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Fin
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2
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an
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[
3
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-
[
6
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Hen
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[
1
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[
2
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[
7
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.
Atten
tio
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as
b
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d
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to
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n
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d
u
s
tr
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p
lan
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[
8
]
,
[
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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I
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1
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[
1
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1
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[
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[
1
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[
1
6
]
-
[
1
9
]
.
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[
1
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[
10
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[
1
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M
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[2
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,
[
17
]
,
[
1
8
]
.
T
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tin
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s
.
As
a
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is
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ce
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p
ac
t
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o
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en
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itiv
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ip
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en
t.
T
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er
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o
r
e,
a
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itig
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e
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ice
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u
s
ed
to
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ed
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ce
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s
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ity
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s
im
p
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v
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g
th
e
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wer
q
u
ality
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o
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th
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e
n
d
u
s
er
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er
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ar
e
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y
ty
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e
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f
cu
s
to
m
p
o
we
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m
itig
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d
ev
ices
wh
ich
u
tili
ze
p
o
wer
elec
tr
o
n
ic
[
2
0
]
-
[
2
7
]
.
T
h
e
STAT
C
OM
an
d
d
y
n
am
ic
v
o
ltag
e
r
esto
r
er
(
DVR
)
ar
e
th
e
eq
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ip
m
en
t
th
at
is
co
m
m
o
n
ly
u
s
ed
to
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d
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ess
v
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s
ag
[
2
0
]
-
[
2
4
]
.
T
h
u
s
,
t
h
ese
s
tu
d
ies
aim
to
u
s
e
m
itig
atio
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d
ev
ice
is
DVR.
W
h
en
th
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f
a
u
lts
tak
e
p
lace
,
th
e
DVR
in
jects
a
th
r
ee
-
p
h
ase
v
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l
tag
e
to
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p
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ate
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v
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o
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al
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e.
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n
ce
,
t
h
e
c
o
n
s
id
er
at
io
n
f
o
r
co
r
r
ec
t
s
izin
g
o
f
th
e
D
VR
is
an
im
p
o
r
tan
t
tas
k
d
u
e
to
c
o
s
t
r
ea
s
o
n
s
[
2
8
]
-
[
3
1
]
.
T
h
er
ef
o
r
e,
it
is
im
p
o
r
t
an
t
to
d
ev
elo
p
a
m
eth
o
d
th
at
ca
n
ca
lc
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late
th
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ap
p
r
o
p
r
iate
o
r
o
p
tim
u
m
s
izin
g
o
f
DVR to
m
itig
ate
v
o
lta
g
e
s
a
g
[
3
0
]
,
[
3
1
]
.
I
t
h
as
b
ee
n
h
ig
h
lig
h
ted
b
y
m
a
n
y
au
th
o
r
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th
at
v
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s
ag
is
th
e
m
ain
ca
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s
e
o
f
h
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g
e
f
in
an
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ial
lo
s
s
es
with
in
th
e
m
an
u
f
ac
tu
r
in
g
o
r
p
r
o
d
u
ctio
n
s
ec
to
r
s
[
3
2
]
-
[
3
7
]
.
He
n
ce
,
th
e
s
tu
d
y
is
to
d
ev
elo
p
a
f
in
an
cial
ass
es
s
m
en
t
m
eth
o
d
to
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eter
m
in
e
th
e
b
e
n
e
f
it
o
f
DVR
a
s
wel
l
as
lo
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s
e
s
d
u
e
to
v
o
ltag
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s
ag
with
an
d
with
o
u
t
a
DVR.
T
h
e
d
ev
elo
p
e
d
m
eth
o
d
em
p
lo
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s
two
-
p
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in
t
cr
o
s
s
o
v
e
r
g
en
etic
alg
o
r
ith
m
s
.
T
h
er
e
f
o
r
e,
it
is
im
p
o
r
tan
t
to
co
n
s
id
er
th
e
ac
cu
r
ate
ass
ess
m
en
t
o
f
f
in
a
n
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lo
s
s
es
d
u
e
to
v
o
ltag
e
s
a
g
,
s
o
th
at
a
s
o
u
n
d
d
ec
is
io
n
c
an
b
e
m
ad
e
f
o
r
th
e
in
v
estme
n
t
o
f
m
itig
atio
n
d
e
v
ices.
B
a
s
ed
o
n
th
e
ab
o
v
e
p
r
o
b
lem
s
,
it
is
im
p
er
ativ
e
to
d
ev
elo
p
a
s
to
ch
asti
c
s
im
u
latio
n
m
eth
o
d
th
at
ca
n
p
r
o
v
id
e
ac
cu
r
ate
esti
m
atio
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o
f
t
h
e
ass
ess
m
en
t
o
f
v
o
ltag
e
s
ag
,
s
izin
g
o
f
m
itig
atio
n
d
ev
ices
an
d
p
er
f
o
r
m
f
in
an
cial
an
aly
s
es
f
o
r
u
tili
ties
an
d
en
d
u
s
er
.
T
h
er
e
f
o
r
e,
th
is
s
tu
d
y
aim
s
to
p
r
o
v
id
e
a
n
ec
o
n
o
m
ic
ass
ess
m
en
t
m
eth
o
d
b
ased
o
n
o
p
tim
izatio
n
m
eth
o
d
o
lo
g
ies
b
y
u
s
in
g
a
two
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p
o
in
t
cr
o
s
s
o
v
er
g
en
etic
alg
o
r
ith
m
as th
e
to
o
l f
o
r
v
o
lta
g
e
s
ag
ass
ess
m
en
t a
n
d
m
in
im
izin
g
m
itig
at
io
n
d
ev
ice
co
s
t.
2.
M
E
T
H
O
DO
L
O
G
Y
T
h
e
f
ir
s
t
p
ar
t
o
f
th
is
s
tu
d
y
i
n
v
esti
g
ates
v
o
ltag
e
s
ag
s
ev
en
ts
ca
u
s
ed
b
y
s
h
o
r
t
-
cir
c
u
it
an
d
d
ev
elo
p
s
a
s
to
ch
asti
c
ass
e
s
s
m
en
t
m
eth
o
d
.
