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[
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Var
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I
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Vo
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15
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No
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3
,
Sep
tem
b
er
20
26
:
1
4
3
9
-
1
4
5
7
1440
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r
id
f
ailu
r
es
in
Nig
er
ia
b
etwe
en
2
0
0
0
an
d
2
0
2
2
.
Ad
d
itio
n
ally
,
t
h
e
wo
r
k
in
[
6
]
d
o
c
u
m
en
ted
th
r
ee
f
ailu
r
es
in
2
0
2
3
,
wh
ile
th
e
s
tu
d
y
in
[
7
]
r
ec
o
r
d
ed
f
i
v
e
co
llap
s
es
in
2
0
2
4
,
co
n
s
is
tin
g
o
f
o
n
e
p
ar
tial
f
ailu
r
e
an
d
f
o
u
r
to
tal
b
r
ea
k
d
o
wn
s
.
Data
f
r
o
m
th
e
tr
an
s
m
is
s
io
n
co
m
p
an
y
o
f
n
ig
er
ia
(
T
C
N)
,
an
in
d
e
p
en
d
en
t
s
y
s
tem
o
p
er
ato
r
[
8
]
f
u
r
th
er
r
e
v
ea
led
s
ev
en
s
y
s
tem
co
llap
s
es,
b
r
in
g
in
g
t
h
e
to
tal
f
ailu
r
es
in
2
0
2
4
to
twelv
e
an
d
th
e
cu
m
u
lativ
e
f
ailu
r
es
b
etwe
en
2
0
0
0
an
d
2
0
2
4
to
5
8
8
.
T
wo
s
y
s
tem
co
llap
s
e
ev
en
ts
o
cc
u
r
r
ed
i
n
2
0
2
5
an
d
a
n
ad
d
itio
n
al
two
in
J
an
u
ar
y
2
0
2
6
,
r
esu
ltin
g
in
a
t
o
tal
o
f
5
9
2
r
ec
o
r
d
ed
in
ci
d
en
t
s
o
v
er
th
e
p
ast
2
7
y
ea
r
s
as
r
ep
o
r
ted
b
y
Nig
er
ian
I
n
d
ep
e
n
d
en
t
Sy
s
tem
O
p
er
ato
r
.
T
h
e
f
r
eq
u
e
n
t
g
r
id
f
ailu
r
es
a
r
e
d
u
e
to
m
u
ltip
le
ca
u
s
es;
in
clu
d
in
g
g
en
er
atio
n
lo
s
s
es,
tr
an
s
m
is
s
io
n
lin
e
an
d
tr
an
s
f
o
r
m
er
o
v
e
r
lo
ad
s
.
I
s
s
u
es
li
k
e
h
ig
h
v
o
ltag
es,
ca
s
c
ad
in
g
f
a
u
lts
,
h
ig
h
-
f
r
eq
u
e
n
cy
d
ev
iatio
n
,
a
wea
k
g
r
i
d
n
etwo
r
k
,
in
f
r
astru
ctu
r
e
lim
itatio
n
s
,
p
r
o
tectiv
e
d
e
v
ice
m
alf
u
n
ctio
n
s
,
n
atu
r
al
d
is
aster
s
s
u
ch
as
f
lo
o
d
in
g
,
an
d
in
ten
tio
n
al
s
ab
o
tag
e
a
r
e
h
ig
h
lig
h
ted
in
[
6
]
,
[
8
]
–
[
1
1
]
.
I
f
we
wan
t
to
ac
h
iev
e
lo
n
g
-
ter
m
ec
o
n
o
m
ic
ad
v
an
ce
m
e
n
t
an
d
e
n
er
g
y
s
ec
u
r
ity
,
s
u
b
s
tan
tial
in
v
estme
n
ts
in
p
o
wer
in
f
r
astru
ct
u
r
e
ar
e
n
ec
ess
ar
y
to
en
h
an
ce
g
r
id
s
tab
ilit
y
an
d
r
eliab
ilit
y
.
T
ab
le
1
p
r
esen
ts
a
2
5
-
y
ea
r
s
u
m
m
ar
y
o
f
g
r
id
f
ailu
r
es with
to
tal
b
lack
o
u
ts
su
r
p
ass
in
g
p
ar
tial b
r
ea
k
d
o
wn
s
,
u
n
d
er
s
co
r
in
g
th
e
b
r
o
ad
er
ec
o
n
o
m
ic
im
p
licatio
n
s
o
f
th
e
co
u
n
tr
y
’
s
en
e
r
g
y
cr
is
is
[
5
]
–
[
9
]
.
T
h
e
r
ec
u
r
r
in
g
g
r
id
c
o
llap
s
e
im
p
o
s
e
s
ig
n
if
ican
t
ec
o
n
o
m
ic
co
s
ts
.
T
h
e
W
o
r
ld
B
an
k
esti
m
ates
th
at
u
n
r
eliab
le
elec
tr
icity
s
u
p
p
ly
r
ed
u
ce
s
Nig
er
ia’
s
GDP
b
y
5
%
to
7
%
an
n
u
ally
,
th
is
is
e
q
u
iv
alen
t
to
a
b
o
u
t
7
–
1
0
tr
illi
o
n
n
air
a
(
US$
2
5
b
illi
o
n
)
lo
s
s
in
p
r
o
d
u
ctiv
ity
an
d
in
v
es
tm
en
t
[
1
2
]
.
Similar
ly
,
th
e
Af
r
ican
Dev
elo
p
m
en
t
B
an
k
(
ADP)
r
ep
o
r
ted
th
at
th
e
co
u
n
tr
y
lo
s
es
r
o
u
g
h
ly
US$
2
9
b
illi
o
n
ea
ch
y
ea
r
o
r
a
b
o
u
t
5
.
8
%
o
f
GDP
d
u
e
to
in
ad
eq
u
ate
an
d
u
n
s
tab
le
p
o
wer
s
u
p
p
ly
[
1
3
]
.
E
ac
h
b
lac
k
o
u
t
ca
n
co
s
t
th
e
ec
o
n
o
m
y
o
v
er
US$
1
0
0
m
illi
o
n
p
er
d
a
y
;
d
is
r
u
p
tin
g
m
an
u
f
ac
tu
r
in
g
,
telec
o
m
m
u
n
icatio
n
s
,
an
d
f
in
an
ci
al
s
er
v
ices.
T
h
ese
im
p
ac
ts
r
e
v
ea
l
th
e
u
r
g
en
cy
o
f
s
tr
en
g
th
en
in
g
v
o
ltag
e
s
tab
ilit
y
to
en
h
a
n
ce
b
o
t
h
en
er
g
y
r
eliab
ilit
y
an
d
n
atio
n
al
ec
o
n
o
m
ic
r
e
s
ilien
ce
.
T
ab
le
1
.
Nig
er
ia
n
g
r
id
co
llap
s
e
f
o
r
th
e
p
er
io
d
o
f
y
ea
r
2
0
0
0
–
2026
S
/
N
Y
e
a
r
To
t
a
l
b
l
a
c
k
o
u
t
P
a
r
t
i
a
l
b
l
a
c
k
o
u
t
To
t
a
l
S
/
n
Y
e
a
r
To
t
a
l
b
l
a
c
k
o
u
t
P
a
r
t
i
a
l
b
l
a
c
k
o
u
t
To
t
a
l
1
2
0
0
0
5
6
11
15
2
0
1
4
9
4
13
2
2
0
0
1
14
5
19
16
2
0
1
5
6
4
10
3
2
0
0
2
9
32
41
17
2
0
1
6
22
6
28
4
2
0
0
3
14
39
53
18
2
0
1
7
15
9
24
5
2
0
0
4
22
30
52
19
2
0
1
8
12
1
13
6
2
0
0
5
21
15
36
20
2
0
1
9
7
4
10
7
2
0
0
6
20
10
30
21
2
0
2
0
3
1
4
8
2
0
0
7
18
8
26
22
2
0
2
1
2
2
4
9
2
0
0
8
26
16
42
23
2
0
2
2
6
2
8
10
2
0
0
9
19
20
39
24
2
0
2
3
2
1
3
11
2
0
1
0
22
20
42
25
2
0
2
4
10
2
12
12
2
0
1
1
13
6
19
26
2
0
2
5
2
0
2
13
2
0
1
2
16
8
24
27
2
0
2
6
2
0
2
14
2
0
1
3
22
2
24
To
t
a
l
3
3
9
2
5
3
5
9
2
2.
SUM
M
ARY
O
F
R
E
VI
E
W
E
D
L
I
T
E
R
AT
U
RE
T
h
e
s
tu
d
y
in
[
1
4
]
r
ep
o
r
te
d
th
e
o
cc
u
r
r
e
n
ce
s
o
f
v
o
ltag
e
co
llap
s
e
b
etwe
en
2
0
0
0
a
n
d
2
0
1
7
;
h
o
wev
er
,
it
d
id
n
o
t
p
er
f
o
r
m
an
y
an
aly
tica
l
in
v
esti
g
atio
n
to
p
r
o
p
o
s
e
s
o
l
u
tio
n
s
to
th
e
id
en
tifie
d
p
r
o
b
le
m
s
.
W
h
ile
s
tu
d
y
in
[
1
5
]
illu
s
tr
ated
th
e
u
s
e
o
f
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
to
ad
d
r
ess
v
o
ltag
e
in
s
tab
ilit
y
b
u
t
f
ailed
to
ad
d
r
ess
d
y
n
am
ic
d
is
tu
r
b
a
n
ce
v
ar
iatio
n
.
T
h
e
r
e
p
o
r
t
in
[
1
6
]
ev
alu
ate
d
a
m
o
d
er
n
v
o
ltag
e
s
tab
ilit
y
in
d
ex
f
o
r
p
r
ed
ictin
g
v
o
ltag
e
co
llap
s
e
an
d
id
e
n
tify
i
n
g
wea
k
b
u
s
es
an
d
cr
itical
lin
es.
T
h
is
p
r
o
v
es
th
at
th
er
e
ar
e
ef
f
ec
tiv
e
in
d
ices
b
u
t
th
e
r
esu
lts
lack
s
an
o
p
tim
izati
o
n
tech
n
iq
u
es
in
te
g
r
atio
n
.
