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
. 55
5
~
56
5
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p55
5-5
65
5
55
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
Enhancement of voltage regula
tion using a 7-level inverter
based el
ectri
c spri
ng with
reduced num
ber of switches
K.
K. Deepik
a
1
, J
.
Vi
jay
a
K
u
m
a
r
2
, G
.
K
e
s
a
va
R
a
o
3
1
Dep
a
rtm
e
nt
of
Ele
ctrical
and
El
ectron
i
cs
En
g
i
ne
erin
g,
Vign
an’s In
stitute
of In
fo
r
m
ation
Tech
no
lo
gy, Ind
i
a
1
KL
Deem
ed
to
be Univers
ity,
In
dia
2
Depart
ment of E
l
ect
r
ical
and
El
ect
roni
c
s
Engineering, Ani
l
Neer
ukonda Institute of
Tech
nology
& Science,
In
dia
3
De
part
me
nt
o
f
El
ect
ri
ca
l
an
d
Ele
c
t
r
o
n
i
c
s E
ngi
nee
r
i
n
g,
KL
Deemed
to
be
U
n
iversity
,
In
dia
Ar
ti
cl
e Info
A
B
STRAC
T
A
r
ti
cl
e hi
st
ory:
Re
c
e
iv
e
d
M
a
r 1
7
, 2
019
Re
v
i
se
d
Ju
l 8
,
2
019
A
c
c
e
p
ted
D
e
c 1
5
, 2
019
Ele
c
tric S
p
ring
s
h
a
s be
en
tes
t
i
f
ied re
cen
tly
to
e
n
h
a
nce
vo
lt
age
r
e
g
u
la
tio
n
in
d
i
s
t
ributio
n
sy
stems us
in
g d
e
ma
nd
s
i
d
e
man
a
g
e
ment
. In
th
is
p
a
per,
a 7-
lev
e
l
M
u
ltile
v
el In
ve
rter
(M
LI)
w
i
th
a
r
e
so
nant
sw
itch
ed
cap
acito
r
Con
v
er
ter
b
a
sed
o
n
sinu
soi
d
al PWM
,
is
i
m
plem
en
ted
to
an
alyz
e th
e
p
e
rfo
r
manc
e of
an
e
l
ec
t
r
ic sp
rin
g
u
n
d
e
r volt
a
ge va
ria
t
io
ns at PCC.
By
the
p
r
opo
se
d ML
I b
a
se
d
ES
, vo
ltage
regu
lation
of
critic
a
l
lo
ad
vo
lt
age
is
stud
ied fo
r
vo
lta
g
e sag
an
d
s
w
ell con
d
itio
n
s
. Rem
a
rk
abl
e
featur
es o
f
t
h
e pro
p
o
s
ed t
opo
lo
gy
are
maint
a
ining
vol
t
age
bal
a
n
ce in inpu
t
capa
c
ito
r
s
and
red
u
c
t
io
n
of
po
wer
c
o
m
p
o
n
e
n
ts.
Sim
u
la
tio
ns
ha
ve
be
e
n
do
ne
in M
A
T
L
AB/
Sim
u
li
nk
on
d
i
s
t
ributio
n s
y
s
t
em with
DGs
equ
i
p
p
ed w
ith
M
L
I b
a
sed ES
un
der lin
e
v
o
ltag
e ano
m
alies
.
T
e
sted res
u
lts
are
an
aly
z
e
d
w
i
th THD
%
in
critica
l
lo
ad
v
o
ltag
e.
K
eyw
ords
:
Cr
it
ica
l
lo
a
d
El
ec
tric
sp
ri
n
g
M
u
lt
ile
v
e
l
i
n
v
e
r
t
e
r
R
e
sona
nt
s
w
i
t
c
hi
n
g
c
a
p
ac
it
or
c
onve
rt
er
T
h
is is
an
op
e
n
acces
s a
r
ticle
un
der
th
e
CC B
Y
-SA
l
i
cen
se
.
C
o
rre
s
pon
di
n
g
Au
th
or:
K.
K.
De
e
p
i
k
a
,
Department of
EEE, Vignan’s
I
n
stitute
of
Infor
m
ation
T
e
chnol
ogy,
Vi
sak
h
a
p
a
t
na
m, A
n
d
h
ra
P
r
a
d
es
h,
In
di
a.
Emai
l
:
kee
r
t
h
i.
deepi
k
a@
gma
i
l
.
c
o
m
1.
IN
TR
O
DUCTION
D
u
e
t
o
t
h
e
hi
gh
pene
t
r
at
ion
of
re
newa
bl
e
sou
r
ces
o
f
e
n
e
r
g
y
i
n
di
st
ri
b
u
t
i
on
syst
ems
[1
],
v
o
l
t
a
g
e
v
a
ri
at
ion
s
o
ccur
in
th
e d
i
s
t
r
i
bu
ti
o
n
sy
st
em
[2
, 3].
In
t
h
is
sc
e
n
a
r
io
,
it
is a
ch
a
lle
n
g
i
n
g
ta
sk to
ma
in
ta
in
con
s
ta
n
t
vol
ta
ge
to
h
o
s
p
it
al
and
mil
i
t
a
r
y l
o
a
d
s,
kn
o
w
n
a
s
c
r
i
t
i
c
a
l
l
o
ads as
pe
r t
h
ei
r v
o
lt
a
g
e se
nsit
i
v
it
y re
q
u
i
r
e
m
e
n
t [4]
.
Re
newa
ble
en
erg
y
sou
r
ces a
l
so l
e
a
d
t
o
the
para
dig
m
shi
f
t
from ce
ntral
i
z
e
d c
ont
rol
t
o
t
h
e di
stri
but
e
d
c
ont
rol
i
n
de
ma
nd
si
de
ma
nage
me
nt
[5,
6
]
. El
ec
tric
Spri
n
g
(ES
)
prop
ose
d
i
n
[7]
b
y
Hu
i et.a
l.
when
e
m
b
e
dd
e
d
in
t
h
e
less sens
itive
loads [
8
],
is
one of
the
simple wa
ys
to
m
a
int
a
in constant
vo
ltage
to the
s
e
nsitive loads
,
wi
thout
t
h
e nee
d
o
f
a
n
y c
o
mm
u
n
i
cat
i
o
n
syst
em
[9
,
10]. ES
re
gul
at
es t
h
e i
n
p
u
t
vo
lt
a
g
e w
h
i
l
e
al
low
i
ng
fl
uct
u
at
i
ons
i
n
l
o
ad
vol
t
a
ge
[
11]
.
Ini
t
i
a
l
ve
rsi
ons
of ES
impl
ement
e
d
hal
f
-
b
rid
g
e
i
n
ve
rte
r
s
fo
r t
h
i
s
[1
2, 1
3
]
, b
u
t
suf
f
ere
d
wit
h
hi
gh T
H
D
of
2
.
19%
. Wi
t
h
t
h
e
a
dve
nt
o
f
m
u
l
t
i
l
evel
i
nvert
e
r
s (ML
I
) i
n
P
o
w
e
r El
ect
roni
c
s
, the
y
e
x
te
n
d
a
g
r
eat
su
pp
o
r
t to
hand
l
e
the
i
n
t
e
r
m
itte
n
t
r
e
n
e
w
a
b
l
e
so
urc
e
s
w
ith
in
cr
ea
sed
pow
e
r
ra
ti
ng
s and
red
u
c
e
d
THD [1
4].
