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
. 93
1
~
94
1
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p93
1-9
41
9
31
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
Stabilit
y analysis of photovolta
ic syst
em under grid faults
Ni
vedi
ta
Pa
ti
1
,
Ba
bi
t
a
Pa
nda
2
, Bhag
abat
Pa
nda
3
1,
2
S
c
hoo
l
of
Ele
ctri
cal Eng
i
n
e
e
r
i
n
g
,
K
I
IT
U
n
iv
er
sity
, Ind
i
a
1
Dep
a
rtm
e
nt o
f
Ele
c
trical
and
El
ectro
n
i
cs
Eng
i
ne
ering,
S
I
T Bh
ub
anesw
a
r,
In
dia
3
De
p
a
r
t
m
e
n
t
o
f
E
l
e
c
t
r
ic
a
l
E
n
gi
ne
e
r
i
n
g,
P
M
E
C
,
In
d
i
a
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
M
a
y
2
6
,
2
019
Re
vise
d
Oc
t 2
2
, 2
019
A
c
ce
p
t
ed
D
e
c
5
,
20
19
Th
is
work
in
clu
d
e
s the est
a
blis
h
m
ent of
a P
h
o
t
o
v
o
ltai
c sys
t
em
c
o
n
n
ect
ed to
t
h
e
gri
d
by me
an
s of
a
n
in
ve
rter.
T
h
e
fun
d
a
m
ent
a
l go
a
l
o
f
th
e wo
rk
is
t
o
in
corp
ora
t
e
an
a
dvan
ced
ac
tive
p
o
wer flow
ma
n
a
gem
e
nt sch
e
me
in o
r
der
to
ado
p
t lo
ad a
t
an
y
weath
e
r
con
d
i
t
ion
alon
g w
i
th
the ad
v
a
n
t
age o
f
maxi
mu
m
a
c
tiv
e p
o
we
r flo
w
a
nd ze
ro harm
on
ic
s
from PV i
n
ver
t
er
to t
h
e gr
id. Th
e
ou
tco
m
e
of
ana
l
y
s
is and
con
t
rol
d
e
sign of
gr
id
co
nnect
ed
PV
inv
e
rter
u
s
ing
a
P
r
op
ortion
al-In
teg
r
al (P
I)
co
n
t
r
o
l te
chn
i
qu
e
is
b
a
sed
on s
y
n
c
h
r
on
ou
s dq
rotating
ref
e
ren
c
e fra
me
so
as
to
achi
e
ve
max
i
mu
m
ou
tp
ut
vo
ltag
e
and
r
ecord
th
e
ac
tive
pow
er
. I
t
h
a
s
b
een
ob
serv
ed
tha
t
th
e
m
o
d
e
l p
r
ov
id
es
a
b
e
tt
er r
a
te
of
stabili
t
y
as
co
mp
ared
to
th
e existi
ng
to
po
lo
gy
.
Ke
yw
ords:
Boost
c
o
nve
rt
e
r
MPP
T
Ph
ot
o
vol
ta
ic
m
odel
Pro
porti
o
n
al
-i
n
t
egra
l
c
ont
rol
l
e
r
P
u
lse
w
i
d
t
h
mo
du
la
tio
n
(PWM
)
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
Ni
ve
di
ta
P
a
t
i
,
Sc
h
ool o
f
El
e
c
t
ri
cal
En
gine
eri
ng,
K
I
IT Uni
v
ersi
t
y
,
Bh
ub
a
n
e
w
sar, 7
510
24
, Ind
i
a
.
Ema
i
l
:
n
i
v
e
d
i
ta
.p
a
ti@
si
lic
on
.ac
.
i
n
1.
IN
TR
O
DUCTION
A
s
fossi
l fue
l
s
are
de
ple
t
i
n
g
da
y
b
y
da
y,
m
o
re re
searc
h
is
g
o
i
n
g o
n
har
v
es
t
i
ng el
ec
tric
al
ener
gy from
re
ne
wa
bl
e ene
r
g
y
. A
m
o
ng al
l
ot
he
r
re
ne
wa
ble
e
n
e
r
gy
so
u
r
ce
s, S
o
l
a
r a
n
d
wi
nd e
n
e
r
gi
es, are
the
ma
xi
mum
ac
cessi
ble
a
n
d
di
spe
r
se
d
a
l
l
ove
r the
u
n
i
v
e
r
se
.
Ut
il
i
z
a
t
i
on of p
hot
ov
ol
ta
ic
(P
V) ha
s
be
e
n
ri
si
ng n
o
t
a
bl
y b
y
vi
rt
ue
of the
fa
st ad
va
nc
eme
n
t
of p
o
w
e
r el
ect
roni
c
t
ech
ni
que
s.
He
re
t
h
e
o
b
je
ct
ive
o
f
t
h
e
st
udy
i
s
to
get
t
h
e
ma
x
i
mu
m
en
erg
y
e
f
f
i
ci
en
cy
u
n
d
e
r
th
e
d
i
ff
ere
n
t op
e
r
a
t
i
n
g
c
o
nd
it
io
n
a
n
d to
ap
pro
a
ch t
h
e
d
e
si
g
n
o
f
a
ro
bu
s
t
cont
rol
l
e
r
ha
vi
ng t
h
e
a
b
il
i
t
y
t
o
re
je
ct
the
n
o
i
s
es. T
h
e
mai
n
obje
c
t
i
ve
of th
e
st
ud
y is t
o
c
o
ordi
nat
e
t
h
e
v
o
l
t
a
ge
,
t
h
e powe
r
i
n
j
e
ct
ed int
o
t
h
e
u
t
i
lit
y. Ma
n
y
e
a
r
l
i
er
wor
k
s
ha
ve
i
n
s
p
ect
ed
d
i
ffe
re
nt
co
nt
rol
aspe
ct
s of
In
ve
rt
er
t
h
at
a
r
e
co
n
n
e
c
t
ed to
t
h
e
g
r
i
d
. M
o
st
of t
h
e
a
n
al
ysis
i
s
do
ne
t
o
re
duce
t
h
e
THD
of t
h
e
syst
em.
B
u
t
ve
ry
fe
w
of
t
h
em
foc
u
s o
n
st
abi
l
i
t
y
issues of gri
d
co
o
n
ec
te
d
P
V
s
y
s
t
em. Di
ffe
r
e
n
t
P
o
wer qual
i
t
y i
s
sue
s
of t
h
e
gri
d
con
n
ec
t
e
d
P
V
syst
em
a
r
e
des
c
ri
b
e
d by
Vi
k
a
s
k
h
are
[1].
T
h
e aut
h
o
r
herse
l
f
e
xpl
ai
ne
d a
b
out
t
h
e
di
ffe
r
e
n
t
t
y
pes
of
fa
ul
t
a
n
al
y
s
i
s
i
n
g
r
i
d
c
o
n
n
e
ct
ed p
hot
o
vol
ta
ic
syst
em [2
]. M
.
G.
Mol
i
n
a an
d L
.
E. Ju
a
n
ic
o
e
xpl
a
i
ne
d
t
h
e
desi
g
n
in
g
o
f
the
p
hot
ov
olt
a
i
c
st
ruct
u
r
e
c
o
n
n
e
c
t
e
d
to
t
h
e
gri
d
[3
].
The
dy
na
mi
c
beha
vi
o
r
of
gri
d
c
onne
ct
e
d
Ph
ot
o
vol
ta
ic
s
y
st
e
m
i
s
st
udi
e
d
u
nde
r t
h
e
L
LLG
fa
ult
by
aut
h
or
K
.
Man
oha
r
[4] a
nd
[
5
]. T
h
e
prop
os
ed
w
o
r
k
gi
ves
the
i
n
for
m
a
t
i
on a
b
out
a
t
h
ree
-
p
h
ase
P
u
lse
Wi
dth
M
o
dula
t
e
d
in
ve
rt
e
r
m
o
del
i
ng a
n
d
i
t
s co
nt
rol
st
ra
te
gy.
Th
e
sin
g
l
e
stag
e
d
gr
id
c
o
n
n
ec
te
d
in
v
e
r
t
e
r
g
e
ts i
t
s
in
pu
t
fr
om
a d
c
-d
c
co
nv
er
ter
fed
thro
ug
h
a
pho
t
o
v
o
lta
ic
i
nput
[
6
]. P
a
rti
c
ul
arly
, t
h
e
co
nt
rol
de
si
gn
o
f
gri
d
c
o
n
n
ect
e
d
i
n
verte
r
usi
n
g the
PI
co
nt
ro
l
t
echni
q
u
e
ha
s
bee
n
pro
pose
d
i
n
t
h
e
d
q
rot
a
t
i
ng
f
r
ame
i
n
o
r
de
r t
o
ac
hi
e
v
e
max
i
mum
o
u
t
put
v
o
l
t
a
g
e
a
n
d
ma
ximu
m
act
i
v
e
po
we
r
.
A c
u
rre
n
t
c
o
nt
rol
P
W
M t
e
c
h
ni
que
ha
s
been
s
u
g
g
e
s
te
d t
o
p
r
ovi
de
t
h
e
p
u
l
s
e
for
vol
t
a
ge
s
o
urce
i
n
verte
r
.
