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s
tem
ef
f
icien
cy
b
y
u
s
in
g
a
7
-
lev
el
m
u
ltil
ev
el
in
v
er
ter
ar
ch
itectu
r
e
with
o
n
ly
5
s
witch
es
in
s
tead
o
f
1
2
.
T
h
e
s
y
s
tem
h
as
m
o
r
e
en
er
g
y
-
an
d
co
s
t
-
ef
f
icien
t
a
s
a
r
esu
lt
o
f
th
e
f
ewe
r
s
witch
es,
wh
ich
also
r
esu
lts
in
lo
wer
p
o
wer
l
o
s
s
es.
T
h
e
d
if
f
icu
lties
p
o
s
ed
b
y
tr
an
s
f
o
r
m
er
less
in
v
er
ter
s
'
d
ec
r
ea
s
e
d
s
witch
in
g
,
esp
ec
ially
wh
en
it
co
m
es
to
g
r
id
-
co
n
n
ec
ted
p
h
o
t
o
v
o
ltaic
(
PV)
s
y
s
tem
s
.
T
r
an
s
f
o
r
m
er
les
s
in
v
er
ter
s
h
av
e
b
en
ef
its
lik
e
lo
w
co
s
t,
co
m
p
ac
t
s
ize,
an
d
g
r
ea
t
ef
f
icien
c
y
,
b
u
t
th
ey
also
h
a
v
e
p
r
o
b
lem
s
with
ea
r
th
leak
ag
e
cu
r
r
en
t,
wh
ic
h
p
o
s
es
elec
tr
ical
an
d
s
ec
u
r
ity
r
is
k
s
.
Nu
m
er
o
u
s
s
tu
d
i
es
[
1
7
]
,
[
2
1
]
,
[
2
2
]
h
a
v
e
s
u
g
g
ested
ap
p
r
o
ac
h
es
to
d
ea
l
with
th
e
s
e
is
s
u
es,
in
clu
d
in
g
th
e
d
ev
elo
p
m
e
n
t
o
f
cr
ea
tiv
e
i
n
v
er
ter
co
n
ce
p
ts
,
f
au
lt
-
to
ler
a
n
t
to
p
o
lo
g
ies,
an
d
co
n
tr
o
l
s
tr
ateg
ies.
T
o
g
u
ar
an
tee
d
ep
en
d
a
b
le
an
d
ef
f
ec
tiv
e
f
u
n
ctio
n
in
g
,
m
o
r
e
r
esear
ch
an
d
o
p
tim
izatio
n
o
f
th
ese
s
o
lu
tio
n
s
ar
e
n
ec
ess
ar
y
,
p
ar
ticu
lar
ly
wh
e
n
n
o
n
-
lin
ea
r
lo
ad
s
an
d
f
lu
ct
u
atin
g
g
r
id
cir
cu
m
s
tan
ce
s
ar
e
p
r
esen
t.
T
o
d
eter
m
in
e
th
e
b
est
m
eth
o
d
f
o
r
b
r
o
ad
im
p
lem
e
n
tatio
n
in
PV
g
r
id
-
co
n
n
ec
ted
s
y
s
tem
s
,
a
co
m
p
ar
is
o
n
o
f
v
a
r
io
u
s
in
v
er
ter
t
o
p
o
lo
g
ies,
co
n
tr
o
l
s
ch
em
es,
f
au
lt
to
ler
a
n
c
e
tech
n
iq
u
es
a
n
d
u
s
in
g
en
e
r
g
y
-
s
to
r
ag
e
co
m
b
in
atio
n
s
tr
u
ctu
r
e
s
an
d
s
o
p
h
is
ticated
co
n
tr
o
l
m
eth
o
d
s
s
u
ch
as
f
u
zz
y
lo
g
ic
-
b
ased
s
witch
in
g
,
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
MPC
)
,
an
d
s
elec
tiv
e
h
ar
m
o
n
ic
elim
in
atio
n
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SHE
-
PW
M)
i
s
also
n
e
ce
s
s
ar
y
.
T
o
o
v
er
co
m
e
th
e
ab
o
v
e
lim
itatio
n
s
h
er
e
co
m
es
an
ef
f
ec
tiv
e
tr
an
s
f
o
r
m
er
less
7
-
lev
el
in
v
e
r
ter
with
o
p
tim
ized
PID
a
n
d
b
u
c
k
b
o
o
s
t
co
n
tr
o
ller
f
o
r
g
r
id
co
n
n
ec
ted
PV
s
y
s
tem
s
wh
ich
is
im
p
lem
en
ted
in
th
is
in
v
esti
g
atio
n
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
r
es
ea
r
ch
is
to
im
p
r
o
v
e
tr
an
s
f
o
r
m
er
less
in
v
er
ter
s
af
ety
,
d
ep
e
n
d
ab
ilit
y
,
a
n
d
ef
f
icien
c
y
.
2.
M
E
T
H
O
D
T
r
an
s
f
o
r
m
e
r
less
in
v
er
ter
s
f
r
eq
u
en
tly
h
a
v
e
s
witch
in
g
lo
s
s
es
,
wh
ich
ca
n
lead
to
d
if
f
icu
ltie
s
with
h
ea
t
d
is
s
ip
atio
n
.
I
n
ac
c
u
r
ate
tu
n
in
g
m
ay
lead
t
o
is
s
u
es
in
clu
d
i
n
g
h
ar
m
o
n
ic
d
is
to
r
tio
n
,
v
o
ltag
e
in
s
tab
ilit
y
,
o
r
p
o
o
r
p
o
wer
tr
a
n
s
m
is
s
io
n
.
An
y
d
e
v
iatio
n
s
o
r
is
s
u
es
with
n
o
n
-
co
m
p
lian
ce
c
o
u
ld
h
in
d
e
r
th
e
in
v
er
ter
d
esig
n
'
s
im
p
lem
en
tatio
n
an
d
wid
esp
r
e
ad
ac
ce
p
tan
ce
.
T
o
o
v
er
co
m
e
th
ese
ch
allen
g
es,
th
e
s
u
g
g
ested
m
o
d
el
p
u
r
s
u
es
in
teg
r
atin
g
PV
an
d
b
atter
ies
i
n
to
a
h
y
b
r
i
d
p
o
wer
s
y
s
tem
w
h
ile
ac
h
iev
in
g
o
p
tim
al
p
o
wer
q
u
ali
ty
.
