Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 81
0
~
82
2
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p81
0-8
22
8
10
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Single phase 21 level
hybrid multi
l
evel i
n
vert
er wit
h
reduced
power componen
ts employing
low f
r
equency m
o
dulation
technique
Sh
ei
kh
T
a
nzi
m
Me
r
a
j
1
,
No
r
Z
a
ih
ar
Ya
h
a
y
a
2
, Ka
m
r
u
l
H
a
s
a
n
3
, A
m
ma
r
M
a
s
a
o
u
d
4
1,
2
Dep
a
rtm
e
nt
of
Electr
i
c
a
l and
Elec
t
ron
i
cs
En
gin
eer
in
g
,
Un
iv
ers
i
t
i
T
e
kn
olog
i P
E
TRON
AS
, M
a
lays
ia
3
Facul
t
y
of E
l
ect
rical Engineering,
Uni
v
ersiti T
e
knologi
MARA,
Malaysi
a
4
F
acu
lty
o
f
M
e
c
h
an
ic
al
a
n
d
Ele
c
t
ric
a
l
En
gin
eerin
g,
Al-Ba
a
th
U
n
i
v
ersity
, S
y
ria
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Jun
30
, 20
19
Re
vise
d
Oc
t 1
0
, 2
019
Acc
e
pt
e
d
Dec 15
, 20
19
T
h
i
s
p
a
per i
n
tro
d
u
c
e
s
a
ne
w hy
b
r
id
t
o
p
o
l
o
gy of
m
u
lt
il
e
v
el
in
v
e
rte
r
ca
p
a
ble
of
gen
e
ra
ting 2
1
-
l
ev
el o
u
tpu
t
vo
lta
g
e.
Th
e
p
r
op
os
ed
to
po
log
y
is bu
ilt us
in
g
th
e
comb
in
a
t
io
n
o
f
cro
s
s
-
sw
itched
b
r
id
ge
and
a
conv
ent
i
o
n
al fu
ll H-bridg
e
.
Comp
ared
to
th
e
con
v
en
tiona
l
top
o
log
i
es
an
d
o
t
her
hy
brid
topo
lo
gies, th
e
new
l
y
in
trod
uc
e
d
mu
lt
ile
ve
l
i
nve
rte
r
ha
s t
h
e
a
b
ili
t
y
t
o
ma
xi
miz
e
th
e
n
u
m
b
e
r
of vo
lt
age lev
e
l
s
utili
z
in
g
lo
wer
n
u
mb
e
r
of DC
voltag
e
s
our
ces
,
in
tegr
ated
bipo
lar
tran
sis
t
o
r
(IG
BT) sw
itch
es and
g
a
te
drivers.
A
low
freq
u
en
cy
mod
u
lation t
ech
niqu
e is
u
s
ed
to
g
e
nera
te
the ideal
multi
le
vel
ou
tpu
t
v
o
l
t
a
g
e
a
n
d g
a
te
p
u
l
s
e
s
.
F
u
rt
he
rm
o
r
e,
t
h
e pro
p
o
se
d
to
pol
o
g
y is
v
a
li
da
te
d
by bu
il
di
n
g
a
h
a
rd
wa
re
pr
o
t
ot
yp
e a
n
d o
b
ta
in
in
g re
l
e
v
a
n
t
e
xpe
rim
e
nta
l
re
sul
t
s. The
acqu
i
r
e
d
simulat
e
d an
d ex
p
e
ri
men
t
a
l
resu
lts ind
i
ca
te
th
e
prop
er
fun
c
tion
ing
of the proposed
hybri
d
t
o
pology along
wi
t
h
t
h
e
compat
ibilit
y of
t
h
e
appl
ied
m
o
du
la
tio
n
t
e
c
hni
qu
e
.
Ke
yw
ords:
Hy
bri
d
mul
t
i
l
e
ve
l in
ve
rt
e
r
Nea
r
est
le
vel
c
ont
rol
(N
LC)
Po
we
r el
ect
ro
n
i
cs
Po
we
r i
n
ve
rt
er
s
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
S
h
ei
kh
Ta
n
z
im
M
e
ra
j,
Depa
rt
me
nt o
f
Ele
c
t
r
i
c
a
l
and
El
e
c
t
r
oni
cs
E
n
gi
nee
r
i
n
g
,
Uni
v
ersi
t
i
Te
k
nol
ogi PETR
O
N
A
S
, M
a
l
a
ysia
Ema
i
l
:
m
e
r
a
j.tan
z
im
@g
ma
il.co
m
1.
IN
TR
O
DUCTION
Mul
t
i
l
e
ve
l i
n
v
e
rt
ers (M
LI
) h
a
ve eme
r
ge
d
a
s
a p
r
ospec
t
i
v
e co
nc
ept
i
n
t
h
e fi
el
d
of hi
g
h
pow
er an
d
medi
u
m
vol
t
a
ge re
g
u
l
a
t
i
on.
As a
po
p
u
l
a
r
po
w
e
r e
l
e
c
t
r
o
n
i
c devi
c
e
m
u
lt
i
l
e
v
el
i
nve
rt
er
has a
d
v
a
nta
g
e
s
an
d
di
sa
d
v
a
n
t
a
ges.
The
m
o
st
c
o
mmo
n
d
r
awba
c
k
of
c
o
n
v
e
n
t
i
ona
l
m
u
lt
i
l
evel
inve
rt
ers
i
s
t
h
e i
n
cre
a
se
d
u
s
age
o
f
po
we
r co
m
pone
nt
s
w
h
il
e g
e
nera
t
i
n
g
hi
g
h
l
e
vel
o
u
t
p
ut
vol
t
a
ge
.
Thi
s
speci
fi
c
d
r
a
w
ba
c
k
c
a
n
l
e
ad t
o
c
o
mp
u
t
ati
o
n
a
l c
o
mp
l
e
x
i
tie
s,
low
e
r
eff
i
c
i
e
n
ci
es, pr
e
s
ence
of
h
a
r
m
on
ics
a
nd mo
st
impor
ta
n
t
l
y
h
i
nd
er
t
h
e
o
v
e
r
al
l
pe
rformanc
e
of
a
n
i
nve
rt
er [1
, 2]. The
i
d
ea
of
mu
l
t
i
l
e
vel
i
nvert
e
r
wa
s
fi
rst
p
r
o
pose
d
i
n
1
9
7
5
[
3
].
S
i
nce t
h
e
n
vari
ous
MLI
t
o
p
o
l
ogi
es
we
re
p
r
op
ose
d
wi
t
h
di
ffe
rent
a
b
il
i
t
i
e
s a
n
d
fu
nc
ti
o
n
a
l
i
ti
es.
Ea
ch
i
of
i
the
s
e
i
to
po
lo
g
i
e
s
i
was
i
desi
gne
d
to
i
im
prov
e
i
it
s
i
a
b
il
ity
i
of
i
prod
uci
n
g
i
in
c
r
ea
se
d
i
le
v
e
l
i
ou
tpu
t
i
vo
lt
ag
e
i
usi
n
g
i
lo
w
i
am
o
unt
i
of
i
po
w
e
r
i
e
qui
pme
n
t
s
,
I
co
mpa
r
ed
i
to
i
its
i
pre
v
io
us
i
ve
rsi
o
n
s
.
i
Ne
ut
ra
l
i
po
i
n
t
i
cl
ampe
d
i
(N
P
C
)
,
I
fl
yi
ng
i
ca
p
aci
t
o
r
i
(F
C
)
I
and
i
th
e
i
casc
a
de
d
i
H
b
ri
dge
i
(C
H
B
)
;
I
the
s
e
i
are
i
th
e
i
thr
e
e
i
fundamental
i
multilevel
i
in
ve
rt
er
i
to
po
lo
g
i
e
s
.
i
Th
e
i
firs
t
i
NPC
i
i
nverte
r
i
wa
s
i
a
i
3 l
e
vel
i
in
ve
r
t
e
r
i
c
o
n
s
is
te
d
i
of
i
four
i
switching
i
de
vi
ce
s,
i
tw
o
i
ca
sc
ade
d
ca
p
aci
to
r
s
i
an
d
i
one
i
DC
i
suppl
y
i
[4]
.
i
Th
e
i
vo
lt
ag
e
i
ba
l
a
nci
n
g
i
of
i
the
i
DC
li
n
k
i
ca
paci
t
o
rs
i
in
i
NP
C
i
i
nverte
r
,
i
is
i
a
i
dec
i
si
ve
i
ta
sk
i
si
nce
i
the
i
vo
lta
g
e
i
at
i
the
i
neu
t
ra
l
i
poi
nt
i
is
i
al
way
s
i
devi
a
t
i
n
g.
i
The
i
FC
i
ML
Is
i
use
i
ca
paci
t
o
rs
i
of
i
cl
ampi
ng
i
di
ode
s.
i
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Si
n
g
l
e
p
hase
2
1
l
e
vel
h
y
bri
d
mul
t
i
l
eve
l
i
n
ve
rt
er
wi
t
h
red
u
c
e
d
pow
er
…
(
She
ik
h
T
a
nzi
m
Meraj
)
8
11
These
i
cl
am
pi
ng
i
di
o
d
es
i
can
i
cl
amp
i
th
e
i
de
v
i
ce
i
volt
a
ge
i
to
i
one
i
capa
c
i
t
or
i
volt
a
ge
i
le
vel
.
