I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
s
(
I
J
P
E
DS
)
Vo
l.
1
2
,
No
.
1
,
Ma
r
2
0
2
1
,
p
p
.
325
~
3
3
3
I
SS
N:
2088
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
ijp
ed
s
.
v
1
2
.i
1
.
pp
3
25
-
333
325
J
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ur
na
l ho
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e
:
h
ttp
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De
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Ah
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Da
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Yo
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y:
R
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J
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20
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ev
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J
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1
9
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2
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Acc
ep
ted
Feb
5
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2
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21
Th
is
p
a
p
e
r
re
c
o
m
m
e
n
d
s
th
e
u
s
e
o
f
g
ra
ss
h
o
p
p
e
r
o
p
t
imiz
a
ti
o
n
a
lg
o
rit
h
m
(G
OA
),
a
n
a
tu
re
-
in
sp
ired
o
p
ti
m
i
z
a
ti
o
n
a
lg
o
rit
h
m
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fo
r
o
p
ti
m
izin
g
sw
it
c
h
in
g
-
a
n
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le
a
p
p
li
e
d
t
o
c
a
sc
a
d
e
d
H
-
b
rid
g
e
m
u
lt
i
lev
e
l
i
n
v
e
rter
(CHBML
I).
S
witch
in
g
a
n
g
les
a
re
se
lec
ted
b
a
se
d
o
n
th
e
m
i
n
imu
m
v
a
l
u
e
o
f
th
e
o
b
jec
ti
v
e
fu
n
c
ti
o
n
fo
rm
u
late
d
u
si
n
g
t
h
e
c
o
n
c
e
p
t
o
f
se
lec
ti
v
e
h
a
rm
o
n
ic
m
in
imiz
a
ti
o
n
p
u
lse
wi
d
t
h
m
o
d
u
latio
n
(
S
HMP
WM
)
tec
h
n
i
q
u
e
.
M
ATLAB/S
imu
li
n
k
-
P
S
I
M
d
y
n
a
m
ic
c
o
-
sim
u
latio
n
c
o
n
d
u
c
te
d
o
n
a
3
-
p
h
a
se
9
-
lev
e
l
CHBM
LI
sh
o
ws
t
h
a
t
th
e
CHBML
I
c
o
n
tro
ll
e
d
u
sin
g
G
O
A
d
e
riv
e
d
sw
it
c
h
i
n
g
-
a
n
g
le
i
s
a
b
le
t
o
re
sp
o
n
d
to
v
a
ry
in
g
m
o
d
u
lati
o
n
in
d
e
x
d
e
m
a
n
d
a
n
d
sy
n
th
e
siz
e
a
n
A
C
sta
irca
se
o
u
t
p
u
t
v
o
lt
a
g
e
wa
v
e
fo
rm
with
th
e
d
e
sire
d
f
u
n
d
a
m
e
n
tal
h
a
rm
o
n
ic
a
n
d
m
in
imiz
e
d
se
lec
ted
lo
w
-
o
r
d
e
r
h
a
rm
o
n
ics
.
Co
m
p
a
re
d
t
o
Ne
wto
n
Ra
p
h
so
n
(NR)
tec
h
n
iq
u
e
,
G
OA
is
a
b
le
to
f
in
d
o
p
ti
m
u
m
sw
it
c
h
i
n
g
-
a
n
g
le
s
o
l
u
ti
o
n
s
o
v
e
r
a
wid
e
r
m
o
d
u
latio
n
in
d
e
x
ra
n
g
e
.
Co
m
p
a
re
d
to
G
e
n
e
ti
c
Alg
o
ri
th
m
(G
A),
G
O
A
is
a
b
le
to
fi
n
d
g
l
o
b
a
l
m
i
n
i
m
a
with
h
ig
h
e
r
p
r
o
b
a
b
il
it
y
.
T
h
e
sim
u
latio
n
re
su
lt
s
v
a
li
d
a
te
t
h
e
p
e
rf
o
rm
a
n
c
e
o
f
G
OA
fo
r
sw
it
c
h
i
n
g
-
a
n
g
le
c
a
lcu
latio
n
b
a
se
d
o
n
th
e
c
o
n
c
e
p
t
o
f
S
H
M
P
W
M
.
K
ey
w
o
r
d
s
:
Dy
n
am
ic
s
im
u
latio
n
GA
GOA
Mu
ltil
ev
el
i
n
v
er
ter
NR
SHMP
W
M
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
J
.
H.
L
eo
n
g
Sch
o
o
l o
f
E
lectr
ical
Sy
s
tem
s
E
n
g
in
ee
r
in
g
Un
iv
er
s
ity
Ma
lay
s
ia
Per
lis
0
2
6
0
0
Ar
au
,
Per
lis
,
Ma
lay
s
ia
E
m
ail:
n
ick
.
u
n
im
a
p
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
No
wad
ay
s
,
m
u
ltil
ev
el
in
v
er
t
er
(
ML
I
)
h
as
b
ee
n
ap
p
lied
in
m
ed
iu
m
-
v
o
ltag
e
a
n
d
h
i
g
h
-
p
o
wer
ap
p
licatio
n
s
s
u
ch
as
ac
tiv
e
f
i
lter
s
,
elec
tr
ical
m
o
to
r
d
r
iv
es
an
d
p
h
o
to
v
o
ltaic
g
r
i
d
-
co
n
n
ec
ted
s
y
s
tem
[
1
]
-
[
7
]
.
Mu
ltil
ev
el
in
v
er
ter
h
as
s
ev
er
al
ad
v
an
tag
es
s
u
c
h
as
lo
wer
s
witch
in
g
lo
s
s
es,
lo
wer
v
o
lta
g
e
s
tr
ess
o
n
p
o
wer
s
witch
es,
an
d
lo
wer
elec
tr
o
m
ag
n
etic
in
ter
f
e
r
en
ce
(
E
MI
)
co
m
p
ar
ed
to
two
-
lev
el
h
i
g
h
-
f
r
e
q
u
en
cy
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
PW
M)
in
v
er
ter
[
8
]
,
[
9
]
.
T
h
e
r
e
a
r
e
th
r
ee
m
ain
M
L
I
to
p
o
lo
g
ies
wh
ic
h
a
r
e
d
io
d
e
-
clam
p
ed
,
f
l
y
in
g
ca
p
ac
ito
r
an
d
ca
s
ca
d
e
d
H
-
b
r
id
g
e
[
6
]
.
Am
o
n
g
th
e
m
,
ca
s
ca
d
e
d
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
v
er
ter
(
C
HB
ML
I
)
,
wh
ich
h
as
th
e
b
e
n
ef
its
o
f
f
lex
ib
ilit
y
an
d
m
o
d
u
lar
ity
,
h
as
g
ain
ed
in
cr
ea
s
in
g
atten
tio
n
in
wid
e
r
an
g
e
o
f
ap
p
licatio
n
s
[6
]
,
[
8
]
.
C
HB
ML
I
is
co
n
tr
o
lle
d
b
y
ap
p
ly
in
g
a
s
et
o
f
o
p
tim
u
m
s
witch
in
g
an
g
les
to
s
y
n
t
h
esize
a
n
ea
r
s
in
u
s
o
id
al
s
tair
ca
s
e
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
.
Ho
we
v
er
,
th
e
o
p
tim
u
m
s
witch
in
g
an
g
les
th
at
ca
n
p
r
o
v
i
d
e
an
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
with
lo
w
t
o
tal
h
ar
m
o
n
ic
d
i
s
to
r
tio
n
(
T
HD)
ar
e
n
o
t e
asy
t
o
b
e
d
eter
m
in
ed
[
8
]
,
[
9
]
.
Sev
er
al
m
eth
o
d
s
to
c
o
n
tr
o
l
t
h
e
ML
I
h
av
e
b
ee
n
r
ep
o
r
ted
i
n
th
e
p
ast.
Sin
u
s
o
id
al
PW
M
an
d
s
p
ac
e
v
ec
to
r
PW
M
ar
e
th
e
co
m
m
o
n
h
ig
h
-
f
r
eq
u
en
c
y
PW
M
m
eth
o
d
s
to
co
n
tr
o
l
th
e
ML
I
[
6
]
,
[
1
0
]
.
Ho
we
v
er
,
h
ig
h
s
witch
in
g
lo
s
s
is
th
e
m
ain
d
r
a
wb
ac
k
in
b
o
th
m
eth
o
d
s
.
An
o
t
h
er
m
eth
o
d
is
th
e
f
u
n
d
am
en
ta
l
-
f
r
eq
u
e
n
cy
PW
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
325
–
3
3
3
326
m
eth
o
d
wh
ic
h
h
as
lo
wer
s
witch
in
g
lo
s
s
es
[
6
]
.
Op
tim
al
m
i
n
im
izatio
n
o
f
to
tal
h
ar
m
o
n
ic
d
i
s
to
r
tio
n
(
OM
T
HD)
is
o
n
e
o
f
th
e
f
u
n
d
a
m
en
tal
-
f
r
e
q
u
en
cy
PW
M
m
eth
o
d
th
at
ca
n
m
in
im
ize
th
e
T
HD
[
1
1
]
.
