I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
(
I
J
P
E
DS)
Vo
l.
1
6
,
No
.
3
,
Sep
tem
b
er
2
0
2
5
,
p
p
.
1
6
0
8
~
1
6
1
9
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
6
.
i3
.
p
p
1
6
0
8
-
1
6
1
9
1608
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Lo
w vo
ltag
e f
a
ult
ride
-
throug
h ope
ra
tion o
f
a
photo
-
v
o
ltaic
sy
stem conn
ect
ed
utilit
y
grid
by usi
ng
dyna
mic
v
o
ltag
e suppo
rt
s
cheme
Sa
t
y
a
na
ra
y
a
na
B
ura
da
1
,
K
o
t
t
a
la
P
a
dm
a
2
1
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
a
n
d
El
e
c
t
r
o
n
i
c
s
E
n
g
i
n
e
e
r
i
n
g
,
A
n
i
l
N
e
e
r
u
k
o
n
d
a
I
n
st
i
t
u
t
e
o
f
T
e
c
h
n
o
l
o
g
y
&
S
c
i
e
n
c
e
s
(
A
N
I
TS)
,
V
i
sak
h
a
p
a
t
n
a
m
,
I
n
d
i
a
2
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
,
A
n
d
h
r
a
U
n
i
v
e
r
si
t
y
,
V
i
sa
k
h
a
p
a
t
n
a
m,
I
n
d
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
1
6
,
2
0
2
4
R
ev
is
ed
Ma
y
3
1
,
2
0
2
5
Acc
ep
ted
J
u
l 2
3
,
2
0
2
5
Th
is
re
se
a
rc
h
su
g
g
e
sts
a
c
o
n
tro
l
tec
h
n
iq
u
e
th
a
t
m
a
k
e
s
u
se
o
f
a
m
icro
g
ri
d
'
s
e
n
e
rg
y
st
o
ra
g
e
a
n
d
to
e
n
a
b
le
l
o
w
v
o
lt
a
g
e
rid
e
t
h
ro
u
g
h
(LVRT)
p
ro
c
e
ss
with
a
flex
ib
le
d
y
n
a
m
ic
v
o
lt
a
g
e
s
u
p
p
o
rt
(DV
S
)
sy
ste
m
.
F
irst,
th
e
re
q
u
ire
m
e
n
ts
fo
r
th
e
m
icro
g
rid
'
s
m
a
x
imu
m
DV
S
a
r
e
sta
ted
,
to
g
e
th
e
r
with
a
n
e
x
p
lan
a
ti
o
n
o
f
h
o
w
th
e
se
re
q
u
irem
e
n
ts
d
e
p
e
n
d
o
n
th
e
c
h
a
ra
c
teristics
o
f
t
h
e
a
n
a
lo
g
o
u
s
n
e
two
rk
th
a
t
th
e
m
icro
g
ri
d
se
e
s.
In
o
rd
e
r
to
c
re
a
te
a
flex
ib
le
DV
S
re
g
a
rd
l
e
ss
o
f
th
e
c
h
a
n
g
i
n
g
sy
ste
m
c
ircu
m
sta
n
c
e
s,
re
fe
re
n
c
e
sig
n
a
ls
fo
r
c
u
rre
n
ts
th
a
t
a
re
d
e
riv
e
d
fro
m
m
a
x
imu
m
v
o
lt
a
g
e
trac
k
i
n
g
tec
h
n
iq
u
e
a
re
su
g
g
e
ste
d
i
n
th
is
re
se
a
rc
h
.
Th
e
se
sig
n
a
ls
tak
e
i
n
to
a
c
c
o
u
n
t
th
e
c
h
a
ll
e
n
g
e
s
in
v
o
l
v
e
d
with
re
a
l
ti
m
e
p
a
ra
m
e
ter
a
ss
e
ss
m
e
n
t
in
th
e
c
o
n
t
e
x
t
o
f
tran
sie
n
t
v
o
lt
a
g
e
d
isru
p
ti
o
n
s.
S
e
c
o
n
d
,
a
c
o
n
tro
l
sc
h
e
m
e
is
su
g
g
e
ste
d
t
o
a
ll
o
w
a
m
icro
g
r
id
'
s
e
n
e
rg
y
sto
r
a
g
e
-
b
a
se
d
LVRT
o
p
e
ra
ti
o
n
.
T
h
ir
d
ly
,
a
n
o
v
e
l
a
p
p
ro
a
c
h
to
e
n
e
rg
y
st
o
ra
g
e
siz
i
n
g
fo
r
LVRT
o
p
e
ra
ti
o
n
is
o
ffe
re
d
,
tak
i
n
g
i
n
to
a
c
c
o
u
n
t
th
e
c
o
rre
sp
o
n
d
in
g
n
e
two
r
k
c
h
a
ra
c
teristics
,
g
rid
c
o
d
e
re
q
u
ire
m
e
n
ts,
a
n
d
t
h
e
ra
te
d
c
u
rre
n
t
v
a
lu
e
o
f
t
h
e
p
o
we
r
e
lec
tro
n
ic c
o
n
v
e
rter.
Re
a
l
-
t
ime
M
ATLAB
sim
u
latio
n
s f
o
r
lo
w
-
v
o
lt
a
g
e
sy
m
m
e
tri
c
a
l
fa
u
lt
s a
re
u
se
d
to
v
a
l
id
a
te t
h
e
su
g
g
e
ste
d
c
o
n
tr
o
l
tec
h
n
i
q
u
e
.
K
ey
w
o
r
d
s
:
Activ
e
cu
r
r
en
t
D
y
n
a
m
i
c
v
o
l
t
a
g
e
s
u
p
p
o
r
t
s
y
s
t
em
E
n
er
g
y
s
to
r
ag
e
u
n
it
Gr
id
n
etwo
r
k
L
o
w
v
o
ltag
e
r
id
e
th
r
o
u
g
h
R
ea
ctiv
e
cu
r
r
en
t
T
r
ip
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Saty
an
ar
ay
an
a
B
u
r
a
d
a
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics
E
n
g
in
ee
r
i
n
g
An
il Ne
er
u
k
o
n
d
a
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
&
Scien
ce
s
(
ANI
T
S)
Vis
ak
h
ap
atn
am
,
An
d
h
r
a
Pra
d
e
s
h
5
3
1
1
6
2
,
I
n
d
ia
E
m
ail:
s
aty
an
ar
ay
an
a.
ee
e@
an
its
.
ed
u
.
in
1.
I
NT
RO
D
UCT
I
O
N
I
n
lig
h
t
o
f
th
eir
g
r
o
win
g
p
e
n
etr
atio
n
,
th
e
r
eq
u
ir
e
m
en
t
f
o
r
m
a
n
d
ated
s
er
v
ices
s
u
ch
as
v
o
ltag
e
f
au
lt
r
id
e
-
th
r
o
u
g
h
(
VFR
T
)
f
u
n
ctio
n
in
g
f
r
o
m
m
icr
o
g
r
id
/
p
h
o
to
v
o
ltaic
u
n
it
(
PV
u
n
it)
is
in
cr
ea
s
in
g
ly
es
s
en
tial
to
p
r
eser
v
in
g
th
e
u
tili
ty
g
r
id
'
s
r
eliab
ilit
y
an
d
p
er
m
a
n
en
ce
.
Acc
o
r
d
in
g
to
th
e
g
r
id
co
d
e
[
1
]
,
th
e
VFR
T
tec
h
n
iq
u
e
n
ec
ess
itates
th
at
th
e
g
r
id
-
c
o
n
n
ec
te
d
p
h
o
to
v
o
ltaic
u
n
it r
em
ain
lin
k
ed
to
th
e
m
icr
o
g
r
id
u
n
til th
e
v
o
ltag
e
d
if
f
er
en
ce
s
m
ain
tai
n
with
in
a
VFR
T
ch
ar
ac
ter
is
tic
cu
r
v
e.
T
h
e
g
en
e
r
ato
r
u
n
it
is
also
r
esp
o
n
s
ib
le
f
o
r
m
ain
tain
in
g
th
e
n
ea
r
b
y
v
o
ltag
e
b
y
r
e
g
u
latin
g
th
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
o
f
its
to
tal
p
o
wer
p
r
o
d
u
ctio
n
.
I
n
a
d
d
itio
n
t
o
r
eq
u
ir
in
g
VFR
T
o
p
er
atio
n
f
r
o
m
th
e
DE
R
,
th
e
I
E
E
E
1
5
4
7
:
2
0
1
8
n
o
r
m
,
wh
ich
was ju
s
t r
elea
s
ed
,
also
in
clu
d
ed
a
n
u
m
b
er
o
f
o
th
e
r
f
ea
tu
r
es,
s
u
ch
as
m
u
ltip
le
p
e
r
f
o
r
m
an
ce
ar
ea
s
th
at
co
m
e
u
n
d
er
th
e
VFR
T
ch
ar
ac
ter
is
tics
,
n
ee
d
s
f
o
r
d
y
n
am
ic
v
o
ltag
e
s
u
p
p
o
r
t
(
DVS)
,
m
icr
o
g
r
id
u
n
u
s
u
al
p
e
r
f
o
r
m
an
ce
g
r
o
u
p
class
if
icatio
n
,
an
d
co
n
s
ec
u
t
iv
e
VFR
T
n
ee
d
s
[
2
]
.
T
h
e
p
o
ten
tial
o
f
th
e
g
r
id
-
f
o
llo
win
g
PV
u
n
it
with
in
v
er
ter
-
co
n
n
ec
ted
DVS
to
s
wap
an
ap
p
r
o
p
r
iate
am
o
u
n
t
o
f
cu
r
r
en
t
with
th
e
n
etwo
r
k
d
u
r
in
g
ex
tr
em
e
v
o
ltag
e
f
l
u
ctu
atio
n
s
en
h
an
ce
s
th
e
n
etwo
r
k
'
s
v
o
ltag
e
p
r
o
f
ile
a
n
d
av
e
r
ts
s
itu
atio
n
s
th
at
ca
n
ca
u
s
e
VFR
T
o
r
tr
ip
o
p
er
atio
n
s
.
T
h
e
m
ain
v
ar
iab
les
th
at
d
ictate
h
o
w
m
u
ch
v
o
ltag
e
s
u
p
p
o
r
t
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
Lo
w
vo
lta
g
e
fa
u
lt
r
id
e
-
th
r
o
u
g
h
o
p
era
tio
n
o
f a
p
h
o
t
o
-
vo
lta
ic
s
ystem
co
n
n
ec
ted
…
(
S
a
ty
a
n
a
r
a
ya
n
a
B
u
r
a
d
a
)
1609
th
e
g
r
id
-
f
o
llo
win
g
PV u
n
it c
an
p
r
o
v
id
e
a
r
e
its
cu
r
r
en
t
o
u
tp
u
t's
m
ag
n
itu
d
e
an
d
p
h
ase
an
g
le
[
3
]
.
Fo
r
th
e
p
u
r
p
o
s
e
o
f
m
ain
tain
in
g
v
o
lta
g
e
with
in
lim
its
d
u
r
in
g
th
e
VFR
T
o
p
er
atio
n
,
a
v
ar
iety
o
f
ce
n
tr
alize
d
an
d
d
ec
en
tr
alize
d
tech
n
iq
u
es
th
at
d
e
p
en
d
o
n
th
e
cu
r
r
en
t
co
n
tr
o
l
o
f
th
e
p
o
wer
el
ec
tr
o
n
ic
c
o
n
v
e
r
ter
a
r
e
o
u
tlin
ed
in
t
h
e
wo
r
k
s
.
T
h
is
ad
d
r
ess
es
co
n
tr
o
l
t
h
at
r
elies
o
n
a
s
tead
y
r
ea
ctiv
e
cu
r
r
e
n
t
[
4
]
,
v
o
ltag
e
v
ar
iatio
n
with
r
ea
ctiv
e
cu
r
r
en
t
[
5
]
,
[
6
]
.