Seco
n
d
p
ar
t
o
f
th
e
s
tu
d
y
in
v
es
tig
ates
alter
n
ativ
e
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
DVR
an
d
im
p
lem
en
ts
a
tech
n
iq
u
e
th
at
p
r
o
v
id
es
f
o
r
th
e
a
n
aly
s
is
o
f
s
u
i
tab
le
m
itig
atio
n
s
tr
ateg
ies
an
d
s
izes
f
o
r
b
alan
ce
d
an
d
u
n
b
alan
ce
d
f
au
lts
at
ea
ch
lo
ca
tio
n
o
n
b
u
s
es o
r
lin
es.
T
h
e
th
ir
d
p
a
r
t o
f
th
e
s
tu
d
ies in
v
est
ig
ates th
e
f
in
an
cial
lo
s
s
es e
x
p
er
ien
ce
d
b
y
u
tili
ties
an
d
en
d
co
n
s
u
m
e
r
s
.
2
.
1
.
Vo
lt
a
g
e
s
a
g
a
s
s
ess
m
ent
2
.
1
.
1
.
Re
m
a
in
in
g
v
o
lta
g
e
d
e
te
r
m
in
a
t
io
n
a
t
b
u
se
s a
n
d
li
n
e
s
T
h
e
Z
-
b
u
s
m
atr
ix
ca
n
b
e
u
s
ed
to
d
eter
m
in
e
th
e
m
ag
n
itu
d
e
o
f
th
e
v
o
ltag
e
s
ag
at
th
e
b
u
s
a
n
d
alo
n
g
th
e
lin
e
wh
en
f
au
lts
o
cc
u
r
at
a
b
u
s
in
a
p
o
wer
s
y
s
tem
.
T
h
e
(
1
)
an
d
(
2
)
u
s
ed
to
ca
lcu
late,
if
th
e
f
au
lts
tak
e
p
lace
o
n
a
b
u
s
an
d
t
h
e
lin
e
ar
e
g
iv
en
b
y
[
3
8
]
-
[
4
0
]
.
012
=
012
−
[
012
]
012
(
1
)
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
S
to
ch
a
s
tic
a
s
s
ess
men
t o
f v
o
lta
g
e
s
a
g
s
a
n
d
tech
n
o
-
ec
o
n
o
mic
o
p
timiz
a
tio
n
(
Je
ya
g
o
p
i R
a
m
a
n
)
2503
012
=
012
−
[
012
]
012
(
2
)
2
.
1
.
2
.
Vo
lt
a
g
e
s
a
g
co
m
pens
a
t
io
n t
ec
hn
iqu
e
s
by
DVR
-
Vo
ltag
e
s
ag
co
m
p
e
n
s
atio
n
ca
l
cu
latio
n
T
h
e
DVR
in
ject
s
v
o
ltag
e
ac
co
r
d
in
g
to
th
e
f
a
u
lt'
s
lo
ca
tio
n
,
n
atu
r
e,
an
d
im
p
e
d
an
ce
o
f
th
e
s
y
s
tem
.
Dif
f
er
en
t
tech
n
iq
u
es
a
r
e
u
tili
ze
d
b
y
DVR
to
co
r
r
ec
t
v
o
lt
ag
e
s
ag
[
2
3
]
,
[
2
4
]
.
T
h
e
p
r
e
-
f
au
lt
co
m
p
en
s
atio
n
tech
n
iq
u
e
is
ap
p
lied
in
th
is
in
v
esti
g
atio
n
.
T
h
e
(
3
)
p
r
o
v
id
es th
e
lo
ad
v
o
ltag
e
r
elatio
n
s
h
ip
.
1
=
+
(
3
)
W
h
er
e:
V
l
-
lo
ad
v
o
ltag
e,
V
sag
-
v
o
ltag
e
s
ag
,
an
d
V
DVR
-
in
ject
ed
v
o
ltag
e
b
y
DVR.
-
R
ea
ctiv
e
p
o
wer
i
n
jectio
n
T
h
e
p
o
wer
eq
u
atio
n
is
as
(
4
)
a
n
d
(
5
)
,
wh
en
DVR in
jects o
n
ly
r
ea
ctiv
e
p
o
wer
.
=
+
(
4
)
=
+
(
5
)
W
h
er
e:
Q
:
r
ea
ctiv
e
p
o
wer
in
jecte
d
;
S
l
:
lo
ad
b
u
s
;
an
d
I
l
:
lo
ad
cu
r
r
en
t.
T
h
e
DVR's
s
ize
an
d
an
g
le
ar
e
d
eter
m
in
e
d
by
(
6
)
an
d
(
7
)
.
=
√
2
+
2
−
2
(
6
)
=
ta
n
−
1
(
−
)
(
7
)
W
h
er
e:
V
DVR
:
in
jecte
d
v
o
ltag
e
m
ag
n
itu
d
e
b
y
DVR
;
δ
DVR
:
in
j
ec
ted
p
h
ase
an
g
le
b
y
DVR
;
V
pf
:
p
r
e
-
f
au
lt
v
o
ltag
e
;
an
d
V
sag
:
v
o
ltag
e
s
ag
.
-
Activ
e
p
o
wer
in
jectio
n
T
h
e
p
o
wer
eq
u
atio
n
is
as
in
(
8
)
,
wh
en
DVR in
jects o
n
ly
ac
ti
v
e
p
o
wer
.
=
+
(
8
)
W
h
er
e:
Q
:
r
ea
ctiv
e
p
o
wer
in
je
cted
;
S
l
:
lo
ad
bus
;
an
d
I
l
:
l
o
ad
cu
r
r
en
t.
I
f
r
ea
ctiv
e
p
o
wer
f
ails
to
co
m
p
en
s
ate
f
o
r
th
e
v
o
lta
g
e
s
ag
,
ac
ti
v
e
p
o
wer
in
jectio
n
co
n
tin
u
es
r
esto
r
atio
n
.
