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6
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4
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I
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IJ
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4
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2
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1
6
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4
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[
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te
d
in
liter
atu
r
e
[
1
4
]
-
[
1
5
]
.
T
h
e
g
r
id
-
s
id
e
co
n
v
er
ter
(G
S
C)
co
n
tr
o
ls
t
h
e
D
C
b
u
s
v
o
ltag
e
a
n
d
r
ea
cti
v
e
p
o
w
er
tr
a
n
s
f
er
to
t
h
e
u
tili
t
y
g
r
id
[
1
2
]
.
T
h
e
co
n
tr
o
l
o
f
G
S
C
i
s
b
id
ir
ec
tio
n
al
to
f
ac
ilit
ate
t
h
e
f
lo
w
o
f
p
o
w
er
f
r
o
m
th
e
m
icr
o
-
g
r
id
to
u
tili
t
y
a
n
d
v
ice
v
er
s
a
i
n
s
tead
o
f
o
n
e
-
w
a
y
o
p
er
atio
n
as in
d
icate
d
in
[
1
3
]
.
As
in
m
an
y
o
th
er
p
o
w
er
ap
p
li
ca
tio
n
s
,
elec
tr
o
l
y
tic
ca
p
ac
ito
r
s
an
d
p
o
w
er
s
w
i
tch
e
s
ar
e
th
e
m
o
s
t
li
k
el
y
co
m
p
o
n
e
n
t
s
to
f
ail
in
p
o
w
e
r
co
n
v
er
ter
s
,
b
ec
au
s
e
th
e
y
ar
e
ex
p
o
s
ed
to
h
ig
h
m
ec
h
a
n
ical
a
n
d
t
h
er
m
al
s
tr
ess
e
s
[
1
6
]
-
[
1
7
]
.
A
n
ex
ce
s
s
o
f
elec
tr
ical
an
d
th
er
m
al
s
tr
ess
es
is
t
h
e
m
ai
n
ca
u
s
e
f
o
r
th
e
f
ail
u
r
e
o
f
p
o
w
er
s
w
itc
h
es,
w
h
ic
h
ca
n
b
e
class
i
f
ied
as
o
p
en
-
cir
cu
it
an
d
s
h
o
r
t
-
c
ir
cu
it
f
a
u
lt
s
[
1
8
]
.
Sh
o
r
t
-
cir
cu
i
t
f
au
lt
p
r
o
tectio
n
is
alr
ea
d
y
a
s
ta
n
d
ar
d
p
r
ac
tice
in
t
eg
r
ated
in
m
o
s
t p
o
w
er
s
w
i
tch
e
s
d
r
iv
es [
1
9
]
.
A
f
ailu
r
e
i
n
th
e
DC
–
D
C
co
n
v
er
ter
w
ill
af
f
ec
t
th
e
w
h
o
le
P
V
s
y
s
te
m
a
n
d
it
m
i
g
h
t
lead
to
its
s
to
p
p
ag
e,
s
in
ce
it
i
s
d
ir
ec
tl
y
co
n
n
ec
ted
to
th
e
ar
r
ay
s
[
4
]
.
Fu
r
th
er
m
o
r
e
,
a
f
ailu
r
e
i
n
th
e
G
SC
ca
n
en
d
an
g
er
s
t
h
e
o
v
er
all
sy
s
te
m
a
n
d
lead
s
to
it
d
is
co
n
n
ec
t
in
g
[
2
0
]
.
Hen
ce
,
to
r
ed
u
ce
th
e
f
ail
u
r
e
r
ate
an
d
to
p
r
ev
en
t
u
n
s
ch
ed
u
led
s
h
u
td
o
w
n
,
r
ea
l
-
ti
m
e
f
a
u
lt
d
ete
ctio
n
,
is
o
latio
n
a
n
d
co
m
p
en
s
a
tio
n
s
ch
e
m
e
i
s
n
ec
es
s
ar
y
to
e
n
s
u
r
e
co
n
ti
n
u
i
t
y
o
f
s
er
v
ice.
R
ec
en
t
l
y
,
s
ev
er
al
p
ap
er
s
h
av
e
s
tu
d
ied
f
a
u
lt
d
ia
g
n
o
s
is
m
et
h
o
d
s
in
p
o
w
er
elec
tr
o
n
ic
co
n
v
er
ter
s
.
Fau
l
t
d
iag
n
o
s
i
s
i
n
th
e
p
o
w
er
co
n
v
e
r
s
io
n
s
tag
e
o
f
a
g
r
id
-
co
n
n
ec
te
d
P
V
s
y
s
te
m
is
p
r
esen
ted
in
[
3
]
.
A
f
a
u
lt
-
to
ler
an
t
s
tr
ateg
y
f
o
r
a
P
V
DC
–
DC
co
n
v
er
ter
is
s
tu
d
ied
in
[
4
]
.
T
h
e
g
r
id
cu
r
r
en
ts
a
n
d
r
o
o
t
m
ea
n
s
q
u
ar
e
cu
r
r
en
ts
ar
e
u
s
ed
f
o
r
o
p
en
-
s
w
itc
h
f
a
u
lt
-
to
ler
an
t
co
n
tr
o
l
in
a
g
r
id
-
s
id
e
co
n
v
er
ter
o
f
a
w
in
d
p
o
w
er
g
en
er
atio
n
s
y
s
te
m
in
[
2
0
]
.
A
FP
GA
-
b
ased
o
p
en
-
an
d
s
h
o
r
t
-
cir
c
u
it
s
w
itc
h
f
a
u
lt
d
iag
n
o
s
is
f
o
r
n
o
n
-
is
o
lated
DC
–
DC
co
n
v
er
ter
s
w
a
s
p
r
o
p
o
s
ed
in
[
2
1
]
.
A
f
a
u
lt
s
d
ia
g
n
o
s
is
i
n
f
i
v
e
-
le
v
el
t
h
r
ee
-
p
h
ase
s
h
u
n
t
ac
ti
v
e
p
o
w
er
f
ilter
u
s
in
g
o
u
tp
u
t
v
o
ltag
e
s
to
d
eter
m
i
n
e
th
e
o
p
en
f
a
u
lt
tr
an
s
is
to
r
is
p
r
o
p
o
s
ed
in
[
2
2
]
.
A
f
a
u
lt
-
to
ler
an
t
DC
–
DC
co
n
v
er
ter
to
p
o
lo
g
y
b
ased
o
n
r
ed
u
n
d
an
c
y
i
s
p
r
o
p
o
s
ed
in
[
2
3
]
.
A
f
a
u
lt
d
iag
n
o
s
i
s
b
ased
o
n
DC
-
lin
k
c
u
r
r
en
t
p
u
l
s
e
s
h
ap
es
o
f
a
Z
V
S
DC
–
D
C
co
n
v
er
ter
is
p
r
o
p
o
s
ed
in
[
2
4
]
.
