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STAT
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C
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Dep
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1
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.
T
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also
a
p
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s
m
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Evaluation Warning : The document was created with Spire.PDF for Python.
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52
I
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J
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&
C
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Sci
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Vo
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o
wer
d
is
tr
ib
u
tio
n
,
tr
a
n
s
f
o
r
m
atio
n
,
tr
an
s
m
is
s
io
n
,
an
d
s
u
b
tr
an
s
m
is
s
io
n
is
th
e
ca
u
s
e
o
f
th
e
tech
n
ical
lo
s
s
es.
T
h
ese
tech
n
o
lo
g
ical
lo
s
s
es
ar
e
in
h
er
en
t
in
th
e
s
y
s
tem
an
d
ca
n
b
e
r
ed
u
ce
d
to
an
o
p
tim
u
m
l
ev
el.
No
n
-
tech
n
ical
lo
s
s
es,
o
n
th
e
o
th
er
h
an
d
,
ar
e
b
r
o
u
g
h
t
o
n
b
y
h
u
m
an
m
is
tak
e,
en
er
g
y
m
eter
f
r
au
d
,
a
v
ar
iety
o
f
r
ea
d
i
n
g
s
,
an
d
f
l
aws
in
th
e
en
er
g
y
m
ea
s
u
r
em
en
t
p
r
o
ce
d
u
r
es
[
9
]
.
Fas
t
r
esp
o
n
s
e
p
o
wer
elec
tr
o
n
i
cs
h
av
e
b
ee
n
d
is
co
v
e
r
ed
as
a
r
esu
lt
o
f
ef
f
o
r
ts
to
s
o
lv
e
p
o
wer
s
y
s
tem
lo
s
s
es
in
th
e
tr
an
s
m
is
s
io
n
n
etwo
r
k
[
1
5
]
,
[
1
6
]
.
T
o
in
c
r
ea
s
e
th
e
cu
r
r
en
t
g
ea
r
b
o
x
s
y
s
tem
’
s
u
s
ef
u
l
ca
p
ac
ity
,
th
ese
d
ev
ices
ca
n
lo
wer
g
ea
r
b
o
x
lin
e
lo
s
s
es
an
d
r
e
g
u
late
b
o
th
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
.
Flex
ib
le
alter
n
atin
g
cu
r
r
en
t
(
AC
)
tr
an
s
m
is
s
io
n
s
y
s
tem
s
(
F
AC
T
S),
a
n
am
e
f
o
r
th
ese
q
u
i
ck
-
r
esp
o
n
s
e
p
o
wer
elec
tr
o
n
ics d
ev
ices,
ca
n
in
c
r
ea
s
e
o
p
er
atin
g
v
o
ltag
es a
n
d
l
o
wer
tr
an
s
m
is
s
io
n
lin
e
lo
s
s
es [
1
7
]
,
[
1
8
]
.
A
v
ec
to
r
co
n
tr
o
l
ap
p
r
o
ac
h
f
o
r
co
n
tr
o
llin
g
r
ea
ctiv
e
cu
r
r
e
n
t
u
s
in
g
s
tatic
s
y
n
ch
r
o
n
o
u
s
co
m
p
en
s
ato
r
s
(
STAT
C
OM
)
was
p
r
esen
ted
b
y
Sch
a
d
u
er
an
d
Me
h
ta
[
1
9
]
.
T
wo
STAT
C
OM
co
n
tr
o
l
ler
s
tr
u
ctu
r
es
wer
e
in
tr
o
d
u
ce
d
th
er
e
.
On
e
s
tr
u
ctu
r
e
em
p
lo
y
s
an
in
v
er
ter
f
o
r
b
o
th
p
h
ase
an
d
m
a
g
n
itu
d
e
co
n
tr
o
l,
wh
ile
th
e
o
th
e
r
s
o
lely
m
ak
es
u
s
e
o
f
p
h
ase
a
n
g
le
co
n
tr
o
l.
Nev
er
th
eless
,
n
o
t
all
o
p
er
atio
n
al
r
eg
io
n
s
o
f
th
e
s
y
s
tem
ca
n
b
e
co
n
tr
o
lled
b
y
a
lin
ea
r
o
u
t
put
f
ee
d
b
ac
k
co
n
tr
o
ller
d
u
e
to
th
e
later
co
n
tr
o
ller
co
n
s
tr
u
ctio
n
.
T
o
s
o
lv
e
t
h
is
is
s
u
e,
th
e
au
th
o
r
s
p
r
o
p
o
s
ed
a
n
o
n
lin
ea
r
s
tate
f
ee
d
b
ac
k
co
n
t
r
o
ller
.
T
h
e
co
n
tr
o
l
m
eth
o
d
’
s
in
tr
icac
y
an
d
th
e
s
y
s
tem
’
s
in
jectio
n
o
f
h
ig
h
f
r
e
q
u
en
c
y
n
o
is
e
ar
e
its
d
r
awb
ac
k
s
.
T
h
e
f
u
n
d
am
e
n
tal
id
ea
o
f
STAT
C
OM
,
it
s
b
asi
c
f
u
n
ctio
n
in
g
,
an
d
its
f
u
n
ctio
n
a
l
co
n
tr
o
l
s
y
s
tem
ar
e
p
r
o
v
id
ed
b
y
Gy
u
g
i
[
2
0
]
.
A
t
h
r
ee
-
p
h
ase
s
y
s
tem
’
s
r
ea
ctiv
e
an
d
ac
tu
al
p
o
wer
ad
ju
s
tm
en
t
was
m
o
d
elled
.
T
h
e
s
tu
d
y
,
h
o
wev
er
,
f
o
cu
s
es
o
n
u
s
in
g
STA
T
C
OM
to
co
n
tr
o
l
t
h
e
v
o
ltag
e
at
th
e
m
id
p
o
in
t
o
f
a
lo
n
g
t
r
an
s
m
is
s
io
n
lin
e
i
n
o
r
d
er
to
co
m
p
e
n
s
ate
f
o
r
r
ea
ctiv
e
p
o
wer
.