T
h
e
au
th
o
r
s
in
[
7
]
u
s
e
a
r
ea
ctiv
e
p
o
wer
m
o
d
u
lato
r
a
p
p
r
o
ac
h
to
ass
is
t
an
d
im
p
r
o
v
e
th
e
v
o
l
tag
e
b
y
co
m
p
u
tin
g
th
e
s
tan
d
ar
d
o
r
r
e
f
er
en
ce
v
alu
e
f
o
r
r
ea
ctiv
e
p
o
wer
.
T
h
is
ap
p
r
o
ac
h
tak
es
in
t
o
c
o
n
s
id
er
atio
n
b
o
th
t
h
e
r
ea
ctiv
e
p
o
wer
p
r
o
d
u
ce
d
b
y
th
e
p
o
s
itiv
e
s
eq
u
en
ce
v
o
ltag
e
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
PC
C
)
an
d
th
e
ca
p
ac
ito
r
u
s
ed
in
th
e
f
ilter
.
W
h
en
n
ec
ess
ar
y
,
th
e
af
o
r
e
m
en
tio
n
e
d
tech
n
i
q
u
es
r
ed
u
ce
r
ea
l
p
o
wer
in
o
r
d
e
r
to
m
ak
e
s
p
ac
e
to
p
r
o
v
id
e
t
h
e
co
n
tin
u
o
u
s
r
ea
ctiv
e
p
o
wer
n
ee
d
e
d
in
th
e
ev
en
t
o
f
s
ev
er
e
v
o
ltag
e
s
win
g
s
.
T
h
e
u
t
ilit
y
g
r
id
'
s
m
ed
iu
m
an
d
h
ig
h
v
o
ltag
e
p
o
r
tio
n
,
wh
e
n
th
e
r
atio
o
f
th
e
lin
es'
r
ea
ctan
ce
to
r
esis
tan
ce
(
X/
R
)
is
lar
g
e,
is
th
e
o
n
ly
ar
ea
wh
er
e
DVS
o
p
er
atio
n
h
as
p
r
o
v
en
ef
f
ec
tiv
e,
d
esp
ite
en
c
o
u
r
ag
in
g
f
i
n
d
in
g
s
.
R
ea
ctiv
e
cu
r
r
en
t
d
ep
en
d
en
c
y
o
n
v
o
ltag
e
s
u
p
p
o
r
t
is
s
h
if
ted
to
r
e
al
cu
r
r
en
t
in
jectio
n
th
r
o
u
g
h
d
is
tr
ib
u
tio
n
f
ee
d
er
s
o
f
th
e
m
icr
o
g
r
id
with
lo
w
v
alu
es
o
f
X/R
.
A
f
ew
p
iece
s
o
f
liter
a
tu
r
e
d
is
cu
s
s
th
e
DV
S
f
r
o
m
th
e
PV
u
n
it
th
at
i
s
in
teg
r
ated
to
t
h
e
g
r
id
with
f
ac
in
g
lo
w
v
o
ltag
e
p
r
o
f
ile.
A
s
en
s
itiv
ity
ev
alu
atio
n
is
p
er
f
o
r
m
e
d
[
8
]
,
an
d
th
e
m
ax
im
u
m
cu
r
r
en
t
lim
it
o
f
th
e
i
n
v
er
te
r
[9
]
is
u
s
ed
to
o
p
tim
ize
r
ea
l
cu
r
r
en
t
in
f
u
s
io
n
o
v
er
th
e
v
o
ltag
e
s
ag
as
th
e
b
asi
s
f
o
r
cu
r
r
en
t
co
n
tr
o
l.
T
h
is
im
p
r
o
v
e
d
th
e
v
o
ltag
e;
H
o
wev
er
,
it
is
n
o
t
to
th
e
m
ax
im
u
m
o
r
p
ea
k
v
o
l
tag
e
th
at
is
n
ec
ess
ar
y
f
o
r
VF
R
T
o
p
er
atio
n
u
n
d
er
s
u
b
s
tan
tial
f
lu
ctu
atio
n
s
in
v
o
ltag
e.
Fu
r
th
er
m
o
r
e,
n
o
t
o
n
e
o
f
th
e
af
o
r
em
en
tio
n
e
d
tech
n
iq
u
es
ca
n
p
r
o
v
i
d
e
th
e
DVS
wh
ile
ad
ap
tin
g
to
ch
an
g
in
g
n
e
two
r
k
co
n
d
itio
n
s
.
T
h
e
s
t
u
d
y
b
y
C
a
m
a
c
h
o
e
t
a
l
.
[
3
]
s
h
o
w
s
h
o
w
t
h
e
i
n
v
e
r
t
e
r
'
s
m
a
x
i
m
u
m
v
o
l
t
a
g
e
s
u
p
p
o
r
t
d
e
p
e
n
d
s
o
n
t
h
e
n
e
t
w
o
r
k
'
s
X
/R
r
at
i
o
.
I
f
a
m
o
s
t
l
y
a
c
c
u
r
a
t
e
r
e
a
l
-
ti
m
e
ass
e
s
s
m
e
n
t
o
f
t
h
e
f
l
u
c
t
u
a
ti
n
g
i
m
p
ed
a
n
c
e
o
f
t
h
e
g
r
i
d
i
s
e
s
t
a
b
li
s
h
e
d
,
c
a
n
t
h
e
h
i
g
h
es
t
D
VS
b
e
r
e
a
l
i
ze
d
.
A
n
i
d
e
a
l
v
o
l
t
a
g
e
s
u
p
p
o
r
t
c
o
n
t
r
o
l
f
o
r
l
o
w
-
v
o
l
t
a
g
e
g
r
i
d
s
e
x
p
e
r
i
e
n
c
i
n
g
f
a
u
l
t
s
is
s
u
g
g
es
t
e
d
i
n
[
1
0
]
.
T
o
m
a
k
e
t
h
e
D
V
S
o
p
e
r
a
ti
o
n
a
l
wh
i
l
e
p
e
r
f
o
r
m
i
n
g
t
h
e
V
FR
T
p
r
o
c
e
d
u
r
e
,
t
h
e
a
u
t
h
o
r
s
,
h
o
w
e
v
e
r
,
m
a
d
e
t
h
e
ass
u
m
p
t
i
o
n
t
h
a
t
t
h
e
g
r
i
d
'
s
X
/R
r
a
ti
o
w
as
k
n
o
w
n
i
n
a
d
v
a
n
c
e
a
n
d
p
r
o
p
o
s
e
d
t
h
a
t
w
i
d
e
-
b
a
n
d
s
y
s
te
m
i
d
e
n
t
i
f
ic
a
t
i
o
n
t
ec
h
n
i
q
u
e
s
b
e
u
s
e
d
t
o
g
e
t
t
h
e
g
r
i
d
'
s
X
/R
r
a
t
i
o
[
1
1
]
,
[
1
2
]
.
N
e
v
e
r
t
h
e
l
e
s
s
,
a
n
u
m
b
e
r
o
f
v
a
r
i
a
b
l
e
s
,
s
u
c
h
a
s
t
h
e
p
e
r
t
u
r
b
a
t
i
o
n
s
i
g
n
a
l'
s
m
a
g
n
i
t
u
d
e
a
n
d
b
a
n
d
w
i
d
t
h
a
n
d
t
h
e
e
x
i
s
t
e
n
c
e
o
f
d
y
n
a
m
i
c
c
o
m
p
o
n
e
n
t
s
w
it
h
i
n
t
h
e
s
y
s
te
m
,
a
f
f
e
c
t
h
o
w
a
c
c
u
r
a
t
e
t
h
e
s
e
a
p
p
r
o
a
c
h
e
s
a
r
e
.
A
f
t
e
r
c
o
n
d
u
c
t
i
n
g
a
t
h
o
r
o
u
g
h
q
u
a
n
t
i
t
a
t
i
v
e
e
x
a
m
i
n
a
t
i
o
n
,
t
h
e
w
r
i
t
e
r
s
h
a
v
e
as
c
e
r
ta
i
n
e
d
t
h
at
a
c
o
u
p
l
e
o
f
a
d
d
i
t
i
o
n
a
l
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
o
f
t
h
e
c
o
m
p
a
r
a
b
le
n
e
tw
o
r
k
s
e
e
n
b
y
t
h
e
P
V
u
n
i
t,
w
h
i
c
h
t
h
e
f
o
l
l
o
w
i
n
g
s
e
c
ti
o
n
a
d
d
r
e
s
s
es
,
a
s
w
el
l
a
s
t
h
e
r
e
a
ct
an
c
e
t
o
r
e
s
i
s
ta
n
c
e
r
a
t
i
o
o
f
t
h
e
T
h
e
v
e
n
i
n
i
m
p
e
d
a
n
c
e
a
c
r
o
s
s
t
h
e
m
i
c
r
o
g
r
i
d
n
e
tw
o
r
k
,
d
e
t
e
r
m
i
n
e
t
h
e
p
e
a
k
v
o
l
t
a
g
e
t
h
a
t
th
e
P
V
u
n
i
t
c
a
n
s
u
p
p
o
r
t
.
T
h
e
el
ec
t
r
i
c
g
r
i
d
'
s
d
y
n
a
m
ic
n
a
t
u
r
e
a
n
d
t
h
e
f
a
u
l
t
v
o
l
t
a
g
e'
s
b
r
i
e
f
d
u
r
a
t
i
o
n
m
a
k
e
i
t
e
x
t
r
e
m
e
l
y
d
i
f
f
i
c
u
l
t
t
o
m
e
as
u
r
e
o
r
e
s
ti
m
a
t
e
n
e
a
r
-
a
c
c
u
r
at
e
e
q
u
i
v
a
l
e
n
t
n
et
w
o
r
k
m
e
t
r
i
c
s
i
n
r
e
a
l
-
t
i
m
e
.
I
n
o
r
d
e
r
t
o
p
r
o
v
i
d
e
m
ax
i
m
a
l
DV
S
d
e
s
p
i
t
e
f
l
u
c
t
u
a
ti
n
g
n
e
t
w
o
r
k
c
o
n
d
i
t
i
o
n
s
,
t
h
e
r
e
is
a
n
i
m
m
e
d
i
at
e
r
e
q
u
i
r
em
e
n
t
t
o
g
e
n
e
r
at
e
i
n
v
e
r
t
e
r
c
u
r
r
en
t
c
o
m
p
a
r
i
s
o
n
s
d
es
p
i
t
e
g
e
n
u
i
n
e
l
y
a
n
a
l
y
z
i
n
g
s
i
m
i
l
ar
s
y
s
te
m
c
h
a
r
a
c
te
r
i
s
t
i
cs
.
I
t
m
a
y
o
c
c
a
s
i
o
n
a
ll
y
b
e
n
e
c
ess
a
r
y
t
o
co
n
s
t
r
a
i
n
r
e
al
c
u
r
r
e
n
t
d
u
r
i
n
g
v
o
l
t
a
g
e
s
u
p
p
o
r
t
d
u
r
i
n
g
V
FR
T
o
p
e
r
a
t
i
o
n
i
n
o
r
d
e
r
t
o
al
l
o
w
s
p
a
c
e
f
o
r
r
e
a
ct
i
v
e
c
u
r
r
e
n
t
,
p
r
o
v
i
d
e
d
t
h
a
t
t
h
e
P
V
s
y
s
t
em
f
u
n
c
t
i
o
n
s
a
t
t
h
e
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
(
M
P
P
T
)
s
ta
t
e
[
1
3
]
.
T
h
i
s
w
o
u
l
d
r
e
s
u
l
t
a
t
t
h
e
i
n
v
e
r
t
e
r
'
s
DC
l
i
n
k
,
t
h
e
r
e
i
s
a
d
i
s
p
a
r
it
y
.
u
s
i
n
g
a
n
e
l
e
c
t
r
i
c
a
l
e
n
e
r
g
y
s
t
o
r
ag
e
d
e
v
i
c
e
a
t
t
h
e
D
C
b
u
s
o
r
a
c
r
o
w
b
a
r
n
e
t
w
o
r
k
[
1
4
]
,
[
1
5
]
,
u
s
i
n
g
o
f
f
-
M
P
P
T
s
t
a
t
e
f
o
r
t
h
e
P
V
s
o
u
r
c
e
,
a
n
d
o
v
e
r
s
i
z
i
n
g
t
h
e
i
n
v
e
r
t
e
r
s
[
1
6
]
a
r
e
a
f
ew
p
o
t
e
n
t
i
al
o
p
t
i
o
n
s
.
