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In
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[
1
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.
Am
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2
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[
3
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ate
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[
4
]
.
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t [
5
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.
T
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tr
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6
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7
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9
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
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8
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I
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9
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2
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Fo
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1
4
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r
th
i
s
t
y
p
e
o
f
ap
p
licatio
n
s
,
in
v
er
ter
u
s
ed
w
i
t
h
s
y
m
m
etr
ic
v
o
ltag
e
m
a
g
n
it
u
d
e
an
d
f
r
eq
u
en
c
y
a
n
d
n
ee
d
s
o
f
lar
g
e
d
c
lin
k
ca
p
ac
ito
r
s
a
n
d
r
ec
tifie
r
cir
cu
it
.
B
u
t
m
atr
ix
co
n
v
er
ter
ac
t
a
s
a
d
ir
ec
t
ac
-
ac
co
n
v
er
ter
,
w
h
ic
h
h
as
s
i
n
u
s
o
id
al
i
n
p
u
t
c
u
r
r
en
t
a
n
d
ad
j
u
s
tab
l
e
o
u
tp
u
t
v
o
ltag
e
a
n
d
f
r
eq
u
e
n
c
y
.
T
h
is
p
r
o
j
ec
ted
w
o
r
k
elu
cid
ate
s
p
er
f
o
r
m
a
n
ce
o
f
3
-
p
h
ase
m
a
tr
ix
co
n
v
er
ter
u
s
i
n
g
s
p
ac
e
v
e
cto
r
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
to
co
n
tr
o
l
o
p
er
atio
n
o
f
th
r
ee
p
h
ase
in
d
u
ctio
n
m
o
to
r
.
I
t
m
i
n
i
m
izes
th
e
ef
f
ec
t
o
n
t
h
e
h
ar
m
o
n
ic
f
l
u
ct
u
atio
n
in
AC
o
u
tp
u
t v
o
lta
g
e
an
d
s
tr
e
s
s
o
n
t
h
e
p
o
w
er
s
w
itc
h
is
r
ed
u
ce
d
.
2.
T
H
RE
E
P
H
ASE
M
AT
RI
X
CO
NVER
T
E
R
2
.
1
.
Str
uct
ure
T
h
e
m
atr
ix
co
n
v
er
ter
in
c
lu
d
e
s
9
b
id
ir
ec
tio
n
al
s
w
itc
h
es,
wh
ich
allo
w
s
an
y
o
u
tp
u
t
p
h
ase
v
o
lta
g
e
i
s
co
n
n
ec
ted
to
an
y
i
n
p
u
t
p
h
a
s
e
v
o
ltag
e.
T
h
e
in
p
u
t
3
p
h
ase
ter
m
in
a
l
v
o
lta
g
e
is
co
n
n
ec
te
d
w
it
h
th
r
ee
p
h
a
s
e
b
id
ir
ec
tio
n
al
s
w
itc
h
t
h
at
r
ed
u
ctio
n
in
h
ar
m
o
n
ic
f
l
u
ct
u
atio
n
.
DC
li
n
k
f
i
lter
s
ar
e
ca
p
ac
itiv
e
f
ilter
a
n
d
in
d
u
cti
v
e
f
ilter
ar
e
er
ad
icate
d
,
d
u
e
to
th
at
co
s
t o
f
s
y
s
te
m
is
d
ec
r
ea
s
e.
3
-
p
h
ase
m
a
tr
ix
co
n
v
er
ter
is
s
h
o
w
n
i
n
F
ig
u
r
e
1
.
Fig
u
r
e
1
.
T
h
r
ee
-
p
h
ase
m
atr
i
x
co
n
v
er
ter
2
.
2
.
O
pera
t
io
n
o
f
m
a
t
rix
co
nv
er
t
er
T
h
e
ap
p
lied
in
p
u
t
in
s
tan
tan
eo
u
s
p
o
w
er
w
ill
n
o
t
b
e
eq
u
al
to
o
u
tp
u
t
p
o
w
er
.