Af
ter
r
esto
r
atio
n
with
r
ea
ctiv
e
p
o
wer
,
v
ar
io
u
s
s
ag
m
ag
n
itu
d
e
v
alu
es
ca
n
b
e
o
b
tain
ed
f
r
o
m
(
9
)
.
T
h
e
DVR's
s
ize
an
d
an
g
le
ar
e
d
eter
m
in
ed
b
y
(
9
)
.
=
√
2
+
1
2
−
2
1
(
9
)
2
.
2
.
G
enet
ic
a
lg
o
rit
hm
T
h
e
g
e
n
etic
alg
o
r
it
h
m
(
GA)
is
a
p
r
o
b
lem
-
s
o
lv
in
g
alg
o
r
ith
m
t
h
at
m
ay
b
e
m
o
d
if
ie
d
to
ad
d
r
ess
a
v
ar
iety
o
f
is
s
u
es.
T
h
e
GA
p
ar
am
eter
s
af
f
ec
t
th
e
co
m
p
u
tatio
n
tim
e
a
n
d
o
v
e
r
all
ef
f
icien
cy
.
T
h
e
p
r
o
ce
s
s
o
f
co
m
p
u
tin
g
GA
is
d
eter
m
in
ed
b
y
p
o
p
u
latio
n
s
ize,
s
elec
tio
n
o
f
v
alu
e,
cr
o
s
s
o
v
er
r
ate,
m
u
tatio
n
r
ate,
a
n
d
s
to
p
cr
iter
ia.
T
h
e
s
ize
o
f
th
e
p
o
p
u
latio
n
is
a
cr
u
cial
co
n
s
id
er
atio
n
in
th
e
esta
b
lis
h
m
en
t
o
f
a
GA.
Alth
o
u
g
h
GA
m
ay
ca
lcu
late
p
o
p
u
latio
n
s
o
f
an
y
s
ize,
an
id
ea
l
p
o
p
u
latio
n
s
ize
w
o
u
ld
y
iel
d
an
id
ea
l
tim
e.
T
h
e
m
eth
o
d
o
f
s
elec
tin
g
th
e
b
est
s
o
lu
tio
n
f
r
o
m
a
p
o
p
u
latio
n
estab
lis
h
es
th
e
lev
el
o
f
s
u
p
e
r
io
r
it
y
an
d
is
k
n
o
wn
as
th
e
s
elec
tio
n
v
alu
e.
T
h
e
in
itial
co
n
v
er
g
en
ce
is
ca
u
s
ed
b
y
s
u
p
er
io
r
in
d
i
v
id
u
als
wh
o
h
ea
v
ily
d
o
m
in
ate
in
f
er
io
r
in
d
iv
id
u
als,
as
in
d
icate
d
b
y
th
e
h
ig
h
s
elec
tio
n
v
alu
e
.
T
h
e
cr
o
s
s
o
v
er
r
ate
is
d
ef
in
e
d
as
th
e
p
er
ce
n
tag
e
o
f
s
o
lu
ti
o
n
s
f
r
o
m
a
p
r
ed
e
f
in
ed
p
o
p
u
latio
n
th
at
ca
n
cr
ea
te
o
f
f
s
p
r
i
n
g
.
T
h
e
f
r
ac
tio
n
o
f
th
e
p
o
p
u
latio
n
'
s
to
tal
n
u
m
b
er
o
f
g
en
es
th
at
d
eter
m
in
es
h
o
w
m
an
y
n
ew
g
en
es
ar
e
in
tr
o
d
u
ce
d
in
to
th
e
p
o
p
u
l
atio
n
f
o
r
test
in
g
is
k
n
o
wn
as
th
e
m
u
tatio
n
r
ate,
o
n
th
e
o
t
h
er
h
an
d
.
W
h
en
th
e
m
u
tatio
n
r
ate
is
to
o
lo
w,
a
co
n
s
id
er
ab
le
p
o
r
tio
n
o
f
th
e
s
o
lu
tio
n
s
p
ac
e
is
n
o
t
s
tu
d
ied
.
T
h
e
GA
p
r
o
ce
s
s
'
s
s
to
p
p
in
g
p
o
in
t
is
d
ef
in
ed
b
y
s
to
p
cr
iter
i
a.
T
h
e
GA
w
ill
n
o
t
b
e
a
b
le
to
f
in
d
e
n
o
u
g
h
s
o
lu
tio
n
s
t
o
f
i
n
d
a
u
n
iv
er
s
al
s
o
lu
tio
n
if
th
e
p
r
o
ce
s
s
en
d
s
to
o
s
o
o
n
.
I
n
co
n
tr
ast,
if
th
e
an
al
y
s
is
tak
es to
o
lo
n
g
,
th
e
c
o
m
p
u
tin
g
tim
e
will in
cr
ea
s
e.
Mo
s
t
GA
s
y
s
tem
s
u
s
e
f
in
is
h
in
g
cr
iter
ia
th
at
ar
e
a
d
e
f
in
ed
n
u
m
b
er
o
f
g
en
er
atio
n
s
o
r
iter
atio
n
s
r
ea
c
h
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
15
,
No
.
4
,
Dec
em
b
er
20
24
:
2501
-
2
5
1
6
2504
2
.
2
.
1
.
Vo
lt
a
g
e
s
a
g
co
m
pens
a
t
io
n t
ec
hn
iqu
e
s
by
DVR
T
h
e
m
eth
o
d
o
lo
g
y
u
s
ed
to
ass
ess
th
e
o
p
tim
u
m
co
s
t
o
f
in
v
est
m
en
t
b
y
u
tili
ties
o
r
e
n
d
-
u
s
er
s
t
o
d
eter
m
i
n
e
f
in
an
cial
d
ec
is
io
n
s
is
d
ep
icted
in
Fig
u
r
e
1
.
T
h
e
f
o
llo
win
g
p
r
o
ce
d
u
r
es c
an
b
e
u
s
ed
to
d
escr
ib
e
Fig
u
r
e
1
:
-
T
h
e
in
itial
p
o
p
u
latio
n
h
as
b
ee
n
g
en
e
r
ated
to
en
s
u
r
e
u
n
if
o
r
m
d
is
tr
ib
u
tio
n
.
