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
. 68
5
~
69
1
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
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jp
e
d
s.v
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.
p
p68
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91
6
85
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
Optimal distribution of power
under stress on power grid in
real-time by rea
ctive comp
ensation-management and
development in balance
Ta
dj
edd
i
ne Ali A
.
1
, A
r
b
a
o
u
i
I
.
2
, H
a
mi
an
i
H.
3
, Ch
ak
er
A
4
1,
4
S
C
A
M
RE Laboratory
,
Nat
i
o
n
a
l P
o
lyt
e
c
h
n
i
c
S
c
ho
ol of
O
r
an,
A
l
g
e
ria.
2
LES
E
M
L
a
b
o
r
a
t
o
r
y
,
Un
iv
er
s
ity
O
r
an1
,
Algeri
a.
3
L
A
AS Laboratory,
National Polyte
chn
i
c
S
c
ho
ol
of
Oran
,
Alg
e
ria
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Ju
l
17
,
20
19
Re
vise
d N
o
v
9
,
20
19
Acc
e
pt
e
d
Fe
b 7, 2
0
2
0
T
h
e
i
n
d
u
st
ria
l
d
e
v
e
lo
pm
e
n
t,
li
fest
yl
e
a
n
d m
o
de
rn
i
z
ati
on
of t
h
e m
a
na
ge
m
e
nt
sectors
in Alg
e
ri
a
h
a
v
e
led
to
an
incr
ease
in de
m
a
nd
for
ele
c
tricit
y po
wer in
recen
t
y
ears
an
d an
inc
r
ease
i
n
d
e
m
a
nd
for t
h
e en
ergy
secto
r
. This
h
i
gh
deman
d
for
po
wer has
led
to
p
r
oblems wi
th
v
o
ltag
e
d
r
ops
,
p
a
rticular
ly
as
r
e
gar
d
s th
e
q
u
a
li
ty
of
th
is v
o
lt
age du
r
i
n
g
p
e
r
i
ods
peak lo
ad
.
T
h
ank
s
to
research
on
th
e
d
e
v
e
lo
pm
en
t o
f
th
e
electr
i
ci
ty
tr
ans
m
is
sion s
y
s
t
em
in
th
e
So
ut
h-W
e
st re
g
i
o
n
o
f
Alg
e
ria
a
n
d
ba
se
d on the
the
o
re
ti
c
a
l re
su
lts.
We ha
v
e
ob
tai
n
ed an
op
ti
mal so
lu
t
i
o
n
f
o
r
the
lo
c
a
ti
on
o
f
th
e r
e
g
u
l
a
tio
n
sy
st
ems
f
o
r
vo
ltag
e an
d
the
f
r
equen
c
y
in
th
e
su
bs
tation
s th
a
t
ex
hibit
s
t
ro
ng
vi
ola
t
io
ns
and
periodic st
at
ic dest
abi
lizat
ion
,
i
n
par
ticular,
the
st
at
ions at t
h
e end
of the
22
0K
v tran
smis
sion
lin
e
s.
Th
e
techn
i
qu
es of
m
o
d
e
ling
and
c
o
n
t
rolling
th
e
vo
ltag
e per
freq
u
en
cy (H
z
/
V
)
a
s
well as
th
e cri
tic
al an
aly
s
is v
a
rian
ts
h
a
v
e
b
een
stud
ied
and
con
f
ir
med
u
s
ing
adv
a
n
ced
re
a
l
-ti
m
e nu
merica
l
simu
lat
i
o
n
.
Ke
yw
ords:
D
e
ce
n
t
r
a
liz
ed
Pr
odu
c
t
i
on
Di
spat
c
h
i
n
g
P
o
w
e
r
In
t
e
gr
a
tio
n
PV
Re
al
Ti
me
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:
Tadj
ed
di
ne
Al
i
A.,
SC
A
M
RE
La
b
o
ra
t
o
r
y
, De
part
ment
of
El
ec
t
r
i
cal
En
g
i
ne
e
r
i
n
g,
Nat
i
onal
P
o
l
y
t
e
c
hnic
S
c
h
o
o
l
of O
r
a
n
- Ma
u
r
i
c
e
Au
di
n
,
Al
ge
ri
a.
Emai
l:
at
adj
1
@g
ma
il
.com
1.
IN
TR
O
DUCTION
The
g
r
owi
ng d
e
ma
n
d
for e
n
e
r
g
y
an
d t
h
e
de
ve
lo
pme
n
t
o
f
de
cent
r
a
l
i
z
e
d
g
e
nerat
i
on s
y
st
e
m
s h
a
ve l
e
d
to
g
r
ea
t
p
r
o
g
ress
in
t
h
e
fi
el
d
of
qu
al
ity
c
o
n
t
r
o
l
o
f
vo
lt
ag
e a
nd
ac
ti
v
e
a
n
d
r
e
ac
tiv
e
po
w
e
r
.
N
e
v
e
r
t
he
le
ss,
th
e
reg
u
l
a
tio
n
o
f
t
h
e qu
a
lity
of
e
n
ergy
an
d
the
ap
p
e
aran
c
e
of
n
e
w
c
o
mp
en
sa
tio
n
d
e
v
i
c
e
s ha
v
e
a
llo
w
e
d
a
b
e
tt
er
cont
rol
o
f
t
h
e
el
ec
tric
al
e
n
e
r
g
y
. T
h
e
m
o
re
the
net
w
ork gr
ow
s
t
h
e
mo
re
c
o
mpl
e
x
it
be
co
mes, di
ffi
c
ul
t
t
o
cont
rol
a
n
d i
t
s
ma
rgi
n
o
f
st
abi
l
i
t
y de
cre
a
se
s
[1,
2
]
.
F
o
r t
h
i
s
, t
h
e
str
u
ct
u
r
e
o
f
the
so
ut
h
e
rn
net
w
ork re
qui
re
s
th
e
o
p
e
r
a
tor t
o
fi
nd an
op
t
i
ma
l so
lu
ti
on to
th
e pro
b
l
e
m
s
re
la
ti
n
g
to
c
o
mp
en
sat
i
o
n
in or
d
e
r
to m
a
i
n
ta
in
th
e
st
ab
il
ity
o
f
th
e
e
l
e
c
tr
ic
a
l
sy
st
em
and
con
t
i
n
u
i
ty of
serv
ic
e.
In
t
e
r
e
st in
t
h
e
i
n
sta
lla
ti
o
n
of e
l
e
c
t
ro
n
i
c
po
w
e
r
devi
ce
s i
n
s
u
bsta
t
i
ons
ha
s
i
n
cre
a
se
d
sig
n
i
fi
ca
ntl
y
i
n
re
c
e
nt
ye
ars
.
