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t
o a
dj
us
t
t
he
l
i
n
e
i
m
p
ed
a
n
ce,
r
ed
u
ce
p
o
t
e
nt
i
a
l
d
e
vi
a
t
i
o
n a
nd
r
e
g
ul
a
t
e
t
he
p
o
w
e
r
gr
i
d
.
P
o
w
e
r
s
ys
t
e
m
s
w
e
r
e
d
e
s
i
g
ne
d
c
o
nc
e
r
ni
n
g t
he
e
xt
e
ns
i
ve
s
t
ab
l
e r
an
g
e t
o
r
e
t
ur
n
f
r
o
m
une
xp
e
c
t
e
d
w
o
r
k c
o
nd
i
t
i
o
n
s
uc
h a
s
p
h
ys
i
c
a
l
e
r
r
o
r
a
nd ge
ne
r
a
t
o
r
o
r
l
i
ne
d
i
s
co
n
n
ect
ed
[
4
]
.
T
h
e s
m
al
l
w
a
y
h
a
s
m
a
n
y
c
o
m
p
le
x
i
tie
s
a
n
d
c
o
s
tl
y
e
s
ta
b
lis
h
m
e
n
t
s
.
I
t is
b
a
s
e
d
o
n
t
h
e
d
ir
e
c
t r
e
la
tio
n
b
e
t
w
e
e
n d
i
s
t
r
i
b
ut
i
o
n
ge
ne
r
a
t
i
o
n i
n
t
he
m
ic
r
o
g
r
id
s
a
nd
t
he
m
a
i
n
gr
i
d
s
.
U
s
i
n
g t
he
r
e
m
o
t
e
m
e
t
ho
d
r
e
q
ui
r
e
s
h
av
i
n
g
a g
o
o
d
an
d
s
af
e co
m
m
u
n
i
cat
i
o
n
s
y
s
t
e
m
.
T
h
e l
o
cal
w
a
y
h
as
t
w
o
act
i
v
e an
d
i
n
act
i
v
e
m
o
d
es
.
T
h
i
s
m
et
h
o
d
i
s
act
i
v
e
m
o
d
e b
ecau
s
e i
t
r
eco
g
n
i
ze
s
t
h
e i
s
l
a
n
d
i
n
g
m
o
d
e b
y
i
n
t
en
t
i
o
n
al
l
y
cr
eat
i
n
g
a
s
y
s
t
e
m
d
i
s
t
u
r
b
an
ce ac
co
r
d
i
n
g
t
o
s
y
s
t
e
m
r
eact
i
o
n
.
T
h
e co
n
s
t
a
n
t
t
r
o
u
b
l
e i
n
t
h
e s
y
s
t
e
m
i
s
co
n
s
i
d
er
ed
as
t
h
e
m
ai
n
d
i
s
ad
v
an
t
a
g
e o
f
t
h
i
s
m
e
t
h
o
d
.
T
h
e i
n
act
i
v
e
m
o
d
e i
s
b
as
ed
o
n
m
ea
s
u
r
e
m
e
n
t
.
I
t
m
ea
s
u
r
e
s
t
h
e l
o
cal
p
ar
a
m
et
er
s
s
u
c
h
a
s
v
ol
t
a
g
e
,
f
r
e
qu
e
n
c
y
,
t
ot
a
l
h
a
r
m
oni
c
di
s
t
or
t
i
on
,
pow
e
r
f
r
eq
u
en
c
y
d
ev
i
at
i
o
n
r
at
e
,
an
d
p
o
w
er
s
i
g
n
al
d
ev
i
at
i
o
n
r
at
e.
T
h
es
e v
al
u
es
s
h
o
u
l
d
b
e co
m
p
ar
ed
t
o
i
d
en
t
i
f
y
t
h
e i
s
l
a
n
d
i
n
g
m
o
d
e t
h
r
es
h
o
l
d
[
5
]
.
O
n
e o
f
t
h
e
g
r
i
d
'
s
es
s
e
n
t
i
al
v
o
l
t
ag
e co
n
t
r
o
l
l
er
s
i
s
a t
ap
c
h
an
g
e
r
t
r
an
s
f
o
r
m
er
t
h
at
ca
n
b
e co
n
v
er
t
ed
i
n
t
o
a
n
a
u
to
m
a
tic
p
o
t
e
n
tia
l c
o
n
tr
o
lle
r
.
T
h
y
r
is
to
r
s
a
r
e
u
s
e
d
f
o
r
t
h
i
s
p
u
r
p
o
s
e
.
D
-
U
P
F
C
is
s
t
r
u
c
tu
r
a
l
ly
d
if
f
e
r
e
n
t
f
r
o
m
U
P
F
C
.
I
t
s
co
m
p
o
n
e
n
t
s
co
n
t
a
i
n
a p
ar
al
l
el
t
r
an
s
f
o
r
m
er
t
h
at
s
u
p
p
l
i
es
t
h
e i
n
p
u
t
cu
r
r
en
t
a
n
d
a s
er
i
es
t
r
an
s
f
o
r
m
er
th
a
t i
n
j
e
c
ts
th
e
c
h
o
p
p
e
r
c
ir
c
u
it'
s
o
u
tp
u
t
v
o
lta
g
e
i
n
t
o
t
he
s
c
he
m
e
.