T
h
e
p
la
n
t
tr
an
s
f
er
f
u
n
ctio
n
is
o
f
th
e
m
i
n
im
al
p
h
ase
ty
p
e,
it
h
as
b
ee
n
d
is
co
v
er
ed
.
Pad
iy
ar
a
n
d
Ku
lk
a
r
n
i
[
2
1
]
,
th
e
d
esig
n
o
f
th
e
v
o
ltag
e
c
o
n
tr
o
ller
as
well
as
th
e
s
im
u
latio
n
an
d
E
i
g
en
v
alu
e
a
n
aly
s
is
o
f
its
d
y
n
am
ic
b
eh
a
v
io
r
wer
e
d
escr
i
b
ed
.
T
o
s
o
l
v
e
th
is
is
s
u
e,
eig
en
v
alu
e
a
n
aly
s
is
u
tili
zin
g
a
lin
ea
r
ized
m
o
d
el
was
u
s
ed
to
co
n
s
tr
u
ct
a
co
m
p
en
s
ato
r
in
ca
s
ca
d
e
with
a
n
in
teg
r
al
co
n
tr
o
ller
.
L
ec
h
ev
in
an
d
R
ajag
o
p
alan
[
2
2
]
p
r
o
p
o
s
ed
th
e
c
o
n
s
tr
u
ctio
n
o
f
a
n
o
n
lin
ea
r
co
n
tr
o
ller
f
o
r
STAT
C
OM
b
ased
o
n
d
if
f
er
en
tial
alg
eb
r
a
th
eo
r
y
.
B
y
u
s
in
g
th
is
ap
p
r
o
ac
h
o
f
co
n
tr
o
ller
d
esig
n
,
th
e
co
m
p
e
n
s
ato
r
ca
n
b
e
lin
ea
r
ized
an
d
th
e
ca
p
ac
ito
r
v
o
ltag
e
an
d
STAT
C
OM
’
s
out
put
r
ea
ctiv
e
p
o
wer
m
ay
b
e
d
ir
ec
tly
co
n
tr
o
lled
.
T
h
is
k
in
d
o
f
co
n
tr
o
l
m
a
k
es
it
p
o
s
s
ib
le
to
s
tab
ilize
th
e
co
m
p
en
s
atio
n
s
y
s
tem
,
wh
ic
h
s
ig
n
if
ican
tly
en
h
an
ce
s
th
e
g
lo
b
al
s
y
s
tem
’
s
tr
an
s
ien
t
p
er
f
o
r
m
a
n
ce
.
T
h
e
m
eth
o
d
’
s
d
is
ad
v
an
tag
e
is
th
at
it
ca
u
s
es
h
ar
m
o
n
ics
to
e
n
ter
t
h
e
s
y
s
tem
.
An
o
v
er
v
iew
o
f
STAT
C
OM
co
n
v
er
te
r
s
an
d
co
n
tr
o
l,
as
well
as
th
e
n
ew,
d
ev
elo
p
in
g
tech
n
o
l
o
g
ies
in
th
e
s
y
s
tem
,
wer
e
p
r
esen
ted
b
y
Sh
in
d
e
an
d
pu
lav
a
r
th
i
[
2
3
]
.
I
n
ad
d
itio
n
to
c
o
m
p
en
s
at
in
g
,
STAT
C
OM
ca
n
also
b
e
u
s
ed
to
in
cr
ea
s
e
s
y
s
tem
s
tab
ilit
y
b
y
im
p
lem
en
tin
g
d
if
f
er
e
n
t
c
o
n
tr
o
l
alg
o
r
ith
m
s
a
n
d
s
witch
in
g
s
tr
ateg
ies.
Nik
a
m
an
d
Kalk
h
am
b
k
ar
[
2
4
]
,
th
e
m
u
ltil
ev
el
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
(
VSC
)
ar
ch
itectu
r
e
an
d
STAT
C
OM
wer
e
r
ev
iewe
d
.
Dif
f
er
e
n
t
s
witch
in
g
s
y
s
tem
s
,
co
n
v
er
ter
to
p
o
lo
g
ies,
an
d
co
n
tr
o
l
alg
o
r
i
th
m
s
wer
e
ca
teg
o
r
ized
b
y
th
e
au
th
o
r
s
.
Var
io
u
s
m
u
ltil
ay
er
co
n
v
er
ter
s
tr
ateg
ies
ar
e
s
u
g
g
ested
to
im
p
r
o
v
e
th
e
VSC
s
p
er
f
o
r
m
a
n
ce
.
T
h
e
m
o
th
-
f
lam
e
o
p
tim
izatio
n
(
MFO)
alg
o
r
ith
m
,
an
e
f
f
ec
tiv
e
o
p
tim
izatio
n
tech
n
iq
u
e,
was
p
r
o
p
o
s
ed
b
y
E
b
ee
d
et
a
l.
[
2
5
]
in
o
r
d
e
r
to
d
eter
m
in
e
t
h
e
b
est
lo
ca
ti
o
n
an
d
p
a
r
am
eter
s
ettin
g
s
f
o
r
STAT
C
OM
.
T
h
e
tr
an
s
v
er
s
e
d
ir
ec
tio
n
o
f
a
m
o
th
f
lam
e
s
er
v
es
as
an
in
s
p
ir
atio
n
f
o
r
th
e
MFO
o
p
tim
izatio
n
tec
h
n
iq
u
e.
I
n
o
r
d
er
to
m
in
im
ize
p
o
wer
lo
s
s
,
im
p
r
o
v
e
v
o
ltag
e
s
tab
ilit
y
,
a
n
d
im
p
r
o
v
e
v
o
ltag
e
p
r
o
f
ile,
STAT
C
OM
is
in
teg
r
ated
in
to
t
h
e
p
o
wer
s
y
s
tem
.
I
n
o
r
d
e
r
to
im
p
r
o
v
e
v
o
ltag
e
p
r
o
f
ile,
a
tec
h
n
o
lo
g
y
ev
alu
atio
n
o
f
STAT
C
OM
was
co
n
d
u
cted
in
[
2
6
]
.