I
n
fa
ct
, sta
t
i
c
c
o
n
v
e
r
t
e
rs
can
meet
t
h
e q
u
al
i
t
y
re
qui
reme
nt
s i
m
pos
ed
b
y
t
h
e
el
e
c
t
r
i
c
po
we
r su
ppli
e
r
an
d
ens
u
re
the
p
r
o
p
er f
unct
i
on
i
ng
of
t
h
e subst
a
t
i
o
ns [3]. The
c
ont
rol
as
pec
t
s o
f
re
act
i
v
e p
o
we
r
a
n
d
v
o
l
t
a
ge
st
ab
i
l
i
t
y are
effe
ct
i
v
e fo
r t
h
e
re
li
a
b
i
l
i
t
y
o
f
pow
e
r
gr
id
s.
V
o
lt
ag
e in
st
a
b
i
lity
u
s
u
a
l
l
y oc
cu
r
s
b
e
c
a
u
s
e
o
f
a re
ac
ti
v
e
po
w
e
r
d
e
f
i
c
i
t
.
Th
e
r
ef
or
e, th
e c
o
n
t
ro
l
o
f
th
e
r
e
ac
ti
v
e
p
o
w
e
r and
the
v
o
l
ta
g
e
i
s
on
e of
th
e
m
a
jo
r ch
al
le
ng
es
f
o
r
th
e
d
i
sp
a
t
ch
er
o
f
th
e e
l
e
c
tr
ic
a
l
net
w
orks
[4,
5]. El
ec
tric
al
g
r
i
d
a
n
al
y
s
i
s
a
n
d
pl
a
nni
n
g
has
n
o
t
onl
y
hel
p
e
d
t
o
c
ont
rol
po
w
e
r s
y
ste
m
s,
b
u
t a
l
so
t
o
de
ve
l
o
p
t
h
ese
sy
ste
m
s,
i
n
cl
u
d
i
ng
l
i
ne
s, t
r
a
n
sf
ormers,
an
d
rea
c
t
i
ve
co
mpe
n
sa
ti
o
n
[6]. C
o
nse
q
u
e
nt
l
y
,
t
h
e opt
i
m
al
s
u
per
v
isi
o
n of i
n
te
grat
i
o
n of re
newa
ble
e
n
erg
y
reso
u
r
c
e
s (p
hot
ov
ol
t
a
i
c
an
d
win
d
)
a
nd
re
act
i
v
e
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
85
– 69
1
68
6
po
we
r co
nt
r
o
l
devi
ce
s
in
el
ec
t
r
i
c
a
l
net
w
or
ks
ca
ll
f
o
r
re
al
-t
ime
st
at
us i
n
f
o
r
m
at
i
on t
o
sy
nc
hr
o
n
iz
e be
t
w
e
e
n
a
l
l
t
h
e sou
r
ces
i
n
t
h
e ne
tw
or
k,
s
o
i
m
pr
o
v
e
e
n
e
r
g
y
e
ffi
c
i
e
n
cy
and
vol
t
a
ge
pr
ofi
l
e
s of
s
u
b
s
t
a
t
i
o
ns u
nde
r di
ffe
rent
o
p
e
r
a
ting
c
ond
it
io
n
s
[
7
,8]
.
Th
e
good
qu
al
ity
o
f
el
ec
tr
ic
a
l
p
o
w
e
r
s
a
n
d
th
e
co
n
tin
u
i
t
y
o
f
ser
v
ic
es
p
l
ay
th
e
c
r
uci
a
l
r
o
le
i
n
t
h
e o
p
t
i
m
a
l
ma
nage
ment
o
f
t
h
e
el
e
c
t
r
i
c
ne
tw
or
k
o
n
t
h
e
o
n
e
han
d
,
an
d
o
n
t
h
e
ot
he
r
ha
nd
,
t
h
e
co
mp
ens
a
ti
o
n
o
f
the
r
e
a
c
t
i
v
e
p
o
w
e
r
t
r
a
n
smi
tte
d
is t
h
e m
e
a
n
s th
a
t
en
sure
s th
e
sta
b
il
ity
o
f
th
e
vo
lt
age
a
n
d
in
c
r
e
a
s
ing th
e f
l
ow of
a
c
tive p
o
we
r [9
].
Th
e
shun
t comp
en
sa
tion
can
b
e
in
sta
l
l
e
d n
e
ar th
e lo
a
d
, in a
di
st
ri
b
u
t
i
o
n
st
at
i
on,
al
o
ng t
h
e di
st
ri
b
u
ti
o
n
o
u
t
l
e
t
o
r
i
n
a
t
r
a
n
sp
or
t
sta
t
i
on.
Eac
h
a
p
pl
i
c
a
t
i
on ha
s
di
ffe
re
nt
obj
ec
ti
ve
s.
Re
act
i
v
e s
h
u
n
t
c
o
mpe
n
sat
i
o
n ca
n
be
in
duct
i
v
e
or
c
a
p
a
ci
ti
ve.
At
t
h
e
l
o
a
d
l
e
v
e
l
,
a
t
the
dist
ri
but
io
n
sta
tio
n
an
d a
l
on
g
th
e
st
ar
t
of
t
h
e
d
i
str
i
bu
t
i
on
, c
o
mp
en
sa
tion
is
g
e
n
e
r
a
l
l
y
cap
a
c
it
iv
e
[10
,
1
2
].
2.
L
I
TE
RAT
U
R
E
RE
VIE
W
2.
1.
R
e
ac
t
i
ve
e
n
er
gy
c
o
m
p
e
n
s
a
ti
on
The
t
r
ans
m
i
s
si
on
of rea
c
t
i
v
e
pow
e
r
by
dist
ri
but
io
n
l
i
ne
s
a
n
d
t
r
a
n
s
f
o
r
me
rs has man
y
d
r
aw
ba
ck
s wit
h
re
g
a
rd
to t
h
e
c
o
n
s
tr
u
c
ti
on a
n
d
op
e
r
ati
on of t
h
e
ele
c
t
r
i
c
a
l sy
ste
m
.
A
c
tiv
e lo
s
s
es a
r
e
i
n
cr
ea
se
d an
d a hig
h
e
r
c
r
oss
-
sec
t
i
o
n o
f
t
h
e
l
i
n
es is somet
i
m
es re
q
u
i
r
e
d.
R
eac
ti
ve
l
o
sse
s
(t
ra
nsf
o
rmer
s) a
r
e
a
l
so
inc
r
ea
se
d
[
1
3,
14
]
.
The
re
ac
ti
ve
p
o
we
r
has
a
l
w
a
ys be
e
n
di
f
f
i
c
u
l
t
t
o
ac
hi
eve
a
bal
a
nc
e be
tw
e
e
n a
mi
ni
mu
m
a
m
ou
nt
of
re
a
c
t
i
v
e
p
o
w
e
r
f
l
o
w
Q a
n
d a
su
ff
ic
ie
n
t
a
m
o
u
n
t
of
rea
c
t
i
v
e
po
w
e
r
f
l
ow
t
o
ma
in
t
a
in
a
prop
er
volt
a
g
e
p
r
of
ile
of
th
e
ne
tw
or
k
(ma
x
i
m
i
z
i
n
g
ac
ti
ve
po
we
r
fl
o
w
ca
pac
i
t
y
P)
[1
5,
16
].
