Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 62
5
~
63
3
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p62
5-6
33
6
25
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Adv
a
nced control scheme of a
uni
f
iedpower fl
ow controll
er
using sli
d
ing m
o
de control
Ab
del
l
a
ti
f Hi
n
d
a
1
, Mo
un
ir
K
h
iat
2
, Zinelaa
b
idine
Bo
udjema
3
1,
2
S
C
A
M
RE Laboratory
,
Dep
a
r
t
ment
o
f
El
e
c
tr
i
c
al
En
gi
ne
er
i
n
g
,
Al
ger
i
a
3
Electrical
En
g
i
neerin
g
D
e
par
t
men
t
,
Un
iv
e
r
s
ity o
f
Chlef
,
A
l
g
e
ri
a
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Re
ce
ive
d
A
p
r 10
, 20
19
Rev
i
sed
D
e
c
28
, 20
19
A
c
ce
p
t
ed
Jan
23
, 20
20
T
h
i
s
pa
pe
r pre
s
e
n
t
s
a
n
a
d
va
nce
d
c
o
n
t
ro
l sc
hem
e
b
a
se
d on
slid
in
g m
ode
con
t
ro
l of
a un
ified po
wer
flo
w
con
t
rol
l
er (U
PFC
)
. This
cont
rol
l
er can
g
e
ne
rat
e
a
n
u
m
b
e
r
of be
ne
fi
ts
i
n
t
e
rm
s of stat
ic an
d dy
na
m
i
c
op
e
r
a
t
io
n of
th
e
po
wer sys
t
em
su
ch
as
the
con
t
rol
l
a
w
is sy
nt
hesized
with
tw
o kind
s of
con
t
ro
ll
ers
:
s
l
idin
g mo
de
contro
ller
(S
M
C
),
and
p
r
op
ortion
al in
teg
r
a
l
(P
I)
.
Th
eir r
e
spec
tiv
e
perfo
rm
anc
e
s are comp
ar
e
d
in ter
m
s
of refer
e
nce
m
o
ni
to
rin
g
,
se
n
s
i
t
i
v
it
y
t
o
di
st
urba
n
c
e
s
a
n
d rob
u
s
tne
s
s.
We h
a
ve
to
stu
dy t
h
e
p
r
ob
le
m
of c
o
n
t
rol
l
i
ng p
o
w
e
r
in el
e
c
t
r
ic
sy
st
em b
y
U
PFC
.
T
h
e
si
m
u
la
tio
n
resu
lts s
h
o
w
t
h
e e
ffec
t
ive
n
es
s
of th
e p
r
op
osed
strateg
y
es
pecially
in
chat
tering-fr
ee b
e
hav
i
or
,
respo
n
s
e
to
su
dden
lo
ad
v
a
ria
t
ion
s
an
d
r
o
bus
tn
ess
.
All th
e simu
lat
i
o
n
s
fo
r th
e
a
b
o
v
e wo
rk h
a
v
e
be
en
carr
i
ed
o
u
t using
MATL
AB/Si
m
ul
in
k
.
Va
rio
u
s sim
u
l
a
tio
ns ha
ve
gi
ve
n
v
e
ry sa
t
i
sfa
c
t
o
r
y
re
su
lt
s
and
w
e
h
a
ve
suc
ces
sfu
l
ly
impro
v
e
d
th
e
activ
e
an
d
reactiv
e p
o
w
e
r
flows
o
n
a
line o
f
tran
sm
ission
, as
well as
to
con
t
rol vo
lt
age
at th
e bu
s
wh
ere it
is
con
n
ec
ted
,
the
st
udies
and
illu
str
a
te
th
e
effect
iv
e
n
ess
an
d
cap
abi
lity
of
UP
F
C
in
i
m
p
r
ov
in
g p
o
w
er
.
Ke
yw
ords:
FA
CTS
Sl
i
d
ing
mode
c
o
n
t
rol
pow
e
r
UP
FC
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
A
b
d
e
lla
tif
H
i
nd
a
,
Depa
rt
me
nt o
f
Ele
c
t
r
i
c
a
l
Engi
ne
eri
n
g
,
Lab
o
ra
t
o
r
y
(S
CA
M
R
E
)
Si
m
u
la
ti
on,
C
o
mm
ande
d,
A
n
a
l
y
s
i
s
a
n
d
Mai
n
t
e
na
nce
El
ec
t
r
i
cal
Net
w
ork.
EN
P of
O
r
an
, BP
15
23
El Mn
a
o
u
e
r
,
O
r
a
n
, Al
g
e
r
i
a
.
Emai
l:
abdel
l
a
t
i
f.hi
nda
2@
gm
ai
l
.
com
1.
IN
TR
O
DUCTION
In
re
cent
y
e
ars, t
h
e
el
ec
tric
al
po
we
r
di
st
ri
b
u
ti
on s
y
st
em a
r
e
suffe
r
in
g
as
of si
gni
fic
a
n
t
po
we
r fl
o
w
qual
i
t
y (P
Q)
pro
b
le
ms, w
h
i
c
h
a
r
e
c
h
ara
c
t
e
ri
z
e
d usi
n
g
low
p
o
w
e
r
fac
t
or,
p
o
o
r v
o
l
t
a
g
e qual
i
t
y
,
v
o
l
t
a
g
e
st
ab
i
lity
,
s
upp
ly
in
te
rru
p
t
ion
s
,
a
n
d
lo
ad
un
ba
la
n
c
i
n
g.
Th
e
s
e
po
w
e
r p
r
o
f
i
l
e
iss
u
es h
a
v
e
a
t
tr
ac
te
d
a
t
t
e
n
t
io
n
to
t
h
e rese
arc
h
e
r
s
in t
h
e aca
de
mi
c and i
n
d
u
st
ri
al
se
ct
ors. T
h
i
s
di
ffi
c
u
l
t
y
a
nd
a
u
gme
n
t i
n
po
we
r s
uppl
y
needs
p
r
ov
id
i
n
g
t
h
e
sy
st
em
w
ith
re
cen
t
con
t
ro
l
sy
st
em
s wh
ic
h c
o
n
t
r
i
bu
te
to
th
e
imp
r
ov
e
m
en
t of
t
h
e
e
l
e
c
t
r
i
ca
l g
r
id
s
perfor
m
ances [1].
The use
of
flexible AC
tr
a
n
s
m
ission
s
y
st
em (FACTS
)
c
o
n
t
r
o
lle
rs in
pow
e
r
sy
st
e
m
h
a
s b
een
of w
o
rld
w
ide
i
n
te
rest
fo
r e
nha
nci
n
g
po
wer
sy
ste
m
c
o
nt
rol
l
a
b
i
l
i
t
y
an
d
st
abi
l
i
t
y
an
d i
n
creasi
n
g
t
h
e
p
o
w
e
r
tr
a
n
sf
er
cap
a
b
i
l
i
t
y
d
u
e
to
t
h
eir
f
l
ex
i
b
ili
ty
a
n
d
sp
e
e
d
.
