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[
4
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I
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liter
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I
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in
[
5
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in
[
7
]
,
th
e
au
t
h
o
r
s
p
r
esen
t
a
m
et
h
o
d
th
at
allo
w
s
o
b
tain
in
g
th
e
o
p
ti
m
a
l
p
lace
m
e
n
t
an
d
s
izi
n
g
o
f
w
in
d
p
o
w
er
g
en
er
ato
r
s
in
p
o
w
er
g
r
id
s
w
i
th
t
h
e
p
u
r
p
o
s
e
to
r
ed
u
ce
r
ea
ctiv
e
p
o
w
er
lo
s
s
e
s
a
n
d
c
o
p
i
n
g
m
a
x
i
m
u
m
lo
ad
ab
ilit
y
m
ar
g
in
.
A
ls
o
,
Sin
g
h
et
al.
[
8
]
p
r
esen
ts
an
ap
p
r
o
ac
h
th
at
p
er
m
its
g
etti
n
g
t
h
e
o
p
ti
m
u
m
v
al
u
e
o
f
r
ea
ctiv
e
p
o
w
e
r
o
u
tp
u
t
b
y
a
w
i
n
d
f
ar
m
w
i
th
t
h
e
o
b
j
ec
tiv
e
to
m
i
n
i
m
ize
p
o
w
er
lo
s
s
es
a
n
d
to
im
p
r
o
v
e
v
o
lta
g
e
p
r
o
f
ile
b
y
u
s
i
n
g
g
e
n
etic
al
g
o
r
ith
m
.
B
esid
es,
th
e
a
u
th
o
r
s
i
n
[
9
]
d
is
cu
s
s
a
n
o
p
ti
m
izatio
n
p
r
o
b
le
m
in
w
h
ic
h
th
e
g
o
al
is
to
f
i
n
d
t
h
e
o
p
ti
m
al
p
lace
m
e
n
t
an
d
s
izi
n
g
o
f
w
i
n
d
tu
r
b
i
n
es
i
n
t
h
e
elec
tr
ical
n
et
w
o
r
k
i
n
o
r
d
er
to
m
i
n
i
m
ize
t
h
e
ac
ti
v
e
p
o
w
er
lo
s
s
e
s
,
an
d
to
m
ax
i
m
ize
th
e
s
y
s
te
m
lo
ad
b
ilit
y
w
it
h
in
s
ec
u
r
it
y
m
ar
g
i
n
.
Ho
w
e
v
er
,
i
n
ca
s
e
o
f
i
n
s
tal
lin
g
s
m
a
ll
w
i
n
d
f
ar
m
s
in
to
p
o
w
er
g
r
id
s
h
a
v
i
n
g
n
o
t
s
u
f
f
icie
n
t
r
ea
cti
v
e
p
o
w
er
ca
p
ab
ilit
y
i
n
o
r
d
er
to
co
n
tr
ib
u
te
to
r
ea
cti
v
e
p
o
w
er
s
u
p
p
o
r
t,
it
w
ill
b
e
b
en
e
f
it
to
u
s
e
a
n
o
p
ti
m
izatio
n
m
et
h
o
d
in
o
r
d
er
t
o
f
in
d
th
e
o
p
ti
m
al
p
lace
m
e
n
t
an
d
r
ea
ctiv
e
p
o
w
er
in
j
ec
tio
n
o
f
b
o
th
w
i
n
d
f
ar
m
s
a
n
d
F
A
C
T
S
d
ev
ices.
I
n
th
is
w
o
r
k
,
w
e
p
r
o
p
o
s
e
an
o
b
j
ec
tiv
e
f
u
n
ctio
n
th
at
allo
w
s
g
etti
n
g
th
e
o
p
ti
m
al
n
u
m
b
er
o
f
SV
C
to
in
s
ta
ll
in
t
h
e
g
r
id
.
T
h
e
o
b
j
ec
ti
v
e
f
u
n
c
tio
n
p
r
esen
ted
i
n
th
i
s
p
ap
er
aim
s
also
to
f
i
n
d
th
e
o
p
ti
m
al
lo
ca
tio
n
an
d
r
ea
ctiv
e
p
o
w
er
in
j
ec
tio
n
o
f
b
o
th
th
e
SV
C
’
s
u
n
its
a
n
d
th
e
w
i
n
d
f
ar
m
w
i
th
t
h
e
tar
g
et
to
r
ed
u
ce
p
o
w
er
lo
s
s
e
s
an
d
to
en
h
a
n
ce
v
o
lta
g
e
s
tab
ili
t
y
.
T
h
is
w
o
r
k
i
s
o
r
g
a
n
i
ze
d
as
f
o
llo
w
s
:
f
ir
s
t,
t
h
e
m
et
h
o
d
u
s
ed
in
o
r
d
er
to
g
et
t
h
e
r
ea
ct
iv
e
p
o
w
er
ca
p
ab
ilit
y
o
f
t
h
e
w
i
n
d
f
ar
m
m
ad
e
u
p
w
it
h
DFI
G
w
i
n
d
tu
r
b
in
e
is
p
r
esen
ted
.
Seco
n
d
,
t
h
e
v
o
ltag
e
s
tab
il
it
y
in
d
ices
a
n
d
t
h
e
P
SO
al
g
o
r
ith
m
u
s
ed
i
n
t
h
is
w
o
r
k
ar
e
p
r
ese
n
ted
f
o
llo
w
ed
b
y
th
e
f
o
r
m
u
la
t
io
n
o
f
t
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
f
o
r
o
p
ti
m
al
p
lace
m
e
n
t
an
d
r
ea
cti
v
e
p
o
w
er
i
n
j
ec
tio
n
o
f
t
h
e
W
F
a
n
d
t
h
e
SVC
’
s
u
n
i
t
s
.
Fi
n
all
y
,
t
h
e
ca
s
e
s
tu
d
y
a
n
d
th
e
s
i
m
u
la
tio
n
r
es
u
lt
s
ar
e
r
ep
o
r
te
d
.
2.
RE
AC
T
I
V
E
P
O
WE
R
CAP
AB
I
L
T
Y
O
F
T
H
E
W
I
ND
F
ARM
B
ASE
D
DF
I
G
W
I
ND
T
URB
I
N
E
I
n
t
h
is
p
ap
er
,
w
e
u
s
e
th
e
DFI
G
w
i
n
d
tu
r
b
in
e
b
ec
au
s
e
it
is
t
h
e
tech
n
o
lo
g
y
t
h
e
m
o
s
t
in
s
tall
ed
in
w
i
n
d
f
ar
m
s
f
o
r
its
s
ev
er
al
ad
v
a
n
ta
g
es.
