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l J
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lect
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I
J
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Vo
l.
14
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Dec
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er
20
24
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p
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.
6
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I
SS
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DOI
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v
14
i
6
.
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6160
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ttp
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ec
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ia
esco
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co
m
Integ
ra
tion o
f
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en
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ble ene
rg
y
int
o
San Andres
Isla
nd
elect
rica
l gri
d
K
ey
la
New
ba
ll Ar
chbo
ld
,
Al
v
a
ro
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a
m
bra
no
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J
a
v
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a
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:
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a
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i
a
Art
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I
nfo
AB
S
T
RAC
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A
r
ticle
his
to
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y:
R
ec
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Ma
r
2
8
,
2
0
2
4
R
ev
is
ed
J
u
l 1
4
,
2
0
2
4
Acc
ep
ted
Au
g
6
,
2
0
2
4
Re
n
e
wa
b
le
e
n
e
rg
y
(RE)
so
u
rc
e
s
in
teg
ra
ti
o
n
i
n
e
lec
tri
c
a
l
g
ri
d
s
is
c
h
a
n
g
i
n
g
th
e
d
y
n
a
m
ics
o
f
p
lan
n
i
n
g
a
n
d
o
p
e
ra
ti
o
n
.
Ov
e
r
v
o
lt
a
g
e
,
o
v
e
rc
u
rre
n
t,
a
n
d
m
a
lfu
n
c
ti
o
n
o
f
p
ro
tec
ti
o
n
sc
h
e
m
e
s
a
re
so
m
e
e
ffe
c
ts
if
it
i
s
li
m
it
s
a
re
n
o
t
c
o
n
tro
ll
e
d
.
T
h
is arti
c
le p
re
se
n
ts a me
th
o
d
o
lo
g
y
b
a
se
d
o
n
th
e
h
o
stin
g
c
a
p
a
c
it
y
(HC)
c
o
n
c
e
p
t
to
e
stim
a
te
p
e
rfo
rm
a
n
c
e
in
d
e
x
e
s
b
y
c
o
n
si
d
e
rin
g
sto
c
h
a
stic
m
e
th
o
d
s
a
n
d
s
y
ste
m
a
ti
c
sim
u
latio
n
tak
i
n
g
a
s
st
u
d
y
c
a
se
th
e
g
r
id
o
f
S
a
n
An
d
re
s
Isla
n
d
.
RE
is
o
f
sp
e
c
ial
in
tere
st
i
n
islan
d
s
w
h
e
re
d
ies
e
l
g
e
n
e
ra
to
r
s
p
ro
d
u
c
e
e
n
e
rg
y
wit
h
a
h
ig
h
f
o
o
t
p
rin
t
a
n
d
se
c
u
rit
y
o
f
su
p
p
l
y
is
lo
w as
th
e
re
is
a
h
ig
h
d
e
p
e
n
d
e
n
c
e
o
n
fo
ss
il
f
u
e
ls an
d
th
e
ir
tran
s
p
o
rt
re
g
ime
.
Th
e
sim
u
latio
n
s
a
re
c
a
rried
o
u
t
in
Di
g
S
il
e
n
t
P
o
we
rF
a
c
to
ry
i
n
teg
ra
ted
wit
h
P
y
th
o
n
to
a
u
to
m
a
te
th
e
i
tera
ti
o
n
s
o
v
e
r
d
iff
e
re
n
t
p
e
n
e
trati
o
n
lev
e
ls.
T
h
e
m
o
st
li
m
it
in
g
fa
c
to
r
fo
u
n
d
is
tran
sf
o
rm
e
r
ra
ti
n
g
.
Vo
l
tag
e
rise
is
a
fa
c
to
r
t
o
b
e
m
o
n
it
o
re
d
a
t
th
e
e
n
d
o
f
t
h
e
c
ircu
it
s.
Emiss
io
n
s
a
re
re
d
u
c
e
d
with
th
e
in
tro
d
u
c
ti
o
n
o
f
re
n
e
wa
b
le
e
n
e
rg
ies
,
b
u
t
v
a
riab
i
li
t
y
n
e
e
d
s
to
b
e
c
o
n
tr
o
ll
e
d
a
s
it
c
o
u
ld
re
q
u
ire
fa
st
sta
rt
-
u
p
o
f
g
e
n
e
ra
to
rs;
th
is
m
o
d
ifi
e
s
m
o
n
it
o
rin
g
a
n
d
c
o
n
tr
o
l
sc
h
e
m
e
s
to
ma
in
tain
sta
b
il
it
y
.
T
h
e
li
m
it
fo
u
n
d
is
h
i
g
h
e
r
th
a
n
th
e
e
sta
b
li
sh
e
d
r
e
g
u
latio
n
fo
r
n
o
n
-
in
terc
o
n
n
e
c
ted
z
o
n
e
s
(NI
Z)
i
n
C
o
lo
m
b
ia,
s
h
o
wi
n
g
t
h
e
c
a
p
a
b
il
it
y
o
f
th
e
g
ri
d
t
o
i
n
teg
ra
te RE
.
