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So
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Dec
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er
20
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5
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ac
r
o
s
s
a
wid
er
r
an
g
e
o
f
in
p
u
t
v
o
ltag
es,
th
u
s
im
p
r
o
v
in
g
s
y
s
tem
r
eliab
ilit
y
an
d
f
lex
ib
ilit
y
[
1
3
]
.
T
h
is
p
a
p
er
p
r
o
p
o
s
es
a
n
u
n
i
q
u
e
tr
a
n
s
f
o
r
m
er
less
b
u
ck
b
o
o
s
t
in
v
e
r
ter
d
esig
n
,
wh
ich
a
d
d
r
ess
es
th
e
lim
itatio
n
s
o
f
tr
a
d
itio
n
al
d
esig
n
s
b
y
o
f
f
e
r
in
g
h
ig
h
e
f
f
icien
cy
a
n
d
r
e
d
u
ce
d
co
m
p
lex
ity
.
T
h
e
s
y
s
tem
in
teg
r
ates
a
s
o
litar
y
in
p
u
t
in
d
u
ctan
ce
an
d
f
i
v
e
p
o
wer
r
eg
u
l
ato
r
s
to
ac
h
iev
e
a
s
y
m
m
etr
ica
l
o
u
tp
u
t
ac
r
o
s
s
b
o
th
h
alv
es o
f
th
e
AC
cy
cle,
e
n
s
u
r
i
n
g
co
n
ti
n
u
o
u
s
p
o
wer
d
eliv
er
y
with
m
in
im
al
lo
s
s
es [
1
4
]
-
[
1
7
]
.
T
h
e
p
r
o
p
o
s
ed
d
esig
n
also
p
r
o
v
id
es
s
ev
er
al
k
ey
ad
v
a
n
tag
es.
B
y
d
ir
ec
tl
y
g
r
o
u
n
d
in
g
th
e
P
V
n
eg
ativ
e
ter
m
in
al
with
th
e
n
eu
tr
al
g
r
i
d
,
leak
ag
e
cu
r
r
en
ts
ar
e
ef
f
ec
tiv
ely
elim
in
ated
,
th
er
eb
y
e
n
h
an
cin
g
s
af
ety
an
d
r
ed
u
cin
g
o
p
er
atio
n
al
r
is
k
s
.
A
d
d
itio
n
ally
,
th
e
s
y
s
tem
r
ed
u
c
es
DC
cu
r
r
en
t
in
jectio
n
an
d
m
in
im
izes
s
witch
in
g
an
d
co
n
d
u
ctio
n
lo
s
s
es,
wh
ich
ar
e
ty
p
ically
p
r
o
b
lem
atic
in
co
n
v
en
tio
n
al
in
v
er
ter
s
.
T
h
ese
f
ea
tu
r
es
m
ak
e
th
e
p
r
o
p
o
s
ed
in
v
er
ter
d
esig
n
a
v
ia
b
le
s
o
lu
tio
n
f
o
r
in
te
g
r
atin
g
h
y
b
r
id
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
,
s
u
ch
as
s
o
lar
an
d
win
d
,
in
to
th
e
g
r
id
,
co
n
tr
i
b
u
tin
g
to
s
u
s
tain
ab
le
an
d
ef
f
icien
t p
o
wer
g
en
er
atio
n
.
2.
SUG
G
E
S
T
E
D
T
O
P
O
L
O
G
Y
F
O
R
B
UCK
-
B
O
O
ST
T
RA
NSFO
RM
E
RL
E
S
S
I
NV
E
R
T
E
R
(
B
B
T
I
)
2
.
1
.
F
un
ct
io
na
l c
ha
ra
c
t
er
is
t
ics o
f
t
he
pro
po
s
ed
B
B
T
I
T
h
e
p
r
o
p
o
s
ed
d
esig
n
co
m
b
in
e
s
a
v
o
ltag
e
-
ad
ju
s
tab
le
d
ir
ec
t
cu
r
r
en
t
to
d
ir
ec
t
cu
r
r
en
t
co
n
v
e
r
ter
an
d
a
f
u
ll
-
b
r
id
g
e
in
v
er
te
r
to
p
r
o
v
id
e
a
co
m
p
ac
t
an
d
ef
f
icien
t
s
o
lu
tio
n
f
o
r
h
y
b
r
id
en
e
r
g
y
s
y
s
t
em
s
.
