I
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Appl
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I
J
AP
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)
Vo
l.
14
,
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.
3
,
Sep
tem
b
er
20
25
,
p
p
.
5
7
9
~
5
8
7
I
SS
N:
2252
-
8
7
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2
,
DOI
:
1
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v
14
.
i
3
.
pp
579
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587
579
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Para
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0
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4
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J
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1
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with
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it
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d
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x
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sta
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f
0
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0
9
5
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5
p
e
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m
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in
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strial
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K
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[
1
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[
5
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.
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it c
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with
PS
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[
6
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[
8
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
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2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
5
7
9
-
587
580
T
h
is
m
o
d
elin
g
is
co
n
d
u
cte
d
to
en
s
u
r
e
th
e
v
o
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p
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in
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ato
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ca
l
m
o
d
el
u
s
in
g
th
e
Gau
s
s
-
Seid
el
(
GS)
m
eth
o
d
i
s
im
p
lem
en
ted
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d
p
r
o
g
r
am
m
ed
in
t
h
e
MA
T
L
AB
en
v
ir
o
n
m
en
t
a
n
d
PS
S/E
s
im
u
lato
r
.
T
h
e
s
im
u
latio
n
r
esu
lts
will b
e
p
r
esen
ted
alo
n
g
wit
h
d
etailed
d
is
cu
s
s
io
n
s
.
I
n
th
e
f
o
u
r
th
s
tep
,
th
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
s
o
p
tim
ize
th
e
p
o
wer
f
lo
w
an
d
v
o
ltag
e
p
r
o
f
iles
o
f
th
e
n
etwo
r
k
[
1
1
]
-
[
1
6
]
.
T
h
e
f
in
al
p
h
ase
in
v
o
lv
es
d
r
awin
g
c
o
n
clu
s
io
n
s
b
a
s
ed
o
n
th
e
p
r
o
p
o
s
ed
wo
r
k
.
T
h
is
en
s
u
r
es
th
at
th
e
r
esu
lts
ar
e
co
m
p
r
eh
e
n
s
iv
e
an
d
ac
tio
n
ab
le.
I
n
cr
ea
s
in
g
a
t
r
a
n
s
f
o
r
m
er
'
s
ca
p
ac
ity
aim
s
to
s
tab
ilize
th
e
elec
tr
ical
n
etwo
r
k
[
1
7
]
,
[
1
8
]
.
T
h
is
en
s
u
r
es
r
eliab
le
p
o
wer
d
eliv
er
y
to
co
n
s
u
m
e
r
s
.
Su
ch
u
p
g
r
ad
es
ar
e
cr
u
cial
d
u
r
in
g
d
is
tu
r
b
an
ce
s
[
1
9
]
-
[
2
2
]
.
2.
M
E
T
H
O
D
Fig
u
r
e
1
illu
s
tr
ates
th
e
s
in
g
le
-
lin
e
d
iag
r
am
o
f
th
e
3
3
k
V
lo
o
p
n
etwo
r
k
.
T
h
e
lin
e
d
ata,
as
well
as
th
e
in
jecte
d
p
o
wer
s
at
th
e
b
u
s
es
a
n
d
th
e
lo
ad
s
,
ar
e
p
r
o
v
id
ed
in
T
ab
les
1
an
d
2
,
r
esp
ec
tiv
ely
.
T
h
e
elec
tr
ical
n
etwo
r
k
co
m
p
r
is
es
f
o
u
r
tr
an
s
m
is
s
io
n
li
n
es,
f
o
u
r
t
r
an
s
f
o
r
m
er
s
u
b
s
tatio
n
s
f
ed
b
y
a
n
in
f
i
n
ite
s
o
u
r
ce
,
an
d
f
o
u
r
lo
a
d
s
lo
ca
ted
at
b
u
s
es
1
,
2
,
3
,
a
n
d
4
(
Fig
u
r
e
1
)
.
T
h
e
g
en
er
ate
d
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
ar
e
p
r
o
v
id
ed
i
n
MW
an
d
MV
AR
,
r
esp
ec
tiv
ely
.
T
h
e
ac
tiv
e
an
d
r
e
ac
tiv
e
p
o
wer
s
g
en
e
r
ated
ar
e
g
i
v
en
in
MW
an
d
MV
AR
,
r
esp
e
ctiv
ely
.
T
h
e
v
o
ltag
e
at
ea
ch
b
u
s
(
i)
is
g
i
v
en
i
n
p
e
r
u
n
it.
T
h
e
lo
ad
b
u
s
is
ch
ar
ac
ter
ized
b
y
its
ac
tiv
e
p
o
wer
P
a
n
d
r
ea
ctiv
e
p
o
wer
Q.
T
h
er
ef
o
r
e,
(
P,
Q)
ar
e
s
p
ec
if
ie
d
,
wh
ile
(
V)
is
to
b
e
ca
lcu
lated
.
I
n
th
is
co
n
tex
t,
b
u
s
3
(
Kae
d
i
)
is
p
r
o
p
o
s
ed
to
s
er
v
e
as
th
e
s
lack
b
u
s
.
Ad
d
itio
n
ally
,
it
is
im
p
o
r
tan
t
to
n
o
te
th
at
ea
ch
b
u
s
is
n
u
m
b
er
ed
as
(
i)
an
d
is
co
n
n
ec
ted
to
(
k
)
o
th
er
b
u
s
es,
as illu
s
tr
ated
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
Sch
em
atic
d
iag
r
am
o
f
th
e
3
3
k
V
lo
o
p
s
y
s
tem
2
.
1
.
L
ine
pa
ra
m
e
t
er
s
T
ab
le
1
p
r
o
v
id
es
th
e
d
ata,
in
c
lu
d
in
g
th
e
ac
tiv
e
r
esis
tan
ce
s
,
r
ea
ctan
ce
s
o
f
th
e
lin
es
in
p
er
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it,
n
o
d
e
v
o
ltag
es,
an
d
th
e
r
esp
ec
tiv
e
len
g
th
s
o
f
ea
ch
lin
e.
T
h
is
in
f
o
r
m
atio
n
is
cr
u
cial
f
o
r
a
n
aly
zin
g
th
e
elec
tr
ical
ch
ar
ac
ter
is
tics
o
f
th
e
n
etwo
r
k
.
I
t
p
r
o
v
i
d
es
k
ey
in
f
o
r
m
atio
n
n
ee
d
ed
to
ev
alu
ate
th
e
n
etwo
r
k
'
s
p
er
f
o
r
m
an
ce
,
as
s
h
o
wn
b
elo
w.
T
ab
le
1
.
L
in
e
p
ar
am
eter
s
B
u
s
(
i
–
k
)
R
e
si
st
a
n
c
e
(
Ω
)
R
p
u
=
R
/
Z
B
R
e
a
c
t
a
n
c
e
(
Ω
)
X
p
u
=
X
/
Z
B
V
o
l
t
a
g
e
(
k
V)
Le
n
g
t
h
(
k
m)
1
-
2
2
.
1
4
7
0
.
0
0
1
5
2
.
9
3
8
0
0
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0
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2
1
5
33
1
1
3
2
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0
8
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0
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8
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0
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33
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8
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33
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33
44
.
