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,
[
1
6
]
.
R
e
c
e
n
t
s
t
u
d
i
es
r
e
f
l
e
ct
t
h
e
s
e
t
r
ad
e
-
o
f
f
s
:
SR
F
i
m
p
r
o
v
e
s
h
a
r
m
o
n
i
c
s
u
p
p
r
e
s
s
i
o
n
a
n
d
t
r
a
n
s
i
e
n
t
c
o
n
t
r
o
l
[
1
2
]
,
[
1
3
]
,
w
h
e
r
e
a
s
a
d
a
p
t
i
v
e
V
SGs
e
n
h
a
n
c
e
f
a
u
l
t
r
i
d
e
-
t
h
r
o
u
g
h
a
n
d
i
n
e
r
t
i
a
s
u
p
p
o
r
t
[
1
7
]
–
[
2
0
]
.
H
o
w
e
v
e
r
,
V
S
G
p
e
r
f
o
r
m
a
n
c
e
i
s
h
i
g
h
l
y
d
e
p
e
n
d
en
t
o
n
t
h
e
i
n
e
r
t
i
a
a
n
d
d
a
m
p
i
n
g
c
o
e
f
f
i
c
i
e
n
ts
[
2
1
]
,
[
2
2
]
,
a
n
d
c
o
m
p
a
r
a
t
i
v
e
e
v
a
l
u
at
i
o
n
s
r
e
m
a
i
n
s
c
a
r
ce
,
o
f
t
e
n
a
s
s
es
s
i
n
g
th
e
S
R
F
f
o
r
p
o
w
e
r
q
u
a
l
i
t
y
a
n
d
V
S
G
f
o
r
s
t
a
b
i
li
t
y
u
n
d
e
r
d
i
f
f
e
r
en
t
c
o
n
d
i
t
i
o
n
s
[
2
3
]
.
Desp
ite
th
ese
ad
v
an
ce
m
en
ts
,
s
ev
er
al
lim
itatio
n
s
r
em
ain
in
th
e
f
ield
.
Ma
n
y
ex
is
tin
g
s
tu
d
ies
ad
o
p
t
s
im
p
lifie
d
DC
-
lin
k
r
ep
r
esen
ta
tio
n
s
o
r
id
ea
l
DC
s
o
u
r
ce
s
,
n
e
g
lectin
g
th
e
in
f
lu
en
ce
o
f
p
h
o
t
o
v
o
ltaic
o
p
e
r
atin
g
co
n
d
itio
n
s
,
s
u
ch
as
ir
r
ad
ian
ce
an
d
tem
p
er
atu
r
e,
o
n
s
y
s
tem
p
er
f
o
r
m
an
ce
.
I
n
ad
d
itio
n
,
co
m
p
ar
ativ
e
an
aly
s
es
b
etwe
en
th
e
SR
F
an
d
VSG
co
n
tr
o
ller
s
ar
e
o
f
ten
co
n
d
u
cte
d
u
n
d
er
n
o
n
-
u
n
if
o
r
m
o
p
er
atin
g
co
n
d
itio
n
s
,
lim
itin
g
th
e
v
alid
ity
o
f
th
e
c
o
n
clu
s
io
n
s
.
Fu
r
th
er
m
o
r
e
,
co
m
p
r
eh
e
n
s
iv
e
ev
alu
atio
n
s
u
n
d
er
s
h
o
r
t
-
cir
c
u
it
f
au
lt
s
ce
n
ar
io
s
ar
e
lim
ited
,
p
ar
ticu
lar
ly
t
h
o
s
e
u
s
in
g
s
tan
d
a
r
d
ized
p
er
f
o
r
m
a
n
ce
m
etr
ics
s
u
ch
as
r
ec
o
v
e
r
y
tim
e,
R
o
C
o
F,
an
d
f
au
lt
r
id
e
-
th
r
o
u
g
h
ca
p
ab
ilit
y
.
T
h
is
lim
its
th
e
ab
ilit
y
to
ass
es
s
r
ea
lis
tic
g
r
id
b
eh
av
io
r
u
n
d
er
d
is
tu
r
b
an
ce
co
n
d
itio
n
s
in
th
e
f
ield
.
T
h
is
s
tu
d
y
ad
d
r
ess
es
th
ese
g
ap
s
b
y
i)
D
ev
elo
p
in
g
a
PV
m
o
d
el
in
co
r
p
o
r
atin
g
ir
r
ad
ian
ce
an
d
tem
p
er
atu
r
e
ef
f
ec
ts
with
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
;
ii)
I
n
teg
r
atin
g
a
b
atter
y
en
er
g
y
s
to
r
ag
e
s
y
s
tem
(
B
E
SS
)
f
o
r
co
o
r
d
in
at
ed
co
n
tr
o
l;
an
d
iii)
C
o
n
d
u
ctin
g
a
s
y
s
tem
atic
f
au
lt
-
b
ased
e
v
alu
atio
n
ac
r
o
s
s
PV
p
en
etr
atio
n
lev
els
r
an
g
in
g
f
r
o
m
3
0
%
to
1
5
0
%.
