Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol.
4, No. 4, Decem
ber
2014, pp. 439~
450
I
S
SN
: 208
8-8
6
9
4
4
39
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Islanding Detection of Invert
er Based DG Unit Usi
n
g PV
System
M.Divyasree, L.Venk
ata Narasimha
Rao
Departm
e
nt o
f
E
l
ec
tric
al
a
nd
Electronics Engin
e
ering, K
L Univ
er
sity
, A.P
,
India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 13, 2014
Rev
i
sed
Jun
31,
201
4
Accepte
d
J
u
l 20, 2014
Distributed g
e
neration (DG) units are
rapid
l
y
in
creasing
and most of them
are interconn
ected with distrib
u
tion
network
to supply
power into th
e
network as well as local loads Isla
nding operations of DG usu
a
lly
occu
r
when power supply
from the main utility
is interr
upted due to sev
e
ral reason
s
but the DG keeps supply
i
ng power into the dis
t
ribution networ
ks. a new
method for islan
d
ing detection of
invert
er-based d
i
stributed
gener
a
tion (DG).
Although active islanding detection tec
hniques
have smaller no
n detection
zones than passive techniques
,
activ
e methods could degrad
e the s
y
stem
power quality
and are not
as simple
and eas
y to
im
plem
ent
as
pas
s
i
ve
methods. Th
e
phenomenon of
unintention
a
l
islanding
occur
s
when
a
distributed gen
e
r
a
tor (DG) continues to feed power into the grid when power
flow from
the centra
l
util
it
y sou
r
ce has
be
en int
e
rrupted
. A simple island
ing
detection sch
e
me has been d
e
signed base
d on this idea.
The prop
osed method
has been studied under m
u
ltipl
e
-DG
operation
m
odes and the UL 1741
islanding tests
co
nd
itio
ns an
d
also
u
s
ing
a PV system
. The
sim
u
lations
results, car
ried
out b
y
MATLAB/Simuli
nk, show that the prop
osed method
has a small Non
detection
zon
e
.
Keyword:
Di
st
ri
b
u
t
e
d ge
nerat
i
o
n (D
G
)
I
s
land
ing
No
n det
ect
i
o
n zone
(
N
DZ)
Pho
t
ov
o
ltaic (PV)
Vol
t
a
ge
-s
ou
rce
i
nve
rt
er
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M.Divyasree,
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
K L Un
iv
ersity,
A.P
,
I
n
dia.
Em
a
il: d
i
v
y
asree.m
a
d
i
v
a
d
a
@g
m
a
i
l
.co
m
1
.
IN
TR
OD
UC
TI
ON
Di
st
ri
b
u
t
e
d
ge
nerat
i
o
n (
D
G
)
pr
ovi
des m
a
ny
pot
e
n
t
i
a
l
bene
fi
t
s
, suc
h
as Lowe
r ener
gy
cost
s,
Im
p
r
o
v
e
d reliab
ility, i
m
p
r
ov
ed
po
wer
qu
ality, Greater au
t
o
no
m
y
, u
p
t
u
r
n efficien
cy.In
th
e last few years,
sm
all DGs in the range of 100
kW
ha
ve
gained popularity
am
ongst
indust
r
y and
utilities. Anti-islandi
ng
det
ect
i
on m
e
t
hods ca
n be
di
vi
ded i
n
t
o
t
w
o m
a
i
n
gr
o
ups:
pa
s
s
i
v
e an
d act
i
v
e
m
e
t
hods. I
n
p
a
ssi
ve m
e
t
hod
s
,
t
h
e
deci
si
o
n
w
h
et
h
e
r an i
s
l
a
ndi
ng
con
d
i
t
i
on occ
u
r
r
ed
or n
o
t
i
s
based o
n
m
e
asuri
ng a cert
a
i
n
sy
st
em
param
e
t
e
r
and c
o
m
p
ari
n
g
i
t
wi
t
h
a prede
t
erm
i
ned t
h
res
hol
d. Act
i
v
e m
e
t
h
o
d
s are
desi
gne
d t
o
f
o
r
ce t
h
e D
G
t
o
be
un
st
abl
e
du
ri
n
g
a
n
i
s
l
a
ndi
ng
si
t
u
at
i
o
n
.
I
n
g
e
ne
ral
,
i
s
l
a
ndi
ng
det
e
c
t
i
on m
e
t
hods
coul
d
be cl
ass
i
fi
ed i
n
t
o
t
h
re
e m
a
i
n
t
y
pes t
h
at
i
n
cl
ude
act
i
v
e,
pa
ssi
ve, a
n
d
co
m
m
uni
cat
i
on-
b
a
sed m
e
t
hods
.
Passi
ve m
e
t
hods
,
whi
c
h are
sim
p
l
e
and
easy
t
o
i
m
pl
em
ent
,
det
ect
i
s
l
a
ndi
ng
by
s
e
t
t
i
ng an
u
p
p
er
an
d l
o
we
r t
h
re
shol
d
o
n
a sy
st
em
param
e
t
e
r.
Act
i
v
e m
e
t
hod
s, o
n
t
h
e ot
her
han
d
,
rel
y
on i
n
ject
i
n
g
del
i
b
e
r
at
e di
st
ur
ba
nc
es t
o
t
h
e co
nne
ct
ed ci
rcui
t
an
d th
en
m
o
n
ito
ri
n
g
t
h
e
respon
se to d
e
term
i
n
e an
island
ing con
d
ition
[8
].
Activ
e m
e
th
o
d
s in
clud
e slid
e-m
o
d
e
fre
que
ncy
s
h
i
f
t
(SM
S
)
[9]
,
a
c
t
i
v
e fre
q
u
en
cy
d
r
i
f
t
(
A
F
D
)
o
r
f
r
e
que
ncy
bi
as [
10]
,
an
d
S
a
ndi
a
fre
q
u
en
c
y
shi
f
t
(SFS
)
[3]. Acti
ve m
e
thods
ha
ve sm
aller NDZ,
but, on
t
h
e othe
r hand,
ca
n degra
d
e
the
powe
r quality
of
the
po
we
r sy
st
em
[8]
.
