In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
Vol.
11, No.
1, Mar
ch 2020,
pp.
1
~9
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
5
9
1
/ij
ped
s
.
v11
.
i
1.pp
1-9
1
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Three phase PUC5 inverter fed i
nducti
on m
ot
or for renew
able
energy applic
ations
G
.
V
. V
.
N
a
garaju
1
,
G
.
S
amb
a
s
i
v
a
R
ao
2
1
Dep
artm
en
t
o
f
Elect
rical
and
El
e
c
t
ro
nic
s
E
ng
in
e
e
ring
, Ac
h
a
r
ya
Nag
a
rju
n
a U
n
iversi
ty, India
2
Dep
a
rtm
e
nt of Elect
rical
and
Elect
ro
nic
s
E
ng
in
e
e
ring
,
R
V
R &
JC
Co
lle
ge
o
f
En
gine
e
r
in
g, Ind
ia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Ju
l
1
7,
201
9
Re
vise
d S
e
pt 9
,
2019
Ac
ce
p
t
ed
Oc
t
2
5
,
2
019
Th
is
p
aper
g
ives
t
h
e
o
verv
iew
t
h
ree
ph
ase
5
l
e
vel
p
acked
U
cel
l
(
P
U
C
5
)
in
vert
er
f
ed
I
nd
ucti
on
M
o
t
or
f
eed
f
ro
m
ren
e
wabl
e
en
ergy
s
o
u
rces
f
or
e
lectri
c
veh
i
cl
es
a
nd
w
ater
p
um
p
s
e
t
i
n
a
g
r
i
c
ul
tu
re
a
p
p
l
i
cation
s
.
PUC5
i
nv
e
r
t
e
r
requ
ires
a
m
in
im
um
num
ber
of
s
em
i
c
on
duct
o
r
dev
i
ces
,
o
n
e
P
V
p
a
n
e
l
and
on
ly
o
n
e
cap
acito
r
i
n
each
p
h
a
se.
M
a
xi
mum
a
l
l
pos
si
b
l
e
sw
it
chin
g
seq
u
ences
are
an
aly
zed
a
n
d
sens
or
l
ess
vol
tag
e
b
alan
cin
g
t
ech
niq
u
e
d
e
p
e
nd
in
g
on
sim
p
l
e
s
w
i
tching
m
o
des
w
a
s
i
n
tegrated
a
s
l
e
vel
shifted
PWM
co
nt
rol
l
e
r
f
or
con
t
ro
l
t
h
e
P
U
C
5
i
nvert
er
s
w
i
t
c
hes.
S
ens
o
r
l
e
ss
v
o
ltag
e
b
al
anci
ng
f
i
xes
th
e
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
(
V
c
)
a
t
h
a
l
f
o
f
t
h
e
P
V
s
o
u
r
c
e
(
V
d
c
)
m
a
g
n
i
t
u
d
e
i
n
e
ach
ph
ase,
w
hi
ch
r
e
s
ults
t
h
e
s
ymm
e
t
r
ic
f
i
v
e
l
e
vel
wave
i
n
phas
e
v
o
l
t
a
ge
o
utp
u
t
a
n
d
se
v
e
n
le
ve
l
wa
ve
form
i
n
lin
e
vo
lta
g
e
with
l
e
s
s
ha
rm
on
ic
s
.
T
his
to
po
log
y
m
i
nim
i
zes
t
he
c
om
plicatio
n
in
t
he
c
o
n
t
r
ol
s
yst
e
m
w
h
i
c
h
creat
es
the
PUC5
in
vert
er
m
o
s
t
s
u
i
t
able
f
or
i
n
d
u
s
t
r
ial
ap
p
l
icati
o
n
s
a
nd
m
ark
e
t
r
equ
i
rem
e
nt
s.
I
t
is
c
ompared
with
o
ther
p
opular
m
ul
tilevel
inver
t
ers
In
t
erms
o
f
c
o
m
pon
ent
cou
n
t
,
v
o
l
t
a
ge
r
ati
n
g
,
volt
a
ge
b
alanci
ng
a
nd
c
o
m
pl
ex
i
t
y
etc.
I
n
o
r
d
e
r
t
o
t
e
s
t
th
e
perf
o
r
m
a
n
ce
p
r
o
p
o
s
ed
P
UC
i
nv
erter
i
t
i
s
test
ed
w
it
h
rat
e
d
l
oad
wi
th
M
a
tl
ab
/Si
m
u
lin
k
.
T
he
r
e
s
ults
o
b
t
ai
ned
have
s
h
o
w
n
g
ood
d
y
n
a
m
i
c
perf
o
r
man
ce un
der d
i
ff
erent
con
d
i
t
i
o
n
s
.
K
eyw
ord
s
:
CH
B
NPC
Pow
e
r Q
u
alit
y
PUC5
S
e
nsor
l
ess
v
o
lta
ge
b
a
l
a
n
c
i
ng
Mu
lt
ieve
l
Inve
rte
r
Sin
g
le
D
C
So
urce
Th
is
is a
n
o
p
en acces
s a
r
ti
cle u
n
d
e
r t
h
e
CC
B
Y
-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
V V Nag
a
raj
u
G
o
r
i
p
arthi
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
a
n
d
El
ect
ro
ni
c
s
Eng
in
e
e
ring
,
A
c
ha
rya
N
a
ga
rjuna
U
ni
ver
s
i
t
y
,
G
unt
u
r
, Indi
a.
Em
ail:
nagar
a
j
u00
6@
gm
ai
l.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
The
w
o
rl
d
pow
er
d
em
and
i
n
t
h
e
e
ne
rg
y
m
a
r
k
et
l
ea
ds
t
o
re
des
i
g
n
o
f
pow
er
c
on
ver
t
e
r
s.
T
he
pow
e
r
con
v
er
sio
n
q
ua
lit
y
is broa
d
l
y
div
ide
d
in
t
o
tw
o
c
a
te
g
o
ries.
The
fir
s
t
c
o
n
v
er
te
rs
i
n
j
ec
t
po
l
l
u
t
i
o
n
i
n
to
t
he
s
ystem
in
t
e
r
m
of
p
owe
r
f
a
c
t
o
r
and
ha
rm
oni
c
s
,
re
sear
cher
s
are
tryi
n
g
t
o
e
nha
nce
the
p
o
w
e
r
qua
l
i
t
y
b
y
us
i
ng
fil
t
e
r
s.
G
e
ne
rall
y,
t
his
reduc
e
s
t
he
e
f
f
ic
ie
ncy
o
f
p
o
w
er
c
on
ver
s
io
n
a
n
d
i
n
c
r
ea
se
c
os
t
of
i
ns
ta
lla
t
i
o
n
s.
T
he
m
ai
n
aim of
the
sec
ond
o
n
e
is
t
o
de
li
ve
r
a
le
ss
c
ost,
h
igh
e
n
erg
y
e
ffic
ie
n
t
i
n
v
er
t
e
r
w
i
t
h
o
u
t
po
l
l
u
tio
n,
m
ul
tile
v
e
l
in
v
e
rters
bel
o
ng
s
t
o
t
hi
s
c
a
teg
o
ry
[
1]
.
The
mul
t
i
l
e
ve
l
in
ve
rters
role
h
as
b
ee
n
i
n
cre
a
si
n
g
i
n
m
e
d
i
um
a
nd
hi
g
h
pow
er
app
l
ica
t
i
o
ns
i
n
t
h
e
pow
e
r
m
arke
t
,
b
e
c
a
u
se
o
f
a
dva
n
t
ages,
l
i
ke
t
he
ir
c
apac
i
t
y
t
o
s
y
n
t
h
es
i
ze
a
w
a
ve
for
m
w
it
h
mor
e
numbe
r
of
l
eve
l
s,
b
e
t
t
e
r
vol
ta
ge
p
r
o
file
,
reduc
e
d
s
w
i
t
c
hin
g
stres
s
es,
m
i
nimize
d
o
u
t
p
ut
f
il
ter
size
.
Mu
lt
ile
ve
l
fo
u
n
d
the
so
l
u
tio
n
to
e
xte
n
d
the
inve
rter
o
p
e
ra
ting
v
o
lta
g
e
h
i
gher
t
h
an
t
he
v
olta
ge
l
im
i
t
o
f
sem
i
c
o
nd
uc
tor
de
v
i
ces
[
2].
N
P
C
to
po
log
y
w
a
s
first
pr
op
ose
d
b
y
N
abae
a
nd
Ta
ka
hash
i
i
n
1
981.
T
en
y
e
a
rs
l
a
t
e
r
fl
yi
ng
c
ap
ac
ito
r
c
o
n
v
e
r
t
e
r
to
po
l
ogy
w
a
s
i
n
t
ro
du
c
e
d
b
y
M
ey
nar
d
a
nd
F
och,
i
n
t
h
is
c
onve
rter
t
h
e
t
w
o
c
l
a
m
p
i
n
g
d
i
o
d
e
s
o
f
N
P
C
w
a
s
r
e
p
l
a
c
e
d
b
y
c
a
p
a
c
i
t
o
r
s
[
3
]
.
