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T
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I
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4
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d
s
to
th
e
o
s
cillatio
n
o
f
s
y
s
te
m
v
ar
iab
le
[
7
]
.
T
h
er
ef
o
r
e,
a
P
W
M
A
C
-
D
C
co
n
v
er
ter
u
n
d
er
u
n
b
alan
ce
d
o
p
er
atin
g
co
n
d
itio
n
s
n
ec
es
s
itates
t
h
e
u
s
e
o
f
f
ilter
s
to
r
ed
u
ce
t
h
e
h
ar
m
o
n
ics at
th
e
A
C
i
n
p
u
t
s
id
e
r
esp
ec
tiv
el
y
.
T
h
u
s
,
to
ac
h
ie
v
e
a
lo
w
e
r
d
is
tu
r
b
an
ce
s
a
n
d
en
h
a
n
ce
d
p
o
w
er
q
u
alit
y
b
y
e
l
i
m
i
n
ate
th
e
h
ar
m
o
n
ics
u
n
d
er
u
n
b
ala
n
ce
d
v
o
ltag
e
i
n
p
u
t
s
u
p
p
ly
,
a
f
e
w
s
o
lu
tio
n
s
h
av
e
b
ee
n
ap
p
r
o
ac
h
i
n
t
h
ese
ca
s
es.
As
a
r
e
s
u
l
t,
it
is
e
s
s
en
tial
to
h
a
v
e
a
n
ad
eq
u
ate
m
o
d
el
to
d
ea
l
w
it
h
th
e
n
e
g
ati
v
e
s
eq
u
en
ce
i
n
p
u
t
v
o
ltag
e
a
s
w
ell
as p
o
s
it
iv
e
s
eq
u
en
ce
in
p
u
t v
o
lta
g
es.
Su
b
s
eq
u
e
n
tl
y
,
th
i
s
p
ap
er
is
m
ain
l
y
f
o
cu
s
s
i
n
g
o
n
th
e
Dir
ec
t
P
o
w
er
C
o
n
tr
o
l
(
DP
C
)
s
tr
ateg
y
,
w
h
ic
h
it
b
ased
o
n
th
e
in
s
ta
n
tan
eo
u
s
o
f
ac
ti
v
e
an
d
r
ea
cti
v
e
p
o
w
e
r
co
n
tr
o
l
lo
o
p
s
[
8
,
9
]
.
Ho
w
ev
er
,
co
n
v
e
n
tio
n
al
ap
p
r
o
ac
h
es
o
f
DP
C
ca
n
n
o
t
b
e
ap
p
lied
f
o
r
g
en
er
alize
d
u
n
b
al
an
ce
d
o
p
er
atin
g
co
n
d
itio
n
s
.
I
n
th
is
p
ap
er
,
D
P
C
is
m
o
d
i
f
ied
to
m
a
n
a
g
e
p
o
w
er
f
l
o
w
d
u
r
i
n
g
u
n
b
ala
n
ce
d
v
o
lta
g
e
s
u
p
p
l
y
s
o
t
h
at
s
i
n
u
s
o
id
al
b
alan
ce
d
g
r
id
cu
r
r
en
t
s
ar
e
o
b
tain
ed
.
W
ith
t
h
i
s
n
e
w
s
t
r
ateg
y
,
DP
C
o
v
er
co
m
e
s
t
h
e
p
r
o
b
lem
s
r
elate
d
to
g
r
id
v
o
ltag
e
i
m
b
alan
ce
an
d
ca
n
ac
co
m
p
li
s
h
ed
n
e
w
r
eg
u
lat
io
n
la
w
s
.
A
t
th
e
en
d
o
f
t
h
i
s
p
ap
er
,
th
e
co
n
v
er
ter
p
er
f
o
r
m
a
n
ce
w
ill
b
e
ev
a
lu
ated
u
n
d
er
s
tead
y
s
tate
an
d
d
y
n
a
m
ic
co
n
d
itio
n
s
.
T
h
e
co
n
v
er
t
er
’
s
d
y
n
a
m
ic
s
t
u
d
y
is
p
er
f
o
r
m
ed
b
y
ev
a
lu
at
in
g
t
h
e
tr
an
s
ien
t r
esp
o
n
s
e
d
u
r
i
n
g
t
h
e
m
a
g
n
it
u
d
e
v
ar
iatio
n
s
o
f
D
C
v
o
lta
g
e
r
ef
er
en
ce
a
n
d
lo
ad
r
esis
ta
n
ce
.
2.
B
ASI
C
S
T
RUC
T
UR
E
DIR
E
CT
P
O
WE
R
CO
N
T
RO
L
T
h
e
Dir
ec
t
P
o
w
er
C
o
n
tr
o
l
(
D
P
C
)
is
b
ased
o
n
th
e
Dir
ec
t
T
o
r
q
u
e
C
o
n
tr
o
l
(
DT
C
)
co
n
ce
p
t
in
elec
tr
ical
m
ac
h
in
e
s
.
T
h
e
in
te
n
tio
n
f
o
r
DP
C
is
to
co
n
tr
o
l
th
e
in
s
t
an
tan
eo
u
s
o
f
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
co
n
tr
o
l
lo
o
p
s
[
10
]
as
th
e
s
a
m
e
d
ir
ec
ti
o
n
f
o
r
DT
C
in
co
n
tr
o
lli
n
g
t
h
e
to
r
q
u
e
a
n
d
f
lu
x
o
f
i
n
d
u
c
tio
n
m
ac
h
in
e
s
.
I
n
t
h
i
s
DP
C
s
c
h
e
m
e
as
s
h
o
w
n
in
Fi
g
u
r
e
1
,
s
w
i
tch
i
n
g
tab
le
p
la
y
s
a
m
aj
o
r
p
ar
t
[
11
]
.
