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
(
I
J
P
E
DS)
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
,
p
p
.
1
9
1
4
~
1
9
2
5
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
7
.
i
3
.
p
p
1
9
1
4
-
1
9
2
5
1914
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Rea
l
-
time
selec
tive ha
rmo
nic elimi
na
tion in mul
tilev
el inverte
rs
using
embedde
d
metah
euristi
c opt
imiza
tion
o
n P
YN
Q
-
Z2
T
a
ha
Ahm
a
d H
us
s
ein
1
,
Da
ha
m
a
n Is
ha
k
2
1
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
Te
c
h
n
i
q
u
e
s
,
N
o
r
t
h
e
r
n
Te
c
h
n
i
c
a
l
U
n
i
v
e
r
si
t
y
,
M
o
su
l
,
I
r
a
q
2
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
,
P
r
i
n
c
e
M
o
h
a
mm
a
d
B
i
n
F
a
h
d
U
n
i
v
e
r
si
t
y
,
Ea
s
t
e
r
n
P
r
o
v
i
n
c
e
,
S
a
u
d
i
A
r
a
b
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
1
2
,
2
0
2
5
R
ev
is
ed
J
u
l 1
4
,
2
0
2
6
Acc
ep
ted
J
u
l 2
1
,
2
0
2
6
Th
is
p
a
p
e
r
o
ffe
rs
a
stru
c
tu
re
d
m
e
th
o
d
o
l
o
g
y
fo
r
re
g
u
latin
g
o
p
ti
m
a
l
c
o
n
tro
l
sw
it
c
h
in
g
a
n
g
les
i
n
m
u
lt
il
e
v
e
l
in
v
e
rters
to
a
c
h
iev
e
se
lec
ti
v
e
h
a
rm
o
n
ic
e
li
m
in
a
ti
o
n
(S
HE)
u
sin
g
e
m
b
e
d
d
e
d
o
p
t
imiz
a
ti
o
n
a
l
g
o
ri
th
m
s
o
n
th
e
P
YN
Q‑Z2
F
P
G
A
o
p
e
ra
ti
n
g
b
a
se
.
Th
e
p
ro
p
o
se
d
a
p
p
r
o
a
c
h
e
m
p
lo
y
s
m
e
tah
e
u
risti
c
tec
h
n
i
q
u
e
s
i
n
c
lu
d
in
g
p
a
rti
c
le
sw
a
rm
o
p
t
imiz
a
ti
o
n
(P
S
O)
,
g
e
n
e
ti
c
a
lg
o
rit
h
m
(G
A),
g
ra
y
wo
lf
o
p
ti
m
iza
ti
o
n
(G
WO),
slim
e
m
o
u
ld
a
lg
o
rit
h
m
(S
M
A),
a
n
d
wh
a
le
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
(W
OA
)
t
o
g
e
n
e
ra
te
c
a
n
d
id
a
te
sw
it
c
h
in
g
a
n
g
les
a
c
ro
s
s
a
wid
e
ra
n
g
e
o
f
m
o
d
u
lati
o
n
i
n
d
ice
s.
F
o
r
e
a
c
h
m
o
d
u
lati
o
n
in
d
e
x
,
th
e
m
o
st
e
ffe
c
ti
v
e
so
l
u
ti
o
n
t
o
wa
rd
s
h
a
rm
o
n
ic
re
d
u
c
ti
o
n
a
n
d
wa
v
e
fo
rm
q
u
a
li
ty
is
se
lec
ted
a
n
d
im
p
lem
e
n
ted
o
n
t
h
e
F
P
G
A
c
o
n
tro
ll
e
r,
e
n
a
b
li
n
g
re
li
a
b
le
re
a
l‑t
ime
o
p
e
ra
ti
o
n
wit
h
v
e
ry
l
o
w
d
e
lay
.
Ex
p
e
rime
n
tal
v
a
li
d
a
ti
o
n
o
f
a
3
1
‑lev
e
l
sin
g
le‑p
h
a
se
in
v
e
rter
c
o
n
firms
th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
t
h
e
m
e
th
o
d
i
n
e
l
imin
a
ti
n
g
se
lec
ted
h
a
rm
o
n
ics
a
n
d
re
fi
n
in
g
th
e
fu
n
d
a
m
e
n
tal
o
u
tp
u
t.
Co
m
b
i
n
i
n
g
c
o
m
p
a
ra
ti
v
e
a
l
g
o
ri
th
m
ic
se
lec
ti
o
n
with
F
P
G
A‑b
a
se
d
c
o
n
tro
l
d
e
m
o
n
stra
t
e
s
a
sy
ste
m
a
ti
c
a
n
d
e
fficie
n
t
st
ra
teg
y
fo
r
a
d
v
a
n
c
e
d
in
v
e
rter
sy
ste
m
s.
A
M
ATLAB/S
imu
li
n
k
m
o
d
e
l
is
c
o
n
s
tru
c
ted
t
o
re
p
re
se
n
t
th
e
3
1
-
lev
e
l
i
n
v
e
rter
t
o
e
n
h
a
n
c
e
th
e
p
ra
c
ti
c
a
l
a
sp
e
c
t
a
n
d
stu
d
y
t
h
e
fre
q
u
e
n
c
y
s
p
e
c
tru
m
,
wh
e
re
m
a
n
y
h
a
rm
o
n
ics
th
a
t
c
o
n
tri
b
u
te
t
o
o
b
tai
n
in
g
THD
with
in
t
h
e
IEE
E
sta
n
d
a
rd
s
a
re
e
li
m
in
a
ted
.
Also
,
th
e
d
iffere
n
t
ty
p
e
s
o
f
lo
ss
e
s a
re
c
a
lcu
late
d
b
a
se
d
o
n
th
e
g
o
v
e
rn
i
n
g
m
a
th
e
m
a
ti
c
a
l
ra
tes
.
K
ey
w
o
r
d
s
:
FP
GA
MLI
Op
tim
izatio
n
SHE
T
HD
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
:
T
ah
a
Ah
m
ad
H
u
s
s
ein
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
T
ec
h
n
iq
u
es
,
No
r
th
er
n
T
ec
h
n
ical
Un
iv
er
s
ity
Mo
s
u
l,
I
r
aq
E
m
ail: ta
h
a.
h
u
s
s
ien
@
n
tu
.
ed
u
.
i
q
1.
I
NT
RO
D
UCT
I
O
N
Mu
ltil
ev
el
in
v
er
ter
s
(
ML
I
s
)
h
av
e
b
ec
o
m
e
ce
n
tr
al
to
m
o
d
er
n
p
o
wer
elec
tr
o
n
ics,
o
f
f
e
r
i
n
g
s
u
p
er
io
r
wav
ef
o
r
m
q
u
ality
,
r
e
d
u
ce
d
s
w
itch
in
g
lo
s
s
es,
an
d
en
h
a
n
ce
d
v
o
ltag
e
ad
ap
tab
ilit
y
f
o
r
m
e
d
iu
m
-
an
d
h
ig
h
-
v
o
ltag
e
ap
p
licatio
n
s
[
1
]
-
[
3
]
.
T
h
ei
r
ab
i
lity
to
s
y
n
th
esize
s
tep
p
ed
v
o
lt
ag
e
wav
ef
o
r
m
s
m
ak
es
th
e
m
i
d
ea
l
f
o
r
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
,
m
o
to
r
d
r
iv
e
s
,
an
d
s
m
ar
t
g
r
id
in
te
r
f
ac
es
[
4
]
.
Ho
wev
e
r
,
as
th
e
n
u
m
b
e
r
o
f
v
o
ltag
e
lev
els
in
cr
ea
s
es,
s
o
d
o
es
th
e
co
m
p
l
ex
ity
o
f
c
o
n
tr
o
llin
g
s
witch
in
g
an
g
les
to
s
u
p
p
r
ess
s
p
ec
if
ic
h
ar
m
o
n
ics
wh
ile
m
ain
tain
in
g
th
e
d
esire
d
o
u
tp
u
t
v
o
ltag
e.