64
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
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8
7
9
2
P
a
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fo
r
mers
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K
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(
E
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r
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581
2
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Ca
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o
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t a
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q
u
a
n
titi
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p
er
u
n
it (
p
.
u
.
)
lis
ted
in
T
ab
le
1
,
it is
n
ec
ess
ar
y
to
ar
b
itra
r
ily
s
elec
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in
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ep
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en
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ase
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th
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ical
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ically
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h
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ase
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e
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ase
im
p
ed
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ce
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wh
ic
h
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tr
o
d
u
ce
d
v
ia
Oh
m
'
s
law.
T
h
e
b
ase
im
p
ed
an
ce
is
g
iv
en
b
y
th
e
f
o
llo
win
g
e
x
p
r
ess
io
n
:
=
2
=
33
2
800
=
1361
Ω
ℎ
=
33
=
800
T
ab
le
2
p
r
esen
ts
th
e
g
iv
e
n
d
at
a
o
f
th
e
i
n
itial
v
o
ltag
es
a
n
d
th
e
ir
an
g
les,
t
h
e
in
jecte
d
p
o
wer
s
,
an
d
p
o
wer
d
em
an
d
in
2
0
2
2
.
T
h
is
d
ata
is
ess
en
tial
f
o
r
ev
alu
atin
g
s
y
s
tem
p
er
f
o
r
m
an
ce
an
d
ef
f
icien
c
y
.
An
aly
zin
g
it
h
elp
s
en
s
u
r
e
n
etwo
r
k
r
eliab
ilit
y
.
T
ab
le
3
p
r
o
v
i
d
es
th
e
p
r
o
jecte
d
s
y
s
tem
d
em
an
d
f
r
o
m
2
0
2
5
to
2
0
4
0
b
ased
o
n
ex
tr
a
p
o
latio
n
.
T
h
is
f
o
r
ec
ast
is
cr
u
cial
f
o
r
ef
f
ec
tiv
e
s
tr
ateg
i
c
p
lan
n
i
n
g
a
n
d
r
eso
u
r
ce
allo
c
atio
n
.
I
t
allo
ws
f
o
r
an
ticip
atin
g
f
u
t
u
r
e
n
ee
d
s
a
n
d
m
ak
in
g
in
f
o
r
m
e
d
p
r
ep
a
r
atio
n
s
.
T
ab
le
4
d
is
p
lay
s
th
e
s
im
u
latio
n
r
esu
lts
f
o
r
th
e
ad
m
ittan
ce
m
atr
ix
o
f
b
u
s
es 1
,
2
,
3
,
an
d
4
.
T
h
is
d
ata
u
n
d
e
r
s
co
r
e
s
th
e
in
ter
ac
tio
n
s
an
d
p
er
f
o
r
m
an
ce
o
f
th
ese
b
u
s
es
with
in
th
e
s
y
s
tem
.
An
aly
zin
g
th
ese
r
esu
lts
is
es
s
en
tial f
o
r
g
r
asp
in
g
s
y
s
tem
d
y
n
am
ics.
T
ab
le
2
.
I
n
itial
d
ata
o
f
t
h
e
s
y
s
tem
B
u
s
N
o.
B
u
s
v
o
l
t
a
g
e
I
n
j
e
c
t
e
d
p
o
w
e
r
Lo
a
d
V
o
l
t
a
g
e
m
a
g
n
i
t
u
d
e
(p
.
u
.
)
A
n
g
l
e
(
d
e
g
)
P
(
k
W
)
Q
(
k
V
A
r
)
P
(
k
W
)
Q
(
k
V
A
r
)
1
1
.
0
5
0
6
3
4
.
5
3
1
0
.
2
5
6
4
4
2
3
2
1
0
3
3
3
1
6
2
.
8
2
9
6
2
2
2
3
1
0
7
2
0
3
5
2
6
4
0
4
8
0
4
1
0
2
8
8
1
4
0
.
8
2
5
6
1
9
2
T
ab
le
3
.
Fo
r
ec
asted
s
y
s
tem
d
e
m
an
d
f
r
o
m
2
0
2
2
to
2
0
4
0
C
o
u
n
t
r
y
2
0
2
5
-
2
0
3
0
2
0
3
0
-
2
0
3
5
2
0
3
5
-
2
0
4
0
P
D
(
M
w
)
Q
D
(
M
v
a
r
)
P
D
(
M
w
)
Q
D
(
M
v
a
r
)
P
D
(
M
w
)
Q
D
(
M
v
a
r
)
S
é
l
i
b
a
b
i
1
0
.
3
3
7
.
5
2
4
1
1
.
5
3
7
8
.
6
5
3
1
3
.
2
6
8
9
.
9
5
1
M
’
B
o
u
t
4
.
7
5
1
4
.
3
4
5
5
.
4
6
4
4
.
9
9
7
6
.
2
8
4
5
.
7
4
6
K
a
é
d
i
1
1
.
3
8
5
8
.
5
3
8
1
3
.
0
9
9
.
8
1
9
1
5
.
0
5
6
1
1
.
2
9
2
G
o
u
r
a
y
4
.
1
0
9
3
.
4
2
4
.
7
2
6
3
.
9
3
5
.
4
3
5
4
.
5
2
3
T
ab
le
4
.
Sy
s
tem
'
s
ad
m
ittan
ce
m
atr
ix
in
p
.
u
.
B
u
s
N
o
.
1
2
3
4
1
0
.
7
8
0
7
-
j1
.
0
6
9
5
-
0
.
2
2
0
6
+
j
0
.
3
0
1
6
0
-
0
.
5
6
0
1
+
j
0
.
7
6
7
9
2
-
0
.
2
2
0
6
+
j
0
.
3
0
1
6
0
.
4
4
7
2
-
j0
.
6
1
2
7
-
0
.
2
2
0
6
+
j
0
.
3
0
1
6
0
3
0
-
0
.
2
2
6
7
+
j0
.
3
1
1
1
0
.
3
5
0
7
-
j
0
,
4
8
0
7
-
0
.
1
2
4
1
+
j
0
.
1
6
9
6
4
-
0
.
5
6
0
1
+
j
0
.
7
6
7
9
0
-
0
.
1
2
4
1
+
j
0
.
1
6
9
6
0
.
6
8
4
2
-
j0
.
9
3
7
5
2
.
3
.
Num
er
ic
a
l m
o
del o
f
re
s
o
lutio
n
L
o
ad
f
lo
w
s
tu
d
ies
ar
e
o
n
e
o
f
t
h
e
m
o
s
t
im
p
o
r
tan
t
asp
ec
ts
o
f
p
o
wer
s
y
s
tem
p
lan
n
in
g
an
d
o
p
e
r
atio
n
.
T
h
e
m
ain
o
b
jectiv
e
o
f
th
e
lo
a
d
f
lo
w
is
to
f
in
d
th
e
v
o
ltag
e
m
ag
n
itu
d
e
at
ea
ch
b
u
s
an
d
its
an
g
l
e
wh
en
th
e
p
o
wer
s
g
en
er
ated
an
d
lo
ad
s
a
r
e
p
r
e
-
s
p
ec
if
ied
.
