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12
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20
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:
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n
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ge
n
e
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y
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ll
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r
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t
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d
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a
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t
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m
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o
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o
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r
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A
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s
i
g
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l
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t
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l
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m
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t
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nk,
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e
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pe
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t
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ly
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h
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ld
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o
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l
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o
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r
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t
uni
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g
b
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d
t
h
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L
F
C
s
c
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m
e
[
1]
we
r
e
a
pp
l
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e
d
to
r
e
gul
a
t
e
f
r
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que
n
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t
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tr
o
l
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n
de
gr
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d
[
1]
.
R
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c
e
n
t
l
y
,
t
h
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de
v
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o
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m
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t
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w
hi
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h
we
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e
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us
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i
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[
2
]
-
[
9]
.
As
po
we
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y
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t
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m
b
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o
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r
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m
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h
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li
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h
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h
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l
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g
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us
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M
A
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ur
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Gu
o
[
10]
t
h
e
a
u
t
h
o
r
a
ppl
i
e
d
s
l
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d
in
g
m
o
de
c
o
n
t
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l
(
S
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to
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o
n
t
r
o
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f
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nc
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po
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y
s
t
e
m
.
Ho
we
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M
C
s
we
r
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h
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vi
ng
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h
a
t
t
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g
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f
f
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t
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t
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l
.
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h
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f
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M
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ne
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t
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r
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h
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n
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m
i
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z
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r
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C
E
we
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d
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s
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u
s
s
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d
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n
[
11
]
-
[
20]
.
L
i
n
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a
r
qua
dr
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t
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c
Ga
us
s
i
a
n
t
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h
ni
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l
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g
n
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d
a
n
d
d
i
s
c
us
s
e
d
i
n
[
21
]
-
[
25]
f
o
r
t
h
e
c
o
m
p
l
e
x
w
i
d
e
a
r
e
a
po
we
r
s
y
s
t
e
m
.
H
-
i
nf
i
n
i
t
y
s
c
h
e
m
e
wa
s
a
l
s
o
d
i
s
c
u
s
s
e
d
i
n
[
26
]
-
[
27]
.
T
h
e
s
e
c
o
n
t
r
o
l
l
e
r
s
pr
o
vi
de
d
go
o
d
pe
r
f
o
r
m
a
n
c
e
a
n
d
r
o
b
us
t
L
F
C
i
n
t
h
e
wi
d
e
a
r
e
a
p
o
we
r
s
y
s
t
e
m
.
B
ot
h
S
M
C
,
l
i
ne
a
r
qua
dr
a
t
i
c
Ga
us
s
i
a
n
(
L
QG
)
,
H
-
i
nf
i
n
i
t
y
s
c
h
e
m
e
s
wo
r
ke
d
we
l
l
u
n
d
e
r
po
we
r
s
y
s
t
e
m
w
i
t
h
m
o
r
e
t
uni
n
g
v
a
r
i
a
bl
e
s
.
Ho
we
v
e
r
,
t
h
e
c
o
n
s
i
de
r
a
t
i
o
n
o
f
c
o
m
m
u
ni
c
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t
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o
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de
l
a
y
h
a
s
b
r
o
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t
a
n
e
w
e
r
a
f
o
r
t
h
e
L
F
C
o
f
M
A
P
S
.
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h
e
s
e
de
l
a
y
s
e
xi
s
t
i
n
po
we
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s
y
s
t
e
m
s
a
n
d
v
a
r
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f
r
o
m
t
e
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t
o
s
e
v
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r
a
l
h
u
n
dr
e
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o
n
mi
l
li
s
e
c
o
n
ds
.
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o
m
m
u
ni
c
a
t
i
o
n
li
nks
a
r
e
u
s
e
d
t
o
c
o
n
n
e
c
t
a
n
c
il
l
a
r
y
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o
m
po
n
e
n
t
s
t
h
a
t
a
r
e
l
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n
k
c
o
nn
e
c
t
i
n
g
l
o
a
d
f
r
e
que
nc
y
s
e
ns
o
r
p
o
i
n
t
to
t
h
e
r
e
m
o
t
e
c
o
n
tr
o
l
u
ni
t
(
R
C
U)
do
wn
to
t
h
e
ge
n
e
r
a
t
i
n
g
uni
t
.
I
n
r
e
a
l
i
t
y
,
t
h
e
R
C
U
s
o
m
e
t
i
m
e
s
m
i
g
h
t
e
x
pe
r
i
e
n
c
e
de
l
a
y
i
n
t
he
r
e
c
e
i
vi
ng
A
C
E
s
i
gn
a
l
.
