Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
8
, No
.
6
,
Decem
ber
201
8
, p
p.
48
80
~
489
1
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v8
i
6
.
pp
48
80
-
489
1
4880
Journ
al h
om
e
page
:
http:
//
ia
es
core
.c
om/
journa
ls
/i
ndex.
ph
p/IJECE
New De
ad
-
Time
Compen
sation M
ethod of P
owe
r Invert
er
Using
Car
rier
B
ased Sin
usoidal
Pul
se
-
W
idth
Modu
lation
Suro
s
o
1
,
D
aru T
ri
N
u
gr
oho
2
,
Tos
hihi
ko N
oguchi
3
1
,2
El
e
ct
ri
ca
l
Eng
i
nee
ring
Depa
r
tment, Jende
r
al Soe
dirman
Univer
sit
y
,
Indone
si
a
3
Gradua
te Schoo
l
of Engin
ee
ring
,
Shizuoka Univers
ity
,
Jap
an
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Ma
r
9
, 2
01
8
Re
vised
Ju
l
6
,
201
8
Accepte
d
J
ul
21
, 2
01
8
A
new
dea
d
-
tim
e
compensat
i
on
m
et
hod
of
power
inv
ert
e
r
ci
r
cui
ts
is
suggested
and
p
rese
nte
d
in
thi
s
pape
r.
The
prop
osed
m
et
hod
utilizes
ca
rr
ier
base
d
sinusoidal pulse
width
m
odula
ti
on
t
ec
hniq
ue
to
produ
ce driving signa
l
s
of
the
inve
rt
er
power
sw
it
che
s
with
dea
d
-
ti
m
e
cor
rec
t
ion
ca
p
abi
lit
y
.
Th
e
proposed
m
et
hod
abl
e
to
e
li
m
in
at
e
de
ad
-
t
ime
ef
fec
ts
such
as
re
duci
ng
the
wave
form
distort
ion
of
the
in
ver
te
r
output
c
urre
nt,
and
increa
sing
th
e
funda
m
ent
al
co
m
ponent
amplitude
of
output
cur
ren
t
.
An
anal
y
sis
of
th
e
proposed
m
et
hod
is
pre
sente
d.
S
om
e
computer
sim
ula
ti
ons
were
ca
rrie
d
ou
t
to
inve
stigate
th
e
princ
ip
le
oper
at
ion
,
and
to
tes
t
per
form
anc
e
of
the
new
m
et
hod.
Th
e
de
vel
oped
m
e
thod
was
val
id
ated
t
hrough
expe
r
imental
t
est
of
H
-
bridge
vol
ta
g
e
source
inv
erter
c
irc
ui
ts.
The
d
ata
obt
ai
n
ed
from
the
computer
sim
ula
ti
on
and
proto
t
ype
expe
r
iments
have
conf
irmed
tha
t
th
at
th
e
proposed
m
et
hod
worked
well
compensat
ing
th
e
dea
d
-
t
ime
in
the
volt
ag
e
source
power
in
ver
te
r
c
irc
ui
ts.
Ke
yw
or
d:
Dead
-
ti
m
e
Har
m
on
ic
s
Inver
te
r
Modula
ti
on
Copyright
©
201
8
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Su
r
oso,
Ele
ct
rical
En
gi
neer
i
ng D
e
par
t
m
ent,
Jen
der
al
S
oe
dirm
an
Un
i
ver
sit
y,
Jl. May
j
en
S
ungkono km
.5
, P
urbali
ngga
, J
a
wa
Te
ngah
, In
donesia.
Em
a
il
:
su
ro
s
o.
t
e.uns
oed@g
m
ai
l.com
1.
INTROD
U
CTION
Be
cause
of
pa
ro
c
hial
tur
n
-
on
and
t
urn
-
off
c
apab
il
it
y
of
power
sem
ic
on
duct
or
switc
hi
ng
de
vices,
a
tim
e d
el
ay
h
as to b
e a
dded bet
ween
t
he
tu
rn
-
on
a
nd tu
rn
-
off
g
at
ing
sig
nals
of
t
he
tw
o
swit
chin
g
de
vices i
n
the
sam
e
le
g
of
a
vo
lt
age
sou
rce
inv
e
rter
ci
rc
ui
t
s.
This
ti
m
e
delay
is
cal
le
d
as
dea
d
-
ti
m
e
,
wh
ic
h
is
in
he
ren
tl
y
need
e
d
in
a
volt
age
s
ource
ty
pe
inv
e
rter
t
o
av
oid
short
ci
rcu
it
s
betw
e
en
the
s
witc
he
s
in
the
sam
e
le
g
of
inv
e
rter
duri
ng
switc
hing
ope
rati
on
[
1]
-
[4
].