T
r
a
p
ez
o
id
al
PW
M
is
u
s
ed
to
m
in
im
ize
T
H
D,
wh
ile
a
7
-
lev
el
in
v
er
ter
with
5
s
witch
es
r
ed
u
ce
s
s
witch
in
g
lo
s
s
es.
T
h
e
UPQC
-
PQ
is
d
ev
elo
p
ed
u
s
in
g
th
e
h
y
b
r
id
m
etah
eu
r
is
tic
alg
o
r
ith
m
,
HB
E
O,
wh
ich
o
p
tim
izes
th
e
PID
co
n
tr
o
ller
f
o
r
a
h
ig
h
ly
ef
f
icien
t
h
y
b
r
i
d
r
en
ew
a
b
le
en
er
g
y
s
y
s
tem
.
T
r
a
p
ez
o
i
d
al
PW
M
i
s
em
p
lo
y
ed
f
o
r
v
o
ltag
e
r
eg
u
lar
izatio
n
,
m
in
im
izin
g
T
HD.
T
h
e
m
o
d
el
also
in
co
r
p
o
r
ates
a
b
u
ck
-
b
o
o
s
t
co
n
tr
o
ller
to
ad
ju
s
t
th
e
v
o
ltag
e
lev
el,
in
cr
ea
s
in
g
o
r
d
ec
r
ea
s
in
g
it
b
ased
o
n
th
e
PV
in
p
u
t
v
o
ltag
e,
wh
ile
a
7
-
lev
el
m
u
ltil
ev
e
l
in
v
e
r
ter
wit
h
m
in
im
al
s
witch
es
(
5
in
s
tead
o
f
1
2
)
en
s
u
r
es
m
in
i
m
al
s
witch
in
g
lo
s
s
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
is
im
p
lem
en
ted
an
d
v
er
if
ie
d
u
s
in
g
th
e
MA
T
L
AB
/S
im
u
lin
k
p
latf
o
r
m
u
n
d
er
v
a
r
io
u
s
tem
p
er
atu
r
e
an
d
s
o
lar
ir
r
ad
ian
ce
c
o
n
d
itio
n
s
,
co
m
p
ar
ed
with
ex
is
tin
g
tech
n
iq
u
e
s
lik
e
PS
O,
GA,
an
d
MO
.
T
h
e
b
lo
ck
d
iag
r
am
f
o
r
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
is
s
h
o
wn
in
Fig
u
r
e
1
.
2
.
1
.
M
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delin
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P
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A
f
e
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e
d
in
p
ar
allel,
ac
tin
g
as
a
s
ec
o
n
d
-
o
r
d
er
lo
w
-
p
ass
f
ilter
to
ef
f
icien
tly
r
e
d
u
ce
th
e
v
o
ltag
e
r
ip
p
le
at
th
e
o
u
tp
u
t.
I
n
a
cir
cu
it
u
tili
zin
g
a
n
in
v
er
ti
n
g
c
o
n
v
er
te
r
to
p
o
lo
g
y
,
th
e
m
e
asu
r
ed
o
u
tp
u
t
v
o
ltag
e
ac
r
o
s
s
t
h
e
lo
ad
ex
h
ib
its
a
r
ev
er
s
ed
p
o
lar
ity
co
m
p
ar
ed
to
t
h
e
in
p
u
t
v
o
ltag
e
.
T
h
is
p
h
en
o
m
e
n
o
n
a
r
is
es
b
ec
au
s
e
o
f
th
e
way
th
e
in
d
u
cto
r
d
is
ch
ar
g
es c
h
ar
g
e
in
a
b
u
ck
-
b
o
o
s
t c
o
n
v
er
ter
,
th
e
ac
r
o
s
s
th
e
lo
ad
is
d
ef
in
e
d
as
(
5
)
.
=
−
1
−
(
5
)
Her
e,
i
s
th
e
in
p
u
t
v
o
ltag
e
an
d
d
u
ty
c
y
cle
o
f
th
e
s
witch
in
g
tr
an
s
is
to
r
.
I
n
th
e
b
o
o
s
t
m
o
d
e
o
f
th
e
b
u
c
k
-
b
o
o
s
t
co
n
v
er
ter
,
th
e
d
u
ty
r
atio
is
g
r
ea
ter
th
an
in
b
u
ck
m
o
d
e.
B
o
o
s
t
m
o
d
e
h
as
a
lo
n
g
er
o
n
-
s
tate
f
o
r
th
e
s
witch
,
allo
win
g
m
o
r
e
en
er
g
y
to
b
e
s
to
r
ed
in
th
e
in
d
u
cto
r
b
ef
o
r
e
tr
an
s
f
er
r
in
g
it
to
th
e
ca
p
ac
ito
r
.
T
h
is
in
cr
ea
s
e
in
en
er
g
y
lead
s
to
a
h
ig
h
e
r
o
u
t
p
u
t v
o
ltag
e.
I
n
th
e
cir
cu
it,
th
e
MO
SF
E
T
s
witch
an
d
d
io
d
e
co
n
tr
o
l
th
e
f
l
o
w
o
f
ch
ar
g
e.
W
h
en
th
e
MO
SF
E
T
s
witch
is
o
n
,
c
u
r
r
en
t
f
lo
ws
to
th
e
i
n
d
u
cto
r
,
w
h
ile
th
e
d
io
d
e
p
r
e
v
en
t
s
cu
r
r
en
t
f
r
o
m
r
ea
c
h
in
g
th
e
o
u
tp
u
t.
T
h
e
in
d
u
cto
r
s
to
r
es
en
er
g
y
as
a
m
ag
n
etic
f
ield
.
W
h
en
th
e
MO
SF
E
T
s
witch
is
o
f
f
,
th
e
d
i
o
d
e
allo
ws
cu
r
r
e
n
t
to
f
lo
w
f
r
o
m
th
e
in
d
u
cto
r
t
o
th
e
r
est
o
f
th
e
cir
c
u
it,
r
ev
er
s
in
g
th
e
in
d
u
ct
o
r
'
s
p
o
lar
ity
,
an
d
r
esu
ltin
g
in
an
in
d
u
ce
d
v
o
ltag
e
at
th
e
o
u
tp
u
t.
