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
)
V
o
l.
10, N
o.
1, Mar
ch 20
19,
p
p.
530~
5
3
7
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
5
30-
53
7
530
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
Droop c
ontrol te
c
hnique for equ
al power sharing in islanded
microgrid
A
.
W
.
N
.
H
us
n
a
1
,
M
. A
.
R
o
sl
an
2
,
M
.
H
. Mat
3
1
Cent
re of
Excellen
t
f
o
r
Renew
able
E
nerg
y,
S
choo
l
of
E
lectri
cal
Syst
e
m
s E
n
g
i
neeri
n
g,
Universiti
Mal
a
y
s
ia
P
erlis, Malaysia
2
School
o
f Electrical
S
y
s
te
ms
E
n
g
ineering,
U
ni
ve
rsiti Malays
i
a
P
erlis,
Mal
a
ysia
3
Cent
re
f
or
D
ip
lo
ma
S
tudies
,
U
n
i
v
ersiti
M
a
l
ay
si
a
P
e
rlis, M
a
l
a
ysi
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Sep
1
7
,
2
018
Re
vise
d N
ov
2
9
,
201
8
A
c
c
e
pte
d
D
ec 14,
2
0
1
8
Th
is
p
aper
p
res
e
nt
s
a
dro
o
p
co
nt
rol
t
echn
i
qu
e
f
o
r
equ
a
l
po
wer
s
ha
ring
i
n
islan
d
ed
m
i
c
rogrid.
In
t
his
st
udy,
t
he
p
ro
po
sed
cont
roller
is
b
as
ed
o
n
th
e
f
r
equ
e
ncy
dro
op
m
e
th
od,
i
s
ap
p
lied
to
a
r
o
b
u
s
t
dro
o
p
co
ntro
ll
er
i
n
pa
ra
lle
l
con
n
ect
ed
i
n
v
ert
e
rs
.
The
p
r
evio
us
r
obu
st
d
roo
p
c
on
tro
l
ler
d
eals
w
it
h
vo
lt
ag
e
d
r
oo
p
m
e
th
od
.
A
m
o
d
i
fic
a
tio
n
h
a
s
b
e
e
n
f
orm
e
d
a
g
a
i
n
s
t
thi
s
c
on
tr
oller
by
add
i
n
g
a
f
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zzy
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c
con
t
ro
ll
er
w
ith
t
he
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u
en
cy
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roop
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eth
o
d
.
Th
e
only
sharing
error
which
is
c
on
centrat
ed
i
n
this
p
aper
i
s
th
e
error
in
s
ha
rin
g
t
he
rated
f
r
eq
uen
c
y
am
ong
t
h
e
i
nv
erters.
By
a
dapt
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u
zzy
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h
e
r
obu
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roo
p
,
it
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r
ies
to
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li
mi
n
a
te
t
he
f
requ
enc
y
e
rror,
h
en
ce
th
at
t
h
e
f
requ
ency
r
ef
erence
o
f
the
inver
t
ers
keeps
ma
inta
in
a
t
5
0
Hz. A
d
erivation of g
enerali
z
ed m
o
d
els of
a
si
ngle-p
h
ase
paral
l
el-co
n
n
e
c
t
ed
i
n
v
erter
sy
st
em
i
s
s
h
o
w
n
.
T
h
e
s
im
ulati
on
results
s
how
tha
t
t
he
p
roposed
co
nt
rol
l
er
w
it
h
F
L
C
is
a
bl
e
t
o
i
m
p
rove
t
h
e
st
abili
t
y
o
f
f
req
u
en
c
y
r
ef
erenc
e
a
n
d
t
he
p
erf
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rm
ance
of
p
ow
e
r
s
ha
r
i
n
g
bet
w
een
t
h
e
in
v
erters
un
d
er t
he i
n
d
uct
i
ve li
n
e im
p
e
dan
c
e.
K
eyw
ord
s
:
Fu
zz
y
co
nt
rol
Rob
u
s
t
dro
op
Islan
d
ed
m
ic
ro
gri
d
Pa
rallel-c
o
nne
cted
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n
v
e
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ters
P
r
op
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na
l
l
o
a
d
shar
i
ng
F
r
equenc
y
re
gu
la
tio
n
Re
duc
t
i
on
b
l
oc
k
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:
A
.
W.N. H
usna,
Ce
ntre
o
f Exc
e
lle
n
t
for
R
e
n
e
w
a
b
l
e
Ene
rg
y,
S
c
hoo
l
o
f
Ele
c
t
rica
l
S
y
stem
s En
gi
neer
ing,
U
ni
versi
t
i Ma
lay
s
ia
P
er
l
i
s,
P
a
uh P
u
tra
Cam
pus,
0260
0
A
r
au,
P
e
rlis,
M
a
lay
s
ia
.
Em
ail:
nur
ulh
u
s
na.
a
w
b
@
g
m
a
il.c
o
m
W
1.
I
N
TR
OD
U
C
TI
O
N
Ad
v
a
n
c
e
d
d
e
v
e
l
op
ment
o
f
di
st
ri
but
e
d
g
e
n
era
t
io
n
(DG
)
u
nit
s
i
n
ma
ny
c
o
unt
ri
e
s
nowad
a
y
s
h
a
s
attrac
ted
m
o
st
r
esea
rche
rs
i
n
all
over
the
w
o
rl
d
due
t
o
the
ava
i
l
a
bil
i
t
y
o
f
di
ff
ere
n
t
en
erg
y
r
esou
rc
es
s
u
c
h
a
s
p
hot
ovo
lt
ai
c
pan
e
ls,
f
u
e
l
c
ells,
an
d
w
i
nd
t
urb
i
n
e
s
[1
].
T
h
r
o
ugh
t
he
c
onc
ept
o
f
a
m
i
c
ro
gri
d
w
h
i
c
h
i
s
t
h
e
be
st
op
tio
n
to
r
ed
u
c
e
a
depe
n
d
e
n
cy
o
n
the
loca
l
uti
l
i
t
y,
c
ons
is
ts
o
f
a
t
leas
t
o
n
e
D
G
,
e
ne
rgy
stora
g
e
de
vic
e
s
a
nd
assoc
i
ate
d
l
oa
ds.
M
i
cro
g
ri
d
w
i
t
h
t
w
o
m
ode
oper
a
tio
ns
e
ither
i
n
gri
d
c
on
nec
t
e
d
o
r
isla
n
d
ed
;
ha
s
be
e
n
con
s
i
d
ere
d
a
s
one
o
f
t
h
e
no
m
i
ness
t
o
s
up
por
t
smo
o
t
h
in
sta
lla
t
i
o
n
o
f
D
G
s
a
s
the
i
n
s
t
a
l
l
a
ti
on
o
f
ma
ny
D
G
s
itse
l
f
c
o
u
l
d
be
h
arm
f
u
l
t
o
th
e
pow
er
q
u
a
lit
y
o
f
u
ti
li
ty
p
o
w
er
s
ystem
s
[
2]
–[4].
