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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Vo
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15
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No
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3
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J
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20
25
:
2
5
8
3
-
2
5
9
8
2584
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s
in
teg
r
ated
with
AC
g
r
id
s
.
T
h
e
s
tu
d
y
ad
d
r
ess
es
th
e
cr
itical
p
r
o
b
lem
o
f
i
n
ef
f
icien
cy
,
p
o
o
r
p
o
wer
q
u
ality
,
a
n
d
g
r
id
s
y
n
ch
r
o
n
izatio
n
ch
allen
g
es
th
at
p
lag
u
e
c
o
n
v
e
n
tio
n
al
in
v
e
r
ter
s
.
B
y
in
tr
o
d
u
ci
n
g
a
h
y
b
r
id
p
h
ase
-
lo
c
k
ed
lo
o
p
(
PLL
)
c
o
n
tr
o
ller
e
n
h
an
ce
d
with
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
S
MC)
,
th
e
p
r
o
p
o
s
ed
in
v
er
ter
a
ch
iev
es
s
u
p
er
io
r
p
e
r
f
o
r
m
an
ce
in
MPPT
ef
f
icien
cy
an
d
r
ed
u
ce
s
t
o
tal
h
a
r
m
o
n
ic
d
i
s
to
r
tio
n
(
T
HD)
.
T
h
e
p
a
p
er
ac
cu
r
ate
ex
a
m
in
es
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
in
v
er
ter
ac
r
o
s
s
v
ar
io
u
s
s
ce
n
ar
io
s
,
in
clu
d
in
g
s
tan
d
alo
n
e
o
p
er
atio
n
with
o
u
t
g
r
id
co
n
n
ec
tio
n
,
g
r
i
d
d
is
co
n
n
ec
tio
n
an
d
r
ec
o
n
n
ec
tio
n
,
f
r
eq
u
e
n
cy
d
is
tu
r
b
an
ce
s
,
a
n
d
am
p
litu
d
e
ch
a
n
g
es
in
g
r
id
s
u
p
p
ly
.
T
h
ese
ca
s
es
h
ig
h
lig
h
t
th
e
r
o
b
u
s
tn
ess
an
d
r
esil
ien
ce
o
f
th
e
p
r
o
p
o
s
ed
in
v
er
ter
d
esig
n
u
n
d
er
r
ea
l
-
wo
r
l
d
co
n
d
itio
n
s
.
T
h
e
r
esear
ch
s
ets
a
n
ew
b
en
c
h
m
ar
k
f
o
r
PV
s
y
s
tem
in
teg
r
atio
n
,
co
n
tr
ib
u
tin
g
to
t
h
e
b
r
o
ad
e
r
a
d
o
p
tio
n
o
f
r
en
ewa
b
le
en
er
g
y
tech
n
o
lo
g
ies an
d
s
u
p
p
o
r
tin
g
t
h
e
s
u
s
tain
ab
le
d
ev
elo
p
m
en
t o
f
en
er
g
y
s
y
s
tem
s
g
lo
b
ally
.
2.
M
E
T
H
O
D
T
h
e
b
o
o
s
t
co
n
v
e
r
ter
is
a
DC
-
DC
co
n
v
er
ter
u
tili
ze
d
i
n
PV
s
y
s
tem
s
to
elev
ate
th
e
v
o
ltag
e
o
f
th
e
DC
p
o
wer
g
en
e
r
ated
b
y
th
e
PV
p
an
els
to
lev
els
co
m
p
atib
le
with
th
e
g
r
id
o
r
o
th
er
lo
a
d
s
.
T
h
e
d
u
ty
cy
cle
o
f
th
e
b
o
o
s
t
co
n
v
er
ter
is
ad
ju
s
tab
le
to
p
r
o
v
id
e
c
o
n
tr
o
l,
an
d
it
m
ay
in
co
r
p
o
r
ate
p
r
o
tectiv
e
f
ea
tu
r
e
s
to
p
r
ev
en
t
s
y
s
tem
d
am
ag
e
[
2
]
.
T
h
e
ef
f
icien
cy
o
f
th
e
b
o
o
s
t
co
n
v
er
ter
is
a
c
r
itical
f
ac
to
r
in
PV
s
y
s
tem
d
esig
n
,
u
s
ed
in
co
n
ju
n
ctio
n
with
an
MPPT
co
n
tr
o
ller
t
o
o
p
tim
ize
th
e
en
er
g
y
o
u
tp
u
t
f
r
o
m
th
e
PV
p
an
els.
Po
wer
in
v
er
ter
s
,
wh
ich
co
n
v
er
t
DC
in
to
AC
,
p
lay
an
ess
en
tial
r
o
le
i
n
PV
s
y
s
tem
s
b
y
tr
a
n
s
f
o
r
m
in
g
th
e
DC
p
o
wer
f
r
o
m
PV
p
an
els
in
to
AC
p
o
wer
n
ec
ess
ar
y
f
o
r
g
r
id
c
o
n
n
ec
tio
n
o
r
p
o
wer
in
g
AC
lo
ad
s
.
Var
io
u
s
c
o
n
tr
o
l
s
ch
e
m
es
o
p
tim
ize
th
ese
in
v
er
ter
s
'
p
er
f
o
r
m
an
ce
a
n
d
ef
f
icien
cy
[
3
]
.
GaN
tr
an
s
is
to
r
s
ar
e
p
r
e
f
er
r
ed
in
p
o
wer
co
n
v
e
r
ter
s
f
o
r
r
en
ewa
b
le
en
er
g
y
s
y
s
tem
s
b
ec
au
s
e
o
f
th
eir
s
u
p
er
io
r
e
f
f
icien
cy
,
p
o
wer
d
en
s
ity
,
s
witch
in
g
s
p
ee
d
,
th
e
r
m
al
p
er
f
o
r
m
an
ce
,
an
d
p
o
te
n
tial c
o
s
t
-
ef
f
ec
tiv
en
es
s
[
4
]
.
T
h
is
s
tu
d
y
in
co
r
p
o
r
ates
a
C
u
k
s
witch
in
g
m
o
d
e
p
o
wer
s
u
p
p
ly
(
SMPS)
an
d
a
s
lid
in
g
m
o
d
e
co
n
tr
o
l
s
ch
em
e
in
th
e
p
h
o
t
o
v
o
ltaic
i
n
v
er
ter
d
esig
n
t
o
ac
h
iev
e
r
eliab
le
clo
s
ed
-
lo
o
p
p
er
f
o
r
m
a
n
ce
.
T
h
is
m
eth
o
d
o
l
o
g
y
en
ab
les
th
e
u
s
e
o
f
s
m
aller
,
m
o
r
e
r
eliab
le
n
o
n
-
elec
tr
o
ly
tic
ca
p
ac
ito
r
s
.
A
p
r
o
to
ty
p
e
in
v
e
r
ter
was
d
ev
elo
p
ed
to
test
th
e
d
esig
n
[
5
]
.
T
h
e
r
e
s
ea
r
ch
d
is
cu
s
s
es
an
MPPT
m
eth
o
d
b
ased
o
n
ad
ap
tiv
e
s
lid
i
n
g
m
o
d
e
co
n
tr
o
l.
T
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
u
s
es
an
ad
ap
tiv
e
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
(
ASMC)
to
d
r
iv
e
a
b
o
o
s
t
co
n
v
e
r
ter
th
at
co
n
n
ec
ts
th
e
PV
g
en
er
at
o
r
to
th
e
lo
ad
.
T
h
e
ef
f
icien
c
y
o
f
t
h
is
tech
n
iq
u
e
is
v
alid
ated
b
y
s
im
u
latio
n
r
esu
lts
u
s
in
g
r
ea
l
d
ata
in
MA
T
L
AB
/
Simu
lin
k
,
an
d
th
e
ASMC
co
n
tr
o
ller
'
s
d
u
r
ab
ilit
y
an
d
s
tab
ilit
y
ar
e
test
ed
u
n
d
er
v
ar
iab
le
wea
th
e
r
co
n
d
itio
n
s
[
6
]
.
L
i
u
et
a
l.
[
7
]
p
r
o
p
o
s
e
a
two
-
m
o
d
e
co
n
tr
o
l
s
tr
ateg
y
f
o
r
b
id
ir
ec
tio
n
al
p
o
wer
co
n
v
er
ter
s
in
AC
/DC
h
y
b
r
id
m
icr
o
g
r
id
s
o
p
e
r
atin
g
u
n
d
er
wea
k
g
r
id
co
n
d
itio
n
s
.
T
h
ey
ac
h
iev
e
s
tab
ilit
y
b
y
m
an
ag
in
g
th
e
s
h
o
r
t
-
cir
c
u
it
r
atio
,
co
n
t
r
o
llin
g
v
o
ltag
e
an
d
cu
r
r
e
n
t
s
o
u
r
ce
s
,
an
d
m
itig
atin
g
s
y
s
tem
in
e
r
tia.
Simu
latio
n
r
esu
lts
d
em
o
n
s
tr
ate
th
is
s
tr
ateg
y
's
ef
f
ec
tiv
en
ess
.
A
r
o
b
u
s
t
n
o
n
-
lin
ea
r
co
n
t
r
o
ller
f
o
r
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
s
(
VSC
s
)
co
n
n
ec
te
d
to
u
n
r
eliab
le
AC
n
etwo
r
k
s
.
T
h
is
co
n
tr
o
ller
,
d
esig
n
e
d
u
s
in
g
f
ee
d
b
ac
k
lin
ea
r
izatio
n
tech
n
iq
u
e,
m
a
n
a
g
es
th
e
ac
tiv
e
p
o
wer
an
d
o
u
tp
u
t
v
o
ltag
e
o
f
g
r
id
-
c
o
n
n
ec
te
d
co
n
v
er
ter
s
.
I
t
is
ca
p
ab
le
o
f
h
an
d
lin
g
f
a
u
lts
an
d
s
u
s
tain
in
g
p
er
f
o
r
m
an
ce
u
n
d
er
u
n
ex
p
ec
ted
ac
tiv
e
p
o
wer
d
em
an
d
s
in
h
ig
h
ly
u
n
s
tab
le
AC
g
r
id
co
n
d
itio
n
s
.