Fo
r
in
s
tan
ce
,
w
it
h
th
e
DF
I
G
tech
n
o
lo
g
y
,
it
is
p
o
s
s
ib
le
to
g
et
th
e
r
eq
u
ir
ed
r
ea
ctiv
e
p
o
w
er
at
th
e
s
tato
r
s
id
e
b
y
co
n
tr
o
lli
n
g
th
e
r
o
to
r
cu
r
r
en
ts
b
y
t
h
e
r
o
to
r
s
id
e
co
n
v
er
te
r
[
1
0
]
.
T
h
e
m
et
h
o
d
p
r
o
p
o
s
ed
in
[
1
1
]
is
u
s
ed
to
g
et
t
h
e
r
ea
cti
v
e
p
o
w
er
ca
p
ab
ilit
y
o
f
th
e
D
FIG
b
ased
w
i
n
d
tu
r
b
in
e
Q
WT
m
ax
an
d
Q
WT
m
i
n
.
I
n
th
is
m
et
h
o
d
,
it
is
s
u
g
g
ested
th
a
t
th
e
r
ea
ctiv
e
p
o
w
er
ca
p
ab
ilit
y
is
b
o
u
n
d
ed
b
y
t
h
r
ee
p
ar
am
eter
s
:
r
o
to
r
v
o
ltag
e
V
r
,
r
o
to
r
I
r
an
d
s
ta
to
r
cu
r
r
en
ts
I
s
.
T
h
e
p
ar
am
eter
s
cited
in
[
1
2
]
ar
e
u
s
ed
to
g
et
t
h
e
P
Q
d
iag
r
am
o
f
2
MW
DFI
G
w
i
n
d
tu
r
b
in
e
u
s
ed
i
n
th
i
s
w
o
r
k
.
Fo
r
m
o
r
e
d
etails,
r
ef
er
to
[
1
3
]
.
I
n
th
is
w
o
r
k
,
th
e
r
ea
ctiv
e
p
o
w
er
lo
s
s
e
s
ar
e
n
eg
l
ec
ted
w
it
h
i
n
th
e
w
i
n
d
f
ar
m
,
s
o
th
e
r
ea
ctiv
e
p
o
w
er
ca
p
ab
ilit
y
o
f
th
e
W
P
P
(
Q
WF
m
ax
an
d
Q
WF
m
i
n
)
is
ca
lcu
lated
as b
elo
w
:
Q
WF
m
ax
=
∑
Q
WT
m
ax
(
1
)
Q
WF
m
i
n
=
∑
Q
WT
m
i
n
(
2
)
3.
L
I
N
E
VO
L
T
A
G
E
ST
AB
I
L
I
T
Y
I
ND
I
C
E
S
[
1
4
,
15]
I
n
th
i
s
w
o
r
k
,
t
h
e
v
o
lta
g
e
s
tab
i
lit
y
i
n
d
ices
L
mn
,
L
QP
an
d
FVSI
ar
e
u
s
ed
.
T
h
ese
in
d
ices
ar
e
f
o
r
m
u
lat
ed
b
ased
o
n
p
o
w
er
tr
an
s
m
is
s
io
n
i
n
a
s
i
n
g
le
li
n
e
a
s
ill
u
s
tr
ated
i
n
F
ig
u
r
e
1
.
A
tr
an
s
m
is
s
io
n
li
n
e
is
s
tab
le
a
s
lo
n
g
a
s
th
e
v
al
u
es
o
f
t
h
ese
i
n
d
ices
r
e
m
ai
n
b
elo
w
1
.
I
f
t
h
e
v
al
u
e
o
f
o
n
e
o
f
t
h
e
m
ex
ce
ed
s
1
,
t
h
e
s
y
s
te
m
lo
s
es
its
s
tab
ilit
y
a
n
d
th
e
v
o
ltag
e
co
llap
s
es
[
1
5
]
.
T
h
ese
in
d
ices a
r
e
o
b
tain
ed
as
f
o
llo
w
s
:
L
mn
=
4X
Q
r
(
V
s
s
i
n
(
θ
−
δ
)
)
2
(
3
)
L
QP
=
4
(
X
V
s
2
)
(
Q
s
+
P
s
2
X
V
s
2
)
(
4
)
F
VS
I
=
4
Z
2
Q
r
V
s
2
X
(
5
)
w
h
er
e
X
: lin
e
r
ea
ctan
ce
.
Q
r
: r
ea
ctiv
e
p
o
w
er
at
th
e
r
ec
ei
v
i
n
g
b
u
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Op
tima
l lo
ca
tio
n
a
n
d
r
ea
cti
ve
p
o
w
er in
jectio
n
o
f wi
n
d
fa
r
ms a
n
d
S
V
C
’
s
u
n
i
ts
u
s
in
g
..
.
(
N
a
z
h
a
C
h
erka
o
u
i)
3409
Vs
: v
o
ltag
e
m
a
g
n
i
tu
d
e
at
t
h
e
s
en
d
in
g
b
u
s
.
θ
: lin
e
i
m
p
ed
a
n
ce
an
g
le.
δ
: th
e
an
g
le
d
i
f
f
er
e
n
ce
b
et
w
ee
n
th
e
v
o
lta
g
e
an
g
le
at
t
h
e
s
e
n
d
in
g
a
n
d
r
ec
eiv
i
n
g
b
u
s
.
Qs
: r
ea
ctiv
e
p
o
w
er
at
th
e
s
en
d
i
n
g
b
u
s
.
Ps
: a
ctiv
e
p
o
w
er
at
t
h
e
s
e
n
d
in
g
b
u
s
.
Z
: th
e
li
n
e
i
m
p
ed
an
ce
a
m
p
lit
u
d
e.
Fig
u
r
e
1.
On
e
lin
e
d
ia
g
r
a
m
o
f
tr
an
s
m
is
s
io
n
li
n
e
4.
P
ARTI
C
L
E
SWA
RM
O
P
T
I
M
I
SAT
I
O
N
T
E
CH
NO
Q
UE
(
P
SO
)
T
h
e
p
ar
ticle
s
w
ar
m
o
p
ti
m
is
a
ti
o
n
(
P
SO)
tech
n
iq
u
e
is
a
m
e
ta
h
eu
r
i
s
tic
al
g
o
r
ith
m
in
v
e
n
ted
b
y
Ke
n
n
ed
y
an
d
E
b
er
h
ar
t
in
1
9
9
5
[
1
6
]
.