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
:
9
3
1
–
941
93
2
B
y
vi
rt
ue
o
f
t
h
e h
uge
am
ou
n
t
of
int
e
rc
o
nnec
t
i
on
of di
s
p
ers
e
d
po
w
e
r
ge
ne
ra
ti
on
t
o
t
h
e
gri
d
in
so
m
e
re
gi
ons
,
unc
e
r
t
a
i
n
t
y
a
n
d fl
uct
u
at
ion
of a
di
ff
ere
n
t
pa
ramet
e
r
of t
h
e
pow
e
r
syste
m
ma
y a
ppe
ar w
h
i
c
h re
q
u
i
r
es
pro
p
er de
si
g
n
o
f
c
o
ntr
o
ll
ers
for st
abi
l
it
y ana
l
ysi
s
u
n
d
er
va
r
i
a
b
le
c
o
ndit
i
o
n
s
[7]. more
i
m
po
rt
ance
i
s
put
o
n
t
h
e
ca
pabi
li
t
y
of a
Di
strib
u
t
e
d
P
o
w
e
r
Ge
ne
ra
ti
on
Sy
st
em (D
P
G
S
)
t
o
o
v
erc
o
me
sha
r
p
g
r
i
d
di
s
r
upt
i
ons s
u
ch
a
s
varia
t
i
o
ns
in v
o
l
t
a
g
e
a
nd fre
q
uenc
y
.
This pa
pe
r foc
u
se
s
o
n
some
desi
ra
bl
e
cont
rol
t
e
c
hni
que
s
tha
t
D
P
G
S
c
a
n
fol
l
o
w
d
u
ri
n
g
da
ma
ged
gri
d
ci
rc
umst
a
n
c
e
s. F
i
rst
,
a
gro
u
p
i
ng
o
f
di
ffe
ren
t
k
i
n
d
s
of
gri
d
fa
ul
t
s
i
s
i
l
l
ust
r
a
t
e
d
,
and
i
t
e
n
s
u
re
d
b
y
so
me
a
p
pl
i
c
a
t
i
ons
of t
h
e
co
nt
rol
t
e
c
hni
que
du
rin
g
da
ma
ge
d
g
r
i
d
c
i
rcu
m
sta
n
ces
.
A.
V
.
Ti
mb
us [8
] a
n
d
[
9
]ana
l
y
z
e
d
some
p
o
ssi
b
l
e
co
nt
rol
t
e
c
hni
ques t
h
at
D
P
GS ca
n fol
l
o
w
du
rin
g
faul
t
y
gri
d
con
d
i
t
i
on
s
fol
l
owe
d
b
y
t
h
e g
r
ou
pi
n
g
of di
ff
ere
n
t ki
n
d
s
o
f
gri
d
fa
ul
ts
i
n
t
h
is pa
pe
r .The
prima
r
y
o
b
je
ct
ive
o
f
th
e
con
t
r
o
l te
c
h
n
i
q
u
e
is
repro
d
u
c
tion
of pow
e
r
,
and a
l
so
th
e
g
e
n
e
ra
tio
n of th
e cu
rr
en
ts r
e
f
e
r
r
ed wh
ich
ca
n
me
e
t
t
h
e
gr
id po
w
e
r
r
e
q
u
iremen
t.
M
.
Cai [1
0]
ad
op
te
d a
shun
t co
n
t
ro
ll
er for
v
o
l
ta
g
e
d
i
p co
mp
ensa
ti
o
n
wh
e
n
a
f
a
u
l
t is
i
n
tro
d
u
c
ed i
n
th
e grid
.
In [11
,
12
] dyn
a
m
ic
stab
il
ity
o
f
a
Pho
t
o
v
o
lta
ic
stru
c
t
u
r
e
c
onn
e
c
t
ed
wi
th
a
di
st
ri
b
u
t
i
on
sy
st
em i
s
a
n
a
l
yz
ed. R
e
fe
re
nc
e
[13]
an
d
[14
]
ha
s
a
d
opt
e
d
a
co
nt
rol
t
e
c
h
ni
que
t
o
a
n
al
yz
e
t
h
e
dy
namic
st
abi
l
i
t
y
of
t
h
e P
V
S
y
st
em.
2.
PROP
OS
E
D
ACT
I
V
E P
O
WE
R FL
OW CO
NT
R
O
L
S
C
HE
M
E
FOR
ST
AB
ILIT
Y AN
A
L
Y
S
IS
Thi
s
se
ct
io
n d
e
scribe
s t
h
e
i
n
t
e
rna
l
str
u
ct
u
r
e
pro
pose
d
c
o
ntrol
desi
g
n
whi
c
h
c
o
nsist
s
of
an
e
x
t
e
rna
l
vol
ta
ge
c
i
rc
ui
t
a
n
d
an
i
n
te
rnal
curre
nt
c
i
rcui
t
[1
5
]
.
T
h
e
pr
o
p
o
se
d m
odel
i
s
disc
u
s
s
e
d
i
n
F
i
gu
re
1.
It
c
onsi
s
t
s
of
a S
o
l
a
r (P
V)
syst
em, ste
p
u
p
c
o
nve
rte
r
,
whi
c
h is
t
h
e
n
int
e
r
f
ac
ed
wit
h
a
n
i
nve
rt
er (VS
I), a
dist
ri
b
u
ti
on
net
w
ork,
l
o
ad
an
d gri
d
wi
t
h
a
po
we
r
fl
ow
co
nt
rol
l
e
r
.
F
i
g
u
re 1
des
c
ribe
s
t
h
e ci
rc
uit
d
i
a
g
ram of
t
h
e
pro
pose
d
st
ruc
t
ure
.
Fi
gu
re
1.
B
l
oc
k di
ag
ra
m
of G
r
i
d
c
o
nne
ct
e
d
P
V
syst
e
m
The
s
u
g
g
est
e
d
struct
u
r
e
i
s
b
u
i
l
t
t
o
c
ont
rol
t
h
e
va
ri
o
u
s pa
rame
te
rs l
i
k
e
c
u
rrent
,
v
o
l
t
a
g
e
and
pow
e
r
in
j
e
c
t
e
d
in
to th
e
u
t
ili
ty
[16
]
.
Th
e
305
S
o
l
a
r Pa
n
e
l is b
e
i
n
g se
le
ct
ed
fo
r
d
e
si
gn
ing
o
f
PV sys
t
e
m
usi
ng
MA
TLAB
.
M
P
P
T
a
p
p
r
oac
h
i
s
e
m
pl
o
y
e
d
fo
r en
ha
nci
n
g
t
h
e
effi
ci
en
c
y
of t
h
e sol
a
r
p
a
nel
.
T
h
e P
e
rt
urb
&
Obse
rve
(P&
O
) met
h
o
d
i
s
se
le
ct
ed
as t
h
e
M
PPT
t
r
ac
ker
wh
ose
p
r
imar
y
g
o
al
i
s
t
o
obt
ai
n ra
pi
d a
nd
correct
t
r
ac
kin
g
act
and re
duce
s
osci
l
l
a
t
i
ons w
i
t
h
respec
t
t
o
c
h
an
gea
b
l
e
we
at
he
r co
n
d
i
t
i
ons. P
&
O
me
th
o
d
i
m
pl
eme
n
t
a
t
i
on is q
u
it
e
c
h
ea
p.
T
h
e
o
u
t
p
ut
of
t
h
e b
o
o
s
t c
onve
rt
er
whi
c
h i
s
120
0 V
DC
i
s
con
v
e
r
t
e
d i
n
t
o
80
0
V
AC
b
y
a
vol
t
a
g
e
source
i
n
vert
er, t
h
e
n
t
h
at
vo
l
t
a
g
e is inc
r
ea
s
e
d
t
o
11
K
V
by a
ste
p
-u
p de
lt
a/
st
ar t
r
ans
f
orme
r.
2.1 In
te
rn
al
stru
ct
ure of
co
ntr
o
l
sy
stem
F
i
gure
2 re
pr
es
ent
s
t
h
e c
i
rc
ui
t di
ag
ra
m rep
r
e
s
e
n
ta
ti
on
o
f
t
h
e co
nt
rol
st
ruc
t
ure
.
It
i
n
cl
ude
s
the
a
b
c
-
dq
t
r
ans
f
o
r
ma
ti
o
n
bl
oc
k,
P
LL
bl
oc
k, P
I
c
ont
rol
l
er an
d the
P
W
M ge
ne
ra
to
r.
T
h
e st
e
p
-
u
p
c
o
n
v
e
r
t
e
r t
o
st
e
p
s
up t
h
e
v
o
l
t
a
g
e
of
t
h
e so
la
r M
PPT sy
ste
m
w
h
il
e
th
e
M
PPT g
e
n
e
ra
t
e
s t
h
e
pu
lse
for
th
e
c
onv
er
ter
.