I
ts
to
p
o
lo
g
y
,
c
o
m
p
o
n
en
t
p
ar
ts
,
co
n
f
ig
u
r
atio
n
,
an
d
f
u
n
d
am
e
n
tal
s
tr
u
ctu
r
e
we
r
e
al
l
d
escr
ib
ed
.
I
n
t
h
e
MA
T
L
AB
/
S
im
u
lin
k
en
v
ir
o
n
m
en
t,
a
STAT
C
OM
is
s
im
u
lated
to
r
e
g
u
late
v
o
ltag
e
in
a
n
o
m
in
al
π
-
m
ed
iu
m
tr
an
s
m
is
s
io
n
lin
e.
T
h
e
r
esu
lt
s
o
f
th
e
s
im
u
latio
n
s
h
o
w
th
a
t
STAT
C
OM
is
a
v
er
y
g
o
o
d
v
o
ltag
e
r
e
g
u
lato
r
,
esp
ec
ially
wh
en
it
is
u
s
ed
wit
h
o
u
t
a
d
r
o
p
an
d
p
r
ec
is
ely
tr
ac
k
s
th
e
r
ef
er
en
ce
v
o
ltag
e.
STA
T
C
OM
co
n
tr
o
l
f
o
r
im
p
r
o
v
in
g
v
o
ltag
e
s
tab
ilit
y
at
a
f
i
x
ed
s
p
ee
d
win
d
f
ar
m
with
u
n
b
alan
ce
d
f
a
u
lts
was
g
iv
e
n
b
y
Vim
alr
aj
et
a
l.
[
2
7
]
.
T
h
e
au
th
o
r
s
co
n
d
u
cted
r
esear
ch
o
n
a
f
i
x
ed
s
p
ee
d
wi
n
d
f
ar
m
u
s
in
g
a
STAT
C
OM
in
co
n
ju
n
ctio
n
with
s
q
u
ir
r
el
ca
g
e
in
d
u
ctio
n
g
en
er
ato
r
s
th
at
wer
e
d
ir
e
ctly
co
n
n
ec
ted
to
th
e
g
r
i
d
.
A
STAT
C
OM
-
b
ased
co
n
tr
o
l
s
tr
ateg
y
was
p
r
esen
ted
in
[
2
8
]
f
o
r
g
r
i
d
-
co
n
n
ec
ted
win
d
g
en
e
r
atin
g
s
y
s
tem
s
s
er
v
in
g
n
o
n
-
li
n
ea
r
lo
ad
s
.
I
ts
g
o
als
wer
e
r
ea
ctiv
e
p
o
we
r
ad
ju
s
tm
en
t
an
d
h
ar
m
o
n
ic
r
ed
u
ctio
n
.
Ad
d
itio
n
ally
,
th
e
is
s
u
es
with
p
o
wer
q
u
a
lity
,
th
eir
ef
f
ec
ts
,
an
d
s
o
lu
tio
n
s
wer
e
d
i
s
cu
s
s
ed
.
I
n
o
r
d
er
t
o
m
ain
tain
p
o
wer
q
u
ality
at
th
e
p
o
in
t
o
f
co
m
m
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c
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p
lin
g
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th
e
au
th
o
r
s
em
p
lo
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ed
STAT
C
OM
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b
atter
y
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d
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e
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g
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av
in
g
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o
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em
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e
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ar
m
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ic
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cu
r
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en
t.
A
u
n
i
q
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e
m
eth
o
d
f
o
r
im
p
r
o
v
in
g
v
o
ltag
e
r
eg
u
latio
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th
r
o
u
g
h
a
u
to
m
atic
co
n
tr
o
l
b
ased
o
n
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
I
mp
r
o
ve
men
t o
f e
lectricity reli
a
b
ilit
y
o
n
th
e
330
kV
N
ig
eria
tr
a
n
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mis
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io
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n
etw
o
r
k
…
(
Lu
ke
Uw
a
kwe O
meje
)
735
g
en
etic
alg
o
r
ith
m
in
STAT
C
OM
was
g
iv
en
b
y
Gan
jef
ar
a
n
d
T
ajali
[
2
9
]
.
T
esti
n
g
h
as
b
e
en
d
o
n
e
o
n
th
e
n
ew
tech
n
iq
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f
o
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in
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e
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en
ce
.
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h
e
ST
AT
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OM
ca
p
ac
ito
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v
o
ltag
e
w
as
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eg
u
lated
u
s
in
g
a
lin
ea
r
q
u
ad
r
atic
r
eg
u
lato
r
(
L
QR
)
.
T
h
e
s
elec
tio
n
o
f
m
atr
ix
co
ef
f
icien
ts
is
d
o
n
e
u
s
in
g
a
g
en
etic
al
g
o
r
ith
m
.
Ho
wev
er
,
it
is
d
eter
m
in
ed
th
at
th
is
m
eth
o
d
’
s
s
lo
w
r
esp
o
n
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e
is
it
s
f
law.
Vo
ltag
e
p
r
o
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il
e
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d
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o
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lo
s
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aly
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is
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y
Pad
h
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et
a
l.
[
3
0
]
with
s
u
itab
le
u
s
e
o
f
STAT
C
OM
;
an
I
E
E
E
5
7
-
b
u
s
test
s
y
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tem
with
an
d
with
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t
STAT
C
OM
was
co
m
p
ar
ed
.
Her
e,
th
e
a
u
th
o
r
s
e
m
p
lo
y
ed
STAT
C
OM
as
a
v
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l
tag
e
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co
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iv
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e
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m
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en
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y
d
escr
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th
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p
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licatio
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o
f
a
s
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FAC
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S
d
ev
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ca
lled
a
STAT
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OM
to
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s
m
is
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io
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lo
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d
en
h
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ce
th
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v
o
ltag
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p
r
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ile
o
f
Nig
er
ia
’
s
3
3
0
kV
tr
an
s
m
is
s
io
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etwo
r
k
.