A
s
tr
in
g
o
f
0
s
a
n
d
1
s
is
u
s
ed
to
r
ep
r
esen
t th
e
ch
r
o
m
o
s
o
m
e
b
its
,
an
d
ea
c
h
b
it o
f
a
ch
r
o
m
o
s
o
m
e
is
d
escr
ib
ed
b
y
a
g
en
e.
-
Fo
r
ea
ch
in
d
i
v
id
u
al
p
o
p
u
latio
n
,
th
e
f
in
a
n
cial
eq
u
atio
n
is
u
s
ed
to
co
m
p
u
te
th
e
f
itn
ess
v
alu
e.
-
T
h
e
p
o
p
u
latio
n
'
s
tar
g
et
f
u
n
ctio
n
is
d
eter
m
in
ed
at
two
cr
o
s
s
o
v
er
p
o
in
ts
u
s
in
g
t
h
e
r
o
u
lette
wh
ee
l m
eth
o
d
.
-
T
h
e
two
-
cr
o
s
s
o
v
er
p
o
in
t
p
r
o
c
ess
will
d
etec
t
ev
er
y
g
e
n
e
an
d
cr
o
s
s
o
v
er
b
etwe
en
two
d
if
f
er
en
t
p
ar
e
n
ts
to
p
r
o
d
u
ce
a
p
air
o
f
ch
r
o
m
o
s
o
m
e
s
.
T
h
is
ca
n
b
e
r
eso
lv
ed
b
y
ex
c
h
an
g
in
g
g
e
n
es b
etwe
en
th
e
two
p
ar
e
n
ts
.
Fro
m
ea
ch
s
et
o
f
p
ar
e
n
ts
,
cr
o
s
s
o
v
er
p
o
in
ts
ar
e
p
r
o
d
u
ce
d
a
t r
a
n
d
o
m
.
-
I
n
d
iv
id
u
al
p
o
p
u
latio
n
m
u
tatio
n
s
ar
e
m
u
tated
as a
r
esu
lt o
f
cr
o
s
s
o
v
er
.
-
Gen
er
ate
th
e
b
est
-
f
it v
alu
e
f
r
o
m
th
e
p
o
p
u
latio
n
f
o
r
e
v
er
y
o
n
e
’
s
co
n
v
er
g
en
ce
p
o
in
t.
-
T
h
e
p
r
e
v
io
u
s
p
r
o
ce
s
s
es will b
e
p
er
f
o
r
m
ed
u
n
til th
e
b
est co
n
v
er
g
en
ce
p
o
in
t is r
ea
ch
e
d
.
-
Af
ter
an
iter
atio
n
,
t
h
e
g
en
etic
alg
o
r
ith
m
ter
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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
S
to
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k
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
15
,
No
.
4
,
Dec
em
b
er
20
24
:
2501
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2
5
1
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d
i
s
le
s
s
t
h
a
n
t
h
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m
a
x
i
m
u
m
m
a
g
n
i
t
u
d
e
o
f
t
h
e
r
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m
a
i
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i
n
g
v
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l
t
a
g
e
e
q
u
a
t
i
o
n
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o
r
0
≤
q
≤
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n
d
g
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e
a
t
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t
h
a
n
t
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l
t
a
g
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s
ag
m
a
g
n
i
t
u
d
e
s
a
t
b
o
t
h
q
=
0
a
n
d
q
=
1
,
i
t
s
u
g
g
e
s
t
s
t
w
o
c
r
i
ti
c
a
l
s
ite
s
a
r
e
o
n
t
h
e
li
n
e
.
-
Fin
ally
,
th
e
to
tal
n
u
m
b
er
o
f
v
o
ltag
e
s
ag
s
ca
n
b
e
co
m
p
u
ted
b
y
a
d
d
in
g
th
e
esti
m
ated
v
o
lta
g
e
s
ag
s
f
o
r
ea
ch
n
etwo
r
k
lin
e.
3
.
1
.
Ass
es
s
m
ent
o
f
v
o
lt
a
g
e
s
a
g
T
h
e
f
o
cu
s
o
f
th
is
s
tu
d
y
is
to
d
em
o
n
s
tr
ate
th
e
ab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
in
lo
wer
in
g
b
alan
ce
d
an
d
u
n
b
alan
ce
d
f
au
lts
b
y
tak
i
n
g
in
to
co
n
s
id
er
atio
n
v
a
r
io
u
s
ty
p
es
o
f
f
au
lts
.
T
ab
le
2
co
n
tain
s
a
lis
t
o
f
th
e
s
ag
d
u
r
atio
n
tim
es
n
ee
d
ed
to
clea
r
th
e
f
au
lts
in
th
e
ca
s
e
s
tu
d
ies.
T
h
e
th
r
ee
-
d
im
e
n
s
io
n
al
b
ar
ch
ar
t
in
Fig
u
r
e
3
d
ep
icts
th
e
to
tal
n
u
m
b
e
r
o
f
v
o
ltag
e
s
a
g
s
th
at
o
cc
u
r
y
ea
r
ly
f
o
r
th
r
ee
p
h
ase
f
au
lt
(
3
PF
)
b
u
s
es
in
ter
m
s
o
f
m
ag
n
itu
d
e
an
d
d
u
r
atio
n
o
f
th
e
v
o
ltag
e
.
T
h
e
x
an
d
y
ax
es,
wh
ich
in
d
icate
al
l
th
e
b
u
s
es,
an
d
th
e
v
o
ltag
e
s
ag
m
ag
n
itu
d
e
r
a
n
g
e
an
d
th
e
z
ax
is
,
wh
ich
s
h
o
ws
th
e
q
u
an
tity
o
f
v
o
ltag
e
s
ag
m
ag
n
itu
d
e.
T
h
e
f
o
llo
win
g
co
l
o
u
r
s
ar
e
u
s
ed
to
s
h
o
w
th
e
v
ar
io
u
s
v
o
lta
g
e
d
u
r
atio
n
lev
el
s
: 6
0
m
s
is
b
y
b
lu
e,
8
0
m
s
b
y
g
r
ee
n
,
1
5
0
m
s
b
y
y
ell
o
w,
an
d
3
0
0
m
s
b
y
r
ed
.