T
h
e
to
p
o
lo
g
y
f
ea
tu
r
es
f
iv
e
co
n
t
r
o
llab
le
s
wi
tch
es
(
S1
-
S5
)
,
a
p
o
wer
d
io
d
e
,
an
in
p
u
t
in
d
u
cto
r
,
an
d
an
a
u
x
iliar
y
ca
p
ac
ito
r
.
Hig
h
-
f
r
eq
u
en
cy
s
witch
es
(
S1
,
S3
,
an
d
S4
)
ar
e
u
tili
ze
d
f
o
r
r
ap
id
e
n
er
g
y
tr
an
s
itio
n
s
,
wh
ile
lin
e
-
f
r
eq
u
en
cy
s
witch
es
(
S2
an
d
S5
)
en
s
u
r
e
p
r
o
p
er
g
r
id
s
y
n
c
h
r
o
n
izatio
n
[
1
8
]
.
A
d
is
tin
g
u
is
h
in
g
f
ea
tu
r
e
o
f
th
is
d
esig
n
is
th
e
d
ir
ec
t
g
r
o
u
n
d
in
g
o
f
th
e
PV
n
eg
ativ
e
ter
m
in
al,
ef
f
ec
tiv
ely
elim
in
atin
g
leak
ag
e
cu
r
r
en
ts
an
d
m
ee
tin
g
I
E
E
E
h
ar
m
o
n
ic
s
tan
d
a
r
d
s
[
1
9
]
,
[
2
0
]
.
T
h
e
s
y
s
tem
o
p
e
r
ates
s
ea
m
less
ly
in
f
o
u
r
m
o
d
es,
en
s
u
r
i
n
g
ef
f
icien
t
e
n
er
g
y
s
to
r
ag
e
an
d
d
eliv
er
y
.
T
h
e
g
r
id
is
co
n
n
ec
ted
th
r
o
u
g
h
b
o
th
n
e
g
ativ
e
an
d
p
o
s
itiv
e
c
y
cles.
Fig
u
r
e
1
illu
s
tr
ates
th
e
p
r
o
p
o
s
ed
to
p
o
l
o
g
y
f
o
r
a
b
u
c
k
-
b
o
o
s
t tr
an
s
f
o
r
m
er
less
in
v
er
ter
(
B
B
T
I
)
.
Fig
u
r
e
1
.
T
h
e
r
ec
o
m
m
en
d
e
d
c
o
n
f
ig
u
r
atio
n
f
o
r
a
B
B
T
I
2
.
2
.
O
pera
t
io
na
l mo
des
o
f
t
he
t
ra
ns
f
o
rm
er
less
inv
er
t
er
T
h
e
f
o
u
r
d
if
f
er
en
t
m
o
d
es
o
f
th
e
B
B
T
I
'
s
co
n
tin
u
o
u
s
co
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
f
u
n
cti
o
n
in
g
ar
e
d
esig
n
ated
Mo
d
e
(
a
)
th
r
o
u
g
h
Mo
d
e
(
d
)
,
wh
ich
r
ep
r
esen
t
th
e
g
r
id
'
s
p
o
s
itiv
e
an
d
n
eg
ati
v
e
h
alf
-
cy
cles.
I
n
p
ar
ticu
lar
,
M
o
d
es
(
a)
an
d
(
b
)
s
tan
d
f
o
r
th
e
p
o
s
itiv
e
h
alf
-
cy
c
le,
an
d
Mo
d
es
(
c
)
an
d
(
d
)
f
o
r
th
e
n
e
g
ativ
e
h
alf
-
cy
cle
,
as
illu
s
tr
ated
in
Fig
u
r
es
2
(
a)
–
2
(
d
)
.
E
ac
h
m
o
d
e
is
d
ef
i
n
ed
b
y
a
u
n
iq
u
e
co
n
f
ig
u
r
atio
n
o
f
s
witch
in
g
s
tates,
en
ab
lin
g
co
n
tr
o
lled
e
n
er
g
y
tr
a
n
s
f
er
an
d
e
f
f
icien
t g
r
id
in
ter
ac
tio
n
.
