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33
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[
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–
[
1
6
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.
I
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co
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I
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I
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Vo
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11
,
No
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1
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Ma
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2
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2
2
:
33
-
51
34
liter
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[
4
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–
[
7
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.
T
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au
lty
p
o
in
t
.
T
h
e
p
o
wer
s
y
s
tem
is
r
eq
u
ir
ed
to
b
e
o
p
e
r
ated
u
n
d
er
th
is
co
n
d
itio
n
.
E
q
u
ip
m
en
t
in
v
o
l
v
ed
in
t
h
e
p
o
wer
s
y
s
tem
m
u
s
t
h
av
e
th
e
ab
ilit
y
to
s
u
s
tain
its
o
p
er
atio
n
u
n
d
er
s
u
ch
ab
n
o
r
m
alities
.
Pro
tectiv
e
eq
u
ip
m
en
t
in
s
talled
m
u
s
t
h
a
v
e
t
h
e
ab
ilit
y
to
r
esp
o
n
d
to
s
u
c
h
ab
n
o
r
m
alities
as
d
esire
d
.
I
n
a
d
d
itio
n
to
th
is
,
th
is
an
aly
s
is
also
h
elp
s
t
o
d
eter
m
in
e
th
e
o
p
er
atin
g
lim
its
o
f
t
h
e
s
y
s
tem
,
s
iz
in
g
o
f
eq
u
ip
m
en
t,
an
d
r
atin
g
o
f
p
o
wer
s
y
s
tem
co
m
p
o
n
en
ts
[
1
1
]
,
[
1
7
]
–
[
1
9
]
.
T
h
e
p
h
en
o
m
en
o
n
o
f
m
o
to
r
s
tar
tin
g
is
also
an
im
p
o
r
tan
t
ev
en
t
in
th
e
p
o
wer
s
y
s
tem
b
ec
au
s
e
o
f
s
tar
tin
g
ch
ar
ac
ter
is
tics
o
f
th
e
m
o
to
r
.
8
5
p
er
ce
n
t
o
f
m
o
to
r
s
i
n
s
talled
in
p
o
wer
s
y
s
tem
s
ar
e
in
d
u
ctio
n
m
o
to
r
s
.
I
t
d
r
aws
s
ix
to
ei
g
h
t
tim
es
lar
g
e
r
cu
r
r
en
t
as
c
o
m
p
a
r
ed
t
o
its
r
a
ted
cu
r
r
en
t
at
th
e
tim
e
o
f
s
tar
tin
g
.
An
in
cr
ea
s
e
i
n
cu
r
r
en
t
m
ak
es
th
is
ev
e
n
t
v
e
r
y
s
im
ilar
to
th
e
ev
en
t
o
f
a
f
a
u
lt.
T
h
er
ef
o
r
e,
it
n
ee
d
s
t
o
b
e
d
i
s
cr
im
in
ated
am
o
n
g
th
ese
ev
en
ts
[
2
0
]
–
[
2
3
]
.
T
h
er
e
ar
e
ev
en
ts
in
th
e
p
o
we
r
s
y
s
tem
wh
ich
in
cr
ea
s
e
cu
r
r
en
t
f
o
r
a
v
er
y
s
h
o
r
t
in
ter
v
al
o
f
ti
m
e.
T
h
ese
ev
en
ts
ar
e
m
o
s
tly
ter
m
ed
tr
an
s
ien
ts
.
T
h
ese
ev
en
ts
d
ec
ay
d
o
wn
o
n
th
eir
o
wn
o
r
it
n
ee
d
s
j
u
s
t
a
r
estar
t
o
f
th
e
s
y
s
tem
at
a
lo
w
s
ca
le.
T
h
er
ef
o
r
e,
s
tead
y
-
s
tate
ev
en
ts
m
u
s
t
b
e
d
if
f
er
e
n
tiated
f
r
o
m
tr
an
s
ie
n
t
ev
en
ts
as
s
tead
y
-
s
tate
ev
en
ts
ar
e
r
eq
u
ir
ed
to
b
e
r
ec
tifie
d
[
2
4
]
–
[
3
9
]
.
C
o
s
t
o
f
g
en
er
atio
n
is
an
im
p
o
r
tan
t
p
illar
o
f
an
y
p
o
wer
g
e
n
er
atin
g
u
n
it.
New
in
s
tallatio
n
s
m
u
s
t
b
e
r
ea
s
o
n
ab
ly
ec
o
n
o
m
ical
s
o
th
at
co
n
s
u
m
er
s
an
d
s
u
p
p
ly
co
m
p
a
n
y
’
s
r
elatio
n
s
h
ip
co
u
ld
b
e
d
e
r
iv
ed
in
an
o
p
tim
u
m
way
.
E
co
n
o
m
ic
d
is
p
atch
is
a
way
to
d
eter
m
in
e
th
e
o
p
tim
al
g
en
er
atin
g
co
s
t
f
r
o
m
a
p
ar
ticu
lar
p
lan
t
wh
ile
tak
e
n
in
to
co
n
s
id
er
atio
n
o
t
h
er
p
o
we
r
g
en
e
r
atin
g
u
n
its
.
T
h
is
an
aly
s
is
h
elp
s
to
d
eter
m
in
e
th
e
o
p
er
atin
g
co
n
d
itio
n
s
o
f
th
e
p
o
wer
p
lan
t
u
n
d
er
m
i
n
im
u
m
f
u
el
c
o
s
t
[
4
0
]
,
[
4
1
]
.