Ot
he
r a
c
t
i
v
e m
e
t
hods
rel
y
on
del
i
b
erat
el
y
i
n
ject
i
ng
negat
i
ve
seq
u
ence c
u
rr
ent
an
d
d
i
stu
r
b
a
n
ce sig
n
a
ls in
to
th
e syste
m
th
ro
ug
h
eith
er th
e d
i
rect axis (d-axis) or the
q
u
ad
ratu
re axis
(q-a
xis
)
cur
r
ent
c
o
nt
r
o
l
l
e
rs [
1
]
,
[
3
]
t
o
det
ect
i
s
l
a
ndi
n
g
. C
o
m
m
uni
cat
i
on-
base
d m
e
tho
d
s
ha
ve
negl
i
g
i
b
l
e
N
D
Z
,
b
u
t
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
4
,
D
ecem
b
er
2
014
:
43
9 – 450
44
0
m
u
ch m
o
re ex
pen
s
i
v
e t
h
an
t
h
e f
o
rm
er m
e
t
h
ods
.
A
su
rvey
on
t
h
e
di
ffe
ren
t
i
s
l
a
ndi
n
g
det
ect
i
on m
e
t
hods
co
ul
d
be
fo
u
n
d
i
n
[
8
]
and
[
9
]
.
T
h
u
s
,
passi
ve
i
s
l
a
ndi
ng
d
e
t
ect
i
on m
e
t
hods
s
u
f
f
er
fr
om
l
a
rge
N
o
n
det
ect
i
o
n
zo
nes
(NDZs). NDZs are d
e
fi
n
e
d
as th
e lo
ad
ing
con
d
ition
s
fo
r
wh
ich
an
islan
d
i
n
g
d
e
tectio
n
m
e
th
od
wou
l
d
fail to
ope
rat
e
i
n
a t
i
m
el
y
m
a
nner.
To en
ha
nce t
h
e per
f
o
r
m
a
nce of
passi
ve m
e
tho
d
s, a
hy
b
r
i
d
passi
ve m
e
t
h
o
d
base
d
on
m
oni
t
o
ri
n
g
t
h
e v
o
l
t
a
ge
u
n
b
al
ance
an
d t
o
t
a
l
harm
oni
c
di
st
ort
i
o
n
(TH
D
)
was
p
r
o
p
o
se
d
i
n
[
7
]
.
Thi
s
pa
per p
r
e
s
ent
s
a new i
s
l
a
ndi
ng
det
ect
i
on m
e
t
hod,
w
h
i
c
h ha
s t
h
e i
m
provem
e
nt
s
of act
i
v
e an
d
passi
ve i
s
l
a
n
d
i
ng m
e
t
hods
, m
i
no
r N
D
Z, a
n
d
excel
l
e
nt
prec
i
s
i
on. T
h
e c
o
n
t
rol
st
rat
e
gy
o
f
t
h
e vol
t
a
ge-s
o
u
rc
e
i
nve
rt
er
has
b
een
desi
g
n
e
d
t
o
ope
rat
e
at
u
n
i
t
y
po
we
r fa
ct
or.
Al
s
o
, t
h
e
dc si
de
has
been
m
odel
l
e
d
by
a
cont
rol
l
a
bl
e dc
vol
t
a
ge s
o
u
r
c
e
. The m
a
i
n
conce
p
t
o
f
t
h
i
s
pape
r i
s
t
o
cha
nge t
h
e
dc-l
i
n
k v
o
l
t
a
ge co
ns
i
d
eri
n
g
th
e PCC
v
o
ltage ch
an
g
e
s
d
u
rin
g
th
e islan
d
i
ng
co
nd
itio
n.
A si
m
p
l
e
and easy
m
e
t
hod l
i
k
e o
v
er/
u
n
d
e
r
vol
t
a
ge
pr
ot
ect
i
on (
O
VP/
U
V
P
), ca
n be u
s
e
d
t
o
det
ect
an
islanding c
o
ndition.
Once
the scale of
vol
tage excee
d
s
a
d
e
term
in
ed
startin
g
po
in
t v
a
lu
e,
an
islan
d
i
ng
co
nd
itio
n
is d
e
tected
and
DG is
d
i
sconn
ected.
In t
h
i
s
pa
per
,
t
h
e sy
st
em
i
s
m
odel
l
e
d i
n
S
ect
i
on I
I
.
The
pr
o
pose
d
i
s
l
a
ndi
ng
det
ect
i
o
n m
e
t
hod i
s
di
scuss
e
d i
n
Se
ct
i
on I
II.
The
p
e
rf
orm
a
nce of
t
h
e pr
o
p
o
s
ed
m
e
t
hod i
s
eval
uat
e
d i
n
Sect
i
o
n I
V
. T
h
e l
a
st
sect
i
o
n
co
nsists of
co
nclu
sion
s.
2
.
SYSTEM
UN
D
E
R
STUDY
The sy
st
em
, whi
c
h has
been
st
udi
e
d
i
n
t
h
i
s
pape
r, i
s
sh
ow
n i
n
Fi
g
u
re 1
.
Thi
s
sy
st
em
consi
s
t
s
o
f
a
di
st
ri
b
u
t
i
o
n
net
w
o
r
k
m
odel
l
e
d
by
a t
h
ree-
p
h
a
s
e v
o
l
t
a
ge s
o
ur
ce be
hi
n
d
i
m
pedance
,
a l
o
ad
m
odel
l
e
d by
a
t
h
ree-
pha
se co
nst
a
nt
im
pedance
,
a
n
d a
DG
sy
st
em
. The
D
G
i
s
m
odel
l
e
d
by
a
co
nt
r
o
l
l
a
bl
e dc
v
o
l
t
a
ge s
o
urce
b
e
hi
n
d
a t
h
ree
-
p
h
ase
i
nve
rt
er
w
h
o
s
e
rat
i
n
g
i
s
1
0
0
k
W
.
The
ot
her
p
a
ram
e
t
e
rs have
bee
n
gi
ve
n i
n
[3]
,
[
4
]
,
an
d
[
5
]
.
Fi
gu
re
1.
M
o
d
e
l
l
e
d sy
st
em
Fig
u
r
e
2
sh
ow
s th
e con
t
ro
l sche
m
e
b
a
sed
on
d
q
syn
c
h
r
o
nous r
e
f
e
r
e
n
ce fr
ame. I
n
t
h
is sche
m
e
, th
e d
c
-
l
i
nk v
o
l
t
a
ge co
nt
r
o
l
l
e
r and r
e
act
i
v
e-p
o
w
er c
ont
rol
l
e
r det
e
r
m
i
n
e d and q c
o
m
pone
nt
s, res
p
ect
i
v
el
y
.