T
o
s
o
lv
e
t
h
e
p
r
o
b
lem
o
f
lo
a
d
f
lo
w,
we
u
s
e
th
e
iter
ati
v
e
m
eth
o
d
o
f
Gau
s
s
-
Seid
el
b
ec
au
s
e
th
e
s
ize
o
f
th
e
s
tu
d
ied
s
y
s
tem
.
T
h
e
s
im
u
latio
n
was c
ar
r
ied
o
u
t o
n
MA
T
L
A
B
an
d
PS
SE.
2
.
3
.
1
.
G
a
us
s
-
Seidel
re
s
o
lutio
n
Usi
n
g
Kir
ch
h
o
f
f
cu
r
r
en
t
law
(
KC
L
)
f
r
o
m
Fig
u
r
e
1
,
we
o
b
tain
.
Usi
n
g
Y
Bus
,
we
ca
n
wr
it
e
a
n
o
d
al
eq
u
atio
n
f
o
r
p
o
wer
s
y
s
tem
as
(
1
)
.
I
=
Y
B
V
(
1
)
W
h
er
e
(
I
)
is
th
e
(
n
)
co
lu
m
n
v
e
cto
r
o
f
s
o
u
r
ce
cu
r
r
en
ts
in
jecte
d
in
to
ea
ch
b
u
s
a
n
d
(
V)
is
th
e
(
n
)
co
l
u
m
n
v
ec
to
r
o
f
b
u
s
v
o
ltag
es.
Fo
r
b
u
s
(
k
)
,
th
e
k
th
in
(
2
)
is
:
I
i
=
∑
Y
ik
V
k
n
k
=
1
(
2
)
t
h
e
co
n
ju
g
ate
co
m
p
le
x
p
o
wer
d
eliv
er
ed
to
b
u
s
(
i)
is
g
iv
e
n
b
y
(
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.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
5
7
9
-
587
582
P
i
−
j
Q
i
=
V
i
∗
I
i
(
3
)
Pu
ttin
g
in
(
2
)
in
(
3
)
,
we
o
b
tain
,
th
e
v
o
ltag
e
at
b
u
s
(
i)
is
d
ef
i
n
e
d
b
y
(
4
)
.
V
i
=
1
Y
ii
[
P
i
−
jQ
i
∗
−
∑
n
k
=
1
]
(
4
)
Hen
ce
,
th
e
f
o
llo
win
g
cu
r
r
en
t b
etwe
en
b
u
s
(
i)
an
d
b
u
s
(
k
)
is
d
e
f
in
ed
b
y
(
5
)
.
I
ik
=
−
Y
ik
(
V
i
−
V
k
)
,
i
≠
k
(
5
)
W
h
er
e
V
i
=
|
V
i
|
∠
δ
i
is
th
e
v
o
ltag
e
m
ag
n
it
u
d
e
an
d
it
a
n
g
le
in
jecte
d
at
b
u
s
(
i)
;
V
k
=
|
V
k
|
∠
δ
k
is
a
v
o
ltag
e
m
ag
n
itu
d
e
an
d
it a
n
g
le
at
b
u
s
(
k
)
;
Y
ii
=
|
Y
ii
|
∠
θ
ii
i
s
s
elf
-
ad
m
ittan
ce
; a
n
d
Y
ik
=
|
Y
ik
|
∠
θ
ik
is
ad
m
ittan
ce
b
etwe
en
b
u
s
(
i)
an
d
(
k
)
.
V
i
=
|
V
i
|
∠
δ
i
,
V
k
=
|
V
k
|
∠
δ
k
,
Y
ii
=
|
Y
ii
|
∠
θ
ii
,
Y
ik
=
|
Y
ik
|
∠
θ
ik
(
6
)
E
x
ten
d
ed
in
(
3
)
,
we
f
in
d
(
7
)
.
P
i
−
j
Q
i
=
V
i
∗
I
i
=
V
i
∗
∑
Y
ik
V
k
n
k
=
1
=
∑
|
Y
ik
V
i
V
k
|
n
k
=
1
(
c
os
(
θ
ik
+
δ
k
−
δ
i
)
−
j
s
in
(
θ
ik
+
δ
k
−
δ
i
)
)
(
7
)
T
h
e
in
jecte
d
p
o
wer
s
at
b
u
s
(
i)
ar
e
d
ef
in
e
d
b
y
(
8
)
an
d
(
9
)
i
n
r
ec
tan
g
u
lar
co
o
r
d
i
n
ates
.
P
i
=
∑
|
Y
ik
V
i
V
k
|
c
os
(
θ
ik
+
δ
k
−
δ
i
)
n
k
=
1
(
8
)
Q
i
=
−
∑
|
Y
ik
V
i
V
k
|
s
in
(
θ
ik
+
δ
k
−
δ
i
n
k
=
1
)
(
9
)
Sin
ce
th
e
v
o
ltag
e
at
th
e
b
u
s
es
m
u
s
t
b
e
m
ain
tain
ed
with
in
ce
r
tain
s
p
ec
if
ied
s
tatu
to
r
y
lim
it.
Hen
ce
,
th
e
v
o
ltag
e
b
o
u
n
d
co
n
s
tr
ain
t lim
it a
t b
u
s
(
i)
is
th
en
d
ef
in
e
d
b
y
(
1
0
)
.
(
m
i
n
)
≤
≤
(
m
ax
)
(
1
0
)
W
h
er
e
Vi
(
m
in
)
an
d
Vi
(
m
ax
)
ar
e
m
in
im
u
m
an
d
m
a
x
im
u
m
v
o
ltag
e
v
alu
es a
t b
u
s
i.
T
h
e
r
ea
ctiv
e
p
o
wer
s
u
p
p
ly
co
n
s
tr
ain
t a
t b
u
s
(
i)
is
s
p
ec
if
ied
b
y
(
1
1
)
.
(
m
i
n
)
≤
≤
(
m
ax
)
(
1
1
)
W
ith
Qg
i(
m
in
)
an
d
Q
g
i(
m
ax
)
ar
e
th
e
m
in
im
u
m
an
d
m
ax
im
u
m
r
ea
ctiv
e
p
o
we
r
v
alu
es g
e
n
er
ated
at
b
u
s
(
i)
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
ab
le
5
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
in
PS
S/E
s
im
u
lato
r
at
y
ea
r
2
0
4
0
.
C
ase
b
ef
o
r
e
i
n
s
er
tio
n
th
e
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
ato
r
i
n
th
e
s
y
s
tem
.
W
e
ca
n
o
b
s
er
v
e
th
e
v
o
ltag
e
m
ag
n
it
u
d
e
p
r
o
f
i
le
an
d
th
e
v
o
ltag
e
an
g
les.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
v
o
ltag
e
m
a
g
n
itu
d
e
v
alu
es
ar
e
b
elo
w
th
e
s
tab
ilit
y
r
an
g
e
(
0
.
9
5
an
d
1
.
0
5
p
.
u
.
)
f
o
r
all
s
y
s
tem
s
ex
ce
p
t th
e
s
lac
k
b
u
s
.
T
ab
le
5
.