T
h
e
c
o
s
t
o
f
e
n
e
r
g
y
s
t
o
r
a
g
e
t
e
c
h
n
o
l
o
g
i
e
s
h
as
d
e
c
r
e
a
s
e
d
,
a
n
d
t
h
e
i
r
a
p
p
l
i
c
a
t
i
o
n
a
r
e
as
h
a
v
e
e
x
p
a
n
d
e
d
d
u
e
t
o
r
e
c
e
n
t
a
d
v
a
n
c
e
m
e
n
t
s
i
n
t
h
e
f
ie
l
d
[
1
7
]
.
T
h
e
t
e
c
h
n
i
q
u
e
,
w
h
i
c
h
i
s
c
o
n
n
e
c
t
e
d
w
i
t
h
a
n
e
n
e
r
g
y
s
t
o
r
a
g
e
d
e
v
i
c
e
u
s
e
d
a
t
t
h
e
i
n
v
e
r
t
e
r
’
s
D
C
b
u
s
,
s
t
o
r
e
s
s
o
l
ar
p
o
w
e
r
t
h
a
t
w
o
u
l
d
o
t
h
e
r
wi
s
e
b
e
w
as
t
e
d
a
n
d
c
a
n
o
f
f
e
r
e
x
t
r
a
f
u
n
c
t
i
o
n
s
t
o
t
h
e
u
ti
l
it
y
g
r
i
d
o
r
m
i
c
r
o
g
r
i
d
,
s
u
c
h
a
s
e
l
e
c
t
r
ic
a
l
i
n
e
r
t
i
a
,
b
l
a
c
k
s
t
a
r
t
o
p
e
r
a
t
i
o
n
,
f
a
s
t
f
r
e
q
u
e
n
c
y
r
e
s
e
r
v
e
s
,
a
n
d
f
r
e
q
u
e
n
c
y
f
a
u
l
t
r
i
d
e
-
t
h
r
o
u
g
h
a
s
s
is
t
a
n
ce
.
A
d
d
i
t
i
o
n
a
l
l
y
,
t
h
e
n
e
tw
o
r
k
v
o
l
t
a
g
e
c
a
n
b
e
s
u
p
p
o
r
t
e
d
b
y
t
h
e
e
n
e
r
g
y
s
t
o
r
a
g
e
d
u
r
i
n
g
p
e
r
i
o
d
s
o
f
l
o
w
g
e
n
e
r
a
t
i
n
g
o
u
t
p
u
t
s
f
r
o
m
s
o
l
a
r
P
V
u
n
i
t
s
[
1
8
]
.
T
h
e
r
e
i
s
c
u
r
r
e
n
t
l
y
n
o
g
e
n
e
r
a
l
a
p
p
r
o
a
c
h
t
h
a
t
m
e
a
s
u
r
e
s
t
h
e
e
n
e
r
g
y
s
to
r
a
g
e
'
s
c
o
n
t
r
i
b
u
t
i
o
n
t
o
f
a
u
l
t
r
i
d
e
-
t
h
r
o
u
g
h
o
p
e
r
a
t
i
o
n
a
n
d
i
ts
s
i
z
i
n
g
d
es
i
g
n
f
o
r
t
h
is
a
p
p
r
o
a
c
h
.
F
u
r
t
h
e
r
m
o
r
e
,
i
n
l
i
g
h
t o
f
f
a
u
l
t
r
i
d
e
-
t
h
r
o
u
g
h
p
e
r
f
o
r
m
a
n
c
e
u
s
i
n
g
e
n
e
r
g
y
s
t
o
r
a
g
e
d
e
v
i
c
e
s
,
m
a
n
a
g
i
n
g
t
h
e
s
t
o
r
a
g
e
o
f
e
l
e
c
t
r
i
c
a
l
e
n
e
r
g
y
i
n
c
o
n
c
e
r
t
w
it
h
a
d
d
i
t
i
o
n
al
r
e
n
e
w
a
b
l
e
e
n
e
r
g
y
s
o
u
r
c
e
s
a
n
d
s
t
o
r
i
n
g
e
l
e
m
e
n
ts
es
s
e
n
ti
a
l
t
o
a
ch
i
e
v
i
n
g
a
d
a
p
t
i
v
e
D
VS
-
b
a
s
e
d
VF
R
T
o
p
e
r
a
ti
o
n
[
1
9
]
.
T
h
e
d
is
cu
s
s
io
n
ab
o
v
e
m
ak
es
i
t
clea
r
th
at
a
co
n
tr
o
l
s
tr
ateg
y
t
h
at
en
s
u
r
es
a
DVS
th
at
is
r
esp
o
n
s
iv
e
to
s
h
if
tin
g
n
etwo
r
k
in
g
ci
r
cu
m
s
tan
ce
s
am
id
s
ig
n
if
ican
t
v
o
lta
g
e
f
lu
ctu
atio
n
s
an
d
p
er
m
its
VFR
T
m
icr
o
g
r
id
p
er
f
o
r
m
an
ce
in
f
lu
ctu
atin
g
s
y
s
tem
co
n
d
itio
n
s
,
wh
ile
tak
in
g
in
to
ac
co
u
n
t
p
er
h
ap
s
th
e
in
v
o
lv
em
e
n
t
o
f
th
e
m
icr
o
g
r
id
'
s
b
u
ilt
-
in
p
o
wer
r
e
s
er
v
e
,
h
as
n
o
t
y
et
b
ee
n
ac
k
n
o
wled
g
ed
.
B
elo
w
is
th
e
s
u
m
m
ar
y
o
f
th
e
wo
r
k
’
s
p
r
in
cip
al
ac
co
m
p
lis
h
m
en
ts
.
−
Utilizin
g
th
e
ex
tr
em
e
v
o
lta
g
e
tr
ac
k
in
g
(
E
VT
)
m
eth
o
d
,
a
f
le
x
ib
le
DVS
ap
p
r
o
ac
h
d
eter
m
in
es
th
e
m
icr
o
g
r
id
o
u
tp
u
t
ch
ar
ac
ter
is
tics
o
f
ac
tiv
e
cu
r
r
en
t
to
en
ab
le
o
p
tim
al
v
o
lt
ag
e
s
u
p
p
o
r
t
at
th
e
in
ter
co
n
n
ec
t
ed
p
o
in
t
o
f
g
r
id
an
d
in
v
er
ter
,
ca
lled
as
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
PC
C
)
,
an
d
p
r
o
d
u
ce
s
r
ef
e
r
en
ce
v
alu
e
s
f
o
r
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
e
n
t in
th
e
e
v
en
t o
f
an
ex
ter
n
al
v
o
ltag
e
d
ef
ec
t.
−
Flex
ib
le
DVS
with
b
aselin
e
p
ar
am
eter
s
f
o
r
cu
r
r
en
ts
,
f
a
u
lt
d
etec
tio
n
,
a
n
d
en
er
g
y
s
to
r
ag
e
co
n
tr
o
l
ar
e
al
l
co
m
b
in
ed
in
th
is
co
n
tr
o
l m
eth
o
d
to
e
n
ab
le
lo
w
-
v
o
ltag
e
f
a
u
lt
r
id
e
-
th
r
o
u
g
h
f
u
n
ctio
n
in
g
o
f
th
e
s
y
s
tem
.
−
A
n
o
v
el
a
p
p
r
o
ac
h
to
ass
ess
in
g
th
e
r
o
le
o
f
a
m
icr
o
g
r
id
's
en
er
g
y
s
to
r
ag
e
b
ased
o
n
th
e
in
v
er
ter
m
ax
im
u
m
cu
r
r
en
t
r
atin
g
,
th
e
VFR
T
ch
ar
ac
ter
is
tic,
an
d
p
o
ten
tial
ad
v
er
s
e
co
m
p
ar
ab
le
n
etwo
r
k
co
n
f
ig
u
r
atio
n
s
to
ass
e
s
s
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
1608
-
1
6
1
9
1610
wh
eth
er
th
er
e
is
en
o
u
g
h
s
to
r
ag
e
ca
p
ac
ity
o
f
elec
tr
ic
en
er
g
y
to
s
u
p
p
o
r
t
th
e
f
a
u
lt
r
id
e
-
th
r
o
u
g
h
o
p
er
atio
n
with
th
e
s
u
g
g
ested
DVS
ap
p
r
o
ac
h
.
2.
VO
L
T
AG
E
CO
NT
RO
L
AN
D
RE
AC
T
I
V
E
P
O
WE
R
M
A
NAG
E
M
E
N
T
B
Y
M
I
CRO
G
RID
Fig
u
r
e
1
[
4
]
s
h
o
ws
an
id
en
tic
al
n
etwo
r
k
o
f
th
e
s
y
s
tem
.
T
h
e
PV
u
n
it
an
d
in
v
er
ter
r
ep
r
esen
t
a
cu
r
r
en
t
r
eso
u
r
ce
(
⃗
,
)
,
th
e
f
ilter
im
p
ed
a
n
ce
an
d
im
p
ed
a
n
ce
o
f
th
e
lo
c
al
lo
ad
ar
e
m
o
d
elled
with
,
,
th
e
lin
e
im
p
ed
an
ce
th
at
jo
in
s
th
e
s
u
b
s
t
atio
n
with
th
e
m
icr
o
g
r
id
is
d
es
ig
n
ed
as
,
,
th
e
r
em
ain
in
g
lo
ad
im
p
ed
an
ce
a
t
th
e
s
u
b
s
tatio
n
is
tak
en
as
,
,
th
e
f
au
lt
im
p
ed
an
ce
is
g
iv
en
as
,
,
at
th
e
s
u
b
s
tatio
n
,
an
d
it
is
,
b
ey
o
n
d
it
an
d
,
.
T
h
e
f
o
llo
win
g
ex
p
r
ess
io
n
p
r
o
v
id
es
th
e
c
o
r
r
esp
o
n
d
in
g
T
h
ev
e
n
in
im
p
e
d
an
ce
o
b
s
er
v
ed
ac
r
o
s
s
th
e
in
v
er
ter
p
o
in
ts
at
th
e
tim
e
o
f
f
au
lt c
o
n
d
itio
n
s
.
|
ℎ
,
|
∠
=
ℎ
,
+
ℎ
,
=
,
,
+
,
,
,
+
,
+
,
(
1
)
Wh
e
re
(2
):
,
=
,
,
,
,
,
+
.
,
+
,
,
(
2
)
i
n
a
s
im
ilar
v
ein
,
th
e
m
icr
o
g
r
id
'
s
T
h
ev
en
in
v
o
ltag
e
is
lis
te
d
as (
3
)
.
|
ℎ
,
|
∠
=
,
2
,
+
,
,
,
(
,
+
,
)
(
,
2
+
,
2
)
+
×
,
(
3
)
I
n
(
4
)
an
d
(
5
)
.
,
=
,
,
,
+
,
(
4
)
=
2
,
(
,
,
+
,
,
)
+
,
,
,
+
,
,
,
(
5
)
Fig
u
r
e
2
d
ep
icts
a
m
o
d
if
ied
co
m
p
ar
ab
le
cir
c
u
it
with
a
b
alan
ce
d
f
au
lt,
tak
in
g
in
t
o
ac
co
u
n
t
|
ℎ
,
|
∠
an
d
|
ℎ
,
|
∠
.
As a
r
esu
lt,
th
e
in
v
er
ter
v
o
lta
g
e
is
ex
p
r
ess
ed
as
(
6
)
.
,
=
|
ℎ
,
|
∠
+
|
,
×
ℎ
,
|
∠
(
+
)
(
6
)
W
h
er
e
β
is
th
e
an
g
le
m
ad
e
b
y
th
e
in
v
er
ter
cu
r
r
e
n
t
with
th
e
v
o
ltag
e
an
d
|
ℎ
,
|
∠
is
th
e
T
h
ev
en
in
eq
u
iv
alen
t
v
o
ltag
e
n
o
tice
d
at
th
e
co
m
m
o
n
co
u
p
lin
g
p
o
in
t
wh
en
th
e
m
icr
o
g
r
id
is
n
o
t
p
r
o
v
id
in
g
a
n
y
cu
r
r
en
t,
an
d
th
e
s
u
b
s
eq
u
en
t
ter
m
is
th
e
s
u
p
p
o
r
t
v
o
ltag
e
th
at
ca
m
e
ab
o
u
t
as
a
r
esu
lt
o
f
th
e
m
icr
o
g
r
id
's
cu
r
r
en
t
p
r
o
v
is
io
n
.
