I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
201
9
,
p
p
.
4
5
9
8
~4
6
0
9
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v9
i
6
.
p
p
4
5
9
8
-
4609
4598
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e
.
co
m/
jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JE
C
E
Active an
d
reacti
v
e po
w
er f
lo
w
m
a
na
g
e
m
en
t
in
pa
ra
llel
trans
m
iss
io
n l
ines
using
s
tatic
serie
s co
m
p
ensa
tion (S
SC)
w
ith
energy
stora
g
e
M
o
ha
m
m
e
d Y.
Su
li
m
a
n
Co
ll
e
g
e
o
f
T
e
c
h
n
ica
l
En
g
in
e
e
rin
g
,
No
rt
h
e
rn
T
e
c
h
n
ica
l
Un
iv
e
rsity
,
I
ra
q
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Feb
1
4
,
2
0
1
9
R
ev
i
s
ed
A
p
r
17
,
2
0
1
9
A
cc
ep
ted
J
u
n
26
,
2
0
1
9
T
h
e
p
o
w
e
r
f
lo
w
c
o
n
tro
ll
e
d
i
n
t
h
e
e
lec
tri
c
p
o
w
e
r
n
e
tw
o
rk
is
o
n
e
o
f
th
e
m
a
in
f
a
c
to
rs
th
a
t
a
ff
e
c
ted
th
e
m
o
d
e
rn
p
o
w
e
r
s
y
ste
m
s
d
e
v
e
lo
p
m
e
n
t.
T
h
e
S
tatic
S
e
ries
Co
m
p
e
n
sa
ti
o
r
w
it
h
sto
ra
g
e
e
n
e
rg
y
,
is
a
F
A
C
T
S
p
o
w
e
r
f
u
l
d
e
v
ice
th
a
t
c
a
n
c
o
n
tro
l
th
e
a
c
ti
v
e
p
o
w
e
r
f
lo
w
c
o
n
tro
l
o
f
m
u
lt
ip
le
tran
sm
is
sio
n
li
n
e
s
b
ra
n
c
h
e
s.
I
n
t
h
is
p
a
p
e
r,
a
sim
u
latio
n
m
o
d
e
l
o
f
p
o
w
e
r
c
o
n
tr
o
l
u
sin
g
sta
ti
c
se
ries
c
o
m
p
e
n
sa
to
r
w
it
h
p
a
ra
ll
e
l
tran
sm
issio
n
li
n
e
s
is
p
re
se
n
te
d
.
T
h
e
c
o
n
tr
o
l
s
y
ste
m
u
sin
g
a
d
a
p
ti
v
e
n
e
u
ro
-
f
u
z
z
y
lo
g
ic
is
p
ro
p
o
se
d
.
T
h
e
re
s
u
lt
s
sh
o
w
th
e
a
b
il
it
y
o
f
sta
ti
c
se
ries
c
o
m
p
e
n
sa
to
r
w
it
h
sto
ra
g
e
e
n
e
rg
y
to
c
o
n
tro
l
th
e
f
lo
w
o
f
p
o
w
e
rs
c
o
m
p
o
n
e
n
ts
"
a
c
ti
v
e
a
n
d
re
a
c
ti
v
e
p
o
w
e
r"
in
th
e
c
o
n
tro
ll
e
d
li
n
e
a
n
d
th
u
s t
h
e
o
v
e
ra
ll
p
o
w
e
r
re
g
u
late
d
b
e
tw
e
e
n
li
n
e
s.
K
ey
w
o
r
d
s
:
A
N
FIS
D
-
q
th
eo
r
y
E
S
F
A
C
T
S
SS
C
Co
p
y
rig
h
t
©
2
0
1
9
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mo
h
a
m
m
ed
Y.
Su
li
m
an
,
C
o
lleg
e
o
f
T
ec
h
n
ical
E
n
g
i
n
ee
r
in
g
,
No
r
th
er
n
T
ec
h
n
ical
U
n
i
v
er
s
it
y
,
Mo
s
u
l,
I
r
aq
.
E
m
ail:
m
o
h
a
m
m
ed
.
y
a
h
y
a
@
n
t
u
.
ed
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
p
o
w
er
f
lo
w
co
n
tr
o
l
i
m
p
o
r
tan
ce
h
as
b
ec
o
m
e
m
o
r
e
ev
id
en
t
w
i
th
d
er
eg
u
latio
n
an
d
co
m
p
e
titi
v
e
en
v
ir
o
n
m
e
n
t
i
n
th
e
p
o
w
er
n
et
w
o
r
k
s
.
Der
eg
u
latio
n
i
s
th
e
o
p
en
in
g
u
p
o
f
a
s
er
v
ice
o
r
p
r
o
d
u
ct
to
co
m
p
etitio
n
.
T
h
is
p
er
m
i
ts
t
h
e
en
d
cu
s
to
m
er
s
to
s
elec
t
th
e
ir
s
er
v
ice
o
f
e
n
e
r
g
y
p
r
o
v
id
er
[
1
]
.
T
h
e
f
lo
w
o
f
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
w
er
in
a
n
in
ter
co
n
n
ec
ted
s
y
s
te
m
,
t
h
at
tr
a
n
s
f
er
th
r
o
u
g
h
t
h
e
tr
a
n
s
m
is
s
io
n
li
n
es
ar
e
g
o
v
er
n
ed
b
y
th
e
m
a
g
n
it
u
d
e
o
f
th
e
s
en
d
i
n
g
an
d
r
ec
eiv
in
g
en
d
v
o
lta
g
es
an
d
p
h
ase
an
g
le
b
et
w
ee
n
t
h
ese
t
w
o
en
d
v
o
lta
g
es
an
d
in
d
u
cta
n
ce
o
f
t
h
e
li
n
e
[
2
]
.
T
h
e
li
m
its
o
f
p
o
w
er
tr
an
s
f
er
in
th
e
tr
a
n
s
m
is
s
io
n
li
n
es
ca
n
b
e
s
p
ec
if
ied
b
y
t
h
r
ee
m
ai
n
asp
ec
ts
[
3
]
:
a.
Un
co
n
tr
o
lled
th
e
le
v
el
o
f
p
o
wer
f
lo
w
.
b.
T
h
e
lev
el
o
f
Stab
ilit
y
a
n
d
t
h
is
is
d
u
e
to
t
h
e
li
m
i
tatio
n
i
m
p
o
s
ed
b
y
t
h
e
r
eg
u
l
at
io
n
s
f
o
r
a
s
ec
u
r
e
a
n
d
th
e
d
y
n
a
m
ical
s
tab
le
o
f
p
o
w
er
tr
an
s
f
er
.
c.