K
ey
w
o
r
d
s
:
Dis
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
Dy
n
am
ics o
f
p
la
n
n
in
g
an
d
o
p
er
atio
n
E
s
tim
ate
p
er
f
o
r
m
an
c
e
in
d
e
x
es
Ho
s
tin
g
ca
p
ac
ity
R
en
ewa
b
le
en
er
g
y
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
J
av
ier
R
o
s
er
o
-
Gar
cia
Gr
u
p
o
d
e
I
n
v
esti
g
ac
ió
n
: E
lect
r
ical
Ma
ch
in
es
an
d
Dr
iv
es,
Fa
cu
lty
o
f
E
n
g
in
ee
r
i
n
g
,
Un
i
v
er
s
id
ad
Nac
io
n
al
d
e
C
o
lo
m
b
ia
E
d
if
icio
4
5
3
,
Of
icin
a
2
0
8
,
B
o
g
o
ta,
C
o
lo
m
b
ia
E
m
ail: ja
r
o
s
er
o
g
@
u
n
al.
ed
u
.
co
1.
I
NT
RO
D
UCT
I
O
N
So
u
r
ce
s
o
f
r
en
ewa
b
le
en
er
g
y
(
R
E
)
h
av
e
a
g
r
o
win
g
p
a
r
ticip
atio
n
in
elec
tr
ical
g
r
id
s
.
I
n
C
o
lo
m
b
ia,
it
h
as
b
ee
n
p
r
o
m
o
te
d
b
y
L
aws
1
7
1
5
o
f
2
0
1
4
a
n
d
2
0
9
9
o
f
2
0
2
1
,
wh
ich
estab
lis
h
r
u
les
f
o
r
th
e
in
teg
r
atio
n
in
to
th
e
Natio
n
al
I
n
ter
co
n
n
ec
ted
Sy
s
tem
(
SIN
)
an
d
n
o
n
-
in
ter
c
o
n
n
ec
t
ed
zo
n
es (
NI
Z
)
to
r
e
d
u
ce
g
as
em
is
s
io
n
s
,
d
iv
er
s
if
y
th
e
en
er
g
y
m
atr
ix
,
an
d
p
r
o
m
o
te
s
u
s
tain
ab
le
ec
o
n
o
m
ic
d
e
v
elo
p
m
en
t
[
1
]
,
[
2
]
.
T
h
e
r
e
ar
e
s
o
m
e
s
p
ec
if
ic
ar
ea
s
ca
lled
ex
clu
s
iv
e
s
er
v
ice
ar
ea
s
s
u
ch
as
San
An
d
r
es
I
s
lan
d
,
w
h
er
e
d
iesel
g
en
e
r
ato
r
s
m
ain
ly
f
ee
d
th
e
p
o
wer
g
r
id
an
d
th
er
e
a
r
e
n
atio
n
al
g
o
v
er
n
m
en
t
s
u
b
s
id
ies
th
at
r
ea
ch
ed
m
o
r
e
th
an
5
7
b
illi
o
n
C
o
lo
m
b
i
an
p
eso
s
in
th
e
f
i
r
s
t
s
em
ester
o
f
2
0
2
3
[
3
]
,
[
4
]
.
T
h
e
p
r
ice
p
er
k
W
h
is
also
o
n
e
o
f
t
h
e
h
ig
h
est
in
th
e
c
o
u
n
tr
y
.
An
en
er
g
y
tr
an
s
itio
n
is
n
ec
ess
ar
y
in
th
ese
ar
ea
s
to
r
ed
u
ce
co
s
ts
an
d
m
ak
e
th
e
en
er
g
y
m
ar
k
et
m
o
r
e
s
u
s
tain
ab
le.
T
h
e
en
er
g
etic
tr
an
s
f
o
r
m
atio
n
m
is
s
io
n
r
aises
th
e
n
ee
d
to
in
tr
o
d
u
ce
n
e
w
tech
n
o
lo
g
ies
ag
ilely
with
o
u
t
co
m
p
r
o
m
is
in
g
r
eliab
ilit
y
[
5
]
.
So
m
e
o
f
th
e
b
e
n
ef
its
in
tr
o
d
u
ce
d
b
y
R
E
ar
e
s
ec
u
r
ity
ag
ain
s
t
s
h
o
r
tag
es
o
f
f
o
s
s
il
f
u
els,
r
ed
u
ctio
n
o
f
p
o
wer
lo
s
s
es
an
d
c
o
n
g
esti
o
n
at
th
e
tr
an
s
m
is
s
io
n
lev
el,
d
y
n
am
izatio
n
o
f
th
e
elec
tr
ical
m
ar
k
et
as
th
er
e
ar
e
n
ew
ag
en
ts
an
d
r
ed
u
ctio
n
o
f
g
r
ee
n
h
o
u
s
e
g
ass
es e
m
is
s
io
n
[
6
]
,
[
7
]
.
T
h
e
in
teg
r
atio
n
o
f
R
E
also
p
o
s
es
ch
allen
g
es
f
o
r
th
e
g
r
i
d
o
p
er
ato
r
s
u
c
h
as
th
e
d
y
n
am
ic
o
r
n
o
n
-
lin
ea
r
b
eh
av
io
r
o
f
g
r
id
p
ar
am
eter
s
,
wh
ich
s
h
o
u
ld
b
e
s
tu
d
ied
u
n
d
er
p
en
etr
atio
n
lev
els
an
d
g
r
id
t
o
p
o
lo
g
y
[
8
]
.
