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5
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th
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r
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8
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er
ate
au
to
n
o
m
o
u
s
ly
b
y
is
o
latin
g
th
e
DC
s
id
e.
W
h
en
co
n
f
ig
u
r
ed
i
n
th
is
m
a
n
n
er
,
th
e
s
h
u
n
t
i
n
v
er
ter
p
er
f
o
r
m
s
as
a
s
tatic
s
y
n
ch
r
o
n
o
u
s
co
m
p
en
s
ato
r
(
STAT
C
OM
)
[
1
1
]
-
[
1
4
]
.
I
ts
m
ain
r
o
le
is
to
g
en
er
ate
o
r
ab
s
o
r
b
r
ea
ctiv
e
p
o
wer
in
o
r
d
er
to
r
eg
u
late
th
e
v
o
ltag
e
m
ag
n
itu
d
e
at
th
e
p
o
in
t
o
f
co
n
n
ec
tio
n
.
On
th
e
o
th
er
h
an
d
,
th
e
s
er
ies
in
v
er
ter
f
u
n
ctio
n
s
as
a
s
tat
ic
s
y
n
ch
r
o
n
o
u
s
s
er
ies
co
m
p
en
s
ato
r
(
SS
SC
)
.
I
t
i
s
r
esp
o
n
s
ib
le
f
o
r
g
en
er
atin
g
o
r
ab
s
o
r
b
in
g
r
ea
ctiv
e
p
o
wer
to
co
n
tr
o
l
t
h
e
cu
r
r
en
t
f
lo
w
a
n
d
s
u
b
s
eq
u
en
tly
r
eg
u
late
t
h
e
p
o
wer
f
lo
w
o
n
t
h
e
tr
a
n
s
m
is
s
io
n
lin
e
[
1
5
]
-
[
1
8
]
.
T
h
is
ar
r
an
g
em
e
n
t
en
s
u
r
es
th
at
th
e
v
o
ltag
e
an
d
p
o
wer
c
h
ar
ac
ter
is
tics
o
f
th
e
s
y
s
tem
a
r
e
ef
f
ec
tiv
ely
m
an
a
g
ed
wh
ile
ad
d
r
ess
in
g
p
o
wer
q
u
ality
is
s
u
es.
T
h
e
UPQC
o
f
f
er
s
th
e
ad
v
an
tag
e
o
f
s
ep
ar
ately
c
o
n
tr
o
lli
n
g
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
,
m
a
k
in
g
it
s
u
itab
le
f
o
r
im
p
r
o
v
in
g
p
o
wer
q
u
ality
.
I
n
t
h
is
p
r
o
p
o
s
ed
s
tu
d
y
,
a
two
-
b
u
s
s
y
s
tem
is
m
o
d
eled
an
d
s
im
u
lated
with
th
e
in
clu
s
i
o
n
o
f
UPQC
.
Ad
d
itio
n
ally
,
a
1
4
-
b
u
s
s
y
s
tem
i
s
m
o
d
eled
an
d
s
im
u
lated
with
an
d
with
o
u
t
UPQC
.
T
h
e
in
v
esti
g
a
tio
n
o
f
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
r
ev
ea
ls
th
at
th
e
r
ea
l
p
o
wer
in
cr
ea
s
es
with
th
e
in
jectio
n
an
g
le,
w
h
ile
th
e
r
ea
c
tiv
e
p
o
wer
in
c
r
ea
s
es with
th
e
s
h
u
n
t v
o
ltag
e
i
n
jectio
n
[
1
9
]
-
[
2
5
]
.
Simu
lin
k
m
o
d
els
ar
e
d
ev
el
o
p
ed
f
o
r
t
h
r
ee
t
y
p
es
o
f
UPQC
:
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M
)
in
v
e
r
ter
-
b
ased
UPQC
,
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
(
SVM
)
in
v
er
ter
-
b
ased
UPQC
,
an
d
m
u
ltil
ev
el
in
v
er
ter
(
MLI
)
-
b
ased
UPQC
.
T
h
e
r
esu
lts
f
r
o
m
th
ese
th
r
ee
ca
s
es
ar
e
co
m
p
ar
ed
.
Fu
r
th
er
m
o
r
e,
th
e
co
n
ce
p
t
o
f
m
u
lti
p
le
an
d
d
is
tr
ib
u
ted
d
y
n
am
ic
v
o
ltag
e
r
esto
r
er
(
D
VR
)
is
in
tr
o
d
u
ce
d
to
en
h
a
n
ce
th
e
v
o
ltag
e
p
r
o
f
ile
o
f
th
e
s
y
s
tem
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws
:
s
ec
tio
n
1
d
escr
ib
es
th
e
in
t
r
o
d
u
ctio
n
,
s
ec
tio
n
2
d
escr
ib
es
th
e
m
eth
o
d
o
lo
g
y
,
s
ec
tio
n
3
p
r
esen
ts
th
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
s
,
an
d
s
ec
tio
n
4
p
r
o
v
id
es th
e
co
n
clu
s
io
n
.
2.
M
E
T
H
O
DO
L
O
G
Y
T
h
e
ab
o
v
e
liter
atu
r
e
d
o
es
n
o
t
d
ea
l
with
m
o
d
eli
n
g
1
4
an
d
30
-
bus
s
y
s
tem
s
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
.
T
h
is
wo
r
k
p
r
o
p
o
s
es
m
o
d
els
f
o
r
1
4
an
d
30
-
bus
s
y
s
tem
s
em
p
lo
y
in
g
UPQC
.
T
h
e
ef
f
ec
ts
o
n
r
ea
l
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
an
d
v
o
ltag
e
ar
e
in
v
esti
g
ated
.
T
h
is
wo
r
k
d
ea
ls
with
th
e
co
n
tr
o
l
o
f
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
in
p
o
wer
s
y
s
tem
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
.
A
u
n
if
ied
p
o
wer
f
lo
w
c
o
n
tr
o
ller
(
UPQC
)
is
a
s
h
u
n
t
-
s
er
ies
ty
p
e
co
n
v
er
ter
u
s
ed
f
o
r
im
p
r
o
v
in
g
p
o
wer
q
u
ality
.