T
h
er
m
al
li
m
i
t d
u
e
to
tr
an
s
m
i
s
s
io
n
lin
e
p
h
y
s
ical
li
m
itatio
n
.
A
t
a
p
ar
ticu
lar
ti
m
e,
t
h
er
e
ar
e
a
ce
r
tain
p
o
w
er
f
lo
w
a
m
o
u
n
t
a
n
d
d
ir
ec
tio
n
t
h
at
n
ee
d
ed
to
b
e
in
cr
ea
s
ed
o
r
d
ec
r
ea
s
ed
to
th
e
d
es
ir
ed
l
ev
el
a
n
d
d
esire
d
p
at
h
s
d
ep
en
d
in
g
o
n
th
e
co
n
s
u
m
er
d
e
m
an
d
.
A
t
t
h
is
in
s
ta
n
ce
,
th
e
ab
ilit
y
f
o
r
co
n
tr
o
llin
g
t
h
e
f
lo
w
o
f
p
o
w
er
is
i
m
p
o
r
ta
n
t.
Usu
all
y
,
th
i
s
is
i
m
p
le
m
en
te
d
b
y
m
ec
h
an
ical
l
y
co
n
tr
o
lled
d
ev
ices,
lik
e
tap
c
h
an
g
er
,
p
h
ase
s
h
i
f
ti
n
g
tr
an
s
f
o
r
m
er
s
,
ca
p
ac
ito
r
s
an
d
in
d
u
cto
r
s
b
an
k
s
.
Ho
w
e
v
er
,
th
e
d
is
ad
v
a
n
tag
e
o
f
th
ese
d
ev
ices
ar
e
s
lo
w
r
esp
o
n
s
e
r
ea
ctio
n
th
at
n
ee
d
ed
d
u
r
in
g
d
is
t
u
r
b
an
ce
s
.
T
h
e
d
ev
elo
p
m
e
n
t
i
n
p
o
w
er
elec
tr
o
n
ics
s
w
i
tch
in
g
d
ev
ice
s
h
av
e
p
r
o
v
id
in
g
a
f
aster
r
es
p
o
n
s
e
co
m
p
ar
ed
to
th
e
co
n
v
e
n
tio
n
al
t
h
e
m
ec
h
an
ic
al
t
y
p
e
s
,
a
n
d
also
n
ee
d
s
le
s
s
m
ai
n
te
n
an
ce
[
4
]
.
T
h
e
F
AC
T
S
(
Flex
ib
le
A
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
ctive
a
n
d
r
ea
ctive
p
o
w
er flo
w
ma
n
a
g
eme
n
t in
p
a
r
a
llel tra
n
s
mis
s
io
n
lin
es
…
(
Mo
h
a
mme
d
Y.
S
u
lima
n
)
4599
T
r
an
s
m
is
s
io
n
S
y
s
te
m
)
d
ev
ice
s
d
ev
elo
p
m
e
n
t
h
a
s
s
tar
ted
w
i
th
t
h
e
g
r
o
w
i
n
g
ca
p
ab
ilit
ies
o
f
p
o
w
er
elec
tr
o
n
ic
d
ev
ices f
o
r
h
ig
h
p
o
w
er
r
ati
n
g
s
b
ee
n
m
ad
e
av
ailab
le
i
n
co
n
v
e
r
ter
s
w
it
h
lo
w
s
w
i
tch
in
g
lo
s
s
e
s
.
F
A
C
T
S
d
ev
ice
s
ca
n
b
e
d
iv
id
e
d
in
to
2
-
g
r
o
u
p
s
w
h
ic
h
ar
e
co
n
v
er
ter
an
d
No
n
-
co
n
v
er
ter
b
as
ed
FAC
T
S
co
n
tr
o
ller
.
No
n
-
C
o
n
v
er
ter
t
y
p
e
is
co
n
tai
n
T
h
y
r
is
to
r
-
co
n
t
r
o
lled
s
er
ies
ca
p
ac
ito
r
(
T
C
SC
)
an
d
Static
Var
c
o
m
p
e
n
s
ato
r
(
S
VC
)
w
h
ic
h
h
av
e
o
f
ab
s
o
r
b
in
g
o
r
g
en
er
ati
n
g
r
ea
cti
v
e
p
o
w
er
w
it
h
u
s
e
t
h
e
ac
r
ea
cto
r
s
an
d
ca
p
ac
ito
r
s
.
W
h
ile
C
o
n
v
er
ter
F
A
C
T
S
g
r
o
u
p
co
n
tain
SS
C
,
ST
A
T
C
OM
,
I
P
FC
an
d
UP
FC
th
e
s
e
d
ev
ice
s
ca
p
ab
ilit
y
o
f
in
d
ep
en
d
e
n
tl
y
c
o
n
tr
o
ls
th
e
r
ea
cti
v
e
an
d
also
a
c
tiv
e
p
o
w
er
f
lo
w
in
t
h
e
li
n
e
[
5
]
.
T
h
e
tr
an
s
m
i
tted
p
o
w
er
th
r
o
u
g
h
t
h
e
li
n
e
is
a
f
u
n
ctio
n
o
f
th
e,
t
h
e
s
e
n
d
in
g
an
d
r
ec
eiv
in
g
en
d
v
o
lta
g
e
s
m
a
g
n
itu
d
e,
p
h
ase
a
n
g
le
(
lo
ad
an
g
le)
an
d
tr
an
s
m
is
s
io
n
lin
e
i
m
p
ed
an
ce
.
T
h
e
d
is
tr
ib
u
te
d
p
o
w
er
i
n
tr
an
s
m
is
s
io
n
li
n
e
s
s
y
s
te
m
d
ep
en
d
s
o
n
th
e
i
m
p
ed
an
ce
o
f
th
e
lin
e
s
i
n
t
h
e
s
y
s
te
m
.
T
h
e
Sta
tic
Ser
ies
C
o
m
p
e
n
s
ato
r
(
SS
C
)
is
a
m
e
m
b
e
r
o
f
2
nd
g
e
n
er
atio
n
o
f
FAC
T
S
w
h
ic
h
u
s
e
th
e
co
n
ce
p
t
o
f
s
y
n
ch
r
o
n
o
u
s
v
o
lta
g
e
s
o
u
r
ce
co
n
v
er
ter
(
VSC
)
f
o
r
g
iv
i
n
g
a
u
n
iq
u
e
l
y
co
m
p
r
e
h
en
s
iv
e
ab
ilit
y
f
o
r
tr
an
s
m
i
s
s
io
n
li
n
e
co
n
tr
o
l
[
6
]
.
