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C
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AC
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,
Un
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f
Nig
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Nsu
k
k
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m
ail:
ch
ib
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u
@
u
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u
.
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g
1.
I
NT
RO
D
UCT
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O
N
T
h
e
b
en
ef
its
o
f
h
av
i
n
g
a
d
ep
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ab
le
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ical
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wer
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k
ca
n
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o
t
b
e
o
v
e
r
s
tated
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t
o
f
th
e
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is
in
g
elec
tr
icity
d
em
an
d
.
Stre
n
g
th
en
in
g
th
e
to
p
o
lo
g
y
o
f
th
e
p
o
wer
s
y
s
tem
an
d
o
p
tim
izin
g
its
o
p
er
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n
s
ar
e
ess
en
tial
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th
e
lik
elih
o
o
d
o
f
s
y
s
tem
b
r
ea
k
d
o
wn
s
[
1
]
.
R
estru
ctu
r
in
g
th
e
n
etwo
r
k
i
s
v
ital
to
en
s
u
r
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g
r
esil
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s
tab
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,
p
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o
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p
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ity
,
an
d
s
u
s
tain
ab
ilit
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in
th
e
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n
er
g
y
s
ec
to
r
[
2
]
.
Stab
ilit
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is
a
cr
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f
ac
to
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in
ass
es
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in
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th
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r
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f
a
p
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tem
d
u
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in
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tag
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[
3
]
.
Po
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tem
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tab
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ef
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d
b
y
th
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task
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s
tem
,
f
o
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a
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iv
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in
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co
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itio
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,
to
r
eg
ain
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s
tate
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eq
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at
p
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ac
tically
th
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en
tire
s
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s
te
m
r
em
ain
s
in
tact”
[
4
]
.
T
h
e
g
o
al
is
to
en
s
u
r
e
th
at
i
t
r
em
ain
s
a
f
o
ca
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p
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tr
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esear
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n
h
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s
tab
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o
f
th
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p
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wer
s
y
s
tem
r
eq
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ir
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.
Nig
e
r
ia's
p
o
wer
in
f
r
astru
ctu
r
e
f
ac
es
s
ev
er
al
ch
allen
g
es
as
elec
tr
icity
u
s
ag
e
in
cr
ea
s
es.
T
h
e
f
r
eq
u
en
cy
o
f
p
ar
tial
an
d
to
tal
g
r
id
d
is
r
u
p
tio
n
s
is
o
f
s
ig
n
if
ican
t
co
n
ce
r
n
.
T
h
is
p
r
im
ar
i
ly
r
esu
lts
f
r
o
m
th
e
g
r
i
d
'
s
o
u
td
ated
in
f
r
astru
ctu
r
e,
ca
s
ca
d
ed
tr
an
s
m
is
s
io
n
lin
e
tr
ip
p
in
g
d
u
e
t
o
o
v
er
lo
a
d
,
lo
s
s
o
f
s
y
n
ch
r
o
n
izatio
n
am
o
n
g
m
u
ltip
le
n
etwo
r
k
alter
n
ato
r
s
,
n
etw
o
r
k
to
p
o
lo
g
y
,
lo
n
g
-
d
is
tan
ce
t
r
an
s
m
is
s
io
n
lin
es,
in
f
r
astru
ctu
r
e
d
ef
icien
cies,
o
v
er
-
v
o
lta
g
es,
v
an
d
alis
m
,
an
d
p
r
o
tectiv
e
d
ev
ice
m
al
f
u
n
ctio
n
s
[
5
]
.
As
th
e
g
r
id
ex
p
an
d
s
to
m
ee
t
ex
p
an
d
in
g
d
em
an
d
an
d
s
u
p
p
o
r
t
th
e
co
u
n
t
r
y
'
s
ec
o
n
o
m
y
,
m
o
r
e
g
en
er
at
o
r
s
an
d
tr
an
s
m
is
s
io
n
lin
es
ar
e
ad
d
ed
,
co
m
p
licatin
g
th
e
s
y
s
tem
an
d
in
cr
ea
s
in
g
th
e
r
is
k
o
f
s
h
o
r
t
cir
cu
its
o
cc
u
r
r
in
g
a
n
d
s
y
s
tem
co
llap
s
e.
T
o
ad
d
r
ess
th
ese
ch
allen
g
es,
th
is
s
tu
d
y
aim
s
to
in
v
esti
g
ate
th
e
o
p
tim
al
r
ec
o
n
f
ig
u
r
atio
n
o
f
th
e
W
ester
n
Nig
er
ian
1
4
-
b
u
s
r
e
g
io
n
al
p
o
wer
n
etwo
r
k
u
s
in
g
h
y
b
r
i
d
wh
ale
alg
o
r
ith
m
an
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
W
APSO)
tech
n
iq
u
es,
f
o
cu
s
in
g
o
n
p
o
wer
lo
s
s
r
ed
u
ctio
n
,
v
o
ltag
e
p
r
o
f
ile
im
p
r
o
v
em
en
t,
an
d
r
o
to
r
an
g
le
s
tab
ilit
y
ass
ess
m
en
t
u
n
d
er
v
a
r
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
.
T
h
e
W
ester
n
Nig
er
ian
1
4
-
b
u
s
r
eg
i
o
n
al
p
o
wer
n
etwo
r
k
is
an
ess
en
tial
co
m
p
o
n
en
t
o
f
th
e
Nig
er
ian
n
ati
o
n
al
g
r
id
.
I
m
p
r
o
v
i
n
g
s
tab
ilit
y
,
ef
f
icien
c
y
,
an
d
d
ep
en
d
a
b
ilit
y
is
im
p
o
r
ta
n
t
f
o
r
en
co
u
r
ag
in
g
ec
o
n
o
m
ic
g
r
o
wt
h
an
d
d
ev
el
o
p
m
en
t,
en
h
a
n
cin
g
elec
tr
icity
q
u
ality
,
an
d
g
u
ar
an
teein
g
s
y
s
tem
r
es
ilien
ce
.
Op
tim
izin
g
r
e
g
io
n
al
n
etwo
r
k
s
will
en
s
u
r
e
t
h
e
o
v
er
all
g
r
id
s
y
s
tem
'
s
s
ec
u
r
ity
an
d
r
eliab
ilit
y
.
Nu
m
er
o
u
s
s
tu
d
ies
h
av
e
b
ee
n
u
n
d
er
tak
e
n
to
o
p
tim
ize
n
etwo
r
k
r
ec
o
n
f
ig
u
r
atio
n
f
o
r
im
p
r
o
v
ed
s
tab
ilit
y
an
d
r
esil
ien
ce
.
Stu
d
y
[
6
]
p
r
o
p
o
s
ed
an
im
p
r
o
v
ed
b
r
u
te
-
f
o
r
ce
m
eth
o
d
f
o
r
o
p
tim
izin
g
th
e
r
ec
o
n
f
ig
u
r
atio
n
o
f
ex
tr
a
-
h
ig
h
v
o
ltag
e
tr
a
n
s
m
is
s
i
o
n
n
etwo
r
k
s
.
