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d
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CC B
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SA
li
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.
C
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s
p
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A
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d
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AGC,
Facu
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Djilali B
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Un
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f
r
1.
I
NT
RO
D
UCT
I
O
N
E
lectr
icity
h
as
b
ec
o
m
e
in
cr
ea
s
in
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ly
in
teg
r
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to
m
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estab
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m
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E
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L
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C
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m
p
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,
wh
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in
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th
e
d
ev
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p
m
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t
o
f
s
team
-
p
o
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e
d
p
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wer
s
tatio
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s
o
n
Pear
l
Stre
et
i
n
New
Yo
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k
C
ity
u
n
d
er
t
h
e
lea
d
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s
h
ip
o
f
in
v
e
n
to
r
T
h
o
m
as
E
d
is
o
n
[1
]
,
[
2
]
.
O
v
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th
e
p
as
t
ce
n
tu
r
y
,
th
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h
as
b
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a
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r
k
ab
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s
u
r
g
e
in
b
o
th
th
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co
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s
u
m
p
tio
n
an
d
g
en
er
atio
n
o
f
elec
tr
icity
[
3
]
,
[
4
]
.
Fo
r
in
s
tan
ce
,
g
lo
b
al
elec
tr
icity
co
n
s
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m
p
tio
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as r
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h
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f
ig
u
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e
c
o
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tin
u
es to
g
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o
w
[
5
]
-
[
7
]
.
An
elec
tr
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p
o
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s
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s
tem
c
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m
p
r
is
es
th
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p
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ce
s
s
es
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f
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e
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er
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tr
an
s
m
is
s
io
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,
d
is
tr
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a
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d
en
d
-
u
s
e
o
f
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y
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v
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as
th
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f
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d
am
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s
.
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icity
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ically
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o
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d
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tr
alize
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g
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atin
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s
tatio
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an
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tr
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s
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ted
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ter
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ted
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m
is
s
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d
is
tr
ib
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tio
n
n
etwo
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k
s
to
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.
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th
e
tr
a
n
s
m
is
s
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p
h
ase,
p
o
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f
lo
w
—
r
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r
in
g
to
th
e
m
o
v
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n
t o
f
b
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ac
tiv
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p
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s
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is
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p
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m
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in
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y
s
tem
ef
f
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y
an
d
s
tab
ilit
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[
8
]
-
[
1
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]
.
Ov
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p
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s
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th
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la
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Evaluation Warning : The document was created with Spire.PDF for Python.
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I
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16
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3
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180
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a
d
v
e
n
t
o
f
r
ev
o
l
u
t
io
n
ar
y
d
e
v
i
ce
s
l
ik
e
e
lect
r
i
c
v
e
h
ic
les
an
d
d
is
t
r
i
b
u
te
d
g
e
n
e
r
a
ti
o
n
,
h
e
r
al
d
i
n
g
a
n
ew
e
r
a
i
n
w
h
i
ch
t
h
e
p
o
wer
s
y
s
t
em
is
i
n
t
r
i
ca
t
el
y
i
n
te
r
t
win
ed
w
it
h
d
iv
er
s
e
an
d
d
e
ce
n
t
r
a
liz
e
d
s
o
u
r
c
es
o
f
en
er
g
y
.
T
h
e
d
y
n
a
m
i
c
e
v
o
l
u
ti
o
n
o
f
t
h
e
e
n
e
r
g
y
la
n
d
s
c
ap
e
c
o
n
ti
n
u
es
to
r
esh
a
p
e
p
o
we
r
d
y
n
am
ics
,
wit
h
th
e
s
m
ar
t
g
r
i
d
p
a
r
a
d
i
g
m
s
t
an
d
i
n
g
o
u
t
as
a
test
am
en
t
t
o
t
h
is
o
n
g
o
i
n
g
t
r
a
n
s
f
o
r
m
at
io
n
.
I
n
co
n
t
r
as
t
t
o
t
h
e
tr
ad
iti
o
n
al
m
o
d
el
,
wh
er
e
p
o
we
r
f
o
ll
o
we
d
a
u
n
i
d
i
r
e
cti
o
n
al
p
at
h
f
r
o
m
g
en
e
r
a
tio
n
t
o
tr
an
s
m
is
s
i
o
n
to
d
is
t
r
i
b
u
ti
o
n
,
t
h
e
co
n
t
em
p
o
r
ar
y
g
r
i
d
o
p
er
at
es
o
n
a
m
o
r
e
a
g
il
e
a
n
d
r
es
p
o
n
s
i
v
e
p
lat
f
o
r
m
.
T
h
is
s
h
i
f
t
h
as
b
e
en
p
a
r
ti
c
u
la
r
l
y
p
r
o
n
o
u
n
ce
d
o
v
e
r
t
h
e
las
t d
e
ca
d
e
[
1
5
]
,
as a
d
v
an
c
em
e
n
ts
i
n
tec
h
n
o
l
o
g
y
h
a
v
e
f
a
c
ilit
a
te
d
b
i
d
i
r
e
cti
o
n
a
l
p
o
we
r
f
l
o
w
,
u
s
h
e
r
i
n
g
in
a
l
ev
e
l
o
f
f
le
x
i
b
il
it
y
a
n
d
a
d
a
p
t
a
b
ili
ty
p
r
e
v
i
o
u
s
l
y
u
n
s
e
e
n
i
n
t
h
e
e
n
e
r
g
y
s
e
ct
o
r
[
1
6
]
-
[
1
8
]
.
Dis
tr
ib
u
ted
g
en
er
atio
n
(
DG)
h
as
b
ec
o
m
e
a
p
i
v
o
tal
elem
e
n
t
in
th
e
tr
an
s
f
o
r
m
atio
n
o
f
t
h
e
elec
tr
ical
p
o
wer
s
y
s
tem
,
p
ar
ticu
lar
ly
with
in
th
e
d
is
tr
ib
u
tio
n
s
ec
to
r
.
