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n
g
r
id
,
alo
n
g
w
it
h
h
ar
m
o
n
ics i
n
tr
o
d
u
c
ed
in
th
e
li
n
es.
Ho
w
e
v
er
th
e
f
ilter
co
n
n
ec
ted
to
S
T
A
T
C
OM
r
ed
u
ce
s
th
e
h
ar
m
o
n
ics
to
a
ce
r
tain
ex
te
n
t.
Fu
r
th
er
h
ar
m
o
n
ics
in
tr
o
d
u
ce
d
b
y
t
h
e
VSC
ca
n
b
e
r
ed
u
ce
d
b
y
i
n
cr
ea
s
in
g
t
h
e
n
u
m
b
er
le
v
el
s
[
8
]
o
f
t
h
e
co
n
v
er
ter
.
I
n
th
i
s
p
ap
er
w
e
i
n
tr
o
d
u
ce
a
m
u
lti
-
le
v
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
co
n
v
er
ter
w
it
h
s
i
x
H
-
b
r
id
g
es
[
6
]
as
th
e
n
u
m
b
er
o
f
le
v
el
s
ar
e
f
o
r
m
u
lated
as
2
n
+1
w
h
er
e,
n
=
n
u
m
b
er
o
f
ca
s
ca
d
ed
H
-
b
r
id
g
es.
T
h
e
m
o
d
el
o
f
th
e
m
u
lti
-
le
v
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
co
n
v
er
ter
s
h
o
w
n
i
n
Fi
g
u
r
e
2.
E
ac
h
H
-
b
r
id
g
e
co
m
p
r
i
s
es
o
f
a
D
C
ca
p
ac
ito
r
w
h
ic
h
i
s
co
n
s
id
er
ed
as
t
h
e
r
ea
ctiv
e
p
o
w
er
co
m
p
en
s
atio
n
ele
m
e
n
t.
P
W
M
[
4
,
5
]
g
en
er
ati
o
n
r
ef
er
e
n
ce
w
a
v
ef
o
r
m
s
to
o
p
er
ate
th
e
H
-
b
r
id
g
e
s
w
itc
h
es a
r
e
s
h
o
w
n
i
n
Fi
g
u
r
e
3
.
Fig
u
r
e
2
.
Mu
lti le
v
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
co
n
v
er
ter
o
f
o
n
e
p
h
ase
Fig
u
r
e
3
.
R
ef
er
en
ce
w
a
v
e
f
o
r
m
s
f
o
r
1
3
-
lev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
co
n
v
er
ter
2.
P
RE
DIC
T
I
VE
CO
N
T
RO
L
AL
G
O
RI
T
H
M
T
h
e
co
n
tr
o
ller
o
f
th
e
ST
A
T
C
OM
p
r
ed
icts
th
e
o
u
tp
u
t c
u
r
r
en
t o
f
th
e
co
n
v
er
ter
an
d
g
e
n
er
ate
p
u
ls
es
f
o
r
th
e
p
o
w
er
elec
tr
o
n
ic
s
d
ev
ices.
P
r
ed
ictiv
e
co
n
tr
o
ller
h
as c
o
s
t f
u
n
ctio
n
o
p
ti
m
izatio
n
alg
o
r
it
h
m
w
h
er
e
th
e
s
y
s
te
m
h
as to
b
e
o
p
er
ated
in
a
d
is
cr
ete
ti
m
e
d
o
m
ai
n
.
W
ith
r
e
s
p
ec
t to
d
is
cr
ete
ti
m
e
T
s
[
3
]
v
alu
es a
r
e
g
e
n
er
ated
f
o
r
iter
atio
n
‘
k
+1
’
,
w
h
ic
h
is
t
h
e
p
r
ed
ictiv
e
v
alu
e
o
f
th
e
iter
ati
o
n
‘
k
’
[
6
]
.