Un
lik
e
p
r
io
r
s
tu
d
ies
with
s
im
p
lifie
d
m
o
d
els
o
r
n
o
n
-
s
tan
d
a
r
d
test
co
n
d
itio
n
s
,
th
is
s
tu
d
y
em
p
lo
y
s
I
E
E
E
/I
E
C
-
alig
n
ed
b
en
ch
m
ar
k
i
n
g
m
etr
ics,
in
clu
d
in
g
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
r
ec
o
v
er
y
tim
e,
an
d
FR
T
co
m
p
lian
ce
,
with
s
tr
ess
s
ce
n
ar
io
s
u
p
to
1
5
0
%
p
en
etr
atio
n
to
em
u
late
o
v
er
-
g
en
er
ati
o
n
co
n
d
i
tio
n
s
.
T
h
e
co
n
tr
ib
u
tio
n
o
f
th
is
s
tu
d
y
s
tem
s
f
r
o
m
ass
ess
in
g
th
e
SR
F
an
d
VSG
co
n
tr
o
l
s
tr
ateg
ies
u
n
d
er
th
e
s
am
e
o
p
er
atin
g
co
n
d
itio
n
s
wi
th
in
a
u
n
if
ied
b
en
ch
m
ar
k
in
g
f
r
am
ewo
r
k
.
T
h
e
r
esu
lts
s
h
o
w
th
at
SR
F
co
n
tr
o
l
is
b
etter
s
u
ited
f
o
r
s
tr
o
n
g
g
r
id
s
wh
er
e
h
ig
h
p
o
wer
q
u
ality
is
e
s
s
en
tial,
wh
ile
VSG
co
n
tr
o
l
d
em
o
n
s
tr
ates
g
r
ea
ter
r
o
b
u
s
tn
ess
in
wea
k
o
r
lo
w
-
in
er
tia
s
y
s
tem
s
.
T
h
ese
f
in
d
in
g
s
p
r
o
v
id
e
p
r
ac
tical
g
u
i
d
an
ce
f
o
r
th
e
d
esig
n
a
n
d
o
p
er
atio
n
o
f
s
tab
le
PV
-
d
o
m
in
ated
p
o
wer
s
y
s
tem
s
ac
r
o
s
s
a
r
an
g
e
o
f
g
r
id
co
n
d
itio
n
s
.
2.
M
E
T
H
O
D
T
h
is
s
tu
d
y
e
m
p
lo
y
s
a
MA
T
L
AB
/Si
m
u
lin
k
-
b
ased
s
im
u
latio
n
f
r
a
m
ewo
r
k
to
ev
alu
ate
an
d
c
o
m
p
ar
e
th
e
p
er
f
o
r
m
an
ce
o
f
SR
F
an
d
VSG
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
g
r
id
-
co
n
n
ec
ted
PV
s
y
s
tem
s
.
T
h
e
an
al
y
s
is
was
co
n
d
u
cte
d
u
n
d
er
id
en
tical
o
p
er
atin
g
an
d
d
is
tu
r
b
an
ce
c
o
n
d
itio
n
s
t
o
en
s
u
r
e
a
f
air
an
d
co
n
s
is
ten
t
co
m
p
a
r
is
o
n
in
ac
c
o
r
d
a
n
ce
with
th
e
I
E
E
E
/I
E
C
r
eq
u
ir
em
e
n
ts
.
2
.
1
.
Sy
s
t
e
m
o
v
er
v
iew
T
h
e
s
im
u
lated
s
y
s
tem
co
n
s
is
t
ed
o
f
a
g
r
i
d
-
co
n
n
ec
ted
PV
g
e
n
er
atio
n
u
n
it
in
ter
f
a
ce
d
th
r
o
u
g
h
a
DC
–
DC
b
o
o
s
t
co
n
v
e
r
ter
a
n
d
a
v
o
lt
ag
e
s
o
u
r
ce
in
v
er
te
r
(
VSI
)
,
wh
i
ch
was
co
n
n
ec
ted
to
th
e
g
r
id
v
ia
an
L
C
L
f
ilter
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
PC
C
)
.
T
h
e
PV
ar
r
ay
o
p
er
ates
u
n
d
er
f
ix
ed
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
with
ir
r
ad
ian
ce
s
et
to
1
0
0
0
W
/m
²
a
n
d
tem
p
er
at
u
r
e
m
ain
tain
e
d
at
2
5
°C
.
MPPT
was
im
p
lem
en
ted
u
s
in
g
th
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
alg
o
r
ith
m
.
A
b
atter
y
en
e
r
g
y
s
to
r
ag
e
s
y
s
tem
(
B
E
SS
)
r
ated
at
6
0
k
W
was
in
teg
r
ated
o
n
th
e
DC
s
id
e
to
s
u
p
p
o
r
t th
e
tr
a
n
s
ien
t p
o
wer
e
x
ch
an
g
e
d
u
r
in
g
d
is
tu
r
b
an
ce
s
.
I
n
th
is
s
tu
d
y
,
th
e
PV
g
en
e
r
atio
n
was
m
ain
tain
e
d
c
o
n
s
tan
t
at
3
6
k
W
f
o
r
all
s
im
u
latio
n
s
ce
n
ar
io
s
.
T
h
e
PV
p
en
etr
atio
n
lev
el
is
d
ef
in
ed
b
y
v
ar
y
in
g
th
e
lo
ad
d
em
a
n
d
wh
ile
k
ee
p
in
g
th
e
PV
o
u
tp
u
t
co
n
s
tan
t.
