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e
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m
o
to
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ter
MCP
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PMSM
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wid
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T
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s
a
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a
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u
n
d
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r th
e
CC B
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C
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uth
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K.
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Go
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Dep
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tm
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g
in
ee
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St.
Ma
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E
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r
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C
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Secu
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k
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g
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co
m
1.
I
NT
RO
D
UCT
I
O
N
Mu
ltil
ev
el
in
v
er
ter
s
ar
e
ca
p
ab
le
o
f
c
o
n
tr
o
llin
g
h
ig
h
v
o
ltag
e
an
d
p
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wer
d
r
iv
es
m
o
r
e
e
f
f
ici
en
tly
an
d
with
less
e
lectr
o
m
ag
n
etic
in
ter
f
er
en
ce
[
1
]
.
T
h
e
y
h
av
e
b
ec
o
m
e
q
u
ite
p
o
p
u
lar
in
th
e
p
o
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in
d
u
s
tr
y
.
Mu
lti
-
ca
r
r
ier
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
M
C
PW
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ap
p
r
o
ac
h
es
ca
n
f
u
r
th
er
im
p
r
o
v
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th
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p
er
f
o
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m
a
n
ce
o
f
n
e
u
tr
al
p
o
in
t
clam
p
ed
(
NPC
)
in
v
er
ter
s
[
2
]
,
wh
ich
ar
e
f
r
eq
u
e
n
tly
em
p
l
o
y
ed
in
c
o
m
m
er
cial
u
s
es.
Mu
ltil
ev
el
in
v
er
ter
s
u
tili
zin
g
MCP
W
M
tech
n
iq
u
es,
s
u
ch
as
i
n
ter
leav
ed
ca
r
r
ie
r
s
(
I
C
)
,
p
h
ase
s
h
if
tin
g
ca
r
r
ie
r
s
(
PS
C
)
,
v
ar
iab
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f
r
eq
u
e
n
cy
ca
r
r
ier
s
(
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,
an
d
alter
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ativ
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p
h
ase
o
p
p
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s
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d
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p
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s
itio
n
(
APOD)
,
ca
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e
f
f
ec
tiv
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m
itig
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wer
q
u
ality
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s
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es,
co
m
m
o
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m
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d
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v
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ltag
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a
n
d
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k
c
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wev
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en
co
m
p
ar
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PD
PW
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m
eth
o
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[
3
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,
th
e
s
e
m
eth
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s
m
ay
also
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lt
in
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cr
ea
s
ed
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tal
h
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m
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is
to
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tio
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(
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HD)
.
T
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p
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p
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is
to
im
p
r
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h
e
T
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o
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ce
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a
3
-
l
e
v
el,
5
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p
h
ase
NPC
in
v
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ter
[
4
]
.
L
o
we
r
T
HD
lev
els in
th
e
in
v
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ter
'
s
o
u
tp
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t
wav
ef
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r
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ar
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d
esire
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b
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au
s
e
th
ey
ca
n
r
es
u
lt
in
in
cr
ea
s
ed
ef
f
icien
cy
,
d
e
cr
ea
s
ed
lo
s
s
es,
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
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8
7
9
2
P
erfo
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ce
a
n
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lysi
s
o
f m
u
lti ca
r
r
ier P
W
M tec
h
n
iq
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es fo
r
a
5
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(
V
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1265
h
ig
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ality
p
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wer
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tp
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[
5
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,
[
6
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.
Mu
ltip
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ase
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ter
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Var
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,
in
clu
d
in
g
h
ig
h
v
o
ltag
e
DC
tr
an
s
m
is
s
io
n
,
co
n
v
ey
o
r
s
,
p
u
m
p
s
,
u
n
in
ter
r
u
p
tib
le
p
o
wer
s
u
p
p
ly
(
UPS)
s
y
s
tem
s
,
an
d
h
ig
h
-
p
o
wer
ap
p
licatio
n
s
[
7
]
.
E
lectr
ic
v
eh
ic
les
(
E
Vs),
wh
er
e
th
er
e
is
a
g
r
o
win
g
n
ee
d
f
o
r
d
ep
en
d
a
b
le
an
d
h
ig
h
-
p
o
wer
elec
tr
ical
d
r
iv
es,
ar
e
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
ap
p
licatio
n
s
f
o
r
m
u
ltip
h
ase
in
v
er
ter
s
.
I
n
d
u
ctio
n
m
o
to
r
s
a
r
e
f
r
eq
u
e
n
tly
em
p
lo
y
ed
as
t
h
e
p
r
im
ar
y
d
r
iv
e
in
E
Vs,
an
d
f
o
r
b
est
r
esu
lts
,
ac
cu
r
ate
s
p
ee
d
co
n
t
r
o
l
is
cr
u
c
ial.
Ad
v
an
ce
d
co
n
tr
o
l
tech
n
iq
u
es
lik
e
f
ield
-
o
r
ien
ted
co
n
tr
o
l
(
FOC
)
an
d
d
ir
ec
t
to
r
q
u
e
c
o
n
tr
o
l
(
DT
C
)
en
ab
le
th
is
ca
p
ab
ilit
y
[
1
]
.
Fu
r
th
er
m
o
r
e,
f
iv
e
-
p
h
ase
m
o
t
o
r
d
r
iv
es
a
r
e
esp
ec
ially
well
-
s
u
ited
f
o
r
in
d
u
s
tr
ies
lik
e
ae
r
o
s
p
ac
e,
au
t
o
m
o
tiv
e,
an
d
r
e
n
e
wab
le
en
er
g
y
s
y
s
tem
s
th
at
d
em
an
d
h
ig
h
p
o
wer
d
en
s
ity
,
h
ig
h
s
p
ee
d
,
an
d
h
ig
h
d
ep
en
d
a
b
ilit
y
[
8
]
.
Ad
d
itio
n
ally
u
tili
ze
d
in
E
V
ap
p
licatio
n
s
,
p
er
m
an
en
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
(
PMSM
)
m
o
to
r
s
u
s
e
FOC
f
o
r
s
p
ee
d
c
o
n
tr
o
l,
wh
ic
h
h
as
b
en
e
f
its
in
clu
d
in
g
h
i
g
h
p
o
wer
d
en
s
ity
an
d
g
r
ea
t
ef
f
icien
cy
a
t
lo
w
s
p
ee
d
s
.
Mu
ltip
h
ase
m
o
t
o
r
s
ar
e
b
ec
o
m
in
g
m
o
r
e
p
o
p
u
l
ar
b
ec
au
s
e
th
e
y
ar
e
b
etter
th
an
s
tan
d
ar
d
th
r
ee
-
p
h
ase
m
o
to
r
s
in
m
an
y
way
s
,
m
ak
in
g
t
h
em
a
n
attr
ac
tiv
e
ch
o
i
ce
.
T
h
ese
b
en
ef
its
in
clu
d
e
h
ig
h
er
p
o
wer
d
e
n
s
ity
,
en
h
an
ce
d
f
au
lt
to
ler
a
n
ce
,
in
cr
ea
s
ed
ef
f
icien
cy
,
a
n
d
m
o
r
e
co
n
tr
o
l
f
le
x
ib
ilit
y
,
wh
ich
r
esu
lts
in
s
m
o
o
th
er
o
p
er
atio
n
.
T
h
e
y
ar
e
esp
ec
ially
u
s
ef
u
l
in
tr
ac
tio
n
(
i
n
clu
d
in
g
elec
tr
ic
an
d
h
y
b
r
id
ca
r
s
)
,
elec
tr
ic
s
h
ip
p
r
o
p
u
ls
io
n
,
an
d
ai
r
cr
af
t
[
9
]
.
