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
)
Vo
l
.
1
0
, No
.
2
, Ju
n
e
20
1
9
, p
p
.
1
0
2
2
~
1
033
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
2.pp1022-1033
1022
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Cu
rrent control of gri
d-conn
ected in
v
erter u
s
ing
integral slidi
ng
mode c
ontrol and res
onant
compensation
S
e
ung-Jin
Yo
o
n
, Thanh
V
an Nguyen, Kyeon
g
-
H
w
a
Kim
Departm
e
nt of E
l
ect
rical
and Info
rmatio
n E
n
g
i
n
e
eri
n
g
,
S
eo
ul Nat
ional Un
i
v
ersi
ty
o
f Scien
ce
a
n
d
Techn
o
l
o
g
y
, K
ore
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
No
v
1
7
,
2
018
Re
vise
d Jan
2
2
, 2019
Ac
ce
p
t
ed
M
ar 7
, 2
0
19
To
e
limin
ate
t
h
e
adv
e
rs
e
ef
f
ect
f
rom
p
a
ram
e
t
e
r
v
a
riati
o
n
s
a
s
w
e
ll
a
s
di
st
orted
gri
d
c
o
nditi
ons,
a
cu
rrent
c
ont
rol
sch
e
me
o
f
an
L
CL-f
iltered
gr
id
-con
nected
in
vert
er
u
sin
g
a
d
is
crete
Integ
r
al
S
li
di
ng
M
o
d
e
C
o
n
t
r
ol
(
IS
M
C
)
an
d
reso
nant
c
o
mpe
n
sa
tion
i
s
pr
e
s
e
n
te
d
.
T
he
p
rop
o
se
d
sc
he
me
i
s
c
o
n
s
truc
te
d
b
as
ed
on
th
e
cascad
ed
m
ul
ti
lo
op
s
t
r
u
c
tu
re,
in
w
h
i
ch
t
h
r
ee
co
n
t
rol
lo
op
s
are
c
o
m
pos
ed
o
f
gri
d
-sid
e
cu
rrent
c
o
n
t
r
ol
,
capacitor
v
o
lt
age
con
t
ro
l,
a
n
d
i
n
v
er
t
e
r-
side
c
urrent
con
t
ro
l.
A
n
activ
e
dam
p
i
n
g
to
s
u
p
p
r
ess
th
e
resonance
c
a
u
s
ed
b
y
L
C
L
f
ilt
er
can
b
e
ef
f
ecti
v
e
l
y
realized
by
m
eans
of
t
h
e
i
n
v
erter-si
d
e
f
eed
b
ack
c
on
trol
lo
op
.
F
u
rthermo
r
e,
t
he
s
eam
less
t
ra
n
s
f
e
r
operat
i
o
n
b
etw
een
t
he
grid-
con
n
ect
ed
m
od
e
and
islan
d
ed
m
od
e
is
achi
e
v
e
d
by
t
h
e
capaci
tor
v
oltag
e
con
t
ro
l
lo
op.
T
o
retai
n
a
h
ig
h
track
in
g
perf
orm
a
n
ce
an
d
rob
u
st
n
es
s
o
f
t
h
e
IS
M
C
a
s
well
a
s
an
e
xc
el
lent
h
arm
o
n
i
c
com
p
ens
a
tio
n
capab
ilit
y
o
f
t
h
e
Reso
nant
C
o
n
t
r
ol
(
RC)
s
chem
e
at
t
he
s
am
e
tim
e
,
tw
o
con
t
ro
l
m
e
t
h
ods
a
re
com
b
ined
i
n
the
prop
os
ed
c
u
rren
t
c
o
n
tro
l
l
e
r.
A
s
a
resul
t
,
th
e
p
ropos
e
d
scheme
y
i
e
lds
a
high
q
uality
o
f
the
inject
ed
g
rid
current
s
and
fas
t
d
ynam
i
c
resp
on
se
e
ven
und
er
d
i
s
t
o
rted
g
ri
d
con
d
iti
ons
.
F
u
rt
herm
ore,
t
o
red
u
ce
th
e
nu
m
b
er o
f
sen
s
ors, a di
s
crete-time red
u
ced-o
rd
er s
tate ob
s
erver
i
s i
n
t
r
od
uced
.
S
i
m
u
la
ti
on
a
nd
exp
e
rim
e
nt
al
r
es
ul
ts
a
re
p
re
sen
t
ed
t
o
demon
s
t
r
at
e
th
e
ef
f
ecti
v
enes
s of th
e
p
ro
po
sed
schem
e
.
K
eyw
ord
s
:
D
i
st
r
i
b
u
te
d
ge
ner
a
t
i
o
n
Gri
d
-co
n
n
ect
ed
i
nv
ert
e
r
Indirect cur
rent cont
r
ol
Inte
gra
l
sl
i
d
i
ng
m
ode
c
ontr
o
l
P
o
w
e
r qua
lit
y
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Kyeo
ng-H
w
a K
i
m
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
and
Inform
ati
on E
n
gi
neer
in
g,
S
e
oul
N
at
io
na
l
U
n
iver
si
t
y
of
S
c
ience
and
Te
c
hno
lo
g
y
,
23
2 G
o
n
g
n
eu
n
g
-r
o, N
ow
on-gu,
S
eoul,
018
1
1
,
K
o
rea
.
Em
ail:
k2h
1@
se
o
u
ltec
h
.ac
.
kr
1.
I
N
TR
OD
U
C
TI
O
N
In
r
e
c
e
nt
y
ea
rs,
re
n
e
wa
b
l
e
e
n
ergy
s
o
u
rc
es
(
R
E
Ss
)
s
u
c
h
a
s
wi
nd
a
nd
so
lar
a
r
e
a
t
tr
a
c
ti
n
g
g
r
eat
atte
n
t
ions
d
ue
t
o
the
d
e
p
l
e
t
i
on
of
f
oss
i
l
ene
r
gy
a
n
d
e
n
vi
r
onm
en
ta
l
i
s
sue
s
[
1-
3].
To
i
n
t
e
g
ra
te
v
ari
o
us
R
ES
s
in
to
t
he
u
til
it
y
grid,
D
i
st
r
i
b
u
t
ed
G
ener
a
tio
n
(DG
)
s
yst
e
ms
a
s
a
c
om
ponen
t
o
f
m
i
c
r
o
g
ri
d
(MG
)
h
as
b
e
e
n
deve
l
ope
d [4].
Wit
h the
a
dva
n
t
a
g
e
s
o
f e
a
sy i
nte
g
ra
ti
on of r
e
s
ou
r
ces,
fle
x
ible
i
nsta
l
l
a
t
i
o
n
loca
tio
n, an
d
relia
b
l
e
opera
tio
n,
D
G
-
based
MG
b
e
c
om
es
a
f
u
t
ure
tren
d
o
f
c
ons
t
r
uct
i
n
g
t
he
e
l
e
ctric
p
o
wer
sy
stem
[
5].
Bas
i
c
a
ll
y,
MG
i
s
f
o
rm
ed
b
y
c
o
n
n
ec
t
i
n
g
D
G
un
i
t
s
w
i
t
h
e
ne
rg
y
s
t
ora
g
e
sys
t
em
a
n
d
l
o
ca
l
l
o
a
d
s.
T
o
in
terface
D
G
un
its
w
ith
t
he
u
ti
l
ity
g
r
i
d,
t
he
I
n
t
er
l
i
n
k
i
n
g
C
o
n
v
e
r
ters
(
I
C
s)
a
re
u
s
u
a
l
l
y
e
m
pl
o
y
ed.
Cur
r
en
tl
y,
m
ost
of
I
C
s
a
do
p
t
a
V
o
l
t
a
g
e
S
o
urc
e
I
nverte
r
(
V
S
I)
w
ith
c
urre
n
t
c
on
tro
l
t
o
reg
u
la
te
th
e
curre
nt
i
nj
e
c
t
e
d
i
nt
o
the
gri
d
.
Th
e
gri
d
-
con
n
ec
ted
V
S
I
sh
ou
l
d
b
e
c
o
n
t
r
o
l
l
e
d
t
o
ac
hi
e
v
e
a
h
i
gh
per
f
o
r
ma
nc
e
of
i
n
j
ecte
d
g
ri
d
c
u
r
r
e
nts
i
n
t
he
s
e
n
se
o
f
fa
st
d
yna
m
i
c
respo
n
se,
robus
t
n
ess
t
o
p
er
tur
b
a
t
ion,
z
e
r
o
tra
c
k
i
n
g
er
ror,
a
nd
low
Tot
a
l
H
a
rm
onic
Di
st
o
r
t
i
o
n
(
T
HD)
.