T
h
e
o
p
er
atio
n
al
b
e
h
av
io
r
o
f
th
e
B
B
T
I
u
n
d
e
r
th
ese
f
o
u
r
m
o
d
es is
d
escr
ib
ed
b
elo
w.
−
Mo
d
e
A:
en
er
g
y
co
llectio
n
an
d
o
u
tp
u
t su
p
p
ly
(
p
o
s
itiv
e
cy
cl
e
)
Du
r
in
g
t
h
is
m
o
d
e
,
as
s
ee
n
in
Fig
u
r
e
2
(
a)
,
S1
,
S3
,
a
n
d
S5
ar
e
tu
r
n
ed
ON
to
d
eliv
er
p
o
wer
to
th
e
g
r
id
.
T
h
e
in
d
u
cto
r
L
s
to
r
es
p
o
wer
f
r
o
m
th
e
r
en
ewa
b
le
s
o
u
r
ce
(
s
u
ch
as
PV)
th
r
o
u
g
h
S1
,
wh
ile
th
e
ca
p
ac
ito
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
h
yb
r
id
o
n
e
s
tep
vo
lta
g
e
-
a
d
j
u
s
ta
b
le
tr
a
n
s
fo
r
merles
s
in
ve
r
t
er fo
r
a
o
n
e
-
p
h
a
s
e
g
r
id
…
(
B
o
n
ig
a
la
R
a
mesh
)
953
s
u
p
p
lies
p
o
wer
to
m
ain
tain
o
u
tp
u
t
co
n
tin
u
ity
.
T
h
e
cu
r
r
e
n
t
f
lo
w
p
ath
to
th
e
g
r
id
is
estab
lis
h
ed
v
ia
s
witch
es
S3
an
d
S5
.
T
h
is
s
witch
in
g
ar
r
an
g
e
m
en
t
e
n
s
u
r
es
ef
f
icien
t
en
er
g
y
tr
an
s
f
er
an
d
m
in
im
izes
p
o
wer
lo
s
s
d
u
r
in
g
th
e
p
o
s
itiv
e
h
alf
c
y
cle.
−
Mo
d
e
B
:
in
d
u
cto
r
en
er
g
y
tr
an
s
f
er
(
p
o
s
itiv
e
cy
cle
)
I
n
th
is
m
o
d
e,
as
illu
s
tr
ated
in
Fig
u
r
e
2
(
b
)
,
o
n
ly
S
5
is
tu
r
n
e
d
ON,
wh
ile
all
o
th
er
s
witch
es
r
em
ain
OFF.
T
h
e
ca
p
ac
ito
r
r
ec
eiv
es
th
e
s
to
r
ed
p
o
wer
f
r
o
m
th
e
in
d
u
cto
r
L
v
ia
d
io
d
e
D
a
n
d
s
witch
S
2
'
s
a
n
tip
ar
allel
d
io
d
e.
Simu
ltan
e
o
u
s
ly
,
th
e
in
d
u
cto
r
allo
ws
cu
r
r
en
t
to
f
r
ee
wh
ee
l
v
ia
S
5
an
d
th
e
an
tip
a
r
a
llel
d
io
d
e
o
f
S
2
.
T
h
e
co
m
p
lete
co
n
d
u
ctio
n
p
ath
f
o
r
th
is
f
r
ee
wh
ee
lin
g
p
h
a
s
e
is
m
ar
k
ed
with
in
Fig
u
r
e
2
(
b
)
,
e
n
s
u
r
in
g
ef
f
icien
t e
n
er
g
y
r
e
d
ir
ec
tio
n
a
n
d
r
ed
u
ce
d
s
witch
in
g
lo
s
s
es.
−
Mo
d
e
C
:
r
ev
er
s
e
cy
cle
p
o
wer
d
eliv
er
y
(
n
eg
ativ
e
c
y
cle
)
T
h
is
m
o
d
e,
s
h
o
wn
in
Fig
u
r
e
2
(
c)
,
co
r
r
esp
o
n
d
s
to
th
e
n
eg
at
iv
e
h
alf
-
cy
cle
p
o
wer
d
eliv
er
y
.