Selectiv
e
h
ar
m
o
n
ic
e
lim
in
atio
n
(
SHE
)
is
a
well
-
est
ab
lis
h
ed
tech
n
iq
u
e
f
o
r
m
itig
atin
g
lo
w
-
o
r
d
e
r
h
ar
m
o
n
ics
b
y
s
o
lv
in
g
n
o
n
lin
ea
r
tr
an
s
ce
n
d
e
n
tal
eq
u
ati
o
n
s
d
e
r
iv
ed
f
r
o
m
Fo
u
r
ie
r
an
aly
s
is
[
5
]
-
[9
]
.
T
r
ad
itio
n
al
n
u
m
er
ical
m
eth
o
d
s
s
u
ch
as
New
to
n
–
R
ap
h
s
o
n
an
d
r
esu
lt
-
b
ased
lo
o
k
u
p
tab
les
o
f
ten
s
tr
u
g
g
le
with
c
o
n
v
e
r
g
e
n
ce
an
d
ad
ap
ta
b
ilit
y
u
n
d
er
d
y
n
am
ic
co
n
d
itio
n
s
.
T
o
a
d
d
r
e
s
s
th
ese
lim
itatio
n
s
,
r
ec
en
t
r
esear
ch
h
as
in
cr
ea
s
in
g
ly
tu
r
n
ed
to
m
etah
eu
r
is
tic
o
p
tim
izatio
n
alg
o
r
ith
m
s
,
wh
ich
o
f
f
er
r
o
b
u
s
t,
f
lex
ib
le,
an
d
s
u
s
tain
ab
le
s
o
lu
tio
n
s
f
o
r
s
o
lv
in
g
th
e
SHE
p
r
o
b
lem
.
R
ec
en
t stu
d
ies h
av
e
d
em
o
n
s
tr
ated
t
h
e
ef
f
ec
tiv
en
ess
o
f
v
ar
io
u
s
m
etah
eu
r
is
tics
in
SH
E
ap
p
licatio
n
s
[
1
0
]
.
Yiğ
it
et
a
l.
[
11
]
co
n
d
u
cted
a
co
m
p
r
eh
e
n
s
iv
e
co
m
p
ar
is
o
n
o
f
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
6
9
4
R
ea
l
-
time
s
elec
tive
h
a
r
mo
n
ic
elimin
a
tio
n
in
mu
ltil
ev
el
in
ve
r
ters
u
s
in
g
emb
ed
d
ed
…
(
Ta
h
a
A
h
ma
d
Hu
s
s
ein
)
1915
2
2
alg
o
r
ith
m
s
f
o
r
SHE
in
ML
I
s
,
h
ig
h
lig
h
tin
g
th
e
s
u
p
er
io
r
p
er
f
o
r
m
a
n
ce
o
f
g
e
n
etic
alg
o
r
ith
m
(
GA)
,
g
r
ay
wo
lf
o
p
tim
izatio
n
(
GW
O)
,
an
d
SP
SA
in
ter
m
s
o
f
T
HD
r
e
d
u
cti
o
n
.
Sajid
et
a
l.
[1
2
]
in
tr
o
d
u
c
ed
th
e
R
u
n
g
e
–
Ku
tta
o
p
tim
izatio
n
(
R
KO)
m
eth
o
d
f
o
r
H
-
b
r
i
d
g
e
in
v
er
ter
s
,
o
u
tp
er
f
o
r
m
in
g
class
ical
an
d
m
eta
h
eu
r
is
tic
tech
n
iq
u
es
in
co
n
v
er
g
en
ce
s
p
ee
d
a
n
d
h
a
r
m
o
n
ic
s
u
p
p
r
ess
io
n
.
Sad
o
u
g
h
i
et
a
l.
[1
3
]
ap
p
lied
a
h
y
b
r
id
PS
O
s
tr
ateg
y
to
SHE
in
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
te
r
s
,
ac
h
iev
in
g
e
n
h
an
ce
d
s
tab
ilit
y
ac
r
o
s
s
m
o
d
u
latio
n
in
d
ices.
B
u
ild
in
g
o
n
th
ese
ad
v
an
ce
m
e
n
ts
,
th
is
p
ap
er
p
r
esen
ts
a
r
ea
l
-
tim
e
SHE
p
lat
f
o
r
m
f
o
r
a
3
1
-
lev
el
i
n
v
er
ter
u
s
in
g
em
b
ed
d
e
d
m
etah
eu
r
is
tic
o
p
tim
izatio
n
o
n
th
e
PYNQ
-
Z
2
p
latf
o
r
m
.
Fi
v
e
alg
o
r
ith
m
s
:
g
en
etic
alg
o
r
i
th
m
(
GA)
,
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
,
g
r
ey
wo
lf
o
p
tim
izer
(
GW
O)
,
s
lim
e
m
o
u
ld
alg
o
r
ith
m
(
SMA)
,
an
d
wh
ale
o
p
tim
izatio
n
alg
o
r
ith
m
(
W
OA)
[1
4]
-
[
1
7
]
a
r
e
im
p
lem
e
n
te
d
an
d
ev
alu
ated
.
Fo
r
ea
ch
m
o
d
u
latio
n
in
d
ex
,
th
e
s
y
s
tem
d
y
n
am
ically
s
elec
ts
th
e
alg
o
r
ith
m
t
h
at
y
ield
s
t
h
e
m
in
im
u
m
t
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
.
T
h
e
o
p
tim
izatio
n
r
o
u
tin
es
ar
e
s
y
n
th
esized
u
s
in
g
Viv
ad
o
an
d
d
e
p
lo
y
ed
o
n
th
e
Z
y
n
q
-
7
0
0
0
So
C
[
1
8]
,
[
1
9
]
,
e
n
ab
lin
g
p
ar
allel
co
m
p
u
tatio
n
an
d
lo
w
-
laten
cy
co
n
tr
o
l.
2.
M
E
T
H
O
D
T
h
is
wo
r
k
p
r
esen
ts
a
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
o
f
SHE
f
o
r
a
3
1
-
lev
el
in
v
e
r
ter
u
s
in
g
m
et
ah
eu
r
is
tic
o
p
tim
izatio
n
alg
o
r
ith
m
s
s
y
n
th
esized
an
d
d
ep
lo
y
ed
th
r
o
u
g
h
th
e
Viv
ad
o
Desig
n
Su
ite.
T
h
e
m
eth
o
d
o
lo
g
y
is
s
tr
u
ctu
r
ed
in
t
o
f
o
u
r
s
tag
es:
h
ar
m
o
n
ic
m
o
d
ellin
g
,
alg
o
r
ith
m
d
esig
n
,
HDL
in
teg
r
atio
n
,
an
d
d
y
n
am
ic
T
HD
-
b
ased
alg
o
r
ith
m
s
elec
tio
n
.
I
n
th
e
h
ar
m
o
n
ic
m
o
d
ellin
g
s
tag
e,
th
e
in
v
e
r
ter
wav
ef
o
r
m
is
c
o
n
s
tr
u
cted
with
1
5
s
witch
in
g
an
g
les
p
er
q
u
ar
te
r
cy
cle,
ex
p
l
o
itin
g
s
y
m
m
etr
y
to
r
ed
u
ce
co
m
p
u
tatio
n
al
c
o
m
p
lex
ity
.
Fo
u
r
ie
r
an
aly
s
is
y
ield
s
n
o
n
lin
ea
r
tr
an
s
ce
n
d
en
tal
eq
u
atio
n
s
tar
g
etin
g
th
e
elim
in
atio
n
o
f
f
o
u
r
tee
n
lo
w
-
o
r
d
er
h
ar
m
o
n
ics
(
3
r
d
–
2
9
th
)
wh
ile
m
ai
n
tain
in
g
th
e
f
u
n
d
am
en
tal
v
o
ltag
e.
T
h
e
m
o
d
u
latio
n
in
d
ex
is
tr
ea
ted
as
a
co
n
tr
o
l
p
ar
am
eter
,
with
s
witch
in
g
a
n
g
les
o
p
tim
ized
ac
c
o
r
d
in
g
ly
.
T
h
e
alg
o
r
ith
m
d
esig
n
s
tag
e
im
p
lem
en
ts
f
iv
e
m
etah
eu
r
is
tic
m
eth
o
d
s
,
GA
[
2
0
]
,
PS
O
[
2
1
]
,
GW
O
[
2
2
]
,
SMA
[
2
3
]
,
W
OA
[
2
4
]
,
ad
ap
ted
f
o
r
f
ix
e
d
-
p
o
in
t
ar
ith
m
etic
an
d
p
ar
allel
co
m
p
u
tatio
n
to
s
u
it
FP
G
A
d
ep
lo
y
m
en
t.