The
dea
d
-
tim
e
value
de
pe
nd
s
on
ty
pe
a
nd
the
powe
r
rati
ng
of
dev
ic
es
use
d
to
bu
il
d
the
po
wer
in
ver
te
r
ci
rcu
it
[5
]
,
[
6]
.
The
highe
r
the
switc
hi
ng
s
pe
ed,
a
prop
e
r
de
ad
-
ti
m
e
m
us
t
be
pr
oper
ly
sel
ect
ed
to
ensure
the
in
ve
r
te
r
ci
rcu
it
s
w
orks
pro
per
ly
[7]
.
Im
pr
op
e
r
sel
ect
ion
of
dea
d
-
tim
e
will
cause
t
he
i
nv
e
rter
fail
s
to
work a
nd m
ake
dam
age to
t
he
inv
e
rter
ci
rcui
ts [8
]
.
In
fact,
th
e
val
ue
of
dea
d
-
ti
m
e
is
com
par
at
ively
sm
a
ll
if
com
par
ed
to
the
fun
dam
ental
per
io
d
of
c
urrent
or
volt
age
wa
vefor
m
.
Howe
ver,
in
a
vo
lt
a
ge
-
so
ur
ce
pow
er
inv
e
rter,
the
cum
ulati
ve
dead
-
ti
m
e
in
on
e
cy
cle
will
giv
e
si
gn
if
ic
ant
ne
gative
eff
ect
s
uch
as
i
ncr
easi
ng
wa
ve
form
distor
ti
on
of
th
e
outp
u
t
curre
nt
an
d
volt
age
,
reducin
g
t
he
f
undam
ental
am
pl
it
ud
e
of
outp
ut
vo
lt
age
and
cu
rren
ts,
and
m
aking
t
he
pha
se
e
rro
r
[9
]
-
[11].
Wh
e
n
a
n
ac
m
oto
r
is
supp
l
ie
d
by
a
volt
age
s
ource
pow
er
in
ver
te
r,
th
e
sta
tor
volt
ag
e
s
of
the
m
oto
r
will
con
ta
in
ha
rm
on
ic
s
ge
ne
rated
by
dea
d
-
ti
m
e
eff
ect
.
T
he
m
otor
oper
at
ion
will
be
ba
dly
influ
e
nce
d
by
these
har
m
on
ic
s,
part
ic
ularly
at
no
-
l
oad
a
nd
lo
w
f
reque
ncies
ope
rati
on
s
,
m
aking
m
or
e
losses
of
m
achine,
re
du
ci
ng
eff
ic
ie
ncy a
nd
m
ake to
r
que
pulsa
ti
on of th
e
m
oto
r
[12]
,
[1
3
]
.
The
a
ddit
ion
al
m
oto
r
losse
s
and
to
rque
rip
ple
dep
e
nd
on
the
har
m
on
ic
l
evel
of
t
he
volt
age
a
nd
cu
rr
e
nt
su
ppli
ed
by
th
e
power
i
nv
e
rt
er
[
14
]
,
[15]
.
F
or
a
m
plifie
r
ap
plica
ti
on
,
th
e
de
ad
-
ti
m
e
gen
er
at
es
m
or
e
disto
rtion
s
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Ne
w Dead
-
Tim
e Co
mp
e
nsati
on Met
hod of P
ower
In
vert
er
Using C
ar
rie
r
Base
d Sin
usoid
al
…
(
Sur
os
o
)
4881
of
the
outp
ut
wav
e
f
or
m
[1
6]
.
In
the
ren
e
wab
le
e
nergy
app
li
cat
io
n,
es
pecial
ly
in
a
gr
i
d
co
nn
e
ct
ed
powe
r
inv
e
rter,
th
e
ha
rm
on
ic
s
of
t
he
inv
e
rter’
s
A
C
ou
t
pu
t
c
urre
nt
will
al
so
be
trans
ferred
i
nto
the
AC
po
w
er
gri
d
[17].
The
harm
on
ic
s
will
p
ollute
the
AC
power
gr
id
a
nd
powe
r
load
.
Hen
ce
,
re
duct
ion
,
el
im
inati
on
a
nd
com
pen
sat
ion
are r
e
quire
d
to
pr
e
ve
nt the ne
gative e
ff
ect
s
of
dead
-
tim
e
in
a
powe
r
i
nv
e
rter’
s
dri
ving
sig
nals.
So
m
e
m
e
tho
ds
hav
e
bee
n
dev
el
op
e
d
a
nd
prese
nted
by
m
any
research
e
rs
to
el
i
m
inate
and
counter
balance
the
eff
ect
s
of
dea
d
-
ti
m
e
.
Ba
sic
al
ly
,
t
he
tradit
ion
al
de
ad
-
ti
m
e
cou
nt
erb
al
a
nce
m
eth
ods
of
inv
e
rter
can
be
cl
assifi
ed
into
two
m
ajo
r
ty
pes
dep
e
ndin
g
on
the
m
ann
er
of
dea
d
-
ti
m
e
eff
ect
s
ad
dr
e
ss
ed
.
