I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
15
,
No
.
4
,
A
u
g
u
s
t
20
25
,
p
p
.
3
6
6
0
~
3
6
8
2
I
SS
N:
2088
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/ijece.
v
15
i
4
.
pp
3
6
6
0
-
3
6
8
2
3660
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
H
y
brid
pa
ss
iv
e d
a
mping
f
ilter
of si
ng
le
-
pha
se g
rid
-
ti
ed
PV
-
mic
ro
inverte
r
F
o
uzey
Sa
lem
Aa
m
a
r
a
1
,
P
ra
v
ee
n K
um
a
r
B
a
la
cha
nd
ra
n
1
,
Yus
ha
iza
d Yu
s
o
f
1
,
M
o
hd
Am
ra
n M
o
o
hd
Ra
dzi
2
,
M
uh
a
m
m
a
d Amm
irrul
At
iqi
M
o
hd
Z
a
inu
ri
1
1
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
,
E
l
e
c
t
r
o
n
i
c
s
a
n
d
S
y
s
t
e
m
En
g
i
n
e
e
r
i
n
g
,
F
a
c
u
l
t
y
o
f
En
g
i
n
e
e
r
i
n
g
a
n
d
B
u
i
l
t
En
v
i
r
o
n
me
n
t
,
U
n
i
v
e
r
si
t
i
K
e
b
a
n
g
s
a
a
n
M
a
l
a
y
si
a
,
S
e
l
a
n
g
o
r
,
M
a
l
a
y
s
i
a
2
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
,
F
a
c
u
l
t
y
o
f
E
n
g
i
n
e
e
r
i
n
g
,
U
n
i
v
e
r
si
t
i
P
u
t
r
a
M
a
l
a
y
s
i
a
,
S
e
l
a
n
g
o
r
,
M
a
l
a
y
si
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
2
6
,
2
0
2
4
R
ev
is
ed
Ma
r
2
5
,
2
0
2
5
Acc
ep
ted
Ma
y
2
3
,
2
0
2
5
P
h
o
t
o
v
o
lt
a
ic
(P
V)
m
icro
in
v
e
rter
with
i
n
d
u
c
to
r
-
c
a
p
a
c
it
o
r
-
in
d
u
c
t
o
r
(LCL
)
fil
ter
h
a
s
m
a
n
y
a
d
v
a
n
tag
e
s,
b
u
t
it
h
a
s
re
so
n
a
n
c
e
with
th
e
g
ri
d
c
u
rre
n
t
situ
a
ti
o
n
c
o
u
l
d
p
o
te
n
ti
a
ll
y
lea
d
to
sta
b
il
it
y
issu
e
s
to
e
n
h
a
n
c
e
th
e
p
o
we
r
q
u
a
li
t
y
;
re
d
u
c
in
g
th
e
g
rid
c
u
rre
n
t
to
tal
h
a
rm
o
n
ic
d
ist
o
rti
o
n
(
THD)
is
c
ru
c
ial,
a
s
it
c
u
rre
n
tl
y
e
x
c
e
e
d
s
t
h
e
li
m
it
s
se
t
b
y
th
e
IEE
E
p
o
we
r
sy
ste
m
sta
n
d
a
r
d
s
.
Th
a
t
imp
r
o
v
e
s
t
h
e
h
y
b
r
id
p
a
ss
iv
e
d
a
m
p
i
n
g
fil
ter
t
o
p
o
l
o
g
y
,
w
h
ich
c
a
n
p
e
rfo
rm
b
e
tt
e
r
th
a
n
t
h
e
LCL
o
u
t
p
u
t
fil
ter.
T
h
e
d
a
m
p
i
n
g
fil
ter
is
e
ffe
c
ti
v
e
in
a
ll
e
v
iatin
g
t
h
e
re
so
n
a
n
c
e
p
e
a
k
o
c
c
u
rrin
g
a
t
t
h
e
re
so
n
a
n
t
fre
q
u
e
n
c
y
o
f
th
e
LCL
fil
ter,
t
h
e
re
b
y
m
in
imiz
in
g
v
o
lt
a
g
e
o
v
e
rsh
o
o
ts
a
n
d
ri
n
g
i
n
g
;
b
y
u
t
il
izin
g
sm
a
ll
e
r
c
a
p
a
c
it
o
rs,
th
e
d
a
m
p
i
n
g
f
il
ter
e
n
h
a
n
c
e
s
sy
ste
m
re
li
a
b
il
i
ty
wh
il
e
a
lso
re
d
u
c
in
g
th
e
c
o
st
a
n
d
siz
e
o
f
t
h
e
LCL
fil
ter.
S
imu
latio
n
re
se
a
rc
h
h
a
s
b
e
e
n
d
o
n
e
to
p
ro
p
o
se
a
h
y
b
ri
d
p
a
ss
iv
e
d
a
m
p
in
g
fil
ter
u
si
n
g
M
ATLA
B/S
imu
li
n
k
to
o
ls
u
n
d
e
r
b
o
t
h
c
o
n
d
it
i
o
n
s,
t
h
e
ste
a
d
y
-
sta
te
a
n
d
d
y
n
a
m
ic
re
sp
o
n
se
.
S
imu
latio
n
re
su
lt
s
in
d
ica
te
th
a
t
t
h
e
p
a
ss
iv
e
d
a
m
p
i
n
g
fil
ter
wo
r
k
s
we
ll
u
n
d
e
r
b
o
t
h
c
o
n
d
it
i
o
n
s wit
h
lo
w T
HD
c
o
m
p
a
re
d
to
LCL
a
n
d
H
-
Bri
d
g
e
(H
-
B)
fil
ters
.
M
a
n
y
m
e
th
o
d
s
a
re
u
se
d
t
o
s
o
lv
e
th
e
p
r
o
b
lem
o
f
h
ig
h
THD
g
rid
c
u
rre
n
t.
T
h
e
p
a
ss
iv
e
d
a
m
p
i
n
g
fil
ter
m
e
th
o
d
si
m
p
li
fies
th
e
P
V
m
icro
i
n
v
e
rter.
T
h
is
stu
d
y
a
ims
to
a
c
h
iev
e
a
h
i
g
h
-
e
fficie
n
c
y
P
V
m
icro
i
n
v
e
rter
b
y
m
in
imi
z
in
g
t
o
ta
l
p
o
we
r
lo
ss
e
s.
K
ey
w
o
r
d
s
:
H
-
B
r
id
g
e
in
v
er
ter
L
C
L
o
u
tp
u
t f
ilter
Pas
s
iv
e
d
am
p
in
g
f
ilter
PV
-
m
icr
o
in
v
er
ter
Q
-
B
o
o
s
t c
o
n
v
er
ter
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
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
:
Mu
h
am
m
ad
Am
m
ir
r
u
l A
tiq
i
Mo
h
d
Z
ain
u
r
i
Dep
ar
tm
en
t o
f
E
lectr
ical,
E
lec
tr
o
n
ics an
d
Sy
s
tem
E
n
g
in
ee
r
in
g
,
Facu
lty
o
f
E
n
g
i
n
ee
r
in
g
a
n
d
B
u
ilt
E
n
v
ir
o
n
m
en
t,
Un
i
v
er
s
iti Ke
b
an
g
s
aa
n
Ma
lay
s
ia
(
UKM
)
4
3
6
0
0
UKM
,
B
an
g
i Sela
n
g
o
r
,
Ma
lay
s
ia
E
m
ail: a
m
m
ir
r
u
latiq
i@
u
k
m
.
e
d
u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
s
u
p
p
ly
o
f
n
o
n
-
r
e
n
ewa
b
l
e
en
er
g
y
s
o
u
r
ce
s
lik
e
co
al
an
d
o
il
is
d
win
d
lin
g
d
u
e
to
th
eir
f
in
ite
av
ailab
ilit
y
an
d
th
e
r
is
in
g
elec
tr
icity
d
em
an
d
[
1
]
,
[
2
]
.
As
a
r
e
s
u
lt,
u
s
er
s
n
ee
d
to
tr
an
s
itio
n
t
o
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
lik
e
s
o
lar
e
n
er
g
y
.
E
n
er
g
y
is
t
h
e
f
o
u
n
d
atio
n
o
f
m
o
d
er
n
s
o
ciety
,
p
o
wer
in
g
m
y
r
iad
ac
tiv
ities
ess
en
tial
f
o
r
d
aily
life
.
Ho
wev
er
,
as
g
lo
b
al
en
er
g
y
d
em
an
d
s
c
o
n
tin
u
e
to
r
is
e,
co
n
ce
r
n
s
a
b
o
u
t
en
v
ir
o
n
m
en
tal
Su
s
tain
ab
ilit
y
an
d
r
eso
u
r
ce
d
e
p
letio
n
h
av
e
p
r
o
m
p
te
d
a
s
h
if
t
to
war
d
s
u
s
tain
ab
le
an
d
r
en
ew
ab
le
en
er
g
y
s
o
u
r
ce
s
[
3
]
.
T
h
e
S
ev
en
t
h
Su
s
tain
ab
le
Dev
elo
p
m
en
t
Go
al
(
SDG
7
)
is
f
o
cu
s
ed
o
n
en
s
u
r
in
g
u
n
iv
er
s
al
ac
ce
s
s
to
af
f
o
r
d
a
b
le,
r
eliab
le,
s
u
s
tain
ab
l
e,
an
d
m
o
d
er
n
en
er
g
y
.
T
h
is
g
o
al
u
n
d
er
s
co
r
es
th
e
im
p
o
r
tan
c
e
o
f
tr
an
s
itio
n
in
g
to
en
er
g
y
s
y
s
tem
s
th
at
s
u
p
p
o
r
t e
c
o
n
o
m
ic
g
r
o
wth
a
n
d
d
e
v
elo
p
m
en
t w
h
ile
m
in
im
izin
g
e
n
v
ir
o
n
m
en
tal
im
p
ac
t
[
4
]
.
Ad
d
itio
n
al
in
d
icato
r
s
h
i
g
h
lig
h
t
th
e
f
o
cu
s
o
n
in
cr
ea
s
in
g
t
h
e
p
r
o
p
o
r
tio
n
o
f
r
en
ewa
b
le
en
er
g
y
a
n
d
im
p
r
o
v
in
g
e
n
er
g
y
ef
f
icien
cy
.
T
h
e
m
ain
g
o
als
ar
e
to
o
f
f
er
c
o
st
-
ef
f
ec
tiv
e
an
d
d
ep
en
d
ab
le
en
er
g
y
ac
ce
s
s
wh
ile
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
Hyb
r
id
p
a
s
s
ive
d
a
mp
in
g
filt
er
o
f sin
g
le
-
p
h
a
s
e
g
r
id
-
tied
P
V
-
micro
in
ve
r
ter
(
F
o
u
z
ey
S
a
lem
A
a
ma
r
a
)
3661
in
cr
ea
s
in
g
th
e
g
lo
b
al
p
r
o
p
o
r
tio
n
o
f
r
en
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
s
.
T
h
ese
o
b
jectiv
es
ad
d
itio
n
ally
h
ig
h
lig
h
t
th
e
en
h
an
ce
m
e
n
t
o
f
en
er
g
y
ef
f
ici
en
cy
,
th
e
ad
v
an
c
em
en
t
o
f
in
t
er
n
atio
n
al
co
o
p
er
atio
n
,
an
d
in
v
estme
n
t
in
clea
n
en
er
g
y
i
n
f
r
astru
ctu
r
e
.
Am
o
n
g
th
ese
s
o
u
r
ce
s
,
s
o
l
ar
e
n
er
g
y
is
d
is
ti
n
g
u
is
h
e
d
b
y
i
ts
a
b
u
n
d
an
ce
,
o
f
f
er
in
g
t
h
e
p
o
te
n
ti
al
to
m
e
et
a
h
u
g
e
p
o
r
ti
o
n
o
f
e
n
e
r
g
y
n
ee
d
s
.
So
l
ar
e
n
e
r
g
y
,
r
ec
o
g
n
iz
ed
as
o
n
e
o
f
t
h
e
m
o
s
t
p
le
n
ti
f
u
l
r
e
n
e
wab
le
r
es
o
u
r
ce
s
,
is
ca
p
t
u
r
ed
t
h
r
o
u
g
h
p
h
o
t
o
v
o
lt
aic
(
PV
)
s
y
s
t
em
s
.
T
h
es
e
s
y
s
te
m
s
c
o
n
s
is
t
o
f
s
o
la
r
p
an
els
m
ad
e
o
f
s
e
m
ic
o
n
d
u
ct
o
r
m
at
er
ials
t
h
at
c
a
p
t
u
r
e
s
u
n
li
g
h
t a
n
d
tr
an
s
f
o
r
m
it
d
ir
ec
t
ly
i
n
t
o
e
lect
r
i
cit
y
v
i
a
th
e
p
h
o
t
o
v
o
l
tai
c
ef
f
e
ct.
PV
i
n
v
e
r
te
r
s
ar
e
c
r
u
c
ial
c
o
m
p
o
n
e
n
ts
i
n
s
o
l
ar
e
n
e
r
g
y
s
y
s
te
ms
th
at
a
r
e
u
s
ab
l
e
b
y
h
o
u
s
e
h
o
l
d
ap
p
l
ia
n
c
es
an
d
s
u
i
ta
b
l
e
f
o
r
t
h
e
ele
ctr
ic
al
g
r
i
d
.
PV
i
n
v
e
r
te
r
s
a
r
e
cr
u
cia
l
c
o
m
p
o
n
e
n
ts
o
f
s
o
la
r
en
er
g
y
s
y
s
te
m
s
.
T
h
e
y
tr
a
n
s
f
o
r
m
th
e
d
ir
ec
t
c
u
r
r
e
n
t
p
r
o
d
u
c
ed
b
y
s
o
la
r
p
a
n
els
i
n
t
o
alte
r
n
at
in
g
c
u
r
r
en
t,
e
n
ab
li
n
g
s
e
am
l
ess
in
te
g
r
ati
o
n
wit
h
th
e
el
e
ctr
ica
l
g
r
i
d
.
Ad
d
itio
n
ally
,
th
ey
en
s
u
r
e
th
at
th
e
elec
tr
icity
g
e
n
er
ated
alig
n
s
with
th
e
g
r
id
’
s
f
r
e
q
u
en
c
y
a
n
d
v
o
ltag
e.
PV
in
v
er
ter
s
ar
e
eq
u
ip
p
e
d
with
f
ea
tu
r
es
lik
e
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
,
wh
ich
o
p
tim
izes
th
e
p
o
wer
o
u
tp
u
t
f
r
o
m
s
o
lar
p
an
els
b
y
co
n
tin
u
ally
a
d
ju
s
tin
g
th
eir
p
er
f
o
r
m
an
ce
to
a
d
ap
t
to
c
h
an
g
in
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
[
5
]
.