T
h
e
v
o
l
t
a
g
e
set
t
i
ng
o
n
a
n
e
l
e
c
t
r
i
c
a
l
ne
t
w
o
r
k
is
str
o
n
g
l
y
r
e
l
a
t
e
d
to
r
e
ac
tiv
e
po
w
e
r
tr
an
sits [1
7]
. Th
e
fi
rst
ste
p
t
o
main
ta
in
th
e
vo
lta
g
e
at a
c
o
rr
ec
t le
v
e
l
is to
min
i
miz
e
the
s
e
tr
an
sit
s
,
fo
rc
in
g cu
s
t
o
m
ers
c
onn
e
c
t
e
d to
t
h
e
n
e
two
r
k
t
o
li
mit the
i
r
r
e
ac
tiv
e
po
w
e
r
c
o
n
s
u
m
pt
io
n
(
t
he
l
o
ads
a
r
e
i
n
fac
t
mai
n
l
y
in
duc
ti
ve
)
[
2
0
]
.
Thi
s
rea
c
t
i
v
e
p
o
we
r c
o
mpe
n
sa
ti
on i
s
us
ua
ll
y
d
o
n
e
t
h
r
o
u
g
h
ca
pac
i
t
y
ban
k
s
c
o
n
n
e
c
t
e
d t
o
t
h
e
b
u
s
ba
r
o
f
the
ar
r
i
va
l
of
the
sta
t
ion
.
A
n
al
t
e
r
n
a
t
or
ca
n a
l
so
pe
r
f
o
r
m
it,
a
t
le
ast
p
a
rtia
lly
.
Th
e p
o
we
r
f
a
cto
r
(PF
)
is
eq
ua
l
to
t
h
e r
a
t
i
o
o
f
th
e
ac
tiv
e
po
w
e
r
P
MW
to
th
e
app
a
r
e
n
t
po
we
r S
M
V
A
[1
1]
.
T
h
e
p
o
we
r
f
act
or
o
r
a
l
most
C
o
s
(
φ
) and ta
n
(
φ
)
a
r
e
linke
d
b
y
th
e
fo
l
l
ow
ing
re
la
ti
o
n
:
(1
)
w
ith
:
The
re
ac
ti
ve
p
o
we
r
pl
ant
Q,
a
nd ap
pa
rent
p
o
we
r S
,
a
ba
n
k
o
f
c
a
p
ac
it
ors
Qc
pow
e
r
is i
n
st
al
l
e
d.
The
re
ac
ti
ve
p
o
we
r
g
o
es f
r
o
m
Q
to
Q ':
The
a
p
pa
re
nt
pow
e
r
g
o
es f
r
o
m S t
o
S
'
.
The
a
p
pa
re
nt
pow
e
r
a
f
t
e
r
c
o
mpe
n
sa
ti
on
S 'i
s t
h
er
ef
o
r
e de
cre
a
sed.
T
h
e
cap
a
c
i
t
y
of
c
o
mp
e
n
sat
i
o
n
by
th
e
ca
p
acit
o
rs is
c
a
l
c
u
l
ated
b
y
:
3
.
².
.
…
.
².
…
(2
)
w
ith
:
′
–
Fi
g
u
re
1 s
h
ows
t
h
e
dia
g
ram
o
f
t
h
e
c
o
m
p
en
sat
i
on
o
f
the
reac
t
i
v
e
ene
r
gy
b
y
t
h
e
c
o
m
p
en
sa
ti
on
c
a
pa
ci
t
o
rs.
F
i
gu
re.
1
F
r
es
n
e
l
rep
r
ese
n
t
a
t
i
on of
ac
ti
ve,
r
e
a
c
t
i
v
e an
d a
p
par
e
nt
p
o
w
e
r
ve
ct
ors
T
h
e
m
a
x
i
mu
m
tr
an
s
f
e
r
ab
l
e
pow
er
g
i
v
e
n by
[2
1]:
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Opt
i
m
a
l
di
st
rib
u
t
i
o
n
of
p
o
w
e
r un
de
r stre
ss
on
p
o
w
e
r gri
d
i
n
re
al-
t
i
m
e
by
…
(Ta
dj
e
ddi
ne Al
i A)
6
87
%
(3
)
S
o
, Th
e r
e
l
a
ti
ve lo
ss
of
t
r
an
smi
ssib
l
e pow
er
∆
is [17
]
:
∆
(4
)
2.
2.
Vo
ltag
e
dr
op i
n
a ps l
o
ad
W
h
e
n
th
e cur
r
en
t
s
are
v
e
ry
h
i
gh
, t
h
e
v
o
lta
g
e
d
r
op
s
i
n
t
h
e
Oh
mic r
e
sist
a
n
c
e
s of th
e
pr
im
ary
and
se
co
nda
ry
t
r
a
n
sf
or
mer
wi
n
d
in
gs a
n
d i
n
t
h
e
l
e
a
k
age
,
ind
u
c
t
o
r
s
m
u
st
be t
a
ke
n i
n
t
o
acc
o
unt
[2
2,
2
5
]
.
Th
e
mag
n
e
t
i
z
i
n
g
cu
rr
en
t a
n
d
t
h
e
i
r
on lo
sses
rem
a
i
n
li
nk
ed
to
th
e
f
l
ux
. In
pra
c
tic
e, t
h
e
vo
lta
g
e
dr
op
in
th
e
p
r
imar
y resi
sta
n
ce
s and
re
ac
tan
c
e
is w
e
a
k
i
n
f
r
on
t
o
f
t
h
e
vo
lta
g
e
by
u
s
ing th
e
K
a
pp
equ
a
tio
n,
w
e
w
ill h
a
v
e
[2
4]:
.
(5
)
w
ith
:
U1
an
d
U
2
: P
r
imar
y
a
n
d
seco
nda
r
y
vol
t
a
ges
,
Rs
an
d
ls
: R
e
sista
n
c
e
o
f
t
h
e
wi
n
d
i
ng
s
and
t
h
e
in
du
c
t
an
c
e
o
f
le
ak
s b
r
o
ugh
t b
a
c
k
to
s
e
c
onda
ry.
n1
an
d n
2
:
N
u
mbe
r
of
p
r
i
m
ar
y a
n
d
se
c
o
n
d
ar
y t
u
r
n
s.