T
ab
le
2
.
Fau
lt c
lear
in
g
tim
e
[
6
]
,
[
7
]
V
o
l
t
a
g
e
l
e
v
e
l
F
a
u
l
t
c
l
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a
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me
B
u
s
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a
u
l
t
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6
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1
3
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k
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8
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3
3
k
V
1
5
0
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s
1
1
k
V
3
0
0
m
s
Fig
u
r
e
3
.
Vo
ltag
e
s
ag
at
b
u
s
4
wh
en
th
e
f
a
u
lts
at
lin
e
s
2
-
6
F
i
g
u
r
e
3
d
e
p
i
ct
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h
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m
a
i
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v
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f
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b
u
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es
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et
w
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t
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e
f
a
u
l
t
s
t
a
k
e
p
l
a
c
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n
li
n
e
2
–
6
.
As
c
a
n
b
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o
b
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v
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r
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Fi
g
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s
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a
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t
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f
S
L
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u
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r
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4
a
n
d
2
1
e
x
p
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i
e
n
c
e
t
h
e
h
i
g
h
e
s
t
a
n
d
l
o
w
e
s
t
y
e
a
r
l
y
v
o
l
t
a
g
e
s
a
g
r
a
t
es
w
h
i
c
h
a
r
e
2
4
2
5
a
n
d
8
9
3
,
r
e
s
p
e
c
ti
v
e
l
y
.
T
h
e
v
o
l
t
a
g
e
d
r
o
p
s
f
o
r
3
PF
a
t
b
u
s
es
4
a
n
d
2
1
,
w
h
i
c
h
a
r
e
1
4
9
6
a
n
d
4
9
6
,
r
e
s
p
e
c
t
i
v
e
l
y
.
A
ll
b
u
s
e
s
h
a
v
e
v
a
l
u
e
s
t
h
at
a
r
e
l
ess
th
a
n
1
5
0
0
.
I
n
th
is
s
tu
d
y
,
d
if
f
er
e
n
t
ty
p
es
o
f
f
au
lts
a
r
e
co
n
s
id
er
ed
to
s
h
o
w
th
e
p
o
ten
tial
o
f
q
u
ad
r
atic
in
ter
p
o
latio
n
tech
n
iq
u
es
o
v
e
r
th
e
an
al
y
tical
m
eth
o
d
s
in
d
ea
lin
g
with
b
ala
n
ce
d
an
d
u
n
b
alan
ce
d
f
a
u
lts
.
Fo
r
ca
s
es
o
f
SLGF,
d
o
u
b
le
lin
e
-
to
-
g
r
o
u
n
d
f
au
lt
(
D
L
GF)
,
lin
e
-
to
-
lin
e
f
au
lt
(
L
L
F),
an
d
3
PF
in
Fig
u
r
e
5
,
th
e
v
ar
ia
tio
n
in
a
n
u
m
b
e
r
o
f
v
o
ltag
e
s
ag
s
ca
n
b
e
d
escr
ib
ed
as
ex
p
o
n
en
tial.
T
h
e
in
ter
p
o
latio
n
m
eth
o
d
h
as
b
ee
n
co
m
p
ar
ed
with
an
an
aly
tica
l
m
eth
o
d
[
3
7
]
.
T
h
ese
two
m
eth
o
d
s
(
an
aly
tical
an
d
in
ter
p
o
latio
n
)
ar
e
c
o
m
p
a
r
ab
le
as b
o
th
s
h
o
w
a
s
im
ilar
n
u
m
b
er
o
f
v
o
ltag
e
s
ag
in
Fig
u
r
e
5
.
Fo
r
all
th
e
f
au
lt
c
o
n
d
itio
n
s
,
th
e
a
n
aly
tical
m
eth
o
d
s
y
ield
ed
alm
o
s
t
s
im
ilar
v
o
ltag
e
s
ag
m
ag
n
itu
d
es,
b
u
t
th
e
in
te
r
p
o
latio
n
m
eth
o
d
ex
h
ib
ited
a
co
n
tin
u
o
u
s
ly
h
ig
h
er
v
alu
e
th
an
th
e
an
aly
tical
m
eth
o
d
s
.
As
a
n
e
x
am
p
le,
in
t
h
e
ca
s
e
o
f
SLGF,
th
e
h
ig
h
est
p
er
ce
n
tag
e
d
if
f
e
r
en
ce
in
ter
m
s
o
f
th
e
n
u
m
b
er
o
f
v
o
ltag
e
s
ag
was
f
o
u
n
d
to
o
cc
u
r
at
th
e
m
ag
n
itu
d
e
o
f
0
.
3
p
.
u
.
a
n
d
0
.
4
p
.
u
.
with
a
d
if
f
er
en
ce
o
f
2
8
.
6
%
an
d
2
9
.
2
%,
r
esp
ec
tiv
ely
.
T
h
e
r
o
o
ts
o
f
t
h
e
in
ter
p
o
latio
n
cu
r
v
e
ar
e
u
s
ed
to
d
eter
m
in
e
th
e
two
p
o
s
s
ib
le
f
a
u
lt
lo
ca
tio
n
p
o
in
ts
.
T
h
e
in
ter
p
o
latio
n
m
eth
o
d
is
s
h
o
wn
to
y
ield
a
m
o
r
e
ac
cu
r
at
e
n
u
m
b
e
r
o
f
v
o
lta
g
e
s
ag
p
e
r
y
ea
r
f
o
r
SLGF,
L
L
F,
DL
GF,
an
d
3
PF
f
o
r
s
en
s
itiv
e
cu
s
to
m
er
s
lo
ca
ted
at
b
u
s
4
.
T
h
e
in
ter
p
o
latio
n
m
eth
o
d
was
also
s
h
o
wn
to
b
e
m
o
r
e
ac
cu
r
ate
b
y
5
%
f
o
r
SLGF,
1
0
%
f
o
r
L
L
F,
1
1
%
f
o
r
DL
GF,
an
d
3
PF
wh
en
co
m
p
ar
ed
to
an
aly
tical
m
eth
o
d
s
.
