I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
s
(
I
J
P
E
DS)
Vo
l.
1
6
,
No
.
1
,
Ma
r
ch
2
0
2
5
,
p
p
.
2
8
7
~
2
9
7
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
6
.
i1
.
p
p
2
8
7
-
297
287
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
To
rg
ue and flu
x
r
ipple mit
ig
a
tion t
echnique
using
m
ulti
-
lev
el
inv
erte
r
for sequ
e
ntial mo
del pr
edi
ctive contro
lle
d
induction
mo
tor
Abo
ba
k
er
K
ikk
i A
bo
ba
k
er
,
No
rj
uli
a
M
o
ha
m
a
d No
rdin,
Aziz
a
h Abdu
l R
a
za
k
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
P
o
w
e
r
En
g
i
n
e
e
r
i
n
g
,
F
a
c
u
l
t
y
o
f
E
l
e
c
t
r
i
c
a
l
E
n
g
i
n
e
e
r
i
n
g
,
U
n
i
v
e
r
si
t
i
Te
k
n
o
l
o
g
i
M
a
l
a
y
si
a
,
J
o
h
o
r
B
a
h
r
u
,
M
a
l
a
y
si
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ma
y
2
1
,
2
0
2
4
R
ev
is
ed
Dec
1
,
2
0
2
4
Acc
ep
ted
Dec
9
,
2
0
2
4
Th
e
c
o
n
tro
l
o
f
e
lec
tri
c
m
o
to
rs
p
re
se
n
ts
a
fa
sc
in
a
ti
n
g
t
o
p
ic
i
n
t
h
e
field
o
f
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
.
Th
re
e
-
p
h
a
se
in
d
u
c
ti
o
n
m
o
t
o
rs
a
re
e
x
ten
siv
e
l
y
e
m
p
lo
y
e
d
i
n
in
d
u
str
ial
a
p
p
l
ica
ti
o
n
s,
b
e
c
a
u
se
o
f
th
e
ir
d
u
ra
b
il
i
ty
a
n
d
c
o
st
-
e
ffe
c
ti
v
e
n
e
ss
.
He
n
c
e
,
in
d
u
c
ti
o
n
m
o
to
r
c
o
n
tr
o
l
re
se
a
rc
h
re
m
a
in
s
a
m
a
jo
r
p
rio
ri
ty
in
e
lec
tri
c
a
l
d
riv
e
tec
h
n
o
l
o
g
y
.
F
ield
-
o
rien
ted
c
o
n
tro
l
(F
OC)
a
n
d
d
irec
t
to
rq
u
e
c
o
n
tro
l
(DTC)
a
re
t
h
e
m
o
st
c
o
m
m
o
n
c
o
n
tr
o
l
m
e
th
o
d
s
fo
r
in
d
u
strial
a
p
p
li
c
a
ti
o
n
s
u
p
to
n
o
w.
Re
c
e
n
tl
y
d
e
v
e
lo
p
e
d
m
icro
c
o
n
tro
ll
e
r
p
ro
c
e
ss
in
g
c
a
p
a
b
il
it
ies
h
a
v
e
e
n
a
b
le
d
n
o
v
e
l
c
o
n
tro
l
t
e
c
h
n
o
lo
g
y
li
k
e
m
o
d
e
l
p
re
d
ictiv
e
c
o
n
tro
l
(M
P
C)
.
Hig
h
-
p
e
rf
o
rm
a
n
c
e
d
riv
e
sy
ste
m
s
c
o
u
ld
b
e
n
e
fit
fro
m
th
is
n
e
w
c
o
n
tro
l
m
e
th
o
d
.
On
e
o
f
M
P
C
a
p
p
ro
a
c
h
,
re
fe
rre
d
to
a
s
fi
n
it
e
c
o
n
tro
l
se
t
-
m
o
d
e
l
p
re
d
ictiv
e
c
o
n
tro
l
(F
C
S
-
M
P
C)
,
f
o
c
u
se
s
o
n
re
d
u
c
i
n
g
a
si
n
g
le
c
o
st
fu
n
c
ti
o
n
.
Th
is
is
a
c
h
iev
e
d
b
y
a
d
ju
st
in
g
a
we
ig
h
ti
n
g
fa
c
to
r
to
p
rio
r
it
ize
e
it
h
e
r
to
rq
u
e
o
r
flu
x
e
rr
o
r
re
d
u
c
ti
o
n
.
Ho
we
v
e
r,
th
e
p
rima
ry
d
ra
wb
a
c
k
s
o
f
th
e
sta
n
d
a
rd
F
CS
-
M
P
C
li
e
in
d
e
term
in
i
n
g
t
h
e
se
we
ig
h
ti
n
g
fa
c
to
rs
a
n
d
th
e
v
a
riab
le
sw
it
c
h
in
g
fre
q
u
e
n
c
y
,
wh
ic
h
g
re
a
tl
y
v
a
r
ies
b
a
se
d
o
n
t
h
e
o
p
e
ra
ti
o
n
a
l
c
o
n
d
i
ti
o
n
s.
A
c
o
n
tr
o
l
a
p
p
ro
a
c
h
th
a
t
e
li
m
in
a
ted
th
e
we
ig
h
i
n
g
fa
c
to
r
wa
s
p
ro
p
o
se
d
.
T
h
e
p
ro
p
o
se
d
se
q
u
e
n
ti
a
l
m
o
d
e
l
p
re
d
ictiv
e
c
o
n
tr
o
l
(S
M
P
C)
m
e
th
o
d
is
a
p
p
li
e
d
to
a
3
-
p
h
a
se
in
d
u
c
ti
o
n
m
o
t
o
r
o
p
e
ra
ted
b
y
a
5
-
lev
e
l
CHB
i
n
v
e
rter.
S
imu
lat
i
o
n
re
su
lt
s
m
a
tch
e
d
th
e
o
re
ti
c
a
l
a
n
a
ly
sis.
Re
s
u
lt
s
d
e
m
o
n
stra
ted
th
a
t
sta
t
o
r
fl
u
x
a
n
d
to
r
q
u
e
a
re
in
d
e
p
e
n
d
e
n
tl
y
c
o
n
tr
o
ll
e
d
wi
t
h
o
u
t
we
ig
h
ti
n
g
fa
c
to
r
,
a
n
d
l
o
w
h
a
rm
o
n
ic
d
isto
rti
o
n
lev
e
ls.
K
ey
w
o
r
d
s
:
Dir
ec
t to
r
q
u
e
c
o
n
tr
o
l
Field
-
o
r
ien
ted
co
n
tr
o
l
I
n
d
u
ctio
n
m
o
to
r
Mu
ltil
ev
el
in
v
er
ter
Seq
u
en
tial m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
No
r
ju
lia
Mo
h
am
a
d
No
r
d
i
n
Dep
ar
tm
en
t o
f
E
lectr
ical
Po
wer
E
n
g
in
ee
r
in
g
,
Facu
lty
o
f
E
le
ctr
ical
E
n
g
in
ee
r
in
g
Un
iv
er
s
iti
T
ek
n
o
lo
g
i M
ala
y
s
ia
8
1
3
1
0
,
UT
M
J
o
h
o
r
B
ah
r
u
,
J
o
h
o
r
,
Ma
lay
s
ia
E
m
ail:
n
o
r
ju
lia@
u
tm
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
Mo
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
MPC
)
h
as
attr
ac
ted
s
ig
n
if
ican
t
in
t
er
est
in
m
o
to
r
d
r
iv
e
co
n
tr
o
l,
b
ec
au
s
e
its
s
im
p
le
p
r
in
cip
les
q
u
ic
k
an
d
a
cc
u
r
ate
r
esp
o
n
s
e
.