T
o
en
h
an
ce
p
o
wer
q
u
ality
[
1
7
]
,
[
1
8
]
a
p
p
lied
a
g
l
o
w
-
wo
r
m
s
war
m
o
p
tim
izer
,
y
et
f
u
r
th
er
o
p
tim
izatio
n
an
d
m
u
lti
-
in
d
ex
ap
p
r
o
ac
h
es
r
em
ain
u
n
ex
p
lo
r
ed
.
Stu
d
y
in
[
1
9
]
p
r
o
p
o
s
ed
a
r
elay
-
b
ased
lo
ca
l
in
d
ex
ad
d
r
ess
in
g
b
o
th
v
o
ltag
e
s
tab
ilit
y
an
d
lin
e
p
r
o
t
ec
tio
n
,
ef
f
ec
tiv
ely
d
is
tin
g
u
is
h
in
g
b
etwe
en
s
tab
l
e
an
d
u
n
s
tab
le
ca
s
es
d
u
r
in
g
d
is
tu
r
b
a
n
ce
s
.
R
esear
ch
er
s
in
[
2
0
]
em
p
lo
y
e
d
Mo
d
al/E
ig
en
v
alu
e
an
aly
s
is
to
ass
ess
Nig
er
ian
p
o
wer
s
y
s
tem
s
tab
ilit
y
.
C
o
n
tr
astl
y
,
[
2
1
]
v
alid
ated
a
q
u
ad
r
atic
ap
p
r
o
x
im
atio
n
f
o
r
lo
ad
m
a
r
g
i
n
esti
m
atio
n
,
p
r
o
p
o
s
in
g
p
o
wer
f
lo
w
eq
u
atio
n
m
o
d
if
icatio
n
s
to
id
en
tify
cr
itical
co
n
tin
g
en
cies,
th
o
u
g
h
r
an
k
in
g
s
r
em
ain
ed
im
p
r
ec
is
e.
Ar
ticl
e
in
[
2
2
]
im
p
r
o
v
e
d
d
is
tr
ib
u
ti
o
n
n
etwo
r
k
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
V
o
lta
g
e
s
ta
b
ilit
y
a
n
a
lysi
s
o
f p
o
w
er tr
a
n
s
mi
s
s
io
n
s
yste
ms u
s
i
n
g
mu
lti
-
in
d
ex
…
(
Tit
u
s
Ter
w
a
s
e
A
ko
r
)
1441
s
tab
ilit
y
b
y
tu
n
in
g
a
v
o
ltag
e
s
tab
ilit
y
in
d
ex
u
s
in
g
th
e
f
ast
v
o
ltag
e
s
tab
ilit
y
in
d
icato
r
an
d
s
im
u
lated
an
n
ea
lin
g
o
p
tim
izatio
n
.
B
ad
r
u
d
ee
n
et
a
l.
[
2
3
]
in
tr
o
d
u
ce
d
a
n
o
v
el
v
o
lta
g
e
s
tab
ilit
y
p
o
in
ter
(
NVSP)
tr
ain
ed
with
SVM
an
d
th
e
m
ed
iu
m
Ga
u
s
s
ian
k
er
n
el
class
if
icatio
n
to
o
lb
o
x
(
m
G
k
C
T
)
in
MA
T
L
AB
,
ef
f
ec
tiv
el
y
d
is
tin
g
u
is
h
in
g
s
tab
le
an
d
u
n
s
tab
le
lin
es.
Stu
d
ies
in
[
2
4
]
,
[
2
5
]
an
al
y
ze
d
v
o
ltag
e
s
tab
ilit
y
in
d
ices
to
id
e
n
tify
wea
k
b
u
s
es
an
d
em
p
lo
y
ed
PS
O
to
m
itig
ate
p
o
wer
lo
s
s
es.
Ho
wev
er
,
th
e
s
tu
d
ies
in
[
2
6
]
,
[
2
7
]
r
elied
o
n
a
s
in
g
le
s
tab
ilit
y
in
d
ex
,
d
esp
ite
m
u
lti
-
in
d
ex
a
p
p
r
o
ac
h
es o
f
f
e
r
i
n
g
g
r
ea
te
r
ac
cu
r
ac
y
,
s
en
s
itiv
ity
,
an
d
ad
ap
tab
ilit
y
.
2
.
1
.
St
a
t
em
ent
o
f
pro
blem
s
a
nd
re
s
ea
rc
h c
o
ntr
ibu
t
io
ns
T
h
e
p
r
o
b
lem
s
id
en
tifie
d
i
n
th
i
s
r
esear
ch
af
ter
an
e
x
ten
s
iv
e
liter
atu
r
e
r
ev
iew
in
d
icate
th
e
f
o
l
lo
win
g
:
˗
T
r
ad
itio
n
al
s
tatic
s
tab
ilit
y
in
d
ices
lik
e
lin
e
s
tab
ilit
y
in
d
ex
(
L
SI)
,
v
o
ltag
e
s
tab
ilit
y
in
d
e
x
(
VSI
)
,
lo
ad
in
g
m
ar
g
in
(
L
M)
,
FVSI
o
f
te
n
f
ail
to
ac
co
u
n
t
f
o
r
r
ea
l
-
tim
e
d
y
n
a
m
ic
v
ar
iatio
n
s
s
u
ch
as
l
o
ad
g
r
o
wth
,
r
en
ewa
b
le
en
er
g
y
f
lu
ctu
atio
n
s
,
N
-
1
co
n
tin
g
en
cies,
o
r
s
u
d
d
en
s
p
ik
es.
˗
C
o
n
v
en
tio
n
al
s
tatic
o
p
tim
izatio
n
ap
p
r
o
ac
h
es
s
u
c
h
as
d
eter
m
in
is
tic
MI
S
m
in
im
izatio
n
ex
h
ib
it
o
v
er
-
o
p
tim
is
m
,
p
r
o
d
u
cin
g
s
o
l
u
tio
n
s
th
at
d
eg
r
ad
e
u
n
d
e
r
d
is
tu
r
b
a
n
c
es
an
d
r
esu
lt
in
h
ig
h
v
ar
iab
ilit
y
(
co
ef
f
icien
t
o
f
v
ar
iatio
n
,
C
V)
in
s
tab
ilit
y
m
ar
g
in
s
with
lim
ited
ad
ap
ta
b
ilit
y
.
W
h
ile
h
y
b
r
id
m
etah
eu
r
is
tics
lik
e
W
APSO
i
s
ef
f
ec
tiv
e
f
o
r
m
u
lti
-
d
im
en
s
io
n
al
p
r
o
b
lem
s
s
u
ch
as
r
ea
ctiv
e
p
o
wer
s
ca
lin
g
ac
r
o
s
s
lar
g
e
n
etwo
r
k
s
,
th
eir
ef
f
ec
tiv
en
ess
r
em
ain
s
h
ig
h
ly
s
en
s
itiv
e
to
p
ar
am
eter
s
ettin
g
s
,
p
ar
ticu
lar
ly
th
e
in
er
tia
wei
g
h
t
(
w)
an
d
t
h
e
co
g
n
itiv
e/so
cial
co
ef
f
icien
ts
(
c
₁,
c₂)
.
T
h
e
af
o
r
m
en
tio
n
ed
p
r
o
b
lem
s
f
o
r
m
ed
t
h
e
g
a
p
s
in
th
is
p
a
p
er
,
th
er
ef
o
r
e
,
th
e
m
ain
o
b
jectiv
e
o
f
th
is
p
ap
er
is
to
f
ill
th
is
g
ap
b
y
ex
p
lo
r
in
g
v
o
ltag
e
s
tab
ilit
y
an
aly
s
is
th
r
o
u
g
h
th
e
i
n
teg
r
ati
o
n
o
f
h
y
b
r
i
d
wh
ale
an
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
alg
o
r
ith
m
s
with
m
u
lti
-
in
d
ex
in
d
ices
(
f
ast
v
o
ltag
e
s
tab
ilit
y
in
d
ex
an
d
lin
e
s
tab
ilit
y
in
d
ex
)
to
en
h
an
ce
n
etwo
r
k
s
tab
ilit
y
u
n
d
er
r
ea
l
-
tim
e
d
y
n
am
ic
v
ar
i
atio
n
s
.
T
h
is
p
ap
er
d
e
m
o
n
s
tr
at
es
th
at
th
e
p
r
o
p
o
s
ed
W
AP
SO
ap
p
r
o
ac
h
d
eliv
e
r
s
m
o
r
e
r
eliab
le
an
d
s
ca
lab
le
s
tab
ilit
y
im
p
r
o
v
em
en
ts
th
an
th
e
PS
O
-
GA
m
eth
o
d
,
o
win
g
to
its
s
u
p
er
io
r
r
o
b
u
s
tn
ess
u
n
d
e
r
d
y
n
am
ic
co
n
d
itio
n
s
,
r
e
d
u
ce
d
p
ar
am
eter
s
en
s
itiv
ity
,
an
d
e
n
h
an
ce
d
a
d
ap
tab
ilit
y
to
r
ea
l
-
ti
m
e
d
is
tu
r
b
a
n
ce
s
.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
s
o
f
th
is
r
esear
ch
ar
e
s
u
m
m
a
r
ized
as f
o
llo
w
s
:
˗
Mu
ltip
le
s
ce
n
ar
io
d
y
n
am
ic
ev
alu
atio
n
:
T
h
is
s
tu
d
y
d
e
v
elo
p
ed
f
iv
e
r
ea
lis
tic
o
p
er
atin
g
s
ce
n
ar
io
s
in
clu
d
in
g
g
r
ad
u
al
g
r
o
wth
,
s
u
d
d
e
n
d
e
m
an
d
s
p
ik
es,
cy
clic
lo
ad
f
l
u
ctu
atio
n
s
,
r
en
ewa
b
le
u
n
ce
r
t
ain
ty
,
an
d
N
-
1
co
n
tin
g
en
cies to
test
MI
S p
e
r
f
o
r
m
an
ce
u
n
d
er
d
iv
er
s
e
c
o
n
d
iti
o
n
s
.