So
m
e
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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I
SS
N:
2088
-
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to
S
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A
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s
la
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d
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(
K
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ll A
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c
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b
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ld
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6161
th
e
ch
an
g
es
in
tr
o
d
u
ce
d
b
y
R
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ar
e
v
o
ltag
e
lev
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is
e,
th
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m
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r
is
k
o
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ee
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h
o
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t
cir
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p
ac
ity
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a
n
d
w
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n
g
o
p
er
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n
o
f
p
r
o
tectio
n
eq
u
ip
m
en
t
[
9
]
.
Vo
ltag
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r
is
e
ca
n
d
a
m
ag
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ap
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ce
s
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d
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f
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ctu
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s
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u
e
to
in
ter
m
itte
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o
f
s
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ca
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ac
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ler
at
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th
e
u
s
ag
e
o
f
lo
ad
tap
c
h
an
g
er
s
an
d
r
eg
u
lato
r
s
[
1
0
]
.
Vo
ltag
e
u
n
b
alan
ce
is
an
o
th
er
p
r
o
b
lem
s
tu
d
ied
,
as
m
an
y
r
esid
en
tial
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
in
s
talled
ar
e
s
in
g
le
-
p
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ased
.
Hig
h
v
o
ltag
e
u
n
b
alan
ce
in
c
r
ea
s
es
v
o
ltag
e
lev
els
[
1
1
]
.
Oth
er
c
o
n
s
eq
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en
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ar
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f
lick
er
s
,
an
d
in
cr
ea
s
in
g
p
o
we
r
lo
s
s
es
[
1
2
]
.
Me
th
o
d
o
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ies
h
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e
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n
d
ev
elo
p
ed
to
s
tu
d
y
th
e
in
teg
r
atio
n
o
f
R
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in
elec
tr
ical
g
r
id
s
with
its
ef
f
ec
ts
o
n
p
er
f
o
r
m
an
ce
in
d
e
x
es a
n
d
th
e
lim
its
t
o
m
ain
tain
in
g
p
o
wer
q
u
ality
.
Sin
ce
2
0
0
4
,
h
o
s
tin
g
ca
p
ac
ity
(
HC
)
h
as
b
ee
n
u
s
ed
to
r
ef
er
to
th
e
to
tal
ca
p
ac
ity
o
f
d
is
tr
ib
u
ted
g
en
er
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ab
o
v
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wh
ich
n
etw
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o
r
m
an
ce
b
ec
o
m
es
u
n
ac
ce
p
tab
le.
I
t
in
d
icate
s
th
e
li
m
it
o
f
in
teg
r
atio
n
o
f
R
E
in
to
a
g
r
id
an
d
m
u
s
t
b
e
ca
lcu
lated
f
o
r
ea
ch
in
d
icato
r
o
f
in
ter
est
f
o
r
th
e
g
r
id
o
p
e
r
ato
r
[
1
2
]
.
T
h
er
e
a
r
e
s
ev
er
al
ap
p
r
o
ac
h
es
u
s
ed
in
th
e
ca
lcu
latio
n
o
f
HC
th
at
ca
n
b
e
class
if
ied
in
to
th
r
ee
m
ain
ca
teg
o
r
ies:
d
eter
m
in
is
tic,
s
to
ch
asti
c,
an
d
t
im
e
-
s
er
ies.
T
r
ad
itio
n
al
n
etwo
r
k
p
lan
n
in
g
an
d
o
p
e
r
atio
n
u
s
ed
d
eter
m
in
i
s
tic
lo
ad
f
lo
ws
th
at
d
o
n
o
t
co
n
s
id
er
th
e
v
ar
iab
ilit
y
o
f
n
atu
r
al
r
eso
u
r
c
es
in
v
o
lv
ed
in
R
E
s
u
ch
as
ir
r
ad
ian
ce
an
d
win
d
.
T
h
e
d
eter
m
in
is
tic
ap
p
r
o
ac
h
ty
p
ically
co
n
s
id
er
s
th
e
wo
r
s
t
-
ca
s
e
s
ce
n
ar
io
,
u
s
u
ally
with
m
in
im
u
m
d
em
a
n
d
an
d
m
a
x
i
m
u
m
g
en
er
atio
n
.
I
n
tim
e
-
s
er
ies
ap
p
r
o
ac
h
es,
t
h
er
e
ar
e
p
r
o
f
iles
o
f
th
e
d
y
n
am
i
c
co
m
p
o
n
en
ts
o
f
th
e
g
r
id
,
a
n
d
lo
a
d
f
lo
ws
ar
e
ca
lcu
lated
f
o
r
th
e
s
h
o
r
test
p
o
s
s
ib
le
tim
e
in
ter
v
al.
Sev
er
al
p
ar
am
eter
s
,
lik
e
lo
ca
tio
n
,
s
ize,
o
r
n
u
m
b
e
r
o
f
R
E
g
en
er
ato
r
s
,
a
r
e
ad
ju
s
ted
u
n
til th
e
HC
is
o
b
tain
ed
[
1
3
]
.
