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m
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w
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p
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tio
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[
1
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-
s
w
itc
h
M
L
I
to
p
o
lo
g
y
i
s
p
r
o
p
o
s
ed
.
T
h
is
in
v
er
ter
is
u
s
ed
as
a
s
h
u
n
t
ac
ti
v
e
p
o
w
er
f
il
ter
to
co
m
p
en
s
a
te
h
ar
m
o
n
ic
cu
r
r
en
ts
g
e
n
er
a
ted
b
y
n
o
n
l
in
ea
r
lo
a
d
s
an
d
at
t
h
e
s
a
m
e
ti
m
e
to
co
m
p
e
n
s
ate
t
h
e
r
ea
ctiv
e
p
o
w
er
.
T
h
e
p
r
o
p
o
s
ed
to
p
o
l
o
g
y
co
n
s
i
s
ts
o
f
f
o
u
r
DC
s
o
u
r
c
es
an
d
b
u
ilt
o
f
th
r
ee
id
en
tical
s
tr
u
ct
u
r
es,
ea
ch
o
n
e
is
p
lace
d
o
n
a
s
ep
ar
ate
p
h
ases
w
ith
a
r
ed
u
ce
d
n
u
m
b
er
o
f
p
o
w
er
s
w
itc
h
es
(
3
0
I
GB
T
)
r
elativ
e
to
co
n
v
en
tio
n
a
l
s
y
s
te
m
s
(
4
8
I
GB
T
)
.
T
h
e
ac
ti
v
e
f
ilter
co
n
tr
o
l
u
s
ed
in
t
h
is
s
t
u
d
y
i
s
d
i
v
id
ed
in
to
t
w
o
p
ar
ts
.
T
h
e
f
ir
s
t
d
ea
ls
w
it
h
t
h
e
h
ar
m
o
n
ic
is
o
lato
r
b
ased
o
n
th
e
in
s
ta
n
tan
eo
u
s
p
o
w
er
t
h
eo
r
y
(
pq
th
eo
r
y
)
,
[
2
1
]
-
[
2
2
]
in
o
r
d
er
to
ex
tr
ac
t
h
ar
m
o
n
ic
c
u
r
r
en
t
s
.
T
h
e
s
ec
o
n
d
p
ar
t
is
d
ev
o
ted
to
t
h
e
lo
g
ic
s
i
g
n
al
s
g
en
er
at
io
n
to
co
n
tr
o
l
th
e
f
il
ter
s
w
itc
h
es
u
s
i
n
g
t
h
e
P
u
ls
e
W
id
th
Mo
d
u
lati
o
n
(
P
W
M)
tech
n
iq
u
e.
T
h
is
t
y
p
e
o
f
co
n
tr
o
l
allo
w
s
th
e
in
j
ec
tio
n
o
f
a
co
m
p
e
n
s
at
i
o
n
cu
r
r
en
t
eq
u
al
to
t
h
e
r
ef
er
e
n
ce
o
n
e
to
o
b
tain
a
s
in
u
s
o
id
al
f
o
r
m
o
f
t
h
e
s
u
p
p
l
y
cu
r
r
en
t
i
n
to
th
e
n
et
w
o
r
k
.
T
h
e
co
n
tr
o
l
o
f
th
e
DC
b
u
s
v
o
lta
g
e
is
p
er
f
o
r
m
ed
b
y
a
P
r
o
p
o
r
t
io
n
al
I
n
te
g
r
al
(
P
I
)
r
eg
u
lato
r
u
s
ed
to
co
r
r
ec
t th
e
ap
p
r
o
p
r
iate
er
r
o
r
v
alu
e
b
et
w
ee
n
th
e
r
e
f
er
en
ce
a
n
d
th
e
i
n
j
ec
ted
cu
r
r
en
ts
.
T
h
e
s
i
m
u
latio
n
te
s
t
s
w
er
e
p
er
f
o
r
m
ed
in
Ma
tlab
/Si
m
u
li
n
k
e
n
v
ir
o
n
m
e
n
t.
T
h
e
r
esu
l
ts
s
h
o
wed
th
at
th
e
f
ilter
i
n
g
p
er
f
o
r
m
an
ce
s
h
a
v
e
b
ee
n
w
ell
i
m
p
r
o
v
ed
u
s
i
n
g
t
h
e
p
r
o
p
o
s
ed
n
in
e
lev
el
M
L
I
to
p
o
lo
g
y
w
i
th
te
n
-
s
w
itc
h
.