T
h
e
co
n
tr
o
ller
'
s
r
o
b
u
s
tn
ess
is
ev
alu
ated
th
r
o
u
g
h
tim
e
-
d
o
m
ain
s
im
u
latio
n
s
an
d
eig
en
v
alu
e
a
n
aly
s
is
[
9
]
.
Mic
r
o
g
r
id
s
ar
e
co
n
s
id
er
e
d
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
ts
o
f
a
s
m
ar
t
g
r
id
,
in
v
o
lv
in
g
p
r
o
ce
d
u
r
es
an
d
co
n
tr
o
ls
s
u
ch
as
lo
ad
s
h
ar
in
g
,
f
au
lt
is
o
latio
n
,
an
d
v
o
ltag
e
m
atch
in
g
.
T
h
e
p
ap
er
r
e
v
iews
th
e
f
o
u
r
p
r
im
ar
y
co
n
tr
o
l
s
tr
ateg
ies
em
p
lo
y
e
d
in
m
icr
o
g
r
i
d
s
an
d
th
e
ch
allen
g
es
en
co
u
n
ter
e
d
d
u
r
in
g
o
p
er
atio
n
in
b
o
th
g
r
id
-
co
n
n
ec
ted
an
d
s
tan
d
alo
n
e
m
o
d
es.
I
t
also
ex
p
l
o
r
es
alter
n
ati
v
e
s
tr
ateg
ies
f
o
r
m
ic
r
o
g
r
i
d
in
t
eg
r
atio
n
an
d
f
u
t
u
r
e
r
esear
ch
d
ir
ec
tio
n
s
[
1
0
]
.
A
b
o
o
s
t
co
n
v
er
te
r
lin
k
s
t
h
e
PV
p
a
n
els
to
th
e
lo
ad
,
an
d
an
in
v
er
t
er
eq
u
i
p
p
ed
with
a
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
(
PI)
c
o
n
tr
o
ller
co
n
v
e
r
ts
th
e
v
o
ltag
e
f
r
o
m
DC
to
AC
.
MA
T
L
AB
/S
im
u
lin
k
s
im
u
latio
n
r
esu
lts
af
f
ir
m
th
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
s
u
g
g
ested
c
o
n
tr
o
l
[
1
1
]
,
[
1
2
]
.
Ph
o
to
v
o
ltaic
s
y
s
tem
s
o
p
er
ate
b
ased
o
n
th
e
p
h
o
to
v
o
ltaic
ef
f
ec
t,
wh
er
e
e
lectr
o
n
-
h
o
le
p
air
s
a
r
e
g
e
n
er
ated
in
s
em
ico
n
d
u
cto
r
m
ate
r
ials
u
p
o
n
p
h
o
to
n
ab
s
o
r
p
tio
n
f
r
o
m
s
u
n
lig
h
t.
T
h
e
s
ep
ar
atio
n
o
f
elec
tr
o
n
s
an
d
h
o
les
b
y
an
elec
tr
ic
f
ield
with
in
a
s
o
lar
ce
ll
p
r
o
d
u
ce
s
v
o
ltag
e
a
n
d
elec
tr
ic
cu
r
r
en
t,
tr
a
n
s
f
o
r
m
i
n
g
s
o
lar
e
n
er
g
y
in
to
elec
tr
ical
en
er
g
y
.
P
V
s
y
s
tem
s
u
s
e
th
i
s
m
ec
h
an
is
m
to
d
ir
ec
tly
c
o
n
v
er
t
s
u
n
lig
h
t
in
to
p
o
wer
,
em
p
l
o
y
in
g
s
em
ico
n
d
u
cto
r
m
ater
ials
lik
e
s
ilico
n
in
s
o
la
r
p
an
els
to
h
ar
n
ess
elec
tr
ical
en
er
g
y
f
r
o
m
s
o
lar
r
ad
iatio
n
.
Du
e
to
tech
n
o
lo
g
ical
ad
v
an
c
em
en
ts
an
d
r
e
d
u
ce
d
co
s
ts
,
p
h
o
to
v
o
ltaic
s
y
s
tem
s
h
av
e
b
ec
o
m
e
m
o
r
e
ac
ce
s
s
ib
le
an
d
co
s
t
-
ef
f
ec
tiv
e,
p
la
y
in
g
a
cr
u
cial
r
o
le
in
th
e
g
lo
b
al
tr
an
s
itio
n
to
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
[
1
3
]
–
[
1
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Dev
elo
p
in
g
g
a
lliu
m
n
itr
id
e
-
b
a
s
ed
in
ve
r
ters
fo
r
h
ig
h
-
p
erfo
r
ma
n
ce
…
(
A
r
s
a
la
n
Mu
h
a
mma
d
S
o
o
m
a
r
)
2585
2
.
1
.
P
rinciple o
pera
t
io
n
T
h
e
p
h
o
t
o
v
o
ltaic
ef
f
ec
t
in
s
e
m
ico
n
d
u
ct
o
r
m
ater
ials
lead
s
to
th
e
cr
ea
tio
n
o
f
elec
tr
o
n
-
h
o
le
p
air
s
u
p
o
n
th
e
ab
s
o
r
p
tio
n
o
f
s
u
n
lig
h
t,
a
k
ey
p
r
o
ce
s
s
f
o
r
c
o
n
v
e
r
tin
g
s
o
lar
en
er
g
y
in
to
elec
tr
icity
.
W
ith
in
a
s
o
lar
ce
ll,
a
n
elec
tr
ic
f
ield
s
ep
ar
ates
th
ese
elec
tr
o
n
s
an
d
h
o
les,
g
en
e
r
atin
g
v
o
ltag
e
an
d
c
u
r
r
en
t.
PV
s
y
s
tem
s
ca
p
italize
o
n
th
is
p
h
en
o
m
en
o
n
to
p
r
o
d
u
ce
elec
tr
icity
d
ir
ec
tly
f
r
o
m
s
u
n
lig
h
t,
u
s
in
g
s
ilico
n
s
o
lar
p
an
el
s
to
co
n
v
er
t
s
o
la
r
r
ad
iatio
n
in
to
elec
tr
ical
en
er
g
y
.
Du
e
to
tech
n
o
lo
g
ical
ad
v
a
n
ce
m
en
ts
an
d
d
ec
r
ea
s
in
g
co
s
t
s
,
PV
s
y
s
tem
s
h
av
e
g
r
o
wn
in
p
o
p
u
lar
ity
an
d
af
f
o
r
d
ab
ilit
y
,
m
ak
in
g
th
em
a
co
r
n
e
r
s
to
n
e
in
th
e
s
h
if
t
to
war
d
r
en
ewa
b
le
en
er
g
y
.
T
h
e
y
f
in
d
wid
esp
r
ea
d
u
s
e
in
r
esid
en
tial,
co
m
m
er
cial,
an
d
u
tili
ty
-
s
ca
le
ap
p
licatio
n
s
.
E
s
s
en
tial
co
m
p
o
n
e
n
ts
o
f
a
p
h
o
to
v
o
ltaic
s
y
s
tem
in
clu
d
e
s
o
lar
p
an
els,
in
v
er
ter
s
,
ch
ar
g
e
co
n
tr
o
ller
s
s
u
ch
as
MPPT,
b
a
tter
ies
f
o
r
b
ac
k
u
p
p
o
wer
s
to
r
a
g
e,
a
n
d
m
o
u
n
tin
g
s
tr
u
ctu
r
es.
So
lar
p
a
n
els
f
u
n
ctio
n
b
y
a
b
s
o
r
b
in
g
s
u
n
lig
h
t
an
d
p
r
o
d
u
cin
g
DC
elec
tr
icity
.
I
n
v
e
r
ter
s
ar
e
cr
iti
ca
l
as
th
ey
co
n
v
er
t
th
is
DC
elec
tr
icity
in
to
AC
,
wh
ich
is
s
u
itab
le
f
o
r
u
s
e
in
h
o
m
es
an
d
b
u
s
in
ess
es.
C
h
ar
g
e
co
n
tr
o
ller
s
ef
f
ec
tiv
ely
r
eg
u
l
ate
th
e
v
o
ltag
e
an
d
c
u
r
r
en
t
c
o
m
in
g
f
r
o
m
th
e
s
o
lar
p
an
els
to
s
af
ely
ch
ar
g
e
b
atter
i
es,
p
r
ev
en
tin
g
o
v
er
ch
a
r
g
in
g
a
n
d
ex
ten
d
i
n
g
b
atter
y
life
.
B
atter
ies
s
to
r
e
s
u
r
p
lu
s
elec
tr
icity
g
en
er
ated
d
u
r
in
g
p
ea
k
s
u
n
lig
h
t
h
o
u
r
s
f
o
r
u
s
e
at
o
th
er
tim
es,
en
h
an
cin
g
th
e
s
y
s
tem
'
s
ef
f
icien
cy
an
d
r
eliab
ilit
y
.
Fin
ally
,
m
o
u
n
tin
g
s
tr
u
ctu
r
es
p
r
o
v
id
e
th
e
n
ec
ess
ar
y
s
u
p
p
o
r
t
an
d
s
tab
ilit
y
,
allo
w
in
g
th
e
s
o
lar
p
an
els
to
b
e
in
s
talled
s
ec
u
r
ely
an
d
p
o
s
itio
n
ed
o
p
tim
ally
f
o
r
m
ax
i
m
u
m
s
u
n
lig
h
t e
x
p
o
s
u
r
e.
2
.
2
.
Desig
n o
f
inv
er
t
er
T
h
e
in
itial
s
tag
e
o
f
th
e
co
n
v
er
ter
p
r
esen
ted
i
n
Fig
u
r
e
1
c
en
ter
s
ar
o
u
n
d
th
e
DC
b
o
o
s
t,
u
tili
zin
g
a
tr
ad
itio
n
al
b
o
o
s
t
co
n
v
e
r
ter
s
etu
p
.