C
h
ar
ac
ter
ized
b
y
th
e
in
te
g
r
atio
n
o
f
s
m
all
to
m
ed
iu
m
-
s
ca
le
g
e
n
er
atio
n
u
n
it
s
o
f
ten
b
ased
o
n
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
s
u
ch
as
s
o
lar
a
n
d
win
d
[
1
9
]
,
DG
is
in
cr
ea
s
in
g
ly
co
n
n
ec
ted
d
ir
ec
tly
to
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
[
2
0
]
-
[
2
2
]
.
T
h
is
s
h
if
t
alig
n
s
with
in
ter
n
atio
n
a
l
s
u
s
tain
ab
ilit
y
in
itiativ
es,
in
clu
d
in
g
th
e
Ky
o
to
Pro
to
co
l,
wh
i
ch
ad
v
o
ca
tes
f
o
r
th
e
r
e
d
u
ctio
n
o
f
g
r
ee
n
h
o
u
s
e
g
as
em
is
s
io
n
s
an
d
th
e
p
r
o
m
o
tio
n
o
f
clea
n
en
e
r
g
y
tech
n
o
l
o
g
ies
to
ad
d
r
ess
clim
ate
ch
an
g
e
[
2
3
]
,
[
2
4
]
.
T
h
e
wid
esp
r
ea
d
d
e
p
lo
y
m
e
n
t
o
f
g
r
id
-
co
n
n
ec
ted
DG
u
n
its
h
as
s
ig
n
if
ican
tly
alter
ed
tr
ad
itio
n
al
p
o
wer
f
lo
w
p
atter
n
s
,
tr
an
s
itio
n
in
g
f
r
o
m
a
ce
n
tr
alize
d
an
d
u
n
id
ir
ec
tio
n
al
m
o
d
el
to
a
m
o
r
e
d
ec
en
tr
alize
d
an
d
d
y
n
am
ic
co
n
f
ig
u
r
atio
n
.
T
h
is
ev
o
lu
tio
n
e
n
h
an
ce
s
g
r
id
r
esil
ien
ce
an
d
s
u
p
p
o
r
ts
o
v
e
r
ar
ch
in
g
g
o
als
r
elate
d
to
en
v
ir
o
n
m
en
tal
p
r
o
tectio
n
an
d
s
u
s
tain
ab
le
r
eso
u
r
ce
m
an
a
g
em
en
t
[
2
5
]
-
[
2
7
]
.
E
n
s
u
r
in
g
p
o
wer
q
u
ality
is
a
p
ar
am
o
u
n
t
c
o
n
ce
r
n
,
esp
ec
i
ally
wh
en
ca
ter
i
n
g
to
lar
g
e
in
d
u
s
tr
ial
co
n
s
u
m
er
s
.
T
h
e
p
o
wer
s
ec
to
r
h
as
b
ee
n
u
n
d
er
g
o
i
n
g
r
ef
o
r
m
s
aim
ed
at
ac
h
iev
in
g
its
r
estru
ct
u
r
in
g
g
o
als.
Hig
h
-
p
o
wer
,
h
i
g
h
-
v
o
ltag
e
co
n
v
er
ter
s
lik
e
u
n
if
ied
p
o
wer
f
lo
w
co
n
t
r
o
ller
(
UPFC
)
an
d
in
ter
lin
e
p
o
wer
f
lo
w
co
n
tr
o
ller
(
I
PF
C
)
h
av
e
b
ee
n
tr
a
d
itio
n
all
y
em
p
lo
y
ed
in
tr
a
n
s
m
is
s
io
n
an
d
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
[
2
8
]
,
[
2
9
]
.
Ho
wev
er
,
a
n
ew
en
tr
an
t
in
th
e
f
lex
ib
le
AC
tr
an
s
m
is
s
io
n
s
y
s
tem
s
(
FAC
T
S
)
f
am
ily
,
th
e
d
is
tr
ib
u
ted
f
lex
i
b
le
AC
tr
an
s
m
is
s
io
n
s
y
s
tem
(
DFAC
T
S)
[
3
0
]
,
[
3
1
]
,
h
as
g
a
r
n
er
e
d
atten
tio
n
d
u
e
to
its
v
ar
i
o
u
s
ad
v
an
tag
es
o
v
er
co
n
v
en
tio
n
al
FAC
T
S
d
ev
ices.
DFAC
T
S
o
f
f
er
s
co
s
t
-
ef
f
icien
cy
,
e
n
h
an
ce
d
r
eliab
ilit
y
,
an
d
im
p
r
o
v
e
d
p
o
we
r
q
u
ality
co
m
p
ar
ed
to
its
p
r
ed
e
ce
s
s
o
r
s
,
esp
ec
ially
UPFC
.
W
h
ile
UPFC
an
d
I
PF
C
ar
e
s
till
u
tili
ze
d
in
p
r
ac
tical
ap
p
licatio
n
s
,
p
h
ase
-
s
h
if
tin
g
tr
an
s
f
o
r
m
er
s
,
with
lim
ited
co
n
t
r
o
l
ca
p
a
b
ilit
ies,
ar
e
o
f
ten
ch
o
s
en
f
o
r
ec
o
n
o
m
ic
r
ea
s
o
n
s
wh
en
p
o
wer
co
n
t
r
o
l d
em
an
d
s
ar
e
h
i
g
h
[
3
2
]
-
[
3
4
]
.
I
n
th
e
c
o
n
tex
t
o
f
FAC
T
S,
th
e
d
is
tr
ib
u
ted
p
o
wer
f
lo
w
c
o
n
tr
o
ller
(
DPFC
)
r
ep
r
esen
ts
a
n
o
tab
le
ad
v
an
ce
m
e
n
t.
Der
iv
ed
f
r
o
m
th
e
UPF
C
,
th
e
DP
FC
d
if
f
er
en
tiates
it
s
elf
b
y
elim
in
atin
g
th
e
DC
lin
k
b
etwe
en
th
e
s
h
u
n
t
an
d
s
er
ies
co
n
v
er
te
r
s
.
I
ts
co
r
e
in
n
o
v
atio
n
lies
in
th
e
d
is
tr
ib
u
tio
n
o
f
s
in
g
le
-
p
h
ase
s
er
ies
co
n
v
er
ter
s
alo
n
g
th
e
tr
an
s
m
is
s
io
n
lin
e,
co
llectiv
ely
o
p
e
r
atin
g
as
a
d
is
tr
ib
u
ted
s
tatic
s
er
ies
co
m
p
en
s
ato
r
.
