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.
11
,
No.
2
,
A
pr
il
2021, p
p. 11
30
~
1142
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v11
i
2
.
pp1130
-
11
42
1130
Journ
al h
om
e
page
:
http:
//
ij
ece.i
aesc
or
e.c
om
A
n
ovel
f
uzzy bas
ed
c
ont
rolle
r to
r
educe
c
i
rc
ul
ating
c
ur
re
n
ts in
p
arallel
i
nterleav
ed
c
onve
rter
c
onnected t
o t
h
e
g
rid
Sravanth
y
G
addame
edhi
1
,
P. S
ri
ni
va
s
2
1
Depa
rtment of
El
e
ct
ri
ca
l
and
E
l
ec
tron
ic
s E
ng
ineeri
ng
,
S
ree
N
idh
i
I
nstit
u
te of
S
c
i
enc
e
and
T
ec
hno
lo
gy
,
H
y
der
aba
d
,
T
ela
ngana
,
Indi
a
2
Depa
rtment of
El
e
ct
ri
ca
l
Eng
in
ee
ring
,
Univ
ersity
Co
llege
o
f
Eng
ine
er
ing, Osm
ani
a
Univ
esity
,
H
y
der
aba
d
,
T
ela
ngana
,
Indi
a
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Feb
28
, 202
0
Re
vised
A
ug
1
2
, 2
020
Accepte
d
Se
p 22
,
2020
Thi
s
pape
r
exhi
b
it
s
suppress
ion
s
tra
t
eg
y
of
low
fr
eque
nc
y
c
irc
u
la
t
ing
cur
ren
t
c
o
m
p
o
n
e
n
t
s
f
o
r
p
a
r
a
l
l
e
l
i
n
t
e
r
-
l
e
a
v
e
d
c
o
n
v
e
r
t
e
r
s
.
H
e
r
e
i
n
v
e
r
t
e
r
s
a
r
e
p
a
r
a
l
l
e
l
i
z
e
d
b
y
m
a
g
n
e
t
i
c
a
l
l
y
c
o
u
p
l
e
d
i
n
d
u
c
t
o
r
s
.
T
r
a
d
i
t
i
o
n
a
l
l
y
,
c
a
r
r
i
e
r
int
erlea
v
ed
tec
hnique
was
u
s
e
d
t
o
g
e
t
l
o
w
e
r
d
i
s
t
o
r
t
e
d
o
u
t
p
u
t
v
o
l
t
a
g
e
,
b
u
t
i
t
g
i
v
e
s
a
h
i
g
h
e
r
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
s
t
o
f
l
o
w
t
h
r
o
u
g
h
t
h
e
T
w
o
-
V
S
C
‘
s
.
T
h
e
m
u
t
u
a
l
i
n
d
u
c
t
a
n
c
e
o
f
t
he
coupl
e
d
induc
tors
(CI)
is
uti
l
ized
for
m
ini
m
iz
ing
circul
a
ti
ng
cur
ren
ts
of
hig
h
fre
quency
components.
Neve
r
th
el
ess,
CI
ca
n‘
t
have
ca
p
ability
to
riddl
e
th
e
components
gen
era
t
ed
b
y
low
f
req
uency
.
W
hen
the
se
ci
r
culati
n
g
cur
ren
ts
ext
remel
y
in
crea
ses
m
ay
leads
to
CI
satura
ti
on,
e
l
eva
t
ed
sw
it
chi
ng
losses
a
n
d
d
i
m
i
n
i
s
h
e
s
t
h
e
e
n
t
i
r
e
p
e
r
f
o
r
m
a
n
c
e
o
f
s
y
s
t
e
m
.
H
e
r
e
a
u
t
h
o
r
i
d
e
n
t
i
f
i
e
d
a
n
o
v
e
l
c
o
n
t
r
o
l
t
e
c
h
n
i
q
u
e
f
o
r
a
g
r
i
d
-
c
o
n
n
e
c
t
e
d
p
a
r
a
l
l
e
l
i
n
t
e
r
-
l
e
a
v
e
d
c
o
n
v
e
r
t
e
r
d
e
p
e
n
d
i
n
g
o
n
a
p
p
r
o
a
c
h
o
f
e
n
e
r
g
y
s
h
a
p
i
n
g
c
o
n
t
r
o
l
(
E
C
S
)
.
T
h
i
s
c
o
n
t
r
o
l
l
e
r
diminishes
th
e
val
ue
of
the
low
fre
quency
components
of
ci
rcu
la
ti
ng
cur
ren
t
(L
FC
C).
The
per
form
anc
e
of
th
e
proposed
c
i
rcu
it
is
eva
lu
ate
d
in
sim
ula
ti
on
m
ode
and
cor
relate
d
with
the
conve
n
ti
ona
l
proporti
onal
in
t
egr
al
con
trol
(
P
I
C
)
a
n
d
t
h
e
l
i
n
e
a
r
q
u
a
d
r
a
t
i
c
c
o
n
t
r
o
l
(
L
Q
C
)
.
T
h
e
F
u
z
z
y
c
o
n
t
r
o
l
l
e
r
i
s
a
l
s
o
i
n
c
l
u
d
e
d
i
n
t
h
i
s
w
o
r
k
t
o
e
n
h
a
n
c
e
t
h
e
c
o
n
v
e
r
t
e
r
p
e
r
f
o
r
m
a
n
c
e
e
f
f
e
c
t
i
v
e
l
y
a
n
d
t
o
d
i
m
i
n
i
s
h
t
h
e
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
s
a
l
o
n
g
w
i
t
h
t
h
e
h
e
a
l
t
h
y
h
a
r
m
o
n
i
c
p
erf
orm
an
ce
anal
y
sis
.
Ke
yw
or
d
s
:
Ci
rcu
la
ti
ng cur
ren
t
Energy s
ha
ping
Fu
zzy
c
on
t
ro
l
Parall
el
interle
aved co
nverte
r
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Sr
a
van
t
hy G
a
ddam
eedh
i
Dep
a
rtm
ent o
f El
ect
rical
an
d
Ele
ct
ro
nics
E
nginee
rin
g
Sr
ee
Nidhi I
ns
t
it
ute o
f
Scienc
e an
d
Tec
hnol
og
y
Yam
na
m
pet, Ghatkesa
r,
Hyde
rab
a
d
-
5013
01
, T
e
la
ng
a
na,
I
nd
ia
Em
a
il
:
srav
ant
hig@sree
nidhi.
edu.in
1.
INTROD
U
CTION
In
rece
nt
tim
es
,
with
t
he
dev
e
lop
m
ent
of
po
wer
s
em
i
-
con
duct
or
de
vices,
powe
r
co
nvert
ers
are
use
d
in
num
ero
us
a
pp
li
cat
io
n
s
li
ke
RES
a
nd
F
A
CTS.
