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.
9
, No
.
4
,
Aug
us
t
201
9
, p
p.
2314~
2320
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v9
i
4
.
pp2314
-
23
20
2314
Journ
al h
om
e
page
:
http:
//
ia
es
core
.c
om/
journa
ls
/i
ndex.
ph
p/IJECE
Analysis
and imp
rovemen
t o
f
the e
ffici
ency
of frequ
ency
co
n
verte
rs with pu
lse w
idt
h modu
lation
Bog
d
an V
as
il
e
v
Depa
rt
m
ent
o
f
e
l
ec
tr
ic
pow
er and
elec
trome
cha
ni
c
s
,
Saint
-
Pe
te
rsbu
rg
Mining
Univ
e
rsit
y
,
Russ
ia
n
Fe
der
ation
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
J
an
1
9
, 2
01
9
Re
vised
Ma
r
4
,
201
9
Accepte
d
Ma
r
12
, 201
9
In
orde
r
to
id
e
nti
f
y
th
e
b
est
c
ontrol
al
gori
thm,
th
e
ef
fects
of
m
odula
ti
on
cont
rol
a
lgori
th
m
s
on
the
ene
rg
y
ch
ara
c
te
r
isti
cs
of
a
two
-
le
vel
aut
onom
ous
fre
quency
conv
e
rte
r
inve
r
te
r
wer
e
studie
d.
Th
e
rese
arc
h
was
ca
r
rie
d
out
b
y
the
m
et
hods
of
m
at
hemati
c
al
an
d
sim
ula
ti
on
m
odel
ing
.
Th
e
eq
ua
-
ti
ons
of
m
at
hemati
c
al
de
script
ion
were
c
om
pil
ed
ta
king
int
o
account
a
num
ber
of
gene
ra
lly
acce
p
te
d
assum
pti
ons.
An
equi
v
ale
nt
c
irc
ui
t
of
a
two
-
le
v
el
aut
onom
ous
inv
ert
er
was
cr
eate
d.
Com
par
isons
of
pulse
-
wid
th
m
odula
ti
on
al
gorit
hm
s
with
ca
rri
er
signa
ls
of
var
ious
shape
s
and
fre
quen
cies
were
m
ade.
Thre
e
different
f
orm
s
of
ca
rrier
sig
nal
w
ere
used
:
tri
angu
la
r
,
sawt
ooth
with
a
fal
li
ng
edg
e
and
sawtooth
wi
th
a
l
ea
ding
edg
e.
Studie
s
were
co
nduct
ed
at
fre
quencie
s
of
3
,
000,
6,
000
and
9,
000
Hz.
Con
clus
ions
were
m
ade
about
the
ide
ntit
y
of
th
e
spec
tral
compos
it
ion
of
the
front
and
rea
r
ed
ges
o
f
the
sawtooth
signal
,
it
was
al
so
note
d
tha
t
with
th
e
tri
angular
wave
form
,
bei
ng
the
p
art
of
th
e
h
ar
-
m
onic
s,
pr
ese
nt
in
the
sawtoo
th
form
is
r
emoved,
so
,
th
e
tri
angular
shap
e
provide
s
the
best
result
of
the
au
t
onom
ous
inve
rter.
Also,
b
y
inc
re
asing
in
the
ca
rrie
r
fre
qu
ency
,
i
t
was
note
d
tha
t
pulse
pac
k
ets
appe
ar
at
diffe
ren
t
h
armonic
num
ber
s,
shift,
and
the
amplit
ude
and
disto
rti
on
f
ac
to
r
dec
re
ase
,
th
at
m
ea
ns,
th
e
best
p
erf
orm
anc
e
was
obta
ine
d
at
th
e
m
axi
m
u
m
fre
quency
stud
ied.
In
the
stud
y
o
f
the
voltage
a
t
the
output
of
th
e
choke
s
a
t
diffe
ren
t
fre
que
nci
es
of
the
c
a
rrie
r
signal,
it
was
note
d
tha
t
at
a
highe
r
fre
quency
,
the
rippl
e
of
the
o
utput
volt
ag
e
dec
re
ase
s.
Thrott
le
s
do
not
el
iminate
har
m
onic
s,
but
onl
y
re
duce
their
a
m
plitude.
Based
on
t
he
result
s,
it
w
as
conc
lud
e
d
tha
t
th
e
al
gor
i
thm
with
a
tri
an
gula
r
c
arr
ie
r
sig
nal
and
th
e
m
axi
m
um
fre
qu
ency
provid
es
the
best
har
m
oni
c
compos
it
ion
o
f
the
output
volt
ag
e
of
the fr
eque
nc
y
conv
erter.
Ke
yw
or
d
s
:
Ele
ct
ric d
ri
ve
Fr
e
qu
e
ncy c
onver
te
r
Pu
lse
-
widt
h
m
odulati
on
Si
m
ulati
on
m
od
el
Tw
o
-
le
vel a
ut
onom
ou
s
in
ver
t
er
Copyright
©
201
9
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
:
Bogda
n Vasil
ev,
Dep
a
rtm
ent o
f
el
ect
ric p
owe
r a
nd elec
trom
echan
ic
s
,
Saint
-
Pete
r
sbu
rg Mi
ning
Un
i
ver
sit
y
,
2,
21st Li
ne
, S
t
Peters
bur
g 19910
6,
R
us
sia
.
Em
a
il
:
vasile
v.
bu@yan
de
x.
r
u
1.
INTROD
U
CTION
Nowa
days,
in
m
od
er
n
el
ect
ric
dr
ives
f
r
equ
e
ncy
co
nverters
are
use
d
for
sm
oo
th
con
tr
ol
of
el
ect
ro
m
agn
et
ic
and
m
echani
cal
var
ia
bles
of
the
el
ect
ric
dr
ive
[1
-
5]
.
A
diag
ram
of
a
ty
pical
fr
equ
e
ncy
conve
rter
is
s
how
n
in
Fig
ur
e
1.
A
tw
o
-
le
vel
aut
onom
ou
s
i
nv
e
rter
(AI)
is
instal
le
d
at
the
out
pu
t
of
th
e
fr
e
qu
e
ncy
c
onver
te
r
[6
-
10]
.