T
h
is
co
n
f
ig
u
r
atio
n
m
ain
tain
s
th
e
p
o
wer
f
l
o
w
co
n
tr
o
l
f
u
n
ctio
n
alities
o
f
th
e
UPFC
wh
ile
o
f
f
er
in
g
im
p
r
o
v
ed
r
eliab
ilit
y
,
en
h
an
ce
d
o
p
er
atio
n
al
f
lex
ib
ilit
y
,
a
n
d
r
ed
u
ce
d
im
p
lem
e
n
tatio
n
c
o
s
ts
.
T
h
e
DPFC
ar
ch
itectu
r
e
co
m
p
r
is
es
s
h
u
n
t
an
d
s
er
ies
co
n
v
er
ter
s
,
ea
ch
g
o
v
e
r
n
ed
b
y
d
ed
icate
d
co
n
tr
o
l
cir
cu
its
,
an
d
co
o
r
d
in
ated
b
y
a
ce
n
tr
al
co
n
tr
o
l
u
n
it
th
at
s
u
p
p
lies
th
e
r
ef
er
en
ce
s
ig
n
als.
T
h
is
s
tu
d
y
p
r
esen
ts
th
e
d
ev
elo
p
m
en
t
o
f
a
DPFC
m
o
d
el
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
an
d
ev
al
u
ates
its
p
er
f
o
r
m
an
ce
th
r
o
u
g
h
s
im
u
latio
n
,
em
p
h
asizin
g
its
ca
p
ab
ilit
y
to
en
h
a
n
ce
v
o
ltag
e
s
tab
ilit
y
an
d
o
p
tim
ize
p
o
wer
tr
an
s
f
er
.
2.
DIS
T
RI
B
U
T
E
D
P
O
W
E
R
F
L
O
W
CO
NT
RO
L
L
E
R
2
.
1
.
T
o
po
lo
g
y
T
h
e
in
teg
r
atio
n
o
f
th
e
DPFC
p
r
esen
ts
an
ad
v
an
ce
d
ap
p
r
o
ac
h
f
o
r
en
h
an
cin
g
co
n
tr
o
l
an
d
s
tab
ilit
y
with
in
p
o
wer
s
y
s
tem
s
.
T
h
is
te
ch
n
o
lo
g
y
lev
er
ag
es
a
co
o
r
d
in
ated
co
n
f
ig
u
r
atio
n
o
f
s
h
u
n
t
an
d
s
er
ies
co
n
v
er
ter
s
,
p
r
o
v
id
i
n
g
a
v
er
s
atile
an
d
ef
f
ec
tiv
e
m
ea
n
s
o
f
im
p
r
o
v
in
g
g
r
id
p
er
f
o
r
m
an
ce
.
T
h
e
s
h
u
n
t
co
n
v
er
ter
o
p
e
r
ates
an
alo
g
o
u
s
ly
to
a
STAT
C
OM
,
d
eliv
er
in
g
r
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t
an
d
m
ai
n
tain
in
g
v
o
ltag
e
r
eg
u
latio
n
.
Me
an
wh
ile,
th
e
s
er
ies
co
m
p
o
n
en
t
is
b
ased
o
n
th
e
d
is
tr
ib
u
ted
s
tatic
s
er
ie
s
co
m
p
en
s
ato
r
(
DSSC
)
p
r
in
cip
le,
wh
er
ein
m
u
ltip
le
au
to
n
o
m
o
u
s
s
in
g
le
-
p
h
ase
co
n
v
er
te
r
s
ar
e
s
tr
ateg
ically
d
ep
lo
y
e
d
alo
n
g
t
h
e
tr
an
s
m
is
s
io
n
lin
e,
r
ep
lacin
g
th
e
tr
ad
itio
n
al
ce
n
t
r
alize
d
th
r
ee
-
p
h
ase
co
n
v
er
ter
ar
r
an
g
em
e
n
t
[
3
5]
-
[
3
7
]
.
E
ac
h
DPFC
co
n
v
er
ter
o
p
er
ates
in
d
e
p
en
d
e
n
tly
an
d
i
n
clu
d
es
its
o
wn
DC
ca
p
ac
ito
r
,
en
ab
li
n
g
th
e
g
en
e
r
atio
n
o
f
th
e
n
ec
ess
ar
y
DC
v
o
ltag
e
with
o
u
t
r
eq
u
ir
in
g
a
s
h
ar
ed
DC
lin
k
.
T
h
is
d
ec
en
tr
aliz
ed
d
esig
n
e
n
h
an
ce
s
s
y
s
tem
f
le
x
ib
ilit
y
,
r
eliab
ilit
y
,
an
d
f
au
lt to
le
r
an
ce
.
T
h
e
DPFC
co
n
f
ig
u
r
atio
n
is
d
e
p
icted
in
F
ig
u
r
e
1
.
T
h
e
d
ev
elo
p
m
en
t
o
f
p
o
we
r
f
lo
w
co
n
tr
o
l
s
y
s
tem
s
r
eq
u
i
r
e
s
ca
r
ef
u
l
co
n
s
id
er
atio
n
o
f
c
o
m
p
o
n
en
t
s
elec
tio
n
an
d
s
p
atial
ar
r
an
g
e
m
en
t.
T
h
e
DPFC
,
wh
ich
in
teg
r
ates
s
h
u
n
t
an
d
s
er
ies
co
n
v
e
r
ter
s
,
n
ec
ess
itates
a
s
h
u
n
t
-
co
n
n
ec
ted
h
i
g
h
-
p
ass
f
ilter
s
tr
ateg
ically
p
lace
d
o
n
th
e
o
p
p
o
s
ite
s
id
e
o
f
th
e
tr
an
s
m
is
s
io
n
lin
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
d
va
n
cin
g
p
o
w
er q
u
a
lity v
ia
d
is
tr
ib
u
ted
p
o
w
er flo
w
co
n
tr
o
l so
lu
tio
n
s
(
A
b
d
elka
d
er Yo
u
s
fi
)
1803
Ad
d
itio
n
ally
,
Y
-
Δ
tr
an
s
f
o
r
m
e
r
s
ar
e
in
s
talled
at
b
o
th
en
d
s
o
f
th
e
lin
e
to
s
u
p
p
o
r
t
s
y
s
tem
f
u
n
ctio
n
ality
.