F
or
high
-
pow
er
a
ppli
an
ces,
the
co
nver
te
rs
are
co
nnec
te
d
in
par
al
le
l
are
co
nf
i
gured
as
on
e
of
the
m
os
t
chall
eng
i
ng
to
po
l
og
y,
pr
im
aril
y
du
e
to
it
s
capab
il
it
y
of
ha
nd
li
ng
la
rg
e
rati
ng
of
power
,
netw
ork
reli
abili
ty
with
eff
ic
ie
nc
y
[1
]
.
Howe
ve
r,
due
to
the
presence
of
ci
rc
ulati
ng
currents
,
it
m
a
y
le
ad
to
dis
to
r
ti
on
in
ou
t
pu
t
currents
flo
wing
th
rou
gh
i
nd
i
vidual
co
nv
e
rt
er,
m
al
-
fu
nctio
ning
of
t
h
e
p
o
w
e
r
c
o
n
v
e
r
t
e
r
d
e
v
i
c
e
s
a
n
d
d
e
d
u
c
t
i
o
n
i
n
t
h
e
e
f
f
i
c
i
e
n
c
y
[
2
]
.
H
e
n
c
e
,
t
o
t
a
l
h
a
r
m
o
n
i
c
d
i
s
t
o
r
t
i
o
n
w
i
l
l
i
n
c
r
e
a
s
e
.
In
a
volt
age
s
ource
in
ve
rter,
joinin
g
eac
h
le
g
in
pa
rall
el
is
an
ap
proac
h
to
a
m
plify
the
ou
tp
ut
curre
nt
and,
fi
nally
rated
power.
T
his
ty
pe
of
a
rr
a
nge
m
ent
is
done
by
co
uple
d
or
un
c
ouple
d
in
duct
ors,
a
nd
at
ta
inin
g
an
eq
ual
con
t
r
ibu
ti
on
to
the
ou
tp
ut
cu
rr
e
nt
fr
om
all
the
le
gs
is
a
vit
al
issue.
Pow
er
switc
hing
de
vice
s
su
bject
e
d
to
add
it
io
nal
losse
s
and
stres
s
du
e
to
these
ci
rcu
la
ti
ng
c
urren
t
s.
Conseq
ue
ntly
,
in
order
m
i
nim
iz
e
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
A
n
ovel
f
uzzy
base
d
c
on
tr
oller t
o
r
e
duce
c
irc
ula
ti
ng
c
ur
re
nts i
n
…
(
S
ra
v
an
thy
G
adda
mee
dh
i
)
1131
the
ef
fect
of
th
ese
cu
rr
e
nts;
a
n
ef
fecti
ve
st
ra
te
gy
is
i
m
ple
m
ented
t
o
ob
ta
in
balance
,
wh
e
n
co
up
le
d
in
duc
tors
are
us
ed
is
give
n
in
[3].
CI
prov
i
d
es
lo
w
co
nductance
with
resp
ect
to
ci
rcu
la
ti
ng
currents
.
So
,
without
need
of
add
it
io
nal
c
o
n
t
r
o
l
e
q
u
i
p
m
e
n
t
i
t
c
a
n
b
e
a
b
l
e
t
o
r
e
d
u
c
e
t
h
e
s
e
c
u
r
r
e
n
t
s
f
o
r
b
a
l
a
n
c
i
n
g
.
T
h
i
s
c
o
n
f
i
g
u
r
a
t
i
o
n
r
e
g
u
l
a
t
e
s
t
h
e
h
a
r
m
o
n
i
c
p
e
r
f
o
r
m
a
n
c
e
a
n
a
l
y
s
i
s
o
f
o
u
t
p
u
t
v
o
l
t
a
g
e
s
b
y
a
d
o
p
t
i
n
g
e
x
a
c
t
m
o
d
u
l
a
t
i
o
n
m
e
t
h
o
d
s
[
4
]
.
O
f
t
e
n
,
par
al
le
li
zed
in
ver
te
r
carrier
pulse
s
are
ph
as
e
s
hift
ed
by
1800,
w
hich
pro
vid
e
s
sever
al
ad
va
ntages
t
o
the
sys
tem
su
ch
a
s
es
cal
at
ing
no of le
vels in ou
t
pu
t
volt
age,
d
e
gr
a
ding i
n
s
iz
e o
f
f
il
te
r
a
nd CM
V
[
5].
Fu
rt
her
m
or
e,
a
ut
hors
in
m
any
pap
e
rs
exte
nded
their
rese
arc
h
on
m
ini
m
iz
i
ng
the
ci
rc
ulati
ng
c
urren
ts
,
wh
ic
h
are
flo
wing
th
rou
gh
the
CI.
I
n
[
6],
it
is
descr
ibe
d
that
c
omm
o
n
dc
bus
pa
rall
el
inv
erter
syst
e
m
for
m
ini
m
iz
at
ion
of
ci
rc
ulati
ng
c
urre
nt
us
i
ng
sin
us
oi
dal
pulse
width
m
od
ulati
on
(SP
W
M
)
to
overc
om
e
the
dead
-
tim
e
eff
ect
s.
D
esi
gn
an
d
reas
on
s
f
or
hav
i
ng
zer
o
se
quence
ci
rcu
la
ti
ng
c
urre
nts
(
ZSCC
)
in
the
pa
rall
el
gr
i
d
-
connecte
d
thre
e
-
phase
i
nv
e
rters
an
d
reducti
on
of
the
se
cu
rrents
us
i
ng
PI
c
on
t
ro
ll
er
a
re
presented
i
n
detai
l
[7
]
.
I
n
[
8
]
,
t
h
e
a
u
t
h
o
r
r
e
p
r
e
s
e
n
t
s
a
n
o
v
e
l
z
e
r
o
s
e
q
u
e
n
c
e
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
r
e
d
u
c
t
i
o
n
m
e
t
h
o
d
b
a
s
e
d
o
n
t
h
e
de
vel
op
i
ng
sel
ect
ive
ha
rm
on
ic
el
im
inati
on
pu
lse
-
wi
dth
m
od
ulati
on
(SHEP
WM)
f
or
par
al
le
l
th
ree
-
l
evel
T
-
ty
pe
in
ver
te
r
s,
wh
ic
h
is
us
e
d
t
o
inc
rease t
he c
apac
it
y of t
he dist
rib
uted ge
ne
rati
on syst
em
.
A
m
od
ifie
d
D
P
W
M
te
ch
niqu
e
was
presente
d
in
[
9]
to
dim
inish
the
ove
ra
ll
Peak
to
peak
at
value
of
the
ci
rcu
la
ti
ng
currents
a
nd
CM
V.
To
ge
ner
at
e
re
fer
e
nce
sig
nals
f
or
each
par
ti
cu
la
r
le
g
of
indi
vid
ua
l
conve
rter,
D
ongs
ul
S
hin
et
al
.
de
velo
pe
d
ba
la
ncing
te
ch
ni
qu
e
.