I
m
p
r
o
v
e
d
to
r
q
u
e
-
s
p
ee
d
c
h
ar
ac
ter
is
tics
,
lo
wer
h
ar
m
o
n
ic
cu
r
r
en
t,
an
d
r
e
d
u
ce
d
ea
ch
p
h
ase's
cu
r
r
en
t
with
o
u
t
in
c
r
ea
s
in
g
ea
c
h
p
h
ase'
s
v
o
ltag
e
ar
e
a
ll
b
en
ef
its
o
f
m
u
lti
-
p
h
ase
m
o
to
r
s
.
Du
e
t
o
its
d
ep
e
n
d
ab
ilit
y
an
d
s
af
ety
,
m
u
ltip
h
a
s
e
in
d
u
ctio
n
m
o
to
r
s
with
m
o
r
e
p
h
ases
ar
e
u
tili
ze
d
in
a
wid
e
r
an
g
e
o
f
ap
p
licatio
n
s
[
1
0
]
,
[1
1
]
.
T
h
e
ex
is
tin
g
liter
atu
r
e
o
n
m
u
l
tilev
el
an
d
m
u
ltip
h
ase
in
v
e
r
te
r
s
h
as
p
r
ed
o
m
i
n
an
tly
f
o
cu
s
ed
o
n
th
r
ee
-
p
h
ase
s
y
s
tem
s
o
r
h
ig
h
er
-
lev
el
in
v
er
ter
s
,
with
r
elativ
ely
lim
it
ed
atten
tio
n
g
i
v
en
to
f
iv
e
-
p
h
ase,
th
r
ee
-
lev
el
NPC
in
v
er
ter
c
o
n
f
ig
u
r
atio
n
s
[1
2
]
.
Mo
s
t
p
r
io
r
s
tu
d
ies
ev
alu
ate
m
u
lti
-
ca
r
r
ier
PW
M
(
MCP
W
M)
tech
n
iq
u
es
p
r
im
ar
ily
in
ter
m
s
o
f
v
o
ltag
e
wa
v
ef
o
r
m
q
u
ality
o
r
T
HD
u
n
d
er
s
i
m
p
lifie
d
r
esis
tiv
e
o
r
R
L
lo
ad
co
n
d
itio
n
s
,
with
o
u
t
ex
ten
d
in
g
th
e
an
aly
s
is
to
r
ea
lis
tic
m
o
to
r
-
d
r
iv
e
ap
p
l
icatio
n
s
[1
3
]
,
[
1
4
]
.
Fu
r
th
e
r
m
o
r
e,
c
o
m
p
a
r
ativ
e
in
v
esti
g
atio
n
s
o
f
ten
co
n
s
id
er
o
n
ly
a
lim
ited
s
u
b
s
et
o
f
PW
M
s
tr
ateg
ies,
s
u
ch
as
PD,
P
OD,
o
r
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
,
leav
in
g
a
clea
r
g
ap
in
c
o
m
p
r
e
h
en
s
iv
e
p
er
f
o
r
m
an
ce
b
en
c
h
m
ar
k
in
g
ac
r
o
s
s
m
u
ltip
le
MCP
W
M
tech
n
iq
u
es
with
in
a
u
n
if
ied
f
r
am
ewo
r
k
[1
5
]
,
[
1
6
]
.
I
n
a
d
d
itio
n
,
th
e
m
ajo
r
ity
o
f
r
ep
o
r
ted
wo
r
k
s
d
o
n
o
t
s
im
u
ltan
eo
u
s
ly
ass
ess
b
o
th
el
ec
tr
ical
(
v
o
ltag
e
an
d
c
u
r
r
en
t
T
HD)
an
d
elec
tr
o
m
ec
h
an
ical
(
to
r
q
u
e
,
s
p
ee
d
,
an
d
s
tato
r
cu
r
r
en
t
d
y
n
am
ics)
p
e
r
f
o
r
m
an
ce
m
etr
ics,
wh
ich
a
r
e
cr
i
tical
f
o
r
E
V
d
r
iv
e
s
y
s
tem
s
[1
7
]
.
An
o
th
er
n
o
tab
le
lim
itatio
n
in
ea
r
lier
r
esear
ch
is
th
e
lack
o
f
i
n
teg
r
ated
ev
alu
atio
n
o
f
d
if
f
er
en
t
m
o
to
r
ty
p
es
,
p
ar
ticu
lar
l
y
f
iv
e
-
p
h
ase
in
d
u
ctio
n
m
o
to
r
s
an
d
PMSMs,
wh
en
f
ed
f
r
o
m
t
h
e
s
a
m
e
m
u
ltil
ev
el
m
u
ltip
h
ase
in
v
er
ter
to
p
o
lo
g
y
[1
8
]
,
[
19
]
.
T
o
ad
d
r
ess
th
ese
r
esear
c
h
g
a
p
s
,
th
e
p
r
esen
t
s
tu
d
y
o
f
f
er
s
a
d
is
tin
ct
an
d
o
r
ig
in
al
c
o
n
tr
i
b
u
tio
n
b
y
p
r
o
v
id
in
g
a
s
y
s
tem
atic
an
d
u
n
if
ied
co
m
p
ar
ativ
e
an
aly
s
is
o
f
s
ix
wid
ely
u
s
ed
MCP
W
M
tech
n
iq
u
es
,
P
D,
POD,
AP
OD,
I
C
,
PS
C
,
an
d
VFC
ap
p
lied
t
o
a
f
i
v
e
-
p
h
ase,
th
r
ee
-
lev
el
NPC
in
v
er
ter
[
20
]
,
[
2
1
]
.
Un
lik
e
p
r
ev
io
u
s
wo
r
k
s
,
t
h
is
s
tu
d
y
ex
ten
d
s
b
ey
o
n
d
s
tatic
lo
ad
an
aly
s
is
b
y
in
co
r
p
o
r
atin
g
b
o
th
a
f
iv
e
-
p
h
ase
in
d
u
ctio
n
m
o
to
r
an
d
a
PMSM
as
d
y
n
am
ic
l
o
ad
s
,
th
e
r
eb
y
clo
s
ely
r
ef
lectin
g
p
r
ac
tical
E
V
o
p
er
atin
g
co
n
d
itio
n
s
.
T
h
e
u
n
iq
u
e
n
ess
o
f
th
is
wo
r
k
lies
in
its
in
teg
r
ated
in
v
e
r
ter
–
m
o
to
r
p
e
r
f
o
r
m
an
ce
ev
alu
atio
n
,
w
h
er
e
v
o
ltag
e
a
n
d
cu
r
r
e
n
t
T
H
D
ch
ar
ac
ter
is
tics
ar
e
d
ir
ec
tly
co
r
r
elate
d
with
m
o
to
r
d
y
n
a
m
ic
r
esp
o
n
s
es
s
u
ch
as
to
r
q
u
e
r
ip
p
le,
s
p
ee
d
s
tab
ilit
y
,
an
d
s
tato
r
cu
r
r
en
t
q
u
ality
.
T
h
is
c
o
m
p
r
e
h
en
s
iv
e
ass
es
s
m
en
t
estab
lis
h
es
clea
r
g
u
id
elin
es
f
o
r
s
elec
tin
g
an
o
p
ti
m
al
PW
M
s
tr
ateg
y
f
o
r
h
ig
h
-
p
er
f
o
r
m
an
ce
,
lo
w
-
d
is
to
r
tio
n
,
an
d
r
eliab
le
elec
tr
ic
v
eh
icle
d
r
iv
e
a
p
p
licatio
n
s
.
T
h
is
s
tu
d
y
will
p
r
im
ar
ily
f
o
c
u
s
o
n
m
u
lti
-
ca
r
r
i
er
PW
M
ap
p
r
o
ac
h
es,
in
clu
d
in
g
PD,
POD,
A
POD,
I
C
,
PS
C
,
an
d
VFC
.