T
h
e
(
7
)
is
a
d
is
p
lay
o
f
th
e
PC
C
v
o
ltag
e
in
d
icate
d
in
(
6
)
.
|
,
|
=
√
ℎ
,
2
+
2
+
2
|
ℎ
,
×
|
(
−
−
)
(
7
)
W
h
er
e
(
8
)
:
=
,
×
ℎ
,
(
8
)
h
er
e
β
s
tated
p
o
s
itiv
e
s
eq
u
en
c
e
cu
r
r
en
t c
o
m
p
o
n
en
ts
o
f
th
e
m
icr
o
g
r
id
’
s
cu
r
r
en
t.
=
−
1
(
,
(
)
,
(
)
)
(
8
)
W
h
er
e
,
(
)
,
,
(
)
r
ep
r
esen
ts
th
e
r
esp
ec
tiv
e
p
o
s
itiv
e
s
eq
u
en
ce
co
m
p
o
n
en
ts
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
en
ts
o
f
th
e
m
icr
o
g
r
id
.
Usi
n
g
(
7
)
an
d
(
8
)
,
th
e
r
elatio
n
s
h
i
p
th
at
en
s
u
es is
cr
ea
ted
to
attain
h
ig
h
er
v
o
ltag
e
s
ce
n
ar
io
s
.
(
,
(
)
,
(
)
)
=
(
−
)
(
9
)
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
Lo
w
vo
lta
g
e
fa
u
lt
r
id
e
-
th
r
o
u
g
h
o
p
era
tio
n
o
f a
p
h
o
t
o
-
vo
lta
ic
s
ystem
co
n
n
ec
ted
…
(
S
a
ty
a
n
a
r
a
ya
n
a
B
u
r
a
d
a
)
1611
I
t
is
r
ec
o
m
m
en
d
ed
to
o
p
er
ate
t
h
e
m
icr
o
g
r
i
d
as
an
ac
tiv
e
p
o
w
er
s
in
k
at
lo
wer
f
ield
ex
citatio
n
ca
s
es
an
d
an
ac
tiv
e
s
o
u
r
ce
o
f
en
er
g
y
at
h
ig
h
er
ex
c
itatio
n
ca
s
es,
r
esp
ec
tiv
ely
,
to
ac
h
iev
e
th
e
h
ig
h
e
r
an
d
lo
wer
v
alu
es
o
f
v
o
ltag
e
at
th
e
co
m
m
o
n
c
o
u
p
lin
g
p
o
in
t
a
cc
o
r
d
in
g
to
(
9
)
.
T
h
is
in
d
icate
s
th
at
th
e
r
ef
er
en
ce
v
alu
es
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
en
t
s
h
o
u
ld
b
e
n
eg
ativ
e
an
d
p
o
s
itiv
e
f
o
r
th
e
u
n
d
er
-
ex
cita
tio
n
ca
s
es,
an
d
th
e
o
th
e
r
way
ar
o
u
n
d
f
o
r
th
e
o
v
er
-
ex
citatio
n
s
ce
n
ar
io
o
f
th
e
m
ic
r
o
g
r
id
.
T
h
e
cu
r
r
en
t
p
r
o
d
u
ce
d
b
y
th
e
m
icr
o
g
r
id
at
e
x
ce
s
s
iv
e
v
o
l
tag
e
at
th
e
co
m
m
o
n
co
u
p
lin
g
p
o
in
t
is
s
o
lely
d
eter
m
in
ed
b
y
=
−
1
(
ℎ
,
ℎ
,
)
wh
ich
is
ca
lled
as
im
p
ed
an
ce
an
g
le
wh
en
δ
≈
0
(
b
ec
au
s
e
o
f
PLL
s
y
n
ch
r
o
n
izat
io
n
o
r
n
etwo
r
k
co
n
d
itio
n
s
)
.
B
u
t
u
s
u
ally
tan
(
δ
−
ζ
)
is
u
s
ed
to
g
en
er
ate
c
u
r
r
e
n
t
r
ef
er
en
ce
s
in
s
tead
o
f
t
a
n
,
wh
en
δ
≠
0
(
d
u
r
in
g
tr
an
s
ien
ts
)
.
W
ith
r
ef
er
en
ce
to
(
6
)
,
th
e
m
a
x
im
u
m
an
d
lo
west
v
o
ltag
e
m
ag
n
itu
d
es a
r
e
d
ep
en
d
en
t o
n
th
e
v
al
u
es o
f
|
ℎ
,
|
,
|
,
|
an
d
|
ℎ
,
|
.
T
h
ey
r
em
ain
co
n
s
tan
t d
esp
ite
v
ar
iatio
n
s
in
δ
a
n
d
ζ
,
p
r
o
v
id
ed
th
at
,
th
p
u
Z
r
em
ain
s
co
n
s
tan
t.
T
h
e
m
ax
im
u
m
DVS
is
f
ac
ilit
ated
b
y
alter
in
g
th
e
r
ef
er
en
ce
v
alu
es
f
o
r
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
en
ts
(
,
(
)
∗
,
,
(
)
∗
)
o
f
th
e
in
v
er
ter
in
ac
co
r
d
an
ce
with
(
9
)
,
d
ep
en
d
i
n
g
o
n
th
e
o
p
tim
u
m
cu
r
r
en
t
ca
p
ab
ilit
y
o
f
th
e
in
v
er
ter
|
,
|
|
|
lis
ted
b
elo
w
.
T
h
is
is
b
ec
au
s
e
t
h
e
r
atio
o
f
th
e
d
ir
ec
t
an
d
q
u
ad
r
at
u
r
e
co
m
p
o
n
en
ts
o
f
cu
r
r
en
t
in
th
e
in
v
e
r
ter
(
,
(
)
,
,
(
)
)
wh
en
th
e
h
ig
h
est
v
o
ltag
e
is
ac
h
iev
ed
is
r
elied
o
n
δ
o
r
ζ
,
o
r
two
o
f
th
em
,
as sh
o
wn
in
(
9
)
.
√
(
,
(
)
)
2
+
(
,
(
)
)
2
=
|
,
|
|
|
(
1
0
)
V
g
I
i
n
v
M
i
c
r
o
g
r
i
d
L
o
c
a
l
l
o
a
d
a
n
d
f
i
l
t
e
r
s
P
C
C
D
i
s
t
r
i
b
u
t
i
o
n
l
i
n
e
s
a
n
d
s
u
b
s
t
a
t
i
o
n
l
o
a
d
s
F
a
u
l
t
R
e
m
a
i
n
i
n
g
N
e
t
w
o
r
k
Z
f
i
l
t
Z
l
n
Z
e
x
Z
F
Z
m
I
i
n
v
V
t
h
Z
t
h
P
C
C
V
i
n
v
M
I
C
R
O
G
R
I
D
Fig
u
r
e
1
.
An
id
e
n
tical
n
etwo
r
k
o
f
a
m
icr
o
g
r
id
in
ter
f
ac
ed
to
t
h
e
g
r
id
Fig
u
r
e
2
.
Mo
d
if
ied
c
o
m
p
ar
a
b
l
e
cir
cu
it
with
b
alan
ce
d
f
a
u
lt
3.
CO
NT
RO
L
D
E
S
I
G
N
F
O
R
L
VR
T
T
E
CH
NIQU
E
O
F
A
M
I
CRO
G
R
I
D
Fig
u
r
e
3
p
r
esen
ts
an
an
aly
ze
d
s
y
s
tem
f
o
r
g
r
id
g
r
id
-
in
ter
f
ac
e
d
m
icr
o
g
r
id
an
d
a
s
u
g
g
ested
c
o
n
tr
o
llin
g
ap
p
r
o
ac
h
.
I
t
ex
p
a
n
d
s
th
e
an
al
o
g
o
u
s
cir
c
u
it
o
f
Fig
u
r
e
1
.
A
g
r
id
-
co
n
n
ec
ted
in
v
er
te
r
co
n
n
e
cts
th
e
PV
u
n
it
a
n
d
en
er
g
y
s
to
r
ag
e
d
ev
ice,
wh
ich
m
ak
e
u
p
th
e
m
icr
o
g
r
id
,
to
th
e
r
em
ain
in
g
n
etwo
r
k
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
v
ia
th
eir
r
esp
ec
tiv
e
co
n
v
er
ter
s
[
4
]
.
T
h
is
g
r
ap
h
ic
s
h
o
ws th
e
co
n
tr
o
l sch
em
e
u
s
ed
to
allo
w
VFR
T
f
u
n
ctio
n
in
g
o
f
a
m
icr
o
g
r
id
with
an
ad
a
p
tiv
e
d
y
n
am
ic
v
o
lta
g
e
s
u
p
p
o
r
t sch
em
e.
T
h
e
co
n
tr
o
l stra
teg
y
p
r
im
ar
i
ly
co
v
er
s
th
e
g
r
id
-
co
n
n
ec
ted
i
n
v
er
ter
,
en
er
g
y
s
to
r
ag
e
co
n
v
er
ter
,
a
n
d
PV u
n
it c
o
n
v
er
ter
c
o
n
tr
o
ller
s
.
3
.
1
.
P
V
u
nit
c
o
ntr
o
ller
T
h
e
MPPT
alg
o
r
ith
m
is
u
s
ed
to
r
eg
u
late
th
e
u
n
id
ir
ec
tio
n
al
c
o
n
v
er
ter
(
DC
-
DC
)
co
n
n
ec
tin
g
a
PV u
n
it,
allo
win
g
it
to
d
r
aw
th
e
m
ax
im
u
m
p
o
wer
o
u
t
o
f
th
e
PV
u
n
it
ev
en
wh
en
th
e
VFR
T
f
u
n
ctio
n
is
in
p
r
o
g
r
ess
.
T
o
d
o
th
is
,
th
e
MPPT
co
n
tr
o
ller
r
ec
eiv
es
m
ea
s
u
r
ed
d
ata
f
r
o
m
th
e
PV
ter
m
in
al
v
o
ltag
e
an
d
cu
r
r
en
t
(
,
)
wh
ich
it u
s
es to
cr
ea
te
th
e
s
witch
in
g
p
u
ls
es to
th
e
u
n
id
ir
ec
tio
n
al
D
C
-
DC
co
n
v
er
ter
th
r
o
u
g
h
t
h
e
d
u
ty
cy
cle
(
).
3
.
2
.
Co
ntr
o
ller
f
o
r
s
t
o
r
a
g
e
o
f
e
lect
rica
l
e
nerg
y
Pre
d
icate
d
o
n
th
e
DC
b
u
s
s
ig
n
alin
g
m
eth
o
d
o
lo
g
y
,
a
co
n
tr
o
l
m
ec
h
an
is
m
s
ch
em
e
[
20
]
is
d
ev
elo
p
ed
t
o
r
eg
u
late
th
e
in
p
u
t
v
o
ltag
e
f
o
r
th
e
in
v
er
ter
an
d
en
a
b
le
th
e
p
o
wer
co
n
tr
o
l
b
etwe
en
d
if
f
er
en
t
g
ad
g
ets
th
at
co
m
m
u
n
icate
with
th
e
DC
lin
e
.
T
h
e
en
er
g
y
s
to
r
ag
e
o
n
ly
ac
tiv
ates
as
s
o
o
n
as
t
h
e
v
o
ltag
e
at
t
h
e
DC
lin
e
c
h
an
g
es
f
r
o
m
th
e
n
o
m
i
n
al
v
o
ltag
e
(
,
∗
)
b
y
m
o
r
e
th
an
±
2
.
5
%
an
d
r
eg
u
lates
it
with
in
±
5
%.