T
h
e
UPQC
co
n
tr
o
ls
th
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
s
b
y
v
a
r
y
in
g
th
e
f
ir
in
g
an
g
le
o
f
th
e
r
ec
tifie
r
an
d
in
v
er
ter
.
T
h
e
cir
cu
it
m
o
d
el
f
o
r
UPQC
i
s
d
ev
elo
p
ed
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
an
d
it
is
u
s
ed
f
o
r
s
im
u
latio
n
s
tu
d
ies
f
o
r
v
a
r
io
u
s
s
y
s
tem
s
.
Mu
ltil
ev
el
in
v
er
ter
-
b
ased
UPQC
is
n
o
t p
r
esen
t
in
th
e
liter
atu
r
e.
SVM
-
b
ased
UPQC
s
y
s
tem
d
o
es
n
o
t
ex
is
t
in
th
e
li
ter
atu
r
e.
T
h
is
wo
r
k
p
r
o
p
o
s
es
SVM
-
b
ased
UPQ
C
s
y
s
tem
an
d
m
u
ltil
ev
el
in
v
er
ter
f
o
r
th
e
co
n
tr
o
l
o
f
p
o
wer
.
T
h
e
co
n
ce
p
t
o
f
UPQC
wi
th
d
is
tr
ib
u
ted
DVR
i
s
p
r
o
p
o
s
ed
to
im
p
r
o
v
e
t
h
e
v
o
lta
g
e
q
u
ality
.
2
.
1
.
L
it
er
a
t
ure
s
urv
ey
Kim
an
d
Su
l
[
1
]
d
is
cu
s
s
ed
th
e
co
n
tr
o
l
o
f
co
m
p
e
n
s
atio
n
v
o
ltag
es
in
d
y
n
am
ic
v
o
ltag
e
r
esto
r
er
s
(
DVRs
)
.
T
h
ey
an
aly
ze
d
th
e
p
o
wer
cir
cu
it
o
f
a
DVR
s
y
s
te
m
to
estab
lis
h
co
n
tr
o
l
lim
itati
o
n
s
an
d
tar
g
ets
f
o
r
co
m
p
en
s
atio
n
v
o
ltag
e
c
o
n
tr
o
l.
T
h
ey
d
ev
elo
p
e
d
a
c
o
m
b
in
e
d
f
ee
d
f
o
r
war
d
an
d
s
tate
f
ee
d
b
ac
k
co
n
tr
o
l
s
tr
u
ctu
r
e
f
o
r
th
e
co
m
p
en
s
atio
n
v
o
ltag
e
s
,
co
n
s
id
er
in
g
co
n
tr
o
l
d
ela
y
an
d
clo
s
ed
-
l
o
o
p
d
am
p
i
n
g
f
ac
to
r
.
Gao
et
a
l
.
[
2
]
an
aly
ze
d
Z
-
s
o
u
r
ce
in
v
er
ter
m
o
d
u
latio
n
a
n
d
d
em
o
n
s
tr
ated
h
o
w
co
n
v
e
n
tio
n
al
PW
M
s
tr
ateg
ies
f
o
r
v
o
ltag
e
s
o
u
r
ce
in
v
er
te
r
s
ca
n
b
e
m
o
d
if
ied
f
o
r
Z
-
s
o
u
r
ce
in
v
er
ter
s
.
T
h
ey
v
e
r
if
ied
th
eir
th
eo
r
etic
al
an
d
m
o
d
u
latio
n
co
n
ce
p
ts
th
r
o
u
g
h
s
im
u
latio
n
s
an
d
ex
p
er
im
en
ts
.
Vilath
g
am
u
wa
et
a
l
.
[
3
]
p
r
o
p
o
s
ed
a
n
ew
to
p
o
lo
g
y
b
ased
o
n
th
e
Z
-
s
o
u
r
ce
in
v
er
ter
f
o
r
DVRs
to
en
h
an
ce
v
o
ltag
e
r
esto
r
atio
n
.
T
h
e
p
r
o
p
o
s
ed
to
p
o
l
o
g
y
u
tili
z
ed
th
e
s
h
o
o
t
-
th
r
o
u
g
h
ca
p
ab
ili
ty
o
f
th
e
in
v
er
ter
to
en
s
u
r
e
a
co
n
s
tan
t
DC
v
o
ltag
e
ac
r
o
s
s
th
e
DC
lin
k
,
im
p
r
o
v
in
g
en
er
g
y
u
tili
za
tio
n
.
T
h
e
s
y
s
tem
an
d
its
co
n
tr
o
ller
wer
e
test
ed
th
r
o
u
g
h
s
im
u
latio
n
s
an
d
ex
p
e
r
im
en
ts
,
d
e
m
o
n
s
tr
atin
g
ef
f
ec
tiv
e
c
o
m
p
e
n
s
atio
n
o
f
v
o
ltag
e
s
ag
s
wh
ile
f
u
lly
u
tili
zin
g
s
to
r
e
d
e
n
er
g
y
.
R
am
asam
y
et
a
l
.
[
4
]
p
r
esen
ted
a
DVR
s
y
s
tem
u
s
in
g
th
r
ee
-
d
im
en
s
io
n
al
s
p
ac
e
v
ec
to
r
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
3
D
-
SVPW
M)
.
T
h
eir
co
n
tr
o
l
s
ch
em
e
m
itig
ated
ze
r
o
s
eq
u
e
n
ce
co
m
p
o
n
en
ts
b
y
in
clu
d
in
g
a
ze
r
o
-
ax
is
in
ad
d
itio
n
to
th
e
co
n
v
en
tio
n
al
alp
h
a
-
b
eta
ax
es.
T
h
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
o
f
f
er
ed
v
er
s
atile
v
o
ltag
e
s
ag
c
o
m
p
en
s
atio
n
f
o
r
f
au
lt
-
af
f
ec
ted
th
r
ee
-
p
h
ase
p
o
wer
s
y
s
tem
s
.
Om
ar
an
d
R
ah
im
[
5
]
d
is
cu
s
s
ed
DVR
co
n
tr
o
l
b
ased
o
n
d
-
q
t
r
an
s
f
o
r
m
atio
n
.