T
h
e
b
o
o
s
ted
DC
o
u
tp
u
t
is
s
u
b
s
eq
u
en
tly
co
n
n
ec
te
d
to
a
h
ig
h
elec
tr
o
n
m
o
b
ilit
y
tr
an
s
is
to
r
(
HE
MT
)
b
ased
o
n
GaN
,
wh
ich
is
r
eg
u
lated
b
y
a
PLL
.
T
h
e
PLL
's
p
r
i
m
ar
y
f
u
n
ctio
n
is
to
s
y
n
ch
r
o
n
ize
th
e
i
n
v
er
ter
with
th
e
g
r
id
'
s
AC
v
o
ltag
e.
T
h
e
o
u
tp
u
t
f
r
o
m
th
e
PLL
is
th
e
n
d
ir
ec
ted
to
th
e
co
n
tr
o
l
b
lo
ck
,
w
h
er
e
SMC
is
ap
p
lied
f
o
r
I
n
teg
r
atio
n
o
f
e
n
er
g
y
p
r
o
d
u
ce
d
f
r
o
m
s
o
lar
p
o
wer
ca
n
lead
to
d
is
astro
u
s
d
is
to
r
tio
n
in
v
o
ltag
e
an
d
cu
r
r
en
t
p
r
o
f
ile
o
f
th
e
AC
g
r
id
als
o
it
m
ay
lead
to
d
e
g
r
ad
i
n
g
th
e
ef
f
icien
cy
o
f
th
e
s
y
s
tem
[
1
6
]
.
T
h
is
co
n
tr
o
l
s
tr
at
eg
y
is
r
esp
o
n
s
ib
le
f
o
r
m
a
n
ag
i
n
g
th
e
p
o
wer
d
eliv
er
y
to
all
f
i
v
e
s
witch
es
in
b
o
t
h
th
e
DC
b
o
o
s
t
co
n
v
er
ter
an
d
t
h
e
in
v
er
ter
s
ec
tio
n
.
Fo
llo
win
g
th
e
co
n
tr
o
l
p
h
ase,
th
e
o
u
tp
u
t
f
r
o
m
th
e
in
v
e
r
ter
p
ass
es
th
r
o
u
g
h
an
L
C
L
f
ilter
co
n
f
ig
u
r
atio
n
,
c
o
m
p
r
is
in
g
an
in
d
u
cto
r
-
ca
p
ac
ito
r
-
in
d
u
cto
r
ar
r
a
n
g
em
en
t.
T
h
e
n
ec
ess
itates
th
e
d
ep
lo
y
m
e
n
t
o
f
L
C
L
f
ilter
s
as
a
s
tr
ateg
ic
ap
p
r
o
ac
h
t
o
lim
it
c
u
r
r
e
n
t
h
a
r
m
o
n
i
cs
ef
f
ec
tiv
ely
[
1
7
]
.
T
h
is
s
etu
p
is
wid
ely
u
s
ed
in
g
r
id
-
co
n
n
ec
ted
i
n
v
er
ter
s
d
u
e
to
its
ef
f
ec
tiv
en
ess
in
m
in
im
izin
g
g
r
i
d
in
te
r
f
er
en
ce
an
d
s
m
o
o
th
i
n
g
th
e
o
u
tp
u
t sig
n
al.
Fig
u
r
e
1
.
Sch
em
atic
v
iew
o
f
t
h
e
GaN
b
ased
in
v
er
te
r
T
h
e
in
n
o
v
ativ
e
asp
ec
t
o
f
th
e
p
r
o
p
o
s
ed
b
o
o
s
t
in
v
e
r
ter
lies
i
n
its
d
if
f
er
e
n
tial
co
n
n
ec
tio
n
a
cr
o
s
s
th
e
s
witch
es
o
f
th
e
DC
-
A
C
co
n
v
er
ter
to
f
ac
ilit
ate
th
e
DC
to
A
C
co
n
v
er
s
io
n
.
T
h
e
o
u
tp
u
t
v
o
ltag
es
f
r
o
m
th
e
DC
-
AC
co
n
v
er
ter
ar
e
s
in
u
s
o
id
all
y
m
o
d
u
lated
,
as
d
etailed
in
Fig
u
r
e
1
.
T
h
is
m
o
d
u
latio
n
a
p
p
r
o
ac
h
h
as
b
ee
n
p
r
ev
io
u
s
ly
ex
p
lo
r
ed
with
in
t
h
e
co
n
tex
t
o
f
b
o
o
s
t
co
n
v
er
te
r
s
.
T
h
e
co
n
v
er
te
r
s
g
en
er
ate
a
u
n
ip
o
lar
v
o
ltag
e
o
u
tp
u
t,
d
r
iv
e
n
b
y
t
h
e
s
in
u
s
o
id
al
m
o
d
u
latio
n
,
with
ea
ch
co
n
v
er
ter
’
s
m
o
d
u
latio
n
p
h
ase
s
h
if
ted
b
y
1
8
0
d
eg
r
ee
s
r
elativ
e
to
th
e
o
th
er
.
T
h
is
p
h
ase
s
h
if
t
m
ax
im
izes
th
e
v
o
ltag
e
ex
cu
r
s
io
n
ac
r
o
s
s
th
e
lo
ad
.
A
d
if
f
e
r
en
tial
co
n
n
ec
tio
n
ac
r
o
s
s
th
e
co
n
v
e
r
ter
s
is
e
s
tab
lis
h
ed
,
an
d
b
y
em
p
lo
y
in
g
th
e
av
er
ag
in
g
co
n
ce
p
t,
th
e
v
o
ltag
e
r
elatio
n
s
h
ip
in
co
n
tin
u
o
u
s
c
o
n
d
u
ctio
n
m
o
d
e
is
d
ef
in
e
d
.
Des
p
ite
th
e
p
r
esen
ce
o
f
an
AC
s
in
e
wav
e
at
ea
c
h
en
d
o
f
th
e
lo
ad
,
th
e
d
if
f
e
r
en
tial
DC
v
o
ltag
e
ac
r
o
s
s
th
e
co
n
n
ec
tio
n
r
em
ain
s
ze
r
o
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
is
d
eter
m
in
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
5
8
3
-
2
5
9
8
2586
th
r
o
u
g
h
a
s
p
ec
if
ic
f
o
r
m
u
la,
a
n
d
th
e
v
o
ltag
e
g
ain
f
o
r
th
e
b
o
o
s
t
in
v
er
ter
is
in
f
er
r
e
d
f
r
o
m
t
h
e
d
u
ty
c
y
cle
wh
en
th
e
co
n
v
er
ter
s
ar
e
p
h
ased
1
8
0
d
eg
r
ee
s
ap
ar
t,
as
s
tip
u
lated
in
(
1
)
.
On
e
in
tr
ig
u
in
g
ch
ar
ac
ter
i
s
tic
to
ac
h
iev
e
is
a
ze
r
o
-
o
u
tp
u
t
v
o
ltag
e,
with
v
ar
i
atio
n
s
in
th
e
d
u
ty
cy
cle
ar
o
u
n
d
th
is
p
o
in
t
r
esu
ltin
g
in
th
e
g
en
er
atio
n
o
f
an
AC
v
o
ltag
e
at
th
e
o
u
tp
u
t te
r
m
in
al.
V
1
V
in
=
1
1
−
D
(
1
)
2
.
3
.
Dev
el
o
pm
ent
o
f
a
r
o
bu
s
t
m
o
del o
f
t
he
inv
er
t
er
T
h
e
in
v
er
ter
'
s
co
n
tr
o
l
s
ch
em
e
an
d
s
ch
em
atic
ar
e
illu
s
tr
ated
in
Fig
u
r
e
1
,
wh
ic
h
also
r
ep
r
esen
ts
th
e
s
witch
f
ee
d
b
ac
k
co
n
tr
o
l
im
p
l
em
en
ted
v
ia
PLL
s
.
T
h
ese
PL
L
s
,
cr
u
cial
f
o
r
e
n
s
u
r
in
g
s
y
n
c
h
r
o
n
izatio
n
with
th
e
g
r
id
'
s
f
r
eq
u
en
cy
an
d
p
h
ase,
th
e
m
o
d
el
o
f
th
e
b
o
o
s
t
in
v
e
r
ter
h
as
b
ee
n
co
n
f
ig
u
r
ed
in
M
AT
L
AB
/Si
m
u
lin
k
,
s
h
o
win
g
th
e
in
v
er
ter
co
n
n
ec
te
d
to
a
lo
ad
an
d
th
e
g
r
id
,
co
n
t
r
o
lled
b
y
a
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
.
T
h
is
s
ch
em
ati
c
in
clu
d
es
co
m
p
r
eh
e
n
s
iv
e
co
m
p
o
n
en
ts
alo
n
g
with
m
ea
s
u
r
e
m
en
t
an
d
co
n
tr
o
l
u
n
its
,
wh
ich
ar
e
ess
en
tial
f
o
r
m
o
n
ito
r
in
g
an
d
m
an
ag
i
n
g
th
e
o
p
er
atio
n
o
f
th
is
GaN
-
b
ased
i
n
v
er
ter
m
o
d
el.
T
h
e
s
p
ec
if
ic
p
ar
am
eter
s
o
f
th
e
d
esig
n
ed
co
n
v
er
ter
ar
e
d
etailed
in
T
a
b
le
1
.
T
h
ese
p
ar
am
et
er
s
p
lay
a
cr
itical
r
o
le
in
th
e
f
u
n
ctio
n
ality
an
d
ef
f
icien
cy
o
f
t
h
e
in
v
e
r
ter
,
p
r
o
v
id
in
g
in
s
ig
h
ts
in
to
its
p
er
f
o
r
m
an
ce
u
n
d
er
v
ar
io
u
s
o
p
e
r
atio
n
al
co
n
d
itio
n
s
.
Strin
g
co
n
f
ig
u
r
atio
n
two
p
a
r
allel
an
d
s
ix
s
er
ies.
T
ab
le
1
.