T
h
e
d
is
cr
ete
ch
an
g
e
in
th
e
p
r
ese
n
t
an
d
n
ex
t iter
atio
n
ca
n
b
e
g
iv
e
n
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i S
y
s
t,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
2
0
1
8
:
150
–
1
5
6
152
dy
dt
⩳
y
(
k
+
1
)
−
y
(
k
)
Ts
(
1
)
T
h
e
‘
k
+1
’
p
r
ed
ictiv
e
o
u
tp
u
t c
u
r
r
en
t o
f
t
h
e
co
n
v
er
ter
is
g
i
v
e
n
as
Io (
k
+1
)
=
[
(
)
−
(
)
]
+
(
1
−
∗
)
∗
(
)
(
2
)
W
h
er
e,
Vx
n
(
k
)
is
th
e
p
h
ase
v
o
ltag
e
f
o
r
th
e
p
r
ese
n
t iter
atio
n
an
d
Vo
(
k
)
is
g
iv
e
n
as
Vo
=
Vxn
−
(
R
e
q
∗
io
)
−
L
e
q
(
d
i
o
dt
)
(
3
)
W
ith
th
e
ab
o
v
e
c
u
r
r
en
ts
p
r
ed
ictio
n
o
f
all
t
h
e
th
r
ee
p
h
a
s
es t
h
e
co
s
t f
u
n
ctio
n
o
p
ti
m
izatio
n
is
(
+
1
)
=
[
∗
(
+
1
)
−
(
+
1
)
]
2
+
[
∗
(
+
1
)
−
(
+
1
)
]
2
+
[
∗
(
+
1
)
−
(
+
1
)
]
2
+
[
∗
(
+
1
)
−
(
+
1
)
]
2
(
4
)
T
h
e
g
en
er
ated
r
e
f
er
en
ce
wav
ef
o
r
m
i
s
co
n
s
id
er
ed
as
f
u
n
d
a
m
en
tal
w
a
v
e
f
o
r
m
co
m
p
ar
ed
w
it
h
tr
ian
g
u
lar
ca
r
r
ier
w
a
v
ef
o
r
m
s
to
g
e
n
er
ate
P
W
M
s
ig
n
als.
T
h
e
b
lo
ck
d
iag
r
a
m
o
f
t
h
e
p
r
o
p
o
s
ed
p
r
ed
ictiv
e
co
n
tr
o
ller
[
5
]
to
co
n
tr
o
l th
e
r
ea
ctiv
e
p
o
w
er
o
u
tp
u
t o
f
t
h
e
ST
A
T
C
OM
is
s
h
o
w
n
i
n
Fi
g
u
r
e
4.
Fig
u
r
e
4.
P
r
o
p
o
s
ed
p
r
ed
ictiv
e
co
n
tr
o
ller
s
ch
e
m
e
T
h
e
cu
r
r
en
t
r
ef
er
en
ce
(
io
*
)
g
e
n
er
ato
r
b
lo
ck
d
iag
r
a
m
is
s
h
o
wn
in
Fig
u
r
e
5
w
i
th
a
f
ee
d
b
ac
k
o
f
s
o
u
r
ce
v
o
ltag
e
an
d
lo
ad
c
u
r
r
en
t
f
r
o
m
t
h
e
d
is
tr
ib
u
tio
n
g
r
id
.
V
dc
i
s
t
h
e
co
m
b
i
n
ed
D
C
v
o
lta
g
e
o
f
t
h
e
s
i
x
ca
p
ac
ito
r
s
co
n
n
ec
ted
o
n
t
h
e
DC
s
id
e
o
f
t
h
e
H
-
b
r
id
g
e
s
.
Fig
u
r
e
5.
C
u
r
r
en
t r
e
f
er
en
ce
g
e
n
er
ato
r
f
o
r
p
r
ed
ictiv
e
co
n
tr
o
ller
3.
SWI
T
CH
F
AUL
T
I
D
E
N
T
I
F
I
CAT
I
O
N
AND
M
I
T
I
G
A
T
I
O
N
M
O
DE
L
I
N
G
As
r
ef
er
e
n
ce
to
th
e
p
r
ev
io
u
s
s
ec
tio
n
I
th
e
n
u
m
b
er
o
f
ca
s
ca
d
ed
H
-
b
r
id
g
e
co
n
v
er
ter
s
ar
e
s
ix
w
it
h
ea
c
h
co
n
v
er
ter
co
m
p
r
is
i
n
g
o
f
f
o
u
r
p
o
w
er
elec
tr
o
n
ic
d
ev
ices
(
I
G
B
T
)
[
9
]
.