H
o
wev
er
,
it
ca
n
n
o
t
g
u
ar
an
tee
th
at
t
h
e
lo
w
-
o
r
d
e
r
h
ar
m
o
n
ics
ar
e
m
in
im
ized
.
Selectiv
e
h
ar
m
o
n
ic
m
i
n
im
i
za
tio
n
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
SHMPW
M)
is
t
h
e
co
m
m
o
n
f
u
n
d
a
m
en
tal
-
f
r
e
q
u
en
cy
PW
M
m
eth
o
d
th
at
ca
n
b
e
em
p
lo
y
e
d
to
o
b
tain
th
e
o
p
tim
u
m
s
witch
in
g
an
g
l
es
with
o
u
t
h
av
in
g
th
e
p
r
o
b
lem
o
f
h
i
g
h
s
witch
in
g
lo
s
s
es
[
1
2
]
.
SHMPW
M
ca
n
m
in
im
ize
th
e
l
o
w
-
o
r
d
er
h
ar
m
o
n
ics
an
d
m
ain
tain
th
e
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
t
at
t
h
e
s
am
e
tim
e.
I
n
t
h
is
m
eth
o
d
,
a
s
et
o
f
n
o
n
-
lin
ea
r
tr
an
s
ce
n
d
en
tal
e
q
u
atio
n
s
o
f
th
e
s
elec
ted
h
a
r
m
o
n
ics
t
h
at
co
n
s
is
t
o
f
tr
ig
o
n
o
m
etr
ic
ter
m
s
is
to
b
e
s
o
lv
ed
.
New
to
n
R
ap
h
s
o
n
(
NR
)
tech
n
iq
u
e
is
a
co
m
m
o
n
iter
ativ
e
m
ath
em
ati
ca
l
m
eth
o
d
u
s
ed
t
o
s
o
lv
e
th
e
eq
u
atio
n
s
[
1
3
]
.
Ho
wev
er
,
NR
is
h
ig
h
ly
d
ep
en
d
e
n
t
o
n
g
o
o
d
in
itial
s
witch
in
g
-
an
g
le
g
u
ess
es
an
d
it
o
f
ten
p
r
o
v
id
es
s
o
lu
tio
n
f
o
r
a
ce
r
tain
r
an
g
e
o
f
m
o
d
u
latio
n
i
n
d
ex
o
n
ly
.
An
o
th
er
tec
h
n
iq
u
e
to
s
o
lv
e
th
e
n
o
n
-
lin
ea
r
eq
u
atio
n
s
is
b
y
c
o
n
v
er
tin
g
th
e
n
o
n
-
lin
ea
r
eq
u
atio
n
s
to
p
o
l
y
n
o
m
ial
eq
u
atio
n
s
an
d
th
en
s
o
lv
in
g
th
e
m
u
s
in
g
r
esu
ltan
t
th
eo
r
y
(
R
T
)
[
1
4
]
-
[
1
6
]
.
W
h
ile
th
is
tec
h
n
iq
u
e
ca
n
p
r
o
v
id
e
a
wid
e
r
a
n
g
e
o
f
s
o
lu
tio
n
s
,
it
is
co
m
p
u
tatio
n
ally
co
m
p
lex
an
d
tim
e
-
co
n
s
u
m
i
n
g
f
o
r
h
ig
h
-
d
i
m
en
s
io
n
s
witch
in
g
-
a
n
g
le
ca
lc
u
latio
n
.
Hen
ce
,
NR
an
d
R
T
ar
e
r
ath
er
d
if
f
icu
lt
to
b
e
im
p
lem
en
ted
.
An
o
th
er
m
et
h
o
d
to
o
p
tim
ize
th
e
ML
I
s
wit
ch
in
g
an
g
les
is
b
y
em
p
lo
y
in
g
s
o
f
t
-
c
o
m
p
u
tin
g
ap
p
r
o
ac
h
[
1
7
]
.
T
h
e
ad
v
a
n
tag
e
o
f
s
o
f
t
-
co
m
p
u
tin
g
ap
p
r
o
ac
h
is
th
at
th
e
alg
o
r
ith
m
u
s
u
ally
d
o
es
n
o
t
r
eq
u
ir
e
a
g
o
o
d
g
u
ess
o
f
i
n
itial
s
witch
in
g
an
g
les.
Gen
etic
alg
o
r
ith
m
(
G
A)
,
wh
ich
is
a
well
-
k
n
o
wn
s
o
f
t
-
co
m
p
u
tin
g
m
eth
o
d
,
h
as
b
ee
n
ap
p
lied
s
u
cc
ess
f
u
lly
in
a
wid
e
r
an
g
e
o
f
ap
p
licatio
n
s
,
e.
g
.
n
etwo
r
k
r
o
u
tin
g
a
n
d
im
a
g
e
p
r
o
ce
s
s
in
g
[
1
8
]
.
I
t
h
as
also
b
ee
n
em
p
lo
y
ed
to
o
p
tim
ize
th
e
s
witch
in
g
a
n
g
les
o
f
ML
I
[
1
9
]
.
Ho
wev
er
,
GA
is
ea
s
ily
tr
ap
p
ed
in
th
e
lo
ca
l
o
p
tim
a
d
u
e
to
th
e
ab
s
en
ce
o
f
ex
p
lo
r
ati
o
n
an
d
ex
p
l
o
itatio
n
ab
ili
ties
.
T
h
u
s
,
GA
h
as lo
wer
p
r
o
b
a
b
ilit
y
to
f
in
d
th
e
g
l
o
b
al
m
in
im
a
[
2
0
].
R
ec
en
tly
,
a
n
atu
r
e
-
in
s
p
ir
ed
s
o
f
t
-
co
m
p
u
tin
g
alg
o
r
ith
m
k
n
o
wn
as
g
r
ass
h
o
p
p
er
o
p
tim
izatio
n
alg
o
r
ith
m
(
GOA)
h
as
b
ee
n
p
r
o
p
o
s
ed
t
o
s
o
lv
e
o
p
tim
izatio
n
p
r
o
b
lem
[
2
1
]
.
I
n
last
f
ew
y
ea
r
s
,
GOA
h
as
b
ee
n
a
p
p
lied
i
n
s
ev
er
al
ap
p
licatio
n
s
s
u
ch
as
el
ec
tr
ical
ch
ar
ac
ter
izatio
n
o
f
p
r
o
to
n
ex
ch
a
n
g
e
m
em
b
r
an
e
f
u
el
ce
lls
s
tack
,
p
o
wer
q
u
ality
en
h
a
n
ce
m
en
t
i
n
an
is
o
lated
m
icr
o
g
r
i
d
,
co
l
o
r
im
ag
e
m
u
ltil
ev
el
th
r
esh
o
ld
in
g
,
m
eta
-
m
atch
in
g
ap
p
r
o
ac
h
f
o
r
o
n
to
lo
g
y
alig
n
m
en
t,
v
o
lt
a
g
e
co
n
t
r
o
l
o
f
s
witch
ed
r
el
u
cta
n
ce
g
en
e
r
ato
r
an
d
o
p
tim
al
r
ec
o
n
f
ig
u
r
atio
n
o
f
PV
ar
r
ay
[
2
0
]
,
[
22
]
-
[
2
6
]
.
T
h
e
ap
p
l
icatio
n
o
f
GOA
in
T
HD
m
in
im
izatio
n
o
f
p
o
wer
elec
tr
o
n
ic
c
o
n
v
er
ter
s
h
as r
ar
ely
b
ee
n
r
e
p
o
r
te
d
.
T
h
er
ef
o
r
e,
GO
A
is
p
r
o
p
o
s
ed
in
th
is
p
a
p
er
t
o
d
eter
m
in
e
th
e
o
p
tim
u
m
s
witch
in
g
a
n
g
les
f
o
r
th
e
ML
I
.
Un
lik
e
NR
,
GOA
co
u
ld
f
in
d
o
p
tim
u
m
s
o
lu
tio
n
s
with
o
u
t
r
eq
u
i
r
in
g
a
g
o
o
d
in
itial
s
witch
in
g
an
g
le
g
u
ess
.
T
h
e
GOA
b
ased
SHMPW
M
h
as b
ee
n
im
p
lem
en
ted
an
d
a
n
al
y
ze
d
u
s
in
g
MA
T
L
AB
,
wh
ils
t th
e
s
witch
in
g
-
an
g
le
s
o
lu
tio
n
is
co
m
p
ar
ed
to
th
at
o
b
tain
ed
u
s
in
g
NR
an
d
GA
m
eth
o
d
.