T
h
e
r
atio
n
ale
b
eh
in
d
th
ese
co
m
p
o
n
en
ts
will b
e
ex
p
lo
r
ed
in
th
e
f
o
l
lo
win
g
d
is
cu
s
s
io
n
.
I
n
c
o
n
tr
ast,
th
e
UPFC
em
p
lo
y
s
a
b
ac
k
-
to
-
b
ac
k
co
n
f
ig
u
r
atio
n
f
o
r
its
s
h
u
n
t
an
d
s
er
ies
c
o
n
v
er
ter
s
,
en
ab
lin
g
s
ea
m
less
ac
tiv
e
p
o
wer
ex
ch
a
n
g
e
[
3
8
]
,
[
3
9
]
.
T
o
en
s
u
r
e
eq
u
iv
ale
n
t
co
n
t
r
o
l
ca
p
a
b
ilit
ies
b
etwe
en
th
e
DPFC
an
d
UPFC
,
a
m
eth
o
d
o
l
o
g
y
m
u
s
t
b
e
d
e
v
elo
p
e
d
th
at
f
a
cilitates
ac
tiv
e
p
o
wer
ex
ch
a
n
g
e
am
o
n
g
c
o
n
v
e
r
ter
s
with
o
u
t
r
ely
in
g
o
n
a
c
o
n
v
e
n
tio
n
al
DC
lin
k
.
T
h
is
s
h
if
t
to
war
d
in
n
o
v
ativ
e
co
n
f
ig
u
r
atio
n
s
h
ig
h
lig
h
ts
th
e
o
n
g
o
in
g
ev
o
lu
tio
n
o
f
p
o
wer
s
y
s
tem
co
n
tr
o
l stra
teg
ies.
Fig
u
r
e
1
.
I
n
ter
n
al
s
ch
em
atic
o
f
th
e
DPFC
2
.
2
.
P
rinciple o
pera
t
io
n
W
ith
in
th
e
DPFC
ar
ch
itectu
r
e
,
th
e
tr
an
s
m
is
s
io
n
lin
e
f
u
n
cti
o
n
s
as
a
s
h
a
r
ed
p
ath
co
n
n
ec
tin
g
th
e
AC
ter
m
in
als
o
f
th
e
s
h
u
n
t
an
d
s
er
ies
co
n
v
er
ter
s
,
th
er
eb
y
f
ac
i
litatin
g
ac
tiv
e
p
o
wer
tr
an
s
f
er
th
r
o
u
g
h
th
eir
AC
in
ter
f
ac
es.
T
h
is
m
ec
h
an
is
m
o
p
er
ates
b
ased
o
n
th
e
th
eo
r
y
o
f
p
o
wer
f
lo
w
u
n
d
er
n
o
n
-
s
in
u
s
o
id
al
co
n
d
itio
n
s
.
T
h
r
o
u
g
h
th
e
ap
p
licatio
n
o
f
Fo
u
r
ier
an
aly
s
is
,
v
o
ltag
e
an
d
cu
r
r
en
t
wav
ef
o
r
m
s
ex
h
ib
it
in
g
n
o
n
-
s
in
u
s
o
id
al
b
eh
av
io
r
ar
e
d
ec
o
m
p
o
s
ed
in
t
o
a
s
er
ies
o
f
s
in
u
s
o
i
d
al
co
m
p
o
n
en
ts
at
m
u
ltip
le
f
r
eq
u
e
n
cies,
ea
ch
ch
a
r
ac
ter
ized
b
y
a
s
p
ec
if
ic
am
p
litu
d
e.
T
h
e
ac
tiv
e
p
o
wer
co
r
r
esp
o
n
d
in
g
to
n
o
n
-
s
in
u
s
o
id
al
v
o
ltag
e
an
d
c
u
r
r
en
t
wav
ef
o
r
m
s
is
d
e
f
in
ed
as
th
e
tim
e
-
av
er
ag
ed
v
alu
e
o
f
th
eir
in
s
tan
tan
eo
u
s
p
r
o
d
u
ct.
T
h
is
d
ef
in
itio
n
r
ef
lects
th
e
av
er
ag
e
p
o
wer
o
v
er
a
co
m
p
lete
cy
cle
o
f
th
e
wav
e
f
o
r
m
.
T
h
e
o
r
t
h
o
g
o
n
ality
o
f
s
in
u
s
o
id
al
f
u
n
ctio
n
s
at
d
is
tin
ct
f
r
eq
u
e
n
cies
is
f
u
n
d
am
e
n
tal
in
th
is
co
n
te
x
t.
L
ev
er
ag
in
g
th
is
p
r
o
p
e
r
ty
,
t
h
e
m
ath
em
atica
l
ex
p
r
ess
io
n
f
o
r
a
ctiv
e
p
o
wer
ca
n
b
e
s
u
cc
in
ctly
ar
ticu
lated
as
th
e
s
u
m
o
f
th
e
i
n
s
tan
tan
eo
u
s
p
r
o
d
u
cts
o
f
co
r
r
esp
o
n
d
in
g
v
o
ltag
e
an
d
c
u
r
r
e
n
t
co
m
p
o
n
en
ts
at
ea
ch
f
r
eq
u
e
n
c
y
.
T
h
is
ap
p
r
o
ac
h
en
ab
les
a
co
m
p
r
eh
en
s
iv
e
u
n
d
er
s
tan
d
i
n
g
a
n
d
r
ep
r
esen
tatio
n
o
f
th
e
ac
tiv
e
p
o
wer
d
y
n
a
m
ics in
th
e
co
n
tex
t
o
f
n
o
n
-
s
in
u
s
o
id
al
wav
ef
o
r
m
s
[
4
0
]
:
P
=
∑
c
os
∞
i
̇
=
1
(
1
)
I
n
(
1
)
,
an
d
co
r
r
esp
o
n
d
to
th
e
v
o
ltag
e
an
d
c
u
r
r
e
n
t a
t th
e
−
ℎ
h
ar
m
o
n
ic
f
r
e
q
u
en
c
y
,
r
esp
ec
tiv
ely
,
wh
ile
d
en
o
tes
th
e
p
h
ase
an
g
le
b
etwe
en
th
ese
q
u
an
titi
es.