A
de
t
a
ils
c
orre
l
a
tio
n
be
t
w
e
e
n
mic
r
ogri
d
a
n
d
D
G
alrea
dy
di
sc
o
v
ere
d
b
y
P
i
ng
e
t
a
l
[5].
B
a
s
i
c
a
l
l
y,
m
i
c
rogri
d
c
o
n
tro
l
i
n
an
i
sla
n
de
d
mode
i
s
mor
e
c
omple
x
t
ha
n
gri
d
c
o
n
n
ec
te
d
m
o
de.
The
vo
l
t
a
g
e
an
d
fr
e
que
nc
y
of
t
he
m
icr
ogr
id
a
re
s
up
por
t
e
d
b
y
t
he
ma
in
g
ri
d
if
i
n
the
gri
d
c
o
n
n
ec
t
e
d
mo
de
.
In
c
on
trast,
t
h
e
v
o
l
t
a
ge
a
nd
fre
que
nc
y
c
o
n
t
r
o
l
a
n
d
eve
n
pow
e
r
ma
nage
me
nt
p
roce
ss
w
ill
be
g
e
n
era
t
e
d
b
y
D
G
uni
ts
i
n
is
l
a
n
d
e
d
m
o
de.
The
oc
curre
nc
e
of
pow
er
m
i
s
m
a
tch
betwee
n
t
h
e
DG
a
nd
t
h
e
loa
d
w
il
l
lead
t
o
the
u
nba
la
nced
a
ll
o
w
ed
v
a
l
ue
o
f
t
h
e
loa
d
v
olta
ge
a
nd
fre
que
n
c
y
dev
i
a
t
i
o
n
as
w
ell
as
uns
ta
bl
e
beha
v
i
o
u
rs
e
spe
c
ial
l
y
t
he
e
x
i
s
t
en
ce
o
f
c
i
rc
u
l
a
t
i
n
g
cur
r
en
t.
T
h
u
s,
i
t
i
s
n
ec
e
ssary
t
o
h
a
v
e
a
goo
d
c
o
nt
roll
er
t
o
su
ppo
rt
v
ol
t
a
g
e
a
n
d
f
r
equ
e
n
c
y
st
ab
i
lit
y
as
w
e
l
l
a
s
s
ui
ta
bl
e
p
o
w
er
s
ha
rin
g
a
mong
D
G
units
i
n is
l
a
nde
d
mode
o
p
e
r
a
tion
[6].
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
D
r
oo
p c
o
n
t
r
o
l te
ch
n
i
que
f
o
r e
qua
l
power
sh
ar
in
g i
n
isl
a
nd
ed m
i
c
r
o
g
r
i
d (A
. W. N. H
u
sna)
53
1
The
e
s
se
n
tia
l
o
b
jec
t
iv
e
of
a
n
i
s
la
n
d
e
d
m
o
d
e
i
s
t
o
kee
p
u
p
pr
eci
se
p
ow
e
r
s
h
a
rin
g
a
mo
ng
v
ario
us
D
G
.
Whe
n
e
v
er
t
he
opera
t
i
o
n
o
f
mic
r
ogri
d
s
h
i
f
t
ed
t
o
isl
a
n
d
m
ode
,
e
l
e
ctric
p
o
te
nt
ial,
E
a
nd
fre
que
nc
y,
a
r
e
con
s
i
d
ere
d
t
o
be
m
ai
nt
a
i
ne
d
w
ith
s
e
v
era
l
i
n
v
e
r
ters
w
or
k
i
n
g
i
n
p
ar
al
l
e
l
a
nd
shar
in
g
the
loa
d
.
The
s
e
in
ve
rters
ac
t
in
r
eg
ula
t
ing
t
h
e
v
o
lta
ge
;
am
pli
t
u
d
e
a
nd
freq
ue
ncy,
i
ns
tea
d
o
f
di
ffe
rent
m
ode
o
f
opera
ti
o
n
l
ike
ot
her
conver
t
e
r
[7];
b
es
i
d
es
p
roviding
t
he
r
e
q
u
i
re
d
c
u
rre
nt
n
ee
de
d.
H
ow
eve
r
,
the
iss
u
e
of
p
o
w
er
qual
i
t
y
[
8]
t
hat
con
t
ri
b
u
te
d
b
y
t
he
e
x
i
s
t
enc
e
o
f
tra
n
sie
n
t
cir
c
ula
tin
g
curr
ent
i
n
l
i
n
e
imp
e
dance
[
9
]
w
ill
lea
d
t
o
the
s
y
ste
m
in
sta
b
il
i
t
y,
t
h
u
s
c
an
h
arm
f
ul
t
he
i
n
v
erter
s
[
1
0
]
d
u
e
to
m
ism
a
tc
h
of
t
he
o
u
t
p
u
t
v
o
l
t
a
ge.
In
a
n
is
l
a
nde
d
mic
r
ogri
d
,
loa
d
s
m
u
st
b
e
pro
p
e
r
l
y
s
ha
red
b
y
m
ul
t
i
p
l
e
D
G
un
its.
G
e
nera
l
l
y,
t
he
c
o
n
t
rol
te
chn
i
que
s
for
para
lle
l
opera
tio
n
o
f
i
nve
r
t
ers
i
n
i
s
l
ande
d
m
i
cr
ogr
i
d
ope
rat
i
o
n
c
a
n
b
e
s
p
l
it
i
n
t
o
tw
o
c
a
t
e
g
o
r
ies;
d
ro
op
c
o
nt
r
o
l
tech
n
i
q
u
es
[1
1]
,
[12] a
nd ac
tiv
e
load s
ha
rin
g
t
echn
i
que
s
[1
3],
[
14].
D
r
oop
c
o
n
t
r
o
l
is
t
he
c
om
mo
n
c
o
n
t
ro
l
t
h
a
t
w
i
d
e
l
y
u
s
ed
i
n
mic
r
ogr
id
d
u
e
t
o
n
o
d
epe
nde
nme
n
t
o
n
com
m
unic
a
t
io
n
a
m
o
n
g
pa
ra
l
l
el-c
onne
c
t
ed
i
nver
t
e
r
s
t
h
us
m
a
k
i
n
g
i
t
h
ighl
y
mo
dul
a
r
a
nd
r
el
i
a
b
l
e
[1
5
]
–
[
17
].
I
t
is
a
pp
l
i
cab
le
w
hen
tw
o
or
m
or
e
in
ve
rters
a
r
e
app
lie
d.
G
ene
r
all
y
,
i
t
d
e
t
e
c
t
s
t
h
e
o
u
t
p
u
t
p
o
w
e
r
a
s
a
f
e
e
d
b
a
c
k
para
me
ter
w
h
il
e
t
h
e
de
via
t
io
n
of
D
C
v
o
lta
g
e
i
s
co
n
t
r
o
l
l
e
d
i
n
pr
o
por
tio
n
to
t
he
o
u
t
p
u
t
p
ow
e
r
.