Th
e
PV
sys
t
em
a
n
d
b
o
o
s
t
con
v
e
rt
er
s a
r
e
co
nn
e
c
t
e
d
to th
e
vo
l
t
ag
e sou
r
ce
c
onv
er
te
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Stability analy
s
is
of
phot
ovoltaic system under
grid
faults (Nivedita P
a
ti)
9
33
Fi
gu
re 2.
Bl
oc
k dia
g
ram o
f
i
n
t
e
rna
l
c
ont
rol
s
t
ruc
t
u
r
e
The
spee
d
o
f
t
h
e c
ontr
o
l
l
o
op
depe
n
d
s
o
n
t
h
e
ba
n
d
w
i
dt
h
of
t
h
e
l
o
op
.
S
o
by
v
a
r
y
i
n
g t
h
e c
u
t-
of
f
f
r
e
que
n
c
y
o
f
o
p
e
n
l
o
o
p
t
r
a
n
sf
er
fu
nc
ti
o
n
(t
ra
nsfe
r
f
unct
i
on
of
i
n
ne
r l
oop
mult
i
p
l
i
e
s
wi
t
h
P
I
t
r
ans
f
e
r
f
u
n
c
t
i
on)
,
t
h
e
di
ffe
r
e
n
ti
a
l
spee
ds
can
b
e
achi
e
ve
d
.
Si
nc
e s
o
me
of t
h
e st
at
e
va
ri
a
b
l
e
s are
mult
i
p
l
i
e
d wit
h
t
h
e
c
ont
rol
i
n
p
u
t
s
,
t
h
e mat
h
emat
i
cal
mod
e
l
of
t
h
e c
o
nve
rt
er
beco
mes
n
onli
n
ea
r.
2.
2.
D
C
-
l
i
n
k
vol
ta
ge c
o
n
t
ro
l
sch
e
m
e
Th
e
ac
tiv
e pow
e
r
i
s
re
st
r
a
ine
d
b
y
th
e vo
lta
g
e
at th
e
D
C
-l
in
k w
ith i
t
s d
e
sir
e
d
v
a
lu
e. F
i
gu
r
e
3 show
s
t
h
e i
n
t
e
r
n
a
l
str
u
c
t
u
r
e o
f
the
dc-l
i
n
k
volt
a
g
e
mana
ge
me
nt
st
ra
te
g
y
.
It
h
a
s si
x c
o
m
p
o
n
e
nt
s:
MP
PT,
v
o
l
t
a
g
e
co
mp
ens
a
to
r,
l
i
mi
te
r,
c
u
rr
en
t
co
mp
on
e
n
t
s
, an
d in
teg
r
ato
r
.
H
e
r
e
dr
ef
u
i
s
a re
fe
renc
e DC v
o
l
t
a
ge rec
o
r
d
ed
by
t
h
e
ma
xi
m
u
m po
we
r
p
o
int
t
e
chni
que
[1
7]
.
dref
u
c
o
rre
la
te
s w
ith
t
h
e
dc
u
a
n
d
t
h
e
o
u
t
put
si
g
n
al
i
s
f
e
d
t
o
t
h
e
P
I
c
o
m
p
e
n
sa
t
o
r
.
The
c
o
m
p
e
n
sa
t
o
r
se
t
s
up
dr
ef
i
w
h
i
c
h
is
t
h
e
r
e
f.
t
h
e
cur
r
e
n
t
v
a
l
u
e
of t
h
e d
-
ax
is co
mp
on
e
n
t
.
Th
e
cu
rr
en
t c
o
n
t
ro
ller
se
ts up
ac
t
u
a
l
d
-
ax
is
cur
r
e
n
t
d
i
fr
om r
e
f.
cu
rren
t
v
a
l
u
e
dref
i
an
d th
en
)
(
d
pv
i
i
is
p
a
sse
d
th
ro
ugh
an
in
teg
r
ato
r
wh
ic
h
ge
n
e
ra
te
s
dc
u
.
F
i
gu
r
e
3.
I
n
si
d
e
str
u
ct
ure
o
f
DC l
i
n
k
vo
l
t
a
g
e
co
nt
r
o
l
sc
he
me
(1
)
(2
)
(3
)
(4
)
(5
)
Modu
l
a
ti
o
n
an
d
PWM
Generator
ab
c
dq
ab
c
dq
PL
L
DC
LI
N
K
PI
CO
N
T
R
O
L
L
E
R
CU
R
R
E
N
T
PI
CO
N
T
RO
L
L
E
R
CURR
EN
T
PI
CO
N
T
RO
L
L
ER
wl
‐
wl
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
:
9
3
1
– 94
1
93
4
W
h
e
r
e C
is th
e c
a
p
ac
it
o
r
, ic
i
s
c
u
r
r
en
t
t
h
rou
g
h
th
e
c
a
p
a
ci
tor,
ipv i
s
th
e PV cu
rr
en
t
,
u
d
c
is th
e
v
o
l
t
a
g
e
ac
r
o
ss D
C
link
,
u
d
r
e
f
th
e
D
C
v
o
lta
g
e
ref
e
r
e
n
c
e
,
i
d
i
s
d
-
ax
is c
o
mp
on
e
n
t o
f
gri
d
cu
rr
e
n
t,
i
d
r
e
f
is it
's a
r
e
fe
renc
e
va
l
u
e
.
2.
3.
In
te
rn
al
cur
r
e
n
t
l
oop
The
d
−
q tr
a
n
sfo
r
ma
tio
n
ma
t
r
ix
is
u
s
e
d
fo
r th
e
con
v
e
r
s
ion
o
f
t
h
re
e
-
ax
is gr
id vo
lta
g
e
a
n
d
c
u
rr
en
t t
o
t
h
e
d
q
re
fe
re
nc
e frame
.
T
h
e
AC
grid
v
o
lt
a
g
e
a
nd c
u
rre
n
t
are
con
v
e
r
t
e
d
int
o
DC
val
u
es wi
t
h
t
h
e
hel
p
of a
b
c
→
dq
t
r
a
n
sf
or
ma
t
i
on
ma
tr
i
x
,
by
r
e
gul
at
in
g t
h
e
va
ri
abl
e
s.
The
p
h
a
s
e a
n
gl
e
i
s
c
a
l
c
ul
at
ed
wi
th t
h
e
hel
p
of
PLL
(
P
h
a
se
L
o
c
k
L
o
o
p
)
[1
8]
whi
c
h i
s
f
u
rt
her
re
qui
re
d f
o
r sy
nc
h
r
o
n
i
zat
i
o
n
of
g
r
id
v
o
l
t
a
g
e
wi
th c
o
nt
rol
l
e
d c
u
rr
e
n
t
.
To
ge
t
the
uni
ty p
o
we
r f
act
o
r
, i
q
ref
*
(re
f
ere
n
ce
re
act
i
v
e
c
u
rre
n
t
)
is se
t
to
zer
o.
The
Pro
p
o
rti
o
nal
-
I
n
t
e
gral
c
ont
r
o
ll
er
s
p
r
o
v
ide
t
h
e v
o
l
t
a
g
e o
u
t
p
uts (
V
d
*
,
V
q
*
)
w
h
ic
h f
e
d t
o
t
h
e P
W
M
gene
rat
o
r t
o
ge
ne
rat
e
s t
h
e
pul
ses
u
s
ed
to fo
r
In
ver
t
er
[
1
9
]
.
I
ୢ
I
୯
I
ൌ
ට
ଶ
ଷ
ൈ
T
ൈ
I
ୟ
I
ୠ
I
ୡ
൩
(6
)
By
usi
n
g t
h
e
abo
v
e
f
o
r
m
ul
a
gi
ven
i
n
(
6
)
,
the
a
b
c
-
d
q
t
r
ansf
o
r
ma
ti
o
n
i
s
ma
de
wh
er
e
T i
s
t
h
e
tr
an
sfor
ma
tio
n
ma
tr
ix
.
As
t
h
e
v
o
l
t
a
g
e
of gr
i
d
i
s
ca
n
n
o
t be
ma
na
ge
d,
t
h
e ul
ti
mat
e
d
e
si
rabl
e c
hoi
ce
of
g
ove
r
n
i
n
g the
a
c
t
i
o
n
o
f
th
e
a
r
r
a
ng
e
m
en
t is by
r
e
g
u
l
a
tin
g
th
e Id
a
n
d Iq
th
a
t
is in
j
e
c
t
i
n
g
to
th
e
g
r
id
.
Fi
gu
r
e
4
d
e
p
i
c
t
s
ou
tpu
t
of
a
c
o
mpe
n
sa
t
o
r
(
U
d
)
,i
s
t
h
e c
ont
rol
si
gnal
f
o
cu
si
n
g
o
n
mi
nimi
zi
ng
e
r
r
o
r as:
(7
)
C
o
r
r
e
s
pon
d
i
n
g
l
y
,
th
e e
rror
si
gn
a
l
th
a
t
ano
t
h
e
r
r
e
gu
la
to
r pr
oc
ess
e
s,
(8
)
T
h
e
er
ro
r comma
nd
s
ar
e
f
e
d to
a
PI reg
u
l
a
t
or
. Th
e
P
I
r
e
g
u
l
at
o
r
c
o
n
s
ta
n
t
s
ar
e
se
le
ct
ed so
th
a
t
,
(9
)
(1
0)
w
h
ere
is
th
e
ti
me
co
n
s
ta
n
t
o
f
t
h
e
ci
rcu
it.