Re
duci
ng
t
h
e n
u
m
b
er
of s
w
i
t
c
h
es, T
H
D a
nd
swi
t
chi
ng l
o
sse
s
ha
s
a
l
w
a
ys c
o
n
s
ti
t
u
te
d
a
ma
jor
a
r
ea
o
f
r
e
sea
r
ch
in
M
u
l
tile
v
e
l i
n
v
e
r
t
e
r
s [1
5,
16
].
A
3-l
e
ve
l Ca
sc
ade
d
H-B
r
i
dge
I
n
vert
e
r
i
s
i
m
pl
eme
n
t
e
d
fo
r ES
c
o
ntr
o
l in
[1
7].
U
n
l
i
ke
t
h
e
c
o
nv
en
tio
n
a
l
M
L
I,
i
t
do
e
s
n
’
t
n
eed
a t
r
an
sfo
r
me
r. I
t
is i
m
p
l
e
m
e
n
ted
in
t
h
e
d
i
str
i
bu
te
d
c
o
n
t
r
o
l of
4 El
ec
tr
ic
spri
ngs
l
o
c
a
t
e
d
a
t
v
a
ri
o
u
s l
o
c
a
t
i
ons
in
t
h
e
di
st
ri
but
io
n s
y
st
em. S
i
mul
a
t
i
ons are
ca
rri
e
d
o
u
t
f
o
r i
n
duct
i
ve
an
d
c
a
p
a
c
iti
v
e
m
odes
of op
er
a
tion
of
ES
,
a
n
d r
e
su
lt
s ar
e
d
i
sc
u
s
se
d
in
te
rm
s of
TH
D%, RM
S
v
a
lu
e
s
o
f
th
e
m
a
i
n
s
vol
ta
ge
s. 5-l
e
v
e
l
Inve
rt
ers i
n
Dio
d
e
-
C
l
a
m
p
e
d
t
o
po
l
o
g
y
a
nd Ne
ut
ra
l P
o
i
n
t
Cl
ampe
d
i
nve
rt
er t
o
p
o
l
o
gy
a
r
e
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
:
5
5
5
–
565
55
6
im
p
l
e
m
en
te
d
i
n
ES c
o
n
t
ro
l
in [
1
8
,
19
] r
e
sp
e
c
ti
v
e
ly
.
Th
ey
ex
h
i
b
i
t l
e
sse
r
TH
D
%
ac
ro
ss the
cr
it
ic
al
lo
a
d
s wh
e
n
c
o
mp
a
r
e
d
w
ith
th
e
3
-
lev
e
l i
nver
t
e
r
co
n
t
r
o
l.
Ac
c
o
rd
ing
to lite
r
a
t
u
re
o
f
fai
l
u
r
es
in
mu
lt
ile
v
e
l i
n
v
e
r
t
er
s, vo
lt
ag
e
u
n
b
a
l
a
n
c
e h
a
s cla
i
m
e
d
th
e
maj
o
ri
ty a
n
d
i
s
cl
osel
y ass
o
ci
at
ed wit
h
st
res
s
i
n
swi
t
chi
ng
com
p
o
n
e
n
t
s
. Vol
t
a
g
e u
n
b
al
an
c
e
i
s
a
l
so due
t
o
t
h
e
t
ype
o
f
c
onne
ct
i
on made
fo
r
t
h
e
v
o
lt
age
di
vi
sio
n
.
T
w
o
maj
o
r
t
ypes
of v
o
lt
age
u
n
b
al
a
n
c
e
p
r
o
b
l
e
ms ar
e
obs
erve
d w
h
i
l
e
the
op
e
r
at
i
o
n of ML
I.
T
h
e
y
a
r
e mi
dp
oi
nt
u
nba
la
nce an
d c
e
n
tral
c
a
pa
ci
to
rs di
sc
har
g
e.
V
o
l
t
age
un
bal
a
nc
e le
a
d
s to re
duce
d
o
u
t
p
ut, co
nse
q
u
e
nt
l
y
i
n
c
r
easi
n
g the
me
c
h
a
n
i
c
a
l
st
ress o
n
the
swi
t
c
hes. T
h
is
l
eads
t
o
po
o
r
pe
rfor
m
a
n
ce
o
f
t
h
e
l
o
ad
s a
n
d
pre
m
a
t
ure
fa
i
l
u
r
e
o
f
c
o
m
p
one
nt
s i
n
i
n
ve
rt
er. S
o
lut
i
ons t
o
t
h
es
e a
r
e
modul
at
i
o
n sc
heme
s
[2
0,
2
1
], use
o
f
sw
it
che
d
ca
paci
t
o
r c
onve
rt
ers
[2
2] a
n
d s
w
i
t
c
he
d
ca
pa
ci
to
r
s
wi
th
re
so
na
nt
ope
ra
t
i
on
[2
3,
24
].
Apa
r
t
from
t
h
e ge
ne
ra
l
di
sc
ussi
on
i
n
t
e
rms o
f
TH
D a
n
a
l
yse
s
,
ot
her so
l
u
t
i
on
met
h
o
d
s
as m
e
nt
ione
d
e
a
r
l
i
er a
r
e
del
i
b
e
r
a
t
e
d
onl
y in
a fe
w
pape
rs
o
n
M
L
I
ba
sed
ES
.
I
n
[25]
, Int
e
r-p
has
e
di
sp
osi
t
i
on
Tec
hni
que
is im
pl
ement
e
d
to
co
n
t
rol
t
h
e
ac
ti
ve s
w
it
c
h
es
i
n
t
h
e
ML
I.
In t
h
is
pa
pe
r, a
7-l
e
vel
M
u
lt
i
l
evel
In
ve
rt
er b
a
se
d ES i
s
i
m
p
l
ement
e
d
.
Volt
a
g
e
u
n
b
al
ance
pro
b
l
e
m acr
oss
t
h
e i
n
put c
a
p
a
c
i
tors
in
a
ML
I i
s
a
n
al
yze
d
a
n
d
sol
v
ed
u
s
i
ng
a R
e
s
o
nant
Sw
it
che
d
Ca
pa
ci
t
o
r C
o
n
v
ert
e
r ba
sed
on
sin
u
s
o
i
d
al
P
W
M. T
h
e
i
m
pro
v
i
s
ed
t
o
pol
ogy
is
i
m
ple
m
e
n
te
d
t
o
a
n
a
l
y
z
e
t
h
e
pe
rformanc
e
o
f
a
n
e
l
e
c
t
r
i
c
spri
ng
un
de
r li
ne
vol
t
a
ge
va
ri
a
t
i
ons. Rema
rk
abl
e
feat
u
r
e
s
o
f
t
h
e
pro
p
o
s
ed
t
o
pol
og
y
are
ma
i
n
ta
ini
n
g
v
o
l
ta
ge
bal
a
nc
e i
n
i
n
p
u
t
c
a
pac
i
t
o
rs a
n
d red
u
ct
i
o
n of
po
we
r c
o
m
p
o
n
e
nt
s.
2.
OPERAT
ING
PRI
N
CIPL
E
OF ES A
N
D MLI
El
ec
t
r
i
c
Sp
rin
g
i
s
t
h
e ne
w v
o
l
t
a
ge
c
o
mpe
n
sa
t
i
ng
devi
ce
e
m
plo
y
ed
i
n
s
m
a
r
t
grid
s u
s
i
ng d
e
ma
n
d
si
de
mana
ge
me
nt.