T
h
er
ef
o
r
e,
it
ca
n
b
e
c
o
n
clu
d
e
d
th
at
f
o
r
all
th
e
s
y
s
tem
s
ev
al
u
a
ted
,
th
e
in
ter
p
o
latio
n
m
et
h
o
d
s
h
o
wed
t
h
e
h
i
g
h
est
v
alu
e
in
ter
m
s
o
f
th
e
n
u
m
b
er
o
f
v
o
ltag
e
s
ag
as
c
o
m
p
ar
e
d
t
o
th
e
a
n
aly
tical
m
et
h
o
d
s
.
Mo
r
e
o
v
er
,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
ab
le
to
ca
lc
u
late
th
e
ex
ac
t f
au
lt p
o
s
itio
n
alo
n
g
th
e
lin
e
f
o
r
a
s
p
ec
if
ie
d
v
o
ltag
e
s
ag
m
ag
n
itu
d
e
.
3
.
2
.
Ass
es
s
m
ent
o
f
DVR
s
izing
Pro
p
er
s
izin
g
o
f
DVR
h
ad
to
b
e
ca
lcu
lated
to
r
ed
u
ce
th
e
s
ev
e
r
ity
o
f
v
o
ltag
e
s
ag
in
th
e
s
y
s
tem
n
etwo
r
k
an
d
to
m
ain
tain
v
o
ltag
e
m
a
g
n
itu
d
e
at
p
ar
ticu
lar
b
u
s
es,
as
w
ell
as
th
e
wh
o
le
n
etwo
r
k
.
T
h
e
r
ef
o
r
e,
th
e
co
s
t
o
f
in
s
tallatio
n
o
f
a
DVR
d
ev
ice
co
u
ld
b
e
lar
g
el
y
r
ed
u
ce
d
in
th
e
s
y
s
tem
n
etwo
r
k
.
T
h
e
in
jectio
n
o
f
v
o
ltag
e
b
y
DVR
d
ep
en
d
s
o
n
f
a
u
lt
ty
p
e,
lo
ca
tio
n
,
an
d
s
y
s
tem
im
p
ed
an
ce
.
A
n
u
m
b
er
o
f
im
p
o
r
tan
t
p
r
o
ce
d
u
r
es
t
h
at
wer
e
co
n
s
id
er
ed
b
ef
o
r
e
t
h
e
in
jectio
n
o
f
v
o
ltag
e
m
ag
n
itu
d
e
was
ca
r
r
ied
o
u
t
ar
e:
i)
All
v
o
ltag
es
wer
e
b
alan
ce
d
b
ef
o
r
e
th
e
o
cc
u
r
r
e
n
ce
o
f
a
f
a
u
lt;
h
en
ce
,
n
eg
ativ
e
an
d
ze
r
o
s
eq
u
en
ce
s
h
ad
b
ee
n
ze
r
o
;
ii)
I
n
th
e
ev
e
n
t
wh
en
a
f
a
u
lt
to
o
k
p
lace
,
r
ea
ctiv
e
p
o
wer
was
in
je
cted
to
co
m
p
en
s
ate
th
e
m
ag
n
itu
d
e
o
f
v
o
ltag
e
;
iii)
I
n
th
e
ca
s
e
wh
en
th
e
r
ea
ctiv
e
p
o
wer
c
o
u
ld
n
o
t
f
u
lly
co
m
p
e
n
s
ate
th
e
v
o
ltag
e
m
a
g
n
itu
d
e
,
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
h
all
b
e
in
jecte
d
;
an
d
iv
)
DVR d
ev
ices sh
o
u
ld
r
esto
r
e
th
e
b
u
s
v
o
ltag
e
to
its
p
r
e
-
f
au
lt v
o
ltag
e
m
ag
n
itu
d
e
an
d
an
g
le.
T
h
e
(
3
)
-
(
7
)
ca
n
b
e
u
s
ed
to
d
ete
r
m
in
e
th
e
s
izin
g
o
f
DVR,
an
d
t
h
e
r
esu
lts
ar
e
s
h
o
wn
in
Fig
u
r
e
6
.
Fo
r
th
e
n
etwo
r
k
s
y
s
tem
s
h
o
w
n
in
Fig
u
r
e
2
,
f
au
lts
ar
e
s
im
u
lated
f
o
r
w
o
r
s
t
-
ca
s
e
p
h
ases
o
f
b
u
s
es
with
an
d
with
o
u
t
DVR,
an
d
v
o
ltag
e
s
ag
m
ag
n
itu
d
es
ar
e
co
m
p
u
ted
an
d
s
h
o
w
n
in
Fig
u
r
e
6
.
T
h
e
o
u
tp
u
t
r
ev
ea
ls
th
e
b
u
s
f
au
lts
an
d
v
o
ltag
e
m
ag
n
itu
d
es
b
etwe
en
0
.
1
a
n
d
0
.
9
p
.
u
.
Acc
o
r
d
in
g
to
th
e
DVR's
s
elec
ted
r
atin
g
,
th
e
v
o
ltag
e
m
ag
n
itu
d
e
f
r
o
m
0
.
5
p
.
u
.
an
d
a
±
3
0
o
p
h
ase
s
h
if
t
ca
n
b
e
r
esto
r
ed
to
a
p
r
e
-
f
au
lt
v
o
l
tag
e
o
f
1
.
0
p
.
u
.
T
h
e
d
e
g
r
ee
o
f
v
o
ltag
e
th
at
ca
n
b
e
r
esto
r
ed
d
ep
e
n
d
s
o
n
th
e
av
aila
b
ilit
y
o
f
r
ea
ctiv
e
a
n
d
ac
tiv
e
p
o
wer
.
T
o
in
v
esti
g
ate
th
e
b
eh
a
v
io
r
o
f
v
o
ltag
e
s
ag
m
ag
n
itu
d
es
f
o
r
v
a
r
io
u
s
ty
p
es
o
f
f
au
lts
,
b
u
s
4
was
in
v
esti
g
ated
.