T
h
e
o
p
tim
izatio
n
p
r
o
b
lem
s
p
an
s
a
1
5
-
d
im
en
s
io
n
al
s
ea
r
ch
s
p
ac
e,
co
n
s
tr
ain
ed
b
y
a
n
g
le
o
r
d
e
r
in
g
a
n
d
m
o
d
u
latio
n
in
d
ex
b
o
u
n
d
s
,
with
f
itn
ess
d
ef
in
e
d
b
y
T
HD
m
in
im
izatio
n
u
n
d
e
r
SHE
co
n
s
tr
ain
ts
.
I
n
th
e
HDL
in
teg
r
atio
n
s
tag
e,
alg
o
r
ith
m
ic
co
r
es
ar
e
m
o
d
u
lar
ly
tr
an
s
lated
in
to
VHDL
an
d
s
y
n
th
esized
o
n
a
Z
y
n
q
-
7
0
0
0
So
C
u
s
in
g
Viv
ad
o
.
Fin
ally
,
d
y
n
am
ic
alg
o
r
ith
m
s
elec
tio
n
is
p
er
f
o
r
m
ed
:
f
o
r
ea
ch
m
o
d
u
latio
n
in
d
e
x
,
all
f
iv
e
alg
o
r
ith
m
s
ar
e
ex
ec
u
ted
,
an
d
t
h
e
o
n
e
y
ield
i
n
g
th
e
lo
west
T
HD
is
ch
o
s
en
to
g
en
er
ate
in
v
er
ter
s
witch
in
g
s
i
g
n
als.
T
h
is
ad
ap
tiv
e
s
elec
tio
n
en
s
u
r
es
o
p
tim
al
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
u
n
d
er
v
ar
y
in
g
o
p
er
atin
g
co
n
d
itio
n
s
.
2.
1.
M
a
t
hema
t
ica
l f
o
rm
ula
t
i
o
n o
f
SH
E
pro
blem
SHE
tech
n
iq
u
e
is
f
o
r
m
u
lated
b
y
r
ep
r
esen
tin
g
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
a
m
u
ltil
ev
el
in
v
er
ter
as
a
Fo
u
r
ier
s
er
ies.
T
h
e
p
r
im
ar
y
o
b
jectiv
e
is
to
elim
in
ate
s
p
ec
if
ic
lo
w
-
o
r
d
er
o
d
d
h
ar
m
o
n
ics,
ty
p
ically
th
e
3
rd
,
5
th
,
7
th
u
p
to
th
e
2
9
th
,
wh
ile
p
r
eser
v
in
g
th
e
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
t.
Fo
r
a
g
en
er
al
s
tair
ca
s
e
wav
ef
o
r
m
,
th
e
o
u
tp
u
t
v
o
ltag
e
(
)
ca
n
b
e
ex
p
r
ess
ed
as [
25
]:
(
)
=
0
+
∑
∞
=
1
(
)
+
s
in
(
)
(
1
)
wh
er
e:
is
th
e
h
ar
m
o
n
ic
o
r
d
er
,
0
,
,
ar
e
th
e
Fo
u
r
ier
co
ef
f
icien
ts
,
is
th
e
an
g
u
lar
f
r
e
q
u
en
c
y
.
Du
e
to
th
e
q
u
a
r
ter
-
s
y
m
m
etr
y
ar
o
u
n
d
π/2
o
f
th
e
s
tair
ca
s
e
wav
ef
o
r
m
,
0
,
,
a
n
d
th
e
s
in
e
ter
m
s
o
f
e
v
en
h
ar
m
o
n
ics
ar
e
ca
n
ce
led
.
As a
r
esu
lt,
th
e
(
1
)
r
ed
u
ce
s
to
(
2
)
.
(
)
=
∑
29
=
1
,
3
,
5
,
7
…
.
s
in
(
)
(
2
)
I
n
a
3
1
-
lev
el
th
r
ee
-
p
h
ase
in
v
er
ter
,
f
if
teen
s
witch
in
g
an
g
le
s
p
er
q
u
ar
te
r
cy
cle
ar
e
av
ail
ab
le,
allo
win
g
th
e
elim
in
atio
n
o
r
s
ig
n
if
ican
t
r
ed
u
ctio
n
o
f
u
p
to
f
o
u
r
teen
h
ar
m
o
n
ics:
3
rd
,
5
th
,
7
th
,
9
th
,
11
th
,
1
3
th
,
1
5
th
,
1
7
th
,
1
9
th
,
2
1
st
,
2
3
rd
,
2
5
th
,
2
7
th
,
an
d
29
th
.
T
h
is
is
wh
y
th
e
lef
t
s
id
e
o
f
(4
)
u
p
to
(
1
7
)
is
s
et
to
ze
r
o
wh
ile
k
ee
p
in
g
t
h
e
f
u
n
d
am
e
n
tal
v
o
lt
ag
e
at
its
m
ax
im
u
m
v
alu
e
in
(
3
)
b
y
s
ettin
g
th
e
lef
t
s
id
e
to
its
m
ax
im
u
m
v
alu
e
(
i.e
.
m
×
V
1(rms)
)
.
T
h
e
o
p
tim
al
f
if
teen
g
atin
g
an
g
les
,
(
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
,
11
,
12
,
13
,
14
,
15
)
t
h
at
co
n
tr
o
l
t
h
e
in
v
e
r
ter
s
witch
es c
an
b
e
f
o
u
n
d
as
(
3
)
.
1
=
[
1
+
2
+
3
+
4
+
5
+
6
+
7
+
8
+
9
+
10
+
11
,
12
+
3
13
+
14
+
15
]
=
∗
1
(
)
(
3
)
wh
er
e
is
th
e
m
o
d
u
latio
n
in
d
e
x
,
an
d
1
is
th
e
f
u
n
d
am
en
tal
c
o
m
p
o
n
e
n
t
:
3
=
[
3
1
+
3
2
+
3
3
+
3
4
+
3
5
+
3
6
+
3
7
+
3
8
+
3
9
+
3
10
+
3
11
+
3
12
+
3
13
+
3
14
+
3
15
]
=
0
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1914
-
1
9
2
5
1916
5
=
[
5
1
+
5
2
+
5
3
+
5
4
+
5
5
+
5
6
+
5
7
+
5
8
+
5
9
+
5
10
+
5
11
+
5
12
+
5
13
+
5
14
+
5
15
]
=
0
(
5
)
7
=
[
7
1
+
7
2
+
7
3
+
7
4
+
7
5
+
7
6
+
7
7
+
7
8
+
7
9
+
7
10
+
7
11
+
7
12
+
7
13
+
7
14
+
7
15
]
=
0
(
6
)
9
=
[
9
1
+
9
2
+
9
3
+
9
4
+
9
5
+
9
6
+
9
7
+
9
8
+
9
9
+
9
10
+
9
11
+
9
12
+
9
13
+
9
14
+
9
15
]
=
0
(
7
)
11
=
[
11
1
+
11
2
+
11
3
+
11
4
+
11
5
+
11
6
+
11
7
+
11
8
+
11
9
+
11
10
+
11
11
+
11
12
+
11
13
+
11
14
+
11
15
]
=
0
(
8
)
13
=
[
13
1
+
13
2
+
13
3
+
13
4
+
13
5
+
13
6
+
13
7
+
13
8
+
13
9
+
13
10
+
13
11
+
13
12
+
13
13
+
13
14
+
13
15
]
=
0
(
9
)
15
=
[
15
1
+
15
2
+
15
3
+
15
4
+
15
5
+
15
6
+
15
7
+
15
8
+
15
9
+
15
10
+
15
11
+
15
12
+
15
13
+
15
14
+
15
15
]
=
0
(
1
0
)
17
=
[
17
1
+
17
2
+
17
3
+
17
4
+
17
5
+
17
6
+
17
7
+
17
8
+
17
9
+
17
10
+
17
11
+
17
12
+
17
13
+
17
14
+
17
15
]
=
0
(
1
1
)
19
=
[
19
1
+
19
2
+
19
3
+
19
4
+
19
5
+
19
6
+
19
7
+
19
8
+
19
9
+
19
10
+
19
11
+
19
12
+
19
13
+
19
14
+
19
15
]
=
0
(
1
2
)
21
=
[
21
1
+
21
2
+
21
3
+
21
4
+
21
5
+
21
6
+
21
7
+
21
8
+
21
9
+
21
10
+
21
11
+
21
12
+
21
13
+
21
14
+
21
15
]
=
0
(
1
3
)
23
=
[
23
1
+
23
2
+
23
3
+
23
4
+
23
5
+
23
6
+
23
7
+
23
8
+
23
9
+
23
10
+
23
11
+
23
12
+
23
13
+
23
14
+
23
15
]
=
0
(
1
4
)
25
=
[
25
1
+
25
2
+
25
3
+
25
4
+
25
5
+
25
6
+
25
7
+
25
8
+
25
9
+
25
10
+
25
11
+
25
12
+
25
13
+
25
14
+
25
15
]
=
0
(
1
5
)
27
=
[
27
1
+
27
2
+
27
3
+
27
4
+
27
5
+
27
6
+
27
7
+
27
8
+
27
9
+
27
10
+
27
11
+
27
12
+
27
13
+
27
14
+
27
15
]
=
0
(
1
6
)
29
=
[
29
1
+
29
2
+
29
3
+
29
4
+
29
5
+
29
6
+
29
7
+
29
8
+
29
9
+
29
10
+
29
11
,
29
12
+
29
13
+
29
14
+
29
15
]
=
0
(
1
7
)
Pro
v
id
ed
th
at
0
<
1
<
2
<
3
<
4
<
5
<
6
<
7
<
8
<
9
<
10
<
11
<
12
<
13
<
14
<
15
<
/
2
(
1
8
)
So
lv
in
g
th
is
s
y
s
tem
y
ield
s
th
e
o
p
tim
al
s
et
o
f
s
witch
in
g
an
g
les
th
at
s
u
p
p
r
ess
th
e
s
p
ec
if
ied
h
ar
m
o
n
ics.