I
n
th
i
s
r
esear
ch
,
in
ter
io
r
p
o
in
t
o
p
ti
m
izatio
n
is
ap
p
lied
b
ec
au
s
e
o
f
its
r
a
p
id
c
o
n
v
e
r
g
e
n
ce
in
lar
g
e
p
o
we
r
s
y
s
tem
s
a
n
d
is
a
n
e
f
f
ec
tiv
e
wa
y
o
f
h
a
n
d
lin
g
lar
g
e
p
o
wer
s
y
s
tem
s
in
E
T
AP so
f
twar
e
[
4
0
]
–
[
5
0
]
.
T
h
er
e
ar
e
d
if
f
er
en
t
ty
p
es
o
f
s
o
f
twar
es
av
ailab
le
f
o
r
th
e
s
im
u
latio
n
o
f
m
o
d
els
o
f
p
o
we
r
s
y
s
tem
s
an
d
p
o
wer
s
tatio
n
s
.
I
n
all
o
f
t
h
ese
s
o
f
twar
es,
E
T
AP
s
o
f
twar
e
is
f
o
u
n
d
m
o
s
t
p
r
o
m
is
in
g
b
ec
au
s
e
o
f
its
r
ea
lis
tic
ap
p
r
o
ac
h
an
d
u
s
er
’
s
co
n
tr
o
l
o
f
d
esig
n
an
d
a
n
aly
s
is
p
ar
am
eter
s
.
T
h
er
ef
o
r
e,
E
T
AP
is
ass
o
ciate
d
with
m
an
y
in
d
u
s
tr
ies f
o
r
s
im
u
latio
n
a
n
d
d
ev
elo
p
m
en
t
[
2
8
]
,
[
5
1
]
–
[
5
9
]
.
I
n
th
is
r
esear
ch
,
a
f
u
r
n
ac
e
o
i
l
-
b
ased
p
o
wer
p
lan
t
c
o
n
s
is
tin
g
o
f
m
o
r
e
th
an
1
6
0
b
u
s
b
ar
s
o
f
h
ig
h
v
o
ltag
e,
m
e
d
iu
m
v
o
ltag
e,
a
n
d
lo
w
v
o
ltag
e
is
d
esig
n
ed
.
Mo
r
eo
v
e
r
,
p
o
s
t
-
d
esig
n
an
aly
s
es
d
is
cu
s
s
ed
in
th
e
co
m
in
g
s
ec
tio
n
ar
e
p
er
f
o
r
m
ed
to
d
ep
ict
th
is
p
o
wer
p
lan
t
d
esig
n
p
er
f
o
r
m
an
ce
.
T
h
is
r
esear
c
h
p
ap
er
c
o
n
s
is
ts
o
f
th
e
f
o
llo
win
g
s
ec
tio
n
s
,
Secti
o
n
I
co
v
er
s
th
e
i
n
tr
o
d
u
ctio
n
an
d
liter
atu
r
e
r
ev
iew.
Sectio
n
I
I
co
n
s
is
ts
o
f
t
h
e
m
eth
o
d
o
l
o
g
y
in
v
o
lv
e
d
f
o
r
th
e
d
esig
n
an
d
a
n
aly
s
is
o
f
f
u
r
n
ac
e
o
il
-
b
ased
p
o
wer
p
lan
ts
co
m
p
r
e
h
en
s
iv
ely
.
Sectio
n
I
I
I
co
n
tain
s
th
e
test
s
y
s
tem
d
esig
n
ed
f
o
r
s
im
u
latio
n
u
n
d
er
d
if
f
er
en
t scen
ar
io
s
.
Sectio
n
I
V
co
n
s
is
ts
o
f
a
d
is
cu
s
s
io
n
o
f
th
e
r
esu
lts
o
f
th
e
s
im
u
latio
n
.
T
h
e
c
o
n
clu
s
io
n
is
p
r
esen
ted
in
Sectio
n
V.
2.
M
E
T
H
O
DO
L
O
G
Y
2
.
1
.
Da
t
a
c
o
llect
io
n
R
elativ
e
d
ata
f
o
r
th
e
d
esig
n
o
f
th
e
p
o
wer
p
lan
t
is
g
ath
er
ed
.
A
s
in
g
le
lin
e
d
iag
r
am
s
h
o
u
l
d
b
e
p
r
o
v
id
e
d
b
y
th
e
v
en
d
o
r
.
I
f
co
llected
d
at
a
is
s
u
f
f
icien
t
f
o
r
th
e
p
o
wer
s
y
s
tem
s
tu
d
ies,
th
en
elec
tr
ical
d
esig
n
an
d
an
aly
s
is
p
r
o
g
r
a
m
(
E
T
AP)
s
o
f
twar
e
is
u
s
ed
to
d
esig
n
a
m
o
d
el.
I
f
s
o
m
e
r
atin
g
s
ar
e
n
o
t
co
r
r
ec
t
o
r
it
is
n
o
t
av
ailab
le,
th
e
s
ite
i
s
v
is
ited
to
g
ath
er
in
f
o
r
m
atio
n
.