T
h
is
ap
p
r
o
ac
h
en
ab
les
a
co
n
tr
o
lled
ev
alu
atio
n
o
f
th
e
s
y
s
tem
p
er
f
o
r
m
an
ce
ac
r
o
s
s
p
en
etr
atio
n
lev
els
r
an
g
in
g
f
r
o
m
3
0
%
to
1
5
0
%,
en
s
u
r
in
g
th
at
v
ar
iatio
n
s
in
th
e
s
y
s
tem
b
eh
av
io
r
ar
e
attr
ib
u
ted
to
th
e
lo
ad
in
g
co
n
d
itio
n
s
r
ath
er
th
an
ch
an
g
es in
g
en
e
r
atio
n
.
T
h
e
s
i
m
u
l
at
i
o
n
w
as
p
e
r
f
o
r
m
e
d
i
n
a
d
i
s
c
r
et
e
e
n
v
i
r
o
n
m
e
n
t
u
s
i
n
g
a
f
i
x
e
d
-
s
t
e
p
s
o
l
v
e
r
w
it
h
a
s
a
m
p
l
i
n
g
t
i
m
e
o
f
1
0
µ
s
,
a
l
l
o
w
i
n
g
a
n
a
c
c
u
r
at
e
r
e
p
r
e
s
e
n
t
at
i
o
n
o
f
t
h
e
s
wi
t
ch
i
n
g
d
y
n
a
m
i
c
s
a
n
d
c
o
n
t
r
o
l
r
e
s
p
o
n
s
e
s
.
T
h
e
t
o
t
al
s
i
m
u
l
at
i
o
n
d
u
r
a
t
i
o
n
w
as
5
s
,
c
o
v
e
r
i
n
g
t
h
e
p
r
e
-
f
a
u
l
t
,
f
a
u
l
t
,
a
n
d
p
o
s
t
-
f
a
u
l
t
o
p
e
r
a
t
i
n
g
i
n
te
r
v
a
l
s
.
T
h
e
o
v
e
r
a
ll
c
o
n
f
i
g
u
r
a
t
i
o
n
o
f
t
h
e
g
r
i
d
-
c
o
n
n
e
c
t
e
d
PV
s
y
s
te
m
is
s
h
o
w
n
i
n
Fi
g
u
r
e
1
,
a
n
d
t
h
e
S
R
F
a
n
d
V
SG
c
o
n
t
r
o
l
i
m
p
l
e
m
e
n
t
a
ti
o
n
s
a
r
e
il
l
u
s
t
r
a
t
e
d
i
n
Fi
g
u
r
e
2
.
T
h
e
m
a
i
n
e
l
e
c
t
r
ic
a
l
a
n
d
c
o
n
t
r
o
l
p
a
r
a
m
e
te
r
s
u
s
ed
i
n
t
h
e
s
i
m
u
l
a
t
i
o
n
a
r
e
l
is
t
e
d
i
n
T
a
b
le
1
.
M
e
as
u
r
em
e
n
t
b
l
o
c
k
s
a
r
e
i
m
p
l
e
m
e
n
t
e
d
a
t
t
h
e
PC
C
t
o
r
e
c
o
r
d
s
y
s
t
e
m
v
a
r
i
a
b
l
e
s
,
i
n
c
l
u
d
i
n
g
v
o
l
t
a
g
e
,
c
u
r
r
e
n
t
,
T
H
D
,
v
o
lt
a
g
e
d
e
v
i
a
t
i
o
n
s
,
a
n
d
t
r
a
n
s
i
e
n
t
r
e
s
p
o
n
s
e
i
n
d
i
c
at
o
r
s
u
s
e
d
i
n
t
h
e
p
e
r
f
o
r
m
a
n
c
e
e
v
a
l
u
a
t
i
o
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
S
ta
b
ilit
y
a
n
a
lysi
s
o
f p
h
o
to
vo
lt
a
ic
g
r
id
-
co
n
n
ec
ted
p
o
w
er sys
t
ems e
mp
lo
yin
g
virt
u
a
l
…
(
A
b
d
a
lla
h
E
l G
h
a
ly
)
1453
Fig
u
r
e
1
.
Gen
e
r
al
m
o
d
el
o
f
th
e
g
r
id
-
c
o
n
n
ec
ted
PV sy
s
tem
Fig
u
r
e
2
.
Mo
d
el
o
f
th
e
g
r
i
d
-
co
n
n
ec
ted
PV sy
s
tem
with
SR
F/
VSG
co
n
tr
o
l c
o
n
f
i
g
u
r
atio
n
s
T
ab
le
1
.
Sy
s
tem
p
ar
a
m
eter
s
f
o
r
SR
F a
n
d
VSG
co
n
tr
o
l im
p
le
m
en
tatio
n
P
a
r
a
me
t
e
r
S
y
mb
o
l
V
a
l
u
e
P
a
r
a
me
t
e
r
S
y
mb
o
l
V
a
l
u
e
R
f
(
i
n
v
e
r
t
e
r
si
d
e
)
Rf
0
.
1
Ω
DC
-
l
i
n
k
v
o
l
t
a
g
e
V
d
c
8
0
0
V
Lf
(
i
n
v
e
r
t
e
r
s
i
d
e
)
Lf
5
mH
Rc
–
f
i
l
t
e
r
b
r
a
n
c
h
Rc
0
.
5
Ω
R
g
(
g
r
i
d
s
i
d
e
)
Rg
0
.