Ad
d
itio
n
all
y
,
MPC
o
f
f
er
s
h
i
g
h
f
le
x
ib
ilit
y
f
o
r
in
co
r
p
o
r
ati
n
g
v
ar
io
u
s
co
n
s
tr
ain
ts
,
m
ak
i
n
g
it
an
ef
f
ec
tiv
e
ap
p
r
o
ac
h
f
o
r
co
m
p
lex
co
n
tr
o
l
s
ce
n
ar
io
s
[
1
]
,
[
2
]
.
T
o
d
ate,
th
e
f
in
ite
co
n
tr
o
l
s
et
m
o
d
el
p
r
e
d
ictiv
e
c
o
n
tr
o
l (
FC
S
-
MPC
)
f
o
r
f
lu
x
a
n
d
to
r
q
u
e
in
th
e
in
d
u
ctio
n
m
o
to
r
(
IM
)
h
as
t
y
p
ically
b
ee
n
ex
ec
u
ted
with
a
s
in
g
u
lar
co
s
t
f
u
n
ctio
n
,
em
p
lo
y
in
g
a
weig
h
tin
g
f
ac
to
r
to
p
r
io
r
itize
th
e
m
in
im
izatio
n
o
f
eith
er
f
lu
x
o
r
t
o
r
q
u
e
e
r
r
o
r
[
3
]
-
[
5
]
.
Dete
r
m
in
in
g
th
e
ap
p
r
o
p
r
iate
weig
h
tin
g
f
ac
to
r
p
r
esen
ts
a
p
r
in
cip
al
ch
allen
g
e
with
in
th
is
co
n
tr
o
l a
p
p
r
o
ac
h
.
T
h
e
d
esig
n
o
f
th
e
weig
h
tin
g
f
ac
to
r
is
in
ten
d
ed
to
n
o
r
m
alize
s
tato
r
f
lu
x
a
n
d
t
o
r
q
u
e
q
u
a
n
titi
es
with
in
th
e
co
s
t
f
u
n
ctio
n
[
6
]
.
Ho
wev
er
,
ch
o
o
s
in
g
an
ap
p
r
o
p
r
iate
weig
h
tin
g
f
ac
to
r
is
a
co
m
p
lex
task
,
s
ig
n
if
ican
tly
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
287
-
297
288
in
f
lu
en
cin
g
h
ar
m
o
n
ic
cu
r
r
e
n
t
d
is
to
r
tio
n
an
d
r
o
b
u
s
tn
ess
ag
ain
s
t
p
ar
am
eter
v
ar
iatio
n
s
.
T
o
a
d
d
r
ess
th
is
ch
allen
g
e,
th
e
liter
atu
r
e
[
7
]
-
[
1
4
]
an
d
h
as
s
u
g
g
ested
n
u
m
er
o
u
s
m
eth
o
d
s
to
m
in
im
ize
o
r
elim
in
ate
th
e
weig
h
tin
g
f
ac
t
o
r
s
in
MPC
.
Acc
o
r
d
in
g
to
[
9
]
,
r
ed
u
c
in
g
th
e
er
r
o
r
in
th
e
v
o
ltag
e
v
e
cto
r
eq
u
ates to
r
ed
u
cin
g
th
e
e
r
r
o
r
in
th
e
s
tato
r
f
lu
x
lin
k
ag
e
v
ec
to
r
.
C
o
n
s
eq
u
e
n
tly
,
em
p
lo
y
in
g
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
ca
n
s
im
p
lify
co
n
tr
o
l
c
o
m
p
lex
d
esig
n
s
a
n
d
r
ed
u
ce
t
h
e
co
m
p
u
tatio
n
al
lo
ad
f
o
r
s
elec
tin
g
th
e
b
est
v
ec
t
o
r
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
i
n
[
1
0
]
,
s
u
g
g
ests
u
s
in
g
a
n
alg
eb
r
aic
s
elec
tio
n
o
f
th
e
weig
h
tin
g
f
ac
to
r
to
ac
h
iev
e
a
p
er
f
o
r
m
an
ce
lev
el
th
at
is
co
m
p
ar
ab
le
to
p
r
ed
ictiv
e
cu
r
r
en
t
c
o
n
tr
o
l.
W
h
ile
th
is
ca
lcu
latio
n
is
less
co
m
p
lex
th
an
t
h
e
o
n
e
in
[
9
]
,
it
s
till
d
ep
en
d
s
o
n
m
ac
h
in
e’
s
s
tates
an
d
p
ar
am
eter
s
.
T
o
ad
d
r
ess
th
e
ch
allen
g
e
o
f
s
elec
tin
g
th
e
weig
h
tin
g
f
ac
to
r
b
y
d
ec
o
u
p
lin
g
t
h
e
co
n
tr
o
l
v
ar
iab
les
an
d
o
p
tim
izin
g
th
em
in
d
iv
i
d
u
ally
u
s
in
g
two
ca
s
ca
d
e
co
s
t
f
u
n
ctio
n
s
in
[
1
1
]
.
H
o
wev
er
,
th
is
ap
p
r
o
ac
h
s
till
en
co
u
n
ter
s
is
s
u
es
s
u
ch
as
an
u
n
d
esire
d
n
on
-
co
n
s
tan
t
s
witch
i
n
g
f
r
eq
u
en
cy
a
n
d
h
i
g
h
r
ip
p
les.
A
two
-
v
ec
to
r
-
b
ase
d
MPC
ap
p
r
o
ac
h
th
at
o
m
its
th
e
u
s
e
o
f
a
weig
h
tin
g
f
ac
to
r
.
w
h
er
e
th
is
m
et
h
o
d
m
ain
tain
s
s
t
ab
le
p
er
f
o
r
m
a
n
ce
in
s
tead
y
-
s
tate
co
n
d
itio
n
s
was
d
i
s
cu
s
s
ed
in
[
1
5
]
,
h
o
wev
e
r
,
th
is
m
eth
o
d
it
in
c
r
ea
s
es
th
e
co
m
p
u
tatio
n
al
co
m
p
lex
ity
.
wh
ich
g
en
er
ally
n
o
t
s
u
itab
le
f
o
r
in
d
u
s
tr
ial
ap
p
licatio
n
s
,
p
a
r
ticu
lar
ly
in
s
ce
n
ar
io
s
in
v
o
lv
in
g
ex
ten
d
ed
h
o
r
izo
n
p
r
ed
ictio
n
s
an
d
m
u
lti
-
lev
el
c
o
n
v
er
ter
s
.
Alter
n
ativ
e
ap
p
r
o
ac
h
es
elim
in
ate
th
e
n
ee
d
f
o
r
a
weig
h
tin
g
f
a
cto
r
.
Pre
v
iew
s
tu
d
y
[
8
]
,
p
r
o
p
o
s
e
a
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
b
ased
o
n
a
r
an
k
in
g
ap
p
r
o
ac
h
.