T
h
e
d
if
f
er
e
n
c
e
b
et
w
ee
n
th
ese
i
n
p
u
t
a
n
d
o
u
tp
u
t
p
o
w
er
s
h
o
u
ld
b
e
ab
s
o
r
b
e
d
o
r
d
is
tr
ib
u
ted
b
y
an
e
n
er
g
y
s
to
r
a
g
e
d
ev
ic
es
lik
e
ca
p
ac
ito
r
o
r
in
d
u
cto
r
w
it
h
i
n
t
h
e
co
n
v
er
ter
s
y
s
te
m
.
B
u
t
m
atr
i
x
co
n
v
er
te
r
h
as
s
in
g
le
s
ta
g
e
co
n
v
er
s
io
n
u
n
it
w
it
h
h
elp
o
f
b
id
ir
ec
tio
n
al
s
w
itc
h
es
i
n
s
tead
o
f
u
s
in
g
m
u
l
tis
ta
g
e
co
n
v
er
s
i
o
n
an
d
en
er
g
y
s
to
r
ag
e
d
ev
ice
s
in
t
h
e
co
n
v
er
ter
.
Ma
tr
ix
co
n
v
er
ter
w
it
h
b
id
ir
e
ctio
n
al
s
w
i
tch
is
s
h
o
w
n
i
n
F
ig
u
r
e
2
.
D
u
e
to
t
h
e
ab
s
en
ce
o
f
en
er
g
y
s
to
r
ag
e
d
ev
ices,
t
h
e
i
n
s
ta
n
ta
n
eo
u
s
in
p
u
t
p
o
w
er
i
s
eq
u
a
l
to
o
u
tp
u
t
p
o
w
er
w
it
h
id
ea
l
ze
r
o
lo
s
s
s
w
i
tch
es.
T
h
e
s
y
s
te
m
co
n
s
is
ts
o
f
9
b
id
ir
ec
tio
n
a
l s
w
it
c
h
es,
w
h
ic
h
ar
e
co
n
n
ec
ted
as
t
h
r
ee
g
r
o
u
p
s
.
E
ac
h
g
r
o
u
p
co
n
ta
in
s
3
s
w
i
tch
e
s
a
n
d
ea
ch
b
id
ir
ec
tio
n
al
s
w
itc
h
is
co
n
n
ec
ted
w
it
h
b
o
th
i
n
p
u
t
v
o
ltag
e
an
d
o
u
tp
u
t v
o
lta
g
e.
T
o
tally
o
p
er
atio
n
o
f
3
p
h
a
s
e
m
atr
i
x
co
n
v
er
ter
h
as
2
7
p
er
m
itted
s
w
itc
h
i
n
g
m
o
d
es,
in
t
h
at
1
8
ac
tiv
e
v
ec
to
r
m
o
d
es,
3
ze
r
o
v
ec
to
r
m
o
d
es,
3
n
o
r
m
al
v
ec
to
r
m
o
d
es
an
d
3
in
v
er
s
e
v
ec
to
r
m
o
d
e
s
.
I
n
F
ig
u
r
e
3
illu
s
tr
ates,
a,
b
,
c
ar
e
i
n
p
u
t
v
o
ltag
es
f
o
r
b
i
-
d
ir
ec
tio
n
al
s
w
it
ch
es
a
n
d
A
,
B
,
C
ar
e
o
u
tp
u
t
v
o
ltag
e
s
o
f
m
atr
ix
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
S
imu
la
tio
n
o
f
3
-
p
h
a
s
e
ma
tr
ix
co
n
ve
r
ter u
s
in
g
s
p
a
ce
ve
cto
r
mo
d
u
la
tio
n
(
K
.
S
elva
ku
ma
r
)
911
co
n
v
er
ter
.
Her
e
all
i
n
p
u
t
p
h
ase
v
o
lta
g
es
ar
e
co
n
n
ec
ted
t
o
o
u
tp
u
t
p
h
a
s
e
v
o
lta
g
e.
An
d
th
ese
b
id
ir
ec
tio
n
a
l
s
w
itc
h
es a
r
e
s
w
itc
h
ed
ON
r
o
tatio
n
al
b
asis
,
w
h
ic
h
av
o
id
s
s
w
it
ch
in
g
o
f
2
s
w
i
tch
e
s
in
a
s
a
m
e
leg
.