Af
ter
th
is
,
if
s
till
d
ata
is
n
o
t
s
u
f
f
icien
t
f
o
r
th
e
m
o
d
e
l
wh
ich
is
co
llected
d
u
r
in
g
th
e
s
ite
s
u
r
v
e
y
,
th
e
n
ass
u
m
p
tio
n
s
ar
e
m
a
d
e
b
ased
o
n
th
e
d
if
f
er
e
n
t
in
ter
n
atio
n
al
s
tan
d
ar
d
s
s
u
ch
as I
E
E
E
s
tan
d
ar
d
s
,
ANSI
s
tan
d
ar
d
s
,
I
E
C
s
tan
d
ar
d
s
.
Dif
f
er
en
t
an
aly
s
es
ar
e
co
n
d
u
cted
u
s
in
g
E
T
AP
to
g
en
er
ate
a
r
ec
o
m
m
en
d
atio
n
r
e
p
o
r
t
f
o
r
th
e
p
o
wer
p
lan
t.
L
o
ad
f
lo
w
an
al
y
s
is
(
L
FA)
is
th
e
f
ir
s
t
an
d
th
e
f
o
r
em
o
s
t
tech
n
iq
u
e
o
f
s
y
s
te
m
s
tu
d
ies.
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
f
u
r
th
er
h
elp
in
th
e
im
p
lem
en
tatio
n
o
f
tech
n
iq
u
e
s
.
2
.
2
.
L
o
a
d f
l
o
w
a
na
ly
s
is
L
o
ad
f
lo
w
an
aly
s
is
is
th
e
s
tu
d
y
o
f
p
o
wer
,
v
o
ltag
es,
an
d
an
g
les
at
d
if
f
er
en
t
n
o
d
es
o
f
b
u
s
an
d
s
p
ec
if
y
th
at
wh
eth
er
th
e
s
y
s
tem
i
s
o
p
er
atin
g
in
n
o
r
m
al
v
o
ltag
es
co
n
d
itio
n
o
r
em
er
g
en
cy
o
p
er
ati
n
g
co
n
d
itio
n
s
,
L
o
ad
f
lo
w
an
aly
s
is
is
p
er
f
o
r
m
ed
t
o
d
esig
n
a
n
ew
p
o
wer
s
y
s
te
m
an
d
m
o
d
if
icatio
n
o
f
t
h
e
e
x
is
tin
g
s
y
s
tem
.
T
h
e
v
o
ltag
e
(
V)
,
v
o
ltag
e
an
g
le
(
δ
)
,
r
ea
l
p
o
wer
(
P),
an
d
r
ea
cti
v
e
p
o
wer
(
Q)
ca
n
b
e
co
m
p
u
te
d
u
s
i
n
g
lo
ad
f
lo
w.
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
C
o
mp
r
eh
en
s
ive
a
n
a
lysi
s
a
n
d
d
esig
n
o
f fu
r
n
a
ce
o
il
-
b
a
s
ed
p
o
w
er st
a
tio
n
u
s
in
g
E
TAP
(
R
a
h
e
el
Mu
z
z
a
mme
)
35
T
h
r
ee
ty
p
es
o
f
b
u
s
es
ar
e
u
s
ed
in
lo
ad
f
lo
w
w
h
ich
ar
e
s
win
g
,
g
en
er
ato
r
,
an
d
l
o
ad
b
u
s
es.
I
n
s
win
g
b
u
s
,
P
an
d
Q
ar
e
f
o
u
n
d
b
ased
o
n
a
n
d
V
an
d
δ.
I
n
th
e
g
e
n
er
ato
r
b
u
s
,
f
o
r
th
e
in
p
u
t o
f
P
a
n
d
V,
th
e
r
eq
u
i
r
ed
o
u
tp
u
t
o
f
Q
an
d
δ
is
ca
lcu
lated
,
an
d
in
t
h
e
lo
a
d
b
u
s
,
P
an
d
Q
a
r
e
k
n
o
wn
an
d
V
an
d
δ
ar
e
u
n
k
n
o
wn
v
alu
es.
All
th
e
u
n
k
n
o
wn
p
ar
am
eter
s
(
V,
δ,
P,
an
d
Q)
ar
e
ac
ce
s
s
ib
le
f
o
r
s
win
g
b
u
s
,
g
e
n
er
ato
r
b
u
s
,
an
d
lo
ad
b
u
s
with
lo
ad
f
lo
w
a
n
aly
s
is
.
T
h
e
o
th
e
r
elec
tr
ical
p
ar
am
eter
s
s
u
ch
as
cu
r
r
en
t,
p
o
wer
f
ac
to
r
,
ap
p
ar
en
t
p
o
wer
f
o
r
th
e
wh
o
le
elec
tr
ical
s
y
s
tem
ca
n
b
e
d
eter
m
in
ed
b
ased
o
n
t
h
ese
f
o
u
r
p
ar
am
ete
r
s
(
V,
δ,
P,
an
d
Q)
an
d
im
p
ed
a
n
ce
b
etwe
en
th
e
b
u
s
es
(
Z
ij).
Fo
r
th
e
ca
lcu
latio
n
o
f
lo
ad
f
l
o
w
an
aly
s
is
,
th
er
e
ar
e
s
o
m
e
m
e
th
o
d
s
i.e
.
Gau
s
s
-
Seid
el
m
eth
o
d
,
New
to
n
R
ap
h
s
o
n
m
eth
o
d
,
A
d
ap
tiv
e
New
to
n
R
ap
h
s
o
n
m
et
h
o
d
.