I
n
a
d
d
i
tion
,
co
nv
er
te
r-b
a
s
e
d
FACTS
c
o
n
t
ro
ll
er
s ar
e
ca
pabl
e
o
f
i
n
de
pen
d
e
n
tl
y c
o
ntroll
i
n
g t
h
e
act
i
v
e
a
n
d
rea
c
t
i
ve
p
o
we
r
flo
w
i
n
t
h
e p
o
w
e
r
sy
st
em [
2
].
U
P
F
C
i
s
t
h
e
m
e
mbe
r
of F
A
CTS
devi
ce
. It
i
s
t
h
e
mai
n
ly
a
d
a
p
ta
ble
a
n
d
p
o
we
rf
ul F
A
CT
S
de
vi
ce
[3].
Th
e
f
und
a
m
enta
l t
h
eo
ry
o
f
U
P
F
C
i
s
th
at,
t
h
e
mag
n
itud
e
o
f
vo
lta
g
e
affe
ct
s f
l
ow
of rea
c
t
i
v
e
po
w
e
r
a
n
d
th
e
pha
se a
n
gl
e a
ffect
s
fl
o
w
o
f
re
al
p
o
w
e
r
[4,
5].
T
h
e
UP
FC
c
o
nsi
s
t
s
o
f
t
w
o ot
h
e
r F
A
CT
S
de
vic
e
s:
t
h
e
St
at
i
c
Sy
nc
h
r
on
o
u
s
C
o
mpe
n
sat
o
r (ST
A
TC
O
M
) a
nd t
h
e
S
t
at
ic
S
ync
h
r
on
ous
Se
ri
es C
o
m
p
ensa
tor
(S
S
S
C
)
, t
h
e S
S
S
C
in
j
e
c
t
s a a
n
a
l
mo
st si
n
u
so
idal
vo
lt
ag
e
,
of
v
a
ri
ab
le
m
a
g
n
itu
d
e
in seri
es using
th
e syste
m
v
o
l
ta
g
e
w
h
ich
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
6
2
5
– 63
3
62
6
p
r
o
v
i
d
e
s th
e
ma
jo
r
i
t
y
c
o
s
t
eff
e
ct
iv
e
so
lu
ti
on
t
o
m
iti
g
a
te
vo
l
t
ag
e
sa
gs th
ro
ugh
i
m
p
r
ov
i
n
g
po
w
e
r qu
a
l
i
t
y
lev
e
l
th
a
t
is r
e
qu
ir
e
d
w
i
th
a
c
u
st
ome
r
. Wh
ile
, the S
T
A
T
C
O
M
is j
o
in
ed
o
r
c
o
nn
e
c
t
ed
wi
th a
c
o
m
m
on
DC l
i
n
k
c
a
pac
i
tor
.
It
c
a
n
, at
t
h
e
sa
me
t
i
me
, to
UP
FC
bus
vol
t
a
ge
/s
h
unt
r
eac
ti
ve
p
o
w
er
c
o
ntr
o
l,
i
n
ad
di
ti
on
pe
rf
o
r
m t
h
e
f
u
n
c
t
i
o
n
of
t
r
a
n
smi
ssi
on
li
ne
re
al
/r
ea
ct
ive
p
o
we
r f
l
o
w
c
ont
rol
[
6
].
Tho
ugh
UPF
C
im
p
lie
s many
a
d
v
a
n
t
ag
es, bu
t its c
o
n
t
ro
lle
r
d
e
sign
st
ill be
in
g
a
ma
tte
r
o
f
c
h
a
l
l
e
ng
e
sin
c
e i
t
is a
mu
lt
i-
v
a
r
i
a
b
le
co
n
t
ro
l
l
e
r
. In
lite
r
a
tu
re
, m
a
ny
w
o
rk
s
h
a
v
e
b
e
e
n
pre
s
en
te
d by
d
i
f
f
e
r
e
n
t
co
n
t
r
o
l
sc
h
e
mes
o
f
U
P
F
C
f
o
r
va
r
i
o
u
s
po
wer
syst
em ap
pl
i
c
a
t
i
o
n
s
. R
e
c
e
nt
ly
,
th
e
sli
d
i
n
g
mod
e
c
o
ntr
o
l
met
h
od
has
be
en
e
x
t
e
nsi
v
e
l
y em
pl
oye
d
f
o
r
c
ontr
o
l
o
f
n
o
nl
i
n
ea
r
sy
st
ems.
Se
ve
ra
l
pa
per
s
have
be
e
n
p
ubl
i
s
he
d
ba
se
d
o
n
S
M
C
o
f
U
P
F
C
[
7
-
9
]
.
Th
e c
l
assi
ca
l SMC
i
s
s
upe
r
i
n
t
e
r
m
s of
par
a
met
e
r
s
va
ri
a
t
i
on,
r
e
sp
onse
t
i
me,
e
x
te
r
n
al
di
st
ur
ba
nce
s
.
I
n
a
d
di
ti
on
, i
t
e
n
su
r
e
s
c
o
n
v
er
g
e
nce i
n
f
i
ni
t
e
ti
me a
n
d
i
t
i
s
ve
r
y
si
mpl
e
t
o
be
i
m
pl
e
m
ent
e
d i
n
a
n
y
lo
w
co
st ma
te
rie
a
l
[
1
0
]
.
Thi
s
art
i
c
l
e
di
scusses t
h
e c
o
mpe
t
e
n
c
e
o
f
UPF
C
o
n
c
o
nt
r
o
ll
i
n
g i
nde
pe
nde
nt
l
y
ac
ti
ve
a
n
d
re
act
i
v
e
p
o
w
e
r
s
i
n
to
the
pow
er
tr
a
n
sm
issi
o
n
li
n
e
, t
h
e
i
m
pr
ov
e
m
en
t
o
f
t
h
e
tr
a
n
sien
t
an
d
d
y
n
a
mi
c
sta
b
ilit
y
o
f
th
e po
w
e
r
syst
em usin
g
the
UP
F
C
. Us
i
ng
t
w
o ki
n
d
of
c
ont
rol
l
e
r
s
PI a
nd S
M
C
,
act
i
v
e
a
n
d
r
e
act
i
v
e
p
o
we
r
s
ar
e
co
n
t
ro
l
l
e
d
. Thei
r
p
e
rf
or
man
c
e
s
ar
e
an
al
y
s
e
d
and
co
mp
ared
i
n
t
e
r
m
s
of
r
e
fer
e
n
c
e
tr
ack
i
n
g
,
se
n
s
iti
v
ity
t
o
r
o
bust
n
ess
pl
us
pe
rt
ur
bat
i
o
ns.
2.