T
h
is
r
elatio
n
s
h
ip
h
ig
h
lig
h
ts
a
k
ey
th
eo
r
etica
l
in
s
ig
h
t: th
e
ac
tiv
e
p
o
wer
co
n
tr
ib
u
tio
n
s
at
d
if
f
er
en
t
h
ar
m
o
n
ic
f
r
eq
u
e
n
cies a
r
e
in
d
ep
en
d
en
t o
f
o
n
e
an
o
t
h
er
.
T
h
a
t
is
,
v
o
ltag
e
o
r
cu
r
r
en
t
at
o
n
e
f
r
eq
u
en
c
y
d
o
es
n
o
t
im
p
ac
t
th
e
ac
tiv
e
p
o
wer
ass
o
ciate
d
with
o
th
er
f
r
eq
u
en
cies.
T
h
is
f
r
eq
u
e
n
cy
-
d
o
m
ain
d
ec
o
u
p
lin
g
e
n
ab
les
a
p
o
wer
elec
tr
o
n
ic
co
n
v
er
ter
t
o
in
ject
ac
tiv
e
p
o
wer
at
o
n
e
f
r
eq
u
e
n
cy
wh
ile
s
im
u
ltan
eo
u
s
ly
ab
s
o
r
b
in
g
it a
t a
n
o
th
er
,
with
o
u
t n
ec
ess
itatin
g
an
ex
ter
n
al
e
n
er
g
y
s
o
u
r
ce
.
W
ith
in
th
e
co
n
tex
t
o
f
th
e
DPFC
,
th
is
p
r
in
cip
le
is
ap
p
lied
b
y
allo
win
g
th
e
s
h
u
n
t
co
n
v
er
t
er
to
d
r
a
w
ac
tiv
e
p
o
wer
f
r
o
m
th
e
g
r
id
at
th
e
f
u
n
d
am
en
tal
f
r
eq
u
en
cy
an
d
r
e
-
in
ject
it
at
a
h
ar
m
o
n
ic
f
r
eq
u
e
n
cy
.
T
h
is
h
ar
m
o
n
ic
p
o
wer
is
th
en
c
o
n
v
ey
ed
th
r
o
u
g
h
th
e
tr
a
n
s
m
is
s
io
n
lin
e
to
th
e
s
er
ies
co
n
v
e
r
ter
s
.
T
h
ese
s
er
ies
co
n
v
er
ter
s
,
b
ased
o
n
th
e
s
y
s
tem
’
s
f
u
n
d
a
m
en
tal
f
r
e
q
u
en
c
y
p
o
wer
r
e
q
u
ir
em
en
ts
,
g
en
er
ate
h
ar
m
o
n
ic
v
o
ltag
es
th
at
en
ab
le
th
em
to
ab
s
o
r
b
th
e
h
ar
m
o
n
ic
ac
tiv
e
p
o
wer
.
Un
d
e
r
th
e
ass
u
m
p
tio
n
o
f
n
eg
lig
ib
le
lo
s
s
es,
th
e
am
o
u
n
t
o
f
p
o
wer
ab
s
o
r
b
ed
at
th
e
h
a
r
m
o
n
ic
f
r
e
q
u
en
c
y
m
atch
es
th
e
p
o
wer
d
r
awn
at
th
e
f
u
n
d
am
en
tal
f
r
eq
u
en
c
y
.
Fig
u
r
e
2
d
ep
icts
th
is
d
y
n
am
ic
ex
ch
an
g
e
o
f
ac
tiv
e
p
o
wer
b
et
wee
n
th
e
s
h
u
n
t
an
d
s
er
ies
co
n
v
er
ter
s
in
th
e
DPF
C
co
n
f
ig
u
r
atio
n
.
A
h
ig
h
-
p
ass
f
ilt
er
in
teg
r
ate
d
in
to
th
e
s
y
s
tem
ar
ch
itectu
r
e
p
r
ev
en
ts
t
h
e
p
ass
ag
e
o
f
f
u
n
d
am
e
n
tal
f
r
eq
u
e
n
cy
co
m
p
o
n
e
n
ts
wh
ile
p
er
m
itti
n
g
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
to
f
lo
w.
T
o
g
eth
e
r
with
th
e
g
r
o
u
n
d
a
n
d
th
e
co
n
v
er
ter
u
n
its
,
th
is
f
ilter
est
ab
lis
h
es
a
clo
s
ed
-
lo
o
p
p
ath
w
ay
f
o
r
th
e
h
ar
m
o
n
ic
cu
r
r
en
t,
en
s
u
r
in
g
ef
f
ec
tiv
e
p
o
wer
tr
an
s
f
er
th
r
o
u
g
h
h
ar
m
o
n
ic
in
ter
ac
tio
n
.
Ad
v
an
tag
es o
f
t
h
e
DPFC
s
y
s
te
m
:
−
Ad
v
an
ce
d
co
n
tr
o
l
f
u
n
ctio
n
al
ity
:
T
h
e
DPFC
p
r
o
v
i
d
es
p
r
ec
is
e
an
d
in
d
e
p
en
d
en
t
r
e
g
u
l
atio
n
o
f
k
ey
tr
an
s
m
is
s
io
n
s
y
s
tem
v
ar
iab
les,
s
u
ch
as
lin
e
im
p
ed
a
n
ce
,
p
o
w
er
f
lo
w
a
n
g
le,
an
d
b
u
s
v
o
ltag
e
m
ag
n
itu
d
es,
th
er
eb
y
e
n
h
an
cin
g
o
v
er
all
n
et
wo
r
k
co
n
tr
o
llab
ilit
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
180
1
-
1
8
1
1
1804
−
I
n
cr
ea
s
ed
o
p
er
atio
n
al
r
eliab
ilit
y
:
T
h
e
m
o
d
u
lar
s
tr
u
ct
u
r
e
o
f
t
h
e
DPFC
allo
ws
co
n
tin
u
o
u
s
o
p
er
atio
n
e
v
en
in
th
e
ev
en
t
o
f
in
d
i
v
id
u
al
s
er
i
es
co
n
v
er
ter
f
ailu
r
es,
as
u
n
af
f
ec
ted
u
n
its
r
em
ain
f
u
n
ctio
n
al
an
d
m
ain
tai
n
s
y
s
tem
p
er
f
o
r
m
a
n
ce
.