T
h
ey
p
r
esen
te
d
a
co
n
tr
o
l
s
y
s
tem
th
at
u
tili
ze
d
a
s
ca
led
er
r
o
r
o
f
th
e
DVR'
s
s
o
u
r
ce
s
id
e
an
d
its
r
ef
er
en
ce
f
o
r
s
ag
/s
well
co
r
r
ec
tio
n
.
T
h
e
DVR
p
r
o
v
id
ed
q
u
ick
co
m
p
e
n
s
atio
n
,
ex
ce
llen
t
v
o
ltag
e
r
eg
u
l
atio
n
,
an
d
c
o
u
ld
h
a
n
d
le
b
alan
ce
d
an
d
u
n
b
alan
ce
d
s
itu
atio
n
s
ef
f
ec
tiv
ely
.
L
am
et
a
l
.
[
6
]
a
d
d
r
ess
ed
v
o
ltag
e
s
well
an
d
o
v
e
r
v
o
ltag
e
c
o
m
p
e
n
s
atio
n
in
a
d
io
d
e
b
r
id
g
e
r
ec
tifie
r
-
s
u
p
p
o
r
ted
tr
a
n
s
f
o
r
m
e
r
-
less
co
u
p
led
DVR.
T
h
ey
p
r
o
p
o
s
ed
a
n
o
v
el
u
n
id
ir
ec
tio
n
al
p
o
wer
f
l
o
w
co
n
tr
o
l
alg
o
r
ith
m
th
at
e
f
f
ec
tiv
ely
s
u
p
p
r
ess
ed
th
e
co
n
tin
u
o
u
s
r
is
e
in
th
e
DC
lin
k
v
o
ltag
e
d
u
r
in
g
s
wells.
Simu
latio
n
an
d
ex
p
er
im
en
tal
r
esu
lts
f
o
r
u
n
b
al
an
ce
d
v
o
ltag
e
s
well
co
m
p
en
s
a
tio
n
wer
e
p
r
esen
ted
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Op
tima
l d
esig
n
o
f th
r
ee
-
p
h
a
s
e
s
o
la
r
P
V
in
teg
r
a
ted
u
n
ified
p
o
w
er q
u
a
lity
… (
Yo
g
esh
S
.
P
a
w
a
r
)
3
B
en
ac
h
aib
a
an
d
Fer
d
i
[
7
]
d
is
cu
s
s
ed
DVR
p
r
in
cip
les
an
d
v
o
l
tag
e
r
esto
r
atio
n
m
eth
o
d
s
at
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
.
T
h
ey
h
ig
h
lig
h
ted
th
e
ef
f
ec
tiv
en
ess
an
d
ef
f
icien
cy
o
f
DVRs
in
s
o
lv
in
g
v
o
ltag
e
s
ag
an
d
s
well
p
r
o
b
lem
s
,
em
p
h
asizin
g
th
eir
lo
wer
co
s
t,
s
m
aller
s
ize,
an
d
f
ast
d
y
n
am
ic
r
esp
o
n
s
e
.
No
u
r
an
d
Hela
l
[
8
]
p
r
esen
ted
a
DVR
b
ased
o
n
a
f
ir
in
g
co
n
tr
o
l
s
tr
ateg
y
f
o
r
a
th
r
ee
s
ix
-
s
witch
v
o
ltag
e
s
o
u
r
ce
i
n
v
er
ter
(
VSI
)
.
T
h
eir
s
tr
ateg
y
co
m
b
i
n
ed
1
8
0
an
d
1
2
0
co
n
d
u
ctio
n
m
o
d
es
to
g
en
e
r
ate
a
n
ew
o
p
e
r
atin
g
m
o
d
e,
r
esu
ltin
g
in
a
s
ev
en
-
lev
el,
1
2
-
s
tep
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
r
esem
b
lin
g
a
s
in
u
s
o
id
al
s
h
ap
e.
Naid
u
[
9
]
d
escr
ib
e
d
th
e
cl
o
s
ed
-
lo
o
p
co
n
t
r
o
l
o
f
a
f
o
u
r
-
leg
v
o
ltag
e
s
o
u
r
ce
c
o
n
v
e
r
ter
(
V
SC
)
-
b
ased
DVR.
T
h
ey
u
s
ed
a
weig
h
ted
,
r
ec
u
r
s
iv
e,
least
s
q
u
ar
e
esti
m
at
o
r
to
r
eso
lv
e
th
e
th
r
ee
-
p
h
ase
in
p
u
t
v
ar
iab
les
in
to
p
o
s
itiv
e,
n
eg
ativ
e,
an
d
ze
r
o
s
eq
u
en
ce
co
m
p
o
n
en
ts
.
T
h
e
y
test
ed
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
DVR
th
r
o
u
g
h
s
im
u
latio
n
s
an
d
ex
p
e
r
im
en
ts
.
Ku
m
ar
a
n
d
Mish
r
a
[
1
0
]
p
r
o
p
o
s
ed
a
f
ilter
s
tr
u
ctu
r
e
to
im
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
a
s
witch
in
g
b
an
d
co
n
tr
o
ller
-
b
ased
DVR.
T
h
ey
p
r
esen
ted
th
e
f
ilter
s
tr
u
ctu
r
e
an
d
an
ad
ap
t
iv
e
b
an
d
co
n
t
r
o
ller
f
o
r
th
e
DVR,
h
ig
h
lig
h
tin
g
th
e
f
ast
d
y
n
am
ic
r
esp
o
n
s
e,
r
o
b
u
s
tn
ess
,
an
d
ea
s
e
o
f
im
p
lem
en
tatio
n
.
T
h
e
p
r
o
p
o
s
e
d
ap
p
r
o
ac
h
was v
alid
ated
th
r
o
u
g
h
p
o
wer
s
y
s
tem
s
co
m
p
u
ter
aid
ed
d
esig
n
(
PS
C
AD
)
s
im
u
latio
n
s
tu
d
ies
.
2
.
2
.
B
a
s
ic
c
ircuit
o
f
UP
Q
C
T
h
e
u
n
if
ie
d
p
o
we
r
f
lo
w
c
o
n
tr
o
ller
(
UPQC
)
is
co
m
p
o
s
ed
o
f
two
s
witch
in
g
co
n
v
er
ter
s
,
s
p
ec
if
ically
v
o
ltag
e
-
s
o
u
r
ce
in
v
e
r
ter
s
,
as
d
e
p
icted
in
Fig
u
r
e
1
.