T
h
e
in
p
u
t
to
th
e
s
w
itc
h
i
n
g
tab
le
w
il
l
b
e
th
e
in
s
ta
n
ta
n
eo
u
s
er
r
o
r
o
f
th
e
ac
tiv
e
p
o
w
er
dP
,
r
ea
ctiv
e
p
o
w
er
Dq
an
d
th
e
v
o
ltag
e
v
ec
to
r
p
o
s
itio
n
θ
n
as sh
o
w
n
i
n
T
ab
le
1
.
T
h
is
s
w
it
ch
in
g
tab
le
en
ab
le
s
th
e
co
n
v
er
ter
to
s
elec
t th
e
ap
p
r
o
p
r
iate
o
f
s
w
itc
h
in
g
s
tates.
Fig
u
r
e
1
.
C
o
n
tr
o
l stru
ct
u
r
e
o
f
d
ir
ec
t p
o
w
er
co
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
n
a
lysi
s
o
f d
ir
ec
t
p
o
w
er c
o
n
tr
o
l A
C
-
DC
co
n
ve
r
ter u
n
d
er u
n
b
a
la
n
ce
v
o
lta
g
e
…
(
N
o
r
A
z
iz
a
h
Yu
s
o
ff
)
3335
T
ab
le
1
.
Sw
itch
in
g
lo
o
k
-
u
p
ta
b
le
f
o
r
d
ir
ec
t p
o
w
er
co
n
tr
o
l
P
o
w
e
r
e
r
r
o
r
st
a
t
u
s
S
e
c
t
o
r
p
o
si
t
i
o
n
(
θ
n
)
a
n
d
c
o
n
v
e
r
t
e
r
v
o
l
t
a
g
e
v
e
c
t
o
r
(
V
n
)
d
P
d
Q
θ
1
θ
2
θ
3
θ
4
θ
5
θ
6
θ
7
θ
8
θ
9
θ
10
θ
11
θ
12
0
0
V
1
V
1
V
2
V
2
V
3
V
3
V
4
V
4
V
5
V
5
V
6
V
6
0
1
V
2
V
2
V
3
V
3
V
4
V
4
V
5
V
5
V
6
V
6
V
1
V
1
1
0
V
6
V
6
V
1
V
1
V
2
V
2
V
3
V
3
V
4
V
4
V
5
V
5
1
1
V
3
V
3
V
4
V
4
V
5
V
5
V
6
V
6
V
1
V
1
V
2
V
2
I
n
co
n
v
e
n
tio
n
al
DP
C
,
a
to
tal
o
f
f
o
u
r
v
o
ltag
e
s
en
s
o
r
s
ar
e
u
s
ed
to
m
ea
s
u
r
e
t
h
e
th
r
ee
-
p
h
ase
AC
in
p
u
t
v
o
ltag
e
a
n
d
DC
o
u
tp
u
t
v
o
lt
ag
e,
w
h
i
le
th
r
ee
c
u
r
r
en
t
s
e
n
s
o
r
s
ar
e
u
s
ed
to
m
ea
s
u
r
e
t
h
e
th
r
ee
-
p
h
ase
i
n
p
u
t
cu
r
r
en
ts
[
12
]
.
T
h
en
,
th
e
m
ea
s
u
r
ed
cu
r
r
en
t
s
a
n
d
v
o
ltag
e
s
ar
e
f
ed
in
to
t
w
o
“
abc
-
αβ
”
b
lo
ck
s
w
h
ich
u
ti
lize
th
e
C
lar
k
e
T
r
an
s
f
o
r
m
atio
n
.
B
o
th
b
lo
ck
s
tr
a
n
s
f
o
r
m
th
e
th
r
ee
-
p
h
ase
v
o
ltag
e
an
d
cu
r
r
en
t
i
n
to
t
h
eir
co
r
r
esp
o
n
d
in
g
α
β
-
r
ef
er
e
n
ce
f
r
a
m
e.
T
h
e
tr
an
s
f
o
r
m
at
io
n
m
atr
ix
to
t
h
e
s
tatio
n
ar
y
f
r
a
m
e
is
u
tili
ze
d
b
y
r
ef
er
r
i
n
g
th
e
eq
u
a
tio
n
in
(
1
)
.
T
h
e
th
r
ee
-
p
h
ase
i
n
p
u
t
co
m
p
o
n
e
n
ts
ar
e
r
ep
r
esen
ted
b
y
x
a
, x
b
an
d
x
c
w
h
il
e
x
α
a
n
d
x
β
i
n
d
icate
t
w
o
-
p
h
a
s
e
co
m
p
o
n
e
n
t
s
i
n
αβ
-
r
ef
er
en
ce
f
r
a
m
e.
T
h
e
a
n
g
le
o
f
s
u
p
p
l
y
v
o
lta
g
e
v
ec
to
r
is
d
ev
i
d
ed
in
to
1
2
s
ec
to
r
an
d
ea
ch
s
ec
to
r
is
30
0
w
id
e
as
s
h
o
w
n
in
F
i
g
u
r
e
2
.
Fig
u
r
e
2
.
Secto
r
s
elec
tio
n
f
o
r
d
ir
ec
t p
o
w
er
co
n
tr
o
l
T
h
e
v
o
ltag
e
a
n
d
cu
r
r
e
n
t
i
n
αβ
-
r
ef
er
e
n
ce
f
r
a
m
e
ar
e
t
h
e
n
f
ed
in
to
t
w
o
b
lo
ck
s
to
o
b
tain
th
e
esti
m
ated
in
s
ta
n
ta
n
eo
u
s
ac
ti
v
e
p
o
w
er
P
inst
,
an
d
r
ea
ctiv
e
p
o
w
er
Q
ins
t
,
as
in
d
icate
d
i
n
(
2
)
an
d
(
3
)
,
r
esp
ec
tiv
el
y
.