T
h
is
ap
p
r
o
ac
h
tr
an
s
f
o
r
m
s
th
e
co
s
t
f
u
n
ct
io
n
v
alu
es
o
f
s
tato
r
f
lu
x
lin
k
ag
e
a
n
d
to
r
q
u
e
f
o
r
ea
c
h
v
o
ltag
e
v
ec
to
r
in
to
r
an
k
in
g
v
alu
es.
I
t
th
en
id
en
tifie
s
v
ec
to
r
with
lo
west
av
er
ag
e
r
an
k
in
g
v
alu
e
as
th
e
id
ea
l
ch
o
i
ce
.
A
s
u
g
g
ested
s
o
lu
tio
n
f
o
r
d
e
cisi
o
n
-
m
ak
in
g
in
v
o
lv
es
s
u
b
s
titu
tin
g
th
e
weig
h
tin
g
elem
en
t
with
a
f
u
zz
y
a
p
p
r
o
ac
h
.
I
n
itially
,
a
m
em
b
er
s
h
ip
f
u
n
ctio
n
tr
an
s
f
o
r
m
s
th
e
c
o
s
t
f
u
n
c
tio
n
f
o
r
s
tato
r
f
lu
x
lin
k
ag
e
a
n
d
t
o
r
q
u
e
in
to
th
e
r
a
n
g
e
o
f
(
0
,
1
)
.
Af
ter
t
h
is
tr
an
s
f
o
r
m
atio
n
,
we
ca
n
u
s
e
v
ar
io
u
s
d
ec
is
io
n
f
u
n
ctio
n
s
to
d
eter
m
in
e
t
h
e
o
p
tim
al
v
o
ltag
e
v
ec
to
r
[
7
]
.
I
g
n
o
r
e
th
e
weig
h
tin
g
f
ac
t
o
r
i
n
[
7
]
-
[
9
]
,
[
1
1
]
,
as
it
in
cr
ea
s
es
b
o
t
h
th
e
co
n
tr
o
l c
o
m
p
lex
d
esig
n
s
an
d
c
o
m
p
u
tatio
n
al
b
u
r
d
en
.
T
h
e
co
s
t
f
u
n
ctio
n
,
s
im
ilar
to
d
ea
d
b
ea
t
c
o
n
tr
o
l,
en
d
s
th
e
s
u
b
s
eq
u
en
t
c
o
n
tr
o
l
p
er
io
d
b
y
r
e
m
o
v
in
g
th
e
weig
h
tin
g
elem
e
n
t
to
r
e
d
u
ce
e
r
r
o
r
s
in
tr
ac
k
in
g
v
ar
iab
les.
Dea
d
b
ea
t
f
l
u
x
an
d
to
r
q
u
e
co
n
tr
o
l
n
o
r
m
alize
s
s
tato
r
f
lu
x
lin
k
ag
e
an
d
to
r
q
u
e
r
ef
er
e
n
ce
s
to
a
s
in
g
le
v
ec
to
r
.
T
h
is
ap
p
r
o
ac
h
was
d
is
cu
s
s
ed
in
[
1
6
]
,
[
1
7
]
.
I
n
s
tead
o
f
r
ed
u
cin
g
f
lu
x
lin
k
ag
e
an
d
to
r
q
u
e
er
r
o
r
s
,
th
e
o
b
jectiv
e
s
h
o
u
ld
b
e
to
r
ed
u
ce
s
tato
r
f
lu
x
lin
k
ag
e
v
ec
t
o
r
er
r
o
r
s
.
g
en
er
alize
d
s
eq
u
en
tial
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
G
-
SMPC
)
[
1
]
m
ain
tain
s
p
er
f
o
r
m
an
ce
r
e
g
ar
d
less
o
f
co
s
t
f
u
n
ctio
n
ev
alu
atio
n
s
eq
u
en
ce
.
G
-
SMPC
r
an
k
s
co
n
tr
o
l
o
b
jec
tiv
es
b
y
c
o
s
t
f
u
n
ctio
n
ev
alu
at
io
n
s
eq
u
e
n
ce
,
with
th
e
f
ir
s
t
f
u
n
ctio
n
b
ein
g
m
o
s
t
ess
en
tial.
Un
lik
e
p
r
io
r
itized
tech
n
iq
u
es,
"e
v
en
-
h
an
d
e
d
"
s
eq
u
en
tial
p
r
ed
ictiv
e
co
n
tr
o
l
as
p
r
o
p
o
s
ed
in
[
1
8
]
,
d
y
n
am
ically
ch
a
n
g
e
th
e
co
n
tr
o
l
o
b
jectiv
es.
T
h
is
m
eth
o
d
u
s
es
m
o
r
e
p
r
o
ce
s
s
o
r
r
eso
u
r
ce
s
an
d
less
cu
s
to
m
izab
le
d
u
e
to
its
er
r
o
r
ev
alu
atio
n
te
r
m
.
R
ec
en
t
r
esear
ch
h
as
p
r
o
p
o
s
ed
th
e
u
s
e
o
f
s
eq
u
en
tial
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
SMPC
)
to
eli
m
in
ate
th
e
n
ee
d
f
o
r
a
weig
h
tin
g
f
ac
to
r
in
m
o
d
el
p
r
ed
ictiv
e
c
o
n
tr
o
l
(
M
PC
)
.
T
h
is
ap
p
r
o
ac
h
in
itially
e
v
alu
ates
th
e
t
o
r
q
u
e
co
s
t
f
u
n
ctio
n
,
s
elec
tin
g
th
e
tw
o
v
ec
to
r
s
with
th
e
s
m
allest
to
r
q
u
e
er
r
o
r
s
f
r
o
m
all
p
o
s
s
ib
le
v
ec
to
r
s
.
T
h
ese
two
v
ec
to
r
s
ar
e
t
h
en
ass
ess
ed
b
y
a
s
ec
o
n
d
ar
y
co
s
t f
u
n
ctio
n
t
o
id
e
n
tify
th
e
o
n
e
th
at
m
in
im
izes th
e
f
lu
x
d
is
cr
ep
an
c
y
.
T
h
is
h
ier
ar
ch
ical
s
tr
u
ctu
r
e
is
s
tr
aig
h
tf
o
r
war
d
an
d
r
em
o
v
e
s
th
e
n
ec
ess
ity
f
o
r
a
wei
g
h
ti
n
g
co
ef
f
icien
t
[
1
2
]
.
Ho
wev
er
,
if
th
e
d
esig
n
p
r
io
r
i
tizes
m
in
im
izin
g
f
lu
x
tr
ac
k
in
g
er
r
o
r
s
as
th
e
p
r
im
ar
y
co
s
t
f
u
n
ctio
n
,
th
e
s
tab
le
o
p
er
atio
n
ac
r
o
s
s
th
e
en
tire
s
p
ee
d
r
an
g
e
is
u
n
ce
r
tain
.
I
n
o
t
h
er
wo
r
d
s
,
th
e
p
r
io
r
SMPC
i
s
n
o
t
a
u
n
iv
er
s
ally
ap
p
licab
le
m
et
h
o
d
an
d
is
ef
f
e
ctiv
e
o
n
l
y
in
s
p
ec
if
ic
c
o
n
d
iti
o
n
s
.
