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Scien
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Dai
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ac
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I
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No
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lan
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elec
tr
icity
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r
o
m
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cu
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to
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(
AC
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with
h
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ca
p
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ity
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f
s
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ically
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u
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e
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s
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m
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ir
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e
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ts
s
u
ch
as
n
eu
tr
al
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p
o
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p
ed
(
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,
ca
s
ca
d
ed
H
-
b
r
id
g
e
(
C
HB
)
,
cla
m
p
d
io
d
e
[
1
]
,
[
2
]
.
Ho
wev
er
,
t
h
ese
co
n
v
er
ter
s
h
a
v
e
m
a
n
y
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ct
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ly
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o
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o
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ig
h
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th
at
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v
o
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e
lev
el
ex
p
an
s
io
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will
b
ec
o
m
e
d
if
f
icu
lt,
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d
th
e
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n
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e
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ter
will
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e
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m
b
er
s
o
m
e,
m
a
k
in
g
th
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a
p
p
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o
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n
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clo
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eth
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s
d
if
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icu
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wh
en
u
s
in
g
m
icr
o
p
r
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ce
s
s
o
r
d
e
v
ices
[
3
]
.
T
h
e
m
o
d
u
lar
m
u
ltil
ev
el
co
n
v
er
te
r
(
MM
C
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m
u
ltil
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co
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v
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te
r
h
as
a
lo
t
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an
tag
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th
at
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n
o
v
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co
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e
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is
ad
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an
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es
o
f
th
e
ab
o
v
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m
u
ltil
ev
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co
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v
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te
r
s
as:
h
as
a
s
im
p
le
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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N:
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co
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ig
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ter
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with
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latio
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a
n
d
c
o
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tr
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l
p
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ce
s
s
[
4
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.
T
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co
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v
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ter
is
ea
s
ily
ap
p
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p
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city
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h
ig
h
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v
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s
o
lar
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o
wer
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lan
ts
to
co
n
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er
t
elec
tr
icity
f
r
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m
DC
to
AC
d
ir
ec
tly
co
n
n
ec
ted
to
t
h
e
g
r
id
[
5
]
.
T
h
e
s
tr
u
ctu
r
al
f
ea
tu
r
e
o
f
t
h
e
MM
C
co
n
v
er
ter
is
th
at
it
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es
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o
t
r
eq
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ir
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a
f
ilter
o
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ter
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iate
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an
s
f
o
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er
o
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p
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th
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y
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tem
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n
n
ec
tin
g
th
e
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ter
t
o
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g
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id
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ec
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y
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p
ac
t
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d
d
o
es
n
o
t
i
n
cu
r
an
y
c
o
s
ts
[
6
]
.
T
h
a
n
k
s
to
t
h
ese
ch
ar
ac
ter
is
tics
,
in
r
ec
en
t y
ea
r
s
,
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C
co
n
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er
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er
s
h
av
e
alwa
y
s
b
ee
n
i
n
ter
ested
in
r
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tis
ts
.
T
h
e
m
ain
to
p
ics
r
esear
ch
ed
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r
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e
m
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u
latio
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n
d
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r
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o
r
ith
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s
ap
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ase
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A
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r
ith
m
s
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b
ee
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ap
p
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s
u
ch
as:
p
u
ls
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wid
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m
o
d
u
latio
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(
PW
M)
,
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
(
SVM)
,
n
ea
r
est
lev
el
m
o
d
u
latio
n
(
NL
M)
,
p
r
o
p
o
r
tio
n
al
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i
n
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r
al
(
PI
)
,
m
o
d
el
p
r
e
d
ictiv
e
co
n
tr
o
l
(
MPC
)
[
7
]
–
[
1
1
]
.
I
n
wh
ich
th
e
m
o
d
u
latio
n
al
g
o
r
it
h
m
s
aim
to
s
o
lv
e
th
e
p
r
o
b
le
m
o
f
g
en
e
r
atin
g
s
witch
in
g
p
u
ls
e
wid
th
s
f
o
r
th
e
in
s
u
lated
-
g
ate
b
ip
o
lar
tr
an
s
is
to
r
(
I
GB
T
)
v
alv
es
o
f
t
h
e
M
MC
co
n
v
er
ter
,
c
o
n
tr
o
l
alg
o
r
i
th
m
s
in
clo
s
ed
-
lo
o
p
cir
cu
its
aim
to
im
p
r
o
v
e
th
e
q
u
ality
o
f
t
h
e
AC
cu
r
r
en
t
a
n
d
v
o
ltag
e
o
f
th
e
MM
C
in
ca
s
es
wh
er
e
th
e
c
u
r
r
e
n
t
an
d
v
o
ltag
e
p
a
r
am
eter
s
ex
p
e
r
ien
c
e
lar
g
e
v
ar
iatio
n
s
o
u
ts
id
e
th
e
allo
wab
le
r
an
g
e
[
1
2
]
,
[
1
3
]
.
N
L
M
m
o
d
u
latio
n
h
as
m
an
y
ad
v
an
tag
es
o
v
e
r
PW
M
m
o
d
u
latio
n
b
ec
au
s
e
it
d
o
es
n
o
t
n
ee
d
to
u
s
e
m
an
y
ca
r
r
i
er
s
an
d
th
e
v
alv
e
s
witch
in
g
f
r
eq
u
e
n
cy
is
lo
w
[
1
4
]
.
C
o
m
p
ar
e
d
with
th
e
ab
o
v
e
-
m
en
tio
n
ed
m
o
d
u
latio
n
m
eth
o
d
s
,
th
e
SVM
m
o
d
u
latio
n
m
et
h
o
d
h
as
m
a
n
y
ad
v
an
ta
g
es
an
d
ca
n
im
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
wh
en
ap
p
lied
to
MM
C
.
Ho
wev
er
,
th
is
m
eth
o
d
is
co
m
p
u
tatio
n
ally
co
m
p
lex
an
d
r
eq
u
ir
es
th
e
estab
lis
h
m
en
t
o
f
a
v
o
ltag
e
v
ec
to
r
s
tate
tab
le
o
n
th
e
o
u
tp
u
t
s
id
e
a
n
d
m
u
s
t
co
m
p
u
te
a
la
r
g
e
n
u
m
b
er
o
f
s
witch
in
g
s
tates
[
1
5
]
.
On
th
e
o
th
er
h
a
n
d
,
d
u
r
in
g
th
e
m
o
d
u
latio
n
p
r
o
ce
s
s
,
th
e
SVM
m
eth
o
d
u
s
es 4
v
er
tices o
f
th
e
p
ar
allelo
g
r
am
to
ca
lcu
late
th
e
s
witch
in
g
s
tate,
wh
ich
in
cr
ea
s
es
th
e
n
u
m
b
er
o
f
ca
lcu
latio
n
s
f
o
r
th
e
m
icr
o
c
o
n
t
r
o
ller
an
d
s
lo
ws
d
o
wn
th
e
s
ig
n
al
r
esp
o
n
s
e
o
f
th
e
MM
C
[
1
5
]
.
T
h
e
p
r
o
b
lem
h
er
e
is
th
at
it is
n
ec
ess
ar
y
to
ap
p
ly
th
e
SVM
m
o
d
u
latio
n
m
et
h
o
d
b
u
t r
ed
u
c
e
th
e
n
u
m
b
e
r
o
f
ca
lcu
latio
n
s
with
o
u
t
h
av
i
n
g
to
lis
t
th
e
s
tate
tab
le
in
d
e
tail.
T
h
er
ef
o
r
e,
i
n
th
is
s
tu
d
y
,
th
e
g
en
er
al
SVM
m
eth
o
d
f
o
r
MM
C
with
an
y
n
u
m
b
er
o
f
lev
els
will
b
e
p
r
o
p
o
s
ed
to
o
v
er
co
m
e
th
e
d
is
ad
v
an
tag
es
o
f
co
n
v
en
tio
n
al
SVM
m
eth
o
d
s
.
T
h
e
p
r
o
ce
s
s
i
s
p
er
f
o
r
m
e
d
b
y
u
s
in
g
th
e
t
h
r
ee
v
er
tices
o
f
t
h
e
tr
ian
g
le
to
ca
lcu
late
th
e
I
GB
T
v
alv
e
s
witch
in
g
s
tate.
I
n
ad
d
i
tio
n
,
th
is
m
eth
o
d
also
u
s
es
t
h
e
co
ef
f
icie
n
t
k
as
a
f
ac
to
r
to
cr
ea
te
th
e
law
to
ex
p
an
d
th
e
SVM
m
o
d
u
latio
n
ca
p
ab
ilit
y
with
an
y
n
u
m
b
e
r
o
f
lev
els
wh
en
th
e
MM
C
ex
p
a
n
d
s
th
e
m
o
d
u
le
to
in
cr
ea
s
e
th
e
n
u
m
b
e
r
o
f
lev
els.
T
h
is
will
r
ed
u
ce
th
e
I
GB
T
v
alv
e
s
witch
in
g
s
tate
an
d
m
in
im
ize
t
h
e
co
m
p
u
tatio
n
al
p
r
ess
u
r
e
o
n
th
e
m
icr
o
p
r
o
ce
s
s
o
r
.