Typ
i
c
a
l
ly,
the
vo
lta
ge
d
r
o
o
p
c
on
tro
l
r
esu
lts
i
n
p
oor
r
eac
tive
pow
e
r
s
h
a
r
i
n
g
w
h
il
st
t
h
e
f
re
qu
en
c
y
d
roo
p
c
o
nt
rol
a
l
wa
ys
ac
hi
e
v
es
a
c
c
u
ra
t
e
r
ea
l
pow
e
r
s
hari
ng.
I
t
is
d
ue
t
o
the
di
ffe
r
e
n
t
offse
t
s
of
l
oca
l
l
oa
ds
a
s
w
e
ll
a
s
the
mis
m
atch
in f
eeder
impe
d
ance
s.
Th
is
p
a
p
er
s
e
e
ks
t
o
ex
pan
d
t
he
m
e
t
h
o
d
of
r
ob
us
t
dro
o
p
p
r
e
sen
t
ed
i
n
[
18]
by
ada
p
t
e
d
w
ith
f
re
que
nc
y
con
t
ro
l i
n
stea
d
of t
he
v
olta
ge c
on
t
r
o
l
u
s
i
n
g
f
uzz
y
l
o
g
i
c
c
on
t
r
o
l (FLC).
It w
ill re
tai
n
t
he fr
e
que
nc
y refere
nce
of
50
H
z
i
n
pa
ral
l
e
l-c
o
nnec
t
e
d
i
nver
t
e
r
s
us
in
g
i
n
d
u
c
t
i
v
e
l
i
n
e
i
m
pe
dance
.
T
h
e
c
on
tro
l
a
p
p
ro
a
c
h
prese
n
t
e
d
by
t
h
e
prev
io
us
a
ut
ho
r
a
pplie
d
Q
−
a
nd
P
−
E
d
roop
t
o
t
h
e
r
e
s
i
s
t
i
v
e
l
i
n
e
i
mp
ed
a
n
c
e
wi
th
s
wit
c
hin
g
acti
o
n
o
f
p
u
l
s
e
-
w
i
d
t
h
m
o
d
u
la
tio
n
(P
WM
)
t
o
i
m
p
rove
t
h
e
s
trate
gy
tha
t
w
or
ks
f
or
g
r
i
d-
con
n
ec
te
d
a
ppl
i
c
a
t
i
o
ns
v
ia
a
d
d
i
n
g
a
u
n
i
t
t
o
r
egul
a
t
e
t
h
e
lo
ad
vol
t
a
g
e
.
In
t
h
i
s
wo
rk
,
an
F
LC
i
s
a
d
j
u
st
ed
t
o
t
h
e
ro
bu
st
c
o
n
t
r
ol
b
y
put
ti
ng
t
h
r
oug
h
th
e
fre
que
nc
y
dro
o
p
prec
i
s
e
l
y
i
n
te
gra
t
ed
i
n
Q
−
.
P
r
ac
ti
c
a
ll
y,
t
he
ope
ra
ti
o
n
o
f
the
co
n
t
ro
ll
e
r
i
s
ro
b
u
s
t
a
ga
in
s
t
loa
d
p
er
tur
b
a
t
ion
an
d
e
v
e
n
a
n
em
erge
nc
y
c
i
r
c
um
sta
n
c
e
s
u
c
h
as
d
i
sc
on
ne
c
tio
n
of
D
G
u
n
i
t
a
nd
t
h
e
pro
pos
ed
con
t
ro
l
l
er
i
s
a
c
tua
l
l
y
b
ei
n
g
de
si
gne
d
for
freque
ncy
c
o
n
t
r
o
l
ind
e
e
d
.
The
pa
ral
l
el
-c
on
necte
d
i
n
v
e
r
ters
inc
o
rp
ora
t
e
w
i
th
a
p
r
o
p
o
rt
io
na
l
-
reso
na
nt
c
ontr
o
l
l
er
(
P
R
)
and
s
i
n
u
s
o
ida
l
pul
se-
w
i
d
t
h
m
odu
la
tio
n
(SP
W
M)
in
ste
a
d
o
f
pr
opor
t
i
o
n
al-i
n
t
e
g
ra
l
(PI
)
a
nd
P
W
M
i
n
t
he
i
s
l
ande
d
m
icro
grid.
V
a
r
i
o
u
s
si
mula
ti
on
s
ha
v
e
b
ee
n
take
n
o
u
t
to
v
e
r
ify an
d
ana
l
y
s
is
t
he c
apab
i
l
i
t
y
of t
he
p
ro
po
s
e
d
c
on
tro
lle
r a
g
ai
nst
the
robu
st dr
oop
co
n
t
ro
ller.
2.
S
Y
S
T
EM
C
O
N
F
I
GU
R
A
TI
O
N
O
F
P
A
RA
LL
E
L
-
C
ON
N
E
C
T
ED
I
N
V
E
R
T
E
R
I
n
t
h
i
s
sec
t
io
n
w
ill
e
x
pl
ai
n
i
n
d
eta
i
ls
o
f
c
o
ns
truct
i
on
of
s
i
n
g
l
e
-ph
a
se
f
ull
-
b
r
id
g
e
i
nv
e
r
ter
a
n
d
th
e
para
l
l
e
l
-c
on
ne
c
t
e
d
i
n
v
erte
rs use
d
i
n
t
he sim
ul
a
tio
n.
2.1.
Mo
d
e
l o
f
s
i
n
g
l
e-pha
se
i
nv
erter
The
s
i
ng
le-p
ha
se
i
nver
t
e
r
i
s
a
n
e
lec
t
r
o
n
i
c
c
i
r
c
ui
t
t
h
at
e
na
b
l
es
a
v
olta
ge
t
o
be
a
pp
l
i
ed
acr
o
ss
a
l
o
ad
i
n
eit
h
er
d
ire
c
t
i
o
n
.
It
c
an
b
e
si
m
p
l
i
fied
j
u
s
t
i
f
i
e
d
w
ith
a
s
wi
tc
hi
n
g
s
c
h
em
e
of
f
u
l
l-
br
idge
c
on
verte
r
.
Typ
i
ca
l
l
y,
i
t
con
s
is
t
s
o
f
a
D
C
p
o
w
er
s
ourc
e
,
a
nd
a
brid
ge
-
t
y
p
e
i
nve
r
t
e
r
w
it
h
LC
L
f
ilte
r
as
s
how
n
in
F
ig
ure
1.
T
he
i
n
v
er
ter
is
a
d
e
v
ice
w
h
i
c
h
c
o
nve
rts
a
D
C
i
np
u
t
s
up
p
l
y
v
o
lta
g
e
i
nto
symm
e
tric
al
A
C
v
o
l
t
a
g
e
b
a
se
d
on
the
m
o
du
la
tio
n
signa
l
fr
om the
S
P
W
M
m
odu
l
a
ti
o
n
. The ind
u
c
t
a
nce
,
r
esis
t
a
n
ce,
a
n
d
c
a
pac
i
t
a
nc
e are
r
e
pre
s
e
n
te
d
b
y
L
f
,
R
f
, and
C
f
.