In
th
is
p
h
ase
,
s
witch
es
S
4
,
S
1
,
an
d
S
2
ar
e
t
u
r
n
ed
ON.
T
h
e
in
d
u
ct
o
r
L
tak
es
p
o
wer
f
r
o
m
t
h
e
r
e
n
ewa
b
le
s
o
u
r
ce
v
ia
S
1
,
wh
ile
th
e
ca
p
ac
ito
r
g
iv
es
p
o
wer
to
th
e
g
r
i
d
th
r
o
u
g
h
S
2
a
n
d
S
4
.
All
cu
r
r
e
n
t
-
co
n
d
u
ctin
g
p
ath
s
ar
e
h
ig
h
lig
h
ted
in
Fig
u
r
e
2
(
c
)
,
en
s
u
r
in
g
e
f
f
icien
t
en
e
r
g
y
t
r
a
n
s
f
er
an
d
m
ain
tain
in
g
s
y
s
tem
s
tab
ilit
y
,
as
d
etailed
in
[
2
1
]
.
−
Mo
d
e
D:
co
n
tr
o
lled
en
er
g
y
d
is
s
ip
atio
n
(
n
eg
ativ
e
c
y
cle
)
T
h
is
m
o
d
e,
s
h
o
wn
in
Fig
u
r
e
2
(
d
)
,
co
r
r
esp
o
n
d
s
to
th
e
n
eg
ati
v
e
h
alf
-
cy
cle
f
r
ee
wh
ee
lin
g
o
p
er
atio
n
.
I
n
th
is
p
h
ase,
o
n
ly
S
2
r
em
ain
s
ON
wh
ile
all
o
th
er
p
o
wer
s
witch
es
ar
e
tu
r
n
ed
OFF.
T
h
e
ca
p
ac
ito
r
r
ec
eiv
es
th
e
s
to
r
ed
p
o
wer
f
r
o
m
th
e
i
n
d
u
cto
r
L
v
ia
d
io
d
e
D
an
d
s
wit
ch
S
5
'
s
an
tip
ar
allel
d
io
d
e.
C
o
n
cu
r
r
e
n
tly
,
th
e
g
r
id
in
d
u
cto
r
cu
r
r
en
t
f
r
ee
wh
e
els
th
r
o
u
g
h
s
witch
S
2
an
d
S
5
'
s
an
tip
ar
allel
d
io
d
e
.
As
in
d
icate
d
in
Fig
u
r
e
2
(
d
)
,
all
ac
tiv
e
co
n
d
u
ctio
n
p
ath
s
ar
e
h
ig
h
lig
h
ted
with
th
ick
l
in
es,
en
s
u
r
in
g
m
in
im
al
s
witch
in
g
lo
s
s
es
an
d
ex
ten
d
ed
c
o
m
p
o
n
en
t lif
e
[
2
2
]
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
2
.
T
h
e
o
p
er
atio
n
al
m
o
d
es: (
a)
p
o
wer
in
g
m
o
d
e
(
p
o
s
itiv
e
h
alf
cy
cle
)
,
(
b
)
f
r
ee
wh
ee
lin
g
m
o
d
e
(
p
o
s
itiv
e
h
alf
cy
cle)
,
(
c)
p
o
wer
in
g
m
o
d
e
(
n
eg
ativ
e
h
alf
cy
cle)
,
an
d
(
d
)
f
r
ee
wh
ee
lin
g
m
o
d
e
(
n
eg
ativ
e
h
alf
cy
cle)
2
.
3
.
Ste
a
dy
-
s
t
a
t
e
e
x
a
m
ina
t
io
n o
f
t
he
s
ug
g
este
d B
B
T
I
T
h
e
s
tab
le
-
s
tate
ev
alu
atio
n
o
f
th
e
r
ec
o
m
m
en
d
ed
B
B
T
I
r
elies
o
n
th
e
s
u
b
s
eq
u
e
n
t
ass
u
m
p
tio
n
s
:
i)
T
h
e
DC
ca
p
ac
ito
r
is
ad
eq
u
ately
s
ized
to
en
s
u
r
e
a
s
tab
le
v
o
lt
ag
e
is
m
ain
tain
ed
ac
r
o
s
s
its
ter
m
in
als
;
ii)
All
s
em
ico
n
d
u
cto
r
d
e
v
ices
o
p
er
at
e
with
o
u
t
an
y
lo
s
s
es
;
an
d
(
iii)
Par
asit
ic
e
lem
en
ts
ar
e
n
eg
lig
ib
le.