The DC
-l
in
k
ca
paci
t
o
rs
o
f
t
h
ese i
nve
rt
ers
are arra
nge
d i
n
a la
d
d
er
stru
ct
ure
,
whe
r
e t
h
e
vol
t
a
ge
di
ffe
rs a
c
ros
s
e
a
c
h
ca
paci
t
o
r
from
t
h
e
next
ca
paci
t
o
r. Si
nc
e
i
t
s
i
n
v
e
nti
o
n,
CH
B
in
vert
e
r
s ha
ve
dra
w
n gre
a
t
i
n
t
e
re
st
ove
r ot
he
r
t
o
p
o
l
ogi
es
bec
a
u
s
e o
f
t
h
e
i
r si
mpli
c
i
t
y
and
mod
u
l
a
rit
y
of c
o
nt
rol.
These i
nve
rt
er
s p
o
ssess
so
m
e
of t
h
e e
x
ce
pti
onal
fe
at
ure
s
i
n
c
l
ud
i
ng
a
b
i
l
i
t
y o
f
ge
n
e
rat
i
n
g hi
g
h
out
put
v
o
l
t
a
ge
wi
t
h
re
duc
e
d
t
o
t
a
l
ha
rmon
i
c
di
st
ort
i
o
ns
(THD
).
Furt
he
rmore,
i
t
ca
n ge
ne
ra
te
c
o
mm
o
n
m
o
de vol
t
a
ge
(C
M) whi
c
h
re
duc
es st
re
ss
on
t
h
e
mot
o
r.
Al
th
oug
h t
h
e
s
e
M
L
I topo
logie
s
h
a
v
e
b
e
t
t
e
r
vo
lt
ag
e cap
a
c
it
y
an
d eff
i
c
i
e
n
cy,
t
h
ey
r
e
quir
e
in
cr
ea
sed
nu
mbe
r
of
p
o
w
er
e
l
e
c
t
r
i
c
c
o
mp
one
nt
s to
p
r
od
uc
e
hig
h
o
u
t
put
v
o
l
t
a
g
e.
T
h
i
s
ca
n l
e
a
d
t
o
hi
g
h
s
w
i
t
chi
n
g los
s
es
a
n
d in
cr
ea
se
t
h
e
ov
e
r
a
ll co
st
o
f
t
h
e
s
y
ste
m
.
A
s
a
r
e
su
lt
, con
s
id
er
ab
l
e
a
m
ou
n
t
s of
r
e
se
a
r
ch
e
s
w
e
r
e
c
o
ndu
ct
ed
.
Re
ce
ntl
y
, di
ff
ere
n
t
va
ri
at
i
o
n
s
o
f
t
h
e
s
e
b
a
si
c M
L
I t
o
p
o
l
o
gie
s
h
a
ve
be
en
deve
l
o
pe
d t
o
i
m
pro
v
e
t
h
ei
r
f
u
n
c
tion
a
lit
ie
s in
a c
o
st-
e
ff
ect
iv
e
w
a
y
.
So
me o
f
th
es
e top
o
l
o
g
i
e
s
i
n
c
l
ud
e
th
e
a
c
t
iv
e
NPC
(
A
N
P
C
)
con
v
e
r
te
r.
In
AN
PC
inve
rt
ers,
c
l
am
pin
g
dio
d
e
s
we
re
use
d
inst
ea
d o
f
p
o
we
r sw
it
che
s
t
o
o
v
e
r
c
o
me t
h
e l
o
ss
ba
l
a
nc
ing
is
su
e
b
e
tw
een
t
h
e
o
u
t
er
an
d inn
e
r sw
it
ch
es [5-
7
]
.
D
u
e
t
o
the
use
of
pow
e
r
swi
t
c
h
es, t
h
e
c
u
rre
nt
at
t
h
e neut
ra
l
poi
nt ca
n be fo
rc
ed t
o
fl
o
w
i
n
bot
h u
p
p
e
r
and
l
o
we
r
pa
t
h
of t
h
e
in
ve
rt
er. T
h
i
s
re
s
u
l
t
s i
n
di
stri
but
i
o
n
o
f
e
qual
l
o
sses a
m
on
g a
l
l
the
semi
co
n
duct
o
r
d
e
v
i
c
e
s. A
n
e
w
v
a
ri
ati
o
n
o
f
FC
in
ve
r
t
e
r
w
a
s
pr
opo
se
d
in
[8
]
wh
ic
h
u
s
ed
a
c
o
mb
in
a
tio
n o
f
se
ri
al
a
n
d
pa
r
a
l
l
e
l
con
n
ec
t
e
d
fl
yi
ng ca
paci
t
o
rs.
Thi
s
ve
rsio
n
o
f
FC
i
n
vert
er
h
a
s be
tt
er v
o
l
t
a
g
e ca
pac
i
t
y
an
d
hi
gh
-qua
li
t
y
out
put
com
p
are
d
t
o
i
t
s
tradi
t
i
o
nal
c
o
u
n
te
rpart.
T
r
a
d
it
i
onal
C
H
B
in
ve
rt
ers
req
u
i
r
es
isol
at
ed
DC s
o
urc
e
s
of
eq
ual
ma
gn
it
u
d
e
a
nd mu
l
tip
l
e
tr
a
n
sf
or
mers fo
r
e
a
c
h
ce
ll i
n
ord
e
r
to
p
r
o
v
i
d
e
elec
tr
ic
al
iso
l
a
t
i
o
n
[9
,1
0]
.
A
va
ri
ati
o
n
o
f
tr
ad
iti
on
al
CH
B
in
v
e
rt
er
s
k
now
n
as a
s
ym
me
tr
ic
al
CHB
u
s
e DC
vo
lt
ag
e
so
ur
c
e
s o
f
d
i
f
f
er
e
n
t
r
a
ti
ngs.
Sin
c
e
th
e
D
C
s
upp
lie
s fo
llo
w
a
c
e
r
t
a
i
n
vo
l
t
a
g
e
r
a
tio
,
it c
a
n in
c
r
e
a
se t
h
e
v
o
l
tag
e
l
e
v
e
ls
o
f
th
e i
n
v
e
r
t
e
r
s
i
g
n
i
f
i
c
a
n
tly.
I
n
201
1
,
a
n
e
w MLI w
a
s i
n
t
r
od
u
ced k
n
o
w
n as mu
l
tist
r
i
n
g mu
ltil
ev
e
l
i
n
ver
t
e
r
w
h
ich
u
t
ilis
e
s
th
e fun
d
a
men
t
al
s
of CHB
i
nve
rte
r
s [11]
.
The
basi
c st
ru
ct
ure
of t
h
i
s
t
o
pol
og
y i
s
base
d
on
spec
ific
c
r
oss
co
n
n
ec
t
i
n
g
l
o
w
vol
ta
ge
swi
t
c
h
es a
n
d
DC
v
o
l
t
a
ge
so
urc
e
s
.
Al
t
h
oug
h
ma
ny
MLI t
o
p
o
l
o
gi
es
ha
v
e
b
e
e
n
de
vel
o
ped
,
t
h
e
o
p
t
i
m
i
zat
i
on
of t
h
e
p
o
w
e
r
equi
pme
n
t
re
q
u
i
r
e
d
for t
h
e
s
e i
nve
rte
r
s
we
re
gi
ve
n a
ne
w he
i
ght
vi
a
the
de
ve
lo
pm
e
n
t
o
f
the
fi
rst
hy
b
r
i
d
i
nve
rt
er
[1
2].
Thi
s
newl
y
fo
un
d c
o
nc
ept
o
f
h
y
b
r
i
d
to
pol
o
g
y
al
o
n
g
wi
th
t
h
e m
u
l
t
i
s
t
r
i
ng ML
I
was t
h
e
pri
m
a
r
y
moti
vat
i
o
n be
hi
n
d
de
si
g
n
i
n
g t
h
e
prop
ose
d
hy
brid
t
o
p
o
l
og
y.
Di
ffe
re
n
t
mod
u
l
a
t
i
on
strat
e
gi
es
we
re
a
l
so
d
e
v
e
lo
p
e
d
w
i
t
h
t
h
e
n
e
w mu
ltil
ev
e
l
in
v
e
rt
er to
po
lo
g
i
es
i
n
o
r
d
e
r t
o
co
n
t
r
o
l th
e
s
e inv
e
r
t
e
r
s
.
G
e
n
e
r
a
lly
, all the
modul
at
i
o
n te
c
hni
que
s can
be
c
l
a
s
si
fi
e
d
i
n
t
o
two c
a
t
e
g
o
r
i
e
s:
low
a
n
d hi
g
h
swi
t
c
h
in
g fre
q
u
enc
i
e
s
[13
]
.
B
a
sed
on t
h
is c
l
a
ssifi
c
a
t
i
on, t
h
is pa
per
use
s
a
mo
di
fi
ed l
o
w s
w
i
t
c
h
i
n
g
fre
que
n
c
y m
o
d
u
la
t
i
o
n
t
e
c
hniq
u
e
t
o
g
e
nerat
e
t
h
e de
si
red
s
w
i
t
c
h
ing
p
u
l
s
es.