T
h
e
SS
C
w
i
th
e
n
er
g
y
s
to
r
ag
e
(
E
S)
is
ab
le
f
o
r
co
n
tr
o
llin
g
s
elec
ti
v
el
y
o
r
s
i
m
u
lta
n
eo
u
s
l
y
all
t
h
e
e
f
f
ec
t
in
g
p
ar
a
m
eter
s
to
th
e
p
o
w
er
f
lo
w
i
n
th
e
tr
a
n
s
m
i
s
s
io
n
s
y
s
te
m
.
A
lter
n
ati
v
el
y
,
SS
C
a
b
le
to
co
n
tr
o
l
in
d
ep
en
d
e
n
tl
y
f
lo
w
o
f
b
o
th
ac
ti
v
e
p
o
w
er
a
n
d
r
ea
ctiv
e
p
o
w
er
in
co
n
tr
o
lled
tr
an
s
m
is
s
io
n
lin
e
[
7
]
.
SS
C
is
s
er
ies
co
n
n
ec
ted
w
it
h
a
tr
an
s
m
i
s
s
io
n
li
n
e
a
n
d
co
n
s
tr
u
ct
o
f
a
t
h
r
e
e
p
h
ase
b
r
id
g
e
in
v
er
ter
w
h
ich
is
co
n
tr
o
lled
b
y
th
e
S
SC
co
n
tr
o
ller
to
in
j
ec
t
a
th
r
ee
-
p
h
ase
s
y
n
c
h
r
o
n
o
u
s
v
o
ltag
e
[
8
]
.
SS
C
o
p
er
ates
b
y
ad
d
in
g
a
co
n
tr
o
lled
v
o
ltag
e
o
f
v
ar
iab
le
m
a
g
n
it
u
d
e
an
d
p
h
ase
an
g
le
at
t
h
e
p
o
w
er
s
y
s
te
m
f
r
eq
u
en
c
y
(
V
pq
)
a
s
s
h
o
w
n
i
n
F
ig
u
r
e
1
.
S
SC
ca
n
o
p
er
ate
in
t
w
o
m
o
d
es
r
ea
ctive
co
m
p
en
s
a
tio
n
an
d
lo
a
d
a
n
g
le
co
n
tr
o
l
d
e
p
en
d
in
g
o
n
t
h
e
r
ef
er
e
n
ce
s
i
g
n
al
li
n
e
cu
r
r
e
n
t
o
r
p
h
ase
v
o
ltag
e
[
9
]
.
I
n
th
i
s
p
ap
er
SS
C
o
p
er
ate
as
a
lo
ad
a
n
g
le
co
n
tr
o
l
b
y
tak
i
n
g
th
e
p
h
a
s
e
v
o
ltag
e
a
s
a
r
e
f
e
r
en
ce
f
o
r
i
n
j
ec
tio
n
,
t
h
is
d
o
n
e
b
y
k
ep
t
th
e
in
j
ec
ted
v
o
ltag
e
p
h
ase
a
n
g
le
(
γ
)
in
q
u
ad
r
atu
r
e
p
h
a
s
e
s
h
i
f
t
w
it
h
t
h
e
s
y
s
te
m
p
h
ase
v
o
lta
g
e
i
n
s
te
ad
o
f
t
h
e
c
u
r
r
en
t.
C
o
n
s
eq
u
en
tl
y
,
S
SC
i
s
co
n
tr
o
l
th
e
p
h
a
s
e
an
g
le
"
lo
ad
an
g
l
e"
b
etw
ee
n
s
e
n
d
in
g
en
d
a
n
d
r
ec
eiv
in
g
e
n
d
s
o
f
tr
an
s
m
is
s
io
n
s
y
s
te
m
.
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
f
lo
w
ca
n
b
e
r
eg
u
la
ted
b
et
w
ee
n
th
e
t
w
o
en
d
s
o
f
tr
an
s
m
is
s
io
n
s
y
s
te
m
b
y
co
n
tr
o
llin
g
SS
C
i
n
j
ec
ted
v
o
ltag
e
m
a
g
n
i
tu
d
e
an
d
p
h
a
s
e
an
g
le:
V
pq
=
|
V
pq
|
<
±
(
1
)
T
r
a
n
s
m
i
s
s
i
o
n
L
i
n
e
V
A
V
B
V
C
P
&
Q
i
s
C
o
n
t
r
o
l
l
e
d
bus
C
o
n
t
r
o
l
l
e
d
TL
Load
r
e
f
q
r
e
f
P
V
ol
t
ag
e
S
ou
r
c
e
I
n
ve
r
t
e
r
E
n
e
r
gy
S
t
or
ag
e
C
on
t
r
ol
p
q
p
V
pq
=
V
pq
s
i
n
(
ω
t
+
γ
)
Fig
u
r
e
1
.
Sch
e
m
atic
d
iag
r
a
m
o
f
SS
C
an
d
th
e
p
h
aso
r
d
iag
r
am
o
f
i
n
j
ec
ted
v
o
ltag
e
Fro
m
F
i
g
u
r
e
1
,
th
e
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
f
lo
w
i
n
co
n
tr
o
lled
tr
an
s
m
is
s
io
n
s
y
s
te
m
a
f
te
r
in
j
ec
t
t
h
e
co
n
tr
o
llab
le
v
o
ltag
e
(
V
pq
):
=
s
in
(
±
)
(
2
)
An
d
:
=
2
−
c
os
(
±
)
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
5
9
8
-
4
6
0
9
4600
W
h
er
e
V
C
is
th
e
co
n
tr
o
lled
b
u
s
v
o
ltag
e
a
n
d
γ
th
e
p
h
ase
an
g
l
e
o
f
th
e
in
j
ec
ted
v
o
ltag
e,
V
B
i
s
th
e
r
ec
eiv
i
n
g
en
d
v
o
ltag
e
a
n
d
X
is
th
e
r
ea
cta
n
ce
o
f
tr
an
s
m
i
s
s
io
n
l
in
e
.
F
ig
u
r
e
2
s
h
o
w
s
,
co
n
n
ec
t
o
f
SS
C
in
s
er
ies
w
it
h
th
e
o
n
e
o
f
p
ar
allel
tr
an
s
m
i
s
s
io
n
.
T
h
e
SS
C
i
n
i
n
j
ec
t
a
co
n
tr
o
llab
le
v
o
lt
ag
e
s
o
t
h
at
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
ad
d
o
r
s
u
b
tr
ac
t
w
it
h
th
e
p
o
w
er
f
lo
w
i
n
th
e
co
n
tr
o
l
tr
an
s
m
i
s
s
io
n
lin
e
an
d
.