W
h
ile
h
ig
h
er
-
o
r
d
e
r
h
ar
m
o
n
ics
s
u
ch
as
th
e
1
7
th
,
1
9
th
,
2
3
rd
,
2
5
th
,
2
7
th
,
an
d
2
9
th
co
n
tr
ib
u
te
less
to
o
v
er
all
d
is
to
r
tio
n
d
u
e
to
th
eir
l
o
wer
am
p
litu
d
e,
t
h
eir
elim
in
atio
n
f
u
r
th
er
im
p
r
o
v
es
wav
ef
o
r
m
q
u
ality
an
d
r
ed
u
ce
s
f
ilter
in
g
r
eq
u
ir
em
e
n
ts
.
2
.
2
.
Co
m
pa
ra
t
iv
e
s
elec
t
io
n o
f
o
ptim
a
l
a
ng
les
Fo
r
ea
c
h
m
o
d
u
lat
io
n
i
n
d
e
x
a
n
d
f
o
r
t
h
e
f
i
v
e
al
g
o
r
i
th
m
s
u
s
ed
i
n
t
h
is
wo
r
k
,
t
h
e
s
wi
tc
h
i
n
g
a
n
g
le
s
et
y
ie
ld
s
t
h
e
lo
west
T
H
D,
as
s
h
o
wn
f
o
r
G
A,
P
SO,
GW
O,
W
OA,
a
n
d
S
MA
as
s
h
o
wn
i
n
Fi
g
u
r
es
1
(
a
)
-
1
(
e
)
,
r
es
p
e
cti
v
e
ly
.
F
o
r
t
h
e
m
o
d
u
lati
o
n
i
n
d
e
x
(
m
)
,
wit
h
i
n
t
h
e
r
a
n
g
e
f
r
o
m
0
t
o
1
0
,
te
n
m
e
asu
r
e
m
e
n
ts
w
e
r
e
co
n
d
u
ct
ed
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
6
9
4
R
ea
l
-
time
s
elec
tive
h
a
r
mo
n
ic
elimin
a
tio
n
in
mu
ltil
ev
el
in
ve
r
ters
u
s
in
g
emb
ed
d
ed
…
(
Ta
h
a
A
h
ma
d
Hu
s
s
ein
)
1917
wit
h
an
i
n
c
r
e
m
e
n
t
al
s
te
p
o
f
0
.
1
f
o
r
e
ac
h
r
ea
d
i
n
g
ac
r
o
s
s
all
f
i
v
e
al
g
o
r
it
h
m
s
.
T
h
e
m
i
n
im
u
m
v
al
u
e
o
f
th
e
T
HD
,
as
o
b
tai
n
ed
f
r
o
m
t
h
ese
a
lg
o
r
it
h
m
s
,
was
ad
o
p
t
ed
.
T
h
e
f
in
al
r
es
u
lt
is
r
e
p
r
ese
n
t
ed
b
y
t
h
e
d
o
t
te
d
c
u
r
v
e
i
n
F
ig
u
r
e
2
,
wh
i
ch
ill
u
s
t
r
ates
th
e
o
p
ti
m
u
m
v
a
lu
es
o
f
t
h
e
f
i
f
t
ee
n
an
g
l
es
co
r
r
es
p
o
n
d
i
n
g
t
o
an
y
s
ele
ct
ed
v
a
lu
e
o
f
m
.
T
h
is
co
m
p
a
r
at
iv
e
s
e
le
cti
o
n
e
n
s
u
r
es
th
a
t
o
n
l
y
t
h
e
m
o
s
t
e
f
f
ec
t
iv
e
s
o
lu
t
io
n
,
r
e
g
a
r
d
less
o
f
al
g
o
r
it
h
m
o
r
i
g
i
n
,
is
u
s
e
d
f
o
r
h
a
r
d
wa
r
e
d
e
p
l
o
y
m
e
n
t
.
T
h
e
s
e
lect
e
d
a
n
g
le
s
ets
a
r
e
s
to
r
e
d
i
n
l
o
o
k
u
p
t
ab
les
i
n
d
e
x
e
d
b
y
m
o
d
u
lat
io
n
l
e
v
el
.
F
o
r
in
s
t
an
ce
,
m
o
d
u
l
ati
o
n
in
d
e
x
m
=
0
.
8
0
is
s
el
ec
te
d
,
a
n
d
t
h
e
o
p
ti
m
al
a
n
g
les
we
r
e
e
x
t
r
a
ct
ed
f
r
o
m
t
h
e
o
p
tim
u
m
T
HD
cu
r
v
e
as
f
o
l
lo
ws:
1
=
2°
,
2
=
7
.
3°
,
3
=
14
.
5°
,
4
=
15
.
2°
,
5
=
22
.
1°
,
6
=
24
.
2°
,
7
=
30
.
4°
,
8
=
35
.
9°
,
9
=
38
.
7°
,
,
10
=
44
.
6°
,
11
=
47
.
6°
,
12
=
56
.
5°
,
13
=
67
.
2°
,
14
=
76
.
1°
,
15
=
85°
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
Fig
u
r
e
1
.
C
o
m
p
a
r
is
o
n
o
f
T
HD
v
er
s
u
s
m
o
d
u
latio
n
in
d
e
x
f
o
r
f
iv
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
: (
a)
GA,
(
b
)
PS
O,
(
c)
GW
O,
(
d
)
W
OA,
an
d
(
e
)
SMA
Fig
u
r
e
2.
Op
tim
u
m
(
d
o
tted
)
T
HD
cu
r
v
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1914
-
1
9
2
5
1918
2
.
3
.
E
m
bedd
ed
im
plem
ent
a
t
io
n o
f
P
YNQ
-
Z2
co
ntr
o
ller
T
h
e
o
p
tim
al
s
witch
in
g
an
g
les
ar
e
em
b
ed
d
e
d
in
t
o
th
e
PYNQ
-
Z
2
p
latf
o
r
m
u
s
in
g
a
h
y
b
r
id
h
ar
d
war
e
-
s
o
f
twar
e
ar
ch
itectu
r
e.