This c
u
st
om
po
we
r
d
e
vic
e
i
s
con
n
ec
t
e
d i
n
se
ri
es
wi
t
h
a l
e
ss volt
a
ge
sensi
t
i
v
e l
o
a
d
l
i
k
e
r
e
fr
ig
e
r
at
o
r
,
mu
sic
syste
m
,
e
t
c
.
th
a
t
h
a
v
e
inb
u
ilt S
w
i
t
ch
ed Mo
d
e
Pow
e
r
S
u
p
p
l
y
c
i
r
c
u
i
t to
wi
th
stan
d
vo
lt
ag
e
varia
t
i
o
ns.
Thi
s
com
p
rise
s
a
sma
r
t
loa
d
. Smart l
o
a
d
i
s
c
o
n
n
ec
te
d
a
c
ros
s
v
o
l
t
a
g
e se
nsi
t
i
v
e l
o
ad
, te
rm
ed as
crit
i
cal
l
o
ad, t
o
ma
i
n
ta
in
v
o
l
t
a
g
e c
o
n
s
t
a
nt
.
E
S
se
nse
s
t
h
e
v
o
l
t
age
fl
uct
u
a
t
i
ons
in
PC
C
a
n
d ope
rat
e
s a
n
a
l
o
g
o
u
s
to
me
ch
an
i
c
a
l
sp
r
i
n
g
.
O
p
e
r
at
i
o
n o
f
ES
wi
th
ha
lf-bri
dge i
n
ve
rt
er, f
u
ll
bri
dge
i
nve
rte
r
,
ne
ut
r
a
l
point
c
l
a
m
pe
d i
nve
rt
e
r
su
ff
er
ed fr
om h
i
gh
TH
D
,
d
i
st
o
r
tion
i
n
ou
tput
vo
l
t
ag
e
a
n
d
hig
h
e
r
st
ress on
s
w
i
t
c
h
es. M
L
I i
m
p
l
e
m
en
te
d in
t
h
is
pape
r
is a
7
-
l
e
ve
l
i
n
ve
rte
r
t
o
ove
rc
ome
t
h
e
dra
w
ba
cks
of t
h
e
ea
rli
e
r
me
n
t
i
one
d t
o
p
o
lo
gi
es.
Vol
t
a
ge
s
o
b
t
a
i
n
ed
are
,2
,
,0
,
,
2
,
. A
not
her maj
o
r bene
fi
t of
real
i
z
i
n
g
7
-
le
vel
o
u
tp
ut
volt
a
ge
wi
th
t
h
is to
pol
og
y i
s
red
u
c
t
i
o
n i
n
nu
mbe
r
of
pow
e
r
s
w
i
t
c
h
e
s
. It
is ac
hie
v
ed
wit
h
onl
y
8
p
o
w
e
r s
w
i
t
c
h
es
i
n
com
p
ari
s
on
w
i
th t
h
e
12 s
w
i
t
c
he
s req
u
i
r
e
d
w
i
t
h
a c
a
s
c
a
d
ed
mult
i
-
ce
l
l
i
nverte
r
, di
o
d
e-cl
am
pe
d i
n
vert
er
,
ca
paci
t
o
r
cl
am
ped i
nve
rte
r
.
P
h
a
s
e
dis
p
osit
i
on t
e
c
h
niq
u
e
i
s
a
ppli
e
d
t
o
ge
ne
rat
e
7 c
a
rrie
r
t
r
i
a
n
g
ul
ar si
g
n
al
s suc
h
t
h
at
t
h
e ba
nd
s t
h
ey
occ
u
p
y
ar
e
c
ont
in
u
o
u
s
a
nd
t
h
ei
r fre
que
ncy is a
b
out
3
00 ti
mes
mo
re
t
h
an t
h
e refe
renc
e
signa
l.
Re
fere
nce
si
g
n
al
i
s
a
si
ne
wave
o
f
50
Hz
fre
q
uenc
y
gene
rat
e
d
b
y
t
h
e
c
ont
rol
l
er
of
ES,
a
s
s
h
o
w
n
i
n
Fi
gu
re
1.
R
e
fe
renc
e
si
g
n
al
i
s
cont
i
n
u
o
u
sl
y com
p
a
r
e
d
w
i
t
h
ea
ch of t
h
e
ca
rri
e
r w
a
ves
t
o
gene
rat
e
ga
te
s
i
gna
l
s
to
th
e
sw
itc
h
e
s i
n
th
e
MLI.
Fi
gu
re 2
i
l
lust
ra
te
s
th
e si
ng
le
p
h
a
se
7
-
lev
e
l DC
-AC
co
nv
er
ter
w
ith v
o
lta
g
e
bal
a
nc
in
g
ci
rc
u
i
t
an
d
Ta
ble
1
pre
s
e
n
ts t
h
e swi
t
c
hi
n
g
c
o
mbi
n
at
i
o
ns re
qui
red
to
ge
nerat
e
t
h
e
7-
l
e
ve
l
out
put
vol
ta
ge
o
f
the
ML
I. Fi
gu
re
3 i
l
l
ust
r
at
e
s
t
h
e com
p
aris
on
of t
h
e n
u
mbe
r
of
vari
ou
s
c
o
mp
one
nts re
qu
i
r
e
d
in
vari
ous
t
y
pe of
i
nve
rt
ers
t
o
o
b
t
a
in
7
-
l
e
vel
MLI
out
put v
o
lt
age
.
DC
S
1
S
3
S
5
S
7
S
8
S
6
S
4
L
r1
L
r2
C
r1
C
r2
S
b1
S
b2
S
b3
S
b4
S
b5
S
b6
C
1
C
2
C
3
D
4
D
1
D
3
D
2
Lo
a
d
S
2
Fi
gu
re
1.
S
i
m
u
l
a
t
e
d
mo
del
of mul
t
i
l
eve
l
in
ve
rt
er
wi
th RS
C
C
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
o
w
Elec &
Dri Sy
st
I
SSN
: 2
0
8
8
-8
69
4
En
ha
nce
m
ent
of
v
o
lt
a
g
e
reg
u
l
ati
on usi
n
g
a
7-l
eve
l i
n
ve
rt
er b
a
se
d
e
l
e
c
t
r
ic
spri
ng w
i
t
h
…
(K.
K
.
Dee
p
i
k
a
)
5
57
Fig
u
r
e
2
.
Sch
e
m
a
t
i
c
d
i
st
ri
bu
tio
n
syst
em
ES
, M
L
I
an
d r
e
sistiv
e
lo
ad
Fi
gu
re
3.
C
o
mpa
r
i
s
on o
f
c
o
m
pone
nts f
o
r
7-l
e
vel
in
ve
rt
e
r
Not
a
ti
o
n
s use
d
in Fi
gu
re
2 a
r
e
:
V
dc
: i
n
pu
t
DC vo
lta
g
e
S
b1
, S
b2
, S
b3
,
S
b4
, S
b5
, S
b6
: B
r
i
d
g
e
sw
it
che
s
L
r1
,
C
r1
:
reso
na
nt
el
em
ent
s
fo
r
R
S
C
C
1
L
r2
,
C
r2
:
reso
na
nt
el
em
ent
s
fo
r
R
S
C
C
2
I
b1,
I
b2
:
bri
dge
c
u
rre
n
t
s
I
n1,
I
n2
:
no
d
e
c
u
rre
nts
,
,
:
c
a
p
ac
ito
r
vo
lta
g
e
s
=
= V
dc
/3 (
1
)
F
o
r th
e
si
mu
late
d
Mu
lti
lev
e
l I
n
v
e
r
t
er
w
i
t
h
R
S
C
C
a
s
show
n
in
t
h
e
Fi
gure
2, th
e
sw
it
c
h
i
n
g
t
a
b
l
e
is
d
e
t
a
i
l
ed
in
Ta
bl
e 1
.