I
n
AC
tr
an
s
m
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io
n
n
etwo
r
k
s
,
th
e
s
ta
ti
c
s
y
n
ch
r
o
n
o
u
s
co
m
p
en
s
ato
r
,
o
r
STAT
C
OM
,
is
a
r
eg
u
latin
g
d
ev
ice
th
at
ca
n
b
e
em
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lo
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ed
as
a
s
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ce
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r
s
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k
o
f
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.
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e
3
3
0
kV
Nig
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ian
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s
m
is
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io
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wo
r
k
’
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ize
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v
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ln
er
ab
le
b
u
s
es a
r
e
s
u
b
ject
to
th
e
STAT
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OM
.
2.
M
AT
E
R
I
AL
S AN
D
M
E
T
H
O
D
Usi
n
g
th
e
New
to
n
-
R
ap
h
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n
m
eth
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d
in
MA
T
L
AB
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d
th
e
p
o
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y
s
tem
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aly
s
is
to
o
lb
o
x
(
PS
AT
)
,
th
e
p
o
wer
f
lo
w
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aly
s
is
is
c
ar
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ied
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u
t
o
n
th
e
Nig
er
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n
3
3
0
kV
tr
an
s
m
is
s
io
n
n
e
two
r
k
.
T
h
is
ap
p
r
o
ac
h
was
ch
o
s
en
b
ec
au
s
e
it
p
r
o
d
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ce
d
co
n
s
is
ten
t
f
in
d
in
g
s
,
ac
ce
ler
ated
co
n
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er
g
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ce
,
an
d
s
im
p
lifie
d
th
e
ca
lcu
latio
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s
.
W
ith
a
to
tal
in
s
talled
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p
ac
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f
6
5
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MW,
th
e
Nig
er
ian
n
etwo
r
k
c
o
n
s
is
ts
o
f
s
ev
en
te
en
(
1
7
)
g
e
n
er
atin
g
s
tatio
n
s
,
f
if
ty
-
two
(
5
2
)
b
u
s
es,
th
ir
ty
-
f
iv
e
(
3
5
)
lo
ad
s
tatio
n
s
,
s
ix
ty
-
s
ix
(
6
6
)
tr
an
s
m
is
s
io
n
lin
e
s
,
an
d
8
,
9
8
5
.
2
8
k
m
g
r
id
tr
an
s
m
is
s
io
n
lin
es.
T
h
r
ee
(
3
)
s
ec
to
r
s
co
m
p
r
is
e
th
e
elec
tr
icity
s
y
s
tem
: N
o
r
th
,
So
u
th
-
E
a
s
t,
an
d
So
u
th
-
W
est.
B
etwe
en
Oso
g
b
o
an
d
J
eb
b
a
T
r
an
s
m
is
s
io
n
Statio
n
,
th
er
e
is
a
s
in
g
le
d
o
u
b
le
cir
cu
it
th
a
t
co
n
n
ec
ts
th
e
No
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th
er
n
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d
So
u
th
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est.
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s
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e
f
r
o
m
Oso
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b
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t
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B
en
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an
d
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s
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o
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le
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cu
it
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f
r
o
m
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k
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to
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en
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co
n
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ec
t
th
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th
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a
s
t
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d
So
u
th
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W
est
r
esp
ec
tiv
ely
.
Fig
u
r
e
1
d
is
p
lay
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th
e
s
in
g
le
lin
e
d
iag
r
am
.
Yo
u
ca
n
f
i
n
d
th
e
b
u
s
d
ata
a
n
d
lin
e
p
ar
am
eter
s
u
s
ed
in
[
2
]
.
Fig
u
r
e
1
.
Sin
g
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lin
e
d
iag
r
a
m
o
f
a
52
-
b
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s
Nig
er
ia
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3
3
0
kV
t
r
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m
is
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etwo
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e
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o
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p
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No
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eth
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it
is
s
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ec
if
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t
h
a
t
v
alu
es
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o
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f
0
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9
5
≤
|
V|
≤
1
.
0
5
pu
a
r
e
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with
in
th
e
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atin
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s
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s
b
e
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r
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te
d
u
s
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OM
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ased
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ag
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d
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ical
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d
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m
p
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p
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icien
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d
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tab
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th
e
s
y
s
tem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
36
,
No
.
2
,
No
v
em
b
er
20
24
:
7
3
3
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7
4
0
736
2
.
1
.
T
he
o
pera
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princip
les o
f
ST
AT
CO
M
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n t
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3
3
0
kV
Nig
er
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n t
ra
ns
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is
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io
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v
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ce
d
e
n
er
g
y
s
to
r
ag
e
f
ac
i
liti
es
ar
e
well
s
u
ited
f
o
r
STAT
C
OM
,
wh
ich
o
f
f
er
s
u
p
a
h
o
s
t
o
f
n
ew
ap
p
licatio
n
s
,
in
clu
d
in
g
n
etw
o
r
k
s
ec
u
r
ity
an
d
en
e
r
g
y
m
a
r
k
ets.
B
y
ap
p
r
o
p
r
iately
co
n
tr
o
llin
g
th
e
in
v
er
te
r
v
o
ltag
e
|
ℎ
|
∠
ℎ
in
r
elatio
n
to
th
e
A
C
v
o
ltag
e
o
n
th
e
h
i
gh
-
v
o
ltag
e
s
id
e
o
f
th
e
STAT
C
OM
tr
an
s
f
o
r
m
er
,
STAT
C
OM
ca
n
p
r
o
d
u
ce
o
r
a
b
s
o
r
b
r
ea
ctiv
e
p
o
wer
.
T
h
e
r
e
ac
tiv
e
p
o
wer
(
1
)
a
n
d
(
2
)
p
r
o
v
id
e
h
elp
f
u
l
in
s
ig
h
t
in
to
h
o
w
th
e
r
ea
ctiv
e
p
o
wer
ex
ch
an
g
e
with
th
e
AC
s
y
s
t
em
is
d
o
n
e
in
a
p
er
f
ec
t
ST
AT
C
OM
,
h
o
wev
er
,
wh
en
th
er
e
i
s
n
o
ac
tiv
e
p
o
wer
lo
s
s
in
v
o
lv
ed
as (
1
)
an
d
(
2
)
.