In
re
a
lit
y, R
s
I2
, a
nd I
s
ar
e w
e
a
k
i
n
f
r
o
n
t
o
f
U
2
a
n
d w
e
ca
n
of
te
n us
e a
simp
l
i
f
i
ed
r
e
la
ti
o
n
,
we c
a
n bu
i
l
d
t
h
e in ad
di
ti
on
, the
v
o
l
t
a
g
e
d
r
o
p
s in the
syst
e
m
are
i
n
cre
a
s
ed, henc
e
t
h
e ne
ed
t
o
c
h
o
o
se
a high
e
r
re
g
u
la
ti
o
n
r
a
n
g
e
o
f
t
a
p c
h
an
ge
r
s
f
o
r
a
u
t
o
t
r
ans
f
or
me
rs
i
n
no
r
m
a
l
si
t
u
at
i
on
(
N
)
o
r
a
not
he
r
met
h
o
d
of
w
h
i
c
h
t
h
e m
o
st
reco
g
n
i
z
e
d
i
s
the
disc
o
n
n
ect
of cha
r
g
e
i
n
cr
it
i
cal
si
t
u
a
t
i
o
n
(N-1
) ca
ll
ed
t
h
e
el
ec
tric
al
l
o
a
d
s
h
e
ddi
ng
[2
6
-
2
8
]
.
Th
e vo
lta
g
e
d
r
op
of
a
tr
a
n
smiss
i
o
n
li
n
e
f
o
r
th
e
th
ree-
ph
a
s
e AC
sy
ste
m
i
s
g
i
ven
by
t
h
e fo
llo
w
i
n
g
eq
u
a
ti
on
[2
9]
:
%
%
√
(6
)
w
ith
: A
= cro
s
s-
se
c
tion
,
l
=
lin
e
le
ng
th
,
I
l
= lin
e
cu
rr
en
t
,
P = a
c
t
i
v
e
p
o
w
e
r to
b
e
t
r
ansm
itte
d
,
κ
=
el
ec
tri
cal
co
nd
u
c
ti
v
ity
, U
=
ph
a
s
e-
t
o
-ph
a
se
vo
l
t
ag
e
,
u
=
re
la
tiv
e
vo
lta
g
e
(
%
),
co
s
ϕ
1 =
p
o
we
r
fa
ct
or
F
r
e
s
n
e
l v
e
c
t
or
s
asso
cia
t
e
d
w
i
th
th
e vo
lt
ag
e
s
, th
e
eq
u
a
tion
of th
e
vo
lta
g
e
dro
p
:
\Th
e
vo
lta
g
e
d
r
op
i
s
a
di
ff
e
r
e
n
ce o
f
the
RMS
val
u
es of
t
h
e
u
n
l
o
ade
d
a
n
d u
n
l
o
ade
d
se
c
o
nda
r
y
vol
t
a
ge
f
o
r
t
h
e sa
me
pri
m
a
r
y
vol
t
a
ge
U
1
.
∆
(7
)
F
i
gu
r
e
2.
F
r
e
s
n
e
l rep
r
ese
n
t
a
t
i
on of
v
o
lt
a
g
e ve
ct
ors [
30]
.
Usi
n
g
Fi
g
u
re
2
the
pr
oj
ec
t
i
on
on t
h
e
a
x
i
s
a
b
,
t
h
e de
vel
o
p
m
e
n
t
o
f
t
h
e
e
quat
i
o
n
gi
ve
s [2
6
]
:
∆
co
s
si
n
(8
)
The
v
o
lt
age
dr
op
i
s
pr
op
o
r
t
i
o
nal
t
o
t
h
e c
u
r
r
e
nt
o
u
t
p
ut a
n
d
t
h
e
nat
u
re
of t
h
e
l
o
a
d
.
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
8
5
–
691
68
8
B
y
a
d
j
u
sti
n
g
t
h
e
re
act
i
v
e
po
we
r
.
in
low vo
ltag
e
b
u
s
d
e
li
v
e
r
e
d to th
e e
l
e
c
tri
c
a
l
n
e
t
w
ork
,
a
TSC
ma
k
e
s
i
t
po
ssi
b
l
e to
a
d
j
u
st the
vo
lt
ag
e
of
th
e n
e
t
w
ork a
c
c
o
r
d
i
n
g to
th
e form
u
l
a
[
2
8
]
:
∆
.
(9
)
wi
th:
∆
,
R
e
prese
n
t
s
t
h
e
rel
a
t
i
ve
v
o
lt
ag
e
va
ria
t
ion,
,
Th
e s
hort
-
c
i
r
c
u
i
t
po
w
e
r
o
f
the
n
e
twor
k.
3.
RE
SUL
T
S
3.1.
Sy
ste
m
de
sc
ri
pti
o
n
The
st
udie
d
s
y
ste
m
i
s
co
mp
o
s
ed as
i
n
dic
a
t
e
d i
n
Ta
bl
e 1
be
low:
Tab
l
e 1
.
D
e
s
c
r
i
p
t
i
o
n of
t
h
e
e
l
ect
ri
ca
l
sy
ste
m
Ge
n
e
r
a
to
r
Ce
ntral TG/C
C
02
buse
s
L
oad buse
s
G
e
nerator buse
s
17
02
T
r
ansform
ers
10
L
ines
22
3.2.
V
o
l
t
ag
e
co
ntro
l
and
t
r
a
n
si
t li
mi
ts
Ta
ble
2
bel
o
w i
l
lust
ra
te
s
t
h
e
vol
t
a
ge
a
n
d
tra
n
si
t l
i
mi
ts;
Tabl
e
2. Li
mi
t
of n
o
d
e
vo
l
t
ag
e
s
an
d tra
n
si
ts
unde
r no
rma
l
c
o
n
d
i
t
i
on
s
V
o
ltage
Low
e
r
li
m
i
t
uppe
r l
i
m
i
t
220
K
V
0
.
93 p
u
1.
09
pu
60 K
V
0
.
93
p
u
1.
09
pu
Tr
ans
its
Li
ne 80
%
Tr
ans
f
orm
e
r
80
%
Fi
gu
re
3 sh
ows
the
i
m
ple
m
e
n
ta
ti
on
of
t
h
e st
u
d
y
mode
l i
n
t
h
e
R
T
si
m
u
la
tor
.
F
i
gu
re
3.
The
mo
del
t
o
st
u
d
y
u
nde
r t
h
e
RT
si
mul
a
t
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Opt
i
m
a
l
di
st
rib
u
t
i
o
n
of
p
o
w
e
r un
de
r stre
ss
on
p
o
w
e
r gri
d
i
n
re
al-
t
i
m
e
by
…
(Ta
dj
e
ddi
ne Al
i A)
6
89
3.
3.
S
i
m
u
la
t
i
o
n
s re
s
u
l
t
s
The resul
t
s we
re
ca
lc
ula
t
e
d
b
y
t
h
e
a
cce
le
ra
t
e
d Gaus
s-Sei
d
el
met
h
o
d
wi
th the
ac
cel
erat
i
on fac
t
o
r
of
1.