A
Simu
lin
k
/PS
I
M
co
-
s
im
u
latio
n
m
o
d
el
h
as
also
b
ee
n
d
ev
elo
p
ed
to
e
v
alu
ate
an
d
v
er
if
y
th
e
d
y
n
am
ic
p
er
f
o
r
m
a
n
ce
o
f
a
3
-
p
h
ase
9
-
le
v
el
C
HB
ML
I
with
GOA
o
p
tim
ized
s
witch
in
g
an
g
les u
n
d
er
d
y
n
am
ic
m
o
d
u
latio
n
in
d
ex
d
em
an
d
.
2.
I
M
P
L
E
M
E
NT
A
T
I
O
N
O
F
G
O
A
-
SH
M
P
W
M
F
O
R
3
-
P
H
A
SE
9
-
L
E
VE
L
CH
B
M
L
I
A
C
HB
ML
I
i
s
co
n
s
tr
u
cted
b
y
a
s
er
ies
o
f
H
-
b
r
id
g
e
cir
cu
its
.
E
ac
h
H
-
b
r
i
d
g
e
cir
cu
it
c
o
n
s
is
ts
o
f
a
DC
v
o
ltag
e
s
o
u
r
ce
an
d
f
o
u
r
p
o
we
r
s
em
ico
n
d
u
cto
r
s
witch
es
th
at
ar
e
ab
le
to
p
r
o
d
u
ce
v
o
ltag
e
le
v
els
+V
dc
,
0
or
-
V
dc
.
A
(
2
k+1
)
-
le
v
el
o
f
s
tair
ca
s
e
o
u
tp
u
t
p
h
ase
v
o
ltag
e
wav
ef
o
r
m
ca
n
b
e
p
r
o
d
u
ce
d
b
y
a
co
m
b
i
n
a
tio
n
o
f
k
n
u
m
b
er
o
f
H
-
b
r
id
g
e
cir
cu
its
.
Fig
u
r
e
1
(
a)
s
h
o
ws
th
e
co
n
s
tr
u
ctio
n
o
f
o
n
e
o
f
th
e
p
h
ases
an
d
Fig
u
r
e
1
(
b
)
s
h
o
ws
th
e
o
u
t
p
u
t
p
h
ase
v
o
ltag
e
wav
e
f
o
r
m
s
y
n
t
h
esized
f
r
o
m
f
o
u
r
H
-
b
r
i
d
g
e
ci
r
cu
its
.
I
n
th
is
p
ap
e
r
,
th
e
p
h
as
es
o
f
th
e
C
HB
ML
I
ar
e
co
n
n
ec
ted
t
o
f
o
r
m
a
b
a
lan
ce
d
3
-
p
h
ase
Y
-
co
n
n
ec
tio
n
cir
cu
it
with
1
2
0
˚
o
f
p
h
ase
s
h
if
t.
B
ased
o
n
Fig
u
r
e
1
(
b
)
,
th
e
o
u
tp
u
t p
h
ase
v
o
ltag
e
wav
ef
o
r
m
c
o
u
ld
b
e
r
e
p
r
esen
ted
in
Fo
u
r
ier
s
er
ies as
(
1
)
[
7
]
:
ℎ
(
)
=
∑
4
∞
=
1
[
(
1
)
+
(
2
)
+
(
3
)
+
(
4
)
]
(
)
(
1
)
wh
er
e
n
is
alwa
y
s
an
o
d
d
n
u
m
b
er
an
d
it
also
r
ep
r
esen
ts
th
e
n
-
th
h
a
r
m
o
n
ics,
V
dc
r
e
p
r
ese
n
ts
th
e
m
ag
n
itu
d
e
o
f
DC
v
o
ltag
e
s
o
u
r
ce
i
n
ea
c
h
H
-
b
r
id
g
e
cir
cu
it,
an
d
ω
is
th
e
an
g
u
lar
f
r
eq
u
en
cy
o
f
th
e
f
u
n
d
am
en
tal
h
ar
m
o
n
ic.
T
h
e
s
witch
in
g
an
g
les
α
1
,
α
2
,
α
3
an
d
α
4
ar
e
in
u
n
it
r
ad
ian
an
d
m
u
s
t
s
atis
f
y
th
e
co
n
d
itio
n
o
f
1
2
3
4
0
/
2
[
1
9
]
.
Fro
m
(
1
)
,
t
h
e
n
-
th
h
ar
m
o
n
ic
ca
n
b
e
ex
p
r
ess
ed
as
(
2
)
[
7
]
:
=
4
[
(
1
)
+
(
2
)
+
(
3
)
+
(
4
)
]
(
2
)
T
h
e
o
b
jectiv
e
o
f
th
e
SHMPW
M
is
to
m
in
im
ize
t
h
e
u
n
d
esire
d
lo
w
-
o
r
d
er
h
ar
m
o
n
ics
an
d
m
ain
tain
th
e
d
esire
d
f
u
n
d
am
e
n
tal
co
m
p
o
n
e
n
t
o
f
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
.
I
n
a
b
alan
ce
d
3
-
p
h
ase
9
-
l
ev
el
C
HB
ML
I
,
5
th
,
7
th
an
d
1
1
th
h
ar
m
o
n
ics
ar
e
c
h
o
s
en
to
b
e
m
in
im
ized
wh
ile
th
e
f
ir
s
t
h
ar
m
o
n
ic
is
m
ain
tain
ed
at
th
e
d
esire
d
v
alu
e.
T
h
e
tr
ip
len
o
d
d
h
ar
m
o
n
is
ar
e
n
o
t
r
e
q
u
ir
ed
to
b
e
m
in
i
m
ized
b
ec
au
s
e
th
e
y
ar
e
elim
in
ated
n
atu
r
ally
in
th
e
3
-
p
h
ase
s
y
s
tem
.
I
n
th
is
p
ap
er
,
GOA
is
ap
p
lied
in
SHMPW
M
to
o
p
tim
ize
th
e
s
witch
in
g
an
g
les.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
Dyn
a
mic
s
imu
la
tio
n
o
f th
r
ee
-
p
h
a
s
e
n
in
e
-
leve
l m
u
ltil
ev
el
in
ve
r
ter w
ith
s
w
i
tch
in
g
a
n
g
les
.
.
.
.
(
W.
T.
C
h
ew)
327
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
s
h
o
win
g
a
3
-
p
h
ase
9
-
le
v
el
C
HB
ML
I
an
d
ty
p
ical
p
h
ase
v
o
ltag
e
wa
v
ef
o
r
m
GOA
is
a
p
o
p
u
latio
n
-
b
ased
n
atu
r
e
-
in
s
p
ir
e
d
alg
o
r
ith
m
wh
ich
is
b
ased
o
n
th
e
s
war
m
b
eh
av
io
r
o
f
g
r
ass
h
o
p
p
er
s
.
T
h
e
alg
o
r
ith
m
m
im
ics
th
e
m
o
v
em
en
ts
o
f
th
e
g
r
ass
h
o
p
p
er
s
in
m
ig
r
atio
n
an
d
f
o
o
d
f
o
r
a
g
in
g
p
r
o
ce
s
s
.
T
h
e
m
ath
e
m
atica
l m
o
d
el
f
o
r
im
p
lem
en
tin
g
th
e
m
o
v
em
en
t o
f
g
r
ass
h
o
p
p
e
r
s
is
g
iv
en
b
y
(
3
)
[2
1
]:
=
[
∑
−
2
(
|
−
|
)
−
=
1
≠
]
+
(
3
)
wh
er
e
ubd
is
th
e
u
p
p
er
b
o
u
n
d
in
th
e
d
-
th
d
im
e
n
s
io
n
,
lb
d
is
th
e
lo
wer
b
o
u
n
d
in
th
e
d
-
th
d
i
m
en
s
io
n
,
T
d
is
t
h
e
b
est
tar
g
et
v
alu
e
a
n
d
d
ij
is
th
e
d
is
tan
ce
b
etwe
en
i
-
th
g
r
ass
h
o
p
p
er
a
n
d
j
-
th
g
r
ass
h
o
p
p
er
.
T
h
e
c
is
a
d
ec
r
ea
s
in
g
co
ef
f
icien
t w
h
ich
is
ex
p
r
ess
ed
as
(
4
)
[2
1
]:
=
(
/
)
(
4
)
wh
er
e
c
max
is
th
e
m
ax
im
u
m
v
alu
e
o
f
th
e
co
e
f
f
icien
t,
c
min
is
th
e
m
in
im
u
m
v
alu
e
o
f
co
e
f
f
icien
t,
iter
is
th
e
cu
r
r
en
t n
u
m
b
e
r
o
f
iter
atio
n
an
d
iter
max
is
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
.
T
h
e
f
u
n
ctio
n
s
is
th
e
s
o
cial
f
o
r
ce
u
s
ed
to
d
ec
id
e
t
h
e
m
o
v
em
en
t
o
f
g
r
ass
h
o
p
p
er
a
n
d
i
t is p
r
esen
ted
as
(
5
)
[2
1
]:
(
)
=
−
/
−
−
(
5
)
wh
er
e
r
is
th
e
n
o
r
m
alize
d
d
is
tan
ce
b
etwe
en
i
-
th
an
d
j
-
th
g
r
a
s
s
h
o
p
p
er
s
,
l
is
th
e
attr
ac
tiv
e
l
en
g
th
s
ca
le
an
d
f
is
th
e
in
ten
s
ity
o
f
attr
ac
tio
n
.