D
-
U
P
F
C
c
ou
l
d c
ont
r
ol
t
h
e
v
ol
t
a
g
e
dr
op
pr
ov
i
de
d by
a
s
ho
r
t
ci
r
cu
i
t
o
r
s
u
b
s
t
a
n
t
i
al
p
o
w
er
co
n
n
ect
i
o
n
t
o
t
h
e g
r
i
d
.
U
P
F
C
can
b
e i
n
s
t
al
l
ed
at
t
h
e b
ack
o
f
a
p
o
w
er
t
r
an
s
f
o
r
m
er
o
r
an
y
w
h
er
e el
s
e i
n
t
h
e g
r
i
d
[
6
]
.
T
he
r
es
ear
ch
p
r
es
en
t
ed
i
n
[
7
]
ex
a
m
i
n
ed
t
h
e U
P
F
C
ap
p
l
i
cat
i
o
n
as
a l
i
m
i
t
er
o
f
er
r
o
r
cu
r
r
en
t
.
T
h
e
y
a
d
d
e
d
th
e
c
o
n
tr
o
l f
u
n
c
tio
n
t
o
U
P
F
C
a
t th
e
t
i
me
o
f t
h
e
e
rro
r
.
I
t
co
n
t
r
o
l
s
t
h
e r
eal
an
d
i
m
a
g
i
n
ar
y
p
o
w
er
m
o
ve
m
e
nt
o
ve
r
t
he
l
i
ne
i
n t
he
r
eg
u
l
ar
o
p
er
at
i
o
n
o
f
t
h
e
g
r
i
d
.
T
h
ey
ar
e al
s
o
u
s
ed
a
s
t
h
e l
i
m
i
t
er
o
f
er
r
o
r
f
l
o
w
i
n
a t
i
m
e o
f
t
h
e
s
ho
r
t
ci
r
cu
i
t
.
R
es
ear
ch
i
n
[
8
]
i
n
v
e
s
t
i
g
at
es
t
h
e ex
cel
l
e
n
t
p
er
f
o
r
m
a
n
ce o
f
f
u
zz
y
co
n
t
r
o
l
l
er
s
i
n
m
in
im
i
z
in
g
t
he
f
l
uc
t
ua
t
i
o
ns
.
A
f
t
e
r
o
p
t
i
m
i
z
i
ng
t
he
f
uz
z
y
c
o
nt
r
o
l
l
e
r
s
d
e
s
i
g
ne
d
b
y
f
uz
z
y c
-
m
ean
s
,
cl
u
s
t
er
i
n
g
o
s
ci
l
l
at
i
o
n
s
w
er
e
h
i
g
h
l
y
r
ed
u
ced
f
o
l
l
o
w
i
n
g
s
i
m
i
l
ar
d
i
s
t
u
r
b
an
ces
.
T
h
e r
es
ear
ch
ex
a
m
i
n
e
d
t
h
e
co
n
t
r
o
l
o
f
t
h
e
tr
a
n
s
m
is
s
io
n
li
n
e
p
o
w
e
r
s
w
it
h
th
e
title
o
f
c
o
nt
r
o
l
a
na
l
ys
i
s
o
f
t
r
a
ns
m
i
s
s
i
o
n l
i
ne
p
o
w
e
r
b
y
U
P
F
C
[
9
]
.
A
no
t
he
r
s
t
ud
y
w
a
s
c
o
nd
uc
t
e
d
us
i
n
g a
ne
w
m
e
t
ho
d
t
o
c
o
nt
r
o
l
D
-
U
P
F
C
w
i
t
h
o
u
t
de
l
a
y
i
n pow
e
r
g
r
i
ds
.
T
h
e
m
os
t
be
n
e
f
i
t
s
of
t
h
i
s
m
e
t
h
od
ar
e
r
e
d
u
c
in
g
t
h
e
ti
m
e
d
e
la
y
a
s
m
u
c
h
a
s
p
o
s
s
ib
le
a
n
d
o
m
i
tti
n
g
d
is
to
r
tio
n
f
r
o
m
t
h
e
c
o
m
pe
n
s
a
t
e
d
v
ol
t
a
g
e
[
10]
.
A
s
t
u
d
y
w
a
s
pr
e
s
e
n
t
e
d i
n
[
11]
t
o e
x
a
m
i
ne
t
he
a
ng
l
e
a
nd
va
l
ue
o
f
o
ut
p
u
t
t
er
m
i
n
al
v
o
l
t
ag
e o
f
s
o
m
e
g
e
n
er
at
o
r
s
,
w
h
i
c
h
ar
e co
n
s
i
d
er
ed
as
t
h
e
m
ai
n
p
ar
a
m
e
t
er
s
o
f
t
h
e p
o
w
er
s
y
s
t
e
m
s
s
ta
b
ilit
y
,
i
n
d
ic
a
te
th
a
t
h
o
w
m
u
c
h
t
h
e
tr
a
n
s
ie
n
t
s
ta
b
il
it
y
o
f
t
h
e
g
r
id
is
o
p
ti
m
iz
e
d
a
f
te
r
r
e
m
o
v
i
n
g
e
r
r
o
r
s
w
i
th
c
on
s
i
de
r
i
ng
U
P
F
C
p
r
es
en
ce
a
n
d
w
i
t
h
o
u
t
U
P
F
C
p
r
es
e
n
ce.