T
h
e
g
o
al
was
to
r
ed
u
ce
s
h
o
r
t
cir
c
u
its
wh
ile
s
t
ill
m
ee
tin
g
s
tead
y
-
s
tate
an
d
tr
an
s
ien
t
co
n
s
tr
ain
t
s
.
T
h
is
co
s
t
-
ef
f
ec
tiv
e
m
eth
o
d
id
en
tifie
s
th
e
o
p
tim
al
g
r
id
r
ec
o
n
f
i
g
u
r
atio
n
to
r
ed
u
ce
s
h
o
r
t
cir
c
u
its
wh
ile
m
ee
tin
g
o
p
er
atio
n
al
r
eq
u
ir
e
m
en
t
s
.
Ho
wev
er
,
a
k
ey
lim
itatio
n
o
f
th
e
s
tu
d
y
was
its
f
ailu
r
e
to
ad
eq
u
ately
ad
d
r
ess
r
o
to
r
a
n
g
le
s
tab
ilit
y
.
T
h
is
d
is
ad
v
an
tag
e
was
ev
id
en
t
in
th
e
a
d
ju
s
tm
en
ts
m
ad
e
to
p
ar
am
eter
s
s
u
ch
as
g
en
er
ato
r
ex
citer
g
ain
,
v
o
ltag
e
s
ch
ed
u
les,
an
d
d
is
p
atch
s
tr
ateg
ies,
with
o
u
t
ad
d
r
ess
in
g
cr
itical
clea
r
in
g
tim
es
o
r
im
p
r
o
v
in
g
p
o
wer
o
s
cillatio
n
s
tab
ilit
y
in
tr
a
n
s
m
is
s
io
n
lin
es
an
d
g
e
n
er
ato
r
s
.
I
n
co
n
tr
ast,
Nad
er
ip
o
u
r
et
a
l.
[
7
]
ex
p
lo
r
ed
o
p
tim
al
r
ec
o
n
f
ig
u
r
a
tio
n
f
o
r
u
n
b
alan
ce
d
d
is
tr
ib
u
tio
n
s
y
s
tem
s
aim
ed
at
lo
s
s
r
ed
u
ctio
n
,
im
p
r
o
v
ed
p
o
wer
q
u
ality
,
an
d
m
in
im
izin
g
u
n
s
er
v
ed
en
er
g
y
u
s
in
g
a
f
u
zz
y
m
u
lti
-
cr
iter
ia
ap
p
r
o
ac
h
a
n
d
an
i
n
n
o
v
ativ
e
e
n
h
an
ce
d
co
r
o
n
a
v
ir
u
s
h
e
r
d
im
m
u
n
ity
o
p
tim
izer
.
T
h
is
m
eth
o
d
wo
r
k
ed
b
etter
th
an
o
th
er
m
eth
o
d
s
w
h
en
test
ed
o
n
I
E
E
E
3
3
a
n
d
6
9
-
b
u
s
s
y
s
tem
s
f
o
r
b
o
t
h
s
in
g
le
-
o
b
jectiv
e
an
d
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
.
Ho
wev
er
,
it
d
i
d
n
o
t
in
clu
d
e
f
a
u
lt
an
aly
s
is
o
r
s
tab
ilit
y
ass
es
s
m
en
ts
.
Sim
ilar
ly
,
Alan
az
i
an
d
Alan
az
i
[
8
]
ap
p
lied
an
in
tellig
en
t
ar
tific
ial
elec
tr
ic
f
ield
alg
o
r
ith
m
-
p
atter
n
s
ea
r
c
h
to
u
n
ev
e
n
I
E
E
E
3
3
-
b
u
s
an
d
r
ea
l
u
n
b
alan
ce
d
1
3
-
b
u
s
s
y
s
tem
s
,
f
o
cu
s
in
g
o
n
lo
s
s
r
ed
u
ctio
n
an
d
v
o
ltag
e
im
p
r
o
v
em
en
t.
Ho
wev
er
,
N
-
1
s
ec
u
r
ity
co
n
s
tr
ain
ts
,
s
h
o
r
t
cir
cu
it
an
al
y
s
is
,
an
d
s
tab
ilit
y
ass
ess
m
en
t
s
wer
e
n
o
t
ad
d
r
ess
ed
.
Ad
d
iti
o
n
ally
,
C
ik
an
a
n
d
Kek
ez
o
g
lu
[
3
]
ex
a
m
in
ed
eq
u
ilib
r
iu
m
o
p
tim
izatio
n
a
n
d
o
t
h
er
m
eta
-
h
eu
r
is
tic
o
p
tim
izatio
n
tech
n
iq
u
es
in
a
r
ec
o
n
f
ig
u
r
ed
d
is
tr
ib
u
tio
n
n
et
wo
r
k
with
th
e
s
o
le
p
u
r
p
o
s
e
o
f
r
ea
l
p
o
wer
lo
s
s
r
ed
u
ctio
n
,
im
p
r
o
v
in
g
th
e
v
o
ltag
e
lev
el,
an
d
r
aisi
n
g
th
e
r
eliab
ilit
y
in
d
ex
.
Nev
er
th
eless
,
N
-
1
s
ec
u
r
ity
co
n
s
tr
ain
ts
,
s
h
o
r
t
cir
cu
it
an
aly
s
is
,
an
d
s
tab
ilit
y
an
aly
s
is
wer
e
n
o
t
ad
d
r
ess
ed
.
Sev
er
al
a
p
p
r
o
ac
h
es
ad
d
r
ess
ed
tr
an
s
m
is
s
io
n
n
etwo
r
k
is
s
u
es:
Sik
ir
u
et
a
l.
[
9
]
id
en
tifie
d
wea
k
b
u
s
es
b
u
t
n
e
g
lecte
d
s
tab
ilit
y
,
wh
ile
in
[
1
0
]
,
co
-
o
p
tim
ized
e
n
er
g
y
a
n
d
r
eser
v
es
with
o
u
t
AC
p
o
wer
f
lo
w
ar
e
co
n
s
id
er
ed
.
Stab
ilit
y
co
n
ce
r
n
s
wer
e
also
o
v
er
lo
o
k
e
d
in
[
1
1
]
an
d
[
1
2
]
,
wh
ich
ex
p
lo
r
ed
co
n
tin
g
en
cy
-
co
n
s
tr
ai
n
ed
o
p
tim
al
p
o
wer
f
lo
w.
R
ec
o
n
f
ig
u
r
in
g
th
e
n
etwo
r
k
to
in
cr
ea
s
e
s
y
s
tem
s
tab
ilit
y
an
d
r
ed
u
ce
s
h
o
r
t
cir
cu
its
h
as
b
ee
n
d
is
cu
s
s
ed
in
p
r
ev
i
o
u
s
wo
r
k
s
in
cl
u
d
in
g
[
1
3
]
–
[
1
9
]
.
T
h
e
co
n
ce
p
ts
o
f
b
u
s
s
p
litt
in
g
an
d
lin
e
elim
in
atio
n
was
ex
p
lo
r
e
d
in
[
1
3
]
.
