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in
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tly
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s
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n
in
g
o
f
m
o
d
er
n
p
o
wer
s
y
s
tem
s
[
1
]
.
W
h
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th
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tech
n
o
lo
g
ies
co
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tr
ib
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to
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w
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-
cir
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[
2
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,
r
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[
3
]
,
an
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co
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n
s
[
4
]
,
all
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co
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f
th
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tu
d
y
,
is
v
o
ltag
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s
tab
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y
[
5
]
,
[
6
]
.
Vo
ltag
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s
tab
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r
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s
to
th
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ab
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f
a
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s
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s
[
7
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.
T
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co
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[
8
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.
Sev
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tu
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s
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es th
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is
k
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f
v
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-
r
elate
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f
ailu
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9
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-
[
1
2
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.
T
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ass
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tab
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v
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aly
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m
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s
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ap
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[
5
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,
[
1
3
]
.
Am
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tatic
m
eth
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d
s
,
P
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Q
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m
itted
b
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e
v
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ltag
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in
s
tab
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I
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T
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as r
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1
4
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1
7
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Giv
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A
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I
n
th
is
co
n
tex
t,
it
is
ess
en
tial
t
o
ex
p
lo
r
e
s
o
lu
tio
n
s
th
at
m
itig
ate
th
e
v
o
ltag
e
s
tab
ilit
y
is
s
u
es
ass
o
ciate
d
with
th
e
in
teg
r
atio
n
.
O
n
e
s
u
ch
s
o
lu
tio
n
,
ex
am
i
n
ed
in
th
is
s
tu
d
y
,
is
th
e
u
s
e
o
f
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
(
SC
s
)
.
T
h
ese
d
ev
ices
ar
e
s
elec
ted
d
u
e
to
th
eir
i
n
h
er
en
t
ca
p
ab
ilit
y
a
s
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
ato
r
s
.
Pre
v
io
u
s
s
tu
d
ies
h
av
e
d
e
m
o
n
s
tr
ated
t
h
at
r
ea
cti
v
e
p
o
wer
m
an
a
g
em
en
t
h
as
a
d
ir
ec
t
im
p
ac
t
o
n
v
o
ltag
e
s
tab
ilit
y
m
ar
g
in
s
[
2
2
]
,
[
2
3
]
.
Mo
r
e
o
v
er
,
SC
s
h
av
e
p
r
o
v
en
t
o
b
e
an
e
f
f
ec
tiv
e
s
o
lu
t
io
n
to
s
ev
e
r
al
ch
allen
g
es
in
tr
o
d
u
ce
d
b
y
R
E
S
in
p
o
wer
s
y
s
tem
s
[
2
4
]
.
T
h
eir
d
y
n
am
ic
p
er
f
o
r
m
an
ce
h
as
ev
en
b
ee
n
s
h
o
wn
to
s
u
r
p
ass
th
at
o
f
o
th
er
co
m
p
en
s
ato
r
s
,
s
u
ch
as
s
tatic
v
ar
co
m
p
en
s
at
o
r
s
(
SVC
s
)
[
2
5
]
,
[
2
6
]
.
I
n
ad
d
itio
n
to
th
eir
a
p
p
licatio
n
in
s
y
s
tem
s
with
h
ig
h
r
en
ewa
b
le
p
en
etr
atio
n
,
th
e
y
ar
e
also
b
en
ef
icial
in
o
th
e
r
lo
w
-
in
er
tia
en
v
ir
o
n
m
en
ts
,
s
u
ch
as
h
ig
h
v
o
ltag
e
d
ir
ec
t
cu
r
r
en
t
(
HVDC)
co
n
n
ec
tio
n
p
o
in
ts
[
2
7
]
,
[
2
8
]
.
T
h
is
p
ap
er
p
r
esen
ts
an
an
aly
s
is
o
f
th
e
im
p
ac
t
o
f
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
o
n
v
o
ltag
e
s
tab
ilit
y
in
p
o
wer
s
y
s
tem
s
with
h
ig
h
p
en
etr
atio
n
o
f
R
E
S.
T
h
e
ass
ess
m
en
t
o
f
lo
ad
a
b
ilit
y
m
ar
g
in
s
is
ca
r
r
ied
o
u
t
u
s
in
g
PV
cu
r
v
es,
wh
ile
u
n
ce
r
tain
t
y
in
r
e
n
ewa
b
le
g
e
n
er
atio
n
is
ad
d
r
ess
ed
th
r
o
u
g
h
th
e
2
m
+
1
p
o
in
t
est
im
ate
m
eth
o
d
.
T
h
e
IEEE
r
eliab
ilit
y
test
s
y
s
tem
(
R
T
S)
is
u
s
ed
as
th
e
tes
t
ca
s
e,
an
d
s
im
u
latio
n
s
ar
e
p
er
f
o
r
m
e
d
u
s
in
g
th
e
NE
PLAN
3
6
0
s
o
f
twar
e.
T
h
e
an
aly
s
is
co
m
p
ar
es
m
u
ltip
le
s
y
s
tem
s
ce
n
ar
io
s
an
d
h
ig
h
lig
h
ts
th
e
b
en
e
f
its
o
f
in
co
r
p
o
r
atin
g
s
y
n
c
h
r
o
n
o
u
s
co
n
d
en
s
er
s
to
en
h
an
ce
v
o
ltag
e
s
tab
ilit
y
.
2.
M
E
T
H
O
D
T
h
e
an
aly
s
is
o
f
th
e
im
p
ac
t
o
f
s
y
n
ch
r
o
n
o
u
s
co
n
d
e
n
s
er
s
o
n
v
o
ltag
e
s
tab
ilit
y
in
p
o
wer
s
y
s
tem
s
with
h
ig
h
r
en
ewa
b
le
en
er
g
y
p
en
etr
atio
n
r
eq
u
ir
es
a
co
m
p
r
eh
en
s
i
v
e
f
r
a
m
ewo
r
k
.
T
h
is
f
r
am
ewo
r
k
in
clu
d
es
s
ev
er
al
k
ey
co
m
p
o
n
en
ts
:
th
e
m
eth
o
d
u
s
ed
f
o
r
v
o
ltag
e
s
tab
ilit
y
an
aly
s
is
,
th
e
p
r
o
b
ab
ilis
tic
ap
p
r
o
ac
h
to
ac
co
u
n
t
f
o
r
u
n
ce
r
tain
ty
,
an
d
th
e
s
izin
g
cr
it
er
ia
f
o
r
b
o
t
h
R
E
S
an
d
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
.
E
ac
h
o
f
th
es
e
elem
en
ts
p
lay
s
a
cr
itical
r
o
le
in
ac
cu
r
ately
ass
es
s
in
g
s
y
s
tem
b
eh
av
io
r
u
n
d
e
r
v
a
r
y
in
g
o
p
er
atio
n
al
co
n
d
itio
n
s
.
T
h
is
s
ec
tio
n
d
etails
th
e
k
ey
c
o
m
p
o
n
en
ts
r
eq
u
ir
ed
f
o
r
an
aly
s
is
.
I
t
b
eg
in
s
with
a
n
ex
p
lan
at
io
n
o
f
P
-
V
cu
r
v
es
an
d
two
lo
a
d
ab
ilit
y
m
a
r
g
in
s
u
s
ed
to
ass
ess
v
o
ltag
e
s
tab
ilit
y
.