T
h
e
f
o
llo
win
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
9
5
1
-
959
954
ex
p
r
ess
io
n
is
o
b
tain
ed
b
y
u
s
in
g
th
e
p
r
in
cip
le
of
v
o
ltag
e
m
ain
tain
in
g
o
v
e
r
an
in
d
u
cto
r
L
.
T
h
e
au
x
iliar
y
ca
p
ac
ito
r
’
s
v
o
ltag
e
(
C
A)
ca
n
b
e
f
o
u
n
d
u
s
in
g
(
1
)
.
∫
+
∫
(
−
)
=
0
0
(
1
)
=
(
1
−
)
(
2
)
T
h
e
f
o
llo
win
g
is
an
ex
p
r
ess
io
n
f
o
r
th
e
h
ig
h
est
AC
o
u
tp
u
t
v
o
ltag
e
.
T
h
e
p
r
e
d
icted
B
B
T
I
g
ain
ca
n
b
e
attain
ed
b
y
ch
a
n
g
in
g
(
2
)
i
n
(
3
)
.
=
×
(
3
)
=
=
(
2
1
−
)
(
4
)
W
h
er
e
is
th
e
v
o
ltag
e
f
r
o
m
th
e
p
h
o
to
v
o
ltaic
(
PV)
p
an
el,
is
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
au
x
ilia
r
y
ca
p
ac
ito
r
,
is
th
e
p
ea
k
AC
o
u
tp
u
t v
o
ltag
e
,
is
th
e
v
o
ltag
e
g
ain
/
,
is
th
e
m
o
d
u
latio
n
in
d
e
x
(
d
u
ty
r
atio
in
th
e
s
witch
in
g
cy
cle)
,
an
d
is
s
witc
h
in
g
tim
e
p
e
r
io
d
.
2
.
4
.
Desig
n o
f
B
B
T
I
t
o
po
lo
g
y
ener
g
y
re
t
ent
io
n
c
o
m
po
ne
nts
2
.
4
.
1
.
I
nd
uct
o
r
(
L
)
f
o
r
ener
g
y
re
t
ent
io
n
T
h
e
d
esig
n
o
f
th
e
in
p
u
t e
n
er
g
y
r
eten
tio
n
in
d
u
cto
r
(
L
)
f
o
r
th
e
p
r
o
p
o
s
ed
B
B
T
I
is
an
alo
g
o
u
s
t
o
th
at
o
f
a
ty
p
ical
b
u
c
k
-
b
o
o
s
t
d
i
r
ec
t
cu
r
r
en
t
to
d
ir
ec
t
c
u
r
r
e
n
t
co
n
v
er
ter
.
T
h
e
in
d
u
ctan
ce
v
alu
e
is
s
elec
ted
to
en
s
u
r
e
th
at
th
e
B
B
T
I
o
p
er
ates
in
co
n
ti
n
u
o
u
s
c
o
n
d
u
ctio
n
m
o
d
e
(
C
C
M)
.
T
o
ac
h
ie
v
e
C
C
M
o
p
er
atio
n
,
th
e
cr
itical
in
d
u
ctan
ce
(
L
c
)
m
u
s
t
b
e
less
th
an
th
e
in
d
u
ctan
ce
.
T
h
e
f
o
llo
win
g
f
o
r
m
u
la
is
u
s
ed
to
ca
lcu
late
cr
itical
in
d
u
ctan
ce
.
=
(
)
2
2
0
(
5
)
W
h
er
e
M
i
is
th
e
m
o
d
u
latio
n
in
d
ex
,
V
pv
is
PV
v
o
ltag
e
in
p
u
t,
P
o
is
AC
en
er
g
y
o
u
tp
u
t
,
an
d
f
s
is
s
witch
in
g
f
r
eq
u
e
n
cy
.
2
.
4
.
2
.