T
o
o
b
tain
th
e
wav
ef
o
r
m
s
o
f
th
e
lo
ad
v
o
ltag
e,
cu
r
r
en
t,
a
n
d
T
HD
an
aly
s
is
,
a
s
im
u
latio
n
an
aly
s
is
u
s
in
g
Simu
lin
k
with
R
an
d
R
L
lo
ad
s
will
b
e
co
n
d
u
c
ted
.
T
o
illu
s
tr
ate
p
o
ten
tial
E
V
ap
p
licatio
n
s
,
a
5
-
p
h
ase
in
d
u
ctio
n
m
o
t
o
r
an
d
a
PMSM
m
o
to
r
will
also
b
e
m
o
d
eled
.
T
h
e
o
u
tco
m
es
o
f
th
is
s
tu
d
y
will
h
elp
ch
o
o
s
e
th
e
b
est
PW
M
s
tr
ateg
y
f
o
r
h
ig
h
-
p
o
wer
a
p
p
licatio
n
s
b
y
T
HD
p
er
f
o
r
m
an
ce
o
f
v
ar
io
u
s
m
u
lti
-
ca
r
r
ier
PW
M
s
tr
ateg
ies
in
NPC
in
v
er
ter
s
.
T
h
e
r
em
ain
in
g
p
ap
er
is
o
r
g
a
n
ized
in
to
v
ar
io
u
s
s
ec
tio
n
s
as
f
o
llo
ws.
Sectio
n
two
d
is
cu
s
s
es
th
e
m
u
lti
-
p
h
ase
m
u
lti
-
lev
el
in
v
er
ter
,
s
ec
tio
n
th
r
ee
tal
k
s
ab
o
u
t th
e
s
im
u
latio
n
r
esu
lts
an
d
co
n
clu
s
io
n
s
p
r
esen
ted
in
s
ec
tio
n
f
o
u
r
.
2.
M
UL
T
I
P
H
A
SE
M
UL
T
I
L
E
VE
L
I
NV
E
RT
E
R
2
.
1
.
B
lo
c
k
d
ia
g
ra
m
Fig
u
r
e
1
d
e
p
icts
th
e
s
tr
u
ctu
r
e
o
f
th
e
3
-
lev
el,
5
-
p
h
ase
in
v
er
ter
[2
2
]
.
I
t
f
ea
tu
r
es
5
leg
s
,
with
f
o
u
r
s
witch
es
o
n
ea
ch
leg
th
at
ca
n
o
n
ly
b
e
u
s
ed
in
two
c
o
m
p
l
em
en
tar
y
c
o
m
b
in
atio
n
p
air
s
.
T
ab
le
1
d
e
p
icts
th
e
p
h
ase
A
s
witch
in
g
co
n
f
ig
u
r
ati
o
n
s
f
o
r
5
-
p
h
ase
NPC
I
n
v
er
ter
.
A
3
L
in
v
er
ter
em
p
lo
y
s
a
DC
-
lin
k
ca
p
ac
ito
r
a
n
d
n
eu
tr
al
p
o
in
t
to
clam
p
th
e
v
o
l
tag
e
s
tr
ess
on
s
witch
e
s
at
Vd
c
/2
.
T
h
er
e
is
an
NPC
leg
f
o
r
ea
ch
o
f
th
e
5
p
h
ases
(
d
esig
n
ated
A,
B
,
C
,
D,
an
d
E
)
.
T
h
r
ee
o
u
tp
u
t
v
o
ltag
e
lev
el
s
ca
n
b
e
g
en
e
r
ated
b
y
th
e
in
v
er
ter
d
u
e
to
th
e
tw
o
clam
p
in
g
d
io
d
es
a
n
d
f
o
u
r
s
w
itch
es
u
s
ed
to
s
et
u
p
ea
ch
le
g
:
+V
d
c/2
,
0
,
an
d
-
Vd
c/
2
.
E
f
f
ec
tiv
e
m
u
ltil
ev
el
in
v
er
s
io
n
an
d
c
o
n
tr
o
l
ar
e
m
a
d
e
p
o
s
s
ib
le
b
y
s
p
ec
if
ically
tu
r
n
in
g
o
n
s
witch
es
S1
A
an
d
S
2
A
,
wh
ich
p
r
o
d
u
c
e
+V
d
c/2
,
an
d
tu
r
n
in
g
o
n
s
w
itch
es
S3
A
an
d
S4
A,
wh
ich
p
r
o
d
u
ce
-
Vd
c/
2
.
W
h
en
S1
A
an
d
S4
A
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
26
4
-
1
27
4
1266
s
im
u
ltan
eo
u
s
ly
tu
r
n
e
d
o
n
,
th
e
o
u
tp
u
t
b
ec
o
m
es
ze
r
o
.
Me
an
wh
ile,
s
witch
p
air
s
S2
A
-
S4
A
an
d
S1
A
-
S3
A
o
p
er
ate
in
a
c
o
m
p
lem
e
n
tar
y
m
an
n
er
.
T
h
e
s
witch
in
g
tab
le
f
o
r
th
e
o
th
er
p
h
ases
will b
e
id
en
tical.
Fig
u
r
e
1
.
Simp
le
d
iag
r
am
o
f
t
h
e
th
r
ee
-
lev
el
NPC
in
v
er
ter
f
o
r
a
lo
ad
with
f
iv
e
p
h
ases
T
ab
le
1
.
Ph
ase
A
s
witch
in
g
co
n
f
ig
u
r
atio
n
s
f
o
r
5
-
p
h
ase
NPC
in
v
er
ter
S
1
A
S
2
A
S
3
A
S
4
A
O
u
t
p
u
t
v
o
l
t
a
g
e
M
o
d
e
ON
ON
O
F
F
O
F
F
V
d
c
/
2
H
i
g
h
O
F
F
ON
ON
O
F
F
0
N
e
u
t
r
a
l
O
F
F
O
F
F
ON
ON
-
V
d
c
/
2
Lo
w
2
.
2
.
Co
ntr
o
l
l
o
g
ic
Mu
ltil
ev
el
in
v
er
ter
s
y
s
tem
s
o
f
ten
em
p
lo
y
s
in
u
s
o
i
d
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
.
A
s
in
u
s
o
id
al
wav
ef
o
r
m
'
s
wid
th
is
ch
an
g
ed
to
ad
ju
s
t
th
e
o
u
tp
u
t
v
o
ltag
e
lev
el.
C
o
m
p
ar
ed
to
co
n
v
en
ti
o
n
al
b
in
ar
y
PW
M
tech
n
iq
u
es,
th
is
m
eth
o
d
o
f
f
er
s
m
o
r
e
v
o
ltag
e
lev
els,
wh
ich
im
p
r
o
v
es
p
o
wer
q
u
ality
a
n
d
lo
wer
s
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
Sin
u
s
o
i
d
al
PW
M
is
also
s
u
itab
le
f
o
r
m
o
t
o
r
d
r
iv
es
[2
2
]
,
[
2
3
]
,
elec
tr
ic
ca
r
ch
a
r
g
i
n
g
,
a
n
d
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
th
at
n
ee
d
a
s
tead
y
an
d
s
m
o
o
t
h
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
[
24
]
,
[
2
5
]
.
Mu
ltil
ev
el
in
v
er
ter
s
y
s
tem
s
ca
n
o
p
er
ate
m
o
r
e
d
ep
en
d
ab
l
y
,
ef
f
icien
tly
,
a
n
d
with
im
p
r
o
v
ed
p
o
wer
co
n
s
u
m
p
tio
n
b
y
u
tili
zin
g
s
in
u
s
o
id
al
PW
M.