Ad
d
itio
n
ally
,
th
e
u
s
e
o
f
a
two
-
lev
el
v
o
ltag
e
s
o
u
r
ce
in
v
er
te
r
r
esu
lts
in
h
ig
h
er
lev
els o
f
to
tal
h
a
r
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
.
Pre
v
iew
s
tu
d
y
[
1
4
]
,
a
p
ar
allel
p
r
ed
ictiv
e
to
r
q
u
e
co
n
tr
o
l (
PP
T
C
)
m
eth
o
d
th
at
elim
in
ates th
e
n
ee
d
f
o
r
a
weig
h
tin
g
f
ac
to
r
was
in
tr
o
d
u
c
ed
.
T
h
e
tech
n
iq
u
e
o
p
tim
izes
b
o
th
to
r
q
u
e
an
d
f
lu
x
co
s
t
f
u
n
ctio
n
s
in
a
p
ar
allel
co
n
f
ig
u
r
atio
n
co
n
c
u
r
r
en
tly
,
th
er
eb
y
p
r
ev
e
n
tin
g
th
e
r
eq
u
ir
e
m
en
t
f
o
r
a
weig
h
tin
g
f
ac
to
r
.
H
o
wev
er
,
th
is
m
eth
o
d
r
esu
lts
in
an
in
cr
ea
s
ed
co
m
p
u
t
atio
n
al
co
m
p
lex
ity
.
T
h
er
ef
o
r
e,
t
h
is
p
ap
e
r
in
tr
o
d
u
ce
s
a
s
eq
u
en
tial
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
SMPC
)
with
a
5
-
lev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
(
5
L
C
HB
M)
in
v
er
ter
.
T
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
s
im
u
ltan
eo
u
s
ly
o
p
tim
izes
to
r
q
u
e
a
n
d
f
lu
x
co
s
t
f
u
n
ctio
n
s
in
a
s
eq
u
en
tial
co
n
f
ig
u
r
atio
n
,
th
er
eb
y
elim
in
ati
n
g
th
e
r
eq
u
ir
em
en
t
f
o
r
a
weig
h
tin
g
f
ac
to
r
an
d
r
ed
u
ce
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
.
A
cr
itical
asp
ec
t
o
f
th
is
m
eth
o
d
is
its
ab
ilit
y
to
k
ee
p
th
e
to
r
q
u
e
an
d
f
lu
x
tr
ac
k
i
n
g
er
r
o
r
s
with
in
p
r
ed
e
f
in
ed
lim
it
s
.
T
h
e
r
em
ain
d
er
o
f
th
e
p
ap
e
r
is
o
r
g
an
ized
as
f
o
llo
ws:
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
with
5
L
ev
el
-
C
HB
MI
is
d
is
cu
s
s
ed
in
s
ec
t
io
n
2
.
T
h
e
co
m
p
ar
is
o
n
o
f
p
r
o
p
o
s
ed
m
eth
o
d
with
DT
C
-
5
L
C
HB
I
m
eth
o
d
o
lo
g
y
is
p
r
e
s
en
ted
in
s
ec
tio
n
3
.
Simu
latio
n
r
esu
lts
ar
e
s
h
o
wca
s
ed
i
n
s
ec
tio
n
4
.
Sectio
n
5
co
n
clu
d
es th
e
p
ap
er
.
2.
P
RO
P
O
SE
D
CO
NT
RO
L
S
T
RAT
E
G
Y
WI
T
H
5
L
E
V
E
L
-
CH
B
M
I
T
h
is
s
ec
tio
n
d
escr
ib
es
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
(
s
eq
u
e
n
tial
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
SMPC
)
)
with
a
5
-
lev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
v
e
r
ter
(
C
H
B
M)
to
d
r
i
v
e
a
th
r
ee
-
p
h
ase
i
n
d
u
ctio
n
m
o
t
o
r
i
n
r
eg
u
latin
g
s
p
ee
d
,
f
lu
x
,
to
r
q
u
e,
s
tato
r
cu
r
r
en
t
,
a
n
d
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
To
r
g
u
e
a
n
d
flu
x
r
ip
p
le
mitig
a
t
io
n
tech
n
iq
u
e
u
s
in
g
m
u
lti
-
leve
l in
ve
r
ter fo
r
…
(
A
b
o
b
a
ke
r
K
ikki
A
b
o
b
a
ke
r
)
289
2
.
1
.
Ca
s
ca
ded H
-
bridg
e
m
ultilev
el
inv
er
t
er
A
m
u
ltil
ev
el
ca
s
ca
d
ed
H
-
b
r
i
d
g
e
(
C
HB
M)
in
v
er
ter
o
f
f
er
s
n
u
m
er
o
u
s
b
e
n
ef
its
co
m
p
ar
e
d
to
m
u
ltil
ev
el
n
eu
tr
al
p
o
in
t
-
clam
p
e
d
a
n
d
m
u
ltil
ev
el
f
ly
in
g
ca
p
ac
ito
r
s
in
v
er
ter
s
.
T
h
e
C
HB
M
in
v
er
ter
is
m
o
d
u
lar
a
n
d
m
o
r
e
s
tr
aig
h
tf
o
r
war
d
t
o
m
an
ag
e
d
u
e
to
th
e
u
n
if
o
r
m
s
tr
u
ctu
r
e
o
f
e
ac
h
ce
ll.
Ad
d
itio
n
ally
,
it
en
a
b
l
es
ac
h
iev
in
g
a
h
ig
h
n
u
m
b
er
o
f
lev
els
with
a
m
in
i
m
al
q
u
an
tity
o
f
r
eq
u
ir
e
d
co
m
p
o
n
en
ts
.
T
h
ese
co
m
p
o
n
en
ts
h
elp
r
ed
u
ce
s
witch
in
g
lo
s
s
es
in
th
e
d
ev
ices,
en
h
an
ci
n
g
b
o
th
th
e
r
eliab
ilit
y
an
d
ef
f
icien
cy
o
f
th
e
cir
c
u
it.
C
o
n
s
eq
u
en
tly
,
th
is
to
p
o
lo
g
y
is
ex
ten
s
iv
ely
em
p
lo
y
e
d
in
in
d
u
s
tr
ial
ap
p
licatio
n
s
,
p
ar
ticu
lar
l
y
in
p
h
o
to
v
o
ltaic
s
y
s
tem
s
[
1
9
]
.
Fig
u
r
e
1
s
h
o
ws
a
th
r
ee
-
p
h
ase
5
-
lev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
(
C
H
B
M)
in
v
er
ter
.
I
n
th
is
c
o
n
f
ig
u
r
a
tio
n
,
ea
ch
p
h
ase
co
m
p
r
is
es
o
f
s
ev
er
al
p
o
wer
ce
lls
s
er
ially
ar
r
an
g
ed
wh
er
e
ea
ch
p
o
wer
ce
ll
is
a
s
in
g
le
-
p
h
ase
H
-
b
r
id
g
e
in
v
er
ter
.
I
t
is
ass
u
m
ed
th
at
ea
c
h
p
h
ase
co
n
tain
s
'
n
'
n
u
m
b
er
o
f
s
u
ch
ce
lls
,
an
d
ea
ch
ce
ll
is
s
u
p
p
lie
d
b
y
a
s
ep
ar
ate
d
c
s
o
u
r
ce
,
d
en
o
ted
as
V
_
d
c.