By
util
iz
i
ng
the
outp
ut
currents
of
in
di
vid
ual
conve
rter
[10],
we
can
deter
m
ine
the
ref
er
ence
sign
al
s
at
su
it
able
tim
e
intervals,
wh
ic
h
are
eq
ualed
to
the
switc
hing
per
i
od.
A
uthor
s
ha
ve
sug
gested
de
creasin
g
the
m
agn
it
ud
e
of
the
ci
rc
ulati
ng
currents
with
de
adb
eat
con
t
ro
l
te
c
hn
i
qu
e
in
[
11
]
.
F
ur
t
her
m
or
e,
s
upplem
entary
li
te
ratur
e
‘s
ha
ve
f
ocu
se
d
on
t
heir
resear
ch
f
or
the
m
ini
m
iz
at
ion
of
the
ZSCC
,
w
hich
gi
ves
a
ne
t
su
m
of
ci
rcu
l
at
ing
cu
rr
e
nts
is
flow
i
ng
th
r
ough
al
l
th
ree
phases
com
par
at
ively
the
in
div
id
ual
diff
e
re
ntial
m
od
e
c
urren
ts
.
T
he
auth
or
[
12]
,
was
pro
po
se
d
t
hat,
to
r
e
s
t
r
a
i
n
t
h
e
s
e
c
u
r
r
e
n
t
s
a
C
a
r
r
i
e
r
p
h
a
s
e
s
h
i
f
t
e
d
P
W
M
w
a
s
u
s
e
d
i
n
m
o
d
u
l
a
r
b
i
-
l
e
v
e
l
i
n
t
e
r
-
l
e
a
v
e
d
c
o
n
v
e
r
t
e
r
s
.
M
o
r
e
o
v
e
r
,
t
w
o
m
o
r
e
s
c
h
e
m
e
s
w
e
r
e
i
n
t
r
o
d
u
c
e
d
i
n
[
1
3
,
1
4
]
f
o
r
d
e
c
r
e
a
s
i
n
g
t
h
e
Z
S
C
C
b
a
s
e
d
o
n
t
h
e
HE
P
W
M
te
c
hn
i
qu
e
.
Re
sea
r
cher
s
exten
d
thei
r
w
ork
t
o
re
duce
t
he
Z
SCC
ef
fec
ti
vely
;
Kar
thik
ey
an
et
al
.
,
int
rod
uced
a
strat
egy
that
by
ad
justi
ng
the
distrib
utio
n
of
the
nu
ll
ve
ct
or
s
in
t
he
c
onve
ntion
al
(SVM)
sc
hem
e
t
hro
ugh
P
I
co
nt
ro
ll
er
[15].
All
these
sp
eci
fied
tech
ni
qu
es
exhibit
t
he
m
agn
it
ude
of circulat
in
g
c
urren
ts
are
i
n
a
ll
ow
able
pe
rm
i
ts
In
the
pro
po
se
d
w
ork,
it
is
reco
m
m
end
e
d
to
restrict
the
LFCC
by
ESC.
Her
e
,
in
ord
er
to
sat
isf
y
energy
bala
nc
e
eq
uation,
th
e
struct
ur
e
is
t
aken
as
a
n
e
ne
rg
y
tra
nsfo
rm
at
ion
ar
ra
ng
e
m
ent.
It
acco
m
pl
ishes
sta
bili
zat
ion
of
pas
sive
netw
ork
by
m
eans
of
HS
with
a
su
it
able
sto
ra
ge
f
unct
ion
,
si
gn
i
fies
the
ess
entia
l
energy
of
t
he
c
losed
-
lo
op
syst
e
m
.
In
al
l
pow
er
s
witc
hing
c
onve
rters
this
t
ype
of
c
on
t
ro
l
te
chn
iq
ue
bee
n
us
e
d.
In
[
16
]
,
to
co
nt
ro
l
the
op
e
rati
on
of
a
th
ree
-
phase
fro
nt
e
nd
conve
rter
t
his
con
t
ro
l
te
c
hn
i
que
was
us
e
d.
It
was
us
e
d
in
m
ic
ro
gr
i
d
ap
plica
ti
on
s
[
17
]
by
co
nt
ro
ll
ing
back
-
to
-
bac
k
co
nv
e
rters.
I
n
[
18
]
,
f
or
a
Tri
-
le
vel
T
-
ty
pe
conve
rter
with
energy
stora
ge
syst
e
m
,
an
ESC
is
dev
el
op
ed.
T
o
co
ntr
ol
the
ci
rcu
la
ti
ng
cu
rr
e
nts
in
pa
rall
el
interl
eave
d
co
nn
ect
e
d
po
wer
inv
erte
rs
a
ne
w
dea
d
-
ti
m
e
c
om
pen
sat
ion
m
et
ho
d
us
in
g
carrier
base
d
s
inu
s
oid
a
l
pu
lse
wi
dth
m
odulati
on
a
nd
m
od
ifie
d
disco
nti
nuous
P
W
M
te
chn
iq
ues
are
giv
en
in
[19
,
2
0
].
T
he
inv
e
rt
ers
are
connecte
d
i
n
pa
rall
el
fo
r
distr
i
b
uted
ge
ner
at
i
on
a
ppli
cat
ion
that
op
e
rates
unde
r
diff
e
ren
t
load
c
o
n
d
i
t
i
o
n
s
w
a
s
i
n
v
e
s
t
i
g
a
t
e
d
i
n
[
2
1
]
a
n
d
i
m
p
r
o
v
e
d
d
r
o
o
p
c
o
n
t
r
o
l
s
t
r
a
t
e
g
y
f
o
r
t
h
e
s
e
c
o
n
v
e
r
t
e
r
s
a
r
e
d
e
v
e
l
o
p
e
d
i
n
[
22
]
.
P
a
r
a
l
l
e
l
o
p
e
r
a
t
i
o
n
o
f
i
n
v
e
r
t
e
r
s
w
i
t
h
a
c
t
i
v
e
p
o
w
e
r
f
i
l
t
e
r
s
a
n
d
t
h
e
i
r
c
o
n
t
r
o
l
t
e
c
h
n
i
q
u
e
s
a
r
e
d
i
s
c
u
s
s
e
d
i
n
d
e
t
a
i
l
[
23
,
2
4
].
T
he
auth
or
desires
to
prom
ote
an
ESC
for
a
PL
-
IC.
It
can
be
a
m
al
ga
m
at
ed
fo
r
huge
po
wer
app
li
cat
io
ns
suc
h
as
RES
an
d
F
AC
TS.
T
he
sug
ge
ste
d
te
chn
i
que
in
this
pap
e
r
end
ea
vors
a
de
sired
c
on
tr
oll
of
LFCC
wit
h
the
apprecia
ble c
ur
ren
ts i
nj
ect
e
d
t
o
the
gri
d
.