An
o
b
jectiv
e
f
u
n
ctio
n
(
OF)
,
wh
ic
h
is
u
s
ed
in
th
e
GOA
-
SHM
P
W
M
to
m
in
im
ize
th
e
u
n
d
esire
d
h
ar
m
o
n
ics an
d
m
ain
tain
th
e
d
esire
d
f
u
n
d
am
e
n
tal
c
o
m
p
o
n
en
t,
is
ad
ap
ted
f
r
o
m
[
1
9
]
as
(
6
)
:
=
(
100
×
−
1
)
4
+
1
5
(
50
5
1
)
2
+
1
7
(
50
7
1
)
2
+
1
11
(
50
11
1
)
2
(
6
)
wh
er
e
V
D
=
(
4
kMV
dc
)/
π
is
d
es
ir
ed
f
u
n
d
am
e
n
tal
h
a
r
m
o
n
ic
th
at
is
co
n
tr
o
lled
b
y
th
e
m
o
d
u
la
tio
n
in
d
e
x
,
M
,
an
d
V
1
,
V
5
,
V
7
an
d
V
11
ar
e
f
u
n
d
am
en
tal,
5
th
,
7
th
an
d
1
1
t
h
h
a
r
m
o
n
ics
o
f
th
e
p
h
ase
v
o
ltag
e
wav
ef
o
r
m
,
r
esp
ec
tiv
ely
.
T
h
e
f
ir
s
t
ter
m
o
f
(
6
)
is
u
s
ed
t
o
r
eg
u
late
th
e
d
esire
d
f
u
n
d
am
en
t
al
h
ar
m
o
n
ics,
wh
ils
t
th
e
s
a
m
e
tim
e
th
e
s
ec
o
n
d
,
th
ir
d
a
n
d
f
o
r
th
ter
m
s
a
r
e
u
s
ed
to
r
ed
u
ce
th
e
5
th
,
7
th
an
d
1
1
th
h
ar
m
o
n
ics,
r
esp
ec
tiv
ely
.
T
h
e
o
b
jectiv
e
o
f
th
e
f
ir
s
t
ter
m
is
to
lim
it
th
e
r
elativ
e
er
r
o
r
b
etwe
en
th
e
V
D
an
d
V
1
b
y
1
%
.
Fo
r
th
e
s
ec
o
n
d
,
th
ir
d
a
n
d
f
o
r
th
ter
m
s
,
th
e
5
th
,
7
t
h
an
d
1
1
th
h
a
r
m
o
n
ic
s
ar
e
k
ep
t
u
n
d
e
r
2
%
o
f
th
e
f
u
n
d
am
en
tal
h
a
r
m
o
n
ic.
T
h
e
r
ef
o
r
e,
all
d
esire
d
co
n
d
itio
n
s
co
u
l
d
b
e
co
n
tr
o
lle
d
with
th
e
p
r
o
p
o
s
ed
OF
wh
ile
th
e
o
p
tim
u
m
s
o
lu
tio
n
f
o
r
al
l
m
o
d
u
latio
n
i
n
d
ex
co
u
ld
b
e
d
eter
m
in
e
d
b
y
u
s
in
g
th
e
im
p
lem
e
n
tatio
n
o
f
GOA.
B
ased
o
n
(
2
)
,
V
1
,
V
5
,
V
7
an
d
V
11
ca
n
b
e
ex
p
r
ess
ed
as
(
7
)
:
HB
1
HB
2
HB
3
HB
4
HB
1
HB
2
HB
3
HB
4
HB
1
HB
2
HB
3
HB
4
P
h
a
s
e
A
P
h
a
s
e
B
P
h
a
s
e
C
V
d
c
S3
S1
S4
S2
L
o
a
d
L
o
a
d
L
o
a
d
4
V
d
c
3
V
d
c
2
V
d
c
V
d
c
0
-
4
V
d
c
-
3
V
d
c
-
2
V
d
c
-
V
d
c
V
ph
π
/2
π
3
π
/
2
2
π
α1
α2
α3
α4
V
d
c
0
-
V
d
c
V
HB
π
2
π
V
ph
V
HB
1
V
HB
2
V
HB
3
V
HB
4
H
-
B
r
id
g
e
C
ir
c
u
it
wt
wt
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
325
–
3
3
3
328
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
4
c
os
c
os
c
os
c
os
1
2
3
4
1
4
c
os
5
c
os
5
c
os
5
c
os
5
1
2
3
4
5
5
4
c
os
7
c
os
7
c
os
7
c
os
7
1
2
3
4
7
7
4
c
os
11
c
os
11
c
os
11
c
os
11
1
2
3
4
11
11
V
dc
V
V
dc
V
V
dc
V
V
dc
V
=
+
+
+
=
+
+
+
=
+
+
+
=
+
+
+
(
7
)
GOA
-
SHMP
W
M
h
as
b
ee
n
i
m
p
lem
en
ted
u
s
in
g
MA
T
L
AB
to
ca
lcu
late
th
e
o
p
tim
u
m
s
witch
in
g
an
g
les,
wh
ile
th
e
im
p
lem
en
ta
tio
n
o
f
GOA
-
SHMPW
M
i
s
i
llu
s
tr
ated
in
Fig
u
r
e
2
.
I
n
th
e
GOA
-
SHMP
W
M
im
p
lem
en
tatio
n
,
th
e
p
ar
am
eter
s
u
s
ed
f
o
r
GOA
ar
e
as
f
o
llo
ws
:
l
=
1
.
5
,
f
=
0
.
5
,
c
min
=
0
.
0
0
0
0
1
,
c
max
=
0
.
5
,
N
=
100
an
d
iter
max
=
100
.
Swi
tch
in
g
-
an
g
le
ca
lcu
latio
n
is
p
er
f
o
r
m
e
d
f
o
r
a
3
-
p
h
ase
9
-
le
v
el
C
HB
ML
I
f
o
r
m
o
d
u
latio
n
in
d
ex
r
an
g
e
f
r
o
m
0
.
0
1
to
1
.
0
0
in
s
tep
s
ize
o
f
0
.
0
1
.
Fig
u
r
e
2
.
Flo
wch
ar
t
o
f
GOA
-
SHMP
W
M
im
p
lem
en
tatio
n
i
n
a
wid
e
m
o
d
u
l
atio
n
in
d
ex
r
a
n
g
e
I
n
o
r
d
er
to
v
alid
ate
wh
eth
er
th
e
C
HB
ML
I
co
n
tr
o
lle
d
u
s
in
g
GOA
-
SHMPW
M
o
p
tim
u
m
s
witch
in
g
an
g
les
is
ca
p
ab
le
to
r
esp
o
n
d
to
th
e
ch
a
n
g
e
o
f
m
o
d
u
latio
n
in
d
e
x
d
em
an
d
,
a
d
y
n
am
ic
co
-
s
im
u
latio
n
o
f
MA
T
L
AB
/SIM
UL
I
NK
-
PS
I
M
is
im
p
lem
en
ted
o
n
3
-
p
h
ase
9
-
lev
el
C
HB
ML
I
.
Fig
u
r
e
3
s
h
o
ws
th
e
Simu
lin
k
m
o
d
el
o
f
s
witch
in
g
-
an
g
le
g
e
n
er
ato
r
f
o
r
3
-
p
h
ase
9
-
lev
el
C
H
B
ML
I
,
wh
ils
t
Fig
u
r
e
4
s
h
o
ws
th
e
b
lo
c
k
d
ia
g
r
am
o
f
3
-
p
h
ase
9
-
lev
el
C
HB
ML
I
s
im
u
latio
n
m
o
d
el
a
n
d
its
PS
I
M
im
p
lem
en
tatio
n
.
Prio
r
to
th
e
s
im
u
latio
n
,
th
e
s
witch
in
g
an
g
les
th
at
ar
e
o
p
tim
iz
ed
b
y
GOA
-
SHMPW
M
ar
e
s
to
r
ed
in
l
o
o
k
-
u
p
tab
les
as
s
h
o
wn
in
Fig
u
r
e
3
.
Du
r
in
g
s
im
u
latio
n
,
t
h
e
o
p
tim
ized
s
witch
in
g
an
g
les
ar
e
in
t
er
p
o
lated
f
r
o
m
th
e
l
o
o
k
-
u
p
t
ab
les
b
ased
o
n
th
e
d
y
n
am
ically
ch
a
n
g
in
g
m
o
d
u
la
tio
n
in
d
ex
d
em
an
d
.
T
h
e
s
witch
in
g
an
g
les
ar
e
d
is
tr
ib
u
ted
i
n
t
o
2
4
s
ig
n
als
(
g
1
t
o
g
2
4
)
th
r
o
u
g
h
g
ate
s
ig
n
al
g
en
e
r
ato
r
.