I
n
th
is
r
esear
c
h
,
th
e
New
to
n
R
ap
h
s
o
n
m
eth
o
d
is
im
p
lem
en
te
d
b
ec
au
s
e
its
r
esu
lts
ar
e
ac
cu
r
ate
an
d
it
r
eq
u
ir
es
f
ewe
r
iter
atio
n
s
.
B
asic
m
o
d
el
o
f
p
o
wer
s
y
s
tem
is
p
r
esen
ted
in
Fig
u
r
e
1
in
wh
ich
cu
r
r
en
t
I
i
is
en
ter
in
g
f
r
o
m
th
e
b
u
s
(
Vi)
an
d
is
f
lo
win
g
to
war
d
s
d
if
f
er
e
n
t
b
u
s
es
(
V1
,
V2
,
…,
Vn
)
v
ia
ad
m
ittan
ce
s
(
y
i1
,
y
i
2
,
…,
y
in
)
.
G
N
D
yi
1
yi
2
yi
n
yi
0
V
1
V
2
Vn
Vi
Ii
Fig
u
r
e
1
.
B
asic p
o
wer
s
y
s
tem
2
.
2
.
1
.
New
t
o
n r
a
ph
s
o
n
New
to
n
'
s
m
eth
o
d
,
n
am
ed
a
f
ter
I
s
aa
c
New
to
n
an
d
J
o
s
ep
h
R
ap
h
s
o
n
,
is
a
m
eth
o
d
f
o
r
f
in
d
in
g
s
u
cc
ess
iv
ely
b
etter
ap
p
r
o
x
im
a
tio
n
s
to
th
e
r
o
o
ts
o
f
a
r
ea
l
-
v
alu
ed
f
u
n
ctio
n
.
T
h
e
ap
p
r
o
ac
h
t
o
New
to
n
-
R
ap
h
s
o
n
lo
ad
f
lo
w
is
s
im
ilar
to
th
at
o
f
s
o
lv
in
g
a
s
y
s
tem
o
f
n
o
n
lin
ea
r
e
q
u
atio
n
s
u
s
in
g
t
h
e
New
to
n
-
R
ap
h
s
o
n
m
eth
o
d
[
4
]
–
[
7
]
.
I
t
is
an
iter
ati
v
e
m
eth
o
d
th
at
ap
p
r
o
x
im
ates
a
s
et
o
f
n
o
n
-
lin
ea
r
s
im
u
ltan
eo
u
s
eq
u
atio
n
s
to
a
s
et
o
f
lin
ea
r
s
im
u
ltan
e
o
u
s
eq
u
at
io
n
s
u
s
in
g
T
a
y
lo
r
’
s
s
er
ies
e
x
p
an
s
io
n
.
R
ef
er
r
in
g
to
Fig
u
r
e
1
,
p
o
wer
f
lo
w
eq
u
atio
n
s
ar
e
f
o
r
m
u
late
d
in
p
o
lar
f
o
r
m
f
o
r
t
h
e
n
b
u
s
s
y
s
tem
in
ter
m
s
o
f
b
u
s
ad
m
ittan
ce
m
at
r
ix
Y
as:
=
∑
=
1
(
1
)
W
h
er
e
ith
an
d
jth
b
u
s
es a
r
e
d
o
n
ated
b
y
i a
n
d
j.
E
x
p
r
ess
in
g
it in
p
o
lar
f
o
r
m
as:
=
∑
|
|
|
|
<
+
=
1
(
2
)
T
h
e
cu
r
r
e
n
t is
ex
p
r
ess
ed
in
ter
m
s
o
f
th
e
ac
tiv
e
a
n
d
th
e
r
ea
ctiv
e
p
o
wer
at
t
h
e
b
u
s
I
as:
=
−
(
3
)
Su
b
s
titu
tin
g
f
o
r
I
i
f
r
o
m
(
2
)
in
(
3
)
as:
P
i
−
JQ
i
=
|
V
i
|
<
−
δ
∑
|
V
i
|
|
V
IJ
|
<
θ
ij
+
δ
j
i
=
1
(
4
)
Sep
ar
atin
g
th
e
r
ea
l a
n
d
im
a
g
in
ar
y
p
ar
ts
as:
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.
11
,
No
.