T
h
is
i
m
p
r
o
v
e
m
e
n
t
ap
p
ea
r
s
in
th
e
r
e
m
ar
k
ab
le
r
ed
u
ctio
n
o
f
t
h
e
h
ar
m
o
n
ic
cu
r
r
en
t
s
an
d
in
t
h
e
w
a
v
e
f
o
r
m
o
f
th
e
s
u
p
p
l
y
cu
r
r
e
n
t
w
h
ic
h
b
ec
o
m
e
s
p
u
r
el
y
s
i
n
u
s
o
id
al
an
d
in
p
h
ase
w
it
h
th
e
v
o
ltag
e.
T
h
e
s
i
m
u
latio
n
s
h
o
w
s
also
th
at
t
h
e
th
r
ee
p
h
a
s
e
v
o
lta
g
es
h
av
e
th
e
s
a
m
e
a
m
p
lit
u
d
es.
2.
NINE
L
E
VE
L
T
E
N
-
SW
I
T
C
H
T
O
P
O
L
O
G
Y
D
E
SC
RIPT
I
O
N
T
h
e
lo
ca
tio
n
o
f
th
e
n
e
w
ac
ti
v
e
p
o
w
er
f
ilter
p
r
o
p
o
s
ed
in
t
h
is
w
o
r
k
i
s
il
lu
s
tr
ated
i
n
Fi
g
u
r
e
1
.
I
t
i
s
p
lace
d
in
p
ar
allel
to
th
e
n
o
n
li
n
ea
r
lo
ad
an
d
th
e
t
h
r
ee
-
p
h
a
s
e
s
u
p
p
l
y
s
o
u
r
ce
.
I
t i
s
p
laca
ted
a
s
clo
s
e
as p
o
s
s
ib
le
to
th
e
n
o
n
li
n
ea
r
lo
ad
in
o
r
d
er
t
o
p
r
ev
en
t
h
ar
m
o
n
ics
p
r
o
p
ag
a
t
io
n
in
t
h
e
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
an
d
g
ett
in
g
h
ig
h
p
o
w
er
q
u
alit
y
[
2
2
]
.
Fig
u
r
e
1
.
T
h
e
p
r
o
p
o
s
ed
n
in
e
lev
el
ac
ti
v
e
p
o
w
er
f
i
lter
lo
ca
tio
n
in
th
e
n
et
w
o
r
k
.
T
h
e
b
lo
ck
d
iag
r
a
m
o
f
t
h
e
n
in
e
le
v
el
te
n
-
s
w
itc
h
i
n
v
er
t
er
t
o
p
o
lo
g
y
is
i
llu
s
tr
ated
i
n
Fig
u
r
e
2
.
I
t
is
m
ai
n
l
y
co
m
p
o
s
ed
o
f
th
r
e
e
id
en
tical
s
tr
u
c
tu
r
es
b
y
p
h
as
e.
E
ac
h
s
tr
u
ct
u
r
e
is
co
m
p
o
s
ed
o
f
1
0
I
GB
T
p
o
w
er
s
w
itc
h
es
i
n
s
tead
to
1
6
I
GB
T
p
o
w
er
s
w
itc
h
es
in
t
h
e
co
n
v
e
n
t
io
n
al
s
y
s
te
m
[
2
3
]
.
T
h
e
DC
b
u
s
v
o
lta
g
e
(V
DC
)
ca
n
g
en
er
ate
n
i
n
e
lev
e
ls
,
n
a
m
el
y
:
V
DC
,
V
DC
/2
,
V
DC
/3
,
V
DC
/4
,
0
,
-
V
DC
/4
,
-
V
DC
/3
,
-
V
DC
/2
an
d
–
V
DC
.
T
h
e
V
DC
v
o
ltag
e
is
u
n
i
f
o
r
m
l
y
d
is
tr
ib
u
ted
o
v
er
f
o
u
r
id
e
n
tical
ca
p
ac
ito
r
s
(
C
1
,
C
2
,
C
3
a
n
d
C4
)
co
n
n
ec
ted
i
n
s
er
ie
s
.
T
h
e
f
o
u
r
s
w
itc
h
es
k1
,
k2
,
k3
an
d
k4
ar
e
u
s
ed
to
f
o
r
m
t
h
e
H
-
b
r
id
g
e,
wh
ile
th
e
s
w
itc
h
es
k5
,
k7
an
d
k9
ar
e
c
o
n
n
ec
ted
in
s
er
ies
w
it
h
k6
,
k8
an
d
k1
0
,
r
esp
ec
tiv
el
y
.
T
o
m
ain
ta
in
t
h
e
ze
r
o
lev
el
at
th
e
i
n
v
er
ter
o
u
t
let,
k1
an
d
k3
ar
e
tu
r
n
ed
o
n
(
Fi
g
u
r
e
3
-
i
)
.