The
l
i
n
e
i
m
pe
dance
rep
r
esente
d
R
line
a
nd
L
li
n
e
b
e
t
w
e
en
t
he
i
n
v
er
te
r
and
t
h
e
l
o
ad
i
s
the
e
q
ui
vale
nt
impe
da
nce
d
u
e
t
o
c
on
nec
tin
g
l
i
nes
or c
abl
e
s.
F
i
gure
1.
B
l
o
c
k
d
i
a
gram
of an
i
nve
rter
2.2.
Pa
ra
ll
el
-c
o
n
nec
t
ed
i
nv
e
r
te
r
Thr
ee
para
lle
l
-
con
n
ec
t
e
d
i
n
v
e
rter
s
are
used
t
o
fil
l
i
n
t
h
e
m
i
cr
ogrid
c
on
fig
u
rat
i
o
n
a
s
dep
i
c
t
ed
i
n
F
i
gure
2.
T
h
e
m
ode
l
o
f
p
a
r
al
lel-c
onne
c
t
ed
i
nver
t
er
s
is
a
n
ec
ess
ary
in
o
r
d
er
t
o
a
p
pl
y
d
r
oop
m
e
t
h
o
d
i
n
th
e
syste
m
.
Pr
evio
us
l
y
,
a
co
nv
en
ti
ona
l
PI
c
o
n
tr
ol
ler
is
u
se
d
w
i
t
h
t
he
v
olta
ge
f
e
e
d
b
ac
k
lo
op
[
1
3
]
t
o
r
e
g
u
l
a
t
e
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
53
0 –
53
7
53
2
ou
p
u
t
vo
lta
ge
.
The
r
efor
e,
i
t
is
s
e
n
s
i
b
l
e
t
o
u
se
d
P
R
c
on
tr
olle
r
in
st
ead
o
f
PI
c
o
n
t
r
ol
l
e
r
d
u
e
to
i
t
s
s
up
erio
r
perform
ance
i
n
te
rms
of
l
e
s
s
stea
dy-s
t
a
t
e
er
ror,
good
dy
na
mic
r
espo
nse,
a
s
well
as
i
t
s
c
apab
i
lit
y
in
r
e
duc
in
g
st
e
a
dy-s
t
ate
de
via
t
io
n
of
f
re
q
u
e
n
c
y
a
nd
am
pl
itu
de
[
1
9
].
I
n
orde
r
t
o
e
ns
ure
in-
phase
s
im
il
a
r
i
t
y
of
t
he
o
u
t
pu
t
vo
lta
ge
o
f
eac
h
in
ver
t
e
r
,
t
h
e
sam
e
v
o
lta
ge
r
efere
n
ce
is
u
se
d,
0
V
.
P
R
c
o
n
t
r
o
ller
ga
in
t
he
f
e
e
dbac
k
v
a
l
ue
s
o
f
ou
tpu
t
v
ol
ta
ge
a
n
d
c
urrent
from
t
h
e
in
ver
t
e
r
,
t
hus,
gene
ra
t
e
a
pr
ope
r
c
o
n
t
r
o
lle
d
si
gna
l
be
fore
t
ra
nsm
itte
d
to
S
P
WM.
Then,
S
P
W
M
used
t
o
pu
t
thr
o
u
g
h
t
he
s
w
i
tc
hi
n
g
p
roc
e
ss
a
n
d
pa
ss
a
p
rac
tic
al
c
o
n
d
it
io
n
of
t
h
e
mic
r
ogri
d
.
Th
e
a
c
t
i
ve
a
nd
rea
c
ti
ve
p
ow
e
r
o
f
ea
c
h
i
nver
t
e
r
i
s
o
b
ta
i
n
ed
b
ase
d
o
n
t
h
e
vo
l
t
a
g
e
an
d
c
u
rrent
me
asure
m
e
n
t
aft
e
r
filter
i
n
g
,
late
r
w
i
ll
be
f
e
d
t
o
t
h
e
pro
pos
ed
c
o
n
t
r
o
ll
er
b
loc
k
t
o
prod
uce
new
va
lue
of
reference volt
a
g
e,
V
re
f
and
an
gu
l
a
r
freque
nc
y,
i
which
will
be led
t
o
propor
tiona
l power
s
h
aring.
Lo
ad
PR
SP
W
M
+
-
V
o
i
re
f
+
-
+
+
V
o
D
r
oo
p
C
ont
r
o
l
V
o
l
t
ag
e
C
o
nt
r
o
l
l
er
In
v
e
r
t
e
r
Io
IL
PR
SPW
M
+
-
V
o
i
re
f
+
-
+
+
V
o
D
r
oo
p
C
ont
r
o
l
V
o
l
t
ag
e
C
ont
r
o
l
l
er
In
v
e
r
t
e
r
Io
IL
PR
SPW
M
+
-
V
o
i
re
f
+
-
+
+
V
o
D
r
oo
p
C
o
n
t
r
o
l
V
o
l
t
ag
e
C
ont
r
o
l
l
er
In
v
e
r
t
e
r
Io
IL
F
i
gure
2.
P
arallel-c
onne
c
t
ed
i
nve
r
t
ers
i
n
m
ic
rogri
d
c
onf
i
g
ur
ati
on
3.
CONT
ROL S
C
H
E
ME
3.1.
R
ob
u
s
t
d
r
oop
c
on
trol
A
s
p
re
sente
d
i
n
[1
8],
the
q
u
a
n
ti
tat
i
ve
a
na
l
y
s
i
s
of
t
he
e
rr
or
i
n
p
ow
e
r
s
harin
g
h
as
b
ee
n
c
a
rr
ied
o
u
t
by
the
au
t
hor.
F
r
om
t
he
p
a
p
er,
t
h
e
sha
r
i
ng
e
rror
w
h
ic
h
is
f
rom
the
e
r
r
o
r
i
n
m
e
a
s
u
r
i
n
g
t
h
e
l
o
a
d
v
o
l
t
a
g
e
i
s
c
a
r
r
i
e
d
o
u
t
t
o
a
d
a
pt
t
o
th
e
robu
st
d
ro
op
m
e
t
hod
.
In
p
ra
ct
i
c
e,
w
h
e
n
t
h
er
e
are
e
rrors
i
n
t
h
e
v
o
l
t
age
m
e
a
s
u
r
e
d
,
a
fu
n
d
am
enta
l
tra
d
eo
ff
b
e
t
ween
t
he
v
olta
ge
d
rop
an
d
t
h
e
s
h
ar
i
n
g
a
cc
urac
y
appea
r
s
t
hus
w
il
l
lea
d
t
o
th
e
er
rors
in
p
r
o
p
o
r
t
i
ona
l
l
o
a
d
s
ha
ri
ng.
U
nsi
m
i
l
ar
w
i
t
h
t
h
e
c
on
ve
nti
ona
l
d
roop
c
on
t
r
o
l
,
t
h
e
au
th
o
r
p
ropo
se
d
a
ro
bu
s
t
dro
op
c
o
n
t
ro
l
l
e
r
by
i
m
p
l
em
ent
i
n
g
Q
−ω
a
nd
P
−
E
d
r
oop
a
n
a
l
ysis
a
nd
R
M
S
vo
lta
ge
s
e
t
-
p
o
i
nts
for
t
h
e
in
verter
s
t
h
ro
u
gh
vo
lta
ge
d
ro
op.