T
h
en
,
th
e
P
inst
an
d
Q
inst
ar
e
co
m
p
ar
ed
w
it
h
th
e
r
ef
er
e
n
ce
o
f
ac
tiv
e
p
o
w
er
,
P
ref
an
d
r
ea
ctiv
e
p
o
w
er
,
Q
ref
v
al
u
es
.
T
h
e
er
r
o
r
q
u
an
titi
es
w
h
ic
h
ar
e
d
en
o
ted
b
y
ΔP
a
n
d
ΔQ
,
ar
e
p
r
o
ce
s
s
ed
b
y
t
w
o
h
y
s
ter
esis
c
o
n
tr
o
ller
s
to
o
b
tain
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
w
er
er
r
o
r
s
w
h
ich
i
s
g
i
v
e
n
b
y
d
P
an
d
d
Q
r
esp
ec
tiv
el
y
.
S
u
b
s
eq
u
e
n
tl
y
,
th
e
an
g
le
o
f
i
n
p
u
t
v
o
ltag
e
v
ec
to
r
θ
n
,
is
d
eter
m
i
n
ed
b
y
t
h
e
v
o
ltag
e
v
ec
to
r
a
n
g
le
co
n
v
er
ter
b
lo
c
k
r
eg
ar
d
i
n
g
to
th
e
eq
u
atio
n
in
(
6
)
.
A
t
th
a
t
p
o
in
t,
t
h
e
s
u
i
tab
l
e
s
w
itc
h
i
n
g
s
ta
tes
o
f
t
h
e
co
n
v
er
ter
w
i
ll
b
e
g
en
er
ated
b
y
th
e
s
w
itc
h
in
g
tab
le
a
n
d
th
e
o
u
tp
u
t v
o
lta
g
e
is
k
ep
t c
lo
s
e
to
th
e
r
ef
er
en
ce
D
C
v
o
lta
g
e
b
y
t
u
n
in
g
t
h
e
PI
co
n
tr
o
ller
ap
p
r
o
p
r
iately
[1
3
,
1
4
]
.
11
1
2
22
3
33
0
22
x
x
(
1
)
(
2
)
(
3
)
I
V
I
V
P
i
n
s
t
2
3
I
V
I
V
Q
i
n
s
t
2
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
4
,
A
u
g
u
s
t 2
0
2
0
:
3
3
3
3
-
3342
3336
2
.
1
.
Dev
elo
pm
e
nt
o
f
s
w
it
ching
t
a
ble f
o
r
DP
C
I
n
DP
C
,
th
e
d
ig
it
ized
s
ig
n
al
θ
n
ca
lcu
late
f
r
o
m
th
e
p
h
ase
o
f
v
o
ltag
e
v
ec
to
r
,
w
h
ic
h
it
m
ea
s
u
r
ed
f
r
o
m
th
e
th
r
ee
-
p
h
ase
p
o
w
er
s
o
u
r
ce
u
s
i
n
g
(
4
)
.
Fr
o
m
t
h
e
eq
u
atio
n
,
th
e
alp
h
a
-
b
eth
a
s
tat
io
n
ar
y
-
f
r
a
m
e
is
o
b
tain
ed
f
r
o
m
th
e
p
o
s
iti
v
e
s
eq
u
e
n
ce
.
1
t
a
n
n
v
v
(
4
)
T
h
e
s
w
itc
h
i
n
g
tab
le
i
n
th
e
ci
r
cu
it
s
i
m
u
latio
n
i
s
cr
ea
tin
g
u
s
in
g
“
Ma
tlab
Fu
n
ctio
n
”
b
lo
ck
.
T
h
e
ac
tiv
e
p
o
w
er
er
r
o
r
,
ΔP
an
d
r
ea
ctiv
e
p
o
w
er
er
o
r
,
ΔQ
ar
e
f
ed
in
to
t
w
o
h
y
s
ter
es
is
b
lo
ck
s
to
o
b
tain
th
e
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
w
er
er
r
o
r
s
s
tatu
s
g
iv
e
n
b
y
d
P
a
n
d
d
Q
r
esp
ec
tiv
el
y
.
3.
P
O
WE
R
ANA
L
YS
I
S
UN
DE
R
UNB
AL
ANC
E
G
RID VO
L
T
A
G
E
Ho
w
e
v
er
,
alth
o
u
g
h
DP
C
o
f
f
er
s
i
m
p
le
co
n
tr
o
l
s
tr
u
c
tu
r
e
a
n
d
f
ast
d
y
n
a
m
ic
r
esp
o
n
s
e,
it
g
e
n
e
r
ates
h
i
g
h
r
ip
p
les
an
d
h
i
g
h
er
n
u
m
b
er
o
f
T
o
tal
Har
m
o
n
ic
Dis
to
r
tio
n
(
T
HD)
d
u
r
in
g
i
m
b
a
lan
ce
in
p
u
t
v
o
lta
g
e
[
1
5
,
1
6
]
.
I
n
o
r
d
er
to
m
ak
e
th
e
co
n
tr
o
ll
er
to
b
e
m
o
r
e
r
o
b
u
s
t
i
n
s
u
c
h
ca
s
es,
i
n
v
esti
g
atio
n
s
o
f
p
o
w
er
co
n
v
er
ter
s
u
n
d
er
u
n
b
ala
n
ce
d
in
p
u
t
v
o
lta
g
e
co
n
d
itio
n
s
ar
e
p
r
esen
ted
i
n
r
ef
er
e
n
ce
s
[
1
7
]
.