I
n
co
n
tr
ast,
th
e
in
v
er
ter
r
eg
u
lates
th
e
v
o
ltag
e
at
th
e
D
C
lin
k
u
n
til
±
2
.
5
%
o
f
1
p
u
.
W
ith
r
ef
er
en
ce
to
Fig
u
r
e
3
,
t
h
e
v
o
ltag
e
d
e
v
iatio
n
ass
o
ciate
d
with
th
e
DC
b
u
s
v
o
ltag
e
(
)
is
co
m
p
u
ted
o
n
ce
it
is
ca
lcu
lated
an
d
tr
an
s
f
o
r
m
ed
i
n
to
th
e
p
er
u
n
it
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
1608
-
1
6
1
9
1612
v
alu
e
(
,
)
.
T
h
e
d
ea
d
-
zo
n
e
b
lo
c
k
g
u
ar
an
tees
th
e
d
ev
iatio
n
in
v
o
l
tag
e
th
at
is
g
r
ea
ter
th
a
n
±
2
.
5
%
o
f
,
∗
ar
e
o
n
ly
s
en
t
to
th
e
co
n
tr
o
ller
o
r
r
e
g
u
lato
r
,
wh
ich
u
s
es
th
e
PI
co
n
tr
o
ller
to
g
en
er
ate
,
∗
wh
ich
is
r
ef
er
en
ce
v
alu
e
o
f
th
e
cu
r
r
en
t
in
th
e
e
n
er
g
y
s
to
r
ag
e
d
e
v
ice.
T
h
e
c
u
r
r
en
t
c
o
n
tr
o
llin
g
tech
n
iq
u
e
en
s
u
r
es
th
at
th
e
en
er
g
y
s
to
r
ag
e
u
n
it o
b
s
er
v
ed
p
e
r
u
n
it
cu
r
r
en
t
(
,
)
,
co
m
p
lies
with
th
e
s
u
p
p
lied
b
aselin
e
an
d
p
r
o
d
u
ce
s
th
e
ap
p
r
o
p
r
iate
d
u
ty
cy
cle
(
)
,
wh
ich
g
e
n
er
ates
p
u
ls
e
wid
th
m
o
d
u
latio
n
p
u
ls
es.
T
h
e
DC
cr
o
wb
a
r
tech
n
o
lo
g
y
d
i
s
s
ip
ates
s
u
r
p
lu
s
p
o
wer
in
to
h
ea
t e
n
er
g
y
,
r
estrictin
g
th
e
DC
lin
k
v
o
ltag
e
at
+5
% [
21
].
3
.
3
.
G
rid
-
co
nn
ec
t
ed
inv
er
t
er
co
ntr
o
ller
Acc
o
r
d
in
g
t
o
Fi
g
u
r
e
3
,
t
h
e
in
v
e
r
t
er
co
n
n
e
cte
d
t
o
t
h
e
DC
li
n
k
o
p
e
r
a
tes
d
u
r
i
n
g
VFR
T
o
p
er
ati
o
n
b
y
o
b
tai
n
i
n
g
t
r
i
g
g
er
in
g
p
u
ls
es
t
h
r
o
u
g
h
a
p
u
ls
e
wi
d
t
h
m
o
d
u
lati
o
n
a
p
p
r
o
a
c
h
ac
co
r
d
i
n
g
t
o
t
h
e
r
ec
o
m
m
en
d
ed
r
e
f
e
r
e
n
c
e
v
al
u
es
f
o
r
ac
ti
v
e
a
n
d
r
ea
cti
v
e
c
u
r
r
en
t.
T
h
e
v
o
l
ta
g
e
an
d
cu
r
r
e
n
t
v
al
u
es
o
f
t
h
e
f
il
te
r
(
,
)
,
w
h
i
c
h
a
r
e
t
h
e
lo
ca
l
v
a
r
i
ab
les
,
ar
e
t
r
a
n
s
f
o
r
m
e
d
in
to
v
al
u
es
p
e
r
u
n
i
t
a
n
d
s
u
p
p
lie
d
t
o
t
h
e
c
o
n
t
r
o
lle
r
.
Usi
n
g
t
h
e
P
ar
k
tr
a
n
s
f
o
r
m
ati
o
n
,
a
n
en
h
a
n
ce
d
p
h
ase
-
l
o
c
k
e
d
lo
o
p
(
PLL
)
d
et
er
m
i
n
es t
h
e
d
at
a
r
e
g
a
r
d
in
g
γ
w
h
i
ch
is
t
h
e
p
h
as
e
a
n
g
le
o
f
i
n
v
v
a
n
d
u
s
es
it
to
co
m
p
u
te
th
e
cu
r
r
e
n
t
a
n
d
v
o
lta
g
e
c
o
m
p
o
n
e
n
t
v
a
lu
es
i
n
t
h
e
f
o
r
m
o
f
d
q
-
a
x
is
(
,
(
)
,
,
(
)
)
[
2
2
]
.
I
n
a
d
d
it
io
n
,
,
is
c
o
m
p
ar
ed
t
o
t
h
e
I
E
E
E
1
5
4
7
:
2
0
1
8
s
t
a
n
d
ar
d
s
'
APC
-
I
I
VFR
T
ch
ar
ac
t
er
is
ti
c
i
n
o
r
d
er
t
o
i
d
e
n
ti
f
y
t
h
e
VFR
T
s
tate
an
d
t
o
ac
ti
v
at
e
o
r
d
ea
cti
v
at
e
t
h
e
T
R
I
P
s
i
g
n
al
,
as
wel
l
as
a
s
tr
i
n
g
o
f
VFR
T
ev
en
ts
[
2
]
.
W
h
ile
t
h
e
ac
t
iv
e
cu
r
r
e
n
t
r
ef
er
e
n
c
e
(
,
(
)
∗
)
o
f
th
e
in
v
e
r
te
r
is
o
b
t
ai
n
e
d
d
u
r
i
n
g
s
ta
b
le
o
p
e
r
a
ti
o
n
o
f
t
h
e
s
y
s
t
em
,
th
e
r
ef
er
en
ce
v
al
u
e
f
o
r
r
ea
c
ti
v
e
c
u
r
r
en
t
(
,
(
)
∗
)
c
an
b
e
p
r
o
d
u
c
e
d
t
h
r
o
u
g
h
ap
p
r
o
p
r
i
ate
P
I
co
n
t
r
o
ll
er
s
.
T
h
e
c
u
r
r
e
n
t
c
o
n
t
r
o
ll
er
d
e
v
ic
e,
f
le
x
i
b
l
e
d
y
n
a
m
i
c
v
o
lta
g
e
s
u
p
p
o
r
t
a
p
p
r
o
a
c
h
ta
k
es
t
h
e
u
s
e
o
f
v
o
lt
ag
es
a
lo
n
g
wi
th
in
v
er
t
e
r
c
u
r
r
e
n
ts
i
n
d
q
a
x
is
f
o
r
m
(
,
(
)
,
,
(
)
)
t
o
p
r
o
d
u
c
e
,
(
)
,
(
)
a
n
d
to
m
o
n
it
o
r
t
h
e
r
e
f
e
r
e
n
c
e
v
a
lu
es
o
f
c
u
r
r
e
n
t
s
ig
n
als
[
2
3
]
.
G
R
I
D
M
P
P
T
A
l
g
o
r
i
t
h
i
m
P
W
M
E
n
e
r
g
y
s
t
o
r
a
g
e
d
e
v
i
c
e
p
u
c
o
n
v
e
r
s
i
o
n
S
P
W
M
I
n
v
e
r
t
e
r
d
c
b
u
s
v
o
l
t
a
g
e
c
o
n
t
r
o
l
l
e
r
C
u
r
r
e
n
t
c
o
n
t
r
o
l
l
e
r
A
d
a
p
t
i
v
e
d
y
n
a
m
i
c
v
o
l
t
a
g
e
s
u
p
p
o
r
t
s
c
h
e
m
e
P
u
c
o
n
v
e
r
s
i
o
n
a
b
c
t
o
d
q
c
o
n
v
e
r
s
i
o
n
E
-
P
L
L
D
e
a
d
Z
o
n
e
P
W
M
C
u
r
r
e
n
t
c
o
n
t
r
o
l
l
e
r
E
n
e
r
g
y
s
t
o
r
a
g
e
d
c
b
u
s
v
o
l
t
a
g
e
c
o
n
t
r
o
l
l
e
r
D
C
-
A
C
b
i
d
i
r
e
c
t
i
o
n
a
l
c
o
n
v
e
r
t
e
r
(
g
r
i
d
-
c
o
n
n
e
c
t
e
d
i
n
v
e
r
t
e
r
)
T
r
i
p
V
F
R
T
/
/
/
R
e
a
l
p
o
w
e
r
c
o
n
t
r
o
l
l
e
r
R
e
a
c
t
i
v
e
p
o
w
e
r
c
o
n
t
r
o
l
l
e
r
V
F
R
T
a
n
d
T
R
I
P
d
e
t
e
c
t
i
o
n
P
C
C
V
O
L
T
A
G
E
C
O
N
T
R
O
L
L
E
R
V
F
R
T
V
F
R
T
V
F
R
T
T
R
I
P
V
F
R
T
c
h
a
r
a
c
t
e
r
s
t
i
c
/
/
/
P
V
B
L
O
C
K
~
D
C
-
D
C
b
i
-
d
i
r
e
c
t
i
o
n
a
l
c
o
n
v
e
r
t
e
r
D
C
b
u
s
D
C
-
D
C
u
n
i
d
i
r
e
c
t
i
o
n
a
l
c
o
n
v
e
r
t
e
r
pu
C
o
n
v
e
rs
i
o
n
d
q
t
o
a
b
c
c
o
n
v
e
rs
i
o
n
pv
i
pv
v
pv
D
e
ss
i
,
e
s
s
pu
i
,
e
s
s
pu
i
e
s
s
D
,
dc
pu
v
,
dc
pu
v
dc
v
,
dc
pu
v
()
,
d
pi
pu
i
,
inv
pu
v
()
,
dq
inv
pu
v
()
,
dq
inv
pu
i
()
,
d
inv
pu
i
()
,
q
inv
pu
i
()
,
()
,
q
e
st
pu
d
e
st
pu
I
I
m
a
x
,
inv
pu
I
m
a
x
,
inv
pu
I
()
,
d
inv
pu
i
()
,
q
pi
pu
i
inv
i
inv
v
,
inv
pu
i
,
inv
pu
v
()
,
dq
inv
pu
i
()
,
dq
inv
pu
v
(
)
,
d
inv
pu
v
()
,
()
,
q
e
st
pu
d
e
st
pu
I
I
P
a
s
s
i
v
e
f
i
l
t
e
r
s
P
C
C
Fig
u
r
e
3
.
S
u
g
g
ested
a
co
n
tr
o
ll
er
to
r
eg
u
late
th
e
VFR
T
f
u
n
cti
o
n
in
g
o
f
th
e
s
y
s
tem
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
Lo
w
vo
lta
g
e
fa
u
lt
r
id
e
-
th
r
o
u
g
h
o
p
era
tio
n
o
f a
p
h
o
t
o
-
vo
lta
ic
s
ystem
co
n
n
ec
ted
…
(
S
a
ty
a
n
a
r
a
ya
n
a
B
u
r
a
d
a
)
1613
T
h
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
c
o
n
tr
o
ller
s
,
r
esp
ec
tiv
ely
,
cr
ea
te
th
e
in
v
er
ter
'
s
s
u
itab
le
r
ef
er
en
ce
v
alu
es
f
o
r
th
e
cu
r
r
en
ts
(
()
,
d
i
n
v
p
u
i
,
()
,
q
i
n
v
p
u
i
)
d
ep
en
d
o
n
th
e
s
u
g
g
ested
f
lex
ib
le
DVS
ap
p
r
o
ac
h
,
wh
en
f
au
lt
r
id
e
t
h
r
o
u
g
h
is
o
cc
u
r
r
in
g
cir
c
u
m
s
tan
ce
s
o
n
t
h
e
n
etwo
r
k
(
VFR
T
=
1
)
.