I
n
or
der
t
o
m
a
k
e
sure
t
hat
the
v
o
l
t
a
g
e
r
em
a
i
ns
w
it
hin
a
c
e
rta
i
n
re
qu
ired
range
,
the
loa
d
v
o
lta
ge
d
ro
p
E
*
−
V
o
n
ee
d
s
t
o
be
f
ed
b
ac
k
i
n
a
cer
t
a
in
w
a
y
,
acc
ordi
ng
to
t
he
b
a
s
i
c
pr
inc
i
ple
s
o
f
control
theory.
It
c
an
b
e
added
to
∆
E
i
v
ia
a
n
a
m
p
l
i
f
ier
,
K
e
a
nd
r
esu
l
t
e
d
t
h
e
ro
bus
t
c
o
nt
rol
l
er
a
s
i
n
d
i
ca
ted
in
F
i
gure
3 (a)
.
T
his co
n
t
rol sch
e
me
i
s
a
be
nch
m
a
r
kin
g
t
o the
pro
p
ose
d
c
on
tr
ol
l
e
r in th
i
s pa
per
.
H
ow
ever
,
i
n
t
his
pape
r
w
ill
be
f
oc
us
in
g
o
n
t
he
f
r
e
q
u
e
n
cy
r
egu
l
a
t
i
o
n;
u
si
n
g
t
h
e
f
r
e
q
u
enc
y
d
r
o
o
p
.
Ther
efor
e,
t
he
f
re
q
u
e
n
cy
dro
op
w
i
l
l
b
e
re
pl
a
c
i
ng
the
v
o
l
t
a
g
e
dr
oo
p
m
e
tho
d
by
m
o
d
i
fyi
n
g
t
he
e
q
u
at
ion
o
f
r
ob
u
s
t
droo
p
c
o
n
t
r
o
l
l
e
r
(
1)
.
H
o
w
e
ve
r,
t
he
pos
sib
i
l
i
t
y
o
f
m
easur
ed
f
re
q
u
enc
y
t
o
r
e
m
a
in
w
ith
i
n
a
c
e
r
tai
n
r
eq
u
i
red
ra
nge
i
n
the
p
a
ralle
l-
con
n
ec
ted
in
ve
r
t
e
r
s usual
l
y a
r
e
quite
u
nma
n
a
g
ea
b
l
e
a
n
d w
i
l
l
c
on
d
u
c
t
in
c
o
n
t
ri
but
in
g of er
r
or
v
a
l
ue.
si
n(
)
ref
VE
t
(
1
)
I
n
e
st
a
b
lis
h
i
n
g
t
he
p
ar
al
le
l-con
n
e
c
t
ed
i
nve
r
t
ers
ena
b
l
e
t
o
shar
e
t
h
e
lo
ad
,
t
h
e
rep
r
ese
n
t
a
t
i
o
n
of
t
h
e
con
v
e
n
t
i
ona
l d
r
oo
p co
n
t
rol
l
er
i
n (
2
) and (
3
) are
use
d
.
T
h
e
a
n
g
u
l
a
r
frequency,
ω
i
is
w
ide
l
y
u
t
il
i
z
e
d
t
o ge
ner
a
te
the
freq
u
enc
y
o
f
t
h
e
fr
eq
uen
c
y
re
fer
e
nce
for
the
i
nver
t
e
r
s,
w
he
re
ω
*
i
s
the
ra
t
e
d
fr
e
que
nc
y
an
d
m
i
is
a
dro
op c
o
e
f
f
i
c
i
e
n
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
D
r
oo
p c
o
n
t
r
o
l te
ch
n
i
que
f
o
r e
qua
l
power
sh
ar
in
g i
n
isl
a
nd
ed m
i
c
r
o
g
r
i
d (A
. W. N. H
u
sna)
53
3
*
ii
i
E
En
P
(
2
)
*
ii
i
mQ
(
3
)
F
r
om
(
3),
the
repre
s
en
tat
i
o
n
o
f
t
he
fr
e
q
u
e
n
c
y
droo
p
c
on
t
r
o
l
c
a
n
be
writt
e
n
as
*
ii
i
i
mQ
(
4
)
and
the
fr
eq
ue
nc
y
ω
i
c
a
n
be
implem
en
ted
v
i
a
inte
gra
t
i
ng
Δ
ω
i
as
0
t
ii
dt
(
5
)
n
i
m
i
1/s
Vr
e
f
E
ω
t+
δ
ω
*
-
Q
P
i
v
o
RM
S
K
e
E*
-
n
i
m
i
1/s
Vr
e
f
E
ω
t+
δ
ω
*
-
Q
P
i
v
o
RM
S
K
e
E*
-
Fr
e
q
*
e
de
Ga
i
n
+
(a)
(b)
F
i
gure
3.
C
o
n
tr
ol sc
h
e
m
e
(a) Rob
u
s
t
dro
op
(b) Ro
bus
t
dro
o
p
w
it
h
F
LC
3.2.
FLC
-
b
a
sed
rob
u
s
t d
r
oop
c
on
t
r
ol
I
n
o
rde
r
t
o
impro
v
e
t
h
e
as
m
e
n
tio
ne
d
co
n
t
ro
ller
i
n
t
he
p
revi
ous
s
e
c
t
i
on,
s
om
e
cha
nge
s
ha
ve
b
ee
n
ma
de
t
o
rea
l
i
z
e
i
t
.
Re
gard
i
n
g
t
o
t
he
p
r
o
p
o
se
d
c
o
n
t
ro
l
l
e
r
,
th
e
c
on
c
e
p
t
a
n
d
mo
d
e
lin
g
o
f
the
b
a
si
c
robu
st
d
roop
c
o
nt
roll
e
r
a
re
a
l
r
ea
dy
h
ig
hl
ig
ht
ed
i
n
[1
8
]
.
In
t
hi
s
p
a
p
e
r,
F
LC
me
th
od
i
s
i
m
pl
ement
e
d
b
a
sed
on
f
requ
e
n
cy
err
o
r,
rr
e
o
f
eac
h
i
n
v
e
r
t
er.
The
vol
ta
ge
r
efere
n
c
e
,
V
ref
a
nd
new
freque
n
c
y
re
fere
nce
(base
d
o
n
the
per
un
it
o
f
o
u
t
p
ut
vol
t
a
g
e
)
o
f
vol
t
a
g
e
c
on
t
r
o
l
uni
t
i
s
b
ro
ugh
t
out
b
y
th
e
f
r
e
q
u
enc
y
c
on
tro
l
u
ni
t
as
i
nd
i
c
a
t
ed
i
n
F
i
gur
e
3
(b).
T
he
i
nit
i
a
t
io
n
of
t
he
f
re
q
u
enc
y
c
o
n
tr
ol
u
n
i
t
is
d
ro
op
m
e
t
h
o
d
.