A
n
d
o
p
en
s
w
itc
h
f
a
u
lt
to
ler
an
t
s
ix
-
le
g
s
A
C
-
DC
-
AC
in
DFI
G
b
ased
W
E
C
S is
p
r
esen
ted
in
[
2
5
]
.
T
h
is
p
ap
er
p
r
esen
ts
a
n
e
w
d
ev
elo
p
ed
ap
p
r
o
ac
h
f
au
lt
-
to
ler
an
t
co
n
tr
o
l
o
f
a
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
te
m
.
W
e
ex
a
m
i
n
e
th
e
f
a
u
lt
-
to
ler
an
t
co
n
tr
o
l
an
d
th
e
r
esp
o
n
s
e
o
f
th
e
P
V
s
y
s
te
m
w
h
e
n
an
o
p
en
-
s
w
itc
h
f
au
l
t
h
as
o
cc
u
r
r
ed
in
o
n
e
o
f
th
e
p
o
w
er
s
w
itc
h
es
i
n
D
C
–
DC
co
n
v
er
ter
o
r
G
SC
co
n
v
er
ter
.
A
b
r
ief
d
escr
ip
tio
n
o
f
th
e
s
y
s
te
m
in
c
l
u
d
in
g
its
m
o
d
elli
n
g
a
n
d
co
n
tr
o
l
s
tr
ateg
ies
ar
e
p
r
esen
ted
in
s
ec
tio
n
s
2
,
f
o
llo
w
ed
b
y
a
d
etailed
e
x
p
la
n
atio
n
o
f
t
h
e
f
a
u
lt
-
to
ler
an
t
s
tr
ate
g
y
an
d
th
e
f
a
u
lt
-
d
etec
tio
n
m
et
h
o
d
i
n
s
ec
tio
n
s
3
a
n
d
4
,
r
esp
ec
tiv
el
y
.
T
h
e
r
esu
lt
s
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
ies
ar
e
p
r
esen
ted
an
d
d
is
c
u
s
s
ed
in
s
e
ctio
n
5
to
v
alid
at
e
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
2.
G
RI
D
-
CO
NNE
CT
E
D
P
H
O
T
O
VO
L
T
AIC
SYS
T
E
M
O
VE
RVI
E
W
T
h
e
s
tu
d
ied
s
y
s
te
m
i
s
s
h
o
w
n
in
Fi
g
u
r
e
1
.
T
h
e
P
V
ar
r
ay
is
c
o
n
n
ec
ted
t
h
r
o
u
g
h
a
u
n
id
ir
ec
ti
o
n
al
b
o
o
s
t
DC
-
DC
co
n
v
er
ter
w
it
h
m
o
d
u
lar
d
esig
n
.
T
h
is
m
o
d
u
lar
c
o
n
v
er
ter
tr
an
s
f
er
t
h
e
a
v
ailab
l
e
m
ax
i
m
u
m
p
o
w
er
g
en
er
ated
b
y
P
V
ar
r
ay
to
DC
b
u
s
.
T
h
e
g
en
er
ated
P
V
p
o
w
er
d
ep
en
d
s
o
n
th
e
s
o
l
ar
ir
r
ad
iatio
n
(
S
)
an
d
te
m
p
er
atu
r
e
(
T
)
.
T
h
e
DC
b
u
s
i
s
co
n
n
ec
ted
to
th
e
u
t
ilit
y
g
r
id
th
r
o
u
g
h
a
b
id
ir
ec
ti
o
n
al
6
-
p
u
l
s
e
P
W
M
co
n
v
er
ter
.
Fig
u
r
e
1
.
Gr
id
-
co
n
n
ec
ted
p
h
o
t
o
v
o
ltaic
s
y
s
te
m
2
.
1
.
M
o
delin
g
o
f
P
ho
t
o
v
o
lt
a
ic
So
la
r
Cell
Sin
g
le
-
d
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d
e
an
d
t
w
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d
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cu
it
m
o
d
els
ar
e
th
e
m
o
s
t
w
i
d
ely
u
s
ed
f
o
r
th
e
P
V
s
o
lar
ce
ll.
As
th
e
s
in
g
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d
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cir
cu
it
m
o
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is
ac
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r
ate
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o
u
g
h
an
d
u
s
ed
in
m
an
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liter
at
u
r
e
[
3
]
-
[
8
]
-
[
1
2
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it
is
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ed
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ip
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u
r
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3
s
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o
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a
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ter
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u
r
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3
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(
a)
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t c
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d
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2
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3
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Co
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V
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t
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lar
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iatio
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n
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r
d
e
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en
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ate
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a
x
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m
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m
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m
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h
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n
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ter
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s
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MP
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ely
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l
m
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n
tr
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l [
6
]
-
[
8
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g
u
r
e
4
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th
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ay
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t
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pv
(
n
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n
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t c
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r
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en
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d
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t p
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P
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t
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d
v
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t
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m
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le
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er
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n
d
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e
s
V
(n
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,
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o
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d
er
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et
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d
ΔV
.
Fig
u
r
e
4
.
Flo
w
c
h
ar
t o
f
P
&
O
a
lg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
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0
8
8
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8
694
O
p
en
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s
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F
a
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t
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t Co
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f P
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er C
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ve
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ters
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Gri
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1298
T
h
en
ac
co
r
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g
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e
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ig
n
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f
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d
ΔV
,
th
e
r
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ce
v
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ag
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o
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th
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co
n
v
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ter
is
ch
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g
e
d
to
tr
ac
k
M
P
P
as su
m
m
ar
ized
b
elo
w
[
9
]
-
[
1
1
]
.
a.
I
f
th
e
v
al
u
e
o
f
ΔP
is
ze
r
o
,
t
h
e
s
y
s
te
m
i
s
w
o
r
k
in
g
at
MP
P
an
d
n
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ch
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g
e
in
r
ef
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en
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e
v
o
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e
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r
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b.
I
f
th
e
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e
o
f
Δ
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d
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e
r
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ce
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g
e
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e
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cr
ea
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ed
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o
as to
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ch
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f
th
e
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e
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f
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d
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lta
g
e
m
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s
t
b
e
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ea
s
ed
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ch
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d.
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f
th
e
v
alu
e
o
f
Δ
P
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d
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V<
0
,
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e
r
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er
en
ce
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o
lta
g
e
is
to
b
e
in
cr
ea
s
ed
to
r
ea
ch
MP
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.
e.
if
t
h
e
v
al
u
e
o
f
Δ
P
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an
d
Δ
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0
,
th
e
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en
ce
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g
e
t
h
is
ti
m
e
is
to
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e
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ec
r
ea
s
ed
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ch
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P
.