The
i
n
p
u
t
p
o
wer ex
tracted
fro
m
th
e DG u
n
it is fed
in
t
o
th
e d
c
lin
k. He
nce, the
voltage cont
ro
ller cou
n
t
eracts th
e vo
ltage
vari
at
i
o
n by
sp
eci
fy
i
ng an a
d
equat
e
val
u
e o
f
t
h
e d a
x
i
s
i
n
vert
er c
u
r
r
e
n
t
t
o
bal
a
nce t
h
e
po
we
r fl
o
w
o
f
t
h
e dc
l
i
nk [
6
]
.
The r
eact
i
v
e po
wer
cont
rol
l
e
r, s
h
o
w
n i
n
Fi
gu
re 2
,
speci
fi
es t
h
e
refe
rence
val
u
e for t
h
e
q co
m
ponent
of t
h
e converte
r curre
nt. T
h
e reactive powe
r
refe
rence
value
Q
ref
is set to
zero
i
n
ord
e
r to
m
o
d
e
l a u
n
ity p
o
wer
fact
or
DG
ope
rat
i
o
n
.
Al
so
, F
i
gu
re 2 sh
o
w
s
t
w
o pr
o
p
o
r
t
i
o
nal
-
i
n
t
e
gral
(P
I) co
nt
r
o
l
l
e
rs f
o
r t
h
e d
-
an
d q-a
x
i
s
cur
r
ent
c
ont
rol
s
. The
out
p
u
t
s
of c
ont
rol
l
e
rs
obt
ai
n t
h
e re
fe
rence
vol
t
a
ges
fo
r t
h
e P
W
M
s
i
gnal
ge
ne
rat
o
r
.
The
main features of the curre
nt cont
ro
l strategy are th
e li
mi
t
a
tio
n
o
f
th
e con
v
e
rter ou
tpu
t
cu
rren
t du
ri
n
g
a fau
l
t
co
nd
itio
n,
p
r
o
v
id
in
g ov
er curren
t pro
t
ection
,
an
d d
e
creas
ing th
e fau
lt curren
t
con
t
ribu
tion o
f
t
h
e
u
n
it [6
]. The
in
stan
tan
e
ou
s real an
d reactive po
wer co
u
l
d b
e
written
i
n
term
s o
f
th
e
dq
ax
is co
m
p
onen
t
s, as
fo
llo
ws [7
],
[8]
:
.
(1)
Q =
.
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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S
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8-8
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9
4
Islan
d
i
n
g
Detectio
n
o
f
In
verter Ba
sed DG
Un
it Usi
n
g PV
System (M.Divya
sree)
44
1
Whe
r
e,
V
dpcc
i
s
t
h
e
pha
se
pe
ak
val
u
e
of
t
h
e PC
C
v
o
l
t
a
ge
. i
dt
and i
qt
are
ort
h
o
g
o
n
a
l
co
m
ponent
s
of
i
nve
rt
er cu
rre
n
t
s. The d
q
co
m
ponent
s o
f
t
h
e v
o
l
t
a
ge an
d cu
rre
nt
are con
s
t
a
nt
val
u
e
s
i
n
t
h
e st
eady
-
st
at
e
condition. T
h
e
r
efore
,
the controller provi
de
s the inde
pe
ndent regulation
d of q a
n
d com
ponents [7],
[8]. T
h
e
i
n
st
ant
a
ne
o
u
s vol
t
a
ge
s of
t
h
e t
h
ree p
h
ases
c
o
ul
d be
e
x
pres
s
e
d by
t
h
e f
o
l
l
o
wi
n
g
e
quat
i
o
n [7]
,
[
8
]
:
(3)
Whe
r
e i
t(abc)
rep
r
esen
ts th
e
DG cu
rren
t three-p
h
a
se co
m
p
on
en
ts. R
f
a
nd L
f
are th
e
filter resistan
ce an
d
inductance
, re
spectively. V
t(
abc)
and
Vpcc(abc)
repre
s
ent the DG term
inal and PCC three phase voltages,
respectively.
Fi
gu
re
2.
B
l
oc
k
di
ag
ram
of t
h
e D
G
i
n
ve
rt
er
cont
rol
l
e
r.
B
y
usi
ng Pa
rk
’s t
r
ans
f
orm
a
t
i
on
[7]
,
(
3
) ca
n
be t
r
ans
f
o
r
m
e
d t
o
t
h
e r
o
t
a
t
i
ng sy
nch
r
o
n
o
u
s
refere
nc
e
f
r
a
m
e
,
as fo
llow
s
[
3
],
[7
] and
[
8
]:
(4)
Or,
0
0
(5
)
Whe
r
e,
=
+
(6)
=
–
(7)
The DG inte
rface control is
m
odified
by
using
the set
of e
quations
shown in Fi
gure 2. T
h
e
m
a
gni
t
ude a
n
d
angl
e
of t
h
e m
o
d
u
l
a
t
i
ng
si
g
n
a
l
are cal
cul
a
t
e
d
and t
h
en t
h
e s
w
i
t
c
hi
n
g
pat
t
e
r
n
o
f
t
h
e i
n
ve
rt
er has
b
een
d
e
term
in
ed
. PWM th
re
e-phase invert
ers should sha
p
e and cont
ro
l th
e th
ree-ph
ase o
u
t
p
u
t
vo
ltag
e
i
n
m
a
gni
t
ude
a
n
d
fr
eq
ue
ncy
wi
t
h
t
h
e esse
nt
i
a
l
l
y
const
a
nt
i
n
p
u
t
dc
vol
t
a
g
e
[
9
]
.
In
t
h
e
l
i
n
e
a
r
regi
on
(i
.e
.,
m
a
≤
1
.
0
)
, th
e fun
d
a
m
en
tal freq
u
en
cy co
m
p
on
en
t in
t
h
e
ou
tpu
t
vo
ltag
e
((V_
AN
)1
)
d
e
termin
es th
e amp
litu
d
e
-
m
odul
at
i
on rat
i
o
(m
a)
, by
t
h
e fol
l
o
wi
n
g
e
q
ua
t
i
on [9]
:
(V
AN
1
) =
m
a
(8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
4
,
D
ecem
b
er
2
014
:
43
9 – 450
44
2
m
a
=
(9
)
Whe
r
e V
contrrol
is th
e
p
eak amp
litu
d
e
of th
e co
n
t
ro
l si
g
n
a
l
an
d th
e
V
tri
is t
h
e am
p
litu
d
e
o
f
th
e triangu
lar sig
n
a
l.