R
es
ear
ch
t
o
i
m
p
r
o
v
e
v
o
l
t
a
g
e s
t
ab
i
l
i
t
y
b
y
U
P
F
C
b
y
a
ppl
y
i
ng
t
h
e
a
l
g
or
i
t
hm
o
f
c
o
n
t
i
n
u
o
u
s
po
w
e
r
f
l
o
w
w
a
s
pe
r
f
or
m
e
d.
S
i
m
ul
a
t
i
on'
s
f
i
n
di
ngs
w
i
l
l
i
n
c
r
e
a
s
e
t
h
e
p
o
w
e
r
s
ys
t
e
m
s
s
t
a
b
i
l
i
t
y
i
n
us
i
ng U
P
F
C
[
1
2
]
,
[
13]
.
I
n
2016,
r
e
s
ear
ch
i
n
[
1
4
]
w
a
s
p
er
f
o
r
m
ed
t
o
ex
a
m
i
n
e a s
p
ec
i
f
i
c
w
a
y
.
T
h
e o
p
t
i
m
i
zat
i
o
n
o
f
t
h
e s
o
l
ar
en
er
g
y
l
o
cat
i
o
n
i
s
p
er
f
o
r
m
ed
b
as
ed
o
n
a
gr
i
d
w
i
t
h
a s
i
m
i
l
ar
cab
l
e cr
o
s
s
-
s
ec
t
i
o
n
.
H
o
w
e
v
er
,
w
e i
n
v
es
t
i
g
at
e t
h
e
t
ech
n
i
cal
an
d
eco
n
o
m
i
c ef
f
e
ct
s
o
f
t
h
e cab
l
e cr
o
s
s
-
s
e
c
t
i
on
,
ope
r
a
t
i
o
n ho
ur
s
a
nd
p
o
w
e
r
p
e
r
i
od
s
a
nd
t
he
o
p
p
or
t
uni
t
y o
f
us
i
ng
s
e
ve
r
a
l
s
o
l
a
r
p
a
ne
l
s
w
i
t
h
m
u
l
t
i
p
a
r
t
e
d
gr
i
d
s
.
T
he
s
o
ur
c
e
p
o
i
nt
,
w
hi
c
h c
o
r
r
e
s
p
o
nd
s
t
o
t
he
m
i
n
i
m
um
t
ot
a
l
f
i
n
a
n
c
e
,
i
s
c
ons
i
de
r
e
d a
n
opt
i
m
i
z
e
d
l
oa
d di
s
t
r
i
bu
t
i
on
.
I
t
c
a
n
be
n
a
m
e
d opt
i
m
i
z
e
d (
O
V
C
)
.
T
h
e
r
es
ear
ch
w
as
p
er
f
o
r
m
ed
i
n
[
1
5
]
p
r
es
en
t
s
an
ad
v
a
n
ced
el
e
m
en
t
o
f
F
A
C
T
S
n
a
m
ed
d
i
s
t
r
i
b
u
t
ed
p
o
w
er
f
l
o
w
r
eg
u
l
at
o
r
w
as
ad
ap
t
ed
w
i
t
h
U
P
F
C
co
n
cep
t
i
o
n
.
D
F
P
C
co
u
l
d
b
e t
r
eat
ed
as
a
U
P
F
C
w
i
t
h
a
n
ab
s
en
t
D
C
b
u
s
.
A
s
ig
n
i
f
ic
a
n
t n
u
m
b
e
r
o
f
s
e
r
ie
s
co
n
v
er
t
er
s
cr
eat
e
r
e
dun
da
n
c
y
t
ha
t
i
n
cr
eas
es
s
y
s
te
m
s
ta
b
ili
t
y
.
D
-
F
A
CT
S
a
r
e
f
l
oa
t
i
n
g t
o t
h
e
g
r
oun
d,
a
n
d
no s
e
pa
r
a
t
i
on
w
i
t
h hug
e
v
ol
t
a
g
e
a
m
ong
p
h
a
s
e
s
i
s
n
ot
r
e
qu
i
r
e
d.
T
h
e
M
A
T
L
A
B
en
v
i
r
o
n
m
e
n
t
e
x
a
m
i
n
es
t
h
e
f
u
n
ct
i
o
n
o
f
D
P
F
C
.
A
n
o
t
h
er
r
es
ear
ch
p
er
f
o
r
m
ed
i
n
[
1
6
]
t
h
at
t
h
e el
ect
r
i
f
i
cat
i
o
n
t
o
ru
ra
l
a
r
e
a
s
i
s
p
o
s
s
i
b
l
e
b
y
r
e
d
uc
i
n
g t
he
t
r
a
ns
m
i
s
s
i
o
n d
r
o
p.
T
he
a
ut
ho
r
s
i
n [
1
6
]
s
ug
ge
s
t
e
d
t
he
c
o
m
b
i
ni
n
g
F
A
C
T
S
c
o
n
tr
o
lle
r
w
it
h
t
h
e
tr
a
n
s
m
is
s
io
n
s
y
s
t
e
m
.
I
t
ca
n
es
t
i
m
at
e t
h
e p
er
f
o
r
m
a
n
ce a
n
d
f
u
n
ct
i
o
n
o
f
t
h
e
t
r
a
ns
m
i
s
s
i
o
n
gr
i
d
.