T
h
is
o
p
ti
m
is
a
tio
n
m
et
h
o
d
ai
m
s
to
f
i
n
d
th
e
p
ar
a
m
eter
s
t
h
at
g
iv
e
th
e
m
in
i
m
u
m
(
o
r
m
a
x
i
m
u
m
)
o
f
a
n
o
b
j
ec
tiv
e
f
u
n
ctio
n
[
1
7
]
.
W
e
o
p
t to
u
s
e
th
e
P
SO a
lg
o
r
ith
m
i
n
t
h
is
w
o
r
k
d
u
e
to
th
e
f
ac
t t
h
at
it
co
n
v
er
g
es
m
o
r
e
to
t
h
e
o
p
ti
m
al
s
o
lu
tio
n
w
it
h
le
s
s
o
v
er
h
e
ad
o
f
p
ar
a
m
eter
s
et
tin
g
a
n
d
le
s
s
co
m
p
u
tatio
n
ti
m
e
in
co
m
p
ar
aiso
n
w
i
th
o
t
h
er
m
et
ah
eu
r
i
s
tic
m
eth
o
d
s
[
1
8
]
.
I
n
t
h
e
P
SO
m
e
th
o
d
,
a
g
r
o
u
p
o
f
p
ar
ticles
ar
e
i
n
itialized
in
a
r
an
d
o
m
m
a
n
n
er
i
n
t
h
e
d
-
d
i
m
en
s
io
n
a
l
s
ea
r
ch
s
p
ac
e,
w
h
er
e
d
is
th
e
n
u
m
b
er
o
f
th
e
d
ec
is
io
n
v
ar
iab
les
in
th
e
o
p
ti
m
i
s
atio
n
p
r
o
b
lem
.
A
p
o
s
itio
n
v
ec
to
r
x
i
,
a
v
elo
cit
y
v
ec
to
r
v
i
an
d
a
p
o
s
itio
n
Pb
e
s
t
i
ar
e
ass
o
cia
ted
to
ea
ch
i
-
t
h
p
ar
ticle.
I
n
o
r
d
er
to
f
in
d
t
h
e
o
p
ti
m
al
s
o
lu
tio
n
,
t
h
e
p
ar
ticles
ex
c
h
a
n
g
e
ef
f
ec
ti
v
el
y
i
n
f
o
r
m
atio
n
d
u
r
i
n
g
an
iter
ati
v
e
p
r
o
ce
s
s
.
I
n
ea
c
h
iter
atio
n
,
t
h
e
b
es
t
g
lo
b
al
p
o
s
itio
n
g
b
e
s
t
f
o
u
n
d
b
y
a
n
y
p
ar
ticle
i
n
th
e
s
w
ar
m
is
s
h
ar
ed
w
it
h
all
t
h
e
r
est
o
f
t
h
e
p
ar
ticles.
I
n
ea
c
h
k
-
th
iter
atio
n
,
th
e
v
elo
cit
y
a
n
d
th
e
p
o
s
itio
n
ar
e
u
p
d
ated
u
s
i
n
g
th
e
eq
u
atio
n
s
b
elo
w
[
1
9
]
:
v
i
k
+
1
=
w
k
v
i
k
+
c
1
r
1
(
Pb
e
s
t
i
k
−
x
i
k
)
+
c
2
r
2
(
gb
e
s
t
k
−
x
i
k
)
(
6
)
x
i
k
+
1
=
x
i
k
+
v
i
k
+
1
(
7
)
w
h
er
e
r
1
an
d
r
2
:
u
n
i
f
o
r
m
l
y
d
is
tr
ib
u
ted
r
an
d
o
m
n
u
m
b
er
s
in
t
h
e
r
an
g
e
[
0
1
]
.
w
: in
er
tia
w
ei
g
h
t.
c
1
an
d
c
2
: a
cc
eler
atio
n
co
ef
f
icien
ts
.
T
h
er
e
ar
e
s
ev
er
al
in
er
tia
w
e
ig
h
ti
n
g
f
ac
to
r
s
,
in
t
h
i
s
p
ap
er
,
w
e
u
s
e
t
h
e
f
o
llo
w
i
n
g
o
n
e
[
1
9
]
:
w
k
=
w
m
ax
−
w
m
ax
−
w
m
in
k
m
ax
x
k
(
8
)
w
h
er
e
k
m
ax
: th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
.
k
: th
e
cu
r
r
en
t n
u
m
b
er
o
f
iter
ati
o
n
s
.
w
min
a
n
d
w
wax
: a
r
e
th
e
lo
w
er
an
d
t
h
e
u
p
p
er
b
o
u
n
d
s
o
f
t
h
e
i
n
er
tia
w
ei
g
h
t
in
g
f
ac
to
r
s
,
r
esp
ec
tiv
el
y
.
5.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
T
h
e
p
u
r
p
o
s
e
o
f
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
p
r
o
p
o
s
ed
i
n
t
h
is
w
o
r
k
i
s
to
f
in
d
t
h
e
o
p
ti
m
al
n
u
m
b
er
n
s
v
c
o
f
SVC
to
in
s
tall
i
n
th
e
n
e
t
w
o
r
k
.
I
n
ad
d
itio
n
to
th
at,
th
e
o
b
j
ec
ti
v
e
f
u
n
c
tio
n
ai
m
s
to
f
i
n
d
th
e
o
p
ti
m
al
lo
ca
tio
n
an
d
th
e
r
ea
ctiv
e
p
o
w
er
in
j
ec
tio
n
o
f
b
o
th
a
w
in
d
f
ar
m
b
ased
DFI
G
W
T
an
d
th
e
n
u
m
b
er
n
svc
o
f
S
VC
.
T
h
e
f
o
u
n
d
p
ar
am
eter
s
r
ed
u
ce
th
e
p
o
w
er
lo
s
s
es
an
d
en
h
a
n
ce
th
e
v
o
lta
g
e
s
tab
ilit
y
in
t
h
e
g
r
id
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
to
m
i
n
i
m
ize
in
t
h
i
s
w
o
r
k
is
r
ep
r
esen
ted
as:
F
(
X
)
=
λ
1
.
P
l
o
s
s
es
+
λ
2
.
∑
L
QP
(
i
)
+
L
mn
(
i
)
+
F
V
S
I
(
i
)
3
N
l
ine
s
i
=
1
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
5
,
Octo
b
er
2
0
1
9
:
3
4
0
7
-
3414
3410
w
h
er
e
P
los
ses
:
p
o
w
er
lo
s
s
es i
n
t
h
e
elec
tr
ical
g
r
id
.