T
h
ese
in
v
e
r
ter
s
,
r
ef
er
r
ed
t
o
as
"Co
n
v
er
ter
1
"
a
n
d
"Co
n
v
er
te
r
2
"
ar
e
s
h
o
wn
in
Fig
u
r
e
1
an
d
o
p
er
ate
u
s
in
g
a
s
h
ar
ed
DC
lin
k
p
r
o
v
id
e
d
b
y
a
DC
s
to
r
ag
e
ca
p
ac
ito
r
.
T
h
is
co
n
f
ig
u
r
atio
n
f
u
n
ctio
n
s
as
a
n
id
ea
l
AC
-
to
-
AC
p
o
wer
co
n
v
e
r
ter
,
allo
win
g
r
ea
l
p
o
wer
to
f
l
o
w
b
id
ir
ec
tio
n
ally
b
etwe
en
th
e
AC
ter
m
in
als
o
f
th
e
two
in
v
er
ter
s
.
E
ac
h
i
n
v
er
t
er
ca
n
in
d
e
p
en
d
e
n
tly
g
e
n
er
ate
o
r
ab
s
o
r
b
r
ea
ctiv
e
p
o
wer
at
its
r
esp
ec
tiv
e
AC
o
u
t
p
u
t te
r
m
in
al.
Fig
u
r
e
1
s
h
o
ws UPQC
co
n
n
ec
ted
to
a
tr
an
s
m
i
s
s
io
n
lin
e.
2.
3
.
Co
ntr
o
l
s
t
ra
t
eg
y
f
o
r
s
hu
nt
co
nv
er
t
er
T
h
e
m
ea
s
u
r
ed
lo
ad
cu
r
r
en
t
is
co
n
v
er
ted
in
to
a
s
y
n
ch
r
o
n
o
u
s
d
u
o
-
r
e
f
er
en
ce
s
y
s
tem
.
W
ith
th
is
tr
an
s
f
o
r
m
atio
n
,
th
e
u
n
d
er
ly
i
n
g
p
o
s
itiv
e
-
s
eq
u
en
ce
co
m
p
o
n
e
n
ts
co
n
v
er
ted
to
d
-
an
d
q
-
ax
is
DC
am
p
litu
d
es
ca
n
b
e
ea
s
ily
ex
tr
ac
te
d
b
y
a
lo
w
-
p
ass
f
ilter
(
L
PF
)
.
Fu
r
t
h
er
m
o
r
e,
all
h
ar
m
o
n
ic
co
m
p
o
n
e
n
ts
ar
e
tr
an
s
f
o
r
m
ed
in
to
AC
q
u
an
titi
es with
a
f
u
n
d
am
e
n
tal
f
r
eq
u
e
n
cy
s
h
if
t
[
3
]
.
T
h
e
s
h
u
n
t
co
m
p
en
s
ato
r
o
p
er
ates
at
m
ax
im
u
m
p
o
wer
a
n
d
d
r
aws
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
PV
s
y
s
tem
.
T
h
e
m
ax
im
u
m
p
o
we
r
p
o
i
n
t
tr
ac
k
in
g
(
MPPT)
al
g
o
r
ith
m
cr
ea
tes
a
DC
lin
k
v
o
ltag
e
r
ef
er
e
n
ce
f
o
r
UPQC
.
C
u
r
r
en
t
f
r
o
m
th
e
in
ter
m
ed
iate
cir
cu
it
is
tr
an
s
f
er
r
ed
t
o
th
e
n
etwo
r
k
b
y
elec
tr
icity
.
T
h
e
m
ain
s
cu
r
r
en
t
is
co
m
p
ar
ed
with
th
e
tar
g
et
cu
r
r
en
t
an
d
f
ed
t
o
th
e
h
y
s
ter
esis
co
n
tr
o
ller
.
A
h
y
s
ter
esis
co
n
t
r
o
ller
g
en
e
r
ates
th
e
g
ate
p
u
ls
e
f
o
r
th
e
s
h
u
n
t c
o
n
v
e
r
ter
[
8
]
.
Fig
u
r
e
2
d
ea
ls
with
th
e
co
n
tr
o
l stru
ctu
r
e
o
f
th
e
s
h
u
n
t c
o
m
p
en
s
ato
r
.
Fig
u
r
e
1
.
UPQC
co
n
n
ec
ted
t
o
a
tr
an
s
m
is
s
io
n
lin
e
2.
4.
Co
ntr
o
l o
f
s
er
ies co
m
pens
a
t
o
r
T
h
e
b
u
s
v
o
ltag
e
is
s
en
s
ed
a
n
d
co
n
v
er
ted
to
a
s
y
n
ch
r
o
n
o
u
s
d
q
0
r
e
f
er
en
ce
f
r
a
m
e.
Ser
ies
c
o
m
p
en
s
ato
r
co
n
tr
o
l
s
tr
ateg
ies
in
clu
d
e
p
r
e
-
em
b
ed
d
e
d
co
m
p
en
s
atio
n
,
co
m
m
o
n
-
m
o
d
e
co
m
p
en
s
atio
n
,
a
n
d
p
o
wer
-
o
p
tim
ize
d
co
m
p
en
s
atio
n
.
I
n
th
is
s
tu
d
y
,
th
e
s
er
ies
co
m
p
en
s
ato
r
ap
p
lies
a
v
o
ltag
e
th
at
is
in
p
h
ase
with
th
e
s
u
p
p
ly
v
o
ltag
e,
wh
ich
h
elp
s
t
o
p
r
o
d
u
ce
th
e
m
in
im
u
m
v
o
ltag
e
a
p
p
lied
to
th
e
s
er
ies
co
m
p
en
s
ato
r
.
Fig
u
r
e
3
s
h
o
ws
th
e
c
o
n
tr
o
l
s
tr
u
ctu
r
e
o
f
th
e
s
er
ies co
m
p
en
s
ato
r
.