I
n
the
first
ty
pe,
the
ave
rag
i
ng
t
heory
is
us
ed.
In
this
te
ch
nique,
the
total
de
ad
-
ti
m
e
eff
ect
s
in
on
e
cy
cl
e
of
the
m
od
ulati
ng
w
a
vefor
m
is
rev
ie
wed
[
18
]
-
[
20
]
. H
owe
ver,
in
t
hi
s
m
et
ho
d,
the sp
ee
d
of
t
he
c
om
pen
sat
ing
process
is
sli
gh
tl
y
slow
.
F
or
the
sec
ond
m
et
ho
d
,
the
com
pen
sat
ion
is
co
nducte
d
on
a
sing
le
pu
lse
ba
sis,
pe
r
tim
e
-
switc
hing
rate,
hen
ce
t
he c
om
pensat
ion
sp
ee
d
ca
n be
faster
and m
or
e accu
rate [
21
]
,
[2
2
].
Howe
ver,
in
t
he
se
co
nv
e
ntio
na
l
te
chn
iq
ues
,
the
dea
d
-
ti
m
e
com
pen
sat
ion
is
accom
plished
ei
ther
by
decr
easi
ng
or
i
ncr
easi
ng
t
he
width
of
dr
i
vin
g
pu
lse
s
of
t
he
inve
rter
’s
powe
r
switc
he
s,
based
on
t
he
curren
t
po
la
rity
of
the
inv
e
rter.
T
herefo
re,
in
t
hese
m
et
ho
ds
th
e
current
se
ns
in
g
beco
m
es
ver
y
i
m
po
rtant
[
23]
.
T
he
po
la
rity
detect
ion
of
t
he
c
urre
nt
w
ave
form
i
s
ve
ry
cr
ucial
rou
nd
zer
o
c
r
ossi
ng
to
m
ake
the
dead
-
ti
m
e
eff
ect
com
pen
sat
ion
works
ef
fecti
ve
ly
.
To
ad
dr
e
ss
this
issue,
so
m
e
dead
-
ti
m
e
co
m
pen
sat
ing
m
et
ho
ds
app
l
y
al
gorithm
s
fo
r
curre
nt
est
im
at
ion
as
disc
usse
d
i
n
re
fer
e
nces
[2
4
]
,
[25
]
,
[26]
an
d
[27].
H
oweve
r,
these
te
chn
iq
ues
ope
rate
ef
fecti
vely
only
at
lo
w
m
odulati
on
in
de
x
or
lo
w
c
urre
nt
c
onditi
on.
I
n
t
he
lo
w
m
odulati
on
ind
e
x,
it
is
pos
sible
to
m
od
ify
the
pulse
-
widt
h
of
th
e
in
ver
te
r
gatin
g
si
gn
al
s
with
ou
t
reachi
ng
t
he
m
ini
m
u
m
or
m
axi
m
u
m
pu
lse
width
si
gn
al
s.
Acc
ur
at
e
s
m
al
l
-
sign
al
m
od
el
of
the
vo
lt
age
so
urce
powe
r
in
ver
te
r
ci
rcu
it
s
wh
ic
h
incl
ud
e
s
m
od
el
non
-
li
ne
arit
ie
s
as
wel
l
as
m
od
ulati
on
a
nd
dea
d
-
ti
m
e
eff
ect
s
is
ve
ry
im
po
rtant
in
this
m
et
ho
d [
28
]
.
In
t
his
researc
h
publica
ti
on,
a
dif
fer
e
nt
dea
d
-
ti
m
e
co
m
pensat
ion
m
et
ho
d
su
it
able
for
volt
age
sou
rce
ty
pe
inv
e
rter
ci
rcu
it
s
is
ex
pl
ai
ned
.
T
he
pr
opos
e
d
m
et
ho
d
based
on
ca
rr
ie
r
base
d
si
nuso
i
dal
pulse
widt
h
m
od
ulati
on
(CSP
W
M
)
strat
e
gy
with
le
vel
-
s
hifted
.
T
he
pr
i
nciple
op
e
rati
ons
of
the
pro
pose
d
ne
w
m
et
ho
d
ar
e
pr
ese
nted
a
nd
discusse
d.
Vali
dation
th
ro
ug
h
the
com
pu
te
r
si
m
ulati
on
s
wer
e
co
nd
ucted
for
the
three
-
le
ve
l
vo
lt
age
sou
rce
inv
e
rter.
F
ur
t
her
m
or
e,
t
he
pro
posed
com
pen
sat
io
n
m
et
ho
d
was
im
ple
m
ented
to
t
he
prototype
of th
ree
-
le
vel
H
-
br
i
dg
e
volt
age s
ource i
nv
e
r
te
r.
2.