A
4
0
MV
A
DVR
is
co
n
n
ec
ted
wh
e
n
b
u
s
4
is
tak
en
in
to
c
o
n
s
id
er
atio
n
to
d
ete
r
m
in
e
h
o
w
m
u
ch
it
ca
n
co
n
tr
ib
u
te
to
r
esto
r
in
g
v
o
ltag
e
s
ag
.
Ass
es
s
m
en
t
o
f
th
e
D
VR
i
s
ca
r
r
ied
o
u
t
u
s
in
g
th
e
two
s
am
e
s
ize
o
f
ap
p
ar
en
t
p
o
wer
(
4
0
MV
A)
with
d
if
f
e
r
en
t
p
o
wer
r
atin
g
s
o
f
a
ctiv
e
an
d
r
ea
ctiv
e
p
o
wer
(
3
5
MW
+
j2
0
Mv
ar
a
n
d
5
MW
+
j4
0
Mv
ar
)
to
in
v
esti
g
ate
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
DVR
s
ize.
Fig
u
r
e
5
d
ep
icts
an
an
aly
s
is
o
f
th
e
v
o
ltag
e
m
ag
n
itu
d
e
with
a
n
d
with
o
u
t D
VR
b
ased
o
n
2
4
b
u
s
es.
Fig
u
r
e
6
s
h
o
ws
th
e
th
r
ee
s
ce
n
ar
io
s
with
an
d
with
o
u
t
DVR
t
h
at
wer
e
em
p
lo
y
ed
o
n
th
e
2
4
-
b
u
s
s
y
s
tem
to
in
v
esti
g
ate
th
e
f
au
lt a
t b
u
s
n
u
m
b
er
4
.
As ca
n
b
e
o
b
s
er
v
e
d
wh
en
co
m
p
a
r
in
g
t
h
e
h
is
to
g
r
a
m
p
lo
ts
,
b
u
s
n
u
m
b
er
4
was
id
en
tifie
d
to
h
av
e
th
e
lo
west
v
o
ltag
e
m
ag
n
itu
d
e
v
alu
e
o
f
0
.
1
3
2
p
.
u
.
W
h
en
u
s
in
g
th
e
s
am
e
b
u
s
with
a
DVR
an
d
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
r
atin
g
s
o
f
5
MW
+
j4
0
Mv
ar
in
s
ce
n
ar
io
1
,
th
is
v
alu
e
clim
b
ed
to
0
.
2
2
3
p
.
u
.
T
h
is
is
an
in
cr
ea
s
e
o
f
9
%,
wh
ile
in
s
ce
n
ar
io
2
,
wh
er
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
is
r
ated
at
3
5
MW
+
j2
0
Mv
ar
,
t
h
e
v
alu
e
g
r
ew
to
0
.
7
0
5
p
.
u
,
r
ep
r
esen
tin
g
a
2
7
% in
cr
ea
s
e.
Acc
o
r
d
in
g
to
Fig
u
r
e
6
,
t
h
e
m
a
g
n
itu
d
e
o
f
th
e
v
o
ltag
e
r
an
g
e
d
f
r
o
m
0
.
1
3
2
p
.
u
.
to
0
.
8
6
3
p
.
u
.
(
0
.
7
3
1
p
.
u
.
)
in
th
e
ev
e
n
t th
at
t
h
er
e
was n
o
DVR.
T
h
is
v
alu
e
d
ec
r
ea
s
ed
in
s
ce
n
ar
io
1
with
DVR,
as sh
o
wn
in
Fig
u
r
e
5
,
f
r
o
m
0
.
9
4
1
p
.
u
.
to
0
.
2
2
3
p
.
u
.
(
0
.
7
1
8
p
.
u
.
)
an
d
s
h
o
ws
a
1
.
3
%
d
ec
r
ea
s
e.
T
h
is
v
alu
e
d
e
cr
ea
s
ed
in
s
ce
n
ar
io
2
to
b
etwe
en
0
.
7
0
5
p
.
u
.
a
n
d
0
.
9
6
1
p
.
u
.
u
n
i
ts
(
0
.
2
5
6
p
.
u
.
)
,
as
s
h
o
wn
in
Fig
u
r
e
5
.
T
h
is
r
esu
lts
in
a
4
8
%
d
r
o
p
in
v
o
ltag
e
m
ag
n
itu
d
e.
W
ith
o
u
t
DVR,
th
e
av
er
ag
e
was
0
.
5
4
6
p
.
u
.
;
with
DVR,
th
e
av
er
ag
e
was
0
.
6
3
9
p
.
u
.
f
o
r
s
ce
n
ar
io
1
an
d
0
.
8
2
1
p
.
u
.
f
o
r
s
ce
n
a
r
io
2
.
T
h
is
d
em
o
n
s
tr
ates
th
at,
in
t
er
m
s
o
f
th
e
p
r
o
b
ab
ilit
y
o
f
r
e
ac
h
in
g
t
h
e
v
o
ltag
e
th
r
esh
o
ld
,
th
e
av
er
ag
e
in
jecte
d
p
o
wer
in
cr
ea
s
ed
b
y
9
% f
o
r
s
c
en
ar
io
1
a
n
d
b
y
2
8
% f
o
r
s
ce
n
a
r
io
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
15
,
No
.
4
,
Dec
em
b
er
20
24
:
2501
-
2
5
1
6
2508
Fig
u
r
e
4
.
Nu
m
b
er
o
f
v
o
ltag
e
s
ag
s
d
u
e
to
SLGF
an
d
3
PF
Fig
u
r
e
5
.
C
o
m
p
a
r
is
o
n
s
in
g
le
li
n
e
-
to
-
g
r
o
u
n
d
f
a
u
lt
Fig
u
r
e
6
.
Vo
ltag
e
s
ag
m
ag
n
itu
d
es a
t b
u
s
4
with
an
d
with
o
u
t
DVR f
o
r
th
r
ee
-
p
h
ase
f
au
lt
0
5
10
15
20
24
0
500
1000
1500
2000
2500
b
u
s
e
s
n
u
m
b
e
r
o
f
s
a
g
/
y
e
a
r
SL
GF
3PF
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1.
