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n
v
er
ter
[
8
]
.
I
n
th
is
w
o
r
k
SVP
W
M
alg
o
r
i
th
m
s
ar
e
d
ev
e
lo
p
ed
in
o
r
d
er
to
co
m
p
ar
e
t
h
e
p
er
f
o
r
m
a
n
ce
s
o
f
d
io
d
e
cla
m
p
ed
m
u
lt
ilev
e
l
i
n
v
er
ter
s
(
f
i
v
e
a
n
d
s
e
v
en
le
v
els)
i
n
h
ar
m
o
n
ics
r
ed
u
c
tio
n
,
m
o
to
r
ti
m
e
r
e
s
p
o
n
s
e
a
n
d
to
r
q
u
e
f
l
u
ctu
a
tio
n
s
.
T
h
e
alg
o
r
it
h
m
s
d
ev
elo
p
ed
f
o
r
th
ese
t
w
o
to
p
o
lo
g
ies
ar
e
test
ed
o
n
i
n
d
u
ct
io
n
m
o
to
r
f
o
r
v
alid
atio
n
.
T
h
e
o
b
tain
ed
r
esu
lts
h
a
v
e
s
h
o
w
ed
t
h
at
h
ar
m
o
n
ics
ar
e
r
ed
u
c
ed
to
a
lo
w
er
v
al
u
e
w
h
e
n
s
e
v
en
le
v
els
i
n
v
er
ter
is
u
s
ed
b
u
t t
h
e
in
v
er
ter
co
m
m
u
ta
tio
n
lo
s
s
e
s
ar
e
less
w
h
en
f
i
v
e
l
ev
el
in
v
er
ter
s
ar
e
u
s
ed
.
2.
SVPWM
T
H
E
O
RE
T
I
CA
L
DE
V
E
L
O
P
M
E
NT
S
T
h
e
co
n
v
en
t
io
n
al
t
w
o
-
le
v
el
i
n
v
er
ter
is
u
s
ed
f
o
r
t
h
eo
r
etica
l
d
ev
elo
p
m
e
n
ts
w
h
ic
h
ca
n
b
e
ex
t
en
d
ed
f
o
r
o
th
er
m
u
ltil
e
v
el
in
v
er
ter
s
.
I
t
is
ass
u
m
ed
t
h
at
th
e
co
n
tr
o
l
o
f
ea
ch
ar
m
s
o
f
t
h
e
in
v
er
ter
is
co
m
p
le
m
e
n
tar
y
,
t
h
u
s
as to
r
ep
lace
s
tatic
s
w
itc
h
es
with
t
w
o
p
o
s
itio
n
s
[
5
]
-
[
6
]
Fig
u
r
e
1.
Fig
u
r
e
1
.
C
o
n
v
e
n
tio
n
al
th
r
ee
p
h
ase
i
n
v
er
ter
B
ased
o
n
th
e
co
n
ce
p
t o
f
r
o
tatin
g
v
ec
to
r
,
it c
an
b
e
co
n
s
id
er
ed
th
at
th
e
i
n
v
er
ter
o
u
tp
u
t i
s
a
v
o
ltag
e
v
ec
to
r
.
e
j
V
e
j
V
V
V
cn
bn
an
r
ef
n
3
4
.
3
2
.
3
2
0
0
0
0
(
1
)
T
h
e
in
v
er
ter
s
w
itc
h
e
s
ar
e
s
u
p
p
o
s
ed
to
b
e
id
ea
l a
n
d
ca
n
b
e
r
e
p
r
esen
ted
as f
o
llo
w
s
: S
j
(
j
=a
,
b
,
c)
s
u
ch
as,
S
j
=1
i
f
p
h
ase
a,
is
co
n
n
ec
ted
to
th
e
p
o
s
itiv
e
r
ail
o
f
th
e
d
c
s
o
u
r
ce
,
S
j
=0
if
p
h
ase
a
is
co
n
n
ec
ted
to
th
e
n
e
g
ati
v
e
r
ail
o
f
th
e
DC
s
o
u
r
ce
.
T
h
e
s
a
m
e
p
r
in
cip
le
is
ap
p
lied
to
th
e
o
th
er
t
w
o
p
h
ases
s
u
ch
a
s
:
V
ino
= S
j
.U
-
U
/2
(
2
)
T
h
e
f
o
llo
w
i
n
g
E
q
u
atio
n
i
s
o
b
tain
ed
:
e
S
e
S
S
3
2
V
3
4
.
j
c
3
2
.
j
b
a
r
ef
(
3
)
T
h
e
d
if
f
er
en
t
co
m
b
i
n
atio
n
s
o
f
S
a
,
S
b
,
S
c
en
ab
le
to
g
e
n
er
ate
eig
h
t
p
o
s
s
ib
le
v
ec
to
r
p
o
s
itio
n
s
V
ref
w
it
h
t
w
o
p
o
s
itio
n
s
co
r
r
esp
o
n
d
in
g
to
ze
r
o
v
ec
to
r
as sh
o
w
n
i
n
Fi
g
u
r
e
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
C
o
mp
a
r
a
tive
S
tu
d
y
o
f F
ive
-
Leve
l a
n
d
S
ev
en
-
Leve
l I
n
ve
r
ter
C
o
n
tr
o
l
led
b
y
S
p
a
ce
…
(
A
b
d
el
ma
lik
B
en
d
a
ikh
a
)
757
Fig
u
r
e
2
.