Sto
ch
asti
c
m
eth
o
d
s
a
r
e
th
e
m
o
s
t
u
s
ed
as
th
ey
co
n
s
id
er
u
n
c
er
tain
ty
.
On
e
ap
p
r
o
ac
h
is
t
o
c
alcu
late
th
e
cu
m
u
lativ
e
d
is
tr
ib
u
tio
n
o
f
o
v
er
v
o
ltag
e
a
n
d
o
v
er
c
u
r
r
en
t
b
y
co
n
s
id
er
in
g
d
is
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
(
DE
R
)
lo
ca
tio
n
[
1
4
]
.
Oth
er
wo
r
k
s
u
s
e
th
e
ter
m
s
b
est
an
d
wo
r
s
t
HC
[
1
5
]
.
T
h
e
p
r
o
b
ab
ilit
y
o
f
ea
ch
c
o
n
s
u
m
er
ac
q
u
ir
in
g
s
o
lar
in
s
tallatio
n
s
is
s
tu
d
ied
t
h
r
o
u
g
h
a
B
ass
m
o
d
el
to
ca
lcu
late
th
e
y
ea
r
in
wh
ich
th
ey
will
r
ea
ch
t
h
e
f
ee
d
er
’
s
lim
it
an
d
th
e
tr
an
s
f
o
r
m
er
s
with
a
h
ig
h
er
p
r
o
b
ab
ilit
y
o
f
h
av
in
g
o
v
er
v
o
ltag
e
p
r
o
b
lem
s
[
1
6
]
.
Oth
e
r
s
tu
d
ies
co
n
s
id
er
th
e
co
n
ce
p
ts
o
f
tim
e
o
f
th
e
d
ay
an
d
tim
e
o
f
th
e
y
ea
r
with
h
ig
h
er
p
r
o
d
u
ctio
n
p
r
o
b
ab
ilit
y
to
m
ak
e
ca
lcu
latio
n
s
less
ex
ten
s
iv
e
[
1
7
]
.
A
d
ata
-
d
r
iv
e
n
HC
f
r
a
m
ewo
r
k
an
d
ac
tiv
e
lear
n
in
g
alg
o
r
it
h
m
s
ar
e
d
ev
elo
p
e
d
tak
i
n
g
in
to
ac
co
u
n
t
f
ac
to
r
s
lik
e
s
o
cio
ec
o
n
o
m
ic
b
e
h
av
io
r
s
an
d
h
o
w
DE
R
s
ar
e
m
an
ag
ed
a
n
d
co
n
tr
o
lled
s
h
o
win
g
th
at
in
te
r
p
r
etatio
n
an
d
r
esu
lts
ar
e
s
u
b
ject
to
t
h
e
s
e
f
ac
to
r
s
[
1
8
]
.
So
m
e
m
eth
o
d
s
co
m
b
in
e
d
etailed
ass
ess
m
en
t
b
ased
o
n
p
o
wer
f
lo
ws
o
r
s
h
o
r
t
-
cir
cu
it
s
tu
d
ies
with
s
tr
ea
m
lin
ed
as
s
ess
m
en
t
th
at
u
s
es
d
ir
ec
t
ca
lcu
latio
n
s
cr
ea
tin
g
h
y
b
r
id
ass
es
s
m
en
t
f
o
cu
s
ed
o
n
s
tead
y
-
s
tate
v
o
ltag
e
an
d
th
er
m
al
m
e
tr
ics,
r
ed
u
cin
g
tim
e
ca
lcu
latio
n
[
1
9
]
.
Alg
o
r
ith
m
s
s
u
ch
as
p
ar
ticle
s
war
m
o
p
tim
i
za
tio
n
(
PS
O)
,
g
e
n
etic
alg
o
r
ith
m
(
GA)
,
a
n
d
d
if
f
er
e
n
tial
ev
o
l
u
tio
n
(
DE
)
ar
e
u
s
ed
f
o
r
HC
an
al
y
s
is
to
d
eter
m
i
n
e
th
e
o
p
tim
al
l
o
ca
tio
n
an
d
m
ax
im
u
m
p
e
n
etr
atio
n
lev
el
co
n
s
id
er
in
g
lan
d
av
ailab
ilit
y
wh
ich
is
a
co
n
s
tr
ain
f
o
r
s
o
lar
p
h
o
t
o
v
o
ltaic
in
t
eg
r
atio
n
to
th
e
g
r
id
,
f
in
d
in
g
f
o
r
th
e
s
tu
d
y
ca
s
e
m
id
-
f
ee
d
er
lo
ca
tio
n
is
o
p
tim
al
co
m
p
ar
e
d
to
h
ea
d
o
r
en
d
f
ee
d
er
[
2
0
]
.
Sto
ch
asti
c
m
eth
o
d
s
ar
e
b
ased
o
n
p
r
o
b
a
b
ilis
tic
lo
ad
f
lo
ws
(
P
L
F)
cr
ea
tin
g
r
an
d
o
m
s
ce
n
ar
io
s
f
o
r
DE
R
n
u
m
b
er
,
ca
p
ac
ity
,
a
n
d
lo
ca
tio
n
.