Sh
o
r
t
cir
cu
it
r
estrictio
n
was
as
s
ess
ed
in
th
e
s
tu
d
y
to
m
in
im
ize
th
e
f
ast
v
o
lta
g
e
s
tab
ilit
y
in
d
ex
'
s
m
ax
im
u
m
v
al
u
e
ac
r
o
s
s
all
ex
am
in
ed
lin
es.
Utilizin
g
an
alter
ed
I
E
E
E
2
4
-
b
u
s
s
y
s
tem
,
th
e
wo
r
k
was
ev
alu
ated
.
T
h
e
o
b
jectiv
e
o
f
m
in
im
izin
g
s
h
o
r
t
cir
cu
it
lev
els
wh
ile
also
o
f
f
er
in
g
s
p
litt
in
g
r
eliab
le
ap
p
r
o
ac
h
es
was
ev
alu
ated
in
[
1
4
]
.
T
h
is
was
d
o
n
e
to
r
estrict
th
e
s
p
litt
in
g
to
th
e
s
u
b
s
tatio
n
s
with
th
e
g
r
ea
test
s
h
o
r
t
cir
cu
it
cu
r
r
en
ts
alo
n
e
an
d
m
ain
tain
a
lim
ited
p
o
wer
f
lo
w
in
th
e
s
p
litt
in
g
p
o
in
t.
An
I
E
E
E
2
5
-
b
u
s
s
y
s
tem
an
d
th
e
I
r
aq
i
400
k
V
p
o
wer
in
f
r
astru
ctu
r
e
wer
e
u
tili
ze
d
f
o
r
t
h
e
in
q
u
ir
y
.
T
o
s
o
lv
e
th
e
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
o
f
N
-
1
co
n
tin
g
en
c
y
r
eq
u
ir
em
e
n
t
a
n
d
s
h
o
r
t
cir
cu
it
cu
r
r
e
n
t
lim
itatio
n
in
th
e
o
p
tim
izatio
n
is
s
u
e,
Do
ğ
an
a
n
d
Y
ö
r
ü
k
er
e
n
[
1
5
]
u
s
ed
a
h
y
b
r
i
d
g
e
n
etic
al
g
o
r
ith
m
(
GA)
a
n
d
b
in
ar
y
PS
O
to
o
p
tim
ally
d
eter
m
in
e
th
e
p
o
s
itio
n
f
o
r
a
b
u
s
ar
ch
itectu
r
e.
Ho
wev
er
,
th
e
p
ar
am
eter
s
o
f
GA
an
d
b
in
ar
y
PS
O
wer
e
n
o
t
em
p
lo
y
ed
to
o
p
ti
m
ize
th
e
to
p
o
lo
g
y
o
f
th
e
tr
an
s
m
is
s
io
n
s
y
s
tem
in
q
u
esti
o
n
.
T
h
e
im
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ce
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p
litt
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was
co
v
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ed
in
[
1
6
]
.
A
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tic
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tili
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Evaluation Warning : The document was created with Spire.PDF for Python.
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2
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I
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t J E
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Vo
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15
,
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6
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Decem
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r
20
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6
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6
6014
an
aly
s
is
an
d
o
t
h
er
f
o
r
m
s
o
f
f
au
lt
wer
e
o
v
e
r
lo
o
k
e
d
b
y
t
h
e
au
th
o
r
s
.
T
h
e
Ku
wait
h
i
g
h
v
o
ltag
e
n
etwo
r
k
'
s
ex
ce
s
s
iv
e
s
h
o
r
t
cir
c
u
it
cu
r
r
en
t
was
ad
d
r
ess
ed
in
[
1
7
]
u
s
in
g
a
v
ar
iety
o
f
s
tr
ateg
ies.
Alth
o
u
g
h
d
iv
id
in
g
th
e
cu
r
r
en
t
2
7
5
k
V
n
etwo
r
k
is
th
e
b
est
way
to
ad
d
r
ess
th
e
r
ap
id
ly
r
is
in
g
s
h
o
r
t
cir
cu
it
lev
els,
it
is
n
o
t
clea
r
wh
er
e
th
e
s
p
litt
in
g
s
h
o
u
ld
b
e
d
o
n
e.
T
wo
s
tr
ateg
ies
f
o
r
r
ed
u
cin
g
v
o
ltag
e
s
tab
ilit
y
an
d
s
h
o
r
t
cir
c
u
it
v
io
latio
n
s
wer
e
co
v
er
ed
i
n
[
1
8
]
.
T
h
e
f
ir
s
t
a
p
p
r
o
ac
h
u
s
es
a
q
u
ick
m
ath
e
m
atica
l
p
r
o
ce
s
s
to
d
eter
m
in
e
th
e
ch
an
g
e
in
th
e
im
p
ed
an
ce
m
at
r
ix
elem
en
t.
T
h
e
s
ec
o
n
d
a
p
p
r
o
ac
h
m
i
n
im
izes
th
e
s
h
o
r
t
cir
cu
it
ca
p
ac
it
y
wh
ile
tak
in
g
b
u
s
v
o
ltag
e
lim
its
in
to
ac
co
u
n
t
b
y
u
s
in
g
a
lin
ea
r
p
r
o
g
r
a
m
m
in
g
m
eth
o
d
o
l
o
g
y
.
T
h
e
au
th
o
r
s
d
id
n
o
t,
h
o
wev
er
,
tak
e
in
to
ac
co
u
n
t
h
o
w
th
e
r
ec
o
n
f
i
g
u
r
atio
n
wo
u
ld
af
f
ec
t
th
e
g
e
n
er
ato
r
s
'
r
o
to
r
an
g
le
s
tab
ilit
y
with
in
th
e
p
o
wer
s
y
s
tem
.
T
o
ac
h
ie
v
e
s
h
o
r
t
cir
c
u
it
r
estrictio
n
s
wh
ile
m
ain
tain
in
g
p
o
wer
f
l
o
w
co
n
s
tr
ain
ts
o
n
b
u
s
b
ar
s
witch
in
g
,
Van
Ack
er
et
a
l.
[
1
9
]
s
h
o
we
d
h
o
w
to
em
p
lo
y
a
m
ix
e
d
in
teg
er
n
o
n
-
co
n
v
ex
q
u
a
d
r
atic
co
n
s
tr
ain
t
alg
o
r
ith
m
.
W
h
ile
s
tu
d
y
[
2
0
]
ad
d
r
ess
ed
tr
an
s
ien
t
s
tab
ilit
y
is
s
u
e
s
b
y
co
m
b
in
in
g
g
r
id
to
p
o
lo
g
y
with
m
ac
h
in
e
lear
n
in
g
tech
n
iq
u
es.