T
h
e
s
ix
ca
t
eg
o
r
ies
o
f
lev
el
-
s
h
if
ted
PW
M
ap
p
r
o
ac
h
es
ar
e
‘
PD,
POD,
A
POD,
I
C
,
PS
C
,
an
d
VFC
’
.
2.
2
.1
.
In
-
ph
a
s
e
ca
rr
ier
dis
po
s
it
io
n
P
WM
I
n
th
e
PD
PW
M
m
eth
o
d
,
m
u
ltip
le
ca
r
r
ier
s
ig
n
als
with
id
en
tical
f
r
eq
u
e
n
cy
an
d
am
p
litu
d
e
ar
e
p
o
s
itio
n
ed
at
d
if
f
er
en
t
lev
els.
T
h
is
tech
n
iq
u
e
u
s
es h
ig
h
-
f
r
eq
u
en
cy
ca
r
r
ier
s
[2
6
]
.
A
ce
r
tain
f
o
r
m
u
la
ca
n
b
e
u
s
ed
to
q
u
an
titativ
ely
r
ep
r
esen
t
th
e
r
atio
o
f
f
r
eq
u
e
n
cy
a
n
d
in
d
ex
o
f
m
o
d
u
latio
n
.
M
a
=
A
m
(
m
−
1
)
.
A
c
(
1
)
M
f
=
c
.
f
m
(
2
)
W
h
er
e
p
r
o
v
id
es
a
way
to
q
u
an
tify
th
e
lev
el
o
f
m
o
d
u
latio
n
an
d
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
m
o
d
u
latin
g
an
d
ca
r
r
ier
f
r
eq
u
en
cies
[2
7
]
.
T
h
e
ca
r
r
ier
a
n
d
m
o
d
u
latin
g
s
ig
n
al
f
r
eq
u
e
n
cies
ar
e
in
d
icate
d
b
y
th
e
p
ar
am
eter
s
f
c
an
d
f
m
,
a
n
d
th
eir
c
o
r
r
esp
o
n
d
i
n
g
am
p
litu
d
es
ar
e
in
d
icate
d
b
y
A
c
an
d
A
m
.
Fig
u
r
e
2
(
a)
s
h
o
ws
th
e
wav
ef
o
r
m
s
o
f
th
ese
s
ig
n
als u
s
in
g
th
e
p
h
ase
PD
-
PW
M
ap
p
r
o
ac
h
.
2
.
2
.
2
.
Ant
i
-
ph
a
s
e
ca
rr
ier
dis
po
s
it
io
n
P
WM
T
h
e
POD
PW
M
tech
n
iq
u
e
em
p
lo
y
s
ca
r
r
ier
s
ig
n
als
with
u
n
if
o
r
m
f
r
eq
u
e
n
cy
an
d
am
p
lit
u
d
e,
wh
er
e
ca
r
r
ier
s
ab
o
v
e
th
e
ze
r
o
r
ef
er
e
n
ce
ar
e
in
v
er
ted
(
1
8
0
-
d
e
g
r
ee
p
h
ase
s
h
if
t)
r
elativ
e
to
th
o
s
e
b
elo
w
[
28
]
-
[3
0
]
.
T
h
e
p
h
ase
o
p
p
o
s
itio
n
an
d
p
h
ase
d
is
p
o
s
itio
n
ap
p
r
o
ac
h
es
ar
e
b
o
th
in
co
r
p
o
r
ated
in
t
o
th
is
ap
p
r
o
ac
h
.
C
ar
r
ier
s
p
o
s
itio
n
ed
ab
o
v
e
th
e
ze
r
o
ax
i
s
g
en
er
ate
p
o
s
itiv
e
o
u
tp
u
t
le
v
els,
wh
er
ea
s
th
o
s
e
b
elo
w
th
e
ze
r
o
ax
is
p
r
o
d
u
ce
n
eg
ativ
e
o
u
tp
u
t
lev
els.
No
c
ar
r
ier
s
ig
n
als
ar
e
u
s
ed
i
n
th
e
p
r
o
d
u
ctio
n
o
f
th
e
ze
r
o
lev
el
.
T
h
e
POD
PW
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f m
u
lti ca
r
r
ier P
W
M tec
h
n
iq
u
es fo
r
a
5
-
p
h
a
s
e
th
r
ee
leve
l …
(
V
en
u
Ya
r
la
g
a
d
d
a
)
1267
tech
n
iq
u
e'
s
m
o
d
u
latin
g
an
d
c
ar
r
ier
s
ig
n
als
ar
e
d
is
p
lay
ed
i
n
Fig
u
r
e
2
(
b
)
.
Fig
u
r
e
2
illu
s
tr
ates
th
e
r
ef
e
r
en
ce
s
in
u
s
o
id
al
s
ig
n
al
an
d
th
e
co
r
r
e
s
p
o
n
d
in
g
ca
r
r
ier
s
ig
n
al
ar
r
an
g
em
en
ts
f
o
r
th
e
s
ix
m
u
lti
-
ca
r
r
ie
r
PW
M
tech
n
iq
u
es
co
n
s
id
er
ed
in
t
h
is
s
tu
d
y
,
n
a
m
ely
PD,
POD,
APOD,
I
C
,
PS
C
,
an
d
VFC
.
T
h
ese
ca
r
r
ie
r
co
n
f
ig
u
r
atio
n
s
ar
e
cr
itical,
as
th
eir
p
h
ase
r
elatio
n
s
h
ip
s
an
d
f
r
eq
u
e
n
cy
ch
a
r
ac
ter
i
s
tics
d
ir
ec
tly
in
f
lu
en
ce
th
e
h
ar
m
o
n
ic
d
is
tr
ib
u
tio
n
an
d
T
HD
p
er
f
o
r
m
a
n
ce
o
f
th
e
f
iv
e
-
p
h
ase,
th
r
ee
-
lev
el
NPC
in
v
er
ter
.
2.
2
.3
.
P
ha
s
e
o
pp
o
s
it
io
n
P
WM
wit
h a
lt
er
na
t
ing
ca
rr
iers
All
ca
r
r
ier
s
in
APOD
-
PW
M
h
av
e
u
n
if
o
r
m
f
r
eq
u
en
cy
an
d
a
m
p
litu
d
e,
b
u
t
th
eir
p
h
ase
an
g
l
es
ar
e
1
8
0
d
eg
r
ee
s
ap
a
r
t
.
T
h
is
m
ak
es
it
p
o
s
s
ib
le
to
p
r
o
d
u
ce
b
o
th
p
o
s
itiv
e
an
d
n
eg
ativ
e
le
v
els
b
y
u
s
in
g
ca
r
r
ie
r
s
ab
o
v
e
a
n
d
b
elo
w
ze
r
o
r
e
f
er
en
ce
s
.
Fig
u
r
e
2
(
c)
d
e
p
icts
th
e
APOD
P
W
M
ca
r
r
ier
an
d
m
o
d
u
latin
g
s
ig
n
als.
W
ith
th
is
m
eth
o
d
,
th
e
v
o
ltag
e
s
tr
ess
is
s
o
m
ewh
at
d
ec
r
ea
s
ed
.
Fo
r
3
l
ev
el
in
v
er
ter
s
,
POD
an
d
APOD
ap
p
r
o
ac
h
es
will
y
ield
co
m
p
a
r
ab
le
f
in
d
in
g
s
; h
o
wev
er
,
f
o
r
h
ig
h
er
lev
el
in
v
er
te
r
s
,
th
ey
will y
ield
d
if
f
er
en
t o
u
t
co
m
es.
2.
2
.4
.