I
n
th
i
s
w
o
r
k
,
w
e
n
e
g
lect
t
h
e
p
o
w
er
lo
s
s
e
s
in
t
h
e
w
i
n
d
f
ar
m
.
N
lines
:
th
e
n
u
m
b
er
o
f
l
in
e
s
in
t
h
e
g
r
id
.
L
QP
,
L
mn
an
d
FV
SI
:
v
o
ltag
e
s
tab
ilit
y
in
d
ice
s
.
X=
(
x
1
,x
2
,x
3
,x
4
,x
5
,x
6
,x
7
)
:
th
e
p
o
s
itio
n
o
f
ea
c
h
p
ar
t
icle.
λ
1
,
λ
2
:
w
ei
g
h
t c
o
ef
f
icie
n
ts
w
it
h
L
WF
=
x
1
,
Q
WF
=
x
2
,
n
S
V
C
=
x
3
,
L
S
V
C
1
=
x
4
,
L
S
V
C
2
=
x
5
,
Q
S
V
C
1
=
x
6
,
Q
S
V
C
2
=
x
7
L
WF
: o
p
tim
a
l lo
ca
tio
n
o
f
t
h
e
w
i
n
d
f
ar
m
Q
WF
: r
ea
ctiv
e
p
o
w
er
to
p
r
o
d
u
ce
o
r
to
ab
s
o
r
b
b
y
t
h
e
w
i
n
d
f
ar
m
L
S
VCi
: o
p
tim
a
l lo
ca
tio
n
o
f
t
h
e
SV
C
(
lo
ad
b
u
s
es in
th
e
g
r
id
)
Q
S
V
Ci
: r
ea
ctiv
e
p
o
w
er
to
in
j
ec
t b
y
th
e
SVC
.
I
n
t
h
is
w
o
r
k
,
t
h
e
SV
C
is
co
n
s
id
er
ed
as a
v
ar
iab
le
lo
ad
.
n
S
VC
: o
p
tim
a
l n
u
m
b
er
o
f
t
h
e
SV
C
t
o
b
e
in
s
talled
in
t
h
e
n
et
w
o
r
k
,
w
it
h
0
≤
n
s
v
c≤
2
I
f
n
S
V
C
=
0
the
n
L
S
V
C
1
=
0
,
L
S
V
C
2
=
0
,
Q
S
V
C
1
=
0
a
n
d
Q
S
V
C
2
=
0
I
f
n
S
V
C
=
1
the
n
L
S
V
C
2
=
0
a
n
d
Q
S
V
C
2
=
0
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
p
r
o
p
o
s
ed
in
th
i
s
w
o
r
k
is
s
u
b
j
ec
t to
th
e
f
o
llo
w
in
g
co
n
s
tr
ain
t
s
:
1)
W
in
d
f
ar
m
r
ea
ctiv
e
p
o
w
er
l
i
m
it
s
Q
wf
m
i
n
≤
Q
wf
≤
Q
wf
m
ax
(
1
0
)
2)
Nu
m
b
er
o
f
SV
C
n
S
V
C
0
≤
n
s
vc
≤
2
(
1
1
)
3)
SVC
r
ea
ctiv
e
p
o
w
er
ca
p
ac
it
y
Q
s
v
c
m
i
n
≤
Q
svc
≤
Q
svc
m
ax
(
1
2
)
I
n
th
i
s
w
o
r
k
,
th
e
o
p
er
atin
g
r
an
g
e
o
f
t
h
e
SV
C
is
co
n
s
id
er
ed
to
b
e
±
5
0
MV
A
R
First,
th
e
p
o
s
itio
n
o
f
th
e
P
S
O
alg
o
r
ith
m
is
i
n
itial
ized
r
an
d
o
m
l
y
w
it
h
p
o
s
s
ib
le
v
al
u
es
i
n
th
e
s
p
ac
e
[
N1
,
N2
,
…NP
Q]
(
lo
ad
b
u
s
es
p
lace
d
in
th
e
elec
tr
ical
g
r
id
)
,
[
Q
WF
m
i
n
,
Q
WF
m
ax
]
,
[
0
,
1
,
2
]
,
[
N1
,
N2
,
…,
NP
Q]
,
[
Q
svc
m
i
n
,
Q
svc
m
ax
]
.
T
h
en
,
at
ea
c
h
it
er
at
io
n
,
as
illu
s
tr
ated
in
F
ig
u
r
e
2
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
lo
o
k
s
f
o
r
th
e
o
p
ti
m
al
s
o
lu
tio
n
b
y
u
p
d
ati
n
g
t
h
e
p
o
s
it
io
n
an
d
th
e
v
elo
cit
y
o
f
ea
ch
i
-
t
h
p
ar
ticle
tak
i
n
g
i
n
to
ac
co
u
n
t
its
p
r
ev
io
u
s
b
est
p
o
s
itio
n
Pb
e
s
ti
an
d
th
e
b
est p
o
s
itio
n
o
f
th
e
g
r
o
u
p
g
b
est.
6.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
I
n
o
r
d
er
to
v
alid
ate
th
e
p
r
o
p
o
s
ed
o
p
ti
m
is
at
io
n
al
g
o
r
ith
m
,
t
h
r
ee
d
if
f
er
e
n
t
ca
s
e
s
ar
e
s
i
m
u
lat
ed
u
s
i
n
g
a
w
i
n
d
f
ar
m
co
n
s
titu
ted
o
f
te
n
2
MW
DFI
G
b
ased
w
i
n
d
t
u
r
b
in
e
an
d
t
h
e
I
E
E
E
1
4
b
u
s
s
y
s
te
m
.
W
e
co
n
s
id
er
t
h
at
th
e
w
i
n
d
t
u
r
b
in
e
s
w
i
th
i
n
th
e
W
PP
o
p
er
ate
at
f
u
l
l
ac
ti
v
e
p
o
w
er
a
n
d
w
e
n
e
g
lect
th
e
p
o
w
e
r
lo
s
s
es
w
it
h
i
n
t
h
e
w
i
n
d
f
ar
m
.
T
h
e
ac
tiv
e
lo
ad
s
in
b
u
s
es
9
an
d
1
3
ar
e
in
cr
ea
s
ed
to
2
4
5
MW
an
d
6
7
,
5
MW
,
r
esp
ec
tiv
ely
.