The
m
odulati
on
c
on
tr
ol
syst
e
m
is
us
ed
to
c
ontr
ol
a
tw
o
-
le
ve
l
AI
,
w
hich
is
par
t
of
an
el
e
ct
ric
dri
ve
c
on
tr
ol
sys
tem
,
on
the
al
gorithm
s
of
w
hich
t
he
ene
r
gy
char
act
erist
i
cs
of
the
fr
e
quency
conve
rter
(F
C
)
and
the
w
hole
el
ect
ric
dr
ive
as
well
.
The
m
os
t
widely
us
e
d
al
gorithm
s
a
re
sinusoi
dal
PWM,
wh
ic
h
can
be
m
od
ifie
d
by
c
hangin
g
the
sha
pe
of
the
c
a
rri
er
sign
al
[11
-
15]
.
T
he
st
ud
y
of
this
t
op
ic
a
ll
ow
s
us
to for
m
ulate
r
e
com
m
end
at
io
ns o
n
t
he
c
ho
ic
e
of the
for
m
and
fr
e
qu
e
ncy
of
the car
rier 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
An
alysis a
nd i
mp
r
ove
me
nt o
f
the eff
ic
ie
ncy
of freq
ue
ncy c
on
ve
r
te
rs…
(
B
ogdan V
as
il
ev
)
2315
Figure
1.
Dia
gra
m
o
f
a
ty
pical
f
re
quency c
on
ver
te
r
To
c
ontr
ol
tw
o
-
le
vel
A
I
tra
ns
ist
ors,
t
he
P
WM
syst
em
gen
erates
switc
hing
functi
ons
,
w
hich
are
con
t
ro
l
sig
nals.
Tw
o
sign
al
s
are
us
ed
to
fo
rm
the
switc
hin
g
f
unct
ion
s:
co
ntr
oller;
carrying
[16
-
18]
.
The
e
ne
rg
y
c
ha
racteri
sti
cs
of
an
aut
onom
ou
s
i
nv
e
rter
de
pend
on
t
he
f
or
m
and
pa
ra
m
et
ers
of
the
carrier
sign
al
,
s
uc
h
as:
vo
lt
age
f
or
m
;
vo
lt
age
sp
ect
ra
l
factor
;
dist
or
t
ion
f
act
or
[
19
-
21]
.
Using
tria
ngular
a
nd
saw
too
t
h
sign
al
s
a
nd
ch
ang
i
ng
t
heir
frequ
e
ncy,
we
r
esearch
by
us
ing
Ma
tl
ab
Sim
ul
ink
by
m
eans
of
sim
ulatio
n
a
nd
m
at
he
m
at
ic
a
l m
od
el
ing
.
2.
RESEA
R
CH MET
HO
D
Fo
r
sim
ulati
ng
the
op
e
rati
on
of
a
tw
o
-
le
ve
l
AI
with
t
he
abili
ty
to
rese
arch
the
c
har
a
ct
erist
ic
s
of
var
i
ou
s
co
ntr
ol
al
gorithm
s,
it
is
necessa
ry
to
so
lv
e
the
f
ollo
wing
ta
s
ks
:
to
acce
pt
an
ass
um
pt
ion
s;
to
m
a
ke
a
n
equ
i
valent
ci
rc
uit;
to
m
ake
a
m
at
he
m
at
ic
a
l
des
cri
ptio
n
of
the
AI
;
to
pe
rfor
m
an
syn
thesis
of
the
P
WM
al
gorithm
; t
o
create
a b
l
ock d
i
agr
am
o
f
a m
at
hem
atical
d
escripti
on a
nd
c
on
trol syst
em
;
to r
el
ease a sim
ulati
on
m
od
el
u
sin
g
th
e Ma
tl
ab
pro
gr
a
m
; t
o
m
ake r
e
search
and a
na
ly
sis of
e
nergy
char
act
e
risti
cs.
In
com
pili
ng
the
eq
uations
of
the
m
at
he
m
a
ti
cal
m
od
el
of
a
two
-
le
vel
A
I,
the
ge
ner
al
l
y
ac
-
cepted
assum
ption
s
a
bout
the
ideal
it
y
of
sem
ic
on
duct
or
s
witc
hes
are
us
ed
,
a
nd
the
tra
ns
it
ion
to
an
e
quivale
nt
ci
rcu
it
is
per
f
or
m
ed
[
22
-
25]
.
T
he
equ
i
valent
sche
m
e
of
a
two
-
l
evel
AI
is
show
n
in
Fi
gure
2.
I
n
Fig
ur
e
2
th
e
fo
ll
owin
g
nota
ti
on
s
are
ta
ke
n:
K
1
,
K
2
,
K
3
,
K
4
,
K
5
,
K
6
—
ideal
inv
erte
r
s
witc
hes;
U
dc
—
equ
i
va
-
le
nt
vo
lt
ag
e
so
urce;
S
1
,
S
2
,
S
3
,
S
4
,
S
5
,
S
6
—
switc
hing
f
un
ct
io
ns
of
th
e
keys;
U
A
,
U
B
,
U
C
—
ph
ase
vo
lt
ages;
U
AB
,
U
ВС
,
U
СА
—
li
nea
r vo
lt
age;
Z
—
e
qu
i
valent l
oad.
Figure
2
.
Eq
ui
valent circ
uit o
f
tw
o
-
le
vel au
t
onom
ou
s i
nv
e
r
te
r
The
m
at
he
m
at
i
cal
m
od
el
of
m
otor c
hokes
ca
n be
represe
nted
as
foll
ows
(1)
:
sC
iC
dr
dr
sC
sB
iB
dr
dr
sB
sA
iA
dr
dr
sA
U
U
L
R
dt
dU
U
U
L
R
dt
dU
U
U
L
R
dt
dU
(1)
wh
e
re R
dr
a
nd
L
dr
—
re
sist
an
ce an
d
in
duct
a
nce
of the
windin
g of t
he
c
ho
ke.
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.
9
, N
o.