The
o
p
erat
in
g
pri
n
ci
pl
es
of th
e
p
r
o
pose
d
i
n
v
e
rte
r
a
r
e
v
e
ri
fi
ed
by
b
o
t
h
co
mp
ute
r
simul
a
t
i
on, usi
n
g
M
A
T
L
AB
a
n
d
t
h
e
ha
rd
wa
re
prot
oty
p
e
.
2.
P
R
OPO
S
ED TO
P
O
LO
GY
AND
OP
ERAT
IN
G PR
INCIP
L
E
The
p
r
o
pose
d
hy
b
r
i
d
i
nve
rt
er wa
s
de
sig
n
ed
usi
n
g
t
h
e ca
sca
d
e
d
c
o
mbi
n
at
i
o
n
of a
si
n
g
l
e
-pha
se c
r
oss
-
swi
t
c
h
e
d
b
r
id
g
e
an
d
a
si
ngle
ce
l
l
con
v
e
n
t
i
onal
ful
l
H-br
idge
. The
c
r
os
s-swi
t
c
h
ed b
r
i
dge
is impl
em
ent
e
d
fol
l
o
w
i
n
g
t
h
e
fu
n
d
a
m
e
n
ta
ls
of
t
h
e
p
r
o
p
o
se
d in
ve
rt
er i
n
[14
]
.
The
cr
oss
b
r
i
d
ge
c
onta
i
ns
2 ba
c
k
t
o
b
a
ck
DC
su
pp
l
i
e
s
(V
C
1
a
n
d V
C
2
)
and
a
to
ta
l of
si
x po
w
e
r sw
itc
h
e
s
(S
1,
S
2
, S3
, S
4
,
S5
and
S6)
a
s
sh
ow
n in
F
i
g
u
r
e
.1
.
The
mi
d
d
le
t
w
o
sw
it
che
s
(S
5
a
n
d
S
6
)
of t
h
e
cr
oss
bri
dge
a
r
e
c
r
oss
c
o
n
n
e
c
t
e
d a
nd
act
as
a
me
di
um
be
t
w
e
e
n
t
h
e t
w
o DC
s
o
urce
s
(
V
C1
a
n
d VC
2). T
h
e
c
r
o
s
s
b
r
i
d
ge
ca
n be
b
u
il
t
ei
t
h
er
b
y
usi
n
g t
w
o DC
su
p
p
li
es ha
vi
ng
same
o
r
dif
f
er
ent
v
o
lt
age
ra
ti
ngs
. W
h
e
n
t
h
e
c
r
oss
bri
dge
fol
l
ow
s s
y
mme
t
r
i
c
a
l
co
nfi
g
u
r
at
i
on, i
t
i
s
ca
p
a
ble
of
gene
rat
i
n
g
5
-
l
e
ve
l
v
o
l
t
a
g
e o
u
t
put
.
O
n
the
c
o
ntrary,
i
f
t
h
is b
r
i
d
ge is b
u
il
t
ut
i
l
i
z
ing asym
me
tric
al
confi
g
u
r
at
i
o
n
,
i
t
i
s
ca
pabl
e of ge
nera
ti
n
g
7-le
vel
v
o
l
t
age o
u
tp
ut
.
T
h
e hy
b
r
i
d
iz
at
i
on i
s
d
o
n
e usi
ng t
h
e
as
ym
met
r
i
cal
con
f
i
g
ura
t
i
o
n
.
The s
w
it
c
h
i
n
g
se
q
u
ence
o
f
t
h
e
7
-
le
vel
out
pu
t vol
ta
ge
i
s
s
h
o
w
n
in
Tabl
e
1.
Table 1
.
V
o
l
t
a
ge le
vel
s
a
nd s
w
i
t
c
h
in
g se
q
u
e
n
ce
s of a si
ngl
e-p
h
a
s
e 7
-
le
vel
asymmet
r
ic
al
c
r
oss-s
w
it
c
h
e
d
bri
dge
.
Switc
hin
g
S
t
at
es
(
a
) ON/OF
F
Switc
h
e
s
Ou
tp
u
t
Vo
lta
g
e (
V
ab
)
S1
S
5
S3
6 1
0
0
3
E
5 1
0
1
2
E
4 0
0
0
E
3
1 1
0
0
0 0
1
2 1
1
1
-
E
1 0
1
0
-
2
E
0 0
1
1
-
3
E
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
8
10
– 82
2
81
2
F
i
gu
r
e
1.
S
i
ngl
e-
p
h
ase
NLe
v
e
l
cr
oss-s
w
i
t
c
he
d m
u
lt
i
l
e
v
el
i
n
ver
t
e
r
T
h
e
cr
oss-
sw
itc
h
e
d in
v
e
r
t
er
can
b
e
ex
te
nd
e
d
in
t
o
N
Level
b
y
fo
llo
w
i
n
g
(1
), (
2
)
and
(
3
) r
e
s
p
ectiv
ely
.
N
Level
=
6
n
+
1
(1
)
N
Swi
t
ch
=
N
Le
vel
1 (
2
)
N
D
C
_
s
up
pl
i
e
s
=
N
Swi
t
c
h
3
(3
)
Her
e
,
n
=
1
,
2
,
3……
.
a
n
d i
t
r
e
pre
s
e
n
t
s
t
h
e
n
u
mbe
r
o
f
c
e
l
l
of
t
h
e
cr
oss-
sw
it
che
d
bri
dge
.
T
h
e
b
o
t
t
om
br
i
dge
i
s
a t
r
a
d
i
t
i
ona
l 3-l
e
v
e
l
f
u
ll
H
-
b
r
id
ge
whi
c
h c
o
nsi
s
t
s
of
onl
y o
n
e
D
C
sup
p
l
y
de
si
g
n
at
e
d
a
s
V
C3
a
nd
fo
u
r
se
mi
co
nd
uct
o
r swi
t
c
h
es
(
S7
,
S8
,
S9
an
d
S10
).
Th
e
f
i
n
a
l
d
e
sign
of
th
e hy
br
id
mu
lt
ile
v
e
l
in
ve
r
t
e
r
h
a
s
a
to
t
a
l
o
f
t
e
n
se
m
i
c
o
n
d
u
c
tor
sw
it
che
s
and
th
r
ee
DC
vol
t
a
ge
so
urc
e
s
a
s
i
l
l
ust
r
a
t
e
d
i
n
F
i
g
u
re
.
2
.
T
h
e
w
hole
t
o
p
o
l
o
g
y
o
f
t
h
e
h
y
b
ri
d i
nve
rt
e
r
ca
n
f
o
l
l
o
w ei
the
r
sym
m
e
t
ri
c o
r
asym
me
t
r
i
c
c
o
nfi
gur
at
i
o
n
.
F
o
r t
h
e
sy
mmet
ri
c
co
nfi
g
u
r
a
t
i
o
n t
h
e
h
y
b
ri
d t
o
pol
og
y i
s
c
a
pa
bl
e
o
f
ge
ne
ra
ti
n
g
7-l
e
ve
l vol
t
a
ge
ou
t
put
.
Ho
w
e
ver
,
fo
r
t
h
e
ne
xt
se
ct
i
ons of
t
h
is p
a
pe
r
,
as
ymmet
r
ic
c
o
n
f
i
g
ura
t
i
o
n
o
f
t
h
e hyb
r
i
d t
o
p
o
l
o
gy was f
o
ll
owe
d
a
nd ut
i
l
i
z
e
d
.
T
h
i
s
c
o
n
f
igu
r
at
io
n is
i
m
ple
m
e
n
t
e
d by mai
n
t
a
i
n
in
g
a
vol
ta
ge
ra
ti
o
of
2
:
1
:
7
a
m
on
g
t
h
e
t
h
re
e
DC su
p
p
lies. Wh
ile
fo
llow
i
ng
t
h
i
s
vo
l
t
ag
e ra
tio
, th
e M
L
I
h
a
s th
e ab
il
ity
to
ge
ne
ra
te
21
v
o
l
ta
ge l
e
ve
ls
using
a
t
o
t
a
l
o
f
2
1
swi
t
c
hi
ng
se
que
nce
s
.
The
s
w
i
t
c
h
in
g
seq
u
e
n
ces
ar
e
prese
n
te
d
i
n
T
a
b
l
e 2
wh
e
r
ea
s, th
e
sw
it
ch
i
n
g
op
e
r
at
ion
o
f
th
e
h
y
b
r
i
d
inv
e
rt
er
fo
r
t
h
e
p
o
s
it
iv
e
h
a
lf
cy
cl
e is ar
e sh
ow
n
i
n
F
i
g
u
r
e
.
3
.
It
ca
n
be
n
o
t
i
ced
f
r
o
m Ta
ble
2,
t
h
a
t
t
h
e
p
r
o
p
o
s
e
d i
n
ve
r
t
e
r
p
o
s
se
sse
s
s
w
i
t
c
hi
ng
re
d
u
n
d
a
n
c
i
e
s
f
o
r
ce
r
t
a
i
n
vo
lta
g
e
l
e
v
e
ls. Th
is fea
t
u
r
e
i
n
cr
e
a
s
e
s th
e r
e
li
ab
i
lity
o
f
th
e inv
e
rt
er
in c
a
se of
m
a
l
f
un
c
t
i
o
n
o
f
a
n
y
sw
itc
h
e
s or
d
r
iv
er
s.