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h
e
r
esu
lted
er
r
o
r
b
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ee
n
th
e
r
ef
er
en
ce
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d
m
ea
s
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r
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is
m
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ip
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lated
u
s
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g
a
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co
n
tr
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ller
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ate
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e
d
u
t
y
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an
d
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n
s
eq
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n
tl
y
t
h
e
P
W
M
g
ate
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ig
n
a
l
g
pv
f
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h
e
co
n
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ter
s
w
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t
ch
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ill
u
s
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ated
i
n
Fig
u
r
e
5
.
Fig
u
r
e
5
.
B
lo
ck
d
iag
r
a
m
o
f
v
o
ltag
e
co
n
tr
o
l
2
.
4
.
Co
ntr
o
l o
f
G
rid
-
Sid
e
Co
nv
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t
er
T
h
e
DC
b
u
s
is
co
n
n
ec
ted
to
th
e
u
tili
t
y
t
h
r
o
u
g
h
T
h
e
GSC
,
wh
ich
i
s
co
n
n
ec
ted
to
th
e
u
t
ilit
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a
th
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o
u
g
h
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to
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it
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h
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en
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ar
m
o
n
ic
s
.
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h
e
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ased
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n
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ca
lc
u
la
ted
:
P
v
i
f
f
f
q
Q
v
i
f
f
f
d
(
6
)
T
h
ese
eq
u
atio
n
s
s
h
o
w
th
a
t
i
n
d
ep
en
d
en
t
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
co
n
tr
o
l
ca
n
b
e
ac
h
ie
v
ed
.
Fig
u
r
e
6
s
h
o
w
s
t
h
e
m
o
d
el
s
c
h
e
m
e
o
f
t
h
e
f
ield
o
r
ien
ted
co
n
tr
o
l o
f
GS
C
.
Fig
u
r
e
6
.
Mo
d
el
s
ch
e
m
e
o
f
G
SC
v
ec
to
r
co
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
:
1
2
9
4
–
1
3
0
8
1299
3.
F
AULT
-
T
O
L
E
RAN
T
CO
N
T
RO
L
T
h
e
s
tu
d
ied
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
te
m
co
n
ta
in
s
a
u
n
id
ir
ec
tio
n
a
l
b
o
o
s
t
DC
–
DC
co
n
v
er
ter
an
d
a
b
id
ir
ec
tio
n
al
6
-
p
u
l
s
e
P
W
M
co
n
v
er
ter
as
it
s
h
o
w
s
in
Fig
u
r
e
7
.
B
o
th
o
f
t
h
e
t
w
o
co
n
v
er
ter
s
ar
e
v
u
l
n
er
ab
le
to
s
e
m
ico
n
d
u
c
to
r
s
s
w
i
tch
e
s
f
au
lts
.
T
h
e
m
o
s
t
co
m
m
o
n
f
ail
u
r
es
i
n
s
e
m
ico
n
d
u
cto
r
s
ar
e
o
p
en
-
cir
c
u
it
f
a
u
lt
s
,
g
ati
n
g
f
au
l
ts
,
an
d
s
h
o
r
t
-
cir
cu
i
t
f
au
lt
s
.
T
h
ese
f
ailu
r
es
m
a
y
h
a
p
p
en
d
u
e
to
ex
ter
n
al
o
r
in
ter
n
al
ev
en
t
s
,
s
u
c
h
as:
in
co
r
r
ec
t
g
ate
v
o
ltag
e,
d
r
iv
er
f
ailu
r
e
o
r
elec
tr
ical
o
v
er
s
tr
ess
(
v
o
ltag
e
o
r
cu
r
r
en
t)
w
h
i
ch
m
a
y
ap
p
ea
r
b
y
elec
tr
o
m
ag
n
etic
p
u
l
s
es,
elec
tr
o
s
tatic
d
is
ch
ar
g
e,
s
y
s
te
m
tr
an
s
ien
t,
an
d
li
g
h
tn
i
n
g
[
1
8
]
[
2
4
]
[
2
5
]
[
2
6
]
.
Fig
u
r
e
7
s
h
o
w
s
t
h
e
f
au
l
t
-
to
l
er
an
t
to
p
o
lo
g
y
w
it
h
r
ed
u
n
d
a
n
c
y
f
o
r
th
e
s
t
u
d
ied
g
r
id
-
co
n
n
ec
ted
P
V
s
y
s
te
m
.
T
h
e
s
w
itc
h
in
g
p
atter
n
f
o
r
th
e
DC
–
DC
co
n
v
er
ter
is
d
ef
i
n
ed
b
y
P
&
O
co
n
tr
o
l
m
et
h
o
d
an
d
th
e
s
w
itc
h
i
n
g
p
atter
n
s
f
o
r
t
h
e
G
SC
ar
e
d
ef
i
n
ed
b
y
v
ec
to
r
co
n
tr
o
l
s
tr
ate
g
y
.
I
n
h
ea
lth
y
co
n
d
itio
n
s
,
t
h
e
o
u
tp
u
ts
o
f
t
h
e
P
&
O
an
d
v
ec
to
r
co
n
tr
o
l a
r
e
d
ir
ec
tly
ap
p
lied
to
th
e
co
n
v
er
ter
s
.
Fig
u
r
e
7
.
Fau
lt to
ler
an
t c
o
n
v
er
ter
to
p
o
lo
g
y
f
o
r
g
r
id
-
co
n
n
ec
te
d
P
V
s
y
s
te
m
3
.
1
.
F
a
ult
-
T
o
lera
nt
Co
ntr
o
l
f
o
r
t
he
B
o
o
s
t
DC
-
DC
Co
nv
er
t
er
I
f
a
p
o
w
er
s
w
i
tch
f
ail
u
r
e
o
cc
u
r
r
ed
in
th
e
DC
-
D
C
co
n
v
er
te
r
,
th
e
f
au
lt
d
etec
tio
n
m
et
h
o
d
d
etec
ts
th
e
f
au
lt
o
cc
u
r
r
en
ce
an
d
th
e
s
w
itc
h
S
pv
w
ill
b
e
r
ep
lace
d
w
ith
t
h
e
r
ed
u
n
d
an
t
s
w
i
tch
S
r
.
T
h
e
f
u
s
ib
le
f
pv
is
ad
d
ed
in
ca
s
e
o
f
d
an
g
er
o
u
s
c
u
r
r
en
t
o
cc
u
r
r
ed
b
y
s
h
o
r
t
-
cir
c
u
i
t
(
S
C
)
.
I
n
s
u
m
m
ar
y
,
i
n
an
o
p
en
-
s
w
it
ch
f
a
u
lt
ca
s
e
o
n
th
e
DC
-
DC
co
n
v
er
ter
,
th
e
co
m
p
e
n
s
atio
n
is
ac
h
ie
v
ed
b
y
th
e
f
o
llo
w
i
n
g
s
tep
s
:
1.
Dete
ctio
n
o
f
t
h
e
f
a
u
lt,
2.