T
h
e
VFR
T
d
etec
tin
g
b
lo
c
k
g
en
er
ates
th
e
T
r
ip
=
0
in
s
tr
u
ctio
n
a
n
d
i
n
ter
r
u
p
ts
th
e
SP
W
M
p
u
ls
es
to
th
e
in
v
er
ter
in
th
e
s
itu
atio
n
w
h
en
t
h
e
v
o
lta
g
e
ch
a
n
g
e
is
g
r
ea
ter
th
an
th
e
s
tan
d
ar
d
d
ev
iatio
n
o
f
VFR
T
[
2
4
]
.
A
DC
b
u
s
an
d
an
ef
f
icien
t
en
er
g
y
s
to
r
ag
e
m
e
ch
an
is
m
attac
h
ed
to
th
e
m
icr
o
g
r
id
ar
e
n
ee
d
ed
f
o
r
t
h
e
s
u
g
g
ested
co
n
tr
o
l
ap
p
r
o
ac
h
u
s
in
g
t
h
e
ad
a
p
tiv
e
DVS
s
ch
e
m
e.
C
o
n
s
eq
u
en
tly
,
th
e
f
o
llo
win
g
s
ec
tio
n
ex
am
i
n
e
s
th
e
f
u
n
ctio
n
o
f
th
e
m
ec
h
a
n
i
s
m
to
s
to
r
e
th
e
en
er
g
y
an
d
th
e
ab
ilit
y
n
ee
d
ed
f
o
r
attain
in
g
th
e
in
ten
d
ed
f
a
u
lt
r
id
e
-
th
r
o
u
g
h
o
p
er
atio
n
.
4.
F
UNCTI
O
N
AND
DE
SI
G
N
O
F
E
NE
RG
Y
S
T
O
RAG
E
D
E
VIC
E
T
o
m
ak
e
th
e
s
u
g
g
ested
DVS
s
ch
em
e
p
o
s
s
ib
le,
en
er
g
y
s
to
r
ag
e
m
u
s
t
p
lay
a
cr
u
cial
r
o
le
in
p
r
eser
v
in
g
th
e
m
icr
o
g
r
id
'
s
DC
b
u
s
v
o
ltag
e.
As
a
r
e
s
u
lt,
th
e
s
to
r
ag
e
d
ev
ice
p
ar
am
eter
s
lik
e
m
ax
im
u
m
en
er
g
y
an
d
m
ax
im
u
m
p
o
wer
ar
e
d
eter
m
i
n
ed
with
a
f
lex
ib
le
d
y
n
am
ic
v
o
ltag
e
ap
p
r
o
ac
h
to
ac
tiv
ate
th
e
f
au
lt
r
id
e
t
h
r
o
u
g
h
p
r
o
ce
s
s
f
o
r
th
e
s
y
s
tem
,
an
d
th
e
am
o
u
n
t o
f
s
to
r
ag
e
o
f
elec
tr
ical
en
er
g
y
th
at
is
av
ailab
le
is
th
en
ass
e
s
s
ed
.
E
n
er
g
y
s
en
t to
th
e
g
r
id
wh
ile
m
ain
tain
in
g
a
c
o
n
s
tan
t
p
o
wer
s
u
p
p
ly
is
f
r
eq
u
en
tl
y
im
p
ac
ted
b
y
v
ar
iatio
n
s
i
n
t
h
e
PC
C
v
o
ltag
e.
A
d
is
p
ar
ity
in
p
o
wer
o
cc
u
r
s
at
th
e
DC
lin
k
wh
en
th
e
m
icr
o
g
r
id
em
p
lo
y
s
th
e
PV
u
n
it'
s
f
u
ll
o
u
tp
u
t
p
o
wer
.
T
h
is
im
b
alan
ce
r
esu
lts
f
r
o
m
th
e
PV
u
n
it'
s
m
ax
im
u
m
p
o
wer
o
u
t
p
u
t
b
ein
g
less
th
an
th
e
p
o
wer
s
u
p
p
lied
u
s
in
g
th
e
in
v
er
ter
.
T
h
e
f
o
llo
win
g
f
o
r
m
u
l
a
p
r
o
v
i
d
es a
ctiv
e
p
o
wer
t
h
at
is
f
ed
in
to
t
h
e
in
v
e
r
ter
.
,
=
,
(
)
×
,
(
)
≤
,
(
1
1
)
W
h
er
e
,
is
th
e
DG
u
n
it's
av
ailab
le
p
o
wer
o
u
t
p
u
t.
No
n
et
h
e
less
,
a
ctiv
e
an
d
r
ea
ctiv
e
cu
r
r
en
ts
m
u
s
t
b
e
m
an
ag
ed
in
o
r
d
er
to
s
u
p
p
ly
f
lex
ib
le
DVS,
o
v
er
VFR
T
p
er
f
o
r
m
an
ce
ac
co
r
d
in
g
t
o
n
etwo
r
k
s
tate
with
in
th
e
in
v
er
ter
c
u
r
r
en
t
ca
p
ac
ity
,
ac
c
o
r
d
in
g
to
t
h
e
s
tu
d
y
co
n
d
u
cted
in
s
ec
tio
n
2
.
I
n
o
r
d
e
r
to
ac
h
i
ev
e
th
e
DVS
wh
ile
en
s
u
r
in
g
th
e
in
v
er
te
r
o
p
er
ates
s
af
ely
,
th
e
v
alu
e
o
f
d
-
a
x
is
cu
r
r
e
n
t
to
q
-
ax
is
cu
r
r
en
t
r
atio
p
u
m
p
ed
f
r
o
m
th
e
in
v
er
te
r
m
u
s
t
th
er
ef
o
r
e
f
o
llo
w
(
9
)
,
an
d
th
e
in
v
er
ter
ca
n
s
u
p
p
l
y
p
e
ak
cu
r
r
e
n
t
th
at
is
s
p
ec
if
ied
i
n
(
1
0
)
.
T
h
e
p
o
wer
im
b
alan
ce
(
,
)
th
at
o
cc
u
r
s
at
th
e
m
icr
o
g
r
id
'
s
DC
b
u
s
d
u
r
in
g
v
o
ltag
e
ch
an
g
es is
p
r
o
v
id
e
d
b
elo
w
u
s
in
g
th
e
ex
p
r
ess
io
n
f
o
r
,
(
)
f
r
o
m
(
1
1
)
,
wh
er
e
r
e
p
r
esen
ts
(
,
−
,
)
lo
w
v
o
ltag
e
co
n
d
itio
n
s
an
d
(
,
+
,
)
r
ep
r
esen
ts
h
ig
h
v
o
ltag
e
c
o
n
d
it
io
n
s
.
,
=
,
∓
,
=
,
∓
,
(
)
×
,
√
1
+
(
,
(
)
,
(
)
)
2
(
1
2
)
T
o
k
ee
p
th
e
DC
b
u
s
v
o
ltag
e
s
tead
y
,
en
er
g
y
s
to
r
ag
e
m
u
s
t
b
e
u
s
ed
to
r
ed
u
ce
t
h
is
b
r
ief
b
u
t
n
o
ticea
b
le
p
o
wer
d
is
p
ar
ity
at
th
e
DC
lin
k
.
Fo
r
l
o
w
v
o
ltag
e
f
au
lt c
o
n
d
itio
n
s
,
(
)
,
d
in
v
p
u
v
is
m
ain
tain
ed
at
1
p
u
,
with
m
a
x
,
i
n
v
p
u
I
=1
.
2
p
u
b
ein
g
th
e
d
ef
au
lt v
al
u
e.
T
h
e
m
in
im
a
l a
n
d
m
ax
im
u
m
g
e
n
er
atio
n
f
r
o
m
th
e
PV u
n
it a
r
e
r
e
p
r
esen
ted
b
y
th
e
co
n
to
u
r
s
f
o
r
,
p
v
p
u
P
=
0
p
u
a
n
d
1
p
u
,
r
e
s
p
e
c
t
i
v
e
l
y
[
2
5
]
.
T
h
e
e
n
e
r
g
y
s
t
o
r
a
g
e
d
e
v
i
c
e
m
u
s
t
c
h
a
r
g
e
i
n
o
r
d
e
r
f
o
r
,
i
m
b
p
u
P
t
o
b
e
p
o
s
i
t
i
v
e
,
a
n
d
v
i
c
e
v
e
r
s
a
.
T
h
e
r
e
f
o
r
e
,
,
i
m
b
p
u
P
c
a
n
b
e
u
s
e
d
t
o
d
e
t
e
r
m
i
n
e
t
h
e
e
n
e
r
g
y
s
t
o
r
a
g
e
d
e
v
i
c
e'
s
m
a
x
i
m
u
m
p
o
w
e
r
r
a
t
i
n
g
.
W
h
e
n
(
)
,
d
in
v
p
u
v
i
s
r
e
p
l
a
c
e
d
i
n
(
1
2
)
w
i
t
h
t
h
e
V
F
R
T
c
h
a
r
a
ct
e
r
is
t
i
c
v
o
l
ta
g
e
,
l
e
t
,
VFRT
im
b
p
u
P
r
e
p
r
e
s
e
n
t
t
h
e
p
o
w
e
r
d
i
s
p
a
r
i
t
y
a
t
t
h
e
D
C
l
i
n
k
o
r
DC
b
u
s
.
t
h
e
e
n
er
g
y
s
t
o
r
a
g
e
d
e
v
i
c
e'
s
n
e
c
es
s
a
r
y
p
o
w
e
r
r
a
t
i
n
g
i
s
p
r
o
v
i
d
e
d
b
y
(
1
3
)
.
,
=
×
(
|
,
|
)
(
1
3
)
W
h
er
e
th
e
s
af
ety
f
ac
to
r
(
s
=1
.
0
5
)
tak
es
in
to
ac
co
u
n
t
th
e
i
m
p
ac
t
o
f
th
e
lo
s
s
es
in
cu
r
r
ed
d
u
r
i
n
g
t
h
e
p
o
wer
co
n
v
er
s
io
n
p
h
ases
.
T
h
e
elec
tr
ical
en
er
g
y
s
wap
p
ed
b
y
th
e
s
to
r
ag
e
d
ev
ice
is
also
p
r
o
v
id
e
d
b
y
(
1
3
)
,
e
n
co
m
p
ass
in
g
th
e
im
p
ac
t
o
f
t
h
e
q
u
a
n
tity
o
f
VFR
T
o
cc
u
r
r
en
ce
s
(
VFRT
N
)
.
T
h
is
is
ex
p
r
ess
ed
in
W
att
-
s
ec
.
=
×
∫
,
×
0
×
(
1
4
)
H
er
e
VFRT
t
is
th
e
VFR
T
ch
ar
ac
ter
is
tic's
tim
e
in
s
ec
o
n
d
s
,
an
d
b
P
is
th
e
b
ase
p
o
wer
to
tr
an
s
f
er
n
o
r
m
al
v
alu
es
in
to
p
er
u
n
it.
T
h
e
n
ec
ess
ar
y
e
n
er
g
y
s
to
r
ag
e
d
e
v
ice'
s
p
o
wer
an
d
en
er
g
y
r
atin
g
s
ar
e
f
o
u
n
d
u
s
in
g
(
1
3
)
an
d
(
1
4
)
.
T
h
is
an
aly
s
is
ca
n
b
e
u
s
ed
as
a
g
u
id
e
to
co
n
f
ir
m
th
at
t
h
e
m
ic
r
o
g
r
id
'
s
cu
r
r
e
n
t
e
n
er
g
y
s
to
r
ag
e
d
ev
ice
is
ad
e
q
u
ate
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
1608
-
1
6
1
9
1614
an
d
,
if
n
ec
ess
ar
y
,
to
u
p
d
ate
it
to
in
co
r
p
o
r
ate
th
e
ap
p
r
o
p
r
iate
en
er
g
y
s
to
r
ag
e
s
o
th
a
t
th
e
f
lex
ib
le
DVS
m
eth
o
d
o
l
o
g
y
ca
n
s
u
p
p
o
r
t V
FR
T
f
u
n
ctio
n
in
g
.