Fi
g
u
re
. 2.
S
i
n
g
le
-
p
h
a
s
e
N
L
e
v
e
l
h
ybr
id
m
u
lti
le
v
e
l
in
ve
r
t
e
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Si
n
g
l
e
p
hase
2
1
l
e
vel
h
y
bri
d
mul
t
i
l
eve
l
i
n
ve
rt
er
wi
t
h
red
u
c
e
d
pow
er
…
(
She
ik
h
T
a
nzi
m
Meraj
)
8
13
Tabl
e 2.
Volt
age
l
e
ve
ls
an
d
swi
t
chi
n
g se
q
u
e
n
ces
of a
si
ngl
e
-
p
h
ase
2
1
-l
e
v
el
asym
met
r
i
cal
h
ybrid
i
n
v
e
rt
er
.
S
w
it
ching
St
a
t
es
(
a
)
ON
/O
FF Sw
itche
s
f
o
r uppe
r br
idge
(
C
)
O
N
/O
F
F
Sw
itc
hes f
o
r
l
o
we
r
br
idge
(
H
)
O
u
tput V
o
ltage
(
V
ab
)
S1 S5
S
3
S7
S9
20
1
0
0
1
0
10
E
19
1
0
1
1
0
9
E
18
0
0
0
1
0
8
E
17
1
1
0
1
0
7
E
16
1
1
1
1
0
6
E
15
0
1
0
1
0
5
E
14
0
1
1
1
0
4
E
13
1 0
0
0
0
3
E
1 0 0
1
1
12
1 0
1
0
0
2
E
1 0 1
1
1
11
0 0
0
0
0
E
0 0 0
1
1
10
0 0
1
0
0
0
0 0 1
1
1
1 1 0
1
1
1 1 0
0
0
9
1 1
1
0
0
-
E
1 1 1
1
1
8
0 1
0
0
0
-2
E
0 1
0
1
1
7
0 1
1
0
0
-3
E
0 1 1
1
1
6 1
0
0
0
1
-4
E
5 1
0
1
0
1
-5
E
4
0
0
0 0 1
-6
E
3 0
0
1
0
1
-7
E
2 1
1
1
0
1
-8
E
1 0
1
0
0
1
-9
E
0 0
1
1
0
1
-
1
0
E
Sim
ila
r
to t
h
e cr
o
s
s-
sw
it
ch
ed in
v
e
r
t
e
r
th
e
hy
br
id M
L
I
ca
n a
l
so
b
e
e
x
ten
d
e
d
in
to
N
L
evel
fol
l
owi
ng (
4
)
,
(5
) an
d (6
) re
s
p
ect
i
v
el
y
.
It
sh
oul
d be
not
e
d
t
h
at
to ap
pl
y
t
h
i
s
e
x
te
nsi
on t
h
e
DC v
o
lt
a
g
e so
urces s
h
ou
l
d
al
ways
fol
l
o
w
2:
1:
7
v
o
lt
age
rat
i
o.
N
Level
=
20
n
+
1
(4
)
N
Sw
it
c
h
=
N
Le
vel
1
2
(5
)
N
DC
_supplies
=
3
N
Switch
10
(6
)
It
ca
n b
e
ob
serv
ed fr
om th
e sw
it
ch
i
n
g
o
p
e
rati
o
n
in F
i
gur
e.3
th
a
t
th
e cu
rre
n
t c
a
n
’t
form
sh
or
t c
i
r
c
u
i
t
l
oops a
r
ou
nd
t
h
e
3 DC
s
u
ppl
i
e
s
be
ca
use
o
f
t
h
e s
w
it
c
h
in
g c
o
m
b
ina
t
i
o
ns. T
hus
, i
t
pre
v
e
n
t
s
sh
ort
c
i
rcui
t
c
u
rrent
to
f
l
o
w
t
h
rou
g
h
t
h
e
21-
lev
e
l h
ybr
id
mu
lt
ile
v
e
l
i
n
v
e
r
t
er
.
The
t
o
t
a
l
st
a
ndi
n
g
v
o
lt
age
o
f
t
h
e
hy
bri
d
t
o
pol
ogy
i
s
c
a
l
c
ul
at
ed
fol
l
o
wing
Tabl
e
2. T
h
e
ma
xi
mum
vol
ta
ge
st
ress
on
e
ach
swi
t
c
h
i
s
ca
l
c
ul
at
ed a
t
of
f st
at
e a
n
d
t
h
e
n
t
h
ese
n
u
m
be
rs
a
r
e
a
d
d
e
d
to
get
h
e
r
t
o
get
t
h
e
t
o
ta
l
st
an
di
ng
vol
ta
ge
(TS
V
)
of
t
h
e
pro
p
o
s
e
d
M
L
I.
T
S
V
ca
l
c
ul
at
i
o
n
i
s
d
e
mo
nst
r
a
t
e
d
b
y
givi
n
g
t
h
e e
x
a
m
pl
e o
f
the
voltage str
e
ss on switch
S1
. T
h
e
DC
su
ppl
y de
sig
n
a
t
e
d
as
V
C1
i
s
ap
p
l
ying
ma
xi
mu
m st
an
di
ng
v
o
l
t
age
on
S1
wh
e
n
it is a
t
o
f
f
s
t
at
e at
V
ab
= -2
E
. T
h
e cal
cul
a
t
i
on
i
s
a
s
fol
l
ows;
V
S1
= 2
E
(A
t;
V
ab
=
-2
E
)
V
S2
= 2
E
(A
t;
V
ab
=
2
E
)
V
S3
=
E
(At
;
V
ab
=
E
)
V
S4
=
E
(At
;
V
ab
= -
E
)
V
S5
= 3
E
(A
t;
V
ab
=
10
E
)
V
S6
= 3
E
(A
t;
V
ab
=
-1
0
E
)
V
S7
=
V
S1
0
= 7
E
(A
t;
V
ab
= -1
0
E
)
V
S8
=
V
S9
=
7
E
(
A
t;
V
ab
= 10
E
)
TSV = 2
E
+ 2
E
+
E
+
E
+ 3
E
+ 3
E
+
7
E
+ 7
E
+ 7
E
+
7
E
=4
0
E
3.
CO
MP
AR
AT
IVE AN
AL
Y
S
IS
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
8
1
0
–
822
81
4
The
c
h
a
r
ac
te
ri
sti
c
s
of t
h
e
hy
bri
d
m
u
l
t
il
eve
l
inve
rt
er
is hi
g
h
l
i
ght
e
d
b
y
c
o
mpa
r
i
n
g i
t
wi
th
tra
d
i
t
i
ona
l
and
rec
e
n
t
l
y
de
ve
lo
pe
d m
u
lt
i
l
e
v
el
i
n
verte
r
to
pol
ogi
es
. T
h
e
com
p
ari
s
on
i
s
do
ne i
n
t
e
rms
o
f
p
o
we
r
c
o
mp
one
nts
suc
h
a
s
IGBT
sw
it
che
s
Fi
g
u
r
e.4a,
di
ode
s
Fi
gu
re
.4
b,
di
ode
s
a
n
d
DC ca
pa
ci
tors/su
p
p
l
i
e
s
Fi
gu
re
.4c.
Al
tho
u
g
h
t
h
e pro
p
o
se
d ML
I
re
qui
res
sa
me
num
ber of DC
su
p
p
l
i
e
s as ACHB
,
by
obse
r
vi
n
g
F
i
gu
re.4
d,
i
t
can be
a
d
dr
ess
e
d
t
h
a
t
th
e
pro
p
o
s
ed
to
po
logy
r
e
qu
i
r
e
d
low
nu
mb
er
of
(a) (b)
(c)
(d)
Fi
gu
re 4.
Com
p
ari
s
on
be
t
w
ee
n diffe
r
e
n
t
M
L
Is
i
n
te
rms
o
f
:
(a) swit
c
h
es
, (b
) dio
d
e
s
,
(
c
) D
C
sup
p
l
i
e
s
/
ca
p
a
ci
to
r
s
a
n
d
(d)
to
ta
l
c
o
mp
on
en
ts.
Ta
bl
e 3.