T
h
ese
r
an
d
o
m
s
ce
n
ar
io
s
a
r
e
cr
ea
ted
th
r
o
u
g
h
m
eth
o
d
s
lik
e
th
e
d
is
p
er
s
ed
g
r
id
tech
n
iq
u
e
a
n
d
q
u
asi
-
Mo
n
te
C
ar
lo
[
1
3
]
.
Mo
n
te
C
ar
lo
s
im
u
latio
n
tech
n
iq
u
e
is
u
s
ed
to
cr
ea
te
s
ce
n
ar
io
s
with
m
ec
h
an
is
m
s
lik
e
t
h
e
r
o
u
lette
wh
ee
l
an
d
th
e
ap
p
licatio
n
o
f
s
ce
n
ar
io
r
ed
u
ctio
n
[
2
1
]
.
C
o
m
b
in
ed
with
Gau
s
s
ian
m
ix
tu
r
e
m
o
d
el
it
is
also
u
s
ed
to
ch
ar
ac
ter
ize
s
to
ch
asti
c
v
ar
iab
les
s
u
ch
as
ir
r
ad
ian
ce
an
d
d
em
an
d
,
an
d
p
o
wer
f
lo
w
r
esu
lts
co
n
ce
r
n
in
g
c
u
r
r
en
ts
,
v
o
ltag
es,
a
n
d
p
o
wer
f
ac
to
r
s
ar
e
a
n
aly
ze
d
to
d
eter
m
i
n
e
h
o
s
tin
g
ca
p
ac
ity
[
2
2
]
.
Mo
n
te
C
ar
lo
is
th
e
m
o
s
t
p
o
p
u
lar
n
u
m
er
ic
ap
p
r
o
ac
h
.
Alth
o
u
g
h
it
r
e
q
u
ir
es
a
g
r
ea
t
co
m
p
u
tatio
n
al
ca
p
ac
ity
,
it
p
r
o
v
id
es
g
r
id
o
p
er
ato
r
s
with
a
s
tr
aig
h
tf
o
r
war
d
ap
p
r
o
ac
h
to
u
n
d
er
s
tan
d
in
g
th
e
HC
an
d
ap
p
l
y
in
g
it
in
d
ec
is
io
n
-
m
ak
in
g
.
T
h
is
s
tu
d
y
ev
alu
ates
th
e
in
te
g
r
atio
n
o
f
R
E
th
r
o
u
g
h
t
h
e
H
C
co
n
ce
p
t
b
y
ca
lc
u
latin
g
in
d
i
ca
to
r
s
th
at
g
u
id
e
g
r
id
p
la
n
n
in
g
an
d
o
p
er
a
tio
n
.
T
h
e
m
o
d
el
o
f
th
e
g
r
i
d
o
f
San
An
d
r
es
I
s
lan
d
is
u
s
ed
as
a
s
tu
d
y
ca
s
e
w
ith
v
alu
ab
le
p
o
in
ts
th
at
p
r
o
v
id
e
i
n
s
ig
h
ts
in
to
th
e
ef
f
ec
ts
an
d
li
m
its
o
f
th
e
p
en
et
r
atio
n
o
f
R
E
in
th
e
g
r
id
.
I
t
is
r
elev
an
t
in
th
e
co
n
tex
t
o
f
San
An
d
r
es
I
s
lan
d
as
en
er
g
y
tr
an
s
itio
n
is
a
r
ea
lity
f
o
r
all
elec
tr
ical
g
r
id
s
,
an
d
m
o
r
e
s
o
f
o
r
a
r
e
g
io
n
c
o
n
s
id
er
ed
a
b
io
s
p
h
er
e
r
eser
v
e
in
n
ee
d
o
f
b
etter
s
ec
u
r
ity
o
f
s
u
p
p
ly
a
n
d
less
d
ep
en
d
en
ce
o
n
f
o
s
s
il f
u
els.
2.
H
O
ST
I
NG
CAP
A
CI
T
Y
So
m
e
o
f
th
e
p
er
f
o
r
m
a
n
ce
in
d
ex
es
ev
alu
ated
ar
e
m
en
tio
n
e
d
b
elo
w.
I
n
ter
m
s
o
f
cu
r
r
en
t,
th
e
r
atin
g
o
f
lin
es
an
d
tr
an
s
f
o
r
m
e
r
s
is
th
e
f
ir
s
t
v
ar
iab
le
m
o
n
ito
r
e
d
,
tak
in
g
th
e
m
ax
im
u
m
r
atin
g
f
o
r
ea
c
h
p
en
etr
atio
n
lev
el,
as d
ef
in
ed
b
y
(
1
)
.
=
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
1
6
0
-
6
1
6
9
6162
w
h
er
e
is
th
e
m
ax
im
u
m
cu
r
r
e
n
t
r
eg
is
ter
ed
in
th
e
lin
e
f
o
r
e
ac
h
p
en
etr
atio
n
lev
el.