I
n
v
er
ter
v
o
lta
g
e
v
ec
t
o
r
s
in
(
-
)
f
r
am
e
T
h
e
ex
p
r
ess
io
n
s
o
f
i
n
s
ta
n
ta
n
eo
u
s
p
h
a
s
e
a
n
d
li
n
e
to
li
n
e
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
s
ac
co
r
d
in
g
to
th
e
u
p
p
er
s
w
itc
h
es c
an
b
e
estab
li
s
h
ed
as
f
o
llo
w
s
:
c
b
a
cn
bn
an
2
1
1
1
2
1
1
1
2
3
V
V
V
S
S
S
U
(
4
)
I
n
o
r
d
er
to
s
i
m
p
lify
t
h
e
co
m
p
u
tatio
n
s
an
d
r
ep
r
esen
t
t
h
ese
v
o
ltag
es
i
n
a
s
i
m
p
l
if
ied
f
o
r
m
,
t
h
e
tr
an
s
f
o
r
m
a
tio
n
o
f
co
o
r
d
in
ates
f
r
o
m
th
e
t
h
r
ee
p
h
ase
s
tatio
n
ar
y
f
r
a
m
e
to
-
f
r
a
m
e
is
ap
p
lied
r
esp
ec
tin
g
th
e
p
o
w
er
tr
a
n
s
f
er
tr
an
s
f
o
r
m
atio
n
(
C
o
n
co
r
d
ia
tr
an
s
f
o
r
m
atio
n
)
:
V
V
V
2
3
2
3
0
2
1
2
1
1
3
2
V
V
cn
bn
an
s
s
(
5
)
T
h
er
e
ar
e
d
if
f
er
en
t
co
n
tr
o
l
s
tr
ateg
ie
s
en
ab
li
n
g
th
e
d
eter
m
in
at
io
n
o
f
t
h
e
th
r
ee
lo
g
ic
f
u
n
c
tio
n
s
Sj
=
(
j
=a
,
b
,
c)
.
I
n
th
is
w
o
r
k
S
VP
W
M
is
u
s
ed
to
d
ev
elo
p
th
e
co
n
tr
o
l stra
teg
y
o
f
t
h
e
in
v
er
ter
.
2
.
1
.
Sp
a
ce
Vec
t
o
r
P
W
M
Rea
liza
t
io
n
SVP
W
M
is
lar
g
el
y
u
s
ed
i
n
m
o
d
er
n
co
n
tr
o
l
o
f
in
d
u
ctio
n
m
o
to
r
s
to
o
b
tain
s
in
u
s
o
id
al
w
a
v
ef
o
r
m
s
a
t
th
e
i
n
v
er
ter
o
u
tp
u
ts
[
1
]
,
[
4
]
-
[
7
]
,
[
9
]
.
I
ts
b
asic
p
r
in
cip
le
is
to
r
ec
o
n
s
tr
u
ct
th
e
v
o
lta
g
e
v
ec
to
r
Vr
ef
f
r
o
m
t
h
e
eig
h
t
v
o
ltag
e
v
ec
to
r
s
.
E
ac
h
v
ec
to
r
co
r
r
esp
o
n
d
s
to
a
s
w
itc
h
i
n
g
s
t
ate
o
f
a
th
r
ee
p
h
a
s
e
v
o
lta
g
e
i
n
v
er
ter
s
w
itc
h
es.
A
r
ef
er
en
ce
v
o
ltag
e
v
ec
to
r
Vr
e
f
i
s
ev
a
lu
ated
ap
p
r
o
x
i
m
atel
y
o
v
er
a
m
o
d
u
latio
n
p
er
io
d
T
m
.
T
h
is
v
ec
to
r
is
esti
m
ated
in
a
s
ec
to
r
b
y
t
h
e
ap
p
licatio
n
o
f
ad
j
ac
en
t v
o
ltag
e
v
ec
to
r
s
an
d
ze
r
o
v
ec
to
r
s
V
8
an
d
V7
.
T
h
e
co
m
p
u
tatio
n
o
f
th
e
r
ef
er
en
ce
v
o
ltag
e
v
ec
to
r
Vr
ef
is
o
b
tain
ed
b
y
an
al
y
zi
n
g
all
th
e
s
w
itc
h
i
n
g
s
tates.