Nex
t,
th
e
2
m
+
1
p
o
i
n
t
esti
m
ate
m
eth
o
d
,
o
r
ig
in
ally
p
r
o
p
o
s
ed
b
y
H
o
n
g
[
2
9
]
,
is
in
tr
o
d
u
ce
d
an
d
ad
a
p
ted
to
t
h
e
co
n
tex
t
o
f
p
o
wer
s
y
s
tem
s
.
T
h
e
s
ec
tio
n
th
en
clar
if
ies
th
e
cr
iter
ia
u
s
ed
f
o
r
s
izin
g
R
E
S
,
r
ef
e
r
en
cin
g
r
e
lev
an
t
C
o
lo
m
b
ian
r
eg
u
latio
n
s
.
Fin
ally
,
it
p
r
esen
ts
th
e
ap
p
r
o
ac
h
f
o
r
s
izin
g
SC
s
,
in
clu
d
in
g
a
b
r
ief
d
escr
ip
tio
n
o
f
th
eir
p
lace
m
en
t w
ith
in
th
e
s
y
s
tem
.
2
.
1
.
P
V
curv
es a
nd
lo
a
d
m
a
rg
ins
T
h
e
P
-
V
cu
r
v
e
is
a
s
tatic
s
tab
ilit
y
an
aly
s
is
m
eth
o
d
u
s
ed
f
o
r
v
o
ltag
e
s
tab
ilit
y
,
w
h
ich
r
e
p
r
esen
ts
th
e
r
elatio
n
b
etwe
en
th
e
v
o
ltag
e
(
V)
an
d
th
e
ac
tiv
e
p
o
wer
(
P)
.
T
h
is
cu
r
v
e
is
o
b
tain
ed
b
y
c
o
m
p
u
tin
g
d
if
f
er
e
n
t
p
o
wer
f
lo
ws
wh
er
e
th
e
lo
a
d
c
h
an
g
es
[
3
0
]
.
T
h
is
f
o
r
m
s
a
“n
o
s
e”
s
h
ap
ed
cu
r
v
e
in
wh
ic
h
th
e
n
o
s
e
is
ca
lled
th
e
cr
itical
p
o
in
t
[
5
]
.
Af
ter
th
is
cr
i
tical
p
o
in
t
th
e
s
y
s
tem
is
in
v
o
l
tag
e
in
s
tab
ilit
y
.
Fro
m
th
is
cu
r
v
e,
two
l
o
ad
ab
ilit
y
m
ar
g
in
s
ca
n
b
e
d
ef
i
n
ed
.
T
h
e
f
i
r
s
t
o
n
e
is
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
tip
o
f
th
e
c
u
r
v
e
an
d
th
e
r
ated
p
o
wer
o
f
t
h
e
s
y
s
tem
’
s
lo
ad
.
T
h
e
s
ec
o
n
d
o
n
e
is
p
r
o
p
o
s
ed
in
t
h
is
d
o
c
u
m
en
t
an
d
is
d
ef
i
n
ed
as
t
h
e
d
i
f
f
er
en
ce
b
etwe
en
th
e
ac
tiv
e
p
o
wer
at
a
m
in
im
u
m
v
o
ltag
e
v
alu
e
an
d
th
e
r
ated
p
o
wer
o
f
th
e
s
y
s
tem
’
s
lo
ad
.
T
h
ese
two
m
ar
g
in
s
ar
e
n
am
ed
in
th
is
d
o
cu
m
e
n
t
as
th
e
m
ax
im
u
m
lo
ad
m
a
r
g
in
(
)
an
d
m
in
im
u
m
v
o
ltag
e
lo
ad
m
ar
g
in
(
)
r
esp
ec
tiv
ely
.
I
n
Fig
u
r
e
1
,
th
ese
two
m
ar
g
in
s
ar
e
illu
s
tr
ated
i
n
th
e
P
-
V
cu
r
v
e.
2
.
2
.
P
o
int
estim
a
t
e
m
et
ho
d
(
P
E
M
)
A
2
m
+1
p
o
in
t
esti
m
ate
m
et
h
o
d
is
u
s
ed
to
o
b
tain
th
ese
lo
ad
m
ar
g
in
s
f
o
r
co
n
s
id
er
in
g
t
h
e
u
n
ce
r
tain
ty
o
f
th
e
R
E
S
.
T
h
is
m
eth
o
d
was
d
ev
elo
p
ed
b
y
Ho
n
g
[
2
9
]
,
wh
er
e
m
is
th
e
n
u
m
b
er
o
f
r
an
d
o
m
v
ar
iab
les
th
at
ar
e
u
s
ed
f
o
r
th
e
a
n
aly
s
is
(
in
th
is
ca
s
e,
th
e
n
u
m
b
e
r
o
f
R
E
S).
T
h
is
m
eth
o
d
r
e
q
u
ir
es
th
e
k
n
o
wled
g
e
o
f
t
h
e
f
o
u
r
ce
n
tr
al
m
o
m
e
n
ts
o
f
ea
ch
r
an
d
o
m
v
ar
iab
le
(
,
,
,
3
,
,
4
)
,
wh
er
e
is
th
e
m
ea
n
v
alu
e,
th
e
s
tan
d
ar
d
d
ev
iatio
n
,
,
3
is
th
e
s
k
ewn
es
s
an
d
,
4
is
th
e
k
u
r
to
s
is
[
3
1
]
o
f
th
e
r
an
d
o
m
v
a
r
iab
le
(
th
e
in
jecte
d
p
o
wer
b
y
a
r
en
ewa
b
le
p
o
we
r
p
lan
t)
.
L
et
Z
b
e
a
r
an
d
o
m
v
a
r
iab
le
f
u
n
ctio
n
(
f
o
r
ex
am
p
le,
th
e
lo
a
d
m
ar
g
i
n
s
)
th
at
d
ep
e
n
d
s
o
n
t
h
e
r
an
d
o
m
v
ar
iab
les
X
(
R
E
S
p
o
wer
in
jec
tio
n
)
,
s
o
=
(
1
,
…
,
)
.
T
h
en
th
e
av
er
a
g
e
v
alu
e
an
d
th
e
s
tan
d
ar
d
d
ev
iatio
n
o
f
th
is
f
u
n
ctio
n
ca
n
b
e
o
b
tain
e
d
as
(
1
)
-
(
3
)
[
3
1
]
.
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Fo
r
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at
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o
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t
h
at
is
c
o
m
p
u
t
e
d
u
s
i
n
g
t
h
e
P
E
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f
o
r
m
u
l
a
t
i
o
n
.
E
a
c
h
c
o
n
c
e
n
t
r
a
t
i
o
n
p
o
i
n
t
c
o
m
p
u
t
e
s
a
v
a
l
u
e
f
o
r
Z
in
a
s
ce
n
ar
io
o
f
th
e
r
an
d
o
m
v
ar
iab
le
X,
(
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.
T
h
e
v
alu
es f
o
r
,
an
d
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ar
e
co
m
p
u
ted
as
(
4
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-
(
6
)
[
3
1
]
.
