
u
ly 19
79
is also
in
teresting
in th
is resp
ect
[1, 2
,
3
]
.
A lo
ss of 100
M
W
lo
ad
al
o
n
g
a tie-lin
e con
n
ection
resu
lt
ed
in
an
in
crease
d active power tra
n
sfer
b
e
tween
th
e two
system
s. Th
e g
e
n
e
rat
o
rs close to
t
h
e in
itial lo
ad lo
ss area
were on
m
a
n
u
al ex
citatio
n
co
n
t
ro
l
(constant field current
)
, whic
h agg
r
av
ated the situ
atio
n.
When
v
o
ltag
e
s started
t
o
fall al
on
g th
e tie-lin
e
d
u
e
to
the increase
d
powe
r trans
f
e
r
, the c
o
n
n
ect
ed l
o
a
d
dec
r
ea
sed p
r
op
ort
i
on
al
l
y
t
o
t
h
e vo
l
t
a
ge sq
uare
d.
Thi
s
in
creased
th
e tie-lin
e tran
sm
i
ssio
n
ev
en m
o
re since there
was no reduct
i
o
n
in
th
e active p
o
wer pro
ductio
n
.
Abou
t on
e m
i
n
u
t
e after t
h
e initial co
n
tin
g
e
ncy, th
e vo
ltag
e
in
th
e m
i
d
d
l
e
o
f
t
h
e tie-lin
e
fell to
app
r
o
x
i
matel
y
0
.
5
Pu
an
d
th
e
tie-lin
e was trip
p
e
d
du
e to
over cu
rren
t at
one end and due to a distan
ce rel
a
y at
the other. The
h
eart
o
f
th
e
voltag
e
stab
ility p
r
ob
lem
is th
e
vo
ltag
e
d
r
op
th
at o
c
curs
when
th
e power
syste
m
ex
p
e
rien
ces a
h
eav
y lo
ad
, and
on
e seri
o
u
s
t
y
p
e
o
f
v
o
ltag
e
in
stab
ility is v
o
ltag
e
co
llapse. Vo
ltag
e
co
llap
s
e is ch
aracterized
b
y
an in
itial slo
w
pro
g
ressive d
eclin
e in the vo
ltag
e
m
a
g
n
itu
d
e
o
f
t
h
e
po
wer system
b
u
s
es and
a fi
n
a
l rapi
d
decline in the
voltage
m
a
gnitude
.
nam
e
d after Isaac
Ne
wton
and J
o
se
ph Raphson,
is a
m
e
thod
for
findi
ng
successi
vel
y
b
e
t
t
e
r ap
pr
o
x
i
m
at
i
ons t
o
t
h
e r
o
ot
s (
o
r ze
roes
)
of
a
real
-v
al
ue
d
fu
nct
i
o
n.
I
n
t
h
e
pr
o
pose
d
v
o
l
t
a
ge
stab
ility an
aly
s
is th
e
Newto
n
–
R
ap
h
s
on
meth
o
d
h
a
s
b
een im
p
l
e
m
e
n
ted
b
ecau
s
e of its accu
r
acy in
approxim
a
tion. In voltage stability, accur
acy in predicting
the voltage m
a
rgi
n
is critical
because low ac
curac
y
may lead
to
fat
a
lity o
f
th
e
who
l
e system
.
2.
R
E
SEARC
H M
ETHOD
Th
e h
e
art o
f
t
h
e vo
ltag
e
stab
ility p
r
o
b
l
em is th
e v
o
ltag
e
d
r
op
th
at o
c
cu
rs
wh
en
th
e
p
o
wer syste
m
expe
riences
a
heavy loa
d
, there are
few t
o
ols can
be
us
ed
to
sim
u
late t
h
e power syst
e
m
lo
ad
flow. In
t
h
e
static v
o
ltag
e
stab
ility stu
d
y
, Co
n
tinu
a
tion Power Fl
o
w
(CPF) and
op
ti
m
i
zatio
n
meth
od
s are t
h
e
m
a
in
an
alysis tech
n
i
q
u
e
s and
th
ey are u
s
ed
to
fi
nd
vo
ltag
e
stab
i
lity
marg
in
o
r
lo
ad
ing
m
a
rg
in (LM) of th
e syste
m
.