B
ey
o
n
d
th
eir
co
r
e
co
n
v
er
s
io
n
f
u
n
ctio
n
,
PV
in
v
er
ter
s
ar
e
v
ital
in
s
o
lar
en
er
g
y
s
y
s
tem
s
'
o
v
er
all
m
an
ag
e
m
en
t a
n
d
s
af
ety
.
T
h
ey
m
o
n
ito
r
t
h
e
s
y
s
tem
’
s
p
er
f
o
r
m
an
ce
,
d
etec
t
f
au
lts
o
r
an
y
d
r
o
p
in
ef
f
icien
cy
,
an
d
ca
n
d
is
co
n
n
ec
t
th
e
s
y
s
tem
in
ca
s
e
o
f
g
r
id
f
ailu
r
es
o
r
o
th
er
elec
tr
ical
is
s
u
es,
en
s
u
r
in
g
s
af
ety
an
d
d
u
r
ab
ilit
y
.
Ad
v
an
ce
d
PV
in
v
er
ter
s
also
o
f
f
e
r
f
ea
tu
r
es
lik
e
r
ea
l
-
tim
e
m
o
n
ito
r
i
n
g
an
d
in
teg
r
atio
n
with
s
m
ar
t g
r
id
tech
n
o
lo
g
y
,
im
p
r
o
v
in
g
th
e
ef
f
icien
cy
an
d
m
an
a
g
e
m
en
t o
f
s
o
lar
p
o
wer
s
y
s
tem
s
.
PV strin
g
in
v
er
ter
s
ar
e
f
r
eq
u
en
tly
u
tili
ze
d
in
s
m
all
to
m
ed
iu
m
-
s
ized
s
o
lar
in
s
tallatio
n
s
,
wh
er
e
s
ev
er
al
s
o
lar
p
an
els
ar
e
co
n
n
ec
ted
in
s
tr
in
g
,
an
d
th
ei
r
co
m
b
i
n
ed
D
C
o
u
tp
u
t
is
f
ed
in
to
a
s
in
g
le
in
v
er
ter
.
T
h
is
ty
p
e
o
f
in
v
er
ter
is
c
o
s
t
-
ef
f
ec
tiv
e
a
n
d
s
im
p
le
to
in
s
tall.
I
t
m
ak
es
a
p
o
p
u
lar
o
p
tio
n
f
o
r
s
m
all
s
o
lar
s
y
s
tem
s
[
6
]
.
Strin
g
in
v
er
ter
s
ar
e
in
s
talled
at
a
ce
n
t
r
al
lo
ca
tio
n
,
t
y
p
ically
clo
s
e
to
th
e
m
ain
elec
tr
ic
s
er
v
ice
p
an
el
.
I
n
th
ese
s
y
s
tem
s
,
th
e
p
an
els'
co
llected
(
DC
)
p
o
wer
is
tr
an
s
f
o
r
m
ed
in
to
(
AC
)
p
o
wer
.
On
e
o
f
th
e
d
r
aw
b
ac
k
s
o
f
s
tr
in
g
in
v
e
r
ter
s
is
th
at
th
e
wea
k
est
p
an
el
with
in
it
in
f
lu
en
ce
s
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
en
tire
s
tr
in
g
[
7
]
.
Fo
r
in
s
tan
ce
,
if
o
n
e
p
an
e
l
is
s
h
ad
ed
,
it
ca
n
s
ig
n
i
f
ican
tly
d
im
in
is
h
th
e
o
v
er
all
o
u
tp
u
t.
H
o
wev
er
,
m
o
d
er
n
s
tr
in
g
i
n
v
er
te
r
s
o
f
ten
in
c
o
r
p
o
r
ate
m
u
ltip
le
MPPTs
to
h
elp
m
itig
ate
th
is
is
s
u
e
to
s
o
m
e
ex
ten
t
b
y
o
p
tim
izin
g
g
r
o
u
p
s
o
f
p
an
els
s
ep
ar
ately
.
Desp
ite
th
ese
lim
itatio
n
s
,
s
tr
in
g
in
v
e
r
ter
s
r
em
ain
a
r
eliab
le
a
n
d
ef
f
icien
t
s
o
lu
tio
n
f
o
r
m
an
y
s
o
lar
in
s
tallatio
n
s
,
p
r
o
v
id
i
n
g
a
g
o
o
d
b
alan
ce
b
et
wee
n
co
s
t a
n
d
p
e
r
f
o
r
m
an
ce
.
PV
-
m
i
c
r
o
i
n
v
e
r
te
r
r
e
p
r
es
e
n
t
s
a
m
o
r
e
r
e
c
e
n
t
a
d
v
a
n
c
e
m
e
n
t
i
n
s
o
l
a
r
t
e
c
h
n
o
l
o
g
y
,
o
f
f
e
r
in
g
s
e
v
e
r
al
a
d
v
a
n
t
a
g
e
s
o
v
e
r
t
r
a
d
i
t
i
o
n
a
l
.
Un
l
i
k
e
s
t
r
i
n
g
i
n
v
e
r
t
e
r
s
,
m
i
c
r
o
i
n
v
e
r
t
e
r
s
a
r
e
i
n
s
t
a
l
le
d
o
n
e
a
c
h
s
o
l
a
r
p
a
n
e
l
,
a
l
l
o
w
i
n
g
f
o
r
t
h
e
c
o
n
v
e
r
s
i
o
n
o
f
DC
t
o
AC
c
u
r
r
e
n
t
at
e
a
c
h
p
a
n
el
[
8
]
.
T
h
is
s
e
t
u
p
a
l
l
o
w
s
e
a
c
h
p
a
n
e
l
t
o
o
p
e
r
a
t
e
a
u
t
o
n
o
m
o
u
s
l
y
,
i
m
p
r
o
v
i
n
g
t
h
e
s
y
s
t
e
m
e
f
f
i
c
i
e
n
cy
b
e
c
a
u
s
e
t
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
o
n
e
p
a
n
e
l
is
n
o
t
a
f
f
e
c
t
e
d
b
y
s
h
ad
i
n
g
o
n
a
n
o
t
h
e
r
[
9
]
.
T
h
a
t
m
a
k
e
s
m
i
c
r
o
i
n
v
e
r
t
e
r
s
p
ar
t
i
c
u
l
a
r
l
y
b
e
n
e
f
ic
i
a
l
i
n
i
n
s
t
a
ll
at
i
o
n
s
w
h
e
r
e
s
h
a
d
i
n
g
,
o
d
d
r
o
o
f
a
n
g
l
e
s
,
o
r
v
a
r
i
a
b
l
e
l
i
g
h
t
c
o
n
d
i
ti
o
n
s
a
r
e
p
r
e
s
e
n
t
.
M
i
c
r
o
i
n
v
e
r
t
e
r
s
a
ls
o
p
r
o
v
i
d
e
en
h
a
n
c
e
d
s
y
s
te
m
m
o
n
i
t
o
r
i
n
g
an
d
t
r
o
u
b
l
e
s
h
o
o
t
i
n
g
c
a
p
a
b
i
l
i
ti
e
s
as
t
h
e
y
a
ll
o
w
f
o
r
p
a
n
e
l
-
l
e
v
e
l
d
at
a
c
o
l
l
e
ct
i
o
n
a
n
d
a
n
a
l
y
t
ic
s
[
1
0
]
.
T
h
i
s
l
e
v
el
o
f
d
e
t
a
i
l
h
e
l
p
s
i
d
e
n
ti
f
y
u
n
d
e
r
p
e
r
f
o
r
m
i
n
g
p
a
n
e
l
s
q
u
i
c
k
l
y
,
m
a
k
i
n
g
m
a
i
n
t
e
n
a
n
c
e
a
n
d
o
p
ti
m
i
z
a
ti
o
n
m
o
r
e
s
t
r
a
i
g
h
t
f
o
r
wa
r
d
.
Ad
d
itio
n
ally
,
b
y
r
ed
u
cin
g
th
e
s
y
s
tem
’
s
DC
v
o
ltag
e,
m
icr
o
in
v
er
ter
s
in
cr
ea
s
e
th
e
s
af
ety
o
f
th
e
s
o
lar
in
s
tallatio
n
.
T
h
e
m
ain
d
r
awb
ac
k
o
f
m
icr
o
in
v
er
ter
s
h
as
h
i
s
to
r
ically
b
ee
n
th
ei
r
h
ig
h
er
i
n
itial
co
s
t
co
m
p
ar
ed
with
s
tr
in
g
in
v
er
ter
s
,
b
u
t
as
tech
n
o
lo
g
y
h
as
ad
v
an
ce
d
,
th
i
s
co
s
t
g
ap
h
as
b
ee
n
n
ar
r
o
win
g
.
On
e
-
s
tag
e
PV
m
icr
o
in
v
er
ter
s
p
er
f
o
r
m
th
e
DC
-
to
-
AC
co
n
v
er
s
io
n
p
r
o
ce
s
s
d
ir
ec
tly
in
a
s
in
g
le
s
tep
[
1
1
]
.
T
h
is
s
tr
aig
h
tf
o
r
war
d
ap
p
r
o
ac
h
s
im
p
lifie
s
th
e
co
n
v
er
s
io
n
p
r
o
ce
s
s
an
d
ca
n
o
f
f
er
ad
v
an
tag
es
in
ter
m
s
o
f
ef
f
icien
cy
an
d
r
eliab
ilit
y
b
ec
au
s
e
f
ewe
r
co
m
p
o
n
en
ts
ca
n
f
ail.
T
h
e
s
im
p
licity
o
f
th
e
o
n
e
-
s
tag
e
co
n
v
er
s
io
n
p
r
o
ce
s
s
en
s
u
r
es
th
at
elec
tr
ica
l
lo
s
s
es a
r
e
m
in
im
ized
,
p
o
ten
tia
lly
b
o
o
s
tin
g
th
e
o
v
e
r
all
en
er
g
y
o
u
tp
u
t
f
r
o
m
th
e
s
o
lar
p
a
n
els
[
1
2
]
–
[
1
4
]
.
H
o
w
e
v
e
r
,
o
n
e
-
s
t
a
g
e
P
V
m
i
c
r
o
i
n
v
e
r
t
e
r
s
m
a
y
b
e
l
i
m
it
e
d
i
n
h
an
d
l
i
n
g
w
i
d
e
v
a
r
i
a
ti
o
n
s
i
n
i
n
p
u
t
v
o
l
t
a
g
e
,
w
h
i
c
h
c
a
n
o
c
c
u
r
d
u
e
t
o
c
h
a
n
g
e
s
i
n
s
u
n
l
i
g
h
t
t
h
r
o
u
g
h
o
u
t
t
h
e
d
a
y
.
T
h
a
t
c
a
n
i
m
p
a
c
t
t
h
e
i
r
e
f
f
e
c
t
i
v
e
n
es
s
i
n
e
n
v
i
r
o
n
m
e
n
t
s
wi
t
h
h
i
g
h
l
y
v
a
r
i
a
b
l
e
s
u
n
l
i
g
h
t
o
r
s
h
a
d
i
n
g
.
D
es
p
i
t
e
t
h
is
l
i
m
it
a
t
i
o
n
,
o
n
e
-
s
t
a
g
e
m
i
c
r
o
i
n
v
e
r
t
e
r
s
a
r
e
a
p
p
r
e
c
i
a
t
e
d
f
o
r
t
h
e
i
r
e
f
f
ic
i
e
n
c
y
a
n
d
a
r
e
g
o
o
d
f
o
r
i
n
s
t
a
l
l
a
ti
o
n
s
w
i
t
h
c
o
n
s
i
s
te
n
t
s
u
n
li
g
h
t
a
n
d
m
in
i
m
a
l
s
h
a
d
i
n
g
[
1
5
]
.
T
wo
-
s
tag
e
PV
m
icr
o
in
v
er
ter
s
ad
d
r
ess
s
o
m
e
o
f
th
e
lim
itatio
n
s
f
o
u
n
d
in
o
n
e
-
s
tag
e
m
o
d
els
b
y
ad
d
in
g
an
in
ter
m
e
d
iate
s
tep
in
th
e
co
n
v
er
s
io
n
p
r
o
ce
s
s
[
1
6
]
.
I
n
a
tw
o
-
s
tag
e
s
y
s
tem
,
th
e
i
n
itial
p
h
a
s
e
g
en
er
ally
f
o
cu
s
es
o
n
co
n
v
er
s
io
n
.
T
h
e
f
ir
s
t
s
tag
e
co
n
v
er
ts
th
e
v
ar
iab
le
DC
v
o
lt
ag
e
p
r
o
d
u
ce
d
b
y
t
h
e
s
o
lar
p
a
n
el
in
to
a
s
tab
le
DC
v
o
ltag
e,
wh
ile
t
h
e
s
ec
o
n
d
s
tag
e
tr
an
s
f
o
r
m
s
th
is
s
tab
le
DC
v
o
ltag
e
in
to
alter
n
atin
g
c
u
r
r
en
t
(
AC
)
.
T
h
is
ad
d
itio
n
al
s
tep
allo
ws
th
e
m
icr
o
in
v
er
ter
t
o
h
an
d
le
a
wid
e
r
r
an
g
e
o
f
in
p
u
t
v
o
ltag
es
m
o
r
e
ef
f
ec
tiv
ely
an
d
m
ain
tain
o
p
tim
al
p
er
f
o
r
m
an
c
e
ev
en
u
n
d
e
r
f
lu
ctu
atin
g
s
u
n
lig
h
t
co
n
d
itio
n
s
.
T
h
e
two
-
s
tag
e
ap
p
r
o
ac
h
ca
n
im
p
r
o
v
e
t
h
e
o
v
er
all
ef
f
icien
c
y
an
d
a
d
ap
tab
ilit
y
o
f
th
e
PV
m
icr
o
in
v
e
r
ter
,
p
a
r
ticu
lar
ly
i
n
in
s
tallatio
n
s
with
v
ar
iab
le
s
h
ad
in
g
o
r
c
h
an
g
i
n
g
wea
th
er
co
n
d
itio
n
s
.
Alth
o
u
g
h
th
is
ad
d
ed
c
o
m
p
lex
ity
ca
n
in
cr
ea
s
e
th
e
c
o
s
t
an
d
th
e
n
u
m
b
er
o
f
co
m
p
o
n
e
n
ts
th
at
co
u
ld
p
o
ten
tially
f
ail,
th
e
b
en
ef
its
o
f
m
o
r
e
r
eliab
le
an
d
ef
f
icien
t
p
o
wer
c
o
n
v
er
s
io
n
o
f
ten
m
itig
ate
th
ese
co
n
ce
r
n
s
.