T
h
e
s
y
n
c
h
r
o
n
o
u
s
g
en
er
ato
r
s
'
r
o
to
r
an
g
le
s
tab
ilit
y
ad
ju
s
tm
en
ts
m
ad
e
to
p
ar
am
eter
s
s
u
ch
as
g
en
er
ato
r
e
x
citer
g
ain
,
v
o
ltag
e
s
ch
ed
u
les,
an
d
d
is
p
atch
s
tr
ate
g
ies,
with
o
u
t a
d
d
r
ess
in
g
cr
itic
al
clea
r
in
g
tim
es o
r
im
p
r
o
v
in
g
p
o
wer
o
s
cillatio
n
s
tab
ilit
y
in
tr
an
s
m
is
s
io
n
lin
e
s
an
d
g
en
er
ato
r
s
f
o
llo
win
g
a
co
n
tin
g
en
cy
wer
e
o
v
er
lo
o
k
ed
b
y
th
e
wr
iter
s
.
T
h
is
s
tu
d
y
p
r
esen
ts
th
e
ap
p
li
ca
tio
n
o
f
a
h
y
b
r
id
weig
h
te
d
ag
g
r
eg
ated
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
(
W
APSO)
tech
n
iq
u
e
f
o
r
th
e
o
p
tim
al
r
ec
o
n
f
ig
u
r
atio
n
o
f
th
e
W
ester
n
Nig
er
ian
1
4
-
b
u
s
r
e
g
i
o
n
al
p
o
wer
n
etwo
r
k
.
T
h
e
p
r
im
ar
y
o
b
jectiv
es
a
r
e
t
o
m
in
im
ize
ac
tiv
e
p
o
wer
lo
s
s
es,
en
h
an
ce
v
o
ltag
e
p
r
o
f
iles
,
an
d
im
p
r
o
v
e
r
o
to
r
an
g
le
s
tab
ilit
y
u
n
d
er
f
au
lt
a
n
d
co
n
tin
g
e
n
cy
co
n
d
itio
n
s
.
T
h
e
s
tab
ilit
y
ass
es
s
m
en
t
f
o
cu
s
es
o
n
tu
n
in
g
g
en
er
ato
r
p
ar
am
eter
s
—
s
p
ec
if
ically
ex
ci
ter
g
ain
,
v
o
ltag
e
s
ch
ed
u
les,
a
n
d
p
o
wer
d
is
p
atch
—
with
o
u
t
alter
in
g
th
e
cr
itical
clea
r
in
g
tim
e
(
C
C
T
)
.
T
h
e
p
r
o
p
o
s
ed
h
y
b
r
id
W
APSO
-
b
ased
r
ec
o
n
f
ig
u
r
atio
n
s
tr
ateg
y
y
ield
s
s
u
b
s
tan
tial
im
p
r
o
v
em
e
n
ts
in
n
etwo
r
k
p
er
f
o
r
m
a
n
ce
.
No
tab
l
y
,
th
e
in
teg
r
atio
n
o
f
two
a
d
d
itio
n
al
tr
an
s
m
is
s
io
n
lin
es
(
L
in
e
5
–
8
a
n
d
L
in
e
1
3
–
1
4
)
en
h
an
ce
s
n
etwo
r
k
co
n
n
ec
tiv
ity
,
allev
iates
lin
e
co
n
g
esti
o
n
,
a
n
d
i
n
tr
o
d
u
ce
s
alter
n
ativ
e
p
o
wer
f
lo
w
p
ath
s
,
th
er
eb
y
in
cr
ea
s
in
g
s
y
s
tem
r
eliab
ilit
y
.
T
h
e
o
p
tim
al
r
ec
o
n
f
ig
u
r
atio
n
r
esu
lts
in
a
2
9
.
5
% r
ed
u
ctio
n
i
n
ac
tiv
e
p
o
wer
lo
s
s
es a
cr
o
s
s
th
e
r
eg
io
n
al
g
r
id
.
Fu
r
th
er
m
o
r
e
,
th
e
s
tu
d
y
d
em
o
n
s
tr
ates
th
e
ef
f
ec
tiv
e
n
ess
o
f
h
y
b
r
id
W
APSO
in
o
p
tim
izin
g
g
e
n
er
ato
r
co
n
tr
o
l
p
ar
am
eter
s
.
E
x
citer
g
ain
s
wer
e
tu
n
ed
with
in
th
e
r
an
g
e
o
f
5
0
t
o
2
5
0
,
v
o
ltag
e
s
ch
ed
u
les
we
r
e
m
ain
tain
ed
b
etwe
en
0
.
9
5
an
d
1
.
0
5
p
.
u
.
,
an
d
p
o
wer
d
is
p
atch
lev
els
wer
e
ad
ju
s
ted
with
in
g
e
n
er
ato
r
o
p
e
r
atio
n
al
lim
its
.
T
h
ese
ad
ju
s
tm
en
ts
led
to
im
p
r
o
v
e
d
tr
an
s
ien
t
an
d
v
o
ltag
e
s
tab
ilit
y
,
with
s
ig
n
if
ican
t
r
ed
u
ctio
n
s
in
r
o
to
r
an
g
le
d
ev
iatio
n
s
.
T
h
e
s
y
s
tem
-
m
ain
tain
ed
s
y
n
c
h
r
o
n
is
m
d
u
r
in
g
f
au
lt
s
ce
n
ar
io
s
,
with
r
o
t
o
r
an
g
le
ex
cu
r
s
io
n
s
r
em
ain
in
g
well
b
elo
w
t
h
e
cr
iti
ca
l
π/2
th
r
esh
o
ld
.
I
m
p
o
r
tan
tly
,
f
au
lt
clea
r
a
n
ce
tim
es
wer
e
p
r
eser
v
ed
with
in
th
e
C
C
T
,
v
alid
atin
g
th
e
r
o
b
u
s
tn
ess
o
f
th
e
o
p
tim
ize
d
co
n
f
ig
u
r
ati
o
n
u
n
d
er
s
ev
er
e
d
is
tu
r
b
an
ce
s
.
T
h
e
r
em
ain
d
er
o
f
th
is
m
an
u
s
cr
ip
t
is
o
r
g
an
ized
as
f
o
llo
ws:
Sectio
n
2
d
etails
th
e
m
ater
ials
an
d
m
eth
o
d
s
em
p
lo
y
ed
,
Sectio
n
3
p
r
esen
ts
th
e
r
esu
lts
an
d
d
is
cu
s
s
es th
eir
im
p
licatio
n
s
,
an
d
Sec
tio
n
4
co
n
clu
d
es th
e
s
tu
d
y
.
2.
M
AT
E
R
I
AL
S AN
D
M
E
T
H
O
D
T
h
is
s
ec
tio
n
ex
p
lain
s
a
way
o
f
r
ec
o
n
f
ig
u
r
in
g
th
e
W
ester
n
Nig
er
ian
1
4
-
b
u
s
r
eg
io
n
al
g
r
i
d
n
etwo
r
k
f
o
r
s
tab
ilit
y
en
h
an
ce
m
en
t.
Utilizin
g
MA
T
L
AB
/MAT
PO
W
E
R
en
v
ir
o
n
m
en
t
a
n
d
m
ath
em
at
ical
f
o
r
m
u
latio
n
s
,
W
AP
SO
an
d
r
o
t
o
r
s
tab
ilit
y
wer
e
m
o
d
elled
.