C
o
mp
a
r
i
s
on
bet
w
ee
n
di
ffe
r
e
n
t
M
L
I
t
o
p
o
lo
gi
es in
t
e
rms o
f
nu
mbe
r
of
l
e
ve
ls (
N
L
e
vel
)
M
L
I
topol
o
g
i
e
s
Le
v
e
l
s
*
(
N
L
evel
)
Sw
it
c
h
es
(
N
Sw
i
t
c
h
)
D
i
odes
(
N
D
io
d
e
)
DC
-li
nks
(
N
D
Cs
u
pp
li
es
/DC
c
a
p
ac
i
t
or
s
)
TSV
T
o
ta
l Com
pone
n
t
s
(
N
To
t
a
l
)
NP
C
20
x
+ 1
2
(
N
L
e
vel
- 1
)
N
L
eve
l
-
1
N
L
evel
- 1
2
(
N
L
evel
-
1
)
4
(
N
L
evel
˗
1
)
FC
2
(
N
L
e
vel
- 1
)
2
(
N
L
eve
l
-
1
)
N
L
evel
- 1
2
(
N
L
evel
-
1
)
5
(
N
L
evel
˗
1
)
AC
H
B
3
(
N
L
ev
el
- 1
)
/5
3
(
N
L
eve
l
-
1
)
/5 3
(
N
L
evel
- 1
)
/20 2
(
N
L
evel
-
1
)
27
(
N
L
evel
˗
1
)
/20
SCML
I [15]
N
L
e
vel
+ 1
N
L
ev
el
+ 10
(
N
L
evel
-
3
)
/2
35
(
N
L
eve
l
˗
1
)
/4
(
5
N
L
evel
+ 19
)
/2
SD
CM
LI
[16]
N
L
e
vel
+ 1
N
L
ev
el
+ 1
(
N
L
evel
-
1
)
/2
35
(
N
L
eve
l
˗
1
)
/4
(
5
N
L
evel
+ 3
)
/2
CM
L
I
[
17]
11(
N
L
evel
-
1
)
/20
11(
N
Le
vel
-
1
)
/20
(
N
L
evel
-
1)
/5
69(
N
L
eve
l
-
1
)
/20
13(
N
L
evel
˗
1)
/10
AH
M
L
I
[
11
]
3
(
N
L
ev
el
- 1
)
/5
3
(
N
L
eve
l
-
1
)
/5 3
(
N
L
evel
- 1
)
/10 5
(
N
L
eve
l
˗
1
)
/2
3
(
N
L
evel
- 1
)
/2
AS
TM
LI
[
18
]
3
(
N
L
ev
el
- 1
)
/4
3
(
N
L
eve
l
-
1
)
/4
(
N
L
evel
-
1
)
/4
5
(
N
L
eve
l
˗
1
)
/2
7
(
N
L
evel
˗
1
)
/4
S
B
SI
ML
I [1
9
]
(
N
L
e
vel
+ 7
)
/2
(
N
L
eve
l
+ 7
)
/2
(
N
L
evel
-
1
)
/5
9
(
N
L
eve
l
˗
1
)
/4
2
(
3
N
L
ev
el
+
1
7
)
/5
N
T
P
M
L
I
[
20]
N
L
e
vel
+ 1
N
L
ev
el
+ 1
(
N
L
evel
+ 1
)
/2 28
(
N
L
evel
- 1
)
/5
5
(
N
L
ev
el
+
1
)
/2
RSM
L
I [14]
18
x
+ 1
(
N
Le
vel
+ 1)/2
(
N
L
eve
l
+ 1
)
/
2
(
N
L
evel
-
1)
/4
99(
N
L
eve
l
-
1
)
/20
(5
N
L
evel
+ 3)
/4
O
R
M
L
I [
21]
16
x
+
1
7(
N
L
evel
-
1
)
/10
7(
N
L
eve
l
-
1)
/10
(
N
L
evel
-
1)
/5
9(
N
L
evel
- 1)
/5
8(
N
Le
ve
l
- 1)/5
Pr
oposed hybr
i
d
MLI
20
x
+ 1
(
N
Lev
e
l
-
1
)
/2
(
N
L
eve
l
-
1)
/2
3(
N
L
evel
-
1)
/20
2(
N
L
evel
-
1)
23(
N
L
evel
- 1)
/20
*
x
=
1,
2,
3
.
.
.
.
.
.
a
nd
it signif
i
e
s
the a
ugm
enta
tion of
N
L
evel
P
o
wer c
o
mp
on
e
n
ts w
h
i
l
e
co
mpa
r
i
n
g wi
t
h
a
l
l
t
h
e t
r
adi
t
i
ona
l
ML
Is.
The
pro
pose
d
hy
b
r
i
d
to
pol
og
y i
s
aga
i
n c
o
mpa
r
e
d
wi
th ni
ne
ot
he
r re
ce
ntl
y
d
e
ve
l
ope
d ML
I
t
o
p
o
l
ogi
e
s
na
med
a
s
red
u
c
e
d
swi
t
c
h mul
t
i
l
evel
in
v
e
r
t
e
r
(
R
SMLI
) [1
5],
swi
t
c
h
ed cap
a
c
i
t
o
r
mu
ltil
ev
e
l
inv
e
rt
er
(
S
C
M
LI)
[1
6]
, sw
itch
e
d
D
C
mu
l
t
il
ev
e
l
in
v
e
rt
er
(S
DC
ML
I)
[1
7], ca
sca
d
e
d
mult
i
l
e
v
el
i
n
v
e
rt
er
(C
M
L
I)
[1
8] i
n
cl
udi
ng
fi
ve
hy
b
r
i
d
t
o
p
o
lo
gi
es
n
a
me
d as
AH
ML
I [
1
1
]
,
AS
T
M
L
I
[
1
9]
,
S
B
S
I
ML
I [
2
0
]
,
NTP
M
L
I
[
2
1]
a
n
d
OR
ML
I
[
2
2].
Det
a
il
ed c
o
mpa
r
i
s
on
wit
h
re
spe
c
t
t
o
n
u
m
be
r of le
vel
s
(N
Level
)
a
r
e
de
mo
nst
r
at
e
d
i
n
Ta
bl
e
3.
Al
l o
f
t
h
e
s
e
ML
I to
p
o
l
o
gi
es
f
o
ll
ow
asym
me
tric
al
con
f
ig
urat
io
n
wi
t
h
a
vol
t
a
ge
rat
i
o
o
f
2:
1:7 t
o
j
u
sti
f
y t
h
e c
o
mpa
r
i
s
on. O
b
servi
ng
fr
om T
a
ble
2
,
f
o
r
[1
5]
vo
lt
age
le
v
e
l
s
NLe
v
el =
1
9
,
37
, 55
, 73
, ...
..
. (18
x
+
1
)
we
re se
le
cte
d
i
n
st
ea
d
o
f
NLe
v
e
l
=
2
1
,
41,
6
1
,
81
,
101
,
.
.
....
(
2
0x+
1).
Si
mil
a
r
l
y, fo
r OR
M
L
I
[22
]
v
o
lt
a
g
e
l
e
ve
ls
NLe
v
el
=
1
7
,
3
3
,
49
, 65
, ......
(
1
6
x
+
1
) we
re
se
le
ct
ed
.
Th
e
s
e v
o
l
t
a
g
e
le
v
e
ls we
r
e
c
h
o
s
e
n
si
n
c
e,
t
h
e
y
ar
e
clo
s
es
t to
t
h
e
desir
e
d
vo
lt
ag
e
le
v
e
ls t
h
at
w
e
r
e
u
s
ed
fo
r c
o
m
p
aris
on
p
u
rpo
s
e in t
h
i
s
sec
t
i
o
n
.
F
u
rt
hermo
r
e
,
it
s
h
o
u
ld
be
not
e
d
th
a
t
t
h
e TS
V o
f
t
h
e
hy
bri
d
i
n
ve
rte
r
i
s
a
s
sa
me
2
(
N
L
ev
el -
1
)
a
s
th
e t
r
a
d
iti
on
al
inv
e
r
t
e
r
s
.
How
e
v
e
r,
it
sti
ll h
a
s
low
e
r TSV c
o
mp
a
r
e
to a
ll o
t
h
e
r M
L
I
s
e
x
ce
p
t
O
R
M
L
I [
2
2
]
. Thu
s
,
it
c
a
n b
e
s
t
a
t
ed
t
h
at
t
h
e
TSV of
th
e
p
r
op
o
s
e
d
inv
e
r
t
e
r
is
in
an
a
c
c
e
p
t
ab
l
e
r
a
ng
e.
Si
nce
,
OR
ML
I
i
s
pro
duci
n
g
v
o
l
t
age
l
e
vel
s
i
n
a
ra
n
g
e
of
(16
x
+
1
), i
t
i
s
e
x
pect
e
d
t
h
at
i
t
has
lo
w
e
r
TS
V
c
o
mp
a
r
e
d
t
o
the
pr
opo
se
d
i
nve
rt
er
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
S
i
ng
l
e
pha
se
21
le
v
e
l hy
b
r
i
d
m
u
ltil
ev
e
l
i
n
verte
r wit
h
re
du
ced
p
o
w
e
r
… (Sh
e
i
k
h
Tan
z
i
m
M
e
ra
j)
8
15
4.
L
O
W F
R
E
Q
UE
N
C
Y
MO
DUL
ATIO
N
The m
o
di
fi
ed
mo
dula
t
io
n m
e
t
h
o
d
ap
pl
i
e
d
t
o
sy
nt
hesiz
e
t
h
e
gat
e
si
gnal
s
of t
h
e s
u
g
g
e
s
t
e
d h
y
b
ri
d
mu
lt
ile
v
e
l
i
nve
rte
r
topo
log
y
i
s
id
en
t
i
f
i
ed
as N
e
a
r
e
s
t Le
v
e
l C
o
n
t
ro
l (N
LC
).