1
,
Ma
r
ch
2
0
2
2
:
33
-
51
36
=
∑
|
|
c
os
(
+
−
)
=
1
(
5
)
=
−
∑
|
|
s
in
(
+
−
)
=
1
(
6
)
Af
ter
ex
p
an
d
in
g
(
5
)
a
n
d
(
6
)
in
T
ay
lo
r
'
s
s
er
ies with
in
itial c
o
n
d
itio
n
an
d
n
e
g
lectin
g
h
ig
h
er
-
o
r
d
er
ter
m
s
as:
[
2
2
⋯
2
⋮
⋱
⋮
2
…
2
|
2
|
…
2
|
|
⋮
⋱
⋮
2
|
2
|
…
2
|
2
|
2
2
…
2
⋮
⋱
⋮
2
⋯
2
|
2
|
…
2
|
|
⋮
⋱
⋮
|
2
|
…
|
|
]
[
∆
2
⋮
⋮
∆
∆
|
2
|
⋮
⋮
∆
|
|
]
=
[
∆
2
⋮
⋮
∆
∆
⋮
⋮
∆
]
(
7
)
T
h
e
J
ac
o
b
i
a
n
m
atr
ix
g
iv
es
th
e
liter
ali
ze
d
r
elatio
n
s
h
ip
b
etwe
en
s
m
all
ch
an
g
es
in
∆
an
d
∆
|
|
v
o
ltag
e
an
g
le
an
d
m
ag
n
itu
d
e
with
th
e
s
m
all
ch
an
g
es in
r
ea
l a
n
d
r
ea
cti
v
e
p
o
wer
∆
an
d
∆
as:
[
∆
∆
]
=
[
1
2
3
4
]
[
∆
∆
|
|
]
(
8
)
T
h
e
d
iag
o
n
al
an
d
th
e
o
f
f
-
d
ia
g
o
n
al
elem
en
ts
o
f
J
1
a
r
e:
=
∑
|
|
c
os
(
+
−
)
=
1
(
9
)
=
∑
|
|
s
in
(
+
−
)
=
1
(
1
0
)
Similar
ly
,
th
e
d
iag
o
n
al
an
d
o
f
f
-
d
iag
o
n
al
elem
e
n
ts
o
f
J
2
,
J
3
,
an
d
J
4
ca
n
b
e
ev
al
u
ated
.
T
h
e
ter
m
s
an
d
ar
e
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
s
ch
ed
u
led
an
d
ca
lcu
lated
v
al
u
es,
k
n
o
wn
as th
e
p
o
wer
r
esid
u
als g
iv
en
as:
∆
=
ℎ
−
(
1
1
)
∆
=
ℎ
−
(
1
2
)
Usi
n
g
th
e
v
alu
es
o
f
th
e
p
o
we
r
r
esid
u
als
an
d
th
e
J
ac
o
b
ia
n
m
atr
ices,
∆
an
d
∆
|
|
ar
e
ca
lcu
lated
f
r
o
m
(
7
)
to
co
m
p
le
te
th
e
p
a
r
ticu
lar
iter
ati
o
n
an
d
th
e
n
ew
v
alu
es
ar
e
ca
lcu
lated
as
s
h
o
wn
b
elo
w
wh
i
ch
ar
e
u
s
ed
as
th
e
in
itial v
alu
es f
o
r
th
e
n
ex
t iter
a
tio
n
.
+
1
=
−
∆
(
1
3
)
|
+
1
|
=
|
|
−
|
∆
|
(
1
4
)
2
.
3
.
Sh
o
rt
circ
uit
a
na
l
y
s
is
Sh
o
r
t
-
cir
cu
it
s
tu
d
ies
ar
e
p
er
f
o
r
m
ed
t
o
d
eter
m
in
e
th
e
p
ea
k
m
ag
n
itu
d
e
o
f
th
e
p
r
o
s
p
ec
tiv
e
cu
r
r
e
n
ts
f
lo
win
g
in
th
e
p
o
wer
s
y
s
tem
at
d
if
f
er
en
t
tim
e
in
ter
v
als
af
ter
a
f
au
lt
o
cc
u
r
s
.
T
h
e
m
ag
n
itu
d
e
o
f
th
e
cu
r
r
en
ts
f
lo
win
g
th
r
o
u
g
h
th
e
p
o
we
r
s
y
s
tem
af
ter
a
f
au
lt
v
ar
ie
s
with
tim
e
u
n
til
th
ey
r
ea
c
h
a
s
tead
y
-
s
tate
co
n
d
itio
n
.
T
h
is
b
eh
av
io
r
o
cc
u
r
s
d
u
e
to
s
y
s
tem
ch
ar
ac
ter
is
tics
an
d
d
y
n
am
ics.
Du
r
in
g
th
is
tim
e,
th
e
p
r
o
tecti
v
e
s
y
s
tem
is
ca
lled
o
n
to
d
etec
t,
in
ter
r
u
p
t,
an
d
is
o
late
th
is
f
au
lty
eq
u
ip
m
en
t.
T
h
e
d
u
ty
e
n
f
o
r
ce
d
o
n
th
is
eq
u
i
p
m
en
t
is
d
ep
en
d
en
t
u
p
o
n
th
e
m
a
g
n
itu
d
e
o
f
th
e
c
u
r
r
en
t,
wh
ich
is
d
e
p
en
d
e
n
t
o
n
th
e
tim
e
f
r
o
m
f
au
lt
i
n
ce
p
ti
o
n
.
T
h
is
is
d
o
n
e
f
o
r
d
if
f
er
en
t
ty
p
es
o
f
f
au
lts
(
th
r
ee
-
p
h
ase,
p
h
ase
-
to
-
p
h
ase,
d
o
u
b
le
-
p
h
ase
-
to
-
g
r
o
u
n
d
,
an
d
p
h
ase
-
to
-
g
r
o
u
n
d
)
at
d
is
s
im
ilar
lo
ca
tio
n
s
th
r
o
u
g
h
o
u
t
th
e
s
y
s
tem
.
T
h
e
in
f
o
r
m
atio
n
is
u
s
ed
to
s
elec
t
th
e
s
ize
o
f
th
e
eq
u
ip
m
e
n
t
lik
e
f
u
s
es,
b
r
ea
k
er
s
,
an
d
s
witch
g
ea
r
r
atin
g
s
in
ad
d
itio
n
to
s
ettin
g
p
r
o
tectiv
e
r
elay
s
.
