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ller
in
clu
d
es
h
y
s
ter
esis
co
n
tr
o
l,
lin
ea
r
ty
p
e
c
o
n
tr
o
l
,
an
d
d
elta
m
o
d
u
lato
r
[
3
6
]
.
Ob
tain
in
g
alter
n
atin
g
cu
r
r
en
t
(
AC
)
o
u
tp
u
t
s
ig
n
als
f
r
o
m
d
ir
ec
t
cu
r
r
en
t
(
DC
)
p
o
wer
s
o
u
r
ce
s
is
th
e
m
ain
task
o
f
p
o
wer
elec
tr
o
n
ic
s
co
n
v
er
ter
s
[
3
6
]
,
[
3
7
]
.
C
o
n
tr
o
lled
AC
p
o
wer
wav
ef
o
r
m
s
a
r
e
n
ee
d
ed
in
m
an
y
ap
p
licatio
n
s
.
T
h
ese
d
if
f
e
r
en
t
a
p
p
licatio
n
s
ca
n
b
e
class
if
ied
b
ased
o
n
th
e
co
n
tr
o
lled
AC
p
ar
am
eter
s
,
wh
ich
ar
e
th
e
m
ag
n
itu
d
e,
f
r
eq
u
en
cy
,
an
d
p
h
ase
an
g
le
o
f
th
e
AC
o
u
t
p
u
t
wav
ef
o
r
m
,
an
d
th
e
ty
p
e
o
f
AC
o
u
t
p
u
t
b
ein
g
co
n
tr
o
lled
.
T
h
e
AC
o
u
tp
u
t
wa
v
ef
o
r
m
will
tak
e
d
is
cr
ete
v
alu
es
s
u
ch
th
at
th
e
f
u
n
d
am
en
tal
co
m
p
o
n
en
t
ap
p
ea
r
s
as a
s
in
u
s
o
id
al
s
ig
n
al,
ev
en
th
o
u
g
h
t
h
e
m
o
d
u
lated
o
u
tp
u
t sig
n
al
is
n
o
t sin
u
s
o
id
al.
Key
ch
ar
ac
ter
is
tics
o
f
th
e
cu
r
r
en
t r
eg
u
lato
r
:
−
“
E
x
tr
em
ely
g
o
o
d
d
y
n
am
ics
”
−
I
n
s
tan
tan
eo
u
s
m
o
n
ito
r
in
g
o
f
l
o
ad
cu
r
r
en
t w
ith
h
i
g
h
(
g
o
o
d
)
a
cc
u
r
ac
y
−
Ov
er
cu
r
r
e
n
t p
r
o
tectio
n
−
Ov
er
-
cu
r
r
e
n
t d
e
v
iatio
n
−
E
r
r
o
r
c
o
m
p
e
n
s
atio
n
wh
en
c
h
a
n
g
in
g
l
o
ad
p
a
r
am
eter
s
−
E
r
r
o
r
c
o
m
p
e
n
s
atio
n
f
o
r
p
ar
am
eter
s
en
s
itiv
ity
−
Ma
in
tain
in
g
co
n
s
tan
t
v
o
ltag
e
i
n
th
e
DC
an
d
AC
lin
k
[
3
8
]
.
In
s
tu
d
y
[
3
6
]
,
a
c
o
n
tr
o
l
d
e
v
ice
with
a
d
elta
m
o
d
u
lato
r
at
z
er
o
h
y
s
ter
esis
an
d
a
m
o
d
if
ied
lin
ea
r
t
y
p
e
c
u
r
r
e
n
t
r
eg
u
lato
r
f
o
r
a
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
ar
e
c
o
n
s
id
er
ed
.
T
h
e
two
r
eg
u
lato
r
s
wer
e
co
m
p
ar
e
d
in
MA
T
L
AB
f
o
r
d
if
f
er
en
t
v
alu
es o
f
lo
a
d
p
a
r
am
eter
s
as sh
o
wn
in
T
ab
le
1
.
T
ab
le
1
.
C
o
m
p
a
r
is
o
n
o
f
cu
r
r
e
n
t r
eg
u
lato
r
s
N
a
me
o
f
t
h
e
p
a
r
a
m
e
t
e
r
s
M
o
d
i
f
i
e
d
l
i
n
e
a
r
t
y
p
e
c
u
r
r
e
n
t
r
e
g
u
l
a
t
o
r
D
e
l
t
a
M
o
d
u
l
a
t
o
r
D
y
n
a
mi
c
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
“
G
o
o
d
o
n
e
s
”
“
G
o
o
d
o
n
e
s
”
C
u
r
r
e
n
t
r
i
p
p
l
e
B
i
g
S
mal
l
e
r
Th
e
c
o
e
f
f
i
c
i
e
n
t
o
f
n
o
n
l
i
n
e
a
r
d
i
st
o
r
t
i
o
n
o
f
t
h
e
l
o
a
d
c
u
r
r
e
n
t
S
mal
l
e
r
B
i
g
Li
mi
t
i
n
g
t
h
e
sw
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
C
a
r
r
i
e
r
f
r
e
q
u
e
n
c
y
l
i
m
i
t
a
t
i
o
n
F
i
x
e
d
a
t
t
h
e
c
u
t
o
f
f
f
r
e
q
u
e
n
c
y
t
h
e
i
n
t
e
g
r
a
t
o
r
In
[
3
9
]
,
a
co
m
p
u
ter
m
o
d
el
o
f
an
AC
elec
tr
ic
d
r
iv
e
with
a
m
u
lti
-
lev
el
v
o
ltag
e
in
v
er
ter
with
f
r
eq
u
en
c
y
co
n
v
er
ter
s
d
ev
elo
p
ed
in
MA
T
L
AB
was
d
escr
ib
ed
(
MV
I
I
F).
T
h
e
s
tu
d
ied
elec
tr
ic
d
r
iv
e
ci
r
cu
it
was
a
1
3
-
lev
el
MV
I
I
F,
co
n
s
is
tin
g
o
f
1
8
s
y
m
m
etr
ical
in
v
er
ter
ce
lls
,
an
d
an
asy
n
ch
r
o
n
o
u
s
m
o
to
r
(
=
8
MW
,
=
10
kV
)
.
T
h
e
co
n
tr
o
l
s
y
s
tem
m
o
d
el
MA
T
L
AB
-
b
ased
in
clu
d
ed
2
s
u
b
s
y
s
tem
u
n
its
:
a
s
p
ee
d
co
n
tr
o
ller
u
n
it
an
d
an
in
v
er
ter
co
n
tr
o
l
s
y
s
tem
u
n
it.
T
h
e
s
p
ee
d
co
n
tr
o
ller
was
a
PI
co
n
tr
o
ller
.
T
h
e
r
esu
lt
o
f
th
e
wo
r
k
was
th
e
ef
f
icien
cy
ca
lcu
latio
n
m
eth
o
d
im
p
lem
en
ted
in
MA
T
L
A
B
,
wh
ich
tak
es
in
to
ac
co
u
n
t
d
y
n
am
ic
l
o
s
s
es
in
s
em
ico
n
d
u
cto
r
d
e
v
ices.
I
n
[
4
0
]
,
th
e
PI
co
n
tr
o
ller
is
d
escr
ib
ed
in
m
o
r
e
d
etail,
an
d
th
e
b
eh
av
io
r
o
f
th
e
d
r
i
v
e
s
y
s
tem
is
co
m
p
ar
ed
with
h
y
b
r
id
f
u
zz
y
PI,
co
n
v
en
tio
n
al
PI
an
d
f
u
zz
y
c
o
n
tr
o
ller
s
,
g
en
eti
c
alg
o
r
ith
m
b
ased
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
(
GA
-
PI
)
an
d
ad
a
p
tiv
e
n
etwo
r
k
-
b
ased
f
u
zz
y
in
f
e
r
en
ce
s
y
s
tem
(
ANFI
S
)
to
r
q
u
e
a
n
d
s
p
ee
d
co
n
tr
o
ller
s
.
Du
e
to
ch
an
g
es
in
en
g
in
e
p
ar
am
eter
s
wh
en
it
s
o
p
er
atin
g
m
o
d
e
is
d
is
tu
r
b
ed
,
th
e
PI
co
n
tr
o
ller
r
eq
u
ir
es
p
r
ec
is
e
ad
ju
s
tm
en
t
o
f
th
e
p
r
o
p
o
r
ti
o
n
al
g
ain
a
n
d
t
h
e
in
teg
r
al
tim
e
co
n
s
tan
t,
b
u
t
th
is
is
d
if
f
icu
lt
to
ac
h
iev
e,
th
is
p
r
o
b
lem
is
o
v
er
co
m
e
b
y
d
e
v
elo
p
in
g
r
e
g
u
lato
r
s
with
f
u
zz
y
lo
g
ic
[
4
1
]
,
b
u
t
th
e
p
er
f
o
r
m
a
n
ce
o
f
s
u
ch
a
r
eg
u
lato
r
s
u
r
p
ass
es
th
e
PI
co
n
tr
o
ller
o
n
ly
in
t
r
an
s
ien
t
co
n
d
itio
n
s
.