PROP
OSE
D DEA
DTIME
COMPE
N
SAT
ION
METH
OD
Fig
ure
1(a)
s
hows
th
e
co
nv
e
ntion
al
le
vel
s
hifted
CSP
W
M
with
two
tr
ia
ngular
car
rier
wa
vefor
m
s,
V
cr1
and
V
cr2
.
These
carrie
r
sign
al
s
ha
ve
the
sam
e
fr
equency,
the
sam
e
ph
ase
a
nd
th
e
sa
m
e
peak
-
to
-
pe
a
k
a
m
plit
ud
e.
T
he
carrier
sig
nals
fr
e
qu
e
ncy
set
s
the
switc
hing
fr
e
qu
e
ncy
of
powe
r
switc
hes
us
e
d
in
the
in
ve
rter
[29],
[
30]
.
T
he
w
a
vefor
m
V
m
is
the
sin
usoi
dal
m
od
ulati
ng
sign
al
.
Its
fr
e
qu
e
ncy
giv
e
s
t
he
m
ai
n
fr
e
qu
e
ncy
of
the
inv
e
rter
outp
ut
volt
age
wav
e
f
or
m
.
Th
is
m
od
ulati
on
m
et
ho
d
is
c
omm
on
ly
us
ed
f
or
gatin
g
sign
al
s
gen
e
rati
on
of
a
three
-
le
vel
i
nv
e
rter
[
31
]
,
[
32
]
.
For
t
he
m
ulti
le
vel
powe
r
in
ver
te
r
ci
rc
uits
with
hi
gher
le
ve
l
nu
m
ber
of
ou
t
pu
t
vo
lt
age
wa
vefor
m
,
m
or
e
tria
ngular
ca
rr
i
ers
are
require
d
with
dif
fer
e
nt
of
fs
et
values
[
33
]
,
[3
4
].
I
n
pract
ic
al
,
fo
r
al
l
volt
age
source
pow
er
inv
e
rter
ci
rc
uits,
a
dead
-
ti
m
e
is
add
ed
to
the
gen
e
rated
sign
al
s
to drive
the
po
wer
sem
ic
on
duct
or
s
witc
hes
.
In
or
der
to
co
m
pen
sat
e
the
eff
ect
of
dea
d
-
tim
e,
Figu
re
1(b)
is
the
sugg
e
ste
d
the
le
vel
sh
ifte
d
C
SP
W
M wit
h
dead
-
ti
m
e
co
m
pensat
ing
f
unc
ti
on
.
T
he
visibl
e
diff
e
re
nce
co
m
par
ed
to
the co
nve
ntion
al
c
arr
ie
r
-
base
d
le
vel
sh
i
fted
SP
WM
is
the
existe
nce
of
intersect
io
n
a
rea
bet
ween
t
he
uppe
r
an
d
lo
wer
ca
rr
ie
r
si
gnal
s.
This c
ro
s
sin
g
a
rea is
no
t a
vail
able in t
he
c
on
ven
ti
onal
m
odulati
on
m
et
hod i
n
Fi
gure
1
(a
)
.
To
m
ake
a
cl
ear
analy
sis,
an
e
nlar
ged
fig
ur
e
of
th
e
pro
po
s
ed
m
od
ulati
on
te
chn
i
qu
e
wit
h
com
pen
sat
ing
capab
il
it
y
of
de
ad
-
ti
m
e
is
pr
esented
i
n
Fi
gure
2.
This
fig
ur
e
de
picts
det
ai
l
op
erati
on
of
the
pro
po
se
d
new
dead
-
ti
m
e
com
pen
sat
ing
m
et
hod.
T
he
vol
ta
ge
V
c
is
the
tria
ngular
ca
r
rier
wa
vefo
rm
of
the
conve
ntion
al
CSP
W
M
.
In
t
he
co
nv
e
ntio
na
l
m
od
ulati
on
strat
egy,
the
m
ini
m
u
m
and
m
axi
m
u
m
peak
of
the
tria
ngular
car
rier
wav
e
f
or
m
do
es
not
cro
ss
t
he
intersect
io
n
area,
A
c
.
I
n
ano
t
her
w
ord
,
there
is
no
par
t
of
a
tria
ngular
ca
rri
er
cr
os
sin
g
e
ach
oth
er
.
T
he
sign
al
V
m
i
s
the
m
od
ulat
ing
s
i
gn
al
w
hi
ch
is
the
si
nuso
i
dal
wav
e
f
or
m
.
Its
fr
e
qu
e
ncy
is
usual
ly
m
uch
lo
wer
tha
n
the
c
arr
ie
r
wa
veform
s
.
Co
m
par
ing
the
tria
ng
ula
r
carrie
r
and
m
odulati
ng
sig
nals
in
the
com
par
at
or
ci
rcu
it
s
will
gen
e
rate
the
P
WM
sig
nal
pa
tt
ern
s
f
or
th
e
powe
r
inv
e
rter
ga
ti
ng
s
ign
al
s.