Giv
en
th
e
co
n
tr
o
l
r
eq
u
ir
em
en
ts
f
o
r
th
e
MM
C
,
th
e
p
r
o
p
o
s
ed
SVM
m
eth
o
d
h
as
ad
v
an
tag
es
s
u
ch
as
it
ca
n
g
e
n
er
ate
a
m
ax
i
m
u
m
n
u
m
b
e
r
o
f
v
o
ltag
e
le
v
el
s
o
f
2
N+
1
,
g
en
er
ate
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
r
esi
d
u
al
s
tates
to
b
alan
ce
th
e
ca
p
ac
ito
r
v
o
ltag
e.
an
d
s
witch
in
g
s
tate
o
p
tim
izatio
n
,
ca
n
b
e
ea
s
ily
ex
ten
d
ed
to
M
MC
with
an
y
n
u
m
b
er
o
f
lev
el
s
an
d
o
p
tim
al
co
m
p
u
tin
g
p
o
w
er
.
T
h
e
p
r
in
ci
p
le
o
f
th
e
m
eth
o
d
is
to
d
etec
t
a
h
e
x
a
g
o
n
with
two
le
v
els
in
th
e
lar
g
e
h
e
x
ag
o
n
to
s
elec
t
ty
p
e
1
a
n
d
ty
p
e
2
tr
ian
g
les,
th
er
eb
y
m
o
d
u
latin
g
th
e
v
o
ltag
e
v
ec
to
r
b
y
th
e
clo
s
est
v
ec
to
r
s
in
th
e
tr
ian
g
le.
d
etec
tab
le
with
o
u
t
lo
o
k
in
g
u
p
th
e
b
u
ilt
-
in
s
tate
tab
le.
C
o
m
p
ar
ed
with
p
r
ev
io
u
s
s
tu
d
ies
o
n
SVM
m
o
d
u
latio
n
,
th
is
m
eth
o
d
o
n
ly
p
er
f
o
r
m
s
th
e
s
tate
s
witch
in
g
p
r
o
ce
s
s
o
f
th
e
v
alv
es
o
n
3
v
er
tices
o
f
a
tr
ian
g
le
in
s
tead
o
f
4
v
er
tices
o
f
a
p
ar
allelo
g
r
am
lik
e
th
e
p
r
ev
io
u
s
m
eth
o
d
[
1
5
]
,
[
1
6
]
,
wh
ich
m
ea
n
s
r
ed
u
cin
g
th
e
n
u
m
b
er
o
f
ca
lcu
latio
n
s
f
o
r
th
e
m
icr
o
co
n
tr
o
ller
an
d
m
ak
in
g
th
e
im
p
ac
t
p
r
o
ce
s
s
f
a
s
ter
.
I
n
a
d
d
itio
n
,
th
is
m
eth
o
d
also
cr
ea
tes
a
r
u
le
to
cr
ea
te
a
n
y
n
u
m
b
e
r
o
f
lev
els
wh
en
th
e
c
o
n
f
ig
u
r
atio
n
o
f
th
e
MM
C
co
n
v
er
ter
is
ex
p
an
d
ed
to
th
e
co
r
r
esp
o
n
d
i
n
g
n
u
m
b
er
o
f
lev
els.
T
h
is
p
r
o
ce
s
s
will
s
av
e
tim
e
an
d
ef
f
o
r
t
wh
e
n
im
p
lem
e
n
tin
g
s
p
ec
i
f
ic
p
r
o
jects
in
p
r
ac
tice.
T
h
e
o
b
tain
ed
r
esu
lts
ar
e
p
r
o
v
e
d
b
y
s
im
u
latio
n
o
n
M
AT
L
AB
/
Simu
lin
k
s
o
f
twar
e
an
d
ex
p
er
im
en
tal
m
o
d
el
o
f
th
r
ee
-
p
h
ase
MM
C
co
n
v
er
ter
s
y
s
tem
b
ased
o
n
Ver
ilo
g
p
r
o
g
r
a
m
m
in
g
lan
g
u
a
g
e
an
d
f
ield
-
p
r
o
g
r
am
m
a
b
le
g
ate
ar
r
ay
(
FP
GA)
m
icr
o
co
n
tr
o
ller
k
it.
T
h
e
f
o
llo
win
g
s
ec
tio
n
s
o
f
t
h
e
p
ap
er
will
clea
r
ly
p
r
esen
t
s
o
m
e
o
f
th
e
co
n
ten
ts
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
u
latio
n
alg
o
r
ith
m
an
d
v
e
r
if
y
th
e
r
esu
lts
o
f
th
e
alg
o
r
it
h
m
.
Sp
ec
if
ically
:
i
n
s
ec
tio
n
2
,
th
e
s
tr
u
ct
u
r
e
an
d
o
p
er
atin
g
p
r
in
cip
le
o
f
MM
C
ar
e
p
r
esen
ted
.
Sectio
n
3
p
r
ese
n
ts
th
e
SVM
m
o
d
u
latio
n
m
et
h
o
d
th
at
ca
n
c
r
ea
te
r
u
les
ap
p
licab
le
to
MM
C
wi
th
an
y
n
u
m
b
er
o
f
lev
els.
Se
ctio
n
4
p
er
f
o
r
m
s
v
er
if
icatio
n
o
f
th
e
r
esu
lts
o
n
s
im
u
latio
n
s
o
f
twar
e.
Sectio
n
5
v
er
if
ies th
e
alg
o
r
ith
m
o
n
an
e
x
p
er
im
en
tal
m
o
d
el.
Fin
ally
,
t
h
e
co
n
clu
s
io
n
.
2.
P
RINCI
P
L
E
O
F
O
P
E
R
AT
I
O
N
AND
DE
S
CRIP
T
I
O
N
O
F
T
H
E
M
M
C
CO
NV
E
R
T
E
R
Fig
u
r
e
1
d
escr
ib
es
th
e
th
r
ee
-
p
h
ase
s
tr
u
ctu
r
e
o
f
th
e
MM
C
.
E
ac
h
p
h
ase
h
as
2
N
SMs.
T
h
e
S
Ms
in
th
e
u
p
p
er
ar
m
ar
e
d
e
n
o
ted
f
r
o
m
SM
j_1
to
SM
j_N
(
j
=
A
,
B
,
C
)
,
th
e
SMs
in
th
e
lo
wer
ar
m
ar
e
d
en
o
ted
f
r
o
m
SM
j_N+
1
to
SM
j_2N
.
T
h
e
DC
s
id
e
o
f
th
e
MM
C
is
co
n
n
ec
ted
to
a
s
in
g
le
VDC
s
o
u
r
ce
with
th
e
co
r
r
esp
o
n
d
in
g
i
DC
cu
r
r
en
t.
I
n
ea
ch
b
r
an
c
h
o
f
t
h
e
MM
C
,
th
er
e
ex
is
t
u
p
p
er
b
r
an
ch
c
u
r
r
e
n
ts
d
en
o
ted
i
j_H
an
d
lo
wer
b
r
an
ch
cu
r
r
e
n
ts
d
en
o
ted
i
j_L
.
T
h
e
AC
s
id
e
cu
r
r
en
t
d
e
n
o
ted
i
j
is
d
r
awn
at
th
e
m
id
p
o
in
t o
f
th
e
in
d
u
cto
r
L
o
o
f
th
e
u
p
p
er
an
d
lo
wer
a
r
m
s
in
ea
ch
p
h
ase.
T
h
is
in
d
u
cto
r
h
as
th
e
ef
f
ec
t
o
f
lim
itin
g
t
h
e
wo
r
k
in
g
tr
a
n
s
ien
ts
o
f
t
h
e
MM
C
.
T
h
e
lo
s
s
es
in
ea
ch
b
r
an
ch
o
f
th
e
MM
C
ar
e
d
esc
r
ib
ed
b
y
th
e
r
esis
to
r
R
o
[
1
7
]
,
[
1
8
]
.
MM
C
co
n
v
er
ter
wo
r
k
s
o
n
th
e
p
r
in
cip
le
o
f
VSM
v
o
ltag
e
ac
cu
m
u
latio
n
o
f
SMs to
g
en
er
ate
AC
v
o
ltag
e
i
n
ea
ch
p
h
ase.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
3
4
-
5
2
4
8
5236
Fo
r
ea
ch
SM,
th
e
o
u
tp
u
t
v
o
ltag
e
will
b
e
ass
o
ciate
d
with
o
n
e
o
f
two
o
p
p
o
s
ite
s
tates
an
d
is
d
ef
in
ed
as
in
s
er
ted
o
r
b
y
p
ass
ed
b
ased
o
n
th
e
s
witch
in
g
s
tates
o
f
th
e
v
al
v
es
in
th
e
d
ir
ec
tio
n
o
f
th
e
cu
r
r
en
t
in
th
e
cir
c
u
it
as
s
h
o
wn
in
Fig
u
r
es 2
,
in
wh
ich
:
Fig
u
r
e
2
(
a
)
s
h
o
ws th
e
cu
r
r
en
t
g
o
in
g
i
n
th
e
p
o
s
itiv
e
d
ir
ec
tio
n
,
Fig
u
r
e
2
(
b
)
s
h
o
ws
th
e
cu
r
r
en
t
g
o
in
g
in
th
e
n
e
g
ativ
e
d
ir
ec
tio
n
.