Aux
ilia
ry
ca
pa
cit
o
r
a
r
chit
ec
t
ure
(
)
T
h
e
au
x
iliar
y
ca
p
ac
ito
r
(
C
A
)
is
d
esig
n
ed
to
m
an
ag
e
en
er
g
y
s
to
r
ag
e
an
d
s
tab
ilize
v
o
ltag
e
lev
els
in
th
e
s
y
s
tem
.
A
v
o
ltag
e
r
ip
p
le
o
f
5
%
is
ty
p
ically
co
n
s
id
er
ed
s
u
f
f
i
cien
t
f
o
r
s
tab
le
o
p
er
atio
n
.
T
h
e
au
x
iliar
y
ca
p
ac
ito
r
v
alu
e
is
ca
lcu
lated
u
s
in
g
(
6
)
.
≥
∆
×
×
(
6
)
W
h
er
e
is
th
e
a
u
x
iliar
y
ca
p
ac
ito
r
(
o
u
tp
u
t
-
s
id
e
ca
p
ac
ito
r
)
v
alu
e,
is
th
e
o
u
tp
u
t
p
o
wer
d
eliv
er
ed
to
th
e
lo
ad
,
∆
is
a
llo
wed
r
ip
p
le
o
r
v
o
ltag
e
d
ev
iatio
n
ac
r
o
s
s
th
e
au
x
iliar
y
c
ap
ac
ito
r
,
is
s
w
itch
in
g
f
r
eq
u
e
n
cy
,
an
d
is
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
a
u
x
iliar
y
ca
p
ac
ito
r
.
W
h
er
e
P
r
e
p
r
esen
ts
th
e
o
u
tp
u
t
p
o
wer
,
V
is
th
e
p
o
ten
tial
alo
n
g
th
e
s
u
p
p
lem
en
tar
y
ca
p
ac
ito
r
,
with
Δ
V
s
er
v
in
g
as
th
e
p
er
m
is
s
ib
le
r
ip
p
le
v
o
ltag
e.
T
h
ese
p
ar
am
eter
s
h
elp
m
ain
tai
n
s
tab
le
v
o
ltag
e
lev
els wh
ile
ac
co
m
m
o
d
atin
g
p
o
wer
f
lu
ctu
atio
n
s
.
3.
M
E
T
H
O
DS
O
F
M
O
D
UL
A
T
I
O
N
AN
D
SUP
E
RVI
SI
O
N
F
O
R
T
H
E
B
B
T
I
A
RC
H
I
T
E
CT
U
RE
DE
S
I
G
N
3
.
1
.
Co
ntr
o
l
a
nd
m
o
du
la
t
io
n
s
t
ra
t
eg
y
f
o
r
t
he
BBTI
t
o
po
lo
g
y
Fig
u
r
e
3
s
h
o
ws
th
e
m
o
d
u
latio
n
tech
n
iq
u
e
f
o
r
th
e
s
u
g
g
ested
T
r
an
s
f
o
r
m
er
less
I
n
v
er
ter
with
B
B
T
I
.
I
t
em
p
lo
y
s
a
tr
ian
g
le
-
s
h
ap
ed
r
ef
er
en
ce
wav
e
f
o
r
m
to
p
r
o
d
u
ce
th
e
f
iv
e
co
n
tr
o
llab
le
s
witch
es'
s
witch
in
g
s
ig
n
als.
(
S1
to
S5
)
.
T
h
is
s
tr
ateg
y
e
n
s
u
r
es
ef
f
icien
t
o
p
e
r
atio
n
w
h
ile
m
ain
tain
in
g
s
y
n
c
h
r
o
n
iza
tio
n
with
th
e
g
r
i
d
,
allo
win
g
s
ea
m
less
p
o
wer
tr
an
s
f
er
f
r
o
m
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
to
th
e
g
r
id
[
2
3
]
.
T
h
e
m
o
d
u
latio
n
p
r
o
ce
s
s
in
v
o
l
v
es th
e
f
o
llo
win
g
s
tep
s
:
−
T
h
e
in
p
u
t
wav
e
f
o
r
m
(
Vin
)
,
it
s
ab
s
o
lu
te
v
alu
e
(
∣
Vin
∣
)
,
a
n
d
its
in
v
er
s
e
(
−V
in
)
ar
e
co
m
p
a
r
ed
ag
ai
n
s
t
a
h
ig
h
-
f
r
eq
u
e
n
cy
tr
ian
g
u
lar
r
ef
e
r
en
ce
wav
ef
o
r
m
.