To ob
ta
in th
e 7 le
v
e
l
s
o
f
ou
tpu
t
vo
l
t
a
g
e
s
,
sta
t
e
s
of
t
h
e sw
itch
e
s
con
s
t
itu
t
i
n
g
RS
CC
- S
b1
,
S
b2
, S
b3,
S
b4
, S
b5
, S
b6
and
the
M
O
S
F
ETs,
d
i
od
e
s
in
M
L
I
ar
e il
lu
str
a
te
d
i
n
Ta
b
l
e
1.
Ta
b
l
e
1
.
S
w
itch
i
ng
Tab
l
e
for
M
u
l
tile
v
e
l I
nve
r
t
er
w
ith
RS
C
C
Sw
it
c
h
Lev
e
l
S
b
1
S
b
2
S
b
3
S
b
4
S
b
5
S
b
6
1
0
1
0
0
0
1
0 0
0 1
0 0 1
0
1
0
0
2
1
0
0
0
1
0
1
0 0
1 1
0 0 1
0
0
0
1
1
0
0
0
0
1
1
1 0
0 1
0 0 1
0
0
0
0
0
0
1
1
1
1
0
0
0 0
0 0
1 0 1
0
0
0
0
0
0
0
1
0
1
0
1 0
0 0
1 1 0
1
0
0
0
2
0
1
0
0
0
1
0
1 1
0 0
1 1 0
0
0
1
0
1
0
0
0
0
1
1
1 0
0 0
1 1 0
0
0
0
0
Fo
r vo
lt
ag
e
lev
e
l
:
S
b1
and
S
b3
of RS
CC
-1
a
r
e
i
n
ON
p
o
siti
o
n
a
n
d th
e c
u
r
r
ent
fl
ows
t
h
ro
ugh
c
a
p
a
c
i
t
o
r
C
1
a
n
d it
g
e
ts
c
h
ar
ge
d. T
h
e
c
a
pac
i
t
o
r
C
1
g
e
ts d
i
sc
h
a
rg
ed
thr
oug
h
sw
itc
h
e
s
S
1,
S
5
a
nd
its
ret
u
rn
p
a
th
i
s
throu
g
h
S
8
a
nd D
1
.
Fo
r vo
lt
ag
e
lev
e
l
2
:
S
b1
and S
b5
of
RSCC
-1 an
d
RSCC
-2 res
p
e
c
t
i
ve
ly a
r
e ON and
he
nc
e ca
p
aci
t
o
r C
1 a
n
d
C
2
a
r
e ch
ar
g
e
d
.
The
c
a
p
ac
it
o
r
s
get
di
sc
har
g
e
d
i
n
f
o
r
w
a
r
d
pa
t
h
of
S
1,
S
5
a
n
d lo
a
d
,
r
e
tu
r
n
p
a
t
h
t
h
ro
ugh
S
4
and
D
4.
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
:
5
5
5
– 56
5
55
8
Fo
r vo
lt
ag
e
lev
e
l
:
Sw
it
che
s
S
b1
and
S
b6
o
f
R
S
C
C
-
1
a
n
d
R
S
CC-2
are
i
n
ON
posi
tio
n
an
d c
h
arg
e
s
al
l th
e C
1,
C
2
, C
3
. T
h
ey
w
ill d
i
s
c
h
a
r
g
e
th
ro
ugh
sw
i
t
ch
es S
1
an
d S
5
a
n
d t
h
e
re
tu
r
n
pa
t
h
t
h
r
o
ug
h
a
nd
. Si
nc
e a
l
l t
h
e
capa
c
i
t
o
rs a
r
e
di
scha
rgi
n
g
.
S
o
, t
h
e
out
put
v
o
l
t
a
g
es
a
r
e
Fo
r vo
lt
ag
e
lev
e
l
-
:
Sw
it
che
s
S
b1
a
nd S
b6
a
r
e
in co
ndu
c
tin
g mode
and
C
3
ge
ts c
h
a
r
ge
d.
It
ge
t
s
di
scha
r
g
e
d
t
h
r
o
u
g
h
D
1
an
d
S
7
i
n
f
o
r
w
ar
d pa
t
h
a
nd
t
h
r
o
u
gh l
o
ad a
n
d S
2
, S
6
is t
h
e re
tur
n
pa
t
h
.
T
h
e
cur
r
e
nt
dir
ect
i
on t
h
r
oug
h t
h
e
l
o
a
d
c
h
an
ges
an
d he
nce t
h
e
v
o
l
t
a
ge
i
s
.
Fo
r vo
lt
ag
e
lev
e
l
-2
:
Sw
it
che
s
S
b2
an
d
S
b6
o
f
R
S
CC-
1 a
nd RS
CC
-2 r
e
sp
ec
ti
v
e
ly ar
e in op
er
at
in
g mod
e
and
t
h
e
c
a
p
a
ci
tor
s
C
2
, C
3
ge
ts di
sc
har
g
e
d
. The
y
di
scha
r
g
e
t
h
ro
ug
h
t
h
e
p
a
t
h
D
3
, S
3
and
S
7
i
n
t
h
e f
o
r
w
a
r
d
di
r
e
c
t
i
on a
n
d
,
are
i
n
r
e
t
u
r
n
di
re
ct
i
on.
Fo
r vo
lt
ag
e
lev
e
l
:
Sw
it
che
s
S
b1
a
nd S
b6
a
r
e in
ON p
o
si
t
i
on a
nd
t
h
e capa
c
i
t
ors
C
1,
C
2
, C
3
g
e
ts ch
ar
g
e
d
.
T
h
e c
a
p
a
ci
to
r
s
w
ill
d
i
sc
h
a
rge
th
ro
ugh
S
1
an
d S
7
i
n
fo
rw
ar
d p
a
t
h
S
2
and
S
6
in r
e
tur
n
p
a
t
h
.
Fo
r vo
lt
ag
e
lev
e
l
ze
ro
:
Sw
it
che
s
S
b2
, S
b3
, S
b4
, S
b5
are
sho
r
t
ci
rc
ui
t
and R
S
C
C
-
1
a
n
d RSCC
-2 are
i
n
w
o
rkin
g m
o
de. T
h
ere
is
no
c
u
rre
n
t
f
l
o
w
t
h
ro
u
g
h
a
n
y of
t
h
e ca
paci
t
o
r
he
nc
e c
h
ar
g
i
ng
or
di
sc
har
g
ing.
D
u
e t
o
t
h
e
gat
e
pulse
s
gi
ven
t
o
switches S
5
an
d S
7
o
f
MLI
a
r
e
in
O
N
po
si
tion
an
d t
h
e
c
u
r
r
e
n
t
f
l
o
w
s
thr
ough
th
e lo
ad
.