0
3
Ω
Cc
–
f
i
l
t
e
r
b
r
a
n
c
h
Cc
4
0
µ
F
Lg
(
g
r
i
d
s
i
d
e
)
Lg
0
.
3
5
mH
J (V
S
G
i
n
e
r
t
i
a
c
o
n
st
a
n
t
)
J
0
.
5
s
F
r
e
q
u
e
n
c
y
f
5
0
H
z
D
(
V
S
G
d
a
m
p
i
n
g
f
a
c
t
o
r
)
D
1
0
p
u
·
s
G
r
i
d
v
o
l
t
a
g
e
(
L
-
L
R
M
S
)
V
g
r
i
d
3
8
0
V
2
.
2
.
Sy
nchro
no
us
re
f
er
ence
f
ra
m
e
(
SRF)
co
ntr
o
l
T
h
e
SR
F
co
n
tr
o
ller
is
a
wid
e
ly
ad
o
p
ted
g
r
i
d
-
f
o
llo
win
g
m
e
th
o
d
th
at
r
eg
u
lates
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
en
ts
b
y
s
y
n
ch
r
o
n
izin
g
wi
th
th
e
g
r
id
u
s
in
g
a
PLL
.
I
n
th
e
d
q
r
o
tatin
g
f
r
am
e
,
p
r
o
p
o
r
t
io
n
al
–
in
teg
r
al
(
PI)
r
eg
u
lato
r
s
in
d
ep
e
n
d
en
tly
c
o
n
tr
o
l
th
e
cu
r
r
en
t
co
m
p
o
n
e
n
ts
,
en
ab
lin
g
ac
cu
r
ate
p
o
wer
r
e
g
u
latio
n
an
d
r
o
b
u
s
t
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
[
2
4
]
.
T
h
is
s
tr
u
ctu
r
e
is
well
-
s
u
ited
f
o
r
s
tiff
g
r
id
s
b
u
t
ex
h
ib
its
r
ed
u
ce
d
r
o
b
u
s
tn
ess
u
n
d
er
weak
-
g
r
id
co
n
d
itio
n
s
o
win
g
t
o
its
r
elian
ce
o
n
th
e
PLL
.
T
h
e
g
en
er
al
co
n
tr
o
l
s
ch
em
e
is
illu
s
tr
ated
in
Fig
u
r
e
3
.
Alth
o
u
g
h
th
e
SR
F
co
n
tr
o
ller
p
r
o
v
id
es
a
r
eliab
le
b
e
n
ch
m
ar
k
f
o
r
h
a
r
m
o
n
ic
p
e
r
f
o
r
m
an
ce
,
it
lack
s
th
e
ca
p
ab
ilit
y
to
em
u
late
p
h
y
s
ical
in
er
tia
o
r
d
am
p
in
g
.
T
h
is
lim
itatio
n
m
o
tiv
ates
th
e
u
s
e
o
f
VSG
co
n
tr
o
l,
wh
ich
is
d
escr
ib
ed
in
th
e
f
o
llo
win
g
s
u
b
s
ec
tio
n
as
th
e
m
ain
f
o
c
u
s
o
f
th
is
s
tu
d
y
.
2
.
3
.
Virt
ua
l sy
nchro
no
us
g
ener
a
t
o
r
(
VSG
)
co
ntr
o
l
T
h
e
VSG
co
n
tr
o
ller
is
a
g
r
id
-
f
o
r
m
in
g
s
tr
ateg
y
th
at
em
u
lates
s
y
n
ch
r
o
n
o
u
s
g
en
e
r
ato
r
d
y
n
am
ics
b
y
in
tr
o
d
u
cin
g
v
ir
tu
al
in
e
r
tia
an
d
d
am
p
in
g
ef
f
ec
ts
.
T
h
e
s
im
p
l
if
ied
co
n
tr
o
l
s
tr
u
ctu
r
e
is
s
h
o
wn
in
Fig
u
r
e
4
.
I
ts
b
eh
av
io
r
is
g
o
v
er
n
ed
b
y
th
e
s
win
g
in
(
1
)
[
2
5
]
.
{
=
−
−
=
−
−
(
−
0
)
=
−
0
(
1
)
I
n
th
is
c
o
n
tex
t,
ω
a
n
d
ω
₀
r
e
p
r
esen
t
th
e
in
s
tan
tan
e
o
u
s
an
g
u
lar
s
p
ee
d
a
n
d
n
o
m
i
n
al
f
r
e
q
u
e
n
cy
o
f
th
e
g
r
id
,
r
esp
ec
tiv
ely
.
T
m
an
d
T
e
c
o
r
r
esp
o
n
d
to
th
e
m
ec
h
an
ical
t
o
r
q
u
e
an
d
elec
tr
o
m
ag
n
etic
to
r
q
u
e,
wh
ile
P
m
an
d
P
d
en
o
te
th
e
m
ec
h
a
n
ical
in
p
u
t
p
o
wer
an
d
elec
tr
ical
o
u
t
p
u
t
p
o
wer
,
r
esp
ec
tiv
ely
.
J
r
ef
er
s
to
th
e
m
o
m
en
t
o
f
in
er
tia,
D
is
th
e
d
am
p
in
g
f
a
cto
r
,
an
d
δ
r
e
p
r
esen
ts
th
e
p
o
wer
an
g
le.