PS
SE
s
im
u
latio
n
o
u
tc
o
m
es f
o
r
th
e
y
ea
r
2
0
4
0
B
u
s
n
a
me
N°
Ty
p
e
V
p
u
ϕ
°
S
e
l
i
b
a
b
i
1
PQ
0
.
9
-
1
.
5
5
M
’
B
o
u
t
2
PQ
0
.
9
3
-
0
.
8
9
K
a
e
d
i
3
S
l
a
c
k
1
0
G
o
u
r
a
y
4
PQ
0
.
9
1
-
1
.
3
7
3
.
1
.
M
o
del o
f
re
a
ct
iv
e
po
we
r
co
m
pens
a
t
io
n
T
ab
le
5
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
f
r
o
m
th
e
PS
S/E
s
im
u
lato
r
with
o
u
t
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
.
T
h
e
v
o
ltag
e
m
ag
n
itu
d
e
p
r
o
f
ile
an
d
v
o
ltag
e
a
n
g
les
f
all
o
u
ts
id
e
th
e
s
tab
ilit
y
m
ar
g
in
.
T
o
a
d
d
r
ess
th
is
is
s
u
e,
we
h
av
e
p
r
o
p
o
s
ed
i
n
(
1
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
P
a
r
a
llel o
p
era
tio
n
o
f tra
n
s
fo
r
mers
to
o
p
timiz
e
a
n
3
3
K
V
lo
o
p
of
…
(
E
th
m
a
n
e
I
s
s
elem
A
r
b
ih
Ma
h
mo
u
d
)
583
=
3
∗
∗
2
∗
ℎ
=
2
(
1
2
)
W
h
er
e
Qc
is
a
r
ea
ctiv
e
p
o
wer
in
MV
Ar
,
U
is
a
b
u
s
b
ar
v
o
ltag
e
,
C
is
a
ca
p
ac
itan
ce
in
μ
F
,
ω
is
a
p
u
ls
e,
an
d
F is
a
n
etwo
r
k
f
r
eq
u
e
n
c
y
.
Giv
en
th
at
C
=
2
0
μ
F,
U
=
3
3
k
V,
an
d
F
=
5
0
Hz,
th
e
r
ea
ctiv
e
p
o
wer
r
eq
u
ir
ed
t
o
m
ain
tain
th
e
s
y
s
tem
with
in
th
e
v
o
ltag
e
co
n
s
tr
ain
ts
(
0
.
9
5
an
d
1
.
0
5
p
.
u
.
)
,
as p
r
eset in
(
1
0
)
,
is
ca
lcu
late
d
u
s
in
g
(
1
3
)
.
=
3
∗
314
∗
33
2
10
6
∗
20
∗
10
−
6
=
20
.
51
ℎ
=
314
/
(
1
3
)
T
h
e
in
jecte
d
r
ea
ctiv
e
p
o
wer
at
th
e
Selib
ab
i
b
u
s
b
a
r
(
1
)
is
Qc
=
2
0
.
5
1
MV
Ar
.
A
s
h
u
n
t
FAC
T
S
d
ev
ice,
s
u
c
h
as
an
SVC
o
r
STAT
C
OM
,
is
co
n
n
ec
ted
to
b
u
s
(
1
)
.
T
h
is
d
ev
ice
ca
n
ab
s
o
r
b
o
r
in
ject
r
ea
ctiv
e
p
o
wer
as n
ee
d
ed
.
3
.
2
.
Ana
ly
s
is
o
f
s
im
ula
t
io
n r
esu
lt
s
T
ab
le
6
p
r
esen
ts
th
e
s
im
u
lati
o
n
r
esu
lts
f
o
r
th
e
v
o
ltag
e
p
r
o
f
ile
an
d
a
n
g
les
af
ter
th
e
in
s
er
tio
n
o
f
th
e
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
s
y
s
tem
.
I
t
al
s
o
d
em
o
n
s
tr
ates
th
at
th
e
v
o
ltag
e
v
alu
es
ar
e
with
in
th
e
s
tab
ilit
y
co
n
s
tr
ain
ts
(
0
.
9
5
to
1
.
0
5
p
.
u
.
)
.
T
h
at
m
ea
n
s
we
h
av
e
p
er
f
o
r
m
e
d
o
n
e
g
o
al.
Fig
u
r
e
2
illu
s
tr
ates
th
e
v
o
ltag
e
p
r
o
f
ile
b
ef
o
r
e
an
d
af
ter
th
e
r
e
ac
tiv
e
p
o
wer
c
o
m
p
en
s
atio
n
,
s
h
o
win
g
a
n
in
cr
ea
s
e
in
v
o
ltag
e
m
ag
n
itu
d
e
s
.
Fo
r
b
u
s
1
,
th
e
v
o
ltag
e
r
is
es f
r
o
m
0
.
9
0
(
o
u
ts
id
e
th
e
lim
it
o
f
[
0
.
9
5
;
1
.
0
5
p
.
u
.
]
)
to
1
p
.
u
.
,
f
o
r
b
u
s
2
f
r
o
m
0
.
9
3
to
0
.
9
8
p
.
u
.
,
an
d
f
o
r
b
u
s
4
f
r
o
m
0
.
9
3
to
0
.
9
9
p
.
u
.
I
t
is
n
o
tewo
r
th
y
th
at
th
e
v
o
ltag
e
an
d
an
g
le
f
o
r
s
lack
b
u
s
3
r
em
ain
u
n
ch
a
n
g
ed
(
1
p
.
u
.
;
0
°).
Fi
g
u
r
e
3
d
is
p
lay
s
th
e
v
o
ltag
e
an
g
le
b
ef
o
r
e
a
n
d
af
ter
th
e
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
,
in
d
icatin
g
a
n
im
p
r
o
v
em
en
t in
v
o
ltag
e
an
g
les.
Fo
r
b
u
s
1
,
th
e
an
g
le
im
p
r
o
v
es
f
r
o
m
-
1
.
5
5
° to
-
5
.
1
5
°,
f
o
r
b
u
s
2
f
r
o
m
-
0
.
8
9
° to
2
.
6
9
°,
a
n
d
f
o
r
b
u
s
4
f
r
o
m
-
1
.
3
7
° to
-
4
.
3
3
°.
T
ab
le
7
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
f
o
r
th
e
to
tal
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
b
ef
o
r
e
an
d
af
ter
th
e
in
s
er
tio
n
o
f
th
e
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
s
y
s
tem
at
Selib
ab
i
b
u
s
(
1
)
.
A
r
e
d
u
ctio
n
in
t
o
tal
p
o
wer
lo
s
s
es
was
o
b
s
er
v
ed
,
h
ig
h
lig
h
tin
g
t
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
c
o
m
p
en
s
at
io
n
s
y
s
tem
.
As
s
h
o
wn
in
Fig
u
r
e
4
,
th
er
e
was
a
d
ec
r
ea
s
e
in
th
e
to
tal
ac
tiv
e
p
o
wer
lo
s
s
o
f
th
e
s
y
s
tem
,
f
r
o
m
1
.
8
MW
to
1
.