W
h
er
ea
s
,
k1
an
d
k4
ar
e
tu
r
n
ed
o
n
to
g
et
V
a
n
=V
DC
o
n
Fig
u
r
e
3
-
a
.
T
o
in
v
er
t
th
e
o
u
tp
u
t
v
o
ltag
e
(
V
a
n
=
-
V
DC
)
,
k2
an
d
k3
ar
e
tu
r
n
ed
o
n
Fi
g
u
r
e
3
-
b
.
k1
,
k7
an
d
k8
ar
e
s
w
itc
h
ed
o
n
to
g
e
n
e
r
ate
3V
DC
/4
o
n
Fi
g
u
r
e
3
-
c
a
n
d
k2
,
k9
an
d
k1
0
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
198
–
2
0
9
200
s
w
itc
h
ed
o
n
to
g
e
n
er
ate
–
3V
DC
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Fig
u
r
e
3
-
d
.
k1
,
k5
an
d
k6
ar
e
tu
r
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ed
o
n
to
g
e
n
er
ate
V
DC
/2
lev
el
Fi
g
u
r
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3
-
e
an
d
to
o
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tain
lo
w
er
i
n
v
er
ter
v
o
ltag
e
-
V
DC
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,
k1
,
k7
an
d
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s
w
itc
h
e
s
ar
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tu
r
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o
n
Fig
u
r
e
3
-
f
.
T
h
e
V
DC
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lev
el
ap
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r
s
w
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th
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1
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g
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r
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ce
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V
DC
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,
k2
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k8
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e
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n
Fig
u
r
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3
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h
.
Fig
u
r
e
2
.
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h
e
s
tr
u
ctu
r
al
d
iag
r
a
m
o
f
t
h
e
p
r
o
p
o
s
ed
n
in
e
lev
el
t
en
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s
w
itc
h
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n
v
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ter
.
Fig
u
r
e
3
.
T
h
e
p
o
s
s
ib
le
co
n
f
ig
u
r
atio
n
s
o
f
t
h
e
p
r
o
p
o
s
ed
n
in
e
lev
el
in
v
er
ter
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
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8
694
A
N
ew S
tr
u
ctu
r
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o
f th
e
N
in
e
L
ev
el
I
n
ve
r
ter Used
a
s
A
ctive
P
o
w
er F
ilter
w
ith
a
.
.
.
(
F
eth
i Ch
o
u
a
f
)
201
3.
I
DE
N
T
I
F
I
CA
T
I
O
N
O
F
T
H
E
H
ARM
O
NIC CU
RREN
T
T
o
g
et
a
h
ig
h
f
il
ter
in
g
q
u
alit
y
,
r
ef
er
en
ce
cu
r
r
e
n
t id
e
n
ti
f
icatio
n
m
et
h
o
d
is
th
e
m
o
s
t e
f
f
icie
n
t
tech
n
iq
u
e
u
s
ed
to
e
x
tr
ac
t
h
ar
m
o
n
ic
cu
r
r
en
ts
.
T
h
er
e
ar
e
s
ev
er
al
alg
o
r
it
h
m
s
w
i
th
d
if
f
er
e
n
t
d
eg
r
ee
o
f
co
m
p
le
x
it
y
,
s
u
c
h
a
s
th
e
tec
h
n
iq
u
e
o
f
i
n
s
tan
tan
eo
u
s
p
o
w
er
s
(
P
Q)
i
n
tr
o
d
u
ce
d
b
y
H.
A
K
A
GI
to
e
x
tr
ac
t
r
e
f
er
en
c
e
h
ar
m
o
n
ic
c
u
r
r
en
t
s
[
2
4
]
-
[
2
5
]
.
T
h
e
C
LAR
K
tr
a
n
s
f
o
r
m
atio
n
is
u
s
ed
to
co
n
v
er
t
t
h
e
b
alan
ce
d
t
h
r
ee
-
p
h
ase
v
o
lta
g
e
s
(
v1
,
v2
,
v3
)
o
r
/an
d
cu
r
r
en
ts
(
i1
,
i2
,
i3
)
to
t
h
e
b
ip
h
ase
s
y
s
te
m
d
e
f
i
n
ed
b
y
co
m
p
o
n
en
ts
(
vα
,
vβ
)
an
d
(
iα
,
i
β
)
,
r
esp
ec
ti
v
el
y
as
p
r
esen
ted
b
y
t
h
e
f
o
llo
w
in
g
eq
u
atio
n
s
.
[
]
=
√
2
3
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
]
[
1
2
3
]
(
1
)
[
]
=
√
2
3
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
]
[
1
2
3
]
(
2
)
W
h
er
e,
α
an
d
β
ax
es
co
in
cid
e
w
it
h
th
e
r
ea
l
an
d
i
m
a
g
i
n
ar
y
ax
es
o
f
t
h
e
co
m
p
lex
p
lan
e.