ℎ
=
ℎ
+
ℎ
(
1
)
ℎ
=
1
ℎ
(
2
)
Als
o
,
f
r
o
m
Fig
u
r
e
2
th
e
n
et
in
j
ec
ted
cu
r
r
e
n
t a
t b
u
s
l
is
Fig
u
r
e
s
2(
a
)
an
d
2
(
b
)
:
=
+
∑
=
1
,
≠
+
ℎ
(
3)
=
∑
=
1
,
≠
1
+
0
(
4
)
w
h
er
e
Y
ll
old
is
th
e
s
elf
-
a
d
m
i
ttan
ce
o
f
t
h
e
b
u
s
l
f
o
r
th
e
o
r
ig
in
al
n
-
b
u
s
s
y
s
tem
with
o
u
t
an
y
STAT
C
OM
c
o
n
n
ec
ted
.
y
lo
ac
c
o
u
n
ts
f
o
r
th
e
s
h
u
n
t c
ap
ac
itan
ce
s
o
f
all
tr
an
s
m
is
s
io
n
lin
es c
o
n
n
ec
ted
to
b
u
s
l.
Seco
n
d
ly
,
ℎ
=
ℎ
(
−
ℎ
)
(
5
)
t
h
e
n
et
in
jecte
d
cu
r
r
en
t a
t
b
u
s
l
f
r
o
m
(
3
)
a
n
d
(
5
)
with
STAT
C
OM
is
:
=
∑
+
1
=
1
(
6
)
=
+
ℎ
(
7
)
w
h
er
e
Y
il
is
th
e
n
ew
v
al
u
e
o
f
s
elf
-
ad
m
ittan
ce
f
o
r
th
e
l
th
b
u
s
with
STAT
C
OM
as (
8
)
.
+
1
=
ℎ
an
d
(
+
1
)
=
−
ℎ
(
8
)
Fro
m
Fig
u
r
e
2
(
b
)
th
e
n
et
in
je
cted
cu
r
r
en
t
at
th
e
n
in
etee
n
(
1
9
)
b
u
s
es
eq
u
als
th
e
cu
r
r
en
t
f
l
o
win
g
in
to
th
e
tr
an
s
m
is
s
io
n
s
y
s
tem
f
r
o
m
t
h
is
b
u
s
an
d
is
o
b
tain
e
d
as
(
9
)
:
(
+
1
)
=
−
ℎ
=
ℎ
ℎ
−
ℎ
=
∑
(
+
1
)
+
1
=
1
(
9
)
t
h
e
n
et
ac
tiv
e
p
o
wer
in
jectio
n
at
an
y
b
u
s
l
i
n
an
n
-
b
u
s
s
y
s
tem
in
s
talled
with
STAT
C
OM
s
is
wr
itten
f
r
o
m
(
3
)
as Wi
th
o
u
t ST
AT
C
OM
co
n
n
ec
ted
to
b
u
s
l
as (
1
0
)
:
=
∑
=
1
(
−
−
)
,
≤
(
1
0
)
w
ith
STAT
C
OM
co
n
n
ec
ted
to
b
u
s
l
as (
1
1
)
.
=
∑
=
1
(
−
−
)
−
ℎ
(
−
ℎ
ℎ
)
,
≤
(
1
1
)
T
h
e
r
ea
ctiv
e
p
o
wer
ab
s
o
r
b
ed
b
y
STAT
C
OM
f
r
o
m
th
e
lo
a
d
b
u
s
l
is
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iv
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1
2
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:
ℎ
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[
ℎ
ℎ
∗
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1
2
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w
h
er
e
th
e
STAT
C
OM
cu
r
r
en
t
I*
sh
is
(
1
3
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an
d
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1
4
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.
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∗
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1
3
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ℎ
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[
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−
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
I
mp
r
o
ve
men
t o
f e
lectricity reli
a
b
ilit
y
o
n
th
e
330
kV
N
ig
eria
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a
n
s
mis
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etw
o
r
k
…
(
Lu
ke
Uw
a
kwe O
meje
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x
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d
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g
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1
2
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g
iv
es
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−
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2
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1
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a
g
ain
,
th
e
r
ea
cti
v
e
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wer
d
eli
v
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ed
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y
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OM
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iv
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w
h
er
e
V
sh
is
th
e
STAT
C
OM
out
p
u
t
v
o
ltag
e
,
I
sh
is
th
e
c
u
r
r
en
t
STAT
C
OM
d
r
aws
f
r
o
m
th
e
s
y
s
tem
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X
sh
r
ep
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ts
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e
leak
ag
e
r
ea
ctan
ce
o
f
th
e
c
o
u
p
lin
g
tr
an
s
f
o
r
m
er
.
(
a)
(
b
)
Fig
u
r
e
2
.
T
h
e
n
et
in
jecte
d
cu
r
r
en
t a
t b
u
s
l is
(
a)
a
STAT
C
OM
co
n
n
ec
ted
t
o
an
y
b
u
s
l
o
f
a
n
n
-
b
u
s
p
o
wer
s
y
s
tem
an
d
(
b
)
t
h
e
eq
u
iv
alen
t
cir
cu
it
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
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O
N
T
h
er
e
ar
e
v
ar
io
u
s
s
im
u
latio
n
tech
n
iq
u
es
av
ailab
le
f
o
r
u
s
e
in
lo
ad
f
lo
w
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v
esti
g
atio
n
s
,
ea
ch
with
u
n
iq
u
e
p
r
o
p
er
ties
.
C
o
m
m
o
n
ch
ar
ac
ter
is
tics
o
f
th
ese
m
e
th
o
d
s
in
clu
d
e
i
n
cr
ea
s
ed
s
p
e
ed
,
p
r
ec
is
io
n
,
a
n
d
v
is
u
alis
atio
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in
co
m
p
ar
is
o
n
to
h
u
m
an
ca
lcu
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d
r
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lt
p
r
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g
.