C
h
an
g
e
in
r
atin
g
is
als
o
m
o
n
ito
r
ed
an
d
is
d
e
f
in
ed
b
y
(
2
)
[
6
]
:
∆
=
−
0
(
2
)
w
h
er
e
∆
is
th
e
m
ax
im
u
m
c
h
an
g
e
in
r
atin
g
o
f
lin
e
f
o
r
a
d
ete
r
m
in
ed
p
en
etr
atio
n
le
v
el,
is
r
atin
g
in
d
ex
d
ef
in
ed
b
y
(
1
)
,
a
n
d
0
is
th
e
lin
e
r
atin
g
with
o
u
t RE
s
o
u
r
ce
s
in
te
g
r
atio
n
.
Vo
ltag
e
v
ar
iatio
n
with
u
n
c
er
tain
ty
an
d
in
s
tan
tan
eo
u
s
ch
an
g
es
in
R
E
g
en
er
atio
n
s
o
u
r
ce
s
is
co
n
s
id
er
ed
o
n
e
o
f
th
e
m
o
s
t
lim
itin
g
f
ac
to
r
s
.
T
h
e
eq
u
atio
n
(
3
)
d
ef
in
es
HC
r
elate
d
to
o
v
e
r
v
o
ltag
e
[
2
3
]
.
Acc
o
r
d
in
g
to
C
o
lo
m
b
ian
r
e
g
u
latio
n
s
,
v
o
ltag
e
f
o
r
d
is
tr
ib
u
ti
o
n
g
r
id
s
m
u
s
t
r
a
n
g
e
b
etwe
en
9
0
%
an
d
1
1
0
%
o
f
n
o
m
in
al
v
o
ltag
e
f
o
r
p
er
i
o
d
s
lo
n
g
er
th
a
n
o
n
e
m
in
u
te
[
2
4
]
.
=
min
{
∑
|
(
[
≥
]
)
=
1
}
(
3
)
L
o
s
s
es a
r
e
r
ec
o
r
d
ed
t
h
r
o
u
g
h
t
h
e
(
4
)
:
=
∑
2
=
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I
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u
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Min
im
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m
v
o
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Fig
u
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4
s
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ax
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m
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eg
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ir
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iatio
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r
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o
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latio
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as
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o
ciate
d
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I
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Fig
u
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5
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Fig
u
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5
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Av
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p
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w
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th
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cir
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I
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e
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R
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ess
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Fo
r
th
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s
e,
it wa
s
f
o
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e
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e
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ctio
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th
at
d
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ib
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o
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th
e
Alm
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s
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it i
s
th
e
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o
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g
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I
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14
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6
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r
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24
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s
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ca
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b
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in
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ed
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ciate
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tain
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en
e
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ch
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e
r
a
m
p
s
.
Fig
u
r
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6
.
Activ
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p
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es
4
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3
.
Ra
t
ing
Fig
u
r
e
7
s
h
o
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th
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m
ax
im
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m
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atin
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f
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r
li
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ter
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lev
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L
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o
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eg
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ed
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Fig
u
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Ma
x
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es
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I
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t J E
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C
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N:
2088
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6167
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r
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s
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atin
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is
th
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m
o
s
t
li
m
itin
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f
ac
to
r
as
s
h
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wn
in
Fig
u
r
e
8
.
T
h
e
HC
ass
o
ciate
d
with
tr
an
s
f
o
r
m
er
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atin
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ca
n
b
e
f
o
u
n
d
at
ap
p
r
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x
im
ately
d
o
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b
le
t
h
e
lo
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co
n
n
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ted
to
th
e
cir
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th
is
p
o
in
t,
tr
an
s
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o
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m
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s
h
av
e
1
0
0
% r
ev
e
r
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e
f
lo
w.
Fig
u
r
e
8
.
Ma
x
im
u
m
r
atin
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in
t
r
an
s
f
o
r
m
er
s
o
f
Alm
en
d
r
o
s
cir
cu
it
4
.
4
.
CO
2
em
is
s
io
ns
W
ith
th
e
in
cr
ea
s
e
in
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
in
th
e
g
r
id
,
C
O
2
em
i
s
s
io
n
s
ar
e
lo
wer
ed
as
s
h
o
wn
in
Fig
u
r
e
9
.
I
n
th
e
s
ce
n
ar
io
o
f
an
av
er
ag
e
lo
ad
with
a
p
en
etr
atio
n
lev
el
o
f
5
.
5
5
MW,
an
av
er
ag
e
o
f
0
.
8
7
to
n
s
o
f
CO
2
i
s
s
av
ed
in
an
h
o
u
r
o
f
g
en
er
atio
n
.
T
h
e
am
o
u
n
t o
f
em
is
s
io
n
s
s
av
in
g
s
also
d
ep
en
d
s
o
n
t
h
e
v
ar
iab
ilit
y
o
f
th
e
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
.
Fig
u
r
e
9
.
C
O
2
em
is
s
io
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
14
,
No
.