Fo
r
MM
C
,
v
o
lta
g
e
is
d
is
tr
ib
u
te
d
ac
r
o
s
s
th
e
ca
p
ac
ito
r
s
o
f
ea
ch
SM
in
all
v
alv
e
ar
m
s
in
ea
c
h
p
h
ase.
SM
1
SM
2
SM
N
SM
N
+
1
SM
N
+
2
SM
2
N
L
o
L
o
i
HA
i
LA
i
DC
i
A
i
C
SM
1
SM
2
SM
N
SM
N
+
1
SM
N
+
2
SM
2
N
SM
1
SM
2
SM
N
SM
N
+
1
SM
N
+
2
SM
2
N
SM
S
1
S
2
R
o
R
o
V
DC
+
_
V
Ha
v
La
+
_
v
C
v
B
v
A
V
C
L
o
L
o
i
HB
i
LB
R
o
R
o
L
o
L
o
i
HC
i
LC
R
o
R
o
i
B
+
_
Fig
u
r
e
1
.
T
h
r
ee
-
p
h
ase
s
tr
u
ctu
r
e
d
iag
r
am
o
f
MM
C
co
n
v
e
r
ter
+
_
+
_
v
C
C
S
1
S
2
D
1
D
2
i
v
out
+
_
+
_
v
C
C
S
1
S
2
D
1
D
2
i
v
out
(
a)
+
_
+
_
v
C
C
S
1
S
2
D
1
D
2
i
v
out
+
_
+
_
v
C
C
S
1
S
2
D
1
D
2
i
v
out
(
b
)
Fig
u
r
e
2
.
Def
in
itio
n
o
f
th
e
in
s
er
ted
an
d
b
y
p
ass
ed
s
tates f
o
r
a
s
u
b
m
o
d
u
le
(
SM)
b
ased
o
n
th
e
s
witch
in
g
s
tates
o
f
its
v
alv
es in
th
e
cu
r
r
en
t
d
ir
e
ctio
n
:
(
a)
in
s
er
ted
s
tate
o
f
SM
an
d
(
b
)
b
y
p
ass
s
tate
o
f
SM
I
f
th
e
to
tal
v
o
ltag
e
o
f
th
e
SMs
is
in
s
er
ted
o
n
ea
ch
ar
m
is
d
if
f
er
en
t,
th
e
cu
r
r
en
t
will
b
e
g
en
e
r
ated
f
r
o
m
th
e
v
o
ltag
e
im
b
alan
ce
ac
r
o
s
s
th
e
ca
p
ac
ito
r
s
.
I
f
in
s
tan
tan
eo
u
s
cu
r
r
en
t f
r
o
m
th
e
AC
co
n
n
ec
ti
o
n
p
o
in
t
f
lo
ws
in
to
th
e
MM
C
C
o
n
v
er
ter
an
d
s
p
li
ts
in
to
th
e
u
p
p
er
an
d
lo
wer
ar
m
s
s
id
e
DC
,
th
en
th
e
ca
p
a
cito
r
s
o
f
ea
ch
SM
in
s
er
ted
in
th
e
u
p
p
er
ar
m
s
wil
l
b
e
in
th
e
d
is
ch
ar
g
e
s
tate,
i
n
t
h
e
lo
wer
a
r
m
s
will
b
e
in
th
e
c
h
ar
g
in
g
s
tate.
I
f
th
e
d
ir
ec
tio
n
o
f
th
e
AC
cu
r
r
e
n
t
is
in
th
e
o
p
p
o
s
ite
d
ir
ec
tio
n
,
th
e
d
is
ch
ar
g
e
an
d
ch
a
r
g
e
s
tates
will
co
r
r
esp
o
n
d
t
o
th
e
ca
p
ac
ito
r
s
in
th
e
lo
wer
an
d
u
p
p
er
ar
m
s
,
r
esp
ec
tiv
ely
.
B
ec
a
u
s
e
o
f
th
e
p
h
ase
d
if
f
e
r
en
ce
b
e
twee
n
th
e
th
r
ee
AC
cu
r
r
en
ts
,
th
e
d
is
ch
ar
g
e
an
d
c
h
ar
g
e
s
tates
o
f
th
e
ca
p
ac
ito
r
s
o
n
ea
ch
p
h
ase
a
r
e
co
n
tin
u
o
u
s
ly
ch
an
g
ed
f
r
o
m
p
h
ase
to
p
h
ase.
Sin
ce
th
e
to
t
al
n
u
m
b
er
o
f
SMs
in
s
er
ted
in
a
b
r
an
ch
is
co
n
s
tan
t,
th
e
to
t
al
v
o
ltag
e
ac
r
o
s
s
a
b
r
an
ch
in
o
n
e
cy
cle
is
a
v
al
u
e
th
at
o
s
cillates
at
th
e
s
am
e
f
r
eq
u
en
cy
as
th
e
ac
s
id
e.
Ho
wev
er
,
t
h
is
v
alu
e
f
lu
ctu
ates
asy
n
ch
r
o
n
o
u
s
ly
in
th
e
ar
m
s
o
f
th
e
c
o
n
v
e
r
ter
,
cr
ea
tin
g
a
v
o
ltag
e
im
b
ala
n
ce
b
etwe
en
th
e
in
s
er
te
d
v
o
ltag
es
in
ea
c
h
ar
m
,
ca
u
s
in
g
cu
r
r
e
n
t
to
f
lo
w
in
t
h
e
ar
m
s
o
f
th
e
MM
C
.
T
h
is
cu
r
r
en
t
is
ca
lled
th
e
cir
cu
latin
g
cu
r
r
en
t
i
v
.
T
h
e
cu
r
r
en
t
i
v
h
as
n
o
ef
f
ec
t
o
n
t
h
e
o
u
ts
id
e
o
f
th
e
MM
C
o
n
b
o
th
th
e
AC
an
d
DC
s
id
es.
Ho
wev
er
,
th
e
cu
r
r
e
n
t
iv
is
th
e
ca
u
s
e
o
f
th
e
lo
s
s
o
f
th
e
MM
C
[
1
9
]
,
[
2
0
]
.
T
h
e
in
d
u
ctan
ce
o
n
ea
ch
a
r
m
h
as
th
e
r
o
le
o
f
r
ed
u
cin
g
th
e
ef
f
ec
t
o
f
cu
r
r
e
n
t
i
v
[
2
1
]
,
[
2
2
]
.
I
f
t
h
e
in
d
u
ctan
ce
L
o
o
f
ea
ch
ar
m
is
lar
g
e,
t
h
e
am
p
litu
d
e
o
f
th
e
cir
cu
latin
g
cu
r
r
en
t
will
b
e
s
m
all.
Ho
wev
er
,
wh
en
th
e
v
al
u
e
o
f
L
o
is
lar
g
e,
th
e
r
esp
o
n
s
e
t
im
e
o
f
th
e
s
y
s
tem
in
cr
ea
s
es,
th
e
co
n
v
er
ter
will
n
o
t
b
e
a
b
le
to
q
u
ick
l
y
ch
a
n
g
e
t
h
e
cu
r
r
en
t
v
alu
e,
s
o
th
e
ca
lcu
l
atio
n
an
d
s
elec
tio
n
o
f
th
e
in
d
u
ctan
ce
v
alu
e
s
h
o
u
l
d
m
atch
th
e
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
[
2
3
]
.
A
p
p
ly
Kir
ch
h
o
f
f
'
s
law
to
Fig
u
r
e
1
,
w
e
h
av
e
s
y
s
tem
o
f
(
1
)
.
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:
2088
-
8
7
0
8
S
imu
la
tio
n
a
n
d
ex
p
erimen
ta
l v
a
lid
a
tio
n
o
f MMC
ca
p
a
b
le
o
f
p
r
o
d
u
cin
g
…
(
Tr
a
n
Hu
n
g
C
u
o
n
g
)
5237
{
=
−
−
+
1
2
=
+
−
1
2
=
−
=
+
+
(
+
)
(
1
)
Fro
m
(
1
)
ad
d
in
g
th
e
f
i
r
s
t two
eq
u
atio
n
s
to
g
eth
e
r
,
th
e
o
u
tp
u
t
v
o
ltag
e
is
ex
p
r
ess
ed
as (
2
)
.
=
1
2
(
−
)
+
2
(
2
)
T
h
er
ef
o
r
e,
th
e
AC
elec
tr
o
m
o
ti
v
e
f
o
r
ce
o
f
th
e
MM
C
is
wr
itte
n
as (
3
)
.
=
1
2
(
−
)
(
3
)
I
f
th
e
s
y
m
b
o
ls
k
H
,
k
L
ar
e
SM
n
u
m
b
er
s
in
th
e
u
p
p
er
an
d
lo
wer
ar
m
s
ar
e
in
s
er
ted
,
th
e
co
r
r
e
s
p
o
n
d
in
g
v
o
ltag
e
is
wr
itten
as (
4
)
.