T
he
d
yna
m
i
c
p
e
r
f
o
r
m
a
nc
e
o
f
t
he
p
o
w
e
r
gr
id
c
o
u
ld
b
e
in
v
e
s
ti
g
a
te
d
w
it
h
a
n
d
w
ith
o
u
t U
P
F
C
.
T
h
e
o
p
t
i
m
al
al
l
o
cat
i
o
n
o
f
U
P
F
C
f
o
r
t
r
an
s
m
i
s
s
i
o
n
n
et
w
o
r
k
an
d
en
h
an
ci
n
g
t
h
e
el
ect
r
i
cal
n
et
w
o
r
k
'
s
d
y
n
a
m
i
c
p
er
f
o
r
m
a
n
ce
h
ad
b
een
d
i
s
cu
s
s
ed
us
i
n
g
ge
ne
t
i
c
a
l
go
r
i
t
h
m
i
n [
1
7
]
,
[
18]
.
T
he
s
t
ud
y'
s
no
ve
l
t
y
r
e
s
i
d
e
s
i
n p
r
e
s
e
n
tin
g
a
m
o
d
if
ie
d
p
a
r
tic
le
s
w
a
r
m
o
p
ti
m
iz
a
tio
n
a
l
g
o
r
ith
m
w
it
h
th
e
N
.
R
m
e
t
h
od f
or
opt
i
m
a
l
a
l
l
oc
a
t
i
on
of
un
i
f
i
e
d po
w
e
r
f
l
o
w
c
on
t
r
ol
l
e
r
i
n
a
n
e
l
e
c
t
r
i
c
a
l
n
e
t
w
or
k
a
ppl
i
e
d on
I
E
E
E
3
0
b
u
s
es
as
a cas
e s
t
u
d
y
.
T
hi
s
s
t
ud
y
f
o
c
u
s
e
d
o
n t
he
f
u
nc
t
i
o
ns
a
nd
b
e
ne
f
i
t
s
o
f
U
P
F
C
f
or
t
h
e
po
w
e
r
s
y
s
t
e
m
,
t
he
c
or
r
e
s
pon
di
n
g
e
f
f
e
c
t
s
o
n
t
r
a
n
s
i
e
n
t
s
t
a
bi
l
i
t
y
.
M
A
T
L
A
B
n
um
e
r
i
c
a
l
s
i
m
ul
a
t
i
on R
2019b h
a
s
be
e
n
pe
r
f
or
m
e
d o
n
IE
E
E
3
0
b
u
s
e
s
.
T
h
e r
es
t
o
f
t
h
i
s
s
t
u
d
y
i
s
p
r
ep
ar
ed
as
:
t
h
e r
e
s
ear
ch
m
et
h
o
d
f
o
r
m
o
d
el
l
i
n
g
o
f
U
P
F
C
w
a
s
d
es
cr
i
b
ed
i
n
s
e
c
tio
n
2
.
S
e
c
tio
n
3
c
o
n
tr
o
ls
te
r
m
i
n
a
l v
o
lta
g
e
,
U
P
F
C
c
o
m
p
e
n
s
a
tio
n
c
o
n
tr
o
l,
p
h
a
s
e
s
h
i
f
t c
o
n
tr
o
l,
m
u
lt
i
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
8708
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
,
V
o
l.
11
, N
o
.
6
,
D
ecem
b
er
2
0
2
1
:
4
698
-
47
07
4700
f
u
n
c
tio
n
c
o
n
tr
o
l,
a
nd
c
ont
r
ol
of
t
h
e
po
w
e
r
f
l
o
w
i
n
o
v
e
r
l
oa
de
d l
i
n
e
s
.
T
h
e
pr
oc
e
s
s
f
or
a
dopt
i
n
g U
P
F
C
h
a
s
be
e
n
c
la
r
if
ie
d
in
s
e
c
tio
n
4
.
N
e
wt
o
n
-
Ra
p
h
s
o
n
p
o
w
e
r
f
lo
w
r
e
s
u
lts
h
ad
b
een
d
i
s
cu
s
s
ed
i
n
p
ar
t
5
.
Re
s
u
l
t
s a
n
d
di
s
c
u
s
s
i
on
pr
e
pa
r
e
d i
n
s
e
c
tio
n
6
.
F
i
n
al
l
y
,
d
ed
i
cat
i
o
n
s
ar
e s
h
o
w
n
i
n
s
e
c
tio
n
7
.
2.
R
ES
EA
R
C
H
M
ETH
O
D
T
h
e
p
r
in
c
ip
le
o
f
U
P
F
C
i
s
w
o
r
ki
n
g i
n t
he
e
x
i
s
t
e
nc
e
o
f
V
S
C
on
bot
h
e
n
ds
[
19]
.
T
h
e
U
P
F
C
c
a
n
l
i
m
i
t
th
e
m
o
m
e
n
t a
n
d
th
e
d
ir
e
c
tio
n
o
f
p
o
w
e
r
f
lo
w
i
n
t
h
e
g
r
id
b
y
t
h
e
r
e
la
tio
n
o
u
tp
u
t
v
o
lta
g
e
o
f
V
S
C
a
s
m
a
g
n
it
u
d
e
an
d
p
h
as
e
an
g
l
e
∠
w
i
t
h A
C
vo
l
t
a
ge
s
up
p
l
y
∠
0
,
a
s
gi
ve
n i
n (
1
)
.