In t
h
i
s
pa
pe
r
,
pr
obl
e
m
o
f
vo
lt
a
g
e u
nbal
a
nc
e i
n
i
n
put
ca
p
a
ci
t
o
rs i
s
ove
r
c
ome
b
y
usi
n
g a
vol
ta
ge
ba
la
nci
n
g
c
i
r
c
ui
t
c
a
l
l
e
d
R
e
s
o
nant
S
w
i
t
c
hi
n
g
C
a
pa
ci
to
r
C
o
n
v
ert
e
r
(
R
S
C
C
)
as sho
w
n
i
n
F
i
gur
e
4
.
Ba
sed
on
t
h
e
v
o
lta
g
e
le
v
e
l
of
mu
lti
le
v
e
l
inv
e
rt
er,
th
e topo
lo
g
y
of
RSCC c
h
a
n
g
e
s. R
S
C
C
c
i
r
c
u
i
t im
ple
m
e
n
ted
i
n
th
is p
a
p
e
r
ha
s se
ve
n m
o
d
e
s of
o
p
er
a
t
i
o
n
whe
n
c
o
mpa
r
ed wi
t
h
the
c
o
nve
nt
i
o
nal
RS
CC
whi
c
h has
onl
y tw
o m
o
de
s.
I
t
i
s
r
eal
i
z
e
d
t
o
ach
i
e
ve
ba
la
nce
of
v
o
l
t
a
ges
a
m
o
n
g
t
h
e
i
n
put
ca
p
aci
t
o
rs
co
n
n
ec
te
d
i
n
seri
es
.
T
hus
,
v
o
l
t
a
ge
ba
l
a
nc
e
of
i
n
put
ca
p
a
ci
t
o
rs i
s
a
c
hi
e
v
e
d
.
Fi
gu
re
4.
C
onv
e
n
ti
onal
R
S
CC
c
i
r
c
ui
t
The v
o
lt
age
b
a
l
a
nce ci
rc
uit
t
r
a
n
s
f
ers el
ec
tr
ic
c
h
arge
bet
w
e
e
n
t
h
e ca
pa
ci
t
o
r mod
u
l
e
s wit
h
a
so
ft
swi
t
c
hi
n
g
o
p
e
r
a
t
i
on w
h
i
c
h
re
sult
s i
n
re
duc
e
d
p
o
w
er
los
s
and e
l
e
c
t
r
oma
gne
ti
c i
n
duct
i
o
n.
A p
h
a
s
e s
h
if
ti
ng
co
n
t
ro
l
me
thod
en
ab
le
s to i
m
pr
ov
e volta
g
e
regu
l
a
ti
o
n
p
e
r
f
or
mance
.
It r
e
du
c
e
s pow
e
r
l
o
ss a
nd
e
l
e
c
t
r
oma
gne
ti
c
ind
u
c
t
i
o
n
.
The ma
in
dif
f
e
r
e
nce
bet
w
e
e
n
swi
t
c
hi
ng
ca
paci
t
o
r c
o
n
v
ert
e
r
a
n
d
re
son
a
nt
swi
t
c
hi
n
g
ca
p
a
ci
tor
co
n
v
er
t
e
r i
s
t
h
at
i
n
RS
CC
, t
h
er
e i
s
a
n
ad
di
ti
ona
l
smal
l i
nduct
o
r t
o
ac
hie
v
e
a soft
swi
t
c
hi
n
g
o
r
r
e
so
nant
o
p
e
r
a
t
ion.
RS
CC
e
n
a
b
l
e
s cha
nge
of
di
re
ct
i
o
n o
f
po
wer
fl
o
w
f
r
o
m hi
g
h
e
r
t
o
lowe
r
vol
t
a
ge
by
usi
n
g
f
i
xe
d pe
ri
o
d
ic
ga
te
si
gnal
.
It
co
nsi
s
t
s
o
f
6 s
w
i
t
c
hi
ng
de
vi
ce
s -
,
,
,
,
,
and
4
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
o
w
Elec &
Dri Sy
st
I
SSN
: 2
0
8
8
-8
69
4
En
ha
nce
m
ent
of
v
o
lt
a
g
e
reg
u
l
ati
on usi
n
g
a
7-l
eve
l i
n
ve
rt
er b
a
se
d
e
l
e
c
t
r
ic
spri
ng w
i
t
h
…
(K.
K
.
Dee
p
i
k
a
)
5
59
reso
na
nt
ci
rc
ui
t
el
ement
s
-
,
,
,
.
Th
is
con
f
i
g
ur
at
io
n
su
p
p
re
sse
s
sp
i
k
e
c
u
rr
en
t
s
a
n
d po
w
e
r
lo
sse
s
an
d
el
ec
tr
o
m
ag
n
e
t
i
c
ind
u
c
t
i
o
n.
Di
ff
e
r
en
t mod
e
s of op
era
t
i
o
n
o
f
RS
CC w
ill
le
ad
t
o
d
i
ff
e
r
en
t
le
v
e
ls
o
f
v
o
lt
ag
e
s
wi
t
h
a
n
e
f
fi
ci
e
n
t
w
a
y
o
f
vol
ta
ge
b
a
l
a
nci
n
g
a
c
ross
the
ca
pac
i
t
o
rs.
Tw
o
mo
d
e
s
are
e
x
pla
i
ne
d
bel
o
w:
Mode-
1
:
I
n
t
h
i
s
mode
,
R
S
C
C
ope
rat
e
s a
s
f
o
l
l
ows
t
o
obt
ai
n a v
o
l
t
a
g
e o
f
. S
w
i
t
c
h
es
S
b1
, S
b
2
are
i
n
cl
ose
d
co
nd
i
tio
n,
and
cu
rr
en
t
w
i
l
l
flo
w
in
th
e
r
e
so
n
a
n
t
c
i
r
c
u
it
of
RSCC
1
,
as
sh
own
i
n
F
i
gur
e 5
.
(2
)
Ap
pl
yi
ng
K
V
L
t
o
F
i
gu
re
3,
w
e
get
0
(3
)
Fr
om (
1
)
(4
)
Mo
de -7
:
In
t
h
is mo
de
o
f
ope
rat
i
o
n, ne
gat
i
v
e v
o
l
t
a
g
e peak
o
f
–
V
dc
is
ob
ta
in
ed
. Sw
itch
i
ng
d
i
a
g
r
a
m
is
as
sh
own
in
Fi
gure
6
.
S
w
itc
h
e
s S
b6
and
S
b1
a
r
e
O
N
po
si
ti
on a
n
d
th
e
c
u
r
r
e
nt
wi
l
l
f
l
ow
t
h
r
o
ug
h
b
o
th
R
S
C
C
-1
an
d RS
CC
-2
.
F
i
g
u
r
e
5
.
O
p
e
r
a
t
i
on of
R
S
C
C
in m
ode
1
Fi
gu
re
6.
O
p
er
at
i
on of
RS
CC
i
n
mode
6
(5
)
Ap
pl
yi
ng
K
V
L
i
n
F
i
gu
re
6,
w
e
get
0
(6
)
Fr
om (
1
)
+
(7
)
Fr
om (
5
), w
e
get
(8
)
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
:
5
5
5
–
565
56
0
3.