STRUC
TU
R
E
O
F
THE UPFC
For
ma
n
y
year
s, UPFC is
co
n
s
i
d
e
r
e
d
as
the
most
ver
s
a
t
il
e of the
FAC
T
S
devi
ce
o
n
e t
h
a
t
ca
n
be
u
s
ed
to
e
n
h
a
n
c
e
stead
y st
at
e st
ab
ility
,
dyn
a
m
ic
st
a
b
ili
ty
a
n
d
tran
si
en
t
s
t
ab
ilit
y
,
wh
ic
h c
o
mb
i
n
e
s
t
h
e
g
ood
fea
t
u
r
es
o
f
S
T
ATCOM and
SSSC. F
i
g
u
r
e
1
sh
ows
th
e
b
a
sic stru
ctu
r
e
o
f
U
PFC
w
h
ic
h
is
co
n
s
ists o
f
t
w
o vo
l
t
ag
e
so
ur
ced
co
nv
e
r
te
r
s
(VS
C
)
an
d emp
l
oy
ed
t
o
g
i
v
e
g
a
lv
an
ic i
s
o
l
a
tio
n a
n
d
r
e
gu
l
a
te
th
e vo
lt
ag
e
lev
e
l
s
in
t
h
e
sup
p
l
y
syste
m
.
It
i
s
c
onsi
s
t
e
d
of
tw
o
P
W
M
(
P
ul
se
Wi
dt
h
Mo
d
u
l
a
t
i
on)
i
n
vert
er
s,
whi
c
h
are
o
p
er
at
e
d
f
r
om
a
DC
l
i
nk
pr
o
v
i
d
ed
b
y
a DC
st
or
a
g
e c
a
p
ac
it
o
r
.
T
h
e fi
rst
i
n
ve
rt
er
is co
u
p
l
e
d i
n
para
ll
e
l
w
h
i
l
e
t
h
e sec
o
nd
one
is
pl
ac
ed i
n
se
ri
es wi
th t
h
e t
r
a
n
smi
s
si
o
n
li
ne
[
11]
.
The
de
ta
il
e
d
st
r
u
c
t
u
r
e a
n
d t
h
e
f
unct
i
ona
l
i
t
y
of t
h
e
UP
F
C
c
a
n
b
e
f
oun
d i
n
[
12]
.
Fi
gure
1. Basi
c
struct
ure
o
f
th
e
UP
FC
3.
THE
U
P
FC
MODE
L
Fi
gu
re
2 re
p
r
e
s
ent
s
t
h
e si
m
p
l
i
f
ie
d
m
o
del
c
i
r
c
ui
t of
the
UP
F
C
. The
UP
F
C
ma
t
h
e
m
at
ic
al
mo
del
can
be
di
vi
de
d i
n
to t
h
re
e set
s
of e
q
u
a
t
i
ons,
nam
e
l
y
:
the
eq
uat
i
o
ns
of
t
h
e
par
a
l
l
e
l
bra
n
c
h
, t
h
e e
q
u
a
t
i
on
s o
f
t
h
e
se
ri
es
b
r
an
ch
an
d
those
of
th
e c
o
n
tinu
o
u
s
on
e
.
Fi
gu
re
2.
Eq
ui
va
l
e
nt
c
i
r
c
ui
t o
f
the
U
P
FC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Adv
ance
d
c
o
nt
rol sc
heme
of
a
u
n
if
i
e
dp
ow
er
f
l
ow co
nt
roll
er
usi
n
g sl
i
d
i
n
g
m
ode
co
nt
rol
(A
bdel
l
a
ti
f
Hi
n
d
a
)
6
27
B
y
a
p
plyi
n
g
K
i
rc
hh
off's
la
w o
n
t
h
e
c
i
rc
ui
t
o
f
F
i
g
u
r
e
2,
w
e
c
a
n
w
r
i
t
e the
fol
l
owi
ng s
y
ste
m
o
f
equa
ti
o
n
s
⎣
⎢
⎢
⎡
00
0
0
00
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
00
0
0
00
⎦
⎥
⎥
⎥
⎤
(1)
B
y
a
ppl
yi
n
g
P
a
rk's
t
r
a
n
sform
a
t
i
on t
o
t
h
e
sys
t
em
(1),
we
ca
n
wri
t
e
:
1
0
0
1
(2)
3.1. Mode
l
i
n
g
o
f
th
e U
P
F
C
shu
n
t
b
r
anc
h
The
c
o
m
p
le
t
e
mat
h
emat
i
c
a
l
mo
del
of
t
h
e
UPF
C
shu
n
t
ca
n be e
s
ta
b
l
i
s
hed si
mil
a
rl
y
usi
ng t
h
e
fol
l
o
w
i
n
g
ma
tr
ix
⎣
⎢
⎢
⎢
⎡
00
0
0
00
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
00
0
0
00
⎦
⎥
⎥
⎥
⎤
(3)
Sin
c
e
th
e sy
st
e
m
i
s
ass
u
me
d
t
o
b
e
a
b
a
lan
c
e
d
on
e
,
it c
a
n
b
e
tran
sf
or
med in
to a
s
y
n
c
h
r
o
nou
s
d-
q-
o
f
r
a
me by
app
l
yi
n
g
P
a
rk
’s tr
a
n
s
f
or
ma
ti
on
. The ma
tr
ix fo
rm
(3
)
is
g
i
v
e
n as
fo
llo
ws:
1
0
0
1
(4)
3
.
2
.
The mo
delin
g
of
t
h
e UPFC
co
n
t
in
ues
branch
Fo
r t
h
e
D
C
-
s
i
d
e
c
i
r
c
u
i
t, b
a
se
d
on
t
h
e powe
r
b
a
la
n
c
e
eq
ua
tio
n
in th
e ou
tpu
t
a
n
d in
put of
U
P
F
C
,
t
h
e ne
t
rea
l
p
o
w
er e
x
cha
n
ged
by
bot
h
t
h
e
c
o
n
v
e
r
t
e
rs t
h
ro
ug
h DC
si
de s
h
o
u
l
d
be
zer
o
to
kee
p
the
ca
paci
t
o
r
vol
ta
ge
c
o
nst
a
n
t
[1
3].
T
h
e
D
C
v
o
l
t
a
g
e
d
y
n
a
mi
cs acr
oss t
h
e
c
a
pac
i
t
o
r i
s
g
i
ve
n b
y
the
fol
l
owi
ng eq
ua
ti
o
n
(5)
W
ith
:
W
ith
:
P
e
: a
c
t
i
ve
po
we
r ab
so
rbe
d
of
t
h
e
AC system
P
ep
:
ac
ti
ve
po
we
r inj
e
c
t
e
d
w
i
t
h
t
h
e
s
h
unt
inve
rt
er
AC
s
y
ste
m
.
B
y
pe
rfo
rmi
ng
Pa
rk
tra
n
sformat
i
on
, t
h
e
DC v
o
l
t
age
dyna
mic
s
ac
ros
s
the
ca
paci
t
o
r ca
n be
descri
be
d
b
y
t
h
e fol
l
o
wi
ng
eq
uat
i
on
s.
(6)
4.
CO
NTR
O
L
S
T
RA
TE
GY
O
F
T
H
E
UPF
C
4
.
1
.
Co
nt
r
o
l
of
th
e
pa
ra
ll
el
c
o
nv
e
r
t
e
r
The
or
dina
ry
wo
rki
n
g
pri
n
c
i
pl
e of
t
h
e pa
ral
l
e
l
c
o
mpe
n
sa
t
i
on
of
S
T
A
T
C
O
M
i
s
de
sc
ri
b
e
d as fol
l
ow
s:
ac
ti
ve
powe
r
c
ont
rol
whic
h means st
a
b
l
i
n
g t
h
e
ca
paci
t
o
r v
o
l
t
age
o
f
t
h
e DC
si
d
e
;
re
act
i
v
e po
we
r c
o
nt
rol
w
h
ich
mean
s
sta
b
lin
g th
e
termi
n
al
vo
l
t
ag
e [1
4
]
.