T
h
u
s
,
th
e
t
h
r
ee
p
h
ase
v
o
ltag
e
a
n
d
cu
r
r
en
t
s
y
s
te
m
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
w
s
:
{
=
+
i
=
+
(
3
)
S
o
,
t
h
e
c
o
m
p
lex
a
p
p
a
re
n
t
p
o
w
e
r
is g
iv
e
n
b
y
:
S
=
(
+
)
(
+
)
(
4
)
T
h
e
in
s
ta
n
ta
n
eo
u
s
ac
ti
v
e
p
o
wer
is
o
b
tain
ed
b
y
eq
u
a
tio
n
(
5
)
an
d
t
h
e
i
n
s
ta
n
ta
n
eo
u
s
r
ea
cti
v
e
p
o
w
er
i
s
ca
lc
u
lated
b
y
eq
u
atio
n
(
6
)
.
P
=
(
+
)
(
5
)
q
=
j
(
−
)
(
6
)
T
h
e
in
s
ta
n
tan
eo
u
s
p
o
w
er
P
an
d
q
ca
n
b
e
d
ec
o
m
p
o
s
ed
in
t
wo
ter
m
s
;
t
h
e
f
ir
s
t
is
co
r
r
esp
o
n
d
in
g
to
it
s
m
ea
n
v
al
u
e
(
̅
,
̅
)
an
d
th
e
s
e
co
n
d
ter
m
i
s
co
r
r
esp
o
n
d
in
g
to
th
e
f
l
u
ctu
at
io
n
p
o
w
er
(
̃
,
̃
)
.
A
s
ec
o
n
d
o
r
d
er
h
ig
h
-
p
ass
f
ilter
i
s
u
s
ed
to
s
ep
ar
ate
th
e
p
o
w
er
co
m
p
o
n
e
n
ts
r
el
ated
to
th
e
h
ar
m
o
n
ic
an
d
to
th
e
f
u
n
d
a
m
e
n
tal.
T
h
e
s
ep
ar
atio
n
s
ch
e
m
e
is
ill
u
s
tr
ated
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
P
o
w
er
s
ep
ar
atio
n
s
h
a
m
e.
T
h
e
cu
to
f
f
f
r
eq
u
e
n
c
y
i
s
s
el
ec
ted
d
ep
en
d
in
g
o
n
th
e
lo
ad
,
allo
w
i
n
g
t
h
e
p
ass
a
g
e
o
f
t
h
e
p
o
w
er
s
h
ar
m
o
n
ic
co
m
p
o
n
e
n
t
s
a
n
d
b
lo
ck
th
e
p
ass
a
g
e
o
f
co
n
ti
n
u
o
u
s
co
m
p
o
n
e
n
ts
o
f
ac
t
iv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
o
f
t
h
e
f
u
n
d
a
m
en
ta
l.
Af
ter
s
ep
ar
atin
g
th
e
p
o
w
er
s
,
w
e
ca
n
ca
lc
u
late
th
e
h
ar
m
o
n
ic
an
d
th
e
r
ea
ctiv
e
cu
r
r
en
t
s
i
m
u
lta
n
eo
u
s
l
y
f
r
o
m
t
h
e
f
o
llo
w
i
n
g
m
atr
i
x
.
[
]
=
1
∆
[
−
]
[
0
q
̅
]
+
[
−
]
[
p
̃
q
̃
]
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
198
–
2
0
9
202
Fig
u
r
e
5
.
I
d
en
tif
icatio
n
s
c
h
e
m
e
o
f
th
e
h
ar
m
o
n
ic
a
n
d
r
ea
ctiv
e
cu
r
r
en
ts
.
4.
ACTI
VE
F
I
L
T
E
R
CO
N
T
R
O
L
ST
R
AT
E
G
Y
Af
ter
d
eter
m
i
n
i
n
g
o
f
r
ef
er
e
n
c
e
cu
r
r
en
ts
b
y
th
e
i
n
s
tan
ta
n
eo
u
s
p
o
w
er
tech
n
iq
u
e
th
e
co
n
tr
o
l
o
f
I
GB
T
s
w
itc
h
es
is
ca
r
r
ied
o
u
t
b
y
th
e
co
m
p
ar
is
o
n
b
et
w
ee
n
r
e
f
er
en
c
e
cu
r
r
en
ts
(
ir
ef
1
,
ir
ef
2
,
ir
ef
3
)
an
d
eig
h
t
tr
ian
g
u
lar
ca
r
r
ier
s
u
s
in
g
t
h
e
P
h
ase
Dis
p
o
s
itio
n
P
u
ls
e
W
id
t
h
Mo
d
u
lat
i
o
n
(
P
DPW
M)
m
et
h
o
d
as
p
r
e
s
en
ted
i
n
Fi
g
u
r
e
6
[
2
6
]
.