B
y
ap
p
ly
in
g
th
e
W
APSO
f
r
am
ewo
r
k
,
th
e
ap
p
r
o
ac
h
e
n
s
u
r
es
r
esil
ien
ce
,
a
ch
iev
in
g
lo
w
v
ar
iab
ilit
y
(
C
V
<
0
.
1
)
a
n
d
h
ig
h
r
eliab
ilit
y
(
s
u
cc
ess
r
ate
>
9
0
%).
˗
C
o
m
p
r
eh
en
s
iv
e
s
en
s
itiv
ity
a
n
aly
s
is
:
T
h
e
s
tu
d
y
s
y
s
tem
atica
lly
ev
alu
ate
d
2
7
p
ar
a
m
eter
c
o
m
b
in
atio
n
s
o
f
in
er
tia
weig
h
t
(
w)
an
d
co
g
n
iti
v
e/so
cial
co
ef
f
icien
ts
(
c₁,
c₂)
ac
r
o
s
s
3
0
in
d
ep
en
d
e
n
t
r
u
n
s
.
A
r
o
b
u
s
tn
ess
in
d
ex
,
d
ef
in
ed
as
μ
×
(
1
+
C
V)
,
is
u
s
ed
to
id
e
n
tify
t
h
e
m
o
s
t
s
tab
le
p
ar
am
eter
s
et
(
lo
we
r
v
alu
es
i
n
d
icate
s
tr
o
n
g
er
p
er
f
o
r
m
an
ce
)
,
th
er
eb
y
ad
d
r
ess
in
g
th
e
co
m
m
o
n
g
ap
i
n
p
ar
am
eter
tu
n
in
g
f
o
r
m
etah
eu
r
is
tic
a
lg
o
r
ith
m
s
.
˗
Re
-
o
p
tim
izatio
n
f
o
r
a
d
ap
tab
ili
ty
:
Simu
lates
r
ea
l
-
tim
e
co
r
r
ec
tiv
e
ac
tio
n
s
with
a
+3
0
%
Qᵣₑ
d
is
tu
r
b
an
ce
an
d
2
0
r
e
-
o
p
tim
izatio
n
r
u
n
s
,
en
s
u
r
in
g
<5
%
p
er
f
o
r
m
an
ce
d
eg
r
ad
atio
n
.
I
t
d
em
o
n
s
tr
ates
~2
0
–
3
0
%
p
er
-
lin
e
M
I
S
im
p
r
o
v
em
e
n
t
th
r
o
u
g
h
a
v
er
ag
e
d
r
esu
lts
an
d
in
ter
p
r
etab
le
v
is
u
aliza
tio
n
s
(
h
ea
tm
ap
s
,
b
o
x
p
lo
ts
)
,
ad
d
r
ess
in
g
th
e
lack
o
f
s
ce
n
ar
io
-
r
o
b
u
s
t m
etr
ic
s
.
2
.
2
.
P
a
per
o
rg
a
niza
t
io
n
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
Sectio
n
1
in
tr
o
d
u
ce
d
th
e
r
esear
ch
to
p
ic
a
n
d
d
is
cu
s
s
ed
th
e
b
ac
k
g
r
o
u
n
d
at
wh
ich
th
e
s
tu
d
y
is
b
ased
.
Sectio
n
2
p
r
esen
ted
an
ex
ten
s
iv
e
liter
atu
r
e
r
ev
ie
w
th
at
h
elp
ed
in
th
e
in
d
en
tific
tio
n
o
f
g
a
p
s
wh
ile
s
ec
tio
n
3
p
r
esen
ts
th
e
m
eth
o
d
o
lo
g
y
,
in
clu
d
in
g
t
h
e
f
o
r
m
u
l
atio
n
o
f
MI
S,
th
e
d
ef
in
itio
n
o
f
d
y
n
am
ic
s
ce
n
ar
i
o
s
,
th
e
W
APSO
alg
o
r
ith
m
,
an
d
I
PF
C
m
o
d
elin
g
.
Sectio
n
4
d
is
cu
s
s
ed
th
e
r
esu
lts
,
co
v
er
in
g
v
o
ltag
e
p
r
o
f
ile
im
p
r
o
v
em
e
n
ts
,
MI
S
r
ed
u
ctio
n
s
,
s
ce
n
ar
io
-
b
ased
p
er
f
o
r
m
an
ce
,
an
d
co
m
p
a
r
ativ
e
ev
alu
atio
n
with
PS
O
-
GA.
Fin
ally
,
s
ec
tio
n
5
s
u
m
m
ar
ized
al
l
th
e
f
in
d
in
g
s
an
d
r
ec
o
m
m
en
d
atio
n
s
o
m
e
f
u
t
u
r
e
r
esear
ch
d
ir
ec
tio
n
s
.
3.
M
AT
E
R
I
AL
S AN
D
M
E
T
H
O
DS
T
h
is
r
esear
ch
u
tili
ze
d
t
h
e
L
SI
an
d
th
e
f
ast v
o
ltag
e
s
tab
ilit
y
in
d
ex
(
FVSI)
as m
u
ltip
le
s
tab
il
ity
in
d
ices.
E
ac
h
in
d
ex
was
m
o
d
ele
d
in
d
iv
id
u
ally
b
ef
o
r
e
c
o
m
b
in
i
n
g
th
em
in
to
a
co
m
p
o
s
ite
s
tab
ilit
y
m
ea
s
u
r
e.
W
ith
r
ef
er
en
ce
to
th
e
lin
e
s
tab
ilit
y
in
d
ex
s
u
g
g
ested
in
[
2
3
]
,
Fig
u
r
e
1
illu
s
tr
ates
a
s
ch
em
atic
o
f
a
2
-
b
u
s
n
etwo
r
k
m
o
d
el.
All
p
ar
am
eter
s
an
d
v
ar
iab
les
ar
e
ex
p
r
ess
ed
in
p
er
-
u
n
it
v
a
lu
es.
T
h
e
p
r
o
b
lem
f
o
r
m
u
latio
n
o
f
L
SI
is
f
u
r
th
er
d
etailed
in
[
2
8
]
.
T
h
e
p
ar
am
eter
s
o
f
Fig
u
r
e
1
ar
e
s
tated
as f
o
llo
ws:
T
h
e
lin
e
im
p
ed
an
ce
is
g
iv
e
n
b
y
:
Z
L
=
R
L
+
jX
L
.
=
+
=
∗
(
1
)
W
h
er
e,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
15
,
No
.
3
,
Sep
tem
b
er
20
26
:
1
4
3
9
-
1
4
5
7
1442
∗
=
̅
̅
̅
̅
̅
=
∠
−
∠
∠
(
2
)
Su
b
s
titu
tin
g
in
(
2
)
in
to
(
1
)
we
h
av
e
(
3
)
.
=
∠
[
∠
−
∠
∠
]
=
|
|
|
|
|
|
∠
(
+
−
)
−
|
|
2
|
|
∠
(
3
)
Af
ter
ap
p
r
o
p
r
iate
m
ath
e
m
atica
l e
v
alu
atio
n
,
we
h
av
e
(
4
)
.
1
−
4
|
|
2
2
(
−
)
≥
0
(
4
)
Hen
ce
,
th
e
lin
e
s
tab
ilit
y
in
d
e
x
will b
e
(
5
)
.
ℎ
=
4
|
|
2
2
(
−
)
,
≤
1
(
5
)
F
o
r
m
u
l
a
t
i
o
n
o
f
t
h
e
F
VS
I
a
s
p
r
o
p
o
s
e
d
i
n
[
2
4
]
:
A
l
s
o
c
o
n
s
i
d
e
r
i
n
g
F
i
g
u
r
e
1
a
n
d
d
e
r
i
v
i
n
g
f
r
o
m
t
h
e
O
h
m
’
s
l
a
w
i
n
(
6
)
.
=
(
6
)
T
h
e
ac
tu
al
cu
r
r
en
t,
is
ex
p
r
ess
ed
as
(
7
)
.
=
(
7
)
Usi
n
g
(
1
)
an
d
(
2
)
,
we
h
a
v
e
(
8
)
.
=
=
=
∠
−
∠
∠
(
8
)
An
d
th
e
r
ec
eiv
i
n
g
en
d
cu
r
r
en
t
is
g
iv
en
b
y
(
9
)
.
=
(
)
∗
=
−
∠
−
(
9
)
Su
b
s
titu
tin
g
(
8
)
in
t
o
(
9
)
,
we
h
av
e
(
1
0
)
.
∠
−
∠
+
=
−
∠
−
(
1
0
)
B
y
ev
alu
atin
g
(
1
1
)
.
4
(
2
)
(
−
)
2
≤
1
(
1
1
)
B
y
ass
u
m
p
tio
n
,
if
→
0
,
→
0
an
d
→
1
.
T
h
e
n
,
(
1
2
)
.
4
2
2
2
≤
1
(
1
2
)
Hen
ce
,
th
e
FVSI
ca
n
b
e
wr
itte
n
as (
1
3
)
.
=
4
2
2
≤
1
(
1
3
)
B
r
in
g
in
g
(
5
)
an
d
(
1
3
)
to
g
et
h
er
y
ield
s
th
e
m
u
lti
-
in
d
e
x
s
tab
ilit
y
in
d
ices (
MI
S)
as sh
o
wn
i
n
(
1
4
)
.
=
4
|
|
2
[
(
|
|
)
2
−
2
(
−
)
(
−
1
)
]
≤
1
=
{
−
1
,
<
0
,
≥
(
1
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
V
o
lta
g
e
s
ta
b
ilit
y
a
n
a
lysi
s
o
f p
o
w
er tr
a
n
s
mi
s
s
io
n
s
yste
ms u
s
i
n
g
mu
lti
-
in
d
ex
…
(
Tit
u
s
Ter
w
a
s
e
A
ko
r
)
1443
W
h
er
e
is
th
e
m
o
d
i
f
ier
an
d
is
th
e
th
r
esh
o
ld
v
alu
e.