Mo
to
r
s
tar
tin
g
a
n
aly
s
is
,
Mo
to
r
s
tar
tin
g
an
aly
s
is
is
u
s
ed
to
c
alcu
late
m
o
to
r
ac
ce
ler
atio
n
ti
m
e
an
d
t
h
e
v
o
ltag
e
im
p
ac
t
o
n
m
o
t
o
r
s
tar
t
in
g
in
elec
tr
ical
p
o
wer
s
y
s
tem
s
.
Ad
v
an
ce
d
p
l
o
ttin
g
an
d
tim
e
-
v
ar
y
in
g
g
r
a
p
h
ical
d
is
p
lay
s
en
ab
le
en
g
in
ee
r
s
to
q
u
ick
ly
ev
alu
ate
r
esu
lts
an
d
t
o
m
ak
e
d
ec
is
io
n
s
.
I
n
an
in
d
u
ctio
n
m
o
to
r
,
wh
e
n
s
u
p
p
ly
is
g
iv
e
n
to
th
e
s
tato
r
w
in
d
in
g
s
,
th
e
r
o
tatin
g
m
ag
n
e
tic
f
ield
f
lu
x
,
an
d
th
e
p
r
o
d
u
c
ed
f
lu
x
in
t
h
e
r
o
to
r
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
C
o
mp
r
eh
en
s
ive
a
n
a
lysi
s
a
n
d
d
esig
n
o
f fu
r
n
a
ce
o
il
-
b
a
s
ed
p
o
w
er st
a
tio
n
u
s
in
g
E
TAP
(
R
a
h
e
el
Mu
z
z
a
mme
)
37
win
d
in
g
s
d
u
e
to
th
e
b
ac
k
e
m
f
,
ca
u
s
e
th
e
m
o
to
r
to
r
q
u
e
to
in
cr
ea
s
e
r
esu
ltin
g
in
h
i
g
h
r
o
to
r
cu
r
r
en
t.
D
u
r
in
g
th
e
tim
e
b
etwe
en
th
e
ap
p
licatio
n
o
f
elec
tr
ic
s
u
p
p
ly
to
t
h
e
m
o
to
r
an
d
th
e
ac
t
u
al
ac
ce
ler
atio
n
o
f
th
e
m
o
to
r
to
its
f
u
ll
s
p
ee
d
,
a
lar
g
e
am
o
u
n
t
o
f
cu
r
r
en
t
is
d
r
awn
b
y
th
e
s
tato
r
f
r
o
m
th
e
s
u
p
p
ly
.
T
h
is
s
tar
tin
g
cu
r
r
en
t
is
ab
o
u
t
5
to
6
tim
es
m
o
r
e
th
an
th
e
f
u
ll
lo
ad
cu
r
r
en
t.
T
h
is
tim
e
d
u
r
atio
n
ca
n
b
e
f
o
r
a
f
ew
m
illi
s
ec
o
n
d
s
o
r
lo
n
g
er
.
T
h
is
ca
u
s
es
th
e
elec
tr
ical
eq
u
ip
m
en
t to
d
a
m
ag
e
b
ec
au
s
e
o
f
th
e
i
n
cr
ea
s
ed
v
o
ltag
e
d
r
o
p
in
elec
tr
ical
s
y
s
tem
s
d
u
e
to
th
e
f
lo
w
o
f
lar
g
er
cu
r
r
e
n
ts
ac
r
o
s
s
th
e
ca
b
le.
Fo
r
th
is
r
ea
s
o
n
,
a
d
ef
in
ite
m
eth
o
d
o
f
s
tar
tin
g
th
e
m
o
to
r
is
n
ee
d
ed
.
2
.
4
.
T
ra
ns
ient
a
na
ly
s
is
T
h
e
ca
p
ac
ity
o
f
a
p
o
wer
s
y
s
tem
,
co
n
tain
in
g
at
least
two
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es,
to
k
ee
p
o
n
wo
r
k
in
g
af
ter
a
c
h
an
g
e
h
ap
p
en
ed
o
n
t
h
e
s
y
s
tem
is
a
ch
ec
k
o
f
its
s
tab
ilit
y
.
T
h
e
s
tab
ilit
y
is
s
u
e
tak
es
two
s
tr
u
ctu
r
es:
s
tead
y
-
s
tate
an
d
tr
an
s
ien
t.
Stead
y
-
s
tate
s
ec
u
r
ity
m
ig
h
t
b
e
ch
ar
ac
ter
ized
as
th
e
ca
p
ac
ity
o
f
a
p
o
wer
s
y
s
tem
to
k
ee
p
u
p
s
y
n
c
h
r
o
n
is
m
b
etwe
en
m
ac
h
in
es
in
s
id
e
th
e
s
y
s
t
em
f
o
llo
win
g
g
en
er
ally
m
o
d
er
ate
lo
ad
ch
an
g
es
.
T
r
an
s
ien
t
s
tab
ilit
y
is
th
e
v
ir
tu
e
o
f
th
e
s
y
s
tem
to
s
tay
in
s
y
n
ch
r
o
n
is
m
u
n
d
e
r
tr
an
s
ien
t
co
n
d
itio
n
s
,
i.e
.
,
ab
n
o
r
m
al
an
d
s
witch
in
g
o
p
er
atio
n
,
etc.