−
E
co
n
o
m
ic
i
n
s
tallatio
n
:
Du
e
t
o
th
e
ab
s
en
ce
o
f
a
d
ir
ec
t
h
i
g
h
-
v
o
ltag
e
is
o
latio
n
r
e
q
u
ir
em
en
t
f
o
r
s
er
ies
co
n
v
er
ter
co
n
n
ec
tio
n
s
to
th
e
t
r
an
s
m
is
s
io
n
lin
e,
th
e
DPFC
f
ac
ilit
ates
th
e
u
s
e
o
f
s
in
g
le
-
tu
r
n
tr
an
s
f
o
r
m
er
s
,
r
esu
ltin
g
in
r
ed
u
ce
d
e
q
u
ip
m
e
n
t c
o
s
ts
an
d
s
im
p
lifie
d
d
ep
lo
y
m
en
t.
Fig
u
r
e
2
.
DPFC
co
n
v
er
ter
s
ex
ch
an
g
in
g
ac
tiv
e
p
o
wer
3.
ST
RA
T
E
G
I
C
CO
N
T
RO
L
D
E
SI
G
N
F
O
R
DP
F
C
3
.
1
.
DP
F
C
s
hu
nt
co
nv
er
s
io
n str
a
t
eg
y
I
n
DPFC
s
y
s
tem
s
,
th
e
s
h
u
n
t
co
n
v
er
ter
is
a
cr
itical
co
m
p
o
n
en
t
th
at
m
u
s
t
b
e
ca
p
ab
le
o
f
p
r
o
d
u
cin
g
v
o
ltag
es
at
b
o
th
th
e
f
u
n
d
am
en
tal
an
d
th
ir
d
h
ar
m
o
n
ic
f
r
e
q
u
e
n
cies.
W
h
ile
a
c
o
n
v
e
n
tio
n
al
t
h
r
ee
-
leg
,
th
r
ee
-
wir
e
co
n
v
er
ter
m
a
y
in
itially
ap
p
ea
r
s
u
itab
le,
it
in
h
er
en
tly
b
eh
av
e
s
as
an
o
p
en
cir
cu
it
f
o
r
th
ir
d
h
ar
m
o
n
ic
cu
r
r
en
ts
,
th
er
eb
y
i
n
h
ib
itin
g
th
eir
g
e
n
er
atio
n
.
T
h
is
co
n
s
tr
ain
t
h
as
p
r
o
m
p
ted
in
v
esti
g
atio
n
s
in
t
o
alte
r
n
ativ
e
th
r
ee
-
p
h
ase
co
n
v
er
ter
c
o
n
f
ig
u
r
atio
n
s
.
O
p
t
i
o
n
s
s
u
c
h
as
m
u
lt
i
-
l
e
g
,
m
u
l
t
i
-
w
i
r
e
c
o
n
v
e
r
t
e
r
s
o
r
m
u
lt
i
p
l
e
s
in
g
l
e
-
p
h
a
s
e
u
n
i
ts
c
an
a
d
d
r
e
s
s
t
h
i
s
is
s
u
e
;
h
o
w
e
v
e
r
,
t
h
e
y
g
e
n
e
r
a
l
l
y
r
e
q
u
i
r
e
a
d
d
i
t
i
o
n
al
h
a
r
d
w
a
r
e
,
i
n
c
r
e
a
s
i
n
g
s
y
s
t
e
m
c
o
m
p
l
e
x
i
t
y
a
n
d
c
o
s
t
.
T
o
o
v
er
co
m
e
th
ese
lim
itatio
n
s
,
an
in
n
o
v
ativ
e
s
h
u
n
t
co
n
v
er
te
r
to
p
o
lo
g
y
h
as
b
ee
n
p
r
o
p
o
s
ed
f
o
r
DPFC
s
y
s
tem
s
.
T
h
is
ap
p
r
o
ac
h
u
tili
ze
s
an
ex
is
tin
g
Y
–
Δ
tr
an
s
f
o
r
m
er
to
f
ac
ilit
ate
th
ir
d
h
ar
m
o
n
ic
cu
r
r
en
t
in
jectio
n
in
to
th
e
p
o
wer
s
y
s
tem
.
A
s
in
g
le
-
p
h
ase
co
n
v
er
ter
is
co
n
n
ec
te
d
b
etwe
en
th
e
tr
an
s
f
o
r
m
er
'
s
n
eu
tr
al
p
o
in
t
an
d
g
r
o
u
n
d
,
en
ab
lin
g
th
e
in
tr
o
d
u
ctio
n
o
f
t
h
ir
d
h
ar
m
o
n
ic
c
u
r
r
e
n
ts
in
to
th
e
n
eu
tr
al.
T
h
ese
cu
r
r
en
ts
ar
e
t
h
en
s
y
m
m
etr
ically
d
is
tr
ib
u
ted
ac
r
o
s
s
th
e
th
r
ee
p
h
ases
b
y
th
e
tr
an
s
f
o
r
m
er
.
An
au
x
iliar
y
b
ac
k
-
to
-
b
ac
k
co
n
v
er
ter
is
in
co
r
p
o
r
ated
o
n
th
e
tr
an
s
f
o
r
m
er
'
s
lo
w
-
v
o
ltag
e
s
id
e
to
s
u
p
p
ly
p
o
wer
to
th
e
s
in
g
le
-
p
h
ase
co
n
v
er
ter
.
Fig
u
r
e
3
illu
s
tr
ates
th
e
co
m
p
lete
s
ch
em
atic
o
f
th
is
co
n
f
ig
u
r
atio
n
.