New
to
n
R
ap
h
s
o
n
’
s
(
NR
)
lo
a
d
f
lo
w
m
eth
o
d
was
ap
p
lied
t
o
d
eter
m
in
e
th
e
s
tead
y
-
s
tate
s
o
lu
tio
n
.
T
h
e
e
x
am
in
ed
n
et
wo
r
k
co
n
s
is
ts
o
f
1
4
b
u
s
es,
in
co
r
p
o
r
atin
g
f
o
u
r
g
en
er
ato
r
s
an
d
1
4
lo
ad
s
.
All
f
o
u
r
g
en
e
r
ato
r
s
ar
e
o
p
er
atio
n
al,
co
llectiv
ely
g
e
n
er
atin
g
a
n
ac
tiv
e
p
o
we
r
o
f
2
,
4
4
4
.
3
MW
an
d
a
r
ea
ctiv
e
p
o
wer
o
f
8
6
6
.
2
MV
Ar
.
T
h
e
d
ata
u
tili
ze
d
in
th
is
s
tu
d
y
,
co
m
p
r
is
in
g
th
e
s
in
g
le
-
lin
e
d
iag
r
am
,
lin
e
d
ata,
b
u
s
d
ata,
g
en
er
at
o
r
d
ata
,
an
d
g
e
n
er
at
o
r
d
y
n
am
ic
p
ar
am
eter
s
,
wer
e
s
o
u
r
ce
d
f
r
o
m
th
e
T
r
an
s
m
is
s
io
n
C
o
m
p
an
y
o
f
Ni
g
er
ia.
2
.
1
.
New
t
o
n
Ra
ph
s
o
n lo
a
d f
lo
w
a
na
ly
s
is
L
o
ad
f
lo
w
an
al
y
s
is
was
f
ir
s
t
ap
p
lied
to
th
e
n
etwo
r
k
s
h
o
w
i
n
Fig
u
r
e
1
to
d
eter
m
in
e
th
e
s
t
ea
d
y
-
s
tate
s
o
lu
tio
n
o
f
th
e
1
4
-
b
u
s
W
ester
n
Nig
er
ian
r
eg
i
o
n
al
p
o
wer
s
y
s
tem
.
T
h
e
an
aly
s
is
p
r
o
v
id
es
a
n
in
itial
ass
es
s
m
en
t
o
f
th
e
p
o
wer
s
y
s
tem
,
wh
ich
is
n
o
n
lin
ea
r
d
u
e
to
t
h
e
d
y
n
am
ic
r
elatio
n
s
h
ip
b
etwe
en
lo
ad
,
v
o
ltag
e
m
a
g
n
itu
d
e,
an
d
cir
cu
it
im
p
ed
an
ce
.
Sin
ce
i
t
is
a
n
o
n
-
lin
ea
r
p
r
o
b
lem
,
it
m
u
s
t
b
e
s
o
lv
ed
iter
ativ
ely
.
T
h
e
m
eth
o
d
h
as
a
b
etter
co
n
v
er
g
en
ce
r
ate
an
d
h
ig
h
lev
el
o
f
ac
cu
r
ac
y
th
an
o
th
er
m
et
h
o
d
s
o
f
lo
ad
f
l
o
w
s
o
lu
tio
n
[
2
1
]
.
T
h
e
eq
u
atio
n
s
o
f
th
e
New
to
n
R
ap
h
s
o
n
’
s
lo
ad
f
l
o
w
tech
n
iq
u
e
ar
e
s
tated
b
elo
w
.
ℎ
=
1
ℎℎ
[
ℎ
−
ℎ
ℎ
∗
−
∑
ℎ
=
1
≠
ℎ
]
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
P
o
w
er lo
s
s
r
ed
u
ctio
n
a
n
d
s
ta
b
ilit
y
en
h
a
n
ce
men
t
o
f p
o
w
er sys
tem
…
(
Tit
u
s
Te
r
w
a
s
e
A
ko
r
)
6015
T
h
e
lo
ad
f
lo
w
f
o
r
m
u
latio
n
is
g
iv
en
b
y
th
e
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win
g
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ets o
f
e
q
u
atio
n
s
.
ℎ
=
∑
|
ℎ
|
|
|
|
ℎ
|
(
ℎ
−
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+
)
=
1
≠
ℎ
(
2
)
ℎ
=
−
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|
ℎ
|
|
|
|
ℎ
|
(
ℎ
−
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=
1
≠
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(
3
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E
q
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atio
n
s
(
2
)
an
d
(
3
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e
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ets o
f
n
o
n
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lin
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aic
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ati
o
n
s
.
Fig
u
r
e
1
.
Sin
g
le
lin
e
d
iag
r
a
m
o
f
th
e
W
ester
n
Nig
er
ian
r
e
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io
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r
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etwo
r
k
2
.
2
.
M
o
dellin
g
o
f
o
pti
m
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l ne
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re
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o
nfig
ura
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io
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T
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e
m
u
lti
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o
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jectiv
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f
u
n
ctio
n
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tated
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n
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id
er
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p
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ctio
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r
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t
.
T
h
e
p
o
wer
l
o
s
s
o
f
th
e
n
etwo
r
k
as e
x
p
r
ess
ed
in
[
3
]
is
g
iv
e
n
as:
min
=
∑
(
2
+
2
2
)
ℎ
,
=
1
ℎ
(
4
)
wh
er
e
is
th
e
p
o
wer
lo
s
s
in
th
e
tr
an
s
m
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io
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e,
ℎ
↔
r
e
p
r
esen
t
s
th
e
b
u
s
n
u
m
b
er
,
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d
d
en
o
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es
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tr
a
n
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m
is
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io
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,
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esis
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ce
o
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etwe
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ℎ
ℎ
ℎ
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s
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ar
e
th
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l
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n
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r
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ctiv
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p
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w
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v
alu
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s
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ℎ
an
d
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ep
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ts
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e
v
o
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a
g
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itu
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o
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t
h
e
b
u
s
.
T
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ac
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wer
lo
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s
r
ed
u
ctio
n
(
∆
)
is
g
iv
en
as e
x
p
r
ess
ed
in
(
5
)
b
y
C
ik
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a
n
d
Kek
ez
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l
u
[
3
]
:
∆
=
(
5
)
wh
er
e,
an
d
ar
e
th
e
p
o
wer
lo
s
s
es
af
ter
an
d
b
ef
o
r
e
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k
r
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n
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ig
u
r
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n
r
esp
ec
tiv
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T
h
e
v
o
ltag
e
d
e
v
iatio
n
(
VD)
in
d
ex
i
s
g
iv
en
as e
x
p
r
ess
ed
in
[
3
]
:
min
=
ma
x
(
−
ℎ
)
∀
ℎ
=
1
,
2
,
3
,
…
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
6
0
1
2
-
6
0
2
6
6016
wh
er
e,
ℎ
ar
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th
e
n
o
m
i
n
al
an
d
b
u
s
v
o
ltag
es
r
esp
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tiv
ely
.
T
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e
g
o
al
is
to
r
ed
u
ce
th
e
v
o
ltag
e
v
ar
iatio
n
as
it
ap
p
r
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ac
h
es
ze
r
o
.