T
h
is
p
r
o
ce
s
s
f
ac
ilit
ates
th
e
tr
an
s
f
er
o
f
e
n
er
g
y
to
th
e
o
u
tp
u
t
a
n
d
c
o
n
tr
ib
u
tes
to
th
e
c
o
n
v
e
r
ter
'
s
f
u
n
ctio
n
ality
.
T
h
e
ch
a
n
g
e
in
c
ap
ac
ito
r
v
o
ltag
e
is
g
iv
en
b
y
(
7
)
.
=
−
+
(
6
)
=
−
(
7
)
2
.
3
.
B
a
t
t
er
y
A
b
atter
y
is
ty
p
ically
m
ad
e
u
p
o
f
o
n
e
o
r
m
o
r
e
elec
tr
o
c
h
em
ic
al
ce
lls
co
n
n
ec
ted
in
p
a
r
allel
o
r
s
er
ies
to
p
r
o
d
u
ce
th
e
r
eq
u
ir
e
d
n
o
m
in
al
v
o
ltag
e
an
d
ca
p
ac
ity
.
T
h
e
b
att
er
y
en
er
g
y
s
to
r
a
g
e
(
B
E
S
)
o
p
e
r
ates
in
ch
ar
g
e
an
d
d
is
ch
ar
g
e
m
o
d
es,
p
r
o
v
id
in
g
b
ac
k
u
p
p
o
wer
to
ad
d
r
ess
s
h
o
r
t
-
in
ter
v
al
d
em
a
n
d
s
n
o
t
m
et
b
y
PV
s
y
s
tem
s
.
I
t
aim
s
to
m
ain
tain
a
s
tab
le
DC
b
u
s
v
o
ltag
e,
r
e
d
u
cin
g
v
o
ltag
e
r
ip
p
le
in
th
e
ca
p
ac
ito
r
.
B
a
t
t
e
r
y
m
o
d
e
l
s
f
a
l
l
i
n
t
o
d
i
f
f
e
r
e
n
t
c
a
t
e
g
o
r
i
e
s
,
w
i
t
h
t
h
e
e
q
u
i
v
a
l
e
n
t
c
i
r
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u
i
t
m
o
d
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l
b
e
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n
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p
r
e
f
e
r
r
e
d
f
o
r
d
y
n
a
m
i
c
s
t
u
d
i
e
s
.
T
y
p
ic
a
l
l
y
,
t
h
e
e
l
e
c
t
r
o
c
h
e
m
i
c
a
l
a
n
d
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l
e
c
t
r
i
c
ci
r
c
u
i
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m
o
d
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ls
d
e
te
r
m
i
n
e
h
o
w
b
a
t
t
e
r
y
m
o
d
e
l
s
a
r
e
c
l
a
s
s
i
f
i
e
d
;
th
e
o
th
er
m
o
d
els
ar
e
ty
p
ically
d
e
r
iv
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
2
0
2
5
:
23
-
36
26
f
r
o
m
t
h
ese
m
o
d
els.
T
o
e
n
h
an
ce
th
e
b
atter
y
m
o
d
el,
f
o
r
i
n
s
tan
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o
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ca
n
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teg
r
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r
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e
n
t
u
s
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g
Sh
e
p
h
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d
’
s
eq
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.
T
h
is
m
o
d
el
r
e
q
u
ir
es
s
p
ec
if
ic
m
ea
s
u
r
em
en
ts
to
d
ete
r
m
in
e
th
e
b
atter
y
'
s
in
ter
n
al
r
esis
tan
ce
.
T
h
e
b
atter
y
v
o
ltag
e
d
u
r
in
g
ch
a
r
g
e/d
is
ch
ar
g
e
is
g
iv
e
n
b
y
(
8
)
.
=
−
(
8
)
T
h
e
v
o
ltag
e
o
f
th
e
in
ter
n
al
b
atter
y
is
r
ep
r
esen
ted
b
y
(
9
)
-
(
1
1
)
.
=
−
+
1
∗
−
−
+
(
)
; Ch
ar
g
e
(
∗
<
0
)
(
9
)
=
−
−
∗
−
−
+
(
)
;
Dis
ch
ar
g
e
(
∗
<
0
)
(
1
0
)
(
)
=
∫
.
(
.
−
(
−
1
)
.
(
1
1
)
W
h
er
e
is
th
e
b
atter
y
v
o
ltag
e
(
)
,
d
en
o
tes
th
e
in
ter
n
al
r
esis
t
an
ce
,
an
d
d
en
o
tes
th
e
b
atter
y
cu
r
r
en
t
.
d
en
o
tes th
e
n
o
-
lo
a
d
v
o
ltag
e
(
)
.
2
.
4
.
P
I
D
co
ntr
o
ller
PID
co
n
tr
o
ller
tech
n
o
lo
g
y
u
til
izes
a
f
ee
d
b
ac
k
co
n
tr
o
l
lo
o
p
t
o
m
in
im
ize
d
is
tu
r
b
a
n
ce
s
im
p
a
ct
o
n
th
e
s
y
s
tem
,
g
u
id
in
g
it
to
war
d
s
th
e
d
esire
d
s
tate
an
d
estab
lis
h
in
g
clea
r
r
elatio
n
s
h
ip
s
b
etwe
en
s
y
s
tem
v
ar
iab
les.
T
h
e
PID
co
n
tr
o
ller
tak
es
th
e
er
r
o
r
at
tim
e
as
in
p
u
t,
wh
ich
is
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
m
ea
s
u
r
ed
an
d
r
ef
er
e
n
ce
v
alu
es.
T
h
e
co
n
tr
o
ller
'
s
o
u
tp
u
t
,
th
e
ac
tu
atio
n
,
r
ep
r
esen
ts
th
e
ac
tio
n
to
b
e
ap
p
lied
to
th
e
s
y
s
t
em
o
r
p
lan
t.