T
h
is
co
m
p
ar
is
o
n
w
i
ll
g
e
n
er
ates
lo
g
ic
s
ig
n
als
to
th
e
I
G
B
T
s
as
ill
u
s
tr
ated
i
n
t
h
e
lo
g
ic
f
lo
w
ch
ar
t
p
r
ese
n
ted
in
Fi
g
u
r
e
7
.
Fig
u
r
e
6
.
E
ig
h
t tr
ia
n
g
u
lar
ca
r
r
i
er
s
d
is
p
o
s
ed
in
p
h
ases
.
5.
DC
B
US V
O
L
T
AG
E
R
E
G
U
L
AT
I
O
N
I
t
is
r
ec
o
m
m
e
n
d
ed
th
at
th
e
DC
b
u
s
v
o
lta
g
e
ac
r
o
s
s
t
h
e
c
ap
ac
ito
r
s
(
C
1
,
C
2
,
C
3
,
a
n
d
C
4
)
o
f
th
e
r
e
m
ain
s
co
n
s
tan
t.
T
h
e
r
eg
u
lat
io
n
o
f
DC
v
o
lta
g
e
is
n
ec
ess
a
r
y
i
n
o
r
d
er
to
lim
it
th
e
f
l
u
ct
u
atio
n
s
a
n
d
p
r
ev
en
t
s
e
m
ico
n
d
u
cto
r
s
f
a
ilu
r
e.
I
t
is
th
er
ef
o
r
e
i
m
p
o
r
tan
t
to
f
in
d
a
co
n
tr
o
ller
w
h
ich
is
i
n
s
e
n
s
iti
v
e
to
p
ar
am
eter
v
ar
iatio
n
s
an
d
d
is
tu
r
b
an
ce
s
a
n
d
also
ap
p
r
o
p
r
iate
to
p
ar
am
eter
s
clo
s
ed
lo
o
p
co
n
tr
o
l.
S
w
itch
es
co
m
m
u
tatio
n
ca
n
g
en
er
ate
f
lu
c
tu
at
io
n
s
i
n
t
h
e
V
DC
v
o
ltag
e,
ca
p
ac
ito
r
lo
s
s
es
a
n
d
a
d
ela
y
in
t
h
e
co
n
tr
o
l
s
y
s
te
m
.
Fo
r
t
h
ese
r
ea
s
o
n
s
,
t
h
e
p
r
o
p
esed
n
in
e
le
v
el
ac
ti
v
e
f
ilter
i
s
u
s
ed
as
a
c
o
n
tr
o
lled
r
ec
tif
ier
,
ai
m
in
g
to
co
m
p
e
n
s
ate
th
e
D
C
b
u
s
v
o
ltag
e
v
ar
iatio
n
s
b
y
tr
an
s
f
er
r
i
n
g
a
s
m
all
q
u
an
tit
y
o
f
A
C
ac
ti
v
e
p
o
w
er
to
th
e
o
t
h
er
s
i
d
e
o
f
th
e
DC
c
u
r
r
en
t
f
ilter
.
Fo
r
th
i
s
p
u
r
p
o
s
e,
th
e
co
n
tr
o
l
o
f
th
e
D
C
b
u
s
v
o
lta
g
e
is
p
er
f
o
r
m
ed
b
y
a
P
r
o
p
o
r
tio
n
al
I
n
te
g
r
al
(
P
I
)
r
eg
u
lato
r
u
s
ed
to
co
r
r
ec
t th
e
ap
p
r
o
p
r
iate
er
r
o
r
v
alu
e
b
et
w
ee
n
th
e
r
e
f
er
en
ce
a
n
d
th
e
i
n
j
ec
ted
cu
r
r
en
ts
.
0
0
.
0
1
0
.
0
2
0
.
0
3
0
.
0
4
0
.
0
5
0
.
0
6
0
.
0
7
0
.
0
8
-6
-4
-2
0
2
4
6
T
i
m
e
(
s
)
M
a
g
n
i
tu
d
e
p1
p2
p3
p4
p5
p6
p7
p8
i
r
e
f
1
i
β
r
e
a
c
va
va
3
i
3
r
e
f
i
2
r
e
f
i
1
r
e
f
b
u
t
t
e
r
b
u
t
t
e
r
V2
5
V3
4
V1
i3
i2
i1
v
β
v
α
i
α
i
β
p
q
p
̃
q
̃
1
/
v
2
α
+
v
2
β
̅
i
α
r
e
a
c
i
α
h
a
r
i
β
h
a
r
i
α
r
e
f
i
β
r
e
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
A
N
ew S
tr
u
ctu
r
e
o
f th
e
N
in
e
L
ev
el
I
n
ve
r
ter Used
a
s
A
ctive
P
o
w
er F
ilter
w
ith
a
.