Fig
u
r
e
2
.
Ma
tr
ix
co
n
v
er
ter
w
it
h
b
i
-
d
ir
ec
tio
n
al
s
w
itc
h
Fig
u
r
e
3
.
Ma
tr
ix
co
n
v
er
ter
–
ze
r
o
v
ec
to
r
m
o
d
es
I
n
F
ig
u
r
e
3
s
h
o
w
s
ze
r
o
v
ec
to
r
m
o
d
es
o
f
3
p
h
a
s
e
m
atr
ix
co
n
v
er
ter
a
n
d
i
n
t
h
at
a
ll
o
u
tp
u
t
p
h
ases
ar
e
co
n
n
ec
ted
in
s
i
n
g
le
in
p
u
t
p
h
as
e,
w
h
ic
h
lead
s
to
d
am
a
g
e
th
e
s
y
s
te
m
b
ec
au
s
e
3
p
h
ase
lo
ad
i
s
co
n
n
ec
ted
w
it
h
1
p
h
ase
i
n
p
u
t.
T
h
e
n
o
r
m
al
ac
t
i
v
e
v
ec
to
r
an
d
o
p
p
o
s
ite
v
ec
to
r
m
o
d
es
ar
e
ap
p
licab
le
f
o
r
f
o
r
w
ar
d
an
d
r
ev
er
s
e
o
p
er
atio
n
o
f
in
d
u
ctio
n
m
o
to
r
.
3.
SPAC
E
V
E
C
T
O
R
M
O
DULAT
I
O
N
(
SVM
)
SVM
is
a
s
w
itc
h
in
g
co
n
tr
o
l
m
eth
o
d
f
o
r
th
e
p
o
w
er
elec
tr
o
n
ic
s
w
i
tch
e
s
w
h
ic
h
r
ec
o
g
n
ize
t
h
e
s
w
i
tch
i
n
g
s
eq
u
en
ce
s
b
y
ass
i
g
n
m
en
t
o
f
a
s
w
i
tch
i
n
g
v
ec
to
r
in
d
-
q
s
p
ac
e
r
eg
io
n
[
1
6
]
.
I
t
is
en
h
an
ce
d
at
h
ar
m
o
n
ic
co
n
ten
t
lev
el
d
i
m
i
n
u
tio
n
a
n
d
in
cr
ea
s
i
n
g
o
u
tp
u
t
v
o
lta
g
e
a
m
p
l
i
tu
d
e
a
s
co
n
tr
ast
to
tr
ad
itio
n
al
SP
W
M
(
Sin
u
s
o
id
al
P
u
ls
e
W
id
th
Mo
d
u
latio
n
)
,
w
h
ic
h
is
g
en
er
all
y
u
s
ed
.
I
t
d
im
i
n
is
h
es
t
h
e
co
m
m
o
n
m
o
d
e
v
o
ltag
e
w
h
i
ch
is
th
e
d
if
f
er
en
c
e
b
et
w
ee
n
v
ec
to
r
s
u
m
o
f
t
h
e
v
o
ltag
e
le
v
el
p
o
te
n
tial
at
p
o
w
er
co
n
v
er
ter
s
y
s
te
m
o
u
tp
u
t
a
n
d
g
r
o
u
n
d
p
o
i
n
t
[
1
7
]
.
T
h
e
v
o
ltag
e
ac
r
o
s
s
p
r
o
p
o
s
ed
m
atr
i
x
co
n
v
er
ter
h
a
s
m
i
n
i
m
is
e
d
v
o
ltag
e
f
l
u
ct
u
atio
n
an
d
r
ed
u
ce
d
h
ar
m
o
n
ic
i
n
p
u
t
cu
r
r
en
t so
u
r
ce
.
Sp
ac
e
v
ec
to
r
r
ep
r
esen
tatio
n
f
o
r
3
-
p
h
a
s
e
p
o
wer
co
n
v
er
ter
is
s
h
o
w
n
i
n
F
ig
u
r
e
4.
Fig
u
r
e
4
.