Th
erefo
r
e, th
e
lin
e-to
-li
n
e rm
s vo
ltag
e
at t
h
e fu
nd
am
en
tal frequ
en
cy can be written
,
as
follo
ws
[9
]:
V
L-L(line-line,r
m
s)
=
√
√
(V
AN
) =
√
√
m
a
0
.612
m
a
(
m
a
1
.0
(
1
0
)
Now, th
e
fo
llowing
eq
u
a
tion
s
can
b
e
written
fo
r
V
dt
an
d V
qt
:
=0.612
m
a
cos
∅
(11)
=0.612
m
a
sin
∅
(12)
Whe
r
e
∅
i
s
t
h
e a
n
gl
e by
w
h
i
c
h t
h
e i
n
ve
rt
er
vol
t
a
ge
vector leads the
lin
e vo
ltag
e
v
ector.
In a
lossless i
n
verter, the i
n
st
antane
ous power at the
ac and d
c
term
in
als of th
e i
n
v
e
rter is equ
a
l. Th
is
p
o
wer b
a
lan
ce can
b
e
written
,
as
fo
llows:
=
)
(1
3)
At
t
h
e dc
l
i
nk
, we have:
=
(1
4)
By u
s
ing
(4) an
d (11
)
–
(
14
), th
e
fo
llowing
st
ate eq
u
a
ti
o
n
s
can
b
e
written
[7
]:
=
+
0
0
00
.
∅
.
sin
∅
.
cos
∅
.
sin
∅
0
(
1
5
)
3
.
ISLANDING DETE
CTION
METHOD
The acce
ptable
voltage
de
viation is in the
range
of
88% to 110% of the
nom
in
al voltage [1], [2].
Any
vol
t
a
g
e
d
e
vi
at
i
on i
n
t
h
i
s
ran
g
e s
h
oul
d
not
be
det
ect
ed an
d t
h
e co
rr
esp
o
n
d
i
n
g l
o
a
d
co
n
d
i
t
i
on
w
oul
d b
e
co
nsid
ered
with
in
the NDZ. It is assu
m
e
d
th
at DG
h
a
s
b
e
en
d
e
sign
ed
t
o
o
p
e
rate at a con
s
tan
t
d
c
vo
ltag
e
of
90
0
V.
I
n
t
h
i
s
sect
i
on, a
ne
w
anal
y
t
i
cal
form
ul
at
i
on i
s
de
ri
v
e
d
by
t
h
e l
i
n
ea
ri
zat
i
on
of
sy
st
em
st
at
e equat
i
o
n
s
.
The
n
,
a new V
dc
-V
pcc
ch
aracteristic o
f
DG will b
e
exp
l
ain
e
d
,
and
th
e p
e
rform
a
n
ce o
f
t
h
is m
e
th
o
d
will be
evaluate
d.
3.
1. L
i
ne
ari
z
ati
o
n
o
f
S
y
s
t
em
St
ate
E
q
u
a
ti
o
n
s
To m
easure t
h
e im
pact
of de
vi
at
i
on
of m
a
on
dc-l
i
n
k v
o
l
t
a
ge,
∅
has bee
n
kept
co
nst
a
nt
and
onl
y
m
a
has bee
n
co
nsi
d
ere
d
as a vari
abl
e
. As a res
u
l
t
,
(15
)
i
s
a no
nl
i
n
ear e
quat
i
o
n. H
o
weve
r, f
o
r a sm
al
l pert
u
r
bat
i
o
n
aroun
d th
e equ
ilib
riu
m
p
o
i
nt
m
a
, th
e
fo
llowing
lin
ear set
of eq
u
a
ti
o
n
s
can
b
e
ob
tain
ed
,
wh
ere su
b
s
crip
t
0
denotes steady
-
state values [7], as
sh
own
in
(16) at th
e b
o
tto
m
o
f
th
e
page. The inve
rter steady-state
m
odel
can
b
e
ob
tain
ed
fro
m
th
e d
yna
m
i
c
m
o
d
e
l b
y
settin
g
th
e d
e
riv
a
tiv
e term
s
e
q
u
a
l to
zero
.
After tran
sform
a
tio
n
fro
m
ab
c to
t
h
e dq
referen
c
e fra
m
e
, th
e vo
ltages and
t
h
e cu
rren
t
s
b
eco
m
e
dc qu
an
tities.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Islan
d
i
n
g
Detectio
n
o
f
In
verter Ba
sed DG
Un
it Usi
n
g PV
System (M.Divya
sree)
44
3
Hen
c
e, sub
s
titu
tin
g
:
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
.
cos
∅
.
sin
∅
.
cos
∅
.
sin
∅
0
∆
0
.
.
.
∅
0
.
.
.
∅
00
.
cos
∅
.
s
i
n
∅
.
V
dpcc
=
,V
dpcc
= 0,i
d
=I
d
,a
nd i
q
=I
q
, and
sim
p
lif
icatio
n
of th
e
stead
y-state mo
d
e
l
resu
lted
i
n
th
e
fo
llowing
equat
i
o
n:
0.612
a
cos
∅
0.
612
a
sin
∅
0
.
612
a
cos
∅
0
.612
a
sin
∅
0
=
l
l
0
0
(1
7)
Fi
gu
re
3.
St
ead
y
-
st
at
e vari
at
i
o
ns
of
V
dc
ve
rsu
s
m
a
(with L
f
=2.1m
H
,
∅
377
/
,
R
f
=0.001
45
Ω
,
∅
=20
0
and V
p
cc
=1
p.u
Fi
gu
re 4.
DC
v
o
l
t
a
ge vers
us
P
C
C
vol
t
a
ge
characte
r
istic (DG and
V
dc-ref
are set to 900
V)
By so
lv
ing
(1
7) for i
dt
, iq
t and V
dc
, we ha
ve:
I
=
∅
|
|
(18)
I
=
∅
|
|
(19)
=
.
∅
.
∅
(2
0)
C
onsi
d
eri
ng (
1
8) a
nd (
1
9)
, i
t
i
s
ob
vi
o
u
s t
h
at
I
dt
and I
qt
d
o
n
o
t
depe
n
d
o
n
t
h
e m
odul
at
i
on
i
nde
x (m
a).
For
t
h
e
gi
ve
n s
y
st
em
, t
h
e vari
at
i
ons
of
V
dc
v
e
rsus
m
a
can be det
e
rm
i
n
ed b
y
usi
n
g (
2
0). B
y
consi
d
eri
ng i
t
as a
constant value
,
(20) be
com
e
s
a hyperbolic equation. B
u
t
the part m
a
<0 is
not acce
ptab
le and
just the pa
rt 0<
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
4
,
D
ecem
b
er
2
014
:
43
9 – 450
44
4
m
a
<1 i
s
t
h
e dom
i
n
ant
.