T
h
is
im
p
r
o
v
es
th
e
n
etwo
r
k
'
s
v
o
ltag
e
p
r
o
f
ile.
T
h
e
f
itn
ess
f
u
n
ctio
n
is
th
e
co
m
b
in
atio
n
o
f
(
5
)
an
d
(
6
)
with
th
e
weig
h
te
d
f
u
n
ctio
n
to
f
o
r
m
a
s
in
g
le
o
b
jectiv
e
f
u
n
ctio
n
.
=
min
(
∆
∗
+
∗
)
(
7
)
wh
er
e,
an
d
r
ep
r
esen
t
th
e
weig
h
t
co
ef
f
icien
ts
o
f
th
e
o
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jecti
v
e
f
u
n
ctio
n
a
n
d
th
eir
s
u
m
m
a
tio
n
s
h
o
u
ld
am
o
u
n
t to
1
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
s
u
b
ject
to
th
e
f
o
llo
win
g
co
n
s
tr
ain
t
s
:
a.
Vo
ltag
e
lim
it: Po
wer
s
y
s
tem
s
n
etwo
r
k
h
as v
o
ltag
e
lev
el
a
n
d
it is
g
iv
en
b
y
its
to
ler
an
ce
b
o
u
n
d
ar
ies.
(
)
≤
ℎ
≤
(
)
(
8
)
wh
er
e
,
ℎ
is
th
e
v
o
ltag
e
m
a
g
n
itu
d
e
at
b
u
s
h
.
f
o
r
th
e
Nig
er
ian
g
r
id
n
etwo
r
k
,
th
e
to
ler
an
ce
is
±
5%
.
T
h
at
is
0
.
95
(
)
≤
ℎ
≤
1
.
05
(
)
at
n
etwo
r
k
b
u
s
.
b.
Activ
e
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
lim
its
:
T
h
ese
ar
e
th
e
e
q
u
ality
co
n
s
tr
ain
ts
o
f
th
e
n
et
wo
r
k
.
A
b
s
o
lu
te
p
o
wer
lim
it: T
h
e
lim
it is
g
iv
en
as
ℎ
<
(
9
)
wh
er
e,
ℎ
is
th
e
tr
an
s
m
is
s
io
n
lin
e
f
lo
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d
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m
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in
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r
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lim
it:
th
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r
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t
m
u
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d
its
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m
is
s
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le
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its
(
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)
an
d
Ω
is
th
e
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et
o
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th
e
n
etwo
r
k
tr
a
n
s
m
is
s
io
n
lin
e
[
2
2
]
.
|
ℎ
|
≤
ℎ
∀
ℎ
∈
Ω
(
1
0
)
2
.
3
.
Ro
t
o
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a
ng
les s
t
a
bil
it
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blem
f
o
r
m
ula
t
io
n
T
h
e
g
o
al
is
to
m
in
im
ize
th
e
r
o
to
r
an
g
le
d
ev
iatio
n
.
T
h
e
s
tar
tin
g
s
tate
o
f
a
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
is
u
s
ed
as
th
e
b
en
ch
m
a
r
k
v
alu
e.
T
h
e
d
e
v
iatio
n
v
al
u
e
is
ca
lcu
la
ted
b
y
d
ed
u
ctin
g
t
h
e
d
if
f
er
en
c
e
at
th
e
s
tar
t
o
f
th
e
f
au
lt
s
tate
f
r
o
m
th
e
d
if
f
er
e
n
ce
at
th
e
en
d
.
T
h
e
m
a
g
n
itu
d
e
o
f
r
o
to
r
an
g
le
v
ar
iatio
n
is
ca
lcu
lated
b
y
s
q
u
ar
i
n
g
th
e
cu
m
u
lativ
e
d
if
f
er
en
ce
[
2
3
]
.
min
∑
(
ℎ
,
−
ℎ
,
0
)
2
ℎ
∈
,
∈
(
1
1
)
wh
er
e
ℎ
,
d
en
o
tes
th
e
r
o
to
r
an
g
l
e;
r
ep
r
esen
ts
th
e
n
u
m
b
er
o
f
g
en
er
ato
r
s
;
T
s
tan
d
s
f
o
r
all
tim
es
ex
ce
p
t
th
e
s
tar
tin
g
p
o
in
t
at
=
0
,
=
∪
.
T
h
is
is
s
u
b
j
ec
t
to
th
e
f
o
llo
win
g
c
o
n
s
tr
ain
ts
as
g
iv
en
[
2
3
]
,
[
1
6
]
:
B
u
s
lo
ad
b
alan
ce
lim
it: T
h
e
lo
ad
b
ala
n
ce
eq
u
atio
n
s
ar
e
g
iv
en
as
(
1
2
)
an
d
(
1
3
)
.
,
ℎ
−
,
ℎ
=
∑
|
ℎ
|
=
1
|
|
|
ℎ
|
c
os
(
ℎ
−
ℎ
+
)
(
1
2
)
,
ℎ
−
,
ℎ
=
∑
|
ℎ
|
=
1
|
|
|
ℎ
|
c
os
(
ℎ
−
−
ℎ
)
(
1
3
)
wh
er
e
,
ℎ
an
d
,
ℎ
ar
e
th
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
o
u
tp
u
t
r
esp
ec
tiv
ely
;
,
ℎ
an
d
,
ℎ
ar
e
th
e
r
ea
l
an
d
r
ea
ctiv
e
lo
ad
;
th
e
s
u
p
er
s
cr
ip
t
o
f
th
e
p
ar
am
eter
s
s
tan
d
s
f
o
r
th
e
in
itial
s
tate.
L
et
ℎ
∈
,
is
th
e
n
u
m
b
er
o
f
th
e
en
tire
b
u
s
es.
T
h
e
p
o
wer
o
u
tp
u
ts
o
f
th
e
g
e
n
er
ato
r
d
u
r
in
g
an
d
a
f
ter
f
a
u
lt
o
cc
u
r
r
en
ce
ar
e
ex
p
r
ess
ed
in
(
1
2
)
an
d
(
1
3
)
.
T
h
e
o
u
tp
u
t p
o
wer
o
f
ea
ch
g
en
e
r
ato
r
is
g
iv
e
n
as
(
1
4
)
.
=
ℎ
2
ℎℎ
ℎℎ
+
∑
|
ℎ
|
|
|
|
ℎ
|
c
os
(
ℎ
−
ℎ
+
)
ℎ
=
1
ℎ
≠
(
1
4
)
T
h
e
s
win
g
eq
u
atio
n
o
f
a
s
y
n
ch
r
o
n
o
u
s
g
en
er
atio
n
is
g
iv
en
as
s
h
o
wn
in
[
2
4
]
:
2
2
2
=
ℎ
−
−
(
1
5
)
wh
er
e
is
th
e
d
am
p
in
g
c
o
ef
f
ici
en
t in
p
er
u
n
it a
n
d
is
th
e
an
g
le
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
g
e
n
er
ato
r
.