R
E
S
U
LTS
AND ANA
LY
S
I
S
To a
n
a
l
yz
e t
h
e o
p
erat
i
o
n
o
f
ES
wit
h
M
L
I
i
n
ne
ut
ral
,
u
nde
rvol
t
a
ge
a
n
d o
v
e
r
vol
ta
ge
con
d
it
i
o
n
s
,
simul
a
t
i
ons are
carri
e
d
out
i
n
MATLAB
20
1
1
. To
kee
p
t
h
e
ana
l
ysi
s
si
mpl
e
, cri
t
i
cal
an
d
non
-cri
t
i
cal
loa
d
s
a
r
e
sel
e
c
t
e
d
t
o
be
re
sist
i
v
e.
S
p
eci
fi
ca
ti
ons
o
f
t
h
e
di
st
ri
b
u
t
i
on l
i
n
e
, ES a
nd l
o
a
d
s i
s
det
a
i
l
ed in
Tabl
e 2
.
The
o
v
era
l
l
ana
l
ysi
s
c
a
n
be
di
vi
de
d
i
n
t
o
3
parts:
i
)
U
n
d
e
rv
ol
t
a
ge
by
2
0
%
from
0
.
5 t
o
1 se
c.
i
i
)
O
v
e
r
volt
a
ge
b
y
2
0
%
from
1.5 t
o
2 sec. ii
i
)
Ne
ut
ral
d
u
ri
n
g
remai
n
in
g t
i
me
. The
ma
in
obj
ec
ti
ve i
s
t
o
certi
fy t
h
e
o
p
e
rat
i
on of
M
L
I
in a
ll
t
h
e m
o
des
o
f
ES.
This
is
de
mo
nst
r
at
ed
i
n
t
e
rms
o
f
T
H
D
anal
ysi
s
an
d
t
h
e v
o
l
t
a
ge
ba
l
a
nci
n
g ac
hi
e
v
ed
i
n
t
h
e
i
nput
c
a
p
a
c
i
t
o
rs. In
put
v
o
lt
ag
e
t
o
the
MLI i
s
4
0
0
V
DC
a
n
d t
h
e
o
u
t
p
ut
v
o
l
t
a
ge
is
2
2
0
V
R
M
S
.
T
h
e
7
vol
t
a
ge
le
v
e
ls ob
ta
in
ed a
r
e
±13
3
V,
± 26
7
V
,
±
40
0
V
,
0
V
.
Th
e
b
l
o
c
k d
i
ag
r
a
m of t
h
e
ov
e
r
al
l test sy
st
em show
n in
Fi
gu
re
7.
Tab
l
e
2
.
Sy
st
e
m
Sp
ec
if
ic
a
tion
s
Spec
if
ica
tions of
Di
str
i
bution L
i
ne,
Non-
cr
itic
al l
o
a
d
u
n
it
S
p
ec
ifi
c
a
tions of Ele
c
t
r
ic
Spr
i
ng
Li
ne I
ndu
c
t
a
n
ce
(
m
H
/
km)
1.
22
Lo
w
-
p
a
ss
fi
lter
I
nduct
a
nc
e (
m
H)
5
Li
ne Re
sista
n
ce
(
/km)
0.
1 C
a
pa
cit
a
nce
(
μ
F) 1
3
.
2
Non-
cr
itic
al Loa
d
(
50.
5
PI
Contr
o
lle
r
(
I
niti
al va
lues)
K
p
2
Cri
tic
al loa
d
Z
(
53
K
i
1.
5
Wi
th
th
e v
a
r
i
ati
o
n
s
in
th
e
rea
l
po
w
e
r
f
e
d
in
t
o
t
h
e
sy
ste
m
by
th
e DG
s, v
o
l
ta
g
e
le
v
e
ls ar
e
aff
e
cte
d
.
Re
sult
s are
sh
o
w
n
f
o
r t
h
e si
mul
a
t
i
o
n
c
a
r
rie
d
o
u
t
for 1.
5 s
econ
d
s
,
i
n
w
h
i
c
h d
u
e t
o
rea
l
po
we
r fe
d b
y
t
h
e D
G
s
is
c
h
a
n
g
e
d
f
r
om 1
.
8
KW
t
o
1.
1 KW a
t
0
.
5
se
c a
nd
th
en b
ack
t
o
1
.
8 KW at
1 se
c
.
Th
is is tr
a
ced w
i
th th
e
R
M
S
val
u
e
o
f
c
r
i
t
i
c
a
l
l
o
ad
v
o
l
t
a
g
e
wi
t
hout
E
S
c
o
nt
rol
hi
ghl
i
g
ht
e
d
i
n
F
i
gu
re
8
a
n
d
F
i
gu
re
9.
Crit
i
cal
l
o
ad
re
qui
res
to
b
e
op
er
at
ed
at
2
2
0
vo
lt
s, bu
t
it
f
a
ll
s t
o
185
v
o
l
t
s
.
Co
n
t
ro
ll
er
o
f
th
e
ES d
e
te
ct
s
th
e
und
e
r
v
o
l
tag
e
an
d
op
e
r
at
e
s
t
o
regu
la
te
th
e
lin
e
v
o
l
t
a
ge
to
220
V
.
Fi
gu
re
10 an
d F
i
gu
re 11
hi
gh
l
i
ghts
t
h
at
ES
ope
rat
e
s
i
n
a
b
out
0.
0
8
sec a
nd re
st
ores
t
h
e
l
i
n
e
v
o
l
t
a
ge t
o
rat
e
d
v
a
lu
e
.
RM
S
Vo
lt
ag
e
a
c
ro
ss
ES
is ill
u
s
tr
at
e
d
in
Fi
g
u
r
e
12
. A
s
th
e vo
lt
age
g
e
ts co
mp
ensat
e
d
t
h
e
r
e
w
i
l
l
b
e
no
e
f
f
e
ct of
ES on
th
e sy
s
t
e
m
fr
om 1 se
c. A
t
t=1
se
c
,
pow
er f
e
d
by
DG
s is
r
e
s
t
o
r
e
d
t
o
no
rmal
.
D
u
e
to t
h
e
su
dd
en
cha
nge
i
n
t
h
e
o
p
era
t
io
n
of
fil
t
e
r ca
paci
t
o
r co
mp
one
nt i
n
ES
,
v
o
l
t
a
ge
spi
k
e
occ
u
rs
i
n
Fi
gu
re 1
3
.
To
val
i
da
te
t
h
e pr
o
pose
d
t
o
pol
o
g
y
f
u
rt
he
r,
re
al
p
o
w
er
fe
d
b
y
t
h
e
D
G
s
is
c
h
a
nge
d
from
1.
8
K
W
to
2.5 K
W
at
1.5
se
c and the
n
ba
ck
t
o
1.8
K
W
at
2 sec
.
It
c
a
n be ob
se
rv
ed at
F
i
gu
re 1
4
t
h
at
thi
s
le
ads to a
v
o
l
t
a
g
e
sw
e
ll c
o
nd
it
io
n in
t
h
e
li
n
e
.
In
swe
l
l
c
o
nd
i
tio
n th
e
v
o
l
t
a
g
e
in
cr
ea
se
s t
o
g
r
ea
t
e
r
th
an
th
e r
e
fer
e
n
c
e
vol
ta
ge
a
t
t
=
1
.
5se
c
s. S
o
, ES
re
duce
s
t
h
e
v
o
l
t
age
dip a
n
d
reg
u
l
a
t
e
s the
l
i
n
e
vol
t
a
ge
o
f
t
h
e
s
y
ste
m
.