45
an
d a
p
r
ec
isi
on of
10
.
Ca
se
01
: c
a
lc
u
l
a
t
i
o
n
w
i
t
h
ou
t c
o
mp
ensa
ti
o
n
Th
e
r
e
su
lts
ob
ta
in
e
d
f
o
r
22
0
/
60
k
V
vo
l
t
ag
e
s
w
ith
ou
t
co
mp
en
sa
tion
a
r
e sh
ow
n in
F
i
gu
r
e
4.
Fi
gu
re
4.
Va
r
i
a
t
ion
of
l
o
a
d
vol
t
a
ges
a
c
c
o
r
d
in
g to
t
h
e
mar
g
in
a
l
and
cri
t
i
c
a
l
no
de
s
wi
th
ou
t co
mp
en
sat
i
on
(P
F)
Ca
se
02
:
Ca
lc
ula
tio
n
w
ith o
p
tima
l
c
o
mp
en
sa
t
i
o
n
The
Fi
g
u
res
5
sho
w
s
t
h
e
c
h
a
nge
i
n
t
h
e
v
o
l
t
a
g
e a
c
c
o
r
d
i
ng
t
o
t
h
e
kn
ow
n
p
o
we
r
s
:
Fi
gu
re
5.
Va
ri
a
t
i
on of
t
h
e l
o
a
d
v
o
l
t
a
g
es acc
o
r
di
ng t
o
t
h
e
ma
r
g
i
n
al
a
n
d
cr
it
i
c
a
l
no
des
wi
th
opt
imal
c
o
m
p
e
n
sat
i
on
(
O
P
F
)
4.
DI
S
C
U
S
SI
ON
S
F
r
om
th
e Fi
gure
4
,
it
is
no
ted
th
at
th
er
e
a
r
e
v
i
o
l
a
tio
n
s
in
vo
lta
g
e
in
08
d
i
f
f
er
e
n
t st
at
ion
s
o
f
le
v
e
ls
22
0/
6
0
kV
r
e
spe
c
t
i
v
el
y
.
We
have
t
w
o
t
ype
s
o
f
vi
ola
t
ions
,
ei
t
h
er
c
r
i
t
i
c
a
l
o
r
mar
g
i
n
al
in
t
h
e
n
o
r
m
al
si
t
u
at
ion
N
a
t
t
h
e
pea
k
of
a su
mme
r
da
y
i
n
Jul
y
2
018
.
T
h
e
r
a
di
al
t
ype
ne
tw
or
k,
an
d
subs
eq
ue
ntl
y
th
e
v
o
l
t
a
ge
d
r
o
p
s
in
t
h
e
re
mo
t
e
sta
tio
n
s
du
e
t
o
th
e lar
g
e
lo
ad
s c
o
n
s
u
m
ed
is
v
e
r
y
lo
g
i
c
a
l. Th
is pro
b
lem
ap
p
e
a
r
s cl
ea
r
l
y in
th
e
n
o
d
e
s
ment
i
o
ned
i
n
f
i
gu
re
4,
a
n
d
in
par
t
i
c
ul
a
r
i
n
t
h
e f
o
l
l
o
w
in
g c
r
i
t
i
cal
no
des:
B
u
s
2,
Bus
3,
B
u
s 6
,
a
n
d
B
u
s
1
4
t
h
ey
ar
e
lo
c
a
t
e
d
i
n
t
h
e
e
n
d
of
th
e
l
i
n
e
.
A
f
te
r
sev
e
r
a
l
al
te
rn
a
t
i
v
e
o
p
t
ima
l
in
sta
l
l
a
tio
n
o
f
th
e c
o
mp
en
sa
tio
n
mean
s
in
t
h
e ne
t
w
o
r
k no
de
s,
t
h
e
o
p
ti
mal
sta
t
ions l
o
ca
t
e
d f
o
r
the
co
mpe
n
sat
i
o
n
a
r
e
a
s
f
o
ll
o
w
s i
n
B
u
s2
, B
u
s
9,
a
n
d
Bus
12
.
The
o
p
t
i
mal
sol
u
ti
on
pr
o
pos
ed
i
s
t
o
ins
t
al
l
a c
a
p
ac
it
y
of
e
i
g
h
t
M
v
a
r
on
t
h
e
t
w
o
n
o
d
e
s
:
b
u
s
t
w
o
a
n
d
ni
ne
an
d a
n
o
t
h
e
r
cap
a
c
it
y
o
f
1
0
Mv
ar
on
th
e node
: Bu
s
1
2
. Th
e op
tim
al
co
mpen
sa
ti
on
o
f
r
e
a
c
ti
v
e
in
t
h
ese
n
o
d
e
s
w
ill
str
e
ng
th
en t
h
e
marg
i
n
of
sta
b
ili
ty
f
o
r
po
we
r t
r
a
n
smi
ssi
o
n
in
t
h
e
so
u
t
he
rn
reg
i
o
n
o
f
Al
g
e
r
i
a
.
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
85
– 69
1
69
0
3.
1.
PE
RT
ES
AC
T
I
VE
S
DU
S
Y
ST
È
M
E
Th
e Fi
gu
re
6 show
s th
e
r
e
s
u
lts
o
f
a
c
ti
v
e
l
o
sses
du
r
i
ng p
e
a
k
hou
r
s
w
i
t
h
ou
t and
w
ith
op
ti
ma
l
co
mp
ens
a
ti
o
n
:
Fi
gu
re
6.
Tot
a
l
ac
t
i
ve
l
o
sse
s
In
Tabl
e 7
p
r
es
e
n
ts the
res
u
lt
s
o
f
t
h
e
act
i
v
e l
o
sses i
n
t
h
e di
ffere
nt ca
ses wi
t
h
t
h
e
rat
e
of re
duc
ti
o
n
.
Tabl
e
7: Re
d
u
c
t
ion T
o
ta
l
ac
t
i
v
e
l
o
sse
s
Loss-
M
W
Loss
-Mvar
L
o
ss-MVA
Wit
h
out
com
p
e
n
sa
tion (
P
F
)
12.
40
83.
69
84.
60
Wit
h
O
PF
10.
92
81.
15
81.
88
Reduc
tion %
11.
91
3.
04
3.
22
The re
sul
t
s
o
b
t
ai
ned s
h
o
w
t
h
at
aft
e
r
c
o
mpe
n
sat
i
o
n
o
f
the
reac
t
i
ve
e
n
e
r
g
y
,
t
h
e ac
ti
v
e
l
o
sse
s
of t
h
e
syst
em a
r
e r
e
duce
d
.