T
h
e
f
o
u
r
s
w
i
tch
e
s
ar
e
lab
eled
as
S1
–
S4
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
er
E
lectr
o
n
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
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8
694
E
cc
en
tr
ic
o
p
era
tio
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o
f
S
TATC
OM u
s
in
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ed
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C
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n
tr
o
ll
er
(
K
.
V
a
r
a
la
ksh
mi
)
153
w
h
er
e
S1
S4
a
n
d
S2
S3
o
p
er
ate
s
i
m
u
ltan
eo
u
s
l
y
ie.
,
t
h
e
s
a
m
e
P
W
M
s
ig
n
al
ar
e
f
ed
to
th
e
s
w
itc
h
e
s
S1
S4
a
n
d
S2
S3
.
A
s
i
n
g
le
H
-
b
r
id
g
e
w
it
h
f
o
u
r
I
GB
T
s
(
S1
-
S4
)
ca
n
b
e
s
ee
n
b
elo
w
in
Fig
u
r
e
6
.
E
ac
h
leg
co
n
tain
s
2
4
I
GB
T
s
an
d
t
h
e
to
tal
n
u
m
b
er
o
f
s
w
itc
h
es
i
n
ST
A
T
C
OM
is
7
2
,
w
h
er
e
t
h
e
r
i
s
k
o
f
f
a
u
lt
o
n
a
n
y
s
w
i
tch
is
m
o
r
e.
T
h
e
f
au
lt
s
o
n
a
s
w
itc
h
ca
n
b
e
eith
er
o
p
en
cir
cu
i
t
o
r
s
h
o
r
t
cir
cu
it,
w
h
ic
h
m
a
y
a
f
f
ec
t
th
e
o
p
er
atio
n
o
f
ST
A
T
C
OM
r
esu
l
tin
g
i
n
d
is
r
u
p
tio
n
s
i
n
t
h
e
g
r
id
p
ar
a
m
e
ter
s
.
T
h
e
f
au
lt
y
s
w
itc
h
h
as
to
b
e
r
e
p
lace
d
o
r
th
e
en
tire
H
-
b
r
id
g
e
h
a
s
to
b
e
b
y
p
ass
ed
[
1
0
,
1
1
]
to
elim
i
n
ate
th
e
f
a
u
lt[1
2
]
.
R
ath
er
p
r
o
v
id
in
g
alter
n
ate
s
w
itc
h
to
ea
ch
an
d
ev
er
y
s
w
i
tch
w
h
ic
h
in
cr
ea
s
e
t
h
e
co
m
p
lex
i
t
y
o
f
t
h
e
d
ev
ice,
s
o
b
y
p
ass
i
n
g
th
e
H
-
b
r
id
g
e
w
i
th
a
b
y
p
ass
s
w
i
tch
is
m
o
r
e
r
eliab
le
an
d
f
lex
ib
le.
T
h
e
b
elo
w
Fi
g
u
r
e
7
is
t
h
e
d
iag
r
a
m
o
f
t
h
e
H
-
b
r
id
g
e
w
ith
a
b
y
p
a
s
s
s
w
i
tch
(
I
GB
T
)
.
Fig
u
r
e
7
.
H
-
b
r
id
g
e
w
it
h
b
y
p
as
s
I
GB
T
s
w
itc
h
Fig
u
r
e
8
.
C
o
n
tr
o
ller
to
g
en
er
at
e
s
ig
n
al
f
o
r
t
h
e
b
y
p
ass
s
w
itc
h
es
T
h
e
s
ig
n
al
to
th
e
b
y
p
ass
s
witch
[
9
]
is
g
en
er
ated
w
it
h
f
e
ed
b
ac
k
o
f
H
-
b
r
id
g
e
DC
s
id
e
ca
p
ac
ito
r
v
o
ltag
e.
A
r
ela
y
is
s
et
w
it
h
i
n
an
o
p
er
atin
g
r
an
g
e
o
f
ca
p
ac
ito
r
v
o
ltag
e,
w
it
h
th
e
c
h
an
g
e
in
v
o
ltag
e
o
f
th
e
ca
p
ac
ito
r
d
u
r
in
g
t
h
e
o
p
en
cir
c
u
it
o
r
s
h
o
r
t
cir
cu
it
f
au
lts
t
h
e
r
ela
y
o
p
er
ates
an
d
s
w
i
tch
e
s
O
N
th
e
b
y
p
as
s
s
w
itch
to
s
u
r
p
ass
th
e
f
au
lt
y
[
1
0
,
1
1
]
H
-
b
r
id
g
e
w
it
h
eli
m
in
at
io
n
o
f
f
au
lt
in
t
h
e
ST
A
T
C
OM
.