T
h
e
s
o
f
t
war
e
lay
er
(
AR
M
C
o
r
tex
-
A9
)
h
an
d
les
m
o
d
u
latio
n
in
d
ex
in
p
u
t,
an
g
le
s
elec
tio
n
,
an
d
wav
ef
o
r
m
m
o
n
ito
r
in
g
,
a
n
d
th
e
h
a
r
d
war
e
lay
e
r
(
FP
GA)
ex
ec
u
tes
PW
M
g
en
er
atio
n
b
ased
o
n
s
elec
ted
s
witch
in
g
an
g
les u
s
in
g
c
u
s
to
m
VHDL
m
o
d
u
les
f
o
r
t
h
e
ten
M
OSFET
s
witch
es
in
th
e
ML
I
d
esig
n
,
as
s
h
o
wn
in
F
ig
u
r
e
3
,
wh
ich
d
em
o
n
s
tr
ates th
e
o
n
an
d
o
f
f
s
witch
s
tatu
s
p
a
tter
n
f
o
r
th
e
3
1
lev
els d
u
r
in
g
o
n
e
co
m
p
lete
cy
cle.
Fig
u
r
e
4
s
h
o
ws th
e
VHDL
d
es
ig
n
co
n
s
tr
ain
t th
at
s
elec
ts
th
e
t
en
o
u
tp
u
t
p
o
r
ts
f
r
o
m
th
e
PYN
Q
-
Z
2
co
n
tr
o
ller
,
as
o
b
tain
ed
f
r
o
m
th
e
r
ef
er
e
n
ce
m
an
u
al
[
2
6
]
.
T
ab
le
1
s
h
o
ws
th
at
t
h
e
PYNQ
-
Z
2
b
o
ar
d
p
r
o
v
id
es
am
p
le
FP
GA
r
eso
u
r
ce
s
,
m
ak
in
g
it
s
u
itab
le
f
o
r
im
p
lem
en
tin
g
an
d
s
ca
lin
g
a
3
1
-
lev
el
in
v
e
r
ter
with
ef
f
icien
t
h
ar
d
war
e
u
tili
za
tio
n
.
Fig
u
r
e
3.
VHDL
r
o
u
tin
e
f
o
r
th
e
ten
s
s
witch
s
tatu
s
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
6
9
4
R
ea
l
-
time
s
elec
tive
h
a
r
mo
n
ic
elimin
a
tio
n
in
mu
ltil
ev
el
in
ve
r
ters
u
s
in
g
emb
ed
d
ed
…
(
Ta
h
a
A
h
ma
d
Hu
s
s
ein
)
1919
Fig
u
r
e
4.
VHDL
Desig
n
co
n
s
tr
ain
t
f
ile
f
o
r
ten
s
witch
es
T
ab
le
1
.
FP
GA
r
eso
u
r
ce
s
o
v
e
r
v
iew
o
n
PYNQ
-
Z
2
u
s
ed
b
y
3
1
-
lev
el
in
v
er
ter
R
e
s
o
u
r
c
e
t
y
p
e
A
v
a
i
l
a
b
l
e
o
n
P
Y
N
Q
-
Z2
U
sed
b
y
t
h
e
3
1
-
l
e
v
e
l
i
n
v
e
r
t
e
r
U
t
i
l
i
z
a
t
i
o
n
(
%)
LU
Ts
5
3
2
0
0
8
4
5
0
1
5
.
9
%
F
l
i
p
-
F
l
o
p
s
1
0
6
4
0
0
1
2
3
0
0
1
1
.
6
%
D
S
P
sl
i
c
e
s
2
2
0
36
1
6
.
4
%
B
l
o
c
k
R
A
M
6
3
0
KB
72
KB
1
1
.
4
%
T
h
ese
f
in
d
in
g
s
in
d
icate
th
at
t
h
e
d
esig
n
u
tili
ze
s
o
n
ly
a
s
m
all
p
o
r
tio
n
o
f
th
e
a
v
ailab
le
FP
GA
r
eso
u
r
ce
s
,
th
er
eb
y
co
n
f
ir
m
in
g
th
e
p
r
ac
ticality
o
f
im
p
lem
en
tin
g
c
o
m
p
l
ex
m
u
ltil
ev
el
in
v
er
ter
ar
c
h
itec
tu
r
es
o
n
m
id
-
r
a
n
g
e
d
ev
ices
wh
ile
p
r
eser
v
in
g
am
p
le
ca
p
ac
ity
f
o
r
ad
d
itio
n
al
c
o
n
t
r
o
l
an
d
m
o
n
ito
r
in
g
f
u
n
ctio
n
s
.
Viv
ad
o
an
d
Xilin
x
SDK
ar
e
u
s
ed
f
o
r
h
a
r
d
war
e
s
y
n
th
esis
an
d
s
o
f
twar
e
in
teg
r
a
tio
n
.
T
h
e
s
y
s
tem
s
u
p
p
o
r
ts
r
ea
l
-
tim
e
m
o
d
u
latio
n
in
d
ex
ad
ju
s
tm
en
t
an
d
d
y
n
am
i
c
an
g
le
s
elec
tio
n
.
T
h
e
PYNQ
-
Z
2
o
p
er
ates
with
a
clo
ck
f
r
eq
u
en
cy
o
f
1
2
5
MH
z,
wh
ile
th
e
tar
g
et
o
u
tp
u
t
f
r
eq
u
en
cy
is
s
et
to
5
0
Hz.
T
h
is
co
n
f
ig
u
r
atio
n
y
ield
s
a
to
tal
o
f
2
,
5
0
0
,
0
0
0
clo
c
k
s
eg
m
en
ts
p
er
o
u
tp
u
t c
y
cle.
T
h
e
n
u
m
b
er
o
f
s
eg
m
en
ts
co
r
r
esp
o
n
d
in
g
to
ea
c
h
s
witch
in
g
s
tate
is
ca
lcu
lated
b
ased
o
n
th
e
an
g
u
lar
d
u
r
atio
n
o
f
th
a
t
s
tate.
Fo
r
in
s
tan
ce
,
at
t
h
e
f
ir
s
t
v
o
ltag
e
lev
el,
t
h
e
s
witch
in
g
p
er
io
d
s
p
an
s
f
r
o
m
(
2
−
1
)
=
(
7
.
3°
−
2°
)
=
5
.
3°
.
T
h
is
tr
an
s
lates to
(
(
2
,
5
0
0
,
0
0
0
/3
6
0
)
×
5
.
3
)
=
3
6
8
0
5
s
eg
m
en
ts
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
P
r
a
ct
ica
l r
esu
lt
s
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
o
u
tco
m
es
o
f
th
e
ex
p
er
im
e
n
tal
v
alid
atio
n
f
o
r
th
e
p
r
o
p
o
s
ed
S
HE
s
tr
ateg
y
ap
p
lied
to
a
3
1
-
lev
el
m
u
ltil
ev
el
in
v
e
r
ter
.
T
h
e
s
y
s
tem
u
tili
ze
s
1
5
o
p
tim
ized
s
witch
in
g
an
g
les
p
er
cy
cle,
s
elec
ted
th
r
o
u
g
h
a
co
m
p
ar
ati
v
e
ev
alu
atio
n
o
f
m
u
ltip
le
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
.
T
h
e
r
esu
lts
ar
e
o
r
g
an
ized
f
o
r
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
o
n
P
YNQ
-
Z
2
.
Fig
u
r
e
5
s
h
o
ws th
e
s
tr
u
ctu
r
al
co
n
f
ig
u
r
atio
n
o
f
th
e
3
1
-
lev
el
m
u
ltil
ev
el
in
v
er
ter
a
n
d
h
ig
h
lig
h
ts
th
e
ar
r
an
g
em
en
t
o
f
s
witch
es,
DC
s
o
u
r
ce
s
,
an
d
o
u
tp
u
t
ter
m
in
als.
Fig
u
r
e
6
d
is
p
lay
s
th
e
tim
in
g
d
iag
r
am
g
en
er
ate
d
b
y
Viv
ad
o
’
s
b
e
h
av
io
r
al
s
im
u
latio
n
en
v
ir
o
n
m
e
n
t,
s
h
o
wca
s
in
g
th
e
Viv
ad
o
s
im
u
lato
r
f
o
r
th
e
g
ate
tr
ig
g
e
r
s
ig
n
als f
o
r
ten
MO
SF
E
T
s
witch
es u
s
ed
in
th
e
m
u
ltil
ev
el
in
v
e
r
ter
.
Fig
u
r
e
5
.
3
1
-
lev
el
ML
I
to
p
o
lo
g
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1914
-
1
9
2
5
1920
Fig
u
r
e
6.