,
=
+
,
(
4
)
,
=
{
(
−
1
)
3
−
,
(
,
1
−
,
2
)
,
=
1
,
2
1
−
1
,
4
−
,
3
2
,
=
3
(
5
)
,
=
{
,
3
2
+
(
−
1
)
3
−
√
,
4
−
3
,
3
2
4
,
=
1
,
2
0
,
=
3
(
6
)
T
h
er
e
ar
e
3
co
n
ce
n
t
r
atio
n
p
o
i
n
ts
f
o
r
ea
ch
r
an
d
o
m
v
ar
iab
le,
h
en
ce
m
ak
in
g
it 3
m
co
n
ce
n
tr
a
tio
n
p
o
in
ts
.
Ho
wev
er
,
wh
en
k
=
3
all
co
n
ce
n
tr
atio
n
p
o
in
ts
s
h
ar
e
th
e
s
am
e
eq
u
atio
n
m
ak
i
n
g
th
em
2
m
+1
co
n
ce
n
tr
atio
n
p
o
in
ts
.
T
h
is
m
eth
o
d
is
u
s
ed
f
o
r
in
d
e
p
en
d
en
t
r
an
d
o
m
v
ar
i
ab
les
,
b
u
t
if
th
is
is
n
o
t
th
e
c
ase,
th
e
co
r
r
elate
d
r
an
d
o
m
v
a
r
iab
les
ar
e
d
ec
o
r
r
elate
d
b
ased
o
n
f
ictitio
u
s
v
ar
iab
les.
T
h
is
is
d
o
n
e
b
y
u
s
in
g
a
C
h
o
lesk
y
tr
an
s
f
o
r
m
atio
n
as
it
is
p
r
esen
ted
in
[
3
1
]
.
I
n
th
is
d
o
cu
m
en
t
,
th
e
r
an
d
o
m
v
ar
iab
les
a
r
e
ass
u
m
ed
to
b
e
in
d
ep
en
d
en
t
,
s
o
th
e
r
e
is
n
o
n
e
ed
to
u
s
e
th
is
p
r
o
ce
d
u
r
e.
No
w
with
th
is
p
r
o
ce
d
u
r
e,
2
m
+1
g
en
er
atio
n
s
ce
n
ar
io
s
ar
e
o
b
tain
ed
.
T
h
ese
s
ce
n
ar
io
s
r
ep
r
esen
t
th
e
ac
tiv
e
p
o
wer
th
at
is
p
r
o
d
u
ce
d
in
ea
ch
o
f
th
e
R
E
S
(
,
)
.
W
ith
th
ese
v
alu
es,
2
m
+1
PV
cu
r
v
es
ar
e
co
m
p
u
ted
,
an
d
all
t
h
e
lo
a
d
m
a
r
g
in
s
a
r
e
o
b
tain
e
d
.
W
ith
ea
c
h
r
esp
e
ctiv
e
weig
h
t,
th
e
m
ea
n
v
alu
e
an
d
th
e
s
tan
d
ar
d
d
ev
iatio
n
o
f
th
e
lo
a
d
m
ar
g
in
s
ar
e
ca
lcu
lated
with
(
1
)
,
(
2
)
,
an
d
(
3
)
.
2
.
3
.
Co
nfidence
inte
rv
a
ls
As
s
tated
b
ef
o
r
e,
u
s
in
g
(
1
)
,
(
2
)
,
an
d
(
3
)
,
th
e
m
ea
n
v
alu
e
an
d
th
e
s
tan
d
ar
d
d
ev
iatio
n
o
f
th
e
lo
ad
m
ar
g
in
s
ar
e
ca
lcu
lated
.
W
ith
th
ese
two
v
alu
es
an
in
ter
v
al
wi
th
a
co
n
f
id
en
ce
lev
el
o
f
9
5
%
ca
n
b
e
o
b
tain
ed
.
I
n
(
7
)
t
h
e
lo
we
r
v
alu
e
o
f
th
e
c
o
n
f
id
en
ce
i
n
ter
v
al
is
s
h
o
wn
,
wh
er
e
τ
tak
es
t
h
e
v
alu
e
o
f
1
.
9
6
f
o
r
9
5
%
co
n
f
id
e
n
ce
;
d
ef
in
ed
as (
7
)
[
1
2
]
.
=
[
µ
−
]
(
7
)
Fig
u
r
e
1.
PV c
u
r
v
e
with
th
e
d
ef
in
ed
lo
ad
m
ar
g
i
n
s
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
I
mp
a
ct
o
f syn
ch
r
o
n
o
u
s
co
n
d
en
s
ers
o
n
vo
lta
g
e
s
ta
b
ilit
y
in
s
ystems
…
(
Ju
a
n
E
s
teb
a
n
R
o
d
r
íg
u
ez Qu
ir
o
g
a
)
763
2
.
4
.
Rea
c
t
iv
e
po
wer
lim
it
s
f
o
r
RE
S
L
ik
e
it
is
s
tated
in
[
3
0
]
,
PV
cu
r
v
es
ar
e
co
m
p
u
ted
u
s
in
g
m
u
ltip
le
p
o
wer
f
lo
ws.
I
t
is
cr
itical
to
estab
lis
h
th
e
p
o
wer
lim
its
R
E
S
h
av
e.
I
n
t
h
is
d
o
c
u
m
en
t
,
th
e
C
o
lo
m
b
ian
r
eg
u
latio
n
is
u
s
e
d
as
a
r
ef
er
en
ce
f
o
r
th
e
r
estrictio
n
r
en
ewa
b
le
en
er
g
ies
h
av
e.
T
h
e
en
er
g
y
an
d
g
a
s
r
eg
u
lato
r
y
co
m
m
is
s
io
n
(
C
R
E
G)
estab
lis
h
es
in
th
e
0
9
0
law
o
f
2
0
1
9
t
h
at
r
en
ewa
b
le
en
er
g
ies
s
h
o
u
ld
h
a
v
e
at
least
a
0
.
9
5
p
o
wer
f
ac
to
r
t
o
in
ject
an
d
ab
s
o
r
b
r
ea
ctiv
e
p
o
wer
i
n
to
th
e
n
atio
n
al
g
r
id
[
3
2
]
.
Usi
n
g
th
ese
r
ea
ctiv
e
lim
its
,
R
E
S
ar
e
co
n
f
ig
u
r
ed
as
a
PV
elem
en
t
f
o
r
p
o
wer
f
lo
w
ca
lcu
la
tio
n
,
with
th
e
ac
tiv
e
p
o
wer
co
n
f
ig
u
r
e
d
d
ep
en
d
in
g
o
n
t
h
e
g
en
er
atio
n
s
c
en
ar
io
ca
lc
u
lated
with
PEM
.
T
h
is
co
n
f
ig
u
r
atio
n
is
u
s
ed
wh
en
th
er
e
ar
e
n
o
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
co
n
n
ec
ted
to
th
e
s
am
e
b
u
s
as
th
e
R
E
S
.
On
th
e
o
th
er
h
an
d
,
wh
en
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
ar
e
u
s
ed
in
th
e
s
am
e
b
u
s
as
th
e
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
,
th
e
co
n
f
ig
u
r
atio
n
ch
an
g
es.
No
w
th
e
y
ar
e
estab
lis
h
ed
as
a
PQ,
wh
er
e
th
eir
ac
ti
v
e
p
o
wer
d
ep
e
n
d
s
o
n
th
e
g
en
e
r
atio
n
s
ce
n
ar
io
,
an
d
th
e
Q
is
f
ix
ed
b
ased
o
n
th
e
v
al
u
es o
b
tain
ed
f
r
o
m
a
p
o
wer
f
lo
w
with
n
o
s
y
n
ch
r
o
n
o
u
s
co
n
d
e
n
s
er
s
.