5.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
A
m
icr
o
g
r
id
th
at
s
to
r
es
en
er
g
y
u
s
in
g
s
u
p
er
ca
p
ac
ito
r
s
(
SC
)
an
d
p
h
o
t
o
v
o
ltaic
s
o
lar
p
o
w
er
(
PV)
as
d
is
tr
ib
u
ted
g
en
e
r
ato
r
s
(
DG)
,
d
ep
icted
in
Fig
u
r
e
3
,
is
ex
a
m
in
ed
u
s
in
g
MA
T
L
AB
s
o
f
twar
e
to
s
im
u
late
th
e
s
u
g
g
ested
co
n
tr
o
l
s
tr
ateg
y
'
s
p
er
f
o
r
m
a
n
ce
.
T
ab
le
1
co
n
tain
s
a
lis
t
o
f
th
e
s
y
s
tem
p
ar
am
eter
s
.
T
h
e
b
asic
v
alu
es
tak
en
in
t
o
ac
c
o
u
n
t
f
o
r
ea
c
h
u
n
it
co
n
v
er
s
io
n
ar
e
5
0
Hz
f
o
r
f
r
eq
u
en
c
y
,
4
1
5
V
f
o
r
AC
v
o
ltag
e,
an
d
1
0
k
VA
f
o
r
AC
p
o
wer
an
d
1
0
k
W
f
o
r
DC
p
o
wer
.
Sin
ce
s
y
m
m
etr
ical
f
au
l
ts
ty
p
ically
h
av
e
th
e
wo
r
s
t
p
o
s
s
ib
le
im
p
ac
t
wi
th
in
th
e
s
y
s
tem
,
in
co
n
tr
ast
to
d
if
f
er
en
t
k
in
d
s
o
f
f
ailu
r
es,
o
n
l
y
s
y
m
m
etr
ical
f
au
lts
ar
e
ta
k
en
i
n
to
ac
co
u
n
t
in
t
h
is
s
im
u
latio
n
s
tu
d
y
.
I
t
is
ass
u
m
e
d
th
at
t
h
e
in
v
er
ter
h
as
a
m
ax
i
m
u
m
c
u
r
r
en
t
r
atin
g
o
f
1
.
2
p
u
.
A
p
o
s
itiv
e
ac
tiv
e
p
o
wer
v
alu
e
is
in
ter
p
r
eted
as
it
is
d
eliv
er
ed
to
th
e
DC
lin
k
o
r
DC
b
u
s
th
r
o
u
g
h
o
u
t
th
is
s
ec
tio
n
,
an
d
co
n
v
er
s
ely
.
C
o
m
p
ar
ab
ly
,
r
ea
ctiv
e
p
o
wer
t
h
at
is
p
o
s
itiv
e
in
d
icate
s
th
at
r
e
ac
tiv
e
p
o
wer
is
b
ei
n
g
ad
d
e
d
to
th
e
g
r
id
.
T
h
is
s
tu
d
y
tak
es in
t
o
ac
co
u
n
t t
h
e
m
ax
im
u
m
PV
u
n
it
g
en
er
atio
n
at
ev
e
r
y
s
tag
e.
5
.
1
.
L
o
w
v
o
lt
a
g
e
f
a
ult
ride
-
t
hro
ug
h
o
pera
t
io
n f
o
r
f
a
ult
v
o
lt
a
g
e
wit
hin
VF
RT
cha
ra
ct
er
is
t
ics
T
h
e
lo
w
-
v
o
ltag
e
r
id
e
-
th
r
o
u
g
h
(
L
VR
T
)
o
p
er
atio
n
o
f
th
e
m
icr
o
g
r
id
is
p
r
esen
ted
i
n
th
is
ch
ap
ter
.
Fig
u
r
e
4
s
h
o
ws
th
e
ir
r
ad
iatio
n
cu
r
v
e
d
u
r
in
g
t
h
e
co
u
r
s
e
o
f
2
0
s
ec
o
n
d
s
.
Fig
u
r
e
5
illu
s
tr
a
tes
h
o
w
th
e
MPPT
co
n
tr
o
ller
tr
ac
k
s
th
e
MPP with
9
9
p
er
ce
n
t e
f
f
icien
cy
.
T
h
e
s
y
s
tem
ex
p
er
ien
ce
s
a
3
-
φ
f
au
lt a
t
3
.
5
s
ec
f
o
r
tim
e
o
f
2
s
,
c
r
ea
tin
g
a
v
o
ltag
e
o
f
0
.
6
7
1
p
e
r
u
n
it a
t
th
e
p
o
in
t
o
f
co
m
m
o
n
c
o
u
p
lin
g
(
PC
C
)
.
T
h
er
ef
o
r
e,
th
e
VFR
T
p
u
ls
e
is
ac
tiv
ated
d
u
r
in
g
th
e
f
au
lt tim
e
,
an
d
th
e
VFR
T
d
etec
tin
g
b
lo
c
k
g
en
er
ates th
e
T
R
I
P=1
in
s
tr
u
ctio
n
an
d
c
o
n
tin
u
es
th
e
SP
W
M
p
u
ls
es
to
th
e
in
v
e
r
ter
if
t
h
er
e
is
a
v
o
ltag
e
d
is
r
u
p
t
io
n
with
in
th
e
VFR
T
ch
ar
ac
te
r
is
tics
(
as
s
h
o
wn
in
Fig
u
r
es 6
(
a
)
-
6
(
c)
)
.
W
h
en
a
lo
w
v
o
ltag
e
f
a
u
lt
o
cc
u
r
s
,
th
e
in
v
er
ter
u
s
es
its
1
.
2
p
u
o
v
e
r
-
cu
r
r
en
t
lim
it
an
d
b
e
g
in
s
in
jectin
g
ac
tu
al
an
d
r
ea
ctiv
e
cu
r
r
en
t
b
ased
o
n
as
s
h
o
wn
in
Fig
u
r
e
7
.
Ac
co
r
d
in
g
l
y
,
as
s
ee
n
in
Fig
u
r
e
8
,
th
e
in
v
e
r
ter
'
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
is
d
eliv
er
ed
in
to
th
e
s
y
s
tem
.
Fu
r
th
er
m
o
r
e,
Fig
u
r
e
9
s
h
o
ws
th
e
ac
tu
a
l
p
o
wer
ex
ch
a
n
g
ed
b
etwe
en
th
e
e
n
er
g
y
s
to
r
ag
e
d
e
v
ice,
th
e
i
n
v
er
ter
,
an
d
th
e
PV
u
n
it.
T
o
k
ee
p
th
e
v
o
ltag
e
at
th
e
DC
lin
k
o
r
DC
b
u
s
ar
o
u
n
d
±
1
.
0
5
p
u
,
th
e
en
er
g
y
s
to
r
ag
e
s
y
s
tem
'
s
e
lectr
ical
p
o
wer
s
u
p
p
ly
is
m
o
d
if
ied
b
ased
o
n
th
e
ch
an
g
e
in
r
ea
l
p
o
wer
o
f
th
e
in
v
er
ter
.
As
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
P
C
C
)
v
o
ltag
e
d
o
es
n
o
t
b
ec
o
m
e
less
th
an
th
e
L
V
R
T
v
o
ltag
e
d
u
r
in
g
th
e
f
au
lt
tim
e,
th
e
in
v
er
ter
r
em
ain
s
c
o
n
n
ec
te
d
to
th
e
g
r
id
,
s
u
p
p
lies
r
ea
ctiv
e
p
o
wer
(
s
ee
Fig
u
r
e
1
0
)
,
a
n
d
p
r
o
v
i
d
es
a
d
ep
e
n
d
ab
le
with
s
tead
y
f
au
lt
r
id
e
-
th
r
o
u
g
h
f
u
n
ctio
n
in
g
with
n
o
ef
f
ec
t
o
n
th
e
PV
ar
r
ay
'
s
MPPT
p
er
f
o
r
m
an
ce
.
W
ith
th
e
s
u
g
g
ested
co
n
tr
o
l
tech
n
iq
u
e,
th
e
v
o
ltag
e
at
th
e
co
m
m
o
n
co
u
p
lin
g
p
o
in
t
is
in
cr
ea
s
ed
to
0
.
9
2
p
u
an
d
th
e
in
v
er
ter
s
u
p
p
lies
r
ea
ctiv
e
p
o
wer
till
th
e
PC
C
v
o
ltag
e
r
ea
ch
es
its
n
o
m
in
al
v
alu
e.
(
r
ef
er
to
Fig
u
r
es 1
1
a
n
d
1
2
)
.
Fig
u
r
e
4
.
I
r
r
ad
iatio
n
cu
r
v
e
Fig
u
r
e
5
.
MPPT
e
f
f
icien
c
y
T
ab
le
1
.
Sy
s
tem
s
p
ec
if
icatio
n
s
P
a
r
a
me
t
e
r
V
a
l
u
e
P
V
U
n
i
t
1
5
mo
d
u
l
e
s
o
f
3
7
.
3
V
(
v
o
l
t
a
g
e
a
t
M
P
P
)
,
8
.
6
6
A
(
c
u
r
r
e
n
t
a
t
M
P
P
)
;
1
0
k
W
(
p
o
w
e
r
a
t
M
P
P
)
S
u
p
e
r
c
a
p
a
c
i
t
o
r
b
a
n
k
2
0
u
n
i
t
s
o
f
1
3
0
F
,
5
0
V
mo
d
u
l
e
s
DC
-
D
C
u
n
i
d
i
r
e
c
t
i
o
n
a
l
c
o
n
v
e
r
t
e
r
10
k
W
,
4
1
5
/
4
1
5
V
,
1
0
k
H
z
I
n
v
e
r
t
e
r
c
o
n
n
e
c
t
e
d
t
o
t
h
e
g
r
i
d
3
p
h
a
se
,
4
1
5
(
D
C
)
/
4
1
5
V
(
A
C
)
,
1
0
k
V
A
,
1
0
k
H
z
F
i
l
t
e
r
s
4
5
0
V
A
R
,
3
p
h
,
C
fi
l
t
e
r
,
L
f
i
l
t
e
r
L
=
6
mH
Th
r
e
e
-
p
h
a
s
e
t
r
a
n
sf
o
r
mers
2
2
0
/
4
1
5
V
,
1
0
k
V
A
,
w
i
n
d
i
n
g
1
c
o
n
n
e
c
t
i
o
n
(
Y
g
)
,
w
i
n
d
i
n
g
2
c
o
n
n
e
c
t
i
o
n
(
D
e
l
t
a
(
D
1
)
)
R
e
st
o
f
t
h
e
n
e
t
w
o
r
k
3
p
h
a
se
,
4
1
5
V
,
5
0
H
z
,
s
h
o
r
t
c
i
r
c
u
i
t
r
a
t
i
o
=
8
,
X
/
R
r
a
t
i
o
=
0
.
5
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
Lo
w
vo
lta
g
e
fa
u
lt
r
id
e
-
th
r
o
u
g
h
o
p
era
tio
n
o
f a
p
h
o
t
o
-
vo
lta
ic
s
ystem
co
n
n
ec
ted
…
(
S
a
ty
a
n
a
r
a
ya
n
a
B
u
r
a
d
a
)
1615
(
a)
(
b
)
(
c)
Fig
u
r
e
6
.
Fau
lt
r
i
d
e
-
th
r
o
u
g
h
p
ar
am
eter
s
:
(
a)
L
VR
T
&
PC
C
v
o
ltag
e
,
(
b
)
L
VR
T
p
u
ls
e
,
an
d
(
c)
T
R
I
P si
g
n
al
Fig
u
r
e
7
.
I
n
v
er
te
r
lin
e
cu
r
r
en
ts
Fig
u
r
e
8
.
I
n
v
er
te
r
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
Fig
u
r
e
9
.
R
ea
l p
o
wer
o
f
m
ic
r
o
g
r
id
co
m
p
o
n
e
n
ts
Fig
u
r
e
1
0
.
R
ea
ctiv
e
p
o
wer
f
r
o
m
th
e
in
v
er
te
r
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
1608
-
1
6
1
9
1616
Fig
u
r
e
1
1
.
PC
C
p
h
ase
v
o
ltag
es
Fig
u
r
e
1
2
.
PC
C
p
h
ase
v
o
ltag
es in
a
m
ag
n
if
ied
v
iew
5
.