=
,
=
(
4
)
W
h
er
e
V
C
=
V
DC
/N
i
s
th
e
v
o
ltag
e
p
er
s
tep
o
n
ea
c
h
ca
p
ac
it
o
r
o
f
SM
ass
u
m
in
g
th
at
th
e
v
o
ltag
e
ac
r
o
s
s
ea
ch
ca
p
ac
ito
r
is
th
e
s
am
e.
T
h
e
n
u
m
b
er
o
f
v
o
ltag
e
lev
els
o
n
ea
c
h
u
p
p
e
r
ar
m
a
n
d
ea
ch
l
o
wer
a
r
m
is
N
+1
.
Fro
m
(
3
)
an
d
(
4
)
,
th
e
o
u
tp
u
t v
o
ltag
e
s
ca
le
will h
av
e
th
e
s
am
e
lev
el
as
(
5
)
.
=
1
2
=
1
2
(
5
)
T
h
en
,
th
e
o
u
tp
u
t v
o
ltag
e
h
as th
e
f
o
r
m
as (
6
)
.
=
(
−
)
1
2
=
;
=
−
(
6
)
T
o
m
a
k
e
a
v
o
l
t
a
g
e
l
e
v
e
l
k
M
,
t
h
e
c
o
r
r
e
s
p
o
n
d
i
n
g
l
e
v
e
l
s
o
f
k
H
,
k
L
a
r
e
c
a
l
c
u
l
a
t
e
d
a
c
c
o
r
d
i
n
g
t
o
(
7
)
.
=
⌊
+
1
+
2
⌋
;
=
⌊
+
1
−
2
⌋
(
7
)
3.
SVM
M
O
DUL
AT
I
O
N
F
O
R
M
M
C
WI
T
H
ANY
NU
M
B
E
R
O
F
L
E
V
E
L
S
SVM
m
o
d
u
latio
n
f
o
r
MM
C
ca
n
b
e
d
o
n
e
b
y
ad
ju
s
tin
g
t
h
e
o
u
tp
u
t
v
o
ltag
e
ac
r
o
s
s
th
e
lo
ad
,
wh
ich
is
ca
lled
th
e
m
o
d
u
latio
n
v
o
ltag
e.
T
o
g
en
er
ate
th
e
m
o
d
u
lated
v
o
ltag
e,
th
e
f
ir
s
t
th
in
g
to
d
o
is
to
d
ef
in
e
th
e
s
p
ac
e
o
f
o
p
er
atin
g
s
tates
o
f
th
e
v
o
ltag
e
v
ec
to
r
in
th
e
co
o
r
d
in
ate
s
y
s
tem
ab
c.
W
h
en
MM
C
h
as
N
n
u
m
b
er
o
f
ac
tiv
e
SMs
in
ea
ch
p
h
ase,
th
e
n
u
m
b
er
o
f
MM
C
lev
els
wi
ll
b
e
M
=
2
N
+1
an
d
th
e
r
ef
er
en
ce
v
o
ltag
e
v
ec
to
r
o
f
th
e
MM
C
is
s
y
n
th
esized
f
r
o
m
th
e
co
o
r
d
in
ates o
f
th
e
v
ec
t
o
r
s
p
ac
e
an
d
is
ex
p
r
ess
ed
b
y
(
8
)
.
=
2
3
(
+
⋅
+
2
⋅
)
(
8
)
I
n
th
er
e:
{
=
.
=
.
=
.
;
=
2
3
;
2
=
4
3
W
ith
,
,
∈
{
−
−
1
2
,
…
,
−
1
,
0
,
1
,
…
,
−
1
2
}
Vo
ltag
e
v
ec
to
r
r
ep
r
esen
tatio
n
o
n
th
e
p
lan
e
α
:
=
+
;
in
th
er
e
=
;
=
1
√
3
(
−
)
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
3
4
-
5
2
4
8
5238
R
ep
r
esen
tin
g
th
e
v
o
ltag
e
v
ec
t
o
r
in
th
e
c
o
o
r
d
in
ate
s
y
s
tem
gh
will b
e
th
e
s
y
s
tem
o
f
(
1
0
)
.
{
=
+
1
2
ℎ
=
√
3
2
ℎ
,
⇒
{
=
−
1
√
3
ℎ
=
2
√
3
(
1
0
)
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
c
o
o
r
d
in
ate
s
y
s
tem
s
is
s
h
o
wn
b
y
(
1
1
)
.
{
=
−
1
√
3
=
−
1
3
(
−
)
=
2
3
(
−
)
ℎ
=
2
√
3
=
2
3
(
−
)
(
1
1
)
Fro
m
(
1
1
)
s
ee
th
at:
−
=
(
−
)
;
−
=
(
−
)
T
h
er
ef
o
r
e
=
2
3
(
−
)
;
ℎ
=
2
3
(
−
)
(
1
2
)
If
2
/3
V
DC
is
tak
en
as
th
e
b
ase
len
g
th
o
f
t
h
e
s
tate
v
ec
to
r
s
k
A
,
k
B
,
k
C
as
in
teg
er
s
,
th
e
co
o
r
d
in
ates
o
f
th
e
[
,
ℎ
]
=
[
(
−
)
,
(
−
)
]
v
ec
to
r
s
ar
e
in
teg
er
s
.
T
h
e
n
th
e
v
er
tex
co
o
r
d
in
ates
o
f
th
e
v
ec
to
r
s
will
cr
ea
te
eq
u
ilater
al
tr
ian
g
les
with
s
id
e
1
as
s
h
o
wn
in
Fig
u
r
e
3
.
E
ac
h
v
ec
to
r
ca
n
co
r
r
esp
o
n
d
to
d
i
f
f
er
en
t
lev
el
s
tates,
ca
lled
r
esid
u
al
s
tates.
Fo
r
ea
ch
s
tate
v
ec
to
r
,
a
co
m
b
in
atio
n
o
f
s
tate
lev
els as (
1
3
)
.
[
ℎ
]
⇔
[
]
=
[
−
−
−
ℎ
]
(
1
3
)
V
1
V
2
V
3
V
4
V
5
V
6
V
7
V
8
V
9
V
10
V
11
V
12
V
13
V
14
V
15
V
16
V
18
V
17
V
0
(
0
,
-
1
,
-
1
)
(
1
,
-
1
,
-
1
)
(
1
,
-
1
,
1
)
(
1
,
-
1
,
0
)
(
0
,
1
,
1
)
(
-
1
,
0
,
0
)
(
-
1
,
1
,
1
)
(
1
,
1
,
0
)
(
0
,
0
,
-
1
)
(
1
,
0
,
-
1
)
(
1
,
1
,
-
1
)
(
0
,
-
1
,
1
)
(
1
,
0
,
1
)
(
0
,
-
1
,
0
)
(
-
1
,
-
1
,
1
)
(
-
1
,
-
1
,
0
)
(
0
,
0
,
1
)
(
-
1
,
0
,
1
)
(
1
-
,
1
,
0
)
(
-
1
,
0
,
-
1
)
(
0
,
1
,
0
)
(
0
,
1
,
-
1
)
(
-
1
,
1
,
-
1
)
(
1
,
1
,
1
)
(
0
,
0
,
0
)
(
-
1
,
-
1
,
-
1
)
Fig
u
r
e
3
.
Switch
in
g
s
tate
in
v
e
cto
r
s
p
ac
e
o
f
m
u
ltil
ev
el
co
n
v
e
r
ter
I
n
th
e
f
ir
s
t
s
ix
th
co
r
n
er
,
v
ec
t
o
r
s
ly
in
g
o
n
th
e
o
u
ter
m
o
s
t
h
ex
ag
o
n
h
a
v
e
k
g
+
k
h
=
M
-
1
,
with
o
n
ly
o
n
e
s
u
itab
le
v
alu
e
o
f
k
=
(M
-
1
)
/2
.
I
n
th
e
n
ex
t
h
e
x
ag
o
n
in
s
id
e
k
g
+
k
h
=
M
-
2
,
k
h
as
two
v
alu
es:
(M
-
1
)
/2
-
1
a
n
d
(M
-
1
)
/2
,
m
ea
n
in
g
th
at
ea
ch
v
ec
to
r
h
as
two
r
esid
u
al
s
tate
s
.
I
n
th
is
way
,
th
e
ze
r
o
-
v
ec
to
r
k
will
h
av
e
M
v
alu
es,
f
r
o
m
-
(M
-
1
)
/2
to
(
M
-
1
)
/2
,
s
o
th
e
ze
r
o
v
ec
to
r
will
h
av
e
M
r
esid
u
als.
Fro
m
th
is
,
it
is
p
o
s
s
ib
le
to
co
m
p
u
te
all
co
m
b
in
atio
n
s
o
f
s
tate
v
ec
to
r
s
in
v
ec
to
r
s
p
ac
e.