Par
am
eter
o
f
th
e
in
v
e
r
ter
d
esig
n
an
d
co
m
p
o
n
e
n
ts
o
f
th
e
s
im
u
latio
n
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
S
o
l
a
r
p
a
n
e
l
p
o
w
e
r
r
a
t
i
n
g
(
Ji
n
k
o
S
o
l
a
r
C
o
.
)
M
a
x
i
m
u
m
p
o
w
e
r
o
f
p
a
n
e
l
(
W
)
2
5
0
.
1
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
(
V
o
c
)
3
7
.
7
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
(
I
sc)
8
.
8
5
M
a
x
i
m
u
m
v
o
l
t
a
g
e
(
V
mp
)
3
0
.
5
P
a
n
e
l
c
u
r
r
e
n
t
(
I
mp
)
8
.
2
I
r
r
a
d
i
a
n
c
e
(
W
/
m
2
)
1
0
0
0
Te
mp
e
r
a
t
u
r
e
(
o
C
)
25
M
a
x
i
m
u
m
p
o
w
e
r
o
f
s
o
l
a
r
3
,
0
0
1
.
2
M
a
x
i
m
u
m
c
u
r
r
e
n
t
1
6
.
4
M
a
x
i
m
u
m
v
o
l
t
a
g
e
1
8
3
B
o
o
st
c
o
n
v
e
r
t
e
r
B
o
o
st
i
n
d
u
c
t
o
r
4
5
0
µH
DC
-
l
i
n
k
c
a
p
a
c
i
t
o
r
1
5
.
6
2
5
µF
B
o
o
st
sw
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
1
0
0
k
H
z
F
e
e
d
b
a
c
k
c
o
n
t
r
o
l
l
e
r
p
a
r
a
m
e
t
e
r
P
r
o
p
o
r
t
i
o
n
a
l
g
a
i
n
(
K
p
1
)
2
.
0
3
P
r
o
p
o
r
t
i
o
n
a
l
g
a
i
n
(
K
d
)
0
.
0
0
0
2
P
r
o
p
o
r
t
i
o
n
a
l
g
a
i
n
(
K
p
2
)
1
I
n
t
e
g
r
a
l
g
a
i
n
(
9
K
i
)
3
,
1
4
2
LC
L
f
i
l
t
e
r
Li
n
v
e
t
e
r
0
.
9
mH
Lg
r
i
d
0
.
8
9
mH
F
i
l
t
e
r
c
a
p
a
c
i
t
o
r
4
0
0
µF
A
v
e
r
a
g
e
o
u
t
p
u
t
v
o
l
t
a
g
e
4
0
0
V
V
i
n
3
5
0
D
e
l
t
a
I
(
R
i
p
p
l
e
c
u
r
r
e
n
t
o
f
i
n
d
u
c
t
o
r
)
0
.
2
%
D
e
l
t
a
V
(
R
i
p
p
l
e
c
u
r
r
e
n
t
o
f
c
a
p
a
c
i
t
o
r
)
0
.
0
6
%
O
u
t
p
u
t
c
u
r
r
e
n
t
(
I
o
u
t
)
7
.
5
O
u
t
p
u
t
v
o
l
t
a
g
e
(
V
o
u
t
)
4
0
0
V
G
r
i
d
v
o
l
t
a
g
e
(
R
M
S
)
2
2
0
V
O
u
t
p
u
t
p
o
w
e
r
(
W
)
2
,
9
9
9
2
.
4
.
Desig
n o
f
L
CL
f
ilte
r
A
d
u
al
-
lo
o
p
c
o
n
tr
o
l
s
tr
u
ctu
r
e
f
o
r
s
in
g
le
-
p
h
ase
s
h
u
n
t
ac
tiv
e
p
o
wer
f
ilter
s
(
SAPF
)
th
at
in
co
r
p
o
r
ates
f
ee
d
f
o
r
war
d
c
o
n
tr
o
l
to
m
itig
at
e
g
r
id
v
o
ltag
e
d
is
tu
r
b
an
ce
s
,
c
o
m
p
lem
en
ted
b
y
a
p
lu
g
-
in
r
ep
etitiv
e
co
n
tr
o
ller
as
th
e
o
u
ter
lo
o
p
co
n
tr
o
ller
.
T
h
e
in
n
er
lo
o
p
u
tili
ze
s
a
PI
co
n
tr
o
ller
to
ad
ju
s
t
th
e
f
r
eq
u
en
c
y
r
e
s
p
o
n
s
e
o
f
th
e
L
C
L
f
ilter
,
f
ac
ilit
atin
g
a
q
u
ick
e
r
tr
an
s
ien
t
r
esp
o
n
s
e
an
d
s
im
p
lify
in
g
th
e
d
esig
n
o
f
th
e
o
u
ter
lo
o
p
co
n
t
r
o
ller
.
T
h
e
p
ap
er
co
n
d
u
cts
a
co
m
p
r
e
h
en
s
iv
e
an
aly
s
is
o
f
th
e
f
ee
d
f
o
r
wa
r
d
co
n
tr
o
l'
s
p
er
f
o
r
m
a
n
ce
,
ass
ess
in
g
th
e
s
tab
ilit
y
an
d
r
o
b
u
s
tn
ess
o
f
t
h
e
d
u
al
-
l
o
o
p
c
o
n
tr
o
l
s
y
s
tem
.
E
x
p
e
r
im
en
tal
r
esu
lts
d
em
o
n
s
tr
ate
th
e
s
y
s
tem
’
s
ef
f
ec
tiv
e
s
tead
y
-
s
tate
p
er
f
o
r
m
a
n
ce
,
r
a
p
id
tr
an
s
ien
t
r
esp
o
n
s
e,
ef
f
ici
en
t
g
r
id
v
o
ltag
e
atten
u
atio
n
,
an
d
r
esil
ien
ce
t
o
v
ar
iatio
n
s
in
L
C
L
f
ilter
p
ar
a
m
eter
s
[
1
5
]
,
[
1
8
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Dev
elo
p
in
g
g
a
lliu
m
n
itr
id
e
-
b
a
s
ed
in
ve
r
ters
fo
r
h
ig
h
-
p
erfo
r
ma
n
ce
…
(
A
r
s
a
la
n
Mu
h
a
mma
d
S
o
o
m
a
r
)
2587
T
h
e
o
u
tp
u
t
o
f
th
e
in
v
er
ter
is
ch
ar
ac
ter
ized
b
y
its
n
o
n
-
s
in
u
s
o
id
al
n
atu
r
e
,
co
n
tain
i
n
g
ad
d
itio
n
al
h
ar
m
o
n
ics
th
at
n
ee
d
f
ilter
in
g
to
elim
in
ate
s
p
ik
es
o
r
o
t
h
er
u
n
wan
ted
s
ig
n
als.
Fo
r
th
is
p
u
r
p
o
s
e,
th
e
well
-
k
n
o
wn
L
C
L
f
ilter
i
s
em
p
lo
y
ed
,
as
ill
u
s
tr
ated
in
Fig
u
r
es
2
(
a)
an
d
2
(
b
)
o
f
th
e
s
ch
em
atic
d
iag
r
am
s
.
T
h
e
L
C
L
f
ilter
i
s
co
m
m
o
n
l
y
u
tili
ze
d
f
o
r
b
u
ild
in
g
an
d
co
n
n
ec
tin
g
in
v
er
ter
s
to
th
e
AC
g
r
id
,
f
av
o
r
e
d
f
o
r
its
a
b
ilit
y
to
ef
f
ec
tiv
ely
s
u
p
p
r
ess
h
ig
h
e
r
-
o
r
d
er
h
ar
m
o
n
ics
o
n
ce
th
e
f
ilter
b
an
d
wid
t
h
an
d
o
th
er
p
ar
am
eter
s
ar
e
p
r
o
p
er
l
y
c
o
n
f
ig
u
r
ed
[
1
9
]
–
[
2
1
]
.
Fig
u
r
e
2
.
Sch
em
atic
r
ep
r
esen
t
atio
n
o
f
a
s
in
g
le
-
p
h
ase
in
v
er
te
r
with
L
C
L
f
ilter
(a
)
d
etailed
c
ir
cu
it o
f
a
g
r
id
-
co
n
n
ec
ted
s
in
g
le
-
p
h
ase
in
v
e
r
t
er
with
L
C
L
f
ilter
,
an
d
(
b
)
b
lo
ck
d
iag
r
am
r
ep
r
esen
tatio
n
o
f
t
h
e
L
C
L
f
ilter
m
o
d
el
Her
e
is
a
co
n
v
en
ie
n
t f
o
r
m
u
la
f
o
r
ca
lcu
latin
g
th
e
L
C
L
f
ilter
c
ap
ac
itan
ce
(
2
)
to
(
8
)
[
2
2
]
,
[
2
3
]
:
1
=
Ω
0
2
(
2
)
wh
er
e
,
0
=
2
0
is
th
e
f
r
eq
u
en
cy
o
f
t
h
e
Gr
id
,
is
th
e
p
o
wer
ab
s
o
r
b
ed
b
y
th
e
in
v
e
r
ter
u
n
d
e
r
r
at
ed
cir
cu
m
s
tan
ce
s
,
U
max
is
th
e
g
r
i
d
v
o
ltag
e
m
ag
n
itu
d
e
(
p
ea
k
v
a
lu
e)
,
an
d
is
th
e
in
ten
d
ed
p
r
o
p
o
r
tio
n
o
f
t
h
e
L
C
L
f
ilter
ca
p
ac
itan
ce
'
s
ab
s
o
r
p
tio
n
o
f
in
v
e
r
ter
p
o
wer
.
Her
e
is
th
e
ca
lcu
latio
n
f
o
r
th
e
in
p
u
t
an
d
o
u
tp
u
t
i
n
d
u
ctan
ce
s
o
f
th
e
L
C
L
f
ilter
:
1
=
6
,
(
3
)
wh
er
e
is
th
e
DC
lin
k
v
o
ltag
e
v
alu
e,
is
th
e
i
n
v
er
ter
p
u
ls
e
wid
th
m
o
d
u
latio
n
s
witch
in
g
f
r
e
q
u
en
c
y
,
Δ
,
.