T
o
em
u
late
th
e
p
r
im
ar
y
f
r
eq
u
e
n
cy
r
eg
u
latio
n
b
e
h
av
io
r
o
f
a
co
n
v
en
tio
n
al
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e,
p
r
im
e
m
o
v
e
r
co
n
tr
o
l
is
in
co
r
p
o
r
ated
in
to
th
e
VSG
s
tr
u
ctu
r
e.
T
h
e
v
ir
tu
al
p
r
i
m
e
m
o
v
er
co
n
tr
o
l is d
escr
ib
ed
b
y
(
2
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
2
,
J
u
n
e
20
2
6
:
1
4
5
1
-
1461
1454
=
+
(
0
−
)
(
2
)
B
y
s
u
b
s
titu
tin
g
(
2
)
in
to
(
1
)
an
d
ap
p
ly
i
n
g
th
e
L
a
p
lace
tr
an
s
f
o
r
m
atio
n
,
th
e
cl
o
s
ed
-
lo
o
p
f
r
e
q
u
en
cy
r
esp
o
n
s
e
is
o
b
tain
ed
as (
3
)
,
wh
er
e
th
e
eq
u
iv
alen
t tim
e
co
n
s
tan
t a
n
d
d
r
o
o
p
co
ef
f
icien
t a
r
e
d
ef
i
n
ed
in
(
4
)
,
r
esp
ec
tiv
ely
.
0
−
−
=
−
1
0
+
0
+
=
−
+
1
(
3
)
{
=
0
0
+
=
1
0
+
(
4
)
As
s
h
o
wn
in
(
3
)
an
d
(
4
)
,
th
e
in
er
tia
co
n
s
tan
t
J
an
d
d
am
p
in
g
f
ac
to
r
D
g
o
v
er
n
th
e
f
r
eq
u
e
n
cy
d
y
n
am
ics
o
f
th
e
s
y
s
tem
.
A
lar
g
e
r
J
p
r
o
v
id
es
s
tr
o
n
g
er
in
er
tial
s
u
p
p
o
r
t
an
d
lim
its
th
e
f
r
eq
u
e
n
cy
d
ev
i
atio
n
b
u
t
s
lo
ws
th
e
tr
an
s
ien
t
r
esp
o
n
s
e,
wh
e
r
ea
s
a
s
m
aller
J
ac
ce
ler
ates
th
e
d
y
n
am
ics
y
et
r
is
k
s
in
s
tab
ilit
y
if
th
e
d
am
p
in
g
is
in
ad
eq
u
ate.
T
h
e
d
am
p
i
n
g
f
ac
to
r
D
c
o
n
tr
o
ls
th
e
o
s
cillatio
n
s
: h
ig
h
er
v
alu
es
s
u
p
p
r
ess
th
e
s
win
g
s
,
wh
er
ea
s
lo
we
r
v
alu
es
m
ay
ca
u
s
e
s
u
s
tain
ed
o
s
cillatio
n
s
.
I
m
p
r
o
p
er
tu
n
in
g
o
f
J
an
d
D
ca
n
d
estab
ilize
th
e
s
y
s
tem
;
in
p
r
ac
tice,
lo
w
in
er
tia
with
o
p
tim
ized
d
am
p
in
g
en
ab
les
f
ast
tr
a
n
s
ien
ts
,
wh
er
ea
s
h
ig
h
in
er
tia
wi
th
ad
d
e
d
d
am
p
in
g
en
h
an
ce
s
r
o
b
u
s
tn
ess
[
2
6
]
.
Vo
ltag
e
r
eg
u
latio
n
is
ac
h
iev
ed
v
ia
r
ea
ctiv
e
p
o
wer
–
v
o
ltag
e
d
r
o
o
p
co
n
tr
o
l a
s
(
5
)
.
=
+
(
−
)
(
5
)
I
n
(
5
)
,
an
d
d
en
o
te
th
e
r
ated
an
d
r
ef
er
e
n
ce
v
o
ltag
es,
r
esp
ec
tiv
ely
.
r
ep
r
esen
ts
th
e
r
e
f
e
r
en
ce
r
ea
ctiv
e
p
o
wer
,
wh
ile
Q
in
d
i
ca
tes
th
e
ac
tu
al
r
ea
ctiv
e
p
o
w
er
d
eliv
er
e
d
b
y
th
e
s
y
s
tem
.
T
h
e
p
ar
a
m
eter
r
ef
er
s
to
th
e
r
ea
ctiv
e
p
o
wer
–
v
o
ltag
e
d
r
o
o
p
co
ef
f
icien
t.
T
h
is
co
n
tr
o
l
m
ec
h
an
is
m
en
a
b
les
d
e
ce
n
tr
alize
d
v
o
lta
g
e
r
eg
u
latio
n
b
y
ad
j
u
s
tin
g
th
e
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
ac
c
o
r
d
in
g
to
th
e
r
ea
ctiv
e
p
o
wer
d
e
m
a
n
d
.
A
n
a
p
p
r
o
p
r
iate
ch
o
ice
o
f
f
ac
ilit
ates
ac
cu
r
ate
r
ea
ctiv
e
p
o
wer
s
h
ar
in
g
am
o
n
g
m
u
ltip
le
in
v
er
ter
s
an
d
im
p
r
o
v
es
th
e
o
v
er
all
v
o
ltag
e
s
tab
ilit
y
o
f
t
h
e
s
y
s
te
m
.