T
h
e
r
eg
u
lated
lin
e
p
o
w
e
r
s
ca
n
b
e
ac
h
iev
ed
w
it
h
a
n
y
p
r
o
p
o
r
tio
n
s
w
a
n
ted
.
Lo
a
d
V
B
V
pq
DC
-
L
i
n
k
(
S
t
o
r
a
g
e
E
n
e
r
g
y
)
2
R
2
L
1
R
1
L
V
A
V
C
p
1
&
q
1
p
2
&
q
2
Fig
u
r
e
2
.
I
n
s
er
tin
g
S
SC
w
it
h
S
E
in
tr
an
s
m
i
s
s
io
n
li
n
e
2.
M
O
DE
L
L
I
N
G
AND
CO
N
T
RO
L
SS
C
SS
C
in
j
ec
ts
a
s
in
u
s
o
id
al
co
n
tr
o
llab
le
v
o
lta
g
e
(
d
ep
en
d
in
g
o
n
f
r
eq
u
en
c
y
o
f
s
w
itc
h
i
n
g
d
ev
ices
an
d
co
n
f
i
g
u
r
atio
n
o
f
th
e
i
n
v
er
ter
)
w
it
h
v
ar
iab
le
a
m
p
li
tu
d
e
[
1
0
]
.
SS
C
ab
le
to
o
p
er
ate
in
p
h
ase
s
h
i
f
t
r
eg
u
lato
r
an
d
e
m
u
late
as
a
co
n
tr
o
ller
o
f
p
o
w
er
f
lo
w
[
1
1
]
.
VSI
(
Vo
lta
g
e
So
u
r
ce
I
n
v
er
ter
)
is
S
SC
h
ea
r
t
th
a
t
is
f
ee
d
ed
f
r
o
m
an
en
er
g
y
s
to
r
ag
e
"
ex
ter
n
al
D
C
lin
k
"
,
th
e
SS
C
v
o
ltag
e
V
pq
h
a
s
2
-
p
ar
a
m
eter
s
t
h
e
a
m
p
lit
u
d
e
(
0
<V
pq
<V
pqm
ax
a
n
d
p
h
ase
an
g
le
(
0
<γ
<3
6
0
0
)
as sh
o
w
n
i
n
F
i
g
u
r
e
3
.
A
d
d
itio
n
ac
t
iv
e
an
d
r
ea
ctiv
e
p
o
w
er
.
v
C
v
B
v
A
v
pq
δ
γ
γ
Fig
u
r
e
3
.
Vec
to
r
d
iag
r
am
=
s
i
n
(
)
(
4
)
=
−
(
)
(
5
)
T
h
e
to
tal
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
in
tr
a
n
s
m
i
s
s
io
n
l
in
e
2
ar
e:
=
2
±
(
6
)
=
2
±
(
7
)
Dep
en
d
in
g
o
n
(
6
)
an
d
(
7
)
t
h
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
ca
n
b
e
r
e
g
u
lated
b
y
ad
d
in
g
o
r
s
u
b
tr
ac
tin
g
th
e
in
j
ec
tio
n
p
o
w
er
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
ctive
a
n
d
r
ea
ctive
p
o
w
er flo
w
ma
n
a
g
eme
n
t in
p
a
r
a
llel tra
n
s
mis
s
io
n
lin
es
…
(
Mo
h
a
mme
d
Y.
S
u
lima
n
)
4601
3.
ACTI
VE
AN
D
RE
A
CT
I
VE
P
O
WE
R
M
E
ASURIM
E
NT
D
-
q
t
h
eo
r
y
w
a
s
ap
p
lied
f
o
r
m
ea
s
u
r
in
g
p
o
w
er
co
m
p
o
n
en
t
s
(
ac
tiv
e
p
o
w
er
&
r
ea
ctiv
e
p
o
w
er
)
.
I
t
i
s
b
ased
o
n
"
ti
m
e
-
d
o
m
a
in
"
also
v
a
lid
f
o
r
o
p
er
atin
g
s
y
s
te
m
i
n
"
s
tead
y
-
s
tate
"
'
an
d
in
"
tr
an
s
ien
t
s
tate
"
,
an
d
ca
n
ap
p
lied
f
o
r
g
en
er
ic
w
a
v
e
f
o
r
m
s
o
f
c
u
r
r
en
t
a
n
d
v
o
lta
g
e
i
n
p
o
w
er
s
y
s
te
m
[
1
2
]
.
T
h
e
s
i
m
p
li
cit
y
ca
lc
u
latio
n
s
i
s
an
o
th
er
ad
v
a
n
tag
e
o
f
t
h
i
s
th
e
o
r
y
,
w
h
ich
i
n
cl
u
d
e
alg
eb
r
aic
ca
lcu
latio
n
in
ex
c
ep
t
t
h
e
r
eq
u
ir
ed
f
o
r
s
ep
ar
atin
g
th
e
alter
n
ated
an
d
m
ea
n
v
a
lu
es
o
f
p
o
w
er
co
m
p
o
n
e
n
ts
ca
lcu
latio
n
[
1
3
]
.
T
h
e
d
-
q
t
h
eo
r
y
i
m
p
le
m
e
n
ts
“
p
ar
k
tr
an
s
f
o
r
m
atio
n
”
to
tr
an
s
f
o
r
m
t
h
e
abc
co
o
r
d
in
ates
(
s
tati
o
n
ar
y
co
o
r
d
in
ate)
to
(
th
e
r
o
tatin
g
co
o
r
d
in
ates)
o
r
dq
co
o
r
d
in
at
es
[
1
4
]
.
T
h
ese
tr
a
n
s
f
o
r
m
atio
n
is
u
ti
lized
f
o
r
cu
r
r
en
ts
an
d
v
o
lta
g
es
in
ti
m
e
d
o
m
ai
n
as
a
s
tan
d
ar
d
f
r
a
m
e
t
h
i
s
m
ea
n
(
v
a,
vb
a
n
d
v
c)
is
as f
o
llo
w
s
:
[
0
]
=
2
3
[
c
os
(
∅
)
c
os
(
∅
−
2
3
)
c
os
(
∅
+
2
3
)
−
s
in
(
∅
)
−
s
in
(
∅
−
2
3
)
−
(
∅
+
2
3
)
1
2
1
2
1
2
]
[
]
(
8
)
[
0
]
=
2
3
[
c
os
(
∅
)
c
os
(
∅
−
2
3
)
c
os
(
∅
+
2
3
)
−
s
in
(
∅
)
−
s
in
(
∅
−
2
3
)
−
(
∅
+
2
3
)
1
2
1
2
1
2
]
[
]
(
9
)
∅
=
(
+
)
(
1
0
)
W
h
er
e
(
∅
)
is
t
h
e
p
h
a
s
e
s
h
i
f
t b
et
wee
n
t
h
e
r
o
tatin
g
a
n
d
f
i
x
ed
co
o
r
d
in
ates i
n
ti
m
e
d
o
m
ain
,
a
ls
o
(
θ)
is
p
h
ase
s
h
if
t
b
et
w
ee
n
th
e
v
o
ltag
e
a
n
d
lo
ad
cu
r
r
en
t [
1
5
]
.