T
h
e
in
ter
ac
tio
n
b
etw
ee
n
t
h
e
h
ar
m
o
n
i
c
co
m
p
o
n
e
n
t
s
o
f
th
e
D
C
o
u
tp
u
t
v
o
lta
g
e
an
d
t
h
e
co
n
v
er
ter
p
o
le
v
o
ltag
es
cr
ea
tes
ev
e
n
-
o
r
d
er
h
ar
m
o
n
ic
s
at
th
e
DC
o
u
tp
u
t
an
d
o
d
d
-
o
r
d
er
h
ar
m
o
n
ic
co
m
p
o
n
e
n
t
s
in
th
e
in
p
u
t
AC
cu
r
r
e
n
t
o
f
t
h
e
P
W
M
A
C
-
DC
co
n
v
er
ter
.
C
o
n
s
eq
u
e
n
tl
y
,
t
h
e
s
e
h
ar
m
o
n
ics
co
m
p
o
n
en
t
s
will
in
cr
ea
s
e
t
h
e
T
HD
o
f
th
e
AC
i
n
p
u
t
cu
r
r
en
t
s
ig
n
i
f
ica
n
tl
y
[
1
8
,
1
9
]
.
I
n
g
e
n
er
al,
th
e
n
o
n
-
id
ea
l
co
n
d
itio
n
s
s
u
ch
as
u
n
b
alan
ce
d
an
d
d
is
to
r
ted
th
r
ee
-
p
h
a
s
e
g
r
id
v
o
ltag
e
s
u
p
p
l
y
h
a
v
e
n
eg
at
iv
e
i
m
p
ac
t
s
to
th
e
p
er
f
o
r
m
a
n
ce
an
d
f
il
ter
s
ize
o
f
AC
-
D
C
co
n
v
er
ter
s
y
s
te
m
[
20
,
21
]
.
T
h
er
ef
o
r
e,
P
W
M
A
C
-
DC
co
n
v
er
ter
s
u
n
d
er
u
n
b
ala
n
ce
d
o
p
er
atin
g
co
n
d
itio
n
s
r
eq
u
ir
e
th
e
u
s
e
o
f
in
p
u
t
o
r
o
u
tp
u
t
f
ilte
s
o
f
a
lar
g
e
s
ize
to
r
ed
u
ce
ev
en
an
d
o
d
d
-
o
r
d
er
h
ar
m
o
n
ic
s
at
th
e
DC
o
u
tp
u
t
a
n
d
AC
i
n
p
u
t
s
u
p
p
l
y
[2
2
,
2
3
]
.
Hen
ce
,
t
h
e
co
n
tr
o
l te
c
h
n
iq
u
es
o
f
an
AC
-
DC
co
n
v
er
ter
n
ee
d
a
d
d
itio
n
al
in
v
est
ig
at
io
n
to
m
i
ti
g
ate
t
h
o
s
e
n
e
g
ati
v
e
i
m
p
ac
ts
d
u
r
i
n
g
v
o
ltag
e
u
n
b
al
an
ce
an
d
d
is
to
r
ted
co
n
d
itio
n
s
[
2
4
]
.
Fo
r
th
at,
it
is
n
ec
ess
ar
y
to
s
p
lit
th
e
v
o
ltag
e
v
ec
to
r
in
to
its
s
eq
u
en
ce
co
m
p
o
n
en
t
s
as
w
ell
as
to
co
m
p
u
te
th
e
p
o
s
iti
v
e
s
eq
u
e
n
ce
v
o
lta
g
e
v
ec
to
r
a
n
g
le
[2
5
]
.
Vo
ltag
e
an
g
le
ca
lc
u
latio
n
is
d
o
n
e
b
y
m
ea
n
s
o
f
a
P
L
L
w
h
i
le
a
v
er
y
s
i
m
p
le
al
g
o
r
ith
m
i
s
u
s
ed
f
o
r
s
eq
u
e
n
ce
ex
tr
ac
tio
n
.
3
.
1
.
Sequ
ence
ex
t
ra
ct
o
r
As
i
n
i
n
tr
o
d
u
ctio
n
p
ar
t,
it
w
as
ex
p
lai
n
ed
th
at
an
u
n
b
alan
ce
i
n
p
u
t
s
u
p
p
l
y
h
as
ca
u
s
i
n
g
n
eg
at
iv
e
o
r
ze
r
o
s
eq
u
en
ce
v
o
ltag
e
co
m
p
o
n
e
n
t
as
w
ell
as
a
p
o
s
itiv
e
s
eq
u
en
c
e
v
o
ltag
e
co
m
p
o
n
e
n
t
o
n
th
e
g
r
id
v
o
ltag
e
v
ec
to
r
.
T
h
er
ef
o
r
e,
n
eg
ati
v
e
s
eq
u
e
n
c
e
co
m
p
o
n
en
t
w
a
s
i
n
tr
o
d
u
ce
d
to
th
e
i
n
p
u
t
c
u
r
r
en
t
i
n
o
r
d
er
to
ad
eq
u
atel
y
co
m
p
e
n
s
ate
f
o
r
t
h
e
u
n
b
alan
ce
d
o
p
er
atin
g
co
n
d
it
io
n
s
o
t
h
at
t
h
e
i
n
s
ta
n
ta
n
eo
u
s
ac
ti
v
e
p
o
w
er
b
ec
o
m
e
s
co
n
s
ta
n
t
w
it
h
o
u
t
o
s
cil
latin
g
co
m
p
o
n
e
n
ts
.