4
,
A
ugust
2019
:
23
14
-
2320
2316
The p
hase
vo
lt
age at th
e
ou
t
put o
f
t
he
tw
o
-
le
vel AI is a
s fol
lows
(
2)
:
C
B
A
dc
iC
C
B
A
dc
iB
C
B
A
dc
i
А
S
S
S
U
U
S
S
S
U
U
S
S
S
U
U
3
2
3
1
3
1
3
1
3
2
3
1
3
1
3
1
3
2
(
2
)
wh
e
re
U
dc
-
volt
age
on
t
he
c
apacit
or
s
of
th
e
DC
li
nk
(in
put
volt
age
of
t
he
in
ver
te
r)
;
U
iA
,
U
iB
,
U
iC
-
outp
ut
ph
a
se
vo
lt
ages
(in
ver
te
r
outp
ut
v
oltage
).
The
e
quat
ions
for descri
bing
rack
s
of a
tw
o
-
le
vel AI are
as
fo
ll
ows
(
3)
:
1
,
0
е
с
л
и
,
0
0
,
1
е
с
л
и
,
1
1
,
0
е
с
л
и
,
0
0
,
1
е
с
л
и
,
1
1
,
0
е
с
л
и
,
0
0
,
1
е
с
л
и
,
1
6
5
6
5
4
3
4
3
2
1
2
1
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
С
С
В
В
А
А
(
3
)
wh
e
re
S
A
, S
B
, S
C
—
the
m
odulati
on
f
un
ct
io
ns
of the
A
I
ra
cks.
The
r
ule
of
c
ontr
ol
of
t
he
sta
tus
of
rac
ks
of
transisto
rs
AI
(
the
r
ule
of
f
orm
at
ion
of
t
he
c
omm
uta
ti
on
functi
on)
is
as
fo
ll
ows
(
4)
:
(
4
)
The
sim
ulati
on
m
od
el
of
tw
o
-
le
vel
AI,
w
hic
h
create
d
in
M
at
la
b
on
the
ba
sis
of
(1)
-
(
4)
,
i
s
pr
e
sente
d
in
Fig
ur
e
3.
T
he
tw
o
-
le
vel
a
utono
m
ou
s
in
ver
te
r
m
od
el
with
the
abili
ty
to
researc
h
the
influ
e
nce
of
th
e
fo
ll
owin
g
fact
or
s
,
su
c
h
as
t
he
fr
e
qu
e
ncy
an
d
f
or
m
of
a
no
n
-
e
xistent
sig
na
l,
var
i
ou
s
al
gorithm
s
and
a
na
ly
sis
of
the ch
a
racteri
st
ic
s o
f
the i
nver
te
r
inclu
des: t
he
P
W
M
, th
e
in
ver
te
r
and t
he c
hokes
.
Figur
e
3
.
Ef
fec
ts of sel
ect
ing
diff
e
re
nt sw
it
c
hing
unde
r dyn
a
m
ic
co
nd
it
io
n
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
An
alysis a
nd i
mp
r
ove
me
nt o
f
the eff
ic
ie
ncy
of freq
ue
ncy c
on
ve
r
te
rs…
(
B
ogdan V
as
il
ev
)
2317
3.
RESU
LT
S
A
ND AN
ALYSIS
Thr
ee
ty
pes
of
sign
al
s
ca
n
be
us
e
d
to
c
o
ntro
l
tw
o
-
le
vel
AI
:
tria
ngular
as
show
n
i
n
F
igure
4
(a),
sawto
oth
with
fron
t
e
dge
as
s
how
n
in
Fig
ure
4
(
b),
sa
wtooth
with
a
fall
ing
e
dge
as
s
how
n
in
Fig
ur
e
4
(c
)
.
In
Fig
ur
e
5
shows
wa
ve
form
os
ci
ll
ogram
s
of
t
he
ou
t
pu
t
volt
age
of
a
n
a
ut
onom
ou
s
in
ve
rter
a
nd
m
oto
r
chokes
at
a f
re
quen
cy
of the ca
rr
ie
r
si
gn
al
of
3000
H
z.
Figure
4
.
Ef
fec
ts of sel
ect
ing
diff
e
re
nt
switc
hing
unde
r
dynam
ic
co
ndit
ion
Figure
5
.
Ef
fec
ts of sel
ect
ing
dif
fe
re
nt sw
it
c
hing
unde
r dynam
ic
co
nd
it
io
n
In the st
ud
y
of
the contr
ol alg
or
it
hm
s o
f
the i
nv
e
rter c
onside
r
the
im
pact o
f:
-
car
rier
wa
vefor
m
o
n t
he
c
ha
racteri
sti
cs of t
he AI;
-
f
re
qu
e
ncy car
rier
si
gn
al
on t
he
c
har
act
e
risti
cs of the
AI;
-
c
hokes o
n
the
h
a
rm
on
ic
co
m
pone
nts
of
t
he vo
lt
age
AI.
In
t
he
sim
ulatio
n
m
od
el
ing
,
the
os
ci
ll
ogram
s
of
the
volt
ag
e
at
the
ou
t
pu
t
of
the
a
uton
om
ou
s
inv
e
rter
an
d
m
oto
r
ch
ok
es
a
re
bu
il
t, a
nd th
ei
r
sp
ect
ral co
m
po
sit
ion
is al
so
i
nv
est
igate
d.
3.1.
In
fluence
of the sh
ap
e
of the c
arrier
si
gnal o
n
th
e c
h
ara
c
teris
tics
of the
freque
nc
y
c
onverter
In
Fi
gure
6
s
hows
t
he
sp
ect
r
al
com
po
sit
ion
of
the
outp
ut
vo
lt
age
at
d
iff
eren
t
wa
ve
for
m
s
:
tria
ng
ular
as
sh
ow
n
in
Fi
gure
6
(a),
saw
too
th
with
a
fa
ll
ing
ed
ge
as
s
how
n
in
Fig
ure
6
(
b)
a
nd
sa
wtooth
with
a
le
adin
g
edg
e
as s
how
n i
n
Fig
ure
6
(c
)
.