Sto
p
th
e
s
w
itc
h
i
n
g
o
r
d
er
s
o
f
t
h
e
s
w
itc
h
S
pv
,
3.
Use th
e
s
w
itc
h
i
n
g
o
r
d
er
s
o
f
th
e
s
w
itch
S
pv
to
th
e
s
w
itch
S
r
,
4.
Sto
p
th
e
f
a
u
lt d
etec
tio
n
s
ch
e
m
e.
3
.
2
.
F
a
ult
-
T
o
lera
nt
Co
ntr
o
l
f
o
r
t
he
G
rid
-
Sid
e
Co
nv
er
t
er
W
h
en
a
f
a
u
lt
o
cc
u
r
r
ed
in
o
n
e
o
f
th
e
s
e
m
ico
n
d
u
cto
r
s
o
r
d
r
iv
er
s
o
f
th
e
t
h
r
ee
-
le
g
s
o
f
th
e
G
S
C
,
th
e
f
au
l
t
d
etec
tio
n
m
et
h
o
d
d
etec
ts
th
e
f
au
lt
o
cc
u
r
r
en
ce
a
n
d
is
o
lates
t
h
e
f
au
l
t
y
le
g
.
T
h
e
f
a
u
lt
y
leg
w
i
ll
b
e
th
en
r
ep
lace
d
w
it
h
th
e
r
ed
u
n
d
an
t
leg
(
co
m
p
o
s
ed
o
f
t
h
e
s
w
itc
h
es
S
d1
a
n
d
S
d2
)
.
I
n
ca
s
e
o
f
a
s
h
o
r
t
-
cir
cu
i
t
f
a
u
lt,
t
h
e
f
a
u
lt
y
leg
is
is
o
lated
b
y
v
er
y
f
ast
ac
tin
g
f
u
s
e
s
;
co
n
s
eq
u
e
n
tl
y
,
th
e
s
h
o
r
t
-
cir
cu
it
f
au
lt
b
ec
o
m
es
an
o
p
e
n
-
c
ir
cu
it.
Fo
r
th
ese
r
ea
s
o
n
s
,
o
n
l
y
o
p
en
-
s
w
itc
h
f
au
l
t
w
i
ll b
e
s
tu
d
ied
f
o
r
th
e
GS
C
[
2
5
]
.
I
n
s
u
m
m
a
r
y
,
i
n
a
n
o
p
en
-
s
w
itc
h
f
a
u
lt c
a
s
e
on
th
e
th
r
ee
-
le
g
s
o
f
t
h
e
GS
C
,
t
h
e
co
m
p
e
n
s
at
io
n
is
ac
h
ie
v
ed
b
y
t
h
e
f
o
llo
w
i
n
g
s
tep
s
:
1.
Dete
ctio
n
o
f
t
h
e
f
a
u
lt
y
le
g
n
u
m
b
er
k
(
k
=1
,
2
,
3
),
2.
Sto
p
th
e
s
w
itc
h
i
n
g
o
r
d
er
s
o
f
t
h
e
t
w
o
s
w
itc
h
i
n
g
d
r
i
v
er
s
o
f
t
h
e
f
au
l
t
y
le
g
,
3.
T
r
ig
g
er
th
e
s
u
it
ed
b
id
ir
ec
tio
n
al
s
w
itc
h
T
rk
o
f
th
e
f
a
u
lt
y
leg
n
u
m
b
er
k
,
4.
Use th
e
s
w
itc
h
i
n
g
o
r
d
er
s
o
f
th
e
f
au
l
t
y
le
g
to
th
e
r
ed
u
n
d
an
t le
g
,
5.
Sto
p
th
e
f
a
u
lt d
etec
tio
n
s
ch
e
m
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
O
p
en
-
s
w
itch
F
a
u
lt
-
t
o
lera
n
t Co
n
tr
o
l
o
f P
o
w
er C
o
n
ve
r
ters
in
a
Gri
d
-
c
o
n
n
ec
te
d
…
(
B
ila
l B
o
u
d
jella
l
)
1300
4.
F
AULT
D
E
T
E
C
T
I
O
N
M
E
T
H
O
DO
L
O
G
Y
4
.
1
.
F
a
ult
Det
ec
t
io
n
M
et
ho
d
o
f
D
C
-
DC
Co
nv
er
t
er
T
h
e
p
r
o
p
o
s
ed
s
w
itc
h
f
au
lt
d
etec
tio
n
o
f
th
e
b
o
o
s
t
D
C
-
DC
co
n
v
er
ter
is
b
ased
o
n
t
h
e
f
o
r
m
o
f
t
h
e
in
d
u
cto
r
cu
r
r
en
t
i
L
,
w
h
ich
is
t
h
e
s
a
m
e
f
o
r
t
h
e
n
o
n
-
i
s
o
lated
s
in
g
le
-
e
n
d
ed
DC
-
DC
co
n
v
er
ter
s
f
a
m
il
y
,
t
h
is
f
au
lt
d
etec
tio
n
m
eth
o
d
ca
n
b
e
g
e
n
er
alize
d
to
t
h
e
o
th
er
n
o
n
-
i
s
o
lated
s
in
g
le
-
en
d
ed
D
C
-
DC
co
n
v
er
ter
s
f
a
m
il
y
.
T
h
e
p
r
o
p
o
s
ed
f
au
lt
d
etec
tio
n
m
et
h
o
d
d
o
es
n
o
t
r
eq
u
ir
e
a
n
y
a
d
d
itio
n
al
cu
r
r
en
t
o
r
v
o
lta
g
e
s
e
n
s
o
r
s
i
n
t
h
e
s
y
s
te
m
,
w
h
ic
h
is
i
n
ter
esti
n
g
b
ec
au
s
e
a
d
d
itio
n
al
s
en
s
o
r
s
af
f
ec
t t
h
e
r
eliab
ilit
y
,
co
s
t,
an
d
w
ei
g
h
t o
f
t
h
e
s
y
s
te
m
.
As
s
h
o
w
n
i
n
Fi
g
u
r
e
8
,
th
e
f
au
lt
d
etec
tio
n
m
eth
o
d
i
s
b
ased
o
n
t
w
o
alg
o
r
it
h
m
s
FD
A
1
a
n
d
F
DA
2
.
T
h
e
f
ir
s
t
al
g
o
r
ith
m
FD
A
1
i
s
f
ast
er
th
a
n
t
h
e
s
ec
o
n
d
al
g
o
r
ith
m
FD
A
2
,
b
u
t
it
is
les
s
r
o
b
u
s
t
at
d
etec
ti
n
g
a
n
o
p
en
-
s
w
i
tch
f
au
l
t
(
OSF)
f
o
r
s
o
m
e
ca
s
e
s
.