B
y
u
s
in
g
th
e
SimCo
u
p
l
er
in
ter
f
ac
e
as
s
h
o
w
n
in
Fig
u
r
e
3
,
th
e
2
4
s
ig
n
als
ar
e
lin
k
ed
to
th
e
PS
I
M
3
-
p
h
a
s
e
9
-
lev
el
C
H
B
ML
I
s
im
u
lati
o
n
m
o
d
el
as
s
h
o
wn
in
Fig
u
r
e
4
.
E
ac
h
H
-
b
r
id
g
e
m
o
d
u
le
em
p
lo
y
s
a
1
2
V
DC
v
o
lt
ag
e
s
o
u
r
ce
a
n
d
th
e
C
HB
M
L
I
is
s
witch
ed
at
5
0
Hz.
Ou
t
p
u
t
v
o
ltag
e
wav
ef
o
r
m
s
ar
e
g
en
er
ate
d
f
r
o
m
th
e
s
im
u
lat
io
n
m
o
d
el
b
ased
o
n
th
e
m
o
d
u
l
atio
n
in
d
ex
d
em
an
d
.
Y
e
s
Ye
s
No
No
i
t
e
r
>
i
t
e
r
m
ax
?
it
e
r
=
it
e
r
+
1
S
T
A
R
T
I
nit
ia
l
iz
e
popu
la
ti
on
X
i
(
i =
1 2
n)
,c
m
ax
, c
m
i
n
, l , f
a
nd
it
e
r
m
ax
M
=
0.01
i
t
e
r
=
0
N
or
ma
li
z
e
the
dis
ta
nc
e
be
twe
e
n s
e
a
r
c
h a
ge
nts
in [
1,4]
.
Upda
t
e
t
he
pos
i
t
i
on o
f
e
a
c
h s
e
a
r
c
h a
ge
nt
us
i
ng E
q.
(
4)
.
B
r
ing t
he
s
e
a
r
c
h a
ge
nt ba
c
k if
it
goe
s
outs
ide
the
boun
da
r
ie
s
.
U
pda
te
T
d
if
t
he
r
e
i
s
a
be
tt
e
r
s
olut
ion.
C
a
l
c
ul
a
t
e
t
he
OF
va
lue
f
or
e
a
c
h
s
e
a
r
c
h a
ge
nt us
ing E
q. (
7)
.
T
d
= the
be
s
t s
e
a
r
c
h a
ge
nt
.
U
pda
te
c
M
>
1
?
T
d
= G
loba
l M
i
nim
um
E
N
D
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
Dyn
a
mic
s
imu
la
tio
n
o
f th
r
ee
-
p
h
a
s
e
n
in
e
-
leve
l m
u
ltil
ev
el
in
ve
r
ter w
ith
s
w
i
tch
in
g
a
n
g
les
.
.
.
.
(
W.
T.
C
h
ew)
329
Fig
u
r
e
3
.
Simu
lin
k
m
o
d
el
o
f
s
witch
in
g
-
an
g
le
g
en
er
ato
r
f
o
r
3
-
p
h
ase
9
-
lev
el
C
HB
ML
I
P
S
I
M mo
d
elin
g
o
f
P
ha
s
e
A
H
B
1
b
lo
ck
Fig
u
r
e
4
.
B
lo
ck
d
iag
r
am
o
f
3
-
p
h
ase
9
-
lev
el
C
HB
ML
I
s
im
u
latio
n
m
o
d
el
a
n
d
its
PS
I
M
im
p
lem
en
tatio
n
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Switch
in
g
an
g
les
o
b
tain
ed
f
r
o
m
GOA
ar
e
b
en
ch
m
a
r
k
ed
a
g
a
in
s
t
th
o
s
e
o
b
tain
ed
f
r
o
m
NR
tech
n
iq
u
e
an
d
GA,
as
s
h
o
wn
in
Fig
u
r
e
5
.
C
o
m
p
a
r
ed
t
o
NR
as
s
h
o
wn
in
Fig
u
r
e
5
(
a)
,
GOA
in
Fig
u
r
e
5
(
b
)
h
as
a
wid
er
m
o
d
u
latio
n
i
n
d
ex
r
an
g
e
o
f
o
p
t
im
u
m
s
witch
in
g
-
an
g
le
s
o
lu
tio
n
s
.
Fi
g
u
r
e
6
(
a)
s
h
o
ws
th
e
m
in
im
u
m
OF
ac
h
iev
ed
b
y
GA
an
d
GOA
f
o
r
t
h
e
m
o
d
u
latio
n
in
d
e
x
r
an
g
e
in
v
est
ig
ated
.
As
s
h
o
w
n
in
Fig
u
r
e
6
(
a)
,
GOA
m
o
s
tly
ac
h
iev
es
lo
wer
OF
co
m
p
ar
ed
to
GA
in
a
wid
e
r
a
n
g
e
o
f
m
o
d
u
latio
n
in
d
ex
.
As
s
h
o
wn
in
Fig
u
r
e
6
(
b
)
,
3
8
%
o
f
th
e
m
o
d
u
latio
n
in
d
e
x
r
an
g
e
ac
h
iev
es
a
m
in
im
u
m
OF
o
f
1
0
-
2
an
d
b
elo
w
b
y
u
s
in
g
GA,
an
d
3
8
%
o
f
t
h
e
m
o
d
u
latio
n
in
d
ex
r
an
g
e
ac
h
ie
v
es
a
m
in
im
u
m
OF
o
f
1
0
-
8
an
d
b
elo
w
b
y
u
s
in
g
GOA.
T
h
is
r
esu
lt
s
u
g
g
ests
th
a
t
GOA
h
as
a
h
ig
h
er
p
r
o
b
ab
ilit
y
th
an
GA
to
r
ea
ch
g
lo
b
al
m
in
im
a
in
th
e
C
HB
ML
I
o
p
t
im
i
za
tio
n
s
ea
r
ch
s
p
ac
e
an
d
th
e
u
n
d
esire
d
5
th
,
7
th
an
d
1
1
th
h
ar
m
o
n
ics
ar
e
n
ea
r
ly
elim
in
ated
.
As
a
r
esu
lt,
GOA
is
ab
le
to
p
r
o
d
u
ce
h
ig
h
er
ac
cu
r
ac
y
o
f
o
p
tim
u
m
s
witch
in
g
an
g
les
th
an
GA.
Fig
u
r
e
6
(
c)
s
h
o
ws
th
e
p
h
ase
v
o
lt
ag
e
T
HD
an
d
lin
e
-
to
-
lin
e
v
o
ltag
e
T
HD
o
f
th
e
C
HB
ML
I
th
at
ac
h
iev
ed
b
y
GOA.
T
h
e
lin
e
-
to
-
lin
e
v
o
ltag
e
T
HD
is
alwa
y
s
lo
wer
th
an
th
e
p
h
ase
v
o
ltag
e
T
HD
b
ec
au
s
e
o
f
th
e
n
at
u
r
al
elim
in
atio
n
o
f
tr
ip
len
h
ar
m
o
n
ics
in
lin
e
-
to
-
lin
e
v
o
ltag
e
wav
ef
o
r
m
.
B
ased
o
n
Fig
u
r
e
6
(
c)
,
th
e
lo
west
p
h
ase
v
o
ltag
e
T
HD
th
at
ca
n
b
e
a
ch
iev
ed
b
y
GOA
is
9
.
6
5
%
f
o
r
M
=
0
.
8
2
.
G
a
t
e
S
i
g
n
a
l
G
e
n
e
r
a
t
o
r
S
i
m
C
o
u
p
l
e
r
I
n
t
e
r
f
a
c
e
To
3
-
p
h
a
s
e
/
9
-
l
e
v
e
l
C
H
BM
L
I
P
S
I
M
Mo
d
el
D
e
s
i
r
e
d
Mo
d
u
l
a
t
i
o
n
I
n
d
ex
C
l
oc
k
α
1
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ook
-
u
p
T
ab
l
e
α
2
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ook
-
u
p
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ab
l
e
α
3
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ook
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u
p
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l
e
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4
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ook
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p
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l
e
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D
T
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u
)
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D
T
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u
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T
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T
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7
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8
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9
g
10
g
11
g
12
g
13
g
14
g
15
g
16
g
17
g
18
g
19
g
20
g
21
g
22
g
23
g
24
V
l
i
n
e
A
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3
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h
a
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2
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h
a
s
e
C
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4
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h
a
s
e
C
H
B
3
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h
a
s
e
C
H
B
2
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h
a
s
e
C
H
B
1
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h
a
s
e
B
H
B
1
R
p
h
A
R
p
h
B
R
p
h
C
V
dc
S1
S3
S2
S4
+
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O
ut
1
I
n 1
I
n 2
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ut
4
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ut
3
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ut
2
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S4
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g1
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dc
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n 1
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n 2
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4
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3
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r
o
m
M
A
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A
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i
m
u
l
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n
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f
a
c
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
1
,
Ma
r
c
h
2
0
2
1
:
325
–
3
3
3
330
(
a)
(
b
)
(
c)
Fig
u
r
e
5
.