I
n
pr
a
c
t
i
c
e
,
t
i
m
e
-
de
l
a
y
f
o
r
t
h
e
c
o
n
tr
o
l
l
e
r
t
o
r
e
c
e
i
v
e
i
n
put
A
C
E
s
i
g
n
a
l
s
h
o
u
l
d
n
ot
b
e
n
e
g
l
e
c
t
e
d
a
n
d
t
hi
s
s
i
g
ni
f
i
e
s
t
h
e
o
p
t
i
m
a
l
c
o
n
t
r
o
l
.
T
h
e
r
e
f
o
r
e
,
c
o
m
m
u
ni
c
a
t
i
o
n
de
l
a
y
s
h
o
u
l
d
b
e
t
a
k
i
n
g
i
n
t
o
a
c
c
o
un
t
i
n
t
h
e
dy
na
m
i
c
mo
de
l
li
ng
o
f
c
o
m
p
l
e
x
po
we
r
s
y
s
t
e
m
.
Ne
w
l
y
pu
bli
s
h
e
d
pa
pe
r
[
28]
a
ddr
e
s
s
e
d
t
h
e
L
F
C
f
o
r
t
h
e
M
A
P
S
w
i
t
h
t
i
m
e
d
e
l
a
y
b
ut
w
i
t
h
a
l
l
s
y
s
t
e
m
v
a
r
i
a
bl
e
s
a
r
e
a
s
s
u
m
e
d
to
b
e
m
e
a
s
u
r
e
d.
I
n
ge
n
e
r
a
l
,
n
o
t
a
l
l
s
y
s
t
e
m
pa
r
a
m
e
t
e
r
s
c
a
n
b
e
m
e
a
s
ur
e
d.
T
h
e
a
ut
h
o
r
w
or
k
i
n
[
29]
s
e
r
v
e
s
a
s
a
m
ot
i
va
t
i
o
n
to
de
s
i
g
n
a
r
e
a
l
c
o
n
c
e
pt
u
a
l
i
z
a
t
i
o
n
c
o
n
tr
o
l
l
e
r
f
o
r
t
h
e
c
o
m
p
l
e
x
i
n
t
e
r
c
o
nn
e
c
t
e
d
po
we
r
pl
a
n
t
s
w
i
t
h
s
i
g
n
a
l
de
l
a
y
.
I
n
t
hi
s
p
a
pe
r
,
t
h
e
L
QR
c
o
m
bi
ne
d
w
i
t
h
K
a
lm
a
n
f
il
t
e
r
tec
hni
qu
e
a
r
e
pr
o
p
o
s
e
d
a
s
L
QG
m
e
t
h
o
d
f
o
r
f
r
e
que
n
c
y
r
e
gu
l
a
to
r
o
f
t
h
e
M
A
P
S
w
i
t
h
c
o
m
m
u
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c
a
t
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o
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s
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g
n
a
l
de
la
y
.
T
h
e
M
A
P
S
m
o
de
l
i
s
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e
pr
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t
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n
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t
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t
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pa
c
e
w
i
t
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t
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t
i
m
e
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de
l
a
y
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o
e
x
t
e
n
d
t
h
e
m
o
de
l
.
T
hi
s
s
t
a
t
e
s
pa
c
e
m
o
de
l
i
s
a
pp
l
i
e
d
t
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o
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t
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i
n
f
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h
e
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QG
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S
i
nc
e
n
o
t
a
l
l
v
a
l
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s
o
f
t
h
e
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F
C
m
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l
's
pa
r
a
m
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t
e
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a
r
e
m
e
a
s
ur
a
bl
e
.
T
h
e
r
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f
o
r
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,
K
a
l
m
a
n
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t
e
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d
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o
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t
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h
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e
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t
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s
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l
a
s
t
i
m
e
-
de
l
a
y
a
r
e
i
n
put
s
i
g
n
a
l
s
.
T
h
e
c
o
n
t
r
i
b
ut
i
o
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o
f
t
h
e
pa
p
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r
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s
s
t
a
t
e
d
b
e
l
o
w:
−
C
o
m
m
u
ni
c
a
t
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o
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t
i
m
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de
l
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n
s
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de
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d
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n
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h
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n
e
t
wo
r
k
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m
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t
a
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s
t
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a
t
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w
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d
b
a
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k
ga
i
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a
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d
t
i
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l
a
y
−
L
y
a
pu
n
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t
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o
r
y
a
n
d
l
i
ne
a
r
m
a
t
r
i
x
i
ne
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t
y
(
L
M
I
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e
c
h
ni
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s
i
s
us
e
d
to
p
r
o
v
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t
h
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M
A
P
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s
t
a
bi
li
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y
−
C
o
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pa
r
i
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o
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pr
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p
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d
c
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tr
o
l
l
e
r
a
n
d
[
29]
.
2.