5
MW,
th
er
eb
y
im
p
r
o
v
i
n
g
th
e
ac
tiv
e
p
o
wer
tr
a
n
s
m
is
s
io
n
th
r
o
u
g
h
t
h
e
lin
es.
T
h
ese
r
esu
lts
d
em
o
n
s
tr
ate
th
e
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
s
y
s
tem
'
s
ab
ilit
y
to
en
h
a
n
ce
th
e
v
o
ltag
e
at
b
u
s
es a
n
d
r
ed
u
ce
ac
tiv
e
p
o
wer
lo
s
s
es in
th
e
p
o
wer
s
y
s
tem
.
Similar
ly
,
Fig
u
r
e
5
s
h
o
ws a
r
e
d
u
ctio
n
in
t
h
e
to
tal
r
ea
ctiv
e
p
o
wer
lo
s
s
o
f
th
e
s
y
s
tem
,
f
r
o
m
2
.
5
MV
AR
to
2
MV
AR
.
T
h
is
r
esu
lts
in
lo
wer
r
ea
ctiv
e
p
o
wer
lo
s
s
es
in
th
e
tr
an
s
m
is
s
io
n
lin
es.
T
h
ese
f
in
d
in
g
s
f
u
r
th
e
r
illu
s
tr
ate
th
e
r
ea
ctiv
e
p
o
wer
c
o
m
p
en
s
atio
n
s
y
s
tem
'
s
ef
f
ec
tiv
en
ess
in
im
p
r
o
v
in
g
v
o
ltag
e
at
b
u
s
es
an
d
r
ed
u
ci
n
g
r
ea
ctiv
e
p
o
wer
l
o
s
s
es a
cr
o
s
s
t
h
e
p
o
wer
s
y
s
tem
.
T
ab
le
6
.
Simu
latio
n
r
esu
lts
af
ter
in
jecte
d
r
ea
ctiv
e
p
o
wer
at
b
u
s
1
B
u
s
N
°
Ty
p
e
V
p
u
ϕ
°
S
e
l
i
b
a
b
i
1
PQ
1
-
5
.
1
5
M
’
B
o
u
t
2
PQ
0
.
9
8
5
-
2
.
6
9
K
a
e
d
i
3
S
l
a
c
k
1
0
G
o
u
r
a
y
4
PQ
0
.
9
9
-
4
.
3
3
Fig
u
r
e
2
.
Vo
ltag
e
m
ag
n
itu
d
e
c
u
r
v
e
in
p
er
u
n
it (
p
u
)
Fig
u
r
e
3
.
Vo
ltag
e
an
g
le
c
u
r
v
e
in
d
eg
r
ee
s
T
ab
le
7
.
T
o
tal
ac
tiv
e
an
d
r
ea
ct
iv
e
p
o
wer
lo
s
s
es in
th
e
s
y
s
tem
C
o
n
n
e
c
t
i
o
n
st
a
t
e
A
c
t
i
v
e
p
o
w
e
r
l
o
sses
R
e
a
c
t
i
v
e
p
o
w
e
r
l
o
sse
s
B
e
f
o
r
e
c
o
m
p
e
n
sa
t
i
o
n
1
.
8
2
.
5
A
f
t
e
r
c
o
m
p
e
n
sa
t
i
o
n
1
.
5
2
0
1
2
3
4
5
0
0
.
2
0
.
4
0
.
6
0
.
8
1
B
u
s
n
u
m
b
e
r
M
a
g
n
i
t
u
d
e
v
o
l
t
a
g
e
(
p
u
)
B
e
f
o
r
e
c
o
m
p
e
n
s
a
t
i
o
n
A
f
t
e
r
c
o
m
p
e
n
s
a
t
i
o
n
0
1
2
3
4
5
-6
-4
-2
0
B
u
s
n
u
m
b
e
r
A
n
g
l
e
i
n
d
e
g
r
e
e
s
A
f
t
e
r
co
m
p
e
n
st
a
t
i
o
n
B
e
f
o
r
e
co
m
p
e
n
sa
t
i
o
n
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.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
5
7
9
-
587
584
Fig
u
r
e
4
.
T
o
tal
ac
tiv
e
p
o
wer
lo
s
s
es in
th
e
s
y
s
tem
Fig
u
r
e
5
.
T
o
tal
r
ea
ctiv
e
p
o
wer
lo
s
s
es in
th
e
s
y
s
tem
3
.
3
.
M
o
del o
f
t
ra
ns
f
o
rm
er
T
o
ad
d
r
ess
th
e
lo
ad
g
r
o
wth
o
f
th
e
3
3
k
V
lo
o
p
b
y
th
e
y
ea
r
2
0
4
0
,
we
p
r
o
p
o
s
e
en
h
an
cin
g
th
e
c
ap
ac
ity
o
f
th
e
tr
an
s
f
o
r
m
er
s
co
n
n
ec
ted
to
th
e
v
ar
io
u
s
b
u
s
es
in
th
e
s
y
s
tem
.
T
h
is
ca
n
b
e
ac
h
ie
v
ed
b
y
c
o
n
n
ec
tin
g
o
n
e
o
r
m
o
r
e
tr
an
s
f
o
r
m
er
s
in
p
ar
allel
with
t
h
e
ex
is
tin
g
o
n
e
s
.
Par
allel
co
n
n
ec
tio
n
o
f
tr
an
s
f
o
r
m
er
s
is
u
s
e
d
wh
en
th
e
lo
a
d
o
n
o
n
e
tr
an
s
f
o
r
m
er
e
x
ce
ed
s
its
ca
p
ac
ity
.
B
y
co
n
n
ec
tin
g
tr
a
n
s
f
o
r
m
er
s
in
p
a
r
allel,
we
ca
n
in
cr
ea
s
e
th
e
av
ailab
le
p
o
wer
with
o
u
t
alter
in
g
th
e
v
o
ltag
e
an
d
d
is
tr
ib
u
te
t
h
e
p
o
wer
d
em
an
d
b
etwe
en
th
e
tw
o
t
r
an
s
f
o
r
m
er
s
.
T
h
e
r
eliab
ilit
y
o
f
th
e
s
y
s
tem
is
e
n
h
an
ce
d
with
p
ar
allel
o
p
er
atio
n
co
m
p
ar
ed
to
u
s
in
g
a
s
in
g
le
lar
g
er
u
n
it
[
2
3
]
,
[
2
4
]
.
Ad
d
itio
n
ally
,
t
h
e
co
s
t
o
f
m
ain
tain
in
g
s
p
a
r
es
is
lo
wer
wh
e
n
two
tr
an
s
f
o
r
m
er
s
a
r
e
co
n
n
ec
t
ed
in
p
ar
allel.
T
h
is
s
etu
p
en
s
u
r
es
th
at
at
least
h
a
lf
o
f
th
e
lo
ad
ca
n
b
e
s
u
p
p
lie
d
ev
en
if
o
n
e
tr
a
n
s
f
o
r
m
e
r
is
o
u
t
o
f
s
er
v
ice.