Stu
dies
wer
e c
onduct
ed
at
a f
reque
ncy of
3000 H
z
.
Figure
6
.
The
inf
l
uen
ce
of th
e
for
m
o
f
t
he
ca
rr
ie
r
sign
al
on the
harm
on
ic
com
po
sit
ion o
f
the
outp
ut
vo
lt
age
AI
Figure
7
.
The
e
ff
ect
of the ca
r
rier
fr
e
qu
e
ncy
on the
har
m
on
ic
c
ompo
sit
io
n of t
he ou
t
pu
t
volt
age
AI
On
the
basis
of
the
resu
lt
s,
we
co
nclu
de
t
hat
the
s
pectral
c
om
po
sit
ion
of
t
he
fron
t
c
oi
ncides
wit
h
t
he
sp
ect
ral
com
posit
ion
of
the
re
ar
fro
nt.
W
it
h
a
sawto
oth
f
or
m
,
the
den
sit
y
of
the sp
ect
ral com
po
sit
ion
is hig
he
r
than wit
h
a
tria
ngular
one.
3.2.
The e
ff
ec
t of
th
e
ca
rri
e
r freq
uenc
y o
n t
he
ch
ar
act
e
ri
stics of
th
e c
onverter
f
req
uency
Since
in
the
fi
rst
par
t
of
the
stud
y
it
was
f
ound
that
the
best
har
m
on
ic
com
po
sit
ion
of
the
outp
ut
vo
lt
age
A
I
is
pro
vid
e
d
with
a
tria
ngular
for
m
of
the
ca
rr
ie
r
sig
nal,
the
e
f
fect
of
t
he
f
re
quency
of
t
he
c
arr
ie
r
sign
al
will
be
co
ns
ide
re
d
only
with
this
f
or
m
.
In
Fi
gur
e
7
sho
ws
t
he
sp
ect
ral
com
po
sit
io
n
of
the
outp
ut
vo
lt
age
w
it
h
a
tria
ngular si
gn
al
at differe
nt freq
ue
ncies.
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.
9
, N
o.
4
,
A
ugust
2019
:
23
14
-
2320
2318
Ba
sed
on
the
r
esults
obta
ined
,
it
can
be
co
nc
lud
e
d
that
the
best
re
gu
la
ti
on
is
pr
ovid
ed
at
a
fr
e
qu
e
ncy
of
9
K
Hz.
P
ulse
pac
kets
a
re
f
or
m
ed
at
a
ca
r
rier
si
gn
al
fr
e
quency
a
nd,
wit
h
inc
reasi
ng
f
r
equ
e
ncy,
are
s
hifted
to the hig
h
-
f
re
qu
e
ncy
reg
i
on.
3.3.
Ef
fect o
f c
ho
kes
on
th
e
ha
rm
on
ic
c
om
po
ne
nt
s
of
th
e
volt
ag
e
In
Fi
gure
8
shows
os
ci
ll
ogra
m
s
of
volt
age
at
the
ou
t
pu
t
of
m
oto
r
ch
ok
es
at
diff
ere
nt
f
r
equ
e
ncies
of
the
carrier
si
gnal
.
I
n
Fig
ur
e
9
t
he
de
pe
nd
e
nce
of
the
no
nl
inear
disto
rtio
n
coe
ff
ic
ie
nt
(
THD)
on
the
r
at
io
of
inducta
nce
to r
esi
sta
nce of
c
hoke
s
Figure
8
.
V
oltage at t
he
out
put of ch
okes
depend
i
ng on t
he
diff
e
re
nt freq
ue
ncy of t
he
ca
r
rier si
gn
al
Fi
gure
9
.
The
dep
e
ndence
of
the no
nlinear
distor
ti
on c
oe
ffi
ci
ent (
TH
D
)
on the
r
at
io
of
inducta
nce
to r
esi
sta
nce of
c
hoke
s
Ba
sed
on
the
resu
lt
s,
it
ca
n
be
c
on
cl
ud
e
d
that
the
best
r
egu
la
ti
on
is
prov
i
ded
at
a
frequ
e
ncy
of
9
KH
z
.
As
the
fr
e
quency
of
the
car
rier
si
gnal
inc
reases,
the
num
ber
of
har
m
on
ic
c
om
po
nen
ts
rem
ai
ns
the
sam
e, o
nly t
heir
am
plit
ud
e d
e
creases.
Power
qu
al
it
y
analy
sis
is
pr
e
sented
i
n
T
abl
es
1
–
4
(
tria
ng
ular
car
rier
(T)
;
sawtoo
t
h
wit
h
f
ront
ed
ge
(F
RE)
;
sawt
oo
t
h wit
h
a
fall
ing ed
ge
(FAE)
).
Table
1.
T
he
va
lue of t
he vo
lt
age
distor
ti
on
coeffic
ie
nt at t
he ou
t
pu
t
of th
e auton
om
ou
s i
nv
e
rter
R
dr
/L
dr
8000
9000
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
3
0
0
0
1
4
0
0
0
1
5
0
0
0
THDi
6
8
,9
6
8
,9
6
8
,9
6
8
,9
6
8
,9
6
8
,9
6
8
,9
6
8
,9
THDdr
(90
0
0
Hz)
6
,1
6
,8
7
,6
8
,3
9
9
,8
1
0
,5
1
1
,2
THDdr
(6
0
0
0
Hz
)
1
1
,9
1
3
,4
1
4
,7
16
17
1
8
,6
1
9
,8
21
Table
2
.