2.
DESIG
N
AND
M
ATHE
MA
TI
C
AL
MO
DELIN
G
OF
THE
PARALL
EL
INTER
-
LE
AVE
D
CONVE
RTER (PL
-
I
C)
2.1.
Mathem
ati
cal
mo
d
el
This
segm
ent
giv
e
s
the
repr
esentat
ion
of
t
he
PL
-
IC,
wh
i
ch
is
ti
ed
to
the
gri
d
by
m
eans
of
a
n
inducti
ve
filt
er
show
n
i
n
Fi
gure
1.
T
he
ou
t
pu
t
volt
ages,
,
,
are
the
f
un
ct
io
n
of
switc
hi
ng
sign
al
s
S
xi
and
excit
at
ion
volt
age
sig
nal
u
dc
.
‘i‘
a
sy
m
bo
l
of
the
tw
o
pa
rall
el
iz
ed
VS
C
(
i
{
1,
2})
and
‘
x‘
i
ndic
at
es
th
e
conve
rter
ph
a
s
es
(
x
{
A
,
B
,
C
}).
T
he
c
urr
ents
fl
ow
i
ng
thr
ough
t
he
gri
d
ar
e
in
dicat
ed
as
i
A
,
i
B
an
d
i
C
.
In
pro
po
se
d
t
opol
og
y,
the
outp
ut
volt
ages
w.r.t
to the m
id
-
poi
nt
‚‘
O‘
is
wr
it
te
n
as:
=
2
(
2
−
1
)
(1)
The
li
ne
to g
round
volt
age
of
conve
rter
is
re
pr
ese
nted
w
it
h
the b
el
ow equa
ti
on
s:
=
1
+
1
+
(2)
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.
11
, No
.
2
,
A
pr
i
l 202
1
:
1130
-
1142
1132
=
2
+
2
+
(3)
Figure
1.
A
rr
a
ng
em
ent of
paral
le
l i
nter
-
le
av
ed
c
onve
rter
Along wit
h t
hi
s,
the
volt
age a
cro
ss
the
cou
plled in
du
ct
or
s
c
an be in
dicat
ed
b
y:
1
=
−
(
1
−
2
)
−
1
−
0
1
2
=
−
(
2
−
1
)
−
1
−
0
2
(4)
In (4)
, L
0
is t
he
m
utu
al
induc
ta
nce and L
L
in
dicat
es lee
ka
ge
inductanc
e.
So,
(
2) p
l
us
(3)
i
m
pl
ie
s:
2
=
−
−
0
+
1
+
1
+
2
(5)
Along wit
h;
1
+
2
=
So
V
AG can
be
w
ritt
en
as
;
=
1
+
2
2
−
2
−
0
2
+
(6)
Likewise,
at th
e two en
ds o
f
A
1
an
d
A
2
,
the
diff
e
re
ntial
v
ol
ta
ge
is f
ound
by
the (4)
:
1
2
=
(
+
2
)
(
1
−
2
)
+
0
(
1
−
2
)
(7)
Abo
ve
e
xpress
ion
ca
n
be re
w
ritt
en
as
;
=
1
−
2
2
Using
we wil
l
get
;
1
−
2
=
2
+
2
0
(8)
w
he
re
2
=
2
+
4
.
.
A
1
C
1
B
1
.
.
.
.
.
.
.
.
A
2
B
2
C
2
.
.
.
.
.
.
A
B
C
L
L
L
R
R
R
N
e
A
e
B
e
C
S
C
1
S
B
1
S
A
1
S
C
2
S
B
2
S
l
A
1
S
l
B
1
S
l
C
1
S
A
2
S
l
A
2
S
l
B
2
S
l
C
2
.
.
.
.
.
.
I
E
n
e
r
g
y
s
o
u
r
c
e
u
dc
2
u
dc
2
O
G
r
i
d
i
A
i
B
i
C
i
A
1
i
A
2
.
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
A
n
ovel
f
uzzy
base
d
c
on
tr
oller t
o
r
e
duce
c
irc
ula
ti
ng
c
ur
re
nts i
n
…
(
S
ra
v
an
thy
G
adda
mee
dh
i
)
1133
In ad
diti
on, wit
h
r
espect
t
o
Fi
gure
1, outp
ut
vo
lt
age
s
deliv
e
red by t
he
PL
-
I
C are:
{
=
+
+
=
+
+
=
+
+
(9)
Her
e
R an
d L a
re ind
uctive
filt
er p
a
ram
et
ers
.
Fr
om
(
9
)
a
nd
(
5
)
we
w
il
l get
;
=
−
−
+
1
+
2
2
−
2
−
0
2
+
=
−
−
+
1
+
2
2
−
2
−
0
2
+
=
−
−
+
1
+
2
2
−
2
−
0
2
+
(10)
By
su
bs
ti
tuti
ng
(1)
i
n
(10), the
foll
ow
i
ng r
el
a
ti
on
s a
re
ob
ta
i
ned.
1
=
−
1
−
+
4
(
2
1
−
1
)
+
4
(
2
2
−
1
)
+
1
=
−
1
−
+
4
(
2
1
−
1
)
+
4
(
2
2
−
1
)
+
1
=
−
1
−
+
4
(
2
1
−
1
)
+
4
(
2
2
−
1
)
+
(11)
Her
e
1
=
(
+
2
)
and
1
=
(
+
0
2
)
Si
m
il
arly
by su
bs
ti
tuti
ng (2) i
n (8),
t
he dyna
m
ic
s o
f
ci
rc
ula
ti
ng
c
urren
ts
c
an be
ob
ta
in
ed
as:
{
2
=
−
2
0
−
+
2
(
2
1
−
1
)
−
2
(
2
2
−
1
)
2
=
−
2
0
−
+
2
(
2
1
−
1
)
−
2
(
2
2
−
1
)
2
=
−
2
0
−
+
2
(
2
1
−
1
)
−
2
(
2
2
−
1
)
(12)
The
ab
ove
ex
pressi
on can be r
ed
uce
d
to m
or
e si
m
ple b
y usi
ng
Pa
rks
trans
f
or
m
at
ion
, wh
ic
h
r
e
n
o
v
a
t
e
s
t
h
e
(
1
1
)
a
n
d
(
1
2
)
i
n
t
o
t
h
e
r
e
v
o
l
v
i
n
g
f
r
a
m
e
d
q
,
c
o
o
r
d
i
n
a
t
e
d
w
i
t
h
r
e
s
p
e
c
t
t
o
a
n
g
l
e
o
f
g
r
i
d
θ
gr
.