I
m
p
l
i
c
a
t
ed
c
el
l
mu
l
t
il
eve
l
t
opo
log
y
h
a
s
b
een
exp
l
a
i
ne
d
i
n
1
993
a
n
d
H
-
brid
ge
c
el
l
s
i
n
1
9
96.
W
h
i
ch
c
o
n
n
e
c
t
se
ve
ra
l
i
n
verter
s
i
n
c
asc
a
d
e
co
n
n
ec
t
i
o
n
w
i
t
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
1
–
9
2
separ
a
te
D
C
s
o
urce
s.
T
his
c
o
n
v
er
t
e
r
can
a
v
o
i
d
c
l
a
m
p
i
n
g
dio
de
s o
r
vo
l
t
a
g
e
b
al
an
ci
ng
cap
aci
t
o
rs.
Du
ri
ng
t
h
e
se
yea
r
s,
s
eve
r
al
o
p
tim
iza
t
i
o
ns
w
e
r
e
pr
opose
d
b
y
re
sear
cher
s
a
n
d
s
h
o
w
e
d
ve
ry
g
oo
d
pe
r
f
or
ma
nce,
s
uc
h
as
a
large
n
u
m
b
er
o
f
le
ve
l
s
w
ith
w
ith
i
mpro
ve
d
o
u
t
p
ut
w
ave
f
orm
s
,
low
t
ot
al
h
a
r
mo
ni
c
di
st
o
r
t
i
o
n
an
d
i
m
p
r
ov
e
d
e
ffi
c
i
en
cy
[
4
-
6].
A
ll
t
h
ese
to
p
o
log
i
es
h
ave
bee
n
i
ntr
o
d
u
ce
d
for
mult
ile
ve
l
c
o
n
v
er
te
rs
t
ha
t
ut
i
l
iz
e
d
t
he
c
o
m
bi
na
tio
n
o
f
ac
t
i
ve sw
i
t
c
hes
a
nd
D
C
so
u
rc
es t
o ge
ne
rate mult
i
l
e
vel
w
a
v
e
for
m
at the
o
u
t
p
u
t
[7,
8
].
T
he
m
ajor cha
lle
n
g
e
s
o
f
the
s
e
mul
tile
ve
l
i
nver
t
e
r
s
are
usage
o
f
m
ore
num
ber
of
i
so
lat
e
d
D
C
source
s
a
nd
t
o
o
m
a
ny
n
u
m
b
ers
of
swit
c
h
i
n
g
dev
i
ce
s,
t
hese
p
ro
b
l
em
s
are
e
l
i
m
i
n
ate
d
i
n
P
U
C
c
o
n
v
ert
er
w
h
i
c
h
i
s
i
nve
n
t
e
d
by
A
l
-H
ad
ded
i
n
2
0
1
0
a
n
d
se
v
e
ral
p
a
p
e
rs
a
re
pub
l
i
s
h
e
d
by
A
l
-Ha
d
d
a
d
and
Ha
ni
v
ah
edi
o
n
the
P
U
C
inve
rt
er
w
i
t
h
R
a
n
d
RL
l
oa
ds
[9].
T
h
i
s
pa
per
pr
opo
se
s
a
thr
ee
p
h
a
s
e
fi
ve
l
eve
l
P
U
C
i
n
v
e
r
ter
fed
i
nduc
ti
on
m
otor
f
ee
d
from
t
he
P
V
sourc
e
thr
o
u
g
h
D
C/D
C
c
on
verter
,
com
p
ar
ed
a
ll
p
opu
la
r
mul
tile
vel
to
po
l
o
g
i
e
s
a
nd
s
i
m
u
l
a
t
e
the
tes
t
s
ys
te
m
usin
g
M
a
t
l
a
b/
Si
mu
lin
k
.
T
hi
s
t
opo
lo
gy
i
s
in
t
e
resti
n
g
i
n
h
yb
rid
e
l
ect
ri
c
ve
hic
l
e
s
a
n
d
a
gr
icu
l
t
u
re
pum
p
se
ts
b
y
ut
iliz
i
n
g
so
lar and w
i
n
d
e
ne
rgy [
10-1
2
]. Fiv
e leve
l PU
C in
ver
t
e
r i
s
es
t
a
b
li
she
d
a
s a s
o
lu
ti
on t
o
t
he
s
e
v
e
n
leve
l
P
U
C
inve
rter
i
ssues.
S
w
i
t
c
h
i
ng
m
o
de
s
o
f
P
U
C
5
c
o
nve
rt
er
a
re
c
ont
r
o
l
l
ed
b
y
se
nsor
l
e
s
s
v
o
l
t
a
g
e
ba
lanc
ing
tech
n
i
q
u
es,
t
h
i
s
t
e
c
h
n
i
que
i
s
re
com
m
e
nded
bec
a
u
s
e
o
f
s
imple
de
s
ig
n
a
nd
d
o
e
s
not
r
e
quire
a
n
y
s
e
n
s
o
r
,
wh
i
c
h
i
n
c
r
ea
se
t
h
e
rel
i
a
bi
l
ity
o
f
t
h
e sy
st
em a
n
d
f
u
ll
f
ill
t
h
e
ind
ust
ri
al
req
ui
re
me
n
t
s.
2.
PUC5
C
O
NVE
RTE
R
Thr
ee
p
h
ase
P
U
C5
i
n
v
erter
f
e
d
in
duc
t
i
o
n
m
ot
or
i
s
s
h
ow
n
i
n
F
ig
ur
e
1.
I
t
c
ons
ists
o
f
fo
ur
l
ow
v
o
l
tag
e
sw
it
c
h
es tw
o
h
i
g
h vo
lta
ge
s
w
i
tche
s i
n
e
a
c
h
p
hase.
A
1.8 k
W
P
V
a
rra
y
c
onnec
t
e
d
to
e
a
c
h
p
hase of thre
e pha
s
e
PUC5
i
n
v
erter
at
V
DC
t
hr
o
u
g
h
D
C
/D
C
b
o
os
t
con
v
e
r
ter.
T
he
P
V
a
r
ra
y
uses
s
ix
s
u
n
m
o
d
u
l
es
(
SRP-3
0
5
E
–
WH
T-
D
)
i
n
ea
ch
pha
se.
T
o
ta
l
18
m
o
dul
e
s
(
6
*
3
*
3
0
5
=
5
.
4
9
kW)
w
i
t
h
ope
n
c
i
r
c
u
it
v
o
l
t
a
g
e
of 64.
2V
a
n
d
s
hor
t
c
i
rcui
t
cu
rre
n
t
o
f
5
.96
A
a
t
10
00
w
/
m
2
s
u
n
i
r
r
a
d
i
a
n
c
e
a
n
d
2
5
o
C
am
b
i
e
n
t
tem
p
er
a
t
ure
[1
3-
15]
.
The
D
C
/
D
C
con
v
er
t
e
r
us
es
i
ncr
e
m
e
n
t
al
c
o
n
d
u
c
t
anc
e
a
nd
in
te
gra
l
r
eg
ula
t
or
M
P
P
T
tec
h
niq
u
e
i
s
u
se
d
to
e
x
t
r
act
m
ax
i
m
u
m
pow
er
f
r
o
m
t
h
e
pa
ne
l
unde
r
i
r
regu
lar
w
e
at
her
c
o
n
d
i
t
ions.
B
o
os
t
c
o
n
v
e
r
t
e
r
bo
osts
t
he
v
o
l
tage
t
o
44
0
V
a
nd
con
n
ec
ted
to
P
U
C
5
in
ve
rter
a
t
V
DC
.
If
t
hi
s
V
DC
i
s
2
E
v
ol
ts,
t
h
en
a
not
her
s
o
u
r
c
e
V
C
m
ust
be
E
v
o
l
ts
[
16]
.
P
r
evio
usl
y
p
u
b
l
i
s
h
e
d
p
a
p
e
r
s
on
7
le
ve
l
P
U
C
i
n
verte
r
w
ith
d
i
ffe
r
en
t
m
o
d
u
la
tio
n
te
chn
i
que
s
sho
w
s
om
e
li
m
i
ta
t
i
o
n
s
w
i
t
h
v
olta
ge
b
a
l
a
n
ci
n
g
p
roc
e
d
u
r
e
in
t
er
ms
o
f
m
o
d
u
la
t
i
on
in
de
x
[
17].
The
s
e
l
i
m
i
ta
tio
ns
a
re
e
l
i
m
in
at
e
d
i
n
se
n
s
o
r
l
e
s
s
vol
t
a
g
e
b
al
an
ci
ng
t
ec
hni
qu
e
a
n
d
d
o
n
o
t
r
e
quire
s
ens
o
rs
o
r
contr
o
llers
t
o
m
ainta
i
n
requ
ire
d
vo
l
ta
g
e
acr
oss ca
pa
c
i
tor V
C
[
18
,
19
]
.
In t
he
d
es
ig
n c
ons
i
d
era
t
i
o
n
p
o
w
e
r ind
u
s
t
ry
u
se
i
den
t
ical
d
evice
s
in
t
he
m
ult
i
l
e
v
el
i
n
v
erter
s
.
It
i
s
di
ffic
ul
t
to
h
a
v
e
e
qua
l
vo
lt
age
ra
nge
s
w
i
tc
hes.