Sp
ac
e
v
ec
to
r
r
ep
r
ese
n
tatio
n
f
o
r
3
-
p
h
ase
p
o
w
er
co
n
v
er
ter
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
.
2
,
A
p
r
il 2
0
1
9
:
9
0
9
-
9
1
6
912
Fig
u
r
e
5
.
Flo
w
c
h
ar
t
f
o
r
s
w
itc
h
in
g
p
u
ls
e
g
en
er
atio
n
u
s
i
n
g
S
V
P
W
M
m
et
h
o
d
Fo
r
d
eter
m
i
n
in
g
t
h
e
s
w
itc
h
i
n
g
s
tate
v
ec
to
r
s
o
f
m
atr
i
x
co
n
v
er
ter
,
th
e
s
p
ac
e
v
ec
to
r
illu
s
tr
atio
n
is
d
iv
id
ed
in
to
T
h
e
f
o
llo
w
i
n
g
s
t
ep
s
ar
e
u
s
ed
to
g
en
er
ate
th
e
g
atin
g
p
u
ls
es
f
o
r
b
i
-
d
ir
ec
tio
n
al
s
w
itc
h
es
o
f
m
a
tr
i
x
co
n
v
er
ter
.
T
h
e
f
o
l
w
c
h
ar
t is
s
h
o
w
n
in
F
ig
u
r
e
5
,
i
n
t
h
at
X
&
Y
p
ar
a
m
eter
s
u
s
ed
to
f
in
d
t
h
e
s
ec
to
r
id
en
ti
f
icatio
n
,
P
1
&
P
2
ar
e
u
s
ed
to
id
en
tify
t
h
e
tr
ian
g
le
f
o
r
r
ef
er
en
ce
v
ec
to
r
ca
lcu
latio
n
.
T
h
e
s
tep
s
ar
e,
a.
Secto
r
id
en
tif
ica
tio
n
f
o
r
r
ef
er
en
ce
v
ec
to
r
p
lace
d
b
ased
o
n
m
a
g
n
i
tu
d
e
an
d
a
n
g
le
ca
lc
u
lat
io
n
b.
T
r
ian
g
le
id
en
ti
f
icatio
n
i
n
t
h
e
s
ec
to
r
r
eg
io
n
c.
S
w
itc
h
in
g
v
ec
to
r
ca
lcu
atio
n
d.
S
w
itc
h
in
g
p
u
l
s
e
g
e
n
er
atio
n
f
o
r
b
i
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.
RE
F
E
R
E
NC
E
S
[1
]
R.
G
u
p
ta,
K.
M
o
h
a
p
a
tra,
A
.
S
o
m
a
n
i
“
Dire
c
t
m
a
tri
x
c
o
n
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e
rter
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b
a
se
d
d
riv
e
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p
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in
g
a
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m
a
c
h
in
e
w
it
h
a
a
d
v
a
n
c
e
d
f
e
a
tu
re
s
,
”
IEE
E
T
r
a
n
s.
I
n
d
.
El
e
c
tro
n
.
,
v
o
l
.
5
7
,
n
o
.
1
2
,
p
p
.
4
0
3
2
-
4
0
4
2
,
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c
.
2
0
1
4
.
[2
]
R.
L
a
i
e
t
a
l.
,
“
A
s
y
ste
m
a
ti
c
to
p
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p
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P
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c
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,
”
IEE
E
T
ra
n
s.
P
o
we
r E
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tro
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., v
o
l
.
2
3
,
n
o
.
6
,
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p
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2
6
6
5
-
2
6
8
0
,
N
o
v
.
2
0
1
0
.
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[3
]
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[4
]
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rid
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,
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,
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.
[5
]
H.
Ke
y
h
a
n
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a
n
d
H.
A
.
T
o
li
y
a
t,
“
A
so
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t
-
s
w
it
c
h
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d
th
re
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p
h
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se
a
c
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w
it
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a
h
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h
-
f
re
q
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c
li
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,
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n
s.
I
n
d
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p
p
l.
,
v
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l.
5
0
,
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4
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p
p
.
2
6
3
7
–
2
6
4
7
,
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l
.
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g
.
2
0
1
4
.