A
c
cor
d
in
g to
th
e sy
ste
m
o
f
(2)
t
h
e
con
t
ro
l
str
a
te
g
y
o
f
pa
r
a
l
l
e
l
com
p
en
sat
i
o
n
(ST
A
TC
O
M
) i
s
dec
o
upli
n
g
o
f
the
t
w
o
cu
rre
nt
lo
op
s c
ont
ro
l
,
t
o
de
cre
a
se
t
h
e c
o
u
p
l
i
n
g be
twe
e
n
th
e
ac
tiv
e
a
n
d
rea
c
t
i
v
e
po
we
r
s
. Blo
c
k
d
i
a
g
ra
m
of
th
e c
o
n
t
r
o
l
s
y
ste
m
is show
n
by
F
i
gu
r
e
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
6
2
5
– 63
3
62
8
Fi
gu
re
3.
C
ont
r
o
l
syst
em of
sh
unt
pa
r
t
4
.
2
.
Co
nt
ro
l of the
se
r
i
es
conv
e
r
te
r
Th
e
SS
SC
r
e
gu
la
te
th
e a
c
tive
and
r
e
ac
tiv
e
p
o
w
e
r f
l
o
w
on th
e
tr
a
n
s
m
issio
n
lin
e
wh
e
r
e
th
e
UP
FC
is
i
n
st
al
le
d by
i
n
j
e
ct
ion
v
o
lt
a
g
e
o
f
w
h
i
c
h t
h
e a
m
pli
t
ude
a
n
d
t
h
e
p
h
ase
b
o
t
h
c
a
n
be
a
d
j
u
st
e
d
.
Th
e
c
o
ntr
o
l
str
a
t
e
gy
of
t
h
e
se
ri
e
s
c
o
m
p
en
sat
o
r
i
s
dec
o
u
p
li
ng
o
f
t
h
e
tw
o c
u
r
r
e
n
t
l
oops c
ont
r
o
l
.
Th
e
dia
g
ra
m
of
c
o
ntr
o
l
ci
rc
ui
t
s
o
f
S
S
S
C
i
s
gi
ve
n i
n
t
h
e
F
i
gu
re
4.
In t
h
is pa
rt
,
w
e
hav
e
dec
i
de
d
t
o
e
v
al
uat
e
the
pe
r
f
o
r
ma
nc
es of
t
h
e U
P
F
C
b
y
t
w
o
di
ve
r
s
e
c
ont
r
o
l
l
e
r
s
:
PI
an
d
S
M
C
.
F
i
gur
e
4.
C
o
nt
r
o
l
s
y
ste
m
of
se
ri
es pa
rt
4.
3.
PI c
o
n
t
r
o
ll
e
r
The P
I
co
nt
r
o
l
l
e
r is easy to
devel
o
p
.
Fi
g
u
r
e
5 il
l
u
str
a
t
e
s
t
h
e t
w
o
l
o
o
p
s of
ou
r
s
y
st
em (c
u
rre
nt an
d
vol
t
a
ge
)
,
c
o
nt
r
o
l
l
e
d b
y
t
h
i
s
t
y
p
e
o
f
re
gul
a
t
or
.
I
n
t
h
is fi
gu
re
,
k
p
and
k
i
su
c
cess
i
v
e
l
y
r
e
pr
e
s
en
t
pr
opo
rt
iona
l
a
nd
in
te
g
r
al
g
a
in
s
o
f
t
h
e
PI
c
o
n
t
ro
l
l
e
r
s. Th
es
e
tw
o
g
a
in
s a
r
e
ca
lc
u
l
a
t
e
d
usin
g th
e
po
le
c
o
mp
ensa
ti
o
n
me
th
od
w
h
e
r
e th
e s
y
ste
m
re
spon
se t
i
me
ha
s b
een
ch
ose
n
e
q
u
a
l
to
5
.
The
cal
cul
a
t
e
d
t
e
rms
are
gi
ven
i
n
Ta
ble
1.
Fig
u
re 5
.
S
y
stem
w
ith
PI
c
o
n
t
r
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Adv
ance
d
c
o
nt
rol sc
heme
of
a
u
n
if
i
e
dp
ow
er
f
l
ow co
nt
roll
er
usi
n
g sl
i
d
i
n
g
m
ode
co
nt
rol
(A
bdel
l
a
ti
f
Hi
n
d
a
)
6
29
Tabl
e
1.
O
p
ti
mal
pa
ra
met
e
rs o
f
t
h
e
p
r
op
ose
d
cont
rol
l
e
rs
C
o
n
t
ro
ll
e
r
s
e
ri
es
p
ar
t
C
ontrol
l
er
shunt p
a
r
t
C
ontroll
er
conti
n
u
e
s bra
n
ch
1
1
2
.
.
ω
It sh
oul
d
be
not
e
d
t
h
at
the
p
o
l
e
c
o
mpe
n
sa
ti
on met
h
o
d
i
s
not t
h
e o
n
l
y met
h
od e
x
i
s
t
i
ng in t
h
e
li
te
ra
tu
r
e
for
cal
cu
l
a
t
i
n
g
th
e g
a
in
s
of
th
e PI
r
e
gu
la
to
r.
B
u
t
it
w
a
s
u
s
ed
b
eca
u
s
e o
f
i
t
s s
i
mp
l
i
ci
ty
.
4
.
4
.
S
lid
in
g mo
d
e
c
o
nt
r
o
l
l
e
r
(SM
C
)
SM
C is on
e o
f
t
h
e
e
f
f
e
c
tiv
e
no
n
lin
e
ar ro
bu
st
c
o
n
t
r
o
l app
r
oac
h
e
s
si
n
c
e
it p
r
ov
id
es
sy
stem
dyn
am
ic
s
b
y
an
inv
a
rian
c
e
pr
op
ert
y
to
u
n
c
e
r
ta
in
ti
e
s
o
n
c
e t
h
e
sy
st
em dy
n
a
m
i
cs
a
r
e
con
t
r
o
lle
d
in
th
e
sl
id
i
n
g
mo
d
e
[1
5-1
7
]
.
Th
e
ma
in
f
e
a
t
u
r
e
of
SM
C
is t
h
at
it
ju
st
re
q
u
i
r
e
s dr
iv
ing
th
e
e
r
r
o
r
to
a
sw
itc
h
i
ng
s
u
rf
a
c
e
i
t
con
s
i
s
ts
of t
h
re
e pa
rt
s F
i
g
u
r
e
6.
F
i
gu
re 6.
P
h
as
e p
o
rt
rai
t
of S
M
C
a.