S
YST
E
M
L
F
C
M
ODE
L
I
N
T
I
M
E
DE
L
AY
I
n
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t
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a
c
o
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pt
ua
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d
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F
C
m
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t
a
ki
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o
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t
a
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s
w
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l
a
y
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d.
A
d
i
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gr
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p
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F
i
gur
e
1
[
29]
.
E
a
c
h
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pr
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0.
1
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1
s
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(
1)
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1)
Ot
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−
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2)
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(
3)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
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Optimal
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whi
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(
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c
o
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put
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m
m
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.
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(
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=
(
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+
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(
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(
5)
F
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1.
T
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s
tr
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t
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)
=
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12
2
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;
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2
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;
=
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
n
t
J
E
l
e
c
&
C
o
m
p
E
n
g,
Vo
l
.
12
,
N
o
.
1
,
F
e
b
r
ua
r
y
20
22
:
157
-
165
160
I
n
t
h
e
r
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a
l
s
y
s
t
e
m
,
e
xa
c
t
m
e
a
s
ur
e
m
e
n
t
o
f
t
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e
pa
r
a
m
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t
e
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v
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l
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e
s
i
s
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m
po
s
s
i
b
l
e
.
T
h
e
r
e
f
o
r
e
,
m
o
s
t
pa
r
a
m
e
t
e
r
s
a
r
e
a
ppr
o
xi
m
a
t
e
d
or
e
s
t
i
m
a
t
e
d.
Al
s
o
,
by
c
o
ns
i
d
e
r
i
n
g
t
i
m
e
de
l
a
y
f
a
c
t
or
,
s
o
t
h
e
d
y
n
a
mi
c
m
o
de
l
in
(
6)
i
s
f
ur
t
h
e
r
r
e
-
wr
i
t
t
e
n
a
s
i
n
(
7)
:
̇
(
)
=
[
+
(
,
)
]
(
)
+
[
1
+
1
]
(
−
1
)
+
[
2
+
2
]
(
−
2
)
+
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+
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,
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)
+
(
)
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)
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−
1
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2
(
−
2
)
+
(
)
+
(
,
)
(
)
=
(
)
+
(
)
(
7)
w
h
e
r
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t
h
e
u
n
k
n
o
wn
m
a
t
r
i
c
e
s
(
,
)
a
n
d
(
,
)
de
n
ot
e
by
s
y
s
t
e
m
v
a
r
i
a
t
i
o
ns
,
t
h
e
m
a
t
r
i
c
e
s
a
n
d
a
r
e
t
h
e
n
o
m
i
na
l
va
l
u
e
s
;
(
,
)
i
s
c
a
ll
e
d
t
h
e
tot
a
l
v
a
r
i
a
t
i
o
ns
whi
c
h
c
a
n
be
e
s
t
i
m
a
t
e
d
a
n
d
we
c
a
n
de
f
i
ne
i
t
i
n
(
8)
:
(
,
)
=
(
,
)
(
)
+
1
(
−
1
)
+
2
(
−
2
)
+
(
,
)
(
)
+
(
)
(
8)
a
n
d
(
)
i
s
a
m
e
a
s
ur
a
bl
e
d
i
s
t
ur
b
a
n
c
e
.
I
de
a
l
ly
,
s
o
m
e
a
s
s
u
m
pt
i
o
n
s
a
r
e
s
t
a
t
e
d
to
de
s
c
r
i
b
e
r
e
a
li
t
y
a
n
d
t
h
e
f
e
a
s
i
b
il
i
t
y
o
f
t
h
e
po
we
r
s
y
s
t
e
m
a
n
d
a
s
we
l
l
t
h
e
pa
r
a
m
e
t
e
r
s
b
a
s
e
d
l
o
a
d
f
r
e
que
n
c
y
c
o
n
t
r
o
l
s
t
r
a
t
e
gi
e
s
un
de
r
c
e
r
t
a
i
n
c
o
n
d
i
t
i
o
ns
.
T
h
e
s
e
a
s
s
u
m
pt
i
o
n
s
a
n
d
s
o
m
e
l
e
mm
a
s
a
r
e
s
t
a
t
e
d
b
e
l
o
w
:
As
s
u
m
pt
i
o
n
1
:
I
f
t
h
e
m
a
t
r
i
x
,
i
s
c
o
n
t
r
o
l
l
a
bil
i
t
y
,
t
h
e
n,
(
,
)
,
(
,
)
c
a
n
be
e
s
t
i
m
a
t
e
d.
As
s
u
m
pt
i
o
n
2
:
T
h
e
l
u
m
p
e
d
(
,
)
,
whi
c
h
i
nc
l
ude
s
de
l
a
y
s
t
a
t
e
m
a
t
r
i
x
a
n
d
t
h
e
di
f
f
e
r
e
n
t
i
a
l
o
f
(
,
)
i
s
b
o
un
de
d.
i
.
e
.