H
e
n
c
e
,
the
dynam
ic
of the
PL
-
IC is
g
ive
n by:
{
1
=
−
1
+
1
−
+
4
1
+
4
2
1
=
−
1
+
1
−
+
4
1
+
4
2
{
2
_
=
−
2
0
_
+
2
_
+
2
1
−
2
2
2
_
=
−
2
0
_
−
2
_
+
2
1
−
2
2
(13)
S
d
1
,
S
d
2
,
S
q
1
a
n
d
S
q
2
a
r
e
S
w
i
t
c
h
i
n
g
F
u
n
c
t
i
o
n
s
o
f
d
i
r
e
c
t
,
q
u
a
d
r
a
t
u
r
e
a
x
i
s
f
o
r
t
h
e
t
w
o
p
a
r
a
l
l
e
l
e
d
c
o
n
v
e
r
t
e
r
s.
2.2.
Port
carr
ey
H
amilto
n
(PCH
)
m
od
el
of t
he
PL
-
IC
The
c
onver
te
r
is
con
si
der
e
d
a
s
an
i
nacti
ve
s
yst
e
m
as
it
can
m
erely
exch
a
ng
e'
s
ene
rg
y,
but
it
do
es
n’t
has
the
capa
bili
ty
of
deliveri
ng
on
it
s
own.
Con
se
qu
e
ntly
,
it
can
be
design
e
d
as
PCH
syst
e
m
that
satisfies
the n
ece
ssit
ie
s o
f
ECS.
Th
e
c
onfig
ur
at
io
n
is:
̇
=
[
(
)
−
(
)
]
(
)
+p(x)
u
y=
(x)
(
)
(14)
In
(
14),
J
(
x
)
is
the
br
i
dg
e
m
a
trix
ta
ke
n
as
a
n
a
nti
-
sym
m
etr
ic
(
J
(
x
)
=
J
(
x
)
T
)
.
R
(
x
),
sym
m
et
ric
m
a
trix
.
p
(
x
),
e
xtern
al
port
m
a
trix
an
E
(
x
),
e
nergy
f
un
ct
io
n
of
the
s
yst
e
m
.
In
(14
),
u
a
nd
y
are
excit
at
ion
an
d
ou
t
pu
t
par
am
et
ers
of t
he
syst
em
. Th
e
r
el
at
ion (
13)
is
r
e
pr
ese
nted
b
y
:
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.
11
, No
.
2
,
A
pr
i
l 202
1
:
1130
-
1142
1134
(
q
c
i
L
d
c
i
L
q
i
L
d
i
L
_
2
_
2
1
1
)
=
(
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
L
L
L
L
)
−
(
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
R
R
R
R
)
(
q
c
i
d
c
i
q
i
d
i
_
_
)
+
4
(
2
0
2
0
0
2
0
2
1
0
1
0
0
1
0
1
)
(
2
2
1
1
q
S
d
S
q
S
d
S
)
_
(
0
0
0
1
)
_
(
0
0
1
0
)
(15)
w
it
h j(x)
=
(
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
L
L
L
L
)
an
d R
(x)=
(
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
R
R
R
R
)
Fr
om
t
he
a
bove
d
isc
us
sio
n, cl
early
(14
)
it
is
c
onsidere
d
a
s
PCH. The
HF,
h
(
̅
)
=
1
2
1
2
+
1
2
1
2
+
1
2
2
_
2
+
1
2
2
_
2
(16)
And x
=
[
1
1
2
_
2
_
]
(17)
The
e
xter
nal
port c
onnecti
on
m
at
rices ar
e s
pe
ci
fied by:
1
=
4
(
2
0
2
0
0
2
0
2
1
0
1
0
0
1
0
1
)
;
2
=
(
0
0
0
1
)
;
3
=
(
0
0
1
0
)
h
(
̅
)
ca
n be
giv
e
n
as:
h
(
̅
)
=
1
2
1
(
1
)
2
+
1
2
1
(
1
′
)
2
+
1
2
2
(
2
_
)
2
+
1
2
2
(
2
_
)
2
(
18)
If
t
he
sta
te
var
i
ables m
ay
b
e r
efer
red as
1
,
2
,
3
4
; (18
) becom
es:
h
(
̅
)=
1
2
1
(
1
)
2
+
1
2
1
(
2
)
2
+
1
2
1
(
3
)
2
+
1
2
1
(
4
)
2
(19)
Ther
e
f
or
e,
the
HF
Gr
a
die
nt is d
e
fine
d
as:
ℎ
(
̅
)
=
[
ℎ
1
ℎ
2
ℎ
3
ℎ
4
]
=
[
_
_
]
(20)
3.
CONTR
OL S
CHE
MES F
O
R
G
RI
D CO
N
NECTED
CO
NV
E
RTER
(
GCC)
3.1.
PIC base
d G
CC
The
c
on
tr
ol
pr
ocess
of
th
e
P
I
-
LC
with
PI
C
is
sh
ow
n
in
F
igure
2.
I
n
ord
er
to
m
easur
e
current
a
nd
vo
lt
age
at
th
e
PCC
to
the
gri
d
,
vo
lt
age
a
nd
current
se
nsors
was
use
d.
By
m
eans
of
PLL,
the
gri
d
ph
ase
ang
l
e
θ
grid
is
ob
ta
ined.
The
ta
r
get
is
at
ta
ined
by
set
ti
ng
the
e
*
grid
d.
to
zero
.
P
I
con
t
ro
le
r
is
util
iz
ed
to
ad
j
us
t
the
gri
d
ang
le
with
r
es
pect
t
o
t
he
er
r
or
betwee
n
e
*
g
ridd
and
e
gridd
.
So
,
t
he
gr
i
d
vo
lt
age
vecto
r
is
associat
ed
with
the
q
axis
of
the
re
vo
l
ving
f
ram
e.
This
c
onve
ntion
al
c
ontrol
is
stud
ie
d
earli
e
r
in
e
norm
ou
s
li
te
ratur
e‘s
[5
]
.
T
he
expressi
on
s
of
P and Q s
uppli
ed
to
gri
d
are
gi
ven
a
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
A
n
ovel
f
uzzy
base
d
c
on
tr
oller t
o
r
e
duce
c
irc
ula
ti
ng
c
ur
re
nts i
n
…
(
S
ra
v
an
thy
G
adda
mee
dh
i
)
1135
{
P
g
rid
=
e
g
ridd
i
d
+
e
g
ridq
i
q
Q
g
rid
=
e
g
ridd
i
d
−
e
g
ridq
i
q
(21)
Ba
sed on (
21),
current
set
poi
nts,
i
d
∗
an
d
i
q
∗
are ac
hieve
d by the
grid
volt
ages,
P
g
rid
∗
an
d
Q
g
rid
∗
∗
=
P
gr
id
∗
e
g
r
idd
+
Q
gr
id
∗
e
gr
idq
e
gr
idd
2
+
e
gr
id
q
2
(22)
∗
=
∗
−
∗
2
+
2
(23)
W
it
h
the
he
lp
of
di
ff
e
ren
ti
a
l
equ
at
io
ns,
t
he
c
on
t
ro
l
pat
te
rn
is
buil
t
f
ro
m
the
el
em
ents
in
the
gri
d
an
d
represe
nted
i
n “
dq”
by:
1
̅
,
+
1
̅
,
=
̅
,
−
1
̅
,
−
̅
,
(24)
In the a
bove
expressi
ons,
̅
,
in
dicat
es the
vo
lt
a
ge vect
or
gen
e
rated
by the
PI
-
LC.