T
wo
-
s
tag
e
PV
m
icr
o
in
v
er
ter
s
ar
e
p
ar
ticu
la
r
ly
b
en
ef
icial
i
n
s
ettin
g
s
wh
er
e
m
ain
tain
in
g
h
ig
h
ef
f
icien
c
y
ac
r
o
s
s
d
iv
er
s
e
co
n
d
itio
n
s
is
ess
en
tial
f
o
r
o
p
tim
izin
g
en
er
g
y
p
r
o
d
u
ctio
n
.
T
h
e
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
ter
is
a
cu
ttin
g
-
ed
g
e
p
o
wer
elec
tr
o
n
ics
co
m
p
o
n
en
t
th
at
o
p
tim
izes
th
e
v
o
ltag
e
co
n
v
er
s
io
n
p
r
o
ce
s
s
in
s
o
lar
s
y
s
tem
s
.
I
t
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
.
4
,
Au
g
u
s
t
20
25
:
3
6
6
0
-
3682
3662
ef
f
icien
tly
b
o
o
s
ts
th
e
DC
v
o
ltag
e
o
u
tp
u
t
o
f
s
o
lar
p
an
els
t
o
th
e
n
ec
ess
ar
y
le
v
els
f
o
r
g
r
i
d
in
teg
r
atio
n
.
T
h
is
tech
n
o
lo
g
y
m
in
im
izes e
n
er
g
y
lo
s
s
es a
n
d
m
ax
im
izes th
e
s
y
s
tem
'
s
en
er
g
y
o
u
tp
u
t
[
1
7
]
.
T
h
e
L
C
L
o
u
tp
u
t
f
ilter
is
a
cr
u
cial
co
m
p
o
n
e
n
t
th
at
en
s
u
r
es
th
e
q
u
ality
o
f
th
e
elec
tr
icity
f
ed
in
to
th
e
g
r
id
.
I
t
r
ed
u
ce
s
T
HD
an
d
f
ilt
er
s
o
u
t
n
o
is
e
f
r
o
m
th
e
AC
o
u
tp
u
t
o
f
th
e
m
icr
o
in
v
er
ter
.
T
h
at
im
p
r
o
v
es
p
o
wer
q
u
ality
a
n
d
m
in
im
izes
th
e
p
o
t
en
tial
f
o
r
d
is
r
u
p
tio
n
s
in
th
e
g
r
id
[
1
8
]
,
[
1
9
]
.
T
h
e
d
a
m
p
in
g
f
ilter
is
d
esig
n
ed
t
o
en
s
u
r
e
s
tab
ilit
y
an
d
o
p
tim
al
p
er
f
o
r
m
a
n
ce
o
f
th
e
s
o
lar
p
o
we
r
s
y
s
tem
.
I
t
d
a
m
p
en
s
o
s
cillatio
n
s
an
d
r
eso
n
an
ce
s
with
in
th
e
s
y
s
tem
,
p
r
ev
e
n
tin
g
u
n
wan
ted
i
n
ter
ac
tio
n
s
b
etwe
en
th
e
s
y
s
tem
an
d
t
h
e
g
r
i
d
[
2
0
]
,
[
2
1
]
.
L
C
L
f
ilter
s
ar
e
co
m
m
o
n
ly
u
tili
ze
d
in
g
r
i
d
-
co
n
n
ec
ted
i
n
v
er
ter
s
t
o
r
e
d
u
ce
h
ig
h
-
f
r
e
q
u
en
c
y
h
a
r
m
o
n
ics
an
d
in
c
r
ea
s
e
p
o
wer
q
u
ality
.
On
e
o
f
th
e
p
r
im
ar
y
a
d
v
an
tag
es
o
f
L
C
L
f
ilter
s
is
th
eir
s
u
p
er
io
r
h
ar
m
o
n
ic
atten
u
at
io
n
ca
p
ab
ilit
y
.
T
h
ey
ar
e
m
o
r
e
e
f
f
ec
tiv
e
at
r
e
d
u
cin
g
th
e
h
ig
h
-
f
r
e
q
u
en
c
y
co
m
p
o
n
en
ts
th
an
s
im
p
l
er
L
C
o
r
L
f
ilter
s
[
2
2
]
,
p
r
im
ar
il
y
d
u
e
to
th
eir
ad
d
itio
n
al
in
d
u
ctiv
e
to
ca
p
ac
itiv
e
s
tag
es.
T
h
e
r
esu
lts
in
cl
ea
n
er
s
in
u
s
o
id
al
o
u
tp
u
t
ar
e
cr
u
cial
f
o
r
g
r
id
co
m
p
lian
ce
an
d
r
ed
u
ce
el
ec
tr
o
m
ag
n
etic
in
ter
f
er
en
ce
(
E
MI
)
[
2
3
]
.
An
o
th
er
s
ig
n
if
ican
t
a
d
v
an
ta
g
e
o
f
L
C
L
f
ilter
s
is
th
eir
ab
ilit
y
to
p
r
o
v
id
e
b
etter
f
ilter
in
g
p
e
r
f
o
r
m
an
ce
with
in
a
c
o
m
p
ac
t
s
ize
an
d
l
o
wer
weig
h
t.
T
h
e
d
esig
n
o
f
L
C
L
f
ilter
s
allo
ws
f
o
r
a
h
i
g
h
er
atten
u
atio
n
o
f
s
witch
in
g
h
ar
m
o
n
ics
with
o
u
t
n
ec
ess
itatin
g
ex
ce
s
s
iv
ely
lar
g
e
f
ilter
co
m
p
o
n
en
ts
[
2
4
]
,
[
2
5
]
.
T
h
is
co
m
p
ac
tn
ess
is
p
ar
ticu
lar
ly
v
alu
ab
le
in
a
p
p
licatio
n
s
with
cr
itical
s
p
ac
e
an
d
weig
h
t
co
n
s
tr
ain
ts
,
s
u
ch
as
s
o
lar
in
v
er
t
er
s
.
Desig
n
in
g
an
d
tu
n
in
g
L
C
L
f
ilter
s
ca
n
b
e
m
o
r
e
c
h
allen
g
i
n
g
.
Desp
ite
t
h
eir
a
d
v
an
ta
g
es,
L
C
L
f
ilter
s
h
a
v
e
p
r
im
ar
y
d
is
ad
v
a
n
tag
es,
s
u
ch
a
s
co
m
p
lex
ity
an
d
th
e
ass
o
ciate
d
co
n
tr
o
l
ch
allen
g
es.
T
h
e
in
clu
s
io
n
o
f
ad
d
itio
n
al
r
ea
ctiv
e
co
m
p
o
n
en
ts
co
m
p
lica
tes th
e
f
ilte
r
d
esig
n
an
d
s
y
s
tem
m
o
d
ellin
g
.
T
h
is
co
m
p
lex
ity
ca
n
lead
to
s
tab
ilit
y
is
s
u
es,
n
ec
ess
itat
in
g
s
o
p
h
is
ticated
co
n
tr
o
l
alg
o
r
ith
m
s
to
en
s
u
r
e
th
e
s
y
s
tem
r
em
ain
s
s
tab
le
u
n
d
e
r
v
a
r
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
.
I
m
p
lem
en
tin
g
th
ese
co
n
tr
o
l
s
tr
ateg
ies
ca
n
b
e
d
em
an
d
in
g
r
eg
a
r
d
in
g
h
ar
d
war
e
an
d
s
o
f
twar
e
r
eso
u
r
ce
s
[
2
6
]
,
[
2
7
]
.
An
o
th
er
d
is
ad
v
an
tag
e
is
th
e
p
o
ten
tial
f
o
r
r
eso
n
an
ce
is
s
u
es.
L
C
L
f
ilter
s
ar
e
p
r
o
n
e
to
r
eso
n
an
ce
at
ce
r
tain
f
r
eq
u
en
cies,
wh
ich
ca
n
am
p
l
if
y
u
n
d
esira
b
le
h
ar
m
o
n
ics
in
s
tead
o
f
atten
u
atin
g
th
em
.
Ad
d
itio
n
al
p
ass
iv
e
o
r
a
ctiv
e
d
am
p
in
g
m
eth
o
d
s
ar
e
o
f
ten
r
eq
u
ir
ed
to
m
itig
ate
r
eso
n
an
ce
p
r
o
b
lem
s
[
2
8
]
,
[
2
9
]
.
T
h
es
e
d
am
p
in
g
s
o
l
u
tio
n
s
m
ay
r
aise
th
e
o
v
er
all
co
s
t
a
n
d
th
e
s
y
s
tem
'
s
co
m
p
lex
ity
.
S
o
m
ewh
at
o
f
f
s
ettin
g
th
e
b
en
ef
its
p
r
o
v
id
e
d
b
y
th
e
e
n
h
an
ce
d
f
ilter
in
g
p
er
f
o
r
m
an
ce
o
f
th
e
L
C
L
f
ilter
.
Pas
s
iv
e
d
am
p
in
g
f
ilter
s
o
f
f
e
r
s
ev
er
al
ad
v
an
tag
es c
o
m
p
ar
ed
t
o
L
C
L
f
ilter
s
an
d
H
-
br
id
g
e
to
p
o
lo
g
ies,
p
ar
ticu
lar
l
y
in
s
im
p
licity
an
d
r
eliab
ilit
y
.
On
e
o
f
th
e
p
r
im
ar
y
b
e
n
ef
its
o
f
p
ass
iv
e
d
am
p
in
g
is
its
s
tr
aig
h
tf
o
r
war
d
im
p
lem
e
n
tatio
n
b
ec
au
s
e
it
r
elies
o
n
p
ass
iv
e
co
m
p
o
n
e
n
ts
,
in
clu
d
in
g
r
esis
to
r
s
,
ca
p
ac
ito
r
s
,
an
d
in
d
u
cto
r
s
.
Un
lik
e
ac
tiv
e
d
a
m
p
in
g
m
eth
o
d
s
[
3
0
]
,
[
3
1
]
,
wh
ich
r
eq
u
ir
e
co
m
p
lex
co
n
tr
o
l
alg
o
r
ith
m
s
an
d
ad
d
itio
n
al
s
en
s
o
r
s
,
p
ass
iv
e
d
am
p
in
g
s
o
l
u
tio
n
s
ar
e
ea
s
ier
t
o
d
esig
n
,
im
p
lem
e
n
t,
an
d
m
ai
n
tain
.
T
h
is
s
im
p
licity
tr
a
n
s
lates
to
in
cr
ea
s
ed
s
y
s
tem
r
o
b
u
s
tn
ess
an
d
lo
wer
ch
an
ce
s
o
f
f
ailu
r
e
d
u
e
to
f
ewe
r
ac
tiv
e
c
o
m
p
o
n
en
t
s
[
3
2
]
.
Pas
s
iv
e
d
am
p
in
g
f
ilter
s
also
ef
f
ec
tiv
ely
m
itig
ate
r
eso
n
an
ce
is
s
u
es
co
m
m
o
n
ly
ass
o
ciate
d
with
L
C
L
f
ilter
s
.
B
y
ca
r
ef
u
lly
d
esig
n
i
n
g
th
e
p
ass
iv
e
elem
en
ts
,
it
is
p
o
s
s
ib
le
to
atten
u
ate
r
eso
n
a
n
ce
f
r
eq
u
e
n
cies
an
d
in
cr
ea
s
e
th
e
s
y
s
tem
s
tab
ilit
y
with
o
u
t
th
e
n
ee
d
f
o
r
ad
v
an
ce
d
co
n
tr
o
l
s
tr
ateg
ies.
C
o
m
p
ar
ed
with
H
-
b
r
id
g
e
f
ilter
s
,
th
e
p
ass
iv
e
d
am
p
in
g
a
p
p
r
o
ac
h
is
o
f
ten
m
o
r
e
co
s
t
-
ef
f
ec
tiv
e
an
d
r
eliab
le,
esp
ec
ially
in
ap
p
licatio
n
s
th
at
r
ed
u
ce
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
a
n
d
im
p
r
o
v
e
p
o
wer
q
u
ality
,
wh
ich
is
cr
itical.
Fu
r
th
er
m
o
r
e,
p
a
s
s
iv
e
d
am
p
in
g
d
o
es
n
o
t
s
u
f
f
er
f
r
o
m
th
e
s
witch
in
g
lo
s
s
es
in
h
er
en
t
in
ac
tiv
e
s
o
lu
tio
n
s
,
en
s
u
r
in
g
h
ig
h
e
r
ef
f
ici
en
cy
o
f
th
e
o
v
er
all
p
o
wer
co
n
v
er
s
io
n
s
y
s
tem
.
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
is
a
c
r
itical
p
ar
am
eter
w
h
en
e
v
alu
atin
g
th
e
ef
f
ec
tiv
e
n
ess
o
f
L
C
L
f
ilter
s
in
p
o
wer
elec
tr
o
n
ic
s
y
s
tem
s
,
p
ar
ticu
lar
ly
in
g
r
id
-
tied
in
v
er
ter
s
[
3
3
]
.
L
C
L
f
ilter
s
ar
e
h
ig
h
ly
ef
f
ec
tiv
e
in
r
ed
u
cin
g
h
ar
m
o
n
ic
d
is
to
r
tio
n
d
u
e
to
th
eir
ab
ilit
y
to
s
u
p
p
r
es
s
h
ig
h
-
f
r
eq
u
en
c
y
s
witch
in
g
h
ar
m
o
n
ics
[
3
4
]
.
T
h
e
co
m
p
o
n
en
t
s
tr
u
ctu
r
e
e
n
ab
les
th
e
L
C
L
f
ilter
to
p
r
o
v
id
e
s
teep
r
o
ll
-
o
f
f
c
h
ar
ac
ter
is
tics
,
s
ig
n
if
ican
tly
m
in
im
izin
g
T
HD
an
d
en
s
u
r
in
g
clea
n
er
s
in
u
s
o
id
al
o
u
tp
u
t.
T
h
is
r
ed
u
ctio
n
in
h
ar
m
o
n
ics is
ess
en
tial
f
o
r
c
o
m
p
ly
in
g
with
g
r
id
co
n
n
ec
tio
n
s
tan
d
ar
d
s
,
th
er
eb
y
im
p
r
o
v
in
g
p
o
wer
q
u
ality
[
3
5
]
.
Ho
wev
er
,
an
L
C
L
f
ilter
ca
n
i
n
tr
o
d
u
ce
r
eso
n
an
ce
is
s
u
es
an
d
,
if
n
o
t
p
r
o
p
er
ly
d
am
p
ed
,
ca
n
lead
to
s
p
ik
es
in
h
ar
m
o
n
ic
d
is
to
r
tio
n
at
ce
r
ta
in
f
r
eq
u
en
cies.
T
o
ad
d
r
ess
th
is
,
d
esig
n
er
s
o
f
ten
in
co
r
p
o
r
ate
p
ass
iv
e
o
r
ac
tiv
e
d
am
p
in
g
tech
n
iq
u
es
to
s
tab
ilize
th
e
f
ilter
an
d
en
s
u
r
e
lo
w
T
HD
lev
els
ac
r
o
s
s
v
ar
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
[
3
6
]
.