Alth
o
u
g
h
,
th
e
s
ec
o
n
d
alg
o
r
ith
m
FD
A
2
is
m
o
r
e
r
o
b
u
s
t
an
d
ef
f
ic
ien
t
,
h
o
w
ev
er
it is
n
o
t a
s
f
ast a
s
th
e
f
ir
s
t a
l
g
o
r
ith
m
FD
A
1
.
Fig
u
r
e
9
s
h
o
w
s
th
e
f
a
u
lt
d
etec
tio
n
s
ig
n
als
f
o
r
t
h
e
D
C
–
DC
co
n
v
er
ter
w
h
en
an
OS
F
h
a
s
o
cc
u
r
r
ed
in
d
if
f
er
e
n
t
t
i
m
e
s
T
F1
an
d
T
F2
,
w
e
ca
n
o
b
s
er
v
e
t
h
at
FD
A
1
i
s
f
a
s
ter
t
h
an
FD
A
2
f
o
r
t
h
e
f
ir
s
t
f
a
u
lt
ca
s
e
(
O
SF
1
)
.
Ho
w
e
v
er
,
in
t
h
e
s
ec
o
n
d
ca
s
e
(
OSF2
)
,
FDA
2
i
s
f
a
s
ter
th
a
n
FD
A
1
in
d
etec
ti
n
g
t
h
e
f
au
l
t.
B
o
th
alg
o
r
ith
m
s
ar
e
d
escr
ib
ed
in
th
e
f
o
llo
w
i
n
g
.
Fig
u
r
e
8
.
Fau
lt d
etec
tio
n
al
g
o
r
ith
m
f
o
r
th
e
DC
–
D
C
co
n
v
er
ter
T
h
e
f
ir
s
t
f
a
u
lt
d
etec
t
io
n
al
g
o
r
ith
m
FD
A
1
u
s
es
th
e
f
o
r
m
o
f
th
e
i
n
d
u
cto
r
c
u
r
r
en
t
i
L
,
to
b
e
m
o
r
e
ac
cu
r
ate
is
u
s
e
s
th
e
s
i
g
n
o
f
t
h
e
s
lo
p
e
o
f
i
L
.
T
h
e
s
ig
n
o
f
t
h
e
cu
r
r
en
t
s
lo
p
e
s
g
n
(
d
i)
is
co
m
p
u
ted
b
y
ca
lc
u
lati
n
g
th
e
d
er
iv
at
iv
e
o
f
t
h
e
i
n
d
u
cto
r
cu
r
r
en
t
i
L
an
d
t
h
e
n
p
ass
it
t
h
r
o
u
g
h
a
s
ig
n
b
lo
ck
.
W
h
en
th
e
s
w
itc
h
S
pv
is
t
u
r
n
ed
o
n
s
g
n
(
g
’
)
=
1
,
i
L
in
cr
ea
s
e
s
an
d
s
g
n
(
d
i)
=
1
.
W
h
en
t
h
e
s
w
i
tc
h
S
pv
i
s
tu
r
n
ed
o
f
f
s
g
n
(
g
’
)
=
-
1
,
i
L
d
ec
r
ea
s
es
an
d
s
g
n
(
d
i)
=
-
1
.
I
f
th
e
t
w
o
s
ig
n
al
s
s
g
n
(
g
’
)
an
d
s
g
n
(
d
i/d
t)
ar
e
d
if
f
er
en
t th
er
e
is
a
s
w
itc
h
f
ai
lu
r
e.
I
n
r
ea
l
ti
m
e
a
n
d
as
a
r
es
u
lt
o
f
n
o
n
-
id
ea
l
b
eh
a
v
io
r
o
f
p
o
w
er
s
w
itc
h
es
a
n
d
d
ela
y
s
,
t
h
e
s
g
n
(
d
i)
w
ill
b
e
d
elay
ed
i
n
r
esp
ec
t
to
s
g
n
(
g
’
)
an
d
th
e
er
r
o
r
s
ig
n
al
“
ε”
i
s
s
et
to
“
1
”
as
s
h
o
w
n
in
Fi
g
u
r
e
9
.
Hen
ce
,
th
e
p
o
w
er
s
e
m
ico
n
d
u
cto
r
s
w
itc
h
i
n
g
,
d
ela
y
s
an
d
d
ea
d
ti
m
es
m
u
s
t
t
o
tak
e
in
to
co
n
s
id
er
atio
n
to
av
o
id
f
alse
f
au
lt
d
etec
tio
n
s
.
T
h
er
ef
o
r
e,
a
co
u
n
t
er
b
lo
ck
is
ad
d
ed
to
ass
u
r
e
th
e
f
au
lt d
etec
tio
n
.
I
n
ca
s
e
o
f
a
s
w
itc
h
f
a
u
lt,
t
h
e
er
r
o
r
s
ig
n
al
“
ε”
w
i
ll
b
e
s
et
to
“
1
”
a
n
d
t
h
e
co
u
n
ter
“
n
”
s
tar
t
s
to
co
u
n
t
f
o
r
en
o
u
g
h
ti
m
e
to
a
s
s
u
r
e
th
e
f
a
u
lt
d
etec
tio
n
,
o
th
er
w
is
e
if
th
e
er
r
o
r
s
ig
n
al
is
s
et
to
“
0
”
th
e
co
u
n
ter
w
il
l
r
es
et
to
ze
r
o
“
0
”.
I
n
ca
s
e
t
h
at
t
h
e
co
u
n
ter
is
g
r
ea
ter
th
an
N
it
m
ea
n
s
t
h
at
a
s
w
i
tc
h
f
au
lt
o
cc
u
r
r
ed
.
T
h
e
co
u
n
tin
g
ti
m
e
m
u
s
t
b
e
lo
n
g
er
t
h
an
t
h
e
o
v
er
all
d
elay
s
ca
u
s
ed
b
y
t
h
e
s
e
n
s
o
r
s
,
d
r
iv
er
s
,
co
n
tr
o
l
ler
s
an
d
s
w
itc
h
es:
N
T
T
sd
(
7
)
W
h
er
e
T
s
is
th
e
s
a
m
p
li
n
g
p
er
i
o
d
an
d
T
d
is
th
e
to
tal
in
h
er
en
t
d
elay
.
T
h
o
u
g
h
,
t
h
e
FD
A
1
al
g
o
r
ith
m
is
v
er
y
f
a
s
t
a
n
d
ca
n
d
etec
t
a
f
au
lt
w
it
h
i
n
N
s
a
m
p
li
n
g
p
er
io
d
,
h
o
w
e
v
e
r
it
s
t
ill
d
ep
en
d
s
o
n
s
e
v
er
al
p
ar
a
m
eter
s
an
d
th
er
e
ar
e
s
o
m
e
n
e
ce
s
s
ar
y
cr
iter
ia
m
u
s
t
to
ta
k
e
i
n
to
co
n
s
id
er
atio
n
to
d
etec
t th
e
f
a
u
lt
s
u
cc
es
s
f
u
ll
y
.