S
o
,
t
h
e ca
s
e o
f
i
m
ag
i
n
ar
y
p
o
w
er
ca
n
al
s
o
b
e ad
j
u
s
t
ed
b
y
cal
i
b
r
at
i
n
g
V
C
R
r
el
at
i
o
n
co
n
cer
n
i
n
g
t
o
∠
a
s
s
ho
w
n i
n (
2
)
,
w
h
er
e i
t
can
b
e g
en
er
at
ed
r
eact
i
v
e p
o
w
er
w
h
e
n
>
an
d
i
t
can
b
e co
n
s
u
m
ed
w
h
en
<
[
20]
.
=
(1
)
=
2
−
(2
)
F
r
o
m
t
h
e s
c
h
e
m
at
i
c d
i
ag
r
a
m
o
f
t
h
e u
n
i
f
i
ed
p
o
w
er
f
l
o
w
co
n
t
r
o
l
l
er
i
n
F
i
g
u
r
e 1
,
o
n
e can
n
o
t
i
ce t
w
o
V
S
C
l
ab
el
l
ed
s
er
i
es
,
an
d
p
ar
a
l
l
el
co
n
v
er
t
er
h
as
f
u
n
ct
i
o
n
ed
w
i
t
h
a d
i
r
ect
c
u
r
r
en
t
b
u
s
.
T
h
e
D
C
-
bus
e
n
e
r
gy
i
s
t
r
a
n
s
f
or
m
e
d t
o A
C
a
n
d l
i
n
k
e
d t
o
t
he
t
r
a
ns
m
i
s
s
i
o
n l
i
ne
t
hr
o
ug
h a
s
h
u
nt
-
t
r
an
s
f
o
r
m
er
.
I
n
f
act
,
t
h
e p
ar
al
l
el
co
n
v
er
t
er
can
w
o
r
k
as
t
h
e s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
t
o
g
en
er
a
t
e i
m
a
g
i
n
ar
y
p
o
w
er
t
o
t
h
e
A
C
n
et
w
o
r
k
.
S
t
ud
yi
n
g
m
at
h
e
m
a
t
i
cal
m
o
d
el
r
eq
u
i
r
es
ex
a
m
i
n
i
n
g
t
h
e r
el
at
i
o
n
b
et
w
ee
n
t
h
e el
ect
r
i
c s
y
s
t
e
m
a
nd U
P
F
C
i
n
n
or
m
a
l
c
o
n
d
itio
n
.
F
i
g
u
r
e
s
1
a
n
d
2
d
e
m
o
n
s
tr
a
te
a
li
n
e
a
r
tr
a
n
s
m
i
s
s
io
n
d
ia
g
r
a
m
w
i
th
r
e
s
is
ta
n
c
e
,
i
nd
uc
t
a
nc
e
,
U
P
F
C
,
a v
o
l
t
ag
e
s
o
u
r
ce o
f
t
h
e t
r
an
s
m
i
t
t
er
en
d
a
n
d
a v
o
l
t
ag
e s
o
u
r
ce o
f
t
h
e r
ecei
v
er
i
s
i
n
d
i
cat
ed
i
n
[2
1
]
.
F
i
g
u
r
e 1
.
T
h
e p
o
w
er
ci
r
cu
i
t
o
f
U
P
F
C
F
i
gu
r
e
2.
M
ode
l
l
i
n
g
of
a
U
P
F
C
3.
C
O
N
TR
O
L O
B
J
EC
TIV
ES
T
h
e p
r
i
m
ar
y
p
u
r
p
o
s
e o
f
t
h
i
s
p
ap
er
t
o
ach
i
ev
e t
h
e
f
o
l
l
o
w
i
n
g
m
ai
n
f
u
n
ct
i
o
n
s
g
i
v
e
n
b
el
o
w
:
CO
1
:
C
o
n
tr
o
lli
n
g
U
P
F
C
te
r
m
in
a
l
v
o
lta
g
e
:
I
t c
a
n
c
o
n
tr
o
l
t
h
e
v
o
lta
g
e
w
it
h
m
i
n
i
m
a
l s
te
p
s
lik
e
ta
p
c
h
a
n
g
i
n
g
t
r
an
s
f
o
r
m
er
s
.
CO
2
:
M
ul
t
i
-
f
unc
t
i
o
n c
o
m
m
a
nd
o
f
U
P
F
C
:
I
t
c
a
n c
o
nt
r
o
l
t
he
c
r
o
s
s
i
n
g p
o
w
e
r
w
i
t
h
s
e
ve
r
a
l
m
e
t
ho
d
s
c
on
c
u
r
r
e
n
t
l
y
.
C
o
m
pe
ns
a
t
i
on
i
s
pe
r
f
or
m
e
d
w
i
t
h
t
e
r
m
i
n
al
v
o
l
t
ag
e co
n
t
r
o
l
,
s
er
i
es
co
m
p
en
s
at
i
o
n
o
f
t
h
e l
i
n
e,
a
nd
a
d
j
us
t
i
n
g t
he
p
ha
s
e
s
hi
f
t
a
ngl
e
.
CO
3
: O
p
ti
m
iz
i
n
g
p
o
w
e
r
f
lo
w
i
n
th
e
e
le
c
tr
ic
a
l p
o
w
e
r
s
y
s
te
m
.