Wit
h
t
he
a
i
m
o
f
a
tte
nua
t
i
n
g
t
he
h
a
r
mon
i
c
c
o
mpo
n
e
n
ts
c
a
u
se
d
b
y
t
h
e
p
u
l
s
e
w
i
d
t
h
m
o
d
u
l
a
t
i
o
n
(PW
M
),
t
h
e
f
ilt
e
r
i
s
c
o
n
n
ect
ed
b
e
t
we
en
t
h
e
u
ti
l
i
t
y
g
ri
d
a
nd
VSI
[
6
]
.
I
n
r
e
c
e
n
t
y
e
a
r
s
,
L
C
L
f
i
l
t
e
r
s
a
r
e
w
i
d
e
l
y
app
l
ied to a gri
d-co
nnec
t
e
d
i
n
v
er
t
e
r sys
t
em
b
e
c
a
u
se
t
he
y prov
i
d
e a b
e
t
t
e
r
harm
o
n
i
c
a
tte
n
u
at
ion ca
p
a
b
ili
ty
[
7].
M
o
r
e
o
v
e
r
,
L
C
L
f
i
l
t
e
r
h
a
s
l
o
w
e
r
c
o
s
t
a
n
d
s
m
a
l
l
e
r
p
h
y
s
i
c
a
l
s
i
z
e
i
n
c
o
m
p
ariso
n
t
o
L
fil
t
e
r
t
o
ach
ie
ve
t
he
s
am
e
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
,
I
S
S
N
:
2088-
86
94
Cu
rr
ent
c
ont
rol
o
f
gri
d
-c
on
n
ect
ed
in
v
e
rt
er
usi
n
g
i
n
t
e
g
r
al
sli
d
i
n
g
mod
e
con
t
rol
an
d…
(S
eu
ng
-J
in
Y
oon
)
1
023
harm
on
ic
a
t
t
en
uat
i
on.
D
ue
t
o
t
h
is
a
d
v
a
n
ta
g
e
,
the
stud
y
o
f
L
CL
f
ilter
ha
s
be
en
a
t
o
p
i
c
o
f
in
tense
r
e
s
e
a
r
ch
ma
inly
i
n
term
s
of
d
es
i
gn
a
n
d
de
ve
lo
pm
ent
of
c
o
n
tr
ol
m
et
ho
ds.
H
ow
eve
r
,
be
cause
t
he
L
C
L
f
ilter
c
a
u
s
es
t
h
e
resona
nce
pro
b
l
em
,
a
current
c
on
tro
l
s
t
r
a
t
eg
y
of
a
n
LCL-filter
e
d
gri
d
-co
n
n
e
c
te
d
i
n
verter
s
ho
ul
d
be
c
ar
e
f
u
lly
d
e
si
gn
ed
t
o
s
t
ab
ili
z
e
th
e
sy
st
em.
Th
e
reso
n
a
n
c
e
p
r
obl
em
o
f
LC
L
fi
lt
e
r
can
b
e
d
e
alt
with
b
y
t
w
o
ma
i
n
m
e
t
h
o
d
s
,
n
a
m
e
l
y
,
t
h
e
p
a
s
s
i
v
e
dam
p
i
ng
a
n
d
a
c
tive
da
mp
i
ng.
T
he
p
a
ssi
ve
d
am
pin
g
i
s
sim
p
l
y
a
c
h
ie
ved
b
y
a
dd
i
n
g
a
r
e
s
i
st
or
i
n
se
r
i
es
w
ith
t
he
fi
l
t
e
r
c
a
p
ac
i
t
or
[
8]
.
D
e
spi
t
e
s
i
mple
i
m
p
l
e
me
nt
a
tio
n,
t
h
i
s
me
t
h
o
d
c
a
u
ses
e
x
tra
l
o
sses
t
h
rou
g
h
h
ea
t
dissi
pat
i
on,
resul
t
i
ng
in
r
educe
d
s
yst
e
m
effic
i
e
n
c
y
.
To
overc
ome
such
a
l
i
m
i
ta
t
i
on,
t
he
a
c
t
i
v
e
dam
p
i
ng
t
e
c
h
n
i
qu
e
w
h
ic
h
dam
p
s
t
h
e
r
e
s
ona
nce
by
a
c
o
n
t
ro
l
a
l
g
o
r
ith
m
h
a
s
been
i
n
t
r
o
duce
d
.
T
o
s
t
ab
i
liz
e
an
i
n
v
e
rte
r
s
yste
m
wit
h
o
u
t
incre
a
s
i
ng
t
h
e
lo
ss,
an
a
ct
ive
dam
p
i
n
g
ap
pro
a
ch
b
a
s
e
d
o
n
a
virt
ua
l
r
e
sis
t
a
n
ce
has
bee
n
s
t
u
d
i
ed
by
us
in
g
t
h
e
fi
l
t
e
r
c
a
p
aci
ta
n
c
e
curre
nt
f
ee
d
b
a
c
k
[9].
H
o
w
ever
,
this
s
che
m
e
r
e
quires
ex
tra
sens
ors
t
o
m
e
a
sure
t
he
c
a
p
ac
it
or
curr
ents,
whi
c
h lea
d
s
to t
he c
os
t
incre
a
se
a
n
d
ha
r
dwar
e c
o
mple
x
it
y
of syst
e
m.
To
p
r
o
vide
u
n
i
nterru
pta
b
le
p
o
w
er
t
o
t
h
e
c
r
i
t
i
c
al
l
oad
e
v
e
n
i
n
t
he
o
cc
urre
nce
of
u
til
i
t
y ou
tage,
t
h
e
gri
d
-
con
n
ec
ted
in
v
e
rter
s
hou
l
d
o
per
a
te
i
n
b
o
t
h
t
he
g
ri
d-co
nn
e
c
ted
m
o
de
a
nd
is
lan
d
e
d
m
o
d
e
[1
0].
In
t
h
e
g
ri
d-
c
o
nn
e
c
t
e
d
mo
de
,
t
h
e
i
n
v
e
rte
r
is
op
e
r
at
ed
w
ith
cu
rre
n
t
-co
n
t
r
ol
l
e
d m
o
de t
o in
jec
t
t
he p
ow
e
r
in
t
o the
u
til
i
t
y
gri
d
,
w
h
i
l
e
t
h
e
cr
it
i
c
a
l
l
oad
vo
lta
g
e
i
s
m
a
i
n
ta
i
n
e
d
b
y
the
gr
id
v
o
l
ta
ge.
O
n
c
e
t
he
u
t
i
l
i
t
y
f
au
l
t
o
cc
urs,
t
he
i
nver
t
e
r
opera
tio
n
i
s
s
w
i
tc
hed
i
n
t
o
t
he
i
slan
de
d
m
ode,
in
w
h
i
ch
t
he
i
n
v
e
r
t
er
i
s
opera
t
e
d
w
i
th
t
he
v
o
l
t
a
ge-c
o
n
tr
ol
le
d
mode
.
The
tran
si
tio
n
be
tw
ee
n
the
s
e
tw
o
co
n
t
rol
m
o
des
s
h
o
u
l
d
b
e
seam
les
s
t
o
preve
n
t
t
h
e
l
o
a
d
d
a
m
a
g
e
due
t
o
uns
t
a
b
l
e
l
o
ad
v
olta
ge
. F
or thi
s
purp
o
se, a mult
i
l
o
o
p
in
d
ire
c
t
c
urrent co
n
t
ro
l m
e
th
od has b
een pre
se
n
t
e
d
a
s one
of
t
he
e
ffec
t
i
v
e
a
pproac
h
es.
The
sea
m
le
ss
t
ra
nsfer
is
ach
i
e
v
e
d
by
c
o
mbi
n
i
ng
the
o
u
ter
c
o
n
t
ro
l
lo
op
of
g
rid-
side
c
urr
e
nt
a
n
d
i
nner
c
ontr
o
l
lo
op
o
f
f
il
t
e
r
ca
paci
t
o
r
vo
l
t
a
g
e
i
n
[1
1].
By
c
on
tro
l
li
ng
t
h
e
c
a
pac
i
t
o
r
v
o
l
t
a
ge
i
n
bo
th
t
he
g
r
i
d-
con
n
ec
te
d
a
n
d
i
s
lan
d
e
d
m
od
es,
t
h
is
m
et
ho
d
i
s
c
a
p
a
bl
e
of
s
upp
ly
i
n
g
the
c
r
i
t
i
c
al
l
o
a
d
wi
th
a
st
a
b
le
a
n
d
s
ea
m
l
ess
v
o
lta
ge
dur
in
g
the
w
h
ole
peri
o
d
.