I
n
[
4
2
]
(
4
o
f
7
)
,
an
im
p
r
o
v
em
e
n
t
o
f
th
e
PI
co
n
tr
o
ller
b
ased
o
n
a
f
u
zz
y
co
n
t
r
o
l
m
o
d
el
was
p
r
o
p
o
s
ed
,
b
u
t
it
is
n
ec
ess
ar
y
t
o
m
an
u
ally
d
eter
m
in
e
th
e
lim
its
o
f
th
e
g
ain
co
ef
f
icien
ts
.
T
h
e
h
y
b
r
id
f
u
zz
y
-
PI
(
f
u
zz
y
PI)
co
n
tr
o
ller
wo
r
k
s
as
a
PI
c
o
n
tr
o
ller
in
s
tead
y
–
s
tate
m
o
d
es,
an
d
as
a
f
u
zz
y
co
n
tr
o
ller
o
n
ly
d
u
r
i
n
g
o
v
er
s
p
e
ed
o
r
u
n
d
er
-
s
p
ee
d
[
4
3
]
(
5
o
f
7
)
.
Ho
wev
er
,
b
o
th
r
eg
u
lato
r
s
h
a
v
e
d
is
ad
v
an
ta
g
es
th
at
ca
n
b
e
elim
in
ated
b
y
e
x
p
an
d
in
g
th
eir
f
u
n
ctio
n
s
.
T
o
e
n
s
u
r
e
in
d
ep
e
n
d
en
t
o
p
er
atio
n
,
t
h
e
PI
co
n
tr
o
ller
m
u
s
t
b
e
ab
le
to
ad
ap
t
to
ch
an
g
e
s
in
th
e
d
y
n
am
ic
ch
ar
ac
ter
is
tics
o
f
th
e
in
s
tallatio
n
.
T
h
e
g
en
etic
alg
o
r
ith
m
(
GA)
allo
ws y
o
u
to
s
ea
r
ch
f
o
r
o
p
tim
al
p
ar
am
eter
s
o
f
th
e
r
eg
u
lato
r
.
T
h
e
m
ain
d
is
ad
v
an
tag
e
o
f
f
u
zz
y
co
n
tr
o
l
is
th
e
lack
o
f
well
-
estab
lis
h
ed
d
esig
n
an
d
co
n
f
ig
u
r
atio
n
tech
n
iq
u
es
[
4
4
]
,
[
4
5
]
.
T
h
e
s
elec
tio
n
o
f
an
ap
p
r
o
p
r
iate
r
u
le
b
ase,
d
ep
en
d
in
g
o
n
th
e
s
itu
atio
n
,
ca
n
b
e
ac
h
iev
e
d
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
.
2
,
Ap
r
il
20
25
:
1
3
3
2
-
1
3
4
7
1334
b
y
u
s
in
g
th
e
ANFI
S
r
eg
u
lato
r
.
Acc
o
r
d
in
g
to
th
e
s
im
u
latio
n
r
esu
lts
,
th
e
AN
FIS
r
eg
u
lato
r
p
r
o
v
id
es
th
e
g
r
ea
test
d
y
n
am
ic
r
esp
o
n
s
e
an
d
g
e
n
er
ally
wo
r
k
s
b
etter
t
h
an
o
th
er
r
eg
u
lato
r
s
[
4
6
]
.
Stu
d
ies
u
s
in
g
tr
ad
itio
n
al
co
n
tr
o
l
m
eth
o
d
s
with
th
e
ad
d
itio
n
o
f
a
PI
r
eg
u
lato
r
wer
e
also
d
escr
ib
ed
in
[
4
7
]
.
Am
o
n
g
t
h
e
tr
ad
i
tio
n
al
m
eth
o
d
s
,
th
e
f
o
llo
win
g
wer
e
co
n
s
id
er
ed
:
a
cu
r
r
en
t
r
e
g
u
lato
r
with
h
y
s
ter
esis
an
d
a
lin
ea
r
ch
an
g
e
co
m
p
ar
is
o
n
cu
r
r
en
t
r
eg
u
lato
r
.
T
h
e
PI
co
n
tr
o
ller
m
ad
e
it
p
o
s
s
ib
le
to
im
p
r
o
v
e
ex
is
tin
g
m
eth
o
d
s
,
to
s
u
p
p
r
ess
h
ig
h
e
r
h
a
r
m
o
n
ics,
to
r
q
u
e
p
u
ls
atio
n
s
,
n
o
is
e,
an
d
elec
tr
o
m
ag
n
etic
in
ter
f
er
en
ce
.
T
h
e
m
o
d
if
ie
d
m
eth
o
d
s
allo
wed
th
e
s
tato
r
cu
r
r
en
t
f
o
r
m
s
to
b
ec
o
m
e
s
m
o
o
th
er
.
Acc
o
r
d
in
g
to
t
h
e
r
esear
ch
r
es
u
lts
,
a
cu
r
r
en
t
r
eg
u
lato
r
with
h
y
s
ter
esis
an
d
a
PI
cu
r
r
en
t
r
e
g
u
lato
r
tu
r
n
e
d
o
u
t
t
o
b
e
m
o
r
e
ef
f
icien
t
th
a
n
a
r
e
g
u
lato
r
b
u
ilt
b
ased
o
n
co
m
p
ar
in
g
th
e
lin
ea
r
c
h
an
g
e
o
f
cu
r
r
en
t w
ith
a
PI
r
e
g
u
lato
r
.
C
u
r
r
en
t
r
eg
u
lato
r
s
with
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
ar
e
co
n
s
id
er
ed
i
n
m
o
d
er
n
s
tu
d
ies
[
3
9
]
,
[
4
8
]
.
PW
M
-
co
n
tr
o
lled
in
v
er
ter
s
h
a
v
e
a
s
ig
n
if
ican
t
ad
v
an
ta
g
e
[
3
9
]
,
[
4
8
]
an
d
as
a
r
esu
lt,
ar
e
wid
ely
u
s
ed
in
AC
d
r
iv
es.
I
n
th
e
ar
ticle
[
3
9
]
,
th
e
p
er
f
o
r
m
an
ce
o
f
a
h
y
s
ter
esis
cu
r
r
en
t
r
eg
u
lato
r
an
d
a
PI
cu
r
r
en
t
r
eg
u
lato
r
u
s
in
g
PW
M
tech
n
o
lo
g
y
f
o
r
a
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
was
test
ed
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
cu
r
r
en
t
r
eg
u
lato
r
s
s
h
o
wed
th
at
b
o
th
r
eg
u
lato
r
s
ca
n
p
r
o
v
i
d
e
th
e
n
ec
ess
ar
y
r
eg
u
la
tio
n
o
f
th
e
o
u
tp
u
t c
u
r
r
e
n
t.
Fo
r
d
ig
ital c
o
n
tr
o
l,
th
e
m
o
s
t
co
m
m
o
n
PW
M
m
eth
o
d
is
th
e
s
in
u
s
o
id
al
PW
M
(
S
P
W
M)
m
eth
o
d
,
b
ec
au
s
e
it
h
as
lo
wer
p
o
wer
lo
s
s
es,
f
ewe
r
h
ar
m
o
n
ics,
an
d
ca
n
b
e
ea
s
ily
im
p
lem
en
ted
[
4
7
]
.
I
n
t
h
is
wo
r
k
,
a
s
im
p
le
m
o
d
el
was
p
r
esen
ted
with
th
e
im
p
lem
en
tatio
n
o
f
d
ig
ital
s
ig
n
al
p
r
o
ce
s
s
in
g
(
DSP
)
b
ased
o
n
th
e
T
MS3
2
0
F2
8
3
3
5
c
h
ip
f
o
r
a
th
r
ee
–
p
h
ase
v
o
ltag
e
s
o
u
r
ce
in
v
e
r
ter
(
VSI
)
u
s
in
g
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SP
W
M)
tech
n
o
lo
g
y
,
im
p
lem
en
te
d
u
s
in
g
MA
T
L
AB
R
2
0
1
9
a.