Ca
rr
ier
inte
rlea
v
ing
P
WM
All
ca
r
r
ier
s
ig
n
als
in
I
C
P
W
M
h
av
e
th
e
s
am
e
f
r
eq
u
en
cy
an
d
am
p
litu
d
e
th
r
o
u
g
h
o
u
t
th
e
en
t
ir
e
s
ig
n
al.
On
th
e
o
t
h
er
h
an
d
,
th
er
e
will
b
e
in
s
tan
ce
s
in
wh
ic
h
th
e
y
o
v
er
lap
o
n
e
an
o
th
er
;
s
p
ec
if
i
ca
lly
,
th
er
e
will
b
e
in
s
tan
ce
s
in
wh
ich
th
e
h
ig
h
er
an
d
lo
we
r
ca
r
r
ier
s
ig
n
als
will
o
v
er
lap
.
T
HD
will
b
e
r
e
d
u
ce
d
with
th
is
m
eth
o
d
,
an
d
th
e
o
u
tp
u
t v
o
ltag
e
will b
e
in
cr
ea
s
ed
.
Fo
r
th
e
p
u
r
p
o
s
e
o
f
g
en
er
atin
g
th
e
p
o
s
itiv
e
an
d
n
eg
ativ
e
lev
els,
u
p
p
er
an
d
lo
wer
ca
r
r
ie
r
s
will
b
e
u
tili
ze
d
.
An
illu
s
tr
atio
n
o
f
th
e
ar
r
an
g
em
en
t
o
f
ca
r
r
ier
a
n
d
r
ef
e
r
en
ce
s
ig
n
als
f
o
r
th
e
th
r
ee
-
lev
el
I
PC
,
PW
M
m
eth
o
d
m
ay
b
e
f
o
u
n
d
in
Fig
u
r
e
2
(
d
)
.
2.
2
.5
.
Ca
rr
ier
ph
a
s
e
s
hift
P
WM
I
n
th
e
PS
C
–
PW
M
tech
n
iq
u
e,
m
u
ltip
le
ca
r
r
ier
s
ig
n
als
with
id
en
tical
f
r
eq
u
e
n
cy
a
n
d
am
p
litu
d
e
ar
e
p
h
ase
-
s
h
if
ted
r
elativ
e
to
ea
c
h
o
th
er
.
T
h
is
p
r
o
ce
s
s
g
en
er
a
tes
a
s
tep
p
ed
o
u
tp
u
t
wav
e
f
o
r
m
th
at
r
ef
lects
th
e
co
m
b
in
ed
ef
f
ec
t
o
f
th
e
s
h
if
ted
ca
r
r
ier
s
.
T
h
e
n
u
m
b
er
o
f
ca
r
r
ier
s
d
eter
m
in
es
th
e
p
h
as
e
s
h
if
t
am
o
u
n
t,
as
illu
s
tr
ated
in
th
e
3
-
lev
el
PS
C
–
PW
M
co
n
f
ig
u
r
atio
n
s
h
o
w
n
in
Fig
u
r
e
2
(
e)
.
2.
2
.6
.
Va
ria
ble c
a
rr
ier
f
re
qu
ency
P
WM
All
ca
r
r
ier
s
ig
n
als
in
I
C
PW
M
h
av
e
th
e
s
am
e
f
r
eq
u
en
cy
an
d
am
p
litu
d
e
th
r
o
u
g
h
o
u
t
th
e
en
t
ir
e
s
ig
n
al
an
d
it
is
s
h
o
wn
in
Fig
u
r
e
2
(
f
)
.
On
th
e
o
th
er
h
a
n
d
,
th
e
r
e
will
b
e
in
s
tan
ce
s
in
wh
ich
th
ey
o
v
er
lap
o
n
e
a
n
o
th
er
;
s
p
ec
if
ically
,
th
er
e
will
b
e
in
s
t
an
ce
s
in
wh
ich
th
e
h
ig
h
er
an
d
lo
wer
ca
r
r
ier
s
ig
n
als
will
o
v
e
r
lap
.
T
HD
will
b
e
r
ed
u
ce
d
with
th
is
m
eth
o
d
,
an
d
th
e
o
u
tp
u
t
v
o
ltag
e
will
b
e
in
c
r
ea
s
ed
.
Fo
r
t
h
e
p
u
r
p
o
s
e
o
f
g
en
er
atin
g
th
e
p
o
s
itiv
e
an
d
n
e
g
ativ
e
lev
els,
u
p
p
er
an
d
lo
wer
ca
r
r
ier
s
will b
e
u
tili
ze
d
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
2
.
T
h
r
ee
lev
el
NPC
in
v
er
ter
r
ef
er
e
n
ce
an
d
ca
r
r
ier
s
ig
n
al
co
n
f
ig
u
r
atio
n
f
o
r
(
a
)
PD,
(
b
)
POD,
(
c)
APOD,
(
d
)
I
C
,
(
e)
PS
C
,
an
d
(
f
)
VFC
PW
M
ap
p
r
o
ac
h
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
26
4
-
1
27
4
1268
An
illu
s
tr
atio
n
o
f
t
h
e
ar
r
a
n
g
e
m
en
t
o
f
ca
r
r
ier
a
n
d
r
ef
er
e
n
ce
s
ig
n
als
f
o
r
th
e
th
r
ee
-
le
v
el
I
PC
,
PW
M
m
eth
o
d
m
ay
b
e
f
o
u
n
d
in
Fig
u
r
e
2
(
d
)
.
A
g
ate
d
r
iv
er
cir
cu
i
t
r
ec
eiv
es
th
is
p
u
ls
e
-
wid
th
m
o
d
u
lated
s
ig
n
al
an
d
u
s
es
it
to
cr
ea
te
th
e
g
ate
p
u
ls
e
f
o
r
ev
e
r
y
s
witch
in
g
d
ev
ice.
T
h
e
PW
M
s
ig
n
al
is
am
p
lifie
d
an
d
tr
an
s
f
o
r
m
ed
i
n
to
a
s
ig
n
al
th
at
m
ay
b
e
u
tili
ze
d
to
r
eg
u
late
th
e
g
ate
v
o
ltag
e
o
f
th
e
s
witch
in
g
d
e
v
ice
b
y
t
h
e
g
ate
d
r
iv
er
cir
cu
it.
T
h
e
g
ate
d
r
iv
er
cir
cu
it
ac
tiv
a
tes
th
e
s
witch
in
g
d
ev
ice
wh
e
n
th
e
PW
M
s
ig
n
al
is
h
ig
h
a
n
d
d
ea
ctiv
ates
th
e
d
ev
ice
wh
e
n
th
e
PW
M
s
ig
n
al
is
lo
w.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
ea
c
h
m
u
lti
-
ca
r
r
ier
PW
M
(
MCP
W
M)
tech
n
iq
u
e
a
n
d
its
co
r
r
esp
o
n
d
i
n
g
im
p
ac
t
o
n
T
HD,
th
e
co
n
tr
o
l
lo
g
ic
,
an
d
r
esu
lts
d
is
cu
s
s
io
n
s
ec
tio
n
s
d
escr
ib
e
th
e
ca
r
r
ier
ar
r
an
g
e
m
en
t,
p
h
ase
d
is
p
o
s
itio
n
,
an
d
f
r
eq
u
en
cy
ch
ar
ac
ter
is
tics
o
f
ea
ch
PW
M
m
eth
o
d
i
n
f
lu
en
ce
h
ar
m
o
n
ic
d
is
tr
ib
u
tio
n
in
th
e
in
v
er
ter
o
u
tp
u
t.
Sp
ec
if
ically
,
t
h
e
PD
tech
n
i
q
u
e
is
e
x
p
lain
e
d
as
y
ield
in
g
lo
wer
T
HD
d
u
e
to
th
e
in
-
p
h
ase
alig
n
m
en
t
o
f
ca
r
r
ier
s
,
wh
ich
p
r
o
m
o
tes
ef
f
ec
tiv
e
h
ar
m
o
n
ic
ca
n
ce
llatio
n
.