As
s
h
o
wn
in
Fig
u
r
e
4
,
th
e
VSG
ap
p
r
o
ac
h
m
im
ics
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e
d
y
n
am
ics,
p
r
o
v
id
in
g
an
in
e
r
tial
r
esp
o
n
s
e,
f
r
eq
u
en
cy
s
tab
ilit
y
,
an
d
r
o
b
u
s
t
f
au
lt
r
id
e
-
th
r
o
u
g
h
.
I
ts
ef
f
ec
tiv
en
ess
d
ep
en
d
s
s
tr
o
n
g
ly
o
n
th
e
p
r
o
p
e
r
tu
n
in
g
o
f
t
h
e
in
er
tia
(
J
)
,
d
am
p
in
g
(
D)
,
an
d
d
r
o
o
p
c
o
ef
f
icien
ts
.
Fig
u
r
e
3
.
C
o
n
tr
o
l stru
ctu
r
e
f
o
r
s
y
n
ch
r
o
n
o
u
s
ly
r
o
tatin
g
r
e
f
er
e
n
ce
f
r
am
e
[
2
4
]
Fig
u
r
e
4
.
Simp
lifie
d
s
win
g
-
b
a
s
ed
v
ir
tu
al
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
2
.
4
.
Sim
ula
t
i
o
n pro
ce
du
re
T
h
e
s
y
s
tem
was
in
itially
o
p
er
ated
u
n
d
er
s
tead
y
-
s
tate
co
n
d
itio
n
s
at
a
s
p
ec
if
ie
d
ir
r
a
d
ian
ce
an
d
tem
p
er
atu
r
e.
A
th
r
ee
-
p
h
ase
s
h
o
r
t
-
cir
cu
it
f
au
lt
was
th
en
a
p
p
li
ed
at
th
e
PC
C
f
o
r
a
d
u
r
atio
n
o
f
0
.
2
s
to
r
e
p
r
esen
t
a
s
ev
er
e
d
is
tu
r
b
a
n
ce
.
Fo
llo
win
g
f
au
lt
clea
r
a
n
ce
,
t
h
e
tr
an
s
ien
t
r
ec
o
v
e
r
y
b
eh
av
io
r
was
r
ec
o
r
d
ed
.
T
h
e
s
im
u
latio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
S
ta
b
ilit
y
a
n
a
lysi
s
o
f p
h
o
to
vo
lt
a
ic
g
r
id
-
co
n
n
ec
ted
p
o
w
er sys
t
ems e
mp
lo
yin
g
virt
u
a
l
…
(
A
b
d
a
lla
h
E
l G
h
a
ly
)
1455
was
r
ep
ea
ted
f
o
r
PV
p
en
etr
a
tio
n
lev
els
r
an
g
in
g
f
r
o
m
3
0
%
to
1
5
0
%
b
y
v
ar
y
in
g
th
e
l
o
ad
d
e
m
an
d
wh
ile
m
ain
tain
in
g
co
n
s
tan
t
PV
g
en
e
r
atio
n
.
I
d
e
n
tical
s
y
s
tem
co
n
f
ig
u
r
atio
n
s
an
d
d
is
tu
r
b
a
n
ce
co
n
d
itio
n
s
wer
e
ap
p
lied
to
b
o
th
t
h
e
SR
F a
n
d
VSG
co
n
tr
o
l stra
teg
ies to
en
s
u
r
e
r
e
p
r
o
d
u
cib
ilit
y
an
d
o
b
jectiv
e
co
m
p
ar
is
o
n
.
2
.
5
.
E
v
a
lua
t
i
o
n m
et
rics
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
c
o
n
tr
o
l
s
tr
ateg
ies
was
ev
alu
ated
u
s
in
g
a
s
et
o
f
m
etr
ics
th
at
ca
p
tu
r
ed
b
o
th
p
o
wer
q
u
ality
a
n
d
d
y
n
am
ic
s
tab
ilit
y
.
T
HD
was
u
s
ed
to
ass
e
s
s
th
e
cu
r
r
en
t
q
u
ality
.
T
h
e
v
o
l
tag
e
o
v
er
s
h
o
o
t
(
%)
an
d
v
o
ltag
e
s
u
r
g
e
(
V)
q
u
an
tif
y
th
e
m
ag
n
itu
d
e
o
f
tr
a
n
s
ien
t v
o
ltag
e
d
ev
iatio
n
s
d
u
r
in
g
d
is
tu
r
b
an
ce
s
,
wh
er
ea
s
th
e
tr
an
s
ien
t r
ec
o
v
er
y
tim
e
(
s
)
r
e
p
r
esen
ts
th
e
tim
e
r
eq
u
ir
ed
f
o
r
th
e
s
y
s
tem
to
r
etu
r
n
to
a
s
tead
y
-
s
tate
o
p
er
atio
n
.
Fre
q
u
en
cy
s
tab
ilit
y
is
ev
alu
ate
d
u
s
in
g
th
e
r
ate
o
f
c
h
an
g
e
o
f
f
r
eq
u
en
c
y
(
R
o
C
o
F)
a
n
d
f
r
eq
u
e
n
cy
n
ad
ir
,
d
ef
in
ed
as
th
e
m
in
im
u
m
f
r
e
q
u
en
cy
r
e
ac
h
ed
d
u
r
in
g
a
d
is
tu
r
b
an
ce
.