H
o
w
e
ve
r,
t
he
c
o
n
tr
ol
d
e
s
ign
i
s
q
ui
te
c
om
plic
a
t
e
d
.
F
u
r
t
he
rm
o
r
e,
t
his
sc
hem
e
r
eq
uires
e
x
tra
se
n
s
i
ng
de
vi
c
e
s
t
o
i
m
p
l
e
m
e
n
t
a
d
di
tio
na
l
c
o
n
t
r
o
l
lo
op
s.
I
n
a
d
d
i
t
i
on,
the a
d
verse
gri
d
vo
l
tage
s
suc
h
a
s
the ha
rm
oni
c
d
i
s
t
or
t
i
o
n
h
a
v
e
no
t
bee
n
a
ddre
s
se
d.
To
c
on
tro
l
t
he
g
ri
d-co
nnec
t
e
d
i
n
v
e
r
ter,
t
he
p
r
opor
t
i
o
n
al-i
nte
g
r
al
(
PI)
d
e
c
o
upl
i
n
g
co
nt
ro
l
h
a
s
been
w
i
de
ly
u
se
d
w
i
t
h
t
he
vol
ta
ge
f
e
e
d
forw
a
r
d
be
ca
use
o
f
i
t
s
s
imp
lic
it
y
a
n
d
st
ab
ili
ty
.
Ho
we
v
e
r,
s
i
n
ce
t
h
e
con
v
e
n
t
i
ona
l
P
I
d
eco
up
l
i
n
g
c
on
t
r
o
l
i
n
h
er
en
t
l
y
ha
s
a
p
oor
d
is
t
u
r
ba
nce
reje
c
tio
n
c
a
p
a
b
i
lit
y,
it
is
not
a
s
u
ita
b
l
e
wa
y
to
c
on
t
r
ol
g
ri
d
-
c
o
n
n
e
c
t
e
d
i
nv
ert
e
rs
u
nde
r
g
r
i
d
vol
t
a
g
e
p
e
r
t
ur
b
e
d
by
d
i
s
t
u
rba
n
ce
s.
T
o
impro
v
e
t
h
e
pow
e
r
qua
l
ity
o
f
i
n
v
e
rter
s
yste
m,
s
e
v
era
l
s
tu
dies
h
a
v
e
bee
n
i
n
v
es
ti
ga
t
e
d
re
ga
rd
i
n
g
th
e
h
a
rmo
n
i
c
co
mp
ens
a
ti
on
st
r
a
te
gy.
T
he
h
ar
monic
com
p
e
n
sa
tio
n
c
a
n
b
e
achie
ve
d
b
y
t
w
o
m
et
h
o
d
s,
n
am
ely,
s
e
l
e
c
t
i
ve
a
nd
no
n-
sel
ecti
v
e
schem
e
s.
A
s
a
selec
t
i
v
e
ha
rm
on
i
c
c
om
pensa
t
i
o
n
sc
hem
e
,
the
p
r
o
p
o
rtio
na
l-
resona
n
t
(
P
R
)
c
ontro
lle
r
is
w
ide
l
y
em
plo
y
e
d
b
e
c
a
u
se
i
t
pr
ovi
de
s
a
g
o
o
d
r
e
fe
ren
c
e
t
r
ack
i
n
g
as
w
ell
as
h
arm
onic
c
o
m
p
ensa
t
i
on
[
1
2
]
.
H
oweve
r
,
as
t
h
e
c
o
mp
en
sate
d
h
a
rmo
n
i
c
t
erms
a
re
i
n
c
re
a
s
ed
,
th
e
comp
u
t
ati
o
n
a
l
b
urde
n
is
a
l
s
o
incre
a
se
d
due
t
o
t
h
e
implem
e
n
ta
t
i
o
n
of separ
a
te
r
e
s
on
an
t
co
ntro
ll
e
r
s.
A
s
a
non-sele
c
tive
harm
o
n
i
c
c
ompe
nsa
tio
n
strate
gy,
t
h
e
p
re
dic
t
i
ve
c
on
tro
l
[
13]
a
n
d
r
e
p
et
iti
v
e
con
t
ro
l
[
1
4]
s
c
h
em
es
h
a
v
e
be
en
s
tu
die
d
.
Alt
h
o
u
gh
the
predic
t
i
ve
c
on
t
r
ol
h
a
s
a
c
ap
a
b
il
it
y
o
f
p
rov
i
di
ng
f
ast
dy
nam
i
c
re
sp
o
n
se
w
i
t
h
m
i
ni
m
u
m
TH
D
l
e
v
e
l,
it
is
v
e
r
y
se
ns
iti
ve
t
o
sy
st
em
p
a
r
amet
er
c
h
a
ng
e
.
T
h
e
r
ep
et
i
t
i
v
e
con
t
ro
l
pro
v
i
d
e
s
a
go
od
harm
onic
re
jec
t
io
n
for
nonl
i
n
ea
r
loads
w
i
t
h
p
erio
dic
di
st
ort
i
ons.
H
o
w
e
ve
r,
s
low
d
y
n
a
mi
c
re
sp
on
se
i
s
t
h
e
ma
i
n
s
ho
rt
co
mi
ng
o
f
thi
s
t
yp
e
o
f
c
o
n
t
r
o
l
l
er d
ue to th
e
le
arn
i
ng
proc
e
ss. T
o
o
v
e
r
c
om
e
the
draw
ba
cks
of
t
he
a
fore
me
nt
ione
d
a
p
proa
che
s
,
a
no
nl
ine
a
r
con
tro
l
s
t
r
at
egy
s
u
c
h
a
s
a
sl
i
d
in
g
mod
e
c
o
n
tr
ol
(S
M
C
) has be
e
n
prese
nte
d
.
S
i
nce t
h
e S
M
C i
s
i
nhere
n
tly i
ns
ens
i
t
i
ve
t
o the
pre
s
e
n
ce
of para
me
ter uncer
ta
in
tie
s
and
ex
ter
n
a
l
d
i
s
t
u
rbance
s,
m
any
st
u
d
i
es
h
av
e
bee
n
c
ar
ried
out
t
o
a
p
p
l
y
th
e
S
M
C
te
c
h
ni
que
t
o
gr
id-c
o
nne
cte
d
in
verter
s
[1
5-1
7
].
A
S
MC sc
h
e
m
e
ba
se
d o
n
d
ua
l-l
oop
co
n
t
rol
str
u
ct
ure
is pre
sen
t
ed
in
[1
5]. This
ap
pr
o
a
ch
not
on
ly
g
uar
a
n
t
ee
s
the
sy
stem
s
tab
i
li
ty,
b
u
t
a
l
so
a
lle
v
i
ate
s
t
he
c
ha
t
t
eri
ng
p
h
e
n
ome
n
o
n
e
ffec
tive
l
y.
I
n
orde
r
t
o
enha
nc
e
t
h
e
t
r
acki
n
g
per
f
orm
a
nce
an
d
r
e
d
u
ce
t
h
e
T
H
D
o
f
i
nje
c
t
ed
g
ri
d
cu
rre
n
t
s
eff
e
c
t
i
v
el
y
,
a
S
MC
s
ch
e
m
e
com
b
i
n
e
d
w
it
h
mult
iple
r
eso
n
a
n
t
te
rms
i
s
p
r
o
p
o
se
d
i
n
[
1
6
]
.
H
o
w
e
ve
r,
t
he
i
mplem
e
n
t
a
t
i
on
of
t
h
i
s
sche
m
e
i
s
c
o
mp
li
cat
ed
i
n
p
r
a
c
t
i
c
e
s
i
n
ce
i
t
empl
oy
s
man
y
re
son
a
n
t
t
e
r
ms
i
n
t
he
s
li
di
ng
s
u
rfa
ce
fu
n
c
tio
n.
M
or
eo
v
e
r,
t
his
appr
oa
ch
r
equ
i
re
s
seve
ral
se
n
s
ing
de
v
i
ce
s
to
m
ea
sure
t
he
i
n
v
e
r
t
e
r
-s
i
d
e
cu
rre
n
t
s
a
nd
cap
aci
t
o
r
v
o
lt
a
g
es,
wh
ich
incre
a
ses
t
h
e
s
y
s
t
em
c
ost
a
n
d
ha
rdw
a
r
e
c
o
m
pl
e
x
ity.