T
h
e
u
n
b
alan
ce
d
d
etec
to
r
an
d
s
y
m
m
e
t
y
r
ical
co
m
p
o
n
en
t
eq
u
a
tio
n
th
at
ac
q
u
ir
es
th
e
p
o
s
iti
v
e
a
n
d
n
eg
ativ
e
s
eq
u
en
ce
co
m
p
o
n
en
t
f
r
o
m
th
r
ee
-
p
h
ase
i
n
s
tan
tan
eo
u
s
q
u
an
titi
e
s
s
u
c
h
as
vo
ltag
e
a
n
d
cu
r
r
en
t
is
r
eg
ar
d
ed
as
an
i
m
p
o
r
tan
t
f
u
n
ct
io
n
al
p
ar
t
o
f
th
e
en
tire
u
n
b
ala
n
ce
co
n
p
en
s
atio
n
co
n
tr
o
l
s
y
s
te
m
.
He
n
ce
,
p
o
s
iti
v
e
a
n
d
n
e
g
ati
v
e
s
eq
u
e
n
ce
eq
u
at
io
n
s
as
s
h
o
w
n
i
n
T
ab
le
2
w
i
ll
b
e
ap
p
lied
in
th
i
s
r
esear
ch
w
o
r
k
i
n
o
r
d
er
to
g
e
n
er
ate
o
r
ex
tr
ac
t
a
n
e
g
ati
v
e
s
eq
u
en
ce
f
r
o
m
th
e
in
p
u
t
s
u
p
p
ly
w
h
ic
h
k
n
o
w
n
a
s
s
eq
u
en
ce
e
x
tr
ac
to
r
.
T
ab
le
2
.
Seq
u
en
ce
ex
tr
ac
to
r
eq
u
atio
n
P
h
a
se
C
o
m
p
o
n
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n
t
M
a
t
r
i
x
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q
u
a
t
i
o
n
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r
o
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q
u
e
n
c
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(
0
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(
0
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0
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bb
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VV
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F
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u
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3
h
a
s
s
h
o
w
n
th
e
b
lo
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ia
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a
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o
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m
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n
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t
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h
e
ex
tr
ac
tio
n
b
lo
ck
d
iag
r
a
m
is
cr
ea
tin
g
b
ased
o
n
th
e
m
atr
ic
eq
u
atio
n
a
s
ca
n
b
e
s
ee
n
i
n
T
ab
le
2
.
Nex
t,
th
e
p
h
ase
o
f
i
n
p
u
t
v
o
ltag
e
a
n
d
cu
r
r
en
t
f
r
o
m
p
h
a
s
e
s
eq
u
en
ce
ar
e
b
ein
g
tr
an
s
f
o
r
m
ed
in
to
alp
h
a
-
b
eta
s
tat
io
n
ar
y
-
f
r
a
m
e.
L
a
s
tl
y
,
t
h
e
s
tat
io
n
ar
y
-
r
e
f
er
en
ce
f
r
a
m
e
f
r
o
m
o
n
l
y
p
o
s
iti
v
e
a
n
d
n
e
g
ati
v
e
s
eq
u
en
ce
is
t
h
e
n
f
ed
i
n
to
a
n
o
th
er
b
lo
ck
i
n
o
r
d
er
to
o
b
tain
t
h
e
e
s
t
i
m
a
ted
in
s
ta
n
ta
n
eo
u
s
ac
tiv
e
p
o
w
er
,
P
out
,
an
d
r
ea
ctiv
e
p
o
w
er
,
Q
out
.
Fig
u
r
e
3
.
B
lo
ck
d
iag
r
a
m
f
o
r
s
e
q
u
en
ce
ex
tr
ac
to
r
T
h
e
in
s
tan
ta
n
eo
u
s
o
f
t
h
e
in
p
u
t
p
o
w
er
P
an
d
r
ea
ctiv
e
p
o
w
er
Q
in
a
s
tatio
n
ar
y
r
ef
er
e
n
c
e
f
r
a
m
a
is
g
iv
e
n
b
y
(
5
)
an
d
(
6
)
,
r
esp
ec
tiv
el
y
.
3
(
)
(
)
2
out
p
t
v
i
v
i
v
i
v
i
v
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4.
RE
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AND
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[2
7
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I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
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m
p
E
n
g
,
Vo
l.
10
,
No
.
4
,
A
u
g
u
s
t 2
0
2
0
:
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3
3
3
-
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r
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s
ien
t r
esp
o
n
s
e
f
o
r
lo
ad
v
ar
iatio
n
f
r
o
m
lo
w
to
h
ig
h
c
u
r
r
en
t d
e
m
a
n
d
;
(
a)
P
h
ase
a
,
(
b
)
DC
-
li
n
k
v
o
ltag
e,
(
c)
E
s
ti
m
ated
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
h
as
p
r
esen
ted
th
e
i
m
p
le
m
e
n
tatio
n
o
f
a
s
eq
u
e
n
ce
ex
tr
ac
to
r
in
to
Dir
ec
t
P
o
w
er
C
o
n
tr
o
l
s
ch
e
m
e.
T
h
e
m
ai
n
g
o
al
f
o
r
t
h
e
ad
d
itio
n
al
s
tr
ateg
y
o
f
s
eq
u
en
ce
e
x
tr
ac
to
r
is
to
ac
h
iev
e
f
o
r
n
ea
r
-
s
i
n
u
s
o
id
al
in
p
u
t
cu
r
r
e
n
t
w
a
v
e
f
o
r
m
o
f
th
e
co
n
v
er
ter
u
n
d
er
d
if
f
er
en
t
a
m
p
li
tu
d
e
i
n
p
u
t
v
o
ltag
e
c
o
n
d
itio
n
s
.