2
.
5
.
Sy
nchro
no
us
co
nd
ens
er
s
s
izing
A
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
(
S
C
)
is
a
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e
th
at
o
p
er
ates
with
o
u
t
a
p
r
im
e
m
o
v
er
o
r
m
ec
h
an
ical
lo
a
d
.
B
y
co
n
tr
o
llin
g
its
ex
citatio
n
f
ield
,
it
ca
n
g
en
er
ate
o
r
ab
s
o
r
b
r
ea
ctiv
e
p
o
wer
.
T
h
e
y
h
a
v
e
b
ee
n
u
s
ed
s
in
ce
1
9
3
0
as
r
ea
cti
v
e
p
o
wer
co
m
p
en
s
ato
r
s
in
tr
a
n
s
m
is
s
io
n
an
d
s
u
b
-
t
r
an
s
m
is
s
io
n
s
y
s
tem
s
[
7
]
.
I
n
r
ec
en
t
y
ea
r
s
,
s
y
n
ch
r
o
n
o
u
s
co
n
d
e
n
s
er
s
h
av
e
b
eg
u
n
to
r
is
e
ag
ain
b
ec
au
s
e
o
f
th
e
in
cl
u
s
io
n
o
f
r
e
n
ewa
b
le
en
er
g
y
.
I
n
C
h
in
a
,
th
eir
ex
ce
llen
t
p
er
f
o
r
m
an
ce
is
r
ef
lecte
d
i
n
s
tr
o
n
g
v
o
ltag
e
s
u
p
p
o
r
t
an
d
o
v
er
lo
a
d
ca
p
a
city
,
an
d
th
er
e
is
a
lo
t o
f
im
p
r
o
v
em
e
n
t in
o
r
d
er
as
p
ec
ts
o
f
th
e
p
o
wer
s
y
s
tem
s
[
3
3
]
.
As
a
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
ato
r
,
it
is
n
ec
ess
ar
y
to
estab
li
s
h
th
e
ca
p
ac
ity
o
f
th
ese
d
ev
ices.
I
n
th
is
d
o
cu
m
e
n
t
,
th
ey
ar
e
u
s
ed
as
a
r
ea
ctiv
e
co
m
p
e
n
s
ato
r
f
o
r
r
e
n
e
wab
le
en
er
g
y
s
o
u
r
ce
s
wh
o
s
e
p
o
wer
f
ac
to
r
tak
es
th
e
v
alu
e
o
f
0
.
9
5
.
A
n
ew
p
o
w
er
f
ac
to
r
is
th
e
o
b
jectiv
e
to
b
e
ac
h
iev
ed
u
s
in
g
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
.
I
n
(
8
)
it
is
s
h
o
wn
th
e
eq
u
atio
n
u
s
ed
to
d
eter
m
in
e
th
e
r
ea
ctiv
e
p
o
we
r
o
f
th
e
s
y
n
c
h
r
o
n
o
u
s
co
n
d
en
s
er
s
.
=
−
(
ta
n
(
c
os
−
1
(
)
)
)
(
8
)
T
h
e
lo
ca
tio
n
o
f
t
h
e
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
i
n
th
is
s
tu
d
y
is
e
s
tab
lis
h
ed
to
b
e
th
e
s
am
e
as
R
E
S
.
T
h
is
is
also
a
ch
o
ice
m
ad
e
b
y
d
if
f
er
en
t stu
d
ies lik
e
[
6
]
.
3.
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
t
h
e
s
tu
d
y
s
y
s
tem
an
d
th
e
v
a
r
iatio
n
s
t
h
at
ar
e
m
ad
e
to
it,
to
in
clu
d
e
R
E
S
an
d
s
y
n
ch
r
o
n
o
u
s
co
n
d
e
n
s
er
s
.
Als
o
,
th
e
r
esu
lts
o
f
th
e
d
if
f
er
en
t
ca
s
es
o
f
s
tu
d
y
ar
e
p
r
esen
ted
.
First,
a
m
ea
n
g
en
er
atio
n
s
ce
n
ar
io
is
s
tu
d
ie
d
to
co
n
clu
d
e
ab
o
u
t
th
e
ef
f
ec
t
o
f
s
y
n
c
h
r
o
n
o
u
s
co
n
d
en
s
e
r
s
.
Af
ter
th
is
,
two
an
aly
s
es
with
an
d
with
o
u
t
s
y
n
ch
r
o
n
o
u
s
c
o
n
d
e
n
s
er
s
ar
e
p
r
e
s
en
ted
u
s
in
g
PEM
to
ca
p
tu
r
e
th
e
u
n
ce
r
tain
ty
a
n
d
co
n
clu
d
e
b
ased
o
n
co
n
f
id
en
ce
in
ter
v
als.
T
h
e
p
o
wer
f
ac
to
r
u
s
ed
f
o
r
R
E
S
is
e
s
tab
lis
h
ed
in
0
.
9
5
an
d
th
e
v
o
ltag
e
cr
iter
ia
f
o
r
th
e
m
ar
g
i
n
(
)
is
9
5
%.
3
.
1
.
T
est
s
y
s
t
em
T
h
e
s
y
s
tem
u
s
ed
f
o
r
th
is
s
tu
d
y
is
th
e
I
E
E
E
-
R
T
S
s
y
s
tem
th
at
h
as
2
4
b
u
s
es
[
2
6
]
.
T
h
e
elec
tr
i
ca
l
s
in
g
le
-
lin
e
d
iag
r
am
o
f
th
e
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
2
.
Fo
r
th
is
s
y
s
tem
th
e
b
u
s
s
elec
ted
as
s
lac
k
is
th
e
eq
u
iv
alen
t
g
en
er
ato
r
o
n
b
u
s
2
3
.
Fin
ally
,
an
ec
o
n
o
m
ic
d
is
p
atch
is
p
er
f
o
r
m
ed
b
ased
o
n
th
e
v
ar
ia
b
le
co
s
t
o
f
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es
o
f
th
e
s
y
s
tem
to
p
e
r
f
o
r
m
a
p
o
wer
f
l
o
w.
All
th
e
p
ar
am
eter
s
o
f
th
e
s
y
s
tem
ar
e
in
clu
d
ed
in
o
r
ig
in
a
l
d
o
cu
m
e
n
t
[
3
4
]
.
3
.
2
.
Renew
a
ble e
nerg
y
info
r
m
a
t
io
n
As
a
s
tu
d
y
ca
s
e
f
o
r
test
in
g
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
l
o
g
y
,
s
o
m
e
co
al
-
b
ased
s
y
n
ch
r
o
n
o
u
s
g
en
er
atio
n
is
r
ep
lace
d
b
y
r
e
n
ewa
b
le
en
er
g
y
g
en
e
r
atio
n
.
T
h
e
two
th
e
r
m
i
c
p
lan
ts
with
a
ca
p
ac
ity
o
f
7
6
MW
co
n
n
ec
ted
to
n
o
d
es
1
an
d
2
,
f
o
r
a
to
tal
o
f
4
m
ac
h
in
es,
g
et
r
ep
lace
d
b
y
two
win
d
p
o
wer
p
ar
k
s
(
W
PP
)
r
ated
with
2
0
0
MW.