Fi
gu
re
7. Bl
oc
k
di
ag
ra
m
of
t
h
e o
v
era
l
l te
st s
y
ste
m
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
o
w
Elec &
Dri Sy
st
I
SSN
: 2
0
8
8
-8
69
4
En
ha
nce
m
ent
of
v
o
lt
a
g
e
reg
u
l
ati
on usi
n
g
a
7-l
eve
l i
n
ve
rt
er b
a
se
d
e
l
e
c
t
r
ic
spri
ng w
i
t
h
…
(K.
K
.
Dee
p
i
k
a
)
5
61
Fi
g
u
re
8
.
RMS
v
a
lu
e of c
r
it
ic
al lo
a
d
vo
lta
g
e
, wi
tho
u
t
ES con
t
ro
l
F
i
gu
re
9.
I
n
sta
n
ta
ne
ou
s va
lue
o
f
cr
it
i
c
a
l
l
o
a
d
v
o
l
t
a
ge,
wi
t
h
o
u
t ES
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Int
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lti
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I
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208
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
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088
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94
I
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t J
P
o
w
El
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D
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i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
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5
5
– 56
5
56
4
F
i
gur
e
1
8
.
C
o
mpa
r
i
s
o
n
of
T
HD%
am
o
ngst
va
ri
o
u
s i
n
ve
r
t
e
r
t
o
p
o
l
o
gie
s
f
o
r
ES
c
o
nt
r
o
l
4.
CO
NCL
US
IO
N
V
o
lt
ag
e
r
e
gu
la
tio
n
for cr
it
ic
a
l
lo
a
d
wi
th
7
-
l
e
v
e
l In
v
e
r
t
e
r
b
a
se
d
Ele
c
t
r
i
c
Spr
i
ng
is
p
r
op
o
s
e
d
and
an
a
l
y
s
ed
in
th
is p
a
p
e
r.
An ov
er
al
l
rev
i
e
w
on
th
e p
e
rfo
rman
c
e
of
M
u
lti
le
v
e
l I
n
v
e
r
t
er
i
s
an
a
l
y
s
ed
fo
r va
ri
ou
s
out
put
v
o
l
t
a
g
e
le
vel
s
, al
so
hi
ghli
g
ht
i
ng t
h
e
volt
a
ge
ba
la
nc
i
ng
a
c
h
i
e
ve
d
wi
th Re
s
ona
nt
S
w
it
c
h
i
ng Ca
paci
t
o
r
C
o
n
v
ert
e
r
.
A
n
y
dist
ri
but
io
n syst
em wi
t
h
fl
uct
u
at
i
n
g
re
ne
wabl
e e
n
er
g
y
sou
r
ces
,
w
h
en ope
rat
e
d
wi
th El
e
c
t
r
i
c
sp
r
i
n
g
w
ill
regu
la
te
th
e
c
r
i
tical
lo
a
d
vo
lta
g
e
ef
f
e
c
t
i
v
ely
u
n
d
e
r
t
h
e
r
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s
u
ltin
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v
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lta
g
e
sag
a
n
d s
w
e
l
l
c
o
nd
itio
n
s
.
I
m
pl
ement
a
t
i
o
n of
t
h
e
7-l
e
ve
l
inve
rt
er
re
d
u
c
ed t
h
e
ha
r
m
o
n
i
c
s i
n
t
h
e o
u
t
put
v
o
l
t
a
ge
l
i
mi
ti
ng t
h
e
n
u
m
be
r
of
po
we
r s
w
i
t
c
h
e
s
. S
i
mul
a
t
i
o
ns
have
be
en
do
n
e
o
n
di
st
ri
but
i
o
n
s
y
st
em
wi
t
h
D
G
s
e
q
uip
p
e
d
w
i
t
h
MLI
ba
se
d
ES
u
n
d
e
r lin
e
v
o
lta
g
e
an
oma
lie
s.
Te
ste
d
r
e
su
lts
a
r
e
an
a
l
y
z
e
d
with
THD
%
i
n
c
r
it
ic
al lo
a
d
v
o
lt
a
g
e.
RE
FE
RE
NC
ES
[1]
RS
Rav
i
San
k
ar
,
S
V
J
a
ya K
u
mar
,
KK
Deep
ik
a,
“
M
od
el P
r
ed
ic
tiv
e
Curren
t
Con
t
ro
l
of G
r
id
Con
n
e
c
t
ed
P
V
S
y
s
t
em”
,
In
do
nesian
Jou
r
n
a
l of
El
ec
tr
ica
l
Eng
i
ne
er
in
g a
n
d
Com
p
u
t
er
Sc
ien
ce (I
JEECS),
Vo
l.
2
,
No.
2.
pp
28
5-29
6,
20
16.
[2]
Yo
sh
i
n
a
g
a
,
J.,
Aka
g
i,
S., It
o,
M.
, Ha
ya
sh
i,
Y.
,
Ish
i
b
a
sh
i,
K., &
Ta
ka
ha
si, N. “
V
ol
ta
g
e
fluc
tu
ati
o
n issu
e
o
n
d
i
s
t
ributio
n
sy
stem
a
t
t
i
me
of d
e
mand
r
e
sp
on
se
an
d
c
o
op
eratin
g vo
ltag
e
co
n
t
ro
l me
th
od be
twe
e
n bat
t
ery
energ
y
st
or
a
g
e
sy
st
em
an
d SV
R
.
”
IE
EJ Tran
sac
t
io
ns
on
Po
we
r
a
n
d
En
e
r
g
y
,
Vo
l.
13
6
,
No.
4
,
pp.
4
0
0
-4
09,
2
0
1
6
.
[3]
S
.
S
a
ntoso
,
R.
D
u
gan,
M
.
F
.
M
c
Granag
han
,
and
H
.
W.
B
e
a
t
y
,
Electrica
l P
o
wer
Sy
stems
Q
u
al
ity
,
3rd ed
. New
York
,
N
Y
, US
A
:
McGraw-H
ill,
20
12.
4
R. E. F
e
hr
, ``
P
o
wer qu
ality
,
''
in
I
n
du
st
ri
a
l
P
o
w
e
r Di
s
t
r
i
b
u
t
i
o
n
.
Ho
bo
k
e
n
, NJ
,
U
S
A: Wiley
,
20
16
.
[4]
R.
E.
Fe
hr
,
`
`
Power qualit
y
,
''
in
In
du
strial Po
w
e
r
D
i
s
t
ribu
tion
.
H
obo
ken
,
NJ, USA:
Wiley,
2
0
1
6
.
[5]
A.
J. Rosc
o
e
a
n
d
G.
Au
lt, “
S
uppo
rt
in
g
h
i
g
h
pe
ne
tr
ati
o
n
s
o
f
re
n
e
wa
bl
e ge
ne
rat
i
on v
i
a im
pl
e
m
e
n
ta
ti
on o
f
re
a
l
-ti
m
e
ele
c
tricity
p
r
i
c
in
g an
d
d
e
m
a
nd
r
e
sp
ons
e,”
I
E
T
Re
n
e
wable
Power
G
e
ner
a
tion
, Vo
l. 4, No.
4
,
pp.
36
9
–
38
2
,
2
0
1
0
.
[6]
C.
K.
Le
e, S
.
N
.
Li,
and
S
.