T
h
e
b
ase
co
m
p
o
n
e
n
t o
f
th
e
PC
C
v
o
ltag
e
was e
x
tr
ac
ted
u
s
in
g
th
e
PLL
an
d
u
s
ed
to
g
en
e
r
ate
r
ef
e
r
en
ce
ax
e
s
in
th
e
d
-
q
-
0
d
o
m
ain
.
T
h
e
r
e
f
er
en
ce
lo
ad
v
o
ltag
e
is
g
e
n
er
at
ed
u
s
in
g
p
h
ase
an
d
f
r
eq
u
e
n
cy
d
etec
tio
n
o
f
t
h
e
PC
C
v
o
ltag
e
o
b
tain
ed
with
th
e
P
L
L
.
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
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
1
-
1
3
4
T
h
e
PC
C
v
o
ltag
e
an
d
th
e
lo
a
d
v
o
ltag
e
ar
e
tr
an
s
f
o
r
m
ed
in
t
o
th
e
d
-
q
-
0
d
o
m
ain
.
T
h
e
lo
a
d
r
ef
er
en
ce
v
o
ltag
e
m
u
s
t
b
e
in
p
h
ase
with
th
e
PC
C
v
o
ltag
e,
s
o
th
e
p
ea
k
lo
ad
r
ef
er
en
ce
v
o
ltag
e
is
th
e
v
alu
e
o
f
th
e
d
-
a
x
is
co
m
p
o
n
en
t
o
f
th
e
l
o
ad
r
ef
er
en
ce
v
o
ltag
e.
T
h
e
q
-
ax
is
co
m
p
o
n
en
t
is
k
ep
t
at
ze
r
o
.
T
h
e
c
h
an
g
e
b
etwe
en
t
h
e
lo
ad
r
ef
er
en
ce
v
o
ltag
e
an
d
th
e
PC
C
v
o
ltag
e
p
r
o
d
u
ce
s
th
e
r
ef
e
r
en
c
e
v
o
ltag
e
f
o
r
th
e
s
er
ies
co
m
p
e
n
s
ato
r
.
T
h
e
ch
a
n
g
e
b
etwe
en
th
e
lo
ad
v
o
ltag
e
an
d
th
e
PC
C
v
o
ltag
e
p
r
o
d
u
ce
s
th
e
ac
tu
al
s
er
ies
co
m
p
en
s
ato
r
v
o
ltag
e.
T
h
e
ch
a
n
g
e
b
etwe
en
th
e
r
ef
e
r
en
ce
v
o
ltag
e
an
d
th
e
ac
tu
al
s
er
ies
co
m
p
en
s
ato
r
v
o
ltag
e
is
f
e
d
to
th
e
PI
c
o
n
tr
o
ller
to
g
e
n
er
ate
th
e
ap
p
r
o
p
r
iate
r
ef
e
r
en
ce
s
ig
n
al.
T
h
ese
s
ig
n
als
ar
e
c
o
n
v
e
r
ted
to
t
h
e
AB
C
d
o
m
ain
an
d
f
ed
th
r
o
u
g
h
a
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
v
o
lt
ag
e
r
e
g
u
lato
r
to
g
en
er
ate
a
s
u
i
tab
le
g
ate
s
ig
n
al
f
o
r
th
e
s
er
ies
co
m
p
en
s
ato
r
[
1
5
]
.
Fig
u
r
e
3
s
h
o
ws th
e
c
o
n
tr
o
l str
u
ctu
r
e
o
f
th
e
s
er
ies co
m
p
e
n
s
ato
r
.
Fig
u
r
e
2
.
C
o
n
tr
o
l stru
ctu
r
e
o
f
s
h
u
n
t c
o
m
p
e
n
s
ato
r
Fig
u
r
e
3
.
C
o
n
tr
o
l stru
ctu
r
e
o
f
s
er
ies co
m
p
en
s
ato
r
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
th
r
ee
-
p
h
ase
s
y
s
tem
is
d
esig
n
ed
f
o
r
th
e
PV
-
B
E
SS
-
UPQC
m
o
d
el.
T
h
e
PV
-
B
E
SS
-
UPQ
C
co
m
p
r
is
es
o
f
s
er
ies
an
d
s
h
u
n
t
APF
co
m
p
en
s
ato
r
lin
k
ed
with
DC
-
lin
k
s
p
lit
ca
p
ac
ito
r
.
T
h
e
b
atter
y
an
d
th
e
PV
ar
r
ay
a
r
e
lin
k
ed
p
ar
allelly
t
o
th
e
DC
-
lin
k
.
T
h
e
PV
is
lin
k
ed
th
r
o
u
g
h
a
b
o
o
s
t
co
n
v
er
t
er
to
th
e
DC
-
lin
k
.
Mo
r
eo
v
er
,
th
e
B
E
SS
is
lin
k
ed
th
r
o
u
g
h
a
b
u
ck
-
b
o
o
s
t
co
n
v
er
t
er
to
th
e
DC
-
lin
k
.
T
h
e
s
er
ies
co
m
p
en
s
ato
r
w
o
r
k
s
lik
ea
co
n
tr
o
lled
v
o
ltag
e
s
o
u
r
ce
m
an
n
er
a
n
d
m
itig
ates
th
e
s
u
p
p
ly
v
o
ltag
e
s
ag
s
,
s
wells,
in
ter
r
u
p
tio
n
s
,
an
d
v
o
ltag
e
h
a
r
m
o
n
ic.
On
th
e
o
th
er
h
an
d
,
th
e
s
h
u
n
t
co
m
p
en
s
at
o
r
m
itig
ates
th
e
cu
r
r
en
t
h
ar
m
o
n
ics
f
o
r
t
h
e
lo
ad
.
B
o
th
th
e
s
er
ies
an
d
s
h
u
n
t
AP
F
co
m
p
en
s
ato
r
ar
e
attac
h
ed
th
r
o
u
g
h
in
ter
f
ac
in
g
in
d
u
cto
r
s
.
I
n
th
e
UPQC
s
y
s
tem
co
n
f
ig
u
r
atio
n
,
d
u
e
to
th
e
co
n
v
er
ter
s
witch
in
g
ac
tio
n
,
h
ar
m
o
n
ics
ar
e
g
en
er
ated
an
d
th
er
e
f
o
r
e
,
a
r
ip
p
le
f
ilter
is
u
tili
ze
d
to
f
ilter
o
u
t
h
ar
m
o
n
ics
.