I
n
thi
s
fig
ur
e
,
the
volt
age
sig
nal
V
c
’
is
the
t
rian
gu
la
r
car
rier
w
aveform
i
m
ple
m
enting
com
pen
sat
ion
of
dead
-
ti
m
e.
I
n
this
m
od
ulati
on
te
ch
nique,
there
is
a
pa
rt
of
the
ca
rr
ie
r
wav
e
f
or
m
s
crossi
ng
each
oth
e
r
in
the inte
rsecti
on
area in
dicat
ed by
A
c
. If
th
e pe
rcen
ta
ge of
t
he
crossin
g
a
rea
denoted
as
C
, we ca
n
wr
it
e:
C = A
c
/A
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
48
80
-
4891
4882
Wh
e
re
A
c
is
t
he
m
agn
it
ud
e
of
t
he
cr
os
se
d
carrier
wa
ve
f
or
m
,
and
A
is
the
rest
m
agni
tud
e
of
t
he
carrier
as
s
ho
wn
in
Fig
ur
e
1(b
)
a
nd
Fig
ure
2.
T
he
∆T
is
t
he
dead
-
ti
m
e
value
ad
de
d
t
o
gating
sig
nal
S
.
T
his
dead
-
ti
m
e
causes
vo
lt
a
ge
sig
nal
loss
es
in
di
cat
ed
as
∆V
.
I
f
the
in
ver
te
r
switc
hing
f
requen
cy
is
f
,
t
he
total
vo
lt
age
dr
op in
one cycl
e out
put v
oltage
i
s:
V
D
= 2.
f.
∆
V
(2)
Wh
e
re,
V
D
is
t
he
total
vo
lt
ag
e
dro
p
pro
duc
ed
by
the
dea
d
-
ti
m
e
in
one
cy
cl
e
P
W
M
outp
ut
volt
age
.
In
one
cy
cl
e
of
switc
hing
f
reque
ncy,
there
will
be
a
turn
-
on
a
nd
a
turn
-
off
tran
sit
ion
.
Co
ns
e
quently
,
the
hi
gher
th
e
switc
hing
fr
e
quency
will
cau
se a
la
r
ger
volt
age
dro
p.
(a)
(b)
Figure
1. (a
)
C
onve
ntion
al
level s
hifted
C
S
P
W
M,
(
b)
pro
pose
d
le
vel s
hift
ed
CSP
WM
wi
th d
ea
d
-
tim
e
com
pen
sat
ing f
un
ct
io
n
In
Fig
ure
2
,
th
e
gatin
g
si
gn
al
w
it
h
dead
-
ti
m
e
com
pen
sat
i
ng capab
il
it
y
is
th
e
S
’
.
It
is
ge
ne
r
at
ed
by
t
he
pro
po
se
d
m
odulati
on
te
c
hn
i
que.
T
he
dead
-
t
i
m
e
value
is
the
sam
e
as
∆T
.
Howe
ver,
the
great
point
in
this
picture
is
that
the
vo
lt
age
s
ign
al
lo
sses
ge
ner
at
e
d
by
th
e
dea
d
-
ti
m
e
is
com
pen
sat
ed
us
in
g
the
s
uggested
m
od
ulati
on
.
T
he
c
om
pen
s
at
ing
volt
age
pu
l
se
com
pen
sat
e
d
by
the
dead
-
tim
e
com
pen
sat
ion
is
in
dica
te
d
as
∆V’
.
Util
iz
ing
the
com
pen
sat
ion
m
et
ho
d,
the
com
pen
sat
e
d
outp
ut
volt
age
V
o
’
will
be
the
sa
m
e
to
t
he
ideal
ou
t
pu
t
vo
lt
age.
Th
e
volt
age l
osse
s pr
oduce
d
by the
dea
d
-
ti
m
e w
il
l no
t
be
gen
e
rated
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Ne
w Dead
-
Tim
e Co
mp
e
nsati
on Met
hod of P
ower
In
vert
er
Using C
ar
rie
r
Base
d Sin
usoid
al
…
(
Sur
os
o
)
4883
Figure
2. Ba
sic
principle
of th
e
sug
gested
m
et
hod.
3.
COMP
UTER
SIMULATI
O
N
TE
ST
RES
ULTS
Com
pu
te
r
sim
ulati
on
s
wer
e
cond
ucted
to
e
xam
ine
the
propose
d
m
od
ul
at
ion
m
et
ho
d
us
in
g
s
of
tw
are
powe
r
PS
IM.
The
th
ree
-
le
ve
l
H
-
br
id
ge
volt
age
s
ource
i
nv
erter
ci
rc
uit
as
show
n
in
Fig
ur
e
3
was
te
ste
d.
T
he
par
am
et
er
te
st
s
are
li
ste
d
in
T
able
1
.