B
y
scal
i
ng bet
w
een
0.8 a
n
d 1, i
t
can be see
n
t
h
at
t
h
e devi
at
i
o
n o
f
m
a
versu
s
V
dc
is
lin
ear an
d usu
a
lly th
e no
rm
al o
p
e
rating
p
o
i
n
t
of th
e inv
e
rt
er is in
t
h
is
range. Th
e
Vd
c-m
a
curv
e of t
h
is ran
g
e
has
bee
n
s
h
o
w
n i
n
Fi
g
u
r
e
3 C
onsi
d
eri
n
g
(
1
0)
, we
ha
ve:
.
.
(2
1)
In
stead
y-state co
nd
itio
n, (10
)
can
b
e
written
as
fo
llows:
.
.
(
2
2
)
B
y
com
b
i
n
i
ng (2
1)
an
d (
2
2
)
, we have:
.
.
(
2
3
)
C
onsi
d
eri
ng (
2
0) an
d Fi
g
u
r
e 3, i
t
i
s
obvi
o
u
s
t
h
at
t
h
e devi
at
i
on o
f
m
a
arou
nd t
h
e
ope
rat
i
n
g p
o
i
n
t
d
o
es
not
have
any
m
a
jor i
m
pact
on
d
r
i
f
t
i
n
g
o
f
t
h
e dc
-l
i
nk
v
o
l
t
a
ge. T
h
e
r
ef
ore
,
t
h
e m
odu
l
a
t
i
on i
n
dex c
a
n b
e
assum
e
d
t
o
be con
s
t
a
nt
(i
.e
.m
a
=m
ao
).
Th
en
, (2
3)
can
b
e
writ
ten
as fo
llows:
.
.
(
2
4
)
3.
2. V
dc
- V
pcc
Ch
arac
teri
sti
c
The V
dc
- V
pcc
(VL
-
L
)
cha
r
act
eri
s
t
i
c
of
DG a
nd
dc
refe
renc
e vol
t
a
ge has
b
een s
h
o
w
n i
n
Fi
gu
re
4.
I
n
th
is figu
re, th
ere are 2
lines
wh
ich
p
r
esen
tin
g th
e l
o
we
r a
n
d
u
p
p
er
dc
v
o
l
t
a
ge l
i
m
i
t
s
. Us
i
ng
(2
4
)
a
nd a
s
sum
i
ng
V
L-Lo
equal
t
o
1 p
.
u
,
t
h
e sl
op
e of t
h
ese l
i
n
e
s
(V
dco
)ca
n
be det
e
rm
i
n
ed
f
o
r
V
rm
dc
=900
V
and t
h
e d
c
v
o
l
t
a
ge
l
i
m
i
t
s
. The i
n
t
e
rsect
poi
nt
o
f
DG
an
d
dc
-l
i
n
k
refe
rence
v
o
l
tag
e
cu
rv
es is
called
th
e island
ing
op
erating
p
o
i
n
t
.
In t
h
i
s
fi
g
u
re
, poi
nt
s “A ” a
nd “ B
”
re
p
r
e
s
ent
t
h
e o
p
e
r
at
i
ng
poi
nt
of t
h
e l
o
wer a
n
d u
ppe
r dc
-l
i
n
k v
o
l
t
a
ge
li
mits, resp
ectiv
ely. Each
op
eratin
g
po
in
t b
e
tween
th
ese
two
lin
es is in
th
e NDZ. In
additio
n
,
in
an
y k
i
n
d
o
f
l
o
adi
n
g
co
n
d
i
t
i
on,
t
h
e
dc
-l
i
n
k
v
o
l
t
a
ge
w
oul
d
be
pl
aced
with
in
or with
ou
t
t
h
ese
bo
und
ar
ies. If
V
dc
is
accomm
odated within these li
m
i
ts, the voltage de
viation
will be in the
allowable val
u
es, and islandi
ng ca
n
o
ccur and
will no
t b
e
d
e
tected
(NDZ).
In this p
a
p
e
r,
th
e
DG referen
c
e d
c
vo
ltag
e
cu
rv
e h
a
s
b
e
en
m
o
dified
and expresse
d
by the
PCC
vol
t
age-depe
ndent
line.
Fi
gu
re 5.
DC
v
o
l
t
a
ge vers
us
t
h
e
PC
C
v
o
l
t
a
g
e
characte
r
istic for DG a
n
d m
odified V
dc-re
f
Fi
gu
re 6.
DC
v
o
l
t
a
ge vers
us
t
h
e
PC
C
v
o
l
t
a
g
e
characte
r
istic, effect
of ne
gative sl
ope
Thi
s
l
i
n
e sho
u
l
d
cro
ss t
h
e poi
nt
whi
c
h has t
h
e rat
e
d dc
vo
l
t
a
ge at
t
h
e rated PC
C
vol
t
a
g
e
. It
can be
exp
r
esse
d by
t
h
e fol
l
o
wi
n
g
e
quat
i
o
n:
.
.
(
2
5
)
Fig
u
re 5
presen
ts
th
e d
c
v
o
l
t
a
g
e
v
e
rsu
s
th
e PCC
vo
ltag
e
li
n
e
s
for t
h
ree (d
c
vo
ltag
e
) con
d
ition
s
. By
changing “
A
”
and “B” points
to “
A
” and “
B
,” the
NDZ i
s
sm
aller,
beca
use the
s
e
new
poi
nts are
outs
ide the
allo
wab
l
e
vo
ltag
e
limits (88
%
an
d 110
%
o
f
no
m
i
n
a
l v
o
ltag
e
), so
t
h
is co
nd
i
tio
n
can
b
e
easily d
e
tected
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Islan
d
i
n
g
Detectio
n
o
f
In
verter Ba
sed DG
Un
it Usi
n
g PV
System (M.Divya
sree)
44
5
As
an
ex
am
p
l
e,
th
e DG referen
ce d
c
v
o
ltag
e
can
b
e
rewritten
as:
450
.
450.
(
2
6
)
The l
o
ad c
o
n
d
i
t
i
on, w
h
i
c
h i
n
t
e
rsect
s t
h
e DG
vol
t
a
ge l
i
n
e at
poi
nt
O,
has an act
i
v
e po
wer
of 1
0
0
k
W
and t
h
e
vol
t
a
ge of
1 p.
u.