T
h
e
b
elo
w
Fi
g
u
r
e
8
is
th
e
f
ee
d
b
ac
k
s
i
g
n
a
l g
e
n
er
ato
r
f
o
r
th
e
b
y
p
a
s
s
s
w
itc
h
.
4.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
I
t
is
im
p
o
r
tan
t
to
d
esig
n
a
s
o
p
h
is
ticated
co
n
tr
o
l
to
p
r
o
d
u
c
e
a
f
au
lt
-
to
ler
an
t
ST
A
T
C
OM
as
h
i
g
h
er
lev
el
co
n
v
er
ter
s
ar
e
u
s
ed
.
A
f
au
lt
y
p
o
w
er
ce
ll
i
n
a
ca
s
ca
d
ed
H
-
B
r
id
g
e
ST
A
T
C
OM
[
1
2
]
ca
n
p
o
ten
tiall
y
ca
u
s
e
s
w
itc
h
m
o
d
u
le
s
to
e
x
p
lo
d
e
lead
in
g
to
t
h
e
f
a
u
lt
co
n
d
it
io
n
s
s
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.
RE
F
E
R
E
NC
E
S
[1
]
C.
-
H.
L
iu
&
Y.
-
Y.
Hs
u
,
“
De
sig
n
o
f
a
se
l
f
-
tu
n
in
g
P
I
c
o
n
tro
ll
e
r
f
o
r
a
S
TA
TCOM
u
sin
g
p
a
rti
c
le sw
a
r
m
o
p
ti
m
iza
ti
o
n
,
”
IEE
E
T
ra
n
s.
I
n
d
.
El
e
c
tro
n
.,
v
o
l
/i
ss
u
e
:
5
7
(2
),
7
0
2
–
7
1
5
,
F
e
b
.
2
0
1
0
.
[2
]
V
e
n
k
a
ta
Ya
ra
m
a
su
,
M
a
rc
o
Riv
e
ra
,
Bin
W
u
,
&
Jo
se
.
Ro
d
rig
u
e
z
,
“
M
o
d
e
l
P
re
d
ictiv
e
Cu
rre
n
t
Co
n
tro
l
o
f
Tw
o
-
L
e
v
e
l
F
o
u
r
-
L
e
g
In
v
e
rters
—
P
a
rt
I:
C
o
n
c
e
p
t,
A
lg
o
rit
h
m
,
a
n
d
S
im
u
lati
o
n
A
n
a
ly
sis,”
IEE
E
T
ra
n
s.
P
o
we
r
El
e
c
tro
n
.,
v
o
l/
issu
e
:
2
8
(7
)
,
3
4
5
9
–
3
4
6
2
,
J
u
l
y
2
0
1
3
.
[3
]
J.
Ro
c
a
b
e
rt,
A
.
L
u
n
a
,
F
.
Blaa
b
jerg
,
&
P
.
Ro
d
r
ig
u
e
z
,
“
Co
n
tro
l
o
f
p
o
w
e
r
c
o
n
v
e
rters
in
A
C
m
icro
g
rid
s,”
IEE
E
T
ra
n
s
.
Po
we
r E
lec
tro
n
.
,
v
o
l/
issu
e
:
2
7
(1
1
),
4
7
3
4
–
4
7
4
9
,
N
o
v
.
2
0
1
2
.
[4
]
V
.
Kh
a
d
k
ik
a
r,
A
.
Ch
a
n
d
ra
,
&
B.
S
in
g
h
,
“
Dig
it
a
l
sig
n
a
l
p
ro
c
e
ss
o
r
im
p
l
e
m
e
n
tatio
n
a
n
d
p
e
rf
o
rm
a
n
c
e
e
v
a
lu
a
ti
o
n
o
f
sp
li
t
c
a
p
a
c
it
o
r,
f
o
u
r
-
leg
a
n
d
th
re
e
h
-
b
rid
g
e
-
b
a
se
d
th
re
e
-
p
h
a
se
f
o
u
r
-
w
ire
sh
u
n
t
a
c
ti
v
e
fi
lt
e
rs,”
Po
we
r
El
e
c
tro
n
.