I
t
s
ho
ul
d
a
na
l
y
z
e
t
he
U
P
F
C
e
q
ui
va
l
e
nt
c
i
r
c
ui
t
a
nd
s
p
e
c
i
f
y
m
o
s
t
o
f
t
he
r
el
at
ed
eq
u
at
i
o
n
s
[2
2
].
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
I
S
S
N
:
2088
-
8708
A
n opt
i
m
al
al
l
oc
at
i
on
of
U
P
F
C
and t
r
ans
i
e
nt
s
t
abi
l
i
t
y
i
m
pr
ov
e
m
e
nt
of
a
n
…
(
A
l
i
A
bdul
R
az
z
aq A
l
t
ahi
r
)
4701
3.
1.
V
ol
t
age
le
v
e
l m
a
in
t
a
in
i
n
g
T
h
e
f
o
llo
w
i
n
g
e
q
u
a
tio
n
s
ill
u
s
t
r
a
te
v
o
lta
g
e
le
v
e
l
m
a
in
te
n
a
n
c
e
:
=
(
+
)
(
3)
=
(
+
)
(4
)
{
−
∗
+
−
∗
}
=
0
(5
)
T
h
e t
r
an
s
f
er
ad
m
i
t
t
an
ce
m
at
r
i
x
co
u
l
d
b
e
w
r
itte
n
a
s
i
n (
6
)
:
=
(
+
)
−
−
−
−
0
(6
)
T
h
e eq
u
at
i
o
n
o
f
act
i
v
e a
n
d
r
eact
i
v
e p
o
w
er
i
n
s
e
n
d
i
n
g
an
d
r
ec
ei
v
i
n
g
b
u
s
es
(
,
) a
re
;
[2
3
]
.
A
t
b
us
k
:
=
2
+
[
(
−
)
+
(
−
)
]
+
[
(
−
)
+
(
−
)
]
+
[
(
−
)
+
(
−
)
]
(7
)
=
−
2
+
[
(
−
)
−
(
−
)
]
+
[
(
−
)
−
(
−
)
]
+
[
(
−
)
+
(
−
)
]
(8
)
A
t
bus
m
:
=
2
+
[
(
−
)
+
(
−
)
]
+
[
(
−
)
+
(
−
)
]
(
9
)
=
−
2
+
[
(
−
)
−
(
−
)
]
+
[
(
−
)
−
(
−
)
]
(
10
)
3
.2
.
P
o
w
er
f
lo
w
in
o
v
e
r
lo
a
d
in
g
lin
e
s
T
o
d
i
m
i
n
i
s
h
t
h
e t
o
t
al
p
o
w
er
i
n
l
i
n
es
,
i
t
w
a
s
r
eco
m
m
e
n
d
ed
t
o
co
m
p
u
t
e t
h
e act
u
al
a
n
d
r
eac
t
i
v
e p
o
w
er
p
e
r
lin
e
a
s
in
(
11)
-
(1
2
)
[
24
]
.
−
=
∑
=
1
−
+
−
(
11)
−
=
∑
=
1
−
+
−
(
12)
3.
3
.
R
e
al
an
d
i
m
agi
n
ar
y p
ow
e
r
l
os
s
e
s
B
y
s
el
ect
i
n
g
t
h
e ap
p
r
o
p
r
i
at
e v
ar
i
ab
l
e f
r
o
m
t
h
e
U
P
F
C
t
h
at
w
i
l
l
b
e i
n
s
er
t
ed
i
n
t
h
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g
r
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d
,
i
t
ca
n
a
tta
in
t
h
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t
ar
g
et
s
t
h
at
w
i
l
l
m
i
n
i
m
i
ze t
h
e
r
eal
an
d
i
m
a
g
i
n
ar
y
l
o
s
s
es
.
T
he
t
o
t
al
ac
t
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al
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d
i
m
a
g
i
n
ar
y
p
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l
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s
ca
n
b
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co
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p
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t
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as
i
n
(
13)
-
(1
4
)
[2
5
]
;
P
L
=
∑
i
N
L
i
=
1
[
V
k
2
+
V
m
2
−
2
V
k
V
m
c
os
(
δ
k
−
δ
m
)
]
(
13)
Q
L
=
∑
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i
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L
i
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1
[
V
k
2
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V
m
2
−
2
V
k
V
m
s
in
(
δ
k
−
δ
m
)
]
(
14)
3.
4.
C
o
ns
t
r
uc
t
i
o
n
o
f
m
o
d
if
ie
d
p
a
r
t
ic
le
s
w
a
r
m
o
p
t
i
m
iz
a
t
io
n
E
ach
b
i
r
d
'
s
f
l
y
i
n
g
n
o
r
m
al
i
zes
i
t
s
p
o
s
i
t
i
o
n
,
g
i
v
i
n
g
a
s
p
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f
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c
ex
p
er
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m
e
n
t
,
cr
eat
i
n
g
t
h
e
b
e
s
t
l
o
cat
i
o
n
don
e
by
i
t
s
e
l
f
a
n
d i
t
s
n
e
i
ghbou
r
i
n
g
bi
r
ds
[
26
]
,
[
2
7]
.
A
c
c
o
r
d
i
ng t
o
t
he
f
und
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p
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tic
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w
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p
ti
m
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tio
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(
P
SO
)
,
o
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f
i
t
s
ap
p
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c
at
i
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f
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p
t
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o
f
U
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d
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w
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r
i
cal
po
w
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y
s
t
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m
.