B
u
t
P
U
C
c
onve
rter
s
h
o
w
n
i
n
F
i
gure
2(a),
h
a
s
a
vo
l
t
a
g
e
o
f
2
E
v
o
l
t
s
ac
ross
S
1,
S
3
an
d
re
ma
i
n
in
g
all
sw
i
t
c
h
e
s
s
u
b
j
ec
t
e
d
to
E
v
ol
ts,
by
add
i
ng
t
w
o
i
de
nt
ica
l
s
w
i
tc
he
s
in
s
e
r
ies
i
n
t
h
e
S
1,
S
2
of
i
n
v
ert
e
r
i
t
c
o
u
l
d
be
d
esi
g
n
e
d
w
i
t
h
i
den
t
i
c
al
v
ol
ta
g
e
r
a
t
i
n
g
s
w
i
t
c
h
e
s
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
2
(
b
)
.
A
n
o
t
h
e
r
d
e
s
i
g
n
c
o
n
s
i
d
e
ra
tion
ab
out
s
w
i
t
c
hes
S
4
,
S
5
a
nd
S6
a
re
w
o
rki
n
g c
o
mp
l
e
m
e
ntar
y to
S
1
,
S
2 a
nd S
3
, S
o thre
e ma
in
p
u
l
se
s de
vise S1, S2 and S3 whi
l
e
th
e
ir N
O
T
se
n
t
to
S4
,
S
5
an
d
S6
[
20
].
F
i
gure
1.
T
hree
pha
se
P
U
C
i
nver
t
er
fe
d
in
d
u
ct
ion
mot
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Th
re
e
p
h
a
s
e
P
U
C
5
in
ve
rt
e
r
fe
d
i
ndu
ct
ion
mo
t
o
r f
o
r r
e
n
ewa
bl
e
e
n
erg
y
app
li
ca
ti
o
n
s (G
.
V
.
V
.
N
a
ga
raju)
3
S
1
1
S1
S4
V
DC
V
C
S2
S3
S5
S6
V
DC
V
C
S1
S2
S3
S4
S5
S6
S4
4
(a
)
(b
)
F
i
gur
e
2.
P
U
C
5
in
ver
t
e
r
w
it
h
(
a
)
uneq
u
a
l
vol
tage
r
a
tin
g
sw
itche
s
(
b
)
equa
l
vo
lta
ge
r
at
in
g
sw
it
c
h
es
3.
S
E
NS
OR-LE
S
S
VO
LTAGE
R
E
G
U
L
ATING TECHNIQUE
Tab
l
e
1
sh
o
w
s
tha
t
t
he
c
a
p
a
c
it
or
m
ay
b
e
c
h
ar
ge
d
or
d
i
s
char
ge
d
i
n
a
ny
one
h
a
l
f
cy
cle
.
O
nl
y
to
m
a
inta
i
n
t
he ca
p
aci
t
o
r v
o
l
ta
ge
c
o
n
stan
t the
s
w
itc
hi
n
g
s
e
q
ue
nce
of
the
c
apa
c
i
t
o
r
is des
ig
ne
d
i
n
s
uch
a
w
a
y th
a
t
it
s
h
oul
d
be
d
i
s
cha
r
ge
d
in
t
h
e
n
e
g
a
t
i
v
e
ha
lf
c
yc
le
a
nd
c
ha
r
g
ed
dur
in
g
t
h
e
p
o
sit
i
v
e
h
a
l
f
cycle.
B
e
c
a
u
se
o
f
t
h
e
sw
itc
h
i
n
g
s
e
q
u
e
nc
e
o
f
c
a
p
ac
i
t
or
a
n
d
o
u
t
pu
t
w
a
vef
o
r
m
f
r
e
que
nc
y
t
he
c
a
p
a
c
it
or
c
har
g
e
i
s
i
ncr
ease
d
t
o
ha
lf
o
f
the
m
a
i
n
s
o
u
rc
e
vo
lta
ge
(
V
dc)
.
A
s
a
r
e
s
u
l
t
t
h
i
s
c
a
p
a
c
i
t
o
r
v
o
l
t
a
g
e
(
V
C
)
incre
a
ses
whe
n
i
t
is
c
on
ne
ct
ed
i
n
se
ries
w
i
t
h
t
he
l
oad
a
nd
V
dc
s
o
u
r
c
e
,
d
e
cre
a
se
s
wh
en
i
t
i
s
c
on
n
ect
ed
i
n
se
r
i
es
w
i
t
h
t
h
e
lo
ad
.
T
h
e
capa
c
i
t
o
r
char
ge
s
in
sw
itc
h
i
n
g
s
ta
te
s
2
a
n
d
7,
s
im
ilar
l
y
ca
pac
i
t
o
r
di
sc
har
g
e
in
s
w
i
t
c
h
i
n
g
st
a
t
e
s
3
a
nd 6.
T
he
capa
c
i
t
o
r
vo
l
t
ag
e
(
V
C
)
dur
in
g
c
h
ar
ge
/
d
i
s
cha
r
ge
i
s
±
E
v
olts
a
s
sh
o
w
n
i
n
T
a
b
le
1
.
Th
is
c
har
g
ing
an
d
d
i
scha
r
g
i
ng
i
s
w
r
i
tte
n
i
n
t
o
t
he
e
qua
t
i
o
n
(
1)
.
2
12
2
2
2
2
out
EV
E
VV
V
V
E
EV
E
(
1
)
I
f
t
he
s
our
c
e
v
o
lta
ge
m
a
g
n
itu
de
V
dc
i
s
fi
xed
at
2
E,
t
o
pr
o
duce
t
h
e
r
e
qu
i
r
ed
l
oa
d
vo
lta
g
e
,
t
h
e
ca
p
a
cit
o
r
v
o
lt
ag
e
V
c
m
us
t
be
m
ain
t
a
i
ne
d
a
t
E
.
S
o
t
he
c
h
a
r
g
i
n
g
a
nd
dis
c
ha
r
g
in
g
tim
e
ke
ep
s
t
h
e
ca
p
acit
o
r
v
o
lt
a
g
e
at
±
E.
T
h
e
re
f
o
re
,
t
o
m
ai
nt
a
i
n
equal
c
h
a
r
gi
ng
a
nd
d
i
s
ch
a
rgi
n
g
t
i
m
es,
swit
c
h
in
g
s
t
a
t
e
2
ch
arg
e
t
h
e
c
a
pac
i
tor
in
t
h
e
pos
iti
ve
h
a
l
f
c
y
cle
a
n
d
sw
i
t
c
h
ing
sta
t
e
6
di
sc
har
g
e
the
capa
c
i
t
o
r
in
n
e
g
a
t
i
v
e
ha
lf
c
yc
le
[
2
1
,
22]
.
Cha
r
g
i
ng
and
d
i
sc
har
g
i
n
g
o
f
c
a
p
ac
it
or
s
d
e
pen
d
s
on
t
h
e
t
ype
o
f
loa
d
o
n
l
y,
n
ot
o
n
th
e
o
u
tp
ut
f
r
e
q
u
e
n
cy
o
r
sw
itc
h
i
n
g
f
r
e
q
u
enc
y
,
t
h
e
size
o
f
t
h
e
c
a
pac
ito
r
depen
d
s
on
t
h
e
t
y
p
e
of
lo
ad
.
The
se
ns
or
l
es
s
vol
ta
ge
r
e
g
u
l
a
t
i
n
g
te
ch
n
i
qu
e
is
i
nt
egr
a
t
e
d
w
i
t
h
m
o
d
u
l
a
ti
on
t
e
c
h
ni
que
[
23-
25]
.
The
leve
l
shi
f
te
d
M
u
l
t
i
c
a
r
r
i
er
s
w
i
tc
hin
g
t
ec
h
n
i
q
u
e
i
s
u
se
d
as
m
odu
l
a
ti
o
n
t
e
c
h
n
i
que
[
2
6
]
.
F
or
i
m
p
lem
e
nt
ati
o
n
o
f
f
i
v
e
l
e
v
e
l
P
W
M
i
n
v
e
r
t
e
r
s
c
h
e
m
e
,
f
o
u
r
c
a
r
r
i
e
r
w
a
v
e
f
o
r
m
s
(
C
r
1
,
C
r
2,
C
r
3
,
and
Cr
4)
a
n
d
r
e
fe
r
e
nc
e
s
i
ne
w
a
v
e
a
r
e
used
s
how
n
i
n
F
ig
ur
e
4.
F
i
gur
e
4.
F
ive-
le
v
e
l
P
W
M
sc
he
me
u
si
ng
f
o
ur
l
eve
l
s
hi
f
t
ed
c
a
r
r
i
e
r
w
a
v
e
s
Hea
r
f
our
t
r
i
a
n
g
u
la
r
si
gna
ls
a
re
v
ertica
lly
s
h
i
fte
d
f
or
m
od
u
l
a
t
i
ng
the
r
e
fer
e
nce
si
ne
w
ave
.
T
h
i
s
mo
d
u
l
a
t
i
o
n
o
u
t
put
p
ul
s
e
i
s
asso
ci
a
t
ed
w
i
t
h
t
h
e
s
w
i
t
c
hi
ng
st
at
es
1
,
2,
5
,
6
an
d
8
sh
o
w
n
i
n
T
a
b
l
e
1
.