C
o
n
s
eq
u
en
tl
y
,
t
h
e
v
o
lta
g
e
a
m
p
litu
d
es i
n
b
u
s
e
s
4
,
5
,
9
,
1
0
an
d
1
4
d
ec
r
ea
s
e
s
ig
n
i
f
ica
n
tl
y
.
-
C
ase
1
:
w
it
h
o
u
t t
h
e
w
i
n
d
f
ar
m
o
r
th
e
SVC
.
-
C
ase
2
: o
n
l
y
w
it
h
th
e
w
i
n
d
f
ar
m
.
w
h
er
e
X=
(
x
1
,x
2
)
,
L
WF
=x
1
a
n
d
Q
WF
=x
2
λ
1
=
λ
2
=
0
,
5
-
C
ase
3
:
w
it
h
b
o
th
th
e
w
i
n
d
f
ar
m
an
d
t
h
e
SV
C
’
s
u
n
it
s
.
w
h
er
e
X=
(
x
1
,x
2
,x
3
,x
4
,x
5,
x
6
,x
7
)
,
L
WF
=
x
1
,
Q
WF
=
x
2
,
n
S
V
C
=
x
3
,
L
S
V
C
1
=
x
4
,
L
S
V
C
2
=
x
5
,
Q
S
V
C
1
=
x
6
,
Q
S
V
C
2
=
x
7
λ
1
=
λ
2
=
0
,
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Op
tima
l lo
ca
tio
n
a
n
d
r
ea
cti
ve
p
o
w
er in
jectio
n
o
f wi
n
d
fa
r
ms a
n
d
S
V
C
’
s
u
n
i
ts
u
s
in
g
..
.
(
N
a
z
h
a
C
h
erka
o
u
i)
3411
Fig
u
r
e
2
.
F
lo
w
c
h
ar
t o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
T
h
e
r
esu
lts
o
b
tain
ed
i
n
th
e
t
h
r
ee
ca
s
es
ar
e
p
r
esen
ted
i
n
T
ab
le
1.
I
n
ca
s
e
3
,
a
s
s
h
o
w
n
i
n
T
ab
le
1
,
th
e
o
p
ti
m
a
l
lo
ca
tio
n
o
f
t
h
e
w
i
n
d
f
ar
m
i
s
b
u
s
n
u
m
b
er
9
,
a
n
d
th
e
o
p
ti
m
al
lo
ca
tio
n
o
f
t
h
e
t
w
o
S
VC
ar
e
b
u
s
e
s
n
u
m
b
er
9
an
d
5
.
N
o
No
C
h
e
c
k
:
(
10
)
,
(
12
)
a
n
d
L
WF
and
L
S
V
C
j
a
r
e
in
load
bu
s
e
s
E
x
e
c
u
te
:
t
h
e
l
oa
d
f
l
ow
E
v
a
lu
a
te
t
h
e
objec
t
iv
e
f
unc
t
i
o
n
v
a
lu
e
o
f
e
a
c
h
pa
r
t
i
c
le
S
e
t
P
bes
t
i
and
g
b
e
st
R
e
a
c
h
m
a
x
im
u
m
i
te
r
a
t
i
o
n
s
≤
S
top
Ye
s
L
S
V
C
1
=
0
,
L
S
V
C
2
=
0
,
Q
S
V
C
1
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0
,
Q
S
V
C
2
=
0
n
=
1
L
S
V
C
2
=
0
,
Q
S
V
C
2
=
0
Ye
s
Ye
s
N
o
C
h
e
c
k
:
(
10
)
,
(
12
)
a
n
d
L
WF
and
L
S
V
C
j
a
r
e
in
load
bu
s
e
s
E
x
e
c
u
te
:
t
h
e
l
oa
d
f
l
ow
E
v
a
lu
a
te
t
h
e
objec
t
iv
e
f
unc
t
i
o
n
o
f
e
a
c
h
pa
r
t
i
c
l
e
I
ni
t
i
a
li
z
e
P
bes
t
i
and
g
b
e
st
Upda
te
th
e
v
e
l
oc
it
y
o
f
e
a
c
h
pa
r
t
i
c
l
e
(
6
)
C
a
l
c
ul
a
te
(7
)
L
WF
=
X
i
k
(
1
)
,
Q
WF
=
X
i
k
(
2
)
,
n
SVC
=
X
i
k
(
3
)
,
L
S
V
C
1
=
X
i
k
(
4
)
L
S
V
C
2
=
X
i
k
(
5
)
,
Q
S
V
C
1
=
X
i
k
(
6
)
,
Q
S
V
C
2
=
X
i
k
(
7
)
n
=
0
n
=
1
L
S
V
C
2
=
0
,
Q
S
V
C
2
=
0
N
o
Ge
n
e
r
a
te
r
a
n
do
ml
y
t
he
pos
it
i
o
n
o
f
e
a
c
h
i
-
t
h
pa
r
ti
c
l
e
X
i
k
=
(
X
i
k
(
1
)
,
X
i
k
(
2
)
,
X
i
k
(
3
)
,
X
i
k
(
4
)
,
X
i
k
(
5
)
,
X
i
k
(
6
)
,
X
i
k
(
7
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)
R
a
n
d
o
m
ly
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n
e
r
a
te
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e
v
e
l
o
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y
o
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e
a
c
h
p
a
r
ti
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l
e
=
X
i
k
(
1
)
,
=
X
i
k
(
2
)
,
=
X
i
k
(
3
)
,
1
=
X
i
k
(
4
)
2
=
X
i
k
(
5
)
,
1
=
X
i
k
(
6
)
,
2
=
X
i
k
(
7
)
n
=
0
L
S
V
C
1
=
0
,
L
S
V
C
2
=
0
,
Q
S
V
C
1
=
0
,
Q
S
V
C
2
=
0
N
o
Ye
s
Yes
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
5
,
Octo
b
er
2
0
1
9
:
3
4
0
7
-
3414
3412
T
ab
le
1.