To
e
li
m
i
na
te
t
he
s
t
e
a
dy-s
t
a
t
e
erro
r
,
a
n
i
n
te
gr
al
s
li
din
g
mo
d
e
c
ont
rol
(I
SM
C)
i
s
d
e
si
gn
ed
b
y
usin
g
th
e
co
nti
nuou
s
-
t
i
m
e
mo
del
[1
7],
in
w
h
i
c
h
t
he
i
n
t
e
g
r
a
l
t
e
rm
i
s
adde
d
i
n
t
o
t
h
e
s
l
i
d
i
ng
fu
nc
tio
n.
F
or
e
a
s
ine
s
s
in
i
m
p
l
e
me
ntat
io
n
b
y
di
g
ita
l
c
o
ntro
l
l
er,
a
discr
e
te
S
M
C
appr
oa
ch is
de
vel
o
ped
for gr
id-
c
o
nnec
t
e
d
in
v
erte
rs [1
8
]
, [19].
Th
is
p
a
p
er
p
re
sen
t
s
a
c
u
r
r
ent
con
t
ro
l
sc
hem
e
f
or
a
t
hree
-p
hase
LC
L-fil
t
e
red
g
r
i
d
-c
on
n
ect
ed
i
nv
ert
e
r
base
d
o
n
a
d
isc
r
ete
in
tegr
a
l
s
lid
i
ng
mo
de
c
on
tro
l
(IS
M
C
)
c
o
mb
i
n
ed
w
it
h
re
sona
nt
c
ompe
nsat
ion
.
T
he
pro
pose
d
c
o
n
tr
ol
s
c
h
e
m
e
i
s
c
onstruc
t
e
d
by
u
sin
g
t
he
m
u
lti
lo
o
p
i
n
d
i
re
ct
c
on
tro
l
s
t
r
uc
t
u
re
w
hic
h
i
s
c
o
m
pose
d
of the
gr
i
d-s
i
de
curr
e
nt c
ontr
o
l loo
p
,
ca
pac
i
t
o
r vo
ltage
c
ont
ro
l lo
op,
a
nd in
verter
-side c
u
rre
nt
c
on
tro
l
l
o
o
p
. By
a
d
din
g
t
h
e
c
a
p
ac
i
t
o
r
v
o
lt
ag
e
co
nt
ro
l
l
o
op
i
nt
o
th
e
c
ont
rol
st
ru
ct
u
r
e
,
t
h
e
s
ea
ml
e
ss
t
r
a
n
sfer
b
et
we
en
t
he
g
rid
-
con
n
ec
ted
m
o
d
e
and i
s
lan
d
e
d
m
ode can be a
c
hie
v
e
d
. In
a
d
d
it
io
n,
a
di
screte-
tim
e
reduced-order
s
tate
o
bser
ver
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
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
1
0
22
–
1
033
1
024
is
i
n
t
r
o
d
u
c
e
d
w
it
h
the
aim
o
f
r
e
duc
i
ng
the
t
o
ta
l
n
u
m
b
er
o
f
se
ns
ing
de
v
i
c
e
s.
I
n
t
h
e
pr
o
p
o
se
d
co
ntr
o
l
sc
he
me
,
the
ac
t
i
ve
d
a
m
pi
n
g
i
s
r
e
a
liz
e
d
t
hr
ou
g
h
a
f
e
e
dbac
k
c
ontr
o
l
l
oop
o
f
i
n
v
erter
-
si
de
c
urre
nt
b
y
u
s
in
g
the
e
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m
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te
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e
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t
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e
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.
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t
h
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p
r
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p
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se
d
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o
l
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o
t
o
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sur
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s
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h
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e
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t
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the
use
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d
d
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t
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l s
e
nsin
g
de
vices
can
b
e
a
v
o
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d.
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it
h
the
m
o
t
i
v
at
io
n
t
o
i
m
p
r
o
ve
t
he
c
ur
r
e
nt
q
u
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li
t
y
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nj
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n
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o
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r
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m
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i
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t
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e
s
o
n
an
t c
ontr
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s
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R
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s
)
ar
e c
o
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ed
w
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t
h
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h
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d
i
s
c
r
e
t
e
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n
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ur
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c
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ol
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e
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t
he
d
isc
r
ete-
tim
e
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ain.
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hi
le
t
he
r
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b
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stne
ss
a
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fa
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dyna
mic
r
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spon
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r
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rmo
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i
c
c
o
mp
en
sat
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o
n
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ased
o
n
t
h
e
RC
.
T
o
v
e
r
i
f
y
t
h
e
e
f
f
e
c
t
iv
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ss
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d
val
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it
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p
r
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p
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d
c
u
r
r
ent
c
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n
t
r
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l
sche
me
,
the
P
S
I
M
sof
t
w
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r
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-
b
ased
s
i
m
ula
t
i
o
n
s
a
n
d
e
xper
i
m
ents
h
a
v
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bee
n
car
r
i
ed
o
ut
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g
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e
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pha
se
2
k
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pr
o
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o
t
ype
g
r
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d
inv
e
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t
er
.
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e
n
t
i
r
e
con
t
r
o
l
a
l
gor
i
t
hm
i
s
im
p
l
e
m
e
n
ted
on
a
d
ig
it
a
l
si
gna
l pr
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r
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D
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TMS32
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2
833
5 a
n
d
t
e
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t
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d
u
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pe
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ized
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s
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e
c
t
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2
pr
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n
t
s
t
h
e
m
odel
i
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g
o
f
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ver
t
e
r
.
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e
c
t
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3
e
xp
l
a
in
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t
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p
r
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d
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ch
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m
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n
s
e
c
t
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t
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s
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ula
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io
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n
d
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x
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MODELING OF
L
C
L-FI
L
TERED GRID-CONNECT
E
D
INVE
R
TER
F
i
gur
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1
sh
o
w
s
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con
f
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g
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ati
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n
of
a
t
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ph
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s
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gr
i
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c
t
ed
inv
e
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c
onne
c
t
e
d
t
o
the
gr
i
d
thr
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g
h
a
n L
C
L f
i
l
t
er
,
i
n
w
h
i
c
h
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sent
s t
h
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D
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l
ink
vo
lta
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R
1
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re t
he
f
ilter res
i
stan
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L
1
an
d
L
2
a
r
e
t
h
e
f
ilt
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c
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a
n
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f
is
t
h
e f
i
l
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r
c
apac
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ce.
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he
s
ta
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qua
t
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t
he gr
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nv
e
r
t
e
r
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expr
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r
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r
enc
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f
r
a
m
e
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S
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a
s fo
l
l
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ws:
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i
gur
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1.
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o
n
f
i
gur
a
tio
n
of
t
h
r
e
e
-
p
h
a
s
e
gr
id-
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on
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t
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d
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n
v
e
r
te
r
with LCL
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ilter
22
22
2
2
22
22
2
2
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qq
c
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c
d
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L
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d
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RL
L
L
dt
(
1
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11
1
1
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11
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1
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c
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d
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v
v
RL
L
L
dt
(
2
)
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21
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0
01
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00
1
/
f
cq
c
q
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q
f
f
cd
c
d
d
d
f
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vv
i
i
C
d
C
vv
i
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C
dt
(3
)
whe
r
e
the
su
b
s
cr
i
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ts
“
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an
d
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[]
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iq
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inve
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a
ng
ular
f
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r
om
(
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,
t
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c
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uo
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s
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t
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mode
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ter
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s;
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(
)
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t
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94
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o
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a
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gita
l
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m
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ta
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,
th
e
c
o
nti
nuo
us-t
i
m
e
mo
d
e
l
o
f
t
h
e
in
vert
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s
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m
ca
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k
k
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6
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(
7
)
w
h
er
e the
m
a
trice
s
d
A
,
d
B
,
d
C
,
and
d
D
can
b
e c
a
l
c
ul
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ed w
i
t
h
t
h
e sa
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p
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.
(
1
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)
3.
PROPO
S
E
D
DISCRE
TE
S
LIDING MODE CONTRO
L WITH
H
ARMONIC
CO
M
PENS
AT
I
ON
F
i
gure
2
s
how
s
t
h
e
o
v
era
ll
b
l
oc
k
d
i
a
g
r
a
m
of
t
h
e
p
ro
p
o
se
d
con
t
ro
l
sc
hem
e
f
or
a
n
L
C
L-fil
t
ere
d
t
hre
e
-
pha
se
g
r
i
d-
co
nnec
t
e
d
i
nve
r
t
er.
The
pr
opose
d
c
on
tro
l
s
chem
e
m
a
in
ly
c
onsist
s
of
a
n
IS
MC
,
r
e
sonant
c
o
mp
e
n
sa
tio
n
,
a
n
d
r
e
d
u
ced
-o
rd
er
o
b
s
erv
e
r
i
n
t
h
e
d
isc
r
et
e-t
i
m
e
d
om
ai
n
.