T
h
e
eig
h
t v
o
lta
g
e
v
ec
to
r
s
an
d
th
e
r
ef
er
e
n
ce
v
ec
to
r
is
r
ep
r
esen
ted
in
a
α
β
-
p
lan
e.
T
h
e
s
w
itc
h
es b
ein
g
O
N
o
r
OFF ar
e
d
eter
m
i
n
ed
b
y
th
e
lo
ca
tio
n
o
f
th
e
r
e
f
er
en
ce
v
ec
to
r
o
n
th
is
α
β
-
p
lan
e
[
1
0
]
Fig
u
r
e
3.
Fig
u
r
e
3
.
R
ep
r
esen
tatio
n
o
f
r
o
tatin
g
v
ec
to
r
i
n
-
f
r
a
m
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
2
,
J
u
n
e
2
0
1
7
:
755
–
7
6
6
758
T
h
e
SVP
W
M
ca
n
b
e
ap
p
lied
a
cc
o
r
d
in
g
to
th
e
f
o
llo
w
i
n
g
s
tep
s
[
5
]
-
[
6
]:
a.
Dete
r
m
i
n
atio
n
o
f
V
, V
,V
ref
,
an
d
th
e
r
o
tatin
g
a
n
g
le
(
θ)
.
b.
A
p
p
lica
tio
n
t
i
m
e
o
f
ad
j
ac
en
t v
ec
to
r
s
x
,
y
,
an
d
z.
c.
Dete
r
m
i
n
atio
n
o
f
th
e
s
w
itc
h
i
n
g
ti
m
e
o
f
ea
ch
s
w
itc
h
(
S
a
,S
b
, S
c
,S
a
’
,
S
b
’
an
d
S
c
’
)
.
Fro
m
Fi
g
u
r
e
4
,
V
, V
, V
ref
,
an
d
th
e
r
o
tatin
g
a
n
g
le
(
θ)
ca
n
b
e
d
eter
m
in
ed
as
f
o
llo
w
s
:
Fig
u
r
e
4
.
Vo
ltag
e
v
ec
to
r
an
d
it
s
co
m
p
o
n
en
ts
i
n
(
-
)
f
r
am
e
V
.
c
o
s
6
0
c
o
s
6
0
11
c
o
s
6
0
22
a
n
b
n
c
n
a
n
b
n
c
n
V
V
V
V
V
V
V
0
.
.
c
o
s
3
0
.
c
o
s
3
0
33
0
.
22
a
n
b
n
c
n
a
n
b
n
c
n
V
V
V
V
V
V
C
o
n
s
er
v
i
n
g
t
h
e
p
o
w
er
tr
an
s
f
er
(
C
o
n
co
r
d
ia
tr
an
s
f
o
r
m
atio
n
)
.
T
h
e
v
o
ltag
e
v
ec
to
r
s
o
n
t
h
e
(
-
)
ax
is
ca
n
t
h
e
n
b
e
d
escr
ib
ed
as
[
1
0
]
:
V
V
V
2
3
2
3
0
2
1
2
1
1
3
2
V
V
cn
bn
an
s
s
(
6
)
22
r
e
f
V
V
V
(
7
)
1
t
a
n
2
V
g
t
f
t
V
(
8
)
W
h
er
e:
f
: is t
h
e
f
u
n
d
a
m
e
n
tal
f
r
eq
u
e
n
c
y
T
h
e
r
ef
er
en
ce
v
ec
to
r
Vr
e
f
i
s
esti
m
ated
o
v
er
a
m
o
d
u
latio
n
p
er
io
d
T
m
,
b
y
g
e
n
er
atin
g
an
a
v
er
ag
e
v
ec
to
r
d
eter
m
in
ed
b
y
t
h
e
ap
p
licatio
n
o
f
i
n
v
er
ter
ad
j
ac
en
t
n
o
n
-
ze
r
o
an
d
ze
r
o
v
ec
to
r
s
.
Fig
u
r
e
4
,
illu
s
tr
ates
th
e
ca
s
e
w
h
er
e
th
e
r
e
f
er
en
ce
v
ec
to
r
is
in
s
ec
to
r
1
.
T
h
e
ap
p
licatio
n
ti
m
e
o
f
ad
j
ac
en
t v
ec
to
r
s
ar
e
g
iv
e
n
as f
o
llo
w
s
:
T
m
=x
+
y
+z
(
9
)
0
2
1
V
V
V
V
m
m
m
r
e
f
T
z
T
y
T
x
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
C
o
mp
a
r
a
tive
S
tu
d
y
o
f F
ive
-
Leve
l a
n
d
S
ev
en
-
Leve
l I
n
ve
r
ter
C
o
n
tr
o
l
led
b
y
S
p
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