P
r
e
v
ious
l
y
,
c
o
n
v
e
n
tio
na
l
dro
op
c
o
ntr
o
l
has
bee
n
u
se
d
as
v
o
lta
ge
a
n
d
f
r
e
que
nc
y
reg
u
l
a
ti
o
n
a
n
d
e
ve
n
pow
e
r
s
h
ar
ing
proc
ess
am
on
g
D
G
un
i
t
s.
I
n
th
i
s
me
tho
d
,
inst
an
tane
ous
a
c
t
i
v
e and
rea
c
t
i
v
e
p
o
w
e
r
com
pone
n
t
s
a
r
e
re
ce
i
v
ed
f
ro
m
t
h
e
lo
c
a
l
me
a
s
u
r
ed
o
f
c
u
rre
n
t
and
vo
lta
ge
. T
h
e
n,
t
he
y a
r
e
passed t
h
ro
ug
h
a low
pass fi
l
t
e
r
w
i
th
c
ut
off
fre
que
nc
y,
c
.
A
s
i
l
l
us
trate
d
i
n
F
i
gur
e
4,
F
LC
w
ith
u
ni
t
y
f
ee
dbac
k
i
s
im
p
l
e
m
e
n
te
d
w
i
t
h
r
ob
ust
dr
oo
p
c
o
n
t
r
o
l
.
T
he
new
re
fer
e
nce
freque
nc
y
is
t
h
e
o
u
t
p
u
t
o
f
f
uz
zy
s
yste
m
w
i
t
h
r
esp
ect
t
o
t
w
o
in
pu
t
s
o
f
fr
eq
uenc
y
e
rror
(
e
rr
)
a
nd
i
t
s
d
eriv
ati
v
e
(
rr
de
dt
).
T
he
m
em
be
r
s
h
i
p
f
u
nct
i
on
f
or
b
o
t
h
i
npu
t
a
n
d
ou
tpu
t
a
re
c
onsid
ered
t
o
wo
rk
w
i
t
h
tria
ng
u
l
ar
m
embe
rsh
i
p
fu
nct
i
o
n.
T
he a
pp
l
i
e
d
rules
a
re
as
i
n
Tab
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
53
0
–
537
53
4
F
i
gur
e
4.
S
im
ul
i
n
k
bloc
k
of
f
uzz
y
l
o
g
i
c
c
ont
r
o
l
l
er
Tab
l
e
1.
F
uzz
y
r
ule
base
De
r
i
v
a
tiv
e
of
fre
que
n
c
y
e
rror
,
(
rr
de
dt
)
F
r
e
que
n
c
y
e
r
r
o
r,
(
rr
e
)
N
B
NS
ZE
PS
PB
NB
NB
NS
ZE
ZE
NS
NS
NS
NS
ZE
NS
PS
ZE
ZE
ZE
ZE
ZE
ZE
PS
ZE
NS
ZE
PS
PS
PB
NS
PS
ZE
PS
PB
4.
GEN
E
RA
L
I
Z
E
D
MODE
L
OF
S
INGL
E-
PHAS
E
I
N
VE
RTER
Th
e
mo
d
e
l
of
s
in
gl
e
-
ph
a
s
e
inv
e
rt
e
r
u
sed
in
t
hi
s
wo
rk
h
as
t
wo
i
n
p
u
ts,
whi
c
h
a
r
e
in
pu
t
v
o
l
t
a
g
e
(
v
i
*)
a
nd
out
p
u
t
c
u
r
r
e
nt
(
i
o
),
a
n
d
on
e
out
p
u
t
,
w
h
i
ch
i
s
th
e
out
put
vol
t
a
g
e
o
f
t
h
e
i
n
v
e
rt
e
r
(
v
o
).
G
v
r
epr
e
sents
the
PR
vo
l
t
age
c
o
nt
r
o
lle
r
of
t
he
v
o
lta
ge
f
ee
d
b
a
c
k
l
o
o
p
,
K
f
i
s
t
h
e
g
a
in
o
f
t
h
e
vo
l
t
a
ge
f
ee
df
or
w
a
r
d
l
o
op,
a
n
d
K
c
i
s
t
h
e
ga
in o
f the
c
u
r
r
e
nt fe
e
d
back
l
oo
p.
I
n
th
is
m
o
d
el,
t
h
e
m
o
d
u
l
ati
o
n i
n
dex of
t
he S
P
W
M
m
odu
la
tor
is assu
m
e
d
t
o
b
e
1
,
i.e. u
n
ity
g
ain
.
Th
e
eq
u
a
t
i
on
fo
r
G
v
i
s
give
n
i
n
(
6)
.
Re
22
2
()
2
s
vP
cc
o
Ks
GK
ss
(
6
)
The
pr
op
or
ti
on
al
g
a
i
n,
r
esona
nt
g
a
i
n,
a
n
d
c
u
t
o
ff
fr
eq
uenc
y
of
t
he
P
R
c
o
n
t
r
o
l
l
er
i
s
r
e
pr
es
ente
d
by
K
P
,
K
Res
,
a
n
d
w
c
r
e
s
pe
ct
ive
l
y,
a
nd
w
o
i
s
the
f
u
nda
me
n
t
a
l
f
r
e
q
u
enc
y
o
f
the
s
y
stem
.
The
c
l
os
ed-
l
oo
p
v
o
lta
ge
g
a
i
n,
G
c
a
n
b
e
de
r
i
ve
d
f
r
o
m
F
i
gur
e
5
usi
n
g
the
r
e
duc
tio
n b
l
oc
k
m
e
tho
d
.
B
y
se
t
tin
g
i
o
t
o be
0
,
and the
m
o
del
c
a
n be
sim
p
li
fie
d
t
o
(7)
.
B
y
se
tti
n
g
v
i
*
t
o
0
,
t
h
e
mode
l
can
b
e
si
m
p
lif
i
e
d
t
o
(
8)
t
o
f
i
nd
t
he
o
u
t
p
u
t
i
m
p
e
d
an
ce
of
t
he
i
nve
r
t
er
2
()
1
iv
f
ff
f
f
f
c
i
v
KG
K
G
CL
s
C
R
C
K
s
K
G
(
7
)
2
()
1
ff
ff
ff
i
c
f
i
v
Ls
R
Z
LC
s
R
C
K
K
C
s
K
G
(
8
)
F
i
gur
e
5.
I
nver
t
e
r
m
odel
w
ith
i
nsta
n
t
ane
o
us
c
ur
r
e
nt
s
ha
r
i
n
g
s
ch
eme
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
D
r
oo
p c
o
n
t
r
o
l te
ch
n
i
que
f
o
r e
qua
l
power
sh
ar
in
g i
n
isl
a
nd
ed m
i
c
r
o
g
r
i
d (A
. W. N. H
u
sna)
53
5
5.