The
a
l
g
o
r
i
t
h
m
s
f
or
g
e
n
era
t
i
n
g
t
h
e
firin
g
pulse
s
a
r
e
p
r
esente
d
in
F
i
gur
e
5.
T
hi
s
pr
o
pose
d
a
l
g
or
it
hm
g
ener
a
t
es
t
he
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
1
–
9
4
fi
ve
l
eve
l
o
u
t
put
o
n
P
U
C5
i
n
v
er
t
e
r
afte
r
set
tin
g
t
h
e
capa
c
i
tor
vo
lt
ag
e
at
a
c
o
rre
ct
v
a
l
u
e
w
i
t
h
out
a
ny
f
ee
d
b
ack
sens
or.
The
capa
c
i
t
o
r
a
n
d
o
u
t
p
u
t
v
ol
ta
ges
do
n’t
de
pe
nd
on
the
t
y
p
e
o
f
t
he
s
ys
t
e
m
mode
l
(e.
g
.
A
v
e
r
a
g
e
mode
l
lin
g),
mod
u
la
ti
on i
n
de
x,
feedba
c
k
se
n
sor
s
,
grid
f
re
q
u
e
n
c
y
an
d sw
it
chi
n
g fr
eque
nc
y.
I
t
can
o
p
e
ra
te
t
he
s
ys
tem
v
o
ltage
t
o
a
ny
a
r
bi
trary
val
u
e.
T
he
P
V
so
urce
v
o
l
t
a
ge
m
ay
b
e
fla
c
uva
tes
bec
a
u
s
e
o
f
c
h
a
nge
s
i
n
c
l
i
ma
ti
c
c
o
nd
iti
o
n
s
.
T
his
se
nsor
l
ess
vo
l
ta
ge
b
alanc
i
ng
perfe
ctl
y
w
ork
w
ith
a
n
y
cha
nge
s
i
n
s
o
u
r
ce
vo
ltag
e
.
W
e
c
an
c
ha
n
g
e
t
h
e
fu
n
d
am
ent
a
l
fr
eq
ue
nc
y
a
s
w
e
l
l
a
s
i
nduc
tion
m
o
tor
s
p
ee
d,
b
y
c
h
an
gi
ng
th
e
V
Ref
s
i
gna
l
fre
q
u
e
ncy.
F
i
gure
5. P
rop
o
se
d
se
nsor-les
s vo
lta
ge
r
egu
l
ati
n
g a
ppr
oac
h
i
nt
e
grate
d
i
n
t
o
sw
itch
i
ng te
c
h
niq
u
e
T
a
b
l
e
1
.
S
w
i
tc
h
i
n
g
s
ta
te
s
,
C
a
p
a
c
i
t
o
r
c
h
a
r
g
i
n
g
/
d
is
c
h
a
r
g
i
n
g
s
t
a
t
e
s an
d
out
put
v
ol
t
a
g
e
of fi
ve
l
e
v
e
l
s P
U
C
in
verte
r
S
t
a
t
e
S
1
S
2
S3
V
output
V
out
v
a
l
u
e
C
a
p
a
c
i
t
o
r
volt
a
g
e
st
a
tus
1
1
0
0
V
DC
+2
E
No
E
f
f
e
c
t
2
1
0
1
V
DC
- V
C
+E
C
h
a
r
ging
3
1
1
0
V
C
+E
D
i
sc
h
a
rging
4
1
1
1
0
0
No
E
f
f
e
c
t
5
0
0
0
0
0
No
E
f
f
e
c
t
6
0
0
1
-
V
C
-E
D
i
sc
h
a
rging
7
0
1
0
V
C
- V
DC
-E
C
h
a
r
ging
8
0
1
1
-
V
DC
-2E
No
E
f
f
e
c
t
4.
COMPARISO
N
B
ETWEEN
P
U
C
5 AN
D
OTH
E
R
TO
POLOGIE
S
Thi
s
P
UC5
t
opo
log
y
i
s
sep
a
rat
e
ly
c
o
m
p
a
re
d
wi
th
f
ul
l
b
r
i
dge
,
CHB
a
n
d
N
P
C
/T
3
c
o
n
v
e
r
te
rs
i
n
ter
m
s
of
c
om
po
ne
nt
c
ou
n
t
,
sw
itc
hi
n
g
freq
u
e
n
c
y
a
nd
v
o
lta
ge
r
ati
n
g.
O
bv
io
us
ly
F
C
i
nver
t
er
h
as
m
or
e
num
be
r
of
c
o
mp
on
en
ts
t
o
c
o
n
t
rol
sin
c
e
t
h
i
s
t
o
pol
ogy
w
a
s
n
o
t
c
on
si
dere
d
.
H
o
w
ev
e
r
,
N
P
C
a
n
d
T3
h
av
e
s
a
me
p
rin
c
ipl
e
conc
e
p
t, the
y
ar
e c
o
mpa
r
ed
i
n
the sa
me
subs
ecti
o
n.
4.1.
C
o
mp
ar
i
s
on
b
etwe
en
sin
gle
p
h
a
s
e
PUC
and
FB in
v
e
r
te
r
s
F
ul
l
bri
dge
i
n
v
er
t
e
r
show
n
i
n
F
i
g
ur
e
6(a
)
i
s
t
h
e
m
o
st
c
o
m
mon
i
n
v
er
ter
to
po
l
o
g
y
i
n
the
ma
rke
t
bec
a
u
s
e
of
s
i
m
ple
s
t
ruc
t
ure
.
I
t
has
o
n
e
i
s
o
l
a
t
ed
D
C
s
ourc
e
,
fou
r
switches
.
However,
e
ac
h
switch
suf
f
er
s
2E
vo
lts
i
f
V
1
w
ou
ld
b
e
e
q
ua
l
t
o
P
U
C
5
i
nver
t
e
r
D
C
so
urce
.
Ba
sed
on
an
e
q
u
a
l
v
o
l
ta
ge
r
at
in
g
desi
g
n
t
he
s
w
i
tche
s
cos
t
o
f
P
U
C
5
w
ou
ld
b
e
l
o
w
e
r
tha
n
f
u
l
l
brid
ge
a
t
e
qua
l
v
o
l
t
age
/
p
ow
e
r
r
a
t
i
ng.
H
ow
e
v
e
r
f
ul
l
bri
d
ge
p
r
o
d
u
ces
three
le
ve
l
o
u
t
pu
t v
o
lta
ge
w
h
ile
P
U
C
5
i
n
ver
t
e
r
h
as
b
e
tte
r
T
H
D
r
e
s
ul
t
s
w
it
h fi
ve l
e
v
el
v
o
l
tage
w
i
t
h
a
dde
d
c
o
st
of
o
ne
c
a
p
ac
i
t
o
r.
M
or
e
eve
r
t
he
quas
i
-sine
w
a
ve
a
t
th
e
ou
tp
u
t
,
r
e
duce
th
e
har
m
onics
w
hi
c
h
w
o
u
l
d
d
im
inis
h
the f
ilter
size
at le
a
s
t
by ha
lf ra
tio
a
n
d
ove
ra
l
l
size
an
d
cos
t of
i
n
v
e
r
ter
w
oul
d
be
r
educ
e
d
.
4.2.
C
o
mp
ar
i
s
on
b
etwe
en
sin
gle
p
h
a
s
e
PUC
and
C
H
B
A
f
i
v
e
l
e
v
e
l
C
H
B
c
o
n
s
i
s
t
s
o
f
t
w
o
f
u
l
l
b
r
i
d
g
e
c
e
l
l
s
c
o
n
n
e
c
t
e
d
i
n
s
e
r
i
e
s
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
6
(
b
)
.
Whe
r
e
a
s
t
he
o
u
t
pu
t
v
o
lta
ge
i
s
t
h
e
sum
of
t
w
o
c
e
l
ls,
s
o
it
inc
l
u
d
e
s
t
w
o
i
so
late
d
D
C
s
o
u
rc
es
o
f
eac
h
E
v
o
lts
and
e
i
gh
t
sw
it
c
h
es
w
i
t
h
a
n
i
de
nt
ica
l
v
ol
ta
g
e
r
ating
of
e
a
c
h
E
v
ol
ts.
Acc
o
rdi
ngl
y
,
i
t
has
ex
a
c
t
l
y
t
h
e
sa
me
d
e
si
gn
a
s
t
h
e
P
U
C5
t
opol
og
y
a
s
s
ho
wn
i
n
Fig
u
r
e
2
(
a).
Th
e
s
e
t
w
o
c
o
n
v
erte
r
s
g
ene
r
ate
fi
v
e
l
eve
l
vo
lta
ge
a
t
t
h
e
ou
tpu
t
.
S
o
t
he
T
H
D
and
o
u
tp
ut
f
i
l
t
e
r
d
esig
n
w
oul
d
be
s
a
m
e
.
O
nly
t
he
d
iffe
rence
b
e
tw
ee
n
five
l
eve
l
C
H
B
a
n
d
PUC5 i
s o
n
e
D
C
sour
ce.