The
swi
t
chin
g
surfac
e c
h
oi
c
e
In o
r
de
r
t
o
al
l
o
w t
h
e
a
p
pli
c
a
t
ion
o
f
t
h
e c
o
m
m
an
d by
sl
i
d
i
ng m
ode
, i
t
is ma
ndat
o
ry
t
h
at
the
c
o
nt
rol
l
e
d
syste
m
mu
st
b
e
w
r
it
t
e
n
in
t
h
e
fol
l
owi
n
g
ca
n
onic
a
l
form
[1
8].
x
,
,
,
,
,
,
(7)
Wh
er
e:
,
;
,
are
t
w
o
c
o
nti
n
uo
us
and
u
n
ce
rta
i
n
no
n
-
l
i
ne
ar
func
t
i
ons, su
p
p
o
s
e
d
li
mi
te
d.
We t
a
ke
t
h
e
g
e
neral
e
qua
ti
o
n
t
o
det
e
rmi
n
e
t
h
e sl
i
d
in
g su
rface
,
p
r
op
ose
d
by J
.
J. S
l
ot
i
n
e [1
9-
20],
gi
ve
n by
;
∗
(8)
Wh
er
e:
e
is
t
h
e
er
ro
r on
th
e sig
n
a
l t
o
b
e
a
d
ju
sted
;
λ
: a
p
o
s
it
iv
e co
ef
fici
en
t
;
n
: sy
s
t
em
or
der
;
x
*
:
desi
re
d si
gna
l;
x
:
st
at
e vari
a
b
l
e
o
f
the
c
ont
rol
si
g
n
al
.
b.
Co
nve
r
g
ence
condi
t
i
o
n
The
c
o
n
v
e
r
ge
n
c
e co
ndi
ti
o
n
is
defi
ned
b
y
t
h
e
Lya
p
u
n
ov e
q
u
a
t
i
on
[1
3]; i
t
m
a
kes the
su
rfac
e
a
t
tract
i
v
e
and
in
va
ri
a
n
t
⋅
(9)
c.
C
o
n
t
ro
l Ca
lc
ula
t
io
n
Th
e
c
o
n
t
r
o
l
a
l
go
r
i
t
h
m
is d
e
f
i
ne
d
b
y
th
e re
la
tio
n [15
]
(10
)
Her
e
V
n
is t
h
e correct
i
on
fac
t
or,
V
eq
is t
h
e equi
val
e
nt
co
nt
rol
ve
ct
o
r
,
V
com
is t
h
e cont
rol
v
ect
or whi
c
h
must
be
c
a
l
c
ul
at
ed in
o
r
de
r
t
h
at
t
h
e sta
b
i
l
i
t
y con
d
i
t
ion
s
fo
r t
h
e
sel
e
c
t
ed
c
o
n
t
rol are
sat
i
sfi
e
d.
Sl
iding p
hase
x(
)
S
Re
aching
Phase
Sliding
surfac
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
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6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
6
2
5
–
633
63
0
/
(11
)
/
|
|
/
|
|
(12
)
H
e
re
, s
a
t
((
S
(
x
)/
δ
)
i
s
t
h
e
prop
o
s
ed sa
t
u
rat
i
o
n func
ti
o
n
,
δ
is
th
e bo
und
a
r
y
laye
r th
ick
n
e
ss.
In our
st
u
d
y
,
t
h
e
er
ro
rs
b
e
twe
e
n
th
e
r
e
f
e
re
nc
es a
nd me
asure
d
I
d
an
d
I
q
c
u
rrent
s
ha
ve
be
e
n
c
h
ose
n
as
sl
id
in
g
mo
d
e
su
rf
a
c
e
s
, so
w
e
c
a
n
w
r
i
t
e
th
e
fo
l
l
o
w
i
n
g
re
la
ti
o
n
:
_
_
(13
)
The
fi
rst
or
der deri
vat
e
o
f
(8
),
o
n
e obt
ai
n
s
_
_
(14
)
Ta
kin
g
i
t
s
d
e
ri
vat
i
v
e a
n
d
re
pl
a
c
i
ng i
t
i
n
t
h
e
current
an
d
ex
pre
s
si
o
n
(
2
)
w
e
ge
t
_
_
(15
)
Re
p
l
a
c
i
n
g th
e
ex
pr
e
ssi
o
n
of
and
i
n
(
10) b
y
t
h
e
i
r
e
x
pressi
on
s gi
ve
n i
n
(1
5
)
,
o
n
e
obt
ai
n
s
(16
)
I
qr
wi
ll
be t
h
e
c
o
mpo
n
e
n
t
of
the
c
ontrol
ve
ct
or
use
d
t
o
c
onst
r
a
i
nt
t
h
e
s
y
st
em
t
o
c
o
nv
erg
e
t
o
S=
0
.
The
c
o
ntr
o
l
ve
ct
or
is o
b
t
a
i
n w
ith
impo
sing
so
t
h
e
e
qui
va
l
e
nt
co
nt
rol
c
o
mp
one
nt
s
a
r
e
gi
ve
n
wi
th
t
h
e f
o
ll
o
w
i
n
g e
xpressi
on
(17
)
U
s
i
n
g
t
h
e sam
e
p
r
oce
dures
a
s
for pa
rt s
hunt
we
get
t
h
e
fol
l
owi
n
g
e
x
p
r
essi
on:
_
_
(18
)
To
ob
t
a
i
n
h
i
gh
-qu
a
lit
y
p
e
rfo
r
ma
n
c
e
s
,
dyna
mi
c a
n
c
o
mm
u
t
a
tio
n
aro
u
n
d
t
h
e su
rf
a
ce,
th
e
con
t
ro
l
v
e
ct
or
is
impo
se
d
a
s
fo
ll
o
w
s [1
7]
⋅
si
gn
(19
)
The
sl
i
d
i
n
g
m
o
de
wi
ll
exi
s
t o
n
l
y i
f
t
h
e fol
l
o
w
i
ng c
o
ndi
ti
o
n
i
s
met
:
0
S
S
(20
)
5.
SIM
U
LAT
I
O
N
RE
SUL
T
S
Th
is se
ssion
i
s
d
e
vo
t
e
d
to t
h
e n
u
m
e
r
i
c
a
l s
i
mu
l
a
t
i
o
n
usin
g M
A
TLAB/SI
MU
LI
NK of
a
U
PFC
c
o
up
le
d to
a
2
2
0
V/
50H
z gri
d
. Th
e
p
a
r
a
m
e
t
e
r
s
o
f
th
e sy
ste
m
use
d
i
n
the
simu
la
tio
n ar
e g
i
v
e
n in Tab
l
e
2
.
Th
r
ee simu
l
a
t
i
o
n
tes
t
s wer
e
pe
rfo
rme
d
i
n
th
is ses
s
ion
t
o
exa
m
in
e
the
p
e
rfo
r
ma
n
c
e
of
th
e
con
t
ro
lle
rs
u
s
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Adv
ance
d
c
o
nt
rol sc
heme
of
a
u
n
if
i
e
dp
ow
er
f
l
ow co
nt
roll
er
usi
n
g sl
i
d
i
n
g
m
ode
co
nt
rol
(A
bdel
l
a
ti
f
Hi
n
d
a
)
6
31
5.1. Re
fe
re
nc
e
tr
ack
i
n
g
te
st
The
o
b
j
e
c
t
i
v
e
of t
h
is
t
e
st
ha
s for
goal
the
s
t
ud
y o
f
t
h
e t
w
o
c
o
ntrol
l
ers
(P
I a
n
d
S
M
C)
be
ha
vi
o
r
i
n
r
e
f
e
r
e
n
c
e tra
c
k
in
g
.