I
n
ad
d
itio
n
,
th
e
p
o
wer
an
g
le
(
δ)
was
m
o
n
ito
r
ed
to
ass
ess
th
e
s
y
s
tem
s
y
n
ch
r
o
n
is
m
an
d
o
v
er
all
s
tab
ilit
y
.
All
m
ea
s
u
r
em
en
ts
w
er
e
o
b
tain
e
d
at
t
h
e
PC
C
u
s
in
g
s
im
u
latio
n
m
o
n
ito
r
in
g
to
o
ls
,
en
s
u
r
i
n
g
co
n
s
is
ten
cy
an
d
ac
c
u
r
ac
y
ac
r
o
s
s
all
s
ce
n
ar
io
s
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
ec
tio
n
ev
alu
ates
th
e
c
o
m
p
ar
ativ
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
SR
F
an
d
VSG
co
n
tr
o
l
s
tr
ate
g
ies
u
n
d
er
PV
p
en
etr
atio
n
v
alu
es
ch
an
g
i
n
g
f
r
o
m
3
0
%
to
1
5
0
%,
d
ep
e
n
d
in
g
o
n
th
e
s
y
s
tem
m
o
d
el
d
e
f
in
ed
in
Sectio
n
2
.
T
h
e
an
aly
s
is
co
n
s
id
er
ed
k
e
y
p
er
f
o
r
m
an
ce
in
d
icato
r
s
,
in
clu
d
in
g
T
HD,
v
o
lta
g
e
r
eg
u
latio
n
(
%VR
)
,
tr
an
s
ien
t
o
v
er
s
h
o
o
t,
r
ec
o
v
er
y
tim
e,
v
o
lt
ag
e
s
u
r
g
e,
f
r
eq
u
en
cy
d
y
n
a
m
ics,
an
d
p
o
wer
an
g
le
δ (
r
ad
)
.
T
h
e
ev
al
u
atio
n
was
co
n
d
u
c
ted
in
ac
co
r
d
a
n
ce
with
th
e
co
n
tr
o
l
s
tr
ateg
ies
an
d
p
er
f
o
r
m
an
ce
ch
ar
ac
ter
is
tics
r
ep
o
r
ted
in
th
e
liter
atu
r
e
[
1
7
]
,
[
2
0
]
,
[
2
7
]
,
as
well
as
in
ter
n
atio
n
al
g
r
id
s
tan
d
ar
d
s
,
in
cl
u
d
in
g
IEEE
-
1
5
4
7
[
2
8
]
,
I
E
E
E
-
5
1
9
[
2
9
]
,
an
d
I
E
C
6
1
7
2
7
[
3
0
]
.
R
ep
r
e
s
en
tativ
e
wav
ef
o
r
m
s
at
1
0
0
% PV
p
en
etr
atio
n
ar
e
p
r
esen
ted
f
o
r
b
o
th
n
o
r
m
al
an
d
f
au
lted
o
p
e
r
atin
g
co
n
d
i
tio
n
s
,
as
s
h
o
wn
in
Fig
u
r
es
5
–
8
.
T
h
e
s
y
s
tem
p
er
f
o
r
m
an
ce
at
lo
wer
(
3
0
%)
an
d
h
ig
h
er
(
1
2
5
%
–
1
5
0
%)
p
e
n
etr
atio
n
lev
els
is
s
u
m
m
ar
ized
in
T
ab
les
2
an
d
3
,
an
d
a
co
m
p
ar
ativ
e
o
v
er
v
iew
o
f
all
s
ce
n
ar
io
s
is
p
r
o
v
id
e
d
in
Fig
u
r
e
9
.
T
h
is
u
n
if
ied
ev
alu
a
tio
n
u
n
d
e
r
id
en
tical
o
p
er
atin
g
co
n
d
itio
n
s
en
a
b
les
a
co
n
s
is
ten
t
ass
ess
m
en
t
o
f
th
e
SR
F
an
d
VSG
p
er
f
o
r
m
an
ce
s
an
d
h
ig
h
lig
h
ts
th
ei
r
o
p
er
atio
n
al
lim
its
u
n
d
er
in
cr
ea
s
in
g
PV p
en
etr
atio
n
.
3
.
1
.
No
r
m
a
l
o
pera
t
io
n per
f
o
rm
a
nce
Un
d
er
s
tead
y
-
s
tate
co
n
d
itio
n
s
,
b
o
th
co
n
tr
o
ller
s
m
ain
tain
ed
s
y
n
ch
r
o
n
is
m
with
th
e
g
r
id
at
all
p
en
etr
atio
n
lev
els.
Ho
wev
er
,
d
is
tin
ct
d
if
f
er
en
ce
s
wer
e
o
b
s
er
v
ed
in
th
e
h
ar
m
o
n
ic
p
er
f
o
r
m
an
ce
an
d
v
o
ltag
e
r
eg
u
latio
n
,
as
illu
s
tr
ated
in
Fi
g
u
r
es
5
an
d
6
a
n
d
s
u
m
m
ar
ize
d
in
T
ab
les
2
an
d
3
.
T
h
e
SR
F
co
n
tr
o
ller
(
Fig
u
r
e
5
an
d
T
ab
le
2
)
d
em
o
n
s
tr
ated
ex
ce
llen
t
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
,
with
th
e
T
HD
co
n
s
is
ten
tly
b
elo
w
0
.
5
%,
th
er
e
b
y
s
atis
f
y
in
g
th
e
lim
its
d
ef
in
ed
in
I
E
E
E
-
5
1
9
[
2
9
]
.