Alth
o
u
g
h
ef
f
ec
tiv
e,
th
ese
s
o
lu
tio
n
s
ad
d
co
m
p
lex
ity
to
th
e
s
y
s
tem
d
esig
n
,
s
o
h
ar
m
o
n
ic
atten
u
atio
n
,
s
tab
ilit
y
,
an
d
o
v
er
all
s
y
s
tem
ef
f
icien
cy
m
u
s
t
b
e
b
alan
ce
d
[
3
7
]
,
[
3
8
]
.
Pas
s
iv
e
d
am
p
in
g
f
ilter
s
ar
e
im
p
o
r
tan
t
f
o
r
r
eg
u
latin
g
T
HD
with
in
p
o
w
er
s
y
s
tem
s
,
o
f
f
er
in
g
a
m
o
r
e
s
tr
aig
h
tf
o
r
war
d
ap
p
r
o
ac
h
th
a
n
L
C
L
f
ilter
s
[
3
9
]
.
B
y
u
s
i
n
g
p
ass
iv
e
f
ilter
c
o
m
p
o
n
en
ts
,
th
e
p
ass
iv
e
d
am
p
in
g
f
ilter
s
ef
f
ec
tiv
ely
r
e
d
u
ce
r
eso
n
an
ce
s
th
at
ca
n
ca
u
s
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
[
4
0
]
.
T
h
e
m
ai
n
a
d
v
an
ta
g
e
o
f
p
ass
iv
e
d
am
p
in
g
is
its
ab
ilit
y
to
m
itig
ate
th
ese
r
eso
n
an
ce
s
with
o
u
t r
eq
u
ir
i
n
g
ac
tiv
e
co
n
tr
o
l
alg
o
r
ith
m
s
,
th
u
s
s
im
p
lify
in
g
th
e
s
y
s
tem
d
esig
n
.
T
h
is
p
ass
iv
e
ap
p
r
o
ac
h
h
elp
s
m
ain
tain
lo
w
T
HD
lev
els
in
t
h
e
o
u
tp
u
t,
e
n
s
u
r
in
g
th
e
p
o
wer
q
u
ality
is
wit
h
in
a
cc
ep
tab
le
lim
its
f
o
r
m
o
s
t
ap
p
licatio
n
s
[
4
1
]
.
Alth
o
u
g
h
p
ass
iv
e
d
am
p
in
g
f
ilter
s
m
ay
n
o
t
o
f
f
er
t
h
e
s
am
e
lev
el
o
f
h
ar
m
o
n
ic
atten
u
atio
n
as
m
eticu
lo
u
s
ly
d
esig
n
ed
L
C
L
f
ilter
s
,
th
ey
b
alan
ce
p
er
f
o
r
m
an
ce
an
d
s
im
p
licity
well.
T
h
e
r
esis
tiv
e
co
m
p
o
n
en
ts
in
p
ass
iv
e
d
am
p
in
g
d
i
r
ec
tly
d
i
s
s
ip
ate
E
n
er
g
y
th
at
co
u
ld
o
th
er
wis
e
co
n
tr
ib
u
te
to
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
th
u
s
p
r
o
v
id
in
g
a
clea
n
er
o
u
tp
u
t
.
T
h
is
m
eth
o
d
is
p
ar
ticu
lar
ly
b
en
e
f
icial
in
ap
p
licatio
n
s
wh
er
e
ea
s
e
o
f
im
p
lem
en
tatio
n
,
r
eliab
ilit
y
,
an
d
m
in
i
m
al
m
ain
ten
an
ce
ar
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
Hyb
r
id
p
a
s
s
ive
d
a
mp
in
g
filt
er
o
f sin
g
le
-
p
h
a
s
e
g
r
id
-
tied
P
V
-
micro
in
ve
r
ter
(
F
o
u
z
ey
S
a
lem
A
a
ma
r
a
)
3663
p
r
io
r
ities
.
Pas
s
iv
e
d
am
p
in
g
f
il
ter
s
ca
n
ef
f
ec
tiv
ely
m
ai
n
tain
l
o
w
T
HD
in
v
ar
io
u
s
p
o
wer
co
n
v
er
s
io
n
s
y
s
tem
s
,
as
well
as
ef
f
icien
cy
,
s
tab
ilit
y
,
an
d
g
r
id
co
m
p
atib
ilit
y
[
4
2
]
.
T
h
is
p
ap
er
is
s
tr
u
ctu
r
e
d
as
f
o
llo
ws:
Sectio
n
2
d
escr
ib
es
th
e
two
-
s
tag
e
PV
-
m
icr
o
in
v
er
ter
an
d
d
am
p
in
g
f
ilter
th
eo
r
y
an
d
e
x
p
lain
s
th
e
m
ath
em
atica
l
d
etails
o
f
th
e
(
R
//LC)
f
ilter
an
d
its
h
ar
m
o
n
ics
-
m
itig
atin
g
c
h
ar
ac
ter
is
tics
.
Sectio
n
3
,
r
esu
lts
an
d
d
is
cu
s
s
io
n
,
p
r
esen
ts
s
im
u
latio
n
s
r
esu
lts
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
,
b
o
d
e
d
iag
r
am
,
an
d
k
ey
p
a
r
am
eter
s
o
f
th
e
g
r
id
-
co
n
n
ec
ted
PV
-
m
icr
o
in
v
er
ter
a
r
e
p
r
o
v
id
ed
.
M
AT
L
AB
s
im
u
latio
n
s
also
co
m
p
ar
e
s
y
s
tem
p
er
f
o
r
m
a
n
ce
with
th
e
L
C
L
f
ilter
,
H
-
B
d
am
p
in
g
f
ilter
,
a
n
d
d
am
p
i
n
g
f
ilter
.
R
esu
lts
en
co
m
p
ass
in
g
g
r
id
cu
r
r
en
t
a
r
e
d
is
cu
s
s
ed
u
n
d
er
s
tead
y
s
tate
an
d
d
y
n
am
ic
o
p
er
atio
n
c
o
n
d
itio
n
s
.
T
h
e
co
n
cl
u
s
io
n
s
h
o
ws
th
e
s
ig
n
if
ican
c
e
o
f
t
h
e
d
am
p
in
g
f
i
lter
.
T
h
is
ap
p
r
o
ac
h
h
o
ld
s
p
r
o
m
is
e
f
o
r
ef
f
icien
t
g
r
id
in
teg
r
atio
n
i
n
PV
s
y
s
tem
s
b
y
im
p
r
o
v
i
n
g
p
o
wer
q
u
ality
an
d
r
e
d
u
cin
g
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
,
co
n
tr
ib
u
tin
g
to
s
u
s
tain
ab
le
en
er
g
y
s
o
lu
tio
n
s
.
2.
T
WO
-
ST
AG
E
P
V
-
M
I
CRO
I
NVER
T
E
R
T
h
e
b
lo
ck
d
iag
r
am
i
n
Fig
u
r
e
1
illu
s
tr
ates a
PV p
an
el
co
n
n
ec
ted
to
a
b
o
o
s
t c
o
n
v
er
te
r
,
wh
ich
r
aises
th
e
v
o
ltag
e
f
r
o
m
th
e
PV
p
a
n
el
to
a
s
u
itab
le
lev
el
f
o
r
a
n
H
-
b
r
id
g
e
in
v
er
ter
.
T
h
is
in
v
er
ter
c
o
n
v
e
r
ts
th
e
DC
in
to
AC
C
u
r
r
en
t
s
u
itab
le
f
o
r
th
e
g
r
id
,
e
n
s
u
r
in
g
t
h
e
o
u
tp
u
t
is
a
p
r
o
p
er
s
in
u
s
o
id
al
wav
ef
o
r
m
[
4
3
]
.
T
h
e
L
C
L
o
u
tp
u
t
f
ilter
is
u
s
ed
to
r
ed
u
ce
th
e
h
ar
m
o
n
ic
s
g
en
er
ated
b
y
th
e
in
v
er
ter
th
r
o
u
g
h
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
PW
M)
tech
n
iq
u
es
[
4
4
]
,
[
4
5
]
.
Ad
d
itio
n
ally
,
th
e
o
v
er
all
s
y
s
tem
in
teg
r
ates
m
a
x
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
an
d
p
h
ase
-
lo
ck
ed
lo
o
p
(
PLL
)
alg
o
r
ith
m
s
to
en
s
u
r
e
ef
f
icien
t
p
o
wer
d
el
iv
er
y
to
th
e
g
r
id
with
a
u
n
ity
p
o
wer
f
ac
to
r
.
T
h
e
two
-
s
tag
e
PV
m
icr
o
in
v
er
ter
w
ith
Q
-
b
o
o
s
t
co
n
v
er
ter
a
n
d
L
C
L
o
u
tp
u
t
f
ilter
s
is
a
m
o
r
e
ad
v
a
n
ce
d
co
n
f
ig
u
r
atio
n
in
h
ig
h
-
p
e
r
f
o
r
m
an
ce
PV
s
y
s
tem
s
.
I
n
th
is
m
icr
o
in
v
er
ter
m
et
h
o
d
o
lo
g
y
,
th
e
PV
p
an
el
is
in
teg
r
ated
with
a
b
o
o
s
t
co
n
v
er
ter
,
wh
ich
is
s
u
b
s
eq
u
e
n
tly
co
n
n
ec
ted
to
an
H
-
b
r
id
g
e
i
n
v
er
ter
th
at
i
n
co
r
p
o
r
ates a
n
L
C
L
o
u
tp
u
t f
ilter
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
tw
o
-
s
tag
e
g
r
id
-
tied
PV
-
m
icr
o
in
v
er
ter
Fig
u
r
e
2
d
e
p
icts
a
cir
cu
it
d
ia
g
r
am
o
f
a
two
-
s
tag
e
g
r
i
d
-
co
n
n
ec
ted
PV
-
m
icr
o
in
v
e
r
ter
,
illu
s
tr
atin
g
a
s
y
s
tem
f
o
r
ef
f
icien
t e
n
er
g
y
co
n
v
er
s
io
n
in
PV a
p
p
licatio
n
s
.
T
h
is
PV
-
m
icr
o
in
v
er
ter
s
y
s
tem
p
r
im
ar
ily
co
m
p
r
is
es
a
PV
ar
r
ay
th
at
ca
p
tu
r
es
s
o
lar
en
er
g
y
.
T
h
e
g
en
er
ate
d
v
o
ltag
e
is
in
itially
s
to
r
ed
in
a
ca
p
ac
it
o
r
,
wh
ich
ac
ts
as
a
b
u
f
f
er
to
s
tab
ilize
th
e
PV
v
o
ltag
e.
Fo
llo
win
g
th
is
s
to
r
ag
e
p
h
ase,
th
e
ca
p
ac
ito
r
is
co
n
n
e
cted
to
a
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
ter
.
T
h
is
co
n
v
e
r
ter
is
ess
en
tial
f
o
r
elev
atin
g
th
e
DC
v
o
ltag
e
to
a
h
i
g
h
er
lev
e
l.
T
h
e
b
o
o
s
ted
DC
v
o
ltag
e
is
t
h
en
f
u
r
th
e
r
s
to
r
ed
i
n
a
DC
-
lin
k
ca
p
ac
ito
r
,
wh
ich
m
ain
tain
s
a
co
n
s
tan
t
v
o
ltag
e
lev
el
at
th
e
in
p
u
t
o
f
th
e
H
-
b
r
id
g
e
in
v
er
ter
.
T
h
e
H
-
b
r
id
g
e
in
v
er
ter
c
o
n
v
er
ts
th
e
s
t
ab
ilized
DC
v
o
ltag
e
in
to
AC
v
o
ltag
e.
L
C
L
o
u
t
p
u
t
f
ilter
is
em
p
lo
y
ed
to
en
s
u
r
e
th
at
th
e
o
u
tp
u
t
c
u
r
r
en
t
is
s
m
o
o
th
.
T
h
is
f
ilter
ef
f
ec
tiv
ely
r
ed
u
ce
s
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
,
p
r
o
v
id
in
g
clea
n
s
in
e
wav
e
o
u
tp
u
t
co
m
p
atib
l
e
with
g
r
id
r
e
q
u
ir
em
e
n
ts
.
T
h
e
q
u
a
d
r
atic
b
o
o
s
t
co
n
v
er
ter
u
s
es
th
e
s
q
u
ar
e
o
f
th
e
in
p
u
t
v
o
lta
g
e
to
in
cr
ea
s
e
th
e
o
u
tp
u
t
v
o
lta
g
e,
o
f
f
e
r
in
g
g
r
e
ater
ef
f
icien
cy
th
an
s
tan
d
ar
d
b
o
o
s
t
co
n
v
er
ter
s
.
Fig
u
r
e
3
d
ep
icts
a
two
-
s
tag
e
g
r
id
-
co
n
n
ec
ted
PV
m
icr
o
in
v
er
ter
with
a
Q
-
b
o
o
s
t
co
n
v
er
ter
an
d
a
n
L
C
L
o
u
tp
u
t f
ilter
.
2
.
1
.
Co
ntr
o
l
s
chem
e
o
f
t
wo
-
s
t
a
g
e
P
V
-
m
icr
o
inv
er
t
er
T
h
e
co
n
tr
o
l
s
tr
ateg
y
o
f
a
two
-
s
tag
e
PV
m
icr
o
in
v
er
te
r
with
a
n
L
C
L
f
ilter
co
n
s
is
t
s
o
f
th
e
c
u
r
r
en
t
an
d
v
o
ltag
e
f
r
o
m
P
-
V
p
a
n
el
d
at
a,
ca
r
r
ied
o
u
t
b
y
an
ap
p
r
o
p
r
iate
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
alg
o
r
ith
m
.
T
h
e
DC
b
u
s
v
o
lta
g
e
co
n
tr
o
l
alg
o
r
ith
m
g
iv
es
a
r
ef
er
en
ce
f
o
r
th
e
cu
r
r
e
n
t
in
je
ctio
n
in
to
th
e
g
r
id
,
wh
ich
is
th
en
s
y
n
ch
r
o
n
ized
with
th
e
g
r
id
an
d
r
elate
d
to
th
e
p
h
ase
-
lo
ck
e
d
lo
o
p
(
PLL
)
alg
o
r
ith
m
.
A
p
r
o
p
o
r
tio
n
al
-
r
eso
n
an
t
(
PR
)
c
o
n
tr
o
ller
ca
n
clo
s
ely
m
o
n
ito
r
th
e
cu
r
r
en
t
s
in
ce
its
g
ain
s
a
r
e
in
f
in
ite
at
s
o
m
e
f
r
eq
u
e
n
cy
[
4
6
]
.