As
a
r
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lt,
PS
AT
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d
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T
L
AB
/S
im
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lin
k
wer
e
u
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ed
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im
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e
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2
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b
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s
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y
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tem
.
PS
AT
s
o
f
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e
is
a
f
e
atu
r
e
-
r
ich
g
r
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h
ical
p
o
wer
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lo
w
ap
p
licatio
n
th
at
c
an
b
e
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s
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ild
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n
aly
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es
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d
alter
p
o
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f
lo
ws
as
well
as
r
ea
d
s
o
lu
tio
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r
ep
o
r
ts
.
Fo
r
b
o
t
h
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ce
n
ar
io
s
(
b
ef
o
r
e
an
d
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ter
co
r
r
ec
tio
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)
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th
e
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ad
f
lo
w
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ch
e
d
a
co
n
v
er
g
en
ce
p
o
i
n
t
af
ter
s
ev
en
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7
)
r
e
p
etitio
n
s
.
I
n
o
r
d
er
to
d
eter
m
in
e
th
e
v
o
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e
m
ag
n
itu
d
es,
a
lo
ad
f
lo
w
s
tu
d
y
was
co
n
d
u
cte
d
,
ac
co
u
n
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g
f
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m
ag
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d
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r
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e
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f
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pu
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t
h
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r
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e
ar
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e
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th
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ated
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r
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ir
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m
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n
s
atio
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.
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h
er
e
ar
e
s
ev
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teen
(
1
7
)
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en
er
atin
g
s
tatio
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s
,
f
if
ty
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two
(
5
2
)
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u
s
es,
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d
th
ir
ty
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f
iv
e
(
3
5
)
l
o
ad
s
tatio
n
s
in
th
e
s
im
u
lated
Nig
er
ian
3
3
0
kV
52
-
b
u
s
n
etwo
r
k
.
T
h
e
Fig
u
r
e
3
d
is
p
lay
s
th
e
v
o
ltag
e
p
r
o
f
ile
r
esu
lts
at
ea
ch
b
u
s
b
o
th
b
ef
o
r
e
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d
af
ter
c
o
m
p
en
s
atio
n
.
T
h
is
d
em
o
n
s
tr
ates
th
at
th
er
e
ar
e
n
in
etee
n
(
1
9
)
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u
s
es
th
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o
n
o
t
o
p
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ate
in
s
id
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al
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9
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en
So
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th
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9
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k
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r
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i
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pu
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a
n
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/Keb
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i
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7
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5
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ar
e
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o
m
e
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f
th
e
b
u
s
es
th
at
f
all
u
n
d
er
t
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teg
o
r
y
.
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d
itio
n
ally
,
Fig
u
r
e
4
d
is
p
lay
s
th
e
n
etwo
r
k
’
s
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es
f
o
llo
win
g
co
m
p
en
s
atio
n
with
STAT
C
OM
s
.
T
h
e
en
h
an
ce
d
v
o
ltag
e
p
r
o
f
ile
s
f
o
llo
win
g
th
e
u
s
e
o
f
STAT
C
OM
f
o
r
co
m
p
en
s
atio
n
a
r
e
d
is
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in
Fig
u
r
e
4
.
T
h
ese
b
u
s
es
’
o
p
e
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atin
g
v
o
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co
n
s
id
er
a
b
ly
im
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r
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e
d
an
d
d
r
o
p
p
ed
in
s
id
e
th
e
o
p
er
atio
n
al
r
a
n
g
e
o
n
ce
STAT
C
OM
co
m
p
en
s
atio
n
was
ap
p
lied
,
a
n
d
th
e
n
et
wo
r
k
g
r
ea
tly
r
ed
u
ce
d
ac
tu
al
an
d
r
ea
ctiv
e
p
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wer
lo
s
s
es.
T
h
is
d
em
o
n
s
tr
ates
th
a
t
STAT
C
OM
ca
n
in
cr
ea
s
e
th
e
s
y
s
tem
’
s
s
tab
ilit
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.
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h
e
f
o
ll
o
win
g
b
u
s
es,
wh
ich
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ad
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ef
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r
e,
h
av
e,
ac
co
r
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to
th
e
r
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,
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ee
n
s
u
f
f
icien
tly
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r
o
u
g
h
t
b
ac
k
t
o
o
p
e
r
atio
n
al
r
a
n
g
e
b
y
u
tili
s
in
g
th
e
STAT
C
OM
.
T
h
ese
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e:
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en
in
No
r
th
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1
.
0
1
1
9
pu
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.
9
5
1
5
pu
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.
9
5
6
6
pu
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Dam
atu
r
u
(
0
.
9
9
8
9
p
u
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m
b
e
(
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.
9
5
7
0
pu
)
,
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d
u
g
ir
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0
.
9
9
2
1
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)
,
Gan
m
o
(
1
.
0
2
0
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pu
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,
J
o
s
(
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.
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0
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,
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9
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,
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ete
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9
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6
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,
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alin
g
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.
9
5
0
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pu
)
,
an
d
Kan
o
(
0
.
9
5
6
5
pu
)
.
T
h
ese
ar
e
Ajah
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0
.
9
7
8
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an
g
b
a
(
1
.
0
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6
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pu
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,
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9
6
1
3
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,
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Hea
v
e
n
(
0
.
9
5
9
4
pu
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,
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ew
Hea
v
e
n
So
u
th
(
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0
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k
u
r
d
i
(
0
.
9
8
3
9
pu
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,
a
n
d
Ma
k
u
r
d
i
(
0
.
9
8
3
9
pu
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.
B
ef
o
r
e
p
a
y
in
g
o
u
t
in
t
h
e
n
etwo
r
k
,
t
h
e
PS
AT
’
s
s
p
ec
if
ied
r
ate
o
f
co
m
p
en
s
atio
n
ca
n
b
e
ch
a
n
g
ed
.
T
h
is
h
as
to
d
o
with
ad
ju
s
tin
g
th
e
PS
AT
’
s
to
ler
an
ce
le
v
el
to
th
e
n
ec
ess
ar
y
d
eg
r
ee
.