6
,
Dec
em
b
e
r
20
24
:
6
1
6
0
-
6
1
6
9
6168
Fro
m
th
e
p
er
f
o
r
m
an
ce
in
d
e
x
e
s
ev
alu
ated
it
is
c
o
n
ce
iv
a
b
le
th
at
f
o
r
th
e
g
r
id
o
f
San
An
d
r
es
I
s
lan
d
s
tu
d
ied
,
th
e
lim
it
o
f
1
5
%
o
f
th
e
cir
cu
it
ca
p
ac
ity
,
tr
an
s
f
o
r
m
er
,
o
r
s
u
b
s
tatio
n
to
wh
ich
th
e
co
n
n
ec
tio
n
is
r
eq
u
ested
,
estab
lis
h
ed
b
y
R
eso
lu
tio
n
0
3
8
o
f
2
0
1
8
[
2
5
]
f
o
r
No
n
-
I
n
te
r
co
n
n
ec
ted
z
o
n
es,
wo
u
ld
n
o
t
h
a
v
e
a
n
eg
ativ
e
im
p
ac
t
o
n
th
e
g
r
id
o
p
er
atio
n
.
I
n
cr
ea
s
in
g
it wo
u
l
d
r
e
d
u
ce
g
as e
m
is
s
io
n
s
an
d
g
e
n
er
a
tio
n
co
s
ts
.
5.
CO
NCLU
SI
O
N
A
m
eth
o
d
o
lo
g
y
b
ased
o
n
M
o
n
te
C
ar
lo
s
im
u
latio
n
in
teg
r
ated
with
Dig
Sil
en
t
Po
wer
F
ac
to
r
y
a
n
d
Py
th
o
n
is
d
ev
elo
p
ed
.
T
h
is
m
eth
o
d
o
lo
g
y
m
a
k
es
it
p
o
s
s
ib
le
to
ev
alu
ate
p
e
r
f
o
r
m
an
ce
in
d
ex
es
an
d
to
f
in
d
th
e
HC
o
f
an
elec
tr
ical
g
r
i
d
.
HC
d
ep
en
d
s
o
n
th
e
to
p
o
lo
g
y
a
n
d
ass
et
ch
ar
ac
ter
is
tics
.
I
t
is
n
ec
ess
ar
y
to
m
o
d
el
lo
w
v
o
ltag
e
cir
cu
its
s
o
th
at
th
e
ef
f
ec
t
in
th
e
tails
o
f
th
e
cir
cu
it
ca
n
b
e
o
b
s
er
v
e
d
,
as
it
s
h
o
ws
g
r
ea
ter
v
ar
iatio
n
s
.
T
h
e
in
teg
r
atio
n
o
f
R
E
ch
a
n
g
es
o
p
er
atin
g
p
ar
a
m
eter
s
b
y
in
tr
o
d
u
cin
g
v
o
ltag
e
r
is
e
an
d
in
cr
ea
s
es
in
lin
es
an
d
tr
an
s
f
o
r
m
er
r
atin
g
.
Fo
r
t
h
e
s
tu
d
ied
g
r
i
d
,
tr
a
n
s
f
o
r
m
er
r
atin
g
i
s
th
e
m
o
s
t
lim
itin
g
f
a
cto
r
wit
h
an
HC
eq
u
iv
alen
t
o
f
ap
p
r
o
x
im
ately
twice
th
e
cir
cu
it
lo
ad
,
r
esu
ltin
g
in
1
0
0
%
r
ev
er
s
e
f
lo
w
f
o
r
s
o
m
e
tr
a
n
s
f
o
r
m
er
s
.
I
t
was
f
o
u
n
d
th
at
n
o
d
es
in
th
e
tail
o
f
th
e
ci
r
cu
it
ca
n
h
a
v
e
u
p
to
1
0
%
v
o
ltag
e
r
is
e,
wh
ich
ca
n
alter
th
e
p
r
o
tectio
n
s
ch
em
es,
Gr
id
o
p
e
r
ato
r
s
n
e
ed
t
o
h
a
v
e
m
o
r
e
o
b
s
er
v
ab
ilit
y
o
f
th
e
s
y
s
t
em
an
d
s
h
o
u
l
d
ad
j
u
s
t
s
ch
em
e
p
r
o
tectio
n
b
ased
o
n
n
ew
o
p
er
atio
n
al
p
ar
a
m
eter
s
.
T
h
e
in
tr
o
d
u
ctio
n
o
f
R
E
r
esu
lts
in
lo
wer
p
o
wer
lo
s
s
es.
Fo
r
th
e
s
tu
d
y
ca
s
e,
a
n
av
er
ag
e
o
f
3
.
3
3
%
o
f
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iv
e
rsit
y
o
f
C
o
lo
m
b
ia.
He
r
re
se
a
rc
h
in
tere
sts
i
n
c
lu
d
e
re
n
e
wa
b
le
e
n
e
rg
y
,
p
o
we
r
q
u
a
li
ty
,
m
e
teo
ro
l
o
g
ica
l
d
a
ta
a
n
a
l
y
ti
c
s,
a
n
d
a
rti
ficia
l
in
telli
g
e
n
c
e
(AI)
a
p
p
li
e
d
to
p
re
d
icti
o
n
sc
h
e
m
e
s.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
k
g
n
e
wb
a
ll
a
r@u
n
a
l.
e
d
u
.
c
o
.
Álv
a
r
o
Z
a
m
b
r
a
n
o
is
a
n
e
lec
tri
c
a
l
e
n
g
in
e
e
r
fr
o
m
Un
iv
e
rsi
d
a
d
Distrit
a
l
F
ra
n
c
isc
o
Jo
se
d
e
Ca
ld
a
s.