I
n
-
f
ac
t,
in
s
ta
n
ta
n
eo
u
s
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
s
p
r
o
v
id
ed
b
y
h
a
r
m
o
n
ic
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m
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t
o
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i
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t
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r
r
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ar
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ir
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tl
y
co
n
tr
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v
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a
s
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Si
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latio
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as
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ex
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t
p
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DP
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al
m
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7
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to
DP
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f
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Un
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s
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T
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n
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Ma
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s
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Me
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(
UT
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)
as
p
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co
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s
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t
o
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is
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esear
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r
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u
lt
an
d
r
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ch
in
ce
n
ti
v
e
g
r
an
t (
J
u
r
n
al/2
0
1
9
/FKE/Q0
0
0
1
6
)
.
RE
F
E
R
E
NC
E
S
[1
]
W
a
n
g
F
e
n
g
a
n
d
L
u
o
Yu
tao
,
“
M
o
d
e
ll
i
n
g
o
f
a
P
o
w
e
r
Co
n
v
e
rter
w
it
h
M
u
lt
i
p
le
Op
e
ra
ti
n
g
M
o
d
e
s
,”
W
o
rld
El
e
c
tric
Veh
icle
J
o
u
rn
a
l
,
p
p
.
1
-
1
7
,
2
0
1
8
.
[2
]
K.
V
e
n
k
a
tes
h
v
a
rlu
a
n
d
Ch
.
Ch
e
n
g
a
iah
,
“
Co
m
p
a
ra
ti
v
e
S
tu
d
y
o
n
DC
M
o
t
o
r
S
p
e
e
d
Co
n
tro
l
u
sin
g
V
a
ri
o
u
s
Co
n
tr
o
ll
e
rs
,”
Glo
b
a
l
J
o
u
r
n
a
l
o
f
Res
e
a
rc
h
e
rs
in
En
g
in
e
e
rin
g
El
e
c
trica
l
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
,
v
o
l.
1
3
,
no.
1
7
,
2
0
1
3
.
[3
]
Bh
im
S
in
g
h
,
Brij
N.
S
i
n
g
h
,
A
m
b
rish
Ch
a
n
d
ra
,
Ka
m
a
l
A
l
-
H
a
d
a
d
,
A
sh
ish
P
a
n
d
e
y
,
a
n
d
Dw
a
r
k
a
P
.
Ko
t
h
a
ri,
“
A
Re
v
ie
w
o
f
T
h
re
e
-
P
h
a
se
Im
p
ro
v
e
d
P
o
w
e
r
Qu
a
li
ty
A
C
–
DC
Co
n
v
e
rters
,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
5
1
(3
),
p
p
.
6
4
1
–
6
6
0
,
J
u
n
e
2
0
0
4
.
[4
]
Y.
Zh
a
n
g
,
J.
Jia
o
,
J.
L
iu
,
a
n
d
J
.
G
a
o
,
“
Dire
c
t
p
o
w
e
r
c
o
n
tro
l
o
f
P
W
M
re
c
ti
f
i
e
r
w
it
h
f
e
e
d
f
o
rwa
rd
c
o
m
p
e
n
sa
ti
o
n
o
f
DC
-
b
u
s v
o
lt
a
g
e
rip
p
le u
n
d
e
r
u
n
b
a
lan
c
e
d
g
rid
c
o
n
d
it
i
o
n
s,”
IEE
E
T
r
a
n
sa
c
ti
o
n
In
d
.
u
stria
l
Ap
p
li
c
a
ti
o
n
.,
v
o
l.
5
5
,
n
o
.
3
,
p
p
.
2
8
9
0
–
2
9
0
1
,
M
a
y
2
0
1
9
.
[5
]
D.
S
u
n
,
X
.
W
a
n
g
,
a
n
d
Y.
F
a
n
g
,
“
Ba
c
k
ste
p
p
in
g
Dire
c
t
P
o
w
e
r
C
o
n
tr
o
l
W
it
h
o
u
t
P
h
a
se
-
L
o
c
k
e
d
Lo
o
p
Of
A
C/DC
Co
n
v
e
rter
Un
d
e
r
Bo
th
Ba
lan
c
e
d
A
n
d
Un
b
a
lan
c
e
d
G
rid
Co
n
d
i
ti
o
n
s
,”
IET
P
o
we
r
El
e
c
tro
n
ic
,
v
o
l.
9
,
n
o
.
8
,
p
p
.
1
6
1
4
-
1
6
2
4
,
2
0
1
6
.
[6
]
Da
w
e
i
Zh
i,
L
ie
X
u
,
a
n
d
Ba
rry
W
.
W
i
ll
ia
m
s,
“
I
m
p
ro
v
e
d
Dire
c
t
P
o
w
e
r
Co
n
tro
l
o
f
G
rid
-
Co
n
n
e
c
ted
DC/A
C
Co
n
v
e
rter
,”
IEE
E
T
r
a
n
s
a
c
ti
o
n
Po
we
r E
lec
tro
n
ic
,
v
o
l.
2
4
,
n
o
.
5
,
2
0
0
9
.
[7
]
Y.
Qu
a
n
,
N.
He
n
g
a
n
d
H.
Jia
b
i
n
g
,
Im
p
ro
v
e
d
Co
n
tr
o
l
o
f
th
e
G
rid
-
c
o
n
n
e
c
ted
Co
n
v
e
rter
u
n
d
e
r
t
h
e
Ha
r
m
o
n
ica
ll
y
Disto
rted
G
rid
V
o
l
tag
e
Co
n
d
it
io
n
s’’,
IEE
E
I
n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
.
p
p
.
2
0
4
-
2
0
9
,
2
0
1
0
.
[8
]
A
.
M
.
Ra
z
a
li
,
M
.
A
.