Sim
u
latio
n
r
esu
lts
C
a
se
1
C
a
se
2
C
a
se
3
(
M
V
A
R
)
(
M
V
A
R
)
(
M
V
A
R
)
-
-
-
-
-
-
-
9
6
,
2
7
7
9
-
-
-
-
-
9
6
,
2
7
7
9
2
9
5
50
50
O
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
-
3
8
,
2
2
5
4
3
6
,
0
3
0
0
As
illu
s
tr
ated
in
F
ig
u
r
e
3
,
th
e
v
o
ltag
e
a
m
p
li
tu
d
es
at
b
u
s
es
4
,
5
,
9
,
1
0
an
d
1
4
in
cr
ea
s
e
r
e
s
p
ec
tiv
el
y
f
r
o
m
0
,
9
2
5
p
.
u
,
0
,
9
3
5
p
.
u
,
0
,
9
3
6
p
.
u
,
0
,
9
4
8
p
.
u
an
d
0
,
9
4
4
p
.
u
.
in
th
e
f
ir
s
t
ca
s
e
to
0
,
9
3
8
p
.
u
,
0
,
9
4
7
p
.
u
,
0
,
9
6
3
p
.
u
,
0
,
9
7
1
p
.
u
.
an
d
0
,
9
6
2
p
.
u
.
in
th
e
s
ec
o
n
d
ca
s
e.
Ho
w
e
v
e
r
,
th
e
s
ig
n
i
f
ica
n
t
i
m
p
r
o
v
e
m
en
t
o
f
t
h
e
v
o
lta
g
e
i
s
o
b
tain
ed
in
t
h
e
t
h
ir
d
ca
s
e.
I
n
f
ac
t,
th
e
v
o
ltag
e
m
a
g
n
it
u
d
es
i
n
ca
s
e
3
at
b
u
s
es
4
,
5
,
9
,
1
0
an
d
1
4
ar
e
0
,
9
6
4
p
.
u
,
0
.
9
7
8
p
.
u
,
1
,
0
3
1
p
.
u
,
1
,
0
2
7
p
.
u
.
an
d
1
,
0
0
5
p
.
u
.
,
r
esp
ec
tiv
ely
.
T
h
is
is
d
u
e
to
th
e
f
ac
t
th
at
th
e
r
ea
cti
v
e
p
o
w
e
r
in
j
ec
ted
in
th
e
g
r
id
in
ca
s
e
3
is
b
ig
g
er
th
a
n
t
h
at
i
n
j
ec
ted
in
ca
s
e
2
,
as
ill
u
s
tr
ated
in
T
ab
le
1
.
A
s
s
h
o
w
n
in
F
ig
u
r
e
4
,
th
e
p
o
w
er
lo
s
s
e
s
ar
e
i
m
p
o
r
tan
t
in
t
h
e
f
ir
s
t
ca
s
e
an
d
d
ec
r
ea
s
e
s
ig
n
i
f
ica
n
tl
y
in
th
e
t
h
ir
d
ca
s
e
b
y
1
6
,
4
1
% in
co
m
p
ar
is
o
n
w
i
t
h
th
e
f
ir
s
t c
a
s
e.
Fig
u
r
e
3
.
Vo
ltag
e
p
r
o
f
ile
Fig
u
r
e
4
.
P
o
w
er
lo
s
s
e
s
A
cc
o
r
d
in
g
to
th
e
r
esu
l
ts
o
b
tain
ed
in
ca
s
e
2
,
lo
o
k
in
g
o
n
l
y
f
o
r
th
e
o
p
ti
m
al
p
lace
m
e
n
t
an
d
r
ea
ctiv
e
p
o
w
er
in
j
ec
tio
n
o
f
a
s
m
al
l
w
i
n
d
f
ar
m
in
o
r
d
er
to
i
m
p
r
o
v
e
t
h
e
v
o
lta
g
e
p
r
o
f
ile
i
s
n
o
t
e
n
o
u
g
h
b
ec
a
u
s
e
it
d
o
es
n
’
t
h
av
e
s
u
f
f
icie
n
t
r
ea
cti
v
e
p
o
w
er
ca
p
ab
ilit
y
to
p
ar
ticip
ate
to
r
e
ac
tiv
e
p
o
w
er
s
u
p
p
o
r
t.
Hen
ce
,
in
ca
s
e
o
f
in
s
talli
n
g
s
m
al
l
w
i
n
d
f
ar
m
s
in
to
p
o
w
er
g
r
id
s
,
it
w
i
ll
b
e
b
en
e
f
icial
to
a
d
d
SVC
’
s
u
n
its
to
t
h
e
n
et
w
o
r
k
.
T
h
e
o
p
ti
m
izatio
n
m
et
h
o
d
p
r
o
p
o
s
ed
in
th
is
s
tu
d
y
ai
m
s
to
d
eter
m
i
n
e
th
e
o
p
ti
m
al
n
u
m
b
er
o
f
SVC
’
s
u
n
it
s
to
in
s
tal
l
in
th
e
g
r
id
in
ad
d
itio
n
to
s
m
all
w
i
n
d
f
ar
m
s
;
also
,
it
ai
m
s
to
f
in
d
t
h
e
o
p
ti
m
al
lo
ca
tio
n
a
n
d
r
ea
ctiv
e
p
o
w
er
i
n
j
ec
tio
n
o
f
th
e
w
i
n
d
f
ar
m
a
n
d
th
s
SV
C
’
s
u
n
it
s
w
it
h
t
h
e
g
o
al
to
m
i
n
i
m
ize
t
h
e
p
o
w
er
lo
s
s
e
s
an
d
to
i
m
p
r
o
v
e
th
e
v
o
ltag
e
p
r
o
f
i
le.
I
n
f
ac
t,
u
s
i
n
g
t
h
e
p
r
o
p
o
s
ed
o
p
t
i
m
izatio
n
m
e
th
o
d
in
ca
s
e
3
all
o
w
s
g
etti
n
g
th
e
b
est r
es
u
lt
s
.
7.
CO
NCLU
SI
O
N
I
n
t
h
is
w
o
r
k
,
an
o
p
ti
m
i
s
atio
n
al
g
o
r
ith
m
b
ased
o
n
p
ar
ticl
e
s
w
ar
m
o
p
ti
m
i
s
atio
n
m
eth
o
d
(
P
SO)
is
p
r
esen
ted
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
p
er
m
i
ts
g
etti
n
g
t
h
e
o
p
ti
m
al
lo
ca
tio
n
a
n
d
r
ea
ctiv
e
p
o
w
er
in
j
ec
tio
n
o
f
b
o
th
a
w
i
n
d
f
ar
m
a
n
d
s
y
n
c
h
r
o
n
o
u
s
v
ar
co
m
p
en
s
ato
r
s
(
SVC
)
.
T
h
e
ai
m
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
to
en
h
an
ce
t
h
e
v
o
ltag
e
p
r
o
f
ile
a
n
d
to
r
ed
u
ce
t
h
e
ac
ti
v
e
p
o
w
er
lo
s
s
es.