Switch
in
g
a
n
g
les d
er
iv
ed
u
s
in
g
(
a)
NR
,
(
b
)
GA,
(
c)
GOA
tech
n
iq
u
es
(
a)
(
b
)
(
c)
Fig
u
r
e
6
.
MA
T
L
AB
an
aly
s
is
: (
a)
OF (
GOA
v
s
GA)
,
(
b
)
C
D
F (
GOA
v
s
GA)
,
(
c)
Vo
ltag
e
T
HD
(
GOA)
T
ab
le
1
s
h
o
ws
th
e
s
elec
ted
m
o
d
u
latio
n
in
d
ex
es
d
em
an
d
f
o
r
th
e
d
y
n
a
m
ic
co
-
s
im
u
lati
o
n
,
wh
ils
t
Fig
u
r
e
7
s
h
o
ws
th
e
s
tep
p
ed
m
o
d
u
latio
n
in
d
e
x
d
em
an
d
,
p
h
ase
v
o
ltag
e
wav
ef
o
r
m
s
an
d
lin
e
-
to
-
lin
e
v
o
ltag
e
wav
ef
o
r
m
s
o
b
tain
ed
f
r
o
m
MA
T
L
AB
/Si
m
u
lin
k
-
PS
I
M
d
y
n
am
ic
co
-
s
im
u
latio
n
.
T
h
e
m
o
d
u
latio
n
in
d
e
x
is
v
a
r
ied
at
ev
er
y
0
.
1
s
tim
e
in
ter
v
al.
F
r
o
m
0
to
0
.
4
s
,
wh
en
th
e
m
o
d
u
latio
n
in
d
ex
is
in
cr
ea
s
ed
f
r
o
m
0
.
1
3
to
0
.
8
2
,
th
e
v
o
ltag
e
lev
el
i
n
cr
ea
s
es
f
r
o
m
3
-
lev
el
to
9
-
lev
el
a
n
d
th
e
p
ea
k
p
h
ase
v
o
ltag
e
in
c
r
ea
s
es
f
r
o
m
1
2
V
to
4
8
V.
At
0
.
4
s
,
th
e
m
o
d
u
latio
n
in
d
e
x
is
d
ec
r
ea
s
ed
f
r
o
m
0
.
8
2
t
o
0
.
2
7
,
t
h
e
v
o
ltag
e
le
v
el
d
ec
r
ea
s
es
9
-
l
ev
el
to
5
-
le
v
el
an
d
th
e
p
ea
k
p
h
ase
v
o
ltag
e
d
ec
r
ea
s
es
f
r
o
m
4
8
V
to
2
4
V.
Du
e
to
th
e
th
r
ee
-
p
h
ase
co
n
f
ig
u
r
atio
n
,
a
1
2
0
˚
p
h
ase
s
h
if
t
with
r
esp
ec
t
to
th
e
ad
jace
n
t
leg
is
o
b
s
er
v
ed
in
th
e
o
u
t
p
u
t
p
h
ase
v
o
ltag
e
an
d
lin
e
-
to
-
lin
e
v
o
ltag
e
wav
ef
o
r
m
s
.
T
h
ese
r
esu
lts
v
er
if
y
th
at
th
e
C
HB
ML
I
co
n
tr
o
lled
u
s
in
g
th
e
GOA
-
SHMP
W
M
o
p
tim
ized
s
witch
in
g
an
g
les
is
ca
p
ab
le
to
r
esp
o
n
d
t
h
e
ch
an
g
e
o
f
m
o
d
u
latio
n
i
n
d
ex
d
em
an
d
.
C
lo
s
e
-
u
p
v
iew
o
f
p
h
ase
an
d
l
i
ne
-
to
-
lin
e
v
o
ltag
e
wa
v
ef
o
r
m
s
f
o
r
ea
ch
m
o
d
u
latio
n
i
n
d
ex
d
em
an
d
a
r
e
s
h
o
wn
in
T
ab
le
2
.
Fas
t
Fo
u
r
ier
T
r
an
s
f
o
r
m
(
FF
T
)
ar
e
ap
p
lied
in
th
e
p
h
ase
an
d
lin
e
-
to
-
lin
e
v
o
ltag
e
wav
ef
o
r
m
s
f
o
r
ea
c
h
m
o
d
u
latio
n
i
n
d
ex
to
s
h
o
w
th
e
h
a
r
m
o
n
ic
co
n
ten
ts
.
T
ab
le
2
s
h
o
ws
th
e
v
o
ltag
e
w
av
ef
o
r
m
s
an
d
FF
T
an
aly
s
is
f
o
r
M
=
0
.
1
3
,
M
=
0
.
2
7
,
M
=
0
.
4
1
an
d
M
=
0
.
8
2
,
r
esp
ec
tiv
ely
.
T
h
e
m
ag
n
itu
d
e
s
o
f
V
1
ar
e
7
.
9
9
V,
1
6
.
5
4
V,
2
5
.
1
0
V
a
n
d
5
0
.
1
0
V,
wh
ich
ar
e
v
e
r
y
clo
s
e
to
V
D
o
f
7
.
9
5
V,
1
6
.
5
0
V,
2
5
.
0
6
V
an
d
5
0
.
1
1
V
as
lis
ted
in
T
ab
le
1
,
r
esp
ec
tiv
ely
,
f
o
r
M
=
0
.
1
3
,
M
=
0
.
2
7
,
M
=
0
.
4
1
an
d
M
=
0
.
8
2
,
r
esp
ec
tiv
el
y
.
I
n
a
d
d
itio
n
,
th
e
m
ag
n
itu
d
e
o
f
f
u
n
d
am
en
tal
h
ar
m
o
n
ic
o
f
t
h
e
lin
e
-
to
-
lin
e
v
o
ltag
e
wav
ef
o
r
m
f
o
r
ea
ch
m
o
d
u
latio
n
in
d
ex
is
ap
p
r
o
x
im
ately
3
V
1
.
Fo
r
M
=
0
.
2
7
,
M
=
0
.
4
1
a
n
d
M
=
0
.
8
2
,
th
e
ch
o
s
en
5
th
,
7
t
h
an
d
1
1
t
h
h
ar
m
o
n
ics
in
th
e
p
h
ase
an
d
lin
e
v
o
ltag
e
wav
ef
o
r
m
s
ar
e
n
ea
r
ly
elim
in
ate
d
.
T
h
is
is
r
ea
s
o
n
ab
le
s
in
ce
th
e
O
F
r
elate
d
with
th
ese
m
o
d
u
latio
n
in
d
e
x
es
ar
e
s
u
cc
e
s
s
f
u
lly
m
in
im
ized
,
wh
i
c
h
ca
n
b
e
c
o
n
f
ir
m
e
d
in
Fig
u
r
e
6
(
a)
.
Nev
er
th
eless
,
th
e
5
th
,
7
th
an
d
1
1
th
h
ar
m
o
n
ics
o
f
th
e
v
o
ltag
e
wav
ef
o
r
m
s
f
o
r
M
=
0
.
1
3
ar
e
o
n
ly
r
ed
u
ce
d
as
m
u
ch
as
p
o
s
s
ib
le
d
u
e
to
th
e
l
o
w
m
o
d
u
latio
n
in
d
e
x
o
f
o
u
tp
u
t
v
o
ltag
e
wav
e
f
o
r
m
th
at
h
as
t
h
e
lo
west
n
u
m
b
er
o
f
v
o
ltag
e
le
v
els.
T
ab
le
3
c
o
m
p
ar
es
t
h
e
MA
T
L
AB
an
d
d
y
n
am
ic
s
im
u
latio
n
r
esu
lts
o
f
f
u
n
d
am
en
tal
h
ar
m
o
n
ic,
p
h
ase
v
o
ltag
e
T
HD
an
d
lin
e
-
to
-
lin
e
v
o
ltag
e
T
HD
f
o
r
ea
ch
m
o
d
u
latio
n
in
d
ex
d
em
a
n
d
.
I
t
ca
n
b
e
o
b
s
er
v
ed
th
at
th
e
r
esu
lts
b
etwe
en
MA
T
L
AB
an
d
d
y
n
a
m
ic
s
im
u
latio
n
ar
e
v
e
r
y
c
lo
s
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
Dyn
a
mic
s
imu
la
tio
n
o
f th
r
ee
-
p
h
a
s
e
n
in
e
-
leve
l m
u
ltil
ev
el
in
ve
r
ter w
ith
s
w
i
tch
in
g
a
n
g
les
.
.
.
.
(
W.
T.