T
he
i
nver
t
er
r
efe
r
enc
e
v
olta
ge
s
by
the
pr
op
ose
d
c
urr
e
nt
c
o
n
t
r
o
ll
er
a
re
a
pp
lie
d
thr
o
u
g
h
t
he
s
p
a
ce
v
ecto
r
P
WM
.
Th
e
p
r
o
pose
d
c
on
t
r
ol
s
c
h
e
me
requ
ire
s
t
he
m
e
a
sure
me
nt
o
f
onl
y
t
h
e
gr
id-s
ide
curr
en
ts
a
n
d
g
ri
d
vo
l
t
age
s
.
The
m
easur
e
d
g
r
i
d
vo
ltag
e
s
a
r
e
u
s
ed
i
n
t
h
e ph
ase
-
l
o
c
k
e
d
l
oo
p
(PLL) sc
h
eme
t
o
d
e
t
ermi
n
e
the
g
ri
d p
h
ase
an
gle.
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
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
1
0
22
–
1
033
1
026
F
i
gur
e
2.
L
CL-
f
i
l
t
er
e
d
t
hr
e
e
-
pha
se
g
r
i
d-
c
o
nn
ecte
d
i
n
v
er
ter
and
t
h
e
pr
op
os
e
d
c
on
tr
o
l
s
c
h
e
m
e
F
i
gur
e
3
sh
ow
s
t
h
e
pr
o
p
o
se
d
c
u
r
r
e
nt
c
o
n
tr
o
l
s
c
h
e
m
e
for
t
h
e
q
-
a
xis
c
u
r
r
ent
ba
se
d
on
t
h
e
mult
i
l
oo
p
struc
t
ure
.
T
o
r
e
aliz
e
a
c
a
sca
d
ed
m
u
lti
lo
o
p
c
o
n
tro
l
ler
,
a
l
l
t
he
s
y
st
e
m
s
t
a
t
e
s
sh
ou
l
d
b
e
a
v
ai
la
bl
e
for
fe
edba
c
k
pur
pose
.
H
ow
ever
,
add
iti
ona
l
se
nsin
g
de
v
i
ces
u
s
u
al
ly
i
nc
r
e
a
s
e
t
he
t
ota
l
c
ost
an
d
ha
r
d
w
a
r
e
c
om
p
l
e
x
ity
i
n
a
pr
act
ica
l
i
n
v
e
r
t
e
r
syste
m
.
The
r
efor
e,
a
d
i
s
c
r
ete-
tim
e
reduc
ed-o
r
d
e
r
s
tate
obs
er
ve
r
is
e
m
p
l
o
yed
t
o
o
b
t
a
i
n
t
h
e
est
i
m
a
t
e
d
s
i
gnal
s
f
o
r
t
h
e
i
nve
rt
e
r
-si
d
e
cu
rren
t
s
an
d
th
e
cap
ac
i
t
o
r
v
o
l
ta
g
e
s
i
n
t
he
p
r
o
pose
d
c
on
t
r
o
l
s
che
m
e
.
The
d
i
scre
t
e
-t
i
m
e
inverte
r
m
odel i
n
(
6) a
nd (7)
c
a
n be
re
w
ritte
n
a
s
F
i
gur
e
3.
P
r
op
ose
d
c
ur
r
e
nt
c
o
n
tr
ol
s
c
h
em
e
;
q
-axi
s
cu
rr
en
t co
n
t
rol
11
1
1
2
1
1
1
22
1
2
2
2
2
2
(1
)
(
)
(
)
(
)
()
()
(1
)
(
)
(
)
(
)
kk
k
k
kk
kk
k
k
xA
A
x
B
D
ue
xA
A
x
B
D
(
11)
1
12
2
()
()
()
k
k
k
x
yC
C
x
(
1
2
)
wh
ere
12
2
[]
T
qd
ii
x
a
nd
21
1
[]
T
q
d
cq
cd
ii
v
v
x
.
Then,
t
h
e
e
s
tim
at
ed
s
tate
v
aria
bles
c
a
n
b
e
o
b
ta
i
n
e
d
b
y
a
p
p
l
yi
n
g
t
h
e
d
i
s
c
r
ete
-
ti
m
e
r
educ
ed-
o
r
d
er
s
ta
te
obser
ver
as
[
20]
21
ˆ
()
(
)
()
kk
k
x
η
Kx
(
1
3
)
22
1
2
22
12
21
1
1
21
2
1
(1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
()
(
)
()
kk
k
k
kk
η
AK
A
η
AK
A
K
y
A
K
A
y
BK
B
u
D
K
D
e
(
14)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
,
I
S
S
N
:
2088-
86
94
Cu
rr
ent
c
ont
rol
o
f
gri
d
-c
on
n
ect
ed
in
v
e
rt
er
usi
n
g
i
n
t
e
g
r
al
sli
d
i
n
g
mod
e
con
t
rol
an
d… (S
eu
ng
-J
in
Y
oon
)
1
027
w
h
e
r
e
t
h
e
s
y
m
b
o
l
“
ˆ
”
d
e
n
o
t
e
s
t
h
e
e
s
t
i
m
a
t
e
d
v
a
r
i
a
b
l
e
s
a
n
d
K
i
s
t
h
e
o
b
se
r
v
e
r
g
ain
m
a
tr
ix.
The
e
s
t
i
m
a
ted
varia
b
l
e
s
2
ˆ
x
ar
e
use
d i
n
the
m
ul
t
ilo
op
co
n
t
ro
l
str
u
ct
ure
in F
igu
r
e
3
i
n
stea
d of
actua
l
me
asurem
e
n
ts.
To
c
o
n
tr
ol
t
he
g
rid-side
c
u
rre
nt
s
w
i
t
h
a
g
o
od
d
i
st
urb
a
nce
re
jec
tio
n,
a
n
I
S
M
C
a
n
d
res
ona
n
t
com
p
en
sat
i
on
a
r
e
desi
gn
e
d
i
n
t
h
e
disc
re
te
-ti
m
e
d
o
ma
i
n
.
F
r
om
(
1
)
,
t
h
e
sta
t
e
mode
l
o
f
a
g
rid-s
i
de
c
ur
rent
i
s
expre
s
se
d i
n
th
e
S
RF
a
s follo
w
s
:
11
()
g
gc
g
t
xA
x
B
v
D
e
(
1
5
)
w
h
er
e
[]
T
cc
q
c
d
vv
v
2
2
/
/
g
RL
R
L
A
,
2
2
1/
0
01
/
g
L
L
B
,
2
2
1/
0
01
/
g
L
L
D
.
(
16)
Th
e
c
o
n
t
i
n
uous-t
i
m
e mo
d
e
l
of g
ri
d
-
si
d
e
c
u
rren
t
c
an
b
e
si
mil
a
rly
discr
e
t
i
z
e
d
b
y
us
in
g
(8) - (
10) a
s
11
(1
)
(
)
(
)
(
)
(
)
dg
dg
c
d
g
kk
k
k
k
xA
x
B
v
D
e
.
(
1
7
)
Le
t
u
s
d
ef
in
e
th
e erro
r st
at
e
v
a
ri
a
b
l
e
E
(
k
)
as
*
11
()
()
()
kk
k
Ex
x
(
1
8
)
w
h
er
e
*
1
()
k
x
i
s
the
referen
c
e
grid-s
ide
curre
nt
v
ect
o
r
.
To
e
li
mi
nat
e
t
h
e
s
t
e
a
dy
-st
a
t
e
e
rro
r
,
a
n
int
e
g
ral
sl
idi
ng
surfa
ce
fu
nc
ti
o
n
S
(
t
)
i
s
sel
ec
t
e
d
a
s
()
()
()
I
k
tt
t
s
S
EE
(
1
9
)
w
h
er
e
k
I
is the
in
t
e
gral
g
a
i
n. Thi
s in
te
g
r
al
sli
d
ing
su
rface
c
an be
di
s
cre
tiz
e
d
by
usi
n
g
t
he
r
e
l
a
t
i
o
n
as
1
1
2(
1
)
(1
)
s
z
s
Tz
.
(
2
0
)
The
n
,
the
i
n
te
g
r
al slidi
n
g
sur
fac
e
func
t
i
o
n
c
a
n
b
e
expre
s
se
d in
t
he
d
i
s
c
r
ete-
t
i
m
e
doma
i
n
as
foll
o
w
s
:
(1
)
(
1
)
(
)
(1
)
(
)
(
)
22
Is
Is
kT
k
T
kk
k
k
k
k
SE
E
E
E
S
.