Th
e CPF techn
i
qu
e in
vo
lv
es in
so
lv
in
g a series of loa
d
flow calculation
with pre
d
ictor and correct
or
steps.
Th
e op
timizati
o
n
techn
i
qu
e in
vo
lv
es in
so
l
v
ing
equ
a
tio
ns o
f
n
ecessary co
nd
itio
ns b
a
sed
on
an
ob
jectiv
e
function a
n
d c
onst
r
aints. Vol
t
age insta
b
ility occ
u
rs
whe
n
t
h
e reactive power
availabl
e
to a
portion of t
h
e
gri
d
fal
l
s
bel
o
w t
h
a
t
requi
re
d by
c
u
st
om
ers, t
r
ans
m
i
ssi
on l
i
n
es, and t
r
a
n
s
f
o
r
m
e
rs i
n
t
h
at
po
rt
i
on
of t
h
e
gri
d
.
The
p
e
ri
o
d
o
f
"i
n
s
t
a
b
ility" is n
o
t
so
m
u
ch
an
i
n
stab
le as it is th
e b
e
h
a
v
i
o
r
an
d
i
n
teraction
o
f
v
a
ri
o
u
s elemen
ts
fo
llowing
th
e i
n
stan
t wh
en
the reactiv
e shortag
e
first
d
e
v
e
l
o
p
s
and
un
til in
terv
en
tion
o
c
cu
rs, vo
ltag
e
co
llap
s
e
occurs,
or,
hopefully, a stable volta
ge is
reache
d
.
Thi
s
peri
od of "s
low
dynam
i
cs
" involves
ge
nerat
o
r
exci
t
a
t
i
on l
i
m
i
t
i
ng co
nt
r
o
l
s
,
on
-l
oa
d t
a
p c
h
ange
rs,
op
erat
or act
i
o
ns, a
n
d
t
h
e resp
o
n
se
of c
u
st
om
er l
o
ads t
o
decaying voltage (e
.g., the
r
mostats an
d m
a
nual activities that respond to
th
e decaying
voltage a
nd atte
m
p
t
to
restore the loa
d
to its origi
n
a
l
dem
a
nd in spite of decayi
n
g voltage).
As
voltage decays, the
resulting drop
in
cust
om
er l
o
ad
al
l
o
ws c
ont
i
nue
d
ope
rat
i
o
n.
Ho
we
ver
,
t
h
e act
i
o
n o
f
di
st
ri
b
u
t
i
o
n
t
r
ansf
o
r
m
e
r on-
l
o
ad
-t
ap
change
rs and s
e
lf-rest
ori
ng l
o
ad elem
ents pull volta
ge
eve
r
lower.
While voltage m
a
y
stabilize in syste
m
s
w
ith
relativ
ely stron
g
ties to
health
y n
e
ig
hbors,
o
t
h
e
rs w
ill req
u
i
re h
e
ro
ic actio
n
b
y
o
p
e
rat
o
rs
o
r
un
d
e
r
v
o
ltag
e
lo
ad
sh
ed
d
i
n
g
to
prev
en
t
v
o
l
t
a
g
e
co
llap
s
e.
To
ov
erco
m
e
o
r
p
r
ed
ict th
is
v
o
ltag
e
co
llap
s
e,
th
e vo
ltag
e
stab
ilit
y
an
alysis tech
n
i
q
u
e
will b
e
u
s
ed
to
p
r
ed
ict or an
alyze th
e syste
m
. Th
e resu
lt o
f
an
alysis
will b
e
u
s
ed
t
o
g
i
v
e
rem
e
di
al
t
o
pre
v
ent
i
t
fr
om
fu
rt
her
dam
a
ge t
o
t
h
e
sy
st
em
. The a
n
al
y
s
i
s
c
a
n
be
d
one
bas
e
d
on
t
h
e
p
o
w
er fl
ow
eq
u
a
tion
in
p
o
wer system
. B
a
sed
on
th
e
p
o
wer fl
o
w
equ
a
tio
n
,
th
e sim
u
latio
n
will b
e
do
n
e
u
s
ing
Matlab
.