.
.
(
F
eth
i Ch
o
u
a
f
)
203
Fig
u
r
e
7
.
L
o
g
ic
s
ig
n
als
g
e
n
er
atio
n
f
lo
w
c
h
ar
t.
6.
M
O
DE
L
I
N
G
AN
D
SI
M
UL
AT
I
O
N
T
h
e
n
in
e
le
v
el
i
n
v
er
ter
to
p
o
lo
g
y
p
r
o
p
o
s
ed
in
t
h
is
w
o
r
k
h
as
b
ee
n
m
o
d
eled
a
s
ill
u
s
tr
ated
in
Fi
g
u
r
e
8
.
T
h
e
s
i
m
u
lated
m
o
d
el
is
co
m
p
o
s
ed
o
f
th
r
ee
-
p
h
a
s
e
s
u
p
p
l
y
s
o
u
r
ce
s
,
a
p
o
llu
ted
lo
ad
an
d
a
n
in
e
le
v
el
p
ar
allel
ac
tiv
e
p
o
w
er
f
il
ter
.
T
h
e
s
im
u
latio
n
is
p
er
f
o
r
m
ed
u
s
i
n
g
Ma
tlab
/Si
m
u
li
n
k
en
v
ir
o
n
m
en
t.
T
h
e
o
b
tain
ed
S
t
a
r
I
r
e
f
,
p
1,
p
2
,
p
3,
p
4,
p
5
,
p
6,
p
7,
p
8.
[k
1,
k
2
,
k
3
,
k
4
,
k
5,
k
6
,
k
7,
k
8
k
9,
k
1
0
]
=
[
01
0
0
0
0
0
0
1
1
]
v
an
=
-
3
v
d
/
4
p
7
>
I
h
≥
p
8
Y
e
s
No
[k
1,
k
2
,
k
3
,
k
4
,
k
5,
k
6
,
k
7,
k
8
k
9,
k
1
0
]
=
[
01
0
01
0
0
0
0
0
]
v
an
=
-
v
d
/2
p
6
>
I
h
≥
p
7
Y
e
s
No
[k
1,
k
2
,
k
3
,
k
4
,
k
5,
k
6
,
k
7,
k
8
k
9,
k
1
0
]
=
[
01
0
0
0
0
1
1
0
0
]
v
an
=
-
v
d
/4
p
5
>
I
h
≥
p
6
Y
e
s
No
[k
1,
k
2
,
k
3
,
k
4
,
k
5,
k
6
,
k
7,
k
8
k
9,
k
1
0
]
=
[
1
0
0
1
0
0
0
0
0
0
]
I
h
≥
p
1
Y
e
s
No
[k
1,
k
2
,
k
3
,
k
4
,
k
5,
k
6
,
k
7,
k
8
k
9,
k
1
0
]
=
[
1
0
0
0
0
0
0
1
1
0
0
]
v
an
=3
v
d/
4
p
1
>
I
h
≥
p
2
Y
e
s
No
v
an
=
v
d
[k
1,
k
2
,
k
3
,
k
4
,
k
5,
k
6
,
k
7,
k
8
k
9,
k
1
0
]
=
[
1
0
0
0
1
1
0
0
0
0
]
v
an
=
v
d
/2
p
2
>
I
h
≥
p
3
Y
e
s
No
[k
1,
k
2
,
k
3
,
k
4
,
k
5,
k
6
,
k
7,
k
8
k
9,
k
1
0
]
=
[
1
0
0
0
0
0
0
0
11
]
v
an
=
v
d
/4
p
3
>
I
h
≥
p
4
Y
e
s
No
[k
1,
k
2
,
k
3
,
k
4
,
k
5,
k
6
,
k
7,
k
8
k
9,
k
1
0
]
=
[
1
0
10
0
0
0
0
0
0
]
v
an
=
0
p
4
>
I
h
≥
p
5
Y
e
s
No
[k
1,
k
2
,
k
3
,
k
4
,
k
5,
k
6
,
k
7,
k
8
k
9,
k
1
0
]
=
[
0
1
1
0
0
0
0
0
0
0
]
v
an
=
-
v
d
P
8
>
I
h
Y
e
s
No
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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E
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1
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RE
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D6
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
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S
y
s
t
I
SS
N:
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
198
–
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0
9
206
s
u
p
p
o
r
ted
b
y
t
h
e
s
e
m
ico
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d
u
c
to
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h
e
r
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ir
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co
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d
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n
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h
at
t
h
e
s
w
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tch
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s
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r
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n
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ct
th
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c
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r
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m
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l
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e
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s
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y
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er
if
ied
to
av
o
id
s
h
o
r
t
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cir
cu
i
t.