Eq
uat
i
on (
2
6)
i
n
t
e
rsect
s t
h
e l
o
wer an
d u
ppe
r l
i
m
i
t
s
at poi
nt
A a
n
d
poi
nt
B
resp
ectiv
ely. Th
ese po
in
ts correspo
n
d
to
voltag
e
lev
e
ls
th
at are b
e
yo
nd
th
e allo
wab
l
e v
o
ltag
e
lev
e
ls. Th
u
s
,
th
ese lo
ad
ing
co
nd
itio
ns can b
e
easily detected
b
y
u
s
i
n
g
th
e
ov
er/und
er vo
ltag
e
p
r
o
t
ectio
n
(OVP/UVP)
m
e
t
hods
.
As a
resul
t
,
a
re
d
u
ct
i
on i
n
t
h
e
ND
Z can
be
achi
e
ved
.
T
h
e
refe
r
e
nce
dc
v
o
l
t
a
g
e
can
be
ex
pre
ssed
b
y
a ne
gative sl
ope as:
450 .
1350.
(
2
7
)
Fig
u
re
6
presen
ts th
e
d
c
vo
ltag
e
v
e
rsu
s
PC
C v
o
ltag
e
lin
es for th
e sam
e
co
nd
itio
ns, sh
own
i
n
Figu
re
5
.
Th
e lo
wer an
d
u
p
p
e
r li
m
i
t
s
in
tersect th
e n
e
w
DG lin
e
by (27) at poi
nts “A’ ” and “B
’,” res
p
ectivel
y. The
v
o
ltag
e
lev
e
ls o
f
th
ese two
po
in
ts are in
th
e NDZ. Th
er
efore, th
ese lo
ad
ing
con
d
ition
s
will n
o
t
b
e
d
e
tected
by
using OVP/UVP m
e
thods.
There
f
ore, th
e
negative slope
in (27) will lead
to an increas
e in the NDZ and the
p
o
s
itiv
e sl
o
p
e
can
red
u
ce t
h
e
NDZ. Th
e v
a
lues o
f
p
a
ram
e
te
rs k1
and
k
2
h
a
v
e
b
e
en
cho
s
en so
th
at th
e DG V
dc
-
V
pcc
slope is
placed highe
r
than t
h
e sl
ope
of all possible
load
lines within
the NDZ. Consi
d
eri
ng (24),
the
fol
l
o
wi
n
g
e
q
ua
t
i
ons ha
ve bee
n
use
d
t
o
t
u
ne k1
an
d k
2
Fi
gu
re 7.
DC
v
o
l
t
a
ge vers
us
t
h
e
PC
C
v
o
l
t
a
g
e
cha
r
act
eristic,with
an
effect
o
f
th
e
Selectio
n
o
f
(3
1)
|
(
2
8
)
(
2
9
)
(
3
0
)
B
a
sed
on t
h
ese
eq
uat
i
ons
, i
t
can
be st
at
ed t
h
at
k1=
V
d
c0/
V
L-L
o
(
V
dco=
9
0
0
v
o
l
t
s
, V
L
-L
O=1
p
.
u
.
)
a
n
d
k2=
0 a
r
e a sui
t
able condition. But it
m
u
st be
m
e
ntione
d th
at k2 ca
nnot be equal to
zero. This is
because if
k
1
=
90
0 and
k2=0
,
t
h
en th
e
syste
m
will b
e
v
e
ry sen
s
itiv
e to
PCC vo
ltag
e
pertu
r
b
a
tion
s
,
And
it will lead
to
un
d
e
sirab
l
e syste
m
trip
p
i
n
g
. To
p
r
o
t
ect th
e system
fro
m
th
is situ
atio
n
b
a
sed
on
the sim
u
lation results a
n
d IEEE 1547 Sta
nda
rd and
othe
r power syste
m
s
t
andards
(the allowable
voltage
devi
at
i
o
n f
o
r
DGs
bel
o
w 5
0
0
k
VA i
s
1
0
% of t
h
e n
o
m
i
nal
vol
t
a
ge
), i
s
su
pp
ose
d
t
o
ha
ve
a goo
d ch
oi
ce
for
k2
,
whe
n
i
t
i
s
a
b
ou
t
10
%
of t
h
e
dc
l
i
nk
v
o
l
t
a
ge.
As a
res
u
l
t
,
(
2
5
)
has
been
cha
nge
d i
n
t
o
t
h
e
f
o
l
l
o
wi
ng
f
o
rm
:
810
.
90.
(
3
1
)
3.
3. Perf
orm
a
nce
E
v
al
u
a
ti
o
n
The pe
rf
orm
a
nce of t
h
e p
r
o
p
o
se
d i
s
l
a
ndi
n
g
det
ect
i
on m
e
tho
d
as wel
l
as i
t
s
NDZ depe
nds
on t
h
e
Vdc
-
Vpcc
DG
characte
r
istic. A PCC voltage
variation (
∆
V) will resu
lt in
a d
c
-link
vo
ltage v
a
riation
(
∆
V) dc
whi
c
h c
oul
d
be
ex
pres
sed
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
4
,
D
ecem
b
er
2
014
:
43
9 – 450
44
6
.
.
(
3
2
)
∆
∆
1
∆
(
3
3
)
∆
∆
∆
(
3
4
)
Tabl
e 1
s
h
ows
t
h
e
cal
cul
a
t
e
d
NDZ
s fo
r di
ff
e
r
ent
val
u
e
s
of
k1
an
d
k
2
.
The
sel
ect
i
on o
f
t
h
e
V
dc
- V
pcc
ch
aracteristic w
ill h
a
ve a
great i
m
p
act
o
n
ND
Z. If th
e boun
d
a
ry
b
e
tw
een lo
w
e
r and
u
pper limits o
f
ND
Z is a
larg
e
n
u
m
b
e
r,
it will lead
to
a wid
e
NDZ.
In
so
m
e
cases, NDZ h
a
s a larg
e g
a
p
(e.g
., case No
.
2
)
, while fo
r
o
t
h
e
r cases, it is relativ
ely
sm
a
ll (e.g
., case No. 3
)
. NDZ can
eith
er b
e
represen
ted
in
term
s o
f
p
o
wer
m
i
sm
atch or in term
s of the
load R,
L, a
n
d C.
A
n
acc
urate
presentation of t
h
e
ND
Z can
b
e
fo
und
in [5
].
Tabl
e
1:
N
d
z
Up
pe
r A
n
dl
o
w
erl
i
m
i
t
s
Fordi
f
f
e
rent
V
dc
- V
pcc
Case
Nu
m
b
e
r
Lower li
m
i
t
of
NDZ
Upper li
m
i
t
of
NDZ
1 450
450
825
1092.
9
2 -
450
1350
675
1478.