T
w
o
DC
so
ur
ce
s
of
M
ag
nit
u
d
e
s
E a
r
e
u
s
ed
i
n
C
H
B
to ge
n
e
ra
t
e
five
le
ve
l w
a
ve
form
.
The
m
a
i
n
q
u
e
s
t
i
o
n
is
t
ha
t
us
ing
tw
o
D
C
s
o
u
rc
es
w
ith
e
ac
h
E
v
o
l
t
s
i
s
b
e
t
t
e
r
o
r
u
s
i
n
g
a
s
i
n
g
l
e
D
C
s
o
u
r
c
e
w
i
t
h
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
T
h
ree
ph
ase PU
C5
i
n
ver
ter fe
d
in
d
u
ct
io
n mot
o
r f
o
r rene
w
a
b
l
e
e
n
er
gy a
p
p
l
i
c
a
t
i
on
s (G.
V.
V.
Nag
a
ra
j
u
)
5
2E
v
o
lts
?
N
o
r
m
ally
i
n
r
e
ne
w
a
ble
e
n
e
r
g
y
c
on
versi
o
n
s
y
stem
o
n
l
y
o
ne
bus
a
va
i
l
a
b
l
e
from
the
P
V
o
r
w
i
n
d
fa
rms
t
h
a
t
s
h
oul
d
be
c
o
nne
c
t
ed
t
o
t
h
e
inv
e
rter.
The
r
efor
e
CH
B
w
i
t
h
m
o
r
e
t
ha
n
one
i
so
la
ted
D
C
s
ourc
e
requ
ire
more
s
pl
i
tti
ng
i
n
t
h
e
P
V
p
a
n
el
o
r
w
i
n
d
t
urb
i
ne
i
nt
o
d
i
f
fer
e
n
t
a
rra
ys
w
it
h
se
p
a
ra
ted
c
o
nnec
tio
ns
t
o
ma
ke
m
or
e
i
s
ola
t
e
d
D
C
b
u
s
es.
S
u
ch
t
y
p
e
c
onf
igur
at
ion
re
q
u
ire
s
p
o
w
er
b
al
an
ci
ng
b
et
we
e
n
D
C
sou
r
c
e
s,
part
icu
l
ar
ly
d
uri
ng
a
n
y
re
n
e
w
a
bl
e
e
n
erg
y
gen
e
r
a
tio
n
le
vel
varia
t
i
on
c
a
use
d
b
y
e
n
v
i
r
onm
en
ta
l
fac
t
ors.
H
o
w
e
ve
r,
r
eplac
i
n
g
t
he
e
x
i
s
t
in
g
tw
o
leve
l
t
o
p
o
l
o
g
y
w
ith
t
hos
e
i
n
v
erter
s
t
ha
t
ha
ve
m
ore
is
ola
t
e
d
D
C
sour
ce
s
wo
ul
d
b
e
m
o
r
e
d
i
f
f
i
c
ul
t
du
e
t
o
c
ha
ng
e
t
h
e
DC
s
id
e
st
ru
c
t
u
r
e
.
B
e
cause
o
f
t
h
e
a
bove
d
isc
u
sse
d
m
e
r
its,
P
U
C5
in
verter
w
it
h si
ngle
D
C
so
u
rc
e is the
bes
t so
l
u
ti
on.
F
i
gure
6.
(
a) Ful
l br
id
ge
in
v
e
r
ter
,
(
b) F
ive le
vel
CH
B i
nver
t
er
4.3.
C
o
mp
ar
i
s
on
b
etwe
en
sin
gle
p
h
a
s
e
PUC
and
N
P
C
/
T3
N
P
C
a
nd
T
3
a
re
t
he
m
ost
p
o
p
u
l
ar
i
n
a
p
p
l
i
cati
o
ns
a
s
a
t
h
ree
lev
e
l
i
n
v
e
r
ter,
w
hile
l
i
n
e
vo
l
t
age
w
ill
gene
ra
te
f
ive
l
e
vel
s
o
f
o
u
t
p
ut
w
hen
tw
o
le
gs
a
n
d
one
D
C
sourc
e
a
r
e
use
d
i
n
si
n
g
le
a
s
show
n
i
n
F
ig
ur
e
7(
a)
and
7(b).
A
n
N
P
C
c
on
tai
n
s
eig
h
t
s
w
i
tch
e
s
and
fo
ur
d
i
o
de
s
w
h
ic
h
is
c
ons
i
d
era
b
ly
m
or
e
t
h
a
n
P
U
C
5
c
o
mp
on
en
ts.
T3
i
nv
ert
e
r
ha
s
e
i
ght
s
wi
t
c
h
e
s
as
s
ho
wn
i
n
Fi
g
u
r
e
7
(
b
)
.
O
u
t
o
f
e
i
g
h
t
S
1
,
S
2
,
S
3
a
n
d
S
4
a
r
e
requ
ire
d
t
o
be
ar
t
he
w
h
o
l
e
D
C
b
u
s
v
o
l
t
a
ge
2
E
v
o
lts.
Th
is
u
ne
qua
l
vo
l
t
a
g
e
ra
ti
n
g
sw
itc
hes
i
s
t
h
e
m
ain
di
sa
d
v
a
n
ta
ge
i
n
T3
i
nvert
e
r
.
More
over,
b
o
t
h
N
P
C
an
d
T3
i
n
v
erte
r
s
requ
ire
t
w
o
ca
pa
ci
t
o
r
s
t
o
sp
l
i
t
th
e
sin
g
l
e
D
C
s
our
ce
v
o
l
t
a
ge,
it
is
o
ne
e
xtra
c
apac
itor
tha
n
P
U
C
5
in
ver
t
e
r
c
a
p
aci
t
o
rs.
Eve
n
tua
l
l
y
t
he
v
o
lta
ge
b
al
anc
i
n
g
als
o
di
f
fic
u
lt i
n
N
P
C
/T3
w
h
en
c
om
pare
d w
i
t
h
P
U
C
5.
F
i
gure
7. (
a) F
ive
leve
l
N
P
C inver
t
e
r
, (b) F
ive
level T
3
i
n
v
e
r
t
er
4.4.
C
o
mp
ar
is
on
b
et
we
en
t
h
r
e
e
p
h
a
s
e
P
UC
a
nd
N
PC
/T3
I
n
b
o
t
h
N
P
C
a
n
d
T
3
i
n
v
e
r
ters
o
n
l
y
o
n
e
le
g
a
dde
d
to
t
he
s
i
n
g
l
e
p
hase
t
w
o
l
eg
s
truc
tu
re
s
how
n
i
n
F
i
gure
7
(a)
a
nd
(b)
and
a
n
o
t
he
r
adva
n
t
a
g
e
w
ith
t
hre
e
pha
se
N
P
C
i
s
on
l
y
one
D
C
so
ur
ce
a
nd
tw
o
c
a
pa
c
i
t
o
r
s
are
require
d
f
o
r
al
l
t
h
re
e
p
h
a
ses.
B
ut
t
he
v
o
l
tage
b
a
l
a
n
c
i
n
g
i
s
m
uc
h
more
c
om
p
l
e
x
i
n
the
s
e
tw
o
in
ve
rters
com
p
are
d
t
o P
U
C5. S
o
m
any
me
thods ha
v
e
bee
n
a
ppe
are
d
in li
tera
t
u
r
e
to
b
al
an
c
e
t
h
e
c
ap
ac
ito
r
v
o
lt
a
g
e a
t
D
C
source
s
uch
a
s
l
i
n
ea
r
P
I
r
egula
t
or
,
non
l
i
nea
r
c
on
t
r
o
lle
r
s
a
nd
z
e
r
o
c
o
mpo
n
e
n
t
i
n
je
ctio
n.
T
he
s
i
m
ple
s
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w El
ec &
D
ri S
y
s
t
Vo
l. 1
1
,
No
. 1
,
Mar
2
0
2
0
:
1
–
9
6
c
o
n
t
r
o
ller
used
i
n
N
P
C
or
T
3
is
s
pa
ce
v
ec
to
r
c
ont
r
o
lle
r
,
t
h
i
s
c
an
b
e
int
e
grat
ed
i
n
t
o
sp
ace
v
ec
to
r
mo
du
l
a
t
i
on
t
e
chni
qu
e.
H
owev
e
r
,
i
n
t
h
r
e
e
p
h
a
se
P
UC
5
in
ve
rt
er
s
i
m
p
l
e
se
n
s
o
r
l
e
ss
v
ol
t
a
g
e
b
a
l
an
ci
ng
i
s
int
e
g
r
at
ed
i
n
t
o
v
e
ry
s
i
m
pl
e
mo
dul
a
tio
n
th
at
i
s
P
W
M
mod
u
l
a
tio
n
to
r
e
gula
t
e
t
h
e
c
a
p
ac
i
t
o
r
v
o
lta
ge
.
F
u
r
t
he
r
m
or
e,
t
he
t
hr
e
e
pha
se
N
P
C
/
T
3
in
ver
t
er
p
r
o
duc
es
t
hr
ee
le
v
e
l
w
a
v
e
f
o
r
m
i
n
ea
ch
pha
se,
f
u
r
t
her
i
n
cr
e
a
se
i
n
le
ve
ls
r
e
q
ui
r
e
a
n
e
x
t
r
em
e
n
u
m
b
er
o
f
sw
itc
he
s
and
is
ola
t
e
d
s
o
u
r
c
e
s
.