T
h
ese
cr
iter
ia
ca
n
b
e
s
u
m
m
ar
iz
ed
as:
D
T
T
N
T
Fs
D
T
N
T
s
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
:
1
2
9
4
–
1
3
0
8
1301
W
h
er
e
T
F
is
th
e
f
a
u
lt
o
cc
u
r
r
en
ce
ti
m
e.
FD
A
1
ca
n
d
etec
t
th
e
f
au
lt
s
u
cc
es
s
f
u
ll
y
if
(
8
)
ar
e
s
i
m
u
lta
n
eo
u
s
l
y
s
a
tis
f
ied
.
H
o
w
e
v
er
,
if
t
h
ese
co
n
d
itio
n
s
ar
e
n
o
t
s
ati
s
f
ied
,
f
a
u
lt
d
etec
tio
n
w
i
ll
f
ail.
C
o
n
s
id
er
in
g
(
8
)
,
th
e
OSF
d
etec
tio
n
w
il
l
f
ail
f
o
r
s
m
al
l
v
alu
e
s
o
f
D
o
r
in
h
i
g
h
-
f
r
eq
u
e
n
c
y
s
w
i
tch
i
n
g
.
B
ec
au
s
e
o
f
th
ese
li
m
i
ts
f
o
r
f
au
l
t d
etec
tio
n
,
a
s
ec
o
n
d
alg
o
r
ith
m
FD
A
2
i
s
p
r
o
p
o
s
ed
.
Fig
u
r
e
9
.
Fau
lt d
etec
tio
n
s
ig
n
a
ls
f
o
r
th
e
D
C
–
DC
co
n
v
er
ter
T
h
e
s
ec
o
n
d
f
au
lt
d
etec
tio
n
al
g
o
r
ith
m
FD
A
2
is
b
ases
o
n
t
h
e
f
o
r
m
o
f
th
e
in
d
u
cto
r
cu
r
r
en
t
i
L
as
w
ell.
T
h
er
e
is
t
w
o
s
tate
s
o
f
t
h
e
s
w
i
t
ch
g
pv
w
h
ic
h
ar
e
s
w
itc
h
tr
i
g
g
e
d
o
n
an
d
s
w
itc
h
tr
ig
g
ed
o
f
f
,
an
d
b
y
ea
ch
p
u
ls
e
o
f
“
T
r
ig
”,
th
e
in
d
u
cto
r
cu
r
r
en
t
i
L
in
cr
ea
s
es
o
r
d
ec
r
ea
s
es,
an
d
th
e
s
lo
p
e
s
ig
n
o
f
i
L
ch
a
n
g
es
b
y
e
v
er
y
T
r
ig
s
i
g
n
al
s
as
s
h
o
w
n
i
n
Fig
u
r
e
9
.
I
f
t
h
e
s
l
o
p
e
o
f
i
L
d
o
es
n
o
t
c
h
a
n
g
e
s
b
y
th
e
T
r
ig
s
ig
n
al
s
it
m
ea
n
s
t
h
at
a
s
w
itc
h
f
ail
u
r
e
h
as
o
cc
u
r
r
ed
.
T
h
e
s
ec
o
n
d
alg
o
r
ith
m
FD
A
2
as it
s
h
o
w
n
i
n
Fi
g
u
r
e
8
ca
n
b
e
s
u
m
m
ar
ize
b
y
t
h
e
f
o
llo
w
i
n
g
s
tep
s
:
1.
Dete
ct
th
e
r
is
i
n
g
an
d
d
ec
lin
in
g
ed
g
e
“
T
r
ig
”
p
u
ls
e;
2.
C
h
ec
k
if
t
h
e
s
lo
p
e
s
ig
n
o
f
i
L
ch
an
g
ed
b
y
co
m
p
ar
in
g
t
h
e
p
r
esen
t
i
L
s
lo
p
e
s
ig
n
w
it
h
th
e
p
r
ev
io
u
s
i
L
s
lo
p
e
s
ig
n
;
3.
I
f
th
e
s
lo
p
e
s
ig
n
o
f
i
L
c
h
an
g
ed
th
en
t
h
er
e
is
n
o
f
a
u
lt a
n
d
ds
is
s
et
to
eq
u
al
d
s
g
n
;
4.
I
f
th
e
s
lo
p
e
s
ig
n
o
f
i
L
d
id
n
o
t c
h
an
g
e
t
h
en
a
f
au
lt h
a
s
o
cc
u
r
r
ed
an
d
f
au
lt
i
s
s
et
to
“
1
”.
T
h
is
alg
o
r
ith
m
i
s
s
lo
w
er
t
h
an
th
e
f
ir
s
t
al
g
o
r
ith
m
,
h
o
w
e
v
er
it
ca
n
d
etec
t
th
e
f
a
u
lt
s
in
a
n
y
c
o
n
d
itio
n
s
,
f
o
r
an
y
D
a
n
d
an
y
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
.
4
.
2
.
F
a
ult
Det
ec
t
io
n
M
et
ho
d
o
f
G
SC
T
h
e
o
p
en
-
s
w
itc
h
f
a
u
lt
d
etec
ti
o
n
o
f
D
C
–
A
C
co
n
v
er
ter
i
s
b
ased
o
n
t
h
e
m
ea
n
v
al
u
e
o
f
c
o
m
p
ar
is
o
n
b
et
w
ee
n
m
ea
s
u
r
ed
an
d
esti
m
ated
s
i
m
p
le
v
o
ltag
e
s
ν
k
an
d
ν
k
_es
(
k
=
1
,
2
,
3
)
as
illu
s
tr
a
ted
in
Fi
g
u
r
e
1
0
.
T
h
e
esti
m
ated
v
o
lta
g
es c
a
n
b
e
ex
p
r
ess
ed
b
y
:
2
1
1
11
1
2
1
22
3
1
1
2
33
vS
V
dc
vS
vS
(
9
)
T
h
e
m
ea
n
v
al
u
e
ca
lcu
lato
r
it
is
th
e
s
u
m
d
i
v
id
ed
b
y
th
e
co
u
n
t
ti
m
e,
in
o
th
er
w
o
r
d
s
,
ad
d
u
p
all
th
e
n
u
m
b
er
s
(
d
ata)
,
th
e
n
d
iv
id
e
b
y
ti
m
e.
Ho
w
ev
er
,
i
n
r
ea
l
ti
m
e
an
d
ca
u
s
e
o
f
t
u
r
n
-
o
n
,
t
u
r
n
-
o
f
f
,
i
n
ter
lo
ck
d
ea
d
,
p
r
o
p
ag
atio
n
ti
m
e
an
d
ti
m
e
g
en
er
ated
b
y
th
e
s
w
itc
h
es
d
r
iv
er
s
,
th
e
v
o
lta
g
e
m
ea
n
v
al
u
e
er
r
o
r
is
n
o
t
n
u
ll.