I
s
th
e
g
r
ea
test
am
o
u
n
t
o
f
f
ilter
cu
r
r
e
n
t
f
l
u
ctu
atio
n
ca
u
s
ed
b
y
s
witch
in
g
ac
tio
n
,
a
n
d
r
i
s
th
e
f
ilter
in
p
u
t/o
u
tp
u
t in
d
u
ctan
ce
r
atio
,
ty
p
ically
b
etwe
en
1
/
4
an
d
1
/6
.
2
=
2
(
4
)
T
h
e
ab
o
v
e
L
C
L
f
ilter
is
ch
ar
a
cter
ized
b
y
its
r
eso
n
a
n
ce
f
r
e
q
u
en
cy
.
Ω
=
2
=
√
1
+
2
1
2
(
5
)
wh
er
ea
s
f
o
llo
win
g
in
e
q
u
ality
co
n
d
itio
n
m
u
s
t a
ls
o
b
e
s
atis
f
ied
b
y
th
e
f
ilter
p
ar
a
m
eter
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
5
8
3
-
2
5
9
8
2588
10
0
<
<
/
2
(
6
)
I
n
o
r
d
er
to
m
i
n
im
ize
th
e
m
ain
v
o
ltag
e/cu
r
r
e
n
t
h
ar
m
o
n
ic
at
t
h
e
f
r
eq
u
en
cy
w
h
ile
also
f
av
o
r
ab
ly
atten
u
atin
g
t
h
e
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
s
witch
in
g
ac
tio
n
.
I
n
o
r
d
er
to
m
in
im
ize
th
e
m
ain
v
o
ltag
e/
cu
r
r
en
t
h
ar
m
o
n
ic
at
th
e
f
r
eq
u
en
cy
wh
ile
also
f
av
o
r
ab
ly
atten
u
atin
g
th
e
PW
M
s
witch
in
g
ac
tio
n
.
Ω
0
=
2
0
.
Fin
ally
,
th
e
s
er
ies
o
f
r
esis
tan
ce
3
o
f
th
e
p
ar
allel
ca
p
a
citan
ce
b
r
an
ch
is
co
m
p
u
te
d
u
s
in
g
th
e
s
u
b
s
eq
u
e
n
t f
o
r
m
u
la:
3
=
2
Ω
(
7
)
wh
er
ein
is
th
e
L
C
L
f
ilter
d
am
p
in
g
at
r
eso
n
an
ce
f
r
eq
u
e
n
c
y
Ω
.
B
y
ch
o
o
s
in
g
Ω
>
0
.
5
,
B
y
m
ak
i
n
g
s
u
r
e
th
e
L
C
L
f
ilter
i
s
d
am
p
en
ed
f
av
o
r
ab
ly
at
th
e
r
eso
n
an
ce
f
r
eq
u
en
c
y
,
lo
w
-
r
ip
p
le
L
C
L
f
ilter
o
p
er
atio
n
is
d
eter
m
in
ed
.
I
f
th
e
ca
p
ac
itiv
e
im
p
ed
an
ce
is
p
r
esen
t
at
t
h
e
p
r
in
cip
al
h
ar
m
o
n
ic
f
r
e
q
u
en
c
y
1
/
(
Ω
0
)
tak
es
o
n
r
elativ
ely
lar
g
e
v
alu
es
(
p
a
r
a
m
eter
<<
1
in
(
2
)
)
,
th
e
ca
p
ac
itan
ce
cu
r
r
en
t
=
1
∗
−
1
m
ay
b
e
n
e
g
lecte
d
co
n
ce
r
n
in
g
f
ilter
o
u
tp
u
t
c
u
r
r
e
n
t
1
,
an
d
t
h
e
f
o
llo
win
g
f
o
r
m
c
an
b
e
u
s
ed
t
o
s
im
p
lify
th
e
L
C
L
f
ilter
tr
an
s
f
er
f
u
n
ctio
n
m
o
d
el:
Au
x
iliar
y
PI
co
n
tr
o
ller
f
o
r
DC
cu
r
r
en
t
s
u
p
p
r
ess
io
n
in
s
in
g
le
p
h
ase
AC
i
n
v
er
ter
cu
r
r
e
n
t
PR
co
n
tr
o
l
.
(
)
=
1
(
)
1
(
)
−
2
(
)
=
1
+
=
+
1
(
8
)
wh
er
e
R
f
=
R
1f
+
R
2f
an
d
L
f
=
L
1f
+
L
2f
ar
e
th
e
eq
u
i
v
alen
t
f
o
r
f
ilter
s
an
d
th
e
co
n
s
tan
t
f
o
r
g
ain
is
K
f
=
1
/
R
f
an
d
th
e
tim
e
co
n
s
tan
t
is
T
f
=
L
f
R
f
.
R
es
p
ec
tiv
ely
.
T
h
e
d
esig
n
o
f
t
h
e
L
C
L
f
ilter
s
ca
lcu
lated
with
th
e
m
ath
em
atica
l d
er
iv
atio
n
is
s
h
o
wn
in
th
e
eq
u
atio
n
.
2
.
5
.
P
ha
s
e
-
lo
c
k
ed
lo
o
p inte
g
ra
t
io
n
A
PLL
-
b
ased
co
n
tr
o
l
m
eth
o
d
was
p
r
o
p
o
s
ed
to
in
teg
r
ate
a
g
r
id
-
co
n
n
ec
ted
s
o
lar
PV
s
y
s
tem
m
o
r
e
ef
f
ec
tiv
ely
,
o
f
f
er
i
n
g
s
wif
ter
g
r
id
in
teg
r
atio
n
an
d
o
p
tim
al
s
y
s
tem
s
y
n
ch
r
o
n
izatio
n
.
R
esea
r
ch
er
s
d
ev
el
o
p
ed
a
h
y
b
r
id
co
n
tr
o
l
m
ec
h
an
is
m
th
at
co
m
b
in
es
PI
a
n
d
p
h
ase
-
s
h
if
t c
o
n
tr
o
l
to
en
s
u
r
e
th
e
p
o
wer
q
u
ality
o
f
th
e
g
r
id
.
I
n
th
is
s
etu
p
,
th
e
PLL
p
lay
s
a
cr
u
cial
r
o
le
b
y
co
n
tr
o
llin
g
a
n
d
s
y
n
ch
r
o
n
izin
g
th
e
i
n
v
er
te
r
’
s
f
ir
in
g
an
g
le.
I
t
p
r
o
v
id
es
c
o
n
tr
o
l
i
n
p
u
ts
to
th
e
s
lid
in
g
m
o
d
e
c
o
n
tr
o
ller
,
wh
ic
h
in
tu
r
n
m
an
a
g
es
th
e
f
ir
i
n
g
a
n
g
les
o
f
th
e
in
v
er
ter
an
d
b
o
o
s
t switch
es,
as we
ll a
s
th
e
r
eg
u
latio
n
o
f
b
o
th
r
ea
ctiv
e
an
d
ac
tiv
e
p
o
wer
f
r
o
m
th
e
g
r
i
d
[
2
4
]
.
F
o
r
s
i
n
g
l
e
-
p
h
a
s
e
s
y
s
t
e
m
s
,
o
b
ta
i
n
i
n
g
a
c
c
u
r
a
t
e
g
r
i
d
v
o
l
t
a
g
e
i
n
f
o
r
m
a
t
i
o
n
i
s
c
r
u
c
i
a
l
.
T
r
a
d
i
t
io
n
a
l
z
e
r
o
-
c
r
o
s
s
i
n
g
d
et
e
c
t
i
o
n
m
et
h
o
d
s
,
a
lth
o
u
g
h
c
o
m
m
o
n
l
y
u
s
e
d
f
o
r
t
h
i
s
p
u
r
p
o
s
e
,
a
r
e
i
m
p
r
a
c
ti
c
a
l
d
u
e
to
t
h
e
i
r
s
e
n
s
i
ti
v
i
t
y
t
o
n
o
i
s
e
.
C
o
n
s
e
q
u
e
n
t
l
y
,
a
n
e
n
h
a
n
c
e
d
a
p
p
r
o
a
c
h
i
n
v
o
l
v
i
n
g
t
h
e
u
s
e
o
f
t
w
o
v
i
r
t
u
a
l
P
L
L
p
h
as
e
s
i
s
r
e
q
u
i
r
e
d
.
R
e
f
e
r
e
n
c
e
f
r
a
m
e
t
h
e
o
r
y
i
s
a
p
p
l
i
e
d
h
e
r
e
,
p
o
s
i
t
i
n
g
t
h
at
t
h
e
s
i
n
g
le
-
p
h
a
s
e
v
o
l
t
a
g
e
s
h
o
u
l
d
b
e
t
r
e
a
t
e
d
a
s
a
v
i
r
t
u
a
l
t
w
o
-
p
h
a
s
e
v
o
l
t
a
g
e
,
w
i
t
h
a
9
0
-
d
e
g
r
e
e
o
u
t
-
of
-
p
h
a
s
e
c
o
m
p
o
n
e
n
t
t
o
f
a
c
i
l
it
a
t
e
s
i
m
p
l
e
r
c
o
n
t
r
o
l
m
e
c
h
a
n
is
m
s
.
B
as
e
d
o
n
t
h
i
s
t
h
e
o
r
y
,
a
s
i
n
g
l
e
-
p
h
a
s
e
P
L
L
s
y
s
t
e
m
is
s
t
r
u
c
t
u
r
e
d
i
n
t
w
o
s
t
a
g
es:
a
tw
o
-
p
h
a
s
e
g
e
n
e
r
at
o
r
a
n
d
a
p
h
a
s
e
c
o
n
t
r
o
l
le
r
,
as
d
e
p
i
c
t
e
d
i
n
F
i
g
u
r
e
3
.