Dete
r
m
in
e
th
e
m
o
d
u
latio
n
f
ac
to
r
f
r
o
m
t
h
e
th
r
ee
n
ea
r
est v
ec
to
r
s
:
T
h
e
NVM
m
eth
o
d
will
g
en
er
ate
th
e
d
esire
d
o
u
tp
u
t
v
ec
to
r
l
o
ca
ted
in
an
y
tr
ian
g
le
s
y
n
th
es
ized
f
r
o
m
th
e
th
r
ee
v
ec
to
r
s
th
at
ar
e
th
e
v
er
tices
o
f
th
is
tr
ian
g
le,
wh
ich
ca
n
en
s
u
r
e
th
e
b
est
h
a
r
m
o
n
ic
c
o
m
p
o
s
itio
n
f
o
r
th
e
o
u
tp
u
t
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:
2088
-
8
7
0
8
S
imu
la
tio
n
a
n
d
ex
p
erimen
ta
l v
a
lid
a
tio
n
o
f MMC
ca
p
a
b
le
o
f
p
r
o
d
u
cin
g
…
(
Tr
a
n
Hu
n
g
C
u
o
n
g
)
5239
v
o
ltag
e
wav
ef
o
r
m
[
6
]
.
T
h
e
e
q
u
ilater
al
tr
ian
g
les
jo
in
to
g
et
h
er
to
cr
ea
te
a
n
eq
u
ilater
al
r
h
o
m
b
u
s
,
wh
o
s
e
s
id
es
ar
e
p
ar
allel
to
th
e
gh
a
x
is
,
th
e
v
er
tices a
r
e
th
e
s
tate
v
ec
to
r
s
p
1
, p
2
, p
3
,
p
4
,
as sh
o
wn
in
Fig
u
r
e
4
.
p
2
(
k
g
+
1
,
k
h
)
p
1
(
k
g
,
k
h
)
p
4
(
k
g
+
1
,
k
h
+
1
)
p
3
(
k
g
,
k
h
+
1
)
m
h
m
g
a
g
h
0
Fig
u
r
e
4
.
Sy
n
th
esis
o
f
th
e
o
u
tp
u
t v
o
ltag
e
v
ec
to
r
f
r
o
m
th
e
th
r
e
e
v
er
tex
v
ec
t
o
r
s
o
f
t
h
e
tr
ian
g
le
T
h
e
d
esire
d
o
u
tp
u
t
v
o
ltag
e
v
e
cto
r
is
also
lin
ea
r
ly
n
o
r
m
alize
d
to
2
/3
V
DC
a
n
d
lin
ea
r
ly
c
o
n
v
er
ted
to
t
h
e
gh
co
o
r
d
in
ate
s
y
s
tem
ac
co
r
d
in
g
to
(
1
4
)
.
[
ℎ
]
=
[
1
−
1
√
3
0
2
√
3
]
⋅
[
]
=
1
[
]
(
1
4
)
w
h
er
e
M
1
is
th
e
tr
a
n
s
f
o
r
m
ati
o
n
m
atr
i
x
.
L
et
m
g
,
m
h
b
e
th
e
d
ec
im
al
p
a
r
ts
ap
ar
t
f
r
o
m
th
e
in
teg
er
p
ar
t
o
f
th
e
co
o
r
d
in
ates
v
rg
, v
rh
r
esp
ec
tiv
el
y
as (
1
5
)
.
{
=
−
⌊
|
|
⌋
=
−
ℎ
=
ℎ
−
⌊
|
ℎ
|
⌋
=
ℎ
−
ℎ
(
1
5
)
wh
er
e
=
⌊
|
|
⌋
,
ℎ
=
⌊
|
ℎ
|
⌋
is
th
e
s
m
allest
in
teg
er
o
f
th
e
c
o
r
r
esp
o
n
d
in
g
ab
s
o
lu
te
v
alu
es.
T
h
e
f
ig
u
r
e
s
h
o
ws th
at
two
tr
ian
g
les co
n
ta
in
in
g
v
ec
to
r
s
V
1
, V
2
h
a
v
e
th
e
s
am
e
in
teg
er
co
o
r
d
i
n
ates
[k
g
, k
h
].
I
t
ca
n
b
e
s
ee
n
t
h
at
th
e
lin
e
+
ℎ
=
1
d
iv
id
es
th
e
r
h
o
m
b
u
s
in
Fig
u
r
e
5
in
to
two
tr
ian
g
les,
wh
e
r
e
v
ec
to
r
V
1
b
elo
n
g
s
to
d
o
m
ain
+
ℎ
≤
1
an
d
v
ec
to
r
V
2
b
el
o
n
g
s
to
d
o
m
ain
+
ℎ
>
1
.
1
is
s
y
n
th
esized
f
r
o
m
3
v
ec
to
r
s
p
1
, p
2
,
p
3
as (
1
6
)
.
1
=
1
+
(
2
−
1
)
+
ℎ
(
3
−
1
)
=
(
1
−
−
ℎ
)
1
+
2
+
ℎ
3
(
1
6
)
V
2
is
s
y
n
th
esized
f
r
o
m
3
v
ec
to
r
s
p
2
, p
3
, p
4
as
(
1
7
)
.
2
=
4
+
(
1
−
)
(
3
−
4
)
+
(
1
−
ℎ
)
(
2
−
4
)
=
(
+
ℎ
−
1
)
4
+
(
1
−
)
3
+
(
1
−
ℎ
)
2
(
1
6
)
Sin
ce
th
e
co
ef
f
icien
ts
co
r
r
esp
o
n
d
in
g
t
o
th
e
v
ec
to
r
s
ar
e
all
p
o
s
itiv
e
an
d
s
u
m
to
1
,
th
ese
will
b
e
th
e
co
ef
f
icien
ts
f
o
r
th
e
m
o
d
u
latio
n
p
r
o
ce
s
s
.
E
q
u
atio
n
s
(
1
6
)
,
(
1
7
)
also
s
h
o
w
th
at
th
e
ca
lcu
latio
n
o
f
th
e
m
o
d
u
latio
n
c
o
ef
f
icien
ts
is
v
er
y
s
im
p
le,
th
r
o
u
g
h
th
e
ca
l
cu
latio
n
o
f
v
rg
,
v
rh
,
t
h
e
in
teg
e
r
p
ar
ts
k
g
,
k
h
a
n
d
th
e
o
d
d
p
a
r
ts
m
g
,
m
h
th
r
o
u
g
h
th
e
(
1
5
)
.
3
.
1
.
L
o
ca
t
e
t
he
v
ec
t
o
r
v
in t
he
la
rg
e
s
ec
t
o
r
W
h
en
th
e
MM
C
co
n
v
e
r
ter
g
r
o
ws
with
an
y
n
u
m
b
e
r
o
f
lev
el
s
M
th
en
th
e
n
u
m
b
er
o
f
s
u
b
-
tr
ian
g
les
o
n
th
e
v
ec
to
r
p
la
n
e
will
in
cr
ea
s
e
r
ap
id
ly
.
T
h
e
ca
lcu
latio
n
b
ec
o
m
es
s
im
p
ler
if
we
u
s
e
th
e
s
y
m
m
etr
y
o
f
t
h
e
s
p
ac
e
v
ec
to
r
s
y
s
tem
in
ea
ch
o
f
t
h
e
s
ix
th
s
.
Sh
o
w
o
n
th
e
v
ec
to
r
p
lan
e
th
r
ee
co
o
r
d
in
ate
s
y
s
tem
s
o
f
th
e
h
ex
ag
o
n
al
an
g
le
(Z
1x
,
Z
1y
)
,
(
Z
2x
,
Z
2y
)
,
(
Z
3x
,
Z
3y
)
,
as
s
h
o
wn
in
Fig
u
r
e
5
.
First,
it
is
n
ec
ess
ar
y
to
d
eter
m
in
e
th
e
p
r
o
jectio
n
o
f
th
e
d
esire
d
o
u
tp
u
t
v
o
ltag
e
v
ec
to
r
o
n
to
th
e
two
b
o
u
n
d
ar
y
v
ec
to
r
s
o
f
th
e
s
ix
th
an
g
le
b
y
p
r
o
ject
in
g
th
e
co
o
r
d
in
ates
=
[
,
]
o
n
to
t
h
e
co
r
r
esp
o
n
d
in
g
co
o
r
d
in
ate
s
y
s
tem
Z
1
,
Z
2
,
Z
3
.
T
h
is
ca
n
b
e
d
o
n
e
with
tr
an
s
f
o
r
m
atio
n
m
atr
ices o
f
th
e
co
o
r
d
in
ate
s
y
s
t
em
M
1
, M
2
, M
3
lik
e
(
1
8
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
3
4
-
5
2
4
8
5240
1
=
[
1
−
1
√
3
0
2
√
3
]
;
2
=
[
1
1
√
3
−
1
1
√
3
]
;
3
=
[
0
2
√
3
−
1
−
1
√
3
]
(
1
8
)
T
h
r
o
u
g
h
a
n
i
n
t
e
r
m
e
d
i
a
t
e
v
a
r
i
ab
l
e
=
∗
/
√
3
,
t
h
e
r
e
m
a
i
n
i
n
g
c
o
m
p
o
n
e
n
t
s
c
a
n
b
e
i
m
m
e
d
i
a
t
el
y
d
e
f
i
n
e
d
a
s
(
1
9
)
:
{
1
=
∗
−
1
=
2
;
{
2
=
1
+
1
2
=
−
1
;
{
3
=
1
3
=
−
2
(
1
9
)
Af
ter
d
eter
m
in
in
g
th
e
z
ij
c
o
o
r
d
in
ates,
th
e
s
ec
to
r
d
eter
m
in
atio
n
alg
o
r
ith
m
is
s
h
o
wn
in
Fig
u
r
e
6
.