B
y
u
s
in
g
th
e
p
er
u
n
it v
al
u
e
o
f
̅
in
(
1
5
)
ab
o
v
e
y
ield
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
P
o
w
er lo
s
s
r
ed
u
ctio
n
a
n
d
s
ta
b
ilit
y
en
h
a
n
ce
men
t
o
f p
o
w
er sys
tem
…
(
Tit
u
s
Te
r
w
a
s
e
A
ko
r
)
6017
2
2
̅
2
=
ℎ
−
−
̅
(
1
6
)
T
h
er
ef
o
r
e,
̅
=
2
=
4
is
th
e
p
er
u
n
it
m
o
m
en
t
o
f
i
n
er
tia.
T
h
e
in
e
r
tia
co
n
s
tan
t
,
wh
ich
s
h
a
p
es
th
e
tu
r
b
in
e
-
g
en
er
ato
r
'
s
d
y
n
am
ic
ch
ar
ac
ter
is
tics
,
is
a
cr
itical
g
en
er
ato
r
p
a
r
am
eter
.
T
h
e
m
o
m
en
t
o
f
in
er
tia
r
ep
r
esen
ts
th
e
in
f
lu
en
ce
o
f
t
h
e
co
m
b
in
e
d
s
p
in
n
in
g
m
ass
es
o
f
th
e
tu
r
b
i
n
e
an
d
g
en
er
ato
r
as
s
tated
in
[
2
5
]
.
Hen
ce
,
th
e
s
win
g
eq
u
atio
n
f
o
r
d
am
p
in
g
b
ec
o
m
es
.
2
2
̅
2
=
ℎ
−
−
−
̅
(
1
7
)
Du
r
in
g
f
a
u
lt c
o
n
d
itio
n
,
th
e
s
w
in
g
eq
u
atio
n
is
g
iv
en
as
(
1
8
)
.
2
2
̅
2
+
̅
=
ℎ
−
−
(
)
(
1
8
)
Af
ter
f
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u
r
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2
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
7
0
8
I
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&
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15
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2
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Hy
b
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APSO tec
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[
2
7
]
3.
RE
SU
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S AN
D
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SCU
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3
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0
1
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3
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,
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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lec
&
C
o
m
p
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g
I
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Net
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Nig
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n 1
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T
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icate
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in
Fig
u
r
e
3
.
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h
e
h
y
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r
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W
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o
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ith
m
u
s
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2
5
0
1
.
0
5
5
.
7
5
0
1
.
2
0
6
4
14
2
5
0
1
.
0
5
4
.
1
3
9
1
.
5
6
5
4
T
h
e
ex
citer
g
ain
v
alu
es
f
o
r
b
u
s
es
1
,
9
,
1
0
,
an
d
1
4
wer
e
s
e
t
at
2
5
0
,
5
0
,
2
5
0
,
a
n
d
2
5
0
,
r
e
s
p
ec
tiv
ely
.
No
tab
ly
,
b
u
s
es
1
,
1
0
,
an
d
1
4
r
ea
ch
ed
th
e
u
p
p
er
lim
it
o
f
th
e
ass
u
m
ed
o
p
tim
izatio
n
r
an
g
e
(
5
0
-
2
5
0
)
.
Hig
h
ex
citer
g
ain
s
e
n
h
an
ce
th
e
r
esp
o
n
s
iv
en
ess
o
f
th
e
au
to
m
atic
v
o
ltag
e
r
eg
u
lato
r
(
AVR)
b
y
in
cr
ea
s
in
g
th
e
f
ield
v
o
ltag
e
(
)
to
m
ain
tain
ter
m
in
al
v
o
ltag
e
n
ea
r
th
e
s
ch
ed
u
led
v
alu
e
(
ℎ
)
.
Ho
wev
er
,
e
x
ce
s
s
iv
e
g
ain
s
ca
n
lead
to
o
v
er
-
ex
citatio
n
,
p
o
ten
tially
ca
u
s
in
g
s
ig
n
if
ican
t
r
o
to
r
an
g
le
s
win
g
s
o
r
ev
en
in
s
tab
ilit
y
.
B
u
s
9
,
o
n
th
e
o
th
e
r
h
an
d
,
h
a
d
a
m
u
ch
l
o
wer
o
f
5
0
,
th
e
lo
west
allo
wab
le
v
alu
e,
s
u
g
g
esti
n
g
th
at
a
lo
w
er
ex
citer
g
ain
at
th
is
lo
ca
tio
n
h
elp
s
d
am
p
en
o
s
cillatio
n
s
.
T
h
is
is
d
u
e
to
its
lo
wer
in
er
tia
(
H
=
4
)
an
d
its
p
o
wer
d
is
p
atch
b
ein
g
at
th
e
m
ax
im
u
m
allo
wab
le
lim
it
(
3
.
3
5
p
u
)
.
T
h
e
h
ig
h
e
x
citer
g
ain
v
alu
es
at
b
u
s
es
1
,
1
0
,
a
n
d
1
4
in
d
icate
a
n
ee
d
f
o
r
s
tr
o
n
g
v
o
ltag
e
s
u
p
p
o
r
t,
d
r
iv
en
b
y
th
eir
s
u
b
s
tan
tial
p
o
wer
d
is
p
atch
es
(
1
0
.
8
4
7
,
5
.
7
5
,
an
d
4
.
1
3
9
p
u
,
r
esp
ec
tiv
ely
)
.
Ho
we
v
er
,
t
h
e
u
n
if
o
r
m
ap
p
licatio
n
o
f
th
e
u
p
p
e
r
lim
it
s
u
g
g
ests
th
at
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
m
ay
h
av
e
b
ee
n
co
n
s
tr
ain
ed
,
p
o
ten
ti
ally
o
v
er
lo
o
k
in
g
m
o
r
e
o
p
tim
a
l
in
ter
m
ed
iate
v
al
u
es.
T
h
e
o
p
t
im
izatio
n
b
alan
ce
d
tr
an
s
ien
t
s
tab
ilit
y
with
s
tead
y
-
s
tate
p
er
f
o
r
m
an
ce
,
th
o
u
g
h
th
e
u
n
if
o
r
m
v
o
ltag
e
s
ch
ed
u
le
an
d
h
ig
h
ex
citer
g
ain
s
at
m
o
s
t
b
u
s
es
s
u
g
g
est
p
o
ten
tial
o
v
er
-
ex
citatio
n
r
is
k
s
.
T
h
e
lo
wer
at
B
u
s
9
ef
f
ec
tiv
ely
d
am
p
en
e
d
o
s
cillatio
n
s
,
lev
er
ag
in
g
its
lo
wer
in
er
tia.
T
h
ese
f
in
d
in
g
s
a
lig
n
with
th
e
s
win
g
eq
u
atio
n
d
y
n
am
ics
(
(4
)
-
(
6
)
,
(
18
)
-
(
19
)
)
an
d
cr
itical
clea
r
in
g
tim
e
(
2
5
)
,
p
r
o
v
id
i
n
g
r
o
b
u
s
t
f
r
am
ewo
r
k
f
o
r
tr
an
s
ien
t
s
tab
ilit
y
an
aly
s
is
.