T
h
e
l
o
ss
red
u
c
t
i
o
n r
a
t
e
u
s
i
n
g c
o
nve
nt
io
na
l
co
m
p
en
sat
i
on
me
a
n
s i
n
s
u
bst
a
t
i
ons
wit
h
v
o
lta
g
e
v
i
o
l
a
tio
n
s
is e
s
tim
at
ed
a
t
11
.9
1%
c
o
mp
ared
to
th
e
firs
t ca
se
, wh
ic
h
i
n
c
r
ea
se
s th
e
c
a
p
a
ci
t
y
o
f
tr
a
n
sit po
w
e
r
.
5.
CO
NCL
US
IO
NS
We
ha
ve st
ud
i
e
d t
h
e
pr
obl
e
m
o
f
opt
i
m
al
c
ont
r
o
l
o
f
v
o
l
t
a
g
e a
n
d
re
ac
t
i
v
e
po
wer
in
ra
dia
l
t
ype
ne
tw
or
k
of
t
h
e S
A
I
D
A-B
e
c
h
e
r
a
r
ea
l
o
ca
t
e
d i
n
so
ut
h-
w
e
st
of
Alge
ri
a.
The
c
h
oi
ce
of
l
o
cat
i
on
of
t
h
e
co
mp
ens
a
ti
o
n
p
o
i
n
t
is
of
cruc
ial
imp
o
r
t
a
n
c
e
fo
r
m
a
i
n
ta
inin
g t
h
e
v
o
lta
ge
wi
t
h
in
th
e
pe
rmi
s
sib
l
e
l
i
mi
ts a
nd
r
e
sol
v
i
n
g t
h
e
volt
a
ge
dr
o
p
s
i
n
the
60
kV
s
ubst
a
ti
o
n
s.
T
h
i
s
sce
n
ari
o
pla
nni
ng
fo
r
t
h
e
S
o
u
t
h
-
West
Al
ge
ri
a
n
po
we
r g
r
i
d
i
s
ve
r
y
usef
ul
,
i
t
wil
l
make
i
t
possi
bl
e t
o
p
r
e
d
et
ermi
ne
the
n
e
xt
st
at
e of
t
h
e
ne
tw
or
k
fo
r
a
gi
ve
n
pr
oduc
ti
o
n
pla
n
a
s
we
ll
as
f
o
r
a
de
ma
n
d
i
n
f
i
xe
d
po
we
r,
t
h
e
r
e
e
x
ist
s
a
pr
io
r
i
a
n
i
n
f
i
ni
t
y
of
pl
a
n
s
of
p
r
od
u
c
ti
on
pos
si
ble
.
F
o
r
t
h
i
s
,
t
h
e
o
p
ti
mal
di
str
i
but
i
o
n o
f
t
h
e
po
wer a
p
pea
r
e
d
to o
p
t
i
m
i
z
e
t
h
e pr
o
d
u
ct
ion
o
n
the
var
i
ous
po
we
r st
at
i
o
ns a
nd t
o
ma
xi
miz
e
the
t
r
a
n
si
t
o
f
po
we
r
whi
l
e
cont
i
nui
n
g
to
s
a
t
i
sf
y
t
h
is
dem
a
nd
in
an
ec
on
omi
cal
a
nd r
e
l
i
a
b
l
e
w
a
y.
T
h
e
a
d
va
nt
age o
f
u
s
i
ng di
git
a
l envi
r
o
nm
ent
s
has made
it
possi
bl
e t
o
i
m
p
r
o
v
e t
h
e
qu
al
it
y of
t
h
e st
ud
y
an
d
t
o
sa
ve
a l
o
t
o
f
ti
me, in
pa
rt
ic
ula
r
i
n
the
te
ch
ni
cal
p
r
obl
em
s
tha
t
it
c
o
nt
ai
n
s
the
al
g
o
ri
th
m
s
an
d
its c
o
nv
erg
e
n
c
e
prob
l
e
m
s
.
RE
FE
RE
NC
ES
[1
]
K
.
To
ng
, Y
.
Ji
a
ngan
g
,
“A Hy
br
id A
ppro
a
ch fo
r
P
o
wer S
y
stem
Secu
rity
Enh
a
nc
emen
t v
i
a
Optimal
Ins
t
a
l
la
tion
of
F
l
exible AC
Tr
a
n
smiss
i
o
n
S
y
stem
(F
ACTS
) Dev
i
ces”
,
Ener
gies
,
1
0
,
13
05
, 2
017
.
[2
]
T. Ay
umu,
Y
.
Hiroaki
,
and
o
t
h
e
r
,
“New H
ybrid
S
t
atic
VA
R Co
mpen
sato
r
with
S
e
ries
Ac
tive
F
ilter
”, En
ergies
1
0
,
16
17
,
2
0
17.
[3
]
T. Ri
ka
nth
,
S
.
Se
l
v
i,
P.
Pu
shy
a
,
“
O
p
t
i
m
a
l
Pl
a
cem
e
n
t
o
f
Sta
tic
VAR
C
o
m
p
e
n
sato
r (SVC)
in
Po
we
r Sy
st
e
m
along
wi
th
Wi
nd
Pow
e
r
Ge
n
e
ra
t
i
o
n
”
,
I
E
EE,
Au
to
matic Co
ntro
l
ICEIC
E
20
17
,
1-6,
20
17.
[4
]
D
.
William
,
“El
e
men
t
s
of
pow
er sy
stem
an
alys
is
”,
Ed
itio
n
D
u
n
o
d
,
paris,
20
01.
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
Opt
i
m
al
di
st
ri
b
u
ti
on
of
pow
er un
der
st
ress
on
p
o
w
e
r gri
d
i
n
re
al
-t
ime
by
…
(T
a
d
j
e
d
d
i
n
e
Al
i
A)
6
91
[5]
M.
G. Mo
li
n
a
,
“Mo
d
e
l
li
n
g
a
nd Con
t
rol
o
f
Gri
d
-c
on
ne
c
t
e
d
So
la
r P
h
ot
o
v
o
l
t
a
ic Sy
st
e
m
s”
,
Ch
a
p3,
Re
ne
wa
bl
e Ene
r
g
y
-
Uti
l
i
z
a
t
i
o
n
a
n
d
S
y
st
e
m
In
t
e
grat
ion
,
p
p
.
53
-8
3
.
2016
.
[6]
A.U
.
Lawan
,
S
.
Bab
a
ni
,
an
d
oth
e
rs,
“P
o
w
er
co
m
p
en
sation
fo
r
v
e
ctor-b
ased
cu
rre
n
t
con
t
ro
l of
a
mod
u
lar
mu
ltile
v
e
l
c
o
nv
e
r
te
r (MMC
) b
a
se
d
STAT
COM”
I
n
tern
at
i
o
na
l Jo
ur
na
l o
f
Po
w
e
r
E
l
ec
t
r
o
n
i
c
s
a
n
d
Dr
ive
Sys
t
em (
I
J
P
ED
S)
, vo
l.
1
0
,
no.
4,
pp.
1
7
8
1
-
17
96
,
2
0
1
9
.
[7]
L
.