T
h
i
s
a
p
p
r
o
a
c
h
a
d
d
r
e
s
s
e
s
t
h
e
i
n
h
e
r
e
n
t
lim
i
t
a
t
i
o
n
s
o
f
s
i
n
g
l
e
-
p
h
a
s
e
s
y
s
t
em
s
a
n
d
p
r
o
v
i
d
e
s
a
r
o
b
u
s
t
f
r
a
m
e
w
o
r
k
f
o
r
m
a
i
n
t
a
i
n
in
g
s
y
n
c
h
r
o
n
i
z
a
t
i
o
n
a
n
d
s
t
a
b
i
l
i
ty
i
n
g
r
i
d
-
c
o
n
n
e
c
t
e
d
s
o
l
a
r
PV
s
y
s
t
e
m
s
.
−
T
wo
-
p
h
ase
g
en
er
ato
r
:
T
h
is
b
l
o
ck
tak
es
th
e
u
tili
ty
v
o
ltag
e
V
utility
.
I
t
p
r
o
d
u
ce
s
two
s
ig
n
als:
o
n
e
th
at
p
ass
es
th
r
o
u
g
h
an
all
-
p
ass
f
ilter
,
y
ield
in
g
V
qs
,
an
d
an
o
th
er
th
at
is
u
s
ed
d
ir
ec
tly
,
V
ds
.
T
h
e
all
-
p
ass
f
ilter
l
ik
ely
en
s
u
r
es th
at
V
qs
ar
e
o
r
th
o
g
o
n
al
to
V
ds
.
−
R
ev
er
s
e
Par
k
tr
an
s
f
o
r
m
atio
n
:
T
h
is
o
p
er
atio
n
ty
p
ically
tak
es
th
e
o
r
th
o
g
o
n
al
co
m
p
o
n
e
n
ts
V
qs
an
d
V
ds
an
d
tr
an
s
f
o
r
m
s
th
em
in
t
o
a
r
o
tatin
g
r
ef
er
e
n
ce
f
r
am
e
(
d
-
q
f
r
a
m
e)
,
r
esu
ltin
g
in
a
d
ir
ec
t
-
ax
is
v
o
lta
g
e,
V
de
.
−
Ph
ase
co
n
tr
o
ller
:
T
h
e
co
r
e
o
f
th
e
PLL
is
wh
er
e
V
de
,
is
f
e
d
i
n
to
a
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI
)
co
n
tr
o
ller
.
T
h
e
PI
co
n
tr
o
ller
aim
s
to
r
ed
u
ce
t
h
e
er
r
o
r
b
etwe
en
V
de
an
d
a
r
ef
er
en
ce
v
alu
e
(
wh
ich
a
p
p
ea
r
s
t
o
b
e
ze
r
o
in
th
is
ca
s
e)
.
T
h
e
o
u
t
p
u
t o
f
th
e
PI
co
n
tr
o
ller
is
an
an
g
u
lar
f
r
eq
u
e
n
c
y
d
ev
iatio
n
∆
.
−
I
n
teg
r
ato
r
:
T
h
e
in
teg
r
atio
n
o
f
th
e
f
r
eq
u
e
n
cy
d
ev
iatio
n
o
v
er
tim
e
to
esti
m
ate
th
e
p
h
ase
a
n
g
le
̂
,
th
en
f
ed
b
ac
k
to
th
e
p
h
ase
d
etec
to
r
.
I
n
ter
m
s
o
f
tr
an
s
f
er
f
u
n
ctio
n
s
,
th
e
all
-
p
ass
f
ilter
will
h
av
e
a
t
r
an
s
f
er
f
u
n
ctio
n
H
ap
(
s
)
,
wh
er
e
(s)
is
th
e
co
m
p
le
x
f
r
eq
u
en
cy
v
ar
iab
le.
T
h
e
PI
c
o
n
tr
o
ller
is
ex
p
r
ess
ed
as (
9
)
[
2
5
]
:
p
(
)
=
+
(
9
)
wh
er
e
th
e
p
r
o
p
o
r
tio
n
al
g
ain
is
,
an
d
in
teg
r
al
g
ain
is
.
T
h
e
tr
a
n
s
f
er
f
u
n
ctio
n
wo
u
ld
ty
p
ically
r
ep
r
esen
t
th
e
in
teg
r
ato
r
1
,
ass
u
m
in
g
it
in
te
g
r
ates
co
n
ce
r
n
i
n
g
tim
e.
Fig
u
r
e
4
s
h
o
ws
th
e
c
o
m
p
lete
p
h
ase
-
lo
ck
ed
l
o
o
p
co
n
f
ig
u
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J E
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&
C
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m
p
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n
g
I
SS
N:
2088
-
8
7
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8
Dev
elo
p
in
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itr
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e
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a
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ters
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Fig
u
r
e
3
.
PLL
b
lo
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d
iag
r
am
f
o
r
a
s
in
g
le
-
p
h
ase
PV in
v
er
ter
co
n
tr
o
ller
Fig
u
r
e
4
.
Ph
ase
lo
ck
lo
o
p
co
n
t
r
o
l b
lo
ck
s
in
th
e
MA
T
L
AB
2
.
6
.
Desig
n o
f
f
ee
db
a
ck
c
o
ntr
o
l
As
d
ep
icted
in
Fig
u
r
e
5
,
t
h
e
in
v
er
ter
’
s
co
n
tr
o
l
ar
ch
ite
ctu
r
e
in
teg
r
ates
a
Feed
b
ac
k
C
o
n
tr
o
ller
co
n
n
ec
ted
to
th
e
i
n
p
u
t
o
f
th
e
PLL
co
n
tr
o
l
s
y
s
tem
.
T
h
is
PLL
is
cr
u
cial
f
o
r
co
n
tr
o
llin
g
an
d
s
y
n
ch
r
o
n
izin
g
th
e
in
v
er
ter
'
s
f
ir
in
g
an
g
le
b
y
p
r
o
v
id
in
g
co
n
tr
o
l
in
p
u
t
f
r
o
m
t
h
e
g
r
id
.
T
h
e
co
n
tr
o
ller
u
s
ed
is
a
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
,
a
n
o
n
-
li
n
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r
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n
t
r
o
l
m
eth
o
d
d
esig
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y
n
am
ics
o
f
a
n
o
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-
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h
d
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u
o
u
s
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o
n
tr
o
l
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tio
n
s
.
T
h
e
o
u
tp
u
t f
r
o
m
th
e
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
is
d
ir
ec
ted
t
o
b
o
th
th
e
in
v
er
ter
an
d
th
e
b
o
o
s
t
in
v
e
r
ter
s
witch
,
tr
a
n
s
f
o
r
m
in
g
th
e
in
v
e
r
ter
in
to
a
f
ee
d
b
ac
k
-
co
n
tr
o
lled
s
y
s
tem
th
at
is
s
y
n
ch
r
o
n
ize
d
with
th
e
g
r
id
v
o
ltag
e.
T
h
e
p
ar
am
eter
s
s
et
f
o
r
th
is
s
y
s
tem
in
Fig
u
r
e
5
ar
e
s
p
ec
if
ied
as
f
o
llo
ws:
th
e
p
r
o
p
o
r
tio
n
al
g
ain
1
is
s
et
at
2
.
0
3
,
th
e
d
e
r
iv
ativ
e
g
ain
K
d
at
0
.
0
0
0
2
,
th
e
s
ec
o
n
d
p
r
o
p
o
r
tio
n
al
g
ain
2
at
1
,
an
d
th
e
in
teg
r
al
g
ain
K
i
at
3
,
1
4
2
.
T
h
ese
s
ettin
g
s
ar
e
ca
lib
r
ated
to
o
p
tim
ize
th
e
s
y
s
tem
'
s
r
esp
o
n
s
e
an
d
ef
f
icien
c
y
,
en
s
u
r
in
g
r
o
b
u
s
t
co
n
tr
o
l
a
n
d
s
tab
le
s
y
n
ch
r
o
n
izatio
n
with
th
e
g
r
id
'
s
f
lu
ctu
atin
g
d
y
n
am
ics.
T
h
is
co
n
f
ig
u
r
atio
n
u
n
d
er
lin
es
th
e
c
o
m
p
lex
ity
a
n
d
p
r
ec
is
io
n
r
e
q
u
ir
ed
i
n
d
esig
n
in
g
co
n
tr
o
l
s
y
s
tem
s
f
o
r
m
o
d
e
r
n
in
v
er
te
r
s
,
aim
in
g
f
o
r
m
a
x
im
u
m
ef
f
icien
cy
a
n
d
r
eliab
ilit
y
in
g
r
id
-
c
o
n
n
ec
ted
ap
p
licatio
n
s
.
Fig
u
r
e
5
.
Sli
d
in
g
m
o
d
e
co
n
tr
o
ller
f
o
r
f
ee
d
b
ac
k
co
n
tr
o
l lo
o
p
f
o
r
in
v
er
ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
5
8
3
-
2
5
9
8
2590
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
e
co
n
tex
t
o
f
th
e
p
ar
am
eter
s
d
is
cu
s
s
ed
ea
r
lier
,
th
e
d
esig
n
o
f
th
e
in
v
er
ter
was
m
eticu
lo
u
s
ly
p
r
ep
ar
e
d
u
s
in
g
MA
T
L
AB
,
as
illu
s
tr
ated
in
Fig
u
r
e
6
.
T
o
e
n
s
u
r
e
th
e
ac
c
u
r
ac
y
a
n
d
f
u
n
ctio
n
ality
o
f
th
e
i
n
v
er
ter
,
it
was
ev
alu
ated
u
n
d
er
f
iv
e
d
is
tin
ct
s
ce
n
ar
io
s
,
ea
ch
aim
ed
at
test
in
g
s
p
ec
if
ic
p
er
f
o
r
m
an
ce
asp
ec
ts
.
T
h
ese
s
ce
n
ar
io
s
wer
e
d
esig
n
e
d
to
e
x
am
in
e
th
e
r
esp
o
n
s
e
o
f
th
e
i
n
v
er
ter
t
o
g
r
id
f
lu
ctu
atio
n
s
,
e
f
f
icien
cy
i
n
p
o
wer
co
n
v
er
s
io
n
,
an
d
s
tab
ilit
y
u
n
d
e
r
d
y
n
a
m
ic
lo
ad
s
,
en
s
u
r
in
g
a
c
o
m
p
r
eh
en
s
iv
e
ass
ess
m
en
t o
f
its
ca
p
ab
ilit
ies.