A
s
lig
h
t
o
v
er
v
o
ltag
e
co
n
d
itio
n
(
%VR
≈
−1
.
5
%)
was
o
b
s
er
v
ed
at
h
ig
h
er
p
en
etr
atio
n
lev
els,
p
r
im
ar
ily
b
ec
au
s
e
o
f
th
e
in
c
r
ea
s
ed
ac
tiv
e
p
o
wer
in
jectio
n
an
d
d
e
p
en
d
e
n
ce
o
n
PLL
d
y
n
am
ics.
T
h
e
p
o
wer
a
n
g
le
δ r
em
ain
ed
s
tab
le
at
a
p
p
r
o
x
im
ately
0
.
2
r
ad
,
i
n
d
icatin
g
s
tr
o
n
g
s
y
n
c
h
r
o
n
is
m
.
I
n
co
n
tr
ast,
th
e
VSG
co
n
tr
o
ll
er
(
Fig
u
r
e
6
an
d
T
ab
le
3
)
ac
h
iev
ed
tig
h
ter
v
o
ltag
e
r
eg
u
lat
io
n
,
with
|
%V
R
|
n
o
t
ex
ce
ed
in
g
1
.
8
1
%
ac
r
o
s
s
all
p
en
etr
atio
n
lev
els
an
d
r
em
ain
in
g
with
in
ap
p
r
o
x
im
a
tely
1
.
5
%
f
o
r
m
o
s
t
o
p
er
atin
g
p
o
i
n
ts
.
T
h
e
T
HD
r
a
n
g
ed
b
etwe
en
1
.
1
4
%
an
d
1
.
7
6
%,
r
em
ain
in
g
with
in
I
E
E
E
-
5
1
9
co
m
p
lian
ce
[
2
9
]
.
T
h
is
b
eh
av
io
r
is
attr
ib
u
ted
t
o
d
r
o
o
p
-
b
ased
v
o
ltag
e
r
eg
u
latio
n
an
d
v
ir
tu
al
in
er
tia,
w
h
ich
en
h
an
ce
p
o
wer
s
h
ar
in
g
an
d
g
r
id
s
u
p
p
o
r
t.
T
h
e
p
o
wer
an
g
le
δ
s
tab
ilized
at
ap
p
r
o
x
im
ately
0
.
2
5
r
a
d
,
r
ef
lecti
n
g
im
p
r
o
v
ed
ac
tiv
e
p
o
wer
tr
an
s
f
er
ca
p
ab
ilit
y
.
T
h
ese
r
esu
lts
co
n
f
ir
m
a
cle
ar
tr
ad
e
-
o
f
f
b
etwe
en
th
e
two
co
n
tr
o
l
s
tr
ateg
ies
u
n
d
er
s
t
ea
d
y
s
tate
co
n
d
itio
n
s
.
T
h
e
SR
F
co
n
tr
o
ll
er
p
r
o
v
id
es
s
u
p
er
i
o
r
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
b
ec
au
s
e
its
cu
r
r
en
t
r
e
g
u
latio
n
is
d
ir
ec
tly
s
y
n
ch
r
o
n
ized
with
th
e
g
r
id
t
h
r
o
u
g
h
th
e
d
q
r
e
f
er
en
ce
f
r
am
e,
wh
er
ea
s
th
e
VSG
co
n
tr
o
ller
ac
h
iev
es
tig
h
ter
v
o
ltag
e
s
u
p
p
o
r
t
t
h
r
o
u
g
h
d
r
o
o
p
-
b
ased
r
eg
u
latio
n
an
d
v
ir
tu
al
in
er
tia.
Acc
o
r
d
in
g
ly
,
th
e
SR
F
is
m
o
r
e
s
u
itab
le
wh
en
p
o
wer
q
u
ality
i
s
th
e
d
o
m
in
an
t
o
b
jectiv
e,
wh
er
ea
s
th
e
VSG
o
f
f
er
s
a
s
tr
o
n
g
er
v
o
ltag
e
s
u
p
p
o
r
t
ca
p
ab
ilit
y
u
n
d
er
v
a
r
y
in
g
o
p
er
a
tin
g
co
n
d
itio
n
s
.
T
ab
le
2
.
Per
f
o
r
m
an
ce
o
f
SR
F c
o
n
tr
o
l u
n
d
er
v
ar
y
i
n
g
PV p
en
etr
atio
n
lev
els d
u
r
in
g
n
o
r
m
al
o
p
er
atio
n
a
n
d
p
o
s
t
-
SC
C
(
0
.
2
s
)
P
V
p
e
n
e
t
r
a
t
i
o
n
l
e
v
e
l
P
V
(
k
W
)
Lo
a
d
(
k
W
)
P
C
C
v
o
l
t
a
g
e
n
o
r
m
a
l
G
r
i
d
v
o
l
t
a
g
e
(V)
TH
D
(
%)
%VR
n
o
r
m
a
l
V
o
l
t
a
g
e
a
t
P
C
C
(
V
)
p
o
s
t
S
C
C
%VR
p
o
st
S
C
C
V
su
r
g
e
p
o
s
t
S
C
C
Tr
a
n
s
i
e
n
t
t
i
m
e
(
s)
O
v
e
r
sh
o
o
t
(
%)
3
0
%
3
6
.
0
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I
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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2088
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ased
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