C
h
ew)
331
I
n
o
r
d
er
to
d
e
m
o
n
s
tr
ate
th
at
th
e
C
HB
ML
I
co
n
tr
o
lled
u
s
in
g
GOA
-
SHMP
W
M
s
witch
in
g
an
g
les
is
ab
le
to
p
r
o
d
u
ce
a
s
tead
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
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E
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&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
Dyn
a
mic
s
imu
la
tio
n
o
f th
r
ee
-
p
h
a
s
e
n
in
e
-
leve
l m
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ter w
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g
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les
.
.
.
.
(
W.
T.
C
h
ew)
333
RE
F
E
R
E
NC
E
S
[1
]
H.
Ab
u
-
Ru
b
,
J.
Ho
l
ts,
J.
Ro
d
rig
u
e
z
,
a
n
d
G
.
Ba
o
m
in
g
,
“
M
e
d
i
u
m
v
o
lt
a
g
e
m
u
l
ti
lev
e
l
c
o
n
v
e
rters
,
sta
te
o
f
th
e
a
rt
,
c
h
a
ll
e
n
g
e
s a
n
d
re
q
u
irem
e
n
ts i
n
in
d
u
strial
a
p
p
li
c
a
ti
o
n
s,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
In
d
u
stri
a
l
El
e
c
tro
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ics
,
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o
l
.
5
7
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o
.
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p
.
2
5
8
1
–
2
5
9
6
,
A
u
g
.
2
0
1
0
.
[2
]
F
.
H.
Kh
a
n
,
L
.
M
.
To
l
b
e
rt
,
a
n
d
W.
E.
Web
b
,
“
Hy
b
r
id
El
e
c
tri
c
Ve
h
icle
P
o
we
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a
n
a
g
e
m
e
n
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S
o
l
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ti
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s
Ba
se
d
o
n
Iso
late
d
a
n
d
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o
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late
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Co
n
fi
g
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ra
ti
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n
s
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f
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M
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lar
Ca
p
a
c
it
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r
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Clam
p
e
d
C
o
n
v
e
rter,
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IE
E
E
T
ra
n
s
a
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
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tro
n
ics
,
v
o
l.
5
6
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o
.
8
,
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p
.
3
0
7
9
–
3
0
9
5
,
A
u
g
.
2
0
0
9
.
[3
]
I.
J.
Ha
sa
n
,
N.
A
b
d
u
l,
J.
S
a
li
h
,
a
n
d
N.
I.
Ab
d
u
l
k
h
a
leq
,
“
Th
re
e
-
p
h
a
se
p
h
o
to
v
o
lt
a
ic
g
r
id
in
v
e
rter
sy
ste
m
d
e
sig
n
b
a
se
d
o
n
P
IC2
4
F
J2
5
6
G
B1
1
0
fo
r
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
,
”
I
n
ter
n
a
t
i
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
ms
(IJ
PE
DS
),
v
o
l.
1
0
,
n
o
.
3
,
p
p
.
1
2
1
5
–
1
2
2
2
,
2
0
1
9
.
[4
]
C.
Lao
u
fi,
Z.
S
a
d
o
u
n
e
,
A.
Ab
b
o
u
,
a
n
d
M
.
A
k
h
e
rra
z
,
“
Ne
w
m
o
d
e
l
o
f
e
lec
tri
c
trac
ti
o
n
d
ri
v
e
b
a
se
d
sli
d
i
n
g
m
o
d
e
c
o
n
tro
ll
e
r
in
field
-
o
rien
te
d
c
o
n
tr
o
l
o
f
in
d
u
c
t
io
n
m
o
t
o
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fe
d
b
y
m
u
l
ti
lev
e
l
i
n
v
e
rter,
”
In
ter
n
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ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
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tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(IJ
PE
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),
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o
l
.
1
1
,
n
o
.
1
,
p
p
.
2
4
2
–
2
5
0
,
2
0
2
0
.
[5
]
G
.
V.
Na
g
a
ra
ju
a
n
d
G
.
S
.
Ra
o
,
“
T
h
re
e
p
h
a
se
P
UC
5
i
n
v
e
rte
r
fe
d
i
n
d
u
c
ti
o
n
m
o
to
r
fo
r
re
n
e
wa
b
le
e
n
e
rg
y
a
p
p
li
c
a
ti
o
n
s,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
D
riv
e
S
y
ste
ms
(IJ
PE
DS
),
v
o
l.
1
1
,
n
o
.
1
,
p
p
.
1
–
9
,
2
0
2
0
.
[6
]
J.
Ro
d
r
ig
u
e
z
,
J.
S
.
Lai
,
a
n
d
F
.
Z
.
P
e
n
g
,
“
M
u
lt
il
e
v
e
l
in
v
e
rters
:
a
su
rv
e
y
o
f
to
p
o
l
o
g
i
e
s,
c
o
n
tr
o
ls,
a
n
d
a
p
p
li
c
a
ti
o
n
s,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
4
9
,
n
o
.
4
,
p
p
.
7
2
4
–
7
3
8
,
Au
g
.
2
0
0
2
.
[7
]
L.
M
.
T
o
lb
e
rt
,
F
.
Z
.
P
e
n
g
,
a
n
d
T.
G
.
Ha
b
e
tl
e
r,
“
M
u
lt
il
e
v
e
l
c
o
n
v
e
rt
e
rs
fo
r
larg
e
e
lec
tri
c
d
riv
e
s,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
I
n
d
u
stry
Ap
p
li
c
a
t
io
n
s
,
v
o
l.
3
5
,
n
o
.
1
,
p
p
.
3
6
–
4
4
,
1
9
9
9
.
[8
]
M
.
M
a
li
n
o
ws
k
i,
K.
G
o
p
a
k
u
m
a
r,
J.
Ro
d
rig
u
e
z
,
a
n
d
M
.
A.
P
é
re
z
,
“
A
S
u
rv
e
y
o
n
Ca
sc
a
d
e
d
M
u
lt
i
l
e
v
e
l
In
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
7
,
n
o
.
7
,
p
p
.
2
1
9
7
–
2
2
0
6
,
Ju
l
.
2
0
1
0
.
[9
]
L.
G
.
F
ra
n
q
u
e
l
o
,
J.
Ro
d
rig
u
e
z
,
J.
I.
Leo
n
,
S
.
Ko
u
ro
,
R.
P
o
rti
l
l
o
,
a
n
d
M
.
A.
M
.
P
ra
ts,
“
T
h
e
a
g
e
o
f
m
u
l
ti
lev
e
l
c
o
n
v
e
rters
a
rriv
e
s,
”
IEE
E
In
d
u
str
ia
l
El
e
c
tro
n
ics
M
a
g
a
zin
e
,
v
o
l.
2
,
n
o
.
2
,
p
p
.
2
8
–
3
9
,
Ju
n
.
2
0
0
8
.
[1
0
]
A.
K
.
G
u
p
ta
a
n
d
A.
M
.
Kh
a
m
b
a
d
k
o
n
e
,
“
A
S
p
a
c
e
Ve
c
to
r
P
WM
S
c
h
e
m
e
fo
r
M
u
lt
il
e
v
e
l
In
v
e
rters
Ba
se
d
o
n
Two
-
Lev
e
l
S
p
a
c
e
Ve
c
t
o
r
P
W
M
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l
.
5
3
,
n
o
.
5
,
p
p
.
1
6
3
1
–
1
6
3
9
,
Oc
t.
2
0
0
6
.
[1
1
]
N.
Yo
u
se
fp
o
o
r,
S
.
F
a
th
i
,
N.
F
a
ro
k
h
n
ia
,
a
n
d
H.
A
b
y
a
n
e
h
,
“
THD
M
in
imiz
a
ti
o
n
Ap
p
li
e
d
Dire
c
tl
y
o
n
t
h
e
Li
n
e
-
to
-
Li
n
e
Vo
lt
a
g
e
o
f
M
u
lt
il
e
v
e
l
I
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
9
,
n
o
.
1
,
p
p
.
3
7
3
–
3
8
0
,
2
0
1
2
.
[1
2
]
G
.
Ko
n
sta
n
ti
n
o
u
,
M
.
Ci
o
b
o
taru
,
a
n
d
V.
Ag
e
li
d
is,
“
S
e
lec
ti
v
e
h
a
rm
o
n
ic
e
li
m
in
a
ti
o
n
p
u
lse
-
wid
t
h
m
o
d
u
lati
o
n
o
f
m
o
d
u
lar m
u
lt
il
e
v
e
l
c
o
n
v
e
rters
,
”
IET
Po
we
r E
lec
tro
n
ics
,
v
o
l.
6
,
n
o
.
1
,
p
p
.
9
6
–
1
0
7
,
Ja
n
.
2
0
1
3
.
[1
3
]
R.
M
.
Ho
ss
a
m
,
G
.
M
.
Ha
sh
e
m
,
a
n
d
M
.
I.
M
a
re
i,
“
Op
ti
m
ize
d
h
a
rm
o
n
ic
e
li
m
in
a
t
io
n
f
o
r
c
a
sc
a
d
e
d
m
u
l
ti
lev
e
l
in
v
e
rter,
”
4
8
t
h
In
ter
n
a
ti
o
n
a
l
U
n
iv
e
rs
it
ies
' P
o
we
r E
n
g
i
n
e
e
rin
g
C
o
n
f
e
re
n
c
e
(UPE
C),
Du
b
li
n
,
p
p
.