O
n
t
he
o
t
h
er
h
a
n
d
t
h
r
e
e
phas
e
P
U
C
5
pr
o
d
u
ces
up
to
n
in
e
leve
ls
i
n
ea
ch
pha
se
by
us
ing
t
h
e
sam
e
c
ompo
ne
nt
s
used
i
n
thr
e
e
l
ev
el
PUC
.
4.
5.
Co
mp
a
r
is
o
n
b
et
w
e
en three
ph
a
s
e
PU
C a
nd CHB
Thr
e
e
p
h
ase
f
i
ve
l
e
v
e
l
C
H
B
c
on
si
s
t
s
of
t
w
o
s
our
c
e
s
a
nd
s
i
x
sw
it
ch
es
i
n
ea
ch
p
h
a
se
t
h
a
t
i
s
t
ot
a
l
s
ix
sour
c
e
s
a
nd
24
s
w
i
t
c
hes.
O
nl
y
t
h
e
d
i
f
f
e
r
enc
e
i
s
t
h
r
e
e
is
ola
t
ed
sw
itche
s
w
h
ich
w
i
l
l
i
ncr
e
as
e
the
ma
nuf
ac
t
u
r
i
ng
c
o
st
a
n
d
s
i
z
e
of
t
he
i
nver
t
er
.
Rem
ain
i
n
g
a
l
l
c
har
acte
r
ist
i
cs,
i
ncl
u
ding
v
o
l
t
a
g
e
r
a
ti
n
g
,
vo
l
t
age
le
ve
l,
a
p
p
lica
tio
ns
a
n
d
T
H
D
value
ar
e
same
i
n
bo
th
C
H
B
a
nd
P
U
C
i
nver
t
e
rs.
Tab
l
e
2
s
how
s
t
h
e
c
o
mpo
n
e
n
t
c
o
unt
c
om
p
a
r
i
so
n
f
o
r
s
i
ng
le
p
h
a
se
f
iv
e
l
e
v
e
l
in
v
e
rt
e
r
s.
A
l
l
a
bov
e
c
o
mpa
r
ison
s
p
r
ove
d
tha
t
t
he P
U
C
i
nver
t
er
i
s
the
bes
t
t
o
p
o
l
og
y
f
or
r
eplac
i
ng
e
x
is
t
i
n
g
t
w
o
,
t
h
r
ee
and
f
i
v
e
l
eve
l
i
n
v
e
r
t
ers on
t
he ma
r
k
e
t
.
Tab
l
e
2.
C
om
pone
n
t
c
ou
n
t
c
o
m
pa
r
i
so
n
for
sing
le
p
hase
f
i
v
e
l
e
vel
inv
er
t
e
rs
I
nve
r
t
e
r
t
y
p
e
D
C
S
ource
s
Ca
p
a
c
i
t
o
r
s
D
i
ode
s
S
w
i
t
c
h
e
s
T
ota
l
c
o
m
pone
nts
C
H
B
2
0
0
8
1
0
N
P
C
wi
thout
volta
ge
c
ont
r
o
l
4
0
6
8
1
8
FC
1
3
0
8
1
2
PU
C
5
1
1
0
6
8
5.
SIMULATION
R
ESULT
S A
ND
DI
S
CU
S
S
IO
N
P
r
opo
se
d
a
th
r
ee
phase
f
i
v
e
leve
l
P
U
C5
i
n
v
er
t
e
r
i
s
b
ui
lt
i
n
M
a
t
l
a
b
/
S
i
mul
i
nk
w
ith
t
h
e
g
ive
n
pa
ram
e
ter
s
.
The
perfor
m
a
n
ce
is
t
este
d
with
s
u
dde
n
l
o
a
d
c
ha
n
g
e
a
t
0.
5
S
e
c
.
I
t
w
a
s
sim
u
l
a
te
d
i
n
Ma
tla
b
/
S
i
m
u
l
i
nk
s
o
f
t
w
a
r
e
a
nd t
h
e
r
e
sul
t
s
s
h
ow
s the
per
f
o
r
m
a
n
ce
of
t
hr
ee
phase
P
U
C
5
inve
r
t
er
s
fed
i
nduc
ti
o
n
m
o
tor.
I
t
is
s
i
m
ulate
d
f
o
r
o
n
e
s
e
c
on
d.
T
h
e
t
es
t
sys
t
e
m
s
i
m
ulat
i
on
pa
r
a
m
e
t
e
r
s
a
r
e
liste
d
i
n
T
ab
le
3
.
F
i
gur
e
8
show
s
t
h
e
t
h
r
e
e
-
phase
l
i
n
e
t
o
line
vo
lta
ge
o
u
t
pu
t
o
f
i
nve
r
t
e
r
w
ith
s
e
v
e
n
l
e
v
els.
F
ig
ure
9
shows
ca
p
acit
o
r
vo
l
t
age
w
h
ic
h
i
s
z
er
o
a
t
s
tar
t
i
ng
a
n
d
i
n
cr
easin
g
u
p
t
o
22
0
vo
l
t
s
an
d
the
n
i
t
is
c
ons
ta
nt,
m
a
inta
i
n
e
d
a
t
ha
lf
o
f
the
V
DC
t
hr
ou
g
h
o
u
t
t
he
s
im
ul
ati
on.
F
i
gur
e
10
show
s
t
h
e
ph
a
s
e
to
g
r
o
un
d
v
ol
t
a
ge
out
p
u
t
w
i
t
h
t
he
f
i
v
e
l
e
vel
s
.
Fi
g
u
r
e
1
1
s
hows
t
h
e
th
re
e
ph
as
e
i
n
v
e
rt
e
r
l
o
a
d
cu
rrent
w
h
i
ch
i
s
al
mo
st
p
u
r
e
sin
e
w
av
e,
F
i
g
u
r
e
12
show
s
t
h
e
loa
d
c
ur
r
e
nt
i
n
B
p
h
ase,
w
h
i
ch
i
s
ve
r
y
h
ig
h
a
t
s
t
a
r
t
i
n
g
b
e
c
a
u
s
e
of
i
ndu
ct
io
n
mo
t
o
r
lo
a
d
a
fte
r
0
.1
se
co
nds
i
t
set
tle
s
t
o
nor
m
a
l
va
l
u
es,
F
i
gur
e
1
3
s
h
o
w
s
t
he
T
H
D
sp
ec
tr
u
m
o
f
l
o
ad
c
ur
r
e
nt
a
nal
y
ze
d
b
y
F
F
T
a
n
al
ys
i
s
.
I
t
i
s
d
one
a
t
0.
5
se
c as
s
ta
r
t
i
n
g
t
i
m
e
a
nd
e
v
a
l
ua
t
e
d
f
o
r
t
h
r
e
e
cyc
l
e
s
.
I
t
s
how
s
t
h
e
TH
D
value
20.
23
%
.
S
i
milar
l
y,
c
ur
r
e
nt
w
ave
s
how
in
g
t
h
e
TH
D
v
a
lue
1.
8
7
%.
W
hi
c
h
i
s
s
h
o
w
i
n
g
v
e
r
y
go
od
p
e
r
f
o
r
m
ance
.
F
i
gur
e
1
4
show
s
t
h
e
spee
d
of
t
he
d
r
i
ve,
w
h
ic
h
is
a
lm
os
t
con
s
ta
n
t
,
at
0
.
5
S
ec
sudde
n
l
o
ad
c
ha
n
g
e
is
a
ppl
ied.
Ta
ble
3.
S
im
ulatio
n
par
a
me
ter
s
P
a
ra
m
e
te
r
V
a
l
u
e
V
DC
440
V
C
0.
015F
Inve
rte
r
f
undam
e
nta
l
f
re
que
n
c
y
50
Hz
Squir
r
e
l
Ca
g
e
Motor
460
V
,
50Hz
,
3730
W]
C
a
rr
i
e
r
f
r
e
que
n
c
y
5
kHz
V
Re
f
m
a
x
1
.
75 V
F
i
g
u
r
e
8
.
T
hr
ee-
phase
line
to
l
i
n
e
v
o
l
t
a
g
e
o
u
t
pu
t
of
in
ver
t
er
w
i
t
h
se
ven
l
e
ve
ls
F
i
gur
e
9.
V
olta
ge
ac
r
o
ss
t
he
c
apa
c
i
t
or
(
V
c
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Th
re
e
p
h
a
s
e
P
U
C
5
in
ve
rt
e
r
fe
d
i
ndu
ct
ion
mo
t
o
r f
o
r r
e
n
ewa
bl
e
e
n
erg
y
app
li
ca
ti
o
n
s (G
.
V
.
V
.
N
a
ga
raju)
7
F
i
gur
e
1
0
.
P
h
a
s
e
t
o
g
r
o
un
d
v
o
l
t
a
g
e
ou
tp
ut
F
i
gur
e
1
1
.
Thr
e
e
pha
se
l
oad
c
u
r
r
ent
F
i
gur
e
1
2
.