T
w
o
p
o
w
er
co
m
p
o
n
en
ts
co
m
p
e
n
s
ated
ca
n
b
e
ca
lcu
lated
b
y
:
=
+
(
1
1
)
=
−
(
1
2
)
4.
CO
NT
RO
L
SCH
E
M
E
O
F
CO
M
P
E
NSAT
O
R
Fig
u
r
e
4
s
h
o
w
s
th
e
co
n
tr
o
l
s
ch
e
m
e
o
f
co
m
p
en
s
a
to
r
.
T
h
e
v
o
ltag
e
s
an
d
cu
r
r
en
t
s
(
th
r
ee
p
h
ase)
ar
e
m
ea
s
u
r
ed
an
d
f
o
r
eli
m
in
a
tin
g
th
e
n
o
is
e
"
h
i
g
h
f
r
eq
u
en
c
y
co
m
p
o
n
en
ts
"
th
e
in
p
u
ts
ar
e
f
il
te
r
ed
th
en
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
ca
lc
u
la
te
d
u
s
i
n
g
p
ar
k
tr
an
s
f
o
r
m
atio
n
(
8
)
to
(
12
)
.
Fro
m
t
h
e
s
y
s
te
m
.
T
h
ese
m
ea
s
u
r
ed
s
ig
n
al
s
in
(
1
)
an
d
(
2
)
w
o
r
k
a
s
in
p
u
t
s
to
th
e
clo
s
ed
lo
o
p
co
n
tr
o
l
(
as
a
f
ee
d
b
ac
k
)
.
T
h
e
d
esire
d
r
ef
er
en
ce
s
v
al
u
e
s
o
f
ac
ti
v
e
an
d
r
ea
cti
v
e
p
o
w
er
"
p
ref
an
d
q
ref
"
ar
e
co
m
p
ar
ed
w
ith
t
h
e
ca
lc
u
lated
v
al
u
es
o
f
m
ea
s
u
r
ed
v
a
lu
e
s
f
o
r
g
en
er
ati
n
g
er
r
o
r
s
ig
n
al
s
"
E
r
r
o
r
p
an
d
E
r
r
o
r
q
"
.
T
h
ese
s
ig
n
als ar
e
p
r
o
ce
s
s
ed
in
th
e
co
n
tr
o
ller
wh
er
e:
=
−
(
1
3
)
=
−
(
1
4
)
i
a
i
b
i
c
v
a
v
b
v
c
q
r
e
f
q
-
N
u
r
o
-
F
u
z
z
y
L
og
i
c
C
on
t
r
ol
P
L
L
P
ar
k
T
r
an
s
f
or
m
at
i
on
C
al
c
u
l
at
e
V
d
,
V
q
an
d
I
d
,
Iq
L
o
w
P
as
s
F
i
l
t
r
v
d
v
q
i
d
i
q
φ
A
c
t
i
ve
an
d
R
e
ac
t
i
ve
P
ow
e
r
c
al
c
u
l
at
i
on
p
-
p
r
e
f
+
γ
S
i
gn
o
f
Δ
p
a
n
d
Δ
q
m
ψ
S
P
WM
Fig
u
r
e
4
.
B
lo
ck
d
iag
r
a
m
f
o
r
S
C
co
n
tr
o
l s
y
s
te
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
5
9
8
-
4
6
0
9
4602
5.
NE
URO
-
F
U
Z
Z
Y
CO
N
T
RO
L
DE
SI
G
N
Neu
r
o
-
f
u
zz
y
co
n
tr
o
ller
ar
e
ad
eq
u
ate
to
u
n
u
n
ce
r
tai
n
s
y
s
te
m
,
esp
ec
iall
y
to
th
e
s
y
s
te
m
w
it
h
m
at
h
e
m
a
tical
m
o
d
el
d
i
f
f
ic
u
lt
to
d
er
iv
e.
Neu
r
o
-
f
u
zz
y
lo
g
ic
p
lay
an
i
m
p
o
r
tan
t
f
u
n
ctio
n
i
n
m
a
n
y
ap
p
licatio
n
s
esp
e
ciall
y
t
h
e
p
r
ac
tical
[
1
6
]
.
T
ak
ag
i
-
S
u
g
e
n
o
“
T
S
"
ch
o
o
s
e
in
th
i
s
s
tu
d
y
a
s
in
f
er
e
n
ce
m
ec
h
a
n
is
m
s
[
1
7
]
.
A
N
N
"
T
h
e
A
r
ti
f
icia
l
Ne
u
r
al
Net
w
o
r
k
"
is
ap
p
lied
f
o
r
tu
n
i
n
g
t
h
e
T
S
-
co
n
tr
o
ller
m
e
m
b
er
s
h
ip
f
u
n
c
tio
n
s
.
T
S
t
y
p
e
h
av
e
v
ar
iab
le
g
ai
n
"
n
o
n
-
l
in
ea
r
g
ai
n
"
.
T
S
ty
p
e
p
r
o
v
id
e
a
wid
e
g
ai
n
v
ar
iatio
n
s
[
1
8
]
.
T
h
e
u
s
i
n
g
o
f
A
NN
f
o
r
ad
ap
tin
g
t
h
e
f
u
zz
y
s
y
s
te
m
p
ar
a
m
eter
s
w
h
ic
h
ca
n
ac
h
iev
e
d
a
b
etter
r
esp
o
n
s
.
C
o
m
b
i
n
e
th
e
f
u
zz
y
s
p
ec
i
f
i
c
ap
p
r
o
ac
h
w
it
h
ad
ap
ti
v
e
lear
n
i
n
g
,
th
i
s
t
y
p
e
o
f
co
n
tr
o
l
ca
n
b
e
tr
ain
ed
ea
s
il
y
an
d
d
o
n
’
t
n
ee
d
f
o
r
a
b
ig
ex
p
er
t
f
o
r
k
n
o
w
led
g
e
as
r
eq
u
ir
ed
in
th
e
co
n
v
en
tio
n
al
Ma
m
d
a
n
i
-
f
u
zz
y
lo
g
ic
[
1
9
]
.