2
.
L
o
w
VF
RT
o
pera
t
io
n f
o
r
f
a
ult
v
o
lt
a
g
e
e
x
ce
eds
VF
RT
c
ha
ra
ct
er
is
t
ics
T
h
e
L
VR
T
p
r
o
ce
s
s
o
f
t
h
e
m
icr
o
g
r
id
,
i
f
th
e
v
o
ltag
e
v
al
u
e
at
P
C
C
ex
ce
ed
s
th
e
VFR
T
ch
ar
ac
ter
is
tics
,
i
s
p
r
esen
ted
in
th
is
ch
ap
ter
.
T
h
e
s
y
s
tem
ex
p
er
ien
ce
s
a
3
-
φ
f
au
lt
with
lo
w
f
au
lt im
p
ed
an
ce
at
3
.
5
s
ec
f
o
r
a
tim
e
o
f
2
s
,
cr
ea
tin
g
a
v
o
ltag
e
at
PC
C
l
ess
th
an
VFR
T
ch
ar
ac
ter
is
tics
as
s
h
o
wn
in
Fig
u
r
e
1
3
.
I
n
F
ig
u
r
e
1
3
,
it
is
o
b
s
er
v
ed
th
at
th
e
PC
C
v
o
ltag
e
at
3
.
8
s
e
c
is
0
.
4
9
p
u
,
wh
ich
is
less
th
an
th
e
VFR
T
ch
ar
ac
ter
is
tics
.
T
h
er
ef
o
r
e,
th
e
VFR
T
p
u
ls
e
is
ac
tiv
ated
d
u
r
in
g
th
e
f
a
u
lt
tim
e
,
an
d
th
e
VFR
T
d
etec
tin
g
b
lo
c
k
g
en
er
ates
th
e
T
R
I
P
=
0
in
s
tr
u
ctio
n
an
d
in
ter
r
u
p
ts
th
e
SP
W
M
p
u
ls
es
t
o
th
e
in
v
er
ter
if
th
e
r
e
is
a
v
o
ltag
e
d
is
r
u
p
tio
n
th
at
ex
ce
ed
s
th
e
VFR
T
ch
ar
ac
ter
is
tics
(
r
ef
er
t
o
Fig
u
r
es
1
4
(
a
)
a
n
d
14
(
b
)
)
.
W
h
en
th
e
VFR
T
d
etec
tin
g
b
l
o
ck
g
en
er
ates
th
e
T
R
I
P
=
0
in
s
tr
u
ctio
n
an
d
i
n
ter
r
u
p
ts
th
e
SP
W
M
p
u
ls
es
to
th
e
in
v
er
ter
,
th
er
e
is
n
o
c
o
n
n
ec
tio
n
b
etwe
en
th
e
in
v
er
ter
an
d
th
e
g
r
id
.
T
h
er
ef
o
r
e,
th
e
in
v
er
te
r
ca
n
n
o
t tr
an
s
f
er
cu
r
r
en
ts
to
th
e
g
r
id
as sh
o
wn
in
Fig
u
r
e
1
5
.
Fu
r
th
er
m
o
r
e
,
Fig
u
r
e
1
6
s
h
o
w
s
th
e
ac
tu
al
p
o
wer
ex
c
h
an
g
e
d
b
etwe
en
th
e
en
er
g
y
s
to
r
ag
e
d
ev
ice,
th
e
in
v
er
ter
,
a
n
d
th
e
PV
u
n
it.
W
h
en
th
e
g
r
i
d
is
d
is
co
n
n
ec
ted
f
r
o
m
th
e
in
v
er
te
r
,
th
e
PV
p
o
wer
i
s
tr
an
s
f
er
r
ed
to
t
h
e
s
to
r
ag
e
d
e
v
ice.
T
o
k
e
ep
t
h
e
v
o
ltag
e
at
t
h
e
DC
lin
k
o
r
DC
b
u
s
ar
o
u
n
d
±
1
.
0
5
p
u
,
th
e
en
er
g
y
s
to
r
ag
e
s
y
s
tem
'
s
elec
tr
ical
p
o
wer
s
u
p
p
ly
is
m
o
d
if
ied
b
ased
o
n
th
e
ch
a
n
g
e
in
r
e
al
p
o
wer
o
f
th
e
in
v
er
ter
.
Fu
r
th
er
m
o
r
e
,
as
s
ee
n
in
Fig
u
r
e
1
7
,
th
e
in
v
er
ter
'
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
is
d
eliv
er
ed
in
t
o
th
e
s
y
s
tem
.
I
t is o
b
s
er
v
ed
i
n
Fig
u
r
e
1
7
t
h
at
th
e
in
v
er
te
r
s
u
p
p
lies
r
ea
ctiv
e
p
o
wer
f
r
o
m
f
a
u
lt o
cc
u
r
r
en
ce
tim
e
(
3
.
5
s
ec
)
to
3
.
8
s
ec
,
wh
en
t
h
e
in
v
er
ter
d
is
co
n
n
ec
ts
f
r
o
m
th
e
g
r
id
n
etwo
r
k
t
h
er
e
is
n
o
p
o
wer
tr
a
n
s
f
er
ta
k
es
p
la
ce
f
r
o
m
th
e
in
v
er
ter
to
th
e
g
r
id
n
etwo
r
k
.
As
th
e
in
v
er
ter
is
d
is
co
n
n
ec
ted
f
r
o
m
th
e
u
tili
ty
g
r
id
at
3
.
8
s
ec
,
af
ter
t
h
e
f
au
lt
clea
r
an
ce
,
th
e
v
o
ltag
e
at
PC
C
will b
e
eq
u
al
t
o
th
e
g
r
id
n
o
m
in
al
v
o
ltag
e
,
th
a
t is 1
p
u
as d
ep
icted
in
Fig
u
r
e
1
8
.
T
h
e
PC
C
p
h
ase
v
o
ltag
es in
th
e
zo
o
m
ed
v
er
s
io
n
ar
e
s
h
o
wn
i
n
Fig
u
r
e
19.
Fig
u
r
e
1
3
.
L
VR
T
an
d
PC
C
v
o
ltag
es
(
a)
(
b
)
Fig
u
r
e
1
4
.
Fau
lt
r
id
e
-
th
r
o
u
g
h
p
ar
am
eter
s
:
(
a)
L
VR
T
p
u
ls
e
a
n
d
(
b
)
T
R
I
P si
g
n
al
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
Lo
w
vo
lta
g
e
fa
u
lt
r
id
e
-
th
r
o
u
g
h
o
p
era
tio
n
o
f a
p
h
o
t
o
-
vo
lta
ic
s
ystem
co
n
n
ec
ted
…
(
S
a
ty
a
n
a
r
a
ya
n
a
B
u
r
a
d
a
)
1617
Fig
u
r
e
1
5
.
I
n
v
e
r
ter
lin
e
c
u
r
r
en
ts
Fig
u
r
e
1
6
.
R
ea
l p
o
wer
o
f
m
icr
o
g
r
id
c
o
m
p
o
n
en
ts
Fig
u
r
e
1
7
.
I
n
v
e
r
ter
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
Fig
u
r
e
1
8
.
PC
C
p
h
ase
v
o
ltag
es
Fig
u
r
e
1
9
.
PC
C
p
h
ase
v
o
ltag
es in
a
m
ag
n
if
ied
v
iew
6.
CO
NCLU
SI
O
N
T
h
e
liter
atu
r
e
th
at
is
n
o
w
ac
ce
s
s
ib
le
ad
d
r
ess
es
VFR
T
p
r
o
b
le
m
s
;
h
o
wev
er
,
its
ap
p
r
o
ac
h
es
d
o
n
o
t
tak
e
in
to
ac
co
u
n
t
th
e
v
ar
y
i
n
g
n
etwo
r
k
s
itu
atio
n
s
p
r
esen
t
am
id
s
y
s
tem
m
alf
u
n
ctio
n
s
.
I
n
s
tead
,
th
e
y
ar
e
s
o
lely
o
n
r
ea
l,
p
u
r
ely
o
n
r
ea
ctiv
e
cu
r
r
en
t,
o
r
a
m
ix
o
f
th
e
two
.
I
n
t
h
is
wo
r
k
,
a
co
n
tr
o
l
ap
p
r
o
ac
h
t
h
at
m
ak
e
s
u
s
e
o
f
th
e
en
er
g
y
s
to
r
ag
e
s
y
s
tem
'
s
as
s
is
tan
ce
is
p
r
o
v
id
e
d
,
a
n
d
its
ef
f
ec
tiv
e
n
ess
is
ass
e
s
s
ed
f
o
r
a
r
a
n
g
e
o
f
o
p
er
atin
g
s
ce
n
ar
i
o
s
,
in
clu
d
in
g
Sev
er
al
is
s
u
es
r
elate
d
to
v
ar
io
u
s
f
a
u
lt
v
o
ltag
es
an
d
lo
w
VFR
T
.
I
n
o
r
d
er
to
en
s
u
r
e
th
e
b
est
DVS
p
o
s
s
ib
le,
th
e
p
r
o
p
o
s
ed
DVS
tech
n
iq
u
e
ad
ap
tiv
ely
d
eter
m
in
es
th
e
m
icr
o
g
r
id
'
s
ac
tu
al
an
d
r
ea
ctiv
e
cu
r
r
en
t
o
u
tp
u
t
ac
co
r
d
in
g
t
o
v
ar
io
u
s
cir
cu
m
s
tan
ce
s
d
ev
elo
p
in
g
th
r
o
u
g
h
o
u
t
th
e
VFR
T
p
r
o
ce
d
u
r
e.
W
ith
th
e
s
u
g
g
ested
co
n
tr
o
l
s
tr
ateg
y
,
it
h
as
b
ee
n
s
h
o
wn
th
at
a
m
icr
o
g
r
id
r
u
n
n
i
n
g
at
m
in
i
m
al
VFR
T
v
alu
es
is
ca
p
ab
le
o
f
s
u
p
p
ly
in
g
f
le
x
ib
le
v
o
ltag
e
ass
is
tan
ce
f
o
r
u
n
a
n
t
icip
ated
f
au
lt
in
cid
e
n
ts
with
in
th
e
g
r
id
,
g
u
a
r
an
teein
g
t
h
e
in
v
er
ter
'
s
s
ec
u
r
e
f
u
n
ctio
n
in
g
b
y
ab
id
i
n
g
b
y
th
e
m
ax
im
u
m
c
u
r
r
e
n
t
lim
it,
an
d
i
m
p
r
o
v
in
g
th
e
u
tili
ty
g
r
id
'
s
VFR
T
ca
p
ab
ilit
y
b
y
to
ler
atin
g
m
o
r
e
s
ev
er
e
f
a
u
lts
.
T
h
is
wo
r
k
'
s
s
izin
g
tech
n
iq
u
e
f
o
r
th
e
s
to
r
ag
e
d
e
v
ice'
s
n
ec
ess
ar
y
p
o
wer
r
atin
g
s
er
v
es
as
a
g
u
id
e
f
o
r
ad
ap
tin
g
t
h
e
en
er
g
y
s
to
r
ag
e
th
at
is
p
r
esen
tly
ac
ce
s
s
ib
le
to
war
d
s
m
o
d
est
VFR
T
r
u
n
n
in
g
o
n
a
m
icr
o
g
r
id
.
Fu
tu
r
e
r
esear
ch
m
ig
h
t
ex
a
m
in
e
h
o
w
th
e
m
icr
o
g
r
id
f
u
n
ctio
n
s
in
u
n
b
alan
ce
d
f
au
lt
s
ce
n
ar
io
s
,
an
d
s
u
g
g
est
a
s
tr
ateg
y
f
o
r
m
an
a
g
in
g
th
e
f
lex
ib
le
DVS
th
at
m
a
k
es
u
s
e
o
f
b
o
t
h
co
m
p
o
n
e
n
ts
o
f
v
o
ltag
e
an
d
c
u
r
r
en
t
i
n
th
e
p
o
s
itiv
e
an
d
n
eg
ativ
e
s
eq
u
en
ce
th
r
o
u
g
h
o
u
t V
FR
T
f
u
n
cti
o
n
in
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.