,
IET
,
v
o
l/
issu
e
:
4
(
4
),
4
6
3
–
4
7
0
,
A
p
r.
2
0
1
1
.
[5
]
R.
d
e
A
r
a
u
jo
Rib
e
iro
,
C.
d
e
A
z
e
v
e
d
o
,
&
R.
d
e
S
o
u
sa
,
“
A
ro
b
u
s
t
a
d
a
p
ti
v
e
c
o
n
tro
l
stra
teg
y
o
f
a
c
ti
v
e
p
o
w
e
r
fi
lt
e
rs
f
o
r
p
o
w
e
r
-
fa
c
to
r
c
o
rre
c
ti
o
n
,
h
a
rm
o
n
i
c
c
o
m
p
e
n
sa
ti
o
n
,
a
n
d
b
a
lan
c
in
g
o
f
n
o
n
li
n
e
a
r
lo
a
d
s,”
IEE
E
T
r
a
n
s.
P
o
we
r
El
e
c
tro
n
.,
v
o
l/
issu
e
:
2
7
(2
),
7
1
8
–
7
3
0
,
F
e
b
.
2
0
1
2
.
[6
]
P
.
Co
rtes
,
A
.
W
il
so
n
,
S
.
Ko
u
ro
,
J.
Ro
d
rig
u
e
z
,
&
H.
A
b
u
-
Ru
b
,
“
M
o
d
e
l
p
re
d
ictiv
e
c
o
n
tr
o
l
o
f
m
u
lt
il
e
v
e
l
c
a
sc
a
d
e
d
H
-
b
rid
g
e
in
v
e
rters
,
”
IEE
E
T
ra
n
s.
In
d
.
El
e
c
tro
n
.,
v
o
l/
issu
e
:
5
7
(
8
),
2
6
9
1
–
2
6
9
9
,
A
u
g
.
2
0
1
0
.
[7
]
S
a
n
th
o
sh
T
K
&
G
o
v
in
d
a
ra
ju
C,
“
De
v
e
lo
p
m
e
n
t
o
f
P
re
d
ictiv
e
Cu
rre
n
t
Co
n
tr
o
ll
e
r
f
o
r
M
u
l
ti
-
P
o
rt
DC/
DC
Co
n
v
e
rter”
,
in
IJ
PE
DS
,
v
o
l/
issu
e
:
6
(
4
),
p
p
.
6
8
3
-
6
9
2
,
De
c
e
m
b
e
r
2
0
1
5
.
[8
]
F
.
F
i
lh
o
,
Y.
Ca
o
,
&
L
.
M
.
T
o
l
b
e
rt,
“
1
1
-
lev
e
l
c
a
sc
a
d
e
d
H
-
b
rid
g
e
g
rid
-
ti
e
d
in
v
e
rte
r
in
ter
fa
c
e
wit
h
s
o
la
r
p
a
n
e
ls,
”
i
n
P
r
o
c
.
IEE
E
A
P
EC
Ex
p
o
.
,
9
6
8
–
9
7
2
,
F
e
b
.
2
0
1
0
[9
]
C.
D.
T
o
w
n
se
n
d
,
T
.
J.
S
u
m
m
e
rs,
&
R.
E.
Be
tz,
“
Co
n
tro
l
a
n
d
mo
d
u
l
a
ti
o
n
sc
h
e
me
fo
r
a
c
a
sc
a
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ro
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.
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,
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sa
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a
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e
:
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(
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t
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,
in
IJ
PE
D
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:
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p
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h
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[1
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K.V
a
ra
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sh
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ra
si
m
h
a
m
.
R.
L
&
G
.
T
u
las
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Ra
m
d
a
s
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e
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lys
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sc
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d
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g
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d
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rin
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switch
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u
lt
,
”
in
P
r
o
c
.
IE
EE
ICIC,
5
3
5
-
5
3
9
,
M
a
y
2
0
1
5
.
`
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