T
h
e
p
o
wer
s
witch
es
with
in
ea
ch
ce
ll
p
r
o
d
u
ce
th
r
ee
d
if
f
er
e
n
t
v
o
ltag
e
lev
els:
V_
d
c,
0
,
an
d
〖
-
V_
d
c,
wh
ich
c
o
r
r
esp
o
n
d
to
th
e
ce
ll
s
tates
{1
,
0
,
−1
}
r
esp
ec
tiv
ely
[
2
0
]
,
[
2
1
]
.
T
h
e
o
v
er
all
v
o
ltag
e
lev
el
o
f
ea
ch
p
h
ase
is
th
e
ag
g
r
eg
ate
o
f
th
e
v
o
ltag
e
lev
els o
f
all
its
ce
lls
g
iv
en
as
(
1
)
.
S
x
=
∑
n
i
=
0
S
xi
(
1
)
T
h
e
to
tal
p
o
s
s
ib
le
n
u
m
b
er
o
f
v
o
ltag
e
lev
els f
o
r
ea
c
h
p
h
ase
ca
n
b
e
ex
p
r
ess
ed
as
(
2
)
.
=
2
+
1
(
2
)
T
h
e
v
o
ltag
es f
o
r
ea
ch
p
h
ase
o
f
th
e
in
v
er
ter
ar
e
d
eter
m
in
ed
th
r
o
u
g
h
(
3
)
-
(
5
)
.
=
[
(
12
−
22
)
+
(
11
−
21
)
]
(
3
)
=
[
(
12
−
22
)
+
(
11
−
21
)
]
(
4
)
=
[
(
12
−
22
)
+
(
11
−
21
)
]
(
5
)
T
h
e
v
o
ltag
e
i
n
th
e
d
−
q
f
r
a
m
e
i
s
ex
p
r
ess
ed
as
(
6
)
an
d
(
7
)
.
=
1
3
(
2
−
−
)
(
6
)
=
1
√
3
(
−
)
(
7
)
Fig
u
r
e
1
.
T
h
r
ee
-
p
h
ase
5
-
lev
el
C
HB
in
v
er
ter
Vb
Vc
CE
L
L
2
CE
L
L
1
Vd
c
2
Vd
c
1
Vd
c
2
Vd
c
1
S
b11
S
b21
S
b31
S
b41
S
b12
S
b22
S
b32
S
b42
S
c
11
S
c
31
S
c
21
S
c
41
S
c
12
S
c
22
S
c
32
S
c
41
C
E
LL
1
C
E
LL
2
CE
L
L
2
CE
L
L
1
M
Va
Vd
c
2
Vd
c
1
S
a11
S
a21
S
a31
S
a41
S
a
1
2
S
a22
S
a32
S
a42
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
287
-
297
290
I
n
a
m
u
ltil
ev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
te
r
,
m
u
ltip
le
co
m
b
i
n
atio
n
s
o
f
s
witch
in
g
s
tates
ca
n
p
r
o
d
u
ce
id
en
tical
v
o
ltag
e
v
ec
to
r
s
.
T
h
er
ef
o
r
e,
th
e
c
o
u
n
t
o
f
u
n
iq
u
e,
n
o
n
r
ed
u
n
d
an
t
v
o
lta
g
e
v
ec
to
r
s
,
ca
n
b
e
ca
lcu
lated
u
s
in
g
(
8
)
,
wh
e
r
e
n
is
th
e
ce
ll
n
u
m
b
e
r
p
er
p
h
ase.
T
h
e
th
r
ee
-
p
h
ase
5
L
C
HB
MI
u
tili
ze
d
in
th
is
r
esear
ch
,
1
2
5
p
o
ten
tial
s
witch
in
g
s
tates
wi
th
in
th
e
s
tatic
d
-
q
co
o
r
d
in
ate
s
y
s
tem
.
T
h
ese
s
witch
in
g
s
tates
co
r
r
esp
o
n
d
to
6
1
d
if
f
er
en
t
v
o
ltag
e
v
ec
to
r
s
[
2
2
]
.
=
12
2
+
6
+
1
(
8
)
2
.
2
.
M
a
t
hema
t
ica
l
m
o
del o
f
ind
uct
io
n m
o
t
o
r
T
h
e
s
tato
r
f
lu
x
is
g
e
n
er
ated
th
r
o
u
g
h
co
u
p
lin
g
o
f
s
tato
r
cu
r
r
en
t a
n
d
r
o
t
o
r
c
u
r
r
e
n
t w
h
ile
th
e
c
o
u
p
lin
g
o
f
r
o
to
r
cu
r
r
en
t
an
d
s
tato
r
cu
r
r
e
n
t
g
en
er
ates
th
e
r
o
to
r
f
lu
x
o
f
a
t
h
r
ee
-
p
h
ase
in
d
u
ctio
n
m
o
to
r
.
T
h
e
f
lu
x
eq
u
atio
n
is
as
(
9
)
an
d
(
1
0
)
.
=
+
(
9
)
=
+
(
1
0
)
W
h
er
e
is
th
e
s
tato
r
f
lu
x
an
d
d
en
o
te
th
e
r
o
to
r
f
lu
x
.
Similar
ly
,
an
d
r
e
p
r
esen
t
t
h
e
s
tato
r
cu
r
r
en
t
a
n
d
r
o
to
r
c
u
r
r
en
t,
r
esp
ec
tiv
ely
.
T
h
e
ter
m
s
,
,
an
d
r
ef
er
to
th
e
s
tato
r
,
r
o
to
r
,
an
d
m
u
tu
al
i
n
d
u
ctan
ce
s
,
r
esp
ec
tiv
ely
.
T
h
e
s
y
s
tem
m
o
d
el
as
ar
ticu
lat
ed
in
a
s
tatio
n
ar
y
f
r
am
e
d
elin
e
ate
as
(
1
1
)
-
(
1
4
)
wh
er
e
is
th
e
r
o
to
r
's
an
g
u
lar
v
elo
city
.
=
⋅
+
(
1
1
)
0
=
⋅
+
−
⋅
⋅
(
1
2
)
=
3
2
|
⊗
|
(
1
3
)
=
−
(
1
4
)
I
n
th
is
co
n
tex
t,
is
th
e
s
tato
r
v
o
ltag
e
v
ec
to
r
,
wh
ile
an
d
in
d
icate
th
e
eq
u
iv
ale
n
t
s
tato
r
an
d
r
o
to
r
r
esis
tan
ce
s
,
r
esp
ec
tiv
ely
.
⊗
r
ep
r
esen
ts
cr
o
s
s
p
r
o
d
u
ct
o
f
t
wo
co
m
p
lex
v
ec
to
r
s
.
T
h
e
l
o
ad
to
r
q
u
e
an
d
elec
tr
o
m
ag
n
etic
to
r
q
u
e
a
r
e
r
ep
r
esen
ted
b
y
an
d
r
esp
ec
tiv
ely
,
wh
ile
is
th
e
elec
tr
ical
s
p
ee
d
.
2
.
3
.