I
n
a
m
o
d
er
n
p
o
wer
s
y
s
tem
,
s
ta
b
ilit
y
m
ay
in
clu
d
e
th
e
p
o
wer
o
r
g
an
izatio
n
s
y
s
tem
an
d
at
least
o
n
e
in
-
p
lan
t
g
en
e
r
ato
r
o
r
s
y
n
c
h
r
o
n
o
u
s
m
ac
h
in
e.
Fo
llo
win
g
ar
e
th
e
p
o
s
s
ib
ilit
ies
i.e
.
,
f
o
r
ex
am
p
le,
lo
ad
d
is
m
is
s
al,
u
n
ex
p
ec
ted
l
o
s
s
o
f
a
g
en
er
ato
r
o
r
u
tili
ty
tie,
s
tar
tin
g
o
f
m
o
to
r
s
o
r
f
a
u
lt
(
an
d
th
eir
tim
e
in
ter
v
al)
,
d
ir
ec
tly
a
f
f
ec
t
s
y
s
tem
s
tab
ilit
y
an
d
ef
f
icien
c
y
.
L
o
ad
-
s
h
ed
d
in
g
s
ch
em
es
an
d
b
asic
f
law
clea
r
in
g
tim
es
ca
n
b
e
r
eso
lv
ed
t
o
ch
o
o
s
e
th
e
b
est
p
o
s
s
ib
le
s
ettin
g
s
f
o
r
p
r
o
tectio
n
r
elay
s
.
T
h
ese
k
in
d
s
o
f
s
tu
d
ies
ar
e
lik
ely
th
e
ab
s
o
lu
te
m
o
s
t
co
m
p
lex
o
n
es
d
o
n
e
o
n
a
p
o
we
r
s
y
s
tem
.
T
h
e
b
eg
in
n
in
g
s
tag
e
f
o
r
an
y
tr
an
s
ien
t
s
tab
ilit
y
s
im
u
latio
n
is
th
e
p
r
e
-
d
is
tu
r
b
an
ce
c
o
n
tr
o
l
p
o
wer
f
l
o
w
ar
r
an
g
em
en
t.
T
h
e
s
y
s
tem
is
co
n
s
tan
tly
th
o
u
g
h
t
to
b
e
in
a
co
n
s
is
ten
t
s
tate
wh
en
th
e
ag
g
r
av
atio
n
h
ap
p
e
n
s
.
Utilizin
g
th
e
p
r
e
-
d
is
tu
r
b
an
ce
p
o
wer
f
lo
w
s
o
lu
tio
n
,
all
th
e
u
n
d
er
ly
in
g
esti
m
atio
n
s
o
f
th
e
s
tate
f
ac
to
r
s
ar
e
d
eter
m
in
ed
af
ter
th
ese
ar
e
ac
q
u
ir
e
d
,
th
e
d
is
tu
r
b
an
ce
is
s
im
u
lated
.
T
h
e
s
im
u
latio
n
o
f
t
h
e
d
is
t
u
r
b
an
ce
ca
u
s
es
a
co
n
f
lict
b
etwe
en
th
e
m
ec
h
an
ical
p
o
wer
co
n
tr
ib
u
tio
n
to
th
e
g
e
n
er
ato
r
s
a
n
d
th
e
elec
tr
ical
p
o
wer
y
ield
o
f
th
e
g
e
n
er
ato
r
s
.
T
h
e
eq
u
ilib
r
iu
m
is
d
is
tu
r
b
e
d
.
T
h
e
s
tate
f
ac
t
o
r
s
ca
lcu
lated
b
y
th
e
d
if
f
er
en
t
d
if
f
er
en
tial
co
n
d
itio
n
s
co
m
b
i
n
ed
with
m
ath
em
atica
l
co
n
d
itio
n
s
ch
an
g
e
th
eir
v
alu
es.
A
tr
an
s
ien
t
s
tab
ilit
y
s
tu
d
y
h
as
b
ee
n
d
o
n
e
b
y
in
t
r
o
d
u
cin
g
a
th
r
ee
-
p
h
ase
an
d
L
-
G
f
a
u
lt
an
d
its
clea
r
an
ce
o
n
d
if
f
er
en
t
b
u
s
es.
T
h
e
s
y
s
tem
is
an
aly
ze
d
u
n
d
er
t
h
e
tr
an
s
ien
t
p
r
o
d
u
ce
d
b
y
th
ese
ab
n
o
r
m
al
co
n
d
itio
n
s
.
T
h
e
s
y
s
tem
g
en
er
ato
r
'
s
r
ea
ctio
n
at
b
eg
in
n
in
g
o
f
th
is
is
s
u
e
an
d
cle
ar
an
ce
o
f
th
is
d
is
tu
r
b
an
ce
h
as b
ee
n
r
ec
o
r
d
ed
.
2
.
5
.
E
co
no
m
ic
dis
pa
t
ch
Du
e
to
t
h
e
in
c
r
ea
s
in
g
p
r
ice
o
f
f
u
el
o
il,
wag
es,
an
d
s
alar
ies,
th
e
elec
tr
ical
en
e
r
g
y
co
s
t
also
in
cr
ea
s
es,
s
o
o
n
e
s
h
o
u
ld
k
ee
p
in
m
in
d
th
e
co
s
t
f
ac
to
r
wh
ile
o
p
er
atin
g
o
r
b
u
ild
i
n
g
a
n
ew
p
o
wer
s
y
s
tem
,
to
m
ee
t
th
e
g
r
o
win
g
lo
ad
d
em
a
n
d
.