Th
is co
n
t
r
o
l
me
tho
d
is
a
low
fr
eq
u
e
n
c
y
te
chn
i
qu
e
wh
ic
h is im
p
l
emen
t
e
d
b
y
ch
oo
sin
g
the
appr
op
r
i
a
t
e vo
lta
g
e
lev
e
ls
th
at
a
r
e
clo
s
est
to
th
e
pr
e
f
e
r
re
d r
e
fe
r
e
nc
e
o
u
tp
ut
vo
lt
a
g
e
[
1
2].
T
h
e
al
g
o
ri
th
m
of
t
h
i
s
c
ont
rol
te
chni
que
i
s
e
a
s
i
l
y e
x
e
c
u
t
a
bl
e c
o
m
p
ar
e
t
o
t
h
e
ot
he
r c
ont
rol
t
e
c
h
niq
u
e
s
.
It
i
s
a
l
so
hi
g
h
ly
u
nde
rst
a
nda
bl
e a
s
i
t
deal
s wi
t
h
l
o
w
f
r
e
q
u
e
nc
y s
w
it
chi
n
g
st
at
es a
n
d
near
est
v
o
lt
age
l
e
v
e
l
sel
e
c
t
i
on.
I
n
t
h
is c
ont
rol
t
e
c
hni
que
the
o
u
t
put
v
o
l
t
a
g
e l
e
ve
l i
s
dec
r
ea
se
d t
o
a
di
st
inc
t
i
v
e si
mpl
e
ex
p
r
e
s
si
o
n
w
h
ic
h
i
s
gi
ve
n by;
N
e
ar
e
s
t v
o
lta
g
e
le
ve
l
=
E
×
a
r
ound
(7
)
E
i
s
de
ma
rca
t
e
d
as t
h
e
v
o
lt
ag
e
al
te
ra
ti
on
bet
w
ee
n
tw
o l
e
ve
l
s
w
h
i
c
h i
s
use
d
to
n
o
r
m
a
l
i
z
e
the
de
si
red
vol
t
a
ge
r
e
fe
re
n
c
e (
V
AB_r
e
f
)
an
d
to
obt
ai
n
t
h
e
s
w
i
t
c
h
in
g c
o
n
d
i
t
ions
desi
g
n
at
e
d
by
a
[22
]
.
Th
e
r
e
su
lti
ng
v
a
lu
e
is
est
i
ma
te
d
by
me
an
s
of t
h
e
ro
und
fun
c
t
i
on
. Th
is
f
u
n
c
t
i
on
w
o
r
k
s
b
y
ro
und
ing
th
e e
l
e
m
en
ts of
a
t
o
th
e
cl
o
s
es
t
d
e
c
i
m
a
l or
i
n
t
e
g
e
r. Th
e
re
su
ltin
g
v
a
l
u
e
fr
om th
i
s
ma
t
h
e
m
atic
al
c
a
l
c
u
lat
i
o
n
w
ill
re
pr
esent t
h
e c
l
o
s
e
s
t
vo
lt
ag
e
l
e
ve
ls t
o
t
h
e
re
f
e
re
nce.
Fi
nal
l
y
, t
h
e e
s
t
i
m
at
ed val
u
es a
r
e f
r
e
que
nt
l
y
e
q
uat
e
d wi
t
h
c
o
rre
s
pon
di
n
g
v
a
l
u
es
of t
h
e
M
L
I
'
s sw
it
ch
i
n
g
co
nd
iti
o
n
s sto
w
ed
in
a
sw
itc
h
i
ng
ta
b
l
e whic
h
is u
s
ed
to
de
te
rm
in
e
t
h
e
ga
te
p
u
l
se
s.
Thus,
th
e
in
it
ial
r
e
fe
r
e
n
c
e
vo
lt
ag
e
i
s
fo
un
d
by
u
s
i
n
g,
(8)
an
d,
(9)
;
V
AB ref
=
mV
dc
2
sin
θ
(8
)
V
dc
=
∑
V
Ci
k
i
=
0
(9
)
Whe
r
e,
m
i
s
t
h
e
mo
dul
at
i
o
n i
nde
x
whi
c
h
ha
s a
r
a
n
g
e
o
f
0
≤
m
≤
1,
θ
is
t
h
e
i
n
v
e
r
t
e
r
's e
l
ec
tr
ic
al
an
g
l
e,
V
dc
t
h
e
to
ta
l
ma
gn
it
ud
e
of
DC
-l
in
k
s
su
pp
l
i
es
an
d
k
t
h
e
num
ber
of DC
sup
p
l
i
e
s. T
h
e e
l
ect
ri
ca
l
angl
e can
be
u
s
ed
to
in
t
r
oduce
p
h
a
se
d
i
f
f
e
re
n
c
e
s
in
case
of
th
r
ee ph
a
s
e
sy
ste
m
s
.
In
a
ddit
i
o
n
,
a
D
C
of
f
s
e
t
h
a
s
b
e
e
n
app
lie
d
w
ith
t
h
e re
f
e
r
e
n
c
e
vo
lt
ag
e
so
th
a
t
th
e
li
n
e
to
gro
und
vo
l
t
a
g
e w
i
ll b
e
i
n
to
le
r
a
b
l
e r
a
n
g
e
o
f
zer
o
t
o
t
h
e
DC
sup
p
l
y
v
o
lt
a
g
e
wi
t
h
o
u
t c
a
usi
ng a
n
y o
v
e
r
-
m
o
dula
t
i
o
n.
A
f
t
e
r
ap
pl
yi
ng
t
h
e
DC
of
fse
t
t
h
e
v
o
lt
age
ha
s be
en
sh
if
te
d a
b
ov
e z
e
ro a
nd all
th
e
ne
g
a
tiv
e v
a
lu
es
a
r
e
e
l
i
m
in
a
t
e
d
. Th
e fin
a
l
i
ze
d
r
e
fere
n
c
e
v
o
l
tag
e
c
a
n
b
e
de
te
rmi
n
e
d
b
y
. (
1
0);
V
A
B
ref(f
i
na
l)
=
mV
dc
2
sin
θ
+
V
dc
2
(1
0)
F
i
n
a
lly
, th
e switc
h
i
n
g
st
at
es
a
is det
e
rmi
n
e
d
by
a
ppl
yi
n
g
t
h
e
r
o
u
n
d
fu
nc
ti
on
wi
th r
e
spe
c
t
t
o
vol
ta
ge
di
ffe
r
e
n
ce
E
w
h
i
c
h ca
n be
de
f
i
ned
b
y
t
h
e
.
(
1
1)
an
d (
1
2)
.
E
=
2
V
dc
N
Le
ve
l
1
(1
1)
a
round
=
ro
un
d
2
V
A
B
r
e
f(fi
nal)
E
(1
2)
Th
e ob
ta
in
ed
sw
itc
h
i
ng s
t
a
t
es
a
i
s
fu
rt
he
r
uti
l
i
zed by
f
r
e
que
nt
l
y
c
o
m
p
a
r
i
n
g wi
t
h
a
p
r
e-
ge
ner
a
t
e
d
ta
b
l
e
in
or
d
e
r
to
p
r
o
d
u
c
e th
e
g
a
t
e
si
gn
a
l
s
an
d th
e
21-l
e
v
e
l
ou
tpu
t
of
th
e
hy
br
id
inv
e
rt
e
r
wh
i
c
h
is show
n
in
Fig
u
re 5
.
(a) (b)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
8
10
– 82
2
81
6
(c)
Fig
u
r
e
.
5.
G
a
t
e
pu
lse
s
a
n
d ou
t
p
u
t
vo
l
t
a
g
e
o
f
:
(
a
) cr
o
s
s
-
sw
i
t
ch
ed br
idg
e
,
(
b
) H
-
br
idg
e
,
(
c
)
2
1
-l
e
v
el
h
ybr
i
d
i
nve
rt
e
r
.
5.
SIMU
LA
TI
ON
RESU
LTS
The si
mul
a
ti
on
of t
h
e p
r
oj
ec
te
d in
ve
rt
e
r
w
a
s com
p
le
te
d
us
ing
M
A
TL
AB
Si
muli
n
k
v
e
r
s
i
on R
201
4a
.
Sim
u
la
tion
w
a
s
don
e
b
y
consid
e
r
ing
a
si
nu
so
id
al
w
a
v
e
a
s
t
h
e
ref
e
r
e
nce
vo
lta
g
e
w
a
v
e
fo
rm w
h
i
c
h
h
a
s a
no
mi
nal
f
r
e
q
ue
ncy
,
f
= 50
H
z
. Th
e
hyb
r
i
d
mu
lti
lev
e
l i
n
v
e
r
t
e
r
w
a
s
b
u
ilt u
s
i
n
g
thr
e
e
u
n
e
qu
a
l
D
C
su
pp
lie
s
whe
r
e
V
C1
= 20
V
,
V
C2
= 1
0
V
an
d
V
C3
=
7
0
V
ma
kin
g
t
h
e w
h
ol
e
DC
v
o
l
ta
ge
of
t
h
e
hy
bri
d
M
L
I
t
o
1
0
0
V
.
A
re
sis
tiv
e
-
i
ndu
ctiv
e
sin
g
l
e
ph
ase
lo
ad
w
a
s c
o
u
p
l
ed
invo
lv
i
n
g
R
=
100
Ω
a
nd
L
=
0.
2
3
H
a
t
t
h
e
o
u
tp
ut
s
i
de
o
f
t
h
e
hyb
r
i
d
M
L
I
.