T
h
e
co
n
tr
o
l
a
lg
o
r
ith
m
is
m
o
d
if
ied
to
r
ea
lize
p
ass
iv
e
d
am
p
e
d
with
th
e
h
e
lp
o
f
s
am
p
lin
g
th
e
cu
r
r
en
t
f
r
o
m
th
e
L
C
L
f
ilter
ca
p
ac
ito
r
,
th
u
s
r
ed
u
ci
n
g
th
e
r
eso
n
an
t
p
ea
k
o
f
L
C
L
f
ilter
s
[
4
7
]
.
I
t
is
al
s
o
ess
en
tia
l
to
co
n
s
id
er
th
e
f
ee
d
f
o
r
war
d
o
f
g
r
id
v
o
ltag
e.
A
d
etailed
d
escr
ip
tio
n
o
f
p
h
ase
-
lo
ck
ed
lo
o
p
(
P
L
L
)
alg
o
r
ith
m
s
f
o
r
s
in
g
le
-
p
h
ase
in
v
er
ter
s
is
av
ail
ab
le
elsewh
er
e
[
4
8
]
,
[
4
9
]
.
T
h
e
co
n
tr
o
l
s
ch
em
e
d
iag
r
am
o
f
th
e
PV
-
m
icr
o
in
v
er
ter
is
s
h
o
wn
in
Fig
u
r
e
4
.
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
.
4
,
Au
g
u
s
t
20
25
:
3
6
6
0
-
3682
3664
Fig
u
r
e
2
.
C
ir
cu
it
d
iag
r
am
o
f
t
wo
-
s
tag
e
g
r
id
-
c
o
n
n
ec
te
d
PV
-
m
icr
o
in
v
er
ter
Fig
u
r
e
3
.
C
ir
cu
it o
f
two
-
s
tag
e
g
r
id
-
co
n
n
ec
ted
PV
-
m
icr
o
in
v
er
ter
Fig
u
r
e
4
.
C
o
n
tr
o
l sch
em
e
o
f
PV
-
m
icr
o
in
v
er
te
r
with
L
C
L
W
h
en
d
ea
lin
g
with
s
in
u
s
o
id
al
r
ef
er
en
ce
s
in
g
r
id
-
co
n
n
ec
ted
PV
-
m
icr
o
in
v
er
ter
,
th
e
PI
co
n
t
r
o
ller
m
ay
s
tr
u
g
g
le
to
tr
ac
k
th
em
p
er
f
ec
t
ly
.
T
h
e
PR
co
n
tr
o
ller
is
o
f
ten
p
r
ef
er
r
e
d
f
o
r
b
etter
tr
ac
k
in
g
p
er
f
o
r
m
an
ce
[
5
0
]
.
T
h
e
g
r
id
-
co
n
n
ec
ted
PV
m
icr
o
in
v
er
ter
'
s
p
r
o
p
o
r
tio
n
al
-
r
eso
n
a
n
t
(
PR
)
co
n
tr
o
ller
r
e
g
u
lates
th
e
p
o
wer
f
lo
w
f
r
o
m
PV
p
an
els
to
th
e
g
r
id
b
y
in
tr
o
d
u
cin
g
h
ig
h
g
ain
at
th
e
r
eso
n
an
t
f
r
e
q
u
en
c
y
.
I
t
ty
p
ically
c
o
n
s
is
ts
o
f
two
p
ar
t
s
.
T
h
e
f
ir
s
t
p
ar
t
is
t
h
e
p
r
o
p
o
r
tio
n
al
co
n
t
r
o
ller
,
wh
ich
h
elp
s
a
d
ju
s
t
th
e
p
o
wer
o
u
tp
u
t
b
ased
o
n
th
e
er
r
o
r
s
ig
n
al
r
ep
r
esen
tin
g
th
e
d
if
f
e
r
en
ce
b
et
wee
n
th
e
d
esire
d
o
u
tp
u
t a
n
d
th
e
ac
tu
al
o
u
tp
u
t.
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
Hyb
r
id
p
a
s
s
ive
d
a
mp
in
g
filt
er
o
f sin
g
le
-
p
h
a
s
e
g
r
id
-
tied
P
V
-
micro
in
ve
r
ter
(
F
o
u
z
ey
S
a
lem
A
a
ma
r
a
)
3665
I
t
p
r
o
v
i
d
es
a
p
r
o
p
o
r
tio
n
al
r
e
s
p
o
n
s
e
to
th
is
er
r
o
r
an
d
ad
ju
s
ts
th
e
p
o
wer
o
u
tp
u
t
ac
co
r
d
i
n
g
ly
.
T
h
e
s
ec
o
n
d
p
ar
t
is
th
e
r
eso
n
an
t
co
n
tr
o
ller
,
wh
ich
is
d
esig
n
ed
to
h
an
d
le
ce
r
tain
f
r
eq
u
en
cy
co
m
p
o
n
en
ts
in
th
e
s
y
s
tem
,
allo
win
g
f
o
r
b
etter
f
ilter
in
g
an
d
c
o
n
tr
o
l
o
f
d
is
tu
r
b
a
n
ce
s
o
r
h
ar
m
o
n
ics
th
at
m
ay
o
cc
u
r
in
th
e
s
y
s
tem
.
T
h
is
ap
p
r
o
ac
h
co
n
tr
ib
u
tes
to
m
ain
tain
in
g
s
tab
ilit
y
an
d
im
p
r
o
v
in
g
th
e
s
y
s
tem
's
o
v
er
all
p
er
f
o
r
m
an
ce
.
Alo
n
g
s
id
e
th
e
PR
co
n
tr
o
ller
,
it
ef
f
ec
tiv
ely
o
p
tim
izes
th
e
p
o
wer
tr
an
s
f
er
f
r
o
m
t
h
e
PV
p
an
els
to
th
e
g
r
id
.
E
n
s
u
r
in
g
ef
f
icien
t o
p
e
r
atio
n
a
n
d
g
r
i
d
in
teg
r
atio
n
wh
ile
m
ain
tain
i
n
g
s
y
s
tem
s
tab
ilit
y
.
T
h
e
PR
co
n
tr
o
ller
ca
n
ef
f
ec
ti
v
ely
tr
ac
k
t
h
e
cu
r
r
en
t.
I
n
co
r
p
o
r
atin
g
a
p
ass
iv
e
d
am
p
in
g
f
ilt
er
th
r
o
u
g
h
s
am
p
lin
g
th
e
L
C
L
f
ilter
ca
p
ac
ito
r
cu
r
r
en
t
also
h
elp
s
t
o
s
m
o
o
th
o
u
t
an
y
r
eso
n
an
ce
p
ea
k
s
t
h
at
m
ay
o
cc
u
r
in
th
e
s
y
s
tem
.
A
PR
co
n
tr
o
ller
is
p
r
ef
er
r
ed
o
v
er
a
PI
co
n
t
r
o
ller
in
g
r
id
-
c
o
n
n
ec
ted
PV
m
icr
o
in
v
e
r
ter
s
b
ec
au
s
e
it
ca
n
h
an
d
le
d
y
n
a
m
ic
ch
a
n
g
es,
f
ilter
o
u
t
h
a
r
m
o
n
ics,
p
r
o
v
id
e
r
o
b
u
s
t
co
n
tr
o
l
in
u
n
ce
r
tain
c
o
n
d
itio
n
s
,
an
d
en
s
u
r
e
co
m
p
lian
ce
with
g
r
i
d
co
d
es.
I
ts
d
u
al
-
ac
tio
n
n
atu
r
e
o
f
f
er
s
im
p
r
o
v
e
d
p
e
r
f
o
r
m
an
ce
an
d
s
tab
ilit
y
co
m
p
a
r
ed
wit
h
th
e
PI
co
n
tr
o
ller
alo
n
e
[
5
1
]
.
On
e
o
f
th
e
m
ajo
r
ad
v
a
n
tag
es
o
f
th
e
PR
co
n
tr
o
ller
is
th
at
i
t
is
a
g
o
o
d
way
o
f
ad
ju
s
tin
g
o
u
t
p
u
t
cu
r
r
en
t
ac
co
r
d
in
g
to
th
e
g
r
id
v
o
ltag
e
s
ettin
g
,
wh
ich
m
o
s
tly
r
e
d
u
ce
s
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
n
th
e
in
jecte
d
g
r
id
s
id
e.
W
e
d
o
th
is
b
y
in
jectin
g
r
eso
n
an
t
co
n
tr
o
l
ac
tio
n
at
th
e
f
u
n
d
am
en
t
al
f
r
eq
u
en
cy
o
f
th
e
g
r
id
,
wh
ich
e
n
ab
les
o
u
r
c
o
n
tr
o
ller
to
ef
f
ec
tiv
ely
r
esp
o
n
d
t
o
b
o
th
n
o
r
m
al
v
ar
iatio
n
s
an
d
d
is
tu
r
b
an
ce
s
in
g
r
id
v
o
ltag
e.
2
.
2
.
L
CL
a
nd
(H
-
B
)
hy
brid f
ilte
r
L
C
L
f
ilter
s
ar
e
im
p
o
r
tan
t
co
m
p
o
n
e
n
ts
in
g
r
id
-
c
o
n
n
ec
te
d
PV
m
icr
o
in
v
er
ter
s
,
wh
ich
a
r
e
cr
u
cial
in
r
ed
u
cin
g
h
a
r
m
o
n
ic
d
is
to
r
tio
n
an
d
im
p
r
o
v
in
g
o
v
er
all
s
y
s
te
m
ef
f
icien
c
y
.
T
h
is
f
ilter
c
o
n
f
ig
u
r
atio
n
ty
p
ically
co
n
s
is
ts
o
f
an
in
d
u
cto
r
,
a
ca
p
a
cito
r
,
an
d
an
o
t
h
er
in
d
u
c
to
r
ar
r
an
g
ed
in
s
er
ies.
T
h
e
L
C
L
f
ilter
h
elp
s
to
m
itig
ate
h
ig
h
-
f
r
eq
u
e
n
cy
r
eso
n
an
ce
s
a
n
d
d
am
p
en
h
ar
m
o
n
ic
c
u
r
r
en
ts
,
en
s
u
r
in
g
t
h
at
th
e
in
v
er
te
r
o
p
e
r
ates
s
m
o
o
th
ly
a
n
d
with
in
g
r
id
co
m
p
lian
ce
r
e
q
u
i
r
em
en
ts
.
I
n
th
e
L
C
L
H
-
leg
’
s
b
r
id
g
e,
th
is
c
o
n
f
ig
u
r
atio
n
is
a
v
a
r
iat
io
n
o
f
th
e
s
tan
d
ar
d
L
C
L
f
ilter
d
esig
n
co
m
m
o
n
ly
u
s
ed
i
n
m
icr
o
in
v
e
r
ter
s
y
s
tem
s
.
B
y
u
tili
zin
g
an
H
-
l
eg
b
r
i
d
g
e
t
o
p
o
lo
g
y
,
as
s
h
o
wn
in
Fig
u
r
e
5
,
th
is
f
ilter
o
f
f
er
s
im
p
r
o
v
ed
atten
u
ati
o
n
o
f
co
m
m
o
n
-
m
o
d
e
n
o
is
e
an
d
b
etter
co
n
tr
o
l
o
f
s
witch
in
g
f
r
eq
u
en
cies.
T
h
e
ad
d
ed
H
-
leg
s
tr
u
ctu
r
e
en
h
a
n
ce
s
th
e
o
v
e
r
all
p
er
f
o
r
m
a
n
ce
o
f
th
e
L
C
L
f
ilter
,
m
ak
in
g
it
s
u
itab
le
f
o
r
d
em
an
d
in
g
g
r
i
d
-
co
n
n
ec
ted
ap
p
licatio
n
s
wh
e
r
e
r
eliab
ilit
y
an
d
ef
f
icien
c
y
a
r
e
p
ar
am
o
u
n
t.
T
h
e
L
C
L
H
-
leg
’
s
b
r
id
g
e
co
n
f
ig
u
r
atio
n
is
a
v
ar
iatio
n
o
f
th
e
tr
ad
itio
n
al
L
C
L
f
ilte
r
d
esig
n
,
o
f
f
er
in
g
en
h
an
ce
d
f
ilter
in
g
p
e
r
f
o
r
m
an
ce
f
o
r
g
r
id
-
co
n
n
ec
te
d
PV
m
icr
o
in
v
er
ter
s
.
T
h
is
s
etu
p
in
c
o
r
p
o
r
ate
s
an
H
-
leg
b
r
id
g
e
to
p
o
lo
g
y
,
wh
er
e
ad
d
itio
n
al
co
m
p
o
n
en
ts
ar
e
ad
d
ed
to
th
e
s
tan
d
ar
d
L
C
L
f
ilter
to
im
p
r
o
v
e
its
f
ilter
in
g
ca
p
ab
ilit
ies
f
u
r
th
er
.
B
y
in
t
r
o
d
u
cin
g
th
is
b
r
id
g
e
s
tr
u
ctu
r
e,
th
e
f
ilter
ac
h
iev
es
b
etter
co
m
m
o
n
-
m
o
d
e
n
o
is
e
atten
u
atio
n
an
d
p
r
o
v
id
es
m
o
r
e
p
r
ec
is
e
co
n
tr
o
l
o
v
er
s
witch
in
g
f
r
eq
u
en
cies,
wh
ich
is
ess
en
tial
f
o
r
m
ain
tain
in
g
s
y
s
tem
ef
f
icien
cy
a
n
d
r
eliab
ilit
y
[
5
2
]
.
T
h
e
H
-
leg
’
s
b
r
id
g
e
d
esig
n
e
n
h
an
ce
s
th
e
f
ilter
’
s
ab
ilit
y
to
r
ed
u
ce
elec
tr
o
m
ag
n
etic
in
ter
f
e
r
en
ce
a
n
d
s
u
p
p
r
ess
v
o
ltag
e
h
ar
m
o
n
ic
s
,
en
s
u
r
in
g
s
m
o
o
th
e
r
p
o
we
r
d
eliv
er
y
to
th
e
g
r
id
.
T
h
e
im
p
r
o
v
e
d
f
ilter
in
g
ch
ar
a
cter
is
tics
o
f
th
e
L
C
L
H
-
leg
s
m
ak
e
th
em
well
-
s
u
ited
f
o
r
ap
p
licatio
n
s
r
eq
u
ir
in
g
s
tr
in
g
en
t
n
o
is
e
r
ed
u
ctio
n
a
n
d
h
ar
m
o
n
ic
m
itig
atio
n
.
B
y
o
p
tim
izin
g
th
e
f
ilter
to
p
o
lo
g
y
wit
h
th
e
H
-
leg
’
s
b
r
id
g
e
,
m
icr
o
in
v
er
ter
s
y
s
tem
s
ca
n
o
p
er
ate
m
o
r
e
ef
f
icien
tly
,
m
ee
tin
g
p
er
f
o
r
m
an
ce
s
tan
d
ar
d
s
an
d
g
r
id
r
eq
u
ir
em
e
n
ts
ef
f
ec
tiv
ely
.