T
h
e
v
ar
iatio
n
in
e
x
citer
g
ain
v
alu
es
ac
r
o
s
s
th
e
g
en
er
ato
r
s
d
e
m
o
n
s
tr
ates
th
e
o
p
tim
izer
’
s
a
ttem
p
t
to
b
alan
ce
d
am
p
in
g
ef
f
o
r
ts
ef
f
ec
tiv
ely
.
T
h
e
v
o
ltag
e
s
ch
ed
u
le
was
u
n
i
f
o
r
m
ly
s
et
at
1
.
0
5
0
p
u
ac
r
o
s
s
all
b
u
s
es,
r
ea
ch
in
g
t
h
e
u
p
p
er
l
im
it
o
f
th
e
o
p
tim
izatio
n
r
a
n
g
e
(
0
.
9
5
to
1
.
0
5
p
u
)
.
T
h
is
v
al
u
e
m
ax
im
izes
v
o
ltag
e
s
u
p
p
o
r
t,
wh
ic
h
in
tu
r
n
en
h
an
ce
s
s
y
n
ch
r
o
n
izi
n
g
to
r
q
u
e
an
d
i
m
p
r
o
v
es
tr
an
s
ien
t
s
tab
ilit
y
b
y
in
cr
ea
s
in
g
elec
tr
ical
p
o
wer
o
u
tp
u
t
(
)
.
Ho
wev
er
,
s
ettin
g
all
v
o
ltag
e
s
ch
ed
u
les
at
th
e
m
ax
im
u
m
m
ay
r
esu
lt
in
o
v
er
-
v
o
ltag
es
in
ce
r
tain
ar
ea
s
o
f
th
e
n
etwo
r
k
,
p
o
ten
tially
s
tr
ess
in
g
eq
u
ip
m
en
t
o
r
lead
in
g
to
v
o
ltag
e
in
s
tab
ilit
y
if
r
ea
ctiv
e
p
o
wer
lim
its
ar
e
ex
ce
ed
ed
.
T
h
e
u
n
if
o
r
m
ity
o
f
ℎ
s
u
g
g
ests
th
at
th
e
o
p
tim
ize
r
p
r
io
r
itized
m
ax
im
izin
g
s
y
n
ch
r
o
n
izin
g
to
r
q
u
e
f
o
r
all
g
e
n
er
ato
r
s
.
T
h
e
to
tal
p
o
wer
d
is
p
atch
ex
ac
tly
m
atch
ed
t
h
e
tar
g
et
lo
ad
d
e
m
an
d
o
f
2
4
.
0
8
6
p
u
,
s
atis
f
y
in
g
th
e
p
o
wer
b
alan
ce
co
n
s
tr
ain
t.
B
u
s
es
9
an
d
1
0
we
r
e
f
u
lly
u
tili
ze
d
,
o
p
er
atin
g
at
th
eir
m
a
x
im
u
m
li
m
its
(
3
.
3
5
p
u
an
d
5
.
7
5
p
u
,
r
esp
ec
tiv
ely
)
,
wh
ile
B
u
s
1
was
n
ea
r
its
lim
it
(
1
0
.
8
4
7
p
u
o
u
t
o
f
1
3
.
2
p
u
)
.
I
n
co
n
t
r
ast,
B
u
s
1
4
o
p
er
ate
d
s
ig
n
if
ican
tly
b
elo
w
its
ca
p
ac
it
y
(
4
.
1
3
9
p
u
o
u
t
o
f
8
.
5
p
u
)
.
T
h
e
d
is
p
atch
d
is
tr
ib
u
tio
n
was
u
n
ev
en
,
with
B
u
s
1
s
h
o
u
ld
er
in
g
th
e
lar
g
est
s
h
ar
e
(
4
5
%
o
f
th
e
to
tal
d
is
p
atch
)
,
f
o
llo
wed
b
y
B
u
s
1
0
(
2
4
%),
B
u
s
1
4
(
1
7
%),
a
n
d
B
u
s
9
(
1
4
%).
T
h
e
h
ea
v
y
r
elian
ce
o
n
B
u
s
1
,
wh
ich
h
as
a
h
i
g
h
in
er
tia
(
H
=
6
.
5
)
,
s
u
g
g
ests
th
at
th
e
o
p
tim
izatio
n
s
tr
ateg
y
lev
er
ag
ed
its
s
tab
ilit
y
to
m
an
ag
e
a
s
ig
n
if
ican
t
p
o
r
tio
n
o
f
th
e
lo
a
d
.
T
h
e
f
ac
t
th
at
B
u
s
es
9
an
d
1
0
r
ea
ch
ed
th
ei
r
m
ax
im
u
m
lim
its
im
p
lies
th
at
th
e
s
y
s
tem
is
co
n
s
tr
ain
ed
b
y
th
eir
ca
p
ac
ities
,
p
o
ten
tially
lim
itin
g
its
ab
ilit
y
to
ac
co
m
m
o
d
ate
ad
d
itio
n
al
co
n
tin
g
e
n
cies.
Me
an
wh
ile,
B
u
s
1
4
,
wh
ich
o
p
er
a
ted
well
b
elo
w
it
s
ca
p
ac
ity
,
co
u
ld
h
av
e
b
ee
n
u
t
ilized
m
o
r
e
ef
f
icien
tly
t
o
b
al
an
ce
th
e
lo
ad
d
is
tr
ib
u
tio
n
.
I
t
is
lik
ely
th
at
th
e
o
p
tim
izer
r
ed
u
ce
d
B
u
s
1
4
’
s
d
is
p
atch
to
m
in
im
ize
r
o
to
r
an
g
le
s
win
g
s
,
as
its
lo
wer
in
er
tia
(
H
=
1
.
3
7
)
m
a
k
es
it
m
o
r
e
s
u
s
ce
p
tib
le
to
o
s
cillatio
n
s
.
T
ab
le
2
f
u
r
th
er
h
ig
h
lig
h
ts
th
a
t
th
e
m
ax
im
u
m
r
o
to
r
a
n
g
le
d
ev
iatio
n
was
1
.
5
6
6
9
r
a
d
at
B
u
s
1
,
ju
s
t
b
elo
w
th
e
s
tab
ilit
y
th
r
esh
o
ld
o
f
π/2
.
T
h
is
c
o
n
f
ir
m
s
th
at
th
e
s
y
s
tem
m
ain
tain
s
s
y
n
ch
r
o
n
is
m
s
in
ce
r
o
to
r
an
g
les
ex
ce
ed
in
g
π/2
ty
p
ically
lead
t
o
lo
s
s
o
f
s
tab
ilit
y
as
co
n
f
ir
m
e
d
in
[
2
0
]
.
B
u
s
9
ex
h
i
b
ited
th
e
s
m
allest
d
ev
iatio
n
(
0
.
7
2
2
2
r
ad
)
,
lik
ely
d
u
e
to
it
s
lo
w
ex
citer
g
ain
a
n
d
f
u
ll
u
tili
za
tio
n
o
f
its
ca
p
ac
ity
,
w
h
ich
m
in
im
ized
its
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