Viv
a
d
o
b
e
h
av
io
r
al
s
im
u
latio
n
f
o
r
th
e
ten
MO
SF
E
T
s
Fig
u
r
es
7
to
1
1
illu
s
tr
ate
th
e
g
ate
s
ig
n
als
g
en
er
ated
f
o
r
ea
c
h
p
air
o
f
s
witch
es
b
ased
o
n
th
e
o
p
tim
ized
an
g
les.
E
ac
h
p
u
ls
e
d
iag
r
a
m
r
e
f
lects
th
e
s
elec
tiv
e
h
ar
m
o
n
ic
elim
in
atio
n
s
tr
ateg
y
,
en
s
u
r
in
g
m
in
im
al
T
HD
an
d
p
r
ec
is
e
lev
el
g
en
er
atio
n
.
T
h
e
e
x
p
er
im
en
tal
s
etu
p
is
s
h
o
wn
in
Fig
u
r
e
1
2
.
F
i
g
u
r
e
1
3
d
is
p
l
a
y
s
t
h
e
s
t
e
p
p
e
d
o
u
t
p
u
t
w
a
v
e
f
o
r
m
o
f
t
h
e
in
v
e
r
t
e
r
a
n
d
d
e
m
o
n
s
t
r
a
t
es
t
h
e
s
u
c
c
ess
f
u
l
s
y
n
t
h
e
s
i
s
o
f
3
1
d
is
c
r
et
e
v
o
l
t
ag
e
l
e
v
e
ls
.
Fi
g
u
r
e
1
4
p
r
e
s
e
n
ts
t
h
e
t
o
t
al
h
a
r
m
o
n
i
c
d
is
t
o
r
ti
o
n
p
e
r
c
e
n
t
a
g
e
(
T
H
D
)
=
3
.
4
%
o
f
t
h
e
o
u
t
p
u
t
v
o
l
t
a
g
e
a
n
d
c
o
n
f
i
r
m
s
t
h
e
h
a
r
m
o
n
i
c
s
u
p
p
r
e
s
s
i
o
n
a
c
h
i
e
v
e
d
t
h
r
o
u
g
h
t
h
e
o
p
t
i
m
i
z
e
d
S
H
E
a
n
g
l
es
.
F
i
g
u
r
e
1
5
s
h
o
w
s
t
h
e
i
n
v
e
r
te
r
’
s
o
u
t
p
u
t
v
o
l
t
a
g
e
a
n
d
c
u
r
r
e
n
t
w
a
v
e
f
o
r
m
s
s
u
p
p
l
y
i
n
g
r
e
s
i
s
t
i
v
e
l
o
a
d
R
=
2
0
0
Ω
a
n
d
h
i
g
h
l
i
g
h
t
s
wa
v
e
f
o
r
m
s
y
m
m
e
t
r
y
,
a
m
p
l
i
t
u
d
e
,
a
n
d
p
h
a
s
e
al
i
g
n
m
en
t
.
Fig
u
r
e
7.
P
u
ls
es f
o
r
s
witch
es 1
an
d
2
Fig
u
r
e
8.
P
u
ls
es f
o
r
s
witch
es 3
an
d
4
Fig
u
r
e
9.
P
u
ls
es f
o
r
s
witch
es 5
an
d
6
Fig
u
r
e
10.
P
u
ls
es f
o
r
s
witch
es 7
an
d
8
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
6
9
4
R
ea
l
-
time
s
elec
tive
h
a
r
mo
n
ic
elimin
a
tio
n
in
mu
ltil
ev
el
in
ve
r
ters
u
s
in
g
emb
ed
d
ed
…
(
Ta
h
a
A
h
ma
d
Hu
s
s
ein
)
1921
Fig
u
r
e
1
1
.
P
u
ls
es f
o
r
s
witch
es 9
an
d
1
0
Fig
u
r
e
1
2.
31
-
ML
I
o
u
tp
u
t v
o
ltag
e
ex
p
er
im
e
n
tal
s
et
Fig
u
r
e
1
3.
31
-
ML
I
v
o
ltag
e
Fig
u
r
e
1
4
.
T
HD%
o
u
tp
u
t
v
o
lt
ag
e
Fig
u
r
e
1
5.
O
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
en
t f
o
r
R
2
0
0
Ω
3
.
2
.
Sim
ula
t
i
o
n r
esu
lt
s
T
o
ev
alu
ate
th
e
p
r
o
p
o
s
ed
3
1
-
lev
el
in
v
e
r
ter
,
a
MA
T
L
AB
/Si
m
u
lin
k
m
o
d
el
is
d
ev
elo
p
ed
to
in
v
esti
g
ate
its
d
y
n
am
ic
p
er
f
o
r
m
an
c
e
u
n
d
e
r
d
if
f
er
en
t
lo
ad
co
n
d
itio
n
s
.
T
h
e
s
im
u
latio
n
r
esu
lts
in
F
ig
u
r
e
1
6
d
em
o
n
s
tr
ate
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
ch
ar
ac
te
r
is
tics
at
th
e
in
v
er
ter
o
u
tp
u
t.
Fo
r
th
e
m
o
to
r
lo
ad
(
s
in
g
le
-
p
h
ase
asy
n
ch
r
o
n
o
u
s
m
ac
h
in
e)
,
th
e
s
p
ee
d
,
v
o
ltag
e
,
an
d
m
o
to
r
cu
r
r
e
n
t
wav
e
f
o
r
m
s
ar
e
s
h
o
w
n
,
with
two
ex
te
r
n
al
lo
ad
d
is
tu
r
b
an
ce
s
ap
p
lied
at
0
.
1
s
an
d
0
.
2
s
;
th
e
m
o
to
r
cu
r
r
e
n
t
is
s
ca
led
b
y
a
f
ac
to
r
o
f
ten
f
o
r
clar
ity
.
I
n
th
e
ca
s
e
o
f
th
e
r
esis
t
iv
e
lo
ad
(R
=
2
Ω)
,
th
e
v
o
ltag
e
a
n
d
cu
r
r
e
n
t
wav
ef
o
r
m
s
ar
e
in
p
h
ase,
r
ef
lectin
g
th
e
ex
p
ec
ted
b
e
h
av
io
r
o
f
a
p
u
r
ely
r
esis
tiv
e
elem
en
t.
Fo
r
th
e
in
d
u
ctiv
e
lo
ad
(
R
=
2
Ω,
L
=1
0
m
H)
,
th
e
cu
r
r
en
t
wav
e
f
o
r
m
lag
s
b
eh
in
d
th
e
v
o
ltag
e,
illu
s
tr
atin
g
th
e
ch
ar
ac
ter
is
tic
p
h
ase
s
h
if
t
ass
o
ciate
d
with
i
n
d
u
ctiv
e
co
m
p
o
n
e
n
ts
.
T
h
ese
r
esu
lts
co
n
f
ir
m
th
e
in
v
er
ter
’
s
ca
p
a
b
ilit
y
to
s
u
p
p
ly
d
if
f
er
en
t
ty
p
es
o
f
lo
a
d
s
wh
ile
m
ain
tain
in
g
d
is
tin
ct
v
o
ltag
e
–
cu
r
r
e
n
t
r
elatio
n
s
h
ip
s
,
th
er
eb
y
v
alid
ati
n
g
th
e
m
o
d
el
f
o
r
d
y
n
am
ic
p
er
f
o
r
m
an
ce
a
n
aly
s
is
.
SHE
r
ed
u
ce
s
lo
w
-
o
r
d
er
h
ar
m
o
n
ics
,
wh
ich
lo
wer
s
witch
in
g
lo
s
s
es.
T
h
is
en
h
an
ce
s
PV
an
d
win
d
in
v
er
ter
s
an
d
im
p
r
o
v
es
ef
f
icien
cy
,
wh
ic
h
im
p
r
o
v
es
p
o
wer
q
u
ality
an
d
ex
ten
d
s
e
q
u
ip
m
e
n
t
life
s
p
an
.
I
t
e
n
ab
les
r
en
ewa
b
le
e
n
er
g
y
in
v
er
ter
s
to
s
atis
f
y
g
r
id
-
co
d
e
r
eq
u
ir
em
en
ts
wh
ile
en
s
u
r
in
g
ef
f
icien
t
en
er
g
y
e
x
tr
ac
tio
n
f
r
o
m
v
ar
iab
le
in
p
u
ts
s
u
ch
as
s
o
lar
ir
r
ad
ian
ce
an
d
win
d
v
el
o
city
.