T
h
e
L
C
L
H
-
leg
’
s
b
r
id
g
e
f
ilter
co
n
f
i
g
u
r
atio
n
o
f
f
e
r
s
ad
v
an
ce
d
f
ilter
in
g
ca
p
ab
ilit
i
es,
en
h
an
ce
d
n
o
is
e
atten
u
atio
n
,
a
n
d
im
p
r
o
v
e
d
co
n
tr
o
l
o
v
er
h
a
r
m
o
n
ic
co
n
ten
t,
m
ak
in
g
it
a
v
alu
ab
le
co
m
p
o
n
e
n
t
in
g
r
id
-
co
n
n
ec
ted
PV m
icr
o
in
v
er
ter
s
y
s
tem
s
.
Fig
u
r
e
5
.
PV
-
m
icr
o
in
v
er
ter
with
(
L
C
L
&
H
-
B
)
h
y
b
r
id
f
ilter
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
.
4
,
Au
g
u
s
t
20
25
:
3
6
6
0
-
3682
3666
2
.
3
.
(
L
CL
a
nd
P
D)
hy
brid f
i
lt
er
T
h
e
H
-
b
r
id
g
e
i
n
v
er
ter
with
L
C
L
f
ilter
an
d
p
ass
iv
e
d
am
p
in
g
f
ilter
co
n
v
er
ts
th
e
DC
v
o
ltag
e
f
r
o
m
th
e
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
ter
in
to
AC
v
o
ltag
e,
wh
ich
is
th
en
co
n
n
ec
ted
t
o
th
e
g
r
id
o
r
lo
ad
.
T
h
e
H
-
b
r
id
g
e
i
n
v
er
te
r
co
n
s
is
ts
o
f
f
o
u
r
s
witch
es
(
two
in
th
e
u
p
p
e
r
ar
m
an
d
two
in
t
h
e
lo
wer
a
r
m
)
a
n
d
u
s
es
h
ig
h
-
f
r
eq
u
en
c
y
PW
M
to
co
n
tr
o
l th
e
s
witch
in
g
o
f
th
e
p
o
wer
d
ev
ices a
n
d
r
eg
u
late
th
e
o
u
tp
u
t v
o
ltag
e
s
h
o
wn
in
Fig
u
r
e
6
.
T
h
e
L
C
L
f
ilter
an
d
d
am
p
in
g
f
ilter
to
g
eth
er
p
r
o
v
i
d
e
b
etter
f
ilter
in
g
p
er
f
o
r
m
an
ce
th
a
n
u
s
in
g
o
n
ly
o
n
e
o
f
t
h
em
.
L
C
L
f
ilter
p
r
o
v
id
es
a
h
ig
h
r
e
d
u
ctio
n
o
f
h
ig
h
-
o
r
d
e
r
h
ar
m
o
n
ics,
r
esu
ltin
g
in
a
cl
ea
n
er
an
d
s
m
o
o
th
er
o
u
tp
u
t
wav
ef
o
r
m
.
I
n
co
n
t
r
ast,
th
e
d
am
p
in
g
f
ilter
p
r
o
v
id
es
an
ef
f
ec
tiv
e
r
ed
u
ctio
n
o
f
h
ig
h
-
o
r
d
er
h
ar
m
o
n
ics.
I
ts
lo
w
co
m
p
o
n
en
t
c
o
u
n
t
m
ak
e
s
it
an
attr
ac
tiv
e
ch
o
ice
f
o
r
ap
p
licatio
n
s
in
v
o
lv
in
g
co
s
t,
weig
h
t,
o
r
s
p
ac
e
co
n
s
tr
ain
ts
.
T
h
e
co
m
b
i
n
atio
n
o
f
th
e
q
u
ad
r
atic
b
o
o
s
t
co
n
v
er
ter
an
d
H
-
b
r
id
g
e
i
n
v
er
ter
with
L
C
L
f
ilter
an
d
d
am
p
in
g
f
ilter
(
R
//LC)
p
r
o
v
i
d
es
a
h
ig
h
-
ef
f
icien
cy
a
n
d
h
i
g
h
-
p
er
f
o
r
m
an
ce
PV
s
y
s
tem
with
b
etter
f
i
lter
in
g
p
er
f
o
r
m
an
ce
,
m
a
k
in
g
it su
itab
l
e
f
o
r
a
p
p
licatio
n
s
th
at
r
eq
u
ir
e
h
ig
h
-
q
u
ality
o
u
t
p
u
t w
av
ef
o
r
m
s
.
Fig
u
r
e
6
.
PV
-
m
icr
o
in
v
er
ter
with
(
L
C
L
&
PD
)
h
y
b
r
id
f
ilter
L
C
L
o
u
tp
u
t
f
ilter
to
p
o
lo
g
y
is
u
s
ed
in
PV
m
icr
o
in
v
er
ter
s
to
r
ed
u
ce
t
h
e
T
HD
o
f
t
h
e
o
u
t
p
u
t
cu
r
r
en
t
wav
ef
o
r
m
.
T
h
e
L
C
L
f
ilter
te
n
d
s
to
r
eso
n
ate
at
a
ce
r
tain
f
r
eq
u
en
c
y
,
wh
ich
co
u
l
d
ca
u
s
e
ef
f
ec
ts
with
in
th
e
s
u
b
s
y
s
tem
.
Deg
r
ad
es
t
h
e
f
ilte
r
in
g
p
er
f
o
r
m
an
ce
.
L
C
L
an
d
(
R
//LC)
p
ass
iv
e
d
am
p
in
g
f
ilter
s
ar
e
u
s
ed
in
PV
m
icr
o
in
v
er
ter
s
to
e
n
h
an
ce
p
o
wer
q
u
a
lity
b
y
m
in
im
izin
g
th
e
g
r
id
cu
r
r
en
t
T
HD.
L
C
L
f
u
n
ctio
n
s
as
a
lo
w
-
p
ass
f
ilter
.
C
o
m
p
ar
ed
with
th
e
(
R
//
L
C
)
p
ass
iv
e
d
am
p
in
g
f
ilter
,
i
m
p
r
o
v
e
d
p
o
wer
q
u
ality
is
ac
h
iev
ed
u
s
in
g
a
n
L
C
L
f
ilter
,
wh
o
s
e
h
ar
m
o
n
ic
f
r
e
q
u
e
n
cy
r
ed
u
ctio
n
is
b
etter
.
O
n
th
e
o
th
er
h
a
n
d
,
u
s
in
g
L
C
L
f
ilter
s
is
m
o
r
e
co
s
tly
in
g
en
er
al,
an
d
d
is
tr
ict
lo
s
s
es wil
l p
o
ten
tially
in
cr
ea
s
e
d
u
e
to
ad
d
in
g
ex
tr
a
in
d
u
ct
o
r
s
.
T
h
e
o
n
ly
s
im
p
le
d
esig
n
o
f
t
h
ese
two
I
s
t
h
e
p
ass
iv
e
d
am
p
in
g
(
R
//LC)
f
ilter
.
I
t
p
r
o
d
u
ce
s
f
ewe
r
h
ar
m
o
n
ic
f
r
eq
u
e
n
cies in
th
is
t
y
p
e
o
f
f
ilter
as c
o
m
p
a
r
ed
to
th
e
L
C
L
f
ilter
,
it is
les
s
co
s
tly
,
a
n
d
p
o
wer
lo
s
s
es a
r
e
lo
w;
ad
d
itio
n
,
d
a
m
p
in
g
f
ilter
s
ar
e
u
s
u
ally
ea
s
ie
r
to
im
p
lem
en
t
an
d
ca
lib
r
ate,
s
o
th
ey
ten
d
to
b
e
th
e
f
av
o
r
ite
s
elec
tio
n
f
o
r
PV
s
m
all
-
s
ca
le
m
icr
o
in
v
er
ter
s
.
T
h
e
p
e
r
f
o
r
m
a
n
ce
o
f
L
C
L
f
ilter
s
is
id
ea
l
f
o
r
g
r
id
-
in
ter
co
n
n
ec
ted
ap
p
licatio
n
s
with
m
o
r
e
s
tr
in
g
en
t
h
ar
m
o
n
ic
f
ilter
in
g
r
e
q
u
ir
em
en
ts
at
lar
g
e
-
s
ca
le
P
V
s
y
s
tem
s
;
o
n
th
e
o
th
er
h
an
d
,
d
am
p
in
g
f
ilter
s
m
ig
h
t
b
e
en
o
u
g
h
f
o
r
s
m
aller
-
s
ized
in
s
talls
,
an
d
co
s
t
-
ef
f
ec
tiv
en
ess
(
an
d
s
im
p
licity
)
ar
e
p
r
im
ar
y
co
n
s
id
er
atio
n
s
.
T
h
e
c
h
o
ice
b
etwe
en
L
C
L
an
d
d
am
p
in
g
f
ilter
s
is
s
u
b
ject
to
v
ar
io
u
s
r
eq
u
ir
em
e
n
ts
o
f
th
e
PV
-
m
icr
o
in
v
er
ter
,
t
h
e
s
ize
o
f
th
e
s
y
s
tem
,
g
r
id
in
ter
co
n
n
ec
tio
n
s
tan
d
ar
d
s
an
d
th
e
e
co
n
o
m
y
o
f
th
e
PV
-
m
icr
o
in
v
er
ter
.
T
h
e
L
C
L
an
d
p
ass
iv
e
d
am
p
in
g
f
ilter
s
ca
n
r
e
d
u
ce
T
HD
in
th
e
g
r
i
d
cu
r
r
en
t.
Ad
d
in
g
a
n
L
C
f
ilter
in
p
ar
allel
with
th
e
R
in
th
e
(
R
//LC)
d
am
p
in
g
f
ilter
an
d
th
e
n
ca
s
ca
d
in
g
it
with
an
L
C
L
f
il
ter
f
u
r
th
er
i
m
p
r
o
v
es
th
e
f
ilter
in
g
p
er
f
o
r
m
an
ce
b
y
atten
u
atin
g
h
ig
h
-
f
r
e
q
u
en
c
y
h
ar
m
o
n
ics
.
T
h
e
L
C
L
f
ilt
er
o
f
f
er
s
ex
ce
llen
t
atten
u
atio
n
o
f
lo
w
-
f
r
eq
u
en
cy
h
ar
m
o
n
ics.
Ho
wev
e
r
,
its
ab
ilit
y
to
atten
u
ate
h
ig
h
-
f
r
eq
u
en
cy
h
ar
m
o
n
ics
is
lim
ited
;
in
co
r
p
o
r
atin
g
an
L
C
f
ilter
in
p
ar
allel
with
th
e
r
esi
s
t
o
r
in
th
e
d
am
p
in
g
f
ilter
ca
n
ef
f
ec
tiv
ely
atten
u
ate
h
ig
h
-
o
r
d
er
h
a
r
m
o
n
ics.
T
h
e
c
o
m
b
in
atio
n
o
f
f
ilter
s
r
esu
lts
in
a
wid
er
atten
u
atio
n
r
an
g
e
,
allo
win
g
f
o
r
ef
f
icien
t
s
u
p
p
r
ess
io
n
o
f
h
ig
h
-
o
r
d
e
r
h
ar
m
o
n
ics an
d
s
u
b
s
eq
u
en
t r
e
d
u
ct
io
n
in
g
r
id
cu
r
r
en
t
T
HD
.
Ad
d
an
(
R
//LC)
d
am
p
in
g
f
ilter
p
ar
allel
to
th
e
L
C
L
f
ilter
t
o
r
eso
lv
e
th
is
lim
itatio
n
.
T
h
e
d
am
p
in
g
r
esis
to
r
h
elp
s
d
is
s
ip
ate
E
n
er
g
y
ac
cu
m
u
lated
in
th
e
r
eso
n
an
t c
ir
cu
it o
f
th
e
L
C
L
f
ilter
,
wh
ile
t
h
e
co
m
b
in
atio
n
o
f
th
e
in
d
u
cto
r
a
n
d
ca
p
ac
ito
r
c
r
e
ates
a
lo
w
-
im
p
ed
an
ce
p
ath
f
o
r
h
ig
h
-
f
r
e
q
u
en
c
y
n
o
is
e,
in
teg
r
a
tin
g
d
am
p
in
g
f
ilter
with
th
e
L
C
L
f
ilter
en
h
an
ce
s
o
v
er
all
p
er
f
o
r
m
a
n
ce
b
y
r
e
d
u
cin
g
r
eso
n
an
ce
p
ea
k
s
an
d
m
in
im
izin
g
h
i
g
h
-
f
r
eq
u
e
n
cy
n
o
is
e,
th
is
im
p
r
o
v
e
m
en
t
also
co
n
tr
ib
u
tes
to
in
cr
e
ased
s
y
s
tem
s
tab
ilit
y
b
y
lo
wer
in
g
th
e
Q
-
f
ac
to
r
o
f
th
e
r
eso
n
an
t c
ir
cu
it,
t
h
e
m
ath
e
m
atica
l a
n
aly
s
is
o
f
th
e
h
y
b
r
id
L
C
L
an
d
(
R
//LC)
d
am
p
in
g
f
ilter
ca
n
b
e
co
m
p
lex
,
an
d
th
e
d
esig
n
o
f
th
e
f
ilter
p
ar
am
eter
s
r
eq
u
ir
es
ca
r
ef
u
l
co
n
s
id
er
atio
n
o
f
th
e
s
y
s
tem
r
eq
u
ir
em
e
n
t
s
an
d
lim
itatio
n
s
.
Ho
wev
er
,
b
y
p
r
o
p
er
ly
s
elec
tin
g
t
h
e
v
alu
es
o
f
th
e
d
am
p
i
n
g
r
esis
to
r
,
in
d
u
ct
o
r
,
an
d
ca
p
ac
ito
r
,
a
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
Hyb
r
id
p
a
s
s
ive
d
a
mp
in
g
filt
er
o
f sin
g
le
-
p
h
a
s
e
g
r
id
-
tied
P
V
-
micro
in
ve
r
ter
(
F
o
u
z
ey
S
a
lem
A
a
ma
r
a
)
3667
s
ig
n
if
ican
t
r
ed
u
ctio
n
in
T
HD
an
d
im
p
r
o
v
e
m
en
t
in
t
h
e
o
v
er
all
p
er
f
o
r
m
an
ce
o
f
th
e
PV
m
icr
o
in
v
e
r
ter
ar
e
p
o
s
s
ib
le.