B
y
u
s
i
n
g
A
NN
lear
n
in
g
alg
o
r
it
h
m
th
e
r
u
le
-
b
ase
ca
n
b
e
r
ed
u
ce
d
.
T
h
e
p
ar
am
e
ter
s
o
f
i
n
p
u
t
an
d
o
u
tp
u
t
MF
"
m
e
m
b
er
s
h
ip
f
u
n
ct
io
n
s
"
ar
e
to
b
e
s
p
ec
if
ied
t
h
r
o
u
g
h
t
h
e
p
er
io
d
o
f
tr
ai
n
i
n
g
.
A
NFI
S
co
n
tr
o
ller
d
esig
n
ed
co
n
s
is
ts
o
f
5
-
la
y
er
s
,
w
h
ic
h
i
n
ea
c
h
la
y
er
h
as
co
n
s
tan
t
n
o
d
es
(
n
o
n
ee
d
to
tu
n
e)
o
r
v
ar
iab
le
n
o
d
e
(
n
ee
d
to
tu
n
e)
th
r
o
u
g
h
tr
ain
i
n
g
p
er
io
d
.
T
h
e
5
-
lay
er
s
o
u
tp
u
ts
e
m
u
la
te
A
N
FIS
d
esi
g
n
p
r
o
ce
d
u
r
e
r
ef
er
r
in
g
to
[
2
0
]
.
T
h
e
ad
v
an
ta
g
e
o
f
u
s
i
n
g
AN
N
alg
o
r
it
h
m
i
s
f
o
r
ad
j
u
s
tin
g
th
e
p
ar
a
m
eter
s
o
f
th
e
m
e
m
b
er
s
h
ip
f
u
n
ct
io
n
s
o
f
o
u
tp
u
t
an
d
i
n
p
u
t
s
o
t
h
at
t
h
e
o
u
t
p
u
t
o
f
Ne
u
r
o
-
f
u
zz
y
b
est
m
atc
h
i
n
g
t
h
e
d
ata
o
f
tr
ai
n
in
g
.
A
h
y
b
r
id
lear
n
i
n
g
"
L
ea
s
e
Sq
u
ar
es
E
s
ti
m
ate
-
L
SE
a
n
d
Gr
ad
ien
t
De
s
ce
n
t
-
GD"
is
u
s
ed
to
id
en
tify
t
h
e
p
ar
am
eter
s
n
et
w
o
r
k
.
I
n
t
h
is
s
tu
d
y
t
h
e
i
n
p
u
ts
ar
e
s
p
lit
to
9
tr
ap
e
zo
id
al
MF
"
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
w
it
h
5
0
%
o
v
er
lap
p
in
g
"
,
s
o
,
t
h
e
t
w
o
v
ec
to
r
in
p
u
ts
an
"
81
-
co
n
tr
o
l
r
u
le
"
r
esu
lta
n
t
li
n
ea
r
f
u
n
ctio
n
s
r
eq
u
ir
ed
to
b
e
d
eter
m
i
n
ed
.
Valid
atio
n
te
s
t
s
h
o
w
n
in
Fi
g
u
r
e
5
.
T
o
tu
n
n
e
t
h
e
r
u
le
s
o
f
T
S
u
s
i
n
g
A
NN
.
T
h
e
v
ec
to
r
s
in
p
u
ts
ar
e
"
E
q
a
n
d
E
p
"
,
th
e
o
u
tp
u
t
m
"
m
o
d
u
l
atio
n
in
d
ex
"
.
Fig
u
r
e
6
an
d
7
s
h
o
w
th
e
v
a
lid
atio
n
s
u
r
f
ac
e
o
f
F
u
zz
y
lo
g
ic
s
y
s
te
m
an
d
th
e
F
u
zz
y
lo
g
ic
r
u
le
s
.
Fig
u
r
e
5
.
Fu
zz
y
lo
g
ic
v
a
lid
ati
o
n
test
Fig
u
r
e
6
.
Neu
r
o
-
f
u
zz
y
lo
g
ic
v
alid
atio
n
s
u
r
f
ac
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
ctive
a
n
d
r
ea
ctive
p
o
w
er flo
w
ma
n
a
g
eme
n
t in
p
a
r
a
llel tra
n
s
mis
s
io
n
lin
es
…
(
Mo
h
a
mme
d
Y.
S
u
lima
n
)
4603
Fig
u
r
e
7
.
Neu
r
o
-
f
u
zz
y
lo
g
ic
r
u
les
6.
SI
M
UL
AT
I
O
N
ST
U
DY
AN
D
RE
SU
L
T
S
T
h
e
T
h
e
s
y
s
te
m
s
t
u
d
y
w
as
c
o
n
s
is
ts
o
f
d
is
tr
ib
u
t
io
n
f
ee
d
er
w
it
h
"
2
-
b
r
an
ch
es
a
n
d
SS
C
"
in
s
tal
led
in
T
r
an
s
m
is
s
io
n
lin
-
2
a
s
s
h
o
wn
i
n
F
ig
u
r
e
8
,
f
o
r
co
n
tr
o
li
n
g
t
h
e
f
lo
w
o
f
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
s
.
T
h
e
co
m
p
e
n
s
ato
r
i
s
p
r
o
v
id
ed
w
it
h
a
DC
v
o
lta
g
e
s
o
u
r
ce
w
h
ich
h
elp
s
i
n
ab
s
o
r
b
in
g
o
r
f
ee
d
in
g
t
h
e
r
ea
cti
v
e
o
r
ac
tiv
e
p
o
w
er
.
T
h
e
s
i
m
u
latio
n
s
tar
t
b
y
s
tep
ch
an
g
i
n
g
t
h
e
lo
ad
an
d
s
en
s
ed
to
tal
cu
r
r
en
t
an
d
th
e
cu
r
r
en
t
in
b
o
th
b
r
an
ch
es
b
ef
o
r
e
co
m
p
en
s
a
tio
n
.
C
o
m
p
en
s
at
io
n
p
r
o
ce
s
s
d
o
n
e
w
it
h
"
in
j
ec
t
V
pq
co
n
tr
o
llab
le
v
o
ltag
e"
w
h
ic
h
w
as
in
m
a
k
e
i
n
q
u
ad
r
atu
r
e
to
th
e
p
h
ase
v
o
ltag
e.
Fig
u
r
e
8
.
T
h
e
test
m
o
d
el
First
t
h
e
te
s
t
d
o
n
e
b
y
"
o
n
e
s
tep
ch
an
g
e
"
in
th
e
lo
ad
,
b
ef
o
r
e
0
.