Load
c
ur
r
e
nt
i
n
ph
a
s
e
B
F
i
gur
e
1
4
.
T
HD
s
pec
t
r
u
m
of
l
i
n
e
v
o
l
t
a
g
e
F
i
gur
e
1
3
.
S
p
e
e
d
of
t
he
i
nd
uc
ti
o
n
m
ot
or
(
P
u
)
6.
CONCLUSION
In
t
hi
s
p
a
p
e
r
se
n
s
o
r
l
ess
vol
t
a
g
e
c
o
n
t
r
oll
i
ng
t
ech
ni
c
i
s
s
ugg
es
te
d
f
o
r
P
U
C
c
o
nve
r
t
er
f
e
d
i
n
duc
t
i
o
n
m
o
tor
w
i
t
h
a
P
V
sour
ce
alo
ng
w
i
t
h
b
o
o
t
c
on
ver
t
e
r
a
nd
a
sin
g
le
c
a
p
ac
itor
in
e
a
c
h
p
hase
w
ith
m
in
imum
num
ber
c
o
mp
o
n
e
n
t
s
.
C
o
m
p
ar
e
d
t
o
a
ll
o
t
her
exi
s
t
i
ng
s
y
s
t
e
m
s,
i
t
r
equir
e
s
on
l
y
s
i
x
s
w
i
t
c
hes
i
n
e
ac
h
p
h
a
se
a
nd
doe
s
n
o
t
r
equ
i
re
a
ny
se
nsor
w
hic
h
w
ill
re
d
u
c
e
t
he
c
ost
a
nd
c
o
m
p
lex
i
t
y
o
f
the
sys
t
em
.
All
t
h
e
de
me
rit
s
o
f
ne
u
t
r
a
l
c
l
am
pe
d
i
nve
r
t
er
s
a
n
d
fly
i
ng
c
a
p
ac
i
t
or
i
n
v
e
r
ter
s
a
r
e
e
l
i
m
i
n
ate
d
i
n
the
P
U
C5
i
nve
rter.
This
s
yste
m
is
si
mu
l
a
t
e
d
in
M
at
l
a
b/
Si
mu
l
i
n
l
,
t
h
e
resul
t
s
sho
w
in
g
good
d
yn
a
m
i
c
p
e
r
f
or
ma
nce
a
n
d
pow
e
r
q
ua
lit
y
is
a
l
s
o
i
m
p
r
ov
e
d
.
It
h
a
s
l
e
ss
wei
ght
b
e
c
a
us
e
of
l
ess
c
o
mp
on
en
ts
a
n
d
mo
r
e
s
u
i
t
a
b
l
e
f
o
r
m
o
v
i
n
g
e
l
e
c
t
r
i
c
v
e
h
i
c
l
e
s
.
B
y
va
r
y
in
g
t
h
e
V
ref
si
ne
w
ave
s
i
gna
l
fr
eq
uenc
y
,
w
e
c
a
n
cha
n
ge
t
he
s
pee
d
o
f
the
mo
to
r
.
T
his
in
ver
t
er
i
s
be
st
su
ita
b
l
e
f
o
r
in
t
e
r
f
a
c
e
t
he
r
e
n
ew
able
e
ne
r
g
y
sour
c
e
w
i
t
h
ind
u
c
t
i
on
m
o
t
o
r
.
REFERE
NC
E
S
[1]
Ou
nej
j
ar,
You
ssef
,
K
a
m
a
l
A
l-Haddad
,
a
n
d
L
uc-
A
nd
re
G
reF
g
o
i
re.
"
P
ack
ed
U
c
e
lls
m
u
ltil
e
vel
convert
er
t
o
p
o
l
o
gy:
th
eoret
i
cal
s
tud
y
a
nd
e
x
p
eri
m
ental
v
a
li
da
t
i
o
n
”
IEEE
T
r
an
sa
c
tions
o
n
Ind
u
strial El
ec
t
r
o
n
i
c
s,
V
ol.
58
,
No.
4
,
p
p.
1
2
9
4
-1
30
6, 2
01
1.
[2]
Babad
i
,
Ad
el
N
azem
i,
e
t
al.
"Mo
d
if
ied
M
u
l
t
ilev
e
l
Invert
ers
wi
th
R
edu
ced
S
t
r
uct
u
res
Based
o
n
P
ack
edU
-
Cell”
IEE
E
Jou
r
n
a
l
o
f
Em
erg
i
n
g
a
nd Sel
ected
T
o
p
i
cs in Power
Electr
onics
,
Vol.
6,
N
o.
2
,
pp.
8
74-8
8
7
,
2
01
8.
[3]
Zi
d
,
A
l
aeddine
B
en,
Abdlekari
m
A
ouiti,
a
nd
F
aouzi
Bacha.
"
Study
a
nd
s
i
m
ulatio
n
of
t
hree-ph
ase
seven
-
le
v
e
l
pack
ed
U
cells
i
nv
erter”
20
17
1
8
th
In
te
rna
tion
a
l Con
f
e
r
e
n
c
e
o
n
Sc
ie
nc
e
s
an
d Te
c
h
n
i
qu
e
s
of Au
to
ma
tic
Co
n
t
rol
a
nd
Com
p
u
t
er
En
g
i
n
eeri
n
g
(
S
TA)
.
IEEE
,
20
17.
[4]
S
a
th
ik,
M
.
J
agabar,
et
a
l.
"
An
I
m
p
ro
ved
S
e
v
e
n
-
Lev
e
l
P
U
C
In
vert
e
r
T
opo
logy
w
it
h
Vo
l
t
age
Bo
os
tin
g”
IE
E
E
Tran
sa
c
tio
ns
o
n
Circ
ui
ts
a
n
d
Sy
ste
m
s II:
Ex
p
r
e
s
s
Brie
fs
,
201
9
.
[5]
Ab
arzadeh
,
M
o
s
t
af
a,
H
an
i
V
a
hed
i
,
an
d
Kam
a
l
Al
-Hadd
a
d.
"
F
a
s
t
s
en
s
o
r-l
e
s
s
volt
a
ge
b
alanci
ng
a
n
d
cap
a
c
ito
r
size
re
d
u
c
t
io
n
in
P
U
C
5 c
o
nv
e
r
te
r
u
s
i
n
g no
v
e
l
mo
du
la
tio
n
me
th
od
”
I
EEE
Trans
a
ctions
on In
dus
t
r
i
a
l
In
for
m
at
i
c
s
(
20
19
).
FF
T
an
alys
is
0
200
400
600
800
1000
Frequ
ency (
Hz)
0
0.05
0.1
Fundament
al
(
50Hz) = 63
4
.3 ,
T
HD= 20.
23%
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
1
–
9
8
[6]
Najafi
,
E
h
s
a
n,
a
nd
A
bdu
l
Hal
i
m
M
o
ham
e
d
Yat
i
m
.
"
D
e
si
gn
a
nd
i
m
p
l
e
mentati
o
n
of
a
n
ew
m
ul
t
ilevel
inverte
r
to
po
lo
gy
”
IEEE
tr
ans
ac
t
i
o
n
s
on in
du
st
rial
electr
o
n
i
cs
,
Vo
l
. 5
9,
No
. 11
, p
p.
4
14
8-
4
1
5
4
, 2
01
1.
[7]
Vahed
i
,
Han
i
,
a
n
d
K
a
m
a
l
Al-Hadd
a
d.
"
R
eal
-time
im
plem
ent
a
ti
on
o
f
a
s
even
-lev
el
p
ack
ed
U
-c
el
l
in
verter
w
i
t
h
a
low
-
s
w
it
chin
g-f
r
eq
uen
c
y
vo
lt
age
regu
lat
o
r”
IEEE T
r
an
sac
t
io
ns
on
Po
wer
El
ectr
oni
cs,
V
ol
.
3
1
,
N
o
.
8
,
pp.
5
9
6
7
-
597
3,
20
1
6
.
[8]
Met
r
i,
J
u
l
ie
I
.,
e
t
al
.
"Real-tim
e
im
p
l
e
m
ent
a
ti
on
o
f
mo
de
l
-
pred
ic
t
i
v
e
c
o
n
trol
o
n
se
v
e
n-le
ve
l
pack
ed
U
-cell
inv
e
rter”
IEEE
T
r
a
n
s
a
c
t
io
n
s
on Industri
a
l
El
ectr
o
n
i
cs,
Vol.
63,
No
.
7
,
pp
.
418
0-4
186
,
2
01
6.
[9]
M
e
tr
i
,
J
u
l
ie
,
e
t
a
l.
"
M
o
de
l
pr
e
d
i
c
t
i
v
e
c
on
tr
o
l
f
o
r
t
he
p
a
c
k
e
d
U
-
C
ell
s
7
-lev
el
g
rid
co
nn
ected
i
n
v
e
rter”
20
16
IEE
E
Inter
n
a
t
i
onal
Co
nf
eren
ce on
Ind
u
s
t
ri
a
l
T
echn
o
l
o
g
y
(
I
CIT)
.
IEE
E
,
20
16
.
[10]
Qash
qai
,
P
ou
ria,
e
t
al.