6
3 810
90
885
938.
5
The D
e
t
a
i
l
s
have bee
n
prese
n
t
e
d i
n
t
h
e
Ap
p
e
ndi
x. T
h
i
s
pa
per e
x
am
i
n
es the N
D
Z
of a
n
OV
P/
U
V
P
an
d OFP/UVP islan
d
i
n
g
sche
m
e
in
case of using
th
e imp
l
em
en
ted
V
dc
-
V
pcc
ch
aracteristic fo
r d
i
fferen
t
am
ount
s
o
f
k1
and
k
2
.
T
h
e re
sul
t
s
ha
ve bee
n
pl
ot
t
e
d
i
n
Fi
g
u
r
e 8.
Fi
gu
re
8.
N
D
Z
o
f
t
h
e
V
dc
-V
pc
c
c
h
aract
eri
s
t
i
c f
o
r a
di
ffe
ren
t
am
ount
o
f
k1
and
k
2
4
.
MATLAB
/
S
IMULINK RESULTS
Tabl
e
2.
Sy
st
em
, DG, a
n
d
l
o
a
d
param
e
t
e
rs
Grid
an
d
In
v
e
rter
Para
m
e
ters
DG Output power
100kW
Switching Fr
equency
8000Hz
I
nput DC Voltage
900V
Voltage (
L
ine to
Line)
480V
Fr
equency 60Hz
Gr
id Resistance
0.
02
Ω
Gr
id I
nductance
0.
3
m
H
Filter Inductance
2.1
m
H
DG Co
n
t
ro
ller P
a
r
a
m
e
te
rs
Q
Contr
o
l
0
.
1
,
0
.
0
1
Contr
o
l
0
.15,
9
.
7
8
PI
Contr
o
l
1
,
1250
Lo
ad
Para
m
e
te
rs
R
2.
304
Ω
L
0.
0034
5 H
C
2037 µF
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Islan
d
i
n
g
Detectio
n
o
f
In
verter Ba
sed DG
Un
it Usi
n
g PV
System (M.Divya
sree)
44
7
In
th
is section
,
th
e test syste
m
p
r
esen
ted
i
n
Fi
gu
re 1
whi
c
h
i
s
sim
u
l
a
t
e
d i
n
M
A
TLAB
/
Si
m
u
li
nk. T
h
e
sy
st
em
, DG, a
nd l
o
a
d
pa
ram
e
t
e
rs are l
i
s
t
e
d
i
n
Tabl
e
2.
T
h
e pa
ram
e
t
e
r Q
ref
has
bee
n
set
t
o
0 M
V
A
r
. T
h
e
Islanding
detection m
e
thod
ha
s bee
n
test
ed for l
o
a
d
wit
h
a
quality factor
(Q
f
)
of
1
.
7
7
. The pr
opo
sed islan
d
i
ng
d
e
tectio
n m
e
th
o
d
h
a
s
b
een also
tested fo
r v
a
rio
u
s
lo
ad
ing
con
d
ition
s
sp
ecifi
ed
in th
e
UL 17
41
Stand
a
rd
[3
].
4
.
1
.
U
L
17
41
Test
ing
Based
on t
h
e
UL
1741 Sta
n
dard, t
h
e active load
powe
r i
s
ad
just
e
d
t
o
s
e
t
t
h
e i
nve
rt
er
at
25%
,
50%
,
10
0%
,an
d
12
5
%
of t
h
e rat
e
d
out
put
po
we
r
of t
h
e i
n
vert
e
r
. T
h
e react
i
v
e
po
wer
has
be
en ad
j
u
st
ed
be
t
w
een
9
5
% an
d 105% of th
e balan
ced cond
ition
(un
ity po
w
e
r
fact
o
r
lo
ad
ing
)
in
1
%
steps [3
]. Th
e isl
a
n
d
i
n
g
detection sc
he
me is tested based on the
procedure
pr
ese
n
t
e
d in [3]. T
h
e
DG i
n
terface
has bee
n
equipped with
the V_(dc
-re
f)
characte
r
istic given i
n
(31)
an
d i
s
l
a
n
d
i
n
g
has
occ
u
r
r
ed
at
t
=
0
.
8
s.
The fi
rst
si
m
u
lat
i
on res
u
l
t
usi
ng t
h
e p
r
op
ose
d
m
e
t
hod i
s
s
h
ow
n i
n
Fi
g
u
re
9. T
h
i
s
fi
gu
re
sho
w
s t
h
e
v
o
ltag
e
at th
e
PCC d
u
ring
an
islan
d
i
n
g
con
d
ition
,
for the activ
e lo
ad
p
o
w
e
r adj
u
sted
at 5
0
%
, 100%, and
1
2
5
%
o
f
its rat
e
d
ou
t
p
u
t
p
o
wer. Th
e
reactive po
wer has b
e
en
ad
ju
sted at 1
0
0
%
o
f
th
e
balan
ced
con
d
itio
n. As
can be s
een i
n
Figure 9, the
PCC voltage e
x
ceeds th
e
OVP/UVP t
h
res
hol
ds in less t
h
an
100m
s (after the
occu
rre
nce o
f
i
s
l
a
ndi
ng
).
Fi
gi
re
9.
PC
C
vol
t
a
ge
u
s
i
n
g t
h
e
pr
o
pose
d
characte
r
istic for differe
n
t loa
d
s
Fig
u
re 10
. PCC
vo
ltag
e
with
characte
r
istic for
three case
s
Fig
u
re
10
sh
ows the
v
o
ltag
e
at th
e PCC
d
u
rin
g
an
islan
d
i
ng
co
nd
itio
n,
for th
e fo
llo
wi
n
g
cases
[4
]:
Case 1) T
h
e load ha
s bee
n
a
d
justed at 100%
of
rated
activ
e p
o
wer
with
10
1% reactiv
e
po
wer in
t
h
e
bal
a
nce
d
c
o
ndi
t
i
on.
Case 2) T
h
e load
has
bee
n
a
d
justed at 100%
of
th
e
rated
activ
e power with 10
0% reactive po
wer.
Case 3) T
h
e load
has
bee
n
a
d
justed at 100%
of
its rated activ
e
p
o
wer
with
9
9
% reactive
po
wer.
Table
3. L
o
a
d
Param
e
ters For UL
1741 TES
TS
P% Q%
R(
Ω
) L
(
H)
C(
µF
)
50
100
4.
603
0.
0034
5
2037
125
100
1.
841
0.
0034
5
2037
100
99
2.
304
0.
0034
88
2037
100
100
2.