Th
e
i
n
tern
a
l
con
t
ro
l
str
u
c
t
u
r
e o
f
t
h
e
sy
st
em
is
sh
own
in
Figur
e
4
.
F
i
gu
re
4.
Ba
si
c
st
ruct
ure
o
f
pu
lse
ge
ne
rat
i
o
n
sche
me
The PWM mo
dul
at
i
n
g
c
o
mm
and
s
a
r
e
,
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Stability analy
s
is
of
phot
ovoltaic system under
grid
faults (Nivedita P
a
ti)
9
35
(1
1)
(1
2)
Whe
r
e
a
r
e
d-
a
x
i
s
a
nd
q
-
a
x
i
s
fa
ct
ors
of
mo
dul
at
i
n
g
c
o
mman
d
s,
Vdc
is
t
h
e
volt
a
ge
at
D
C
l
i
nk,
are
co
nt
r
o
l
si
g
n
al
s o
f
d
-
a
x
is a
n
d
q
-
a
x
is,
Us
d,
Us
q a
r
e
re
f
i
ne
d vol
t
a
ge
of
VSI
,
is t
h
e g
r
i
d
fr
eq
u
e
n
c
y
.
The
pu
lse
s
a
r
e
de
v
e
l
o
p
e
d
by
c
o
nv
er
sion
o
f
d
a
n
d
q
sign
a
l
s in
t
o
a
,
b
,
c si
gnal
s
.
By
r
e
gu
l
a
t
i
n
g
md
a
nd
mq
,
t
h
e i
d
a
nd i
q
qui
c
k
l
y
f
o
ll
o
w
t
h
ei
r
cor
r
e
s
p
o
n
d
i
n
g
r
e
fe
renc
e si
gn
al
s i
d
r
e
f
a
n
d i
q
re
f
[
2
0].
The
n
act
i
v
e
an
d
r
e
a
c
t
i
v
e
pow
e
r
of
Pho
t
ov
o
lta
ic
a
r
r
a
ng
emen
t ar
e g
i
v
e
n a
s
:
(1
3)
(1
4)
A
s
th
e vo
lt
ag
e at
th
e
g
r
id
is un
man
a
g
eab
l
e
, t
h
e
u
l
tima
t
e
p
r
ac
tic
a
b
le
ap
pro
a
ch of
mo
n
i
tor
i
ng
t
h
e
a
rra
nge
ment
i
s
by
re
g
u
la
ti
ng
gr
i
d
cu
rr
e
n
t
s
I
d
a
n
d I
q
.
As a
c
t
i
ve
po
we
r
fl
ow
is r
e
l
i
a
nt
o
n
t
h
e
c
u
r
r
e
n
t
I
d
,
a
n
d
r
eac
ti
ve
p
o
w
e
r
i
n
se
rt
ed t
o
the
gr
id i
s
de
pen
d
e
nt
o
n
t
h
e
c
u
r
r
ent
I
q
a
n
d th
us
Iq
re
f =
0 i
s
se
t f
o
rce
f
ul
ly t
o
ma
ke
z
e
ro
rea
c
t
i
v
e
p
o
w
e
r
[2
1,
2
2
]
.
2.
4.
Si
m
u
l
i
n
k
e
n
vi
r
o
n
m
e
n
t
The
val
i
d
i
t
y
of
t
h
e
syst
em is che
c
k
ed
wi
th
th
e
he
lp
o
f
c
o
mput
e
r
si
m
u
l
a
ti
ons. T
h
e
M
A
T
L
A
B/SIM
U
L
I
N
K
sof
t
w
a
r
e
i
s
u
s
e
d
t
o
simu
la
te th
e fi
n
a
l
sy
st
em
a
n
d fo
r unu
sua
l
ci
rc
u
m
st
a
n
ce
s, th
e
an
a
l
y
s
i
s
is d
one
.
Th
e
s
y
mme
t
r
ic
al
a
nd
un
sym
m
e
t
ri
ca
l f
a
u
lts
a
r
e
cr
e
a
ted
o
n
th
e d
i
str
i
but
io
n
n
e
t
w
ork,
fo
r
th
e
a
n
al
ysis
of
s
y
st
em be
ha
vio
r
u
nde
r
fa
ult
[2
3]
.
3.
S
I
MUL
A
TI
O
N
OUT
C
O
M
E
S
OF
FA
UL
T AN
AL
YSIS
The si
mul
a
ti
on
i
s
con
duct
e
d i
n
o
r
de
r
to a
c
h
i
e
ve
sta
b
il
i
t
y o
f
the
ph
ot
ov
ol
t
a
i
c
syst
em u
nde
r di
f
f
e
r
e
n
t
co
nd
i
tio
ns
o
f
gr
id
f
a
u
lts
.
Th
e tr
an
s
i
en
t
sta
t
e
sta
b
ili
ty
of
t
h
e
syste
m
m
a
y
be
a
n
aly
z
e
d
b
y
ma
ny
me
tho
d
s
;
h
e
re
some
aspec
t
s
a
r
e
t
a
ke
n
i
n
to ac
cou
n
t.
The
f
a
ul
ts on t
h
e
g
r
id c
a
n
be
divi
de
d
i
n
to t
w
o
mai
n
g
r
o
u
p
s.
a)
Sy
mm
et
ri
ca
l fa
u
lt: W
h
en
an equ
a
l d
e
cre
a
s
e
in
th
e
ma
gn
i
t
u
d
e
o
f
t
h
e
g
r
i
d
v
o
lta
g
e
o
ccur
s
in
a
l
l
thr
ee
pha
ses whe
r
ea
s
t
h
e
s
y
st
em r
e
mai
n
s bal
a
nc
ed.
Sy
mmet
r
i
c
a
l
faul
t
s
a
r
e
n
o
t u
n
c
o
mmo
n
(t
he
y
d
o
ha
ppe
n
of
te
n:
b
u
s
fa
ul
ts,
l
i
ght
ni
n
g
st
ri
kes i
n
sub
s
t
a
t
i
ons
et
c)
.
b)
Un
sy
mme
t
r
i
c
a
l
fau
l
t
:
Wh
e
n
a
n
un
e
q
u
a
l d
e
c
r
ea
se in gr
id
v
o
l
tag
e
o
c
cu
rs w
i
th al
te
rn
a
t
i
o
n in
ph
a
s
e in
be
t
w
ee
n.
Thi
s
c
a
t
e
go
ry
o
f
f
a
u
l
t
ar
ise
s
as mo
r
e
t
h
a
n
o
n
e
p
h
a
s
e is sh
o
r
te
d
t
o
g
r
ou
nd
o
r
t
o
one
a
not
he
r
.
T
h
e
e
f
f
e
cti
v
e
n
ess
of
th
e
c
o
n
t
ro
l
sy
ste
m
is ch
ec
k
e
d
b
y
c
onsid
e
r
ing
t
h
re
e
ca
se
s of
gr
id
fa
u
lts.
In
e
ach
o
f
th
e
c
a
s
e
s
,
t
h
e
r
e
su
lt
an
a
l
y
s
is
is c
a
r
r
i
e
d
ou
t th
at
h
a
s
b
een
re
c
o
rd
ed
for
stab
ilit
y
a
n
a
l
y
s
is [
2
4
]
.
c
a
se
-
1
: Th
ree
ph
as
e
t
o
gr
ou
n
d
f
a
ul
t (
L
L
L
G
f
a
ul
t)
: Three
ph
ase
s
to gro
und
f
a
u
l
t is a fa
mil
i
a
r
f
a
u
lt
in
th
e
in
du
st
ri
al c
l
i
m
a
t
e.
T
h
e
o
u
t
come
o
f
th
e
P
V
ci
rc
u
i
t
wi
th a
L
L
L
G f
a
u
lt of
0
.
3
sec to 0
.
4
se
c
is an
al
y
zed in
th
is
se
ct
ion.
c
a
se
-
2
: L
L
G f
a
ul
t
i
n
d
i
st
ri
b
u
t
i
o
n
ne
tw
or
k
: I
n
th
is c
a
s
e,
a do
ub
le
l
i
n
e
to
g
r
ou
nd
fa
u
lt
is s
i
mu
la
te
d
f
r
om 0.
3
se
c to
0.
4
se
c
.
Whe
n
t
h
i
s
t
y
pe
of
f
a
ul
t oc
c
u
rs
a s
udde
n po
w
e
r s
u
r
g
e i
s
e
x
peri
e
n
c
e
d
i
n
t
h
e
c
o
nve
rt
e
r
.
T
h
e
vol
t
a
ge
o
f
t
h
e
con
v
e
r
te
r r
i
se
s
ra
pi
dl
y a
nd
t
h
en r
e
c
o
ve
rs
wi
t
h
an
osc
i
ll
at
i
on t
h
at
l
a
st
s f
o
r
a
fe
w c
y
c
l
es.