Z
1
x
Z
1
y
0
I
II
III
IV
V
VI
Z
2
x
0
I
II
III
IV
V
VI
Z
3
x
Z
3
y
0
I
II
III
IV
V
VI
Fig
u
r
e
5
.
T
h
r
ee
n
o
n
-
p
er
p
e
n
d
ic
u
lar
co
o
r
d
in
ate
s
y
s
tem
s
th
at
m
ak
e
u
p
t
h
e
h
ex
a
g
o
n
s
(
s
ec
to
r
s
)
Z
1
x
.
Z
1
y
<
0
C
oor
di
na
t
e
s
[
g
,
h
]
Z
1
x
>
0
S
e
c
t
or
I
S
e
c
t
or
I
V
Z
2
x
.
Z
2
y
<
0
Z
2
x
>
0
S
e
c
t
or
I
I
S
e
c
t
or
V
Z
1
x
>
0
S
e
c
t
or
I
I
I
S
e
c
t
or
V
I
Y
e
s
No
Y
e
s
No
Y
e
s
No
Y
e
s
No
Y
e
s
No
Fig
u
r
e
6
.
Alg
o
r
ith
m
to
d
eter
m
in
e
lar
g
e
s
ec
to
r
3
.
2
.
Det
er
m
ine t
he
s
t
a
t
e
v
ec
t
o
rs in sect
o
rs
3
.
2
.
1
.
Def
ine st
a
t
e
v
ec
t
o
rs a
t
s
ec
t
o
r
I
T
h
e
s
ix
th
an
g
le
I
,
th
e
c
o
o
r
d
in
a
te
s
y
s
tem
is
Z
1
,
f
r
o
m
(
2
0
)
we
h
av
e:
{
1
=
=
2
3
(
−
)
1
=
ℎ
=
2
3
(
−
)
T
h
en
[
1
1
]
=
[
(
−
)
(
−
)
]
(
2
0
)
I
f
tak
in
g
th
e
co
o
r
d
in
ates
k
A
=
k
th
en
th
e
w
o
r
d
(
2
0
)
will
b
e
o
b
tain
ed
o
n
th
e
co
o
r
d
in
ate
s
y
s
tem
,
th
en
t
h
e
s
tate
v
ec
to
r
co
o
r
d
in
ates w
ill b
e:
[
1
1
]
⇔
[
]
=
[
−
1
−
1
−
1
]
So
th
at:
−
−
1
2
≤
,
−
1
,
−
1
−
1
≤
−
1
2
(
2
1
)
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:
2088
-
8
7
0
8
S
imu
la
tio
n
a
n
d
ex
p
erimen
ta
l v
a
lid
a
tio
n
o
f MMC
ca
p
a
b
le
o
f
p
r
o
d
u
cin
g
…
(
Tr
a
n
Hu
n
g
C
u
o
n
g
)
5241
3
.
2
.
2
.
Def
ine st
a
t
e
v
ec
t
o
rs a
t
s
ec
t
o
r
I
I
Seco
n
d
s
ix
th
an
g
le,
co
o
r
d
in
ate
s
y
s
tem
is
Z
2
,
f
r
o
m
(
1
9
)
we
h
a
v
e:
{
2
=
1
+
1
=
2
3
(
−
)
2
=
−
1
=
2
3
(
−
)
T
h
en
:
[
2
2
]
=
[
(
−
)
(
−
)
]
(
2
2
)
C
h
o
o
s
e
k
B
=
k
t
o
s
a
t
i
s
f
y
t
h
e
c
o
n
d
i
t
i
o
n
(
2
1
)
,
t
h
e
r
e
m
a
i
n
i
n
g
c
o
o
r
d
i
n
a
t
e
s
i
n
s
e
c
t
o
r
I
I
a
r
e
d
e
t
e
r
m
i
n
e
d
a
s
(
2
3
)
.
[
2
2
]
⇔
[
]
=
[
−
2
−
2
−
2
]
(
2
3
)
3
.
2
.
3
.
Def
ine st
a
t
e
v
ec
t
o
rs a
t
s
ec
t
o
r
I
I
I
T
h
e
th
ir
d
s
ix
th
a
n
g
le,
th
e
co
o
r
d
in
ate
s
y
s
tem
is
Z
3
,
f
r
o
m
(
1
9
)
we
h
av
e:
{
3
=
1
=
2
3
(
−
)
3
=
−
2
=
2
3
(
−
)
T
h
en
[
3
3
]
=
[
(
−
)
(
−
)
]
(
2
4
)
C
h
o
o
s
e
k
C
=
k
t
o
s
a
t
i
s
f
y
t
h
e
c
o
n
d
i
t
i
o
n
(
2
1
)
,
t
h
e
r
e
m
a
i
n
i
n
g
c
o
o
r
d
i
n
a
t
e
s
i
n
s
e
c
t
o
r
I
I
I
a
r
e
d
e
t
e
r
m
i
n
e
d
a
s
(
2
5
)
.
[
3
3
]
⇔
[
]
=
[
−
3
−
3
−
3
]
(
2
5
)
Sin
ce
th
e
s
p
ac
e
v
ec
to
r
s
ar
e
s
y
m
m
etr
ical,
it
is
o
b
v
io
u
s
th
at
s
ec
to
r
I
V
is
s
y
m
m
etr
ical
with
s
ec
to
r
I
.
Secto
r
V
is
s
y
m
m
etr
ical
with
s
ec
to
r
I
I
.
Secto
r
VI
is
s
y
m
m
etr
ical
with
s
ec
to
r
I
I
I
.
T
h
er
ef
o
r
e,
th
e
wa
y
to
d
eter
m
in
e
t
h
e
s
tate
v
ec
to
r
s
is
d
o
n
e
s
im
ilar
ly
.
3
.
3
.
O
pti
m
a
l o
rder
f
o
r
nu
mb
er
o
f
s
wit
ches
W
h
en
s
p
ac
e
v
ec
t
o
r
m
o
d
u
latio
n
f
o
r
a
two
-
lev
el
in
v
e
r
to
r
,
Sy
m
m
etr
ical
tr
ian
g
le
m
o
d
u
latio
n
u
s
es
o
n
l
y
two
ed
g
e
v
ec
to
r
s
an
d
ze
r
o
v
ec
to
r
s
,
s
u
ch
th
at
t
h
e
tim
e
u
s
in
g
t
h
e
ze
r
o
-
v
ec
to
r
d
iv
id
e
d
eq
u
ally
in
to
two
p
ar
ts
,
At
th
e
b
eg
i
n
n
in
g
an
d
e
n
d
o
f
ea
ch
m
o
d
u
latio
n
h
alf
cy
cle,
in
th
e
o
th
er
h
alf
th
e
o
r
d
e
r
o
f
v
ec
to
r
e
x
ec
u
tio
n
is
r
ev
er
s
ed
.
T
h
is
will
o
p
tim
ize
th
e
h
ar
m
o
n
ic
co
m
p
o
n
en
t
o
n
th
e
o
u
tp
u
t
v
o
ltag
e
[
2
4
]
.
T
h
is
m
o
d
u
latio
n
is
ca
lled
SVM
m
o
d
u
latio
n
with
ac
tiv
e
v
ec
to
r
s
p
lace
d
b
etwe
en
ea
ch
h
alf
-
cy
cle
o
f
th
e
m
o
d
u
lati
o
n
.
T
h
is
m
eth
o
d
is
eq
u
iv
alen
t to
SP
W
M
b
y
in
s
er
t
in
g
a
ze
r
o
-
o
r
d
er
co
m
p
o
n
en
t,
a
s
f
o
llo
ws
[
2
5
]
.
=
−
(
,
,
,
,
,
)
+
(
,
,
,
,
,
)
2
(
2
6
)
I
n
th
er
e
V
a,
ref
,
V
a
,
ref
,
V
a,
ref
a
r
e
th
e
d
esire
d
s
in
u
s
o
id
al
s
ettin
g
s
,
V
off
is
th
e
ze
r
o
-
o
r
d
er
c
o
m
p
o
n
en
t
ad
d
ed
to
th
e
s
ettin
g
s
.
T
h
e
m
o
d
u
lated
s
ig
n
al
s
will h
av
e
th
e
f
o
r
m
as (
2
7
)
.
′
,
=
,
+
,
=
,
,
.
(
2
7
)
T
h
e
SP
W
W
M
m
o
d
u
latio
n
an
d
s
witch
in
g
p
r
o
ce
s
s
in
SVM
m
o
d
u
latio
n
is
s
h
o
wn
in
Fig
u
r
e
7
.
T
h
e
s
ig
n
al
at
th
e
PW
M
o
u
tp
u
t
th
r
o
u
g
h
th
e
c
o
m
p
ar
at
o
r
with
t
h
e
s
awto
o
th
v
o
ltag
e
in
o
n
e
m
o
d
u
latio
n
cy
cle
is
s
h
o
wn
in
Fig
u
r
e
7
(
a
)
.