T
h
e
s
er
ies
co
m
p
en
s
ato
r
u
s
es
a
s
er
ies
in
jectio
n
tr
an
s
f
o
r
m
er
to
in
s
er
t
v
o
ltag
e
to
th
e
g
r
id
.
I
n
th
is
wo
r
k
,
a
th
r
ee
-
p
h
ase
non
-
lin
ea
r
lo
a
d
is
u
tili
z
ed
.
T
h
e
PV
-
B
E
SS
-
UP
QC
d
esi
g
n
p
r
o
ce
d
u
r
e
s
tar
ts
with
th
e
ac
cu
r
ate
m
ea
s
u
r
e
m
en
t
o
f
PV
ar
r
ay
,
s
p
lit
ca
p
ac
ito
r
,
an
d
r
ef
e
r
en
ce
v
o
ltag
e
o
f
DC
-
lin
k
.
T
h
e
d
esig
n
o
f
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I
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g
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SS
N:
2252
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8
7
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2
Op
tima
l d
esig
n
o
f th
r
ee
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p
h
a
s
e
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o
la
r
P
V
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teg
r
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ted
u
n
ified
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o
w
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a
lity
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P
a
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5
th
e
s
h
u
n
t
co
m
p
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n
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ato
r
f
o
llo
ws
th
e
way
th
at
ap
ar
t
f
r
o
m
m
itig
atin
g
cu
r
r
e
n
t
h
ar
m
o
n
ics
it
co
n
tr
o
ls
th
e
p
ea
k
o
u
tp
u
t
p
o
wer
f
r
o
m
PV
ar
r
a
y
.
Fig
u
r
e
4
s
h
o
ws
MA
T
L
AB
s
im
u
latio
n
f
o
r
th
r
ee
p
h
ase
in
v
e
r
ter
in
teg
r
ated
FC
.
Fig
u
r
e
5
s
h
o
ws
th
r
ee
-
p
h
ase
g
r
id
v
o
ltag
e
a
n
d
c
u
r
r
en
t
f
o
r
in
te
g
r
ated
UPQC
.
Fig
u
r
e
6
s
h
o
ws
th
r
ee
p
h
ase
s
h
u
n
t
in
v
er
ter
v
o
ltag
e
an
d
s
h
u
n
t
in
v
er
ter
cu
r
r
en
t
f
o
r
in
teg
r
ated
UPQC
.
F
ig
u
r
e
7
s
h
o
ws
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o
m
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ar
is
o
n
b
etwe
en
g
r
id
v
o
ltag
e,
lo
a
d
v
o
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e,
a
n
d
v
o
ltag
e
i
n
jectio
n
f
o
r
in
te
g
r
ated
UPQC
.
Fig
u
r
e
8
s
h
o
ws
l
o
a
d
v
o
ltag
e
an
d
lo
ad
cu
r
r
en
t
b
ef
o
r
e
th
e
in
v
eter
in
te
g
r
ated
UPQC
.
Fig
u
r
e
9
s
h
o
ws
p
o
wer
-
v
o
ltag
e
c
u
r
v
e
o
f
PV
s
y
s
tem
f
o
r
d
if
f
er
e
n
t
ir
r
ad
ian
ce
an
d
p
o
wer
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cu
r
r
en
t
cu
r
v
e
o
f
PV sy
s
tem
f
o
r
d
i
f
f
er
e
n
t ir
r
ad
ian
ce
.
Fig
u
r
e
4
.
MA
T
L
AB
s
im
u
latio
n
f
o
r
t
h
r
ee
p
h
ase
in
v
er
ter
in
te
g
r
ated
FC
Fig
u
r
e
5
.
T
h
r
ee
-
p
h
ase
g
r
id
v
o
l
tag
e
an
d
c
u
r
r
en
t
f
o
r
i
n
teg
r
ated
UPQC
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I
SS
N
:
2
2
5
2
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8
7
9
2
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p
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n
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,
Vo
l.
1
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
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-
1
3
6
Fig
u
r
e
6
.
T
h
r
ee
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p
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ase
s
h
u
n
t in
v
er
ter
v
o
ltag
e
an
d
s
h
u
n
t in
v
er
t
er
cu
r
r
e
n
t f
o
r
in
teg
r
ated
UPQC
Fig
u
r
e
7
.
C
o
m
p
a
r
is
o
n
b
etwe
e
n
g
r
id
v
o
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lo
a
d
v
o
ltag
e
,
an
d
v
o
lta
g
e
i
n
jectio
n
f
o
r
in
te
g
r
ated
UPQC
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I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
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8
7
9
2
Op
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l d
esig
n
o
f th
r
ee
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p
h
a
s
e
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o
la
r
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ted
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n
ified
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o
w
er q
u
a
lity
… (
Yo
g
esh
S
.
P
a
w
a
r
)
7
Fig
u
r
e
8
.
L
o
ad
v
o
ltag
e
an
d
lo
a
d
cu
r
r
e
n
t b
ef
o
r
e
th
e
i
n
v
er
ter
i
n
teg
r
ated
UPQC
Fig
u
r
e
9
.
Po
wer
-
v
o
ltag
e
c
u
r
v
e
o
f
PV sy
s
tem
f
o
r
d
if
f
er
en
t i
r
r
ad
ian
ce
an
d
p
o
wer
-
cu
r
r
e
n
t
cu
r
v
e
o
f
PV sy
s
tem
f
o
r
d
if
f
er
en
t ir
r
ad
ian
ce
T
h
e
p
o
wer
v
s
v
o
ltag
e
cu
r
v
e
f
o
r
a
p
h
o
t
o
v
o
ltaic
(
PV)
ar
r
ay
d
escr
ib
es
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
o
u
tp
u
t
p
o
wer
an
d
th
e
o
p
er
at
in
g
v
o
ltag
e
o
f
th
e
a
r
r
ay
.