Thi
s
re
spon
s
e
is g
e
ne
r
a
t
e
d
w
ith
t
h
e P
I
c
o
n
t
ro
lle
r
.
c
a
se
-
3
: LG
f
a
ul
t in
d
i
s
t
ri
bu
ti
on
ne
t
w
ork
: I
n
th
i
s
c
a
s
e
,
a
sin
g
l
e
lin
e t
o
g
r
o
und
fa
u
l
t
is
simu
la
te
d
.
Th
e
Fi
g
u
r
e
5
illu
str
a
t
e
s th
e
Si
mu
la
ti
o
n
m
ode
l o
f
t
h
e
gr
id
co
nn
ec
te
d PV sy
s
t
em
.
Th
e
sub
-
sy
ste
m
o
f
t
h
e P
V
s
o
u
r
c
e
i
n
cl
ude
s a P
V
bl
oc
k,
M
P
PT
c
ont
roll
er al
on
g
wi
th
st
ep
u
p
c
o
n
v
e
r
t
e
r int
e
rfac
ed
t
o
t
h
e g
r
i
d
vi
a
vol
t
a
ge
so
u
r
c
e
inve
rt
er
. T
a
bl
e 1
gi
ves syst
em pa
ra
met
e
rs
dat
a
a
n
d
s
p
e
c
i
fi
cat
i
ons [
2
5]
.
He
re t
h
e s
y
st
em
i
s
ce
r
tif
ie
d
un
d
e
r
t
h
e
le
as
t
f
a
u
lt
c
i
rc
u
m
st
a
n
c
e
s
.
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
:
9
3
1
–
941
93
6
F
i
gu
re
5.
Si
mu
l
a
t
i
on m
o
d
e
l
o
f
t
h
e
pro
pose
d
s
y
st
em
Ta
b
l
e
1
.
S
y
stem
Par
a
m
e
te
r
an
d
Sp
e
c
i
fi
ca
ti
on
s
Pa
ram
e
t
e
r V
a
lue
s
Pa
ram
e
t
e
r
V
a
l
u
es
T
h
e vol
tage
at the
Grid
1
1
KV
V
dc
1200V
Supply f
r
e
quenc
y
50 H
z
F
s
w_i
nv
2 kH
z
Fil
t
er
Induc
to
r
10 m
H
Fi
lter
Ca
pac
itor
100
µ
F
Inve
rte
r
v
o
l
t
a
g
e
1200V
Inve
rt
er
output volta
g
e a
f
ter f
ilter
i
n
g
800V
Thr
e
e phase
line
15 km
len
g
th L
o
a
d
5M
W
,
100V
A
R
3
.
1
.
Th
ree pha
s
e
t
o
g
r
ound
fa
ult
(LLLG
f
a
u
l
t)
The
out
put
wa
ve
forms of pro
pos
ed st
ruct
ure
wi
th a LL
LG
faul
t
are il
l
u
stra
t
e
d bel
o
w
.
At
t
=
0.
3
se
c
t
o
0.4 sec
,
LL
LG
faul
t
is i
n
sert
e
d
i
n
to t
h
e syste
m
. Fi
g
u
re
6(a
)
sho
w
s
t
h
e wa
v
e
fo
rm
of
DC
v
o
l
t
a
ge ge
ne
rat
e
d
b
y
t
h
e bo
ost
c
o
nv
ert
e
r. Fi
g
u
re
s
6
(
b
)
a
n
d
6(c
)
de
pi
ct
w
i
t
h
LLL
G
fa
ult
t
h
e
na
ture
o
f
3-p
h
a
s
e c
u
rre
n
t
an
d
vol
t
a
ge
a
t
t
h
e g
r
id
. F
i
gu
r
e
s 6
(
d
)
a
n
d
6(e
)
s
h
o
w
t
h
e
vari
a
t
i
on
of
p
o
w
e
r
s fe
d t
o
t
h
e
g
r
i
d
.
F
i
gure
6(a
)
i
l
l
u
st
rat
e
s
t
h
e
w
a
vefor
m
of
t
h
e
DC
vol
t
a
ge
p
r
o
d
u
ced
b
y
t
h
e
ste
p
-u
p c
onv
e
r
t
e
r. B
e
fo
re
th
e
a
p
p
l
i
c
a
tio
n
o
f
t
h
e fa
u
l
t
,
D
C
vo
lta
g
e
at
ta
in
s a
v
a
lu
e
of
12
00V
.
D
u
r
i
n
g
t
h
e
f
a
u
l
t
,
D
C
vo
lt
ag
e
inc
r
ea
se
s
su
dd
en
ly
fro
m
1
2
0
0
to
160
0V.
Ju
st
af
te
r
0.
42 se
c
,
12
00V
i
s
a
c
h
ie
v
e
d
.
F
i
gure
6
(
b)
de
pi
ct
s t
h
e
res
p
o
n
se
of
a t
h
re
e
-
p
h
ase
cu
rre
n
t
i
n
t
h
e c
ourse
o
f
th
e
t
h
ree
-
pha
se
faul
t
.
Ahea
d
of the
int
r
od
uc
ti
o
n
of
fa
ult
,
c
u
rre
n
t i
s
set
t
le
d at
5
A
.
Whe
n
a
fa
ul
t
i
s
i
n
t
r
o
d
u
ce
d
a
t
0
.
3 sec
t
h
e c
u
rre
n
t
ri
ses
ne
arl
y
to
18
0A
(ma
x
) a
n
d
ce
rt
ai
nly
t
h
e
c
u
rre
n
t
rec
ove
rs i
t
s
st
ea
dy
val
u
e
of 5
A
a
f
t
e
r
t
h
e fa
ul
t
pe
rio
d
.
Figure 6(c
)
indica
tes the nature
of three-ph
ase
voltages
at th
e time of
LLLG fa
ult.
Ahead
of
the
a
p
p
lic
a
tion
o
f
fau
l
t,
vo
lt
ag
e i
s
k
e
p
t
at 8KV
(m
ax)
.
A
t
th
e ti
me
of
app
l
i
c
a
tio
n
of
f
a
u
l
t, th
e
vo
lta
g
e
a
t
th
e g
r
i
d
i
s
ze
ro
f
r
o
m
0.3
t
o
0.4
sec
.
La
te
r 0.
4 s
e
c
,
v
o
lt
ag
e
set
t
l
e
s t
o
it
s c
onst
a
nt
val
u
e.
Fi
g
u
re
6
(
d) sh
ows
t
h
e
wa
ve
form of act
i
v
e
po
we
r fe
d t
o
t
h
e
gri
d
a
t
t
h
e
t
i
m
e
o
f
t
h
e
fa
ul
t peri
od
fro
m
0.3 se
c t
o
0.4
sec
.
I
n
t
h
e
co
u
r
se
of t
h
e fa
ul
t
p
e
ri
od
,
bot
h a
c
t
i
v
e, as
w
e
l
l
as re
act
i
v
e
p
o
w
e
r
, re
mai
n
s z
e
r
o
.
A
t
0
.
4
5
se
c
po
w
e
r se
tt
les
to
its
no
rma
l
v
a
lu
e.
In
Fi
gu
re
,
6(e
)
it
i
s
o
b
serve
d
t
h
at
t
h
ere
i
s
a
ve
ry sl
i
g
h
t
c
h
an
ge
in
rea
c
t
i
ve
po
wer
j
u
st
aft
e
r
0.4
seco
nds
. T
h
e
n
aft
e
r s
o
me
ti
me, i
t
set
t
l
e
s
t
o
i
t
s st
ead
y-st
at
e
v
a
l
u
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Stability analy
s
is
of
phot
ovoltaic system under
grid
faults (Nivedita P
a
ti)
9
37
(a) (
b
)
(c
)
(d
)
(e)
F
i
gu
r
e
6.
(
a
)
D
C
v
o
lt
a
g
e
ge
ne
ra
te
d vs.t
i
m
e
,
(
b
)
3
-
p
h
ase
cu
r
r
e
nt
vs.
t
ime at
g
r
id,
(
c
)
3-
pha
se
v
o
lt
a
g
e
vs
.t
ime
at
gri
d
,
(d)
Active
powe
r at gri
d
, (e
)
R
e
a
c
tive
powe
r
v
s
.
tim
e
a
t
the grid
with
LLLG fa
ult
3
.
2
.
LLG
fa
ult
at
d
i
s
t
ribut
io
n netw
o
r
k
The F
i
g
u
r
e
7(
a
)
s
h
ows
the
DC vol
t
a
ge
g
e
nera
te
d b
y
t
h
e
St
ep
u
p
c
o
n
v
e
r
t
e
r
a
l
on
g
LL
G
faul
t
.
Fig
u
re
s
7
(
b)
a
n
d
7(c
)
d
e
p
i
ct
3
-
p
h
a
se
cu
r
r
e
n
t a
n
d vo
lt
ag
e
s
a
t
th
e
gr
id a
l
on
g w
i
t
h
LLG
f
a
u
l
t
.
F
i
gur
es
7(d)
an
d
7
(
e)
illu
s
t
r
a
te
t
h
e
c
h
a
n
g
e
s i
n
ac
ti
v
e
a
n
d
re
a
c
t
i
v
e
po
w
e
r
.