L.
G
r
i
g
sby,
"El
e
ct
ri
c
Pow
e
r Genera
t
i
on, T
r
ans
m
i
s
si
on,
and
Distri
buti
on -
T
h
ird editi
on,
"
b
ook,
CRC Pres
s
e
d
it
io
n
,
E
l
e
c
t
ric Po
we
r Ge
n
e
rati
o
n
,
p
p
.
2.
1-2
.
9,
2
0
12
.
[8]
A.
M. Elshe
rb
iny
,
A.
S
.
Na
da
,
Mo
ha
m
m
e
d
Ka
m
a
l,
“
S
m
o
o
t
h tra
n
si
ti
on from gri
d
t
o
sta
n
d
a
l
one
so
la
r die
s
e
l
m
o
d
e
hy
brid g
e
nera
tio
n
sy
stem with
a
battery
”,
In
t
e
rn
a
t
i
o
n
a
l J
o
urna
l of P
o
w
e
r
El
e
c
tron
i
c
s a
n
d
Driv
e
Syst
e
m
(IJPE
DS
)
,
v
o
l
.
1
0
,
n
o
.
4
,
pp.
2
0
6
5
-
20
75,
2019
.
[9]
W
.
Zha
n
g, W. Liu
, a
nd o
t
he
rs,
"
D
istri
b
ut
e
d
m
u
l
t
i
p
l
e
a
g
e
n
t sy
st
em
ba
se
d o
n
l
i
ne
o
p
t
i
m
al
rea
c
t
i
v
e
po
we
r co
nt
rol for
smart gr
ids
,"
I
E
E
E
T
r
ans
. S
m
a
r
t
Gr
id
,
vo
l.
5,
n
o
.
5,
pp
.
2
4
21-2
4
3
1
,
201
4
.
[10]
C.
R. Ba
y
l
i
s
s,
B.
J
.
Ha
rd
y, “T
ransm
i
ssio
n
a
nd D
i
stri
bu
ti
on
E
l
ec
t
r
ic
al
E
n
g
i
ne
e
r
i
ng”
, Bo
ok
,
fou
r
th
e
d
it
io
n
,
Ne
wnes
e
d
it
io
n
,
Cha
p
.
2
8
Fu
nd
a
m
e
n
ta
l
s
, pp
.
1
1
2
4
-
11
31,
20
12
.
[11]
A. A
b
d
u
lk
arim
,
S
.
M
.
Ab
de
lkad
er, an
d
oth
e
rs
, “E
ffect of
we
athe
r
and
the
hy
brid
e
n
erg
y
stor
age
o
n
th
e av
a
i
lab
i
l
i
ty
o
f
sta
n
d
a
lo
ne
m
i
c
r
og
ri
d”
In
tern
at
io
na
l Jo
ur
nal
o
f
Renewa
b
l
e En
er
gy Res
e
arch
(IJ
RER)
,
Vol.
6, n
o
.
1,
p
p
.
18
9-1
98,
20
16
.
[12]
D.P
.
Romm
el,
D. Di M
a
io
, T
.
Tin
g
a
,
“Calcu
la
tin
g
wi
nd tu
rb
in
e
co
m
p
on
ent lo
ads
for impro
v
e
d life
pred
ict
i
on
”,
Elsev
i
er L
t
d,
R
e
newa
ble
En
e
r
g
y
14
6,
20
20,
22
3-2
4
1
.
[13]
I. Vech
iu
, ‘‘M
o
délisat
i
o
n
, Co
m
m
an
d
e
et In
tégrat
io
n
de l
a
P
r
o
ductio
n
Décen
tralisée d
a
n
s
les µréseau
x’
’,
diss
ertation
, G
r
en
ob
le IN
P
,
ch
ap
.
0
1&04
, 2
0
1
3
.
[14]
M.
Ahm
e
d, M.
EL
-Shi
m
y
,
a
nd
ot
he
rs, “
S
iz
in
g
o
f
rea
c
t
i
v
e
po
we
r
c
o
m
p
e
n
sa
t
o
rs fo
r on
sh
ore
a
n
d
offsh
o
re g
r
id
c
o
nn
e
c
t
e
d wi
nd
fa
rm
s”
,
In
du
st
ry Ac
a
d
e
m
i
a
Co
l
l
abo
rat
i
o
n
(IAC)
Con
f
e
r
e
n
ce
,
E
n
ergy
an
d su
st
a
i
n
a
b
l
e
dev
e
l
op
me
n
t
Trac
k
,
Apr. 6 –
8
,
20
15.
[15]
N.M
.
S
a
lg
ado
Herrera
, A.
M
e
dina-R
io
s, R
.
Tapi
a-Sán
c
he
z an
d oth
e
rs,
“R
eac
tive
P
o
wer
Co
mpen
sation
i
n
Distrib
u
ted
Ne
tw
ork
s
with
Win
d
Turbine In
teg
r
atio
n us
in
g R
e
so
nant Correc
t
o
r
”,
IE
E
E
, 9
78-1
-
50
90-4
2
8
1
-4
/17
,
20
17
.
[16]
V.
C
.
Sekhar
, K. Kant, B.
Singh,
"DST
AT
COM
suppor
ted
in
duction
g
e
ner
a
tor
for im
provi
n
g
power quality",
IET
R
e
ne
wa
ble
P
o
we
r
Ge
n
e
ra
ti
o
n
,
v
o
l.
10,
no. 4,
p
p
.
4
9
5
-
50
3
,
4
2
0
16.
[17]
M
.
E
L
-S
h
i
my
,
“
R
eac
tive
p
o
w
e
r
manag
e
men
t
and
con
t
rol
o
f
d
i
sta
n
t l
a
rge-sc
al
e
gri
d
conn
ected
offs
ho
re wind
po
wer
farms”,
In
ter
n
a
t
i
ona
l Jour
na
l
o
f
S
u
s
t
a
i
n
able
Ene
r
g
y
,
iFi
r
st,
20
12,
1
–
1
7
.
[18]
M.
Na
se
r,
A.
Agh
b
o
l
a
g
h
i
,
a
nd
ot
h
e
rs, “
P
owe
r
Sy
ste
m
s R
e
active
Pow
e
r
Control in AC Pow
e
r
System
s
F
u
n
d
ament
a
ls
an
d
Curren
t
Is
su
es”,
Edition springer
,
20
17.
[19]
Ali.A
.
T
a
djed
di
ne, A
.
Ch
ak
er,
M
.
Khia
t,
L. A
b
d
e
lm
alek
,
N.