Figu
r
e
7
sh
ow
s t
h
e
ob
t
a
in
e
d
re
su
l
t
s.
As
sh
own
by
th
is f
i
gu
r
e
, w
e
ca
n
no
ti
ce
tha
t
th
e
po
we
r
s
f
o
l
l
o
w
al
mos
t
pe
rf
ect
l
y
the
i
r
r
e
fe
re
n
c
es
fo
r t
h
e t
w
o t
ypes
of c
o
nt
r
o
l
l
e
rs
wi
th a
v
e
ry
red
u
c
e
d
re
s
p
o
n
s
e
ti
me
f
o
r
th
e
SM
C
co
n
t
r
o
ll
er
co
mp
ar
ed
t
o
the
PI r
e
g
u
l
a
t
or
.
5.2. R
o
b
u
s
tne
s
s
We t
e
st
ed t
h
e
ro
bu
st
ness
of t
h
e
use
d
co
nt
rol
l
e
rs
fo
r
a
v
a
ri
a
t
i
on
of t
h
e
re
act
a
n
ce
XL
. Th
e r
e
su
lts
pre
s
e
n
te
d
i
n
Fi
gu
re
8
sh
ow
t
h
at
thi
s
vari
at
i
o
n pre
s
ent
s
a
c
l
ear
e
ffe
ct
o
n
t
h
e act
i
v
e a
n
d
re
a
c
t
i
v
e p
o
w
ers
fo
r t
h
e
syste
m
wi
t
h
P
I
co
nt
roll
e
r
co
nt
rar
y
t
o
t
h
e
s
y
st
em
wi
t
h
S
M
C where t
h
i
s
vari
at
i
o
n
ha
v
e
al
most
n
o
e
f
fec
t
on
ac
ti
ve
an
d
rea
c
t
ive
p
o
we
rs.
T
hus, i
t
c
a
n
be
c
o
nc
l
ude
d t
h
at
t
h
i
s
l
a
st
i
s
r
obu
st
a
g
ai
nst
t
h
is
p
a
ra
me
te
r
va
ri
at
i
o
n
.
5.3. Se
nsi
t
i
v
it
y to
a
sub
-
v
o
l
t
age
pe
r
t
u
r
b
a
ti
o
n
The
p
u
rp
ose
of t
h
is t
e
st
i
s
t
h
e e
v
al
uat
i
o
n
of
t
h
e
c
o
ntr
o
ll
ers
use
d
a
g
ai
nt
s a
s
u
b-v
o
l
t
a
ge
effect
(+
5
0
%
)
, a
ppl
ie
d
bet
w
ee
n t
h
e
i
n
sta
n
t
s
t
=
0.
6s an
d
t
=
0
.
6
2
s
.
Th
e
ob
ta
in
ed sim
u
la
tion
r
e
su
lts a
r
e exp
o
s
ed
i
n
Fi
gu
re
9
.
T
h
rou
g
h
t
h
is
fig
u
r
e,
we
n
o
t
i
c
e
tha
t
t
h
e a
ppl
i
e
d
di
st
urba
nc
e (su
b
-
v
o
l
t
a
ge
) c
a
u
se
d a
n
a
l
most
n
e
g
lig
ib
le
eff
ect
o
n
th
e
po
w
e
r
c
u
rv
e
s
f
o
r
t
h
e
tw
o t
y
p
e
s o
f
co
n
t
ro
l
l
e
r
s
u
s
e
d
. C
e
r
é
su
lt
at
est
in
té
r
e
ss
a
n
t
po
ur
l
e
sy
st
èm
e U
P
F
C
qu
i
p
e
u
t
ê
t
r
e
so
um
is
à d
e
s
ef
fe
ts
p
a
r
e
ils.
Tabl
e
2
.
U
P
F
C
pa
ra
me
te
rs
us
ed
fo
r sim
u
l
a
t
i
on
P
a
r
a
m
e
te
r
na
m
e
S
y
m
bol
V
a
l
u
e
U
n
it
N
e
tw
or
k vo
l
t
age
V
r
220
V
Volta
ge of
t
h
e rec
e
ive
r
V
s
220
V
D
C
volta
ge
V
dc
280
V
N
e
tw
or
k f
r
eque
ncy
f
50
HZ
T
h
e
c
a
pa
cit
y
of
the
c
o
m
m
on ci
r
c
ui
t D
C
C
2
mF
I
nducta
nce
1
L
1.
125
m
H
Re
sista
n
ce
1
r
100
Ω
I
nducta
nce
2
L
p
1.
125
m
H
Re
sista
n
ce
2
r
p
100
Ω
Fi
gu
re
7.
R
e
fe
renc
e trac
ki
n
g
t
e
st
0
0.
2
0.
4
0.
6
0.
8
1
-
3000
-
2000
-
1000
0
1000
2000
Ti
m
e
(
s
)
A
c
ti
v
e
power
(
w
)
0
0.
2
0.
4
0.
6
0.
8
1
-1
50
0
-1
00
0
-5
00
0
50
0
10
00
15
00
20
00
25
00
Ti
m
e
(
s
)
R
eac
t
i
v
e
po
w
e
r
(
V
a
r
)
0
0.
2
0.
4
0.
6
0.
8
1
-3
-2
-1
0
1
2
3
4
Ti
m
e
(
s
)
C
u
rre
n
t
I
q
s
(
A
)
0
0.
2
0.
4
0.
6
0.
8
1
-3
-2
-1
0
1
2
3
4
Ti
m
e
(
s
)
C
u
rre
n
t
I
d
s
(
A
)
P
s
-re
f
Ps
-
p
i
Ps
-
s
m
c
Q
s
-re
f
Qs
-
p
i
Qs
-
s
m
c
Id
s
-
p
i
I
d
s-
sm
c
Iq
s
-
p
i
I
q
s-
sm
c
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
6
2
5
–
633
63
2
F
i
gu
re
8.
S
e
nsi
t
i
v
i
t
y
t
o
t
h
e
rea
c
t
a
nc
e v
a
ri
at
i
on
(
XL
-30%
)
F
i
gure
9. S
e
nsi
t
ivi
t
y
t
o
s
u
b-vo
l
t
age
pe
rt
u
r
ba
ti
on
(+
5
0
%)
6.