T
h
e
s
im
u
latio
n
r
esu
lt
was
te
s
ted
ex
p
er
im
en
tally
o
n
a
th
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
VSI
t
r
ain
in
g
m
o
d
el
an
d
s
h
o
wed
th
at
t
h
e
s
im
u
lat
io
n
was
p
er
f
o
r
m
e
d
f
air
l
y
ac
cu
r
ately
,
wh
ile
t
h
e
im
p
lem
en
tatio
n
o
f
th
is
d
ev
ice
is
s
im
p
le
T
h
e
f
r
eq
u
e
n
cy
co
n
v
er
ter
a
n
d
t
h
e
m
o
to
r
ar
e
n
o
t
alwa
y
s
clo
s
e
en
o
u
g
h
,
in
th
e
elec
tr
ic
d
r
iv
e
s
y
s
tem
o
f
v
ar
io
u
s
in
d
u
s
tr
ies,
th
e
d
is
tan
ce
b
etwe
en
th
em
ca
n
r
ea
ch
h
u
n
d
r
ed
s
o
r
th
o
u
s
an
d
s
o
f
m
ete
r
s
,
i.e
.
th
e
co
n
v
er
ter
m
u
s
t b
e
co
n
n
ec
ted
u
s
in
g
a
lo
n
g
ca
b
le
[
4
9
]
.
T
o
s
u
p
p
r
ess
th
e
ef
f
ec
t o
f
o
v
er
v
o
ltag
e
o
n
th
e
m
o
to
r
s
id
e,
th
e
ar
ticle
[
5
0
]
d
escr
ib
es
s
ev
er
al
m
eth
o
d
s
f
o
r
s
o
lv
in
g
th
e
p
r
o
b
lem
i
n
an
o
v
er
v
iew,
as
well
as
a
n
ew
m
eth
o
d
f
o
r
s
u
p
p
r
ess
in
g
r
eso
n
an
t
o
v
er
v
o
lt
ag
e
o
f
a
d
r
iv
e
s
y
s
tem
with
a
lo
n
g
ca
b
le,
co
n
s
id
er
in
g
th
e
v
ar
iab
le
f
r
eq
u
en
c
y
o
f
cu
r
r
en
t
an
d
v
o
ltag
e.
B
ased
o
n
th
e
m
ath
em
atica
l
m
o
d
el,
a
n
im
p
r
o
v
e
d
co
n
s
tan
t
ac
tiv
e
p
o
wer
co
n
tr
o
ller
was
d
ev
elo
p
e
d
.
Acc
o
r
d
in
g
to
th
e
r
esu
lts
o
f
th
e
s
tu
d
y
,
th
e
al
g
o
r
ith
m
h
as
h
ig
h
co
n
tr
o
l
ef
f
icien
cy
an
d
g
o
o
d
r
eliab
ilit
y
in
co
n
tr
o
llin
g
th
e
p
h
en
o
m
en
o
n
o
f
r
eso
n
a
n
t
o
v
e
r
v
o
ltag
e
an
d
ca
n
ef
f
ec
tiv
ely
en
s
u
r
e
th
e
s
af
ety
o
f
o
p
er
atio
n
o
f
a
d
r
iv
e
with
a
f
r
e
q
u
en
cy
co
n
v
er
ter
an
d
a
lo
n
g
c
ab
le.
2.
M
E
T
H
O
D
T
h
e
s
ch
em
es
o
f
DC
-
to
-
AC
co
n
v
er
ter
s
th
at
h
a
v
e
f
o
u
n
d
th
e
g
r
ea
test
ap
p
licatio
n
b
y
f
o
r
m
in
g
a
s
in
u
s
o
id
al
th
r
ee
-
p
h
ase
v
o
ltag
e
wh
en
s
o
lv
in
g
p
r
o
b
lem
s
o
f
r
eg
u
latin
g
th
e
ef
f
ec
tiv
e
v
o
lta
g
e
v
alu
e
at
a
f
ix
ed
f
r
eq
u
e
n
cy
m
o
s
t
o
f
te
n
tu
r
n
o
u
t
to
b
e
d
if
f
icu
lt
to
im
p
lem
e
n
t
an
d
p
r
ac
tically
ca
n
n
o
t
m
ain
ta
in
o
p
e
r
ab
ilit
y
with
s
in
g
le
f
ailu
r
es.
So
lv
in
g
th
e
p
r
o
b
lem
o
f
v
o
ltag
e
s
y
m
m
et
r
y
b
y
tr
ad
itio
n
al
m
eth
o
d
s
d
r
am
atic
ally
co
m
p
licates
th
e
cir
cu
it
an
d
alg
o
r
ith
m
s
o
f
th
e
co
n
v
er
ter
,
t
h
er
ef
o
r
e
th
ey
n
e
ed
to
b
e
im
p
r
o
v
ed
to
g
eth
er
with
alg
o
r
ith
m
s
f
o
r
g
en
er
atin
g
alter
n
atin
g
v
o
ltag
e.
W
ith
an
in
c
r
ea
s
e
in
th
e
n
u
m
b
er
o
f
p
h
ases
,
th
e
n
ec
ess
ar
y
e
n
er
g
y
i
n
d
icato
r
s
ar
e
ac
h
iev
ed
b
y
u
s
in
g
a
g
en
er
at
o
r
with
a
clo
s
ed
win
d
in
g
,
w
h
ile
i
t
is
n
ec
ess
ar
y
to
co
n
s
id
er
t
h
at
in
ca
s
es
o
f
d
am
a
g
e
to
o
n
e
o
f
th
e
win
d
in
g
s
o
r
th
e
r
ec
tifie
r
k
ey
,
its
o
p
er
atin
g
m
o
d
e
is
n
o
t
d
is
r
u
p
ted
.
T
h
is
is
ex
p
lain
ed
b
y
th
e
f
ac
t
th
at
d
u
r
in
g
t
h
e
s
witch
in
g
p
r
o
ce
s
s
th
e
co
m
b
in
atio
n
an
d
n
u
m
b
er
o
f
p
h
ases
co
n
n
ec
ted
t
o
th
e
p
o
s
itiv
e
an
d
n
eg
ativ
e
b
u
s
es
o
f
th
e
p
o
wer
s
o
u
r
ce
ch
an
g
es.
I
n
th
is
r
eg
ar
d
,
in
th
e
ca
s
e
o
f
an
asy
m
m
etr
ic
lo
ad
,
th
ese
p
ar
am
eter
s
ar
e
d
if
f
e
r
en
t
at
ea
ch
cy
cle
an
d
,
with
s
ix
-
c
y
cle
s
witch
in
g
o
f
th
e
in
v
e
r
ter
,
a
r
e
r
ep
ea
ted
ev
e
r
y
f
iv
e
cy
cles.
2
.
1
.
Sim
ula
t
i
o
n o
f
a
n inv
er
t
er
a
s
a
v
o
lt
a
g
e
s
o
urce
us
ing
dis
cr
et
e
s
wit
ch
ing
wit
h a
PI
co
ntr
o
ller
L
et's
co
n
s
id
er
th
e
s
im
u
latio
n
o
f
v
o
ltag
e
co
n
v
er
ter
s
with
d
is
cr
ete
s
witch
in
g
b
ased
o
n
a
t
h
r
ee
-
p
h
ase
in
v
er
ter
f
ee
d
in
g
a
s
y
m
m
etr
ical
an
d
u
n
b
alan
ce
d
lo
a
d
.
T
h
e
in
v
er
ter
o
f
th
e
th
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
will
b
e
m
o
d
eled
in
th
e
MA
T
L
AB
/Si
m
u
lin
k
en
v
ir
o
n
m
e
n
t.
Fig
u
r
e
1
s
h
o
ws
a
m
o
d
el
o
f
a
s
y
m
m
etr
y
d
ev
ice
(
SD)
b
ased
o
n
a
PI
c
o
n
tr
o
ller
im
p
lem
en
te
d
in
MA
T
L
AB
/Si
m
u
lin
k
,
f
o
r
m
in
g
a
s
et
v
alu
e
o
f
t
h
e
v
o
lta
g
e
at
a
co
m
m
o
n
p
o
in
t
(
C
P),
an
d
a
co
n
tr
o
l u
n
it f
o
r
ad
d
itio
n
al
tr
an
s
is
to
r
s
(
SD)
is
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
d
is
cr
ete
s
ig
n
al
co
n
tr
o
llin
g
th
e
o
p
er
atio
n
o
f
th
e
in
v
e
r
ter
is
im
p
lem
en
ted
b
y
th
e
co
n
tr
o
l
u
n
it
(
b
lo
ck
p
ar
am
ete
r
s
:
p
u
ls
e
g
e
n
er
ato
r
)
i
n
th
e
MA
T
L
AB
/Si
m
u
lin
k
e
n
v
ir
o
n
m
en
t
an
d
co
m
es
to
ea
c
h
o
f
th
e
s
ix
tr
an
s
is
to
r
s
.
T
o
o
b
tain
a
th
r
ee
-
p
h
ase
o
u
tp
u
t
v
o
ltag
e
,
th
e
s
ix
s
witch
es
m
u
s
t
b
e
co
n
tr
o
lle
d
s
o
t
h
at
th
e
o
u
t
p
u
t
wav
ef
o
r
m
is
clo
s
e
to
s
in
u
s
o
id
al.