T
he
a
m
pl
it
ud
e of t
he
h
a
rm
on
ic
co
m
pone
nts
of
the
aut
onom
ous outp
ut
vo
lt
ag
e t
he
in
ve
rter a
t a carrie
r
si
gnal
f
re
qu
e
ncy
of 3000
Hz
f
f
1
= 30
0
0
Hz
f
3
= 60
0
0
Hz
f
3
= 90
0
0
Hz
n
T
FRE
FAE
n
T
FRE
FAE
n
T
FRE
FAE
0
60
–
–
–
120
–
–
–
180
–
–
–
± 50
5
9
/6
1
–
18
18
1
1
9
/1
2
1
18
7
7
1
7
9
/1
8
1
–
4
4
± 10
0
5
8
/6
2
32
31
31
1
1
8
/1
2
2
–
10
10
1
7
8
/1
8
2
6
5
5
± 15
0
5
7
/6
3
–
–
–
1
1
7
/1
2
3
–
–
–
1
7
7
/1
8
3
–
–
–
± 20
0
5
6
/6
4
2
10
10
1
1
6
/1
2
4
–
10
10
1
7
6
/1
8
4
15
6
6
± 25
0
5
5
/6
5
–
3
3
1
1
5
/1
2
5
3
12
12
1
7
5
/1
8
5
–
3
3
± 30
0
5
4
/6
6
–
–
–
1
1
4
/1
2
6
–
–
–
1
7
4
/1
8
6
–
–
–
Table
3
.
T
he
a
m
pl
it
ud
e of t
he
h
a
rm
on
ic
co
m
pone
nts
of
the au
t
onom
ous outp
ut
vo
lt
ag
e inv
e
rter
with
a carr
ie
r
sig
nal
f
re
quency
of
6000
Hz
f
f
1
= 30
0
0
Hz
f
3
= 60
0
0
Hz
f
3
= 90
0
0
Hz
n
T
FRE
FAE
n
T
FRE
FAE
n
T
FRE
FAE
0
60
–
–
–
120
–
–
–
180
–
–
–
± 50
5
9
/6
1
–
–
–
1
1
9
/1
2
1
–
18
18
1
7
9
/1
8
1
–
–
–
± 10
0
5
8
/6
2
–
–
–
1
1
8
/1
2
2
32
31
31
1
7
8
/1
8
2
–
–
–
± 15
0
5
7
/6
3
–
–
–
1
1
7
/1
2
3
–
–
–
1
7
7
/1
8
3
–
–
–
± 20
0
5
6
/6
4
–
–
–
1
1
6
/1
2
4
2
10
10
1
7
6
/1
8
4
–
–
–
± 25
0
5
5
/6
5
–
–
–
1
1
5
/1
2
5
–
3
3
1
7
5
/1
8
5
–
–
–
± 30
0
5
4
/6
6
–
–
–
1
1
4
/1
2
6
–
–
–
1
7
4
/1
8
6
–
–
–
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
An
alysis a
nd i
mp
r
ove
me
nt o
f
the eff
ic
ie
ncy
of freq
ue
ncy c
on
ve
r
te
rs…
(
B
ogdan V
as
il
ev
)
2319
Table
4
.
T
he
a
m
pl
it
ud
e of t
he
h
a
rm
on
ic
co
m
pone
nts
of
t
he
aut
onom
ous outp
ut
vo
lt
ag
e inv
e
rter
with
a carr
ie
r
f
re
qu
e
ncy
of
9000
H
z
f
f
1
= 30
0
0
Hz
f
3
= 60
0
0
Hz
f
3
= 90
0
0
Hz
n
T
FRE
FAE
n
T
FRE
FAE
n
T
FRE
FAE
0
60
–
–
–
120
–
–
–
180
–
–
–
± 50
5
9
/6
1
–
–
–
1
1
9
/1
2
1
–
–
–
1
7
9
/1
8
1
–
18
18
± 10
0
5
8
/6
2
–
–
–
1
1
8
/1
2
2
–
–
–
1
7
8
/1
8
2
32
31
31
± 15
0
5
7
/6
3
–
–
–
1
1
7
/1
2
3
–
–
–
1
7
7
/1
8
3
–
–
–
± 20
0
5
6
/6
4
–
–
–
1
1
6
/1
2
4
–
–
–
1
7
6
/1
8
4
2
10
10
± 25
0
5
5
/6
5
–
–
–
1
1
5
/1
2
5
–
–
–
1
7
5
/1
8
5
–
3
3
± 30
0
5
4
/6
6
–
–
–
1
1
4
/1
2
6
–
–
–
1
7
4
/1
8
6
–
–
–
4.
CONCL
US
I
O
N
The
aut
onom
ou
s
fr
e
quen
cy
conve
rter
can
draw
the
f
ollo
w
ing
co
nclu
sio
ns:
(
1
)
De
pe
nd
i
ng
on
the
m
od
ific
at
ion
of
the
al
gorith
m
of
pu
lse
-
wi
dth
co
ntr
ol
of
the
ou
tp
ut
vo
lt
age
in
accor
dan
ce
with
th
e
ta
sk
;
(
2
)
The
s
hap
e
of
the
car
rier
si
gn
al
af
fects
the
har
m
on
ic
sta
te
of
the
outp
ut
vo
lt
age
of
a
n
auto
no
m
ou
s
in
ve
rter;
(
3
)
Ca
r
ryi
ng
a
sawto
ot
h
sig
na
l,
re
gardless
of
t
he
fron
t
i
n
the
eq
ually
ha
r
m
on
iou
s
c
o
m
po
sit
ion
of
the
ou
t
pu
t
vo
lt
age;
(
4)
B
y
us
ing
the
pul
se
-
wi
dth
m
od
ul
at
ion
of
a
tria
ngular
car
rier
sign
al
,
the
harm
on
ic
co
m
po
s
it
ion
of
the
ou
t
pu
t
volt
age
is
m
or
e
fa
vora
ble
than
wh
e
n
us
i
ng
a
sawto
o
th
sig
na
l
;
(
5
)
The
f
re
quency
of
the
c
arr
ie
r
sign
al
determ
i
nes
the
s
witc
hi
ng
fr
e
quency
of
an
a
uton
om
ou
s
in
ver
te
r,
whic
h
in
tu
rn
det
erm
ines
the
posit
ion
of
the
sta
ti
ona
ry
pu
lse
packet
s;
(
6
)
T
he
pa
ckag
e
s
of
vo
lt
age
pu
lse
s
a
r
e
form
ed
at
a
fr
e
qu
e
ncy
tha
t
is
a
m
ul
ti
ple
of
the
fr
eq
ue
ncy
of
the
carrier
sign
al
;
(
7
)
By
i
ncr
easi
ng
the
fr
eq
ue
ncy
of
the
pu
lse
pac
ke
ts
are
sh
ifte
d
to
high
fr
e
qu
e
ncies;
(
8
)
To
ha
rm
on
iz
e
the
sh
ape
of
the
ou
t
pu
t
volt
age
of
the
auto
no
m
ou
s
in
ver
t
er
a
nd
load,
it
is
ad
visable
an
d
ef
fici
ent
to
us
e
m
oto
r
ch
okes
;
(
9
)
Using
the
c
hoke
s
it
le
ads
to
a
dec
rease
i
n
the
a
m
plit
ud
e
of
the
har
m
on
ic
c
om
po
ne
nts
of
the
ou
t
pu
t
volt
age
wh
il
e
m
ai
ntaining
the
num
ber
of
ha
r
m
on
ic
com
po
ne
nts in
the s
pectru
m
.