On
th
e
o
th
er
h
an
d
,
a
f
ter
ap
p
ly
in
g
STAT
C
OM
,
th
e
o
v
er
all
lo
s
s
r
ed
u
ctio
n
was
f
o
u
n
d
t
o
b
e
1
2
.
1
5
%
u
s
in
g
th
e
eq
u
atio
n
,
a
n
d
th
e
t
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
d
ec
r
ea
s
ed
f
r
o
m
2
6
% to
4
.
6
4
%.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
36
,
No
.
2
,
No
v
em
b
er
20
24
:
7
3
3
-
7
4
0
738
Fig
u
r
e
3
.
Vo
ltag
e
p
r
o
f
ile
o
f
t
h
e
n
etwo
r
k
b
ef
o
r
e
an
d
a
f
ter
co
m
p
en
s
atio
n
Fig
u
r
e
4
.
R
ea
l a
n
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es a
f
ter
co
m
p
en
s
atio
n
4.
CO
NCLU
SI
O
N
T
h
e
im
p
ac
t
o
f
a
p
p
ly
in
g
STAT
C
OM
to
en
h
an
ce
p
o
wer
s
y
s
tem
p
er
f
o
r
m
an
ce
h
as
b
ee
n
r
esea
r
ch
ed
a
n
d
u
s
ed
in
th
e
3
3
0
kV
,
5
2
-
b
u
s
Nig
er
ian
s
y
s
tem
to
r
ed
u
ce
p
o
wer
lo
s
s
an
d
im
p
r
o
v
e
v
o
ltag
e.
T
h
e
th
r
ee
-
p
h
ase
n
etwo
r
k
m
o
d
el
was
u
tili
ze
d
,
an
d
MA
T
L
AB
/Si
m
u
lin
k
s
o
f
twar
e
was
em
p
lo
y
ed
to
c
o
n
d
u
ct
th
e
s
im
u
latio
n
.
On
ce
m
o
r
e
,
a
th
o
r
o
u
g
h
liter
at
u
r
e
ass
ess
m
en
t
o
f
ea
r
lier
s
tu
d
i
es
o
n
v
o
ltag
e
p
r
o
f
ile
en
h
a
n
ce
m
en
t
an
d
p
o
wer
lo
s
s
r
ed
u
ctio
n
STAT
C
OM
h
as
b
ee
n
co
m
p
leted
in
o
r
d
e
r
to
p
r
o
p
er
ly
ju
s
tify
th
e
s
tu
d
y
.
T
o
a
ch
iev
e
th
e
d
esire
d
o
u
tco
m
es,
a
STAT
C
OM
co
n
t
r
o
ller
was
u
s
ed
in
a
f
u
ll
clo
s
e
d
lo
o
p
co
n
tr
o
l
ar
ch
itectu
r
e
.
T
h
e
s
tu
d
y
’
s
f
in
d
in
g
s
,
h
o
wev
er
,
in
d
icate
th
at
th
e
s
y
s
tem
’
s
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es
wer
e
1
9
.
2
7
5
8
5
pu
an
d
2
2
.
3
4
4
5
4
pu
,
r
esp
ec
tiv
ely
,
u
tili
zin
g
p
r
io
r
to
co
m
p
e
n
s
atio
n
.
Fo
llo
win
g
co
m
p
e
n
s
atio
n
as
a
r
esu
lt
o
f
th
e
STAT
C
OM
ap
p
licatio
n
,
th
e
r
ea
l
a
n
d
r
ea
c
tiv
e
p
o
wer
lo
s
s
es
d
ec
r
ea
s
ed
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[
1
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[
2
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J.
-
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[
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G
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[
9
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M
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[
1
2
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S
.
R
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[
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4
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R.
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1
6
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7]
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9
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3
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4
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2
5
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6
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7
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[
2
8
]
G
.
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2
9
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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52
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B
I
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RAP
H
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S O
F
AUTH
O
RS
Lu
k
e
Uw
a
k
we
O
m
e
je
g
ra
d
u
a
ted
fro
m
th
e
De
p
a
rtme
n
t
o
f
El
e
c
t
rica
l
En
g
i
n
e
e
rin
g
,
Un
iv
e
rsity
o
f
Ni
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k
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it
h
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n
g
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e
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re
e
in
2
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r
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c
e
iv
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d
h
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a
ste
r
’
s
d
e
g
re
e
(M
.
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g
.
)
fro
m
th
e
sa
m
e
d
e
p
a
rtme
n
t
a
n
d
u
n
i
v
e
rsity
i
n
2
0
1
9
.
He
is
c
u
rre
n
tl
y
a
lec
tu
re
r
in
th
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
a
t
t
h
e
Un
i
v
e
rsity
o
f
Nig
e
ria,
Ns
u
k
k
a
.
He
h
a
s a
n
u
m
b
e
r
o
f
p
a
p
e
rs
to
h
is
c
re
d
it
i
n
b
o
t
h
l
o
c
a
l
a
n
d
i
n
tern
a
ti
o
n
a
l
jo
u
rn
a
ls.
His
a
r
e
a
o
f
sp
e
c
ializa
ti
o
n
is
p
o
we
r
sy
ste
m
s
a
n
d
h
ig
h
-
v
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lt
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g
e
e
n
g
i
n
e
e
rin
g
,
a
n
d
h
is
re
se
a
rc
h
in
tere
sts
a
re
p
o
we
r
sy
ste
m
s,
re
n
e
wa
b
l
e
e
n
e
rg
y
,
a
n
d
m
a
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h
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lea
rn
in
g
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
u
wa
k
we
.
o
m
e
je@
u
n
n
.
e
d
u
.
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b
u
ik
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r
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h
a
n
u
e
a
rn
e
d
a
Ba
c
h
e
lo
r
o
f
E
n
g
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n
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e
rin
g
i
n
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tri
c
a
l
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g
i
n
e
e
rin
g
fro
m
th
e
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n
iv
e
rsit
y
o
f
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e
ria,
Ns
u
k
k
a
.