T
o
clar
if
y
th
is
,
a
s
tar
-
c
o
n
n
ec
ted
r
esis
tiv
e
lo
ad
is
co
n
n
ec
ted
to
th
e
i
n
v
er
ter
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
co
r
r
ec
t
n
ess
o
f
th
e
m
o
d
el
u
n
d
er
s
y
m
m
etr
ical
lo
ad
with
t
h
e
wav
ef
o
r
m
s
o
f
th
e
p
h
ase
v
o
l
tag
e
o
f
th
e
in
v
er
ter
is
s
h
o
wn
in
Fig
u
r
es
2
to
4
.
Fo
r
th
e
1
2
0
°
m
o
d
e
o
f
th
e
th
r
ee
-
p
h
ase
v
o
ltag
e
in
v
er
ter
,
ea
ch
o
f
t
h
e
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I
n
t J E
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p
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d
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erter
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Ta
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1335
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em
ico
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u
cto
r
s
witch
es
co
n
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u
cts
1
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th
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1
8
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o
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e,
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e
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e
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ter
in
1
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o
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ir
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s
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o
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m
o
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ter
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ct
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o
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ter
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1
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°
d
eg
r
ee
s
.
I
t
h
as
twelv
e
s
tep
s
,
ea
ch
o
f
wh
ich
h
as
a
d
u
r
atio
n
o
f
3
0
°
d
eg
r
ee
s
to
c
o
m
p
lete
o
n
e
cy
cle
o
f
th
e
o
u
tp
u
t
AC
v
o
ltag
e.
T
h
r
ee
tr
a
n
s
is
to
r
s
co
n
d
u
ct
in
o
n
e
in
ter
v
al,
as
in
th
e
1
8
0
°
m
o
d
e,
wh
ile
o
n
ly
two
tr
an
s
is
to
r
s
co
n
d
u
ct
in
th
e
n
ex
t
in
ter
v
al,
as
in
th
e
1
2
0
°
m
o
d
e.
T
h
e
s
tab
ilit
y
o
f
m
ain
tain
in
g
t
h
e
o
u
tp
u
t
p
a
r
am
eter
s
o
f
a
th
r
ee
-
p
h
ase
v
o
ltag
e
in
v
er
ter
u
n
d
er
an
u
n
b
ala
n
ce
d
lo
ad
is
ca
r
r
ied
o
u
t
u
s
in
g
a
b
lo
c
k
f
o
r
m
in
g
a
s
et
v
o
ltag
e
v
alu
e
(
C
P)
in
Fig
u
r
e
5
.
I
n
th
is
u
n
it,
an
a
d
d
itio
n
al
tr
an
s
is
to
r
is
co
n
tr
o
lled
,
wh
ich
g
en
er
ates
a
r
ef
er
en
ce
s
ig
n
al
o
f
a
s
et
v
al
u
e
o
f
th
e
c
o
m
m
o
n
p
o
i
n
t v
o
ltag
e
Fig
u
r
e
6
.
T
o
ac
h
iev
e
a
r
ef
er
en
c
e
s
ig
n
a
l,
th
e
v
o
ltag
e
at
a
n
u
n
b
alan
c
ed
lo
ad
at
th
e
o
u
tp
u
t
o
f
a
t
h
r
ee
-
p
h
ase
in
v
er
ter
an
d
th
e
v
o
ltag
e
at
a
co
m
m
o
n
p
o
in
t
r
elativ
e
to
th
e
m
in
u
s
b
u
s
ch
an
g
es
its
v
alu
e
an
d
wh
en
co
m
p
ar
in
g
th
e
r
ef
er
en
ce
s
ig
n
al
with
th
e
s
ig
n
al
at
a
co
m
m
o
n
p
o
in
t
r
elativ
e
to
th
e
m
in
u
s
b
u
s
,
th
e
r
e
g
u
lato
r
ac
ts
o
n
t
h
e
co
n
tr
o
l
u
n
it
o
f
ad
d
itio
n
al
t
r
an
s
is
to
r
s
in
Fig
u
r
e
7
(
i
n
Fig
u
r
e
1
,
th
e
b
lo
ck
o
f
th
e
s
y
m
m
etr
y
d
e
v
ice
is
h
ig
h
lig
h
ted
in
r
ed
)
.
Ho
wev
er
,
t
h
e
SD
b
ased
o
n
t
h
e
PI
co
n
t
r
o
ller
o
p
er
at
es
u
n
d
er
ac
tiv
e
l
o
ad
an
d
d
e
p
e
n
d
s
o
n
th
e
v
o
ltag
e
an
d
cu
r
r
e
n
t
in
th
e
ze
r
o
wir
e.
W
h
en
an
in
d
u
ctiv
e
lo
a
d
ap
p
ea
r
s
,
th
e
co
n
tr
o
l
d
e
v
ice
is
to
o
late.
I
n
th
is
ca
s
e,
it
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n
ec
ess
ar
y
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u
s
e
a
d
e
v
ice
with
d
is
cr
ete
s
witch
in
g
an
d
a
P
-
r
e
g
u
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r
as sh
o
wn
i
n
Fig
u
r
e
8
.
Fig
u
r
e
1
.
A
m
o
d
el
o
f
th
e
SD sy
m
m
etr
y
d
ev
ice
b
ased
o
n
a
PI
co
n
tr
o
ller
i
n
MA
T
L
AB
/Si
m
u
lin
k
Fig
u
r
e
2
.
T
h
e
wav
ef
o
r
m
o
f
th
e
p
h
ase
v
o
ltag
e
at
1
2
0
-
d
eg
r
ee
s
witch
in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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u
r
e
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.
T
h
e
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ef
o
r
m
o
f
th
e
p
h
ase
v
o
ltag
e
at
150
-
d
eg
r
ee
s
witch
in
g
Fig
u
r
e
4
.
T
h
e
wav
ef
o
r
m
o
f
th
e
p
h
ase
v
o
ltag
e
at
180
-
d
eg
r
ee
s
witch
in
g
Fig
u
r
e
5
.
A
c
o
m
m
o
n
p
o
i
n
t v
o
l
tag
e
s
etp
o
in
t sh
ap
er
Fig
u
r
e
6
.
T
h
e
r
ef
e
r
en
ce
v
o
ltag
e
s
ig
n
al
at
th
e
co
m
m
o
n
p
o
in
t
Fig
u
r
e
7
.
A
s
y
m
m
et
r
ical
d
ev
ic
e
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ased
o
n
a
PI
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
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n
g
I
SS
N:
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8
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Mo
d
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o
f semico
n
d
u
ct
o
r
co
n
v
erter
s
fo
r
th
e
s
imu
la
tio
n
o
f a
n
a
s
ymm
etri
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lo
a
d
s
in
…
(
S
a
id
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n
Ta
va
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1337
Fig
u
r
e
8
.
A
m
o
d
el
o
f
a
s
y
m
m
e
tr
y
d
ev
ice
(
SD)
b
ased
o
n
a
P
-
r
eg
u
lato
r
in
MA
T
L
AB
/Si
m
u
lin
k
2
.
2
.
I
m
ple
m
ent
a
t
io
n o
f
a
v
o
l
t
a
g
e
co
nv
er
t
er
ba
s
ed
o
n a
t
h
re
e
-
ph
a
s
e
inv
er
t
er
wit
h dis
c
re
t
e
k
ey
s
wit
ching
T
h
e
u
s
e
o
f
d
is
cr
ete
s
witch
in
g
o
f
in
v
e
r
ter
p
o
we
r
k
ey
s
f
o
r
c
o
n
v
er
tin
g
d
ir
ec
t
v
o
ltag
e
in
to
alter
n
atin
g
v
o
ltag
e,
ev
e
n
in
th
e
s
im
p
lest
ca
s
e
with
1
8
0
-
d
e
g
r
ee
s
ix
-
cy
cl
e
s
witch
in
g
,
allo
ws
o
b
tain
in
g
a
p
h
ase
v
o
ltag
e
at
th
e
in
v
er
ter
o
u
tp
u
t w
ith
a
co
n
ten
t o
f
h
ig
h
er
h
ar
m
o
n
ics o
f
n
o
m
o
r
e
th
an
4
.
5
% o
f
th
e
ef
f
ec
tiv
e
v
alu
e
o
f
th
e
to
tal
v
o
ltag
e.
I
n
th
is
ca
s
e,
s
ix
in
s
u
lated
g
ate
b
ip
o
lar
tr
an
s
is
to
r
(
I
GB
T
)
tr
an
s
is
to
r
s
ar
e
r
eq
u
ir
ed
,
as
s
h
o
wn
in
Fig
u
r
e
1
.