Fi
g
u
re
7
(
a
)
show
s th
e D
C
vo
lt
ag
e
g
e
n
e
r
a
t
e
d by
th
e
bo
ost
c
o
n
v
e
r
te
r i
s
dis
r
u
p
t
e
d
mo
re
tha
n
LL
LG
fa
ult
.
Wi
th
0.
3 se
c
DC
vol
ta
ge
o
s
ci
l
l
a
t
e
s
bet
w
ee
n
1
200 t
o
1
600
V a
n
d
t
h
en
d
e
cr
e
a
s
e
s
to 1
200
V a
f
te
r
the
f
a
u
lt.
La
te
r
a
t
0
.
41
sec,
v
o
l
ta
g
e
set
tle
s t
o
i
t
s
ste
a
dy
-
s
ta
te
val
u
e.
F
i
g
u
r
e
7(b)
i
n
dica
te
s
t
h
e n
a
ture
of
t
h
r
ee-
ph
ase
vo
l
t
a
g
es
du
rin
g
L
L
G
f
a
u
l
t
.
T
h
e
vo
l
t
ag
e
a
t
t
h
e g
r
id
is
di
st
ur
be
d f
r
o
m
0.
3
t
o
0.
4
sec
.
A
f
t
e
r
0
.
4
-
se
c v
o
l
t
a
ge
set
t
l
e
s
t
o
i
t
s
re
g
u
la
r va
lue
.
W
h
e
n
a
f
a
u
lt i
s
in
tr
odu
c
e
d at 0
.
3
se
c
t
h
e
cu
rr
en
t
ri
ses
nea
r
ly
t
o
10
0
A
(max
) wh
ic
h
is sh
o
w
n
in
F
i
g
u
r
e
7(
c
)
.
At
0.
42
sec
,
c
u
r
r
ent
a
t
t
a
ins i
t
s
ori
g
i
n
al
val
u
e.
F
r
om
Fi
g
u
r
e
7(
d)
it
i
s
o
b
se
r
v
ed
t
h
at
t
h
e
re
a
l
and
r
eac
ti
ve
po
wer
inse
rt
e
d
t
o
t
h
e
gri
d
i
s
hi
g
h
ly
di
sr
upt
e
d
a
t
th
e
t
i
me
o
f
t
h
e
LLG
fa
ul
t
of
0
.
3 sec
to
0.
4
s
e
c
.
At
0
.
4
3
se
c
po
w
e
r at
ta
in
s its ste
a
d
y
-
s
t
a
te
v
a
lu
e.
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
-
200
-
150
-
100
-5
0
0
50
100
150
200
Ti
m
e
(
s
)
Li
ne
C
u
r
r
en
t
(
A
)
A
B
C
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
:
9
3
1
–
941
93
8
F
i
gure
7(e
)
s
h
ows
t
h
e
c
h
a
n
g
e
s i
n
t
h
e
re
act
i
v
e
po
wer
i
n
t
h
e
co
urse
o
f
th
e
faul
t
peri
od
.
The
o
u
t
put
wave
form
depi
ct
s
t
h
at
t
h
e
re
a
c
t
i
v
e p
o
w
er
i
s
negat
i
ve
du
ri
n
g
t
h
e
faul
t
pe
ri
od. J
u
st
a
f
te
r the
cl
ea
ra
nce
o
f
fa
ul
t
,
g
r
o
w
t
h
is see
n
, t
h
en
af
te
r so
me
ti
me
,
it
set
t
le
s
to
i
t
s n
o
rm
al
v
a
lu
e
.
(
a
)
(b)
(c) (
d
)
(e
)
Figure 7.
(a) C
o
nverter
vol
tage
vs
.
time with LLLG
fa
ult, (
b
) Grid
voltage
vs
. time
with L
LLG
fault
(c)
Gr
id
c
u
rr
e
n
t w
i
th LLG
fault,
(d)
A
c
ti
v
e
po
w
e
r
at
th
e g
r
id
w
i
th
LLG
fau
l
t
,
(e)
R
e
a
c
tive
po
w
e
r
v
s
.
time
at
th
e
gr
id w
ith LLG
f
a
u
l
t
3.3.
L
G
Fa
ul
t
at d
i
stri
bu
ti
on
ne
twor
k
F
i
gure
8
(
a
)
sh
ows
t
h
e
vol
ta
g
e
ge
ne
rat
e
d
b
y
the
c
o
n
v
ert
e
r
w
i
t
h
LG
fa
ul
t
.
Fi
gu
re
s
8
(
b) a
n
d
8(c
)
s
h
ow
3-p
h
ase
c
u
rre
nt
and
vol
ta
ges
at
t
h
e gri
d
wi
th LG
fa
ult
.
F
i
gu
res 8(d
)
a
n
d 8
(
e)
s
h
ow c
h
a
nge
s
i
n
ac
ti
ve an
d
r
e
a
c
tiv
e
p
o
wer f
e
d
t
o
th
e
g
r
id
.
F
i
gure
8(a
)
s
h
ows
t
h
e
v
o
l
t
a
g
e
ge
nera
te
d b
y
the
co
n
v
ert
e
r
wi
t
h
L
G
fa
ul
t
i
s
di
stur
b
e
d l
e
s
s
t
h
a
n
LL
G
fa
ult
d
u
rin
g
t
h
e LG
faul
t
o
f
0
.
3
sec
t
o
0.4 se
c.
A
t
0.42
sec t
h
e v
o
lt
age
rea
c
h
es it
s re
gul
a
r
va
lue
t
h
at
is 1
2
0
0
V
.
W
ith
0.
3
se
c
D
C
vo
lta
g
e
o
s
c
i
lla
te
s b
e
tw
ee
n
120
0
to
1400
V
a
n
d
th
en
dec
r
ea
se
s to
120
0V
a
f
ter th
e
cle
a
r
a
n
c
e
of fa
ul
t
.
A
f
te
r
0.42
sec
vol
ta
g
e
set
t
l
e
s t
o
it
s regul
a
r
va
lue
.
In
Fi
g
u
re
8(
b
)
, i
t
i
s
sho
w
n t
h
at
in
t
h
e
co
u
r
se
of t
h
e
LG
faul
t
t
h
e
gr
id
v
o
lt
a
g
e i
s
di
st
urbed
fro
m
0.
3 t
o
0
.
4
sec
.
A
f
t
e
r
0
.
4
se
c
vo
l
t
age
set
t
l
e
s
t
o
i
t
s re
gula
r
va
lue
.
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0
20
0
40
0
60
0
80
0
10
00
12
00
14
00
16
00
18
00
20
00
Ti
m
e
(
s
)
V
o
l
t
ag
e (
V
)
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
-1
0
-8
-6
-4
-2
0
2
4
6
8
10
Ti
m
e
(
s
)
P
has
e V
o
l
t
age (
k
V
)
A
B
C
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
-
200
-
150
-
100
-5
0
0
50
100
150
200
Ti
m
e
(
s
)
L
i
n
e
C
u
rre
n
t
(A
)
A
B
C
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
-0
.
2
-0
.
1
0
0.
1
0.
2
0.
3
0.
4
Ti
m
e
(
s
)
Ac
t
i
v
e
P
o
w
e
r
(
M
W
))
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
-0
.
2
-0
.
1
5
-0
.
1
-0
.
0
5
0
0.
05
0.
1
0.
15
0.
2
Ti
m
e
(
s
)
R
e
a
c
t
i
v
e
P
o
w
e
r (M
V
A
R
)
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Sta
b
i
l
i
t
y
an
al
y
s
i
s
of
ph
ot
o
v
ol
tai
c
syst
em
un
d
e
r gri
d
f
a
ult
s
(
N
i
v
e
d
it
a
P
a
t
i
)
9
39
F
i
gure
8(c
)
de
pi
ct
s
t
h
e c
u
rre
n
t
re
s
ponse
f
o
r the
SL
G fa
u
l
t
.
The
c
u
rre
n
t rise
s
from
5
A t
o
1
0
0
A
i
n
st
ant
l
y
d
u
ri
n
g
the
fa
ult
.
T
h
e
fa
ul
t
i
s
c
l
e
a
ne
d
1 se
c
l
a
t
e
r a
n
d t
h
e
cu
rre
nt
gra
s
p
t
h
e
no
rma
l
val
u
e
at
t
=
0.
4
2
s.
F
i
gure
8
(
d
)
s
h
ows
t
h
e
w
a
vefor
m
of a
c
t
i
ve
p
o
w
e
r
fe
d
t
o
t
h
e
g
r
i
d
.
It
is
vi
si
bl
e t
h
at
the
p
o
w
e
r i
n
je
ct
ed
t
o
t
h
e
gri
d
i
s
le
ss di
s
r
u
p
te
d
d
u
r
in
g t
h
e
LG
fa
ul
t t
h
an
the
LL
G
fa
ult
fro
m
0.3 sec t
o
0.
4
se
c
.
At
0.