I
n
t
h
e
o
p
er
atio
n
o
f
th
e
p
o
wer
s
y
s
tem
,
th
e
c
o
n
tr
ib
u
tio
n
f
r
o
m
ea
ch
lo
ad
a
n
d
ea
ch
u
n
it
with
in
a
p
lan
t
m
u
s
t
b
e
s
u
c
h
th
at
th
e
co
s
t
o
f
elec
tr
ical
en
er
g
y
p
r
o
d
u
ce
d
is
m
i
n
im
u
m
.
I
n
ter
io
r
p
o
in
t
o
p
tim
izatio
n
is
th
e
tech
n
i
q
u
e
t
h
r
o
u
g
h
ec
o
n
o
m
ic
d
is
p
atch
is
co
n
d
u
cte
d
in
E
T
AP.
T
h
e
r
ed
u
ctio
n
o
f
g
en
e
r
atio
n
co
s
t
is
ca
lled
ec
o
n
o
m
ic
d
i
s
p
atch
as
s
h
o
wn
in
Fig
u
r
e
2
.
I
n
t
h
e
g
en
er
atio
n
,
c
o
s
t
in
clu
d
es
th
e
o
p
er
atio
n
al
co
s
t,
m
ain
te
n
an
ce
,
l
ab
o
r
,
an
d
s
u
p
p
ly
c
o
s
t.
Mo
s
tly
,
th
e
g
en
er
atio
n
co
s
t
is
p
r
esen
t
a
s
q
u
ad
r
atic
o
f
in
p
u
t
f
u
el
an
d
p
o
we
r
g
en
er
atio
n
co
s
t
in
ec
o
n
o
m
ic
d
is
p
atch
an
d
o
th
er
co
n
s
tr
ain
ts
ar
e
v
o
ltag
e
lim
its
,
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
lim
its
,
an
d
p
o
wer
b
ala
n
ce
co
n
d
i
tio
n
[
4
0
]
–
[
4
5
]
.
T
o
u
n
d
er
s
tan
d
t
h
e
ec
o
n
o
m
ic
d
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p
atch
,
a
p
r
o
b
lem
is
p
r
esen
ted
in
th
e
m
ath
em
atica
l d
escr
ip
tio
n
as:
∑
(
+
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1
2
)
Su
b
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to
:
∑
(
=
1
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(
1
5
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≤
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W
h
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α
,
β,
an
d
γ
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e
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e
p
ar
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eter
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ar
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d
ep
en
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t
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e
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y
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tem
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d
th
ey
af
f
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t
r
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l
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atio
n
p
o
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co
s
t.
T
h
e
t
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n
u
m
b
er
o
f
g
e
n
er
ato
r
s
is
r
ep
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th
e
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ea
l
p
o
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en
e
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atio
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a
n
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n
etwo
r
k
r
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T
h
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atic
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ter
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t p
r
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ic
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atch
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r
o
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lem
i
n
th
e
f
o
llo
win
g
f
o
r
m
at
[
4
6
]
–
[
5
0
]
:
(
+
̅
+
1
2
̅
)
Su
b
ject
to
≤
≤
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
5
2
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7
9
2
I
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t J Ap
p
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11
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ch
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(
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Input
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ys
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e
m
D
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t
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P
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rform
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c
onom
i
c
D
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h S
t
udi
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A
re
L
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s
Inc
l
ude
d
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bt
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orre
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Ca
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pt
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t
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ude
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d fl
ow
t
o obt
a
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n ne
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P
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or
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s
pon
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t
o n
e
w
P
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V
ol
t
a
ge
V
i
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a
t
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ons
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D
i
s
pl
a
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i
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um
P
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M
i
ni
m
um
fue
l
c
os
t
S
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P
Y
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S
NO
NO
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S
Fig
u
r
e
2
.
Pro
p
o
s
ed
f
l
o
w
ch
ar
t
o
f
in
ter
-
p
o
in
t o
p
tim
izatio
n
f
o
r
ec
o
n
o
m
ic
d
is
p
atch
3.
T
E
ST
SY
ST
E
M
T
h
e
test
s
y
s
tem
is
co
m
p
o
s
ed
o
f
th
r
ee
m
ain
s
ec
tio
n
s
wh
ich
ar
e
d
escr
ib
ed
b
elo
w.
I
t
co
n
tain
s
n
in
e
f
u
r
n
ac
e
o
il
-
b
ased
g
en
er
at
o
r
s
an
d
o
n
e
co
m
b
in
e
d
cy
cle
-
b
ase
d
g
en
er
ato
r
.
Fu
r
th
er
d
etail
is
f
o
llo
wed
b
y
ea
ch
s
ec
tio
n
.
3
.
1
.
H
i
g
h v
o
lt
a
g
e
s
ide
T
h
e
h
ig
h
v
o
ltag
e
s
id
e
is
co
m
p
o
s
ed
o
f
two
m
ain
b
u
s
es
wh
ich
ar
e
d
ir
ec
tly
f
ed
f
r
o
m
two
u
tili
ty
b
u
s
es
as g
iv
en
in
Fig
u
r
e
3
.
T
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I
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