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o
b
tain
e
d
a
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a
ste
r
’
s
d
e
g
re
e
wit
h
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c
ti
o
n
in
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c
tri
c
a
l
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g
i
n
e
e
rin
g
(
P
o
we
r
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ti
o
n
)
fr
o
m
Riv
e
r
s
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tate
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iv
e
rsity
N
k
p
o
lu
-
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wo
ru
k
wu
,
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o
rt
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rc
o
u
rt.
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is
a
Lec
tu
re
r
in
t
h
e
De
p
a
rtme
n
t
o
f
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e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
,
Un
iv
e
rsity
o
f
Ni
g
e
ria,
Ns
u
k
k
a
.
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re
se
a
rc
h
in
tere
sts
i
n
c
lu
d
e
re
n
e
wa
b
le
e
n
e
rg
y
tec
h
n
o
lo
g
y
,
c
o
m
pu
ter
-
a
id
e
d
a
n
a
ly
sis
o
f
p
o
w
e
r
d
istri
b
u
ti
o
n
n
e
two
rk
s
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o
p
ti
m
iz
a
ti
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o
f
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istri
b
u
ti
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n
s
y
ste
m
s,
p
o
we
r
s
y
ste
m
d
y
n
a
m
ics
a
n
d
c
o
n
tro
l,
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teg
ra
ti
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n
o
f
re
n
e
wa
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le
e
n
e
rg
y
s
o
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rc
e
s
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n
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istri
b
u
ti
o
n
sy
ste
m
s,
a
n
d
sm
a
rt
g
rid
s.
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is
a
re
g
istere
d
e
n
g
in
e
e
r
with
t
h
e
C
o
u
n
c
i
l
fo
r
t
h
e
Re
g
u
lati
o
n
o
f
En
g
i
n
e
e
rin
g
in
Nig
e
ria
(COREN)
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
c
h
ib
u
i
k
e
.
o
h
a
n
u
@
u
n
n
.
e
d
u
.
n
g
.
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n
ifa
c
e
O
n
y
e
m
a
e
c
h
i
An
y
a
k
a
is
c
u
rre
n
tl
y
t
h
e
He
a
d
o
f
De
p
a
rtme
n
t
in
th
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
,
F
a
c
u
lt
y
o
f
En
g
i
n
e
e
rin
g
,
U
n
i
v
e
rsity
o
f
Ni
g
e
ria,
Ns
u
k
k
a
,
Nig
e
ria.
He
is
a
n
As
so
c
iate
P
r
o
f,
a
n
d
h
e
h
o
l
d
s
a
P
h
.
D
.
d
e
g
re
e
fro
m
th
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
ri
n
g
,
U
n
iv
e
rs
it
y
o
f
Ni
g
e
ria,
Ns
u
k
k
a
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
b
o
n
ifac
e
.
a
n
y
a
k
a
@u
n
n
.
e
d
u
.
n
g
.
To
le
S
u
tik
n
o
is
a
lec
tu
re
r
in
E
lec
tri
c
a
l
En
g
i
n
e
e
rin
g
De
p
a
rtme
n
t
a
t
th
e
Un
i
v
e
rsitas
Ah
m
a
d
Da
h
lan
(UA
D),
Y
o
g
y
a
k
a
rta,
In
d
o
n
e
sia
.
He
re
c
e
iv
e
d
h
is
B.
E
n
g
.
,
M
.
En
g
.
a
n
d
P
h
.
D.
d
e
g
re
e
s
in
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
fro
m
Un
iv
e
rsitas
Dip
o
n
e
g
o
ro
,
U
n
iv
e
rsitas
G
a
d
jah
M
a
d
a
a
n
d
Un
iv
e
rsiti
Tek
n
o
l
o
g
i
M
a
lay
si
a
,
in
1
9
9
9
,
2
0
0
4
,
a
n
d
2
0
1
6
,
re
s
p
e
c
ti
v
e
ly
.
He
h
a
s
b
e
e
n
a
n
As
so
c
iate
P
ro
fe
ss
o
r
in
UA
D,
Y
o
g
y
a
k
a
rta,
In
d
o
n
e
sia
sin
c
e
2
0
0
8
.
He
is
c
u
rre
n
tl
y
a
n
E
d
it
o
r
-
in
-
Ch
ief
o
f
t
h
e
TE
LKOMNIKA
a
n
d
th
e
He
a
d
o
f
t
h
e
Emb
e
d
d
e
d
S
y
s
tem
s
a
n
d
P
o
we
r
El
e
c
tro
n
ics
Re
se
a
rc
h
G
ro
u
p
(ES
P
ERG
).
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e
is
a
m
o
n
g
th
e
to
p
2
%
o
f
re
se
a
rc
h
e
rs
n
a
m
e
d
b
y
S
tan
f
o
rd
Un
iv
e
rsity
a
n
d
El
se
v
ier BV as
th
e
m
o
st i
n
flu
e
n
ti
a
l
sc
ien
ti
sts in
t
h
e
wo
rld
f
o
r
2
0
2
1
–
p
re
se
n
t.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
t
h
e
field
o
f
d
i
g
it
a
l
d
e
sig
n
,
i
n
d
u
str
ial
a
p
p
li
c
a
ti
o
n
s,
in
d
u
strial
e
lec
tro
n
ics
,
in
d
u
strial
in
f
o
rm
a
ti
c
s,
p
o
we
r
e
lec
tro
n
ics
,
m
o
t
o
r
d
ri
v
e
s,
re
n
e
wa
b
le
e
n
e
rg
y
,
F
P
G
A
a
p
p
li
c
a
ti
o
n
s,
e
m
b
e
d
d
e
d
s
y
ste
m
,
a
rti
ficia
l
in
telli
g
e
n
c
e
,
in
telli
g
e
n
t
c
o
n
tro
l
,
in
f
o
rm
a
ti
o
n
tec
h
n
o
l
o
g
y
,
a
n
d
d
ig
i
tal
li
b
ra
ry
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
to
le@
te.u
a
d
.
a
c
.
id
,
to
le
@e
e
.
u
a
d
.
a
c
.
id
.
Evaluation Warning : The document was created with Spire.PDF for Python.