T
h
is
n
o
v
el
d
esig
n
n
o
t
o
n
ly
r
eso
lv
es
th
e
s
h
o
r
tco
m
in
g
s
o
f
co
n
v
en
tio
n
al
co
n
v
er
ter
to
p
o
lo
g
ies
b
u
t
also
en
a
b
les
ef
f
icien
t
an
d
co
s
t
-
ef
f
ec
tiv
e
th
ir
d
h
a
r
m
o
n
ic
g
en
er
atio
n
a
n
d
d
is
tr
ib
u
tio
n
with
in
th
e
DPFC
f
r
am
ewo
r
k
.
Fig
u
r
e
3
.
Sh
u
n
t c
o
n
v
er
ter
o
f
D
PF
C
3
.
2
.
T
hree
ph
a
s
e
co
nv
er
t
er
s
o
f
s
hu
nt
T
h
e
p
r
im
ar
y
o
b
jectiv
es
in
th
e
co
n
tr
o
l
s
tr
ateg
y
o
f
th
e
DPFC
s
h
u
n
t
co
n
v
er
te
r
ar
e
two
f
o
ld
:
to
f
ac
ilit
ate
r
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t
b
y
in
je
ctin
g
a
co
n
tr
o
llab
le
r
ea
ctiv
e
c
u
r
r
en
t
at
th
e
f
u
n
d
am
en
tal
f
r
e
q
u
en
cy
in
to
th
e
g
r
id
,
an
d
to
m
ain
tain
a
s
tab
le
DC
-
lin
k
v
o
ltag
e
ac
r
o
s
s
th
e
en
er
g
y
s
to
r
ag
e
ca
p
ac
ito
r
.
As
d
e
p
icted
in
Fig
u
r
e
4
,
th
e
co
n
tr
o
l
s
tr
u
ctu
r
e
co
n
s
is
ts
o
f
two
ess
en
tial
s
u
b
s
y
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tem
s
DC
v
o
ltag
e
r
eg
u
latio
n
an
d
in
jecte
d
cu
r
r
en
t
c
o
n
tr
o
l.
T
h
e
in
n
er
c
u
r
r
e
n
t
co
n
tr
o
l
l
o
o
p
is
r
esp
o
n
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ib
le
f
o
r
r
e
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u
latin
g
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e
s
h
u
n
t
c
u
r
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n
t
ℎ
,
1
,
f
o
r
m
in
g
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e
co
r
e
o
f
th
e
cu
r
r
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n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
d
va
n
cin
g
p
o
w
er q
u
a
lity v
ia
d
is
tr
ib
u
ted
p
o
w
er flo
w
co
n
tr
o
l so
lu
tio
n
s
(
A
b
d
elka
d
er Yo
u
s
fi
)
1805
co
n
tr
o
l
m
o
d
u
le.
T
h
e
r
ef
er
en
ce
f
o
r
th
e
q
-
a
x
is
cu
r
r
en
t
co
m
p
o
n
en
t
is
s
u
p
p
lied
b
y
th
e
ce
n
tr
al
co
n
tr
o
l
u
n
it,
wh
il
e
th
e
r
ef
er
en
ce
f
o
r
th
e
d
-
ax
is
co
m
p
o
n
en
t
o
r
ig
in
ates
f
r
o
m
t
h
e
DC
v
o
ltag
e
co
n
tr
o
l
lo
o
p
.
T
o
p
er
f
o
r
m
Par
k
’
s
tr
an
s
f
o
r
m
atio
n
,
a
s
y
n
c
h
r
o
n
o
u
s
r
ef
er
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ce
f
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am
e
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em
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lo
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ich
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h
ed
u
s
in
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h
ase
-
lo
ck
ed
lo
o
p
(
PLL
)
.
T
h
e
PLL
l
o
ck
s
o
n
to
th
e
g
r
i
d
v
o
ltag
e
wa
v
ef
o
r
m
,
u
s
in
g
th
e
b
u
s
v
o
ltag
e
as
its
in
p
u
t
to
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en
er
ate
th
e
n
ec
ess
ar
y
r
ef
er
e
n
ce
a
n
g
le
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o
r
co
o
r
d
in
ate
tr
a
n
s
f
o
r
m
atio
n
.
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o
r
th
e
DC
v
o
ltag
e
co
n
t
r
o
l
b
lo
ck
,
a
n
d
u
n
d
er
th
e
ass
u
m
p
tio
n
o
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eg
lig
ib
le
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wer
lo
s
s
es,
th
e
r
ef
er
en
ce
cu
r
r
en
t
ca
n
b
e
d
ir
ec
tly
d
er
iv
ed
f
r
o
m
th
e
p
o
wer
b
alan
ce
b
etwe
en
th
e
AC
an
d
DC
s
id
es.
1
2
ℎ
×
ⅆ
2
ⅆ
=
1
−
3
(
2)
Fo
r
th
e
co
n
t
r
o
l b
lo
c
k
in
u
s
e
r
ig
h
t n
o
w:
ℎ
,
ⅆ
,
1
=
3
/
2
(
ℎ
,
1
,
ⅆ
,
ℎ
,
1
,
ⅆ
+
ℎ
,
1
,
,
ℎ
,
1
,
)
(
3
)
Her
e,
th
e
s
tatio
n
ar
y
f
r
am
e
c
o
m
p
o
n
en
ts
(
to
)
ar
e
c
o
n
v
e
r
ted
to
r
o
tatin
g
f
r
am
e
co
m
p
o
n
en
ts
u
s
in
g
Par
k
'
s
tr
an
s
f
o
r
m
atio
n
:
ℎ
,
1
=
,
ℎ
,
1
×
ℎ
,
ⅆ
(
4
)
F
i
g
u
r
e
5
d
e
p
i
c
ts
t
h
e
c
u
r
r
e
n
t
r
e
g
u
l
a
t
i
o
n
l
o
o
p
o
f
t
h
e
th
r
e
e
-
p
h
as
e
s
h
u
n
t
c
o
n
v
e
r
t
e
r
i
n
t
e
g
r
a
t
e
d
i
n
t
o
a
D
P
F
C
s
y
s
t
e
m
.
Fig
u
r
e
4
.