In
th
e sim
u
latio
n
all th
e factors t
h
at cause
v
o
ltag
e
instab
ility can
b
e
im
p
l
e
m
e
n
ted
wh
en an
al
yzin
g
th
e sim
u
latio
n
o
f
vo
ltag
e
stabilit
y. Th
e an
alysis will b
e
do
ne b
a
sed
on
IEEE 30
bu
s system
(Fig
u
r
e
1) [4, 5,
6
,
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
18
9 – 1
9
7
1
91
Fi
gu
re
1.
IEE
E
3
0
bus
sy
st
em
A
s
sh
own
in f
i
g
u
r
e
th
e bu
s
10 and
bu
s
24
h
a
s cap
acitor
b
a
nk
s inj
ecting
r
e
activ
e po
w
e
r
to
su
ppo
r
t
t
h
e
syste
m
. The analysis has be
en carried
out
in four s
ection
s
in
wh
ich
are sectio
n
1
and
section
3
with
the
cap
acito
r b
a
nks
of
bu
s 10
and
bu
s 2
4
su
ppo
r
ting
t
h
e
syst
e
m
an
d
in
th
e sectio
n
2
and
sectio
n
4
w
itho
u
t
th
e
cap
acito
r
b
a
nks. Th
is an
alysis will h
e
lp
t
o
k
now th
e sen
s
itiv
ity o
f
th
e
v
o
ltag
e
stab
ility in
flu
e
n
ced by th
e
cap
acito
r banks in
t
h
e system. Th
e
reactiv
e
p
o
wer (Q)
o
f
each
bu
s
will be in
creased b
y
2
0
%
u
n
til it reach
es
th
e 400
%. Th
en
th
e read
ing
o
f
t
h
e
vo
ltag
e
mag
n
itu
d
e
(V
) of the
bus a
nd the
neares
t
bus connected t
o
it has
been t
a
bul
at
ed
and
gra
ph
pl
o
t
t
e
d. Si
m
i
l
a
rl
y sel
ect
ed bus
r
eact
i
v
e po
wer
(Q
) was i
n
c
r
ea
sed si
m
u
l
t
a
neousl
y
,
th
en
t
h
e ch
an
ges to
t
h
e
v
o
ltage m
a
g
n
itu
d
e
(V)
of th
e bu
ses.
3.
VOLTA
GE
S
T
ABILITY C
A
SES A
N
D
SI
MUL
A
TIO
N
RESULTS
Vo
ltag
e
stab
ility an
alysis h
a
s b
e
en
carried
ou
t in
th
e selected
th
e
bu
ses are selected
b
a
sed
o
n
activ
e
po
we
r great
e
r
t
h
an
1
5
M
W
. I
n
t
h
e pro
p
o
se
d po
we
r sy
st
em
net
w
or
k, 5
bus
es t
o
be anal
y
zed are B
u
s 2
,
5
,
7, 8
and
21
. The a
n
al
y
s
i
s
wi
l
l
be done
by
i
n
creasi
ng t
h
e
Q o
n
b
u
s
5. The
dat
a
g
o
i
n
g t
o
anal
y
s
i
s
are, t
h
e i
n
cre
a
se i
n
Q, t
h
e c
h
an
ges
o
n
t
h
e
v
o
l
t
a
ge
m
a
gni
t
ude
of
bus
5
an
d t
h
e c
h
an
ges
o
n
t
h
e
vol
t
a
ge
m
a
gni
t
ude
o
f
bu
s c
o
n
n
ect
ed
to
bu
s 5 wh
ich
ar
e
b
u
s
2 and
bu
s
7
.
Fig
u
r
e
2
.
QV
of
Bu
s 2 w
i
t
h
r
e
activ
e po
w
e
r
i
n
j
ection
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Vo
ltag
e
S
t
ab
ility Ana
l
ysis and S
t
ab
ility I
m
p
r
o
vem
en
t
o
f
Power S
y
stem
(D
r K. Nith
iyan
an
t
h
an
)
19
2
Fig
u
re 3
.
QV Co
m
p
ariso
n
of
Bu
s 2
with
reactiv
e
po
wer
i
n
jectio
n
Bu
s 2
is
a g
e
ner
a
tin
g
bu
s on
th
e
30
bu
s
syst
e
m
s.