1
–
6
,
2
0
1
3
.
[1
4
]
J.
N.
Ch
ias
so
n
,
L.
M
.
To
l
b
e
rt,
K.
J.
M
c
Ke
n
z
ie
,
a
n
d
Z.
Du
,
“
C
o
n
tr
o
l
o
f
a
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter
u
sin
g
re
su
lt
a
n
t
th
e
o
ry
,
”
IEE
E
T
r
a
n
s
a
c
ti
o
n
s
o
n
Co
n
tr
o
l
S
y
ste
ms
T
e
c
h
n
o
lo
g
y
,
v
o
l.
1
1
,
n
o
.
3
,
p
p
.
3
4
5
-
3
5
4
,
M
a
y
2
0
0
3
,
d
o
i:
1
0
.
1
1
0
9
/
TCS
T.
2
0
0
3
.
8
1
0
3
8
2
.
[1
5
]
J.
N.
Ch
ias
so
n
,
L.
M
.
To
l
b
e
rt,
K.
J.
M
c
Ke
n
z
ie
,
a
n
d
Zh
o
n
g
Du
,
“
A
c
o
m
p
lete
so
lu
ti
o
n
to
t
h
e
h
a
rm
o
n
ic
e
li
m
in
a
ti
o
n
p
ro
b
lem
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
ics
,
v
o
l
.
1
9
,
n
o
.
2
,
p
p
.
4
9
1
–
4
9
9
,
M
a
r.
2
0
0
4
.
[1
6
]
J.
N.
Ch
ias
so
n
,
L
.
M
.
T
o
lb
e
rt,
K.
J.
M
c
Ke
n
z
ie
,
a
n
d
Zh
o
n
g
Du
,
“
El
i
m
in
a
ti
o
n
o
f
h
a
rm
o
n
ics
in
a
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter
u
sin
g
th
e
th
e
o
r
y
o
f
s
y
m
m
e
t
ric
p
o
ly
n
o
m
ials
a
n
d
re
su
lt
a
n
ts,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Co
n
tro
l
S
y
ste
ms
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
1
3
,
n
o
.
2
,
p
p
.
2
1
6
–
2
2
3
,
M
a
r.
2
0
0
5
.
[1
7
]
B.
Ch
o
u
d
h
u
ry
a
n
d
R.
M
.
Jh
a
,
“
S
o
ft
Co
m
p
u
ti
n
g
tec
h
n
iq
u
e
s,
”
S
o
ft
Co
m
p
u
ti
n
g
i
n
El
e
c
tro
m
a
g
n
e
t
ic
s:
M
e
th
o
d
s
a
n
d
Ap
p
li
c
a
ti
o
n
s,
Ca
m
b
ri
d
g
e
:
Ca
m
b
ri
d
g
e
Un
i
v
e
rsity
P
re
ss
,
p
p
.
9
–
4
4
,
2
0
1
6
.
[1
8
]
A.
Lam
b
o
ra
,
K.
G
u
p
ta
,
a
n
d
K.
Ch
o
p
ra
,
“
G
e
n
e
ti
c
Alg
o
rit
h
m
-
A
Li
tera
tu
re
Re
v
iew
,
”
I
n
ter
n
a
t
io
n
a
l
Co
n
fer
e
n
c
e
o
n
M
a
c
h
i
n
e
L
e
a
r
n
in
g
,
B
ig
D
a
ta
,
Clo
u
d
a
n
d
P
a
ra
ll
e
l
C
o
mp
u
ti
n
g
(CO
M
IT
Co
n
)
,
F
a
rid
a
b
a
d
,
In
d
ia,
2
0
1
9
,
p
p
.
3
8
0
–
3
8
4
.
[1
9
]
N.
F
a
ro
k
h
n
ia,
S
.
F
a
t
h
i,
R.
S
a
leh
i,
G
.
G
h
a
re
h
p
e
ti
a
n
,
a
n
d
M
.
Eh
sa
n
i,
“
Im
p
ro
v
e
d
se
lec
ti
v
e
h
a
rm
o
n
ic
e
li
m
in
a
ti
o
n
p
u
lse
-
wid
t
h
m
o
d
u
lati
o
n
st
ra
teg
y
in
m
u
lt
il
e
v
e
l
in
v
e
rters
,
”
IET
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
5
,
n
o
.
9
,
p
p
.
1
9
0
4
–
1
9
1
1
,
2
0
1
2
.
[2
0
]
Z.
Lv
a
n
d
R.
P
e
n
g
,
“
A
n
o
v
e
l
m
e
ta
-
m
a
tch
in
g
a
p
p
ro
a
c
h
f
o
r
o
n
t
o
l
o
g
y
a
li
g
n
m
e
n
t
u
sin
g
g
ra
ss
h
o
p
p
e
r
o
p
t
imiz
a
ti
o
n
,
”
Kn
o
wled
g
e
-
Ba
se
d
S
y
ste
ms
,
v
o
l.
2
0
1
–
2
0
2
,
A
u
g
.
2
0
2
0
.
[2
1
]
S
.
S
a
re
m
i,
S
.
M
irj
a
li
li
,
a
n
d
A.
Le
wis,
“
G
ra
s
sh
o
p
p
e
r
Op
ti
m
isa
ti
o
n
Alg
o
rit
h
m
:
T
h
e
o
r
y
a
n
d
a
p
p
li
c
a
ti
o
n
,
”
A
d
v
a
n
c
e
s
i
n
En
g
i
n
e
e
rin
g
S
o
ft
wa
re
,
v
o
l
.
1
0
5
,
p
p
.
3
0
–
4
7
,
M
a
r.
2
0
1
7
.
[2
2
]
A.
El
-
F
e
rg
a
n
y
,
“
El
e
c
tri
c
a
l
c
h
a
ra
c
terisa
ti
o
n
o
f
p
r
o
to
n
e
x
c
h
a
n
g
e
m
e
m
b
ra
n
e
fu
e
l
c
e
ll
s
sta
c
k
u
si
n
g
g
ra
ss
h
o
p
p
e
r
o
p
ti
m
ise
r,
”
IET
Ren
e
wa
b
le P
o
we
r Ge
n
e
ra
ti
o
n
,
v
o
l.
1
2
,
n
o
.
1
,
p
p
.
9
–
1
7
,
Ja
n
.
2
0
1
8
.
[2
3
]
H.
El
m
e
twa
ly
,
A.
A
.
El
d
e
so
u
k
y
,
a
n
d
A.
A
.
S
a
ll
a
m
,
“
An
A
d
a
p
ti
v
e
D
-
F
ACTS
fo
r
P
o
we
r
Q
u
a
li
ty
En
h
a
n
c
e
m
e
n
t
in
a
n
Iso
late
d
M
icr
o
g
ri
d
,
”
IEE
E
Acc
e
ss
,
v
o
l.
8
,
p
p
.
5
7
9
2
3
–
5
7
9
4
2
,
2
0
2
0
.
[2
4
]
A.
K.
Bh
a
n
d
a
ri
a
n
d
K.
Ra
h
u
l
,
“
A
n
o
v
e
l
l
o
c
a
l
c
o
n
tras
t
f
u
sio
n
-
b
a
se
d
fu
z
z
y
m
o
d
e
l
f
o
r
c
o
lo
r
i
m
a
g
e
m
u
lt
il
e
v
e
l
th
re
sh
o
l
d
i
n
g
u
sin
g
g
ra
ss
h
o
p
p
e
r
o
p
ti
m
iza
ti
o
n
,
”
Ap
p
li
e
d
S
o
ft
C
o
mp
u
ti
n
g
J
o
u
r
n
a
l
,
v
o
l.
8
1
,
Au
g
.
2
0
1
9
.
[2
5
]
M
.
Ba
h
y
,
e
t
a
l
.
,
“
Vo
lt
a
g
e
c
o
n
tr
o
l
o
f
sw
it
c
h
e
d
re
lu
c
ta
n
c
e
g
e
n
e
ra
to
r
u
sin
g
g
ra
s
sh
o
p
p
e
r
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m (IJP
EDS
),
v
o
l.
1
1
,
n
o
.
1
,
p
p
.
7
5
–
8
5
,
2
0
2
0
.
[2
6
]
A.
F
a
th
y
,
“
Re
c
e
n
t
m
e
ta
-
h
e
u
risti
c
g
ra
ss
h
o
p
p
e
r
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
fo
r
o
p
ti
m
a
l
re
c
o
n
fi
g
u
ra
ti
o
n
o
f
p
a
rti
a
ll
y
sh
a
d
e
d
P
V arra
y
,
”
S
o
la
r E
n
e
rg
y
,
v
o
l.
1
7
1
,
p
p
.
6
3
8
–
6
5
1
,
S
e
p
.
2
0
1
8
.
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