T
h
e
(
1
4
)
u
s
es
a
s
witch
in
g
f
u
n
ctio
n
,
σ
,
to
d
eter
m
in
e
v
o
ltag
e
co
llap
s
e
p
r
o
x
im
ity
an
d
co
m
p
ar
es
ea
ch
r
esu
lt
to
a
th
r
e
s
h
o
ld
v
alu
e.
T
h
e
f
u
n
ctio
n
σ
f
o
r
s
witch
in
g
is
b
ased
o
n
th
e
in
s
ig
n
if
ican
t
f
lu
ctu
atio
n
in
an
g
le,
δ,
wh
ich
in
d
icate
s
a
s
ev
er
ely
lo
ad
ed
p
o
wer
s
y
s
tem
g
r
id
.
A
co
n
s
id
er
ab
le
an
g
le
v
ar
iatio
n
in
d
icate
s
h
ig
h
p
o
wer
f
lo
w
o
r
r
esis
tan
ce
.
Stab
ilit
y
is
m
ain
tain
ed
wh
en
MI
S
is
les
s
th
an
1
,
b
u
t
as
it
ap
p
r
o
ac
h
es
1
,
in
s
tab
ilit
y
ar
is
es,
r
esu
ltin
g
in
v
o
ltag
e
co
llap
s
e
as
en
u
m
er
ated
b
y
[
2
8
]
.
A
s
u
m
m
ar
y
o
f
k
ey
eq
u
atio
n
s
is
s
h
o
wn
i
n
T
a
b
le
2
.
T
h
e
p
a
r
am
eter
σ
c
h
ar
ac
ter
izes
th
e
d
o
m
in
an
t
in
s
tab
ilit
y
m
ec
h
a
n
is
m
as
th
e
s
y
s
tem
ap
p
r
o
ac
h
es
v
o
ltag
e
co
llap
s
e.
At
lo
w
lo
ad
s
(
σ
≈
0
)
,
in
s
tab
ilit
y
is
r
ea
ctiv
e
-
p
o
wer
-
lim
ited
,
w
h
er
ea
s
at
h
ig
h
lo
a
d
s
(
σ
≈
1
)
,
it
b
ec
o
m
es
a
n
g
le
-
lim
ite
d
,
am
p
lify
in
g
p
o
wer
s
win
g
s
an
d
r
is
k
in
g
s
y
n
ch
r
o
n
is
m
lo
s
s
.
Fo
r
th
e
Nig
er
ian
g
r
i
d
,
h
ig
h
σ
v
alu
es
u
n
d
er
p
ea
k
d
em
an
d
h
ig
h
lig
h
t
s
tr
ess
ed
o
p
er
atin
g
c
o
n
d
itio
n
s
,
u
n
d
er
s
co
r
in
g
t
h
e
n
ee
d
f
o
r
r
ein
f
o
r
ce
m
e
n
ts
s
u
ch
as
FAC
T
S
d
ev
ices
to
p
r
ev
e
n
t
ca
s
ca
d
in
g
o
u
tag
es.
T
h
e
th
r
esh
o
ld
an
g
l
e
(
)
d
ef
in
es
th
e
cr
itical
s
tab
ilit
y
m
ar
g
in
in
th
e
s
witch
in
g
f
u
n
ctio
n
σ
(
δ)
,
m
a
r
k
in
g
th
e
p
o
in
t
wh
er
e
t
h
e
MI
S
s
h
if
ts
b
etwe
en
L
SI
-
an
d
FVSI
-
d
o
m
in
an
ce
.
I
n
tr
an
s
m
is
s
io
n
s
y
s
tem
s
,
ac
tiv
e
p
o
wer
tr
an
s
f
er
≈
(
)
s
in
(
)
r
ea
ch
es
its
m
ax
im
u
m
,
b
ey
o
n
d
wh
ich
=
90
s
tab
ilit
y
d
eter
io
r
ates.
Fig
u
r
e
1
.
A
tr
a
n
s
m
is
s
io
n
n
etwo
r
k
m
o
d
el
o
f
a
2
-
b
u
s
s
y
s
tem
T
ab
le
2
.
A
s
u
m
m
a
r
y
o
f
k
e
y
eq
u
atio
n
s
I
n
d
e
x
Eq
u
a
t
i
o
n
C
o
n
d
i
t
i
o
n
LSI
4
|
|
2
2
(
−
)
,
≤
1
-
F
V
S
I
4
2
2
≤
1
M
S
I
4
|
|
2
[
(
|
|
)
2
−
2
(
−
)
(
−
1
)
]
≤
1
=
{
−
1
,
<
0
,
≥
,
i
s t
h
e
m
o
d
i
f
i
e
r
a
n
d
i
s t
h
e
t
h
r
e
s
h
o
l
d
v
a
l
u
e
.
Pra
ctica
lly
,
is
s
et
at
o
r
s
lig
h
tl
y
b
elo
w
th
is
v
alu
e
(
ty
p
ically
8
0
°
–
8
5
°)
to
p
r
o
v
i
d
e
a
s
af
ety
m
ar
g
in
.
I
t
d
is
tin
g
u
is
h
es
s
ec
u
r
e
o
p
e
r
atio
n
(
<
)
f
r
o
m
s
tr
ess
ed
o
r
em
er
g
e
n
cy
co
n
d
itio
n
s
(
>
)
,
wh
er
e
s
m
a
ll
d
is
tu
r
b
an
ce
s
ca
n
tr
ig
g
er
v
o
ltag
e
co
llap
s
e.
I
t
is
im
p
o
r
tan
t
to
n
o
te
th
at
t
h
e
ass
u
m
p
tio
n
δ→0
is
in
tr
o
d
u
ce
d
o
n
ly
as
a
m
ath
em
atica
l simp
lific
atio
n
d
u
r
in
g
th
e
d
er
iv
atio
n
o
f
th
e
FVSI
f
o
r
m
u
latio
n
.
I
n
r
ea
l tr
an
s
m
is
s
io
n
s
y
s
tem
s
,
th
e
p
o
wer
an
g
le
d
if
f
er
en
ce
is
s
m
all
b
u
t
n
o
n
-
ze
r
o
,
ty
p
ically
r
an
g
in
g
f
r
o
m
5
°
to
3
0
°
u
n
d
er
n
o
r
m
al
o
p
er
atin
g
co
n
d
itio
n
s
.
T
h
e
r
ef
o
r
e
,
th
is
ap
p
r
o
x
im
atio
n
d
o
es
n
o
t
im
p
ly
ze
r
o
p
o
wer
tr
an
s
f
er
;
r
at
h
er
,
it
s
im
p
lifie
s
th
e
an
aly
tical
ex
p
r
ess
io
n
wh
ile
p
r
eser
v
i
n
g
th
e
p
r
ac
tical
o
p
er
atin
g
ch
a
r
ac
ter
is
tics
o
f
th
e
s
y
s
tem
.
Fu
r
th
er
m
o
r
e
,
alth
o
u
g
h
th
e
m
ax
im
u
m
th
eo
r
etica
l
p
o
wer
tr
an
s
f
er
o
cc
u
r
s
at
δ
=
90
o
,
p
r
ac
tical
tr
an
s
m
is
s
io
n
s
y
s
tem
s
o
p
er
ate
at
s
ig
n
if
ican
tly
s
m
aller
p
o
wer
an
g
les
(
ty
p
ically
5
°
–
4
0
°)
to
m
ain
tain
s
u
f
f
icien
t
s
tab
ilit
y
m
ar
g
in
s
an
d
p
r
e
v
en
t
in
s
tab
ilit
y
.
C
o
n
s
eq
u
en
tly
,
δ
=9
0
o
r
e
p
r
esen
ts
o
n
ly
th
e
th
e
o
r
etica
l
s
tead
y
-
s
tate
s
tab
ilit
y
lim
it
,
r
ath
er
th
an
an
a
ctu
al
o
p
er
atin
g
co
n
d
itio
n
.
L
o
a
d
f
lo
w
an
al
y
s
is
is
ap
p
lied
to
d
eter
m
in
e
th
e
s
tead
y
-
s
tate
s
o
lu
tio
n
o
f
a
p
ar
tic
u
lar
p
o
wer
s
y
s
tem
.
I
t
p
r
o
v
id
es
an
in
itial
ass
ess
m
en
t
o
f
th
e
p
o
w
er
s
y
s
tem
,
wh
ic
h
is
n
o
n
lin
ea
r
d
u
e
to
th
e
d
y
n
am
ic
r
elatio
n
s
h
ip
b
etwe
en
lo
ad
,
v
o
lt
ag
e
m
ag
n
itu
d
e
,
an
d
cir
cu
it im
p
ed
an
ce
.
Sin
ce
it is
a
n
o
n
-
lin
ea
r
p
r
o
b
lem
,
it
h
as
to
b
e
s
o
lv
ed
iter
ativ
ely
.
T
h
e
m
eth
o
d
h
as
a
b
etter
co
n
v
er
g
e
n
ce
r
ate
th
an
o
th
er
m
eth
o
d
s
o
f
l
o
ad
f
l
o
w
s
o
lu
tio
n
as st
ated
in
[
2
5
]
.
T
h
e
lo
ad
f
lo
w
f
o
r
m
u
latio
n
is
g
iv
en
b
y
(
1
5
)
an
d
(
1
6
)
.
ℎ
=
∑
|
ℎ
|
|
|
|
ℎ
|
(
ℎ
−
ℎ
+
)
=
1
≠
ℎ
(
1
5
)
ℎ
=
−
∑
|
ℎ
|
|
|
|
ℎ
|
(
ℎ
−
ℎ
+
)
=
1
≠
ℎ
(
1
6
)
T
h
e
(
1
5
)
an
d
(
1
6
)
f
o
r
m
a
s
et
o
f
n
o
n
-
lin
ea
r
alg
e
b
r
aic
eq
u
ati
o
n
s
.
B
y
ap
p
ly
in
g
a
T
a
y
lo
r
s
er
ies
ex
p
an
s
io
n
a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
15
,
No
.