T
h
i
s
a
l
g
or
i
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b
a
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d
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p
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T
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f
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p
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l
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b
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[
2
8
]
.
T
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t
ep
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t
o
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cu
l
at
e t
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f
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u
m
m
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as
:
St
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p
1
:
P
r
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s
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n
t
pos
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t
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on
a
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d s
pe
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d.
St
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p
2
:
D
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s
t
a
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ce b
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w
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en
t
l
o
cat
i
o
n
an
d
p
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s
o
n
a
l b
e
s
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
20
88
-
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In
t
J
E
l
e
c
&
C
o
m
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V
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11
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6
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D
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b
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2
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2
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4
698
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4702
St
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p
3
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D
i
s
t
a
n
ce b
et
w
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t
h
e p
r
es
en
t
l
o
cat
i
o
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d
t
h
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g
l
o
b
al
b
es
t
.
N
o
w
,
le
t
u
s
c
o
n
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id
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r
th
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p
a
r
tic
le
'
s
lo
c
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tio
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,
an
d
s
p
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c
ou
l
d be
m
odi
f
i
e
d (
15)
a
n
d (
16)
.
+
1
=
+
1
˟
−
+
2
˟
−
(
15)
+
1
=
+
+
1
(
16)
W
h
er
e
1
,
2
a
r
e
p
o
s
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d
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s
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o
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t
a
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c
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t
e
s
t
o r
a
n
do
m
n
um
be
r
bou
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de
d [
0,
1]
.
is
d
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f
in
e
d
as
w
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g
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t
i
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er
t
i
a.
T
h
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s
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(
1
3
)
.
T
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u
al
p
o
w
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o
s
s
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n
d
ex
w
as
g
i
v
en
[
2
9
]
:
,
=
,
,
˟
1
0
0
%
(
17)
a
l
so
,
,
=
,
,
,
˟
1
0
0
%
(
18)
w
h
er
e
,
,
is
th
e
a
c
tu
a
l p
o
w
e
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lo
s
s
w
i
th
U
P
F
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,
,
is
th
e
a
c
tu
a
l p
o
w
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lo
s
s
w
it
h
o
u
t U
P
F
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,
,
i
s
t
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m
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gi
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r
y
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s
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P
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p
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s
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u
t
U
P
F
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T
h
e
m
o
d
if
ie
d
p
a
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tic
le
s
w
a
r
m
o
p
tim
iz
a
tio
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a
l
g
o
r
ith
m
f
o
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th
e
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p
tim
a
l a
llo
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tio
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o
f
U
P
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d
e
v
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e
o
n
I
E
E
E
3
0 b
us
e
s
i
s
gi
ve
n i
n t
he
f
o
l
l
o
w
i
n
g s
t
e
p
s
:
S
t
e
p 1
: S
ta
r
t th
e
m
o
d
i
f
ie
d
P
S
O
a
l
g
or
i
t
hm
a
n
d r
e
a
d bu
s
da
t
a
,
lin
e
d
a
t
a an
d
t
o
l
er
an
ce t
h
r
o
u
g
h
N
.
R
.
St
e
p
2
:
R
u
n
t
h
e
p
r
o
g
r
a
m
to
g
e
n
e
r
a
te
a
n
in
i
tia
l p
o
p
u
la
tio
n
o
f
p
a
r
tic
l
e
s
.
St
e
p
3
: C
o
m
p
u
te
a
c
tu
a
l p
o
w
e
r
lo
s
s
p
e
r
p
a
r
tic
le
St
e
p
4
: S
e
t th
e
c
u
r
r
e
n
t
.
St
e
p
5
: S
e
t th
e
g
lo
b
a
l b
e
s
t c
u
r
r
e
n
t
.
St
e
p
6
:
B
r
i
ng up
-
t
o
-
d
at
e t
h
e v
el
o
ci
t
y
an
d
p
o
s
i
t
i
o
n
o
f
each
p
ar
t
i
cl
e.
St
e
p
7
:
I
f
=
an
d
t
h
e t
i
m
e co
m
p
l
et
e,
s
t
o
p
m
o
d
i
f
i
ed
P
S
O
r
u
n
n
i
n
g
a
n
d
w
r
i
t
e t
h
e b
es
t
s
o
lu
tio
n
,
e
ls
e
s
e
t
n
e
w
ite
r
a
tio
n
,
=
+
1
4.
P
RO
CE
S
S
F
O
R ADO
P
T
I
N
G
UP
F
C
I
ns
e
r
t
i
o
n U
P
F
C
to
th
e
g
r
id
tr
e
a
te
d
th
e
m
o
s
t d
if
f
ic
u
ltie
s
t
h
a
t a
r
e
e
x
p
o
s
e
d
to
th
e
e
le
c
tr
ic
a
l n
e
t
w
o
r
k
.
I
t
w
i
l
l
b
e
at
t
ai
n
ed
b
y
s
el
ect
i
n
g
t
h
e
b
es
t
co
n
s
t
r
ai
n
t
s
o
f
t
h
e U
P
F
C
,
w
h
i
c
h
can
m
i
n
i
m
i
ze t
h
e o
v
er
l
o
ad
l
i
n
e
an
d
m
ak
e t
h
e
v
o
l
t
ag
e
w
i
t
h
i
n
t
h
e p
er
m
i
s
s
i
b
l
e r
an
g
e [
3
0
]
.