(
21)
In
g
e
n
era
l
,
the
S
MC
s
uff
e
rs
f
ro
m
t
h
e
ch
a
t
t
e
ri
ng
p
h
e
no
men
o
n
th
at
c
au
se
s
cu
rre
nt
h
a
rmo
n
i
cs,
incre
a
ses po
w
e
r l
o
sse
s,
a
nd
a
l
so pro
d
u
ces se
v
er
e
e
l
ectr
o
m
a
gne
ti
c
c
o
mp
atib
i
l
i
t
y
noi
se
i
n
i
n
v
e
rt
e
r
a
p
pli
c
a
t
ion
s.
I
n
o
r
d
e
r
t
o
e
l
i
m
i
n
a
t
e
s
u
c
h
a
c
h
a
t
t
e
r
i
n
g
p
r
o
b
l
e
m
,
t
h
e
s
t
u
d
y
i
n
[
21]
g
a
v
e
the
c
o
m
p
le
t
e
d
efin
it
ion
a
nd
d
e
tai
l
e
d
ph
ysic
a
l
e
xpla
n
a
t
ion
for
t
h
e
q
u
as
i-sl
idi
ng
mode
, in
w
h
i
c
h a
re
a
chin
g c
o
n
d
i
t
i
on i
s
expr
ess
e
d a
s
fol
l
o
w
s
:
(
1
)
(
)
(
)
s
gn(
(
)
)
ss
kk
q
T
k
T
k
SS
S
S
,
0
q
,
0
.
(
2
2
)
The
co
ntro
l i
n
p
u
t
o
f the
IS
MC
can
b
e o
b
ta
i
n
e
d
as
*
eq
L
N
uu
u
u
(
2
3
)
w
h
er
e
eq
u
i
s
t
h
e
eq
uiv
a
l
ent
co
nt
ro
l
,
L
u
i
s the line
a
r
c
on
tro
l
,
and
N
u
i
s
t
h
e
no
nli
n
ear
s
wi
t
c
hi
ng
c
on
t
r
o
l
.
Fro
m
(15),
(18)
,
(21),
and
(22), the
se
c
o
n
t
ro
l
inp
ut
s c
a
n
b
e
o
b
t
ai
ne
d as
f
ol
low
s
:
1*
11
2
()
(
)
()
(
)
2
Is
e
q
dg
dg
dg
Is
kT
kk
k
k
kT
uB
x
A
x
D
e
E
(
2
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
102
2 –
1
0
33
1
028
1
2
()
2
Ld
g
s
Is
qT
k
kT
uB
S
(
25)
1
2
s
gn(
(
)
)
2
Nd
g
s
Is
Tk
kT
uB
S
.
(
2
6
)
Th
e
p
r
opo
sed
sc
h
e
me
a
l
s
o
emp
l
oy
s
t
h
e
re
son
a
nt
c
ont
rol
l
e
rs
o
f
g
r
id-
s
ide
c
u
rre
nt
f
o
r
h
arm
onic
com
p
en
sat
i
on.
T
h
e
r
eso
n
a
n
t
con
t
ro
l
l
ers
are
im
ple
m
e
n
t
e
d
in
t
he
S
RF
t
o
t
a
ke
a
d
v
a
n
ta
ge
o
f
the
s
i
mul
t
a
n
eo
us
com
p
en
sat
i
on
for
b
o
t
h
t
he
n
e
g
a
t
ive
a
nd
pos
it
ive
se
que
nce
ha
rmon
ics
by
o
n
e
re
son
a
nt
t
e
r
m
.
T
hu
s,
t
he
harm
on
ical
l
y
d
is
t
o
r
t
e
d
g
ri
d
at
t
he
5
t
h
,
7
t
h
,
1
1
t
h
a
nd
1
3th
c
a
n
be
s
u
ppress
e
d
by
c
o
m
p
en
sat
i
ng
t
h
e
har
m
on
i
c
c
o
mp
on
en
ts a
t
6
t
h
a
n
d
1
2th
i
n t
h
e SRF. Th
e
t
ran
s
fe
r f
u
n
c
tion
o
f
re
s
on
ant
c
o
nt
roll
er i
s e
x
pre
sse
d
a
s
2
22
6,
1
2
()
()
Ih
h
s
Rs
K
sh
(
2
7
)
w
h
er
e
h
d
e
n
ote
s
t
he
h
a
r
mo
n
i
c
or
der
an
d
h
K
i
s
t
h
e
re
so
n
a
nt
g
a
i
n
.
Th
e
t
r
an
sf
e
r
f
un
ct
ion
o
f
t
h
e
r
e
s
on
an
t
c
o
nt
roll
e
r
i
n
(2
7
)
i
s
i
m
pl
e
m
e
n
t
e
d
i
n
t
h
e
d
i
s
cre
t
e-ti
me
doma
i
n
b
y
u
s
i
ng
t
h
e
i
m
pu
lse
in
v
a
ri
ant
me
tho
d
.
A
s
show
n
in
F
i
g
u
r
e
3,
t
he
g
ri
d-s
i
de
c
urre
nt
c
o
n
t
r
o
l
loo
p
g
e
n
e
r
ate
s
t
he
f
i
lte
r
ca
pac
i
t
o
r
r
e
fe
renc
e
v
o
lta
ges
*
c
v
f
o
r
the
q
-
and
d
-
a
x
es.
F
o
r
t
h
e
in
ner-lo
o
p
c
ap
ac
i
t
or
vol
ta
ge
c
on
tro
l
a
n
d
i
n
v
er
t
er-side
c
u
rrent
c
ontrol,
t
he
P
I
con
t
ro
l
l
ers a
r
e em
plo
y
e
d
w
it
h
the
est
i
ma
t
e
d
sta
t
es.
4.
SIMU
L
A
TION
A
ND
E
XPE
R
IMENTAL
RE
S
U
LT
S
I
n
o
rde
r
t
o
ver
i
fy
t
he
f
e
a
s
i
bil
i
t
y
an
d
va
li
d
i
t
y
o
f
the
pr
op
ose
d
c
ur
ren
t
c
on
trol
s
c
h
e
m
e
,
t
he
s
im
u
l
at
ions
have
b
een
car
ried
o
u
t
f
or
a
n
LCL-
fi
l
t
er
e
d
t
hre
e
-phase
g
ri
d-co
nn
e
c
t
e
d
i
n
v
er
t
e
r
ba
se
d
o
n
t
he
P
SI
M
softw
a
re
.
Th
e
sy
st
em
c
on
fig
u
r
at
io
n
a
n
d
th
e
p
r
opo
se
d
co
nt
rol
sc
h
e
me
a
re
d
e
pic
t
ed in F
i
g
u
re
2
and F
i
gure 3. The s
ystem
parameters
a
re
l
is
te
d
in Table 1.
Tab
l
e
1
.
S
yst
e
m
parame
ters of a
grid-c
on
ne
cted
i
nve
rter
P
a
ra
m
e
te
r
V
a
l
u
e
D
C
l
i
nk
v
o
l
t
a
g
e
420
V
Grid
volta
ge
220
V
I
nve
r
t
e
r
-
s
ide
f
i
lte
r induc
ta
n
c
e
1
.
7 m
H
G
r
id-si
d
e
f
i
l
t
e
r
i
nduc
ta
n
c
e
0
.
9 m
H
F
i
l
t
er
c
a
p
a
c
i
t
an
ce
4
.5
µ
F
F
ilte
r
r
e
sist
a
n
ce
0
.5 Ω
L
o
a
d
b
a
nk
24
Ω
Grid
f
r
e
que
nc
y
60
Hz
Sw
it
c
h
ing
f
r
e
que
ncy
10
kHz
F
i
gure
4
show
s
the
sim
u
la
t
i
o
n
r
esul
t
s
o
f
t
h
e
p
rop
o
se
d
curre
nt
c
o
n
t
rol
sc
hem
e
a
t
stea
dy
-state
u
n
d
er
di
st
orte
d
gri
d
c
on
d
i
t
i
on.
F
ig
ure
4(a
)
r
e
p
rese
nts
thr
ee-
ph
a
s
e
di
s
t
orted
gri
d
v
ol
ta
ges
use
d
f
or
t
he
s
imul
a
t
i
o
n
s.
The
a
b
norm
a
l gri
d
v
o
l
t
a
g
e
s
c
on
ta
in
t
he
5
th,
7t
h, 11
t
h
,
an
d
13
t
h
h
armo
ni
c
o
r
d
e
rs
w
i
t
h
t
h
e
ma
g
nit
ud
e
of
5
%
of
the
fu
n
d
am
ent
a
l
c
o
mp
one
n
t
.