3
,
Sep
tem
b
er
20
26
:
1
4
3
9
-
1
4
5
7
1444
n
eg
lectin
g
h
i
g
h
er
-
o
r
d
e
r
ter
m
s
,
th
e
s
y
s
tem
ca
n
b
e
lin
ea
r
ize
d
,
r
esu
ltin
g
i
n
th
e
J
ac
o
b
ian
m
atr
ix
f
o
r
m
u
latio
n
,
wh
ich
d
escr
ib
es th
e
in
ter
ac
tio
n
b
etwe
en
v
o
ltag
e
m
ag
n
itu
d
e,
v
o
ltag
e
an
g
le,
an
d
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
:
[
∆
∆
]
=
[
1
2
3
4
]
[
∆
∆
|
|
]
(
1
7
)
wh
er
e
J
1
,
J
2
,
J
3
,
an
d
J
4
ar
e
th
e
s
u
b
m
atr
ices
o
f
th
e
J
ac
o
b
ian
m
atr
ix
.
∆
P
an
d
∆
Q
r
ep
r
esen
t
th
e
m
is
m
atch
es
b
etwe
en
s
ch
ed
u
le
d
an
d
ca
lcu
lated
v
alu
es
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
,
r
esp
ec
tiv
ely
.
∆
δ
an
d
∆|
V
|
ar
e
th
e
in
cr
em
en
tal
co
r
r
ec
tio
n
s
to
t
h
e
b
u
s
v
o
ltag
e
an
g
les
an
d
m
ag
n
itu
d
es.
T
h
ese
m
is
m
atch
es
at
iter
atio
n
k
a
r
e
ex
p
r
ess
ed
as:
T
h
u
s
,
∆
ℎ
=
ℎ
ℎ
−
ℎ
(
)
(
1
8
)
∆
ℎ
=
ℎ
ℎ
−
ℎ
(
)
(
1
9
)
h
en
ce
,
th
e
m
ea
s
u
r
ed
v
o
ltag
e
m
ag
n
itu
d
e
a
n
d
a
n
g
le
ar
e
g
iv
en
as
(
2
0
)
a
n
d
(
2
1
)
.
ℎ
(
+
1
)
=
ℎ
(
)
+
∆
ℎ
(
)
(
2
0
)
|
ℎ
(
+
1
)
|
=
|
ℎ
(
)
|
+
∆
|
ℎ
(
)
|
(
2
1
)
T
h
is
is
r
ep
ea
ted
u
n
til it
co
n
v
er
g
es
(
2
2
)
a
n
d
(
2
3
)
.
|
∆
ℎ
|
≤
(
2
2
)
|
∆
ℎ
|
≤
(
2
3
)
W
h
er
e
s
tan
d
f
o
r
th
e
to
ler
an
ce
lev
el.
3
.
1
.
Dy
na
m
ic
dis
t
urba
nce
s
c
ena
rio
f
o
r
m
ula
t
io
n
In
th
is
p
ap
e
r
,
f
iv
e
ca
teg
o
r
ies
o
f
d
y
n
am
ic
l
o
ad
d
is
tu
r
b
an
ce
s
ar
e
ex
p
lo
r
e
d
to
s
tr
ess
r
ea
l
wo
r
ld
c
o
n
d
itio
n
s
.
T
h
e
d
y
n
am
ic
l
o
ad
s
in
clu
d
e
i
)
g
r
ad
u
al
lo
ad
g
r
o
wth
(
GL
G)
:
th
e
s
tep
wis
e
in
cr
ea
s
e
in
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
at
lo
ad
b
u
s
es
(
1
0
–
3
0
%)
o
f
b
ase
v
alu
e
;
ii)
Su
d
d
e
n
s
p
ik
es
(
SS
)
:
R
an
d
o
m
in
s
tan
tan
eo
u
s
d
em
an
d
s
u
r
g
es
(5
-
1
0
%
o
f
th
e
to
tal
lo
a
d
)
;
iii)
C
y
clic
f
lu
ctu
atio
n
s
(
C
F):
Per
i
o
d
ic
o
s
cillatio
n
s
in
lo
ad
s
as
s
h
o
wn
in
(
2
4
)
an
d
(
2
5
)
.
(
)
=
(
1
+
s
in
(
)
)
(
2
4
)
(
)
=
(
1
+
s
in
(
)
)
(
2
5
)
W
h
er
e
an
d
ar
e
th
e
s
tead
y
s
tate
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
r
esp
ec
tiv
ely
;
α
is
th
e
f
lu
ctu
atio
n
am
p
litu
d
e
(
r
an
g
e
0
≤
α
≤
1
,
if
α
=
0
.
1
,
it
me
a
n
s
10%
va
r
ia
tion
a
r
ound
the
b
a
s
e
l
oa
d
)
,
is
th
e
o
s
cillatio
n
f
r
eq
u
en
cy
,
(
)
an
d
(
)
ar
e
th
e
tim
e
-
v
ar
y
in
g
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
d
em
a
n
d
a
t
a
lo
ad
b
u
s
,
r
esp
ec
tiv
ely
.
I
n
th
is
s
tu
d
y
,
cy
clic
lo
ad
f
lu
ctu
atio
n
s
wer
e
m
o
d
eled
u
s
in
g
a
s
in
u
s
o
id
al
lo
a
d
v
ar
iatio
n
with
a
f
r
eq
u
en
cy
o
f
ap
p
r
o
x
im
ately
0
.
2
Hz
,
r
ep
r
esen
tin
g
s
lo
w
p
er
io
d
ic
v
ar
iatio
n
s
co
m
m
o
n
ly
o
b
s
er
v
ed
in
in
d
u
s
tr
ial
an
d
ag
g
r
eg
ate
d
d
em
a
n
d
p
atter
n
s
.
T
h
er
ef
o
r
e,
th
e
m
ax
im
u
m
lo
a
d
p
o
wer
co
r
r
esp
o
n
d
s
to
1
1
0
%
o
f
th
e
b
ase
lo
ad
,
wh
ile
t
h
e
m
in
im
u
m
lo
a
d
co
r
r
esp
o
n
d
s
to
9
0
%
o
f
th
e
b
ase
lo
ad
.
I
n
er
tial
lo
ad
s
,
s
u
ch
as
in
d
u
ctio
n
m
o
to
r
s
,
p
r
o
v
i
d
e
tem
p
o
r
ar
y
k
in
etic
en
er
g
y
s
u
p
p
o
r
t
b
u
t
in
cr
ea
s
e
r
ea
ctiv
e
p
o
wer
d
em
an
d
d
u
r
i
n
g
v
o
ltag
e
d
ip
s
,
wh
er
ea
s
n
o
n
-
in
er
tial
lo
a
d
s
r
esp
o
n
d
r
ap
id
ly
to
v
o
ltag
e
v
a
r
iatio
n
s
an
d
m
ay
in
cr
ea
s
e
s
y
s
tem
s
en
s
itiv
ity
,
t
h
er
eb
y
in
f
lu
e
n
cin
g
o
v
er
all
v
o
ltag
e
s
tab
ilit
y
.
iv
)
R
en
ewa
b
le
u
n
ce
r
tain
ty
(
R
U)
:
Var
iab
ilit
y
in
r
en
ewa
b
le
p
o
wer
in
r
en
ewa
b
le
in
jectio
n
m
o
d
eled
as
Gau
s
s
ian
n
o
is
e
in
(
2
6
)
.
(
)
=
+
,
~
(
0
,
2
)
(
2
6
)
W
h
er
e
(
)
r
ep
r
esen
ts
th
e
ac
tu
al
r
en
ewa
b
le
p
o
wer
o
u
t
p
u
t
at
a
tim
e
(
s
o
lar
PV,
win
d
o
r
h
y
d
r
o
with
v
ar
iab
l
e
in
f
lo
w)
,
is
th
e
ex
p
ec
ted
o
r
f
o
r
ec
asted
g
en
er
atio
n
(
m
ea
n
/b
ase
v
alu
e)
,
~
(
0
,
2
)
d
ep
icts
th
e
er
r
o
r
f
o
llo
ws
n
o
r
m
al
(
Gau
s
s
ian
)
d
is
tr
ib
u
tio
n
with
:
m
ea
n
=
0
(
d
ev
iatio
n
s
ar
e
u
n
b
iased
)
,
v
ar
ia
n
ce
=
2
(
th
e
d
eg
r
ee
o
f
u
n
ce
r
tain
ty
,
lar
g
e
r
2
=
)
,
t
=
tim
e
in
d
ex
(
m
in
u
tes,
h
o
u
r
s
o
r
s
tep
s
im
u
latio
n
.
v
.
N
-
1
C
o
n
tin
g
en
cy
(
N1
C
)
:
lin
e
o
r
g
en
er
ato
r
o
u
tag
e
s
im
u
lated
b
y
r
em
o
v
in
g
an
elem
en
t
an
d
r
ee
v
alu
atin
g
th
e
p
o
we
r
f
lo
w.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
V
o
lta
g
e
s
ta
b
ilit
y
a
n
a
lysi
s
o
f p
o
w
er tr
a
n
s
mi
s
s
io
n
s
yste
ms u
s
i
n
g
mu
lti
-
in
d
ex
…
(
Tit
u
s
Ter
w
a
s
e
A
ko
r
)
1445
3
.
2
.
T
he
a
pp
lica
t
io
n o
f
pa
rt
i
cle
s
wa
rm
o
ptim
iza
t
io
n t
ec
hn
iqu
e
T
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
is
m
ath
em
atica
lly
m
o
d
eled
as
p
r
esen
ted
in
[
2
6
]
.
L
et
th
e
p
o
s
itio
n
o
f
a
p
ar
ticle
in
an
n
-
d
im
en
s
io
n
al
s
ea
r
ch
s
p
ac
e
be
d
ef
in
e
d
as
(
2
7
)
.
Let
=
(
1
,
2
…
)
(
2
7
)
W
h
er
e
r
ep
r
esen
ts
th
e
p
ar
ticle
p
o
s
itio
n
in
th
e
n
-
d
im
en
s
io
n
al
s
ea
r
ch
s
p
ac
e.