W
ith
an
ac
tiv
e
-
in
d
u
ctiv
e
s
y
m
m
etr
ical
p
h
ase
lo
ad
in
th
e
ca
s
e
o
f
d
is
cr
ete
s
witch
in
g
,
th
e
s
h
ap
e
o
f
th
e
o
u
tp
u
t
v
o
ltag
es
r
em
ain
s
th
e
s
am
e
as
with
a
p
u
r
ely
ac
tiv
e
lo
ad
.
I
n
th
e
ca
s
e
o
f
a
n
asy
m
m
etr
y
o
f
p
h
ase
lo
ad
s
,
th
e
s
h
ap
e
o
f
th
e
p
h
ase
v
o
ltag
es
is
d
is
to
r
ted
[
1
0
]
.
T
h
er
ef
o
r
e
,
th
e
v
o
ltag
e
o
n
t
h
e
p
a
r
allel
r
esis
to
r
s
is
eq
u
al
to
Us/
3
,
an
d
o
n
th
e
s
er
ies
r
esi
s
t
o
r
-
2
/3
Us
[
1
0
]
.
I
t
is
ass
u
m
e
d
th
at
a
p
u
r
ely
ac
tiv
e
lo
ad
is
co
n
n
ec
ted
to
th
e
co
n
v
er
ter
:
=
=
=
1
0
Oh
m
[
1
0
]
.
T
h
e
d
is
cr
ete
v
alu
es
g
e
n
er
ated
b
y
th
e
in
v
er
ter
im
p
o
s
e
ad
d
itio
n
al
r
estrictio
n
s
o
n
s
o
m
e
ap
p
licatio
n
s
.
Fo
r
ex
am
p
le,
s
en
s
itiv
e
lo
ad
s
ca
n
n
o
t
b
e
co
n
n
ec
ted
d
ir
ec
tly
to
th
e
in
v
er
te
r
o
u
t
p
u
t.
T
h
e
q
u
ality
o
f
th
e
o
u
tp
u
t
s
ig
n
als
m
u
s
t
b
e
im
p
r
o
v
e
d
wit
h
h
ar
m
o
n
ic
f
ilter
s
to
m
ee
t
th
e
r
eq
u
ir
ed
q
u
ality
s
tan
d
ar
d
s
.
I
n
ad
d
itio
n
,
ca
p
ac
itiv
e
lo
ad
s
will in
cr
ea
s
e
th
e
in
f
lu
en
ce
o
f
th
e
d
is
cr
ete
o
u
tp
u
t v
o
lta
g
e
b
y
ad
d
in
g
m
o
r
e
cu
r
r
en
t p
ea
k
s
[
1
0
]
.
T
o
o
b
tain
a
th
r
ee
-
p
h
ase
o
u
tp
u
t
v
o
ltag
e,
th
e
s
ix
s
witch
es
m
u
s
t
b
e
co
n
tr
o
lled
in
s
u
ch
a
wa
y
th
at
th
e
o
u
tp
u
t
wav
e
f
o
r
m
is
clo
s
e
to
s
in
u
s
o
id
al.
T
o
clar
if
y
th
is
,
a
r
esis
t
iv
e
lo
ad
co
n
n
ec
t
ed
in
a
s
tar
is
co
n
n
ec
ted
to
th
e
in
v
er
ter
s
h
o
wn
in
Fig
u
r
e
4
.
I
n
ca
s
es
wh
er
e
t
h
er
e
ar
e
n
o
s
tr
ict
r
eq
u
ir
e
m
en
ts
f
o
r
th
e
c
o
n
ten
t
o
f
h
i
g
h
er
h
ar
m
o
n
ics
in
th
e
s
u
p
p
ly
v
o
ltag
e,
a
s
im
p
le
co
n
v
er
ter
with
d
is
cr
ete
co
m
m
u
tatio
n
ca
n
b
e
u
s
ed
:
i)
E
ac
h
in
v
er
ter
s
witch
is
o
p
en
at
an
in
ter
v
al
o
f
1
2
0
°;
ii)
E
ac
h
in
v
e
r
ter
s
witch
is
o
p
e
n
at
a
n
in
ter
v
al
o
f
1
5
0
°;
an
d
iii)
E
ac
h
in
v
er
ter
k
e
y
is
o
p
en
at
180
° in
ter
v
al.
Fo
r
th
e
1
2
0
°
m
o
d
e
o
f
th
e
th
r
e
e
-
p
h
ase
v
o
ltag
e
in
v
er
ter
,
ea
ch
o
f
th
e
s
em
ico
n
d
u
cto
r
s
witch
es
co
n
d
u
cts
f
o
r
1
2
0
°
o
f
th
e
c
y
cle.
As
in
th
e
1
8
0
°
m
o
d
e,
th
e
in
v
e
r
ter
i
n
t
h
e
1
2
0
°
m
o
d
e
also
r
eq
u
ir
es
s
ix
s
tep
s
o
f
6
0
°
ea
ch
to
co
m
p
lete
o
n
e
cy
cle
o
f
th
e
AC
o
u
tp
u
t
v
o
ltag
e.
T
ab
le
2
s
h
o
ws
th
e
co
n
d
u
ctin
g
tr
an
s
is
to
r
s
d
u
r
in
g
ea
c
h
in
d
iv
id
u
al
in
ter
v
al.
I
n
a
th
r
ee
-
p
h
ase
in
v
er
ter
,
ea
c
h
s
witch
co
n
d
u
cts
1
8
0
°
o
f
th
e
cy
cle,
a
p
ai
r
o
f
s
em
ico
n
d
u
c
to
r
k
e
y
s
in
ea
ch
ar
m
,
i.e
.
VT
1
,
VT
4
;
VT
3
,
VT
6
an
d
VT
5
,
VT
2
ar
e
s
witch
ed
o
n
with
a
tim
e
in
ter
v
al
o
f
1
8
0
°.
T
h
is
is
also
p
r
o
v
e
n
b
y
th
e
lo
wer
g
r
o
u
p
o
f
s
witch
es.
T
ab
le
3
s
h
o
ws
th
e
co
n
d
u
ctin
g
tr
a
n
s
is
to
r
s
d
u
r
i
n
g
ea
ch
in
d
iv
id
u
al
in
ter
v
al
[
1
0
]
.
I
n
th
e
1
5
0
°
s
witch
in
g
m
o
d
e,
ea
ch
in
v
er
ter
s
witch
co
n
d
u
cts
o
v
er
an
in
ter
v
al
o
f
1
5
0
°
d
eg
r
ee
s
.
I
t
h
as
twelv
e
s
tep
s
,
ea
ch
o
f
wh
ic
h
h
as
a
d
u
r
atio
n
o
f
3
0
°
d
e
g
r
ee
s
to
co
m
p
lete
o
n
e
c
y
cle
o
f
t
h
e
o
u
tp
u
t
AC
v
o
ltag
e
.
T
h
r
ee
tr
an
s
is
to
r
s
co
n
d
u
ct
i
n
o
n
e
in
ter
v
al,
as
in
th
e
1
8
0
°
m
o
d
e,
wh
ile
o
n
ly
two
tr
an
s
is
to
r
s
co
n
d
u
ct
in
th
e
n
ex
t
in
ter
v
al,
as in
th
e
1
2
0
° m
o
d
e.
T
ab
le
4
s
h
o
ws th
e
co
n
d
u
ctin
g
tr
an
s
is
to
r
s
d
u
r
in
g
ea
c
h
in
d
iv
i
d
u
al
in
ter
v
al
[
1
0
]
.
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
.
2
,
Ap
r
il
20
25
:
1
3
3
2
-
1
3
4
7
1338
T
ab
le
2
.
Op
e
r
atio
n
in
1
2
0
° c
o
m
m
u
tatio
n
m
o
d
e
N
o
.
I
n
t
e
r
v
a
l
K
e
y
(
o
n
)
P
o
l
a
r
i
t
y
(A)
(
B
)
(
C
)
1
0
-
60
V
T1
,
V
T6
+
0
-
2
60
-
1
2
0
V
T3
,
V
T6
0
+
-
3
1
2
0
-
180
V
T3
,
V
T2
-
+
0
4
1
8
0
,
2
4
0
V
T5
,
V
T2
-
0
+
5
2
4
0
-
300
V
T5
,
V
T4
0
-
+
6
3
0
0
-
360
V
T1
,
V
T6
+
-
0
T
ab
le
3
.
Op
e
r
atio
n
in
1
8
0
° c
o
m
m
u
tatio
n
m
o
d
e
N
o
.