These
ge
nerat
i
n
g
b
u
ses
are
usual
l
y
ve
r
y
st
abl
e
an
d
do not
prone t
o
a
n
y voltage
instab
ility. The
initial reactive powe
r l
o
ad a
t
bus
2 was
12.7 M
V
Ar a
n
d i
t
was
increase
d
by
400% till it reach
es
63.5 MVAr. The
voltage
magnitude
is
not affected
m
u
ch as its drops
1.043
V to
1
.
0
1
3
V.
It do
esn
’
t
go
cl
o
s
e t
o
vo
ltag
e
in
stab
ility. Th
e bu
ses conn
ected
t
o
b
u
s
2
are bu
s
4
,
5
an
d
6. Du
e
to
stab
le
vo
ltage at bu
s
2
t
h
ese bu
se
s a
r
e als
o
not
being a
ffe
c
t
ed m
u
ch.
Fig
u
r
e
4
.
QV
of
Bu
s 2 w
i
t
h
out r
eactiv
e
p
o
w
e
r
inj
ection
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
18
9 – 1
9
7
1
93
Fi
gu
re 5.
Q
V
C
o
m
p
ari
s
on
o
f
B
u
s 2 wi
t
h
out
react
i
v
e po
we
r
i
n
ject
i
o
n
It h
a
s b
e
en
iden
tified
th
at there is a sig
n
i
fi
can
t d
r
op
in
th
e vo
ltag
e
m
a
g
n
itud
e
o
f
all th
e an
alyzed
b
u
s
es withou
t th
e reactiv
e
p
o
wer in
j
ecti
o
n
.
Bu
t
b
u
s
2
still ab
le to
o
p
e
rate in
a stab
le con
d
ition
.
If th
is
co
nd
itio
n con
tin
uou
sly for lon
g
ho
urs th
ere
mig
h
t
b
e
so
m
e
d
a
m
a
g
e
to
th
e g
e
n
e
rator
o
f
bu
s
2
as it’s
o
p
erates
at higher loa
d
and produces
m
o
re heat.
Fig
u
r
e
6
.
QV
of
Bu
s 5 w
i
t
h
r
e
activ
e po
w
e
r
i
n
j
ection
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Vo
ltag
e
S
t
ab
ility Ana
l
ysis and S
t
ab
ility I
m
p
r
o
vem
en
t
o
f
Power S
y
stem
(D
r K. Nith
iyan
an
t
h
an
)
19
4
Fig
u
re 7
.
QV Co
m
p
ariso
n
of
Bu
s 5
with
reactiv
e
po
wer
i
n
jectio
n
B
u
s 5
react
i
v
e
po
we
r l
o
ad
wa
s i
n
crease
d
f
r
o
m
19 M
V
Ar t
o
95 M
V
A
r
. T
h
e vol
t
a
ge m
a
gni
t
ude
d
r
o
p
is 1.01 to
0.96
V.
Afte
r the
increas
e of 160%
of
reacti
v
e powe
r whic
h
is
49.4 MVAr t
h
e
voltage m
a
gnitude
of
b
u
s
5 do
es
no
t d
r
op
. Th
is is
du
e to
t
h
e sy
n
c
hr
ono
u
s
cond
enser
co
nn
ected to
b
u
s
5. Syn
c
hr
ono
u
s
cond
enser
i
s
a de
vice that c
a
n inject a
n
d a
b
sorb
reactiv
e
p
o
wer
b
a
sed on
th
e situ
ation
o
f
th
e system
. Th
e
bu
s co
nn
ected
t
o
bus
5 i
s
bus
2
and
7.
The
r
e i
s
no
si
g
n
i
f
i
can
t
dr
op i
n
t
h
e
v
o
l
t
a
ge o
f
bus
2 w
h
er
eby
i
n
t
h
e b
u
s
7 t
h
e
r
e
was a
dr
o
p
but
i
t
bec
o
m
e
const
a
nt
a
f
t
e
r t
h
e
b
u
s
5
v
o
l
t
a
ge m
a
gni
t
u
de
becom
e
co
n
s
t
a
nt
.
Fig
u
r
e
8
.
QV
of
Bu
s 5 w
i
t
h
out r
eactiv
e
p
o
w
e
r
inj
ection
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
18
9 – 1
9
7
1
95
Fi
gu
re 9.