Als
o
in
n
o
d
e
1
6
,
th
e
1
5
5
M
W
co
al
th
er
m
ic
p
lan
t
is
r
ep
la
ce
d
b
y
a
3
0
0
MW
W
PP
.
W
it
h
th
ese
r
ep
lace
m
e
n
ts
,
th
e
s
y
s
tem
en
d
s
u
p
with
a
2
4
%
r
en
ewa
b
le
en
er
g
y
p
en
etr
ati
o
n
.
Fig
u
r
e
3
s
h
o
ws
th
e
ch
an
g
e
s
m
ad
e
to
th
e
I
E
E
E
-
R
T
S sy
s
tem
.
T
h
e
ap
p
licatio
n
o
f
th
e
PEM
r
eq
u
ir
es
to
k
n
o
w
th
e
s
tatis
tical
in
f
o
r
m
atio
n
o
f
th
ese
th
r
ee
win
d
p
o
wer
p
ar
k
s
.
I
n
T
a
b
le
1
,
th
e
f
o
u
r
s
tatis
tical
ce
n
tr
al
m
o
m
en
ts
o
f
th
e
th
r
ee
W
PP
ar
e
s
h
o
wn
;
th
es
e
ar
e
n
o
r
m
alize
d
to
th
e
r
ated
p
o
wer
o
f
ea
ch
W
PP
.
T
h
is
in
f
o
r
m
atio
n
ca
n
b
e
o
b
tain
e
d
th
r
o
u
g
h
M
o
n
te
C
ar
lo
s
im
u
latio
n
s
to
ch
ar
ac
ter
ize
R
E
S
,
as
s
h
o
wn
[
3
5
]
.
Als
o
,
th
e
ca
p
ac
ity
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
is
ca
lcu
lated
to
ac
h
iev
e
a
0
.
8
5
p
o
wer
f
ac
to
r
in
th
e
p
o
i
n
t
o
f
c
o
n
n
ec
tio
n
o
f
th
e
R
E
S
.
T
h
ese
v
alu
es
ar
e
s
h
o
w
n
in
T
ab
le
2
,
wh
e
r
e
th
e
in
f
o
r
m
atio
n
o
f
t
h
e
r
ea
ctiv
e
lim
its
o
f
th
e
W
PP
is
al
s
o
av
ailab
le.
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
.
2
,
J
u
n
e
20
2
6
:
760
-
769
764
Fig
u
r
e
2
.
I
E
E
E
R
T
S sy
s
tem
[
3
4
]
Fig
u
r
e
3
.
I
E
E
E
-
R
T
S sy
s
tem
with
th
e
r
en
ewa
b
le
r
ep
lace
m
en
ts
T
ab
le
1
.
Statis
tical
in
f
o
r
m
atio
n
o
f
th
e
W
PP
C
e
n
t
r
a
l
m
o
me
n
t
1
2
16
µ
/
0
.
3
0
1
8
0
.
3
0
1
8
0
.
2
9
4
9
/
µ
1
.
0
0
9
6
1
.
0
0
9
6
0
.
5
2
5
5
,
3
0
.
8
4
9
0
0
.
8
4
9
0
-
0
.
3
5
7
3
,
4
2
.
4
2
7
0
2
.
4
2
7
0
1
.
8
3
5
7
T
ab
le
2
.
R
ea
ctiv
e
lim
its
f
o
r
th
e
W
PP
an
d
SC
W
i
n
d
p[
a
r
k
[
M
W
]
[
M
v
a
r
]
[
M
v
a
r
]
S
C
[
M
v
a
r
]
S
C
[
M
v
a
r
]
1
2
0
0
66
-
66
58
-
58
2
2
0
0
66
-
66
58
-
58
16
3
0
0
99
-
99
87
-
87
3
.
3
.
Vo
l
t
a
g
e
s
t
a
bil
it
y
re
s
ults
in a
n a
v
er
a
g
e
g
ener
a
t
io
n sc
ena
rio
I
n
th
is
s
u
b
s
ec
tio
n
,
P
-
V
c
u
r
v
e
s
ar
e
co
m
p
u
ted
f
o
r
a
d
eter
m
i
n
is
tic
av
er
ag
e
g
en
er
atio
n
s
ce
n
ar
io
.
T
h
e
ac
tiv
e
p
o
wer
g
e
n
er
ated
in
th
i
s
ca
s
e
is
6
0
.
3
6
MW
f
o
r
th
e
two
W
PP
s
co
n
n
ec
ted
to
b
u
s
es
1
an
d
2
a
n
d
8
0
.
4
7
MW
f
o
r
th
e
W
PP
co
n
n
ec
ted
to
b
u
s
1
6
.
Fro
m
th
is
s
ce
n
ar
io
,
lo
ad
m
ar
g
in
s
ar
e
o
b
tain
e
d
f
o
r
th
r
ee
d
if
f
er
e
n
t
s
y
s
tem
s
.
Fir
s
t,
f
o
r
th
e
test
s
y
s
t
em
with
o
u
t
R
E
S
an
d
s
y
n
ch
r
o
n
o
u
s
co
n
d
e
n
s
er
s
.
Seco
n
d
,
f
o
r
th
e
s
y
s
tem
with
th
e
in
clu
s
io
n
o
f
R
E
S
b
u
t
with
o
u
t
s
y
n
ch
r
o
n
o
u
s
co
n
d
e
n
s
er
s
.
An
d
f
in
ally
,
f
o
r
th
e
s
y
s
tem
with
R
E
S
an
d
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
.
Als
o
,
f
o
r
th
e
th
r
ee
r
esu
lts
o
b
tain
ed
,
Fig
u
r
e
4
s
h
o
ws
a
co
m
p
ar
ativ
e
cu
r
v
e
o
f
th
e
n
o
d
es th
at
r
ea
ch
th
e
m
in
im
u
m
v
o
ltag
e,
wh
ich
in
th
is
ca
s
e
is
9
5
%,
u
s
ed
to
ca
lcu
late
th
e
m
in
im
u
m
v
o
ltag
e
lo
a
d
m
ar
g
in
(
)
.
All
n
o
d
es
o
f
th
e
s
y
s
tem
s
h
ar
e
th
e
s
am
e
v
alu
e
f
o
r
th
e
m
a
x
im
u
m
lo
a
d
m
ar
g
in
(
)
.
T
ab
le
3
p
r
esen
ts
all
th
e
r
esu
lts
o
b
tain
e
d
f
o
r
t
h
is
av
er
ag
e
s
ce
n
a
r
io
.
T
h
e
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
h
as
a
p
o
s
itiv
e
ef
f
ec
t
o
n
v
o
ltag
e
s
tab
ilit
y
.
T
h
e
ef
f
ec
t
was
s
o
s
ig
n
if
ican
t
th
at
it
ev
en
s
u
r
p
ass
ed
th
e
s
y
s
tem
th
at
o
n
ly
h
as
s
y
n
c
h
r
o
n
o
u
s
g
en
e
r
atio
n
.
Als
o
,
th
e
co
n
g
esti
o
n
b
u
s
o
f
th
e
s
y
s
tem
ch
an
g
ed
f
r
o
m
n
o
d
e
4
t
o
n
o
d
e
6
th
a
n
k
s
to
th
e
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
.
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
I
mp
a
ct
o
f syn
ch
r
o
n
o
u
s
co
n
d
en
s
ers
o
n
vo
lta
g
e
s
ta
b
ilit
y
in
s
ystems
…
(
Ju
a
n
E
s
teb
a
n
R
o
d
r
íg
u
ez Qu
ir
o
g
a
)
765
Fig
u
r
e
4.