T
h
er
ef
o
r
e,
to
av
o
id
f
a
ls
e
f
a
u
lt
d
etec
t
io
n
s
d
u
e
to
p
o
w
er
s
e
m
ico
n
d
u
cto
r
s
w
itc
h
i
n
g
,
w
e
ad
d
t
w
o
s
tep
s
o
f
d
etec
tio
n
.
T
h
e
f
ir
s
t
s
tep
i
s
c
alcu
lati
n
g
t
h
e
m
ea
n
v
al
u
e
o
f
th
e
v
o
lta
g
e
er
r
o
r
s
i
g
n
al
a
n
d
co
m
p
ar
e
it
w
it
h
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
O
p
en
-
s
w
itch
F
a
u
lt
-
t
o
lera
n
t Co
n
tr
o
l
o
f P
o
w
er C
o
n
ve
r
ters
in
a
Gri
d
-
c
o
n
n
ec
te
d
…
(
B
ila
l B
o
u
d
jella
l
)
1302
th
r
es
h
o
ld
v
al
u
e
h
(
T
ab
le
2
)
.
T
h
e
s
ec
o
n
d
s
tep
is
ti
m
e
d
ela
y
to
a
s
s
u
r
e
th
e
f
a
u
lt d
etec
tio
n
it
’
s
d
o
n
e
b
y
co
m
p
ar
in
g
th
e
t
h
r
es
h
o
ld
t
k
w
it
h
th
e
ti
m
e
d
ela
y
v
al
u
e
τ
,
as
s
h
o
w
n
in
Fig
u
r
e
1
0
.
T
h
e
r
esu
ltin
g
s
ig
n
al
f
k
f
r
o
m
t
h
e
f
au
lt
d
etec
tio
n
d
iag
r
a
m
i
s
u
s
ed
to
is
o
late
th
e
f
a
u
lt
y
leg
a
n
d
s
tar
t t
h
e
co
m
p
e
n
s
atio
n
in
f
a
u
lt c
ase.
Fig
u
r
e
10
.
B
lo
ck
d
iag
r
am
o
f
t
h
e
p
r
o
p
o
s
ed
f
au
lt d
etec
tio
n
T
ab
le
2
class
if
ied
th
e
f
a
u
lt
y
s
w
itc
h
d
etec
tio
n
u
s
in
g
ea
ch
p
h
ase
m
ea
n
v
al
u
e
t
h
r
es
h
o
ld
v
alu
e.
T
ab
le
2
.
Fau
lt
y
s
w
i
tch
d
etec
ti
o
n
th
r
es
h
o
ld
F
a
u
l
t
y
s
w
i
t
c
h
P
h
a
se
1
P
h
a
se
2
P
h
a
se
3
S
g
1
>
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<
h
<
h
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g
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<
h
>
h
<
h
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g
3
<
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<
h
>
h
S
g
4
<
h
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h
>
h
S
g
5
>
h
<
h
>
h
S
g
6
>
h
>
h
<
h
5.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
T
h
e
s
y
s
te
m
m
o
d
el
w
a
s
d
ev
el
o
p
ed
an
d
s
i
m
u
lated
in
M
A
T
L
A
B
/SIM
U
L
I
NK
en
v
ir
o
n
m
e
n
t
u
s
in
g
th
e
Si
m
s
ca
p
e
P
o
w
er
S
y
s
te
m
s
to
o
lb
o
x
f
o
r
v
er
if
y
i
n
g
t
h
e
v
a
lid
it
y
o
f
th
e
p
r
o
p
o
s
ed
f
au
lt
-
to
ler
an
t
s
tr
ateg
y
an
d
f
au
l
t
-
d
etec
tio
n
m
eth
o
d
s
.
T
h
e
s
y
s
te
m
p
ar
a
m
e
ter
s
ar
e
g
i
v
en
i
n
T
ab
le
3
.
T
h
e
s
a
m
p
li
n
g
p
er
io
d
h
a
s
b
ee
n
c
h
o
s
e
n
to
b
e
eq
u
al
to
1
μ
s
.
T
h
e
p
u
ls
e
w
id
th
m
o
d
u
la
tio
n
f
r
eq
u
e
n
c
y
is
s
et
t
o
1
0
k
Hz
f
o
r
th
e
DC
–
D
C
co
n
v
er
ter
an
d
5
k
Hz
f
o
r
th
e
G
SC
.
T
h
e
GS
C
i
s
co
n
n
e
cted
to
a
t
h
r
ee
-
p
h
a
s
e
u
til
it
y
g
r
id
o
f
380
v
,
50
Hz
.
T
h
e
n
o
m
i
n
al
p
o
w
er
o
f
P
V
s
y
s
te
m
is
4
0
k
W
at
1
0
0
0
W
/
m
2
o
f
s
o
lar
ir
r
ad
ian
ce
an
d
th
e
te
m
p
er
at
u
r
e
is
ass
u
m
ed
co
n
s
t
an
t
at
th
e
r
ef
er
e
n
ce
v
alu
e.
Fa
u
lt d
etec
tio
n
m
e
th
o
d
s
p
ar
am
eter
s
ar
e
N=
4
0
,
h
=
10
an
d
τ
=1
m
s
.
T
ab
le
3
.
Sim
u
latio
n
p
ar
a
m
eter
s
V
a
r
i
a
b
l
e
V
a
l
u
e
R
p
v
1
0
mΩ
L
p
v
4
mH
C
d
c
6
0
0
0
µ
F
Lf
3
mH
Rf
5
mΩ
T
h
e
s
o
lar
ir
r
ad
iatio
n
S
ch
an
g
e
s
f
r
o
m
5
0
0
W
/
m
2
an
d
1
0
0
0
W
/
m
2
as
s
h
o
w
n
in
Fig
u
r
e
1
1
.
Fig
u
r
e
11
.
So
lar
ir
r
ad
iatio
n
(
S
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
4
,
Dec
em
b
er
2
0
1
6
:
1
2
9
4
–
1
3
0
8
1303
T
h
e
o
p
er
atio
n
o
f
th
e
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
te
m
i
n
clu
d
es
th
r
ee
ca
s
es
o
f
s
t
u
d
ies,
a
n
o
r
m
al
o
p
er
atio
n
m
o
d
e,
an
o
p
en
-
s
w
i
t
ch
f
a
u
lt o
p
er
atio
n
m
o
d
e
in
b
o
t
h
DC
-
D
C
co
n
v
er
ter
an
d
GSC
.
5
.
1
.
Ca
s
e
s
t
ud
y
1
:
No
r
m
a
l
O
pera
t
io
n
M
o
de
I
n
n
o
r
m
al
o
p
er
atio
n
m
o
d
e,
t
h
e
P
V
o
u
tp
u
t
p
o
w
er
P
PV
i
s
v
ar
y
i
n
g
b
et
w
ee
n
2
0
k
W
a
n
d
4
0
k
W
ac
co
r
d
in
g
l
y
to
t
h
e
v
alu
e
o
f
S
.