T
h
e
o
u
tp
ut
vol
t
a
ge
of
t
h
e
i
nve
r
t
e
r
a
l
o
n
g
wi
t
h
i
t
s T
H
D
at
m
=
1 is de
pic
t
e
d
i
n
Fi
g
u
r
e
.6a.
It
c
a
n si
mi
l
a
r
l
y
b
e
det
e
c
t
ed f
r
o
m F
i
g
u
re
.
5
a
t
h
at
t
h
e p
r
op
os
ed
MLI
'
s
out
p
u
t
v
o
l
t
a
g
e ha
s
rea
c
he
d i
t
s
ma
xi
mu
m
va
lue
V
a
b_m
ax
=
10
0.
3 V
gene
r
a
t
i
ng 21
v
o
lt
ag
e
st
eps a
nd t
h
e
si
mul
a
t
e
d
R
M
S
vol
t
a
ge
i
s
V
a
b_rm
s
=
70.
95
V
.
T
h
i
s
va
lue
i
s
ne
a
r
l
y
c
l
ose
t
o
t
h
e
h
y
pot
he
ti
ca
l val
u
e o
f
70
.
7
V
t
h
at
can
be cal
c
u
l
a
te
d
f
r
o
m
[2
3,
2
4
]:
V
ab
_r
m
s
=
0.
70
7
×
m
×
V
pe
a
k
(1
3)
Fi
gu
re
.
6
a a
l
s
o
ap
pr
o
v
e
s
t
h
at
the
T
H
D
i
s
onl
y
3.
9%
wi
t
h
th
e
hi
g
h
er
or
de
r
h
a
rm
o
n
i
c
s re
mo
ve
d
co
mp
le
te
ly
. Thi
s
als
o
sp
ec
if
ies th
e sy
mm
etri
c n
a
t
u
r
e
o
f
th
e vo
lta
g
e
wav
e
fo
rm
. In
Fig
u
r
e.6
b
,
th
e mo
du
lat
i
o
n
i
nde
x i
s
re
duc
e
d
to
m
= 0
.
8
an
d
be
ca
use
o
f
t
h
is bot
h t
h
e out
put
vol
t
a
ge an
d the
R
M
S
vol
t
a
ge
ha
ve de
cl
i
n
ed
t
o
V
ab
=
80.
3
9
V
a
nd
V
a
b_rm
s
=
5
6
.
8
4 V
r
e
s
p
e
c
t
i
v
el
y ge
ner
a
t
i
ng
17 v
o
l
t
a
ge
st
eps. N
e
ve
rt
hel
e
ss,
t
h
e T
H
D has
a
m
pl
i
f
i
e
d
t
o
4.
84%
i
n
t
h
i
s
ca
se
si
nce
,
t
h
e
hyb
r
i
d
t
o
p
o
lo
gy
ha
s
ge
ner
a
t
e
d
le
sser a
m
o
u
n
t
of
vol
ta
ge
sta
g
es
wit
h
re
sp
e
c
t
t
o
t
h
e
e
a
r
lie
r
ci
rcu
m
stan
c
e
.
Fur
t
h
e
r
r
e
du
ci
ng
t
h
e
mo
du
la
tio
n ind
e
x
to
m
=
0.
3
o
u
t
c
ome
s
i
n
an
out
put
vol
t
a
ge
o
f
V
ab
=
30
.
6
2
V
w
i
t
h
o
n
ly
se
v
e
n
v
o
l
t
a
ge st
e
p
s
a
s
s
how
n i
n
Fi
gu
re.
6
c.
F
u
r
t
he
rmor
e
,
i
t
m
u
st
b
e
a
d
d
r
esse
d
f
r
o
m
F
i
gur
e.
6c t
h
a
t
the
si
mu
l
a
te
d
R
M
S
vol
t
a
ge
s
i
n
t
h
is
ca
se
i
s
d
e
cre
a
sed
t
o
V
a
b_r
ms
= 21.6
5
V
whi
l
e
t
h
e TH
D ha
ve
a
m
pl
i
f
i
e
d
e
x
pressi
vel
y
t
o
12
.3
3%
.
The
THD
o
f
t
h
e h
y
b
r
id i
nve
rt
er
wit
h
res
p
ec
t t
o
ot
he
r
mod
u
l
a
t
i
o
n
in
dic
e
s
ar
e
i
llu
st
rate
d
i
n
F
i
gu
r
e
.
7
.
6.
EX
P
E
R
I
M
E
NT
A
L
RE
SU
LTS
The
har
d
w
a
re
ve
r
s
i
o
n
of t
h
e
hy
b
r
i
d
M
L
I
wa
s
e
s
ta
bli
s
hed
p
r
o
d
u
ci
ng
an
i
n
te
g
r
a
t
i
on be
tw
ee
n
MA
TLAB
Si
m
u
li
nk
a
n
d
so
me
ha
rd
wa
r
e
e
q
ui
pme
n
t
.
The
pr
ot
ot
ype
was
deve
l
ope
d
a
p
pl
yi
n
g
T
M
S
3
20
F2
83
3
5
di
gi
ta
l
si
g
n
al
pr
ocess
o
r
(
D
S
P
)
t
o
ge
ne
r
a
t
e
the
ga
te
pul
s
e
s o
f
t
h
e
ML
I
.
The
int
e
gr
at
i
o
n
wa
s
e
s
t
a
bli
s
he
d
ap
p
l
y
i
ng
CC
S v
5
so
f
t
w
a
re
. Th
e g
a
te
d
r
i
v
e
r
sig
n
a
ls
w
e
re
pro
d
u
c
e
d
using
C
C
S
wh
i
c
h
u
tiliz
e
d
t
h
e
pr
e
-
lo
ad
ed
g
a
t
e
pu
ls
es fro
m th
e
DS
P.
Th
ese
g
a
t
e
pu
ls
es w
e
r
e
i
n
iti
al
l
y
lo
ad
ed
i
n
t
o
D
S
P
f
r
o
m
MATLAB
.
Th
e
s
e
s
i
g
n
a
ls
f
r
o
m
t
h
e ga
t
e
d
r
ive
r
s
a
r
e
u
s
ed
t
o
s
ynt
hesi
ze
t
h
e e
xpe
ri
me
nt
al
resul
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
S
i
ng
l
e
pha
se
21
le
v
e
l hy
b
r
i
d
m
u
ltil
ev
e
l
i
n
verte
r wit
h
re
du
ced
p
o
w
e
r
… (Sh
e
i
k
h
Tan
z
i
m
M
e
ra
j)
8
17
(a)
(b)
(c)
F
i
g
u
r
e
6.
S
i
mu
l
a
t
e
d re
sul
t
s
f
o
r
vol
ta
ge
an
d h
a
rm
onic
s
p
ec
tr
um at
di
f
f
e
re
nt
mo
d
u
l
a
t
i
o
n
i
n
di
ces:
(a)
at,
m
=
1
,
(b
)
at
,
m
=
0.
8
a
n
d (c
) at
,
m
=
0.
3.
F
i
gur
e
7.
S
i
mu
l
a
t
e
d
TH
D
a
g
a
i
nst
di
f
f
e
r
e
n
t
mo
dul
at
i
o
n i
n
d
i
c
e
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
8
10
– 82
2
81
8
The
ex
pe
ri
me
nta
l
set
u
p
wa
s
d
o
n
e
f
o
l
l
ow
i
n
g t
h
e
ar
r
a
n
g
e
m
ent
simi
l
a
r t
o
t
h
e
si
mul
a
ti
on
se
t
up.
The
lo
a
d
b
a
n
k
w
a
s
u
s
e
d
to
con
n
e
c
t
a s
i
n
g
l
e
-
phase
lo
ad t
o
the
h
ybr
id
m
u
ltil
ev
e
l
i
n
v
e
r
t
e
r
h
a
v
i
n
g
th
e
f
o
llo
win
g
pa
ra
met
e
r
s
;
R
=
10
0
Ω
an
d
L
= 0.
23 H
.
T
h
e
ha
r
d
wa
re
pa
r
a
met
e
rs
of t
h
e h
ybr
i
d
ML
I a
r
e
speci
fi
ed
i
n
Ta
bl
e 4
.
F
u
rt
her
m
o
r
e
,
the
c
ont
rol
bloc
k
di
ag
ra
m
of
th
e
p
r
ot
ot
y
p
e
i
s
i
l
l
u
st
ra
t
e
d i
n
F
i
gu
re.
8
.
Th
e
p
e
rfo
rman
ce
o
f
th
e hy
br
id
M
L
I and
t
h
e
c
o
mp
at
ib
il
ity
of
t
h
e
m
o
d
u
l
a
tion
met
h
od
w
e
re
ad
d
i
tion
a
lly
ve
r
i
fi
ed
by
ob
ta
in
in
g
th
e e
xpe
r
i
me
n
t
a
l
re
sult
s.
Th
e r
e
su
lts
in
c
l
ud
e t
h
e a
n
al
y
s
is
of
h
a
r
m
o
n
i
c
s
p
ec
t
r
um u
nde
r
di
ffe
rent
mo
d
u
l
a
t
i
on i
ndic
e
s
.