T
h
e
a
c
t
u
a
t
i
o
n
is
d
e
t
e
r
m
i
n
e
d
b
y
c
o
m
b
i
n
i
n
g
t
h
r
e
e
t
e
r
m
s
:
t
h
e
p
r
o
p
o
r
t
i
o
n
a
l
g
a
i
n
m
u
l
t
i
p
l
i
e
d
b
y
t
h
e
e
r
r
o
r
m
a
g
n
i
t
u
d
e
,
t
h
e
i
n
t
e
g
r
a
l
g
a
i
n
m
u
l
t
i
p
l
ie
d
b
y
t
h
e
i
n
t
e
g
r
a
l
o
f
t
h
e
e
r
r
o
r
,
a
n
d
t
h
e
d
e
r
i
v
a
t
i
v
e
g
a
i
n
m
u
l
t
i
p
li
e
d
b
y
t
h
e
d
e
r
i
v
a
t
i
v
e
o
f
t
h
e
e
r
r
o
r
.
T
h
is
cr
ea
tes a
well
-
d
ef
in
ed
c
o
n
tr
o
l sig
n
al
th
at
d
r
iv
es th
e
s
y
s
tem
to
war
d
s
its
d
esire
d
s
tate.
=
+
∫
+
0
(
1
2
)
T
h
e
PID
co
n
tr
o
ller
co
m
b
in
es
t
h
r
ee
ter
m
s
to
c
r
ea
te
th
e
c
o
n
tr
o
l
s
ig
n
al:
p
r
o
p
o
r
tio
n
al
g
ain
in
teg
r
al
g
ain
an
d
d
er
iv
ativ
e
g
ain
.
r
ed
u
ce
s
s
tea
d
y
-
s
tate
er
r
o
r
b
y
r
esp
o
n
d
i
n
g
t
o
t
h
e
p
r
esen
t
er
r
o
r
.
a
d
d
r
ess
es
o
s
cillatio
n
s
b
y
co
n
s
id
er
i
n
g
p
ast
er
r
o
r
ac
c
u
m
u
latio
n
s
.
a
n
ticip
ates
f
u
tu
r
e
er
r
o
r
c
h
an
g
es
an
d
ad
d
s
d
a
m
p
in
g
to
p
r
ev
e
n
t
o
v
er
s
h
o
o
tin
g
with
o
u
t
af
f
ec
tin
g
th
e
s
tead
y
-
s
tate
er
r
o
r
.
2
.
5
.
Sev
en
lev
el
inv
er
t
er
T
h
e
p
u
ls
e
g
e
n
er
atio
n
cir
cu
it
d
esig
n
s
ets
th
is
to
p
o
lo
g
y
a
p
a
r
t
f
r
o
m
o
th
er
s
,
en
s
u
r
in
g
a
u
n
iq
u
e
p
u
ls
e
p
atter
n
to
t
r
ig
g
er
s
witch
es
at
th
e
p
r
ec
is
e
m
o
m
en
t.
Switch
es
S1
,
S2
,
an
d
S3
m
u
s
t
b
e
u
n
id
ir
ec
tio
n
al
to
p
r
ev
en
t
wav
ef
o
r
m
d
is
to
r
tio
n
.
T
h
e
r
ed
u
ce
d
n
u
m
b
e
r
o
f
s
witch
es m
ak
es t
h
e
cir
cu
it m
o
r
e
co
m
p
ac
t a
n
d
u
s
er
-
f
r
ien
d
ly
.
T
h
e
ex
p
r
ess
io
n
ca
n
b
e
s
im
p
lifie
d
a
s
(
1
3
)
.
=
(
2
∗
−
3
)
=
(
2
∗
−
1
)
(
1
3
)
W
h
er
e
is
th
e
v
o
ltag
e
lev
el,
is
th
e
n
u
m
b
er
o
f
s
witch
es,
an
d
is
th
e
n
u
m
b
er
o
f
DC
s
o
u
r
ce
s
.
Alth
o
u
g
h
4
DC
s
o
u
r
ce
s
ar
e
u
s
ed
f
o
r
t
h
e
7
-
le
v
el
ML
I
,
r
e
d
u
ce
d
s
witch
es
lead
to
lo
wer
s
witch
in
g
lo
s
s
es.
T
wo
s
witch
es
ar
e
r
esp
o
n
s
ib
le
f
o
r
p
o
lar
ity
r
ev
er
s
al.
T
ab
le
1
p
r
esen
ts
th
e
s
witch
in
g
s
ch
em
e
f
o
r
th
is
to
p
o
lo
g
y
.
T
ab
le
1
.
Switch
in
g
to
p
o
lo
g
y
o
f
5
s
witch
,
7
lev
el
i
n
v
er
ter
S
.
N
o
S
1
S
2
S
3
S
4
S
5
V
O
1
O
F
F
O
F
F
ON
O
F
F
ON
+V
dc
2
O
F
F
ON
O
F
F
O
F
F
ON
+2
V
dc
3
ON
O
F
F
O
F
F
O
F
F
ON
+3
V
dc
4
O
F
F
O
F
F
O
F
F
O
F
F
O
F
F
0
5
ON
O
F
F
O
F
F
ON
O
F
F
-
V
dc
6
O
F
F
ON
O
F
F
ON
O
F
F
-
2
V
dc
7
O
F
F
O
F
F
ON
ON
O
F
F
-
3
V
dc
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2
2
5
2
-
8
7
9
2
A
n
effec
tive
tr
a
n
s
fo
r
mer le
s
s
7
leve
l in
ve
r
ter w
ith
o
p
timiz
ed
P
I
D
…
(
B
.
Mo
h
a
n
R
a
o
)
27
2
.
6
.
T
ra
ns
f
o
rm
er
less
UP
Q
C
T
h
e
T
L
-
UPQC
is
co
n
n
ec
ted
to
a
lo
w
v
o
ltag
e
(
LV
)
d
is
tr
ib
u
tio
n
n
etwo
r
k
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
PC
C
)
an
d
co
n
s
is
ts
o
f
two
h
alf
-
b
r
id
g
e
b
i
-
d
ir
ec
tio
n
al
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
s
(
VSC
s
)
s
h
ar
in
g
a
co
m
m
o
n
DC
lin
k
,
f
o
r
m
in
g
a
to
p
o
lo
g
y
with
o
n
e
s
h
u
n
t
co
n
v
er
ter
a
n
d
o
n
e
s
er
ies
co
n
v
e
r
ter
.