Ra
h
m
a
n
,
a
n
d
G
l
y
n
G
e
o
rg
e
,
“
A
n
A
n
a
l
y
sis
o
f
Dire
c
t
P
o
w
e
r
c
o
n
tro
l
f
o
r
T
h
re
e
P
h
a
se
A
C
-
DC
Co
n
v
e
rter
,”
In
d
u
stry
Ap
p
li
c
a
t
io
n
s S
o
c
iety
A
n
n
u
a
l
M
e
e
ti
n
g
(
IAS
)
,
p
p
.
1
-
7
,
2
0
1
2
.
[9
]
No
r
A
z
iza
h
M
o
h
d
Yu
so
f
f
,
A
z
z
id
d
i
n
M
u
h
a
m
m
a
d
Ra
z
a
li
,
Ka
sru
l
A
b
d
u
l
Ka
rim
,
L
o
o
n
g
Jie
Ya
n
,
“
A
Dire
c
t
P
o
w
e
r
Co
n
tr
o
l
o
f
A
C/DC Co
n
v
e
rter,”
J
o
u
rn
a
l
o
f
En
g
in
e
e
rin
g
S
c
ien
c
e
s a
n
d
T
e
c
h
o
n
o
lo
g
y
,
p
p
.
13
-
2
1
,
F
e
b
.
20
1
9
.
[1
0
]
No
r
A
z
i
z
a
h
M
o
h
d
Yu
so
f
f
,
A
z
z
i
d
d
i
n
M
u
h
a
m
m
a
d
Ra
z
a
li
,
K
a
sru
l
A
b
d
u
l
Ka
rim
,
T
o
le
S
u
ti
k
n
o
,
a
n
d
A
u
z
a
n
i
Jid
in
,
“
A
Co
n
c
e
p
t
o
f
V
ir
tu
a
l
-
F
l
u
x
Dire
c
t
P
o
w
e
r
Co
n
tro
l
o
f
A
C
-
DC
Co
n
v
e
rter
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m (
IJ
PE
DS
)
,
v
o
l
.
8
,
n
o
.
4
,
p
p
.
1
1
7
6
-
1
7
8
4
,
De
c
2
0
1
7
.
[1
1
]
Zh
a
n
g
,
Y.,
L
i,
Z.
,
Z
h
a
n
g
,
Y.,
X
ie,
W
.
,
P
iao
,
Z.
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n
d
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,
C.
,
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rf
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m
p
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t
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M
Re
c
ti
f
ier
w
it
h
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im
p
le
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lcu
latio
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,”
IEE
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ra
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ti
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s
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l.
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0
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3
.
[1
2
]
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ji
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n
g
,
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a
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o
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Ya
n
g
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d
Jia
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iao
,
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8
.
[1
3
]
J.
Hu
,
J.
Z
h
u
,
a
n
d
D.G
.
Do
rre
ll
,
“
In
-
De
p
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0
1
4
.
[1
4
]
A
.
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.
Ra
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li
,
M
.
A
.
Ra
h
m
a
n
,
“
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m
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n
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l
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si
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re
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P
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se
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Re
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ti
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ier
Us
in
g
Dire
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o
w
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r
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tro
l,
”
in
In
ter
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ti
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l
El
e
c
tric M
a
c
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Dr
ive
s Co
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e
(
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DC
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,
p
p
.
1
6
0
3
-
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6
0
8
,
2
0
1
1
.
[1
5
]
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a
p
a
n
,
“
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Re
v
ie
w
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c
t
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p
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to
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rid
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c
ted
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W
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C
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v
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,
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o
.
4
,
p
p
.
8
4
1
–
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4
9
,
2
0
1
5
.
[1
6
]
Y.
Zh
a
n
g
,
J.
Jia
o
,
a
n
d
J.
L
iu
,
“
Dire
c
t
p
o
w
e
r
c
o
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tro
l
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f
P
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M
re
c
ti
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iers
w
it
h
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li
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n
d
u
c
tan
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id
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t
if
ica
ti
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n
d
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n
b
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la
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d
a
n
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d
isto
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tw
o
rk
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o
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it
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o
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,
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EE
E
T
ra
n
s.
P
o
w
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r
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tro
n
.
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o
l.
3
4
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o
.
1
2
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p
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5
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4
–
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2
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3
7
,
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c
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2
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1
9
.
[1
7
]
Nia
n
,
H.,
S
h
e
n
,
Y.,
Ya
n
g
,
H.
,
a
n
d
Qu
a
n
,
Y.,
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lex
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le
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rid
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n
n
e
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ti
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h
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iq
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ti
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n
s
Ba
se
d
o
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c
t
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tr
o
l
,”
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a
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ti
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n
d
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st
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Ap
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n
s
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51
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2
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1
5
.
[1
8
]
S
u
h
,
Y.,
a
n
d
L
ip
o
,
T
.
A
.
,
“
M
o
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ly
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n
d
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C/DC
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U
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lan
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rk
,
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[1
9
]
X
iao
,
P
.
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o
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,
K.A
.
,
a
n
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V
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,
G
.
K.,
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u
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Re
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re
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e
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ra
m
e
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se
d
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o
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re
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h
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se
P
W
M
Bo
o
st
Re
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ti
f
iers
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n
d
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r
Un
b
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lan
c
e
d
a
n
d
Disto
rted
In
p
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t
Co
n
d
it
io
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s
,”
IEE
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ra
n
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c
tro
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l.
2
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4
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p
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2
0
0
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7
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.
[2
0
]
Nia
n
,
H.,
S
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n
g
,
Y.,
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,
P
.
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n
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He
,
Y.,
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p
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Dire
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ra
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g
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ra
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G
rid
Vo
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g
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Un
b
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lan
c
e
,”
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2
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[2
1
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Zh
a
n
g
,
Y.,
a
n
d
Qu
,
C.