I
n
co
n
t
r
ast,
th
e
POD
an
d
APOD
tech
n
iq
u
es
in
tr
o
d
u
ce
p
h
ase
r
ev
e
r
s
als
b
etwe
en
ca
r
r
ier
s
,
lead
in
g
to
i
n
cr
ea
s
ed
lo
w
-
o
r
d
er
h
ar
m
o
n
ics
an
d
h
ig
h
er
T
HD.
T
h
e
I
C
ap
p
r
o
ac
h
is
d
is
cu
s
s
ed
in
ter
m
s
o
f
h
a
r
m
o
n
ic
s
p
r
ea
d
in
g
ca
u
s
ed
b
y
o
v
er
lap
p
i
n
g
ca
r
r
ier
s
,
r
esu
ltin
g
in
m
o
d
er
ate
T
HD
r
ed
u
ctio
n
.
Similar
ly
,
th
e
PS
C
an
d
V
FC
tech
n
iq
u
es
ar
e
ex
p
lain
ed
as
r
ed
is
tr
ib
u
tin
g
h
ar
m
o
n
ic
en
er
g
y
ac
r
o
s
s
a
wid
er
f
r
eq
u
e
n
cy
s
p
ec
tr
u
m
,
wh
ic
h
r
ed
u
ce
s
d
o
m
in
a
n
t
h
ar
m
o
n
ic
p
ea
k
s
b
u
t d
o
es n
o
t o
u
tp
er
f
o
r
m
PD in
o
v
er
all
T
HD
m
in
im
izatio
n
.
T
h
ese
clar
if
icat
io
n
s
s
tr
en
g
th
en
th
e
p
h
y
s
ical
in
ter
p
r
etatio
n
o
f
t
h
e
s
im
u
latio
n
r
esu
lts
an
d
im
p
r
o
v
e
th
e
r
ea
d
er
’
s
u
n
d
e
r
s
tan
d
in
g
o
f
h
o
w
ea
c
h
PW
M
s
tr
ateg
y
af
f
ec
ts
h
ar
m
o
n
ic
p
er
f
o
r
m
an
ce
.
3.
SI
M
UL
A
T
I
O
N
A
NAL
YSI
S
AND
RE
SUL
T
S
T
h
e
s
o
f
twar
e
m
o
d
el
o
f
t
h
e
5
-
p
h
ase
3
-
lev
el
NPC
in
v
er
ter
h
as
b
ee
n
in
v
esti
g
ated
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
,
an
d
a
n
u
m
b
er
o
f
d
if
f
e
r
en
t
MCP
W
M
tech
n
iq
u
es
h
av
e
b
ee
n
u
tili
z
ed
.
T
h
e
s
witch
in
g
f
r
eq
u
e
n
cy
o
f
th
e
s
y
s
tem
is
1
0
k
Hz,
an
d
it
is
d
r
iv
e
n
b
y
a
3
0
0
V
DC
p
o
wer
s
o
u
r
ce
th
at
is
s
u
p
p
o
r
ted
b
y
a
1
0
0
µF
ca
p
ac
ito
r
d
u
r
i
n
g
o
p
er
atio
n
.
Ass
u
m
in
g
th
at
R
is
e
q
u
al
to
1
0
Ω
an
d
L
is
eq
u
al
to
2
m
H,
we
p
r
o
ce
ed
to
in
v
esti
g
ate
an
R
L
lo
ad
.
Fig
u
r
e
3
s
h
o
ws
th
e
lin
e
v
o
ltag
e
wav
ef
o
r
m
s
an
d
th
eir
co
r
r
esp
o
n
d
in
g
FF
T
-
b
ased
v
o
ltag
e
T
HD
s
p
ec
tr
a
f
o
r
th
e
s
ix
MCP
W
M
tech
n
iq
u
es.
T
h
e
co
m
p
ar
is
o
n
p
r
o
v
id
es
a
q
u
an
tit
ativ
e
ass
ess
m
en
t
o
f
h
o
w
d
if
f
e
r
en
t c
ar
r
ie
r
ar
r
a
n
g
e
m
en
ts
af
f
ec
t h
ar
m
o
n
ic
d
is
to
r
ti
o
n
an
d
o
u
tp
u
t v
o
lta
g
e
q
u
ality
.
A
co
m
p
ar
ativ
ely
s
m
o
o
th
a
n
d
s
y
m
m
etr
ical
lin
e
v
o
ltag
e
wav
ef
o
r
m
with
a
f
u
n
d
am
e
n
tal
v
o
ltag
e
m
ag
n
itu
d
e
o
f
ap
p
r
o
x
im
ately
1
7
0
V
is
s
h
o
wn
in
Fig
u
r
e
3
(
a)
u
s
in
g
th
e
PD,
PW
M
ap
p
r
o
ac
h
.
A
T
HD
o
f
2
0
.
0
7
%,
th
e
lo
west
o
f
all
r
es
ea
r
ch
ed
ap
p
r
o
ac
h
es,
is
s
h
o
wn
b
y
th
e
r
elate
d
FF
T
an
aly
s
i
s
,
em
p
h
asizin
g
PD
PW
M
's
ex
ce
p
tio
n
al
h
ar
m
o
n
ic
p
er
f
o
r
m
an
ce
.
T
h
e
POD,
PW
M
ap
p
r
o
ac
h
,
o
n
th
e
o
th
er
h
an
d
,
s
h
o
ws
r
esu
lts
in
Fig
u
r
e
3
(
b
)
,
wh
er
e
th
e
wav
ef
o
r
m
s
h
o
ws
m
o
r
e
ab
r
u
p
t
tr
an
s
itio
n
s
b
ec
au
s
e
o
f
th
e
1
8
0
°
p
h
ase
s
h
if
t
b
etwe
en
ad
jace
n
t
ca
r
r
ier
s
.
As
a
r
esu
lt,
th
e
T
HD
is
m
u
ch
g
r
ea
ter
at
4
0
.
8
7
%.
T
h
e
o
u
tp
u
t
f
o
r
t
h
e
APOD,
wh
ich
h
as
s
tr
u
ctu
r
al
s
im
ilar
ities
to
POD
an
d
p
r
o
d
u
ce
s
a
T
HD
o
f
3
9
.
8
3
%,
is
s
im
ilar
ly
i
llu
s
tr
ated
i
n
Fig
u
r
e
3
(
c)
.
T
h
e
I
n
ter
leav
ed
c
ar
r
ie
r
PW
M
tec
h
n
iq
u
e,
s
h
o
wn
in
Fig
u
r
e
3
(
d
)
,
h
as
o
v
er
lap
p
in
g
ca
r
r
ier
s
ig
n
als
th
at
s
o
m
ewh
at
lo
wer
h
ar
m
o
n
ic
co
n
te
n
t,
alth
o
u
g
h
th
e
T
HD
is
s
till
m
o
r
e
th
a
n
th
e
PD.
Fig
u
r
e
s
3
(
e)
a
n
d
3
(
f
)
illu
s
tr
ate
th
e
PS
C
an
d
VFC
m
eth
o
d
s
,
r
esp
ec
tiv
ely
.
B
ec
au
s
e
o
f
th
eir
d
is
tin
ct
ca
r
r
ier
ar
r
an
g
e
m
en
ts
,
b
o
th
g
e
n
er
ate
a
v
ar
iety
o
f
h
ar
m
o
n
ic
p
r
o
f
iles
,
b
u
t
n
eith
e
r
o
u
tp
er
f
o
r
m
s
th
e
PD
ap
p
r
o
ac
h
in
ter
m
s
o
f
r
e
d
u
cin
g
d
is
to
r
tio
n
.