Fo
r
PV
an
d
win
d
s
y
s
tem
s
,
SHE
is
a
p
r
ac
tical
m
o
d
u
latio
n
s
tr
ateg
y
th
at
co
n
tr
o
ls
ef
f
icien
cy
,
p
o
wer
q
u
ality
,
an
d
g
r
id
co
m
p
lian
ce
.
I
t
is
esp
ec
ially
ef
f
ec
tiv
e
in
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1914
-
1
9
2
5
1922
m
u
ltil
ev
el
in
v
er
ter
d
esig
n
s
,
wh
er
e
h
ar
m
o
n
ic
co
n
tr
o
l
is
cr
itical
to
s
ca
lab
ilit
y
.
Fo
r
ef
f
icien
t
im
p
lem
en
tatio
n
,
co
m
b
in
in
g
SHE
with
o
p
tim
iz
atio
n
alg
o
r
ith
m
s
a
n
d
FP
GA
-
b
ased
co
n
tr
o
l
e
n
s
u
r
es
r
en
ewa
b
l
e
in
v
er
ter
s
o
p
e
r
ate
ef
f
icien
tly
u
n
d
er
v
a
r
iab
le
co
n
d
itio
n
s
.
T
h
e
co
m
p
ar
ativ
e
a
n
aly
s
is
o
f
th
e
3
1
-
le
v
el
in
v
er
ter
d
em
o
n
s
tr
ates
a
m
ar
k
ed
im
p
r
o
v
e
m
en
t
in
o
u
tp
u
t
q
u
ality
as
s
h
o
wn
in
F
ig
u
r
e
1
7
.
I
n
t
h
e
f
ir
s
t
ca
s
e,
th
e
f
if
te
en
s
witch
in
g
an
g
les
ar
e
ch
o
s
en
with
s
tep
s
o
f
5
d
e
g
r
ee
s
(
i.e
.
5
,
1
0
,
1
5
,
2
0
,
25,
3
0
,
35,
40,
4
5
,
50,
5
5
,
60,
6
5
,
7
0
,
an
d
7
5
d
e
g
r
ee
s
,
r
esp
ec
tiv
ely
,
p
r
o
d
u
cin
g
a
31
-
lev
el
in
v
er
ter
with
a
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
o
f
1
1
.
6
0
%,
in
d
icatin
g
n
o
ticea
b
le
h
ar
m
o
n
ic
p
r
esen
ce
.
I
n
th
e
s
ec
o
n
d
ca
s
e
,
wh
en
th
e
o
p
tim
ized
an
g
les
(
i.e
.
2
,
7
.
3
,
1
4
.
5
,
1
5
.
2
,
2
2
.
1
,
2
4
.
2
,
3
0
.
4
,
3
5
.
9
,
3
8
.
7
,
4
4
.
6
,
4
7
.
6
,
5
6
.
5
,
6
7
.
2
,
7
6
.
1
,
an
d
8
5
d
eg
r
ee
s
,
r
esp
ec
tiv
ely
)
a
r
e
u
s
ed
r
esu
lts
in
a
r
ed
u
ctio
n
o
f
T
HD
to
4
.
0
6
%.
T
h
is
r
ed
u
ctio
n
h
ig
h
li
g
h
ts
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
ap
p
lied
m
o
d
u
latio
n
s
tr
ateg
y
in
s
u
p
p
r
ess
in
g
h
a
r
m
o
n
ics
an
d
e
n
h
an
cin
g
wav
e
f
o
r
m
p
u
r
ity
.
T
h
e
r
esu
lts
co
n
f
ir
m
th
at
th
e
p
r
o
p
o
s
ed
3
1
-
lev
el
in
v
er
ter
ca
n
d
eliv
er
s
tab
le
v
o
l
tag
e
with
s
ig
n
if
ican
tly
im
p
r
o
v
ed
h
ar
m
o
n
ic
p
e
r
f
o
r
m
an
ce
,
m
a
k
in
g
it
s
u
itab
le
f
o
r
h
ig
h
-
q
u
ality
p
o
we
r
ap
p
licatio
n
s
.
(
a)
(
b
)
Fig
u
r
e
1
6
.
Simu
latio
n
r
esu
lts
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
: (
a)
m
o
to
r
s
p
ee
d
r
esp
o
n
s
e
u
n
d
er
two
to
r
q
u
e
c
h
an
g
es
a
n
d
(
b
)
o
u
tp
u
t v
o
ltag
e
an
d
cu
r
r
en
t
wav
ef
o
r
m
s
f
o
r
th
e
m
o
to
r
,
r
esis
tiv
e,
an
d
in
d
u
ctiv
e
lo
ad
s
3.
3
.
T
y
pe
o
f
lo
s
s
es a
nd
ef
f
iciency
T
h
e
lo
s
s
es
in
a
m
u
lti
-
lev
el
i
n
v
er
ter
ar
e:
i
)
C
o
n
d
u
ctio
n
lo
s
s
es
(
s
witch
o
n
-
s
tate
lo
s
s
es)
,
wh
er
e
ea
ch
s
witch
h
as
an
on
-
s
tate
r
esis
ta
n
ce
R
on
.
T
h
e
s
witch
in
g
tr
an
s
is
to
r
u
s
ed
in
th
is
wo
r
k
is
an
N
-
ch
an
n
el
MO
SF
E
T
FHF2
0
N6
0
A
r
ated
as
6
0
0
V
,
2
0
A
with
R
on
=
0
.
3
2
Ω
.
T
h
e
co
n
d
u
ctio
n
lo
s
s
es
ar
e
ca
lcu
lated
as
P
con
=
I
rms
2
.R
on*
N
on
,
wh
er
e
N
on
is
th
e
n
u
m
b
er
o
f
o
n
s
witch
es
f
o
r
th
e
co
r
r
esp
o
n
d
in
g
lev
el.
T
h
e
to
ta
l
co
n
d
u
ctio
n
lo
s
s
es
ar
e
th
e
s
u
m
o
f
all
co
n
d
u
ctin
g
s
witch
es
in
ea
ch
le
v
el
;
ii)
S
witch
in
g
lo
s
s
es
o
cc
u
r
d
u
r
i
n
g
tu
r
n
-
o
n
an
d
tu
r
n
-
o
f
f
tr
an
s
itio
n
s
.
T
h
e
ap
p
r
o
x
im
ate
f
o
r
m
u
la
is
P
sw
=f
sw
.
(
E
on
+E
off
)
,
wh
er
e
f
sw
is
th
e
s
witch
in
g
f
r
e
q
u
en
cy
,
E
on
,
E
off
ar
e
en
er
g
y
lo
s
s
es
p
er
tr
an
s
itio
n
(
d
ep
en
d
o
n
cu
r
r
e
n
t
an
d
v
o
ltag
e
at
th
e
s
witch
in
g
in
s
tan
t)
;
an
d
i
ii)
Dr
iv
er
an
d
co
n
tr
o
l
lo
s
s
es
,
wh
ich
ar
e
co
n
s
u
m
ed
in
g
ate
d
r
iv
e
cir
cu
it
s
an
d
ar
e
s
m
all
co
m
p
ar
e
d
t
o
co
n
d
u
ctio
n
an
d
s
witch
in
g
lo
s
s
es.
Fo
r
illu
s
tr
atio
n
o
f
p
o
wer
lo
s
s
es
ca
lcu
latio
n
,
a
r
esis
tiv
e
lo
ad
with
R
=
50
Ω
is
u
s
ed
,
a
n
d
t
h
e
cu
r
r
en
t
wav
ef
o
r
m
is
s
h
o
wn
in
F
ig
u
r
e
1
8
.
T
h
e
lo
a
d
cu
r
r
en
t
r
m
s
v
alu
e
is
ca
lcu
lated
as
I
rms
=
4
.
6
5
A.
T
h
e
ca
lc
u
latio
n
in
T
ab
le
2
is
f
o
r
th
e
f
ir
s
t
o
u
tp
u
t
lev
el.