Q
V
C
o
m
p
ari
s
on
o
f
B
u
s 5 wi
t
h
out
react
i
v
e po
we
r
i
n
ject
i
o
n
D
u
e to bu
s 10 and
bu
s
24
do
es
no
t h
a
v
e
an
y d
i
r
ect co
nnectio
n
and
it’
s f
r
o
m
th
e bu
s
5
,
it
do
es
no
t
give a
n
y
noticeable c
h
anges
on the
rea
d
ing
as they a
r
e
almost the
sam
e
. Sim
i
lar analysis has
bee
n
c
a
rried
out
o
n
rem
a
in
in
g
selected
bu
ses t
o
an
alyize th
e
syste
m
's resist
an
ce to
vo
ltage in
stab
ility, it
s cap
acity li
m
i
t, th
e
chan
ges
i
n
t
h
e
vol
t
a
ge
m
a
gni
t
ude
o
f
t
h
e
bus
and
t
h
e e
ffe
ct
on
ot
her
nea
r
es
t
bu
ses c
o
n
n
ect
ed t
o
i
t
.
Figure 10.
QV
Com
p
arison of all the a
n
alyzed
bus
wit
h
reac
tive powe
r i
n
je
ction
Ab
o
v
e gra
p
h s
h
o
w
s t
h
e com
p
ari
s
on
of al
l
t
h
e buse
s
anal
yzed. Here the
reactive powe
r increase
d
until 200%
onl
y com
p
are to t
h
e
400% i
n
cre
a
se in
part
1
a
n
d pa
rt 2. Si
nc
e all the
5 buses
reactive power (Q)
were i
n
crease
d
si
m
u
ltaneously it will give
m
o
re i
m
pact
on the
syste
m
, thus the i
n
crea
se of reactive
powe
r
were l
o
we
re
d t
o
200%. In thi
s
case, as
you
can see
bu
s
6
an
d bu
s
21
were th
e
o
n
l
y bu
ses co
llap
s
ed
w
e
r
e
bu
s
6 collapses at reactive were increased m
o
re than
100%
and bus
21 at 180%. Ove
r
all, the
increase in re
active
p
o
w
e
r
o
f
a bu
s no
t on
ly aff
ect
s its ow
n bu
s,
b
u
t
affects all th
e
b
u
ses co
nn
ected
n
e
arb
y
to
it.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
Vo
ltag
e
S
t
ab
ility Ana
l
ysis and S
t
ab
ility I
m
p
r
o
vem
en
t
o
f
Power S
y
stem
(D
r K. Nith
iyan
an
t
h
an
)
19
6
Fig
u
re
11
.
QV
Co
m
p
ariso
n
of all th
e an
al
yzed bus
es with re
ac
tiv
e po
wer i
n
j
ection
In
th
is case the cap
acito
r b
a
n
k
s
were rem
o
v
e
d
,
thu
s
th
e syste
m
is
m
o
re v
u
l
n
e
rab
l
e to
in
stab
ility.
Here m
o
re buses were colla
pse
d
. T
h
e im
p
act being
se
rved
to
th
e
bu
s
connected
nea
r
by to t
h
e capacitor
b
a
nk
s. As you
can
see
bu
s
1
0
and
bu
s
24
collap
s
ed
w
ith
low
p
e
rcen
tag
e
of in
crease in the reactiv
e
o
f
all th
e
bus
es.
The
pre
v
ent
i
o
n o
f
v
o
l
t
a
ge c
o
l
l
a
pse
has be
en di
vi
de
d i
n
t
o
t
w
o sect
i
o
ns
whi
c
h are t
h
e
sy
st
em
desi
g
n
m
easures.
In t
h
e sy
st
em
desi
gn m
easures,
t
h
e t
h
i
n
g
s
wi
l
l
be l
ooki
ng
i
n
t
o
are t
h
e c
h
an
ges t
h
at
ca
n be
im
pl
em
ent
e
d in t
h
e desi
g
n
o
f
an exi
s
t
i
ng p
o
w
er sy
st
em
or a new p
o
we
r s
y
st
em
t
o
preve
n
t
vol
t
a
ge c
o
l
l
a
pse. I
n
th
e system
o
p
eratin
g m
easu
r
es, th
e th
i
n
g
s
t
h
at
will b
e
l
o
ok
ed in
t
o
b
e
ing th
e m
easu
r
es
can
b
e
tak
e
n
on
an
ope
rat
i
n
g
po
w
e
r sy
st
em
and
pre
v
e
n
t
i
t
fr
om
col
l
a
psi
n
g
[
8
.