Th
us
,
the
ch
oi
ce
of
m
e
tho
ds
for
m
od
ify
ing
the
pu
lse
-
wi
dth
co
ntro
l
al
gor
it
h
m
s
sh
ou
l
d
be
carried
out
com
pr
ehe
ns
ive
ly
.
W
he
n
c
hoosi
ng
m
et
hods
i
t
is
necessa
ry
to
ta
ke
into
acc
ount:
car
rier
w
aveform
;
fr
eq
ue
ncy
of
t
he
car
rier
sign
al
;
ch
oke
par
am
et
ers.
All
these
pa
ra
m
et
ers
hav
e
a
sign
ific
a
nt
im
pact
on
the
energy
char
act
e
risti
cs o
f
freq
ue
ncy c
onve
rters a
nd t
heir
c
om
patibilit
y wit
h
the l
oa
d.
In
the
pr
act
ic
al
i
m
ple
m
entation
of
the
co
ntr
ol
syst
e
m
,
the
weigh
t
an
d
dim
e
ns
io
ns
of
ch
ok
es
and
th
e
el
ect
ric
dr
ive
as
a
w
ho
le
,
th
e
eff
ic
ie
ncy
of
an
a
uton
omou
s
in
ver
te
r
m
oto
r
and
t
he
inv
e
rter
as
a
whole
,
insu
la
ti
on
re
quirem
ents
for
the
dri
ve
m
oto
r
windin
gs,
their
a
ging
s
pe
ed
a
nd
ser
vice
li
fe
de
-
pe
nd
on
t
he
correct
ness
of t
he
c
ho
ic
e.
REFERE
NCE
S
[1]
X.
Xu,
L.
Fang,
X.
Xu
and
X.
Lu,
"Control
str
at
eg
y
of
photov
olt
aic
gene
r
ation
inve
rte
r
gri
d
-
co
nnec
t
ed
oper
a
ti
n
g
and
har
m
onic
e
l
iminat
ion
h
y
brid
s
y
stem,"
2017
2nd
Inte
rnation
al
Confe
renc
e
o
n
Powe
r
and
Renewable
En
ergy
(
ICPR
E)
,
Cheng
du,
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,
2017
.
[2]
W
.
Guo,
T
.
Mi
ngxing
and
R.
Ene
n,
"S
truc
tur
e
design
and
i
ts
par
amete
r
opt
imization
of
outpu
t
filter
in
cur
ren
t
bal
an
ce
compen
sati
on
inv
erter
f
or
elec
tr
ifi
ed
ra
ilw
a
y
,
"
The
2nd
I
nte
rnational
Sy
mpos
ium
on
Powe
r
El
e
ct
roni
cs
for
Distribute
d
Gen
erati
on
S
yste
ms
,
Hefe
i, pp. 791
-
7
95
,
2010
.
[3]
H.
M.
Ahn,
W
.
Sung,
M.
Kim
,
B.
K.
Lee,
S.
R
yu
and
C.
Li
m
,
"Control
m
et
hod
of
input
-
par
a
llel
and
output
-
seri
e
s
conne
c
te
d
inve
r
te
rs
for
p
la
sm
a
gene
r
at
or
,
"
20
18
IEEE
App
lie
d
Powe
r
El
e
ct
r
onic
s
Conf
ere
nc
e
and
Ex
posit
io
n
(
AP
EC)
,
San
Antonio, T
X,
pp.
3
563
-
3568
,
2018
.
[4]
M.
Song,
C.
Ga
o,
J.
Yang
and
H.
Yan,
"Ene
rg
y
storage
m
odel
ing
of
inve
rte
r
ai
r
condi
ti
on
ing
for
output
opti
m
iz
in
g
of
wind
gen
erat
ion
in
the
e
le
c
t
ric
ity
m
ark
et,"
i
n
CSEE
Journa
l
of
Powe
r
and
Ene
rgy
Syst
ems
,
vol.
4,
no.
3,
pp.
305
-
315,
Se
pte
m
ber
2018
.
[5]
Xin
Li
and
S.
S.
W
il
li
ams
on,
"Effi
cienc
y
anal
y
s
is
of
hy
br
id
el
e
ct
r
i
c
vehi
c
le
(HEV)
tra
ction
m
otor
-
inve
rte
r
driv
e
fo
r
var
ie
d
driv
ing
l
oad
demands,"
2008
Tw
ent
y
-
Thir
d
Annual
IEEE
Appl
i
ed
Pow
er
El
ectronics
Confe
renc
e
and
Ex
positi
on
,
Aus
t
in,
TX,
pp
.
280
-
285
,
2008
.
[6]
V
.
V.
Alekse
ev,
V.
I. Vershinin
a
nd
B.
Yu.
Vasil
'
e
v,
"D
efi
n
it
ion
of
par
amet
ers
of
v
ec
tors
of
m
agne
t
ic
f
lux
in
e
lectr
i
c
drive
s with
th
e
v
ec
tor
control
,
"
Zapis
ki
Gor
nogo
Instit
uta/Journal
of
M
ini
ng
Institute
,
196,
pp.
222
-
225
,
2012
.
[7]
A.
Anuchin,
D.
Shpak,
A.
Zha
rkov,
V.