4
2
se
c
p
o
w
e
r
at
t
a
i
n
s
i
t
s
ste
a
dy
st
at
e
val
u
e
bec
a
u
s
e of
t
h
e
act
i
o
n
of a
ro
bust
co
nt
rol
l
e
r.
F
i
gu
re 8(e
)
sho
w
s t
h
e
c
h
a
n
ges i
n
r
e
a
c
tiv
e
p
o
wer i
n
th
e
cou
r
se
of
th
e f
a
u
lt
p
e
rio
d
. It
is
le
ss d
i
sr
up
te
d
th
an
LLG
fa
u
l
t
.
(a
)
(b
)
(c
)
(d
)
(e
)
F
i
gu
re
8.
(a
) C
o
n
v
e
r
te
r vol
t
a
g
e
wi
th
LG
fa
ul
t
,
(b),
Gri
d
vol
t
a
ge
wi
t
h
S
L
G
fa
ult
,
(c
) G
r
i
d
c
u
r
r
ent
w
i
t
h
S
L
G
f
a
ul
t,
(
d
) Ac
ti
v
e
p
o
we
r
a
t
t
h
e
gri
d
w
i
t
h
SL
G
faul
t
,
(e)
R
eac
t
i
ve
p
o
w
er
a
t
th
e
g
r
i
d
wit
h
SL
G f
a
ul
t
4.
CO
NCL
U
S
I
O
N
In
i
tia
lly
,
th
e
sy
ste
m
is simu
l
a
t
e
d
w
i
t
hou
t a
n
y f
a
u
lt.
Th
e
t
h
r
e
e
t
y
p
e
s
o
f
fau
l
ts a
r
e
p
r
e
s
en
te
d
and
th
e
i
m
pa
ct
o
n
t
h
e
syste
m
i
s
st
u
d
i
e
d u
n
d
er t
h
e
prese
n
ce o
f
di
ffe
rent
t
y
pes of fa
ul
t
s
. The sim
u
l
a
t
i
on res
u
lt
i
s
gi
ve
n
bel
o
w for
al
l
t
ype
s o
f
fa
ul
ts.
Neve
rt
hel
e
ss
, t
h
e
r
e a
r
e
c
o
u
n
t
l
e
s
s
proces
se
s
t
o
a
n
al
yze
the
dy
nami
c st
a
b
i
l
i
t
y of
t
h
e st
ruc
t
ure
,
onl
y
i
m
po
rt
an
t
a
s
pe
ct
s
a
r
e
t
a
ken i
n
to c
o
nsi
d
e
r
a
t
i
o
n
.
T
h
i
s
pa
p
e
r de
s
c
ribe
s t
h
e eff
ect
i
v
e
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0
20
0
40
0
60
0
80
0
100
0
120
0
140
0
160
0
180
0
200
0
Ti
m
e
(
s
)
V
o
l
t
age (
V
)
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
-10
-8
-6
-4
-2
0
2
4
6
8
10
Ti
m
e
(
s
)
P
h
as
e V
o
l
t
a
g
e
(
k
V
)
A
B
C
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
-2
0
0
-1
5
0
-1
0
0
-5
0
0
50
10
0
15
0
20
0
Ti
m
e
(
s
)
Line C
u
r
r
e
n
t
(
A
)
A
B
C
0
0.
1
0.
2
0.
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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
:
9
3
1
–
941
94
0
ac
hie
v
e
m
ent
o
f
t
h
e
s
y
st
em.
In t
h
is
pape
r, t
h
e struct
u
r
e i
s
c
e
rti
f
i
e
d u
n
d
er
t
h
e l
e
a
s
t dama
g
e
d
c
i
rc
umsta
n
c
e
s i
.
e
.
t
h
e
sy
mmet
r
i
c
al
as
we
l
l
as u
n
sy
mme
t
ri
cal
f
a
ul
t
.
Ju
st
a
f
t
e
r t
h
e
fa
ul
t,
s
y
st
em
pa
ramet
e
rs re
ta
in t
h
ei
r or
igi
n
al
val
u
es
be
ca
use
o
f
t
h
e r
o
b
u
st
ness
of
t
h
e
cont
rol
l
e
r
.
T
h
e co
rrect
ness
of
t
h
e
cu
rr
ent
c
ont
rol
sc
he
me is
dem
o
n
s
trat
ed
by
t
h
e
result
anal
ysi
s
.
T
h
e
out
put
wa
ve
fo
rm
c
o
mpi
l
ed
t
h
e
val
i
dit
y
of
t
h
e
use
d
c
o
ntrol
t
echni
q
u
es
sin
c
e t
h
e
del
i
ve
re
d p
o
w
e
rs
p
u
rs
ue t
h
e
re
g
u
l
a
r
val
u
es
,
pro
v
i
d
ed
b
y
t
h
e
MP
P
T
c
ontr
o
ll
er
of
the
P
V
sy
st
em
, bo
th in a nor
ma
l
an
d
ab
n
o
rm
al
co
nditi
o
n
.
RE
FERE
NC
E
S
[1]
V.
kh
a
r
e,
S.
Nema
,
a
n
d
P
.
Ba
r
e
d
a
r,
"Po
w
e
r
q
u
a
l
i
t
y di
st
urb
a
n
ces
in
g
r
id
con
n
ected
so
lar s
y
s
t
e
m
i
t
s
pre
v
ention
",
Intern
ation
a
l
Jo
u
r
n
a
l of
En
gine
e
r
ing
an
d
In
no
va
t
i
ve
T
echn
o
log
y
(
I
JEIT
)
, Vo
l.
1, Issu
e
.
5, pp
25
2-2
55,
20
16.
[2]
P
.
K.
H
o
t
a
,
Babita
P
a
nd
a
,
Bh
ag
ab
a
t
P
a
n
d
a
, "F
au
lt
an
a
l
y
s
is of
g
r
id
co
nn
ected
p
h
o
t
ov
oltai
c
s
y
s
t
em
”
,
Am
erican
Jour
na
l
o
f
Elec
trical
Po
we
r
a
nd
En
er
gy Syst
ems
, Vo
l.
5,
No.
4
,
pp.
35
-
4
4
,
2
016
.
[3]
M.
G.
Mo
li
na
a
nd
L. E.
Jua
n
ic
o,
“
D
y
n
a
m
ic
m
o
d
e
li
ng
a
n
d
c
ontro
l
d
e
si
gn
o
f
a
n
a
d
va
nc
e
d
p
h
o
t
ov
olta
i
c
so
la
r
sy
st
em
for distr
i
b
u
te
d
genera
tio
n
app
licat
io
n”,
J
o
urna
l
of
E
l
ec
t
r
i
c
al En
gi
nee
r
i
n
g
:
T
h
e
o
ry
a
nd
A
p
p
l
i
c
a
t
i
on (J
EETA
)
,
Vo
l. 1
,
No.
3,
pp
.14
1
-15
0
,
20
15
.
[4]
K.
Ma
no
ha
r a
n
d
P.
So
bh
a
Ra
ni
“M
PPT
an
d s
i
m
u
latio
n
for
a g
r
id-
c
o
nnec
t
ed
ph
ot
o
v
o
l
ta
ic
sy
st
e
m
and
fa
ul
t a
n
a
l
y
s
is”
,
Intern
ation
a
l
Jo
u
r
n
a
l of
En
gine
e
r
ing
an
d
Sc
ien
c
e
(IJES
)
, Vo
l.
1,
Is
su
e.2,
pp
.15
8
-1
6
6
,
20
14
.
[5]
L.
B. G.
Ca
mpa
n
h
o
l1,
S
.
A.
Oliv
eira
d
a
S
ilva
,
V
.
D
.
Ba
con
,
A
.
A.
O.
Ju
nior, "
T
h
r
ee-P
h
ase
Grid
-Con
nected
P
V
S
y
s
t
em O
p
era
t
in
g
with
F
e
ed-F
orw
a
rd Co
ntrol
Loo
p
an
d
A
c
ti
v
e
P
o
wer
-
Li
ne
C
o
nd
it
io
nin
g
U
s
i
n
g
NP
C
I
n
ver
t
er
"
,
IECO
N
An
nua
l
Co
nferen
c
e
of
th
e IEEE In
du
stria
l
Elec
tro
n
ics S
o
c
iet
y
, 20
16
.
[6]
V.
N.
L
a
l;
S
.
N
.
S
i
n
g
h
“Co
n
t
ro
l
and
P
e
rfo
rman
ce
A
n
aly
s
is
of
a S
i
ng
le-S
tag
e
U
t
ility-S
c
al
e G
r
id-Co
n
n
e
c
t
ed
P
V
Sy
st
e
m
",
IEEE Sy
ste
m
s
J
o
urna
l
,
Vo
l. 11
,
is
su
e
3,
pp
.
1
601
-16
1
1
,
20
17
.
[7]
S.
Izu
m
i, Y. Kar
a
kaw
a
,
X.
Xin, T. Yamas
a
ki,
"
S
tab
i
lity
A
n
aly
s
is
of
P
o
wer S
y
stems
w
ith
P
h
otovo
ltaic
G
e
ner
a
tors"
,
IE
EE Con
f
e
r
e
n
ce
on
De
c
i
si
on and Co
nt
ro
l
(CDC)
,
20
16.