P
re
dict
io
n
e
qu
a
t
io
ns
Fo
r
th
e
ev
alu
atio
n
o
f
to
r
q
u
e
an
d
f
lu
x
co
s
t
f
u
n
ctio
n
s
,
ac
cu
r
ate
p
r
ed
ictio
n
o
f
to
r
q
u
e
a
n
d
f
lu
x
co
s
t
f
u
n
ctio
n
s
is
ess
en
tial
f
o
r
all
p
o
s
s
ib
le
s
witch
in
g
s
tate
s
.
T
h
e
to
r
q
u
e
an
d
s
tato
r
f
lu
x
p
r
ed
ictio
n
s
ar
e
d
er
iv
ed
u
s
in
g
d
is
cr
ete
-
tim
e
eq
u
atio
n
s
o
f
f
th
e
r
o
to
r
f
lu
x
ca
lcu
latio
n
ca
n
b
e
d
er
iv
e
d
f
r
o
m
th
e
eq
u
i
v
alen
t
(
1
0
)
an
d
(
1
2
)
wh
ich
d
escr
ib
ed
th
e
r
o
to
r
d
y
n
am
ics
o
f
an
I
M
with
i
n
a
r
o
tatin
g
r
e
f
e
r
en
ce
f
r
am
e,
alig
n
ed
with
th
e
r
o
to
r
win
d
in
g
.
T
h
is
d
er
iv
atio
n
y
ield
s
th
e
v
alu
e
o
f
Ψ
r
.
Ψ
r
+
d
Ψ
r
d
=
i
s
(
1
5
)
W
h
er
e,
=
⁄
d
en
o
tes
th
e
r
o
t
o
r
tim
e
co
n
s
tan
t.
B
y
ap
p
ly
in
g
th
e
f
o
r
war
d
-
E
u
ler
d
is
cr
etiza
tio
n
te
ch
n
iq
u
e
an
d
tak
in
g
as
th
e
s
am
p
lin
g
tim
e,
th
e
d
is
cr
ete
-
tim
e
e
q
u
atio
n
f
o
r
esti
m
atin
g
th
e
r
o
to
r
f
lu
x
is
ar
ticu
lated
is
g
iv
en
b
y
(
1
6
)
.
=
(
1
−
)
−
1
+
−
1
(
1
6
)
B
y
u
s
in
g
(
9
)
a
n
d
(
1
0
)
,
th
e
s
tato
r
f
lu
x
esti
m
atio
n
is
ac
h
iev
ed
u
s
in
g
(
1
7
)
.
Ψ
s
k
=
L
m
L
r
Ψ
r
k
+
(
1
−
L
m
2
L
s
L
r
)
i
s
k
(
1
7
)
Usi
n
g
(
1
1
)
,
th
e
s
tato
r
f
lu
x
p
r
e
d
ictio
n
is
f
o
u
n
d
b
y
u
tili
zin
g
th
e
f
o
r
war
d
-
E
u
ler
d
is
cr
etiza
tio
n
m
eth
o
d
as
(
1
8
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
To
r
g
u
e
a
n
d
flu
x
r
ip
p
le
mitig
a
t
io
n
tech
n
iq
u
e
u
s
in
g
m
u
lti
-
leve
l in
ve
r
ter fo
r
…
(
A
b
o
b
a
ke
r
K
ikki
A
b
o
b
a
ke
r
)
291
Ψ
s
+
1
=
Ψ
s
+
v
s
−
i
s
(
1
8
)
Fu
r
th
er
m
o
r
e
,
th
e
p
r
e
d
ictio
n
o
f
s
tato
r
cu
r
r
en
t
is
d
er
iv
ed
th
r
o
u
g
h
t
h
e
ap
p
licatio
n
o
f
t
h
e
f
o
r
war
d
-
E
u
ler
d
is
cr
etiza
tio
n
m
eth
o
d
,
as in
d
ic
ated
b
y
(
1
9
)
.
i
s
k
+
1
=
C
1
i
s
k
+
C
2
Ψ
s
k
+
T
s
L
σ
v
s
k
(
1
9
)
W
h
er
e,
=
(
+
(
)
2
)
is
th
e
eq
u
iv
ale
n
t
r
esis
tan
ce
as
r
ef
er
r
e
d
to
th
e
s
tato
r
,
with
1
=
(
1
−
(
/
)
)
,
an
d
2
=
(
/
)
/
(
(
1
/
)
−
)
,
in
th
is
f
o
r
m
u
latio
n
,
is
th
e
leak
ag
e
in
d
u
ctan
ce
,
is
th
e
r
o
to
r
tim
e
co
n
s
tan
t,
an
d
σ
is
th
e
to
tal
leak
ag
e
f
ac
to
r
as
s
h
o
wn
in
(
2
0
)
an
d
(
2
1
)
r
esp
ec
tiv
ely
.
=
(
2
0
)
=
(
2
1
)
T
h
e
p
r
e
d
ictio
n
o
f
to
r
q
u
e
is
b
ased
o
n
p
r
ed
icatio
n
o
f
s
tato
r
f
lu
x
an
d
s
tato
r
c
u
r
r
e
n
t,
wh
ich
d
ef
in
ed
as in
(
2
2
)
.
+
1
=
3
2
|
Ψ
s
+
1
⊗
i
s
k
+
1
|
(
2
2
)
2
.
4
.
P
r
o
po
s
ed
co
ntr
o
l st
ra
t
e
g
y
Fig
u
r
e
2
s
h
o
ws
a
b
l
o
ck
d
ia
g
r
a
m
o
f
th
e
p
r
o
p
o
s
ed
in
d
u
ctio
n
m
ac
h
in
e
d
r
iv
es
s
y
s
tem
,
SMPC
with
5
-
lev
el
C
HB
M
in
v
er
ter
f
o
r
m
in
g
a
ca
s
ca
d
e
s
tr
u
ctu
r
e
f
o
r
m
an
ag
i
n
g
m
u
ltip
le
co
n
tr
o
l
o
b
jectiv
es.
T
h
e
s
ch
em
e
u
tili
ze
s
a
s
er
ies
o
f
co
s
t
f
u
n
ctio
n
s
,
ea
ch
t
ailo
r
ed
to
a
s
p
ec
if
i
c
co
n
tr
o
l
o
b
jectiv
e.
R
ath
er
th
an
a
p
p
ly
in
g
a
s
in
g
le
co
s
t
f
u
n
ctio
n
en
co
m
p
ass
in
g
v
ar
i
o
u
s
o
b
jectiv
es
co
n
n
ec
ted
th
r
o
u
g
h
a
weig
h
t
in
g
f
ac
to
r
,
th
e
a
p
p
r
o
ac
h
ad
d
r
ess
es
th
e
p
r
o
b
lem
b
y
em
p
lo
y
in
g
s
ep
ar
ate
co
s
t f
u
n
ctio
n
s
,
with
ea
ch
o
n
e
f
o
cu
s
ed
o
n
a
s
ep
ar
ate
co
n
tr
o
l o
b
je
ctiv
e.
I
t
is
im
p
o
r
tan
t
to
ac
k
n
o
wled
g
e
th
at
wh
en
im
p
lem
en
tin
g
th
e
p
r
ed
ictiv
e
co
n
tr
o
l
s
tr
ateg
y
,
th
er
e
is
n
ee
d
to
co
n
s
id
er
th
e
d
elay
i
n
ap
p
ly
i
n
g
th
e
o
p
tim
al
v
ec
t
o
r
.