Fi
g
u
re
9
(
a
)
, Fi
gu
re
1
0
(a
)
a
n
d
Fi
gu
re
1
1
(a
)
de
mons
t
r
a
t
e
T
a
bl
e 4.
S
p
ec
i
f
i
c
at
ions
of
t
h
e
har
d
w
a
re
p
r
ot
o
t
ype
H
a
r
d
w
a
re S
p
ec
i
f
i
c
a
tion
S
y
m
bol
V
a
lue
/
Model
D
C
volta
ge suppl
i
e
s
V
C1
20 V
V
C2
10 V
V
C3
70 V
F
undam
e
ntal f
r
e
qu
e
n
cy
f
50 H
z
IGB
T
s
w
it
c
h
es
S1-
S10
AB
B
5
S
NG
250A a
nd 3300 V
IGB
T
g
ate drive
o
p
toc
o
u
p
l
e
r
H
C
PL
3120
I
G
BT
gate drive
IC
74H
C04
F
i
gu
r
e
8.
C
o
ntr
o
l bl
ock
di
a
g
r
a
m.
The
p
r
op
ose
d
M
L
I
’
s
out
pu
t
vol
t
a
ge
w
a
vef
o
r
m
s w
i
t
h
re
s
p
e
c
t
t
o
di
f
f
e
r
e
n
t
m
o
dula
t
i
o
n
i
n
dic
e
s.
By
br
ie
f
co
mp
ari
s
on
, i
t
c
a
n
be c
o
n
f
i
r
me
d t
h
at
t
h
e
out
put
w
a
v
e
f
o
r
m
s o
f
t
h
e
hy
b
r
i
d
ML
I
bo
t
h
f
r
o
m
t
h
e
si
mula
ti
on
resul
t
s
a
n
d
t
h
e
e
x
pe
ri
ment
al
re
sult
s
are
a
l
most
i
d
ent
i
cal
.
It
ca
n
be
al
s
o
c
o
n
f
i
r
me
d
fro
m
t
h
e
T
HD s
p
ec
t
r
u
m
s
th
a
t
a
ll
th
e ev
e
n
o
r
d
e
r
h
a
rmon
ic
s ar
e
e
r
ad
ica
t
e
d
.
Fi
gu
re.
9b h
a
s sho
w
n
th
at t
h
e ob
ta
in
ed
TH
D at
m
=
1
is o
n
l
y
4
.
5
%
.
Ad
d
iti
on
al
ly
,
it c
a
n
b
e
o
b
se
rv
ed fr
om
th
e
gra
p
h
th
at
al
l t
h
e t
r
i
p
le
n
h
a
rm
on
ic
comp
on
en
ts (3
rd
, 9th
a
nd
15t
h) are
al
so
el
i
m
i
n
at
ed. T
h
e meas
ure
d
R
M
S
v
o
l
t
a
ge
fro
m
t
h
e
f
u
n
d
ame
n
t
a
l
fre
q
u
e
ncy
com
p
o
n
e
n
t
at
m =
1
,
i
s
69
.
2
V.
Thi
s
va
l
u
e i
s
al
mos
t
sa
me
a
s
t
h
e
si
mul
a
t
e
d
v
a
l
u
e
of
R
M
S
vol
t
a
g
e
7
0
.
95
V
i
ndi
ca
ti
ng
the
va
li
di
ty
of
t
h
e o
u
t
p
u
t
s.
H
o
we
ve
r,
i
n
thi
s
case
pre
s
e
n
ce
of
5t
h ha
r
m
o
n
i
c
c
o
mpo
n
e
n
t
ca
n
be
o
b
ser
v
e
d
ha
vi
ng a
n
o
rm
al
iz
ed
va
lue
o
f
2.
4/6
9
.
2
=
0.
03
5%.
S
e
l
e
c
t
i
v
e
ha
r
m
o
n
i
c
el
i
m
ina
t
i
on
(S
HE)
m
o
d
u
l
a
t
i
on
te
ch
ni
q
u
e ca
n
be
use
d
t
o
c
o
mpl
e
t
e
l
y
re
mo
ve t
h
e
exi
s
t
e
n
c
e
o
f
t
h
e
r
e
mai
n
in
g
ha
rm
oni
cs
(
5
th
,
1
1
t
h
a
n
d
1
3
t
h
)
fr
om
the
out
put
vol
ta
ge
a
nd c
u
r
r
e
n
t
[
25]
.
It
m
u
st
be
a
ddr
esse
d t
h
a
t
the
est
i
m
a
t
ion
and e
r
a
d
i
c
a
t
i
on o
f
har
m
o
n
i
c
s
is not
a
p
u
r
p
ose
of
th
is man
u
s
cri
p
t
.
Th
e
exp
e
r
i
menta
l
re
su
lt
s ob
tain
e
d
i
n
F
i
gu
r
e
.1
0b
th
a
t
t
h
e
R
M
S
v
a
lu
e of
th
e f
und
a
m
en
tal f
r
e
qu
en
cy
c
o
mpo
n
e
n
t
s
h
a
s decr
ea
se
d b
y
2
2
% at
a sl
ight
l
y
hig
h
e
r
T
HD si
nc
e, t
h
e
mo
dula
t
i
o
n i
nde
x is
re
d
u
c
e
d
t
o
m
=
0
.
8
.
R
e
d
u
c
i
n
g
t
h
e
mo
dul
at
i
on i
n
de
x to
m
=
0
.
3
i
n
Fi
g
u
re
.
1
1a,
i
t
c
a
n
be
obse
r
ved
t
h
at
t
h
e
h
y
b
r
i
d
in
ve
rt
er
has
pr
oduc
e
d
7-
l
e
v
e
l
out
put
v
o
l
t
a
g
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
S
i
ng
l
e
pha
se
21
le
v
e
l hy
b
r
i
d
m
u
ltil
ev
e
l
i
n
verte
r wit
h
re
du
ced
p
o
w
e
r
… (Sh
e
i
k
h
Tan
z
i
m
M
e
ra
j)
8
19
(
a
)
(
b
)
Fi
gu
re.
9
.
E
x
p
e
r
i
me
nta
l
re
sul
t
s at
,
m =
1:
(
a
)
o
u
t
put
v
o
lt
age
a
nd
c
u
r
r
e
nt
a
n
d
(b
) har
m
o
n
i
c
s
p
e
c
t
r
um.
(
a
)
(
b
)
F
i
gu
re.
1
0
.
Ex
per
i
me
nt
al
res
u
l
t
s
at
,
m
=
0.
8:
(a)
o
u
t
p
ut v
o
l
t
a
ge
a
n
d
c
u
r
r
e
n
t
an
d
(b
) har
m
o
n
i
c
s
p
e
c
t
r
um.
(
a
)
(
b
)
F
i
g
u
r
e
11
.
Expe
r
i
me
n
t
a
l
re
su
l
t
s a
t
,
m
= 0.
3
:
(a
)
o
u
t
p
u
t
vo
l
t
a
g
e
a
n
d c
u
rr
en
t an
d
(b
) har
m
o
n
i
c
s
p
e
c
t
r
um.
In t
h
i
s
case
,
t
h
e pr
op
ose
d
i
nve
r
t
e
r
wi
ll
o
p
era
t
e
e
x
ac
tl
y
li
ke t
h
e 7
-
l
e
ve
l cr
oss-
sw
it
che
d
i
n
v
e
r
t
e
r
pr
opose
d
i
n
[
1
3
]
.
H
o
we
ve
r,
TH
D
ha
s i
n
cre
a
sed
si
gnif
i
c
a
nt
ly a
t
m
=
0.
3
whi
l
e
t
h
e
R
M
S
v
a
l
u
e o
f
th
e
fun
d
a
men
t
a
l
f
r
e
qu
e
n
cy
ha
s d
ecr
ea
sed
.
Fin
a
ll
y
,
a
b
r
ief c
o
mp
ar
iso
n
b
e
tw
e
e
n th
e
s
e
r
e
su
l
t
s and th
e
si
mu
la
ted
r
e
sul
t
s
f
r
o
m
th
e
p
r
evi
ous
sec
t
i
on i
s
su
mma
r
iz
ed i
n
Ta
ble
5
.
B
y
o
b
se
r
v
i
n
g
Ta
ble
5,
it
c
a
n
be
veri
fi
e
d
t
h
a
t
i
n
te
rm
s
o
f
ou
tput v
o
lta
g
e
,
R
M
S vo
l
t
ag
e
and THD
,
th
e
h
i
gh
est
dev
i
at
ion
b
e
tw
e
e
n
t
h
e
simu
la
te
d
r
e
su
l
t
s a
n
d
t
h
e e
xpe
ri
me
nt
al
r
e
s
u
l
t
s ar
e
r
e
l
a
ti
vel
y
l
o
w
.
There
f
ore
,
i
t
c
a
n
be
co
ncl
u
de
d t
h
at
the
obt
ai
ned
re
sult
s
fr
o
m
b
o
t
h
si
mula
ti
on
an
d
har
d
wa
re
pr
ot
ot
y
p
e i
s
ac
c
u
rat
e
a
n
d
v
a
li
d.
The
det
a
i
l
ed ex
pe
r
i
me
nt
a
l
set
up i
s
s
h
o
w
n
in
Figur
e
1
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.