304
0.
0034
5
2037
100
101
2.
304
0.
0034
19
2037
4.
2.
E
ffec
t
of
L
oad
Sw
i
t
chi
n
g
The p
r
op
ose
d
i
s
l
a
ndi
n
g
det
e
c
t
i
on m
e
t
hod h
a
s been t
e
st
ed
fo
r l
o
a
d
swi
t
c
hi
n
g
i
n
t
h
e
gri
d
-c
o
nnect
e
d
ope
rat
i
o
n m
ode. I
n
pa
ral
l
e
l
wi
t
h
t
h
e
ol
d l
o
ad,
whi
c
h
has
been
p
r
ese
n
t
e
d
i
n
Fi
g
u
re
1,
t
h
e ne
w l
o
ad
h
a
s bee
n
swi
t
c
he
d at
t
=
0.
5 s an
d
di
sco
nnect
e
d
at t= 1s. Three cases
h
a
v
e
b
e
en
simu
lated
in
th
is t
e
st. In
all cases, th
e
l
o
ad a
ppa
rent
po
we
r i
s
equal
t
o
10
0 k
V
A b
u
t
t
h
e p
o
we
r f
act
or i
s
0.
8 l
e
a
d
, 1
.
0 a
n
d 0.
8
l
a
g. The si
m
u
l
a
t
i
on
resu
lts th
at in
clu
d
e
th
e PCC vo
ltag
e
, and
th
e
DG activ
e
and
reactiv
e po
wer o
u
t
pu
ts fo
r three d
i
fferen
t
lo
ad
ing
co
nd
itio
ns
h
a
ve b
e
en
p
r
esen
t
e
d
in Figure
11
.
Th
e vo
ltag
e
v
a
riation
can
be seen wh
en
the lo
ad is switch
e
d
on
and off. For sim
u
la
ted cases,
the voltage
and frequ
en
cy
v
a
ri
atio
n
s
are
within
th
e stan
dard
v
a
lu
es. It is
obv
iou
s
that the
propos
ed m
e
thod
doe
s
no
t interfere
with the
power system
ope
ration during
norm
al conditions
.
0.
5
0.
6
0.
7
0.
8
0.
9
1.
0
1.
1
1.
2
1.
3
1.
4
1.
5
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
T
i
m
e
(s
ec)
P
C
C
V
o
l
t
ag
e (
p
.
u
)
P
l
oa
d
=
50 kW
P
l
oa
d =
1
00 kW
P
l
oa
d =
12
5
k
W
0
0.
5
1
1.
1
1.
2
1.
3
1.
4
1.
5
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
1.
1
1.
2
1.
3
1.
4
Ti
m
e
(
s
e
c
)
P
C
C
V
o
l
t
ag
e (
p
.
u
)
ca
se 2
ca
se
3
ca
se 1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
4
,
D
ecem
b
er
2
014
:
43
9 – 450
44
8
(a)
(b
)
(c)
Fi
gu
re 1
1
. Sy
st
em
resp
on
se d
u
ri
ng
l
o
a
d
s
w
i
t
c
hi
n
g
. (a
)
PCC
v
o
ltage.
(
b
)
I
n
verter
active
p
o
we
r.
(c
) I
n
ver
t
er
reactive powe
r
4.
3. Mul
t
i
p
l
e
-
D
G Oper
ati
o
n
M
o
de
The propose
d islanding detec
tion m
e
thod
has been
tested
in a system
with
m
u
ltiple DGs. F
o
r the
si
m
p
lificatio
n
an
d
d
e
m
o
n
s
tratio
n
o
f
th
e in
teractio
n
s
, tw
o
DG
u
n
its are used
in
th
is stu
dy. Fig
u
r
e
1
3
illu
strates
t
h
e o
p
erat
i
on
of t
w
o
D
G
s
gr
i
d
-c
on
nect
ed
i
nve
rt
ers
.
Ea
c
h
DG is t
h
e sam
e
as the si
ngle
DG system
ca
se and
t
h
e rat
i
n
g
of
e
ach
of t
h
em
i
s
equal
t
o
10
0
k
W
. T
h
ey
a
r
e c
o
nnected to t
h
e PCC in
paral
l
el to supply the load
with 200-kW
a
c
tive
powe
r. E
v
ery DG
interface has
bee
n
e
qui
ppe
d
with t
h
e
V
dc-Vpcc
characteristic prese
n
ted i
n
(3
1)
.
Isl
a
n
d
i
n
g
has
bee
n
si
m
u
l
a
t
e
d at
t
=
0.
8
s. T
h
e si
m
u
l
a
t
i
on
res
u
l
t
has
b
een
pres
ent
e
d i
n
Fi
gu
re
1
4
.
It
can
be
seen
t
h
at DG l
o
ses its stab
le
o
p
e
ration
m
o
de, and an island
ing
co
nd
ition
can
b
e
d
e
tected
b
y
using
OVP/UVP
m
e
t
hods
i
n
l
e
s
s
t
h
a
n
50m
s.
Fi
gu
re
1
3
.
Sch
e
m
a
t
i
c
di
agra
m
of t
h
e t
w
o-
D
G
sy
st
em
0.
2
0.
4
0.6
0.8
1
1.
2
1.
4
1.
6
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
Ti
m
e
(
s
e
c
)
P
C
C
V
o
l
t
a
g
e (p
.
u
)
L
o
a
d
=
1
00 kV
A
@
p
.
f
0.
8
l
e
a
d
L
o
a
d
=
100
k
V
A
@
p
.
f
1
L
o
a
d
=
100
kV
A
@
p
.
f
0.
8 l
a
g
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
Ti
m
e
(
s
e
c
)
Ac
t
i
v
e
P
o
we
r
(
p
.
u
)
L
o
a
d
=
100 kV
A
@
p
.
f
0
.
8 l
e
a
d
L
o
a
d
=
100
k
V
A
@
p
.
f 1
L
o
a
d
=
1
00 kV
A
@
p
.
f
0
.
8
l
a
g
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
-0
.
0
6
-0
.
0
5
-0
.
0
4
-0
.
0
3
-0
.
0
2
-0
.
0
1
0
0.
01
0.
02
0.
03
0.
04
Ti
m
e
(
s
e
c
)
R
e
a
c
t
i
v
e
P
o
w
e
r
(p
.
u
)
L
o
a
d
=
1
00 kV
A
@
p
.
f
1
p
.
f 0.
8
l
e
ad
pf
0
.
8
l
a
g
Evaluation Warning : The document was created with Spire.PDF for Python.