"
A
r
evi
e
w
o
n
m
ult
i
l
e
v
e
l
co
nv
erter
t
opo
l
o
g
i
e
s
f
o
r
electric
tran
sp
ortatio
n
ap
pl
icati
ons”
20
15
IEEE
Veh
i
cl
e
Power a
n
d
Pr
opulsio
n
Co
n
f
erence (
V
PP
C)
.
IE
EE
, 2
01
5.
[11]
Arun
pras
ath,
R
.,
e
t
al
.
"
P
erf
o
rm
an
ce
E
v
al
uati
on
o
f
SE
P
I
C
Based
S
i
ngle-P
h
a
s
e
Sev
e
n-L
e
vel
Inv
e
rter
f
or
R
enewab
le
App
l
i
cati
o
n
s
”
Intern
atio
nal Jo
urn
a
l
o
f
R
e
n
e
wab
l
e E
n
er
gy R
e
s
e
arch
(
I
JRER),
Vo
l.
9
,
N
o
.
2
,
pp
.
704-7
1
1
,
2
0
1
9
.
[12]
R
e
d
d
y
,
C
h
R
a
m
i
,
a
n
d
K
.
H
a
r
i
n
a
d
h
a
R
e
d
d
y
.
"
A
N
e
w
P
a
s
s
i
v
e
I
s
l
a
n
d
i
n
g
D
e
t
ectio
n
T
echn
i
qu
e
f
o
r
In
t
e
grat
ed
Distr
i
buted
Generat
i
on
S
y
s
te
m
U
s
ing
Rat
e
o
f
Change
o
f
Reg
u
lator
V
o
l
t
a
ge
O
v
e
r
Reacti
v
e
P
o
w
e
r
at
B
a
l
an
ced
Isla
nd
in
g”
Jou
r
n
a
l
o
f
El
ectr
i
cal
En
gi
neeri
ng
&
T
echn
o
l
o
g
y
,
Vol
. 1
4, No
. 2
, pp
. 52
7
-5
34
, 20
1
9
.
[13]
Re
d
d
y
,
C
h
Ram
i
,
and
K.
H
arin
adh
a
R
eddy
.
"P
ass
i
ve
I
s
l
an
ding
D
ete
ct
io
n
Techni
qu
e
f
o
r
In
tegrat
ed
D
is
trib
u
t
ed
Generat
i
o
n
a
t
Zero
P
ow
er
B
ala
n
ced
I
slan
di
ng
”
Int
e
rn
atio
nal
J
o
ur
na
l o
f
Int
e
grat
ed Eng
i
n
eeri
n
g,
V
o
l.
1
1,
N
o.
6
,
pp.
1
2
6
-1
37,
2019
.
[14]
Re
d
d
y
,
C
h
,
a
nd
K.
H
ari
n
adh
a
R
edd
y
.
"
I
s
l
an
din
g
d
etect
io
n
f
o
r
in
v
erter
based
d
i
st
rib
u
t
e
d
g
e
nerati
on
w
ith
L
ow
freq
u
en
cy
c
urr
e
nt
h
arm
oni
c
i
n
j
e
cti
on
t
h
rou
g
h
Q
co
nt
roll
er
a
n
d
R
OCOF
a
nal
y
sis
”
Jo
urn
a
l
o
f
electrica
l system
s,
Vo
l
1
4
,
No
. 2
, 2
01
8
.
[15]
CH,
Rami
R
ed
d
y
,
and
K.
H
arinadh
a
R
eddy
.
"Is
l
andi
ng
D
e
t
ection
T
e
chn
i
q
u
es
f
or
G
ri
d
Integ
r
at
ed
D
G–
A
Rev
i
ew”
Inter
n
a
t
i
onal
Jo
ur
na
l o
f
Renewabl
e En
ergy Rese
a
r
ch
(
I
J
R
ER)
,
Vo
l
9
,
No
. 2
, p
p
. 9
6
0
-9
7
7
, 20
1
9
.
[16]
Azeem
,
Ab
du
l,
e
t
al
.
"Perf
o
rm
a
n
ce
of
F
iv
e
P
h
ase
P
U
C
In
vert
er
F
e
d
F
i
ve
P
h
a
se
I
nd
uct
i
on
M
otor
D
ri
ve
U
n
d
er
Diff
eren
t
T
r
iangul
ar
C
arrier
P
WM
S
ch
em
es”
IE
CO
N 20
18
-44
t
h
An
nua
l Co
nf
eren
ce
of
the IEEE Ind
u
s
t
ria
l
Elect
ro
n
i
cs
S
o
cie
t
y
.
IEE
E
,
20
18
.
[17]
Se
pa
h
v
a
n
d,
H
o
s
se
in
,
Jing
she
n
g
Lia
o
,
a
n
d
M
e
hd
i
F
e
rdo
w
s
i
.
"
I
nv
e
s
t
ig
ati
o
n
o
n
cap
aci
to
r
v
o
l
t
a
g
e
reg
u
l
a
ti
on
in
cascad
ed
H
-b
rid
g
e
m
u
l
t
i
l
ev
el
c
o
n
v
e
rters
wit
h
f
und
am
ental
f
r
eque
ncy
swit
ching”
IEEE
T
r
ansacti
o
ns on indust
r
ial
electr
o
n
i
cs,
V
ol.
5
8
,
No
.
1
1,
pp.
51
0
2
-
51
11,
2
0
1
1
.
[18]
Vahed
i
,
Han
i
,
an
d
Kam
a
l
Al
-Hadd
a
d.
"
S
i
n
g
le-D
C-so
urce
f
i
ve-l
evel
C
HB
i
nvert
e
r
w
ith
s
e
n
s
o
r-l
e
s
s
volt
a
g
e
balancing”
IE
CON 2
015
-41
s
t
An
nu
al
Con
f
eren
ce of
th
e I
EEE Indu
st
r
i
al Elect
ro
n
i
cs S
o
ciety. IE
EE
,
20
15
.
[19]
Nagaraj
u
,
G
.
V
.
V
.
,
G
.
S
a
m
basiva
R
ao
,
and
Ch
R
am
i
Redd
y.
"
S
e
ns
o
r
l
e
ss
v
o
l
t
ag
e
co
nt
rol
o
f
C
HB
m
ultilev
e
l
i
n
v
e
r
t
e
r
f
e
d
t
h
r
e
e
p
h
a
s
e
i
n
d
u
c
t
i
o
n
m
o
t
o
r
w
i
t
h
o
n
e
d
c
s
o
u
r
c
e
p
e
r
each
p
h
a
se
”
I
n
ter
natio
nal Jour
na
l o
f
Pu
re and
A
p
pl
ie
d
Ma
th
e
m
a
t
ic
s
1
20
.
06
(2018
):
4
07
9-4
097.
[20]
Vahed
i
,
Han
i
,
and
K
a
m
a
l
A
l
-Hadd
a
d.
"
P
U
C5
i
nv
erter-a
p
rom
i
si
ng
t
o
polo
gy
for
si
ng
le-p
hase
a
nd
t
hre
e
-ph
a
s
e
appl
icat
io
n
s
”
IECON 2
0
1
6
-4
2nd A
nnu
a
l
Confer
e
n
ce o
f
t
h
e
IEEE
Ind
u
s
t
ri
a
l
El
ectron
i
cs
So
c
i
e
t
y.
IEE
E
, 20
1
6
.
[21]
Ajes
h,
P
.
S
.
,
Be
en
a
M
.
V
arg
h
es
e,
a
nd
A
nnie
P
.
O
o
m
m
e
n
.
"
P
e
rfo
r
m
a
nce
anal
ys
is
o
f
cas
cadabl
e
U
-cel
l
m
u
l
t
i
level
inv
e
rter”
2
0
1
7
Int
e
rn
ation
a
l
Co
n
f
er
ence on
T
e
c
h
n
o
lo
gi
ca
l
Ad
va
ncem
ent
s
i
n
P
o
wer a
n
d
En
ergy (
T
AP E
n
er
gy
)
.
IEE
E
,
20
17
.
[22]
Ba
b
a
ie,
M
o
hamm
ad,
et
a
l.
"
Desig
n
o
f
an
A
rt
ifi
c
ial
Neural
N
etw
o
r
k
Con
t
rol
Based
o
n
L
even
berg-M
arq
u
art
Algo
r
i
th
m
fo
r
Grid-C
on
ne
c
t
ed
Packed
U
-Cell
In
v
e
rter”
[23]
Ra
o
,
G
.
S
a
m
b
asiv
a,
a
n
d
K
.
Ch
a
ndra
S
e
kh
ar.
"
A
n
ov
el
f
ive-level
S
PW
M
In
verter
s
yst
e
m
f
o
r
dual
-
f
e
d
in
duction
mo
to
r
dri
v
e”
20
12
IEEE In
t
e
rn
atio
nal Con
f
e
r
ence on
Ad
van
c
ed
Com
m
un
ica
t
i
o
n
Co
n
t
rol a
n
d
Comp
uting
Te
chnologies
(
I
CACCCT).
I
E
E
E
,
2
012
.
[24]
Ra
o
,
G
.
S
a
m
b
a
s
i
v
a,
a
n
d
K
.
Chan
dra
S
e
k
h
ar.
"A
s
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