PV c
u
r
v
es f
o
r
th
e
av
er
ag
e
g
en
e
r
atio
n
s
ce
n
ar
i
o
T
ab
le
3
.
L
o
ad
m
ar
g
in
s
o
b
tain
e
d
f
o
r
t
h
e
av
er
a
g
e
g
e
n
er
atio
n
s
ce
n
ar
io
Lo
a
d
a
b
i
l
i
t
y
m
a
r
g
i
n
s
Te
st
s
y
s
t
e
m
Te
st
s
y
s
t
e
m
w
i
t
h
R
ES
Te
st
s
y
s
t
e
m
w
i
t
h
R
ES
a
n
d
S
C
[
%]
4
0
.
0
3
3
.
0
4
7
.
0
[
%]
5
7
.
0
4
9
.
5
6
1
.
5
[
M
W
]
1
1
4
0
.
0
9
4
0
.
5
1
3
3
9
.
5
[
M
W
]
1
6
2
4
.
5
1
4
1
0
.
0
1
7
5
2
.
8
M
i
n
i
m
u
m
v
o
l
t
a
g
e
b
u
s
(
4
)
(
4
)
(
6
)
3.
4
.
Resul
t
s
f
o
r
t
he
P
E
M
a
na
ly
s
is
in t
he
t
est
s
y
s
t
em
wit
h RG
wit
ho
ut
CS
No
w
th
e
r
esu
lts
f
o
r
th
e
PEM
an
aly
s
is
ar
e
p
r
esen
ted
f
o
r
th
e
s
y
s
tem
with
R
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
with
o
u
t
im
p
lem
e
n
tin
g
s
y
n
ch
r
o
n
o
u
s
c
o
n
d
e
n
s
er
s
.
First
,
all
t
h
e
co
n
ce
n
tr
atio
n
p
o
i
n
ts
ar
e
c
alcu
lated
f
o
r
th
e
3
W
PP
,
wh
ich
lead
s
to
7
co
n
ce
n
tr
atio
n
p
o
in
ts
.
I
n
T
ab
le
4
,
all
th
e
co
n
ce
n
tr
atio
n
p
o
in
ts
ar
e
p
r
esen
ted
,
in
clu
d
in
g
th
e
weig
h
t
o
f
ea
ch
p
o
in
t
an
d
th
e
r
esp
ec
tiv
e
ac
tiv
e
p
o
wer
g
en
er
atio
n
.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
all
th
e
weig
h
t
f
ac
to
r
s
ad
d
u
p
to
1
.
W
ith
th
e
co
n
ce
n
tr
atio
n
p
o
in
ts
,
s
ev
en
PV c
u
r
v
es we
r
e
co
m
p
u
ted
to
ac
q
u
ir
e
th
e
m
ea
n
an
d
th
e
s
tan
d
ar
d
d
ev
iatio
n
o
f
th
e
l
o
ad
m
ar
g
i
n
s
.
I
t
is
wo
r
th
m
en
tio
n
in
g
t
h
at
th
e
co
n
ce
n
tr
atio
n
p
o
in
t
W
0
is
th
e
av
e
r
ag
e
g
en
er
atio
n
s
ce
n
ar
io
an
aly
ze
d
ab
o
v
e.
T
ab
le
5
p
r
esen
ts
th
e
lo
ad
m
ar
g
in
s
in
%
,
wh
ile
T
ab
le
6
p
r
esen
ts
th
e
s
am
e
m
ar
g
in
s
in
MW.
Fin
ally
,
T
ab
le
7
p
r
esen
ts
th
e
m
ea
n
v
alu
e
an
d
th
e
s
tan
d
a
r
d
d
e
v
iatio
n
in
MW
an
d
%
f
o
r
th
e
test
s
y
s
tem
with
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
with
o
u
t
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
.
T
h
is
tab
le
al
s
o
h
as
in
f
o
r
m
atio
n
o
n
th
e
c
o
ef
f
icien
t o
f
v
ar
iatio
n
(
σ
/
µ
)
an
d
th
e
lo
w
v
alu
e
(
m
i
n
i
m
u
m
v
alu
e
)
o
f
th
e
co
n
f
id
en
ce
in
ter
v
al
(
).
T
ab
le
4
.
C
o
n
ce
n
tr
atio
n
p
o
in
ts
ca
lcu
lated
f
o
r
t
h
e
3
W
PP
C
o
n
c
e
n
t
r
a
t
i
o
n
p
o
i
n
t
1
[
M
W
]
2
[
M
W
]
16
[
M
W
]
W
e
i
g
h
t
f
a
c
t
o
r
w0
6
0
.
3
6
6
0
.
3
6
8
8
.
4
7
-
0
.
7
5
7
7
w1
1
6
9
.
9
3
6
0
.
3
6
8
8
.
4
7
0
.
2
0
2
5
w2
2
.
5
3
6
0
.
3
6
8
8
.
4
7
0
.
3
8
3
6
w3
6
0
.
3
6
1
6
9
.
9
3
8
8
.
4
7
0
.
2
0
2
5
w4
6
0
.
3
6
2
.
5
3
8
8
.
4
7
0
.
3
8
3
6
w5
6
0
.
3
6
6
0
.
3
6
1
4
1
.
4
9
0
.
3
3
2
4
w6
6
0
.
3
6
6
0
.
3
6
1
8
.
8
4
0
.
2
5
3
1
T
ab
le
5
.
L
o
ad
m
ar
g
in
s
in
% f
o
r
th
e
test
s
y
s
tem
with
R
E
S wit
h
o
u
t SC
C
o
n
c
e
n
t
r
a
t
i
o
n
p
o
i
n
t
[
%]
[
%]
w0
3
3
.
0
0
4
9
.
6
5
w1
4
3
.
6
0
5
9
.
2
5
w2
2
6
.
1
0
4
3
.
5
0
w3
4
3
.
6
0
5
9
.
2
0
w4
2
6
.
0
0
4
3
.
6
0
w5
3
3
.
4
0
5
0
.
2
0
w6
3
2
.
5
0
4
8
.
8
5
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
.
2
,
J
u
n
e
20
2
6
:
760
-
769
766
T
ab
le
6
.
L
o
ad
m
ar
g
in
s
in
MW f
o
r
th
e
test
s
y
s
tem
with
R
E
S
with
o
u
t SC
C
o
n
c
e
n
t
r
a
t
i
o
n
p
o
i
n
t
[
M
W
]
[
M
W
]
w0
9
4
0
.
5
0
1
4
1
5
.
0
3
w1
1
2
4
2
.
6
0
1
6
8
8
.
6
3
w2
7
4
3
.
8
5
1
2
3
9
.
7
5
w3
1
2
4
2
.
6
0
1
6
8
7
.
2
0
w4
7
4
1
.
0
0
1
2
4
2
.
6
0
w5
9
5
1
.
9
0
1
4
3
0
.
7
0
w6
9
2
6
.
2
5
1
3
9
2
.
2
3
T
ab
le
7
.
Statis
tical
in
f
o
r
m
atio
n
o
f
th
e
lo
ad
m
a
r
g
in
s
f
o
r
th
e
t
est s
y
s
tem
with
R
E
S with
o
u
t SC
S
t
a
t
i
st
i
c
s
[
%]
[
M
W
]
µ
(
)
3
1
.