T
h
e
f
ir
s
t
ca
s
e
f
o
c
u
s
ed
o
n
a
n
aly
zin
g
th
e
s
tan
d
alo
n
e
s
y
s
tem
p
er
f
o
r
m
a
n
ce
with
o
u
t
PL
L
an
d
g
r
id
co
n
n
ec
tio
n
.
I
n
th
e
s
ec
o
n
d
ca
s
e,
th
e
tr
an
s
ien
t
r
esp
o
n
s
e
o
f
th
e
PLL
u
n
d
er
o
p
tim
al
g
r
id
s
u
p
p
ly
co
n
d
itio
n
s
was
ex
am
in
ed
to
ass
ess
i
ts
s
y
n
ch
r
o
n
izatio
n
ac
cu
r
ac
y
.
T
h
e
th
ir
d
ca
s
e
in
v
o
lv
ed
ev
alu
atin
g
t
h
e
b
eh
av
io
r
o
f
th
e
in
v
er
ter
in
th
e
ev
e
n
t
o
f
a
g
r
id
s
u
p
p
ly
lo
s
s
,
wh
ich
is
cr
u
cial
f
o
r
d
eter
m
in
in
g
its
r
esil
ien
ce
an
d
ab
ilit
y
to
h
an
d
le
u
n
ex
p
ec
te
d
d
is
co
n
n
ec
tio
n
s
.
T
h
e
f
o
u
r
th
ca
s
e
s
tu
d
ied
th
e
in
v
er
ter
’
s
r
esp
o
n
s
e
to
f
r
eq
u
en
c
y
d
is
tu
r
b
an
ce
s
in
th
e
g
r
id
s
u
p
p
l
y
,
en
s
u
r
i
n
g
th
at
th
e
s
y
s
tem
r
em
ain
s
s
tab
le
u
n
d
er
f
lu
ctu
atin
g
c
o
n
d
itio
n
s
.
Fin
ally
,
th
e
f
if
th
ca
s
e
in
v
esti
g
ated
th
e
im
p
ac
t
o
f
a
m
p
litu
d
e
v
ar
iatio
n
s
in
th
e
g
r
i
d
s
u
p
p
ly
,
test
in
g
th
e
in
v
e
r
ter
’
s
ab
ilit
y
to
r
eg
u
late
v
o
ltag
e
ef
f
ec
tiv
el
y
.
E
ac
h
o
f
th
ese
ca
s
es
p
r
esen
te
d
u
n
iq
u
e
ch
alle
n
g
es
th
at
th
e
in
v
er
ter
n
ee
d
ed
to
h
a
n
d
le,
v
e
r
if
y
in
g
its
r
o
b
u
s
tn
ess
an
d
ad
a
p
tab
ilit
y
in
r
ea
l
-
wo
r
ld
ap
p
licatio
n
s
.
T
h
e
r
esu
lts
o
b
tain
ed
f
r
o
m
th
ese
te
s
ts
p
r
o
v
id
ed
cr
itical
in
s
ig
h
ts
in
to
th
e
in
v
er
ter
o
v
e
r
all
r
eliab
ilit
y
an
d
ef
f
icien
cy
.
B
y
an
aly
zin
g
its
p
er
f
o
r
m
a
n
ce
ac
r
o
s
s
d
if
f
er
en
t
o
p
er
atin
g
co
n
d
itio
n
s
,
n
ec
ess
ar
y
o
p
tim
izatio
n
s
an
d
r
ef
in
em
en
ts
co
u
ld
b
e
m
ad
e
to
en
h
an
ce
its
s
tab
ilit
y
an
d
ef
f
ec
tiv
en
ess
.
T
h
is
r
ig
o
r
o
u
s
ev
alu
atio
n
m
eth
o
d
o
lo
g
y
en
s
u
r
es
th
at
th
e
in
v
er
ter
is
well
-
s
u
ited
f
o
r
s
ea
m
less
in
teg
r
atio
n
with
s
o
lar
PV
s
y
s
tem
s
,
o
f
f
er
in
g
a
d
ep
en
d
ab
le
an
d
ef
f
icien
t
s
o
lu
tio
n
f
o
r
g
r
id
-
co
n
n
ec
ted
r
e
n
ewa
b
le
en
er
g
y
a
p
p
licatio
n
s
.
Fig
u
r
e
6
.
Deta
iled
MA
T
L
AB
/
Simu
lin
k
m
o
d
el
o
f
a
g
r
id
-
c
o
n
n
ec
ted
PV
in
v
er
ter
with
c
o
n
tr
o
l m
ec
h
an
is
m
s
3
.
1
.
Ca
s
e
1
:
a
na
ly
zing
s
t
a
nd
a
lo
ne
s
y
s
t
em
perf
o
r
m
a
nce
w
it
ho
ut
P
L
L
a
nd
g
rid c
o
nn
ec
t
io
n
T
h
e
an
aly
s
es
wer
e
in
itially
co
n
d
u
cted
with
o
u
t
a
g
r
id
c
o
n
n
e
ctio
n
an
d
with
o
u
t
lin
k
i
n
g
th
e
PLL
to
th
e
in
v
er
ter
.
As
o
b
s
er
v
e
d
in
Fig
u
r
es
7
(
a)
a
n
d
7
(
b
)
,
t
h
e
o
u
tp
u
t
wav
ef
o
r
m
with
o
u
t
PLL
co
n
tr
o
l
ex
h
ib
its
s
ig
n
if
ican
t
d
is
to
r
tio
n
an
d
a
h
ig
h
lev
el
o
f
tr
an
s
ien
ts
.
T
h
is
d
is
to
r
tio
n
is
f
u
r
th
er
ev
id
en
ce
d
b
y
t
h
e
h
a
r
m
o
n
ic
co
n
ten
t,
w
h
ich
r
ea
ch
es u
p
to
2
2
.
2
% a
s
d
ep
ict
ed
in
Fig
u
r
e
7
(
b
)
.
T
o
ad
d
r
ess
th
ese
is
s
u
es
an
d
im
p
r
o
v
e
th
e
q
u
ality
o
f
th
e
o
u
tp
u
t
wav
e
f
o
r
m
,
th
e
PLL
co
n
tr
o
l
was
in
teg
r
ated
in
to
th
e
s
y
s
tem
.
T
h
e
in
clu
s
io
n
o
f
PLL
c
o
n
tr
o
l
a
im
s
to
s
y
n
ch
r
o
n
ize
th
e
in
v
er
t
er
'
s
o
u
tp
u
t
with
th
e
g
r
id
'
s
f
r
eq
u
en
cy
a
n
d
p
h
ase,
th
er
eb
y
s
ig
n
if
ica
n
tly
r
ed
u
c
in
g
h
ar
m
o
n
ic
d
is
to
r
tio
n
an
d
tr
an
s
ien
ts
.
T
h
is
ad
ju
s
tm
en
t
allo
ws
th
e
s
y
s
tem
to
m
ee
t
t
h
e
s
tan
d
ar
d
s
f
o
r
all
o
wab
le
h
ar
m
o
n
ics,
wh
ich
ar
e
ess
en
tial
f
o
r
g
r
id
co
m
p
lian
ce
an
d
ef
f
icien
t
o
p
e
r
atio
n
.
T
h
ese
im
p
r
o
v
em
en
ts
an
d
th
eir
ef
f
ec
ts
ar
e
elab
o
r
ate
d
in
th
e
v
ar
io
u
s
ca
s
es
d
is
cu
s
s
ed
th
r
o
u
g
h
o
u
t
th
e
p
a
p
er
.
B
y
in
co
r
p
o
r
atin
g
PLL
co
n
tr
o
l,
th
e
in
v
er
ter
'
s
p
er
f
o
r
m
an
ce
alig
n
s
with
r
eg
u
lato
r
y
s
tan
d
ar
d
s
an
d
co
n
tr
ib
u
tes
to
a
m
o
r
e
s
tab
le
an
d
r
eliab
le
g
r
id
-
co
n
n
ec
ted
s
o
lar
PV
s
y
s
tem
.
T
h
is
d
em
o
n
s
tr
ates
th
e
cr
itical
r
o
le
o
f
PLL
in
en
h
an
cin
g
in
v
er
te
r
f
u
n
ctio
n
ality
a
n
d
en
s
u
r
in
g
c
o
m
p
atib
ilit
y
with
th
e
g
r
id
in
f
r
astru
ctu
r
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Dev
elo
p
in
g
g
a
lliu
m
n
itr
id
e
-
b
a
s
ed
in
ve
r
ters
fo
r
h
ig
h
-
p
erfo
r
ma
n
ce
…
(
A
r
s
a
la
n
Mu
h
a
mma
d
S
o
o
m
a
r
)
2591
(
a)
(
b
)
Fig
u
r
e
7
.
Vo
ltag
e
o
u
tp
u
t a
n
d
tr
an
s
ien
t r
esp
o
n
s
e
o
f
th
e
s
tan
d
a
lo
n
e
in
v
er
te
r
with
o
u
t PL
L
(
a
)
v
o
ltag
e
o
u
tp
u
t a
n
d
tr
an
s
ien
t r
esp
o
n
s
e
o
f
t
h
e
s
tan
d
alo
n
e
in
v
er
te
r
with
o
u
t PL
L
,
a
n
d
(
b
)
tr
an
s
ien
t
wav
ef
o
r
m
a
n
a
ly
s
is
3
.
2
.
Ca
s
e
2
:
t
r
a
ns
ient
re
s
po
ns
e
o
f
ph
a
s
e
-
lo
ck
ed
lo
o
ps
in o
ptim
um
g
rid su
pp
ly
Du
r
in
g
r
eg
u
lar
o
p
e
r
atio
n
o
f
th
e
g
r
i
d
at
o
p
tim
al
co
n
d
itio
n
s
as
s
h
o
wn
in
Fig
u
r
e
8
,
wh
e
r
e
Fig
u
r
e
8
(
a
)
s
h
o
ws
cu
r
r
en
t
an
d
v
o
ltag
e
o
u
t
p
u
t
o
f
th
e
i
n
v
er
ter
with
PLL
.