He
re
c
e
iv
e
d
a
m
a
ste
r’s
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
fr
o
m
th
e
Na
ti
o
n
a
l
Un
iv
e
rsity
o
f
Co
l
o
m
b
ia.
His
fie
ld
s
o
f
stu
d
y
in
c
lu
d
e
q
u
a
li
ty
p
o
we
r,
m
o
d
e
ll
in
g
o
f
e
lec
tri
c
a
l
p
o
we
r
sy
ste
m
s,
re
li
a
b
il
it
y
in
p
o
we
r
sy
ste
m
s
a
n
d
sm
a
rt
g
ri
d
s.
He
i
s
in
tere
ste
d
in
d
e
m
a
n
d
-
si
d
e
m
a
n
a
g
e
m
e
n
t
fo
r
e
n
e
rg
y
e
fficie
n
c
y
,
p
h
a
so
r
m
e
a
su
re
m
e
n
t
u
n
it
s,
re
n
e
wa
b
le
e
n
e
rg
y
i
n
teg
ra
ti
o
n
,
a
n
d
so
ftwa
re
d
e
v
e
lo
p
m
e
n
t.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
a
a
z
a
m
b
ra
n
o
p
@
u
n
a
l
.
e
d
u
.
c
o
.
J
a
v
ier
Ro
se
r
o
-
G
a
r
c
ia
wa
s
b
o
rn
i
n
P
o
to
si,
Co
l
o
m
b
ia,
i
n
1
9
7
8
.
He
re
c
e
iv
e
d
h
is
B
.
S
c
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
fr
o
m
th
e
Un
iv
e
rsid
a
d
o
f
Va
ll
e
,
C
a
li
,
Co
l
o
m
b
ia,
i
n
2
0
0
2
.
He
wo
rk
e
d
fo
r
c
o
n
str
u
c
ti
o
n
a
n
d
m
a
in
ten
a
n
c
e
o
f
p
o
we
r
sy
ste
m
s
a
n
d
s
u
b
sta
ti
o
n
s
in
Bo
g
o
tá
,
Co
lo
m
b
ia,
b
e
twe
e
n
2
0
0
2
a
n
d
2
0
0
4
.
He
re
c
e
iv
e
d
a
P
h
.
D
.
d
e
g
re
e
fro
m
th
e
Tec
h
n
ica
l
U
n
iv
e
rsit
y
o
f
Ca
talo
n
ia
(UPC)
in
2
0
0
7
a
n
d
m
a
ste
r’s
i
n
a
d
m
i
n
istratio
n
fr
o
m
Na
ti
o
n
a
l
U
n
iv
e
rsit
y
o
f
Co
lo
m
b
ia,
in
2
0
2
0
.
He
re
c
e
iv
e
d
IEE
E
se
n
i
o
r
m
e
m
b
e
r
a
n
d
t
h
e
IEE
E
AES
S
Ha
rry
R
o
we
M
imn
o
a
wa
rd
fo
r
e
x
c
e
ll
e
n
c
e
i
n
t
e
c
h
n
ica
l
c
o
m
m
u
n
ica
ti
o
n
s
f
o
r
2
0
0
7
fro
m
t
h
e
Ae
ro
sp
a
c
e
a
n
d
El
e
c
tro
n
ic
S
y
ste
m
s
S
o
c
iety
(AES
S
)
IEE
E
2
0
0
7
.
He
wo
r
k
e
d
with
As
e
a
Bro
wn
Bo
v
e
ri
(ABB)
,
Ba
rc
e
lo
n
a
,
S
p
a
in
,
fr
o
m
2
0
0
7
to
2
0
0
9
p
r
o
v
i
d
i
n
g
se
rv
ice
a
n
d
tec
h
n
ica
l
su
p
p
o
rt
fo
r
d
r
iv
e
s
f
o
r
in
d
u
strial
a
n
d
wi
n
d
m
il
l
sy
ste
m
s.
He
is
c
u
rre
n
tl
y
a
F
u
l
l
P
ro
fe
ss
o
r
i
n
th
e
Un
i
v
e
rsid
a
d
Na
c
io
n
a
l
d
e
Co
lo
m
b
ia’s
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ic
En
g
in
e
e
ri
n
g
De
p
a
rtme
n
t
i
n
Bo
g
o
ta.
He
h
a
s
p
u
b
li
sh
e
d
m
o
re
th
a
n
1
0
0
re
fe
rre
d
jo
u
rn
a
l
a
n
d
c
o
n
fe
re
n
c
e
p
a
p
e
rs.
His
re
se
a
rc
h
in
tere
sts
a
re
fo
c
u
se
d
o
n
th
e
a
re
a
s
o
f
m
o
d
e
ll
in
g
,
d
iag
n
o
s
is
a
n
d
c
o
n
tr
o
l
o
f
e
lec
tr
ica
l
m
a
c
h
in
e
s
a
n
d
d
ri
v
e
s,
e
lec
tri
c
m
o
b
il
it
y
a
n
d
sm
a
rt
g
ri
d
s.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
jar
o
se
ro
g
@
u
n
a
l.
e
d
u
.
c
o
.
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