[8]
A.
V.
Ti
m
b
us,
P.Ro
dr
ig
ue
z, R.
Te
o
d
o
re
sc
u, M.L
i
se
rre
a
nd F.
Blaa
b
j
e
r
g
,
"Co
n
t
r
o
l
strat
e
gie
s
fo
r
d
i
stri
bu
te
d po
wer
g
e
ne
rat
i
on sy
st
em
s op
e
r
a
t
i
n
g on t
h
e fa
u
l
ty gri
d
"
, IEEE
Internat
iona
l S
y
mp
o
s
ium
on
Indu
st
rial
Ele
ctro
ni
cs
,
p
p
.
1
60
1-1
6
0
7
,
201
6.
[9]
Y.
Shi
,
L
u
.Wa
ng,
Hui
L
i
, "Co
n
t
r
ol sy
st
e
m
d
e
sig
n
a
nd Sta
b
ili
ty
Ana
l
y
s
i
s
for
a
th
re
e pha
se
Si
C-ba
se
d
Fi
lte
r-l
e
s
s
Grid-connected PV
Invert
er
"
,
I
E
EE
App
l
i
e
d Pow
e
r El
ectro
ni
cs
C
o
nferenc
e
and
Exp
o
s
i
tio
n
(APEC
)
, 20
18
.
[10]
W
.
Cai,
H.
Re
n
,
Y.
Ji
a
o
,
M
.
Ca
i,
X.
Che
n
g
,
"Ana
lysi
s
a
n
d
Si
m
u
l
a
tio
n
for
Gri
d
-Co
n
ne
c
t
e
d
Ph
ot
ov
olt
a
ic
Syste
m
ba
se
d
on
M
A
TLA
B
"
,
I
n
ter
n
a
t
i
o
n
a
l
C
onf
eren
c
e
on
El
e
c
tr
ica
l
a
n
d
C
o
n
t
ro
l En
gin
e
eri
ng (
I
C
EC
E)
, Yichang
,
2
0
1
1
,
pp
.63
-
66
.
[11]
IEEE,
“IE
E
E
standard
for
int
e
rconn
e
c
ting
di
stribu
ted
re
s
o
u
r
c
e
s
wi
th
e
l
ec
t
r
i
c
p
o
w
er s
y
s
t
em
s,
” Sta
n
d
a
rd
s
Coo
r
dinating
Co
mmittee
,
IEE
E
S
t
a
nda
rd
s
15
47
,
200
3
.
[12]
A.Y
azdan
i, P
.
P
.
D
a
sh,
"
A
Co
n
t
ro
l M
e
th
odo
lo
gy
a
n
d Char
acter
i
zation
o
f
D
y
n
a
mics
for
a
P
hotov
ol
taic
(P
V) S
y
s
t
em
I
n
te
r
f
a
c
e
d w
i
t
h
a
Di
st
ri
bu
ti
on
Ne
t
w
o
r
k
"
IE
EE
Transactions o
n
Pow
e
r
Deliv
e
r
y
,
Vol.
24
, No
.
3
,
pp.1
5
3
8
-
15
51,
Ju
ly
20
09
.
[13]
F
.
Blaab
jerg
,
R
.
Teod
ores
cu
,
M
.
L
i
s
e
rre
,
A
.
V.
Timbus
,
"O
ver
v
iew of
Con
t
ro
l
and
Grid
S
y
n
c
hro
n
izatio
n
f
o
r
Distributed Pow
e
r Ge
ner
a
tion Systems",
IEE
E
Tran
sac
t
io
ns on
In
d
u
stria
l
E
l
e
c
tronic
s
,
Vo
l.
53
,
No
.5,
pp
.1
3
9
8
-
14
09,
Oct. 2
006
.
[14]
B.S
a
rith
a,
E
.Ch
r
is
S,
H
.
S
h
aw
n
D and
C.Jianwu
, "A
nalys
i
s an
d
Con
t
rol of P
h
o
t
o
voltai
c
Sy
stem
: Ap
plica
t
ion
to
a
high
pen
e
tra
t
ion
Case S
t
ud
y"
,
IEE
E
Sy
st
e
m
s J
o
urna
l
,
Vol.6
,
No
. 2,
2
0
12.
[15]
R.S
u
n
n
y
,
R
.
A
n
t
o
, "H
armo
nics
Co
ntrol and
P
e
r
f
ormanc
e
A
n
a
l
ysi
s
o
f
a
Gri
d
-Co
n
n
e
c
t
e
d
Ph
ot
ov
ol
ta
ic Syste
m
",
In
te
rna
t
io
na
l
Con
f
e
r
e
n
ce
on
A
d
v
a
n
c
e
d
Comp
ut
in
g a
n
d
Co
mmu
n
i
c
a
ti
on Sy
st
e
m
s (IC
ACCS
)
,
Coimbatore,
p
p
.
1
-6, 20
13
.
[16]
Z
.
Dejia,
Z
.
Zhen
gming,
M
.
Elt
awil
,
Y.
Liqi
a
ng
, "D
esign
and
Co
n
t
ro
l o
f
a Thre
e-
P
h
as
e Grid-con
n
ect
ed ph
o
t
ov
olt
a
ic
Sy
st
e
m
with
Deve
l
o
p
e
d Ma
xi
mu
m
Po
we
r Po
in
t
Tra
c
k
i
n
g
"
,
T
w
e
n
ty-
T
h
i
r
d
An
nua
l
I
E
E
E
Ap
pl
i
e
d
Po
w
e
r El
e
c
t
r
o
n
i
c
s
Co
nf
e
r
e
n
ce
a
nd
e
x
p
o
s
i
t
i
o
n
, Aus
t
i
n
, TX
,
pp
.97
3
-9
79,
20
08
.
[17]
S
.
M
e
sh
ram, G
.
Ag
nihotri,
S
.
G
u
p
t
a,
"A
n
Effici
ent Co
nsta
nt
C
u
rrent
Controller for
PV
S
o
lar
Po
wer Genera
t
o
r
Integrat
ed
wit
h
the Gr
id",
Fift
h
I
E
EE Power
India
Conferen
ce
,
M
u
rth
a
l,
pp.
1-6
,
2
0
12
.
[18]
M
.
F
.
S
c
ho
nard
ie
,
D
.
C.M
a
rtins
,
"
A
pp
licatio
n o
f
the d
q
0
Tr
ans
f
or
mation
in
the
T
h
ree-P
h
as
e Grid
-Con
nected
P
V
Sy
st
e
m
s wi
th
Ac
t
i
v
e
a
n
d
Reac
t
i
ve
Po
we
r
Cont
ro
l",
I
E
EE In
tern
atio
na
l Con
f
er
enc
e
on
Su
st
aina
ble
Ener
gy
T
echn
o
lo
gi
es
,
Sin
g
a
p
ore
,
pp
.
18
-23
,
2
0
08.
[19]
S
.
B.
Kjaer
,
J.
K
.
P
e
d
e
rs
en
, F
.
Blaab
jerg
, “A R
e
v
i
ew
of
S
i
ng
le
-
P
has
e
Grid-Con
nected
Inv
e
rters
for P
h
otovo
ltaic
Mo
du
le
s”
,
IEEE Tran
s. In
dA
pp
l.
, Vo
l
.
4
1
,
No.
5
, pp.
1
2
9
2
-1
30
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t
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20
05.
[20]
J.M.Carras
co
, L.G.F
r
an
quel
o
,
J
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T. Bi
alasi
e
wicz,
E.Galv
an
, R
.
C
.
P.Gu
isad
o, M
.
A
.
M
.
P
r
ats
,
J.I
.
L
e
on
,
N.M
o
ren
o
-
Alfon
s
o,
“P
o
w
e
r
Elec
tron
ic S
y
stems for
th
e
G
r
id
In
tegra
t
io
n of
Ren
e
wab
l
e
En
ergy
S
o
ur
ces:
A
s
u
rv
ey
”
,
IEEE T
r
an
s.o
n
I
n
d.
Ele
c
tro
n
,
Vo
l.
53
, No
.4,
Au
g.
2
0
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02
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[21]
J.H.R.Ens
l
in
, P
.
J.M
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H
e
sk
es,
“H
armoni
c In
tera
ction
be
tween
a Large Numb
er
o
f
D
i
s
t
ribu
ted P
o
wer Inver
t
ers an
d
the Distr
i
bution
Network”,
IEEE
Trans.
on Pow
e
r El
ectron
,
Vol
.
19
, N
o
.6
, p
p
.
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5
8
6
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v
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04
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[22]
N.S
r
isaen
,
A
.
S
a
ng
swan
g
, “Ef
f
ec
t
of P
V
Grid
-Co
n
n
ected
S
y
s
t
em
Loca
tio
n
on
a
D
i
strib
u
tio
n
Sy
ste
m
”,
Proc
. of
IE
EE
As
ia
Pa
cif
i
c
C
o
n
f
.
on
C
i
r
c
u
i
t a
n
d
Sys
t
em
s
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