I
n
t
e
r
v
a
l
K
e
y
(
o
n
)
P
o
l
a
r
i
t
y
(A)
(
B
)
(
C
)
1
0
-
60
V
T1
,
V
T5
,
V
T
6
+
-
+
2
60
-
1
2
0
V
T2
,
V
T6
,
V
T
1
+
-
-
3
1
2
0
-
180
V
T3
,
V
T1
,
V
T
2
+
+
-
4
1
8
0
,
2
4
0
V
T4
,
V
T2
,
V
T
3
-
+
-
5
2
4
0
-
300
V
T3
,
V
T4
,
V
T
5
-
+
+
6
3
0
0
-
360
V
T4
,
V
T5
,
V
T
6
-
-
+
T
ab
le
4
.
Op
e
r
atio
n
in
1
5
0
° c
o
m
m
u
tatio
n
m
o
d
e
N
o
.
I
n
t
e
r
v
a
l
K
e
y
(
o
n
)
P
o
l
a
r
i
t
y
(A)
(
B
)
(
C
)
1
0
-
60
V
T1
,
V
T2
,
V
T
6
+
-
-
2
60
-
1
2
0
V
T1
,
V
T2
+
0
-
3
1
2
0
-
180
V
T1
,
V
T2
,
V
T
3
+
+
-
4
1
8
0
-
240
V
T2
,
V
T3
0
+
-
5
2
4
0
-
300
V
T2
,
V
T3
,
V
T
4
-
+
-
6
3
0
0
-
360
V
T3
,
V
T4
-
+
0
7
3
6
0
-
420
V
T3
,
V
T4
,
V
T
5
-
+
+
8
4
2
0
-
480
V
T4
,
V
T5
-
0
+
9
4
8
0
-
540
V
T4
,
V
T5
,
V
T
6
-
-
+
10
5
4
0
-
600
V
T5
,
V
T6
0
-
+
11
6
0
0
-
660
V
T1
,
V
T5
,
V
T
6
+
-
+
12
6
6
0
-
720
V
T1
,
V
T6
+
-
0
2
.
3
.
H
a
rmo
nic a
na
ly
s
is
o
f
t
h
re
e
-
ph
a
s
e
v
o
lt
a
g
e
wit
h dis
cr
et
e
co
nv
er
s
io
n
Fo
r
h
ig
h
ef
f
icie
n
cy
o
f
DC
-
to
-
AC
co
n
v
er
s
io
n
an
d
p
ea
k
p
o
w
er
tr
ac
k
in
g
,
th
e
i
n
v
er
ter
m
u
s
t
h
av
e
lo
w
h
ar
m
o
n
ic
d
is
to
r
tio
n
alo
n
g
wit
h
lo
w
elec
tr
o
m
ag
n
etic
in
ter
f
e
r
en
ce
an
d
h
ig
h
-
p
o
wer
f
ac
to
r
.
I
n
o
r
d
e
r
to
s
u
p
p
r
ess
h
ar
m
o
n
ics an
d
co
n
tr
o
l u
n
b
ala
n
ce
d
lo
ad
s
,
th
e
r
e
ar
e
s
ev
er
al
s
witch
in
g
m
eth
o
d
s
f
o
r
in
v
er
ter
co
n
tr
o
l
[
1
]
–
[
9
]
.
T
h
e
d
is
cr
ete
co
n
tr
o
l
m
eth
o
d
o
f
p
o
wer
k
ey
s
is
o
n
e
o
f
th
em
[1
0
]
–
[
3
0]
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
a
d
is
cr
ete
s
witch
in
g
cir
cu
it
ca
n
b
e
esti
m
ated
b
ased
o
n
th
e
an
aly
s
is
o
f
th
e
d
is
to
r
tio
n
lev
el
at
th
e
in
v
er
ter
o
u
t
p
u
t,
th
e
s
p
ec
tr
u
m
o
f
h
ar
m
o
n
ics
c
o
n
tain
ed
in
t
h
is
v
o
ltag
e
an
d
th
e
co
m
p
le
x
ity
o
f
t
h
e
im
p
lem
e
n
tatio
n
.
Acc
o
r
d
in
g
to
[
1
1
]
–
[
1
5
]
,
b
ased
o
n
th
e
o
b
tain
ed
tim
in
g
d
iag
r
a
m
s
,
we
ca
lcu
late
th
e
ef
f
ec
tiv
e
v
alu
es o
f
th
e
p
h
ase
v
o
ltag
es
[
1
6
]
–
[
2
2
]
.
T
h
is
d
iag
r
am
s
h
o
ws
th
at
th
e
o
u
tp
u
t
v
o
ltag
e
b
etwe
en
th
e
lin
e
s
is
+
Us,
0
o
r
–
Us.
T
h
e
in
s
t
an
tan
eo
u
s
in
ter
f
ac
ial
v
o
ltag
e
ca
n
b
e
e
x
p
r
ess
ed
in
a
Fo
u
r
ier
s
er
ies,
as d
escr
ib
ed
in
:
=
∑
4
∞
=
1
,
3
,
5
∙
(
6
)
∙
(
(
+
6
)
)
(
1
)
T
h
en
an
d
s
h
if
tin
g
o
n
1
2
0
º
a
n
d
2
4
0
º
we
g
et,
=
∑
4
∞
=
1
,
3
,
5
∙
(
6
)
∙
(
(
−
2
)
)
,
(
2
)
=
∑
4
∞
=
1
,
3
,
5
∙
(
6
)
∙
(
−
7
6
)
.
(
3
)
I
t
is
also
s
h
o
wn
th
at
in
(
1
)
,
(
2
)
,
an
d
(
3
)
th
e
h
ar
m
o
n
ics
o
f
th
e
tr
ip
lets
ar
e
ze
r
o
i
n
lin
ea
r
v
o
ltag
e.
T
h
e
r
ated
m
ax
im
u
m
s
in
u
s
o
id
al
(
R
MS)
v
o
ltag
e
b
etwe
en
th
e
lin
es
is
ex
p
r
ess
ed
in
(
4
)
,
wh
er
ea
s
th
e
R
MS
v
o
ltag
e
b
etwe
en
th
e
lin
es a
n
d
th
e
n
eu
tr
al
is
in
(
5
)
:
=
√
[
2
2
∫
2
2
0
]
=
√
2
3
,
(
4
)
.
=
√
3
.
(
5
)
T
h
e
u
s
e
o
f
d
is
cr
ete
s
witch
in
g
o
f
in
v
er
ter
p
o
we
r
k
ey
s
f
o
r
c
o
n
v
er
tin
g
d
ir
ec
t
v
o
ltag
e
in
to
alter
n
atin
g
v
o
ltag
e,
ev
en
in
t
h
e
s
im
p
lest
ca
s
e
with
1
8
0
°
s
ix
-
cy
cle
s
witch
in
g
,
a
llo
ws
o
b
tain
in
g
a
p
h
ase
v
o
ltag
e
at
th
e
i
n
v
er
ter
o
u
tp
u
t w
ith
a
c
o
n
ten
t
o
f
h
ig
h
e
r
h
ar
m
o
n
ics o
f
n
o
m
o
r
e
th
an
4
.
5
% o
f
th
e
e
f
f
ec
tiv
e
v
al
u
e
o
f
t
h
e
to
tal
v
o
ltag
e.
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
Mo
d
el
o
f semico
n
d
u
ct
o
r
co
n
v
erter
s
fo
r
th
e
s
imu
la
tio
n
o
f a
n
a
s
ymm
etri
c
lo
a
d
s
in
…
(
S
a
id
j
o
n
Ta
va
r
o
v
)
1339
2
.
4
.
M
a
t
hema
t
ica
l descript
io
n o
f
v
o
lt
a
g
e
c
o
nv
er
s
io
n und
er
a
ct
iv
e
-
ind
uct
iv
e
lo
a
d
No
w
let
u
s
est
im
ate
th
e
in
f
lu
en
ce
o
f
in
d
u
cta
n
ce
o
n
th
e
v
o
ltag
e
d
iag
r
am
o
n
th
e
n
eu
tr
al
wi
r
e
with
an
ac
tiv
e
-
in
d
u
ctiv
e
lo
ad
.
L
et
u
s
co
n
s
id
er
th
e
ca
s
e
o
f
1
8
0
-
d
eg
r
ee
s
witch
in
g
as
th
e
m
o
s
t
ea
s
il
y
im
p
lem
e
n
ted
a
n
d
q
u
ite
ef
f
ec
tiv
e
f
r
o
m
th
e
p
o
in
t
o
f
v
iew
o
f
th
e
co
n
ten
t o
f
h
ig
h
er
h
ar
m
o
n
ics in
th
e
p
h
ase
v
o
lt
ag
es.