T
h
e
ad
v
an
tag
es
o
f
p
ar
allel
tr
an
s
f
o
r
m
er
o
p
er
atio
n
in
clu
d
e
m
ee
tin
g
lo
ad
d
e
m
an
d
,
im
p
r
o
v
in
g
r
eliab
ilit
y
,
f
ac
ilit
atin
g
s
witch
in
g
o
p
er
atio
n
s
,
a
n
d
p
r
o
v
id
in
g
a
n
u
n
i
n
ter
r
u
p
ted
p
o
w
er
s
u
p
p
ly
in
ca
s
e
o
f
a
u
n
it o
u
tag
e.
T
h
e
co
n
d
itio
n
s
f
o
r
p
ar
allel
o
p
er
atio
n
o
f
tr
a
n
s
f
o
r
m
er
s
ar
e
[
2
5
]
-
[
3
0
]
:
Fo
r
p
ar
allel
co
n
n
ec
tio
n
o
f
tr
an
s
f
o
r
m
er
s
,
p
r
im
a
r
y
win
d
in
g
s
o
f
th
e
tr
an
s
f
o
r
m
er
s
ar
e
co
n
n
ec
ted
to
s
o
u
r
ce
b
u
s
-
b
ar
s
an
d
s
ec
o
n
d
ar
y
win
d
in
g
s
ar
e
co
n
n
ec
ted
to
t
h
e
lo
a
d
b
u
s
-
b
ar
s
.
Sev
er
al
co
n
d
itio
n
s
m
u
s
t
b
e
m
et
f
o
r
t
h
e
s
u
cc
ess
f
u
l
p
a
r
allel
o
p
er
atio
n
o
f
tr
an
s
f
o
r
m
er
s
:
-
B
o
t
h
t
h
e
p
r
i
m
a
r
y
a
n
d
s
ec
o
n
d
ar
y
v
o
lta
g
e
r
at
in
g
s
m
u
s
t
b
e
t
h
e
s
a
m
e
(
i
.
e
.
,
t
h
e
s
am
e
v
o
lt
ag
e
r
at
io
an
d
t
u
r
n
s
r
at
io
)
.
-
T
h
e
tr
an
s
f
o
r
m
atio
n
r
atio
(
k
)
s
h
o
u
ld
b
e
id
en
tical.
-
T
h
e
s
h
o
r
t c
ir
c
u
it v
o
ltag
e
s
h
o
u
l
d
b
e
eq
u
al
to
o
r
less
th
an
1
0
%.
-
T
h
e
p
h
ase
an
g
le
s
h
if
t
m
u
s
t b
e
th
e
s
am
e
(
i.e
.
,
th
e
v
ec
to
r
g
r
o
u
p
s
s
h
o
u
ld
b
e
t
h
e
s
am
e
o
r
c
o
m
p
atib
le)
.
3
.
3
.
1
.
M
o
del pa
ra
llel o
pera
t
io
n o
f
t
ra
ns
f
o
r
m
er
s
T
o
s
h
ar
e
th
e
t
o
tal
lo
ad
b
etwe
en
two
c
o
n
n
ec
te
d
tr
a
n
s
f
o
r
m
e
r
s
in
p
ar
allel,
we
m
u
s
t
k
n
o
w
c
er
tain
k
e
y
p
ar
am
eter
s
.
T
h
ese
in
clu
d
e:
-
T
h
e
tr
an
s
f
o
r
m
er
p
o
wer
T
1
(
MV
A1
)
an
d
th
eir
p
er
ce
n
t im
p
ed
an
ce
(
%Z1
)
-
T
h
e
tr
an
s
f
o
r
m
er
p
o
wer
T
2
(
MV
A2
)
an
d
th
eir
p
er
ce
n
t im
p
ed
an
ce
(
%Z2
)
-
T
h
e
to
tal(
lo
ad
)
d
em
a
n
d
p
o
wer
(
MV
A)
L
o
ad
s
h
ar
in
g
b
y
T
1
is
g
iv
e
n
b
y
(
1
4
)
,
an
d
th
at
b
y
T
2
is
g
i
v
en
b
y
(
1
5
)
.
1
=
1
1
1
1
+
2
2
∗
(
1
4
)
2
=
2
2
1
1
+
2
2
∗
(
1
5
)
T
h
e
(
1
4
)
a
n
d
(
1
5
)
allo
w
u
s
to
ca
lcu
late
th
e
p
o
we
r
v
alu
es
s
h
a
r
ed
b
etwe
en
th
e
co
n
n
ec
ted
tr
a
n
s
f
o
r
m
er
s
in
p
ar
allel
at
b
u
s
3
(
Kae
d
i)
f
o
r
th
e
y
ea
r
2
0
4
0
.
No
te
th
at
o
n
e
o
f
th
ese
tr
an
s
f
o
r
m
er
s
alr
ea
d
y
ex
is
ts
in
th
e
s
y
s
tem
,
with
a
r
atin
g
o
f
T
1
=
1
0
MV
A.
T
h
eo
r
etica
lly
,
t
h
e
t
o
tal
lo
a
d
d
em
an
d
(
MV
A)
m
in
u
s
th
e
p
o
wer
o
f
th
e
ex
is
tin
g
tr
an
s
f
o
r
m
er
(
MV
A1
)
g
iv
es
t
h
e
lo
ad
to
b
e
s
h
ar
e
d
b
y
t
h
e
s
ec
o
n
d
tr
an
s
f
o
r
m
er
(
MV
A2
)
.
T
o
p
er
f
o
r
m
t
h
is
ca
lcu
latio
n
,
we
an
aly
ze
two
ca
s
es: th
e
f
ir
s
t is d
eter
m
in
ed
b
y
s
im
u
latin
g
th
e
to
tal
lo
ad
d
em
a
n
d
o
f
th
e
s
y
s
tem
in
th
e
PS
S/E
s
o
f
twar
e,
an
d
th
e
s
ec
o
n
d
u
s
es
in
(
1
4
)
an
d
(
1
5
)
to
c
alcu
late
th
e
s
h
ar
ed
lo
ad
b
etwe
en
tr
an
s
f
o
r
m
er
s
T
1
an
d
T
2
,
as sh
o
wn
in
T
a
b
le
8
.
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
P
a
r
a
llel o
p
era
tio
n
o
f tra
n
s
fo
r
mers
to
o
p
timiz
e
a
n
3
3
K
V
lo
o
p
of
…
(
E
th
m
a
n
e
I
s
s
elem
A
r
b
ih
Ma
h
mo
u
d
)
585
T
ab
le
8
.
Simu
latio
n
a
n
d
ca
lc
u
latio
n
o
u
tco
m
es f
o
r
th
e
lo
ad
d
is
tr
ib
u
tio
n
at
b
u
s
(
3
)
B
u
s
To
t
a
l
l
o
a
d
(
T)
(
M
V
A
)
i
n
2
0
4
5
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i
s
t
i
n
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o
a
d
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V
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f
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r
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r
e
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y
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10
31
8
10
1
5
.
2
5
2
5
.
6
2
2
0
.
5
2
0
.
5
4.
CO
NCLU
SI
O
N
I
n
th
is
p
a
p
er
,
we
e
x
am
in
e
d
th
e
s
tate
o
f
a
3
3
k
V
l
o
o
p
n
etwo
r
k
o
v
er
two
p
er
io
d
s
.