Fig
u
r
e
1
3
s
h
o
w
s
clea
r
l
y
t
h
e
n
in
e
v
o
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n
a
m
el
y
:
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0
0
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5
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2
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r
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ce
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v
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Fig
u
r
e
1
2
.
Op
en
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g
a
n
d
clo
s
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r
e
s
eq
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en
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o
f
t
h
e
s
w
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h
es (
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).
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u
r
e
1
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.
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tp
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t v
o
lta
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s
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3
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ter
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ated
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ase
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ig
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e
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t
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n
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h
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n
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o
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ateg
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g
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ith
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a
n
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th
e
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L
I
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r
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ase
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h
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p
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l
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u
r
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1
6
illu
s
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ates
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r
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3
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r
e
1
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cu
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w
a
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h pre
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[
2
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]
[
3
0
]
w
h
ic
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r
eq
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i
x
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n
I
GB
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tr
an
s
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to
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o
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8.
CO
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O
N
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n
t
h
is
w
o
r
k
,
a
n
e
w
s
tr
u
ct
u
r
e
o
f
n
in
e
le
v
el
i
n
v
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ter
is
p
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o
p
o
s
ed
u
s
in
g
ten
p
o
w
er
s
w
i
tch
e
s
b
y
p
h
ase
in
s
tead
to
s
i
x
teen
I
GB
T
in
th
e
co
n
v
e
n
tio
n
al
s
y
s
te
m
.
T
h
is
i
n
v
er
ter
i
s
u
s
ed
a
s
a
s
h
u
n
t
ac
t
iv
e
p
o
w
er
f
i
lter
to
co
m
p
e
n
s
ate
t
h
e
h
ar
m
o
n
ic
cu
r
r
en
ts
a
n
d
th
e
r
ea
cti
v
e
p
o
w
er
.
T
h
e
s
i
m
u
la
tio
n
w
a
s
ca
r
r
ied
o
u
t
in
Ma
tlab
/Si
m
u
l
in
k
en
v
ir
o
n
m
en
t
.
Fro
m
th
e
r
es
u
lts
o
b
tain
ed
in
th
e
s
co
p
e
o
f
th
is
s
t
u
d
y
,
th
e
f
o
l
lo
w
i
n
g
co
n
clu
s
io
n
s
m
a
y
b
e
d
r
a
w
n
:
1.
T
h
e
cu
r
r
en
t
w
a
v
e
f
o
r
m
b
ec
o
m
e
p
u
r
el
y
s
i
n
u
s
o
id
al
w
ith
a
r
ed
u
ctio
n
i
n
th
e
h
ar
m
o
n
ic
d
is
to
r
ti
o
n
r
ate
(
T
HD)
f
r
o
m
2
7
.
4
1
% to
2
.
6
8
%.
2.
R
ed
u
ci
n
g
t
h
e
n
u
m
b
er
o
f
s
w
itc
h
es r
ed
u
ce
s
s
w
itc
h
i
n
g
lo
s
s
es.
3.
R
ed
u
ci
n
g
t
h
e
s
w
itch
in
g
n
u
m
b
er
r
ed
u
ce
s
th
e
d
u
r
atio
n
o
f
th
e
ap
p
lied
v
o
ltag
e
o
n
th
e
s
e
m
ico
n
d
u
cto
r
s
.
4.
Desp
ite
th
e
r
ed
u
ce
d
n
u
m
b
er
o
f
s
w
i
tch
e
s
,
th
e
p
r
o
p
o
s
ed
m
o
d
el
is
ab
le
to
p
r
o
v
id
e
n
in
e
lev
el
o
f
v
o
lta
g
e.
5.
T
h
e
th
r
ee
cu
r
r
en
ts
o
f
t
h
e
n
et
wo
r
k
h
av
e
t
h
e
s
a
m
e
a
m
p
l
itu
d
e
s
w
it
h
b
alan
ce
d
p
h
a
s
es.
6.
Go
o
d
c
o
m
p
e
n
s
atio
n
o
f
th
e
h
ar
m
o
n
ic
s
an
d
r
ea
ctiv
e
p
o
w
er
is
o
b
tain
ed
w
it
h
a
p
o
w
er
f
ac
to
r
clo
s
er
to
u
n
it
y
in
ac
co
r
d
an
ce
w
ith
I
E
E
E
s
ta
n
d
ar
d
s
.
7.