T
h
e
p
ar
ticle
ten
d
s
to
ac
h
iev
e
n
ew
p
o
s
itio
n
(
+
1
)
b
y
u
p
d
atin
g
th
eir
v
el
o
city
(
+
1
)
u
s
in
g
s
p
ee
d
c
h
an
g
es.
T
h
is
is
r
ep
r
esen
ted
b
y
th
e
(
2
8
)
an
d
(
2
9
)
.
(
+
1
)
=
.
(
)
+
1
1
(
(
)
−
(
)
)
+
2
2
(
(
)
−
(
)
)
(
2
8
)
(
+
1
)
=
(
)
+
(
+
1
)
(
2
9
)
W
h
er
e
(
)
(
)
ar
e
th
e
p
ar
ticles
an
d
s
war
m
o
p
tim
al
p
o
s
itio
n
s
r
esp
ec
tiv
ely
,
1
2
ar
e
th
e
r
an
d
o
m
v
alu
es
b
etwe
en
0
an
d
1
o
f
th
e
Par
ticle,
an
d
g
r
o
u
p
r
esp
ec
tiv
ely
,
an
d
1
2
ar
e
th
e
ac
c
eler
atio
n
co
ef
f
icien
ts
o
f
th
e
p
ar
ticle
an
d
g
r
o
u
p
r
esp
ec
tiv
ely
.
T
h
e
v
elo
cit
y
v
ec
to
r
h
as
th
r
ee
co
m
p
o
n
en
ts
n
am
ely
:
th
e
in
er
tia
co
m
p
o
n
en
t
g
iv
e
n
as
(
)
,
th
e
c
o
g
n
itiv
e
co
m
p
o
n
e
n
t
1
1
(
(
)
−
(
)
)
an
d
th
e
s
o
cial
co
m
p
o
n
e
n
t
r
ep
r
esen
ted
as
2
2
(
(
)
−
(
)
)
.
(
)
r
ep
r
esen
ts
th
e
in
er
tia
weig
h
t
v
alu
e
at
iter
ati
o
n
(
t)
an
d
it
is
g
iv
en
as
(
3
0
)
.
(
)
=
(
−
−
)
×
(
3
0
)
T
h
e
in
er
tia
ad
ju
s
ted
th
e
ex
p
lo
r
atio
n
a
n
d
ex
p
lo
itatio
n
.
E
x
p
lo
r
atio
n
is
g
r
o
win
g
d
u
r
in
g
th
e
p
r
o
ce
d
u
r
e,
wh
ile
ex
p
lo
itatio
n
is
r
ed
u
cin
g
th
e
e
f
f
icac
y
o
f
th
e
s
ea
r
ch
.
T
h
e
s
ea
r
c
h
p
r
o
ce
d
u
r
e
lo
wer
s
lin
ea
r
ly
f
r
o
m
0
.
9
to
0
.
4
o
r
0
.
2
d
u
r
in
g
th
e
o
p
tim
izatio
n
p
h
ase.
3
.
3
.
Appl
ica
t
io
n o
f
wha
le
o
ptim
iza
t
io
n t
ec
hn
iqu
e
T
h
e
m
ath
em
atica
l
m
o
d
el
was
cr
ea
ted
b
y
th
e
wh
ale
ar
o
u
n
d
th
e
p
r
ey
,
th
e
s
p
ir
al
b
u
b
b
le
-
n
et
ea
tin
g
p
atter
n
,
an
d
th
e
s
ea
r
ch
s
p
ac
e
f
o
r
th
e
p
r
ey
as
d
em
o
n
s
tr
ated
i
n
[
2
9
]
.
T
h
e
wh
ale
ca
n
r
ec
o
g
n
ize
an
d
s
u
r
r
o
u
n
d
its
p
r
ey
.
Du
r
in
g
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
,
it
is
a
s
s
u
m
ed
th
at
th
e
cu
r
r
en
t
ca
n
d
id
ate'
s
b
est
s
o
lu
tio
n
is
th
e
tar
g
et
p
r
ey
.
Af
ter
s
elec
tin
g
th
e
to
p
s
ea
r
ch
a
g
en
t,
th
e
r
e
m
ain
in
g
s
ea
r
c
h
ag
e
n
ts
ad
ju
s
t
th
eir
lo
ca
tio
n
s
to
ac
c
o
m
m
o
d
ate
t
h
e
b
est
s
ea
r
ch
ag
en
t.
T
h
is
is
m
ath
em
atica
lly
m
o
d
el
as
(
3
1
)
an
d
(
3
2
)
.
⃗
⃗
=
|
.
⃗
⃗
⃗
⃗
(
)
−
⃗
⃗
⃗
⃗
⃗
⃗
(
)
|
(
3
1
)
⃗
⃗
⃗
⃗
⃗
⃗
(
+
1
)
=
⃗
⃗
⃗
⃗
(
)
+
.
⃗
⃗
(
3
2
)
W
h
er
e
is
th
e
cu
r
r
en
t
iter
atio
n
,
⃗
⃗
⃗
⃗
is
th
e
p
o
s
itio
n
v
ec
to
r
o
f
th
e
o
p
tim
al
s
o
lu
tio
n
,
⃗
⃗
⃗
⃗
⃗
⃗
is
th
e
p
o
s
iti
o
n
v
ec
to
r
o
f
th
e
s
ea
r
ch
ag
en
t,
ar
e
th
e
c
o
ef
f
icien
t
v
ec
t
o
r
s
o
f
th
e
p
o
s
itio
n
o
p
tim
al
s
o
lu
tio
n
a
n
d
d
is
tan
ce
to
th
e
s
o
lu
tio
n
an
d
|
|
is
th
e
ab
s
o
lu
te
v
alu
e
o
f
⃗
⃗
.
T
h
u
s
ar
e
g
iv
e
n
as
(
3
3
)
an
d
(
3
4
)
.
=
2
.
⃗
⃗
⃗
⃗
−
(
3
3
)
=
2
.
⃗
⃗
⃗
(
3
4
)
W
h
er
e
is
r
ed
u
ce
lin
ea
r
l
y
f
r
o
m
2
to
0
o
v
e
r
n
u
m
b
er
o
f
iter
atio
n
,
⃗
⃗
⃗
⃗
⃗
⃗
⃗
r
ep
r
esen
ts
r
an
d
o
m
v
ec
to
r
s
o
f
r
an
g
e
[
0
,
1
]
.
T
h
e
s
p
ir
al
u
p
d
atin
g
p
o
s
itio
n
is
g
iv
en
as
(
3
5
)
.
⃗
⃗
⃗
⃗
⃗
⃗
(
+
1
)
=
′
⃗
⃗
⃗
⃗
.
.
c
os
(
2
)
+
⃗
⃗
⃗
⃗
(
)
(
3
5
)
W
h
er
e
′
⃗
⃗
⃗
⃗
is
th
e
d
is
tan
ce
o
f
th
e
n
th
h
u
m
p
b
ac
k
wh
ale
to
t
h
e
p
r
ey
o
b
tain
ed
p
o
s
itio
n
,
k
is
a
co
n
s
tan
t
th
at
d
eter
m
in
e
th
e
s
h
ap
e
o
f
th
e
lo
g
ar
ith
m
ic
s
p
ir
al
an
d
s
p
ec
if
ied
t
h
e
r
an
d
o
m
n
u
m
b
er
[
-
1
,
1
]
.
At
th
e
s
am
e
tim
e,
th
e
wh
ales
s
wim
ar
o
u
n
d
th
e
tar
g
et
with
in
a
s
h
r
in
k
in
g
cir
cle
an
d
al
o
n
g
th
e
s
p
ir
al
s
h
ap
e
p
ath
.
T
h
is
is
r
ep
r
esen
ted
b
y
th
e
(
3
6
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
15
,
No
.
3
,
Sep
tem
b
er
20
26
:
1
4
3
9
-
1
4
5
7
1446
⃗
⃗
⃗
⃗
⃗
⃗
(
+
1
)
=
{
⃗
⃗
⃗
⃗
(
)
−
.
⃗
⃗
ℎ
<
0
.
5
′
⃗
⃗
⃗
⃗
.
.
c
os
(
2
)
+
⃗
⃗
⃗
⃗
(
)
ℎ
≥
0
.
5
(3
6
)
W
h
er
e
ℎ
is
a
r
an
d
o
m
n
u
m
b
er
in
[
0
,
1
]
tak
en
as
th
e
5
0
%
ch
an
c
e
th
at
th
e
s
h
r
in
k
in
g
en
cir
clin
g
m
ec
h
an
is
m
o
r
th
e
m
o
d
el
s
p
ir
al
will u
p
d
ate
t
h
e
p
o
s
itio
n
o
f
th
e
wh
ales d
u
r
in
g
th
e
s
ea
r
ch
f
o
r
p
r
ey
.
⃗
⃗
=
|
.
(
)
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
⃗
⃗
⃗
⃗
⃗
⃗
|
(3
7
)
⃗
⃗
⃗
⃗
⃗
⃗
(
+
1
)
=
(
)
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
+
.
⃗
⃗
(3
8
)
Usi
n
g
=
[
−
1
,
1
]
f
r
o
m
(
3
7
)
,
(
)
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
is
a
r
an
d
o
m
p
o
s
itio
n
v
ec
to
r
o
b
tai
n
ed
f
r
o
m
th
e
cu
r
r
en
t
p
o
p
u
latio
n
o
f
t
h
e
wh
ale.
4.
T
H
E
H
YB
R
I
D
WH
A
L
E
A
L
G
O
RIT
H
M
A
ND
P
ART
I
C
L
E
SWAR
M
O
P
T
I
M
I
Z
AT
I
O
N
(
WAP
SO
)
A
L
G
O
RIT
H
M
T
h
e
d
is
tin
ctiv
e
f
ea
tu
r
e
o
f
th
e
h
y
b
r
id
m
eth
o
d
lies
in
th
e
wh
ale
o
p
tim
izatio
n
alg
o
r
ith
m
’
s
(
W
OA)
ab
ilit
y
to
co
m
p
e
n
s
ate
f
o
r
t
h
e
lim
itatio
n
s
o
f
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
.