CO
NCL
U
S
I
O
N
Thi
s
a
r
ti
c
l
e
wa
s de
dic
a
t
e
d
t
o
t
h
e a
ppli
c
a
t
io
n
o
f
a
ro
but
e
co
nt
rol
me
t
h
o
d
b
a
sed
o
n
t
h
e sl
i
d
i
n
g
mo
de
fo
r the
co
nt
rol
o
f
a UPFC
s
y
st
em. A
co
m
p
arat
ive
st
ud
y
by
nu
me
ri
cal
si
mula
ti
o
n
ha
s cl
ea
rl
y sh
o
w
n
t
h
e
sup
e
ri
o
r
i
t
y
o
f
t
h
e c
o
nt
rol
use
d
(S
MC) co
mp
ared
to
t
h
e c
o
n
v
ent
i
ona
l
c
ont
rol
based
on
P
I
reg
u
l
a
t
o
rs es
pe
c
i
a
l
l
y
i
n
t
h
e
ro
b
u
st
ne
ss
t
e
st
a
n
d
t
h
e
deco
u
p
l
i
ng
be
twe
e
n
ac
ti
ve
a
nd
re
ac
ti
ve
p
o
w
ers. Ba
sin
g
o
n
t
h
e
obt
ai
ne
d
re
su
l
t
s
,
t
h
e UP
FC
de
v
i
c
e
ba
se
d
on
S
M
C, ca
n a
d
j
u
st
t
h
e
di
str
i
but
i
o
n o
f
the
syste
m
pow
e
r
fl
o
w
bet
w
e
e
n
t
h
e
t
r
ansmissi
on
l
i
n
es q
u
i
c
kl
y
a
n
d
smo
o
t
h
l
y
, a
n
d
does
n
o
t
ha
ve
a
si
g
n
ifi
c
ant
i
m
pact
on t
h
e
ot
he
r o
p
e
ra
t
i
ng
para
met
e
rs of
t
h
e
s
y
st
em.
RE
FERE
NC
E
S
[1]
G. Abdull
ah Sa
lman, M.
H
a
san
A
l
i
,
and
A. Naji
m Abdullah, "Impl
e
ment
at
ion
Opti
mal
Locati
on a
n
d Sizi
ng
of
UPFC on Iraqi
P
o
wer
System G
r
id
(13
2
kV) Us
in
g
G
e
net
i
c
A
l
g
o
r
i
t
hm,
"
Int
e
rn
at
iona
l
J
o
urna
l o
f
Po
we
r E
l
e
c
t
ron
i
cs
a
n
d
Dr
i
v
e
Sy
s
t
em
(
I
J
PE
DS
)
,
vol.
9
,
no.
4
,
pp.
1
607
-16
1
5
,
20
18.
[2]
M
.
Boudiaf
an
d M. Moudj
a
hed, "Imp
rovement of
transient
sta
b
i
lity of
po
wer system by
IP
FC, SS
SC
and
ST
ATCOM,
"
J
o
urna
l o
f
El
ec
t
r
ical
En
g
i
n
e
e
r
i
n
g
,
v
o
l
.
14,
n
o
.
1, p
p
.
25
7-2
7
2
,
20
14.
[3]
Yang
, S
.,
Liu
Y.,
an
d
Wang
,
X., G
u
n
a
sekar
a
n
,
D.
, Kark
i, U
.
, and
F
a
ng
Z.
P
e
ng
, "M
o
d
u
l
ation
and
Control
of
Tr
ans
f
or
mer
-
les
s
U
P
F
C
,"
I
E
E
E
T
r
a
n
s
a
ct
io
ns on
Po
w
e
r
E
l
ec
tr
on
i
c
s
,
vo
l. 3
1
,
no.
2,
pp.
1
0
5
0
-
10
63,
2
0
1
6
.
[4]
Kris
hn
a, T. M
u
rali,
an
d An
jan
e
yulu,
K
.
S
.
R.
, "Co
o
rd
in
at
i
on of
Int
e
l
l
igent
C
o
ntroll
ers
for s
h
unt
and seri
es
conv
erters
o
f
U
P
F
C
,
"
Pr
oceedi
n
g
s
of
th
e in
t
e
rna
t
ion
a
l
Co
n
f
er
ence
on
Pow
e
r,
Co
ntr
o
l
,
Co
mm
un
icatio
n an
d
Comp
utatio
nal T
echn
o
log
i
es
fo
r
S
u
staina
ble
Gr
owth
(PCCCT
S
G
)
,
p
p
. 1
1
-1
4, 2
015.
[5]
Roun
d S
.
D
,
yu
Q
,
and
Noru
m
L.E
,
and
T.M
,
"P
erfo
rmanc
e
of
a Un
ified
P
o
wer F
l
ow Co
ntro
ller Using
a
D
-
Q
Control S
y
s
t
em
, AC an
d D
C
Po
wer Transmiss
i
o
n
,"
P
r
o
c
ee
di
n
g
s of
th
e Si
xt
h In
te
rna
t
io
na
l Co
nfe
r
e
n
c
e
o
n
A
C
and
DC Power
Transm
is
sion
,
vo
l.
42
3
,
p
p
.
35
7-36
2
,
19
96.
[6]
S
h
arma
N
.
K
an
d
Jagtap P
.
P
,
"
M
o
d
elling
and
a
p
plicat
io
n of
Unified
P
o
wer
F
l
o
w
Controller
(UP
F
C),"
Thi
r
d
Inter
n
a
t
ion
a
l
Co
nferen
c
e
on
Em
e
r
g
i
ng
T
r
en
ds
in
Engine
er
in
g a
n
d
T
echno
lo
g
y
(IC
ET
ET
)
,
p
p
.
35
0-
35
5, 20
10
.
[7]
Umre P
.
B
,
Band
al V.S
,
and
D
h
a
m
n
e
A
.
R, "
D
es
ign
of
con
t
ro
l
l
er for Uni
f
ied Pow
e
r Flow
C
o
ntrol
l
er (UPFC) us
i
n
g
S
lid
in
g M
ode
C
ontrol (S
M
C
)
str
a
teg
i
es
,"
In
: th
e
5
t
h
In¬te
r
na
ti
onal
Con
f
e
r
e
n
ce
on
Co
nf
lue
n
ce
The
Ne
x
t
Ge
n
e
ra
tion
Info
rm
atio
n T
e
c
h
n
o
log
y
Su
mm
it
(Conflu
en
ce)
,
pp
.
89
3-8
9
7
,
20
14
.
0
0.
2
0.
4
0.
6
0.
8
1
-2
000
-1
500
-1
000
-500
0
500
1
000
1
500
Ti
m
e
(
s
)
A
c
t
i
v
e pow
er
(
w
)
0
0.
2
0.
4
0.
6
0.
8
1
-150
0
-100
0
-50
0
0
500
100
0
150
0
Ti
m
e
(
s
)
R
eac
t
i
v
e
pow
er
(
V
ar
)
P
s
-ref
Ps
-
p
i
Ps
-
s
m
c
Q
s
-ref
Qs
-
p
i
Qs
-
s
m
c
0
0.
2
0.
4
0.
6
0.
8
1
-2000
-1500
-1000
-500
0
500
1000
1500
2000
Ti
m
e
(
s
)
A
ct
i
v
e
p
o
w
er
(
w
)
0
0.
2
0.
4
0.
6
0.