9.
1
0
,
1
1
]
.
3.
1 T
h
e
S
y
ste
m
Desi
gn
Me
a
s
ures
(i) Application
of
reactive power-com
p
ensat
i
ng de
vices
•
The si
ze, rat
i
n
gs, l
o
cat
i
o
ns
o
f
t
h
e com
p
ens
a
t
i
ng de
vi
ces
sho
u
l
d
be
bas
e
d o
n
a det
a
i
l
e
d st
u
d
y
of t
h
e
syste
m
d
u
r
i
n
g
all d
i
fferen
t
syste
m
co
nd
itio
ns
•
The desi
g
n
o
f
com
p
ensat
i
n
g
devi
ces
cri
t
e
ri
a
sh
oul
d be base
d on
m
a
xim
u
m
al
l
o
wa
bl
e
v
o
l
t
age dr
o
p
•
Recognize the
voltage
contro
l
areas a
n
d the
weak tra
n
sm
is
s
i
o
n
bo
und
ar
ies of
th
e system
•
There
are
di
ffe
rent ty
pes
o
f
re
active powe
r c
o
m
p
ensating devices:
Shu
n
t
cap
acitor,
regu
lated
shu
n
t
co
m
p
en
satio
n, series cap
a
cito
r
(i
i
)
C
o
or
di
nat
i
on
o
f
pr
ot
ect
i
o
n/
co
nt
r
o
l
s
•
Lack
o
f
c
o
o
r
di
nat
i
o
n
bet
w
een e
q
ui
pm
ent
pr
ot
ect
i
o
ns/
c
ont
rol
s
an
d
p
o
we
r sy
st
em
re
qui
rem
e
nt
s.
Ade
q
uat
e
co
o
r
di
nat
i
o
n s
h
oul
d
be e
n
s
u
re
d
b
a
sed
o
n
dy
nam
i
c sim
u
l
a
t
i
on st
udi
es
.
•
Tripp
i
ng
o
f
equ
i
p
m
en
t to
prev
en
t an
ov
erl
o
ad
ed cond
itio
n sho
u
l
d
b
e
the l
a
st reso
rt.
Wherev
er
po
ssib
l
e,
adeq
uat
e
c
ont
rol
m
easures
(aut
om
ati
c
or m
a
nual
)
s
h
o
u
l
d
be
pr
ovi
de
d f
o
r rel
i
e
vi
n
g
t
h
e
o
v
erl
o
a
d
co
nd
itio
n befo
re iso
l
atin
g t
h
e equ
i
p
m
en
t from
th
e syste
m
.
(iii) Con
t
ro
l
of
tran
sform
e
r tap
ch
an
g
e
r
•
Tap c
h
ange
rs
can be
controlled, eithe
r
local
ly or cent
r
ally, so
as t
o
red
u
c
e th
e risk
of
vo
ltag
e
co
llap
s
e.
Whe
r
e t
a
p c
h
angi
ng i
s
dam
a
gi
n
g
, a si
m
p
le
m
e
t
hod i
s
t
o
bl
o
c
k t
a
p c
h
an
gi
n
g
w
h
e
n
t
h
e sou
r
ce si
de
vol
t
a
ge
d
r
ops
,
and
u
n
b
l
o
c
k
w
h
en
t
h
e
v
o
l
t
a
ge
rec
ove
rs.
•
M
i
crop
r
o
cess
o
r-
base
d ULTC
cont
r
o
l
s
o
ffe
r vi
rt
ual
l
y
unl
im
it
ed fl
exi
b
i
l
i
t
y
for im
pl
em
ent
i
ng UL
T
C
cont
rol
st
rat
e
gi
es so
as t
o
t
a
ke
ad
vanta
g
e
of the loa
d
c
h
a
r
acteristics.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 2, A
p
ri
l
20
15
:
18
9 – 1
9
7
1
97
3.