A
k
n
o
wn
d
r
awb
a
ck
o
f
s
tan
d
ar
d
PS
O
is
th
e
u
s
e
o
f
a
co
n
s
tan
t
in
er
tia
weig
h
t,
wh
ich
r
estricts
th
e
p
a
r
ticles’
s
ea
r
ch
ca
p
ab
ilit
y
in
co
m
p
lex
en
g
i
n
ee
r
in
g
p
r
o
b
lem
s
p
ac
es.
T
o
ad
d
r
ess
th
is
,
th
e
h
y
b
r
i
d
W
OA
–
PS
O
(
W
APSO)
m
eth
o
d
r
ep
lace
s
th
e
c
o
g
n
itiv
e
co
m
p
o
n
en
t
o
f
(
1
8
)
with
th
e
W
OA
-
in
s
p
ir
ed
co
m
p
o
n
en
t
f
r
o
m
(
3
3
)
.
T
h
e
u
p
d
ated
v
elo
city
a
n
d
p
o
s
itio
n
eq
u
atio
n
s
f
o
r
th
e
W
AP
SO a
lg
o
r
ith
m
,
as d
escr
ib
ed
in
[
3
0
]
,
a
r
e:
V
i
(
t
+
1
)
=
ω
.
V
i
(
t
)
+
C
1
r
1
(
X
SA
⃗
⃗
⃗
⃗
⃗
⃗
⃗
(
t
+
1
)
−
X
i
(
t
)
)
+
C
2
r
2
(
g
b
e
st
(
t
)
−
X
i
(
t
)
)
(3
9
)
X
i
(
t
+
1
)
=
X
i
(
t
)
+
V
i
(
t
+
1
)
(
40
)
I
n
th
ese
ex
p
r
ess
io
n
s
,
X
SA
(
t
+
1
)
is
th
e
u
p
d
ated
p
o
s
itio
n
f
r
o
m
th
e
W
OA
m
o
d
el
ac
tin
g
as
a
co
g
n
itiv
e
g
u
id
e
f
o
r
t
h
e
p
a
r
ticle,
ω
is
th
e
in
er
tia
weig
h
t.
T
h
e
h
y
b
r
i
d
alg
o
r
ith
m
u
s
es
an
ad
a
p
tiv
e
in
er
tia
weig
h
t
(
as
g
iv
en
in
eq
u
atio
n
s
3
8
-
3
9
)
f
r
o
m
PS
O
to
en
h
an
ce
g
lo
b
al
ex
p
lo
r
atio
n
wh
ile
m
ain
tain
in
g
th
e
f
u
n
d
a
m
en
tal
s
tr
u
ctu
r
e
o
f
v
elo
city
u
p
d
ate.
r
1
an
d
r
2
ar
e
r
an
d
o
m
n
u
m
b
er
s
u
n
if
o
r
m
ly
d
is
tr
ib
u
ted
in
[
0
,
1
]
,
a
n
d
C
1
,
C
2
ar
e
ac
ce
ler
atio
n
co
ef
f
icien
ts
.
I
n
th
is
h
y
b
r
id
f
r
am
ewo
r
k
1
r
eg
u
lates
th
e
co
g
n
itiv
e
co
m
p
o
n
en
t,
wh
ich
is
ad
a
p
ted
f
r
o
m
W
OA
th
r
o
u
g
h
⃗
⃗
⃗
⃗
⃗
⃗
(
+
1
)
(
3
3
)
i
n
p
lace
o
f
th
e
co
n
v
en
tio
n
al
(
)
,
th
er
e
b
y
le
v
er
a
g
in
g
W
OA’
s
p
r
e
y
-
en
cir
clin
g
m
ec
h
an
is
m
to
en
h
an
ce
lo
c
al
ex
p
lo
itatio
n
.
Me
an
wh
ile,
2
p
r
eser
v
es
th
e
s
o
cial
in
f
lu
en
ce
d
ir
ec
ted
to
war
d
(
)
,
en
s
u
r
in
g
s
war
m
-
wid
e
co
n
v
er
g
en
ce
.
Stan
d
ar
d
p
ar
am
eter
s
ettin
g
s
in
PS
O
h
y
b
r
id
s
(
co
m
m
o
n
l
y
1
=
2
=
2
)
ar
e
ty
p
ically
ass
u
m
ed
,
as
th
ey
p
r
o
v
id
e
a
b
alan
ce
d
tr
ad
e
-
o
f
f
b
etwe
en
in
d
iv
i
d
u
al
lear
n
i
n
g
an
d
co
llectiv
e
in
tellig
en
ce
,
th
er
eb
y
r
ed
u
cin
g
.
T
h
e
ter
m
g
best
(
t
)
d
en
o
tes th
e
g
lo
b
al
b
est s
o
lu
tio
n
f
o
u
n
d
b
y
th
e
s
war
m
at
iter
atio
n
t
.
T
h
is
h
y
b
r
id
a
p
p
r
o
ac
h
e
n
h
an
ce
s
b
o
th
l
o
ca
l
ex
p
lo
itatio
n
an
d
g
lo
b
al
ex
p
lo
r
at
io
n
b
y
s
y
n
er
g
izin
g
PS
O’
s
v
elo
city
-
d
r
iv
en
ex
p
lo
r
a
tio
n
with
W
OA’
s
ad
ap
tiv
e
en
c
ir
clin
g
b
eh
a
v
io
r
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
o
f
t
h
e
o
p
tim
izatio
n
is
to
m
i
n
im
ize
th
e
m
ax
im
u
m
s
tab
ilit
y
in
d
ex
ac
r
o
s
s
all
lin
es
an
d
d
y
n
am
ic
lo
a
d
s
ce
n
ar
io
s
.
Ob
jectiv
e
f
u
n
ctio
n
:
min
=
ma
x
{
(
)
}
∈
{
,
,
,
,
1
}
(4
1
)
Su
b
ject
to
:
i)
B
u
s
v
o
ltag
e
lim
it:
0
.
95
≤
≤
1
.
05
ii)
T
h
er
m
al
lo
ad
i
n
g
:
≤
(
)
iii)
Gen
er
ato
r
s
lim
its
:
(
,
)
Fo
r
ea
ch
o
f
th
e
p
a
r
am
eter
s
et
(
,
1
,
2
,
)
:
i)
3
0
Mo
n
te
C
ar
lo
s
im
u
latio
n
s
ac
r
o
s
s
all
s
ce
n
ar
io
s
was r
u
n
ii)
Me
an
MI
S,
co
ef
f
icien
t
o
f
v
ar
i
atio
n
(
C
V)
an
d
s
u
cc
ess
p
r
o
b
ab
ilit
y
(
SP
)
was c
o
m
p
u
ted
T
h
e
r
o
b
u
s
t in
d
ex
is
r
e
p
r
esen
te
d
as
(
4
2
).
=
.
̅
̅
̅
̅
̅
̅
(
4
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
V
o
lta
g
e
s
ta
b
ilit
y
a
n
a
lysi
s
o
f p
o
w
er tr
a
n
s
mi
s
s
io
n
s
yste
ms u
s
i
n
g
mu
lti
-
in
d
ex
…
(
Tit
u
s
Ter
w
a
s
e
A
ko
r
)
1447
Fo
r
o
p
er
atio
n
al
p
u
r
p
o
s
es,
a
lo
w
C
V
in
d
icate
s
co
n
s
i
s
ten
t
v
o
ltag
e
s
tab
ilit
y
p
er
f
o
r
m
an
ce
ac
r
o
s
s
d
if
f
er
en
t
o
p
er
atin
g
c
o
n
d
itio
n
s
,
wh
ile
a
lo
w
r
o
b
u
s
tn
ess
in
d
ex
r
ef
le
cts
r
eliab
le
an
d
r
ep
ea
ta
b
le
o
p
tim
izatio
n
r
esu
lts
.
T
o
g
eth
er
,
th
ese
m
etr
ics p
r
o
v
id
e
g
r
id
o
p
er
ato
r
s
with
g
r
e
ater
c
o
n
f
id
en
ce
in
s
y
s
tem
s
tab
ilit
y
a
n
d
r
esil
ien
ce
u
n
d
er
u
n
ce
r
tain
ty
.
Step
-
by
-
s
tep
alg
o
r
ith
m
i
)
I
n
itializatio
n
˗
L
o
ad
s
y
s
tem
d
ata.
˗
C
o
m
p
u
te
b
ase
-
ca
s
e
L
SI,
FVSI,
MI
S f
o
r
all
lin
es.
˗
Def
in
e
s
ea
r
ch
s
p
ac
e
b
o
u
n
d
s
f
o
r
r
ea
ctiv
e
p
o
wer
(
,
)
˗
Gen
er
ate
d
y
n
a
m
ic
s
ce
n
ar
io
s
.
ii)
Par
am
eter
s
en
s
itiv
ity
an
aly
s
is
˗
L
o
o
p
o
v
er
ca
n
d
id
ate
v
alu
es o
f
in
er
tia
weig
h
t
,
ac
ce
ler
atio
n
c
o
ef
f
icien
ts
1
,
2
.
˗
Fo
r
ea
ch
p
a
r
am
eter
s
et,
r
ep
ea
t
o
p
tim
izatio
n
f
o
r
_
.
iii)
W
AP
SO
o
p
tim
izatio
n
(
p
er
r
u
n
)
˗
R
an
d
o
m
ly
in
itialize
a
p
o
p
u
lati
o
n
o
f
ca
n
d
id
ate
s
o
lu
tio
n
s
.
˗
Fo
r
ea
ch
iter
atio
n
(
u
p
t
o
m
ax
_
iter
)
:
˗
E
v
alu
ate
f
itn
ess
=
m
ax
im
u
m
MI
S a
cr
o
s
s
all
s
ce
n
ar
io
s
.
˗
Up
d
ate
th
e
b
est s
o
lu
tio
n
.
W
h
ale
p
h
ase
(
ex
p
lo
itatio
n
o
r
e
x
p
lo
r
atio
n
)
: p
o
s
itio
n
u
p
d
ate
u
s
in
g
en
cir
clin
g
p
r
e
y
o
r
s
p
ir
al
s
e
ar
ch
.