Simu
ltan
eo
u
s
ly
,
ad
d
in
g
a
d
am
p
in
g
(
R
//LC)
f
ilter
p
ar
allel
to
L
C
L
ca
n
s
ig
n
if
ican
tly
s
u
p
p
r
ess
th
e
g
r
id
cu
r
r
en
t
r
eso
n
an
ce
p
ea
k
s
an
d
ef
f
ec
tiv
ely
r
e
d
u
ce
h
ig
h
-
f
r
eq
u
en
cy
d
is
tu
r
b
an
ce
,
t
h
u
s
g
r
ea
tly
im
p
r
o
v
i
n
g
th
e
f
ilter
in
g
p
r
o
p
e
r
ty
a
n
d
d
ec
lin
i
n
g
lo
w
T
HD
o
f
g
r
id
cu
r
r
en
t.
I
n
a
d
d
itio
n
,
it
will
im
p
r
o
v
e
s
y
s
tem
s
tab
ilit
y
an
d
r
ed
u
ce
th
e
Q
-
f
ac
to
r
r
eso
n
an
t c
ir
cu
it.
2
.
4
.
M
a
t
hema
t
ica
l
m
o
dellin
g
o
f
(
L
CL
-
P
D)
hy
brid f
ilte
r
An
L
C
L
f
ilter
is
f
r
eq
u
en
tly
u
tili
ze
d
in
g
r
id
-
c
o
n
n
ec
te
d
PV
m
icr
o
in
v
er
ter
s
to
d
ec
r
ea
s
e
h
ig
h
-
f
r
eq
u
en
c
y
h
ar
m
o
n
ics
a
n
d
g
u
a
r
an
tee
t
h
at
th
e
i
n
v
er
ter
’
s
o
u
t
p
u
t
c
o
m
p
li
es
with
g
r
id
r
e
q
u
ir
em
e
n
ts
.
T
h
e
L
C
L
f
ilter
is
a
co
m
p
o
n
en
t
o
f
th
e
i
n
v
er
ter
’
s
p
o
wer
elec
tr
o
n
ics,
wh
ich
is
ess
en
tial
in
im
p
r
o
v
in
g
th
e
en
er
g
y
q
u
ality
s
u
p
p
lied
t
o
th
e
g
r
id
.
T
h
e
b
asic d
esig
n
o
f
th
e
L
C
L
f
ilter
ca
n
b
e
illu
s
tr
ated
as
f
o
llo
ws:
i
s
th
e
(
PV)
DC
-
v
o
ltag
e
in
p
u
t,
t
h
e
in
v
er
ter
r
ep
r
esen
ts
th
e
PV
-
m
icr
o
in
v
er
ter
,
1
an
d
2
ar
e
in
d
u
cto
r
s
,
C
is
th
e
ca
p
ac
ito
r
,
an
d
is
th
e
g
r
id
o
r
lo
ad
r
esis
tan
ce
.
T
h
e
L
C
L
f
ilter
m
ath
em
atica
l
e
q
u
atio
n
ca
n
b
e
o
b
tain
ed
b
y
co
n
s
id
er
i
n
g
t
h
e
im
p
ed
a
n
ce
o
f
th
e
f
ilter
cir
cu
it.
T
h
e
L
C
L
f
ilter
to
tal
im
p
ed
a
n
c
e
ca
n
b
e
d
ef
in
ed
as:
(
)
=
+
2
+
1
+
1
(
1
)
(
s
)
is
th
e
co
m
p
lex
f
r
e
q
u
en
c
y
v
ar
iab
le,
ex
p
r
ess
ed
as
(
s
=
j
ω
)
,
wh
er
e
(
j)
r
ep
r
esen
ts
th
e
im
a
g
in
ar
y
u
n
it
an
d
(
ω
)
d
en
o
tes
th
e
a
n
g
u
lar
f
r
e
q
u
en
c
y
.
(
)
is
th
e
lo
ad
r
esis
tan
ce
,
wh
ile
(
1
)
an
d
(
2
)
r
e
p
r
esen
t
f
ilter
i
n
d
u
ctan
ce
s
,
an
d
C
in
d
icate
s
th
e
f
ilte
r
ca
p
ac
itan
ce
.
T
h
e
L
C
L
f
ilter
tr
an
s
f
er
f
u
n
ctio
n
ca
n
b
e
o
b
tain
e
d
b
y
r
ea
r
r
an
g
i
n
g
th
e
eq
u
atio
n
in
th
e
L
ap
lace
d
o
m
ai
n
:
(
)
=
(
)
(
)
=
1
(
)
(
2
)
Descr
ip
tio
n
o
f
th
e
m
ath
em
atic
al
eq
u
atio
n
an
d
tr
an
s
f
er
f
u
n
cti
o
n
s
tep
-
by
-
s
tep
g
u
id
e
o
f
L
C
L
f
ilter
in
two
-
s
tag
e
PV
-
m
icr
o
in
v
er
ter
i
n
v
o
lv
es a
p
p
ly
in
g
Kir
ch
h
o
f
f
’
s
v
o
ltag
e
la
w
to
th
e
lo
o
p
co
n
s
is
tin
g
o
f
(
1
)
,
(
C
)
an
d
(
):
=
1
−
−
=
0
(
3
)
Th
e
v
o
ltag
e
ac
r
o
s
s
ea
ch
elem
e
n
t c
an
b
e
e
x
p
r
ess
ed
as:
Vo
ltag
e
ac
r
o
s
s
1
:
1
=
1
(
4
)
T
h
e
v
o
ltag
e
ac
r
o
s
s
C
:
=
1
∫
(
5
)
Vo
ltag
e
ac
r
o
s
s
:
=
∙
.
(
6
)
T
h
e
ex
p
r
ess
io
n
s
f
o
r
v
o
ltag
e
a
cr
o
s
s
(
1
)
,
(
C
)
an
d
(
)
ar
e
co
m
b
i
n
ed
to
ex
p
r
ess
th
e
cu
r
r
e
n
t
(
)
in
ter
m
s
o
f
(
)
An
d
its
d
er
iv
ati
v
es:
=
1
+
1
∫
+
∙
(
7
)
T
h
e
L
ap
lace
tr
an
s
f
o
r
m
is
a
tech
n
iq
u
e
th
at
tr
a
n
s
f
o
r
m
s
d
if
f
er
en
tial
eq
u
atio
n
s
f
r
o
m
th
e
tim
e
d
o
m
ain
in
to
al
g
eb
r
aic
eq
u
atio
n
s
in
th
e
s
-
d
o
m
ain
,
co
m
m
o
n
ly
k
n
o
wn
as th
e
co
m
p
lex
f
r
e
q
u
en
c
y
d
o
m
ain
.
T
h
e
tr
an
s
f
o
r
m
atio
n
o
f
th
e
(
)
f
u
n
ctio
n
is
r
e
p
r
esen
ted
as
(
)
.
B
y
ap
p
ly
in
g
t
h
e
L
ap
lace
tr
an
s
f
o
r
m
to
b
o
th
s
id
es
o
f
t
h
e
eq
u
atio
n
,
we
d
er
iv
e
th
e
f
o
llo
win
g
e
x
p
r
e
s
s
io
n
:
ι
{
}
=
1
(
)
+
1
(
)
+
(
)
(
8
)
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
.
4
,
Au
g
u
s
t
20
25
:
3
6
6
0
-
3682
3668
T
o
ex
p
r
ess
f
o
r
th
e
cu
r
r
en
t
th
r
o
u
g
h
th
e
cir
cu
it
in
t
h
e
L
a
p
lac
e
d
o
m
ain
.
T
h
is
m
eth
o
d
en
ab
le
s
u
s
to
ex
am
in
e
th
e
cir
cu
it’s
b
eh
av
io
r
in
th
e
s
-
d
o
m
ain
,
m
ak
in
g
it
ea
s
ier
to
s
o
l
v
e
f
o
r
th
e
cu
r
r
e
n
t
(
)
wh
en
g
iv
e
n
.
(
s
)
.
On
ce
(
)
is
f
o
u
n
d
,
th
e
in
v
er
s
e
L
ap
lace
tr
an
s
f
o
r
m
ca
n
ca
lcu
late
(
)
in
th
e
tim
e
d
o
m
ain
.
I
t
s
o
lv
es
th
e
cu
r
r
e
n
t
(
)
in
ter
m
s
o
f
(
s
)
:
(
)
=
(
)
1
+
1
+
(
9
)
T
o
s
u
m
m
ar
ize,
it
d
er
i
v
ed
th
e
o
u
tp
u
t
v
o
ltag
e.
Usi
n
g
th
e
L
ap
lace
tr
an
s
f
o
r
m
,
(
)
ac
r
o
s
s
t
h
e
lo
ad
an
d
r
esis
to
r
(
)
in
th
e
R
L
C
cir
cu
it.
T
h
e
f
in
al
e
x
p
r
ess
io
n
p
r
o
v
id
e
s
a
clea
r
u
n
d
er
s
tan
d
in
g
o
f
h
o
w
th
e
cir
cu
it
co
m
p
o
n
en
ts
af
f
ec
t
t
h
e
o
u
tp
u
t
in
th
e
s
-
d
o
m
ain
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
(
)
is
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
r
esis
to
r
lo
ad
,
wh
ich
is
s
im
p
ly
(
(
)
)
:
(
)
=
∙
(
)
1
+
1
+
(
1
0
)
T
h
e
tr
an
s
f
e
r
f
u
n
ctio
n
H(
s
)
ch
ar
ac
ter
izes
th
e
s
y
s
tem
as
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
L
ap
la
ce
tr
an
s
f
o
r
m
o
f
t
h
e
o
u
tp
u
t
v
o
ltag
e,
(
)
,
an
d
t
h
e
L
ap
l
ac
e
tr
an
s
f
o
r
m
o
f
th
e
in
p
u
t
v
o
ltag
e,
(
)
.
T
h
is
d
ef
i
n
itio
n
en
a
b
les
th
e
tr
an
s
f
er
f
u
n
ctio
n
to
b
e
r
e
p
r
esen
ted
as H(
s
)
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
is
an
i
m
p
o
r
tan
t
to
o
l
f
o
r
u
n
d
er
s
ta
n
d
i
n
g
h
o
w
t
h
e
s
y
s
tem
r
esp
o
n
d
s
to
v
ar
io
u
s
f
r
eq
u
e
n
cies
in
th
e
in
p
u
t
s
ig
n
a
l,
o
f
f
e
r
in
g
v
alu
ab
le
in
s
ig
h
ts
in
to
its
b
eh
a
v
io
r
a
n
d
s
tab
ilit
y
;
it
en
ca
p
s
u
lates
th
e
s
y
s
tem
’
s
d
y
n
am
ics
in
th
e
s
-
d
o
m
ain
an
d
s
er
v
es
as
an
ess
en
tial
to
o
l
in
co
n
tr
o
l
s
y
s
tem
s
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
H(
s
)
r
ep
r
esen
ts
th
e
r
atio
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
to
th
e
in
p
u
t v
o
ltag
e,
in
d
icatin
g
th
ei
r
r
elatio
n
s
h
ip
.
(
)
=
(
)
(
)
=
1
+
1
+
(
1
1
)
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
H(
s
)
ca
p
tu
r
es
th
e
f
u
n
d
am
e
n
tal
ch
a
r
ac
ter
is
tics
o
f
th
e
R
L
C
cir
c
u
it,
illu
s
tr
atin
g
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
o
u
t
p
u
t
v
o
ltag
e.
(
)
an
d
th
e
in
p
u
t
v
o
ltag
e
(
)
As
g
o
v
er
n
ed
b
y
th
e
cir
cu
it
co
m
p
o
n
en
ts
,
th
e
L
C
L
f
ilter
tr
a
n
s
f
er
f
u
n
cti
o
n
is
g
iv
en
b
y
:
(
)
=
1
+
1
+
(
1
2
)
T
h
at
s
h
o
ws
h
o
w
th
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
an
L
C
L
f
ilter
in
a
two
-
s
tag
e
g
r
id
-
c
o
n
n
ec
ted
PV
m
icr
o
in
v
er
ter
ca
n
h
elp
d
esig
n
an
d
tu
n
e
th
e
o
u
t
p
u
t
f
ilter
f
o
r
d
esire
d
p
er
f
o
r
m
a
n
ce
an
d
s
tab
ilit
y
.
T
h
e
h
y
b
r
i
d
f
il
ter
tr
an
s
f
er
f
u
n
ctio
n
is
d
escr
ib
ed
in
d
etail,
co
n
s
id
er
in
g
th
e
L
C
L
an
d
p
ass
iv
e
d
am
p
in
g
f
ilter
(
PD)
.
2
.
5
.
R
educt
io
n
o
f
g
rid c
urre
nt
T
H
D
in
PV
-
m
icro
inv
er
t
er
T
h
e
h
y
b
r
i
d
L
C
L
f
ilter
an
d
p
ass
iv
e
d
am
p
in
g
PD
f
ilter
ar
e
d
esig
n
ed
to
r
ed
u
ce
g
r
id
cu
r
r
en
t
T
HD
p
r
o
d
u
ce
d
b
y
t
h
e
PV
m
icr
o
in
v
er
ter
.
R
ed
u
ci
n
g
T
HD
is
ess
en
tial
to
co
m
p
l
y
in
g
with
I
E
E
E
s
tan
d
ar
d
s
a
n
d
r
eg
u
latio
n
s
,
wh
ich
ty
p
ically
r
e
s
tr
ict
th
e
lev
els o
f
h
ar
m
o
n
ic
d
i
s
to
r
tio
n
in
th
e
g
r
i
d.
T
h
e
h
y
b
r
id
f
ilter
ca
n
co
n
tr
ib
u
t
e
to
r
ed
u
ci
n
g
g
r
id
cu
r
r
en
t T
H
D
in
th
e
f
o
llo
win
g
way
s
:
a.
Har
m
o
n
ic
f
ilter
in
g
with
L
C
L
f
ilter
:
T
h
e
L
C
L
f
ilter
m
in
im
iz
es
h
ig
h
-
f
r
eq
u
e
n
cy
h
ar
m
o
n
ics
p
r
o
d
u
ce
d
b
y
th
e
in
v
er
ter
'
s
s
witch
in
g
o
p
er
atio
n
.
I
t
p
r
o
v
id
es
a
l
o
w
-
im
p
ed
an
ce
p
ath
f
o
r
h
i
g
h
-
f
r
eq
u
e
n
c
y
co
m
p
o
n
e
n
ts
,
ef
f
ec
tiv
ely
p
r
e
v
en
tin
g
th
ese
h
ar
m
o
n
ics f
r
o
m
b
ein
g
in
jecte
d
i
n
to
th
e
g
r
id
.
b.
Dam
p
in
g
o
f
r
eso
n
a
n
ce
s
:
T
h
e
d
am
p
in
g
elem
en
ts
in
th
e
PD
f
ilter
h
elp
d
am
p
en
r
eso
n
a
n
ce
s
with
in
th
e
s
y
s
tem
.