T
o
m
in
im
ize
s
witch
in
g
h
ar
m
o
n
ics
in
jecte
d
in
to
th
e
g
r
id
,
a
s
h
u
n
t
f
ilter
ca
p
ac
ito
r
ac
ts
as
lo
w
im
p
ed
an
ce
f
o
r
h
ig
h
-
f
r
eq
u
en
cy
co
m
p
o
n
en
ts
in
tr
o
d
u
ce
d
b
y
t
h
e
co
n
v
er
te
r
.
T
h
e
k
e
y
f
ea
tu
r
es
o
f
th
e
T
L
-
UPQC
to
p
o
lo
g
y
in
cl
u
d
e
its
tr
an
s
f
o
r
m
er
less
d
esig
n
,
r
esu
ltin
g
in
h
ig
h
er
ef
f
icien
c
y
an
d
co
s
t
-
ef
f
ec
ti
v
en
ess
,
lo
w
co
m
m
o
n
-
m
o
d
e
v
o
ltag
e
ac
h
iev
e
d
b
y
clam
p
in
g
th
e
p
o
te
n
tial
d
if
f
er
e
n
ce
b
etwe
en
t
h
e
AC
an
d
DC
g
r
o
u
n
d
s
,
ef
f
ec
ti
v
e
m
itig
atio
n
o
f
h
ar
m
o
n
ics
f
r
o
m
n
o
n
lin
ea
r
lo
ad
s
,
p
r
o
v
is
io
n
o
f
r
ea
ctiv
e
p
o
we
r
to
lin
ea
r
lo
ad
s
,
f
ast
d
y
n
am
ic
r
esp
o
n
s
e
p
r
o
te
ctin
g
cr
itical
lo
a
d
s
f
r
o
m
v
o
ltag
e
f
lick
e
r
in
g
an
d
d
is
tu
r
b
an
ce
s
,
an
d
th
e
ab
ilit
y
to
co
n
tr
o
l
am
p
litu
d
e
v
o
ltag
e
v
a
r
iatio
n
f
o
r
en
er
g
y
s
av
in
g
s
at
th
e
lo
a
d
b
u
s
.
I
n
ad
d
itio
n
t
o
its
in
s
tallatio
n
at
a
L
V
d
is
tr
ib
u
tio
n
n
etwo
r
k
,
th
e
T
L
-
UPQC
ca
n
b
e
o
p
tim
ized
to
p
er
f
o
r
m
th
e
f
o
llo
win
g
f
u
n
ctio
n
s
:
p
r
o
v
i
d
in
g
r
ea
ctiv
e
p
o
wer
c
o
m
p
en
s
a
tio
n
f
o
r
r
e
g
u
latin
g
th
e
i
n
p
u
t
g
r
id
v
o
ltag
e
to
l
o
ad
s
co
n
n
ec
ted
at
th
e
PC
C
,
e
n
h
an
cin
g
th
e
P
C
C
v
o
ltag
e
p
r
o
f
ile
,
an
d
lead
in
g
to
an
o
v
e
r
all
im
p
r
o
v
e
m
en
t
in
th
e
u
p
s
tr
ea
m
v
o
ltag
e
q
u
ality
.
I
n
a
t
y
p
ical
T
L
-
UPQC
s
y
s
tem
,
th
e
s
h
u
n
t
c
o
n
v
er
te
r
is
r
esp
o
n
s
ib
le
f
o
r
in
jectin
g
cu
r
r
en
t
h
ar
m
o
n
ics
an
d
r
ea
ctiv
e
cu
r
r
en
t
to
co
m
p
en
s
ate
f
o
r
th
e
d
is
to
r
t
ed
cu
r
r
e
n
t
o
f
th
e
n
o
n
lin
ea
r
lo
a
d
co
n
n
ec
te
d
to
b
u
s
B
.
T
h
is
s
h
ap
in
g
o
f
th
e
in
p
u
t
cu
r
r
en
t
en
s
u
r
es
th
at
it
b
e
co
m
es
s
in
u
s
o
id
al
an
d
i
n
p
h
as
e
with
th
e
PC
C
v
o
ltag
e.
T
h
e
g
r
id
c
u
r
r
en
t
(
)
ca
r
r
ies
th
e
ap
p
ar
en
t
p
o
wer
d
em
a
n
d
o
f
th
e
PC
C
lo
ad
,
r
ep
r
esen
te
d
b
y
th
e
PC
C
lo
ad
cu
r
r
e
n
t
(
)
.
Ad
d
itio
n
ally
,
it
ca
r
r
ies
th
e
ac
tiv
e
p
o
wer
d
em
a
n
d
co
n
s
u
m
e
d
b
y
t
h
e
lo
ad
co
n
n
ec
ted
to
th
e
lo
ad
b
u
s
,
alo
n
g
with
th
e
n
ec
es
s
ar
y
ac
tiv
e
p
o
wer
r
eq
u
ir
e
d
to
m
ain
tain
th
e
DC
lin
k
v
o
ltag
e
an
d
co
m
p
e
n
s
ate
f
o
r
co
n
v
er
ter
lo
s
s
es.
T
h
e
p
r
o
p
o
s
e
d
en
h
a
n
ce
d
co
n
tr
o
l
m
et
h
o
d
o
lo
g
y
in
tr
o
d
u
ce
s
an
e
x
tr
a
co
n
tr
o
l d
eg
r
ee
o
f
f
r
ee
d
o
m
,
allo
win
g
th
e
cr
ea
tio
n
o
f
a
p
h
a
s
e
an
g
le
(
)
b
etwe
en
an
d
at
th
e
g
r
id
s
id
e.
T
h
e
ex
p
r
ess
io
n
s
f
o
r
ac
tiv
e
(
)
an
d
r
ea
ctiv
e
(
)
p
o
wer
at
th
e
PC
C
ca
n
b
e
d
ef
in
e
d
as
(
1
4
)
an
d
(
1
5
)
.