F
i
gure
4(b)
t
hro
u
g
h
F
i
g
ur
e
4
(
d)
s
how
s
th
e
s
i
mul
a
t
i
o
n
res
u
lt
s
of
u
si
ng
the
pro
pose
d
c
ur
rent
c
on
tro
l
u
nd
er
t
he
d
is
t
o
rte
d
g
rid
v
o
l
ta
ge
s
a
s
i
n
F
i
g
u
r
e
4
(a
).
T
he
r
efere
n
ce
va
lue
of
t
he
g
rid-
side
c
urr
e
nt
i
s
set
t
o
7
A
.
Eve
n
t
ho
u
gh
t
h
e
g
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s
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ro
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t
ro
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it
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Fi
gu
re
4
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g
iv
ing
q
uit
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i
da
l
pha
se
c
urre
nts
w
i
t
h
o
u
t
n
o
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ice
a
b
l
e
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ist
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rt
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igure
4
(c
)
sh
ow
s
th
e
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te
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esp
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s
es
o
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r
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t
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s
i
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n
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g
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urr
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g
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r
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rman
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e
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s
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e
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o
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fy
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he
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u
a
li
ty o
f
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t
e
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ri
d
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r
ents,
F
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Tra
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orm
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1
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47
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1
1
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he
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ents
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ffe
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t
i
v
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mpe
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p
r
opose
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e
THD
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lu
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rre
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%,
w
hic
h
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eets th
e
qual
i
t
y
cri
t
er
ia
.
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
C
u
rre
nt
cont
rol
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f
g
r
id
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n
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c
t
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d
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(
S
eu
ng
-J
in
Y
oon
)
1
029
(a)
(b
)
(c)
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)
F
i
gur
e
4.
S
im
ul
a
t
ion
r
e
su
l
t
s
f
o
r
st
e
a
d
y
-
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te
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g
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i
d
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ges,
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ur
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r
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t
t
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o
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id-
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i
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ur
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nt
To
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emon
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te
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h
e
t
ran
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i
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n
t
p
erf
o
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m
an
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h
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r
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n
t
c
o
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t
r
o
l
sc
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i
gu
r
e
5
s
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resul
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t
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e
sa
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d
i
s
t
o
rted
g
ri
d
co
n
d
iti
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as
i
n
Figu
re
4
(a)
wh
en
t
h
e
q
-
a
xi
s
gr
i
d
-
s
i
d
e
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rren
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e
r
enc
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m
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t
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t
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.0
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om
10
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o
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a
t
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s
.
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i
gur
e
5(
a)
a
n
d
F
i
g
u
r
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5(
b)
r
epr
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sen
t
t
he
t
r
a
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ie
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h
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g
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enc
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f
r
a
m
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R
F
,
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e
s
pecti
v
e
l
y.
I
t
ca
n
be
c
lear
ly
o
bser
ve
d
fr
om
t
he
se
f
i
gures,
e
x
cep
t
for
sm
al
l
c
u
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n
t
o
sci
l
l
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tio
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r
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e
l
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new
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dy-
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t
e
val
u
es.
Thi
s
i
n
d
i
c
a
te
s
a go
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d
a
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a
s
t
t
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esp
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n
s
e
o
f the
pr
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ed c
o
n
tro
l
s
ch
em
e.
(a)
(b
)
F
i
gur
e
5.
S
i
m
ulat
i
o
n
r
e
su
l
t
s
f
o
r
transie
n
t
respo
n
ses under dis
t
or
te
d
gr
id
v
o
l
ta
ge
s
w
i
th
t
he
p
r
o
pose
d
c
ur
r
e
nt
con
t
r
o
l
sc
hem
e
,
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a
)
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e
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pha
s
e
g
r
i
d-
side
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ur
r
e
nt
r
esp
o
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es,
(
b
)
gr
id-
s
ide
c
u
r
r
e
nt
r
espo
nse
s
a
t
the
S
R
F
Fi
g
u
r
e
6
shows
th
e
si
mul
a
t
i
on
r
e
s
u
l
t
s
f
or
t
h
e
i
nv
ert
e
r
st
a
t
e
s
a
nd
e
st
ima
t
e
d
s
t
a
t
e
s
by
u
si
ng
t
h
e
d
i
screte-time
red
u
c
ed
-
o
rd
er
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tat
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erver
at
t
h
e
S
RF.
O
b
vi
o
u
sly,
t
he
e
s
tima
t
ed
s
ta
tes
c
a
n
f
o
l
l
ow
t
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l
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e
v
en
unde
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h
a
r
m
o
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i
c
i
n
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ct
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o
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o
ndit
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,
wh
i
c
h
con
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i
r
ms a
st
a
b
le
o
pe
r
a
ti
on
o
f
t
he
o
b
s
er
ver
.
Figure
7
s
h
o
w
s
the
sim
u
l
a
tio
n
re
su
l
t
s
fo
r
the
es
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te
d
thre
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ur
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atur
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.
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e
s
tim
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ti
o
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r
esu
lts
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lear
ly
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e
m
on
stra
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g
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ver
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To
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e
r
ify
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ess
o
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o
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s
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r
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s
ha
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a
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d
ou
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F
igur
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8
show
s
t
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conf
igur
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io
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of
t
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x
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e
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im
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ba
se
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on
D
SP
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28
335.
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
Elec
&
Dr
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Vo
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No
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Ju
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2
019
:
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033
1
030
F
i
gur
e
9
s
h
ow
s
t
h
r
ee-
phase
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i
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tor
t
e
d
g
r
i
d
vo
l
t
age
s
u
sed
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e
x
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eri
m
en
ta
l
ev
a
l
u
a
ti
on
s.
T
h
e
se
g
rid
vo
l
t
age
s
c
o
n
t
a
i
n
the
5
t
h,
7
t
h
,
11
t
h
,
a
nd
13
th
h
a
r
m
oni
c
or
d
e
r
s
w
it
h
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m
a
gn
itu
de
o
f
5
%
o
f
t
h
e
fu
n
d
a
m
ental
c
o
mpo
n
e
n
t
as
t
he
s
i
m
u
l
at
i
on
i
n
F
i
gur
e
4(
a)
.
(a) In
v
e
rter
-si
d
e cu
rren
t
s
a
nd
e
s
t
i
m
a
ted
s
t
ate
s
a
t
th
e
SRF
(b)
C
a
paci
t
o
r vol
ta
ge
s
an
d
estim
ated
s
t
a
te
s a
t
t
he
SR
F
F
i
gur
e
6.
S
i
m
u
lat
i
on
r
e
su
l
t
s
f
o
r
the
e
s
tim
at
i
ng
per
f
or
m
a
nc
e
of
th
e
di
screte-
t
ime
red
u
c
ed-o
rd
er state o
bserv
e
r,
(a)
In
v
e
rter-side cu
rren
t
s
an
d
es
tim
ated
s
t
a
te
s a
t
t
h
e
S
R
F
,
(b)
C
a
p
ac
it
or
v
olta
ge
s an
d
est
i
m
a
te
d s
t
ate
s
a
t the
SR
F
(a)
(b
)
F
i
gur
e
7.
S
imulat
i
on
r
e
su
lts
f
or
e
st
im
ate
d
t
h
r
ee-
phase
s
t
a
te
s,
(
a
)
estima
t
e
d
thre
e
-pha
se
i
n
v
erte
r-side
curre
nt
s,
(b)
e
s
tim
ated
t
hre
e
-
p
h
a
se
cap
a
c
itor
vo
l
t
age
s
F
i
gur
e
8.
C
onf
igur
a
tio
n
of
t
he
e
xpe
r
i
me
nt
a
l
s
ys
t
e
m
F
i
gur
e
9.
T
hr
e
e
-
pha
se
d
is
tor
t
ed
g
r
i
d
vo
lta
ge
s
used
i
n
expe
r
i
me
nts
F
i
gur
e
1
0
s
ho
w
s
t
he
e
x
p
e
r
i
m
e
n
t
a
l
r
e
s
u
lts
o
f
t
h
e
pr
opose
d
c
ur
r
e
n
t
co
ntr
o
l
sc
hem
e
i
n
te
rm
s
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s
te
ad
y-
sta
t
e
a
nd
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n
sie
n
t
re
sp
on
se
s
u
n
d
e
r
the
dist
orted
gr
id
c
on
d
iti
o
n.
I
t
c
a
n
b
e
see
n
f
r
o
m
F
i
gur
e
10(
a)
,
the
pr
opose
d
c
on
t
r
ol
s
c
h
em
e
pr
ov
i
d
e
s
c
ons
i
d
e
r
a
b
ly
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oid
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l
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e
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-
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ase
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w
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orm
s
a
t
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,
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is
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o
n
s
i
ste
n
t
w
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ll
w
i
t
h
t
h
e
simu
la
t
i
o
n
re
sul
t
i
n
F
i
g
u
r
e
4
(
b
)
.