[6
]
Bo
z
tas
,
G
,
“
A
n
o
v
e
l
d
irec
t
A
C
–
A
C
c
o
n
v
e
rter
f
o
r
sin
g
le
a
n
d
t
w
o
-
p
h
a
se
a
s
y
n
c
h
ro
n
o
u
s
m
o
to
rs,”
M
S
c
th
e
sis,
F
irat
Un
iv
e
rsit
y
,
2
0
1
6
.
[7
]
J.
L
e
i,
B.
Zh
o
u
,
X
.
Qi
n
,
J.
W
e
i,
a
n
d
J.
B
ian
,
“
A
c
ti
v
e
d
a
m
p
in
g
c
o
n
tro
l
stra
teg
y
o
f
m
a
tri
x
c
o
n
v
e
rter
v
ia
m
o
d
ify
in
g
in
p
u
t
re
f
e
re
n
c
e
c
u
rr
e
n
ts,
”
IEE
E
T
ra
n
s.
P
o
we
r E
lec
tro
n
.
,
v
o
l.
3
0
,
n
o
.
9
,
p
p
.
5
2
6
0
-
5
2
7
1
,
S
e
p
.
2
0
1
6
.
[8
]
L
.
E
m
p
rin
g
h
a
m
,
J.
Ko
lar,
J.
Ro
d
rig
u
e
z
,
P
.
W
.
W
h
e
e
ler,
a
n
d
J.
C.
Clare
,
“
Tec
h
n
o
lo
g
ica
l
issu
e
s
a
n
d
in
d
u
stria
l
a
p
p
li
c
a
ti
o
n
o
f
m
a
tri
x
c
o
n
v
e
rters
:
A
re
v
ie
w
,
”
IEE
E
T
ra
n
s.
I
n
d
.
El
e
c
tro
n
.
,
v
o
l.
6
0
,
n
o
.
1
0
,
p
p
.
4
2
6
0
-
4
2
7
1
,
Oc
t.
2
0
1
3
.
[9
]
J.
Ro
d
rig
u
e
z
,
M
.
Riv
e
ra
,
J.
W
.
K
o
lar,
a
n
d
P
.
W
.
W
h
e
e
ler,
“
A
re
v
iew
o
f
c
o
n
tro
l
a
n
d
m
o
d
u
latio
n
m
e
th
o
d
s
f
o
r
m
a
tri
x
c
o
n
v
e
rters
,
”
IEE
E
T
ra
n
s.
I
n
d
.
El
e
c
tro
n
.
,
v
o
l.
5
9
,
n
o
.
1
,
p
p
.
5
8
-
7
0
,
J
a
n
.
2
0
1
2
.
[1
0
]
R.
P
a
lan
isa
m
y
,
K.
V
ij
a
y
a
k
u
m
a
r,
“
S
VP
W
M
f
o
r
3
-
p
h
a
se
3
-
lev
e
l
Ne
u
tral
P
o
i
n
t
Clam
p
e
d
In
v
e
r
ter
f
e
d
I
n
d
u
c
t
io
n
M
o
t
o
r
Co
n
tr
o
l
,
”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
Co
m
p
u
ter
S
c
ien
c
e
(
IJ
EE
CS
)
,
v
o
l.
9
,
n
o
.
3
,
p
p
.
7
0
3
-
7
1
0
,
M
a
rc
h
2
0
1
8
.
[1
1
]
B.
M
c
G
ra
th
,
D.
Ho
lm
e
s,
a
n
d
T
.
Li
p
o
,
“
Op
ti
m
ize
d
sp
a
c
e
v
e
c
to
r
s
w
it
c
h
in
g
se
q
u
e
n
c
e
s
f
o
r
m
u
lt
il
e
v
e
l
in
v
e
rters
,
”
IEE
E
T
ra
n
s.
Po
we
r E
lec
tro
n
.
,
v
o
l
.
1
8
,
n
o
.
6
,
p
p
.
1
2
9
3
–
1
3
0
1
,
No
v
.
2
0
1
3
.
[1
2
]
K.
G
u
p
ta
a
n
d
A
.