I
t
p
r
o
v
id
es
v
alu
ab
le
in
f
o
r
m
atio
n
ab
o
u
t
t
h
e
ar
r
ay
'
s
p
er
f
o
r
m
an
ce
u
n
d
er
d
if
f
e
r
en
t
c
o
n
d
itio
n
s
.
T
h
e
p
o
wer
v
s
v
o
lta
g
e
cu
r
v
e
ty
p
ically
ex
h
ib
its
a
ch
ar
ac
ter
is
tic
s
h
ap
e
k
n
o
wn
as
th
e
"
I
-
V
cu
r
v
e"
(
c
u
r
r
en
t
v
s
v
o
ltag
e
cu
r
v
e)
.
T
h
e
s
h
ap
e
o
f
th
e
p
o
wer
v
s
v
o
ltag
e
cu
r
v
e
d
ep
en
d
s
o
n
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I
SS
N
:
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2
5
2
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8
7
9
2
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p
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l.
1
5
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1
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r
ch
20
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3
8
v
ar
io
u
s
f
ac
to
r
s
,
in
clu
d
i
n
g
th
e
PV
m
o
d
u
le
tech
n
o
lo
g
y
,
te
m
p
er
atu
r
e,
s
h
ad
i
n
g
,
an
d
th
e
am
o
u
n
t
o
f
s
u
n
lig
h
t
h
itti
n
g
th
e
ar
r
ay
.
I
t
is
ty
p
ically
a
d
o
wn
war
d
-
s
lo
p
in
g
cu
r
v
e,
with
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
lo
ca
ted
at
a
s
p
ec
if
ic
v
o
ltag
e
an
d
cu
r
r
en
t
c
o
m
b
in
atio
n
.
B
y
an
aly
zin
g
th
e
p
o
wer
v
s
v
o
ltag
e
cu
r
v
e,
en
g
in
ee
r
s
an
d
s
y
s
tem
d
esig
n
er
s
ca
n
o
p
tim
ize
th
e
o
p
er
atio
n
o
f
th
e
PV
ar
r
ay
,
en
s
u
r
in
g
it
o
p
er
ates
at
o
r
n
ea
r
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
f
o
r
m
ax
im
u
m
en
e
r
g
y
co
n
v
er
s
io
n
ef
f
icien
cy
.
Fig
u
r
e
1
0
illu
s
tr
ates
th
e
PV
s
y
s
tem
o
u
t
p
u
t
with
r
esp
ec
t
to
tem
p
er
atu
r
e,
f
o
llo
we
d
b
y
th
e
o
v
er
all
PV p
o
wer
o
u
t
p
u
t d
ep
i
cted
in
Fig
u
r
e
1
1
.
T
h
e
c
o
r
r
esp
o
n
d
in
g
lo
a
d
d
em
an
d
is
p
r
esen
ted
in
Fig
u
r
e
1
2
,
w
h
ile
th
e
g
r
id
p
o
we
r
p
r
o
f
ile
is
s
h
o
wn
in
Fig
u
r
e
1
3
.
Fin
ally
,
Fig
u
r
e
1
4
d
is
p
lay
s
th
e
in
v
er
ter
p
o
wer
.
Fig
u
r
e
1
0
.
PV sy
s
tem
o
u
tp
u
t (
tem
p
er
atu
r
e)
Fig
u
r
e
1
1
.
PV sy
s
tem
o
u
tp
u
t (
Pp
v
,
I
p
v
,
Vp
v
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
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8
7
9
2
Op
tima
l d
esig
n
o
f th
r
ee
-
p
h
a
s
e
s
o
la
r
P
V
in
teg
r
a
ted
u
n
ified
p
o
w
er q
u
a
lity
… (
Yo
g
esh
S
.
P
a
w
a
r
)
9
Fig
u
r
e
1
2
.
L
o
ad
p
o
wer
Fig
u
r
e
1
3
.
Gr
id
p
o
wer
T
h
e
p
er
f
o
r
m
an
ce
o
f
a
PV a
r
r
ay
is
in
f
lu
en
ce
d
b
y
th
e
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
,
p
r
im
ar
ily
t
em
p
er
atu
r
e
an
d
ir
r
ad
ian
ce
(
am
o
u
n
t
o
f
s
u
n
lig
h
t)
.
Her
e'
s
a
d
escr
ip
ti
o
n
o
f
h
o
w
th
ese
f
ac
to
r
s
af
f
ec
t
th
e
PV
ar
r
ay
:
i)
T
em
p
er
atu
r
e:
T
h
e
tem
p
e
r
atu
r
e
o
f
th
e
PV
ar
r
ay
af
f
ec
ts
th
e
ef
f
icien
cy
an
d
p
o
we
r
o
u
tp
u
t
o
f
th
e
s
o
lar
ce
lls
.
Gen
er
ally
,
as
th
e
tem
p
er
atu
r
e
in
cr
ea
s
es,
th
e
ef
f
icien
c
y
o
f
t
h
e
s
o
lar
ce
lls
d
ec
r
ea
s
es.
T
h
is
is
b
ec
au
s
e
h
ig
h
e
r
tem
p
er
atu
r
es
ca
n
ca
u
s
e
an
in
cr
ea
s
e
in
th
e
in
ter
n
al
r
esis
tan
ce
o
f
th
e
ce
lls
an
d
r
e
d
u
ce
t
h
e
v
o
ltag
e
o
u
tp
u
t.
Ho
wev
er
,
th
e
d
ec
r
ea
s
e
in
ef
f
icien
cy
v
ar
ies
d
ep
en
d
in
g
o
n
th
e
s
p
ec
if
ic
tech
n
o
lo
g
y
an
d
d
esig
n
o
f
th
e
PV
m
o
d
u
les.
ii)
I
r
r
a
d
ian
ce
:
T
h
e
am
o
u
n
t
o
f
s
u
n
lig
h
t
o
r
ir
r
ad
ia
n
ce
d
ir
ec
tly
im
p
ac
ts
th
e
p
o
w
er
o
u
t
p
u
t
o
f
th
e
PV
ar
r
ay
.
Hig
h
er
lev
els
o
f
ir
r
a
d
ian
ce
r
esu
lt
in
in
c
r
ea
s
ed
p
o
wer
g
en
er
atio
n
,
wh
ile
lo
wer
le
v
els
o
f
ir
r
ad
ian
ce
lea
d
to
r
ed
u
ce
d
p
o
wer
o
u
tp
u
t.