R
ed
u
ci
n
g
th
e
n
u
m
b
er
o
f
p
o
w
er
s
w
itch
e
s
allo
w
s
to
g
et
s
i
m
p
l
e
s
tr
u
ct
u
r
e
o
f
t
h
e
i
n
v
er
ter
w
it
h
a
r
ed
u
ce
d
co
s
t.
RE
F
E
R
E
NC
E
S
[
1
]
Ch
e
b
a
b
h
i
A
,
F
e
ll
a
h
M
K,
A
b
d
e
lh
a
li
m
K,
B
e
n
k
h
o
ris
M
F
.
F
u
z
z
y
lo
g
ic
c
o
n
tro
ll
e
rs
f
o
r
th
re
e
lev
e
ls
sh
u
n
t
a
c
ti
v
e
p
o
w
e
r
f
il
ter
c
o
m
p
e
n
sa
ted
b
y
th
re
e
-
lev
e
l
s
sta
b
il
izin
g
sp
a
c
e
v
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c
to
r
m
o
d
u
latio
n
t
o
f
ix
e
d
s
w
i
tch
in
g
f
r
e
q
u
e
n
c
y
a
n
d
sw
it
c
h
in
g
las
se
s
re
d
u
c
in
g
u
n
d
e
r
u
n
b
a
lan
c
e
d
lo
a
d
.
T
h
e
M
e
d
it
e
rr
a
n
e
a
n
J
o
u
rn
a
l
o
f
M
e
a
su
re
me
n
t
a
n
d
C
o
n
tr
o
l
.
2
0
1
5
;
1
1
(
1
):
3
5
7
-
3
6
6
.
[
2
]
Ka
n
n
a
n
R,
Ja
g
a
b
a
r
S
a
th
ik
M
A
,
S
e
lv
a
m
S
.
A
Ne
w
S
y
m
m
e
tri
c
M
u
lt
il
e
v
e
l
In
v
e
rter
T
o
p
o
lo
g
y
U
sin
g
S
in
g
le
a
n
d
Do
u
b
le
S
o
u
rc
e
S
u
b
-
M
u
lt
il
e
v
e
l
.
In
v
e
rters
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
.
2
0
1
5
;
1
5
(
1
):
9
6
-
1
0
5
.
[
3
]
Ka
le
M
,
Öz
d
e
m
ir
E.
Co
rrig
e
n
d
u
m
to
Ha
r
m
o
n
ic
a
n
d
re
a
c
ti
v
e
p
o
w
e
r
c
o
m
p
e
n
sa
ti
o
n
w
it
h
sh
u
n
t
a
c
ti
v
e
p
o
w
e
r
f
il
ter
u
n
d
e
r
n
o
n
-
i
d
e
a
l
m
a
in
s v
o
lt
a
g
e
.
El
e
c
tric P
o
we
r S
y
ste
m R
e
se
a
rc
h
.
2
0
0
5
;
7
4
(
3
):
3
6
3
-
3
7
0
.
[
4
]
Ba
ss
i
HM.
A
M
o
d
u
latio
n
S
c
h
e
m
e
f
o
r
F
lo
a
ti
n
g
S
o
u
rc
e
M
u
lt
i
lev
e
l
In
v
e
rter
T
o
p
o
l
o
g
y
w
it
h
In
c
re
a
se
d
Nu
m
b
e
r
o
f
Ou
tp
u
t
L
e
v
e
ls.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
Co
mp
u
ter
E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
.
2
0
1
6
;
6
(5
):
1
9
8
5
-
1
9
9
3
.
[
5
]
J
y
o
th
i
B,
G
o
p
a
la
Ra
o
M
V
.
P
e
rf
o
rm
a
n
c
e
A
n
a
l
y
sis
o
f
3
-
L
e
v
e
l
5
-
P
h
a
se
M
u
lt
il
e
v
e
l
In
v
e
rter
T
o
p
o
lo
g
ies
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
tr
ica
l
a
n
d
C
o
mp
u
t
e
r E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
.
2
0
1
7
;
7
(
4
):
1
6
9
6
-
1
7
0
5
.
[
6
]
Jo
sé
R,
Jih
-
S
h
e
n
g
L
,
F
a
n
g
Zh
e
n
g
P
.
M
u
lt
il
e
v
e
l
In
v
e
rters
:
A
S
u
rv
e
y
o
f
T
o
p
o
l
o
g
ies
,
Co
n
tro
ls,
a
n
d
A
p
p
li
c
a
ti
o
n
s.
IEE
E
tra
n
sa
c
ti
o
n
s
o
n
in
d
u
stri
a
l
e
lec
tro
n
ics
.
2
0
0
2
;
4
9
(
4
):
7
2
4
-
7
3
7
.
0
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