As wa
s
s
h
o
wn
[
1
1
]
,
in
th
is
ca
s
e
f
o
r
th
e
s
y
m
m
etr
ical
m
o
d
e
an
d
ac
tiv
e
lo
ad
o
f
th
e
co
n
v
er
ter
we
h
av
e
th
e
f
o
r
m
o
f
p
h
ase
v
o
ltag
es
(
,
,
)
,
an
d
th
e
ze
r
o
p
o
in
t
v
o
ltag
e
r
elativ
e
to
th
e
m
in
u
s
b
u
s
o
f
th
e
p
o
wer
s
o
u
r
ce
(
0
)
,
co
r
r
esp
o
n
d
in
g
t
o
Fig
u
r
e
1
.
I
n
Fig
u
r
e
9
,
th
e
an
g
u
lar
in
ter
v
al
i
s
p
lo
tted
alo
n
g
th
e
ab
s
ciss
a
ax
is
,
an
d
th
e
r
elativ
e
v
o
ltag
e
v
alu
e
as
a
f
r
ac
tio
n
o
f
th
e
DC
s
o
u
r
ce
v
o
ltag
e
is
p
lo
tt
ed
alo
n
g
t
h
e
o
r
d
in
ate
ax
is
.
Ob
v
io
u
s
ly
,
th
e
task
o
f
s
y
m
m
etr
izatio
n
is
to
en
s
u
r
e
th
at
th
e
v
o
ltag
e
wav
ef
o
r
m
s
h
o
w
n
in
Fig
u
r
e
9
is
p
r
eser
v
ed
o
r
b
r
o
u
g
h
t
clo
s
er
to
it
with
an
y
d
if
f
er
en
ce
a
n
d
an
y
ty
p
e
o
f
p
h
ase
lo
ad
r
esis
tan
ce
.
Fig
u
r
e
9
.
C
o
n
n
ec
tio
n
d
iag
r
am
o
f
th
e
p
h
ase
lo
ad
s
o
f
t
h
e
co
n
v
er
ter
to
a
DC
s
o
u
r
ce
I
n
th
e
ca
s
e
o
f
a
s
y
m
m
et
r
ical
ac
tiv
e
–
in
d
u
ctiv
e
lo
a
d
(
1
=
2
=
3
=
,
1
=
2
=
3
=
)
,
o
n
o
n
e
s
witch
in
g
cy
cle,
th
e
cir
cu
it
f
o
r
co
n
n
ec
tin
g
th
e
win
d
i
n
g
th
r
o
u
g
h
th
e
in
v
e
r
ter
s
witch
es
t
o
a
DC
s
o
u
r
ce
.
T
h
e
d
o
tted
a
r
r
o
w
with
th
e
d
esig
n
a
tio
n
s
h
o
ws
th
e
d
ir
ec
tio
n
o
f
th
e
v
o
ltag
e
v
ec
to
r
at
th
e
co
n
s
id
er
ed
,
p
r
ev
io
u
s
,
a
n
d
s
u
b
s
eq
u
en
t
s
witch
in
g
in
ter
v
al
o
f
th
e
co
n
v
er
ter
k
ey
s
i
n
Fig
u
r
e
9
.
So
lid
ar
r
o
ws
in
d
icate
cu
r
r
en
ts
1
an
d
2
at
th
e
m
ed
ia
co
n
tr
o
l
in
ter
f
ac
e
(
MCI)
in
q
u
esti
o
n
,
an
d
d
o
tted
o
n
es
in
d
icate
th
e
s
am
e
c
u
r
r
en
ts
at
t
h
e
p
r
e
v
io
u
s
m
e
d
ia
co
n
tr
o
l
(
MC)
AND.
T
o
d
escr
i
b
e
elec
tr
o
m
a
g
n
etic
p
r
o
ce
s
s
es,
we
will
d
r
aw
u
p
v
o
ltag
e
eq
u
atio
n
s
to
d
ete
r
m
in
e
th
e
co
n
to
u
r
cu
r
r
en
ts
1
an
d
2
,
n
e
g
lectin
g
th
e
m
u
t
u
al
in
d
u
cta
n
c
es
an
d
ca
p
ac
itan
ce
s
o
f
p
h
ase
lo
ad
s
,
wh
ich
we
will tak
e
in
to
ac
co
u
n
t la
ter
:
=
2
(
+
)
1
+
(
+
)
2
,
(
6
)
w
h
er
e
1
̅
,
2
̅
is
th
e
d
if
f
er
en
tiatio
n
o
p
er
ato
r
,
is
th
e
v
o
ltag
e
o
f
th
e
DC
s
o
u
r
ce
,
an
d
is
th
e
r
elat
iv
e
v
alu
e
o
f
th
e
cu
r
r
e
n
t.
Mo
v
in
g
o
n
to
r
elativ
e
u
n
its
,
w
e
g
et:
1
=
1
̅
(
1
+
)
,
1
=
2
̅
(
1
+
)
,
(
7
)
w
h
er
e:
–
is
th
e
elec
tr
o
m
a
g
n
et
ic
tim
e
co
n
s
tan
t o
f
th
e
win
d
in
g
.
I
n
th
e
f
u
tu
r
e,
th
e
d
ash
es
d
en
o
tin
g
r
elativ
e
u
n
its
will
b
e
o
m
itted
.
T
h
en
th
e
s
o
lu
tio
n
o
f
th
e
v
o
ltag
e
eq
u
atio
n
s
o
f
th
e
cu
r
r
en
t c
ir
cu
it
s
will b
e
wr
itten
as
(
8
)
.
1
(
)
=
(
1
−
−
)
+
10
−
,
2
(
)
=
(
1
−
−
)
+
20
−
,
(
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
.
2
,
Ap
r
il
20
25
:
1
3
3
2
-
1
3
4
7
1340
w
h
er
e
10
an
d
20
ar
e
th
e
in
itial v
alu
es
o
f
th
e
co
n
t
o
u
r
cu
r
r
e
n
ts
in
th
e
co
n
s
id
er
ed
n
th
in
ter
v
al,
eq
u
a
l
to
th
e
f
in
al
v
alu
es o
f
s
im
ilar
cu
r
r
en
ts
in
th
e
p
r
ev
io
u
s
n
-
1
i
n
ter
v
al.
Acc
o
r
d
in
g
t
o
Fig
u
r
e
9
,
y
o
u
ca
n
wr
ite
as
(
9
)
.
10
=
−
1
=
1
−
1
+
2
−
1
,
20
=
−
−
1
=
−
2
−
1
.
(
9
)
w
h
er
e
th
e
u
p
p
e
r
in
d
ex
in
d
icate
s
th
e
s
witch
in
g
cy
cle,
an
d
th
e
lo
wer
o
n
e
in
d
icate
s
th
e
n
am
e
o
f
t
h
e
p
h
ase
with
th
e
f
in
al
v
alu
e
o
f
th
e
cu
r
r
e
n
t i
n
it.
I
n
tu
r
n
,
t
h
e
f
i
n
al
v
alu
es
o
f
th
e
cu
r
r
e
n
ts
o
n
th
e
MC
ar
e
d
et
er
m
in
ed
f
r
o
m
(
7
)
f
o
r
a
tim
e
e
q
u
al
to
th
e
d
u
r
atio
n
o
f
th
e
MCI.
So
lv
in
g
(
8
)
an
d
(
9
)
to
g
eth
er
wh
en
=
Т
к
,
wh
er
e
Т
к
–
th
e
d
u
r
atio
n
o
f
th
e
MCI,
f
o
r
a
s
tead
y
-
s
tate
o
p
er
atio
n
m
o
d
e,
we
g
et:
10
=
(
1
−
)
+
(
1
−
)
(
1
−
)
1
−
+
2
,
20
=
(
1
−
)
+
(
1
−
)
(
1
−
)
1
−
+
2
.
(
1
0
)
w
h
er
e
=
−
.
Su
b
s
titu
tin
g
th
e
in
itial
v
alu
es
o
f
th
e
cu
r
r
e
n
ts
o
b
tain
ed
in
(
7
)
,
we
ca
n
f
in
d
th
e
law
o
f
ch
an
g
e
o
f
co
n
to
u
r
cu
r
r
en
ts
o
n
th
e
MCI
f
o
r
th
e
s
tead
y
-
s
tate
o
p
er
atio
n
m
o
d
e.
Kn
o
win
g
t
h
e
law
o
f
ch
an
g
e
o
f
co
n
t
o
u
r
cu
r
r
en
ts
,
we
ca
n
f
in
d
t
h
e
law
o
f
ch
an
g
e
o
f
p
h
ase
cu
r
r
en
ts
:
=
1
+
2
;
=
−
1
;
=
−
2
,
(
1
1
)
ℎ
=
1
3
ℎ
(
)
(
1
+
)
.
(
1
2
)
Usi
n
g
th
e
p
h
ase
v
o
ltag
e
(
1
2
)
,
we
ca
n
f
i
n
d
t
h
e
law
o
f
c
h
an
g
e
in
p
h
ase
v
o
ltag
es
at
m
icr
o
co
n
tr
o
ller
(
MK
)
.