T
h
e
ad
d
itio
n
o
f
th
e
ze
r
o
-
o
r
d
e
r
co
m
p
o
n
en
t
lik
e
(
26
)
is
to
d
eter
m
in
e
th
e
ze
r
o
v
ec
t
o
r
at
th
e
b
eg
in
n
in
g
o
f
th
e
m
o
d
u
lati
o
n
cy
cle.
Ho
wev
er
,
i
n
a
m
u
lti
-
lev
el
in
v
er
ter
it
is
n
o
t
p
o
s
s
ib
le
to
h
av
e
a
ze
r
o
v
ec
to
r
to
ar
r
a
n
g
e
th
e
s
ig
n
als
as
s
h
o
wn
in
Fig
u
r
e
7
(
a
)
.
I
n
s
tea
d
,
if
a
m
o
d
u
latio
n
m
eth
o
d
is
u
s
ed
with
th
e
th
r
ee
n
ea
r
est
v
ec
to
r
s
in
ea
ch
m
o
d
u
l
atio
n
h
alf
-
cy
cle,
o
n
e
v
ec
to
r
wi
ll
b
e
u
s
ed
as
v
ec
to
r
ze
r
o
,
i.e
.
t
h
e
tim
e
s
p
en
t
u
s
in
g
th
is
v
ec
to
r
is
d
iv
id
ed
in
to
two
eq
u
al
h
alv
es,
eq
u
ally
d
iv
id
ed
f
o
r
th
e
b
e
g
in
n
in
g
o
f
th
e
h
alf
c
y
cle
T
s
an
d
th
e
en
d
o
f
th
e
h
alf
cy
cle
T
s
.
T
o
a
p
p
ly
t
h
e
s
am
e
two
-
lev
el
in
v
e
r
ter
to
a
m
u
lti
-
lev
el
in
v
er
ter
,
it
ca
n
b
e
im
ag
in
ed
th
at
th
e
s
p
atial
v
ec
to
r
o
f
a
m
u
lti
-
lev
el
in
v
er
ter
h
as
as
m
an
y
s
m
all
h
ex
ag
o
n
s
as
th
at
o
f
a
two
-
lev
el
in
v
er
ter
,
an
d
th
e
v
ec
to
r
at
th
e
ce
n
ter
o
f
th
is
s
m
all
h
ex
ag
o
n
h
as
r
o
le
as
ze
r
o
v
ec
to
r
.
C
o
n
s
id
er
s
p
ec
if
icall
y
wh
en
th
e
v
o
ltag
e
v
ec
to
r
m
o
v
es f
r
o
m
tr
ian
g
le
2
t
o
tr
ian
g
le
3
as sh
o
wn
in
Fig
u
r
e
7
(
b
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
3
4
-
5
2
4
8
5242
t
t
t
t
0
1
0
1
0
1
0
1
t
0
/
4
t
0
/
4
t
0
/
4
t
0
/
4
t
1
/
2
t
1
/
2
t
1
/
2
t
2
/
2
t
1
/
2
t
2
/
2
t
2
/
2
t
2
/
2
(
a)
V
1
V
2
V
3
V
4
V
5
V
6
V
7
V
8
V
9
V
10
V
11
V
12
V
13
V
14
V
15
V
16
V
18
V
17
V
0
(
0
,
-
1
,
-
1
)
(
1
,
-
1
,
-
1
)
(
1
,
-
1
,
1
)
(
1
,
-
1
,
0
)
(
0
,
1
,
1
)
(
-
1
,
0
,
0
)
(
-
1
,
1
,
1
)
(
1
,
1
,
0
)
(
0
,
0
,
-
1
)
(
1
,
0
,
-
1
)
(
1
,
1
,
-
1
)
(
0
,
-
1
,
1
)
(
1
,
0
,
1
)
(
0
,
-
1
,
0
)
(
-
1
,
-
1
,
1
)
(
-
1
,
-
1
,
0
)
(
0
,
0
,
1
)
(
-
1
,
0
,
1
)
(
1
-
,
1
,
0
)
(
-
1
,
0
,
-
1
)
(
0
,
1
,
0
)
(
0
,
1
,
-
1
)
(
-
1
,
1
,
-
1
)
(
1
,
1
,
1
)
(
0
,
0
,
0
)
(
-
1
,
-
1
,
-
1
)
1
2
3
4
(
b
)
Fig
u
r
e
7
.
T
h
e
SP
W
W
M
m
o
d
u
latio
n
an
d
s
witch
in
g
p
r
o
ce
s
s
in
SVM
m
o
d
u
latio
n
:
(
a)
PW
M
o
u
tp
u
t sig
n
al
a
n
d
tim
es u
s
in
g
p
o
s
itiv
e
an
d
ze
r
o
v
ec
to
r
s
an
d
(
b
)
o
p
tim
al
s
witch
in
g
o
r
d
er
f
o
r
th
r
ee
-
p
h
ase
3
-
lev
el
in
v
er
ter
s
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
I
n
th
is
s
ec
tio
n
,
th
e
au
th
o
r
will
p
r
esen
t
s
im
u
latio
n
r
esu
lts
wh
en
p
e
r
f
o
r
m
in
g
SVM
m
o
d
u
latio
n
f
o
r
an
MM
C
co
n
v
er
ter
co
n
s
is
tin
g
o
f
1
2
SMs
p
er
p
h
ase.
T
h
e
s
i
m
u
latio
n
p
ar
a
m
eter
s
ar
e
p
r
es
en
ted
in
T
ab
le
1
.
T
h
e
o
u
t
p
u
t
p
a
r
am
eter
s
o
f
t
h
e
AC
s
id
e
o
f
th
e
MM
C
co
n
v
er
t
er
ar
e
s
h
o
wn
in
Fig
u
r
e
8
.
Fig
u
r
e
s
8
(
a)
a
n
d
(
b
)
a
r
e
th
e
r
esu
lts
o
f
p
h
ase
v
o
ltag
e
an
d
cu
r
r
e
n
t
o
n
p
h
ases
A,
B
,
C
o
f
th
e
MM
C
co
n
v
er
ter
wh
en
ap
p
ly
in
g
th
e
SVM
m
o
d
u
latio
n
m
eth
o
d
with
th
e
s
elec
tio
n
o
f
th
e
n
ea
r
est
v
o
l
tag
e
v
ec
to
r
.
T
h
e
p
ictu
r
e
s
h
o
ws
cu
r
r
en
t
v
o
ltag
e
with
o
u
t
g
o
in
g
th
r
o
u
g
h
th
e
f
ilter
g
iv
es
n
o
r
m
al
s
in
u
s
o
id
al
r
esu
lts
,
wh
ich
ar
e
o
b
tain
ed
i
n
th
e
f
ir
s
t
cy
cle
an
d
n
o
tr
an
s
ien
ts
o
cc
u
r
d
u
r
in
g
th
e
s
im
u
latio
n
.
Per
f
o
r
m
i
n
g
e
v
alu
at
io
n
o
f
to
tal
h
a
r
m
o
n
ic
d
is
to
r
tio
n
T
HD
f
o
r
v
o
ltag
e
an
d
cu
r
r
e
n
t
as
s
h
o
wn
in
Fig
u
r
e
9
,
th
e
r
esu
lts
F
ig
u
r
e
s
9
(
a)
an
d
9
(
b
)
s
h
o
w
th
at
th
e
T
HD
in
d
ex
o
f
cu
r
r
e
n
t
an
d
v
o
ltag
e
is
v
er
y
s
m
all.
Sp
ec
if
ically
,
th
e
T
HD
in
d
ex
o
f
th
e
o
u
t
p
u
t
v
o
ltag
e
in
th
e
p
er
io
d
0
.
0
2
to
0
.
0
8
s
is
1
.
8
5
%,
th
e
T
HD
in
d
ex
o
f
th
e
c
u
r
r
en
t
o
n
th
e
lo
ad
is
1
.
0
1
%.
T
h
is
r
es
u
lt
s
h
o
ws
th
at
t
h
e
p
o
wer
q
u
ali
ty
co
r
r
esp
o
n
d
i
n
g
to
th
e
p
r
o
p
o
s
ed
SVM
m
o
d
u
lati
o
n
alg
o
r
ith
m
is
g
u
ar
an
teed
a
s
r
eq
u
ir
ed
,
with
th
e
r
esu
lts
o
f
th
e
T
HD
in
d
ex
s
h
o
win
g
th
at
th
is
m
eth
o
d
ca
n
b
e
u
s
ed
f
o
r
MM
C
to
c
o
n
n
ec
t
d
ir
ec
tly
to
th
e
g
r
id
to
tr
a
n
s
m
it
p
o
wer
to
t
h
e
g
r
id
with
o
u
t
th
e
n
ee
d
f
o
r
v
o
ltag
e
f
ilter
s
an
d
with
o
u
t
th
e
n
ee
d
f
o
r
tr
an
s
f
o
r
m
er
s
.
T
h
is
is
v
er
y
im
p
o
r
tan
t
to
r
e
d
u
ce
eq
u
ip
m
en
t
co
s
ts
,
r
e
d
u
ce
in
v
es
tm
en
t
co
s
ts
f
o
r
th
e
p
r
o
ject
wh
i
le
s
till
en
s
u
r
in
g
tech
n
ical
co
n
d
itio
n
s
ac
co
r
d
i
n
g
t
o
r
eg
u
latio
n
s
.