3.2.
LQC base
d G
CC
Inver
te
r
c
onne
ct
ed
to t
he
gr
i
d
with
LQC is
s
how
n
in
Fig
ure
3. T
he
im
pr
o
vem
ent in th
e
contr
oller is
achieve
d by th
e stat
e sp
ace
r
e
pr
ese
ntati
on which is
g
i
ven by
(
16)
. Hence
,
{
̇
=
A
+
B
=
C
(25)
wh
e
re
Y
yi
el
ds o
utput vect
or i.e, y=
⌊
⌋
is i
nput
vect
or
⌊
−
−
⌋
A=
(
−
1
1
−
1
1
)
; B
=
(
1
1
0
0
1
1
)
; C
=
(
1
0
0
1
)
Stabil
iz
ing
fee
db
ac
k
m
at
rix
K
d
is
eff
ic
ie
ntly
cal
culat
ed
by
LQC
te
ch
ni
qu
e
.
It
sat
is
fies
the
ov
e
rall
perform
ances o
f
en
e
rg
y
c
o
n
t
r
o
l
a
n
d
t
r
a
n
s
i
e
n
t
r
e
s
p
o
n
s
e
.
T
h
e
m
o
d
e
l
l
i
n
g
o
f
th
is co
ntro
l
l
er
is
giv
e
n
in
d
et
ai
l
[25
].
Figure
2. Co
nverter c
onnecte
d t
o
the
grid
w
it
h
P
IC
Figure
3. Co
nverter c
onnecte
d t
o
the
grid
w
i
t
h
L
QC
L
R
I
P
T
i
A
3
2
3
2
v
*
iq
v
*
id
Q
*
g
r
i
d
P
*
g
r
i
d
PLL
e
g
r
i
d
d
e
g
r
i
d
q
P
W
M
1
P
W
M
2
G
e
n
e
ra
ti
o
n
o
f
c
u
rr
e
n
t
s
e
t
p
o
in
ts
O
grid
O
grid
i
B
i
C
e
gri
d
O
g
r
i
d
u
dc
.
.
.
.
.
.
.
.
e
c
_
d
e
c
_
q
PI
PI
i
g
r
i
d
d
i
g
r
i
d
q
i
*
g
r
i
d
d
i
*
g
r
i
d
q
-
-
+
+
+
+
-
-
.
.
.
.
L
o
o
p
D
e
c
o
u
p
li
n
g
L
R
i
A
K
d
3
2
3
2
v
*
iq
v
*
id
Q
*
g
r
id
P
*
g
r
id
P
LL
e
g
r
id
d
e
g
r
id
q
P
W
M
1
P
W
M
2
i
*
d
i
*
q
u
d
G
en
er
a
t
i
o
n
o
f
c
u
rr
en
t
s
et
p
o
i
n
t
s
Tra
j
ec
t
o
ry
G
en
er
a
t
i
o
n
(
i
d
,
i
q
)
(
e
g
r
id
d
,
e
g
r
id
q
)
v
O
g
r
id
O
g
r
id
i
B
i
C
e
g
r
id
O
g
r
id
u
dc
.
.
.
.
.
.
.
.
.
.
.
.
+
+
+
-
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.
11
, No
.
2
,
A
pr
i
l 202
1
:
1130
-
1142
1136
3.3.
ESC base
d G
CC
GCC sat
isfie
s t
he
PC
H n
otati
on g
i
ven in
(
17).
In PCH
, bri
dge a
nd the
dam
ping m
at
rices can
handle
internal e
ne
rg
y
ex
c
hange e
ff
ic
ie
ntly
[
2
6
].
Fin
al
ly
, th
e prefe
r
red co
nf
i
gurati
on is s
how
n be
low:
̇
=
[
(
)
−
(
)
]
(
)
(26)
with
{
(
)
=
J
(
x
)
+
(
)
(
)
=
R
(
x
)
+
(
)
wh
e
re,
(
)
de
note
s
the
pr
e
fer
a
ble
br
i
dg
e
m
a
trix
,
(
)
is
prefe
r
able
dissipati
on
m
at
rix
a
nd
(
)
is
ex
pecte
d
e
nerg
y functi
on r
e
spe
ct
ively
.
(
)
=
(
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
L
L
L
L
)
;
(
)
=
(
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
r
r
r
r
)
r
1
and
r
2
are
a
posit
ive
nu
m
erical
.
ESC
pe
rm
i
t
u
=ɣ
(
x
)
s
uc
h
that
t
he
dynam
ic
beh
avi
or
of
t
he
cl
ose
d
loo
p
syst
e
m
are
ill
us
trat
ed
i
n
(
24)
.
Her
e
,
the
m
ot
ive
is
to
t
rack
the
c
urre
nt
set
po
i
nts
eff
ic
ie
ntly
by
pro
per
desig
ning
of c
on
t
ro
le
r
. Henc
e, the
re
qu
ir
ed
energy f
unct
io
n
of PL
-
IC is
gi
ven
by:
(
)
=
1
2
1
(
−
∗
)
2
+
1
2
1
(
−
∗
)
2
+
1
2
2
(
−
∗
)
2
+
1
2
2
(
−
∗
)
2
(27)
Her
e
_
∗
an
d
_
∗
sho
ws
the
ci
rc
ulati
ng
c
urre
nts
se
t
po
i
nts.
T
he
gradie
nt
of
requ
ired
Ham
ilton
functi
on
(
HF)
and the
disti
nct
stat
e v
ect
or is
represe
nted by:
(
)
=
[
1
2
3
4
]
=
(
*
_
_
*
_
_
*
*
q
c
i
q
c
i
d
c
i
d
c
i
q
i
q
i
d
i
d
i
)
(28)
X=
[
1
(
−
∗
)
1
(
−
∗
)
2
(
_
−
_
∗
)
2
(
_
−
_
∗
)
]
(29)
ESC at
ta
ins th
e stabil
iz
at
ion
gu
i
ded b
y t
he
e
x
pecte
d Hd
(
x)
.