9
7
9
1
1
.
0
8
µ
(
)
4
8
.
8
3
1
3
9
1
.
6
3
σ (
)
9
.
0
3
2
5
7
.
4
7
σ (
)
8
.
0
8
2
3
0
.
2
4
σ (
)
/
µ
(
)
0
.
2
8
0
.
2
8
σ (
)
/
µ
(
)
0
.
1
7
0
.
1
7
(
)
1
4
.
2
6
4
0
6
.
4
4
(
)
3
2
.
9
9
9
4
0
.
3
5
3.
5
.
Resul
t
s
f
o
r
t
he
P
E
M
a
na
ly
s
is
in t
he
t
est
s
y
s
t
em
wit
h RES
a
nd
SC
Af
ter
s
tu
d
y
in
g
th
e
im
p
ac
t
o
f
in
clu
d
in
g
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
o
n
v
o
ltag
e
s
tab
ilit
y
,
th
is
s
ec
t
io
n
p
r
esen
ts
th
e
r
esu
lts
o
f
th
e
ef
f
ec
t
th
at
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
h
av
e.
B
ec
au
s
e
b
o
th
s
itu
atio
n
s
s
h
ar
e
th
e
s
am
e
r
an
d
o
m
v
ar
iab
les,
th
e
co
n
ce
n
t
r
atio
n
p
o
in
ts
s
h
o
wn
in
T
ab
le
4
ar
e
s
h
ar
ed
in
th
ese
two
ca
s
es.
Similar
ly
to
th
e
r
esu
lts
p
r
esen
ted
ab
o
v
e,
T
ab
l
e
8
p
r
esen
ts
th
e
lo
ad
m
ar
g
in
s
in
%
wh
ile
T
ab
le
9
p
r
esen
ts
th
e
lo
ad
m
ar
g
in
s
in
MW
b
o
th
f
o
r
th
e
s
y
s
tem
with
R
E
S
an
d
SC
.
Fo
llo
win
g
th
e
an
aly
s
is
,
th
e
m
ea
n
v
alu
e,
s
tan
d
ar
d
d
ev
iatio
n
,
th
e
co
ef
f
icien
t
o
f
v
ar
iatio
n
,
an
d
th
e
b
o
tto
m
le
v
el
o
f
t
h
e
co
n
f
id
en
ce
in
ter
v
al
is
p
r
esen
ted
o
n
T
a
b
le
1
0
.
Fro
m
th
ese
r
esu
lts
,
it
ca
n
b
e
o
b
s
er
v
ed
th
at
th
e
m
ed
iu
m
v
alu
es
ar
e
s
ig
n
if
ican
tly
h
ig
h
er
wh
en
s
y
n
c
h
r
o
n
o
u
s
co
n
d
e
n
s
er
s
ar
e
in
clu
d
ed
i
n
th
e
s
y
s
tem
,
m
iti
g
atin
g
th
e
e
f
f
ec
t
th
e
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
h
av
e
o
n
v
o
ltag
e
s
tab
ilit
y
.
Similar
ly
,
in
clu
d
in
g
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
s
r
e
d
u
ce
s
th
e
s
tan
d
ar
d
d
e
v
iatio
n
o
f
t
h
e
lo
a
d
m
a
r
g
in
s
,
r
e
d
u
cin
g
th
e
u
n
ce
r
tain
ty
th
ese
v
alu
es h
av
e
i
n
th
e
co
n
f
id
en
ce
i
n
ter
v
al.
T
ab
le
8
.
L
o
ad
m
ar
g
in
s
in
% f
o
r
th
e
test
s
y
s
tem
with
R
E
S a
n
d
SC
C
o
n
c
e
n
t
r
a
t
i
o
n
p
o
i
n
t
[
%]
[
%]
w0
4
6
.
8
0
6
1
.
6
5
w1
5
5
.
1
0
7
0
.
2
0
w2
4
0
.
8
0
5
6
.
2
0
w3
5
5
.
6
0
7
0
.
2
0
w4
4
0
.
8
0
5
6
.
2
5
w5
4
7
.
4
0
6
2
.
4
0
w6
4
6
.
0
0
6
0
.
6
5
T
ab
le
9
.
L
o
ad
m
ar
g
in
s
in
MW f
o
r
th
e
test
s
y
s
tem
with
R
E
S
an
d
SC
C
o
n
c
e
n
t
r
a
t
i
o
n
p
o
i
n
t
[
M
W
]
[
M
W
]
w0
9
4
0
.
5
0
1
4
1
5
.
0
3
w1
1
2
4
2
.
6
0
1
6
8
8
.
6
3
w2
7
4
3
.
8
5
1
2
3
9
.
7
5
w3
1
2
4
2
.
6
0
1
6
8
7
.
2
0
w4
7
4
1
.
0
0
1
2
4
2
.
6
0
w5
9
5
1
.
9
0
1
4
3
0
.
7
0
w6
9
2
6
.
2
5
1
3
9
2
.
2
3
T
ab
le
10.
Statis
tical
in
f
o
r
m
ati
o
n
o
f
th
e
lo
ad
m
ar
g
i
n
s
f
o
r
th
e
test
s
y
s
tem
with
R
E
S a
n
d
SC
S
t
a
t
i
st
i
c
s
[
%]
[
M
W
]
µ
(
)
4
5
.
6
6
1
3
0
1
.
2
3
µ
(
)
6
0
.
9
5
1
7
3
7
.
0
1
σ (
)
7
.
5
0
2
1
3
.
7
0
σ (
)
7
.
2
2
2
0
5
.
7
7
σ (
)
/
µ
(
)
0
.
1
6
0
.
1
6
σ (
)
/
µ
(
)
0
.
1
2
0
.
1
2
(
)
3
0
.
9
6
8
8
2
.
3
8
(
)
4
6
.
8
0
1
3
3
3
.
7
0
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
I
mp
a
ct
o
f syn
ch
r
o
n
o
u
s
co
n
d
en
s
ers
o
n
vo
lta
g
e
s
ta
b
ilit
y
in
s
ystems
…
(
Ju
a
n
E
s
teb
a
n
R
o
d
r
íg
u
ez Qu
ir
o
g
a
)
767
3.
6
.
Co
m
pa
riso
n o
f
t
he
re
s
ults o
bta
ined
T
o
f
ac
ilit
ate
co
m
p
ar
is
o
n
o
f
t
h
e
r
esu
lts
,
T
ab
le
1
1
p
r
esen
ts
th
e
m
ea
n
l
o
ad
m
ar
g
in
v
alu
es
f
o
r
ea
ch
test
s
y
s
tem
s
ce
n
ar
io
.
T
h
e
m
ea
n
v
alu
e
co
r
r
esp
o
n
d
in
g
to
th
e
s
y
s
tem
with
o
u
t
R
E
S
an
d
SC
s
m
atch
es
th
e
o
n
e
o
b
tain
ed
u
n
d
er
th
e
av
er
a
g
e
g
en
er
atio
n
s
ce
n
a
r
io
.
All
v
al
u
es
ar
e
ex
p
r
ess
ed
b
o
th
as
p
er
ce
n
tag
es
an
d
in
m
eg
awa
tts
(
MW),
as in
d
icate
d
in
th
e
tab
le
.