Os
tri
rov
and
Y.
Vaga
pov,
"A
m
et
hod
of
det
erminin
g
the
m
axi
m
um
per
form
anc
e
tor
que
-
spee
d
cha
ra
ct
er
isti
c
f
or
an
i
nduct
ion
m
otor
drive
over
it
s
en
ti
re
spe
ed
ran
g
e,"
2017
IEE
E
58t
h
Inte
rnational
S
cienti
f
ic
Conf
ere
n
ce
on
Powe
r
and
El
ectric
al
Enginee
ring
of
Riga
Techni
ca
l
Univer
sity
(
RTUC
ON
)
,
Riga
,
pp.
1
-
5
,
20
17
.
[8]
G.
Yang,
M.
Li
n
,
G.
Ta
n
and
H.
Li
,
"D
irect
Input
Pow
er
Control
f
or
Drive
Sy
st
em
of
Single
-
Phase
to
Thre
e
-
Phas
e
Pow
er
Convert
e
r
W
it
hout
El
e
ct
r
ol
y
ti
c
C
apaci
tor
,
"
2018
21st
Inte
rnational
Confe
r
enc
e
on
E
lectrical
Mac
hine
s
and
Syste
ms
(
ICEMS)
,
Jeju,
pp
.
1503
-
1507
,
2018
.
[9]
Zhong
y
u
an
Zh
a
o,
Zhe
ng
y
u
Lu,
Gaoxia
n
Jin,
W
a
nm
en
Fei
and
Linghui
Xia,
"D
ev
el
opm
ent
of
ga
t
e
-
drivi
ng
s
y
s
te
m
of
th
y
ristor
v
al
v
e
with
m
ultipl
e
isola
te
d
output
s
used
in
n
ew
-
t
y
p
e
solid
-
sta
te
s
hort
-
ci
r
cui
t
fau
l
t
c
urre
nt
li
m
it
er
in
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.
9
, N
o.
4
,
A
ugust
2019
:
23
14
-
2320
2320
el
e
ct
ri
c
power
sy
st
em,"
2004
IEE
E
35th
Annual
Powe
r
El
e
ct
ronics
Spec
iali
sts
Confe
renc
e
(
IEE
E
Cat
.
No.
0
4CH37551)
,
Aac
hen, Ge
rm
an
y
,
pp.
3233
-
3236
,
2004
.
[10]
B.
Yu.Vasil'ev,
V.
A.
Shpenst,
O.
V.
Kal
ashnik
ov,
and
G
.
N.
U
l'y
a
n
ov,
"P
rovid
ing
ene
rg
y
de
co
upli
ng
of
el
e
ct
ri
c
drive
and
e
lectr
i
c
grids
for
indus
tri
al
e
le
c
trica
l
in
stal
lations,
"
Zapi
ski
Gor
nogo
Instit
uta/Journal
of
Mini
ng
Insti
tute
,
229,
рр
.
41
-
49
,
2018
.
[11]
V.
Ans
al
,
P.
Pa
rthi
ban
and
K
.
Ravi
kum
ar,
"
Per
form
anc
e
stud
y
of
high
fr
eque
n
c
y
li
nk
AC
-
AC
conve
rt
er,
"
201
4
Inte
rnational
Confe
renc
e
on
Adv
anc
es
i
n
Ene
rgy
Co
nve
rs
ion
Tech
nologi
es
(
ICAE
CT
)
,
Manipal,
pp.
164
-
168
,
20
14
.
[12]
P.
Szcz
esnia
k
,
"Basic
Properties
Com
par
at
ive
Stud
y
of
Matri
x
-
Rea
c
ta
nc
e
Freq
uency
Conv
erter
Based
on
Buck
-
Bo
ost
Topol
og
y
wi
th
Ventu
ri
ni
Control
Str
at
eg
ie
s,"
2007
Compatibi
l
it
y
in
Pow
er
E
l
ec
troni
cs
,
Gdan
sk,
pp.
1
-
7
,
2007
.
[13]
T.
Shim
iz
u,
K.
Kunom
ura
,
M.
Kai,
H.
Mi
y
ajim
a
and
T.
Matsui
,
"S
tudy
for
fur
t
her
int
roduc
ti
on
of
the
El
e
ct
roni
c
Freque
nc
y
con
ver
te
rs
to
the
Toka
ido
Shi
nkanse
n,
"
2018
Inte
rnational
Powe
r
El
ectronics
Confe
ren
ce
(
IPE
C
-
Nii
gata
2
018
-
ECCE A
sia
)
,
Niiga
t
a, pp. 18
03
-
1809
,
2018
.
[14]
Toni
,
F.
D.
W
i
jay
a
a
nd
E.
Fir
m
ansy
ah,
"F
ull
-
bridge
inverter
phase
-
shifte
d
P
W
M
(FB
PS
-
PWM)
ze
ro
volt
ag
e
sw
it
chi
ng
(ZVS)
and
high
fre
qu
e
nc
y
tra
nsform
er
as
par
t
of
DC
-
DC
conve
rt
er
311/
100V
300W
,
"
2
014
Inte
rnationa
l
Confe
renc
e
on
E
le
c
tric
al
Engi
n
e
ering
and
Comp
ute
r Sc
ie
nc
e
(
ICEE
CS)
,
Kuta
,
pp
.
298
-
301
,
2014
.
[15]
H.
Zuo,
J.
W
an
g,
J.
Zh
ao
and
L.
Zhou
,
"S
imulat
ion
Stud
y
on
Com
m
uta
ti
on
Le
ad
ing
Angle
Control
of
Sta
tic
Freque
nc
y
Conv
ert
er
for
th
e
Sta
rtup
of
La
rge
-
sc
al
e
S
y
n
chr
onous
Condenser
,
"
2018
IEE
E
Stude
n
t
Confe
renc
e
on
El
e
ct
ric
Mac
h
in
es
and
Syst
ems
,
HuZhou,
Chin
a,
pp.
1
-
4
,
2018
.