,
“
M
o
d
e
l
P
re
d
ictiv
e
Dire
c
t
P
o
w
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r
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n
tro
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f
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W
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Re
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ti
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iers
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r
Un
b
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l
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n
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Ne
tw
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n
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it
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n
s,”
IEE
E
T
ra
n
sa
c
ti
o
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s
o
n
I
n
d
u
stria
l
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e
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tro
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o
l.
6
2
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o
.
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p
p
.
4
0
1
1
–
4
0
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2
,
2
0
1
5
.
[2
2
]
Im
a
d
M
e
rz
o
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k
a
n
d
M
o
h
a
m
e
d
Lo
m
a
n
e
Be
n
d
a
a
s,
“
I
m
p
ro
v
e
d
Dire
c
t
P
o
w
e
r
Co
n
tr
o
l
f
o
r
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-
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e
v
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AC/DC
Co
n
v
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u
n
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e
r
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b
a
l
a
n
c
e
d
a
n
d
/
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r
ted
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o
l
tag
e
S
o
u
rc
e
Co
n
d
it
io
n
s
,
”
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u
rk
ish
J
o
u
rn
a
l
o
f
El
e
c
trica
l
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g
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n
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g
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mp
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ter
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s
,
v
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l.
2
4
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p
p
.
1
8
4
7
-
1
8
6
2
,
2
0
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6
.
[2
3
]
M
e
rz
o
u
k
I,
Be
n
d
a
a
s
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L
,
G
a
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f
a
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A
,
a
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d
Riza
o
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M
.
,
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p
ro
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d
Dire
c
t
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f
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lev
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C
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d
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so
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it
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o
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s
,”
1
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n
ter
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ti
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l
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o
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Po
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tro
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a
n
d
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h
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ir A
p
p
li
c
a
ti
o
n
,
N
o
v
2
0
1
3
.
[2
4
]
Yo
n
g
c
h
a
n
g
Zh
a
n
g
,
Zetin
g
W
a
n
g
,
Jia
n
Jia
o
,
a
n
d
Jie
L
iu
,
“
G
rid
-
v
o
lt
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g
e
S
e
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so
rles
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o
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re
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Co
n
tro
l
o
f
T
h
re
e
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P
h
a
se
P
W
M
Re
c
ti
f
ier
u
n
d
e
r
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b
a
lan
c
e
d
a
n
d
Dist
o
rted
G
rid
Vo
lt
a
g
e
s
”
IEE
E
T
ra
n
sa
c
ti
o
n
in
Po
we
r
El
e
c
tro
n
ic
,
20
19
.
[2
5
]
F
.
Bra
d
a
sc
h
ia,
J.
P
.
A
rru
d
a
,
H.
E.
P
.
S
o
u
z
a
,
G
.
M
.
S
.
A
z
e
v
e
d
o
,
F
.
A
.
S
.
Ne
v
e
s,
a
n
d
M
.
C.
Ca
v
a
lca
n
ti
,
“
A
M
e
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f
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Ex
trac
ti
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n
d
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tal
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Vo
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s
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im
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M
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ra
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o
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m
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ti
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n
s,”
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P
o
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r E
lec
tro
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ic
s S
p
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st C
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,
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l.
1
,
p
p
.
1
1
1
5
–
1
1
2
1
,
Ju
n
e
20
0
8.
[2
6
]
B.
Ka
h
ia,
A
.
Bo
u
a
f
i
a
,
a
n
d
A
.
Ch
a
o
u
i,
“
Dire
c
t
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o
w
e
r
Co
n
tro
l
o
f
T
h
re
e
-
Lev
e
l
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W
M
Re
c
ti
f
ier
u
n
d
e
r
Un
b
a
lan
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e
d
a
n
d
h
a
rm
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n
ica
ll
y
Disto
rted
G
rid
Vo
lt
a
g
e
Co
n
d
it
i
o
n
s,”
IE
EE
T
r
a
n
sa
c
ti
o
n
P
o
we
r E
lec
tro
n
ic
,
20
15
.
[2
7
]
M.
M
a
li
n
o
w
sk
i,
G
.
M
a
rq
u
e
s,
M
.
Cich
o
w
las
,
a
n
d
M
.
P
.
Ka
z
m
ier
k
o
w
s
k
i,
“
Ne
w
d
irec
t
p
o
we
r
c
o
n
tro
l
o
f
th
re
e
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p
h
a
se
p
wm
b
o
o
st
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ti
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iers
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n
d
e
r
d
ist
o
rted
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d
im
b
a
lan
c
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d
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v
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lt
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g
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c
o
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d
it
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o
n
s,”
IE
EE
I
n
ter
n
a
ti
o
n
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S
y
mp
o
si
u
m
o
n
In
d
u
stria
l
El
e
c
tro
n
ics
,
p
p
.
4
3
8
–
4
4
3
,
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u
n
e
2
0
0
3
.
[2
8
]
H.
Ya
n
g
,
Y.
Zh
a
n
g
,
J.
L
ian
g
,
J
.
G
a
o
,
P
.
D.
W
a
lk
e
r,
a
n
d
N.
Zh
a
n
g
,
“
S
li
d
i
n
g
-
M
o
d
e
Ob
se
rv
e
r
Ba
se
d
V
o
lt
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g
e
-
S
e
n
so
rles
s
M
o
d
e
l
P
re
d
ictiv
e
P
o
w
e
r
Co
n
tro
l
o
f
P
W
M
Re
c
ti
f
ier
Un
d
e
r
Un
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[2
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In
ter
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Dr
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[3
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]
No
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a
h
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f
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sru
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Ab
d
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rim
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Dire
c
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b
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g
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it
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,”
In
ter
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o
u
rn
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f
El
e
c
trica
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mp
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(
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,
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c
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1
9
.
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