S
I
M
U
LA
T
I
O
N
R
E
S
U
L
TS
A
N
D
A
NA
LY
S
I
S
In
t
hi
s
sec
t
i
o
n,
s
evera
l
M
A
TLA
B/
S
I
MU
LIN
K
si
m
u
lat
i
o
n
s
ha
ve
b
ee
n
ta
ke
n
to
i
n
v
es
tiga
t
e
th
e
perform
ance
o
f
b
o
t
h
c
on
tro
l
l
e
rs’
schem
e
s.
B
ot
h
o
f
t
he
m
e
t
h
o
d
s
a
r
e
u
s
i
n
g
the
fre
q
uenc
y
dro
op
so
t
ha
t
b
o
t
h
o
f
the
resu
l
t
s
fro
m
bo
th
c
on
tro
llers
c
a
n
b
e
e
x
am
ine
d
i
n
t
h
e
sa
me
a
na
l
y
s
i
s.
T
he
a
na
lys
i
s
i
s
b
ase
d
o
n
t
h
e
fre
que
nc
y
re
fe
re
nce
t
h
a
t
c
a
p
a
b
l
e
i
n
ge
nera
tin
g
the
o
u
t
p
ut
o
f
vo
lta
ge
a
n
d
c
urre
n
t
a
s
w
e
ll
a
s
t
h
e
e
q
ua
li
ty
o
f
loa
d
pow
e
r
s
ha
rin
g
w
he
n
a
l
o
ad
d
isturba
n
c
e
o
cc
urs
in
t
h
e
p
a
r
al
l
el-c
on
n
e
cted
i
nve
r
t
ers.
S
yste
m
para
me
ters
u
s
ed
a
r
e
a
s
s
h
ow
n
i
n
T
a
b
l
e
2
.
Tab
l
e
2.
P
a
r
ameter
list
D
e
s
c
r
i
ption
V
a
lue
Filt
e
r
I
nduc
t
a
n
c
e
1
m
H
F
ilte
r
Re
sist
a
n
ce
5
Ω
F
i
l
t
er
C
ap
acit
a
n
c
e
2
0
µ
F
Ca
p
a
c
itor C
u
rr
e
n
t Gain (
K
c
)
10
No
m
i
n
a
l
Fr
e
que
n
c
y
(
w
o
)
314.
15
r
a
d/s
C
u
t
o
f
f
F
re
que
n
c
y
(
w
c
)
10
Hz
N
u
m
b
e
r
o
f
P
a
r
a
ll
e
l
C
onnec
t
e
d
I
nve
r
t
e
r
(
n
)
3
Am
p
l
i
f
i
e
r
(
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e
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in
k
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ltag
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V
DC
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400V
Nu
m
b
er
o
f
lo
ad
I
m
p
ed
a
n
c
e
(
Z
L
)
2
L
i
ne
Re
s
ist
a
n
c
e
3.
42e
-3
Ω
L
i
ne
I
nduc
t
a
n
c
e
2.
73µF
The
simu
la
ti
o
n
results
o
b
t
a
i
n
e
d
is
d
o
n
e
us
i
ng
the
li
ne
i
m
p
eda
n
c
e
va
lue
s
a
s
show
n
in
T
a
b
l
e
2
.
The
fu
nc
ti
o
n
o
f
bre
a
ker
i
s
a
p
p
l
ie
d
i
n
t
he
s
im
ula
tio
n
t
o
m
a
k
e
i
t
eas
ier
to
p
lu
g
i
n
a
nd
d
isc
o
n
n
e
c
t
the
i
n
ver
t
e
r
s
an
d
the l
o
a
d
s.
The
i
n
v
erter
s
c
o
n
fi
gura
t
i
o
n a
nd l
o
ad
c
on
d
iti
o
n
a
re
s
i
m
ilar
i
n
b
o
t
h
con
t
ro
l m
e
th
ods.
A
s
d
e
p
i
c
t
e
d
i
n
F
ig
u
r
e
6 (
a
)
,
t
h
e
p
r
o
p
o
s
e
d
c
o
n
t
r
o
ll
e
r
i
s
a
b
l
e
t
o
r
e
m
a
i
n
at
t
h
e
r
at
ed
fre
qu
en
cy
o
f
50
H
z
aft
e
r
loa
d
c
han
g
e
a
t
1
.7s.
H
o
w
e
v
er,
t
h
e
fre
q
ue
nc
y
of
t
he
r
ob
us
t
d
r
oop
be
com
e
s
u
n
stab
l
e
a
fter
l
oa
d
c
h
a
nge
a
t
1.7s
a
nd
i
t
ha
s
rem
a
ine
d
o
sc
i
l
l
a
tin
g
more
t
h
a
n
50
H
z
as
r
e
q
u
i
re
d.
T
he
r
e
s
u
l
t
o
f
t
he
f
re
que
nc
y
dev
i
a
t
ion
o
f
bo
th
c
o
n
tro
l
lers
i
s
s
how
n
in
F
ig
u
r
e
6
(b),
i
nd
icate
s
t
he
p
r
o
p
o
s
ed
c
o
n
t
r
oll
e
r
i
s
a
bl
e
in
r
ed
uci
n
g
th
e
e
r
ro
r
wh
en
the l
o
a
d
c
ha
ng
e
ha
p
p
e
n
s.
Th
e
co
rrel
a
ti
o
n
re
sul
t
o
f
an
aly
s
i
s
o
f
t
h
e
ou
tp
ut
v
olt
a
ge
o
f
b
o
t
h
s
y
st
e
m
s
i
s
p
rese
n
t
e
d
i
n
F
i
gur
e
7
(a)
.
F
r
om
t
he
f
i
g
ure
,
it
can
b
e
o
b
s
e
r
ved
t
h
a
t
t
he
v
o
l
t
a
ge
o
f
t
h
e
rob
us
t
dro
o
p
c
on
tro
l
ler
be
co
me
s
unsta
ble
sta
r
t
i
n
g
at
t=1.
4s,
whi
l
e
al
l
t
h
e
inv
e
rters
a
n
d
lo
ad
s
are
d
i
scon
n
e
ct
e
d
f
ro
m
l
i
n
e
i
m
peda
nce.
I
n
F
i
gure
7
(b)
s
h
o
w
s
th
e
ou
tpu
t
c
urr
e
nt
o
f
bot
h
m
e
th
o
d
s.
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ike
w
ise
,
t
he
o
u
t
p
u
t
v
olta
ge
,
t
he
r
e
s
u
l
t
w
i
t
h
o
u
t
F
LC
s
how
s
the
insta
b
i
l
ity
o
f
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resp
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n
se
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spe
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ia
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t
t=1.4
s
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t
h
e
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rre
n
t
s
t
i
l
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i
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ul
at
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al
l
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n
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e
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t
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o
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ds
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disco
nnec
t
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li
ne
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m
p
e
d
anc
e
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A
s
s
how
n
i
n
F
ig
ure
8
an
d
F
i
gure
9,
t
he
re
w
as
a
s
i
g
n
i
fic
a
n
t
di
ff
e
r
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ce
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etwe
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o
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ontro
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t
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h
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t
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ook
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1
8
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t
o
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at
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rt
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t
h
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sie
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t
respo
n
se
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t
h
e
act
ive
p
o
w
e
r
i
n
F
i
gure
8
i
s
o
b
t
a
i
ne
d
us
i
n
g
t
h
e
prop
ose
d
c
o
n
tr
ol
l
e
r
be
t
t
er
t
han
t
h
e
re
sp
o
n
se
b
y
us
i
n
g
the
robu
s
t
dr
oop
co
n
t
rol
l
er.