T
h
is
is
d
u
e
to
th
e
f
ac
t
th
at
th
e
p
r
o
ce
s
s
es
o
f
m
ea
s
u
r
em
en
ts
,
d
ata
p
r
o
ce
s
s
in
g
,
an
d
o
p
tim
izat
io
n
alg
o
r
ith
m
s
ar
e
n
o
t
in
s
tan
tan
eo
u
s
.
T
o
o
f
f
s
et
th
is
d
elay
,
th
e
co
n
tr
o
l
v
ar
ia
b
les
o
u
g
h
t
to
b
e
f
o
r
ec
asted
f
o
r
th
e
f
u
tu
r
e
in
s
tan
t
(
k
+
2
)
.
T
o
ad
d
r
ess
th
is
d
elay
,
c
o
n
s
id
er
t
h
e
c
o
m
p
u
tatio
n
tim
e
an
d
im
p
lem
en
t
th
e
c
h
o
s
en
s
witch
i
n
g
s
tate
af
ter
th
e
f
o
llo
win
g
s
a
m
p
lin
g
in
s
tan
t.
T
h
e
c
o
n
tr
o
l
alg
o
r
ith
m
is
a
d
ju
s
ted
in
th
is
m
an
n
er
.
T
h
e
p
r
o
ce
s
s
in
v
o
lv
es
m
ea
s
u
r
in
g
i
s
an
d
,
ap
p
ly
in
g
th
e
s
witch
in
g
s
tate,
esti
m
atin
g
an
d
v
alu
es
at
tim
e
t
k+
1
,
p
r
ed
ictin
g
an
d
v
alu
es
f
o
r
th
e
n
ex
t
s
am
p
lin
g
in
s
tan
t
t
k+
2
,
ev
alu
atin
g
th
e
co
s
t
f
u
n
ctio
n
,
an
d
s
elec
tin
g
th
e
m
in
i
m
izin
g
s
witch
in
g
s
tate
[
2
3
]
.
Fig
u
r
e
2
.
Pro
p
o
s
ed
c
o
n
tr
o
l m
o
d
el
MP
C
w
T*
N
Vc
Va
Vb
S
b
22
CE
LL
1
CE
LL
2
CE
LL
2
CE
LL
1
CE
LL
1
CE
LL
1
Vd
c
1
Vd
c
2
Vd
c
1
Vdc
1
S
c
11
S
c
12
S
c
41
S
c
22
S
c
41
S
c
21
S
c
31
S
b
41
S
b
11
S
b
31
S
a
41
S
a
21
S
a
11
S
a
31
S
b
21
Vd
c
2
S
b
12
S
b
32
S
b
42
S
c
32
Vdc
2
S
a
12
S
a
22
S
a
32
S
a
42
S
t
a
t
or
/
R
ot
or
Fl
u
x
E
s
t
i
m
a
t
i
on
g
2
=
(
D
Y
)
²
5
-
L
E
V
E
L
M
L
I
IM
T
or
que
/
Fl
ux
P
r
e
di
c
t
i
o
n
g
1
=
(
DT
)
²
PI
w
MP
C
1
0
v
o
l
t
a
g
e
v
e
c
t
o
r
S
e
l
e
c
t
e
d
V
o
l
t
a
g
e
-
+
+
-
i
a
b
c
T
i
a
b
c
y
y*
1
2
3
4
5
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
287
-
297
292
I
n
Fig
u
r
e
2
,
th
e
d
if
f
er
e
n
ce
b
et
wee
n
th
e
r
ef
er
en
ce
s
p
ee
d
(
*
)
a
n
d
th
e
ac
tu
al
m
ea
s
u
r
ed
s
p
ee
d
(
)
is
f
ed
in
to
a
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
al
(
P
I
)
co
n
tr
o
ller
in
b
lo
ck
1
in
Fig
u
r
e
2
.
T
h
e
c
o
n
tr
o
ller
th
e
n
p
r
o
d
u
ce
s
th
e
r
ef
er
en
ce
to
r
q
u
e
(
T*
).
T
h
e
co
s
t f
u
n
cti
o
n
u
tili
ze
d
f
o
r
to
r
q
u
e
c
o
n
tr
o
l (
1
)
is
o
b
tain
ed
as
(
2
3
)
.
1
=
(
∗
−
+
2
)
2
(
2
3
)
W
h
er
e
+
2
r
ep
r
esen
ts
th
e
p
r
ed
icte
d
to
r
q
u
e,
d
eter
m
in
ed
as
(
2
4
)
.
+
2
=
3
2
|
Ψ
s
+
2
⊗
i
s
k
+
2
|
(
2
4
)
C
o
n
s
eq
u
en
tly
,
in
b
lo
ck
2
o
f
th
e
b
lo
ck
d
iag
r
am
in
Fig
u
r
e
2
,
1
is
co
m
p
u
ted
f
o
r
ea
c
h
o
f
th
e
6
1
d
if
f
er
en
t
v
o
ltag
e
v
ec
t
o
r
s
p
r
o
d
u
ce
d
b
y
t
h
e
in
v
er
te
r
.
Ho
wev
e
r
,
ten
v
o
lt
ag
e
v
ec
to
r
s
y
ield
in
g
th
e
lo
wes
t
v
alu
es
o
f
1
(
i.e
.
,
th
e
m
o
s
t
m
in
o
r
er
r
o
r
)
a
r
e
ch
o
s
en
f
o
r
th
e
s
u
b
s
eq
u
en
t
co
n
tr
o
l
s
tep
s
.
T
h
is
s
tep
alig
n
s
with
th
e
m
in
im
izatio
n
o
f
f
lu
x
er
r
o
r
,
ex
ec
u
ted
th
r
o
u
g
h
t
h
e
co
s
t
f
u
n
ctio
n
2
,
wh
ich
is
ass
o
ciate
d
with
th
e
f
lu
x
er
r
o
r
an
d
is
d
ef
in
ed
b
y
(
2
5
)
.
2
=
(
∗
−
|
+
2
|
)
2
(
2
5
)
W
h
er
e
+
2
r
ep
r
esen
ts
th
e
p
r
e
d
icted
f
lu
x
,
wh
ich
is
ca
lcu
lated
as
(
2
6
)
.
Ψ
s
k
+
2
=
Ψ
s
k
+
1
+
T
s
v
s
k
+
1
−
T
s
R
s
i
s
k
+
1
(
2
6
)
T
h
e
co
s
t
f
u
n
ctio
n
is
m
eth
o
d
ica
lly
ass
ess
ed
f
o
r
ea
ch
o
f
th
e
ten
v
o
ltag
e
v
ec
to
r
s
ch
o
s
en
in
t
h
e
p
r
ec
ed
in
g
to
r
q
u
e
c
o
n
tr
o
l
s
tep
.
Ultim
ately
,
th
e
v
o
ltag
e
v
ec
to
r
th
at
o
p
tim
ally
m
in
im
izes
2
is
d
eter
m
in
ed
an
d
s
u
b
s
eq
u
e
n
tly
s
u
p
p
lied
to
th
e
lo
ad
.
T
h
is
p
r
o
ce
s
s
is
d
ep
icted
in
b
lo
ck
3
o
f
Fig
u
r
e
2
.