T
ab
le
1
.
MM
C
p
ar
am
eter
s
u
s
e
d
f
o
r
s
im
u
latio
n
P
a
r
a
me
t
e
r
S
y
mb
o
l
V
a
l
u
e
V
o
l
t
a
g
e
o
f
D
C
p
o
w
e
r
su
p
p
l
y
V
DC
6
0
0
0
V
C
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
V
C
1
0
0
0
V
A
r
m i
n
d
u
c
t
a
n
c
e
L
o
5
mH
C
a
p
a
c
i
t
a
n
c
e
o
f
t
h
e
c
a
p
a
c
i
t
o
r
S
M
C
SM
3
0
0
0
µF
N
u
mb
e
r
o
f
S
M
s
p
e
r
p
h
a
se
2N
12
F
r
e
q
u
e
n
c
y
f
5
0
Hz
0
0
.
1
0
0
.
05
-
3000
3000
T
h
ờ
i
g
i
a
n
(
s
)
Đi
ệ
n
á
p
(
V
)
(
a)
0
.
1
0
0
.
05
T
h
ờ
i
g
i
a
n
(
s
)
-
100
100
D
ò
n
g
đ
i
ệ
n
(
A
)
(
b
)
Fig
u
r
e
8
.
T
h
e
o
u
t
p
u
t p
a
r
am
ete
r
s
o
f
th
e
AC
s
id
e
o
f
th
e
MM
C
co
n
v
er
ter
:
(
a)
p
h
ase
v
o
ltag
e
o
n
th
e
AC
s
id
e
o
f
th
e
MM
C
co
n
v
er
ter
a
n
d
(
b
)
cu
r
r
en
t o
n
th
e
AC
s
id
e
o
f
th
e
M
MC c
o
n
v
er
ter
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:
2088
-
8
7
0
8
S
imu
la
tio
n
a
n
d
ex
p
erimen
ta
l v
a
lid
a
tio
n
o
f MMC
ca
p
a
b
le
o
f
p
r
o
d
u
cin
g
…
(
Tr
a
n
Hu
n
g
C
u
o
n
g
)
5243
(
a)
(
b
)
Fig
u
r
e
9
.
Per
f
o
r
m
in
g
ev
alu
ati
o
n
o
f
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
T
HD
f
o
r
v
o
ltag
e
an
d
cu
r
r
en
t:
(
a)
T
HD
in
d
ex
f
o
r
AC
v
o
ltag
e
an
d
(
b
)
T
HD
in
d
e
x
f
o
r
AC
lo
ad
cu
r
r
e
n
t
T
h
ese
r
esu
lts
p
r
o
v
e
th
at
th
e
s
witch
in
g
o
p
tim
izatio
n
p
r
o
ce
s
s
o
f
th
e
m
eth
o
d
is
g
u
ar
an
teed
to
b
e
in
ac
co
r
d
an
ce
with
th
e
s
et
o
b
jectiv
es
an
d
alwa
y
s
e
n
s
u
r
es
th
e
o
p
er
atio
n
q
u
ality
o
f
th
e
M
MC
co
n
v
er
ter
wh
e
n
ap
p
ly
in
g
th
e
p
r
o
p
o
s
ed
SVM
m
o
d
u
latio
n
alg
o
r
ith
m
.
B
ased
o
n
th
e
co
m
p
ar
is
o
n
o
f
v
o
ltag
e
an
d
cu
r
r
en
t
T
HD
in
d
ex
es
o
f
PW
M
m
eth
o
d
s
w
h
en
ap
p
lied
to
MM
C
co
n
v
er
t
er
s
with
co
r
r
esp
o
n
d
in
g
n
u
m
b
er
o
f
lev
els
in
th
e
d
o
cu
m
e
n
t
[
1
6
]
,
we
f
in
d
th
at
t
h
e
T
HD
in
d
ex
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
in
th
is
p
ap
er
is
alw
ay
s
lo
wer
in
v
alu
e.
T
h
e
d
etails ar
e
s
h
o
wn
in
T
ab
l
e
2
.
T
ab
le
2
.
C
o
m
p
a
r
is
o
n
o
f
T
HD
o
f
v
o
ltag
e
b
etwe
en
m
o
d
u
latio
n
m
eth
o
d
s
M
o
d
u
l
a
t
i
o
n
m
e
t
h
o
d
TH
D
i
n
d
e
x
f
o
r
v
o
l
t
a
g
e
PSC
-
PWM
8
.
2
5
%
N
LC
17
.
2%
N
LC
+
P
W
M
9
.
7%
N
LC
+
C
R
C
17
.
6%
Fig
u
r
e
10
is
th
e
v
o
ltag
e
o
f
ca
p
ac
ito
r
s
in
p
h
ase
A.
Fig
u
r
e
s
1
0
(
a)
a
n
d
1
0
(
b
)
ar
e
th
e
ca
p
ac
ito
r
v
o
ltag
es
o
f
th
e
SM
o
f
t
h
e
u
p
p
er
a
n
d
l
o
wer
ar
m
s
o
n
p
h
ase
A.
Ob
s
e
r
v
in
g
th
e
ca
p
ac
ito
r
v
o
ltag
e
v
a
lu
es
o
f
SMs
o
f
th
e
u
p
p
er
an
d
lo
wer
ar
m
s
o
f
p
h
ase
A
s
h
o
ws
t
h
at
th
e
MM
C
co
n
v
er
ter
ca
p
ac
ito
r
v
o
ltag
e
alwa
y
s
f
lu
ctu
ates
ar
o
u
n
d
th
e
eq
u
ilib
r
iu
m
p
o
s
itio
n
o
f
1
0
0
0
V,
th
e
m
ax
im
u
m
f
l
u
ctu
ati
o
n
v
al
u
e
o
f
th
e
ca
p
ac
ito
r
v
o
lt
ag
e
wh
en
r
ea
ch
in
g
th
e
eq
u
ilib
r
iu
m
p
o
s
itio
n
is
2
5
V,
i.e
.
2
.
5
%.
T
h
is
r
esu
lt
will
h
elp
th
e
ca
p
ac
ito
r
o
p
er
ate
s
tab
l
y
f
o
r
a
lo
n
g
tim
e
to
h
elp
in
cr
ea
s
e
th
e
life
o
f
th
e
M
MC a
n
d
im
p
r
o
v
e
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
th
e
MM
C
.
0
.
1
0
0
.
05
970
1030
T
h
ờ
i
g
i
a
n
(
s
)
Đi
ệ
n
á
p
(
V
)
1000
(
a)
0
.
1
0
0
.
05
960
1040
T
h
ờ
i
g
i
a
n
(
s
)
Đi
ệ
n
á
p
(
V
)
1000
(
b
)
Fig
u
r
e
1
0
.
T
h
e
v
o
ltag
e
o
f
ca
p
a
cito
r
s
in
p
h
ase
A:
(
a)
v
o
ltag
e
o
f
u
p
p
er
an
d
lo
wer
a
r
m
ca
p
ac
i
to
r
s
in
p
h
ase
A
an
d
(
b
)
v
o
lta
g
e
o
f
t
h
e
lo
wer
ar
m
ca
p
ac
ito
r
s
in
p
h
ase
A
5.
E
XP
E
R
I
M
E
N
T
A
L
SYS
T
E
M
AND
R
E
SU
L
T
S
5
.
1
.
Str
uct
ure
o
f
t
he
ex
perim
ent
a
l sy
s
t
em
o
f
t
he
M
M
C
co
nv
er
t
er
T
h
e
ex
p
e
r
im
en
tal
m
o
d
el
o
f
th
e
MM
C
s
y
s
tem
is
p
r
esen
ted
i
n
Fig
u
r
e
1
1
.
T
h
e
ex
p
er
im
e
n
ta
l
s
y
s
tem
is
b
u
ilt
b
ased
o
n
th
e
s
tr
u
ctu
r
e
o
f
th
e
MM
C
co
n
v
er
ter
with
1
2
SMs
p
er
p
h
ase
an
d
is
d
escr
ib
ed
b
y
th
e
s
tr
u
ctu
r
al
d
iag
r
am
as sh
o
wn
i
n
Fig
u
r
e
1
1
(
a
)
.
I
n
wh
ich
:
MM
C
co
n
v
er
ter
is
th
e
m
ain
s
tr
u
ct
u
r
e
to
co
n
v
er
t
e
n
er
g
y
f
r
o
m
DC
to
AC
ac
co
r
d
i
n
g
to
t
h
e
p
r
o
p
o
s
ed
SVM
alg
o
r
ith
m
;
T
h
e
m
ea
s
u
r
em
en
t
b
lo
c
k
is
r
esp
o
n
s
ib
le
f
o
r
m
ea
s
u
r
i
n
g
,
co
llectin
g
,
an
d
e
x
tr
ac
tin
g
s
am
p
les o
f
s
ig
n
als f
r
o
m
th
e
M
MC c
o
n
tr
o
ller
to
s
er
v
e
th
e
s
ig
n
al
p
r
o
ce
s
s
in
g
s
y
s
tem
; Wi
th
th
e
ch
ar
ac
ter
is
tics
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.