,
t
h
e
r
e
e
xi
s
t
t
h
e
kn
o
wn
s
c
a
l
a
r
s
a
n
d
̄
s
uc
h
t
h
a
t
‖
(
,
)
‖
≤
a
n
d
‖
̇
(
,
)
‖
≤
̄
,
wh
e
r
e
‖
.
‖
i
s
m
a
t
r
i
x
n
o
r
m
.
L
e
mm
a
1:
[
13]
Le
t
X
,
Y
a
n
d
F
a
r
e
a
c
t
ua
l
m
a
t
r
i
c
e
s
o
f
a
ppr
o
pr
i
a
t
e
di
m
e
ns
i
o
n
w
i
t
h
≤
1
t
h
e
n
,
f
o
r
a
ny
s
c
a
l
a
r
>
0
,
t
h
e
s
e
que
n
t
m
a
t
r
i
x
i
ne
qua
li
t
y
h
o
l
d
s
.
+
≤
−
1
+
3.
CONT
ROL
L
E
R
DE
S
I
GN
WI
T
H
T
I
M
E
-
DE
L
A
Y
3.
1.
L
in
e
ar
q
u
ad
r
at
ic
r
e
gu
l
at
o
r
(
L
QR)
T
o
de
s
i
g
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3.
2.
P
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9)
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11)
wh
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ℜ
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qua
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ℜ
+
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−
ℜ
−
1
ℜ
+
=
0
(
12)
S
ub
s
t
i
t
ut
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n
g
i
n
t
o
(
6
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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c
&
C
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p
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N:
2088
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8708
Optimal
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−
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
n
t
J
E
l
e
c
&
C
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m
p
E
n
g,
Vo
l
.
12
,
N
o
.
1
,
F
e
b
r
ua
r
y
20
22
:
157
-
165
162
I
n
a
dd
i
t
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n
,
t
h
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L
M
I
s
(
16)
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s
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va
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t
to
t
hi
s
i
ne
qua
l
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y
:
[
1
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=
−
(
20)
a
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d
−
<
0
.
C
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(
16)
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d
(
19)
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:
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−
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(
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2
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21)
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5
1
2
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1
2
2
+
2
3
2
,
t
h
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c
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s
t
a
n
t
v
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(
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√
.
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e
s
y
s
t
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m
(
15)
i
s
a
s
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pt
ot
i
c
a
ll
y
s
t
a
bl
e
.
4.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
I
n
t
hi
s
s
e
c
t
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n
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M
A
P
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f
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a
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b
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y
o
f
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pr
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d
L
QG
c
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1
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d
2
a
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to
b
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f
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d.
T
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pa
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1
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u
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a
r
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o
b
t
a
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d
f
r
o
m
pa
pe
r
[
29]
.
4.
1.
S
im
u
l
at
ion
r
e
s
u
l
t
b
as
e
d
on
n
om
in
al
val
u
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s
T
h
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pa
r
a
m
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t
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r
s
w
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l
v
a
l
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s
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f
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M
A
P
S
a
r
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us
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d.
All
s
t
a
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v
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r
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a
bl
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s
a
r
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us
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d
in
pr
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p
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s
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d
c
o
n
t
r
o
l
l
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r
i
s
ge
t
f
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t
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K
a
lm
a
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f
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.
A
t
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RE
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NC
E
S
[
1]
R
.
K
.
S
a
hu,
S
.
P
a
nda
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nd
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.
K
.
Y
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of
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s
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ol
,
v
o
l.
24,
n
o
.
10,
pp.
1596
-
1608,
O
c
t.
2
014,
do
i:
10.1016/j
.
jp
r
oc
o
nt
.2014.08.006.
[
2]
S
.
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x
e
na
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,
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and E
ne
r
gy
Sy
s
te
m
s
, v
o
l.
81, pp. 4
05
-
415, F
e
b. 2016, d
o
i
:
10.1016/j
.i
j
e
p
e
s
.2016.02.041.
[
3]
T
.
K
.
M
o
ha
pa
tr
a
a
nd
B
.
K
.
S
a
hu,
"
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ta
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m,
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t
-
C
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y
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ne
r
gy
Se
c
u
r
it
y
and
P
o
w
e
r
, pp. 1
-
6, M
a
r
. 2018, doi:
10.1109/I
C
S
E
S
P
.2
018.837669
7.
[
4]
N
. E
. Y
.
K
o
uba
, M
. M
e
na
a
, M
. H
a
s
ni
a
nd M
. B
o
ud
o
ur
,
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nal
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