Th
e
contr
ol in
pu
t
u o
f netw
ork
is
obta
ined
a
s:
[
J
(
)
−
R
(
)
]
(
)
+
(
)
=
[
(
)
−
(
)
]
(
)
(30)
If
t
he
syst
em
fu
nctio
ns
nea
re
st
to
t
he
e
xp
ec
te
d
po
i
nt,
the
n
the
H
d
(
x
)
trie
s
to
m
ai
ntain
at
the
l
ow
e
s
t
value. S
o,
(
15) shoul
d
sat
isfy:
(
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
L
L
L
L
)
-
(
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
R
R
R
R
)
(
q
c
i
d
c
i
q
i
d
i
_
_
)
+
(
1
2
1
2
1
1
q
S
d
S
q
S
d
S
)
4
_
(
2
2
2
2
2
2
q
S
d
S
q
S
d
S
)
4
-
_
(
0
0
g
r
i
d
q
e
g
r
i
d
d
e
)
=0
(31)
At
ste
ady
-
sta
te
po
int,
ou
t
pu
t
currents
are
id
entic
al
ly
distri
bu
te
d
am
on
g
conve
rters
an
d
hen
ce
ze
r
o
ci
rcu
la
ti
ng curr
ents f
l
ow
i
ng th
rou
gh a syste
m
(
i
c
_
d
=
i
c
_
q
=
0).
Stea
dy
-
sta
te
va
lues are
d
et
e
r
m
ined
by
(
31):
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
A
n
ovel
f
uzzy
base
d
c
on
tr
oller t
o
r
e
duce
c
irc
ula
ti
ng
c
ur
re
nts i
n
…
(
S
ra
v
an
thy
G
adda
mee
dh
i
)
1137
{
1
∗
=
2
∗
=
0
∗
=
−
1
∗
+
1
∗
+
2
1
∗
=
2
∗
=
0
∗
=
−
1
∗
+
1
∗
+
2
(32)
The
c
ontr
ol
ac
ti
on
u
=
[
1
∗
2
∗
1
∗
2
∗
]
is
opte
d
by
the
m
at
c
hing
(30).
Assum
ing
_
∗
=
_
∗
=
0,
th
e
so
luti
on
of (2
6)
giv
es:
1
∗
+
2
∗
2
=
0
∗
+
1
(
−
∗
)
+
1
(
(
−
∗
)
2
(33)
1
∗
+
2
∗
2
=
0
∗
−
1
(
−
∗
)
+
1
(
(
−
∗
)
2
(34)
1
∗
−
2
∗
=
2
_
+
2
_
2
(35)
1
∗
−
2
∗
=
−
2
_
−
2
_
2
(36)
The
re
s
pons
e
obta
ined
f
r
om
(
33)
-
(
36)
are
co
ns
ide
red
as
b
1
,
b
2
,
b
3
and
b
4
r
especti
vely
.
Further
,
thes
e
equ
at
io
ns are
e
xpresse
d
as:
=
(
1
∗
2
∗
)
=
1
(37)
=
(
1
∗
2
∗
)
=
2
(38)
i
th
,
=
(
1
2
1
2
1
−
1
)
,
1
=
(
1
3
)
,
1
=
(
2
4
)
S
o
l
u
t
i
o
n
s
f
r
o
m
(
3
7
)
a
n
d
(
3
8
)
g
i
v
e
t
h
e
d
e
s
i
r
e
d
e
x
c
i
t
a
t
i
o
n
f
o
r
t
h
e
t
w
o
p
a
r
a
l
l
e
l
e
d
c
o
n
v
e
r
t
e
r
s
.
T
h
e
switc
hing
functi
on
w
hich
is
ta
ken
as
re
f
eren
ce
is
cal
cu
la
te
d
s
m
oo
thly
with
the
h
el
p
of
the
i
nv
e
rse
of
m
at
rix
A.
Fi
gure
4
sh
ows
the
bl
oc
k
diag
ram
of
a
co
ntr
ol
str
uct
ur
e
f
or
dete
rm
ining
the
re
fere
nce
s
witc
hing
f
un
ct
io
n
with
ESC.
The DC
bus
volt
age contr
olli
ng
is sim
il
ar to
the PIC.
.
.
.
.
.
.
i
C
i
A
i
B
v
g
r
i
d
a
v
g
r
i
d
b
v
g
r
i
d
c
L
R
I
P
T
i
A
L
P
F
i
A
1
i
B
1
i
C
1
i
C
i
B
i
A
3
2
i
C
A
i
C
C
i
C
B
3
2
S
*
q
1
S
*
d
1
S
*
q
2
S
*
d
2
E
q
(
2
9
)
E
q
(
3
0
)
E
q
(
3
1
)
E
q
(
3
2
)
b
3
b
1
b
2
b
4
S
*
d
0
S
*
q
0
E
q
(
2
8
)
i
*
C
_
d
i
*
C
_
q
i
*
d
i
*
q
Q
*
g
r
i
d
P
*
g
r
i
d
v
g
r
i
d
c
v
g
r
i
d
b
v
g
r
i
d
a
P
L
L
e
g
r
i
d
d
e
g
r
i
d
q
A
e
-
1
B
1
A
e
-
1
B
2
C
u
r
r
e
n
t
s
e
t
p
o
i
n
t
s
C
i
r
c
u
l
a
t
i
n
g
C
u
r
r
e
n
t
C
a
l
c
u
l
a
t
i
o
n
P
W
M
1
P
W
M
2
N
.
.
.
.
.
.
i
A
1
i
B
1
i
C
1
3
2
3
2
i
d
i
q
i
c
_
d
i
c
_
q
U
d
c
Figure
4. Co
nverter
c
onnecte
d t
o
the
gri
d
wit
h
E
SC
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.
11
, No
.
2
,
A
pr
i
l 202
1
:
1130
-
1142
1138
(
1
∗
2
∗
)
=
−
1
(
1
3
)
(39)
(
1
∗
2
∗
)
=
−
1
(
2
4
)
(40)
w
he
re
−
1
=
(
1
1
2
1
−
1
2
)
4.
SUMM
A
RY
OF
RESU
LT
S
Her
e
,
the
perform
ance
of
the
conve
rter
with
diff
e
re
nt
co
ntr
ollers
is
gi
v
en
.
The
c
onve
rter
resu
lt
s
with
PI
C,
LQC
an
d
E
SC
a
re
obta
ined
a
nd
with
E
SC
the
pe
rfor
m
ance
of
t
he
c
onve
rter
i
s
achie
ved
bette
r
a
s
com
par
ed
t
o
P
I
C an
d
L
QC in
te
rm
s o
f
re
du
ci
ng the ci
rcu
la
ti
ng curre
nts.
4
.
1.
Conv
er
ter
per
fo
rm
an
ce
wi
t
h PI
C
F
i
g
u
r
e
5
g
i
v
e
s
t
h
e
f
u
n
c
t
i
o
n
o
f
t
h
e
s
y
s
t
e
m
w
i
t
h
P
I
C
.