0
0
25
50
75
100
125
150
175
200
225
250
275
s
a
g
m
a
g
n
i
t
u
d
e
(
p
.
u
.
)
n
u
m
b
e
r
o
f
v
o
l
t
a
g
e
s
a
g
an
aly
t
ic
al
int
erp
ola
t
ion
1
4
5
7
9
14
17
19
20
24
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
F
a
u
l
t
e
d
b
u
s
e
s
V
o
l
t
a
g
e
m
a
g
n
i
t
u
d
e
(
p
.
u
)
w
it
ho
ut
D
VR
w
it
h
D
VR
(5M
W
+
j40
M
v
ar)
w
it
h
D
VR
(35
M
W
+
j20
M
v
ar)
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
S
to
ch
a
s
tic
a
s
s
ess
men
t o
f v
o
lta
g
e
s
a
g
s
a
n
d
tech
n
o
-
ec
o
n
o
mic
o
p
timiz
a
tio
n
(
Je
ya
g
o
p
i R
a
m
a
n
)
2509
3
.
3
.
Vo
lt
a
g
e
s
a
g
wit
h
a
nd
wit
ho
ut
DVR
T
o
ev
al
u
ate
v
o
ltag
e
s
ag
p
er
f
o
r
m
an
ce
with
an
d
with
o
u
t
DVR,
DVR
is
p
lace
d
with
in
th
e
p
o
wer
s
y
s
tem
n
etwo
r
k
.
Fig
u
r
e
7
s
h
o
ws
th
e
th
r
ee
-
d
im
en
s
io
n
al
b
ar
ch
ar
t
to
r
e
p
r
esen
t
th
e
n
u
m
b
er
o
f
v
o
ltag
e
s
ag
p
er
y
ea
r
f
o
r
all
th
e
b
u
s
es
f
o
r
3
PF
with
r
esp
ec
t
to
th
e
v
o
ltag
e
m
ag
n
itu
d
e
an
d
v
o
ltag
e
d
u
r
atio
n
.
T
h
e
x
a
n
d
y
ax
is
r
ep
r
esen
t
all
th
e
b
u
s
es
an
d
th
e
v
o
ltag
e
s
ag
m
ag
n
itu
d
e
r
a
n
g
e
r
esp
ec
tiv
el
y
wh
ile
th
e
n
u
m
b
er
o
f
v
o
ltag
e
s
ag
m
ag
n
itu
d
e
is
r
ep
r
esen
ted
b
y
th
e
z
a
x
is
.
Dif
f
er
en
t
co
lo
r
s
ar
e
u
s
ed
as:
(
b
lu
e
is
0
-
0
.
2
s
,
g
r
ee
n
0
.
2
–
0.
4
s
,
y
ello
w
0
.
4
–
0
.
6
s
,
an
d
r
ed
0
.
6
–
0
.
8
s
)
to
in
d
icate
th
e
d
if
f
er
e
n
t
v
o
ltag
e
d
u
r
atio
n
s
.
W
h
en
a
f
au
lt
o
cc
u
r
s
at
lin
e
s
2
-
6
,
th
e
v
o
ltag
e
s
ag
p
er
f
o
r
m
an
ce
o
f
th
e
e
n
tire
n
etw
o
r
k
o
f
all
th
e
b
u
s
es
ar
e
as
s
h
o
wn
in
Fig
u
r
e
7
.
W
h
en
t
h
e
f
au
lt
s
o
cc
u
r
in
lin
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u
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ize
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ate
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4
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20
24
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2501
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T
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m
b
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f
v
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ev
en
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o
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tai
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was in
i
tialized
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-
GA
p
r
o
ce
s
s
:
GA
p
r
o
ce
s
s
was e
m
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lo
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ed
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o
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en
tify
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h
e
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ti
m
al
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t
o
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ag
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ic
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u
ld
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i
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ize
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e
f
in
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s
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es o
f
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ag
an
d
DVR.
-
C
o
s
ts
o
f
v
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e
s
ag
an
d
DVR:
T
h
e
co
s
t
o
f
v
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ag
wa
s
ca
lcu
lated
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ased
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m
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t,
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ile
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s
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s
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eter
m
in
ed
f
r
o
m
th
e
g
iv
en
eq
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ati
o
n
.
-
Gr
ap
h
ical
r
esu
lts
: T
h
e
o
p
tim
u
m
n
u
m
b
er
o
f
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ag
s
,
as we
ll a
s
co
s
ts
o
f
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d
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VR
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is
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is
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lay
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ia
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ar
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ie
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.
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.
1
.
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lt
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g
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s
a
g
co
s
t
a
s
s
ess
m
ent
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h
e
(
11
)
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d
(
12
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ca
n
b
e
u
s
ed
to
d
eter
m
in
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th
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s
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th
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w
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r
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.
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r
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n
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ip
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s
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y
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illi
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s
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ent
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s
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atio
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e
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n
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ca
lcu
lated
b
y
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l
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g
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n
d
(
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,
wh
er
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m
ain
ten
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ce
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o
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e
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d
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ed
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ased
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ir
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r
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s
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f
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5
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illi
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a
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r
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b
ab
ilit
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ty
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e
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f
3
.
Fro
m
Fig
u
r
e
8
,
it
ca
n
b
e
s
ee
n
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at
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e
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ec
o
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d
to
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4
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d
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ce
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o
s
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th
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ad
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ee
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M
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6
7
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illi
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as sh
o
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Fig
u
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,
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ile
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e
m
a
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s
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ent
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R
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s
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f
v
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with
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ep
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u
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e
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n
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g
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etwe
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cc
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,
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e
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u
e
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k
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e
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m
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v
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e
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f
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2
8
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illi
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.
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we
v
er
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ased
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th
at
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ter
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s
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m
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er
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e
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ec
r
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9
f
r
o
m
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.
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u
r
e
1
0
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e
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e
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l g
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Fi
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