=
c
os
(
1
4
)
=
s
in
(
1
5
)
i
s
th
e
p
h
ase
an
g
le
b
y
wh
ich
th
e
PC
C
cu
r
r
en
t is d
is
p
lace
d
co
n
ce
r
n
in
g
its
v
o
ltag
e.
T
o
o
b
tain
th
e
th
r
ee
-
p
h
ase
v
o
ltag
e
r
ef
er
en
ce
s
ig
n
al
f
o
r
th
e
s
e
r
ies
ac
tiv
e
p
o
wer
f
ilter
(
APF),
a
p
h
ase
-
lo
ck
ed
lo
o
p
(
PLL
)
is
em
p
lo
y
e
d
as
s
h
o
wn
in
F
ig
u
r
e
2
.
=
s
in
(
1
6
)
=
s
in
(
−
120
)
(
1
7
)
=
s
in
(
+
120
)
(
1
8
)
∗
=
∗
(
1
9
)
T
h
e
TL
-
UPQC
h
as
th
e
ca
p
ab
il
ity
to
o
p
er
ate
in
th
r
ee
d
is
tin
ct
m
o
d
es
o
f
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
,
wh
ich
ca
n
b
e
ac
h
iev
ed
b
y
co
n
tr
o
llin
g
th
e
p
h
ase
an
g
le.
I
n
t
h
e
p
o
wer
f
ac
to
r
co
r
r
ec
tio
n
(
PF
C
)
m
o
d
e
,
th
er
e
is
n
o
n
ee
d
f
o
r
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
o
n
th
e
g
r
id
s
id
e.
I
n
th
e
ca
p
ac
i
tiv
e
m
o
d
e,
th
e
r
ea
ctiv
e
p
o
wer
is
in
jecte
d
in
to
th
e
g
r
id
,
wh
ile
in
th
e
in
d
u
ctiv
e
m
o
d
e;
th
e
s
y
s
tem
ab
s
o
r
b
s
r
ea
ctiv
e
p
o
wer
f
r
o
m
th
e
g
r
i
d
.
Prio
r
t
o
ac
tiv
atin
g
th
e
g
r
id
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
,
th
e
s
tead
y
-
s
tate
v
al
u
es
ar
e
r
e
p
r
esen
ted
b
y
′
,
′
,
an
d
′
.
T
h
e
g
r
id
'
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
tr
a
n
s
f
er
r
ed
to
th
e
PC
C
b
u
s
ca
n
b
e
ex
p
r
ess
ed
as
(
2
0
)
an
d
(
2
1
)
.
=
c
os
(
−
+
)
−
2
c
os
(
2
0
)
=
s
in
(
−
+
)
−
2
c
os
(
2
1
)
Her
e
,
th
e
g
r
id
im
p
e
d
an
ce
is
c
h
ar
ac
ter
ized
b
y
a
d
is
p
lace
m
en
t a
n
g
le
o
f
.
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
o
f
th
e
lin
ea
r
lo
ad
c
o
n
n
e
cted
to
th
e
PC
C
i
s
g
iv
en
as
(
2
2
)
.
=
2
c
os
:
=
2
c
os
(
2
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
4
,
No
.
1
,
Ma
r
ch
2
0
2
5
:
23
-
36
28
T
h
e
lo
ad
im
p
e
d
an
ce
co
n
n
ec
te
d
to
th
e
PC
C
,
h
as
a
d
is
p
lace
m
en
t
an
g
le
.
T
h
e
T
L
-
UPQC
s
y
s
tem
p
r
o
v
i
d
es
h
ar
m
o
n
ic
c
o
m
p
e
n
s
atio
n
an
d
a
ctiv
e
p
o
wer
co
n
tr
o
l f
o
r
n
o
n
-
li
n
ea
r
lo
ad
s
,
wh
ic
h
is
g
iv
en
b
y
(
2
3
)
.
=
2
(
2
3
)
T
h
e
T
L
-
UPQC
m
ain
tain
s
a
s
tab
le
v
o
ltag
e
at
th
e
lo
ad
b
u
s
b
y
in
co
r
p
o
r
atin
g
a
f
ictitio
u
s
r
esis
t
an
ce
.
Fig
u
r
e
2
.
C
o
n
tr
o
l b
lo
c
k
d
iag
r
a
m
o
f
s
er
ies APF
Fig
u
r
e
3
s
h
o
ws
th
e
co
n
tr
o
l
b
lo
ck
d
iag
r
a
m
o
f
th
e
s
h
u
n
t
APF.
I
n
th
e
T
L
-
UPQC
s
y
s
tem
,
th
e
p
o
wer
1
f
lo
win
g
th
r
o
u
g
h
th
e
s
h
u
n
t
co
n
v
er
ter
is
u
tili
ze
d
to
ch
ar
g
e
th
e
DC
lin
k
ca
p
ac
ito
r
an
d
m
ai
n
tain
a
s
tead
y
DC
lin
k
v
o
ltag
e.
T
h
is
co
m
p
en
s
ates
f
o
r
th
e
p
o
wer
r
e
q
u
ir
ed
b
y
th
e
s
er
ies
co
n
v
er
ter
2
.
T
h
e
in
d
icato
r
o
f
s
y
s
tem
s
tab
ilit
y
is
th
e
co
n
s
tan
t
v
alu
e
o
f
th
e
DC
lin
k
v
o
ltag
e
r
ea
c
h
ed
d
u
r
in
g
s
tead
y
-
s
tate
o
p
er
atio
n
.
At
eq
u
ilib
r
iu
m
,
th
e
in
p
u
t
p
o
wer
m
atch
es
th
e
o
u
t
p
u
t
p
o
wer
.
I
n
s
h
o
r
t,
th
e
T
L
-
UPQC
ac
h
iev
es
s
tab
ilit
y
b
y
b
alan
cin
g
th
e
p
o
wer
f
lo
w
b
etwe
en
th
e
s
h
u
n
t a
n
d
s
er
ies co
n
v
er
ter
s
,
en
s
u
r
in
g
a
c
o
n
s
tan
t
DC
lin
k
v
o
ltag
e.
c
os
(
−
+
)
−
2
c
os
=
2
+
2
c
os
(
2
4
)
T
h
e
TL
-
UPQC
s
y
s
tem
co
n
tr
o
l
s
th
e
v
o
ltag
e
at
th
e
PC
C
b
y
in
jectin
g
o
r
ab
s
o
r
b
i
n
g
r
e
ac
tiv
e
p
o
wer
in
to
o
r
f
r
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T
h
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h
u
n
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ilter
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it
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r
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en
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h
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late
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l
in
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v
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I
t
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ates
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ly
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APF
b
u
t
with
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k
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er
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r
o
r
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ig
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m
u
ltip
lied
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e
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r
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ig
n
al.