T
h
e
f
o
llo
w
i
n
g
p
r
o
ced
u
r
e i
s
s
u
m
m
ar
i
z
ed
i
n
:
a.
C
on
s
i
de
r
i
n
g
M
A
T
L
A
B
pr
og
r
a
m
m
i
ng
R
2019b
t
o
de
s
c
r
i
be
t
h
e
l
i
n
e
s
a
n
d bu
s
e
s
da
t
a
of
I
E
E
E
-
30
bu
s
e
s
a
l
s
o
t
he
U
P
F
C
c
o
n
s
t
r
a
i
nt
a
nd
s
o
l
ve
t
he
s
ys
t
e
m
i
n N
e
w
t
o
n
R
a
p
hs
o
n t
e
c
hn
i
q
ue
.
b.
A
p
p
lie
d
U
P
F
C
d
e
v
ic
e
i
n
p
a
r
tic
le
s
w
a
r
m
o
p
ti
m
iz
a
tio
n
to
r
e
s
t
r
ic
t th
e
o
v
e
r
lo
a
d
e
d
lin
e
s
.
c.
A
s
s
u
m
e t
h
e s
y
s
t
e
m
e
n
f
o
r
ced
a r
i
s
e i
n
el
ect
r
i
cal
l
o
ad
(
7
%
,
1
4
%
,
2
1
%
)
.
d.
E
le
c
tin
g
th
e
a
p
p
r
o
p
r
ia
te
c
o
n
s
tr
a
in
ts
o
f
U
P
F
C
a
n
d
o
p
ti
m
a
l lo
c
a
tio
n
.
e.
I
t
can
r
ed
u
ce t
h
e o
v
er
l
o
ad
ed
l
i
n
es
,
r
eg
u
l
at
e r
eal
an
d
i
m
ag
i
n
ar
y
p
o
w
er
f
l
o
w
,
an
d
co
n
t
r
o
l
t
h
e
vo
l
t
a
ge
i
n
e
a
c
h b
us
,
d
yna
m
i
c
c
o
m
p
o
s
i
t
i
o
n.
f.
O
n
e
o
f
t
h
e
c
r
itic
a
l i
s
s
u
e
s
in
g
r
id
s
is
th
e
is
la
n
d
i
n
g
p
h
e
n
o
m
e
n
o
n
.
I
s
la
n
d
i
n
g
is
a
c
o
n
d
itio
n
t
h
a
t a
p
a
r
t o
f
a
g
r
i
d
co
n
t
ai
n
s
a p
ar
t
o
f
t
h
e l
o
ad
s
ep
ar
at
ed
f
r
o
m
t
h
e g
r
i
d
w
h
i
l
e
i
t
h
as
el
ect
r
i
ci
t
y
.
5.
N
EW
TO
N
-
RAP
H
S
O
N
P
O
W
ER
F
LO
W
R
E
S
U
L
TS
N
e
wt
o
n
-
R
a
p
h
s
o
n
m
e
t
h
o
d
is
a
s
e
q
u
e
n
tia
l c
a
lc
u
la
t
io
n
a
d
o
p
tin
g
a
p
r
i
m
a
r
y
c
o
n
d
itio
n
o
f
t
h
e
f
ir
s
t
-
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Evaluation Warning : The document was created with Spire.PDF for Python.
In
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I
SSN
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8708
In
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N
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F
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p
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u
s
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1
-
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F
i
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r
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.
I
m
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n
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p
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s
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w
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b
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s
(
1
-
2)
F
i
gu
r
e
6.
R
eal
an
d
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m
a
g
i
n
ar
y
p
o
w
er
l
o
s
s
i
n
d
e
x
i
n
t
h
e ar
ea b
et
w
ee
n
b
u
s
(
1
-
2)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
E
l
e
c
&
C
o
m
p
E
n
g
I
S
S
N
:
2088
-
8708
A
n opt
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m
al
al
l
oc
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on
of
U
P
F
C
and t
r
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[
1]
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.
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u
s
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ei
n
,
G
.
S
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,
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.
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as
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2,
pp.
8
88
-
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9,
20
18
,
do
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p
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[
2]
S
. S
.
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,
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v
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36
-
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201
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11
59
1
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v8
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pp1
3
36
-
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44
.
[
3]
B
.
P
r
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t
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an
d
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.
A
m
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s
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vo
l
.
4,
n
o.
2,
pp.
10
1
-
10
9,
20
13
[
4]
P
.
M
a
jid
,
N
.
B
r
ij,
a
n
d
R
.
P
a
r
v
iz
,
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c
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,
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06
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p
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1
-
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,
doi
:
10
.
11
09
/
P
E
D
E
S
.
20
06
.
3
44
230
.
[
5]
C
.
P
a
p
a
d
im
itr
io
u
,
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.
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le
f
ta
k
is
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a
n
d
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.
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.
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tz
ia
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R
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ch
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l
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121,
p
p.
58
-
66
,
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15
,
doi
:
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0.
1
01
6/
j
.
e
ps
r
.
2
01
4.
1
2.
00
4
[
6]
A
.
N
.
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l
s
a
m
m
ak
an
d
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.
A
.
M
oha
m
m
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d,
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t
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t
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v
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on t
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ni
f
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