T
h
e
s
i
m
u
latio
n
r
es
u
lts
ill
u
s
tr
ate
t
h
e
ef
f
ec
tiv
e
n
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Op
tima
l lo
ca
tio
n
a
n
d
r
ea
cti
ve
p
o
w
er in
jectio
n
o
f wi
n
d
fa
r
ms a
n
d
S
V
C
’
s
u
n
i
ts
u
s
in
g
..
.
(
N
a
z
h
a
C
h
erka
o
u
i)
3413
RE
F
E
R
E
NC
E
S
[1
]
“
G
lo
b
a
l
w
in
d
sta
ti
stics
2
0
1
7
,
”
F
e
b
2
0
1
8
.
A
v
a
il
a
b
le at www
.
g
w
e
c
.
n
e
t.
[2
]
Z.
Ch
e
n
,
“
I
ss
u
e
s
o
f
c
o
n
n
e
c
ti
n
g
w
in
d
fa
r
m
s
in
to
p
o
w
e
r
s
y
st
e
m
,
”
IEE
E/
PE
S
T
ra
n
s
miss
io
n
a
n
d
Distrib
u
ti
o
n
Co
n
fer
e
n
c
e
&
Exh
ib
it
io
n
:
Asi
a
a
n
d
P
a
c
if
ic
,
C
h
in
a
,
2
0
0
5
.
[3
]
H.
Am
a
ris
a
n
d
M
.
A
lo
n
so
,
“
Co
o
rd
in
a
ted
re
a
c
ti
v
e
p
o
w
e
r
m
a
n
a
g
e
m
e
n
t
in
p
o
w
e
r
n
e
t
w
o
rk
s
w
it
h
w
i
n
d
tu
r
b
in
e
s
a
n
d
F
A
C
T
S
d
e
v
ice
s
,
”
En
e
rg
y
Co
n
v
e
rs
io
n
a
n
d
M
a
n
a
g
e
me
n
t
,
v
o
l
.
5
2
,
p
p
.
2
5
7
5
-
2
5
8
6
,
2
0
1
1
.
[4
]
K.
R.
V
a
d
iv
e
lu
,
“
M
u
lt
i
o
b
jec
ti
v
e
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
w
e
r
p
lan
n
in
g
u
sin
g
im
p
ro
v
e
d
d
if
fe
re
n
ti
a
l
e
v
o
lu
ti
o
n
a
lg
o
rit
h
m
in
p
o
w
e
r
s
y
st
e
m
s
,
”
T
h
e
sis,
S
ri
V
e
n
k
a
tes
wa
ra
Un
iv
e
rsit
y
,
T
iru
p
a
ti
,
I
n
d
ia.
S
h
o
d
h
g
a
n
g
a
,
2
0
1
5
.
A
v
a
il
a
b
le:
h
tt
p
:
//
sh
o
d
h
g
a
n
g
a
.
in
f
li
b
n
e
t.
a
c
.
in
/
h
a
n
d
le/
1
0
6
0
3
/1
7
1
7
8
3
.
[5
]
M
.
N.
Da
z
a
h
ra
,
e
t
a
l
.
,
“
Op
ti
m
a
l
L
o
c
a
ti
o
n
o
f
S
V
C
u
sin
g
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
a
n
d
Vo
lt
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g
e
S
tab
il
it
y
In
d
e
x
e
s
,
”
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ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
ol
/
issu
e
:
6
(
6
)
,
p
p
.
2
5
8
1
-
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5
8
8
,
De
c
2
0
1
6
.
[6
]
D.
Ka
rth
ik
a
ik
a
n
n
a
n
a
n
d
G
.
Ra
v
i,
“
Op
ti
m
a
l
lo
c
a
ti
o
n
a
n
d
se
tt
in
g
o
f
F
A
C
T
S
d
e
v
ic
e
s
f
o
r
re
a
c
ti
v
e
p
o
w
e
r
c
o
m
p
e
n
sa
ti
o
n
u
sin
g
h
a
rm
o
n
y
se
a
r
c
h
a
lg
o
rit
h
m
,
”
AUT
OM
AT
IKA
,
v
o
l.
5
2
,
p
p
.
8
8
1
-
8
9
2
,
2
0
1
6
.
[7
]
S
.
M
a
k
h
lo
u
f
i,
e
t
a
l
.
,
“
C
u
c
k
o
o
S
e
a
rc
h
A
l
g
o
rit
h
m
f
o
r
In
teg
ra
ti
o
n
W
in
d
P
o
w
e
r
G
e
n
e
ra
ti
o
n
to
M
e
e
t
L
o
a
d
De
m
a
n
d
G
ro
w
th
,
”
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
E
n
v
iro
n
me
n
t
a
n
d
El
e
c
trica
l
En
g
in
e
e
rin
g
,
M
i
lan
,
Italy
,
2
0
1
7
.
[8
]
S
.
S
in
g
h
,
e
t
a
l
.
,
“
A
No
v
e
l
A
p
p
ro
a
c
h
f
o
r
R
e
a
c
ti
v
e
P
o
w
e
r
Ou
tp
u
t
Op
ti
m
iza
ti
o
n
in
W
in
d
F
a
rm
f
o
r
th
e
Re
d
u
c
ti
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n
o
f
Distrib
u
ti
o
n
L
o
ss
e
s
u
sin
g
G
e
n
e
ti
c
A
lg
o
rit
h
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ad
v
a
n
c
e
d
Res
e
a
rc
h
in
El
e
c
trica
l,
El
e
c
tro
n
ics
a
n
d
I
n
stru
me
n
t
a
ti
o
n
En
g
i
n
e
e
rin
g
,
v
ol
/i
ss
u
e
:
2
(
3
)
,
M
a
r
2
0
1
3
.
[9
]
I.
M
.
W
a
rtan
a
,
et
al
.
,
“
Op
ti
m
a
l
In
teg
ra
ti
o
n
o
f
th
e
Re
n
e
w
a
b
le
E
n
e
rg
y
to
th
e
G
rid
b
y
Co
n
sid
e
rin
g
S
m
a
ll
S
ig
n
a
l
S
tab
il
it
y
Co
n
stra
in
t
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l
/i
ss
u
e
:
7
(
5
)
,
p
p
.
2
3
2
9
-
2
3
3
7
,
Oc
t
2
0
1
7
.
[1
0
]
P
.
V
i
jay
a
n
,
“
Util
izin
g
re
a
c
ti
v
e
c
a
p
a
b
il
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y
o
f
d
o
u
b
ly
fe
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
rs
to
e
n
h
a
n
c
e
s
y
ste
m
v
o
lt
a
g
e
p
e
rf
o
r
m
a
n
c
e
a
n
d
w
it
h
sta
n
d
w
in
d
v
a
riab
il
it
y
,
”
m
a
ste
r
th
e
sis,
2
0
1
0
.