T
h
e
co
ef
f
icien
t
1
/3
tak
es
in
to
ac
c
o
u
n
t
th
at
th
e
b
ase
r
esis
tan
ce
,
ac
co
r
d
in
g
to
(
7
)
,
is
th
r
ee
ti
m
es
g
r
ea
ter
th
an
t
h
e
p
h
ase
r
esis
tan
ce
.
T
h
er
ef
o
r
e,
w
e
ca
n
m
ak
e
s
u
r
e
th
at
th
e
p
h
ase
v
o
ltag
es
at
a
s
y
m
m
etr
ical
ac
tiv
e
-
in
d
u
ctiv
e
lo
a
d
ch
an
g
e
in
s
tead
y
s
tate.
T
h
is
ca
n
b
e
s
ee
n
b
y
ta
k
in
g
th
e
d
u
r
atio
n
o
f
th
e
MCI
lo
n
g
e
n
o
u
g
h
f
o
r
th
e
cu
r
r
en
t
in
th
e
win
d
in
g
to
r
ea
ch
a
s
tead
y
v
alu
e
at
t
h
e
e
n
d
o
f
th
is
in
ter
v
al.
T
o
d
o
t
h
i
s
,
in
th
e
r
esu
ltin
g
eq
u
atio
n
s
,
it
is
en
o
u
g
h
to
tak
e
=
0
.
Fro
m
h
er
e
we
g
et
10
=
2
,
20
=
−
1
¸
a
n
d
th
e
eq
u
atio
n
s
o
f
co
n
t
o
u
r
c
u
r
r
en
ts
will lo
o
k
lik
e:
1
(
)
=
(
1
−
−
)
+
2
−
,
2
(
)
=
(
1
−
−
)
+
−
.
(
1
3
)
T
h
en
ac
co
r
d
in
g
to
(
1
1
)
a
n
d
(
1
3
)
we
g
et
(
1
4
)
:
(
)
=
1
(
)
+
2
(
)
=
2
−
−
.
(
1
4
)
Su
b
s
titu
tin
g
(
)
f
r
o
m
(
1
4
)
in
to
(
1
2
)
an
d
d
if
f
er
en
tiatin
g
,
we
g
et
(
)
=
2
/
3
.
T
h
u
s
,
th
e
p
r
esen
ce
o
f
in
d
u
ctan
ce
in
th
e
lo
ad
in
a
s
y
m
m
etr
ical
m
o
d
e
d
o
es
n
o
t
d
is
t
o
r
t
th
e
p
h
ase
v
o
ltag
e
d
iag
r
am
.
Ph
y
s
ically
,
th
is
i
s
ex
p
lain
ed
b
y
th
e
f
ac
t
th
at
th
e
elec
tr
o
m
ag
n
etic
p
r
o
ce
s
s
es
o
f
cu
r
r
e
n
t
r
is
e
in
th
e
co
n
n
ec
ted
p
h
ase
an
d
cu
r
r
en
t
d
ec
r
ea
s
e
in
th
e
d
is
co
n
n
ec
ted
p
h
ase
o
cc
u
r
at
th
e
s
am
e
s
p
ee
d
,
d
eter
m
in
ed
b
y
th
e
elec
tr
o
m
ag
n
etic
co
n
s
tan
t
τ
.
I
n
th
e
ca
s
e
o
f
an
asy
m
m
etr
ic
i
n
d
u
ctiv
ely
ac
tiv
e
lo
ad
,
ea
ch
p
h
ase
will
h
av
e
its
co
n
s
tan
t
v
al
u
e
.
It
will
lead
to
an
asy
m
m
etr
y
o
f
p
h
a
s
e
v
o
ltag
es
n
o
t
o
n
ly
d
u
e
to
th
e
d
if
f
er
en
ce
in
ac
tiv
e
lo
ad
s
b
u
t
also
d
u
e
to
th
e
d
if
f
er
en
ce
in
th
e
r
ate
o
f
f
lo
w
o
f
elec
tr
o
m
ag
n
etic
p
r
o
ce
s
s
es
o
f
th
e
p
h
ases
b
ein
g
s
witch
ed
o
n
an
d
o
f
f
.
T
h
e
d
iag
r
am
o
f
p
h
ase
v
o
ltag
es
an
d
ze
r
o
p
o
in
t
v
o
ltag
es
r
elativ
e
to
th
e
“m
in
u
s
”
b
u
s
in
s
o
m
e
p
ar
ticu
lar
ca
s
e
will
lo
o
k
lik
e,
as sh
o
wn
in
Fig
u
r
e
1
0
(
s
o
lid
lin
es).
T
o
s
o
lv
e
th
e
is
s
u
es
o
f
o
u
tp
u
t
v
o
ltag
e
s
y
m
m
etr
izatio
n
,
th
e
f
o
llo
win
g
p
r
i
n
cip
le
is
s
h
o
wn
in
Fig
u
r
e
1
1
.
T
h
e
o
r
ig
in
al
r
ep
lace
m
en
t
cir
cu
it
with
o
u
t
s
y
m
m
etr
izatio
n
is
s
h
o
wn
in
Fig
u
r
e
1
1
(
a
)
.
U
s
in
g
th
e
ad
d
itio
n
al
r
esis
tan
ce
in
Fig
u
r
e
1
1
(
b
)
,
th
e
co
n
tr
o
l
k
ey
G8
is
r
ep
lace
d
o
r
th
e
cu
r
r
en
t
is
r
ed
u
ce
d
at
th
e
s
tar
's
m
id
p
o
in
t,
s
o
th
at
in
th
is
ca
s
e
th
e
v
o
ltag
e
d
r
o
p
ac
r
o
s
s
th
e
r
esis
tan
ce
R
2
is
eq
u
al
to
2
/
3
Us.
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
Mo
d
el
o
f semico
n
d
u
ct
o
r
co
n
v
erter
s
fo
r
th
e
s
imu
la
tio
n
o
f a
n
a
s
ymm
etri
c
lo
a
d
s
in
…
(
S
a
id
j
o
n
Ta
va
r
o
v
)
1341
Fig
u
r
e
1
0
.
Z
er
o
-
p
o
in
t
v
o
ltag
e
o
f
th
e
p
o
wer
s
u
p
p
ly
in
s
y
m
m
e
tr
ical
(
s
o
lid
lin
es)
an
d
asy
m
m
etr
ical
(
d
ash
ed
lin
es)
m
o
d
es
(
a)
(
b
)
Fig
u
r
e
1
1
.
Ou
tp
u
t
v
o
ltag
e
s
y
m
m
etr
izatio
n
:
(
a)
t
h
e
o
r
ig
in
al
s
u
b
s
titu
tio
n
s
ch
em
e
with
o
u
t sy
m
m
etr
y
an
d
(
b
)
th
e
e
q
u
iv
alen
t su
b
s
titu
tio
n
s
ch
em
e
with
s
y
m
m
etr
y
T
h
e
r
eq
u
ir
ed
cu
r
r
en
t
v
alu
e
is
d
eter
m
in
ed
b
y
(
1
5
)
:
=
(
2
3
)
2
2
,
(
1
5
)
w
h
er
e
U
R
2
–
th
e
ex
is
tin
g
p
h
ase
v
o
ltag
e
o
n
th
e
r
esis
to
r
R
2
;
2
=
1
∙
2
,
(
1
6
)
1
–
cu
r
r
e
n
t c
o
n
s
u
m
e
d
f
r
o
m
th
e
n
etwo
r
k
;
i
1
=
U
d
U
eq
u
.
w
h
er
e
=
1
∙
2
1
+
2
(
1
7
)
No
w,
k
n
o
win
g
th
e
ad
ju
s
ted
p
h
ase
v
o
ltag
e
ca
n
b
e
ca
lcu
lated
:
2
=
(
1
+
)
2
(
1
8
)
Af
ter
ca
lcu
latio
n
,
we
o
b
tain
a
tim
e
d
iag
r
am
o
f
th
e
s
y
m
m
etr
y
cu
r
r
en
t
in
Fig
u
r
e
1
2
,
an
d
th
e
tim
e
d
iag
r
am
o
f
p
h
ase
v
o
ltag
es
will
h
av
e
th
e
s
am
e
ap
p
ea
r
an
c
e
as
with
a
s
y
m
m
etr
ical
lo
ad
,
as
s
h
o
wn
in
Fig
u
r
e
1
.
Fig
u
r
e
1
3
s
h
o
ws th
e
tr
an
s
ien
t p
r
o
ce
s
s
o
f
th
e
au
to
m
atic
v
o
ltag
e
b
alan
cin
g
s
y
s
tem
at
a
ce
r
tain
v
alu
e
o
f
t
h
e
k
co
e
f
f
icien
t.
Evaluation Warning : The document was created with Spire.PDF for Python.