I
t
ca
n
b
e
s
ee
n
f
r
o
m
Fi
g
u
r
e
1
2
th
at
t
h
e
P
&
O
MP
PT
co
n
tr
o
l
m
et
h
o
d
h
elp
s
to
g
en
er
ate
t
h
e
m
ax
i
m
u
m
p
o
w
er
f
r
o
m
t
h
e
P
V
ar
r
ay
b
y
co
n
tr
o
llin
g
t
h
e
P
V
o
u
tp
u
t
v
o
ltag
e
V
PV
.
Fig
u
r
e
12
.
P
V
o
u
tp
u
t c
u
r
r
en
t (
I
PV
)
,
P
V
o
u
tp
u
t p
o
w
er
(
V
PV
)
an
d
P
V
o
u
tp
u
t p
o
w
er
(
P
PV
)
Fig
u
r
e
1
3
s
h
o
w
,
t
h
e
g
r
id
ac
tiv
e
p
o
w
er
P
f
,
g
r
id
r
ea
cti
v
e
p
o
wer
Q
f
an
d
DC
b
u
s
v
o
lta
g
e
v
dc
.
T
h
e
v
dc
is
w
ell
r
eg
u
lated
to
it
r
e
f
er
en
ce
(
6
0
0
V
)
an
d
s
a
g
s
ar
e
ab
o
u
t
3%
(
1
8
V
)
,
h
o
w
ev
er
,
it
d
ec
r
e
ases
a
n
d
i
n
cr
ea
s
es
in
s
ta
n
tl
y
w
h
en
t
h
e
P
f
in
cr
ea
s
es
an
d
d
ec
r
ea
s
es,
r
esp
ec
tiv
e
l
y
,
an
d
r
ec
o
v
er
s
q
u
ic
k
l
y
b
y
th
e
v
ec
to
r
co
n
tr
o
l
s
tr
ateg
y
.
T
h
e
P
f
is
v
ar
y
i
n
g
b
et
w
ee
n
-
2
0
k
W
an
d
-
4
0
k
W
(
th
e
m
i
n
u
s
s
i
g
n
m
ea
n
s
it’s
a
g
en
er
ated
p
o
w
er
)
ac
co
r
d
in
g
l
y
to
t
h
e
P
V
o
u
tp
u
t
p
o
w
er
P
PV
.
T
h
e
Q
f
is
f
i
x
ed
to
ze
r
o
v
alu
e,
to
m
ai
n
tai
n
th
e
p
o
w
er
f
ac
to
r
at
u
n
i
t
y
.
Fig
u
r
e
13
.
Gr
id
ac
tiv
e
p
o
w
er
(
P
f
)
,
Gr
id
r
ea
ctiv
e
p
o
w
er
(
Q
f
)
a
n
d
DC
b
u
s
v
o
lta
g
e
(
v
dc
)
5
.
2
.
Ca
s
e
Study
2
:
DC
–
DC
Co
nv
er
t
er
O
pen
-
Sw
it
ch
F
a
ult
O
p
er
a
t
io
n
M
o
de
Fig
u
r
e
1
4
s
h
o
w
s
s
i
m
u
latio
n
r
esu
lt
s
o
f
s
tu
d
ied
s
y
s
te
m
w
h
e
n
a
n
o
p
en
-
s
w
itc
h
f
a
u
lt
h
as
o
cc
u
r
r
ed
in
DC
-
DC
co
n
v
er
ter
(
s
w
itc
h
S
pv
)
at
t=2
.
2
s
w
it
h
o
u
t
f
a
u
lt
-
to
ler
an
t
to
p
o
lo
g
y
.
Af
ter
t
h
e
s
w
itc
h
f
au
lt
i
s
o
cc
u
r
r
ed
,
b
o
th
o
f
P
V
o
u
tp
u
t
cu
r
r
e
n
t
I
PV
an
d
P
V
o
u
tp
u
t
p
o
w
er
P
PV
ar
e
d
r
o
p
s
to
ze
r
o
“
0
”
.
A
s
a
r
es
u
lt,
th
e
D
C
b
u
s
v
o
ltag
e
v
dc
d
r
o
p
s
as
w
ell,
b
u
t
r
ec
o
v
er
s
q
u
ick
l
y
b
y
G
SC
.
T
h
e
g
r
id
ac
t
iv
e
p
o
w
er
P
f
b
ec
o
m
es
p
o
s
it
iv
e
,
m
ea
n
in
g
th
at
t
h
e
p
o
w
er
f
lo
w
s
f
r
o
m
t
h
e
g
r
id
to
t
h
e
DC
b
u
s
.
I
n
s
u
m
m
ar
y
,
w
e
c
an
co
n
cl
u
d
e
th
at
a
f
ail
u
r
e
in
t
h
e
DC
-
DC
co
n
v
er
ter
w
il
l
a
f
f
ec
t
th
e
w
h
o
le
P
V
s
y
s
te
m
a
n
d
lead
to
its
s
to
p
p
ag
e
s
i
n
ce
it
is
d
ir
ec
tl
y
co
n
n
ec
ted
to
t
h
e
ar
r
a
y
s
.
Fi
g
u
r
e
1
5
s
h
o
w
s
th
e
DC
–
D
C
co
n
v
er
ter
s
ig
n
al
s
th
a
t
u
s
ed
to
d
etec
t
th
e
f
a
u
lt.
T
h
is
f
i
g
u
r
e
p
r
o
v
es
th
at
th
e
p
r
o
p
o
s
ed
f
au
l
t
d
etec
tio
n
m
et
h
o
d
ca
n
d
etec
t
o
p
en
-
s
w
itc
h
f
a
u
lt
i
n
DC
–
D
C
c
o
n
v
er
ter
(
at
ti
m
e
t=2
.
7
0
0
0
4
2
s
)
.
Fig
u
r
e
1
6
s
h
o
ws
s
i
m
u
lat
io
n
r
e
s
u
l
ts
f
o
r
t
h
e
s
a
m
e
f
a
u
lt
w
h
en
t
h
e
p
r
o
p
o
s
ed
f
au
lt
-
to
ler
an
t
to
p
o
lo
g
y
i
s
u
s
ed
.
O
n
e
ca
n
s
ee
t
h
at
t
h
e
P
V
s
y
s
te
m
ca
n
s
till
o
p
er
ate
in
n
o
m
i
n
al
co
n
d
itio
n
s
ev
e
n
af
ter
o
p
en
-
s
w
itc
h
f
a
u
lt
i
s
o
cc
u
r
r
ed
in
DC
–
D
C
co
n
v
er
ter
.
Evaluation Warning : The document was created with Spire.PDF for Python.