B
ased
o
n
th
e
r
esu
lts
,
th
e
in
te
g
r
atio
n
o
f
s
y
n
ch
r
o
n
o
u
s
co
n
d
e
n
s
er
s
in
to
s
y
s
tem
s
with
R
E
S
lead
s
to
a
s
ig
n
if
ican
t
in
cr
ea
s
e
in
lo
ad
m
ar
g
in
s
.
T
h
is
im
p
r
o
v
em
en
t
is
s
o
s
u
b
s
tan
tial
th
at
ev
en
th
e
av
er
ag
e
m
ar
g
in
s
s
u
r
p
ass
th
o
s
e
o
f
th
e
b
ase
s
y
s
tem
with
o
u
t
R
E
S.
T
h
ese
f
in
d
in
g
s
p
r
o
v
id
e
v
alu
ab
le
in
s
ig
h
ts
in
t
o
th
e
p
lan
n
in
g
a
n
d
o
p
er
atio
n
o
f
p
o
wer
s
y
s
tem
s
,
p
ar
ticu
lar
ly
i
n
s
ce
n
ar
io
s
wh
e
r
e
R
E
S
in
teg
r
atio
n
p
o
s
es
ch
a
llen
g
es
to
v
o
ltag
e
s
tab
ilit
y
.
T
ab
le
11.
C
o
m
p
ar
ativ
e
o
f
th
e
l
o
ad
m
ar
g
in
s
f
o
r
t
h
e
th
r
ee
s
y
s
t
em
v
ar
iatio
n
s
S
t
a
t
i
st
i
c
s
Te
st
s
y
s
t
e
m
Te
st
s
y
s
t
e
m
w
i
t
h
R
ES
Te
st
s
y
s
t
e
m
w
i
t
h
R
ES
a
n
d
S
C
µ
(
)
[
%]
4
0
.
0
3
1
.
9
7
4
5
.
6
6
µ
(
)
[
%]
5
7
.
0
4
8
.
8
3
6
0
.
9
5
µ
(
)
[
M
W
]
1
1
4
0
.
0
9
1
1
.
0
8
1
3
0
1
.
2
3
µ
(
)
[
M
W
]
1
6
2
4
.
5
1
3
9
1
.
6
3
1
7
3
7
.
0
1
4.
CO
NCLU
SI
O
N
T
h
is
d
o
cu
m
en
t
p
r
esen
ted
a
m
eth
o
d
to
s
tu
d
y
th
e
im
p
ac
t
o
f
s
y
n
ch
r
o
n
o
u
s
co
n
d
e
n
s
er
s
o
n
v
o
ltag
e
s
tab
ilit
y
b
ased
o
n
PV
cu
r
v
es
an
d
th
e
co
m
p
u
tatio
n
o
f
th
e
lo
wer
lo
ad
ab
ilit
y
m
ar
g
in
s
b
a
s
ed
o
n
u
n
ce
r
tain
ty
an
aly
s
is
.
T
h
is
u
n
ce
r
tain
ty
an
a
ly
s
is
i
s
b
ased
o
n
th
e
p
o
in
t
esti
m
ate
m
eth
o
d
,
wh
ich
allo
ws
th
e
co
m
p
u
tatio
n
o
f
s
tatis
t
ical
in
f
o
r
m
atio
n
s
u
ch
a
s
th
e
m
ea
n
v
al
u
e,
t
h
e
s
tan
d
a
r
d
d
ev
iatio
n
,
th
e
co
ef
f
icien
t
o
f
v
ar
iatio
n
,
an
d
a
co
n
f
id
en
ce
in
ter
v
al
o
f
th
e
l
o
ad
ab
ilit
y
m
ar
g
in
s
th
at
ca
n
h
elp
t
o
p
lan
a
n
d
o
p
er
ate
p
o
wer
s
y
s
tem
s
.
Fo
r
a
s
p
ec
if
ic
ca
s
e
s
tu
d
y
,
in
th
e
2
4
-
n
o
d
e
I
E
E
E
R
T
S
s
y
s
tem
,
in
clu
d
in
g
r
en
ewa
b
le
en
er
g
y
p
en
etr
atio
n
o
f
2
4
%
o
f
th
e
to
tal
s
y
s
tem
ca
p
ac
ity
,
it
co
u
ld
b
e
id
en
tifie
d
t
h
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[
1
3
]
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.
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1
4
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[
1
5
]
A
.
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6
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1
7
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1
8
]
C.
-
L.
S
u
,
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r
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[
1
9
]
J.
M
.
M
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s,
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B
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A
.
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0
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.
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M
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.
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2
2
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b
e
g
a
n
h
is
st
u
d
ies
in
e
lec
tri
c
a
l
e
n
g
i
n
e
e
rin
g
i
n
2
0
2
1
a
n
d
re
c
e
iv
e
d
a
d
e
g
re
e
in
e
lec
tri
c
a
l
a
n
d
e
lec
tro
n
ics
e
n
g
in
e
e
rin
g
in
2
0
2
5
fro
m
Un
iv
e
rsi
d
a
d
d
e
lo
s
An
d
e
s,
Bo
g
o
tá
,
Co
lo
m
b
ia
.
His
re
se
a
r
c
h
in
tere
sts
a
re
r
e
n
e
wa
b
le
e
n
e
rg
ies
a
n
d
m
a
c
h
in
e
lea
rn
in
g
a
p
p
l
ica
ti
o
n
s
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
je.r
o
d
ri
g
u
e
z
q
1
@u
n
ian
d
e
s.e
d
u
.
c
o
.
Ma
r
io
A.
Ri
o
s
re
c
e
iv
e
d
a
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
i
n
1
9
9
1
a
n
d
a
M
.
S
c
.
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
in
1
9
9
2
,
b
o
th
fro
m
Un
i
v
e
rsid
a
d
d
e
lo
s
An
d
e
s,
Bo
g
o
ta,
Co
lo
m
b
ia.
He
re
c
e
iv
e
d
a
P
h
.
D.
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
f
ro
m
INPG
-
LE
G
,
G
re
n
o
b
le,
F
ra
n
c
e
,
in
1
9
9
8
,
a
n
d
a
d
o
c
t
o
ra
l
d
e
g
re
e
in
e
n
g
i
n
e
e
rin
g
fro
m
Un
i
v
e
rsid
a
d
d
e
l
o
s
An
d
e
s,
i
n
1
9
9
8
.
He
wo
rk
e
d
a
s
a
c
o
n
s
u
lt
a
n
t
e
n
g
i
n
e
e
r
in
Co
n
C
o
l
(n
o
w
WS
P
),
B
o
g
o
tá,
Co
l
o
m
b
ia,
d
u
r
in
g
1
2
y
e
a
rs.
Also
,
h
e
wa
s
a
re
se
a
r
c
h
a
s
so
c
iate
a
t
th
e
Un
iv
e
rsity
o
f
M
a
n
c
h
e
ste
r
(fo
rm
e
rly
,
UMIS
T).
Cu
rre
n
tl
y
,
h
e
is
a
fu
l
l
p
ro
fe
ss
o
r
a
t
t
h
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
S
c
h
o
o
l
o
f
En
g
i
n
e
e
rin
g
,
Un
i
v
e
rsid
a
d
d
e
lo
s
An
d
e
s,
B
o
g
o
tá.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
m
rio
s@
u
n
ian
d
e
s.e
d
u
.
c
o
.
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