T
h
e
o
th
er
1
4
lev
els
ca
n
b
e
esti
m
ated
with
th
e
s
am
e
p
r
o
ce
d
u
r
e
,
n
o
tin
g
t
h
at
th
e
n
u
m
b
er
o
f
o
n
-
s
tate
s
witch
es v
ar
ies d
ep
en
d
in
g
o
n
th
e
o
u
t
p
u
t v
o
ltag
e
lev
el.
E
f
f
icien
cy
is
th
e
r
atio
o
f
th
e
o
u
tp
u
t p
o
wer
P
out
to
th
e
in
p
u
t p
o
wer
P
in
.
=
∗
100%
(
1
9
)
T
h
e
in
p
u
t
p
o
wer
is
ca
lcu
late
d
b
y
m
ea
s
u
r
in
g
ea
c
h
DC
s
o
u
r
ce
v
o
ltag
e
an
d
c
u
r
r
e
n
t
,
th
e
n
m
u
ltip
ly
in
g
an
d
s
u
m
m
in
g
.
T
h
e
in
v
er
ter
is
f
ed
b
y
f
o
u
r
DC
s
u
p
p
lies
:
1
2
V,
2
4
V,
6
0
V,
a
n
d
1
2
0
V.
T
o
tal
in
p
u
t
p
o
we
r
is
th
e
s
u
m
o
f
ea
ch
s
o
u
r
ce
’
s
co
n
tr
ib
u
t
io
n
:
=
∑
(
)
∗
(
)
4
1
(
2
0
)
T
h
is
r
esu
lts
in
P
in
=1
5
0
0
W
.
T
h
e
lo
s
s
es
ar
e
ca
lcu
lated
ac
co
r
d
in
g
to
T
ab
le
2
f
o
r
o
n
-
s
tate
s
witch
es
f
o
r
ea
ch
in
v
er
te
r
o
u
tp
u
t
lev
el
(
f
r
o
m
lev
el
1
t
o
lev
el
1
5
)
an
d
th
e
n
s
u
m
all
1
5
lev
el
l
o
s
s
es.
T
h
is
r
esu
lts
in
P
losses
=
1
3
5
W
.
T
h
e
o
u
tp
u
t p
o
wer
P
out
=Pin
-
P
losses
=
1365
W
.
Acc
o
r
d
in
g
to
(
20
)
,
th
e
3
1
-
le
v
el
in
v
er
t
er
ef
f
icien
cy
is
=
1365
1500
×
100
=
91%
.
Fo
r
r
en
ewa
b
le
en
er
g
y
an
d
g
r
id
-
co
n
n
ec
ted
s
y
s
tem
s
,
ef
f
icien
cy
b
elo
w
8
5
%
is
u
s
u
ally
n
o
t
ac
ce
p
tab
le.
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
6
9
4
R
ea
l
-
time
s
elec
tive
h
a
r
mo
n
ic
elimin
a
tio
n
in
mu
ltil
ev
el
in
ve
r
ters
u
s
in
g
emb
ed
d
ed
…
(
Ta
h
a
A
h
ma
d
Hu
s
s
ein
)
1923
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
7
.
C
o
m
p
ar
is
o
n
o
f
th
e
3
1
-
lev
el
in
v
er
ter
p
e
r
f
o
r
m
an
ce
with
an
d
with
o
u
t
o
p
tim
izatio
n
:
(
a)
o
u
t
p
u
t v
o
ltag
e
with
o
u
t
o
p
ti
m
izatio
n
,
(
b
)
o
u
t
p
u
t v
o
ltag
e
w
ith
o
p
tim
izatio
n
,
(
c)
T
HD
with
o
u
t o
p
tim
izatio
n
,
an
d
(
d
)
T
HD
with
o
p
tim
izatio
n
Fig
u
r
e
18.
I
n
v
e
r
ter
cu
r
r
en
t f
o
r
r
esis
tiv
e
lo
ad
R
=5
0
Ω
T
ab
le
2
.
E
s
tim
ated
lo
s
s
co
m
p
o
n
en
ts
o
f
th
e
3
1
-
lev
el
s
in
g
le
-
p
h
ase
in
v
er
ter
Ty
p
e
o
f
l
o
ss
e
s
P
a
r
a
me
t
e
r
s
Est
i
m
a
t
e
d
l
o
sses
(W)
O
u
t
p
u
t
l
e
v
e
l
On
-
st
a
t
e
sw
i
t
c
h
e
s
Est
i
m
a
t
e
d
l
o
sses
(W)
C
o
n
d
u
c
t
i
o
n
l
o
ss
e
s
I
rm
s
=
4
.
6
5
A
,
R
on
=
0
.
3
2
Ω
6
.
9
2
W
p
e
r
sw
i
t
c
h
1
5
3
4
.
6
S
w
i
t
c
h
i
n
g
l
o
ss
e
s
F
sw
=
5
0
H
z
E
on
+E
o
ff
=
0
.
5
mJ
0
.
0
2
5
W
p
e
r
sw
i
t
c
h
1
5
0
.
1
2
5
D
r
i
v
e
r
l
o
sses
G
a
t
e
d
r
i
v
e
c
o
n
su
m
p
t
i
o
n
~
0
.
1
W
p
e
r
sw
i
t
c
h
1
5
0
.
5
To
t
a
l
l
o
sses
3
5
.
2
2
5
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
in
tr
o
d
u
ce
s
an
e
x
p
an
d
ab
le
a
n
d
ef
f
icien
t
m
o
d
e
l
f
o
r
im
p
lem
en
tin
g
s
elec
tiv
e
SHE
in
m
u
ltil
ev
el
in
v
er
ter
s
u
s
in
g
em
b
ed
d
ed
o
p
tim
izatio
n
alg
o
r
ith
m
s
o
n
th
e
PYNQ
-
Z
2
FP
GA
p
latf
o
r
m
.
A
r
a
n
g
e
o
f
m
etah
eu
r
is
tic
m
eth
o
d
s
,
PS
O,
GA,
GW
O,
S
MA
,
an
d
W
OA
,
ar
e
em
p
lo
y
e
d
to
d
y
n
am
ically
d
eter
m
in
e
o
p
tim
al
s
witch
in
g
an
g
les
th
at
m
in
im
ize
T
HD
wh
ile
m
ain
tain
in
g
th
e
f
u
n
d
am
en
tal
o
u
tp
u
t
v
o
ltag
e.
T
h
e
ap
p
r
o
ac
h
co
m
b
in
es
m
ath
em
atica
l
m
o
d
ellin
g
,
alg
o
r
ith
m
ic
o
p
tim
izatio
n
,
co
m
p
ar
ativ
e
ev
al
u
atio
n
,
an
d
h
ar
d
war
e
d
ep
lo
y
m
e
n
t,
r
esu
ltin
g
in
a
r
ea
l
-
tim
e
co
n
tr
o
l
s
y
s
tem
d
esig
n
e
d
to
m
itig
ate
u
p
to
f
o
u
r
tee
n
lo
w
-
o
r
d
er
h
ar
m
o
n
ics
in
a
3
1
-
le
v
el
in
v
er
ter
co
n
f
ig
u
r
atio
n
.
T
h
r
o
u
g
h
th
e
co
m
p
ar
ativ
e
s
elec
tio
n
p
r
o
ce
s
s
,
th
e
FP
GA
co
n
tr
o
ller
e
m
b
ed
s
th
e
m
o
s
t
ef
f
ec
tiv
e
s
o
lu
tio
n
f
o
r
ea
ch
m
o
d
u
latio
n
i
n
d
ex
,
en
s
u
r
in
g
f
ast
ex
ec
u
tio
n
,
lo
w
d
e
lay
,
an
d
co
n
s
is
ten
t
r
eliab
ilit
y
.
E
x
p
er
im
e
n
tal
r
esu
lts
v
alid
ate
th
e
s
y
s
tem
’
s
ab
il
ity
to
r
ed
u
ce
tar
g
eted
h
ar
m
o
n
ics
an
d
im
p
r
o
v
e
wav
ef
o
r
m
q
u
ality
.
Utilizin
g
t
h
e
PYNQ
-
Z
2
p
latf
o
r
m
en
ab
les
h
ar
d
war
e
-
s
o
f
twar
e
co
-
d
esig
n
,
d
eliv
er
in
g
n
o
tab
le
Evaluation Warning : The document was created with Spire.PDF for Python.