W
h
en
tak
en
as
a
wh
o
le,
th
ese
s
u
b
f
ig
u
r
es
o
f
f
er
a
co
m
p
a
r
ativ
e
v
iew
o
f
th
e
ef
f
ec
ts
o
f
ea
ch
PW
M
s
ch
em
e
o
n
th
e
q
u
ality
o
f
th
e
v
o
ltag
e
wav
ef
o
r
m
.
T
h
e
PD
ap
p
r
o
ac
h
is
th
e
m
o
s
t
ef
f
ec
tiv
e
at
r
ed
u
cin
g
T
HD,
wh
ich
is
cr
u
cial
f
o
r
en
h
an
ci
n
g
in
v
er
ter
p
e
r
f
o
r
m
an
ce
in
E
V
ap
p
licatio
n
s
.
Fig
u
r
e
4
d
ep
icts
th
e
d
y
n
a
m
ic
p
er
f
o
r
m
an
ce
o
f
th
e
P
MSM
d
r
iv
e,
in
clu
d
in
g
m
o
t
o
r
s
p
ee
d
,
elec
tr
o
m
ag
n
etic
to
r
q
u
e,
a
n
d
s
tato
r
cu
r
r
en
t
wav
ef
o
r
m
s
.
T
h
ese
r
esu
lts
d
em
o
n
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
in
v
er
ter
an
d
PW
M
s
tr
ateg
y
i
n
ac
h
iev
in
g
s
m
o
o
th
s
p
ee
d
co
n
tr
o
l
an
d
s
tab
le
to
r
q
u
e
r
esp
o
n
s
e.
T
h
e
s
im
u
latio
n
r
esu
lts
f
o
r
a
th
r
ee
-
p
h
ase
PMSM
o
p
er
atin
g
u
n
d
er
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
ap
p
r
o
ac
h
ar
e
g
iv
en
in
Fig
u
r
e
4
.
Fig
u
r
e
4
(
a)
d
is
p
lay
s
th
e
m
o
t
o
r
s
p
ee
d
in
r
ad
ian
s
p
er
s
ec
o
n
d
to
illu
s
tr
ate
th
e
r
esu
lts
.
T
h
i
s
in
d
icate
s
th
at
th
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
is
ef
f
i
cien
t
an
d
th
at
th
e
r
ea
ctio
n
ti
m
e
is
s
h
o
r
t.
T
h
e
s
p
ee
d
p
r
o
f
ile
d
em
o
n
s
tr
ates
a
co
n
s
is
ten
t
an
d
s
m
o
o
th
clim
b
to
th
e
s
tead
y
-
s
tate
v
alu
e
th
at
is
p
lan
n
ed
.
Fig
u
r
e
4
(
b
)
illu
s
tr
ates
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
th
at
is
p
r
o
d
u
ce
d
b
y
t
h
e
m
o
t
o
r
.
T
h
is
to
r
q
u
e
is
r
elativ
ely
s
tab
le
an
d
g
en
e
r
ates
o
n
ly
a
litt
le
am
o
u
n
t
o
f
r
ip
p
le
,
wh
ich
in
d
icate
s
th
at
th
e
to
r
q
u
e
is
co
n
tr
o
lled
p
r
ec
is
ely
.
T
h
is
is
an
es
s
en
tial
ch
ar
ac
ter
is
tic
f
o
r
e
n
s
u
r
in
g
th
a
t
elec
tr
ic
ca
r
ap
p
licatio
n
s
co
n
t
in
u
e
to
f
u
n
ctio
n
s
m
o
o
th
l
y
.
T
h
e
s
tato
r
cu
r
r
e
n
ts
o
f
th
e
th
r
ee
-
p
h
ase
m
o
to
r
a
r
e
s
h
o
wn
in
Fig
u
r
e
4
(
c)
,
an
d
th
ey
a
r
e
b
alan
ce
d
an
d
s
in
u
s
o
id
al.
T
h
is
d
em
o
n
s
tr
ates
th
at
th
e
in
v
er
ter
is
ca
p
a
b
le
o
f
d
eliv
er
in
g
c
u
r
r
en
t
wa
v
ef
o
r
m
s
o
f
h
ig
h
q
u
ality
.
T
h
e
r
esu
lts
o
f
t
h
e
s
im
u
latio
n
s
h
o
w
th
at
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
is
ef
f
ec
tiv
e
f
o
r
co
n
tr
o
lli
n
g
cu
r
r
e
n
t
as
well
as
s
m
o
o
th
s
p
ee
d
an
d
to
r
q
u
e
m
an
ag
em
en
t.
As a
co
n
s
eq
u
e
n
ce
,
it is
s
u
ited
f
o
r
elec
tr
ic
v
e
h
icle
d
r
iv
es th
at
ar
e
b
ased
o
n
P
MSM
tech
n
o
lo
g
y
.
A
5
-
p
h
ase
in
d
u
ctio
n
m
o
to
r
'
s
s
im
u
latio
n
r
esu
lts
,
in
clu
d
in
g
m
o
to
r
s
p
ee
d
(
r
ad
/s
a
n
d
r
p
m
)
an
d
to
r
q
u
e
v
alu
es
an
d
s
tato
r
c
u
r
r
e
n
ts
,
ar
e
s
h
o
wn
in
Fig
u
r
e
5
.
T
h
ese
r
esu
lts
h
av
e
b
ee
n
o
b
tain
ed
u
s
in
g
t
h
e
p
a
p
er
o
u
tlin
es
a
co
n
tr
o
l
tech
n
i
q
u
e
d
esig
n
e
d
to
m
ax
im
ize
p
er
f
o
r
m
an
ce
in
f
i
v
e
-
p
h
ase
in
d
u
ctio
n
m
o
to
r
s
.
T
h
e
s
im
u
latio
n
r
esu
lt
s
p
r
o
v
id
e
a
d
ee
p
er
u
n
d
er
s
tan
d
in
g
o
f
th
e
m
o
to
r
'
s
b
eh
av
io
r
ac
r
o
s
s
d
if
f
er
en
t o
p
er
atin
g
s
ce
n
ar
io
s
,
in
f
o
r
m
in
g
d
esig
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f m
u
lti ca
r
r
ier P
W
M tec
h
n
iq
u
es fo
r
a
5
-
p
h
a
s
e
th
r
ee
leve
l …
(
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en
u
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la
g
a
d
d
a
)
1269
an
d
co
n
tr
o
l
p
ar
am
eter
o
p
tim
izatio
n
.
Key
m
etr
ics
lik
e
m
o
t
o
r
s
p
ee
d
an
d
to
r
q
u
e
p
r
o
f
ile
r
ev
ea
l
th
e
m
o
to
r
'
s
d
y
n
am
ic
r
esp
o
n
s
e
an
d
l
o
ad
-
h
an
d
lin
g
ca
p
a
b
ilit
ies,
wh
ile
s
t
ato
r
cu
r
r
e
n
t
wav
ef
o
r
m
s
in
d
ic
ate
ef
f
icien
cy
an
d
lo
ad
o
p
e
r
atio
n
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
3
.
Vo
ltag
e
T
HD
an
d
li
n
e
v
o
ltag
e
r
esu
lts
f
o
r
(
a)
PD,
(
b
)
POD,
(
c)
APOD,
(
d
)
I
C
,
(
e)
PS
C
,
an
d
(
f
)
VFC
PW
M
ap
p
r
o
ac
h
Fig
u
r
e
5
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
5
-
p
h
ase
in
d
u
ctio
n
m
o
to
r
f
ed
b
y
th
e
p
r
o
p
o
s
ed
in
v
er
ter
s
y
s
tem
,
in
clu
d
in
g
s
p
ee
d
r
esp
o
n
s
e,
to
r
q
u
e
ch
ar
ac
ter
is
tics
,
an
d
s
tato
r
cu
r
r
en
t
wav
e
f
o
r
m
s
.