Y
.
R.
Hui, “A
des
i
g
n
me
tho
dolog
y
fo
r
smart
ligh
ting
sy
stem
s
p
o
wered
by
weak
ly
re
gu
la
te
d
re
n
e
wa
bl
e po
we
r gird
s,”
I
E
E
E
T
r
an
sa
c
t
io
ns
on
S
m
ar
t
G
r
id
,
Vo
l.
2,
No.
3, pp
.
54
8–
55
4
,
S
e
p
.
2
0
1
1
.
[7]
P
.
P
a
lensk
y
and
D
.
Dietr
i
ch, “De
m
an
d side
man
a
gemen
t
:
D
e
man
d
resp
on
se, in
te
l
l
igen
t ene
r
gy
sy
stems
,
and
s
m
art
loads,
”
IE
E
E
Tr
ans
.
Ind.In
f
o
r
m
at
ics
,
vol
. 7
,
n
o
.
3
,
pp
.
38
1–
388
, 2
0
1
1
.
[8]
Q.
W
a
ng,
M.
Ch
e
n
g
,
Y. Jia
n
g
,
W.
Z
uo a
nd G.
Buj
a
,
"A
Si
m
p
l
e
Ac
ti
ve
a
n
d
Rea
c
tiv
e
P
o
we
r Co
nt
ro
l fo
r
A
p
p
l
icatio
ns
o
f
S
i
n
g
le-P
hase El
ectr
i
c S
p
ring
s,"
i
n
IEEE
T
r
a
n
s
a
ctio
ns
on
In
du
str
i
a
l
El
ectr
oni
cs
,
Vo
l. 65
,
N
o
. 8,
p
p
.
62
91
-6
30
0,
Au
g. 2
0
1
8
.
[9]
S.
Y.
R
.
Hu
i, C
.
K
.
Le
e,
Fu,
“
E
le
ctr
i
c
s
p
rin
g
s
–
A n
e
w smart gr
id tech
no
lo
gy,
”
IEEE T
r
a
n
s
.
Sm
art Grid
, Vo
l. 3,
No
.
3,
S
e
p
t
emb
e
r.
20
12
,
pp
:
155
2–
15
61
.
[10]
Tan, S
i
ew
-Cho
n
g
& Lee
,
Chi
K
w
an
& Hu
i, S
.
Y
.
“G
en
era
l
S
t
e
a
d
y
-S
tate An
alys
is
an
d Con
t
ro
l P
r
incipl
e
o
f
E
l
e
c
tric
S
p
rin
g
s w
i
th
Ac
tive
an
d
R
eactiv
e Po
wer
Comp
e
n
satio
n
s
.
”
Powe
r
Electro
ni
cs, IEEE T
r
a
n
s
a
ction
s
o
n
. Vol. 28
, pp.
39
58
-3
96
9,
20
1
3
.
1
0
.1
1
0
9
/
T
P
EL
.
2
0
1
2
.
22
27
82
3.
[11]
Son
i
,
Ja
ya
nt
ik
a
&
Pa
n
d
a,
Sa
nji
b
. “
E
le
c
t
ri
c Sp
rin
g
fo
r Vol
t
a
g
e a
nd P
o
we
r Sta
b
ili
t
y
a
n
d
Po
we
r Fac
t
o
r
Co
rre
c
ti
o
n
.”
IEE
E
Tran
sac
t
ions on
Ind
u
stry
Ap
pl
ic
a
tio
ns
.
p
p
.
1
-
1,
20
17.
1
0
.1
109
/T
IA.
2
01
7.
2
6
8
1
9
7
1
.
[12]
D
eepika
K
,
V
i
j
a
yaku
mar
J
,
G
K
Rao,
Ch
aitany
a
S
,
"A
dap
t
iv
e PI
cont
rol of
Elect
r
ic Spri
ngs
for
V
o
lt
ag
e Regu
l
a
t
i
o
n
u
n
d
e
r Dy
namic
Lo
ad Ch
ang
e
s
"
,
In
te
rna
t
i
o
n
a
l
J
o
u
r
na
l of
Inn
o
v
a
t
i
v
e
Te
c
h
n
o
lo
gy
and
E
x
p
l
o
r
i
ng Engi
ne
e
r
i
n
g
, Vol
,
8
No
.
1
0
, p
p
. 10
51-1
0
5
6
,
20
19.
[13]
Ji
h-Sheng
Lai and F
a
ng Z
h
en
g P
e
ng, "M
ul
tilevel converter
s-a ne
w br
eed
of power conv
ert
e
rs,
"
i
n
IE
EE
T
r
an
sactio
ns
on
Ind
u
s
t
r
y
Ap
pl
ica
t
io
ns
,
vol. 3
2
, no.
3,
p
p
. 5
0
9
-
51
7,
Ma
y
-
Ju
n
e
1
9
9
6
.
d
o
i
:
1
0
.
1
10
9
/
28.
50
21
61
[14]
Ch
aud
huri
N
R
,
Lee
CK
,
Bal
a
rk
o
Ch
audh
uri
,
“D
yn
amic mod
e
l
i
n
g
of
electr
i
c
s
p
ri
ng
s”
IE
EE
T
r
an
sactio
ns
o
n
Sm
art
Gr
id
,
Vo
l. 5, No
.
5
, Se
pt
. pp
:2
45
0
–
8
,
2
0
1
4
.
[15]
H
a
sabelrasu
l
, H
a
s
h
im &
Yan
,
X
i
an
gw
u. “Com
pariso
n
o
f
M
u
lti
carrier P
W
M
Tech
niqu
es fo
r C
a
scad
ed
H-Brid
g
e
M
u
lt
il
ev
el
I
n
ver
t
er
.
”
In
ter
n
a
t
ion
a
l J
o
ur
na
l o
f
Po
wer Electron
i
cs
an
d Dr
ive
S
y
stem
s (IJPED
S
)
. Vol
,
8,
No.
2,
p
p
.
86
1-8
6
8
,
20
17.
[16]
Ma
dh
u
s
u
d
a
n
a
Re
dd
y, B &
Re
d
d
y
,
Y
&
Vi
ja
ya
Ku
ma
r, M.
“Mod
e
l
i
n
g
a
nd sim
u
l
a
ti
on o
f
1
27
le
v
e
l
o
p
t
i
mal
mul
tilevel
i
nver
t
er
wit
h
lower numb
er of swit
ches and mini
mum T
H
D.
”
Intern
atio
nal
J
o
ur
nal o
f
Po
w
e
r
Ele
c
tron
ics
an
d
Drive Sys
t
em
s (I
JPEDS
)
.
Vo
l. 9,
No.
4, pp
. 17
65
-17
7
3
,
20
18.
[17]
Ch
etn
a
J
a
ng
ad
e, K
a
ly
ani G
a
jb
hi
ye, P
a
v
a
n
F
u
k
e
, P
a
yal
Dah
i
wal
e
,S
amrud
d
h
i
Bh
arat
i, Tin
a
Patil
, S
.
P
.
G
a
w
a
nd
e,
“
V
o
l
t
a
ge
re
g
u
l
a
ti
on
a
n
d
dro
op c
o
nt
ro
l
o
f
Elec
t
r
ic
sp
ri
ng using
sin
g
l
e
p
h
a
s
e c
a
s
ca
de
d H-b
r
id
ge
in
ve
rte
r
for
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