Kh
a
m
b
a
d
k
o
n
e
,
“
A
S
p
a
c
e
V
e
c
to
r
P
W
M
S
c
h
e
m
e
fo
r
M
u
l
ti
lev
e
l
In
v
e
rters
Ba
s
e
d
o
n
th
e
Tw
o
-
L
e
v
e
l
S
p
a
c
e
V
e
c
to
r
P
W
M
,
”
I
n
:
IE
EE
T
ra
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
v
o
l.
5
3
,
n
o
.
5
(
2
0
1
3
).
[1
3
]
Y.
Ya
n
,
H.
A
n
,
T
.
S
h
i,
a
n
d
C.
Xia
,
“
I
m
p
ro
v
e
d
d
o
u
b
le
li
n
e
v
o
lt
a
g
e
s
y
n
th
e
sis
o
f
m
a
tri
x
c
o
n
v
e
rter
fo
r
in
p
u
t
c
u
rre
n
t
e
n
h
a
n
c
e
m
e
n
t
u
n
d
e
r
u
n
b
a
lan
c
e
d
p
o
w
e
r
su
p
p
ly
,
”
IET
Po
we
r E
lec
tro
n
.,
v
o
l
.
6
,
n
o
.
4
,
p
p
.
7
9
8
-
8
0
8
,
A
p
r
.
2
0
1
3
.
[1
4
]
L
i,
X
.
,
S
u
,
M
.
,
S
u
n
,
Y
.
,
e
t
a
l.
,
“
M
o
d
u
latio
n
stra
teg
ies
b
a
se
d
o
n
m
a
th
e
m
a
ti
c
a
l
c
o
n
stru
c
ti
o
n
m
e
t
h
o
d
f
o
r
m
a
tri
x
c
o
n
v
e
rter u
n
d
e
r
u
n
b
a
lan
c
e
d
i
n
p
u
t
v
o
lt
a
g
e
s”
,
IET
Po
we
r E
lec
tro
n
.
,
2
0
1
3
,
6
,
(3
),
p
p
.
4
3
4
-
4
4
5
.
[1
5
]
S
.
A
ld
h
a
h
e
r,
P
.
C.
K.
L
u
k
,
A
.
Ba
ti
,
a
n
d
J.
F
.
W
h
id
b
o
rn
e
,
“
W
irele
ss
p
o
w
e
r
tran
sfe
r
u
sin
g
c
las
s
e
in
v
e
rter
w
it
h
sa
tu
ra
b
le d
c
-
f
e
e
d
in
d
u
c
to
r,
”
IE
EE
T
ra
n
s.
In
d
.
A
p
p
l
.
,
v
o
l
.
5
0
,
n
o
.
4
,
p
p
.
2
7
1
0
-
2
7
1
8
,
Ju
l
.
/A
u
g
.
2
0
1
4
.
[1
6
]
R.
P
a
lan
isa
m
y
,
K.
V
ij
a
y
a
k
u
m
a
r,
D.S
e
lv
a
b
h
a
ra
th
i,
“
M
S
P
W
M
Ba
se
d
I
m
p
lem
e
n
tatio
n
o
f
No
v
e
l
5
-
lev
e
l
In
v
e
rter
w
it
h
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r
E
lec
tro
n
i
c
s
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
)
,
v
o
l.
8
,
n
o
.
4
,
p
p
.
1
4
9
4
-
1
5
0
2
,
De
c
e
m
b
e
r
2
0
1
7
.
[1
7
]
H.
Ng
u
y
e
n
a
n
d
H.
L
e
e
,
“
A
DSV
M
m
e
th
o
d
f
o
r
m
a
tri
x
c
o
n
v
e
rters
to
su
p
p
re
ss
c
o
m
m
o
n
-
m
o
d
e
v
o
lt
a
g
e
w
it
h
re
d
u
c
e
d
sw
it
c
h
in
g
lo
ss
e
s,”
IEE
E
T
ra
n
s
.
P
o
we
r E
lec
tro
n
.
,
v
o
l.
3
1
,
n
o
.
6
,
p
p
.
4
0
2
0
-
4
0
3
0
,
Ju
n
.
2
0
1
6
.
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