2 T
h
e
S
y
ste
m
Oper
ati
n
g
Mea
s
ures
(i) Stab
ility
m
a
rg
i
n
•
The system
shoul
d
be
ope
rat
e
d
with a
n
acc
eptable
volta
ge
stability
•
There a
r
e at present
no
wide
ly accepted guidelines fo
r se
lection of the
degree
of m
a
rgin
before t
h
e
syste
m
goes
unstable
•
For exam
ple, i
n
m
y
research
I ha
ve m
a
de a
ssum
p
tion that
“if a
voltage
magnitude
of
a bus
decrease
d
bel
o
w t
h
an
0
.
9
5
vol
t
a
ge m
a
gni
t
ude
, t
h
e
bu
s
i
s
co
nsi
d
ere
d
col
l
a
pse
d
a
n
d
fai
l
t
o
m
eet
t
h
e dem
a
nd
o
f
t
h
e
powe
r system
”
.
•
If t
h
e
re
qui
red
m
a
rgi
n
ca
nn
o
t
be m
e
t
by
usi
ng a
v
ai
l
a
bl
e r
eact
i
v
e p
o
we
r
reso
u
r
ces an
d
vol
t
a
ge
co
nt
r
o
l
facilities,
ad
d
i
t
i
o
n
a
l g
e
n
e
rating
u
n
its h
a
v
e
to b
e
starte
d
u
p
to prov
id
e vo
ltage supp
ort at cri
tical areas.
(ii) Sp
inn
i
ng
reserv
e
•
The s
p
inning
reactive power
reserv
e
of each ge
nerat
o
r m
u
s
t
be
known
•
It
can
hel
p
t
h
e
ope
rat
o
rs t
o
pr
edi
c
t
o
n
ho
w
m
u
ch po
we
r ea
ch
gene
rat
o
r ca
n s
u
p
p
l
y
•
The s
p
i
n
ni
n
g
reser
v
e m
u
st
be m
a
i
n
t
a
i
n
ed fo
r em
ergenc
y
used “i
n t
h
e event
of s
u
dde
n
dem
a
nd of
reactive powe
r”
(iii) Op
erat
o
r
’s actio
n
•
Op
erators m
u
st b
e
ab
le to
reco
gn
ize and
iden
tify
an
y vo
ltag
e
stab
ility sy
m
p
to
m
s
an
d
tak
e
approp
riat
e
rem
e
d
i
al wh
ich
sh
ou
l
d
so
lv
e
th
e pro
b
l
em
o
r
li
mit th
e d
a
m
a
g
e
.
•
Th
e op
erat
o
r
s
m
u
st b
e
co
nstan
tly
m
o
n
ito
red
and
an
aly
s
is th
e syste
m
to
id
en
tify p
o
t
en
tial v
o
ltage
stab
ility p
r
ob
lem
s
an
d
po
ssi
b
l
e cou
n
t
eractiv
e m
easu
r
es to
ov
erco
m
e
th
e pro
b
l
em
s.
In
th
is section
,
it is ex
p
l
ain
e
d
th
e resu
l
t
s o
f
research an
d
at th
e sam
e
ti
me
is
g
i
v
e
n
the
com
p
rehe
nsi
v
e
di
scus
si
o
n
. R
e
sul
t
s
can
be
pr
esent
e
d i
n
fi
gu
res,
gra
p
hs, t
a
b
l
es and
ot
hers t
h
at
m
a
ke t
h
e r
eade
r
un
de
rst
a
n
d
eas
i
l
y
[2]
,
[
5
]
.
T
h
e di
sc
ussi
o
n
ca
n
be m
a
de i
n
s
e
veral
s
u
b-c
h
a
p
t
e
rs.
4.
CO
NCL
USI
O
N
R
eact
i
v
e po
we
r i
s
i
nversel
y
pr
o
p
o
r
t
i
onal
t
o
t
h
e vol
t
a
ge m
a
gni
t
u
de o
f
a bus
. I
n
crease
on re
act
i
v
e
p
o
wer
lo
ad
on
a
bu
s stresses
th
e p
a
rticu
l
ar bu
s
and
cau
s
es th
e
v
o
ltag
e
to
drop
, if t
h
is co
nd
itio
n con
tinu
e
s th
e
p
a
rticu
l
ar bu
s
w
ill co
llap
s
e.