T
h
is
f
ig
u
r
e
is
c
r
u
cial
f
o
r
ev
alu
atin
g
th
e
s
u
itab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
PW
M
s
tr
ate
g
y
f
o
r
E
V
tr
ac
tio
n
a
p
p
licatio
n
s
.
T
h
e
to
r
q
u
e
an
d
s
tato
r
cu
r
r
en
t
r
esp
o
n
s
es
ar
e
s
h
o
wn
in
Fig
u
r
e
5
,
d
em
o
n
s
tr
atin
g
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
PW
M
s
tr
ateg
y
in
im
p
r
o
v
in
g
th
e
5
-
p
h
ase
in
d
u
ctio
n
m
o
to
r
p
e
r
f
o
r
m
a
n
ce
.
T
h
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
ex
h
ib
its
r
ed
u
ce
d
r
ip
p
le
an
d
f
aster
s
ettlin
g
tim
e,
in
d
icatin
g
im
p
r
o
v
e
d
d
y
n
a
m
ic
s
tab
ilit
y
an
d
s
m
o
o
th
er
o
p
er
atio
n
u
n
d
er
l
o
ad
.
T
h
e
s
tato
r
cu
r
r
en
t
wa
v
ef
o
r
m
s
ar
e
b
alan
ce
d
an
d
n
ea
r
ly
s
in
u
s
o
id
al,
co
n
f
ir
m
i
n
g
r
e
d
u
ce
d
h
ar
m
o
n
ic
in
jectio
n
f
r
o
m
th
e
in
v
er
te
r
.
T
h
ese
c
h
ar
a
cter
is
tics
d
ir
ec
tly
co
n
tr
ib
u
te
to
lo
wer
co
p
p
er
lo
s
s
es,
r
ed
u
ce
d
th
er
m
al
s
tr
ess
,
an
d
en
h
an
ce
d
r
eliab
ilit
y
o
f
th
e
m
o
to
r
d
r
iv
e
,
wh
ich
ar
e
cr
itical
r
eq
u
ir
em
en
ts
f
o
r
elec
tr
ic
v
eh
icle
p
r
o
p
u
ls
io
n
s
y
s
tem
s
.
T
h
e
r
esu
lts
ar
e
s
h
o
wn
in
Fig
u
r
e
5
,
s
h
o
w
h
o
w
ef
f
ec
tiv
ely
t
h
e
s
u
g
g
ested
co
n
tr
o
l
m
eth
o
d
wo
r
k
s
wh
en
co
n
tr
o
llin
g
th
e
s
p
ee
d
an
d
to
r
q
u
e
o
f
a
f
iv
e
-
p
h
ase
i
n
d
u
ctio
n
m
o
to
r
.
W
ith
m
in
im
u
m
to
r
q
u
e
an
d
s
p
ee
d
ch
a
n
g
es,
th
e
m
o
to
r
m
ay
f
u
n
ctio
n
s
m
o
o
th
ly
an
d
ef
f
icien
tly
,
wh
ic
h
i
s
cr
u
cial
f
o
r
n
u
m
er
o
u
s
in
d
u
s
t
r
ial
an
d
r
en
ewa
b
le
en
er
g
y
a
p
p
licatio
n
s
,
ac
co
r
d
in
g
to
th
e
r
esu
lts
o
b
tain
ed
.
All
th
in
g
s
co
n
s
id
er
ed
,
th
e
f
in
d
in
g
s
o
f
f
er
in
s
ig
h
tf
u
l
in
f
o
r
m
atio
n
ab
o
u
t
h
o
w
well
a
f
iv
e
-
p
h
ase
in
d
u
ctio
n
m
o
t
o
r
p
er
f
o
r
m
s
,
allo
win
g
u
s
to
en
h
an
ce
its
d
esig
n
an
d
co
n
tr
o
l p
a
r
am
eter
s
f
o
r
u
s
e
in
e
lectr
ic
v
eh
icles.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
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p
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wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
26
4
-
1
27
4
1270
(
a)
(
b
)
(
c)
Fig
u
r
e
4
.
Simu
latio
n
r
esu
lts
th
r
ee
-
p
h
ase
p
e
r
m
an
en
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
:
(
a
)
s
p
ee
d
i
n
r
ad
/s
,
(
b
)
to
r
q
u
e,
an
d
(
c)
s
tato
r
cu
r
r
e
n
ts
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
5
.
Simu
latio
n
r
esu
lts
,
f
iv
e
p
h
ase
in
d
u
ctio
n
m
o
to
r
:
(a
)
s
p
ee
d
in
r
ad
/s
,
(
b
)
zo
o
m
ed
s
tat
o
r
cu
r
r
en
ts
,
(
c)
to
r
q
u
e,
an
d
(
d
)
s
tato
r
cu
r
r
e
n
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f m
u
lti ca
r
r
ier P
W
M tec
h
n
iq
u
es fo
r
a
5
-
p
h
a
s
e
th
r
ee
leve
l …
(
V
en
u
Ya
r
la
g
a
d
d
a
)
1271
I
n
T
a
b
le
2
,
th
e
v
alu
es
o
f
t
h
e
n
u
m
er
o
u
s
p
ar
a
m
eter
s
th
at
a
r
e
u
tili
ze
d
in
th
e
p
r
o
ce
s
s
o
f
s
im
u
latin
g
an
elec
tr
ic
m
ac
h
in
e
a
r
e
p
r
esen
ted
.
T
h
ese
p
ar
am
eter
s
in
cl
u
d
e
th
e
b
ase
f
r
eq
u
e
n
cy
,
th
e
n
u
m
b
er
o
f
p
o
les,
th
e
m
o
m
en
t
o
f
in
er
tia,
th
e
f
r
ictio
n
f
ac
to
r
,
t
h
e
r
o
to
r
an
d
s
tato
r
r
esis
tan
ce
,
th
e
r
o
t
o
r
a
n
d
s
tato
r
in
d
u
ctan
ce
,
an
d
th
e
m
ag
n
etizin
g
in
d
u
ctan
ce
.
E
x
p
er
im
en
tal
o
r
t
h
eo
r
etica
l
an
aly
s
is
is
o
f
ten
u
s
ed
to
id
en
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1272
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[
29
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in
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fro
m
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sin
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h
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n
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h
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s
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l
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tern
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ti
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ters
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n
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n
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ti
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re
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p
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rs.
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a
re
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o
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n
tere
st
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tri
c
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l
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sy
ste
m
s,
p
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n
d
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l
m
a
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h
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s.
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is
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m
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m
b
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f
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d
ian
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o
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r
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h
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l
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c
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ti
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n
(IS
TE
)
.
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c
a
n
b
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c
o
n
tac
ted
a
t
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m
a
il
:
u
rs
u
n
il
2
5
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m
a
il
.
c
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m
.
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.
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v
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e
n
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g
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s
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n
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ro
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r
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th
e
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p
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rtme
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t
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f
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tri
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l
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n
d
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tro
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g
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ra
sa
r
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o
p
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ta
En
g
in
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rin
g
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ll
e
g
e
(Au
t
o
n
o
m
o
u
s),
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n
d
h
a
s
a
b
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t
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y
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re
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re
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n
g
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a
n
d
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h
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s
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n
d
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r
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Ed
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c
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ti
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).
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h
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s
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e
d
2
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1
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d
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tern
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ti
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6
p
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c
a
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3
1
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.
c
o
m
.
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