F
i
g
u
r
e
5
(
a
)
p
o
r
t
r
a
y
s
t
h
e
c
u
r
r
e
n
t
d
e
l
i
v
e
r
e
d
t
o
t
h
e
g
r
i
d
a
n
d
F
i
g
u
r
e
5
(
b
)
d
e
s
c
r
i
b
e
s
t
h
e
c
u
r
r
e
n
t
s
f
l
o
w
i
n
g
t
h
r
o
u
g
h
t
h
e
c
o
n
v
e
r
t
e
r
d
e
l
i
v
e
r
e
d
b
y
p
h
a
s
e
‘
s
C
1
a
n
d
C
2
.
F
r
o
m
F
i
g
u
r
e
5
(
b
)
,
m
a
g
n
i
t
u
d
e
o
f
t
h
e
c
u
r
r
e
n
t
i
n
c
o
n
v
e
r
t
e
r
1
i
s
c
o
n
s
i
d
e
r
a
b
l
y
l
a
r
g
e
r
t
h
a
n
t
h
e
m
a
g
n
i
t
u
d
e
o
f
t
h
e
c
u
r
r
e
n
t
i
n
c
o
n
v
e
r
t
e
r
2.
Hen
ce
,
the
sh
a
rin
g
of
the
gr
i
d
curre
nts
in
the
two
c
onve
r
te
r
s
are
uneq
ua
l
le
ads
to
LFCC
‘s.
The
dc
offset
com
po
ne
nt
of
ci
rcu
la
ti
ng
c
urren
t
ca
n
at
ta
in
0.5A
(iCC
)
as
exh
i
bited
in
F
igure
5
(
c
)
,
w
hi
ch
is
nea
rly
30%
of
the
m
agn
it
ud
e
of
t
he
gr
i
d
c
urren
t.
Co
ns
e
quently
,
a
band
oned
ci
rcu
la
ti
ng
curre
nts
ar
e
l
arg
e
r
in
m
agni
tud
e,
wh
ic
h
m
ay
le
a
d
to
sat
urat
io
n
of
c
ouplin
g
i
nducto
rs.
A
ddit
ion
al
ly
,
it
rais
es
the
powe
r
c
onve
rters
s
wit
chin
g
losses. P a
nd Q deli
ve
red to t
he
gri
d
a
re
dem
on
st
rated i
n
Fi
gure
5
(
d
)
.
(a)
(b)
(c)
(d)
Figure
5. Per
f
orm
ance o
f
c
on
ver
te
r
w
it
h
P
I
C
,
(a
)
gr
id
curr
ent
,
(
b) c
onve
rter c
urren
ts
,
(c)
dif
fer
e
nce
m
od
e curren
ts
,
(
d)
PQ p
owers
4.2.
Conv
er
ter
per
fo
rm
an
ce
wi
t
h LQC
Figure
6
gi
ves
the
f
un
ct
io
n
of
the
GCC
with
the
L
QC.
T
he
resu
lt
s
a
re
obta
ined
with
L
QC
is
ve
ry
near
e
r
to
the
r
esults
with
PIC
.
Eve
n
s
o,
sti
ll
so
m
e
con
sid
erab
le
am
ount
of
ci
rcu
la
ti
ng
currents
are
pr
esent
in
the tw
o
c
onve
r
te
rs
as s
how
n
i
n
Fi
gure
6
(
a
)
a
nd grid
po
wer
s
shown i
n
Fi
g
ure
6(
b
).
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
A
n
ovel
f
uzzy
base
d
c
on
tr
oller t
o
r
e
duce
c
irc
ula
ti
ng
c
ur
re
nts i
n
…
(
S
ra
v
an
thy
G
adda
mee
dh
i
)
1139
(a)
(b)
Figure
6. Per
f
orm
ance o
f
c
on
ver
t
er
w
it
h L
Q
C
,
(a
) diffe
ren
c
e m
od
e cu
rr
e
nt
s
,
(
b) grid
po
w
ers
4.3.
Conv
er
ter
per
fo
rm
an
ce
wi
t
h ESC
Figure
7
gi
ves
the
beh
a
vio
u
r
of
the
gri
d
wi
th
ESC.
The
c
urren
ts
w
hic
h
are
supp
li
ed
to
the
gr
id
ar
e
i
l
l
u
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
s
7
(
a
)
a
n
d
(
b
)
d
e
s
c
r
i
b
e
s
t
h
e
c
u
r
r
e
n
t
s
f
l
o
w
i
n
g
t
h
r
o
u
g
h
t
h
e
c
o
n
v
e
r
t
e
r
s
d
e
l
i
v
e
r
e
d
b
y
p
h
a
s
e
s
C
1
a
n
d
C
2
.
I
n
t
h
i
s
c
a
s
e
i
t
i
s
n
o
t
i
c
e
d
t
h
a
t
,
c
u
r
r
e
n
t
s
a
r
e
d
i
s
t
r
i
b
u
t
e
d
i
d
e
n
t
i
c
a
l
l
y
b
e
t
w
e
e
n
t
h
e
c
o
n
v
e
r
t
e
r
s
.
Additi
on
al
ly
,
t
he
dc
c
o
m
p
o
n
e
n
t
o
f
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
s
f
o
r
t
h
r
e
e
p
h
a
s
e
s
i
s
d
i
m
i
n
i
s
h
e
d
t
o
z
e
r
o
a
n
d
o
n
l
y
c
i
r
c
u
l
a
t
i
n
g
c
u
r
r
e
n
t
s
w
h
i
c
h
a
r
e
h
a
v
i
n
g
h
i
g
h
f
r
e
q
u
e
n
c
y
t
r
a
v
e
l
s
a
m
o
n
g
t
w
o
C
o
n
v
e
r
t
e
r
s
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
7
(
c
)
a
n
d
F
i
g
u
r
e
(
d
)
s
h
o
w
s
t
h
e
c
onve
rter
powe
rs.
The
DC
bus vo
lt
age
rem
ai
ns
stable a
s r
e
pr
ese
nted
in
Fi
gure
7
(
f
)
.
(a)
(b)
(c)
(d)
(e)
(f)
Figure
7. Per
f
orm
ance
of
c
on
ver
te
r
w
it
h ES
C
,
(a
) gr
id
curr
ent
,
(b)
c
onve
rter c
urren
ts
,
(c)
dif
fer
e
nce
m
od
e curren
ts
,
(
d)
gri
d p
ow
e
r
s
,
(e
) VAB
,
(
f)
dc bus
vo
lt
age
4.4.
Conv
er
ter
be
havior wi
t
h fu
zz
y
control
Figure
8
e
xh
i
bits
gr
id
beh
a
vior
with
f
uzz
y
con
tr
ol.
The
cur
re
nts,
wh
i
c
h
are
sup
pl
ie
d
to
gri
d
ar
e
il
lustrate
d
on
F
igure
8
(
a
)
.
Wh
e
reas,
Fi
gure
8
(
b
)
de
scri
be
t
he
c
urren
t
s
flo
wing
thr
ough
th
e
c
onver
te
r
s
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