A
100
V
DC
vo
lt
a
ge
was
use
d
as
t
he
input
powe
r
so
urce
of
t
he
inv
e
rter
ci
rcu
it
s.
T
he
s
witc
hing
fr
e
quenc
y
was
ch
ose
n
as
22
kH
z
in
order
to
push
the
s
witc
hing
har
m
on
ic
c
ompone
nt
s
into
higher
re
gi
on
an
d
t
o
pr
e
ven
t
au
dib
le
noise
.
The
dea
d
-
tim
e
value
wa
s
3.5µs
.
Ind
uctive
power
loa
d
wit
h
series
resist
a
nc
e
R
20
Ω
a
nd
inducto
r
3
m
H
was
c
onnecte
d
to
t
he
in
ve
rter.
T
he
fun
da
m
e
ntal
ou
tp
ut
vo
lt
age
fr
e
qu
e
ncy
was
60 H
z
.
Figure
4
sho
ws
the
te
st
resu
lt
s
us
in
g
co
m
pu
te
r
si
m
ula
ti
on
of
the
th
ree
-
le
vel
H
-
bri
dg
e
in
ver
te
r
pr
ese
ntin
g
the
wavef
or
m
s
of
load
c
urre
nt
a
nd
outp
ut
volt
age
wh
e
n
the
m
od
ulati
on
in
dex
was
0.9
w
it
h
no
com
pen
sat
ion
.
The
ha
rm
on
ic
sp
ect
ra
of
the
load
cu
rrent
a
nd
P
W
M
ou
t
put
volt
age
are
descr
i
bed
i
n
F
igure
5(
a
)
an
d
Fig
ure
5(b)
.
F
ur
t
herm
or
e
,
Figu
re
6
pr
ese
nts
si
m
ulati
on
te
st
resul
ts
of
the
load
current
an
d
vo
lt
age
wav
e
f
or
m
wh
e
n
the
c
om
pen
sat
ion
m
et
ho
d
was
im
ple
m
ent
ed.
T
he
inter
se
ct
io
n
area
of
t
he
carrier
si
gn
al
s
was
set
to
be
9%.
The
ha
rm
on
ic
sp
ect
ra
of
loa
d
cu
rr
e
nt
an
d
vo
lt
age
wa
vefor
m
are
sh
ow
n
in
Fig
ure
7(a)
a
nd
Fig
ure
7(b
)
,
s
uc
cessi
fely
.
Fig
ure
8
de
note
s
a
relat
ion
bet
we
en
the
inters
ect
ion
a
rea
value
of
t
rian
gu
la
r
c
arr
ie
r
wav
e
f
or
m
s,
C
,
and
the
total
har
m
on
ic
dist
ort
ion
(T
HD)
of
the
loa
d
cu
rr
e
nt
wa
vefor
m
fo
r
t
he
th
ree
-
le
vel
H
-
br
i
dg
e
in
ver
te
r
.
T
he
lo
west
c
urren
t
disto
rtio
n
value
is
achi
eved
at
inter
se
ct
ion
a
rea
valu
e
ar
ound
9%.
This
value
is
u
se
d
i
n
the
co
m
pu
te
r
sim
ulatio
n
a
nd lab
orat
or
y
pr
oto
ty
pe
e
xperi
m
ental
test
.
Figure
3. H
-
bri
dg
e
in
ver
te
r
cir
cuits [
30
]
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
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-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
48
80
-
4891
4884
T
able
1.
C
om
pu
te
r
s
im
ulati
on
t
est
p
aram
et
ers
Variable
Valu
e
DC in
p
u
t vo
ltag
e
100
V
Inv
erter
s
wi
tch
in
g
f
requ
en
cy
2
2
kHz
Dead
-
ti
m
e
valu
e
3
.5µ
s
Po
wer
lo
ad
R
=
20
Ω,
L
=
3
mH
Fu
n
d
a
m
en
tal o
u
tp
u
t vo
ltag
e
f
requ
en
cy
6
0
Hz
Figure
4
.
Lo
a
d cu
rr
e
nt and
vo
lt
age w
a
veform
s o
f
H
-
bri
dge
volt
age s
ource
inv
e
rter
with
no
c
om
pen
sat
io
n
(a)
(b)
Figure
5
.
(
a
)
H
arm
on
ic
sp
ect
r
a of loa
d
c
urre
nt
wa
ve
form
witho
ut c
om
pen
s
at
ion
, (
b
) ha
rm
on
ic
sp
ect
ra
of
vo
lt
age
w
a
ve
form
w
it
ho
ut c
om
pen
sat
ion
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Ne
w Dead
-
Tim
e Co
mp
e
nsati
on Met
hod of P
ower
In
vert
er
Using C
ar
rie
r
Base
d Sin
usoid
al
…
(
Sur
os
o
)
4885
Figure
6
.