T
o
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t
e
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he
t
r
a
n
s
ie
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er
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o
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m
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r
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o
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t
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s
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eme,
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s
t
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ch
ang
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g
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i
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rre
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e
f
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m
4
A
t
o
6
A
i
s
i
n
t
r
o
d
u
c
e
d
.
I
t
c
a
n
be
obser
ve
d
f
r
o
m
F
i
gur
e
10(
b)
t
ha
t
the
gr
id-
s
ide
c
u
r
r
e
nts
c
an
t
ra
ck
n
e
w
r
ef
ere
n
ce
s
ra
p
i
d
l
y
,
w
h
i
ch
i
s
a
l
so
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
C
u
rre
nt
cont
rol
o
f
g
r
id
-con
n
e
c
t
e
d
i
n
ve
rt
e
r
usin
g
int
e
g
r
al
sli
d
in
g
m
o
d
e
con
t
rol
an
d…
(
S
eu
ng
-J
in
Y
oon
)
1
031
m
a
tche
d
w
i
t
h
t
he
b
eh
a
v
ior
as
s
how
n
in
F
igur
e
5(
a)
.
Th
is
c
on
f
i
r
m
s
a
goo
d
dyn
ami
c
a
nd
s
t
e
a
d
y
-
st
at
e
pe
r
f
or
m
a
nc
e
o
f
t
he
p
r
o
p
o
se
d
cur
r
e
n
t
c
o
n
t
r
o
l
sc
he
me
i
n
the
pr
ese
nc
e
of
s
e
v
er
el
y
dis
t
orte
d
c
o
n
d
itio
n
of
gr
id
v
o
ltage
s.
F
i
gur
e
1
1
s
h
o
w
s
t
h
e
ex
pe
r
i
me
nt
a
l
r
esu
l
ts
f
or
t
he
e
s
t
im
ati
n
g
per
f
o
rm
ance
o
f
the
d
i
scr
e
te-t
im
e
r
e
duce
d
-
o
r
d
er
s
ta
te
o
bse
r
ve.
I
n
t
he
se
f
ig
ur
e
s
,
the
es
t
i
m
a
te
d
th
r
ee-
pha
se
i
nve
r
t
er-
s
i
d
e
c
u
r
r
ents
a
n
d
c
a
p
acit
o
r
vo
l
t
age
s
a
r
e
c
a
l
c
u
l
a
t
e
d
i
n
a
D
S
P
by
usi
n
g
t
h
e
est
i
ma
ted
s
t
a
t
es
a
t
t
h
e
S
R
F
.
C
l
e
a
r
l
y
,
t
h
e
e
x
p
e
r
i
m
e
n
t
a
l
r
e
s
u
l
t
s
a
r
e
com
p
ati
b
l
e
w
ith
t
he
s
i
m
u
l
ati
on
r
e
sul
t
s
i
n
F
i
gur
e
7,
s
how
in
g
a
g
o
od
e
s
t
i
m
a
tin
g
per
f
or
m
a
nce
.
(a)
(b
)
F
i
gur
e
1
0
.
Exp
e
r
i
m
e
nta
l
r
esul
ts
f
or
t
he
p
r
o
p
o
s
e
d
c
ur
r
e
nt
c
o
n
t
r
o
l sch
e
me u
nd
er
d
is
t
o
r
t
ed
g
r
i
d
voltag
e
s
,
(
a)
stea
dy-s
t
ate r
e
sponse,
(b
)
transie
n
t r
e
sp
onse
(a)
(
b
)
F
i
gur
e
1
1
.
Exp
e
r
i
m
e
nta
l
r
esul
t
s
f
or
t
he
e
stim
a
tin
g
per
f
o
r
m
ance
of
d
i
s
c
r
ete
-
ti
m
e
r
educ
ed-
o
r
d
e
r
s
ta
t
e
o
bs
er
ve
r
,
(a
)
Estim
ate
d
t
hr
ee-
phase
i
n
v
e
rter-side
cur
r
ent
s
,
(b)
Estim
at
ed
t
hr
ee-
pha
se
c
apa
c
i
t
or
v
o
lta
ges
5.
CONCLUSIONS
T
h
i
s
p
a
p
e
r
h
a
s
p
r
e
s
e
n
t
e
d
a
m
u
l
t
i
l
o
o
p
i
n
d
i
r
e
c
t
c
u
r
r
e
n
t
c
o
n
t
r
o
l
s
ch
eme
fo
r
a
th
ree-p
h
a
s
e
L
C
L
-
f
il
tered
gr
id-
c
on
nec
t
e
d
i
n
v
er
t
e
r
base
d
o
n
a
d
i
s
c
r
et
e
I
S
MC
s
che
m
e
a
nd
a
r
esona
n
t
c
om
pe
n
s
at
io
n.
T
he
p
r
o
p
o
se
d
sc
h
e
m
e
i
s
c
o
n
s
tr
uc
t
e
d
b
y
t
hr
e
e
casc
a
ded
c
o
ntr
o
l
lo
o
p
s
co
ns
ist
i
n
g
of
a
g
r
i
d-
side
c
ur
r
e
n
t
c
o
n
t
r
o
l
,
a
c
a
p
aci
t
o
r
vo
l
t
age
c
o
n
t
rol
,
a
nd
an
i
nve
r
t
er-
s
ide
curr
en
t
con
t
ro
l.
I
n
ge
ner
a
l
,
t
o
i
m
p
l
e
m
e
n
t
t
h
e
m
u
l
t
i
l
o
o
p
c
u
r
r
e
n
t
c
o
n
t
r
o
l
sc
h
e
m
e
,
m
a
ny
se
nsi
n
g
de
v
i
c
e
s
shou
ld
b
e
r
e
qu
ir
e
d
,
w
h
i
c
h
incr
ease
s
t
h
e
cos
t
a
n
d
c
om
p
l
ex
i
t
y
of
s
ys
te
m
.
T
o
ove
r
c
om
e
t
h
is
limi
t
a
t
io
n,
a
d
i
s
cr
e
t
e-
time
r
e
d
u
ce
d-
or
der
sta
t
e
o
bse
r
ver
is
u
sed
t
o
e
stim
ate
both
t
h
e
in
ver
t
er
-
si
de
c
ur
r
e
n
t
s
a
nd
c
a
p
ac
itor
v
o
lta
ges
by
u
s
i
ng
o
n
ly
t
he
m
e
a
sur
e
d
g
r
i
d-
si
de
c
ur
r
e
nts
a
nd
gr
id
vol
ta
ge
s.
T
his
pr
act
ica
l
l
y
r
ed
uc
es
t
he
c
o
s
t
and
c
o
m
p
lex
i
ty
o
f
a
n
L
CL-fil
t
ere
d
g
r
id-
c
on
nec
t
e
d
i
nve
r
t
e
r
s
yste
m.
F
or
t
he
pur
pose
of
s
up
pr
essi
n
g
t
he
r
e
s
on
ance
b
e
h
a
v
ior
d
u
e
to
L
C
L
f
ilt
er
,
an
active
dam
p
ing
h
a
s
bee
n
r
eal
ize
d
b
y
m
e
a
n
s
of the i
nve
r
t
er-side c
u
rr
ent
feed
ba
c
k
l
o
o
p
.
Thi
s
a
p
p
roac
h
i
s
m
o
r
e
f
e
a
si
bl
e
in c
ompa
r
i
s
on
w
i
t
h
t
h
e
fi
l
t
e
r
ca
p
a
cit
o
r
c
u
rre
n
t
f
e
edb
a
ck
s
i
n
ce
t
h
e
i
nv
ert
e
r-si
d
e
c
u
rre
n
t
can
be
e
as
i
l
y
es
t
i
ma
t
e
d
b
y
s
t
a
te
obse
r
v
e
r
.
B
y
in
te
gra
tin
g
t
h
e
ca
pac
i
tor
vo
lt
age
c
o
n
t
ro
l
l
o
op
i
nto
the
co
ntr
o
l
s
t
r
ucture,
the
seam
l
e
ss
transfer
b
e
t
we
en
t
he
gr
id-
c
on
nec
t
e
d
m
ode
a
n
d
i
sl
a
nde
d
mo
de
i
s
eff
e
c
t
i
v
e
l
y
ac
h
i
e
v
e
d
.
To
r
et
a
i
n
a
hi
gh
t
ra
cki
n
g
p
e
rf
o
r
man
c
e
a
n
d
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