PV
ar
r
ay
s
ty
p
ically
h
av
e
a
lin
ea
r
r
elatio
n
s
h
ip
b
etwe
en
i
r
r
ad
ian
ce
an
d
p
o
wer
o
u
tp
u
t,
m
ea
n
in
g
th
at
d
o
u
b
lin
g
th
e
ir
r
a
d
ian
ce
will r
o
u
g
h
ly
d
o
u
b
le
t
h
e
p
o
wer
o
u
tp
u
t.
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
5
,
No
.
1
,
Ma
r
ch
20
2
6
:
1
-
1
3
10
Fig
u
r
e
1
4
.
I
n
v
e
r
ter
p
o
wer
T
h
e
r
esu
lts
p
r
esen
ted
a
r
e
s
tu
d
ied
o
n
a
s
in
g
le
m
ac
h
in
e
i
n
f
i
n
ite
b
u
s
(
SMI
B
)
p
o
wer
n
etw
o
r
k
,
w
h
ich
r
ef
lects
s
u
itab
ilit
y
o
f
th
is
ap
p
r
o
ac
h
in
tu
n
in
g
UPQC
co
n
tr
o
l
p
ar
am
eter
s
an
d
is
also
ex
ten
d
ab
le
to
m
u
lti
-
ar
ea
s
y
s
tem
s
.
I
n
th
is
m
o
d
el
,
two
v
o
ltag
e
s
o
u
r
ce
s
ar
e
u
s
ed
t
o
r
e
p
r
esen
t
th
e
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
ts
o
f
t
h
e
PW
M
-
co
n
tr
o
lled
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
o
f
th
e
two
b
r
an
ch
es
in
th
e
UPQC
.
T
h
e
im
p
ed
an
ce
o
f
th
e
two
co
u
p
lin
g
tr
an
s
f
o
r
m
er
s
is
in
clu
d
ed
in
th
e
p
r
o
p
o
s
ed
m
o
d
el
,
a
n
d
th
e
lo
s
s
es
o
f
UPQC
d
ep
ict
th
e
v
o
ltag
e
s
o
u
r
ce
eq
u
iv
alen
t
cir
cu
it
o
f
UPQC
.
T
h
e
s
er
ie
s
in
jectio
n
b
r
an
ch
es
a
s
er
ies
in
jectio
n
v
o
ltag
e
s
o
u
r
ce
an
d
p
er
f
o
r
m
s
th
e
m
ain
f
u
n
ctio
n
s
o
f
c
o
n
tr
o
llin
g
p
o
we
r
f
lo
w
,
wh
ils
t
th
e
s
h
u
n
t
b
r
an
c
h
is
u
s
ed
to
p
r
o
v
i
d
e
r
ea
l
p
o
w
er
d
em
a
n
d
ed
b
y
th
e
s
er
ies
b
r
an
ch
an
d
th
e
lo
s
s
es
in
th
e
UPQC
.
Ho
wev
er
,
in
th
e
p
r
o
p
o
s
ed
m
o
d
el
,
th
e
f
u
n
ctio
n
o
f
r
ea
ctiv
e
co
m
p
en
s
atio
n
o
f
th
e
s
h
u
n
t b
r
a
n
ch
is
co
m
p
letely
n
eg
lecte
d
.
4.
CO
NCLU
SI
O
N
T
h
is
r
esear
ch
p
ap
e
r
in
tr
o
d
u
ce
s
th
e
n
ew
ca
p
ab
ilit
ies
o
f
p
e
r
f
o
r
m
an
ce
i
n
v
esti
g
atio
n
o
f
o
p
tim
al
d
esig
n
th
r
ee
-
p
h
ase
s
o
lar
PV
in
teg
r
at
ed
u
n
if
ie
d
p
o
wer
q
u
ality
co
n
d
itio
n
er
(
UPQC
)
as
a
h
y
b
r
i
d
r
en
ewa
b
le
e
n
er
g
y
d
ev
ice
with
en
er
g
y
m
an
ag
e
m
en
t
tech
n
iq
u
es.
T
h
e
s
im
u
latio
n
r
esu
lts
s
h
o
w
th
e
ef
f
icien
cy
o
f
th
e
p
o
wer
an
g
le
co
n
tr
o
l
an
d
th
e
e
f
f
icien
cy
o
f
th
e
d
is
tr
ib
u
tio
n
e
q
u
ip
m
e
n
t
f
il
ter
in
g
d
ev
ice
d
u
r
i
n
g
th
e
en
tir
e
UPQC
r
ed
u
ctio
n
test
.
T
h
is
ap
p
r
o
ac
h
also
en
s
u
r
es a
co
n
s
tan
t/re
q
u
ir
ed
lo
w
v
o
l
tag
e
o
f
h
ig
h
q
u
ality
.
T
h
is
d
o
c
u
m
en
t sh
o
ws h
o
w
to
ea
s
ily
tu
n
e
s
er
ial
an
d
p
ar
allel
APF
s
with
o
u
t
lo
s
in
g
th
e
ab
ilit
y
to
im
p
r
o
v
e
p
o
wer
q
u
ality
an
d
elim
in
ate
p
er
s
is
ten
t
cu
r
r
en
ts
.
T
h
is
s
ch
e
m
e
s
h
o
ws
th
at
a
s
m
all
in
d
ex
o
f
th
e
o
p
er
atin
g
lev
el
r
e
d
u
ce
s
th
e
m
ax
im
u
m
v
alu
e
o
f
v
ib
r
atio
n
ass
o
ciate
d
with
th
e
cu
r
r
en
t
p
o
s
itio
n
an
d
th
e
ef
f
ec
tiv
e
f
o
r
ce
s
d
r
awn
f
r
o
m
th
at
p
o
s
itio
n
,
an
d
r
esp
o
n
d
s
to
APF.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
t
h
e
r
esear
c
h
r
esu
lt
s
s
h
o
w
p
o
ten
tial
f
u
tu
r
e
ap
p
licatio
n
s
in
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
an
d
s
m
ar
t
g
r
id
s
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT
)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.