R
e
s
o
n
an
ce
s
ca
n
o
cc
u
r
at
ce
r
tain
f
r
eq
u
en
cies
r
esu
l
tin
g
f
r
o
m
th
e
in
ter
ac
tio
n
b
etwe
e
n
th
e
in
v
er
ter
'
s
im
p
ed
an
ce
an
d
th
e
g
r
id
.
D
am
p
in
g
th
ese
r
eso
n
an
ce
s
r
e
d
u
ce
s
th
e
am
p
litu
d
e
o
f
s
p
e
cif
ic
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
,
co
n
tr
i
b
u
tin
g
t
o
T
HD
r
ed
u
ctio
n
.
c.
I
m
p
r
o
v
ed
co
n
t
r
o
l
an
d
s
tab
ilit
y
:
T
h
e
h
y
b
r
i
d
f
ilter
d
esig
n
,
wh
en
p
r
o
p
er
ly
tu
n
e
d
,
ca
n
im
p
r
o
v
e
th
e
in
v
er
ter
'
s
co
n
tr
o
l
an
d
s
tab
ilit
y
.
T
h
is
im
p
r
o
v
em
e
n
t
ca
n
h
el
p
m
itig
ate
th
e
r
is
k
o
f
g
r
id
cu
r
r
en
t
d
is
to
r
tio
n
,
esp
ec
ially
d
u
r
in
g
tr
an
s
ien
t c
o
n
d
itio
n
s
o
r
g
r
id
v
a
r
iatio
n
s
.
T
h
e
co
m
b
i
n
atio
n
o
f
L
C
L
an
d
PD
elem
en
ts
allo
ws
f
o
r
s
elec
tiv
e
f
ilter
i
n
g
o
f
s
p
ec
i
f
ic
h
ar
m
o
n
ics;
th
e
L
C
L
f
ilter
m
ay
b
e
m
o
r
e
e
f
f
ec
tiv
e
at
ce
r
tain
f
r
eq
u
e
n
cies,
wh
ile
th
e
PD
f
ilter
ad
d
r
ess
es
o
th
er
s
;
th
is
f
lex
ib
ilit
y
in
f
ilter
in
g
ch
a
r
ac
ter
is
tics
h
elp
s
ac
h
iev
e
a
m
o
r
e
c
o
m
p
r
e
h
en
s
iv
e
r
ed
u
ctio
n
in
T
HD.
T
h
e
p
ar
am
eter
s
o
f
th
e
L
C
L
an
d
PD
f
ilter
s
m
u
s
t
b
e
ca
r
e
f
u
lly
s
elec
ted
a
n
d
tu
n
e
d
to
ac
h
iev
e
o
p
tim
al
p
e
r
f
o
r
m
an
ce
,
an
d
th
is
in
v
o
lv
es
co
n
s
id
er
in
g
th
e
r
eso
n
a
n
ce
f
r
e
q
u
en
cies,
d
am
p
in
g
r
atio
s
,
an
d
o
th
er
ch
ar
ac
ter
is
tics
to
en
s
u
r
e
ef
f
ec
tiv
e
h
ar
m
o
n
ic
m
itig
atio
n
with
o
u
t
co
m
p
r
o
m
is
in
g
s
y
s
tem
s
tab
ilit
y
.
T
h
e
d
esig
n
an
d
im
p
lem
en
tatio
n
o
f
th
e
h
y
b
r
id
f
ilter
s
h
o
u
ld
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
Hyb
r
id
p
a
s
s
ive
d
a
mp
in
g
filt
er
o
f sin
g
le
-
p
h
a
s
e
g
r
id
-
tied
P
V
-
micro
in
ve
r
ter
(
F
o
u
z
ey
S
a
lem
A
a
ma
r
a
)
3669
f
o
llo
w
r
elev
a
n
t
I
E
E
E
s
tan
d
ar
d
s
an
d
g
u
id
elin
es,
wh
ic
h
en
s
u
r
e
th
at
t
h
e
g
r
i
d
-
co
n
n
ec
ted
P
V
s
y
s
tem
m
ee
ts
th
e
r
eq
u
ir
ed
lim
its
f
o
r
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
R
ed
u
cin
g
g
r
id
cu
r
r
e
n
t
T
HD
u
s
in
g
a
h
y
b
r
id
f
ilter
i
n
v
o
lv
es
d
es
ig
n
in
g
an
d
tu
n
i
n
g
th
e
f
ilter
to
m
in
im
ize
th
e
am
p
litu
d
e
o
f
t
h
e
g
r
id
cu
r
r
en
t
wav
ef
o
r
m
h
a
r
m
o
n
ic
co
m
p
o
n
en
ts
.
Alth
o
u
g
h
p
r
o
v
id
in
g
a
s
in
g
le
f
o
r
m
u
la
f
o
r
T
HD
r
ed
u
ctio
n
is
ch
allen
g
in
g
d
u
e
to
th
e
c
o
m
p
lex
ity
o
f
th
e
s
y
s
tem
an
d
th
e
in
ter
p
lay
o
f
v
ar
io
u
s
p
ar
am
ete
r
s
,
we
ca
n
ex
p
r
ess
th
e
g
e
n
er
al
co
n
ce
p
t m
ath
em
atica
lly
.
˗
L
et
(
)
b
e
th
e
g
r
id
cu
r
r
en
t.
˗
(
t)
b
e
a
f
u
n
d
a
m
en
tal
f
r
e
q
u
en
c
y
co
m
p
o
n
en
t.
T
HD
is
u
s
u
ally
d
ef
in
e
d
as
t
h
e
r
atio
o
f
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
'
s
r
o
o
t
m
ea
n
s
q
u
ar
e
(
R
MS)
v
alu
e
to
th
e
f
u
n
d
am
e
n
tal
f
r
eq
u
en
cy
co
m
p
o
n
en
t'
s
R
M
S v
alu
e.
=
√
2
−
_
2
_
(
1
3
)
A
well
-
d
esig
n
ed
h
y
b
r
id
f
ilter
s
ig
n
if
ican
tly
r
ed
u
ce
s
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
in
th
e
in
v
er
ter
c
u
r
r
en
t,
b
y
f
ilter
in
g
o
u
t
s
p
ec
if
ic
u
n
wan
ted
f
r
eq
u
e
n
cies,
th
e
g
r
id
cu
r
r
e
n
t
b
ec
o
m
es
clea
n
er
an
d
clo
s
er
to
s
in
u
s
o
id
al
wav
ef
o
r
m
,
wh
ich
is
id
ea
l
f
o
r
g
r
i
d
s
tab
ilit
y
an
d
p
o
we
r
q
u
ality
.
T
h
e
h
y
b
r
id
f
ilter
also
af
f
ec
ts
th
e
d
y
n
am
ic
o
p
er
atio
n
r
esp
o
n
s
e
o
f
th
e
g
r
id
c
u
r
r
e
n
t;
i
f
r
ap
id
ch
an
g
es
o
cc
u
r
in
th
e
i
n
v
er
ter
c
u
r
r
e
n
t,
th
e
f
ilter
m
o
d
u
lates
th
ese
ch
an
g
es
d
ep
en
d
i
n
g
o
n
its
d
esig
n
p
ar
a
m
eter
s
,
s
u
ch
as
c
u
to
f
f
f
r
e
q
u
en
cies
an
d
th
e
s
teep
n
es
s
o
f
th
e
r
o
ll
-
o
f
f
.
W
e
co
n
s
id
er
th
e
im
p
ac
t o
f
t
h
e
h
y
b
r
id
f
ilter
tr
an
s
f
er
f
u
n
ctio
n
.
ℎ
(
)
o
n
th
e
g
r
id
cu
r
r
en
t:
(
)
=
ℎ
(
)
∙
(
)
(
1
4
)
I
n
th
e
f
r
e
q
u
en
c
y
d
o
m
ai
n
,
th
e
h
y
b
r
id
f
ilter
'
s
ef
f
ec
t
o
n
th
e
g
r
i
d
cu
r
r
e
n
t
r
ev
o
lv
es
ar
o
u
n
d
its
ab
ilit
y
to
am
p
lify
o
r
atten
u
ate
th
e
f
u
n
d
am
en
tal
f
r
eq
u
en
cy
c
o
m
p
o
n
en
t
with
in
t
h
e
in
v
er
ter
'
s
g
r
id
cu
r
r
e
n
t,
b
y
f
o
cu
s
in
g
o
n
th
e
f
u
n
d
am
e
n
tal
f
r
eq
u
e
n
cy
co
m
p
o
n
en
t,
th
e
f
ilter
'
s
m
ag
n
itu
d
e
r
esp
o
n
s
e
d
eter
m
in
es
th
e
am
p
litu
d
e
s
ca
lin
g
an
d
h
ar
m
o
n
i
c
r
ed
u
ctio
n
at
th
at
s
p
ec
if
ic
f
r
eq
u
en
cy
,
th
is
en
s
u
r
es
clea
n
s
ig
n
al
at
t
h
e
d
esire
d
f
r
e
q
u
en
cy
,
im
p
r
o
v
in
g
p
o
wer
q
u
ality
an
d
o
v
er
all
s
y
s
tem
ef
f
icien
cy
.
Her
e,
(
)
is
th
e
o
u
t
p
u
t
cu
r
r
en
t
o
f
t
h
e
in
v
er
ter
.
T
o
s
im
p
lify
th
e
d
is
cu
s
s
io
n
,
we
f
o
cu
s
o
n
t
h
e
f
r
eq
u
e
n
cy
d
o
m
ain
(
ω
):
_
(
)
=
|
ℎ
(
)
|
∙
_
(
)
(
1
5
)
H
e
r
e
,
_
(
)
r
e
p
r
e
s
e
n
ts
t
h
e
f
u
n
d
a
m
e
n
t
a
l
f
r
e
q
u
e
n
c
y
c
o
m
p
o
n
e
n
t
as
s
o
c
i
a
t
e
d
wi
t
h
t
h
e
g
r
i
d
c
u
r
r
e
n
t
;
i
t
a
s
s
u
m
es
t
h
a
t
t
h
e
h
y
b
r
i
d
f
i
l
t
e
r
e
f
f
e
c
t
i
v
e
l
y
a
t
te
n
u
a
t
e
s
h
a
r
m
o
n
ic
c
o
m
p
o
n
e
n
t
s
ℎ
(
)
=
0
f
o
r
(
ω
≠
)
,
w
e
c
a
n
e
x
p
r
e
s
s
t
h
e
T
HD
r
e
d
u
ct
i
o
n
:
=
√
_
2
−
_
_
2
_
_
<
(
1
6
)
Her
e,
is
th
e
g
r
id
cu
r
r
en
t
(
T
HD)
af
ter
p
ass
in
g
th
r
o
u
g
h
t
h
e
h
y
b
r
id
f
ilter
,
is
th
e
in
v
er
ter
o
u
t
p
u
t
cu
r
r
e
n
t
(
T
HD
)
,
_
is
th
e
g
r
id
cu
r
r
en
t
af
ter
p
ass
in
g
th
r
o
u
g
h
th
e
h
y
b
r
i
d
f
ilter
,
an
d
_
_
is
th
e
f
u
n
d
am
en
tal
f
r
eq
u
en
c
y
co
m
p
o
n
en
t
o
f
th
e
g
r
id
cu
r
r
en
t
af
ter
p
ass
in
g
th
r
o
u
g
h
th
e
h
y
b
r
id
f
ilter
.
T
h
e
s
p
ec
if
ic
m
ath
em
atica
l
f
o
r
m
o
f
ℎ
(
)
an
d
th
e
r
ed
u
ctio
n
in
T
HD
d
ep
en
d
s
o
n
th
e
d
etailed
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
h
y
b
r
id
f
ilter
.
A
h
y
b
r
id
f
ilter
'
s
ad
v
an
tag
e
o
v
er
an
L
C
L
f
ilter
f
o
r
r
e
d
u
cin
g
g
r
id
c
u
r
r
en
t
T
HD
lies
in
its
ab
ilit
y
to
co
m
b
in
e
th
e
b
en
e
f
its
o
f
L
C
L
an
d
p
a
r
allel
f
ilter
(
PD)
elem
en
ts
.
T
h
e
h
y
b
r
i
d
f
ilter
aim
s
to
ad
d
r
ess
th
e
lim
itatio
n
s
o
f
t
h
e
L
C
L
f
ilter
,
s
u
ch
as
r
eso
n
an
ce
is
s
u
es
an
d
h
ig
h
er
lo
s
s
es
at
ce
r
tain
f
r
e
q
u
en
cies.
T
h
e
g
r
id
b
en
ef
its
f
r
o
m
im
p
r
o
v
ed
p
o
wer
q
u
ality
with
f
ewe
r
h
ar
m
o
n
ics
an
d
n
o
is
e,
lead
in
g
to
b
ette
r
p
er
f
o
r
m
an
ce
PV
-
m
icr
o
in
v
er
t
er
s
co
n
n
ec
ted
to
th
e
g
r
id
.
T
h
e
u
s
e
o
f
h
y
b
r
id
f
ilter
s
h
elp
s
m
ee
t
r
eg
u
lato
r
y
s
tan
d
ar
d
s
f
o
r
h
ar
m
o
n
ic
em
is
s
io
n
s
an
d
p
o
wer
q
u
ality
,
en
s
u
r
i
n
g
th
at
th
e
in
v
er
ter
'
s
co
n
tr
i
b
u
t
io
n
s
to
t
h
e
g
r
id
d
o
n
o
t v
io
late
estab
lis
h
ed
lim
its
.
As
af
f
ec
ted
b
y
t
h
e
h
y
b
r
i
d
f
ilte
r
,
th
e
an
aly
s
is
o
f
f
u
n
d
am
e
n
tal
f
r
eq
u
e
n
cy
c
o
m
p
o
n
en
ts
in
th
e
f
r
eq
u
e
n
cy
d
o
m
ain
h
i
g
h
lig
h
ts
th
e
im
p
o
r
ta
n
ce
o
f
m
ain
tain
i
n
g
clea
n
,
s
tab
ilized
f
u
n
d
am
e
n
tal
f
r
eq
u
en
cy
in
th
e
g
r
id
c
u
r
r
e
n
t.
Fu
r
th
er
m
o
r
e
,
o
p
tim
izin
g
th
e
tr
an
s
m
is
s
io
n
o
f
th
e
f
u
n
d
am
en
ta
l
f
r
eq
u
en
cy
an
d
m
itig
atin
g
h
a
r
m
o
n
ics,
th
e
h
y
b
r
id
f
ilter
(
L
C
L
a
nd
PD)
co
n
t
r
ib
u
tes
s
ig
n
if
ican
tly
t
o
p
o
wer
s
y
s
tem
s
tab
ilit
y
,
ef
f
icien
c
y
,
a
n
d
c
o
m
p
lian
ce
with
in
d
u
s
tr
y
s
tan
d
ar
d
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.