∗
=
∗
(
2
6
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I
n
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Ana
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V
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at
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r
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o
m
e
o
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e
PV
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ar
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o
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PV sy
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Fig
u
r
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p
r
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h
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iatio
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is
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en
tly
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ed
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a
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o
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m
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ar
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o
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.
Fig
u
r
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4
(
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r
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n
s
tan
t
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lar
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ad
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ter
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u
r
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4
(
b
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d
e
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ter
m
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em
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as
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ig
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ican
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o
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m
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im
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ar
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tic
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e
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y
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.
Fig
u
r
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4
(
c)
s
h
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atu
r
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3
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2
.
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ly
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t
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g
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Fig
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5
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atter
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t 2
8
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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Fig
u
r
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6
.
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h
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cir
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o
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s
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p
r
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en
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at
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ter
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r
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t
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en
e
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y
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p
a
n
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to
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o
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m
at
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itab
le
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o
r
co
n
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ec
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g
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licatio
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s
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h
er
ef
o
r
e,
it
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em
o
n
s
tr
ated
th
at
a
s
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y
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o
ltag
e
o
f
2
5
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0
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2
5
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llo
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f
o
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f
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t e
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t
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ag
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an
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h
-
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f
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r
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.
(
a)
(
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(
c)
Fig
u
r
e
4
.
PV
c
h
ar
ac
te
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is
tics
o
f
(
a)
co
n
s
tan
t so
lar
r
ad
ian
ce
,
(
b
)
v
ar
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le
s
o
lar
ir
r
ad
ian
ce
,
an
d
(
c)
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ar
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p
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Fig
u
r
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5
.
B
atter
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a
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ac
ter
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Fig
u
r
e
6
.
DC
lin
k
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2
2
5
2
-
8
7
9
2
A
n
effec
tive
tr
a
n
s
fo
r
mer le
s
s
7
leve
l in
ve
r
ter w
ith
o
p
timiz
ed
P
I
D
…
(
B
.
Mo
h
a
n
R
a
o
)
31
3
.
4
.
Ana
ly
s
is
o
f
s
ev
en
-
lev
el
v
o
lt
a
g
e
o
utput
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n
a
p
h
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to
v
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ltaic
(
PV)
s
y
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tem
,
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e
ter
m
"sev
en
-
lev
el
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o
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e
o
u
tp
u
t"
u
s
u
ally
im
p
lies
th
e
to
tal
q
u
an
tity
o
f
lev
els
o
f
v
o
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e
t
h
at
ar
e
in
clu
d
ed
in
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e
f
o
r
m
t
h
at
co
m
es
o
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t
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th
e
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a
n
s
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er
.
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s
tab
lis
h
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g
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m
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ltil
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o
u
tp
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t
v
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ltag
e
is
a
s
tr
ateg
y
th
at
will
en
h
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ce
th
e
ef
f
icien
cy
o
f
th
e
p
r
o
d
u
ce
d
AC
p
o
wer
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d
elim
in
ate
d
is
to
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tio
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ca
u
s
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b
y
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ar
m
o
n
ic
s
in
th
e
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ettin
g
o
f
p
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wer
cir
cu
i
ts
an
d
p
r
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ce
s
s
o
r
s
u
tili
ze
d
in
p
h
o
to
v
o
ltaic
s
y
s
tem
s
.
T
h
e
o
u
tp
u
t o
f
th
e
s
ev
en
-
le
v
el
in
v
er
ter
is
s
h
o
wn
in
F
ig
u
r
e
7
.
T
h
e
s
ev
en
lev
els ar
e
0
,
±
1
0
V,
±
2
0
V,
a
n
d
±
30
V.
3
.
5
.
Ana
ly
s
is
o
f
s
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urce
re
a
l
a
nd
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a
ct
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e
po
wer
T
er
m
in
o
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r
elate
d
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e
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ctr
icity
p
r
o
d
u
ce
d
an
d
s
u
p
p
lied
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y
th
e
s
y
s
tem
in
q
u
esti
o
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in
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lu
d
es
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l
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o
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ten
r
ef
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r
e
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to
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o
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d
r
ea
ctiv
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wer
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o
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t
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itu
atio
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o
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o
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o
ltaic
(
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s
y
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tem
s
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d
th
eir
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ea
t
u
r
es.
T
h
e
r
ea
l
p
o
wer
in
a
s
y
s
tem
o
f
elec
tr
icity
is
r
ep
r
esen
ted
b
y
t
h
e
letter
P
an
d
r
ep
r
esen
ts
th
e
r
ea
l
s
o
u
r
ce
o
f
en
er
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o
es
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k
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t
is
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e
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er
g
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th
at
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an
s
f
o
r
m
ed
in
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u
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ctio
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ic
o
r
m
ec
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ical
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tiv
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ea
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tex
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o
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p
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al
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er
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y
o
u
tp
u
t
th
at
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s
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o
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m
ed
i
n
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tr
ical
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wer
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at
ca
n
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e
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s
ed
.
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h
e
r
elatio
n
s
h
ip
b
etwe
en
v
o
ltag
e
(
V)
,
cu
r
r
en
t
(
I
)
,
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d
r
ea
l
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o
wer
(
P)
is
g
i
v
en
.
T
h
e
p
o
wer
t
h
at
is
n
'
t
d
o
in
g
an
y
wo
r
k
b
u
t
is
r
eq
u
ir
e
d
f
o
r
th
e
cr
ea
tio
n
a
n
d
u
p
k
ee
p
o
f
elec
tr
o
m
ag
n
etic
wav
es
i
n
th
e
elec
tr
ical
g
r
id
is
k
n
o
wn
as
r
ea
ctiv
e
p
o
wer
,
r
ep
r
esen
ted
b
y
th
e
letter
Q.