7
s
ec
o
n
d
th
e
p
o
w
er
in
u
n
b
alan
c
e
b
et
w
ee
n
t
h
e
p
ar
allel
tr
a
n
s
m
i
s
s
io
n
li
n
e
s
at
t=0
.
7
s
ec
o
n
d
SS
C
i
n
j
ec
t
th
e
co
n
tr
o
llab
le
v
o
lt
ag
e
t
h
e
co
n
tr
o
llab
le
in
j
ec
ted
v
o
ltag
e
s
h
o
w
n
i
n
F
ig
u
r
e
9
.
T
h
e
lin
e
c
u
r
r
en
t
o
f
t
h
e
p
ar
allel
tr
an
s
m
i
s
s
io
n
li
n
es
s
h
o
w
n
i
n
F
i
g
u
r
e
1
0
,
th
e
r
m
s
v
al
u
es
o
f
b
o
th
cu
r
r
e
n
t
s
s
h
o
w
n
in
F
i
g
u
r
e
1
1
.
Fig
u
r
e
1
2
an
d
1
3
s
h
o
w
t
h
e
c
h
a
n
g
e
in
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
w
er
f
lo
w
af
ter
in
j
ec
tio
n
r
es
p
ec
tiv
el
y
.
Fi
g
u
r
e
1
4
a
n
d
1
5
s
h
o
w
t
h
e
c
h
a
n
g
e
in
th
e
v
o
lta
g
e
a
cr
o
s
s
th
e
r
ea
ctan
c
e
o
f
tr
an
s
m
is
s
io
n
l
in
e
V
TL
a
f
ter
in
j
ec
ted
th
e
co
n
tr
o
lled
v
o
lta
g
e
V
pq
,
th
e
r
e
s
u
l
ts
s
h
o
w
th
e
d
ec
r
ea
s
e
th
e
v
o
lta
g
e
V
TL
w
i
th
t
h
e
V
pq
a
n
d
th
e
n
i
n
cr
ea
s
e
in
c
u
r
r
en
t.
Fi
g
u
r
e
1
6
an
d
1
7
s
h
o
w
t
h
e
F
FT
an
al
y
s
i
s
o
f
t
h
e
in
j
ec
ted
v
o
lta
g
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
5
9
8
-
4
6
0
9
4604
V
pq
an
d
th
e
lo
ad
v
o
ltag
e
a
f
ter
in
j
ec
tio
n
,
its
clea
r
f
r
o
m
t
h
e
r
e
s
u
lt
th
at
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
T
HD
o
f
V
pq
w
a
s
3
.
1
1
%
an
d
th
e
lo
ad
v
o
lta
g
e
w
a
s
0
.
1
5
%.
Fig
u
r
e
1
8
s
h
o
w
T
h
e
C
h
ar
a
cter
is
tic
o
f
th
e
en
er
g
y
s
to
r
ag
e
b
atter
y
m
o
d
el,
d
ep
en
d
in
g
o
n
t
h
e
co
n
t
r
o
l
s
y
s
te
m
in
F
i
g
u
r
e
4
,
th
e
p
o
w
er
is
ta
k
en
f
r
o
m
E
S
an
d
co
m
p
e
n
s
ate
th
e
p
o
w
er
s
o
n
th
e
tr
an
s
m
i
s
s
io
n
lin
e
.
Fi
g
u
r
e
1
9
s
h
o
w
s
t
h
e
s
tep
ch
a
n
g
e
r
esp
o
n
s
e
o
f
th
e
s
y
s
te
m
to
t
h
e
"
ac
tiv
e
p
o
w
er
"
.
Fro
m
th
e
f
ig
u
r
e
it
is
clea
r
th
a
t
th
e
n
e
w
co
n
tr
o
ller
d
esig
n
(
Nu
r
o
-
F
u
zz
y
co
n
tr
o
ller
)
h
as
a
"
s
m
o
o
t
h
er
r
esp
o
n
s
e
"
an
d
also
f
as
ter
th
a
n
th
e
co
n
v
e
n
tio
n
al
"
P
I
co
n
tr
o
ller
"
in
r
ea
c
h
es t
h
e
s
tead
y
s
tate.
Fig
u
r
e
9
.
T
h
e
s
i
m
u
la
tio
n
tes
t
(
a)
(
b
)
Fig
u
r
e
1
0
.
T
h
e
cu
r
r
en
ts
b
ef
o
r
e
an
d
af
ter
co
m
p
en
s
atio
n
,
(
a)
li
n
e
cu
r
r
en
t
s
(
b
)
th
e
zo
o
m
in
g
i
n
0
.
6
4
0
.
6
6
0
.
6
8
0
.
7
0
.
7
2
0
.
7
4
0
.
7
6
0
.
7
8
0
.
8
0
.
8
2
-3
-2
-1
0
1
2
3
T
i
m
e
i
n
s
e
c
o
n
d
s
V
o
l
t
a
g
e
i
n
P
U
P
h
a
s
e
v
o
l
t
a
g
e
(
1
/
1
0
0
)
I
n
j
e
c
t
e
d
v
o
l
t
a
g
e
(
1
/
1
0
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
1
.
6
1
.
8
-
1
.
5
-1
-
0
.
5
0
0
.
5
1
1
.
5
T
i
m
e
i
n
s
e
c
o
n
d
s
L
i
n
e
c
u
r
r
e
n
t
i
n
P
U
T
h
e
c
u
r
r
e
n
t
i
n
T
L
1
T
h
e
c
u
r
r
e
n
t
i
n
T
L
2
0
.
5
5
0
.
6
0
.
6
5
0
.
7
0
.
7
5
0
.
8
0
.
8
5
0
.
9
-1
-
0
.
5
0
0
.
5
1
T
i
m
e
i
n
s
e
c
o
n
d
s
L
i
n
e
c
u
r
r
e
n
t
i
n
P
U
T
h
e
c
u
r
r
e
n
t
i
n
T
L
1
T
h
e
c
u
r
r
e
n
t
i
n
T
L
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
ctive
a
n
d
r
ea
ctive
p
o
w
er flo
w
ma
n
a
g
eme
n
t in
p
a
r
a
llel tra
n
s
mis
s
io
n
lin
es
…
(
Mo
h
a
mme
d
Y.
S
u
lima
n
)
4605
Fig
u
r
e
1
1
.
T
h
e
r
m
s
o
f
t
h
e
li
n
e
cu
r
r
en
ts
Fig
u
r
e
1
2
.
T
h
e
ac
tiv
e
p
o
w
er
Fig
u
r
e
1
3
.
T
h
e
r
ea
ctiv
e
p
o
w
er
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
1
.
6
1
.