−
Switch
es
S
2
an
d
S
5
o
p
er
ate
at
th
e
g
r
id
’
s
lin
e
f
r
eq
u
e
n
cy
o
f
5
0
Hz,
e
n
s
u
r
in
g
s
y
n
ch
r
o
n
izatio
n
with
th
e
AC
v
o
ltag
e
cy
cle.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
h
yb
r
id
o
n
e
s
tep
vo
lta
g
e
-
a
d
j
u
s
ta
b
le
tr
a
n
s
fo
r
merles
s
in
ve
r
t
er fo
r
a
o
n
e
-
p
h
a
s
e
g
r
id
…
(
B
o
n
ig
a
la
R
a
mesh
)
955
−
Switch
S
3
p
u
ls
es
ar
e
d
er
iv
ed
b
y
co
m
p
a
r
in
g
∣
Vin
∣
with
th
e
tr
i
an
g
u
lar
r
ef
er
en
ce
wav
ef
o
r
m
.
−
Similar
ly
,
th
e
p
u
ls
es
f
o
r
S
1
a
n
d
S
4
a
r
e
g
en
er
ate
d
b
y
c
o
m
p
ar
in
g
Vin
an
d
−V
in
,
r
esp
ec
ti
v
ely
,
with
th
e
r
ef
er
en
ce
wav
e
f
o
r
m
.
T
h
is
m
o
d
u
latio
n
ap
p
r
o
ac
h
en
ab
les
p
r
ec
is
e
co
n
tr
o
l
o
v
er
en
er
g
y
tr
a
n
s
f
er
,
m
in
im
izi
n
g
s
witch
in
g
lo
s
s
es
an
d
en
s
u
r
in
g
s
tab
le
o
p
er
atio
n
.
T
h
e
cu
r
r
e
n
t
m
o
d
u
latio
n
tech
n
iq
u
e
m
ain
tain
s
s
ea
m
less
p
o
wer
f
lo
w
t
o
th
e
g
r
id
,
o
p
tim
izin
g
en
e
r
g
y
u
s
ag
e
f
r
o
m
r
en
ewa
b
le
s
o
u
r
ce
s
s
u
ch
as so
l
ar
an
d
win
d
[
2
4
]
,
[
2
5
]
.
Fig
u
r
e
3
.
T
h
e
B
B
T
I
to
p
o
lo
g
y
'
s
m
o
d
u
latio
n
a
p
p
r
o
ac
h
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
T
h
e
h
y
b
r
id
s
o
lar
-
win
d
g
r
id
-
co
n
n
ec
ted
b
u
c
k
-
b
o
o
s
t
tr
an
s
f
o
r
m
er
less
in
v
er
ter
(
B
B
T
I
)
s
y
s
tem
was
m
o
d
elled
a
n
d
s
im
u
lated
in
Si
m
u
lin
k
/MAT
L
AB
with
3
0
0
W
en
er
g
y
r
an
g
in
g
.
T
a
b
le
1
lis
ts
th
e
s
p
ec
if
ics
o
f
th
e
s
y
s
tem
th
at
was
u
tili
ze
d
f
o
r
th
e
s
im
u
latio
n
s
.
T
h
e
co
m
b
in
e
d
in
p
u
t
v
o
ltag
e
s
o
u
r
ce
s
,
i
n
clu
d
in
g
b
o
th
s
o
lar
PV
an
d
win
d
e
n
er
g
y
,
d
eliv
er
a
to
t
al
v
o
ltag
e.
T
h
e
s
u
g
g
ested
B
B
T
I
co
n
f
i
g
u
r
atio
n
ef
f
ec
tiv
ely
tr
an
s
f
er
s
th
e
h
ig
h
est
p
o
wer
ac
ce
s
s
ib
le
f
r
o
m
th
e
h
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r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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ates
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N:
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RE
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NC
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S
[
1
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.
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[
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5
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