[16]
Jin
-
H
y
ung
Yoo,
June
-
W
oo
Jo
an
d
Ta
e
-
Uk
Jung,
"A
study
on
desi
gn
a
nd
opti
m
iz
ation
proc
edur
e
of
high
fre
qu
e
n
c
y
tra
nsform
er
for
m
odule
-
integra
te
d
conve
rt
er,
"
2014
16th
Eu
ropean
Confe
re
nce
on
Powe
r
Elec
troni
cs
an
d
Appl
ic
a
ti
ons
,
L
a
ppee
nra
n
ta,
pp
.
1
-
8
,
2014
.
[17]
A.
L.
A.
da
Fons
ec
a
,
J.
A.
La
m
be
rt,
R.
V.
A.
Montei
ro
,
A.
B.
de
Vasc
oncellos
and
B.
C.
Carvalho,
"Beha
vioral
and
stat
isti
ca
l
ana
l
y
s
is
of
tot
al
har
m
onic
distort
ion
i
nput
fre
quency
conve
rt
er
of
a
tr
igge
ring
an
indu
stria
l
fan
:
A
ca
se
stud
y
,
"
2014
16t
h
Inte
rnational
Confe
renc
e
on
Har
monics
and
Qualit
y
of
Power
(
ICHQ
P
)
,
Bucha
rest,
pp
.
152
-
156
,
2014
.
[18]
G.
Gök,
I.
Alişar
and
D.
Gökce
n,
"S
tructura
l
Com
par
ison
of
W
ide
Band
-
Gap
Sem
ic
onduct
o
rs
with
Sili
con
Sem
ic
onduct
ors
and
Perform
anc
e
Orien
te
d
Com
par
ison
for
a
High
Sw
it
chi
ng
Freque
nc
y
Fl
y
ba
c
k
Convert
er,
"
20
18
2nd
Inte
rnation
al
Symposium
on
Mult
idi
sc
ipl
i
nary
Studi
es
a
nd
Innov
ati
v
e
Technol
ogi
es
(
I
SMSIT)
,
Ankar
a,
pp.
1
-
5
,
2018
.
[19]
G.
R.
Kam
at
h
,
"S
imulat
ion
stu
d
y
of
a
sim
ple
f
lux
saturation
c
ontrol
ler
for
hig
h
-
fre
quency
tra
n
sform
er
li
nk
full
-
bridge
DC
-
DC converte
rs,"
2012
IEE
E Inte
rnat
io
nal
Confe
ren
ce
on
Powe
r E
l
ectronics,
Dr
ives and
Ene
rgy
S
yste
m
s
(
PE
DES)
,
Bengaluru,
pp
.
1
-
5
,
20
12
.
[20]
Chen
y
ou
L
i,
Gu
ang
Zh
ang
and
Z.
Yan
,
"S
tud
y
on
four
PW
M
m
odula
ti
on
str
ategie
s
of
th
e
hig
h
fre
quen
c
y
li
n
k
m
at
rix
conve
rt
e
r
with
BLDCM
loa
d,
"
2016
IEE
E
8th
Inte
rn
ati
onal
Powe
r
El
e
ct
ronics
and
Moti
on
Control
Confe
renc
e
(
IPEMC
-
ECCE
Asia)
,
Hef
ei
,
pp.
1854
-
1857
,
2016
.
[21]
Atsus
hi
Hirota
,
Satoshi
Naga
i,
B
ishwaji
t
Saha
an
d
Mutsuo
Naka
o
ka,
"F
undament
al
stud
y
of
a
sim
ple
cont
rol
a
c
-
ac
conve
rt
er
int
rod
uci
ng
de
lt
a
-
sig
m
a
m
o
dula
ti
on
appr
oac
h
,
"
20
08
IEE
E
In
te
rn
ati
onal
Conf
ere
nce
on
Industri
al
Technol
ogy
,
Ch
e
ngdu,
pp
.
1
-
5
,
2
008
.
.
[22]
T.
Shim
ada
and
K.
Ta
nigu
chi
,
"I
GBT/MOS
FET
h
y
brid
br
idge
wi
th
phase
shift
an
d
fre
quency
m
o
dula
ti
on
cont
ro
l
for
a
bi
-
dir
ecti
onal
seri
es
resona
nt
conv
ert
er
,
"
2017
19th
Eu
ropean
Confe
re
nce
on
Pow
er
El
e
ct
ronics
and
Appl
ic
a
ti
ons (
E
PE
'17
ECCE
Eu
rope)
,
W
arsa
w, pp.
P.1
-
P.7
,
201
7
.
[23]
R.
Barr
era
-
C
ard
ena
s
and
M.
Mol
ina
s,
"Com
par
a
tive
stud
y
of
the
c
onver
te
r
eff
i
cien
c
y
and
power
de
nsit
y
in
offshore
wind
ene
rg
y
co
nver
sion
s
y
stem
with
single
-
ph
a
se
tra
nsform
er,
"
Inte
rnational
S
ymposium
on
Powe
r
El
e
ct
ronic
s
Powe
r E
le
c
troni
cs,
E
lectric
a
l
Dr
iv
es,
Au
tomati
on
and
Mot
ion
,
Sorrento, 2012, pp.
1085
-
1090.
[24]
T.
Ibu
chi
and
T.
Funaki,
"A
stud
y
on
par
asitic
in
duct
an
ce
red
uc
tion
d
esign
in
Ga
N
-
base
d
power
c
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BIOGR
AP
H
Y
O
F
AU
TH
OR
Gr
adu
ate
d
from
Uchti
ncski
y
t
ec
hni
ca
l
univ
ersity
in
2010.
Re
ce
iv
ed
P.H.D.
d
egr
ee
in
N
at
ion
al
Minera
l
R
esourc
es
Univer
sit
y
in
2013.
H
e
is
assistant
p
rofe
ss
or
in
ele
ct
ri
ca
l
ene
rg
y
and
el
e
ct
rom
ec
h
ani
c
s
depa
rtment
since
2013.
His
rese
arc
h
int
er
est
include
s
el
ectrom
agnetic
compati
bilit
y
pr
ovidi
ng,
elec
trotec
hni
ca
l
s
y
st
ems
for ener
g
y
industr
y
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