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h
e
f
ir
s
t
p
er
i
o
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e
f
lects
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n
etwo
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k
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a
r
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eter
s
(
v
o
lta
g
es
an
d
p
o
wer
s
)
f
o
r
th
e
y
ea
r
2
0
2
2
,
wh
e
r
e
th
e
s
y
s
tem
is
s
tab
l
e
an
d
th
e
p
ar
am
eter
s
m
ee
t
th
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ir
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s
tan
d
ar
d
s
.
I
n
th
e
s
ec
o
n
d
p
er
io
d
,
we
p
r
o
je
cted
th
e
d
em
an
d
f
r
o
m
2
0
2
5
to
2
0
4
0
.
T
h
e
r
esu
lts
in
d
icate
d
th
at
th
e
s
y
s
tem
f
alls
o
u
ts
id
e
th
e
s
tab
ilit
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n
s
tr
ain
ts
.
T
o
ad
d
r
ess
th
e
in
cr
ea
s
in
g
d
em
an
d
,
we
in
jecte
d
r
ea
ctiv
e
p
o
wer
(
v
ia
a
ca
p
ac
ito
r
b
an
k
)
at
th
e
Selib
ab
i
b
u
s
(
1
)
,
wh
ich
h
elp
e
d
m
a
in
tain
th
e
s
y
s
tem
with
in
th
e
v
o
ltag
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s
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ilit
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m
ar
g
in
(
0
.
9
5
to
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.
0
5
p
.
u
.
)
an
d
r
ed
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ce
d
p
o
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er
m
is
m
atch
es.
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a
r
esu
lt,
th
e
s
y
s
tem
r
em
ain
e
d
s
tab
le
in
ter
m
s
o
f
b
o
th
v
o
ltag
e
an
d
p
o
wer
at
ea
ch
b
u
s
.
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n
th
e
s
ec
o
n
d
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s
e,
th
e
ex
is
tin
g
tr
an
s
f
o
r
m
er
s
b
ec
am
e
o
v
er
lo
ad
ed
.
I
t
was
f
o
u
n
d
to
b
e
m
o
r
e
ec
o
n
o
m
ical
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o
p
er
ate
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tr
a
n
s
f
o
r
m
e
r
s
in
p
ar
allel,
wh
ich
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ld
a
cc
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m
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ate
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ea
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ep
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tr
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s
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o
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m
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h
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ap
p
r
o
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h
e
n
s
u
r
ed
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s
y
s
tem
r
em
ain
ed
s
tab
le
in
v
o
ltag
e
an
d
p
o
wer
.
Ad
d
itio
n
ally
,
wh
e
n
t
h
e
lo
ad
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ec
r
e
ased
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th
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s
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m
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lectr
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Ap
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UNDING
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h
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r
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was
f
u
n
d
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d
in
p
ar
t
b
y
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n
al
Ag
e
n
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f
o
r
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tific
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n
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www.
an
r
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k
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in
an
cial
s
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p
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f
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h
elp
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ce
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k
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AUTHO
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u
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to
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ax
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th
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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.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
5
7
9
-
587
586
E
T
H
I
CAL AP
P
RO
V
AL
T
h
is
r
esear
ch
was
r
ev
iewe
d
an
d
ap
p
r
o
v
e
d
b
y
t
h
e
r
ev
iewe
r
s
o
f
th
is
jo
u
r
n
al.
E
th
ical
ap
p
r
o
v
al
f
o
r
th
is
s
tu
d
y
was
o
b
tain
ed
th
r
o
u
g
h
th
e
r
ev
iew
p
r
o
ce
s
s
o
f
jo
u
r
n
al,
f
o
llo
win
g
its
g
u
id
elin
es
an
d
p
o
licies.
T
h
is
r
esear
ch
also
was
ap
p
r
o
v
ed
b
y
t
h
e
s
cien
tific
co
m
m
ittee
o
f
th
e
Hig
h
er
I
n
s
titu
te
o
f
E
d
u
c
atio
n
al
an
d
T
ec
h
n
o
lo
g
y
,
R
o
s
s
o
,
Ma
u
r
itan
ia.
DATA AV
AI
L
AB
I
L
I
T
Y
T
h
e
s
y
s
tem
d
ata
u
s
ed
in
th
is
s
tu
d
y
a
r
e
in
clu
d
ed
with
in
t
h
e
m
an
u
s
cr
ip
t
an
d
ar
e
av
aila
b
le
in
th
e
s
u
p
p
lem
en
tar
y
m
ater
ials
.
T
h
e
d
ata
s
u
p
p
o
r
tin
g
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
ar
e
p
r
o
v
id
e
d
in
Fig
u
r
e
1
,
T
ab
le
1
,
T
ab
le
2
,
T
ab
le
3
,
a
n
d
T
ab
le
4
,
r
esp
ec
tiv
ely
.
All
r
elev
an
t
d
a
ta
ar
e
in
clu
d
ed
i
n
th
e
m
an
u
s
cr
ip
t
f
o
r
r
e
v
iew
an
d
f
u
r
th
er
r
ef
er
e
n
ce
.
RE
F
E
R
E
NC
E
S
[
1
]
P
.
K
a
u
r
,
M
.
J
a
i
sw
a
l
,
a
n
d
P
.
Ja
i
sw
a
l
,
“
R
e
v
i
e
w
a
n
d
a
n
a
l
y
si
s
o
f
v
o
l
t
a
g
e
c
o
l
l
a
p
se
i
n
p
o
w
e
r
s
y
st
e
m,”
I
n
t
e
rn
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
S
c
i
e
n
t
i
f
i
c
a
n
d
Re
se
a
r
c
h
P
u
b
l
i
c
a
t
i
o
n
s
,
v
o
l
.
2
,
n
o
.
1
,
p
p
.
2
–
5
,
2
0
1
2
.
[
2
]
V
.
C
h
a
y
a
p
a
t
h
i
,
B
.
S
h
a
r
a
t
h
,
a
n
d
G
.
S
.
A
n
i
t
h
a
,
“
V
o
l
t
a
g
e
c
o
l
l
a
p
s
e
m
i
t
i
g
a
t
i
o
n
b
y
r
e
a
c
t
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v
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p
o
w
e
r
c
o
mp
e
n
s
a
t
i
o
n
a
t
t
h
e
l
o
a
d
si
d
e
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
Re
s
e
a
r
c
h
i
n
E
n
g
i
n
e
e
r
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n
g
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l
.
0
2
,
n
o
.
0
9
,
p
p
.
2
5
1
–
2
5
7
,
2
0
1
3
,
d
o
i
:
1
0
.
1
5
6
2
3
/
i
j
r
e
t
.
2
0
1
3
.
0
2
0
9
0
3
7
.
[
3
]
E.
M
a
h
m
o
u
d
,
A
.
K
.
M
a
h
m
o
u
d
,
M
.
M
a
a
r
o
u
f
i
,
a
n
d
A
.
Y
a
h
f
d
h
o
u
,
“
P
e
r
f
o
r
man
c
e
o
f
S
TA
TC
O
M
i
n
a
p
o
w
e
r
g
r
i
d
,
”
i
n
2
0
1
8
6
t
h
I
n
t
e
r
n
a
t
i
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4
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[
1
5
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[
1
6
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0
.