T
h
e
f
r
eq
u
en
cy
is
s
tab
ilized
at
5
0
Hz,
th
e
in
v
e
r
ter
p
er
f
o
r
m
s
ef
f
ec
tiv
ely
,
d
em
o
n
s
tr
atin
g
th
e
ef
f
ec
tiv
en
ess
o
f
its
d
esig
n
.
T
h
e
T
HD
is
m
ain
tain
ed
at
5
%
at
Ny
q
u
is
t
f
r
eq
u
e
n
cy
at
t
h
e
m
a
x
im
u
m
f
r
eq
u
en
c
y
,
as
illu
s
tr
ated
in
Fig
u
r
e
8
(
b
)
,
th
ese
lev
els
ar
e
c
o
m
p
lian
t
with
th
e
s
tan
d
ar
d
s
s
et
b
y
I
E
E
E
5
1
9
,
wh
ich
g
o
v
e
r
n
s
h
ar
m
o
n
ic
co
n
tr
o
l i
n
elec
tr
ical
p
o
wer
s
y
s
tem
s
.
T
h
e
Ny
q
u
is
t
f
r
eq
u
e
n
cy
,
d
ef
i
n
ed
as
h
alf
th
e
s
am
p
le
r
ate
o
f
th
e
s
y
s
tem
,
r
ep
r
esen
ts
th
e
h
ig
h
est
f
r
eq
u
e
n
cy
th
at
th
e
eq
u
i
p
m
en
t
ca
n
ac
cu
r
ately
m
ea
s
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r
e.
T
h
e
ad
h
er
en
ce
to
th
ese
T
HD
v
alu
es
n
o
t
o
n
ly
r
ef
lects
th
e
in
v
er
te
r
'
s
ca
p
ab
ilit
y
to
o
p
er
ate
ef
f
icie
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tly
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er
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tan
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ar
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g
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id
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n
d
itio
n
s
b
u
t
also
u
n
d
er
s
co
r
es
t
h
e
p
r
ec
is
io
n
o
f
th
e
in
v
er
ter
d
esig
n
.
T
h
e
in
teg
r
atio
n
o
f
th
e
PLL
an
d
f
ee
d
b
ac
k
c
o
n
tr
o
l
p
lay
s
a
cr
u
cial
r
o
le
in
th
is
p
er
f
o
r
m
an
ce
,
en
s
u
r
i
n
g
th
at
th
e
in
v
er
ter
'
s
o
u
tp
u
t h
ar
m
o
n
ics ar
e
well
with
in
ac
ce
p
tab
le
lim
it
s
.
Ad
d
itio
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ally
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th
e
MPPT
s
y
s
tem
m
ax
im
izes
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o
w
er
ex
tr
ac
tio
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o
m
th
e
s
o
lar
p
a
n
els,
o
p
tim
izin
g
th
e
o
v
er
all
en
er
g
y
p
r
o
d
u
ctio
n
o
f
th
e
s
y
s
tem
.
T
h
is
o
p
e
r
atio
n
al
ef
f
icien
cy
co
n
f
ir
m
s
th
e
c
o
r
r
ec
tn
ess
o
f
th
e
in
v
er
ter
'
s
d
esig
n
,
h
ig
h
lig
h
tin
g
its
ca
p
ab
ilit
y
to
p
er
f
o
r
m
r
eliab
ly
an
d
ef
f
ec
tiv
ely
in
g
r
id
-
co
n
n
ec
ted
s
ce
n
ar
io
s
wh
ile
ad
h
er
in
g
to
in
d
u
s
tr
y
s
tan
d
ar
d
s
f
o
r
p
o
wer
q
u
ality
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
5
8
3
-
2
5
9
8
2592
(
a)
(
b
)
Fig
u
r
e
8
.
T
r
an
s
ien
t r
esp
o
n
s
e
o
f
p
h
ase
-
lo
ck
e
d
lo
o
p
in
o
p
tim
u
m
g
r
id
s
u
p
p
ly
(
a
)
cu
r
r
en
t a
n
d
v
o
ltag
e
o
u
tp
u
t o
f
th
e
in
v
er
ter
with
PLL
a
n
d
(
b
)
v
o
ltag
e
tr
an
s
ien
t r
esp
o
n
s
e
o
f
t
h
e
in
v
er
ter
in
o
p
tim
u
m
g
r
id
s
u
p
p
ly
3
.
3
.
Ca
s
e
3
:
lo
s
s
o
f
g
rid su
p
ply
I
n
ca
s
e
3
o
f
th
e
s
ce
n
ar
io
s
ev
alu
ated
,
a
s
p
ec
if
ic
f
au
lt
co
n
d
itio
n
was
s
im
u
lated
wh
er
e
th
er
e
is
a
tem
p
o
r
ar
y
in
ter
r
u
p
tio
n
in
t
h
e
g
r
id
s
u
p
p
ly
f
o
r
a
d
u
r
atio
n
o
f
0
.
3
s
ec
o
n
d
s
.
T
h
e
g
r
id
f
r
e
q
u
en
cy
r
em
ain
s
c
o
n
s
tan
t
at
5
0
Hz
th
r
o
u
g
h
o
u
t
th
e
test
,
an
d
th
e
g
r
id
d
is
co
n
n
ec
ts
a
n
d
s
u
b
s
eq
u
en
tly
r
ec
o
n
n
ec
ts
af
ter
0
.
3
s
ec
o
n
d
s
.
T
h
is
tr
an
s
ien
t e
v
en
t a
n
d
its
im
p
ac
t
o
n
th
e
in
v
er
ter
'
s
p
er
f
o
r
m
a
n
ce
ar
e
illu
s
tr
ated
in
Fig
u
r
e
9
.
T
h
e
d
ep
ictio
n
in
Fig
u
r
e
9
(
a)
s
h
o
ws
two
k
ey
wav
ef
o
r
m
s
:
th
e
r
ed
g
r
ap
h
r
ep
r
esen
ts
th
e
g
r
id
s
u
p
p
ly
,
an
d
th
e
b
l
u
e
wav
e
f
o
r
m
s
h
o
ws
th
e
v
o
ltag
e
o
u
tp
u
t
f
r
o
m
t
h
e
in
v
e
r
ter
.
T
h
is
b
l
u
e
wav
e
f
o
r
m
is
c
r
u
cial
as
it
d
em
o
n
s
tr
ates
th
e
r
esp
o
n
s
e
o
f
t
h
e
in
v
er
ter
,
co
n
tr
o
lled
b
y
th
e
PLL
an
d
f
ee
d
b
ac
k
m
ec
h
an
is
m
s
,
d
u
r
in
g
an
d
af
ter
th
e
g
r
id
f
au
lt.
T
h
e
b
l
u
e
wav
ef
o
r
m
b
e
h
av
io
r
d
u
r
in
g
th
e
f
a
u
lt
in
d
icate
s
h
o
w
e
f
f
ec
tiv
ely
th
e
PLL
an
d
f
ee
d
b
ac
k
co
n
tr
o
l
m
an
ag
e
th
e
in
v
e
r
ter
'
s
o
p
e
r
atio
n
am
id
s
t
g
r
id
in
c
o
n
s
is
ten
cies.
T
h
e
PLL
r
o
le
is
t
o
en
s
u
r
e
th
e
in
v
e
r
ter
o
u
tp
u
t
r
em
ain
s
s
y
n
c
h
r
o
n
ized
with
th
e
g
r
i
d
f
r
eq
u
e
n
cy
e
v
en
wh
en
th
e
g
r
id
s
u
p
p
ly
is
u
n
s
ta
b
le
o
r
m
o
m
e
n
tar
ily
u
n
av
ailab
le.
T
h
is
is
cr
itical
f
o
r
m
ain
tain
in
g
th
e
s
tab
ilit
y
o
f
th
e
en
tire
s
y
s
tem
an
d
m
in
im
izin
g
th
e
im
p
ac
t
o
f
d
is
tu
r
b
an
ce
s
o
n
c
o
n
n
ec
te
d
lo
a
d
s
.
T
h
e
ab
ilit
y
o
f
th
e
in
v
er
ter
t
o
co
n
tin
u
e
o
p
e
r
atin
g
ef
f
ec
tiv
el
y
d
u
r
in
g
th
is
f
au
lt,
as
ev
id
en
ce
d
b
y
th
e
co
n
tr
o
lle
d
an
d
s
tab
le
o
u
tp
u
t
v
o
ltag
e,
i
s
a
test
am
en
t
to
th
e
r
o
b
u
s
tn
e
s
s
o
f
th
e
in
v
er
te
r
’
s
d
esig
n
an
d
co
n
tr
o
l
s
ch
em
es.
Fig
u
r
e
9
(
b
)
s
h
o
ws
th
e
p
o
wer
d
e
liv
er
y
to
th
e
l
o
ad
a
n
d
th
e
g
r
id
wh
er
e
it
h
i
g
h
lig
h
ts
th
e
s
y
s
tem
ca
p
ab
ilit
y
to
h
an
d
le
g
r
id
d
is
tu
r
b
a
n
ce
s
wh
ile
m
ain
tain
in
g
o
p
e
r
atio
n
al
co
n
ti
n
u
ity
,
en
s
u
r
in
g
th
at
p
o
wer
d
eliv
e
r
y
is
s
u
s
tain
ed
e
v
en
u
n
d
er
ch
allen
g
i
n
g
c
o
n
d
iti
o
n
s
.
T
h
is
r
esil
ien
ce
is
ess
en
tial
f
o
r
s
y
s
tem
s
th
at
m
u
s
t o
p
er
ate
r
eliab
ly
in
en
v
ir
o
n
m
en
ts
wh
er
e
g
r
id
s
tab
ilit
y
ca
n
n
o
t a
lway
s
b
e
g
u
ar
a
n
teed
.
Evaluation Warning : The document was created with Spire.PDF for Python.