PS
O
p
h
ase
: v
elo
city
u
p
d
ate
u
s
in
g
,
1
,
2
.
Ap
p
ly
b
o
u
n
d
s
(
,
)
to
k
ee
p
f
ea
s
ib
le
s
o
lu
tio
n
s
.
iv
)
Scen
ar
io
e
v
alu
atio
n
˗
C
o
m
p
u
te
p
er
-
s
ce
n
a
r
io
MI
S v
a
lu
es f
o
r
th
e
b
est s
o
lu
tio
n
.
˗
Sto
r
e
r
esu
lts
f
o
r
s
tatis
tical
ag
g
r
eg
atio
n
.
v)
R
o
b
u
s
tn
ess
in
d
ex
c
o
m
p
u
tat
io
n
˗
Fo
r
ea
ch
p
a
r
am
eter
s
et
(
,
1
,
2
)
co
m
p
u
te:
˗
Me
an
MI
S,
Std
Dev
,
C
V
(
co
ef
f
icien
t o
f
v
a
r
iatio
n
)
.
˗
Su
cc
ess
r
ate
(
MI
S <
1
)
.
˗
Av
er
ag
e
im
p
r
o
v
em
e
n
t o
v
e
r
b
a
s
e
-
ca
s
e
MI
S.
˗
R
o
b
u
s
tn
ess
in
d
ex
=
m
ea
n
*
(
1
+CV)
.
˗
Select
b
est p
ar
am
eter
s
et
(
lo
west r
o
b
u
s
tn
ess
in
d
ex
)
.
v
i)
Fin
al
o
p
tim
izatio
n
with
b
e
s
t p
ar
am
eter
s
˗
R
u
n
en
s
em
b
le
o
p
tim
izatio
n
with
b
est (
,
1
,
2
).
˗
E
v
alu
ate
ad
ap
ta
b
ilit
y
b
y
r
e
-
o
p
tim
izin
g
u
n
d
e
r
d
is
tu
r
b
a
n
ce
(
+
3
0
% Q)
.
˗
C
o
m
p
u
te
p
o
s
t
-
d
is
tu
r
b
a
n
ce
d
e
g
r
ad
atio
n
.
v
ii)
R
esu
lts
an
d
Vis
u
aliza
tio
n
R
ep
o
r
t b
ase
-
ca
s
e
v
s
o
p
tim
ized
MI
S (
p
er
lin
e
a
n
d
o
v
er
all)
.
Plo
t:
˗
MI
S a
cr
o
s
s
s
ce
n
ar
io
s
.
˗
B
o
x
p
lo
ts
(
r
o
b
u
s
tn
ess
d
is
tr
ib
u
tio
n
)
.
˗
Sen
s
itiv
ity
h
ea
tm
ap
f
o
r
p
ar
am
eter
s
.
˗
Re
-
o
p
tim
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n
ad
ap
tab
ilit
y
.
˗
MI
S b
ef
o
r
e
v
s
af
ter
o
p
tim
izatio
n
.
4
.
1
.
WAP
SO
pa
ra
m
et
er
s
ens
it
iv
it
y
a
nd
co
m
pu
t
a
t
io
na
l c
o
m
plex
it
y
a
na
ly
s
is
To
g
u
a
r
an
tee
th
e
r
o
b
u
s
tn
ess
o
f
th
e
h
y
b
r
id
wh
ale
an
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
W
APSO)
alg
o
r
ith
m
,
a
s
en
s
itiv
ity
an
aly
s
is
was
u
n
d
er
tak
en
to
v
alid
ate
th
e
ch
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ice
o
f
c
r
itical
p
ar
am
e
ter
s
:
in
er
tia
weig
h
t
(
)
,
co
g
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itiv
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an
d
s
o
cial
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ce
ler
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ef
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icien
ts
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,
2
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,
an
d
th
e
W
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co
n
tr
o
l
p
ar
am
eter
(
)
.
I
n
itial
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alu
es
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e
ass
ig
n
ed
as
=
0
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5
,
1
=
2
=
2
,
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d
α
d
ec
r
ea
s
in
g
lin
ea
r
ly
f
r
o
m
2
t
o
0
,
in
lin
e
with
estab
lis
h
ed
s
tu
d
ies
[
3
1
]
.
T
h
e
s
en
s
itiv
ity
an
aly
s
is
ex
p
lo
r
ed
ω
with
in
th
e
r
an
g
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[
0
.
4
,
0
.
9
]
,
1
2
with
in
[
1
.
5
,
2
.
5
]
,
a
n
d
b
o
th
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ea
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tial
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ay
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er
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/MAT
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h
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m
p
u
tatio
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o
f
th
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APSO
alg
o
r
ith
m
was
b
en
ch
m
ar
k
e
d
ag
ain
s
t
co
n
v
en
tio
n
al
PS
O
an
d
th
e
W
OA
to
ev
alu
ate
s
ca
lab
ilit
y
.
T
h
e
ass
es
s
m
en
t
was
p
er
f
o
r
m
e
d
o
n
th
e
Nig
er
ia
n
4
8
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b
u
s
,
3
3
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k
V
s
y
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tem
u
s
in
g
MA
T
L
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/MAT
PO
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E
R
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a
s
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ar
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m
p
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tin
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etu
p
(
I
n
tel
C
o
r
e
i7
,
1
6
GB
R
AM
)
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Fo
r
1
0
0
iter
atio
n
s
,
th
e
av
e
r
ag
e
r
u
n
tim
es
r
ec
o
r
d
ed
wer
e
1
2
.
5
s
ec
o
n
d
s
f
o
r
W
APS
O,
9
.
6
s
ec
o
n
d
s
f
o
r
PS
O,
an
d
1
5
.
8
s
ec
o
n
d
s
f
o
r
W
OA.
T
h
e
s
lig
h
tly
h
ig
h
er
r
u
n
tim
e
o
f
W
APSO
(
ab
o
u
t
1
.
3
tim
es
th
at
o
f
PS
O)
s
tem
s
f
r
o
m
its
h
y
b
r
id
d
esig
n
,
wh
ich
co
m
b
i
n
es
PS
O’
s
v
elo
city
u
p
d
ate
r
u
le
with
W
OA’
s
en
cir
clin
g
an
d
s
p
ir
al
s
ea
r
ch
m
ec
h
an
is
m
s
.
Desp
ite
th
is
o
v
e
r
h
ea
d
,
W
APSO
ac
h
iev
ed
a
1
0
%
g
r
ea
ter
im
p
r
o
v
e
m
en
t
i
n
MI
S
co
m
p
ar
e
d
to
PS
O
an
d
r
eq
u
ir
e
d
1
5
%
f
ewe
r
iter
at
io
n
s
th
an
W
OA
to
attain
9
0
%
o
f
th
e
o
p
tim
al
MI
S
v
alu
e
.
As
s
h
o
wn
in
T
a
b
le
3
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
15
,
No
.
3
,
Sep
tem
b
er
20
26
:
1
4
3
9
-
1
4
5
7
1448
f
o
r
lar
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er
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s
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ar
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m
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tatio
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tiv
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a
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eter
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s
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t
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r
ec
o
m
m
en
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ed
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o
m
itig
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n
tim
e
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em
an
d
s
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d
s
tr
en
g
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en
th
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o
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ith
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’
s
s
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ig
u
r
e
2
p
r
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a
f
r
am
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o
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th
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ess
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im
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ic
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ased
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id
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Fig
u
r
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3
illu
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ates N
ig
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3
.
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o
m
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tatio
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aly
s
is
o
f
th
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tim
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tech
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iq
u
es
A
l
g
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r
i
t
h
m
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v
g
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me
(
s)
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o
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i
s
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m
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me
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t
K
e
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s
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9
.
6
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se
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e
–
1
0
%
v
s WA
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a
st
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+
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n
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t
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t
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e
b
a
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e
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.
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u
r
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2
.
Dy
n
am
ic
s
ce
n
ar
io
-
b
ased
W
APS
O
o
p
tim
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n
f
r
a
m
ewo
r
k
Fig
u
r
e
3
.
T
h
e
s
in
g
le
-
lin
e
d
iag
r
am
o
f
th
e
Nig
e
r
ian
g
r
id
3
3
0
k
V,
4
8
-
b
u
s
n
etwo
r
k
T
h
e
n
etwo
r
k
is
in
ter
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n
n
ec
ted
an
d
co
m
p
r
is
es
f
o
r
ty
-
ei
g
h
t
(
4
8
)
b
u
s
es,
in
clu
d
in
g
f
o
u
r
teen
(
1
4
)
g
en
er
ato
r
b
u
s
es
an
d
th
ir
ty
-
f
o
u
r
(
3
4
)
lo
a
d
b
u
s
es.
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t
f
ea
tu
r
es
eig
h
t
y
-
eig
h
t
(
8
8
)
t
r
an
s
m
is
s
io
n
lin
es
u
tili
zin
g
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is
o
n
twin
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d
b
ea
r
twin
(
L
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n
)
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n
d
u
cto
r
s
,
ea
ch
with
a
cr
o
s
s
-
s
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tio
n
al
ar
ea
o
f
3
5
0
m
m
2
.
Fo
r
t
h
e
p
u
r
p
o
s
es
o
f
th
is
s
tu
d
y
,
a
s
u
b
s
et
o
f
f
if
ty
-
n
i
n
e
(
5
9
)
tr
an
s
m
is
s
io
n
lin
es,
r
ep
r
esen
tin
g
th
e
o
p
er
atio
n
al
lin
k
s
b
etwe
en
th
e
b
u
s
es,
h
as
b
ee
n
s
elec
ted
an
d
an
aly
ze
d
.
All
r
ele
v
an
t
n
etwo
r
k
an
d
o
p
e
r
atio
n
al
d
ata
wer
e
co
llected
f
r
o
m
th
e
t
r
a
n
s
m
is
s
io
n
co
m
p
an
y
o
f
n
ig
e
r
ia
(
T
C
N)
in
Ab
u
ja
[
3
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.