Sh
u
n
t c
o
n
tr
o
ller
f
o
r
a
th
r
ee
-
p
h
ase
in
v
er
ter
Fig
u
r
e
5
.
C
o
n
tr
o
ller
f
o
r
s
h
u
n
t
cu
r
r
en
t
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
s
i
m
u
latio
n
s
tu
d
y
o
f
th
e
DPFC
m
o
d
el
in
co
r
p
o
r
atin
g
DQ
-
ax
is
co
n
tr
o
l,
ap
p
lied
to
a
7
-
b
u
s
p
o
wer
s
y
s
tem
u
s
in
g
th
e
MA
T
L
A
B
/Si
m
u
lin
k
en
v
ir
o
n
m
en
t.
T
h
e
s
im
u
latio
n
o
u
tco
m
es
v
alid
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
DPFC
in
en
h
an
cin
g
v
o
lta
g
e
s
tab
ilit
y
,
co
n
tr
o
llin
g
p
o
wer
f
lo
w,
an
d
im
p
r
o
v
in
g
en
er
g
y
t
r
an
s
f
er
ef
f
icien
cy
ac
r
o
s
s
th
e
n
etwo
r
k
.
T
h
e
p
ar
am
eter
s
u
s
ed
f
o
r
th
e
s
im
u
latio
n
ar
e
li
s
ted
in
T
ab
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
180
1
-
1
8
1
1
1806
Fig
u
r
e
6
illu
s
tr
ates
th
e
DPFC
s
im
u
latio
n
m
o
d
el
d
ev
elo
p
ed
i
n
MA
T
L
AB
/Si
m
u
lin
k
,
wh
ich
in
teg
r
ates
b
o
th
s
h
u
n
t
an
d
s
er
ies
co
n
v
er
te
r
co
m
p
o
n
en
ts
.
Fig
u
r
e
7
d
e
p
icts
v
o
ltag
e
s
ag
an
d
s
well
in
th
e
g
r
id
v
o
ltag
e
wh
e
n
th
e
DPFC
d
ev
ice
is
n
o
t
p
r
esen
t.
Fu
r
th
er
m
o
r
e,
th
e
r
esu
ltin
g
p
h
ase
s
h
if
t
in
th
e
l
o
ad
v
o
ltag
e
ad
v
er
s
ely
af
f
ec
ts
co
n
n
ec
ted
e
q
u
ip
m
e
n
t,
r
e
d
u
ci
n
g
th
e
r
eliab
ilit
y
a
n
d
q
u
ality
o
f
elec
tr
ical
p
o
wer
tr
an
s
m
is
s
io
n
.
Fig
u
r
e
8
d
em
o
n
s
tr
ates
th
at
th
e
in
co
r
p
o
r
atio
n
o
f
th
e
DPFC
d
ev
ice
ef
f
ec
tiv
ely
m
itig
ates
v
o
ltag
e
s
ag
an
d
s
well.
B
y
elim
in
atin
g
p
h
ase
s
h
if
t
ef
f
ec
ts
,
th
e
DPFC
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u
r
e
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.
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o
d
el
o
f
th
e
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Fig
u
r
e
7
.
Gr
id
v
o
ltag
e
wav
ef
o
r
m
with
o
u
t th
e
DPFC
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
d
va
n
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g
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er q
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lity v
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r
in
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ile
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ter
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ce
th
e
s
y
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tem
's
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o
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e
p
r
o
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Fig
u
r
e
9
p
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esen
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th
e
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er
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u
n
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tiv
e
p
o
wer
r
esp
o
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e
o
f
th
e
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,
d
em
o
n
s
tr
atin
g
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o
w
th
e
co
o
r
d
i
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ated
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th
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ies
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n
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i
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to
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itig
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f
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o
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g
e
s
ag
s
an
d
s
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th
e
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.
Fig
u
r
e
1
0
d
is
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lay
s
th
e
p
er
-
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n
it
r
ea
l
lo
ad
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r
esp
o
n
s
e
o
f
th
e
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,
wh
er
e
th
e
co
n
s
is
ten
t
r
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p
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tp
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is
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.
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u
r
e
1
1
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ates
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er
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u
r
e
1
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ely
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ates
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ateg
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lated
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h
e
m
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ir
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er
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.
Fig
u
r
e
8
.
Gr
id
v
o
ltag
e
wav
ef
o
r
m
with
th
e
DPFC
in
o
p
er
atio
n
Fig
u
r
e
9
.
R
ea
l p
o
wer
s
o
u
r
ce
r
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o
n
s
e
p
er
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n
it o
f
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
180
1
-
1
8
1
1
1808
Fig
u
r
e
1
0
.
R
ea
l p
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ad
r
e
s
p
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n
s
e
p
er
u
n
it o
f
DPFC
Fig
u
r
e
1
1
.
T
h
ir
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
DPFC
lo
ad
cu
r
r
e
n
t
Fig
u
r
e
1
2
.
DC
v
o
ltag
e
ⅆ
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
d
va
n
cin
g
p
o
w
er q
u
a
lity v
ia
d
is
tr
ib
u
ted
p
o
w
er flo
w
co
n
tr
o
l so
lu
tio
n
s
(
A
b
d
elka
d
er Yo
u
s
fi
)
1809
5.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
in
tr
o
d
u
ce
s
an
ad
v
a
n
ce
d
im
p
lem
e
n
tatio
n
o
f
th
e
d
i
s
tr
ib
u
ted
p
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wer
f
lo
w
c
o
n
tr
o
lle
r
(
DPFC
)
,
r
ep
r
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tin
g
a
s
ig
n
if
ica
n
t
ev
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lu
tio
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o
f
th
e
u
n
if
ied
p
o
wer
f
lo
w
c
o
n
tr
o
ller
(
UPFC
)
.
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h
ile
p
r
eser
v
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n
g
t
h
e
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’
s
co
r
e
f
u
n
ctio
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alities
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ch
as
th
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r
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ated
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n
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ag
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elim
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ates
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v
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k
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n
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s
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er
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th
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tr
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an
s
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er
ies
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n
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ter
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ase
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atin
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o
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th
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latio
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s
t
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atin
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ar
m
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r
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h
a
n
ce
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d
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ilit
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r
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in
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