Lo
a
d cu
rr
e
nt and
vo
lt
age w
a
veform
s o
f
H
-
bri
dge
volt
age s
ource
inv
e
rter
with
pro
posed
m
et
ho
d
(a)
(b
)
Figure
7
.
(
a
)
H
arm
on
ic
sp
ect
r
a of loa
d
c
urre
nt w
it
h
com
pe
ns
at
io
n,
(b
) har
m
on
ic
sp
ect
ra
of outp
ut
vo
lt
a
ge
with c
om
pen
sa
ti
on
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
48
80
-
4891
4886
Figure
8
.
A rel
at
ion
betwee
n cros
s
ed
area
of
the tria
ngular
carriers
and
T
HD
of
ou
t
put c
urren
t
Fig
u
r
e
9
repre
sents
the
com
par
is
on
of
pu
l
se
-
wi
dth
of
P
WM
outp
ut
volt
age
wa
vefo
r
m
fo
r
the
idea
l
wav
e
f
or
m
(
no
dead
-
ti
m
e),
with
dead
-
tim
e
but
no
com
pen
s
at
ion
,
an
d
with
dea
d
-
ti
m
e
equi
pp
e
d
with
pro
po
s
e
d
com
pen
sat
ion
m
et
ho
d.
As
ca
n
be
ob
se
r
ved
in
this
fig
ur
e
,
the
s
ugges
te
d
m
et
ho
d
rec
ov
e
red
t
he
l
os
s
of
pulse
-
width
of
P
W
M
ou
tp
ut
vol
ta
ge
to
the
id
eal
wav
ef
orm
.
Figure
10
pr
esents
the
sim
ula
ti
on
res
ults
of
a
com
par
ison
ha
rm
on
ic
order
s
in
case
of
us
i
ng
com
pen
sat
io
n
an
d
without
com
pen
sat
ion
.
The
re
su
lt
s
s
how
that
the
m
agn
it
ud
e
s
of
the
l
ow
fr
e
qu
e
ncy
harm
on
ic
s
beco
m
e
m
uch
lowe
r
by
im
ple
m
en
ti
ng
the
dea
d
-
tim
e
com
pen
sat
ion
m
et
ho
d.
Figure
9.
Enla
r
ged pulse
widt
h of P
W
M
out
pu
t
volt
age
wa
vefor
m
in
case
of
no
dea
d
-
ti
m
e (id
eal
wa
vefor
m
),
with
dead
-
ti
m
e
but no c
om
pen
sat
io
n,
a
nd
c
om
pen
sat
ed
pul
se
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
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88
-
8708
Ne
w Dead
-
Tim
e Co
mp
e
nsati
on Met
hod of P
ower
In
vert
er
Using C
ar
rie
r
Base
d Sin
usoid
al
…
(
Sur
os
o
)
488
7
Figure
10.
A
c
om
par
ison o
f o
utput cu
rr
e
nt
ha
rm
on
ic
co
m
po
ne
nts
of H
-
br
i
dg
e
volt
age
source
in
ver
te
r
(co
m
pu
te
r si
m
ulati
on
test
res
ult)
4.
E
X
PERI
MEN
TAL
TE
ST
RESU
LT
S
Vali
dation
an
d
ver
i
f
ic
at
ion
of
the
pro
pose
d
m
et
ho
d
e
xp
erim
entally
wer
e
do
ne
in
la
borato
ry.
A
la
borat
or
y
pro
toty
pe
of
t
he
H
-
br
i
dg
e
volt
age
s
ource
po
wer
i
nverter
was
m
ade
us
i
ng
po
wer
M
OS
FE
T
FK30SM
-
6.
T
his
sect
io
n
presents
la
bo
rator
y
e
xperim
ental
te
st
resu
lt
s
of
the
pro
po
sed
new
dea
d
-
tim
e
com
pen
sat
ion
te
chn
i
qu
e
.
Ta
bl
e
2
li
sts
the
e
xperim
ental
te
st
pa
ram
et
ers
of
the
in
ver
te
r
prototype.
A
50
V
DC
vo
lt
age
po
wer
source
was
use
d
in
the
in
ve
rter
prototype
ex
per
im
ent.
Figure
.
11(a
)
sh
ows
t
he
m
e
asure
d
tria
ngular
car
ri
ers
an
d
sin
us
oi
dal
m
od
ulati
ng
wa
vefor
m
of
the
conven
ti
onal
SP
W
M
w
it
h
no
c
om
pen
s
at
ion
.
Wh
e
reas,
Fig
ure
11(
b)
pr
e
sen
ts
the
m
easur
e
d
tria
ngula
r
an
d
sin
us
oi
dal
sign
al
s
of
the
s
ugge
ste
d
com
pen
sat
io
n
m
et
ho
d
.