8
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
T
i
m
e
i
n
s
e
c
o
n
d
s
R
m
s
c
u
r
r
e
n
t
s
i
n
P
U
C
u
r
r
e
n
t
i
n
T
L
1
C
u
r
r
e
n
t
i
n
T
l
2
L
o
a
d
C
u
r
r
n
e
t
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
1
.
6
1
.
8
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
1
.
1
1
.
2
T
i
m
e
i
n
s
e
c
o
n
d
s
A
c
t
i
v
e
p
o
w
e
r
i
n
P
U
P
o
w
e
r
i
n
T
L
1
P
o
w
e
r
i
n
T
L
2
T
o
t
a
l
P
o
w
e
r
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
1
.
6
1
.
8
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
1
.
1
T
i
m
e
i
n
s
e
c
o
n
d
s
R
e
a
c
t
i
v
e
p
o
w
e
r
i
n
P
U
R
e
a
c
t
i
v
e
p
o
w
e
r
i
n
T
L
1
R
e
a
c
t
i
v
e
p
o
w
e
r
i
n
T
L
2
T
o
t
a
l
r
e
a
c
t
i
v
e
p
o
w
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
5
9
8
-
4
6
0
9
4606
(
a)
(
b)
Fig
u
r
e
1
4
.
T
h
e
v
o
ltag
e
ac
r
o
s
s
th
e
tr
an
s
m
is
s
io
n
li
n
e
v
er
s
u
s
in
j
ec
ted
v
o
ltag
e
(
a)
V
TL
an
d
V
pq
(
b
)
T
h
e
zo
o
m
i
n
g
i
n
Fig
u
r
e
1
5
.
T
h
e
r
m
s
o
f
v
o
ltag
e
ac
r
o
s
s
th
e
tr
an
s
m
is
s
io
n
li
n
e
an
d
th
e
in
j
ec
ted
v
o
ltag
e
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
1
.
6
1
.
8
2
-
1
.
5
-1
-
0
.
5
0
0
.
5
1
1
.
5
T
i
m
e
i
n
s
e
c
o
n
d
s
V
o
l
t
a
g
e
i
n
P
U
I
n
j
e
c
t
e
d
v
o
l
t
a
g
e
V
o
l
t
a
g
e
a
c
r
o
s
s
T
L
2
0
.
5
0
.
5
5
0
.
6
0
.
6
5
0
.
7
0
.
7
5
0
.
8
0
.
8
5
0
.
9
0
.
9
5
1
-
1
.
5
-1
-
0
.
5
0
0
.
5
1
T
i
m
e
i
n
s
e
c
o
n
d
s
V
o
l
t
a
g
e
i
n
P
U
I
n
j
e
c
t
e
d
v
o
l
t
a
g
e
V
o
l
t
a
g
e
a
c
r
o
s
s
T
L
2
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
1
.
6
1
.
8
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
T
i
m
e
i
n
s
e
c
o
n
d
s
V
o
l
t
a
g
e
i
n
P
U
I
n
j
e
c
t
e
d
v
o
l
t
a
g
e
V
o
l
t
a
g
e
a
c
r
o
s
s
T
L
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
ctive
a
n
d
r
ea
ctive
p
o
w
er flo
w
ma
n
a
g
eme
n
t in
p
a
r
a
llel tra
n
s
mis
s
io
n
lin
es
…
(
Mo
h
a
mme
d
Y.
S
u
lima
n
)
4607
Fig
u
r
e
1
6
.
T
h
e
FF
T
an
al
y
s
i
s
o
f
th
e
i
n
j
ec
ted
v
o
ltag
e
Fig
u
r
e
1
7
.
T
h
e
FF
T
an
al
y
s
i
s
o
f
th
e
lo
ad
v
o
lta
g
e
Fig
u
r
e
1
8
.
T
h
e
ch
ar
ac
ter
is
tic
o
f
th
e
e
n
er
g
y
s
to
r
ag
e
m
o
d
el
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
-
4
0
-
2
0
0
20
40
S
e
l
e
c
t
e
d
s
i
g
n
a
l
:
3
2
.
3
c
y
c
l
e
s
.
FF
T
w
i
n
d
o
w
(
i
n
r
e
d
)
:
1
c
y
c
l
e
s
T
i
m
e
(
s
)
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
1
.
4
Fr
e
q
u
e
n
c
y
(
H
z
)
Fu
n
d
a
m
e
n
t
a
l
(
5
0
H
z
)
=
3
0
.
7
7
,
T
H
D
=
3
.
1
1
%
M
a
g
(
%
o
f
Fu
n
d
a
m
e
n
t
a
l
)
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
-
2
0
0
0
200
S
e
l
e
c
t
e
d
s
i
g
n
a
l
:
3
2
.
3
c
y
c
l
e
s
.
FF
T
w
i
n
d
o
w
(
i
n
r
e
d
)
:
1
c
y
c
l
e
s
T
i
m
e
(
s
)
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0
0
.
0
1
0
.
0
2
0
.
0
3
0
.
0
4
0
.
0
5
0
.
0
6
0
.
0
7
Fr
e
q
u
e
n
c
y
(
H
z
)
Fu
n
d
a
m
e
n
t
a
l
(
5
0
H
z
)
=
3
1
2
.
3
,
T
H
D
=
0
.
1
5
%
M
a
g
(
%
o
f
Fu
n
d
a
m
e
n
t
a
l
)
0
1
2
3
4
5
6
7
8
0
.
9
1
1
.
1
1
.
2
1
.
3
1
.
4
1
.
5
N
o
m
i
n
a
l
C
u
r
r
e
n
t
D
i
s
c
h
a
r
g
e
C
h
a
r
a
c
t
e
r
i
s
t
i
c
a
t
0
.
2
C
(
0
.
3
A
)
T
i
m
e
i
n
h
o
u
r
s
T
e
r
m
i
n
a
l
V
o
l
t
a
g
e
D
i
s
c
h
a
r
g
e
c
u
r
v
e
N
o
m
i
n
a
l
a
r
e
a
E
x
p
o
n
e
n
t
i
a
l
a
r
e
a
0
10
20
30
40
50
60
70
80
90
1
1
.
1
1
.
2
1
.
3
1
.
4
1
.
5
T
i
m
e
i
n
M
i
n
u
t
e
s
T
e
r
m
i
n
a
l
V
o
l
t
a
g
e
E
0
=
1
.
3
2
,
R
=
0
.
0
1
,
K
=
0
.
0
0
7
,
A
=
0
.
2
,
B
=
1
1
1
.
5
A
3
A
Evaluation Warning : The document was created with Spire.PDF for Python.