2
4
0
8
4
/
r
e
p
q
j
0
6
.
3
9
2
.
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
Eth
m
a
n
e
Is
se
lem
Ar
b
ih
M
a
h
m
o
u
d
wa
s
b
o
r
n
i
n
Ti
d
ji
k
ja
,
M
a
u
rit
a
n
ia,
i
n
1
9
6
6
.
He
re
c
e
iv
e
d
a
M
a
ste
r
o
f
S
c
ien
c
e
d
e
g
re
e
in
E
lec
tri
c
a
l
S
y
ste
m
s
a
n
d
N
e
two
rk
s
fr
o
m
Vin
n
it
sa
S
tate
Un
iv
e
rsity
in
1
9
9
4
a
n
d
h
is
P
h
.
D
.
d
e
g
re
e
i
n
E
lec
tri
c
a
l
E
n
g
in
e
e
r
in
g
fro
m
t
h
e
Un
iv
e
rsity
o
f
M
o
h
a
m
m
a
d
V
(UM5
R)
i
n
M
o
ro
c
c
o
in
2
0
1
9
.
Cu
rre
n
tl
y
,
h
e
is
a
lec
tu
re
r
a
ss
istan
t
a
t
th
e
Hig
h
Tec
h
n
o
l
o
g
ica
l
Ed
u
c
a
ti
o
n
a
l
In
stit
u
te
o
f
Ro
ss
o
c
o
u
n
try
.
His
c
u
r
re
n
t
re
se
a
rc
h
in
tere
sts
in
c
l
u
d
e
e
lec
tri
c
n
e
two
rk
s
,
p
o
we
r
sy
ste
m
s
,
e
n
e
rg
y
e
fficie
n
c
y
,
a
n
d
a
u
t
o
m
a
ti
c
c
o
n
tro
l
.
He
is
t
h
e
a
u
th
o
r
o
f
fiv
e
(5
)
m
a
n
u
sc
rip
ts,
two
(
2
)
c
o
n
fe
re
n
c
e
s
,
a
n
d
tw
o
b
o
o
k
s.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
e
th
m
a
n
e
isse
lem
a
rb
ih
1
9
6
6
@g
m
a
il
.
c
o
m
.
Ahm
e
d
A
b
b
o
u
re
c
e
iv
e
d
t
h
e
B
.
E.
d
e
g
re
e
fro
m
ENS
ET
in
Ra
b
a
t,
th
e
M
.
E.
d
e
g
re
e
fro
m
M
o
h
a
m
m
e
d
V Un
iv
e
rsity
i
n
Ra
b
a
t
,
a
n
d
th
e
P
h
.
D.
d
e
g
re
e
fro
m
M
o
h
a
m
m
e
d
V Un
iv
e
rsity
in
Ra
b
a
t,
in
2
0
0
0
,
2
0
0
5
,
a
n
d
2
0
0
9
,
re
sp
e
c
ti
v
e
ly
,
a
ll
in
E
lec
tri
c
a
l
E
n
g
i
n
e
e
rin
g
.
S
in
c
e
2
0
0
9
,
h
e
h
a
s
b
e
e
n
wo
rk
in
g
a
t
M
o
h
a
m
m
a
d
ia
S
c
h
o
o
l
o
f
En
g
i
n
e
e
rs
,
M
o
h
a
m
m
e
d
V
Un
i
v
e
rsity
in
Ra
b
a
t,
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
P
o
we
r
En
g
in
e
e
rin
g
,
wh
e
re
h
e
is
a
fu
ll
P
r
o
f
e
ss
o
r
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
El
e
c
tri
c
Dri
v
e
s
.
He
p
u
b
l
ish
e
d
n
u
m
e
ro
u
s
p
a
p
e
rs
in
sc
ien
ti
fic
in
tern
a
ti
o
n
a
l
jo
u
rn
a
ls
a
n
d
c
o
n
fe
re
n
c
e
p
ro
c
e
e
d
in
g
s.
His
c
u
r
re
n
t
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
i
n
d
u
c
t
io
n
m
a
c
h
in
e
c
o
n
tr
o
l
sy
ste
m
s,
se
lf
-
e
x
c
it
e
d
in
d
u
c
ti
o
n
g
e
n
e
ra
to
r,
p
o
we
r
e
lec
tro
n
ics
,
se
n
so
rles
s
d
riv
e
s
f
o
r
AC
m
a
c
h
in
e
s,
e
lec
tri
c
v
e
h
icle
c
h
a
rg
e
,
d
ro
n
e
c
o
n
tr
o
l
,
a
n
d
re
n
e
wa
b
le
e
n
e
rg
y
c
o
n
v
e
rsio
n
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
a
b
b
o
u
@e
m
i.
a
c
.
m
a
.
Abd
e
l
K
a
d
e
r
Ma
h
m
o
u
d
wa
s
b
o
r
n
in
Ale
g
,
M
a
u
rit
a
n
ia
i
n
1
9
6
0
.
He
re
c
e
iv
e
d
h
is
M
a
ste
r'
s
d
e
g
re
e
o
f
sc
ien
c
e
s
in
p
o
we
r
sta
ti
o
n
s
i
n
1
9
8
8
a
n
d
h
is
P
h
.
D
.
d
e
g
re
e
i
n
E
lec
tri
c
a
l
E
n
g
i
n
e
e
rin
g
fr
o
m
th
e
Tec
h
n
ica
l
Un
iv
e
rsity
o
f
Tas
h
k
e
n
t
i
n
Uz
b
e
k
istan
,
in
1
9
9
1
.
T
h
e
n
h
e
re
c
e
iv
e
d
h
is
se
c
o
n
d
D
o
c
to
ra
te
d
e
g
re
e
in
Re
n
e
wa
b
le
En
e
rg
y
fro
m
th
e
Un
iv
e
rsity
o
f
C
h
e
ik
h
An
ta
Dio
p
(UCA
D),
Da
k
a
r,
S
e
n
e
g
a
l,
i
n
2
0
0
8
.
Cu
rre
n
t
ly
,
h
e
is
i
n
c
h
a
rg
e
o
f
t
h
e
Ap
p
li
e
d
Re
se
a
rc
h
Lab
o
ra
to
r
y
o
f
Re
n
e
wa
b
le
En
e
r
g
y
(LRAER).
He
is
th
e
a
u
th
o
r
a
n
d
c
o
-
a
u
th
o
r
o
f
m
o
re
th
a
n
3
0
sc
ien
ti
fic p
a
p
e
rs
.
Th
e
ir
c
u
rre
n
t
p
r
o
jec
t
is '
Co
m
p
a
riso
n
b
e
twe
e
n
th
e
d
iffere
n
t
n
u
m
e
rica
l
m
o
d
e
ls
a
n
d
d
e
term
in
a
ti
o
n
o
f
p
a
ra
m
e
ters
c
h
a
ra
c
teristics
p
h
y
sic
a
l
m
a
teria
ls.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
n
a
k
a
d
e
r@y
a
h
o
o
.
fr
.
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