8
1
-1
500
-1
000
-500
0
500
1
000
1
500
2
000
Ti
m
e
(
s
)
A
ct
i
v
e
p
o
w
er
(
w
)
Q
s
-re
f
Qs
-
p
i
Qs
-
s
m
c
P
s
-ref
Ps
-
p
i
Ps
-
s
m
c
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Adv
ance
d
c
o
nt
rol sc
heme
of
a
u
n
if
i
e
dp
ow
er
f
l
ow co
nt
roll
er
usi
n
g sl
i
d
i
n
g
m
ode
co
nt
rol
(A
bdel
l
a
ti
f
Hi
n
d
a
)
6
33
[8]
Go
rin
e
vsky
,
D,
Bo
yd
,
S
,
a
n
d Ste
i
n, G., "R
ob
ust t
e
rm
in
al
sl
idin
g
m
o
d
e
po
we
r flo
w
c
o
nt
rolle
r
u
s
in
g u
n
i
f
ie
d p
o
we
r
flow
co
ntro
ller
with
ad
ap
tiv
e
o
b
s
erver an
d
lo
cal
measure
m
en
t,"
IEE
E
I
E
T Ge
ne
ra
t
i
o
n
, Tr
ansmission &
Dis
t
r
i
bution
,
v
o
l
.
53, n
o
.
10,
p
p
.
1
7
1
2
-
17
23,
20
14
.
[9]
Nayeripo
ur,
M
,
Nariman
i
,
M
.
S
,
and
Nik
n
am
,
T,
and
J
a
m,
S
.
,
"
D
es
ign
of s
lid
in
g mod
e
cont
roller
for U
P
FC to
impro
v
e
p
o
w
e
r
os
cilla
t
ion
damp
in
g,"
E
L
SE
VIE
R
A
p
pl
ie
d So
ft
Co
mpu
t
i
n
g
, v
o
l
.
1
1
,
n
o
.
8,
pp.
47
66
-
477
2,
20
11
.
[10]
Ali M
ous
mi,
A
h
med
Ab
bo
u,
Y
a
ssine El Ho
um
,
and
A
n
as
s
Bako
u
r
i,
"
R
ea
l ti
me
i
m
plemen
tatio
n
o
f
a
su
per
twistin
g
control
of
a B
L
DC motor,
"
In
te
r
natio
na
l
Jo
urn
a
l of
Elec
tr
ica
l
an
d Co
mp
uter
En
gineer
in
g
(IJ
ECE)
, v
o
l
.
9
,
no.
4,
pp.
30
32
-30
4
0
,
20
19
.
[11]
Bouanane,
A, Yahi
aoui,
and Me
rzoug,
"Robust
stabi
lity
powe
r
in t
h
e
transmissi
on l
i
ne wi
th t
h
e
use of
a
UPFC
sys
t
em and
neu
r
al co
ntrol
l
ers b
a
s
e
d
ad
ap
tiv
e
con
t
ro
l,"
In
t
e
rn
a
t
i
onal
J
o
u
r
n
a
l o
f
P
o
we
r
Ele
c
t
ron
i
c
s
an
d
Dri
v
e
Sy
stem
(IJ
PE
D
S
)
,
vol
. 1
0
,
no
. 3
,
pp
.12
8
1
-
129
6,
20
19
.
[12]
Kamel,
S
an
d J
u
rad
o
,
F
.
, "
C
omp
a
riso
n
of
vari
ous
UPFC models for power
fl
ow control,
"
EL
S
E
VI
E
R
El
ec
t
r
i
c
Po
w
e
r
S
y
s
t
e
m
s R
e
se
a
r
c
h
,
vo
l.
12
1, p
p
.
2
5
7-
27
2,
20
15.
[13]
Mall
ick R.
K.
,
N
a
hak
N
.
,
and Si
n
h
a R.
R.,
"Fuzzy
Sl
iding Mode C
o
nt
rol for UPFC
t
o
Improve
T
r
ansient Stabili
ty
of
Power System,"
An
nua
l
I
EEE
, In
dia Co
nfer
ence
(
I
ND
ICO
N
), New
D
e
lhi
,
In
d
i
a
,
pp
.
1-6
,
2
015
.
[14]
Men
g
W
an
d Q
i
nx
ian
g
G
.
,
"M
ath
e
ma
tic
a
l M
o
de
l
and
Contro
l S
t
r
a
tegy
of U
P
F
C
,"
In: Sixth In
t
e
rn
ati
o
nal
Confe
r
ence
on Mea
s
ur
in
g
T
ech
no
log
y
an
d
M
echa
t
r
oni
cs Autom
a
tio
n
(ICM
T
M
A
)
,
Zh
an
gj
iaj
i
e,
C
h
in
a
,
2
014
.
[15]
Wai R.
J. an
d
C
h
ang J.
M
.
,
"Im
p
lem
e
nta
t
ion of rob
u
s
t
w
a
vele
t
-
n
e
u
r
al-
n
et
wo
r
k
s
l
id
in
g-
mo
de
con
t
r
o
l f
o
r
in
du
ct
io
n
servo motor
driv
e,"
I
E
EE T
r
ans
actio
n
s
on
Ind
u
s
t
r
i
al
Ele
c
tr
on
ics
,
v
o
l
.
5
0
,
no.
6
,
pp.
1
3
1
7
-
13
34,
2
008
.
[16]
Ut
ki
n,
V.
I.
,
"S
li
di
ng
m
o
de
c
o
n
t
rol
d
e
si
gn
p
r
inci
pl
e
s
a
n
d
a
p
p
lica
t
i
o
n
s
to
e
l
ec
t
r
ic
dri
v
e
s
,
"
I
E
EE
T
r
an
sact
io
ns
o
n
Indu
strial Elec
tr
onics
, v
o
l
.
4
0
,
no.
1
,
p
p
.
23
-36,
19
93
.
[17]
Ast
r
o
m K
.
J
.
an
d
W
i
t
t
en
mar
k
B
.
,
Ad
ap
ti
ve
Cont
ro
l
.
Ne
w Yo
r
k
:
Add
i
s
o
n
-
W
e
s
l
e
y
,
19
95
.
[18]
S
un,
T,
Ch
en,
Z,
and Bl
aabj
e
rg
, F
.
,
"
F
lick
er s
t
ud
y o
n
v
a
riabl
e
sp
ee
d
wind
turb
in
es with
do
ub
ly fed
in
duc
tio
n
generators
,
"
I
E
EE T
r
a
n
s
a
ctio
ns
on
En
ergy
Conv
er
sion
, vo
l.
20
, n
o
.
4
,
p
p
.
896
-90
5
,
20
05
.
[19]
S
l
ot
in
e,
J
.
J
.
E.
a
n
d
Li
,
W
.
,
Appl
ied Nonlinear Co
ntrol.
Engl
ewoo
d
C
l
i
f
f
s
. N
J
:
P
r
e
n
tic
e
–H
all,
19
91
.
[20]
Sl
o
t
i
n
e
,
J.
J. E and
Ste
i
n
,
"Sl
i
d
i
ng c
o
ntro
lle
r de
sign
for no
n-lin
ear syste
m
s,
"
I
J
C In
ter
natio
na
l Jo
u
r
n
a
l
of
Co
ntro
l
,
v
o
l
.
40, n
o
.
2, p
p
.
42
1-4
3
4
,
20
07.
Evaluation Warning : The document was created with Spire.PDF for Python.