Kha
l
fal
a
h, “
A
c
o
ntri
bu
ti
on
to th
e
con
t
r
o
l o
f
vo
l
t
a
g
e
and
p
o
wer
of
th
e inte
r
c
o
n
n
e
ctio
n be
tween
tw
o
decen
traliz
ed
electr
i
ca
l grid
s wi
th
an op
tim
a
l lo
c
a
l
i
za
tio
n
of
th
e
S
V
C devices
in
real-
t
im
e”
,
Int
e
r
n
at
io
na
l J
o
urna
l o
f
Po
we
r E
l
e
c
t
r
o
n
i
c
s
a
nd Driv
e
Sy
st
e
m
(IJ
P
E
D
S
)
, Vol
.
10
,
no
.
1,
p
p
.
17
0~
17
7, 201
9.
[20]
Aya
M.
E
l
sherbi
ny,
Adel
S
.
Nada,
Mo
hammed
Kamal,
“Smoo
t
h t
r
ansition
from
grid t
o
stand
a
l
o
ne solar
diesel
m
o
de
hy
bri
d
gen
e
ra
ti
o
n
syste
m
wi
th
a
ba
t
t
e
r
y
”
,
Inte
rna
t
i
o
n
a
l
J
o
urna
l
of
Po
we
r El
ec
t
r
o
n
ic
s
an
d Driv
e
S
y
stem
(IJP
E
DS)
,
Vol.
1
0
,
n
o
.
4
,
pp.
2065
-20
7
5
,
20
19.
[21]
H. Wolfg
a
ng
,
S
.
J
u
rg
en,
J.
Wolf
gang
,
“Re
a
c
t
iv
e
P
o
wer Co
mpensati
on -
A P
r
actical
Guid
e”
,
Wile
y ed
ition
,
ch
ap.3
Effec
t
of
Re
act
ive
P
o
wer,
pp
.22
-
27
, 20
12
.
[22]
T. S
r
ik
a
n
th
, S
.
C. S
e
lv
i,
V.
N.
P
u
sh
ya, “O
ptim
al
p
l
acem
en
t o
f
static
VA
R com
p
ensator
(SV
C
)
in
po
wer
sys
t
e
m
a
l
on
g wit
h
win
d
po
we
r
g
e
n
e
ra
ti
on
”
,
IEE
E
In
ter
n
a
t
iona
l
Conferen
c
e
on
Ele
c
tr
ica
l
,
In
s
t
ru
men
t
a
t
ion
a
n
d
Com
m
un
ica
t
ion
En
gine
ering
(IC
EICE),
Ka
rur,
pp.
1-6,
2
0
17.
[23]
De
sh
pa
nd
e
Chi
n
m
a
y V., De
sh
pa
nd
e
Chai
ta
n
y
a
V.
,
“
O
p
t
i
m
um
d
e
sig
n
of d
y
n
a
mic
v
o
l
t
a
g
e
re
st
orer fo
r volt
a
ge
sa
g
m
i
ti
g
a
t
i
o
n
in
d
i
stri
bu
ti
on n
e
twor
k”
,
In
tern
atio
na
l
Jou
r
na
l o
f
Po
w
e
r El
ectr
o
n
i
cs a
n
d
D
r
ive S
y
stem
(IJPEDS
)
, Vo
l
.
1
0
,
no.
3,
pp.
1
3
6
4
-
13
72
,
2
0
1
9
.
[24]
S
h
aimaa S
h
ukri
A
.
Alha
lim
,
Lu
b
n
a A
.
A
l
n
a
bi, “
E
nh
anc
e
men
t
tra
n
s
i
ent
stab
ility
o
f
wind
p
o
w
e
r s
y
s
t
em
of Dou
b
ly-
F
e
d indu
ction
g
e
nera
tor us
in
g
S
T
A
T
COM
an
d P
I
con
t
roller”
,
In
ter
natio
na
l Jo
u
r
n
a
l of
Power
Ele
c
tro
n
ic
s
an
d
Dr
ive S
y
st
em (I
J
P
EDS
)
,
Vo
l.
1
0
,
no
.
4
,
pp.
1
9
7
7
-
19
85
,
2
0
19.
[25]
J. M
o
ri
n, “
C
o
o
rd
in
a
t
i
o
n
d
e
s
m
oye
n
s
de ré
g
l
a
g
e
d
e
la
t
e
nsio
n
à
l’i
n
t
e
rfa
c
e
ré
se
a
u
x
de
t
r
a
n
sp
ort et d
e
d
i
stri
buti
o
n
,
é
v
ol
ut
io
n du
rég
l
a
g
e tem
p
s réel d
e
l
a
te
n
s
i
o
n
d
a
ns l
e
s
ré
se
a
ux d
e
di
st
ri
bu
ti
o
n
’’,
Éc
o
l
e
do
ctora
l
e: Sc
ie
n
c
e
des
Mé
t
i
e
r
s d
e
l
’
in
g
é
ni
e
u
r,
20
16.
[26]
J.H. Gridley
,
“
P
rincipl
e
s
of
E
l
e
c
tr
i
cal
Tran
sm
is
sion
Lines
in
P
o
wer
an
d Co
mm
un
ica
t
io
n”
, Perg
a
m
on
Pre
s
s
Ltd
.
Fi
rst
Edition.
[27]
C
.
J.
Wo
ng
, M
.
D
.
M
i
ll
e
,
“G
ui
d
e
li
n
e
s
f
o
r
El
e
c
tr
ica
l
T
r
an
sm
iss
i
on
Lin
e
S
t
ru
ctu
r
al Load
in
g
”
,
Am
eric
an
S
o
cie
t
y
o
f
C
i
v
i
l
En
gi
n
eer
s,
Th
ir
d
Ed
it
i
o
n
,
2
0
1
0
.
[28]
S.
X.
Ch
e
n
,
Y.
S
.
Fo
o.
Ed
dy,
a
n
d o
t
h
e
r, “
A
Ce
ntra
liz
e
d
Rea
c
t
i
v
e
P
o
we
r Co
m
p
e
n
sa
ti
on
Sy
stem
for L
V
Di
st
rib
u
t
i
on
Ne
twor
ks”
,
I
E
E
E
Tr
ans
actions
On Power S
y
stem
s
,
20
14
, pp
1-1
1
.
[29]
S.
Ka
la
g
a
,
P.
Yen
u
m
u
l
a
“
D
e
s
ig
n of
E
l
e
c
tri
c
a
l
T
r
a
n
sm
i
s
si
on
Li
nes,
Stru
ct
ure
s
a
n
d
Fo
un
d
a
ti
on
s”,
T
a
yl
o
r
& Fra
n
cis
Grou
p,
L
o
n
d
o
n
,
UK Vol
u
m
e
1, 201
7
.
[30]
A. Key
h
an
i, M
.
N. M
a
rwali, M
i
n
D
a
i,
“Int
egra
tion
o
f
g
r
e
e
n
an
d
renew
a
bl
e en
erg
y
in
el
ectric p
o
wer
sy
stems”,
Bo
ok
,
e
d
i
t
i
on Wi
le
y,
c
h
a
p
.2,
20
1
0
.
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