T
h
e
u
n
it
o
f
m
e
asu
r
em
en
t
is
VAR,
o
r
v
o
lt
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a
m
p
er
es
r
ea
ctiv
e.
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h
e
s
o
u
r
ce
s
id
e
o
f
r
ea
l a
n
d
r
ea
ctiv
e
p
o
wer
is
s
h
o
wn
in
Fig
u
r
e
8
.
Fig
u
r
e
7
.
Sev
e
n
-
lev
el
v
o
ltag
e
o
u
tp
u
t
Fig
u
r
e
8
.
So
u
r
ce
r
ea
l a
n
d
r
ea
ct
iv
e
p
o
wer
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
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Vo
l.
1
4
,
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r
ch
2
0
2
5
:
23
-
36
32
3
.
6
.
Ana
ly
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g
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luct
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io
n m
it
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n
F
ig
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e
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r
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at
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d
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e
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jecte
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at
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1
s
to
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itig
at
e
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ag
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d
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l
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ctu
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n
.
W
h
en
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r
in
g
to
d
if
f
e
r
en
t
p
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wer
r
eli
ab
ilit
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p
r
o
b
lem
s
in
elec
tr
ical
s
y
s
tem
s
,
p
ar
ticu
lar
ly
th
o
s
e
lin
k
ed
t
o
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h
o
to
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o
ltaic
(
PV)
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y
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s
,
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h
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ases
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ag
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e
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.
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o
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ce
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ts
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e
b
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ief
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ar
iatio
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in
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o
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e
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at
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ay
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av
e
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im
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ac
t
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n
th
e
d
ep
e
n
d
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ilit
y
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d
ef
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icien
cy
o
f
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ical
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A
b
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ief
d
r
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e
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n
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e
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th
e
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m
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e
is
r
ef
e
r
r
ed
to
as
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s
ag
,
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ten
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lled
a
v
o
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e
d
ip
.
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m
e
th
i
n
g
s
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ch
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itiatin
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o
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er
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t
s
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f
ts
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e
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ical
g
r
id
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n
r
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as sh
o
wn
in
Fig
u
r
e
9
(
a)
.
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b
r
ief
r
is
e
in
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o
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e
o
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er
th
e
v
o
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e
t
h
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t is n
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al
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lled
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s
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en
o
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en
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r
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p
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d
is
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n
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tio
n
s
o
f
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v
y
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d
s
,
o
r
m
o
d
if
icatio
n
s
to
th
e
n
etwo
r
k
ca
n
all
r
esu
lt
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s
well
s
as
s
h
o
wn
in
Fig
u
r
e
9
(
b
)
.
Fas
t
an
d
f
r
eq
u
en
t
ch
an
g
es
in
th
e
lev
el
o
f
v
o
ltag
e
ar
e
r
ef
e
r
r
ed
to
as
v
o
ltag
e
f
lu
ctu
ati
o
n
.
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v
y
s
tr
ess
o
p
er
atio
n
s
,
m
o
d
if
icatio
n
s
to
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e
s
y
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tem
s
etu
p
,
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d
s
p
o
r
ad
ic
m
alf
u
n
ctio
n
s
ca
n
all
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u
s
e
f
lu
ctu
atio
n
s
th
at
ca
n
b
e
r
e
p
r
esen
ted
in
Fig
u
r
e
9
(
c)
.
(
a)
(
b
)
(
c)
Fig
u
r
e
9
.
An
al
y
s
is
o
f
(
a)
s
ag
,
(
b
)
s
well
,
an
d
(
c)
f
lu
ctu
atio
n
m
itig
atio
n
3
.
7
.
Co
m
pa
riso
n o
f
s
a
g
,
s
well
,
a
nd
f
luct
ua
t
io
n
Fig
u
r
e
1
0
s
h
o
ws
a
co
m
p
ar
ati
v
e
s
tu
d
y
with
ex
is
tin
g
o
p
tim
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za
tio
n
tech
n
iq
u
es
s
u
ch
as
PS
O,
GA,
an
d
m
o
th
f
lam
e
o
p
tim
izatio
n
(
MFO
)
to
ac
h
iev
e
o
p
tim
u
m
p
o
wer
q
u
ality
(
PQ)
in
a
h
y
b
r
id
p
o
wer
s
y
s
tem
in
teg
r
atin
g
b
atter
y
an
d
PV.
Fig
u
r
e
1
0
(
a)
s
h
o
ws
th
e
s
ag
co
m
p
ar
is
o
n
o
f
th
e
p
r
o
p
o
s
ed
HB
E
O
with
th
e
o
th
er
e
x
is
tin
g
o
p
tim
izatio
n
m
eth
o
d
s
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
ac
h
iev
es
a
r
e
d
u
ce
d
o
u
tp
u
t
v
o
ltag
e
o
f
3
.
8
KV
co
m
p
ar
ed
with
o
th
er
s
th
at
attain
ed
b
etter
ef
f
ic
ien
cy
.
T
h
e
v
o
ltag
e
r
ed
u
ctio
n
c
an
b
e
o
b
tain
e
d
d
u
r
in
g
th
e
s
well
co
m
p
ar
is
o
n
in
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ac
h
iev
es
1
4
V
as
m
o
r
e
c
o
n
v
er
g
en
ce
wh
en
co
m
p
ar
ed
to
th
e
o
th
e
r
o
p
tim
izatio
n
tech
n
iq
u
es
th
at
ca
n
b
e
s
h
o
wn
i
n
Fig
u
r
e
1
0
(
b
)
.
Similar
ly
,
th
e
o
u
tp
u
t
g
en
er
ate
d
in
t
h
e
v
o
ltag
e
r
e
d
u
ce
d
th
r
o
u
g
h
f
l
u
ctu
atio
n
o
n
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ac
h
iev
es a
1
5
V,
wh
en
co
m
p
ar
ed
with
o
th
er
ex
is
tin
g
r
esear
ch
as sh
o
wn
i
n
Fig
u
r
e
1
0
(
c)
,
an
d
also
attain
s
b
etter
o
p
tim
al
in
te
g
r
ity
.
Evaluation Warning : The document was created with Spire.PDF for Python.