T
he
in
te
rsecti
on
a
rea
of
the
tria
ngula
r
carrie
r
wa
vefor
m
s
is
cho
sen
as
9%,
w
hic
h
is
the
op
ti
m
al
valu
e
for
the
outp
ut
cu
r
ren
t
dist
or
ti
on
as
dete
rm
in
ed
in
the
pr
e
vi
ou
s
c
om
pu
te
r
si
m
ulati
on
te
st
resu
lt
s.
Fig
ure
12
i
s
m
easur
ed
d
ea
d
-
tim
e add
e
d
to
the in
ver
te
r gati
ng
sig
nals. T
he
m
easur
ed de
ad
-
ti
m
e w
as 3
.
5
µ
s.
Figure
13(a)
di
sp
la
ys
the
m
ea
su
re
d
wav
e
f
orm
s
of
the
P
WM
AC
volt
age
and
l
oad
cu
rr
e
nt
in
case
of
no
dea
d
-
ti
m
e
c
om
pen
sat
ion.
A
disto
rtio
n
cause
d
by
the
de
adtim
e
eff
ect
can
be
ob
se
r
ve
d
in
the
loa
d
c
urren
t
wav
e
f
or
m
.
Fig
ure
13(b)
pres
ents
the
P
W
M
vo
lt
age
a
nd
l
oad
c
urre
nt
w
aveform
s
of
the
H
-
bri
dge
inv
e
rte
r
wh
e
n
the
p
r
op
os
e
d
m
e
tho
d
was
em
plo
ye
d.
The
load
c
urr
ent
was
al
m
os
t
a
pu
re
sin
usoidal
wa
veform
with
lowe
r
distor
ti
on.
Furthe
rm
or
e,
Fig
ure
14
shows
the
m
or
e
detai
l
com
par
ison
of
t
he
lo
w
fr
e
quency
ha
r
m
on
ic
s
in
case
of
no
com
pen
sat
ion
,
an
d
w
hen
c
om
pen
sat
ion
wa
s
em
plo
ye
d
.
T
he
data
wer
e
obta
ined
by
la
borat
or
y
exp
e
rim
ental
t
est
.
Ex
per
im
ental
ly
,
it
con
fir
m
ed
that
the
ne
w
com
pen
sat
i
ng
m
et
ho
d
of
dead
-
ti
m
e
wo
r
k
ed
well
el
i
m
inati
ng
de
ad
-
ti
m
e eff
ect
, red
ucin
g
t
he h
arm
on
ic
d
ist
ort
ion
pro
duced
by
the d
ea
d
-
tim
e
.
T
able
2.
E
xper
i
m
ental
te
st par
am
et
ers
Variable
Valu
e
DC in
p
u
t vo
ltag
e
5
0
V
Inv
erter
s
wi
tch
in
g
f
requ
en
cy
2
2
kHz
Dead
-
ti
m
e
valu
e
3
.5µ
s
Load
R
=
20
Ω
,
L
=
3
mH
Main f
requ
en
cy
of
o
u
tp
u
t vo
ltag
e
6
0
Hz
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IS
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:
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-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
8
, N
o.
6
,
Dece
m
ber
2
01
8
:
48
80
-
4891
4888
(a)
(b)
Figure
11.
(a)
The
tria
ngular
carrier
and si
nuso
i
dal
m
od
ula
ti
ng
wav
e
f
or
m
s of SP
W
M i
n ca
se of
without
dead
-
ti
m
e co
m
pensat
ion
, (b
) T
he
tria
ngular
carrier
and si
nuso
i
dal m
od
ula
ti
ng
wav
e
f
or
m
s of SP
W
M i
n ca
se
of w
it
h dea
d
-
ti
m
e com
pen
sat
ion
Figure
12
. Dea
d
-
ti
m
e o
f
the
inv
e
rter
gatin
g si
gn
al
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Ne
w Dead
-
Tim
e Co
mp
e
nsati
on Met
hod of P
ower
In
vert
er
Using C
ar
rie
r
Base
d Sin
usoid
al
…
(
Sur
os
o
)
4889
(a)
(b)
Figure
1
3.
(a)
Me
asur
em
ent
r
esult
of
ou
t
pu
t
vo
lt
age
and l
oa
d
c
urren
t
wa
ve
form
s in
case o
f
no
com
pen
sat
ion
,
(b)
T
he
m
easure
d wav
e
f
or
m
s o
f
volt
age a
nd
load
c
urre
nt
w
hen
com
pen
sat
ion
was
appli
ed
Figure
1
4.
C
om
par
ison
of cu
rr
e
nt h
a
rm
on
ic
co
m
po
ne
nts
of H
-
b
ri
dg
e
in
ve
rter in ca
se
of
no c
om
pen
sat
ion an
d
with c
om
pen
sa
ti
on
(experim
ental
test
r
es
ult)
Evaluation Warning : The document was created with Spire.PDF for Python.