Th
is can
b
e
overco
m
e b
y
co
nn
ectin
g syn
c
h
r
o
nou
s co
nd
en
ser to
th
e bu
s as you
can see
o
n
t
h
e
bus
5
an
d
bu
s
8. C
a
paci
t
o
r
ba
nks
o
n
a
sy
st
em
have a m
a
jor i
m
pact
on t
h
e
sy
st
em
s st
abi
l
i
t
y
. A
s
we rem
ove
d t
h
e ca
paci
t
o
r
b
a
nk
s f
o
r
t
h
e
p
a
rt
2 a
n
al
y
s
es
t
h
e sy
st
em
had t
w
o m
a
jor
fai
l
u
res
.
T
h
e c
onst
a
nt
i
n
ject
i
o
n
of
rea
c
t
i
v
e p
o
we
r
gi
ves t
h
e
sy
st
em
a st
abl
e
fl
ow
of
p
o
we
r.
I
n
p
a
rt
3,
we ca
n c
oncl
ude
t
h
at
i
n
creas
e
in reactive
power
of m
o
re than one
bus can have m
a
jor im
pact on the
whole power s
y
ste
m
. The inc
r
ease i
n
the reactive power
on a pa
rticular bus af
fect
s all the nearest bus connected to
the pa
rticular affected bus.
As
fo
r t
h
e pa
rt
4,
rem
ovi
ng
of t
h
e capaci
t
o
r
ba
nks m
a
de
the syste
m
weaker. The system
b
ecom
e
s unstable for
sm
a
ll increase of reactive
power
of all the
bus
es.
In t
h
is
analysis, we c
a
n c
oncl
ude
that
m
a
jor i
n
cre
a
se in
reactiv
e
p
o
wer will h
a
v
e
sev
e
re im
p
act th
e bu
s con
n
ected
t
o
th
e lo
ad
and
may stress th
e
who
l
e system
.
REFERE
NC
ES
[1]
B
y
ung Ha Lee
and Kwang Y. Lee. Senior
Member Department of Electr
ic
al
and Computer Engineering Th
e
Penns
y
l
van
i
a State University
.
A study on
vo
ltage collapse mecha
n
ism in e
l
e
c
tric
power systems
.
[2]
"IEEE
at
a
Glan
ce
> I
EEE
Quick
F
acts".
IEEE
. D
ecem
ber
31, 201
0. Re
tri
e
ved Au
gust 14, 2013
.
[3]
"IEEE 2012
Ann
u
al R
e
port".
IEEE
. October
2011
. Retrieved M
a
y
5, 2013
.
[4]
Jan Veleb
a
University
of
West
Bohemia in
Pils
en, R
e
gion
al In
novation
Centr
e
of Electr
ical Engineer
ing, Pilsen
,
Czech
Republ
ic
, e-m
a
il
:
jvel
eba
@
rice
.zcu
.c
z
[5]
Jose
O.
Pe
ssa
nha
,
7th july
2005,
Te
sting
a
diffe
r
e
n
tia
l
a
l
ge
bric
e
q
ua
tion solve
r
in long
te
rm volta
ge
sta
b
ility
sim
u
lation.
[6]
K.
S.
Sa
stry
Mus
ti,
Unive
r
sity
of We
st Indie
s
,
musti.
sa
stry
@sta.
u
wi.
e
du, Ri
cardo
B. Ramkhelaw
a
n, University
of
West Indies, ricardo.ra
mkhelawan@gmail.com -
Power System Load Flow
Anal
ysis using Microsoft
Excel
.
[7]
Mohd Shahimi
Bin Mohamad Is
a,
Univ
ersity
M
a
lay
s
ia Pahang
,
Power Flow
Analysis Software Using Matlab
.
[8]
N Biglar
i, Iran
,
Static and d
y
na
mic assessment
of vo
ltage stability
.
[9]
Scott gr
eene, I
a
n Doboson.
USA, IEEE,vo
l
12,f
e
b-1997,
S
e
nsitivity of loading
margin to vo
lta
ge co
llapse w
i
th
respect
to arbitr
ary parameters
.
[10]
Stefan
johanson
& Fredrik
siogren, SWEDEN,
Vo
ltage
collapse in
power system_t
heinflu
enc
e
of
g
e
nerator curren
t
limiter
,
on
load
tap changers and
load d
y
namics
.
[11]
The Histor
y
of C
I
GRE –
A key player in
th
e de
velopment of el
ectric power system s
i
nce 1921
.
Evaluation Warning : The document was created with Spire.PDF for Python.