(a)
(
b
)
F
i
gure
6.
S
im
ulat
ion
resu
l
t
s
o
f
(
a)
L
oad
fre
q
uenc
y
o
f
bo
t
h c
o
n
t
ro
ll
e
r
s
t
o
a
ch
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e
v
e
s
t
eady
-
st
a
t
e
at
5
0
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(
b
) F
r
eque
nc
y de
v
i
a
tio
n
of b
o
t
h c
o
n
t
r
o
l
l
er
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
53
0 –
53
7
53
6
(a
)
(
b
)
F
i
gur
e 7.
S
i
m
ulat
i
on re
su
l
t
s o
f
o
u
t
pu
t c
u
rre
n
t
s
of t
hre
e
pa
r
all
el
-conn
e
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rt
e
r
s a
n
d
lo
ad
(a) wi
t
h
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pose
d
t
ec
hn
iq
ue
(
b)
w
i
t
h
pr
evi
ous ro
bus
t dro
op
t
e
c
h
ni
q
u
e
(a
)
(b
)
F
i
gure
8.
S
i
m
ulat
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resu
l
t
s o
f
o
u
t
pu
t p
o
w
e
r of t
hre
e
pa
r
alle
l-
con
n
ect
ed
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nv
ert
e
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d
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wi
t
h
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rop
o
s
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ch
n
i
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(a
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a
cti
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P (b)
re
active
po
wer, Q
(a
)
(b
)
F
i
gur
e 9.
S
i
m
ulat
i
on re
su
l
t
s o
f
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t p
o
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e
r of t
hre
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r
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and l
o
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d
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rev
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st dr
oop
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chn
i
que
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a)
ac
t
ive
p
o
w
e
r
, P
(
b) r
eac
ti
v
e
pow
er
,
Q
6.
CONCL
U
S
ION
T
h
i
s
p
a
p
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t
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re
q
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Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
D
r
oo
p c
o
n
t
r
o
l te
ch
n
i
que
f
o
r e
qua
l
power
sh
ar
in
g i
n
isl
a
nd
ed m
i
c
r
o
g
r
i
d (A
. W. N. H
u
sna)
53
7
dro
op
me
t
hod.
A
s
i
m
pl
ifi
e
d
mode
l
o
f
s
in
g
l
e
-
phase
i
nver
t
e
r
i
s
us
e
d
t
o
i
n
v
e
s
t
i
g
a
t
e
s
y
s
t
e
m
s
t
a
b
i
l
i
t
y
i
n
t
e
r
m
s
o
f
ou
tpu
t
c
urre
nt and
v
o
lta
ge
. The ru
l
e
s
o
f F
L
C a
r
e t
une
d t
o
de
a
l
w
i
t
h
th
e
e
r
r
or a
nd c
h
a
n
g
e
of e
rror
o
f
fr
e
que
nc
y
of
t
he
s
ys
t
e
m
.
A
ccor
d
in
g to t
h
e
r
esul
t
s
a
bo
v
e
,
the pro
p
o
s
ed
c
on
t
r
o
l
st
r
a
t
eg
y is a
ble t
o
pro
vide
a
sta
b
l
e a
n
g
u
l
ar
fre
que
nc
y
f
o
r
m
i
c
r
ogri
d
s
w
o
rki
ng
in
t
h
e
i
s
l
a
n
de
d
m
ode.
The
l
i
mi
te
d
sc
ope
o
f
t
h
e
pre
v
io
us
r
o
b
us
t
d
r
oo
p
con
t
ro
l
l
er
t
ha
t
a
n
al
yze
d
w
it
h
v
o
l
t
age
dr
oop
has
bee
n
n
ot
ic
ed.
M
e
a
nw
h
i
le
,
the
prop
ose
d
c
on
tro
l
l
e
r
has
pro
v
en
tha
t
i
t
is
c
apa
b
l
e
of o
u
tpe
rform
ing t
h
e lacks
of t
he ro
bus
t d
r
o
op
c
ont
rol
l
er
i
n
p
r
ovi
d
i
n
g
a
smo
o
t
h
a
nd
s
t
a
b
l
e
in
line
res
p
o
n
se.
A
d
d
iti
ona
l
l
y
,
w
i
t
h
l
ess
overs
ho
o
t
i
n
r
e
s
p
o
n
s
e
an
d
de
p
e
nd
able
i
n
a
l
i
ne
p
e
r
turba
t
i
on
sho
w
t
h
a
t
t
h
e
p
r
o
p
o
s
e
d
c
o
n
t
r
oll
e
r
a
c
hi
e
v
e
s
g
ood
p
e
rfo
rman
c
e
i
n
s
yste
m
res
ponse
w
i
t
h
less
circ
ula
t
in
g
c
u
rrent
as w
e
ll
a
s
bet
t
er
pow
er
s
hari
ng.
REFE
RENCES
[1]
A.
W
.
N.
H
u
s
n
a
,
S.
F
.
S
i
r
a
j
,
a
nd
M
.
Z.
A
b
M
u
in
,
“Mod
el
i
n
g
o
f
D
C
-DC
conv
erter
f
o
r
sola
r
en
ergy
sys
t
em
a
p
plic
a
t
ion
s
,”
i
n
20
12
IEEE
Symp
os
iu
m o
n
Comput
e
r
s
and Infor
m
a
t
i
c
s
,
I
S
C
I
2
0
1
2
,
20
12.
[2]
T.
H
o
r
ni
k
and
Q
.
-C.
Z
h
o
ng,
“
A
Cu
rrent-Co
n
t
r
ol
S
trat
egy
f
o
r
V
o
lt
age-S
o
urce
In
vert
ers
i
n
M
ic
ro
grid
s
Based
on
$H^{\inf
t
y
}$
and
R
epetiti
ve Control
,
”
IE
EE Tran
s
.
P
o
wer
E
l
e
c
t
r
on
.
,
vol.
26,
no.
3
,
p
p
.
9
43
–9
52,
Mar.
2
01
1.
[3]
P
.
T
enti,
H
.
K.
M
.
P
a
redes
,
a
n
d
P
.
M
a
tt
avelli
,
“
C
on
serv
ati
v
e
P
o
w
e
r
T
h
eo
ry,
a
F
r
am
ework
t
o
A
pp
roach
C
on
trol
a
n
d
Acco
unt
abi
l
i
t
y Iss
u
es in
S
m
art M
i
cro
g
ri
d
s
,”
I
E
EE
T
r
a
n
s
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m
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g
c
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n
t
r
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l
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s
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a
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I
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t
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e
s
o
u
r
c
e
i
s
l
a
n
d
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t
e
m
s
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t
h
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l
l
e
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W
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