[1
1
]
T
.
L
u
n
d
,
e
t
a
l
.
,
“
Re
a
c
ti
v
e
p
o
w
e
r
c
a
p
a
b
il
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y
o
f
a
w
in
d
tu
rb
i
n
e
w
it
h
d
o
u
b
ly
f
e
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r
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”
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in
d
En
e
rg
y
,
v
o
l
.
1
0
,
p
p
.
3
7
9
-
3
9
4
,
A
p
r
2
0
0
7
.
[1
2
]
A
.
A
h
m
id
i
,
“
W
in
d
f
a
r
m
s
p
a
rti
c
ip
a
ti
o
n
a
t
v
o
lt
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g
e
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n
d
re
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c
ti
v
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p
o
we
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re
g
u
lati
o
n
in
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p
o
w
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r
s
y
ste
m
n
e
tw
o
rk
,
”
P
h
d
d
isse
rtatio
n
,
2
0
1
0
.
[1
3
]
N.
Ch
e
rk
a
o
u
i,
e
t
a
l
.
,
“
V
o
l
tag
e
re
g
u
latio
n
i
n
th
e
e
lec
tri
c
a
l
n
e
tw
o
r
k
u
sin
g
re
a
c
ti
v
e
p
o
w
e
r
c
o
n
tro
l
st
ra
teg
y
o
f
W
P
P
b
a
se
d
DFIG
w
in
d
tu
r
b
in
e
,
”
3
rd
Ir
n
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
El
e
c
t
ric
a
l
a
n
d
I
n
fo
rm
a
ti
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T
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s ICE
IT
’2
0
1
7
,
Ra
b
a
t,
M
o
r
o
c
c
o
,
N
o
v
2
0
1
7
.
[1
4
]
H.
H.
G
o
h
,
e
t
a
l
.
,
“
Co
m
p
a
ra
ti
v
e
stu
d
y
o
f
li
n
e
v
o
lt
a
g
e
sta
b
il
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y
i
n
d
ice
s
f
o
r
v
o
lt
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g
e
c
o
ll
a
p
se
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o
re
c
a
s
ti
n
g
in
p
o
w
e
r
tran
sm
issio
n
s
y
ste
m
,
”
W
o
rld
Aca
d
e
my
o
f
S
c
ien
c
e
,
En
g
in
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Civil
a
n
d
En
v
iro
n
me
n
ta
l
En
g
in
e
e
rin
g
,
v
ol
/
i
ss
u
e
:
9
(
2
)
,
2
0
1
5
.
[1
5
]
J.
M
o
d
a
rre
si,
e
t
a
l
.
,
“
A
c
o
m
p
re
h
e
n
siv
e
re
v
ie
w
o
f
th
e
v
o
lt
a
g
e
sta
b
il
it
y
in
d
ice
s
,
”
e
lse
v
ie
r
Ren
e
wa
b
le
a
n
d
S
u
sta
i
n
a
b
le
En
e
rg
y
Rev
iews
,
v
o
l
.
6
3
,
p
p.
1
-
1
2
,
2
0
1
6
.
[1
6
]
A
.
Ersk
in
e
,
e
t
a
l
.
,
“
S
t
o
c
h
a
stic
sta
b
il
it
y
o
f
p
a
rti
c
le
sw
a
r
m
o
p
ti
m
isa
t
io
n
,
”
S
w
a
rm
In
telli
g
e
n
c
e
,
v
o
l
.
1
1
,
p
p
.
2
9
5
-
3
1
5
,
2
0
1
7
.
[1
7
]
J.
Blo
n
d
i
n
,
“
P
a
rti
c
le
sw
a
r
m
o
p
ti
m
iza
ti
o
n
,
a
p
p
li
c
a
ti
o
n
s
o
f
p
a
r
a
m
e
teriz
a
ti
o
n
o
f
c
las
si
f
iers
,
”
2
0
0
9
.
A
v
a
il
a
b
le
:
ww
w
.
c
s.a
r
m
stro
n
g
.
e
d
u
/sa
a
d
.
[1
8
]
L
.
A
.
Be
w
o
o
r,
e
t
a
l
.
,
“
Co
m
p
a
ra
ti
v
e
A
n
a
l
y
sis
o
f
M
e
tah
e
u
risti
c
A
p
p
ro
a
c
h
e
s
f
o
r
M
a
k
e
sp
a
n
M
in
im
iza
ti
o
n
f
o
r
No
W
a
it
F
lo
w
S
h
o
p
S
c
h
e
d
u
li
n
g
P
ro
b
le
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l
/i
ss
u
e
:
7
(
1
)
,
p
p
.
4
1
7
-
4
2
3
,
F
e
b
2
0
1
7
.
[1
9
]
T
.
Krz
e
sz
o
w
sk
i
a
n
d
K.
W
ik
to
r
o
w
icz
,
“
E
v
a
lu
a
ti
o
n
o
f
se
lec
ted
f
u
z
z
y
p
a
rti
c
le
s
wa
r
m
o
p
ti
m
iz
a
ti
o
n
a
lg
o
rit
h
m
s
,
”
Pro
c
e
e
d
in
g
s
o
f
th
e
Fed
e
ra
ted
C
o
n
fer
e
n
c
e
o
n
C
o
mp
u
ter
S
c
ien
c
e
a
n
d
In
f
o
rm
a
ti
o
n
S
y
ste
ms
,
v
o
l.
8
,
p
p
.
5
7
1
-
5
7
5
,
2
0
1
6
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
Na
z
h
a
Ch
e
rk
a
o
u
i
i
s
a
P
h
.
D.
stu
d
e
n
t
a
t
th
e
Na
ti
o
n
a
l
Hig
h
e
r
S
c
h
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o
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tri
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it
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M
e
c
h
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n
ics
(Un
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e
rsit
y
Ha
s
sa
n
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o
f
Ca
sa
b
lan
c
a
-
M
o
ro
c
c
o
).
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r
re
se
a
rc
h
in
tere
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lu
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n
e
w
a
b
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rg
ies
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n
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p
o
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b
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p
ro
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"
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tri
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a
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tati
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sm
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s
.
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I
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N
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2
0
8
8
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8708
I
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C
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g
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l.
9
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.
5
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2
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9
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4
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7
-
3414
3414
F
a
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