B
lo
ck
4
in
Fig
u
r
e
2
s
h
o
ws
th
e
p
o
wer
cir
cu
it
o
f
th
e
5
-
lev
el
C
HB
M
in
v
er
ter
,
b
lo
ck
5
co
r
r
esp
o
n
d
s
to
(
1
6
)
an
d
(
1
7
)
f
o
r
esti
m
atin
g
f
lu
x
,
a
n
d
b
lo
ck
6
g
iv
es (
1
7
)
an
d
(
2
6
)
f
o
r
p
r
e
d
ictin
g
to
r
q
u
e
an
d
f
lu
x
.
T
h
e
f
lo
wch
ar
t o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l stra
teg
y
is
illu
s
tr
ated
i
n
Fig
u
r
e
3
(
s
ee
Ap
p
en
d
ix
)
.
T
h
e
s
tr
ateg
y
co
m
m
en
ce
s
b
y
m
o
n
ito
r
in
g
th
e
s
tato
r
cu
r
r
en
t
(
i
s
)
an
d
th
e
s
p
e
ed
at
a
s
p
ec
if
ied
s
am
p
lin
g
in
ter
v
al
d
en
o
te
d
as
(
k
)
,
as
illu
s
tr
ated
in
s
tep
1
.
T
h
e
v
o
ltag
e
v
ec
to
r
co
m
p
u
ted
d
u
r
in
g
th
e
p
r
ec
ed
in
g
s
am
p
lin
g
in
te
r
v
al
is
s
u
b
s
eq
u
en
tly
ap
p
lied
in
s
tep
2
.
Step
3
in
v
o
l
v
es th
e
esti
m
atio
n
o
f
b
o
th
th
e
s
tato
r
f
lu
x
an
d
r
o
t
o
r
f
l
u
x
at
th
e
s
p
ec
if
ied
s
am
p
lin
g
in
ter
v
al
k
.
Su
b
s
eq
u
en
tl
y
,
in
s
tep
4
,
th
e
p
ar
am
eter
1
is
co
m
p
u
te
d
f
o
r
all
6
1
v
o
ltag
e
v
ec
to
r
s
.
Step
5
in
v
o
l
v
es
th
e
s
elec
tio
n
o
f
ten
v
o
ltag
e
v
ec
to
r
s
ch
ar
ac
ter
ized
b
y
th
e
s
m
allest
v
alu
es
o
f
1
.
I
n
s
tep
6
,
th
e
p
ar
am
eter
1
i
s
co
m
p
u
ted
f
o
r
th
e
ten
p
r
ev
io
u
s
ly
s
elec
ted
v
o
ltag
e
v
ec
to
r
s
.
Ultim
ately
,
in
s
tep
7
,
th
e
v
o
ltag
e
v
ec
to
r
th
a
t
m
in
im
izes th
e
p
ar
am
eter
1
is
ch
o
s
en
to
b
e
a
p
p
lied
in
t
h
e
s
u
b
s
e
q
u
en
t sam
p
lin
g
in
ter
v
al
[
2
4
]
.
3.
CO
M
P
ARI
SO
N
WI
T
H
DT
C
-
5
L
CH
B
I
M
E
T
H
O
DO
L
O
G
Y
T
o
d
eter
m
in
e
th
e
p
o
s
itiv
e
attr
ib
u
tes
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
,
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
o
d
el
is
co
m
p
ar
ed
wi
th
th
at
o
f
DT
C
-
5
L
C
HB
MI
.
A
s
ig
n
if
ican
t
d
if
f
er
en
ce
ex
is
ts
b
etwe
en
th
e
SMPC
-
5
L
C
HB
MI
an
d
DT
C
-
5
L
C
HB
MI
as seen
f
r
o
m
t
h
e
two
b
lo
ck
d
iag
r
am
s
Fig
u
r
e
s
2
an
d
4
.
I
n
DT
C
-
5
L
C
HB
,
eig
h
t
lev
els o
f
h
y
s
ter
esis
ar
e
u
s
ed
f
o
r
to
r
q
u
e
an
d
f
iv
e
h
y
s
ter
esis
u
s
ed
f
o
r
t
h
e
f
lu
x
.
3
.
1
.
DT
C
-
5
L
CH
B
M
I
I
n
tr
a
d
itio
n
al
d
ir
ec
t
to
r
q
u
e
co
n
tr
o
l
(
DT
C
)
,
s
elec
tin
g
th
e
r
ig
h
t
v
o
ltag
e
v
ec
t
o
r
f
r
o
m
a
2
-
lev
el
in
v
er
te
r
r
eg
u
lates
f
lu
x
an
d
to
r
q
u
e.
T
h
i
s
s
o
r
t
o
f
in
v
er
ter
ap
p
lies
th
e
s
am
e
v
o
ltag
e
v
ec
to
r
r
e
g
ar
d
less
o
f
to
r
q
u
e
an
d
f
lu
x
er
r
o
r
d
u
e
to
its
lim
ited
v
o
ltag
e
v
ec
to
r
s
et.
T
h
e
co
n
tr
o
l
s
tr
u
c
tu
r
e
u
s
es
h
y
s
ter
esis
co
n
tr
o
ller
s
,
a
lo
o
k
-
u
p
tab
le,
a
5
-
lev
el
ca
s
ca
d
e
d
H
-
b
r
id
g
e
m
u
l
tilev
el
in
v
er
ter
(
C
HB
MI
)
,
f
lu
x
an
d
to
r
q
u
e
esti
m
ato
r
s
.
T
h
ese
esti
m
ato
r
s
esti
m
ate
to
r
q
u
e,
f
lu
x
,
an
d
s
ec
to
r
u
s
in
g
v
o
ltag
e
an
d
c
u
r
r
e
n
t
d
ata.
E
ig
h
t
-
lev
el
an
d
f
iv
e
-
lev
el
h
y
s
ter
esis
co
n
tr
o
ller
s
r
ep
r
esen
t
to
r
q
u
e
an
d
f
lu
x
co
n
t
r
o
ller
s
.
T
h
e
to
r
q
u
e,
f
lu
x
,
an
d
s
ec
to
r
s
tatu
s
es
in
th
e
lo
o
k
-
u
p
tab
le
d
eter
m
in
e
th
e
in
v
er
ter
v
o
ltag
e
v
ec
to
r
[
2
2
]
.
A
5
-
lev
el
ca
s
ca
d
ed
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
v
er
ter
(
C
HB
MI
)
p
r
o
v
id
es
m
o
r
e
to
r
q
u
e
an
d
f
lu
x
r
eg
u
latio
n
v
o
ltag
e
v
ec
t
o
r
p
o
s
s
ib
ilit
ies.
I
n
cr
ea
s
ed
f
le
x
ib
ilit
y
im
p
r
o
v
e
s
d
ir
ec
t
to
r
q
u
e
co
n
tr
o
l'
s
d
y
n
am
ic
p
er
f
o
r
m
an
ce
.
Fig
u
r
e
4
s
h
o
ws
th
e
s
y
s
tem
b
lo
ck
d
iag
r
am
.
A
5
-
lev
el
C
H
B
MI
h
as
m
an
y
v
o
ltag
e
v
ec
to
r
s
elec
tio
n
o
p
tio
n
s
,
th
er
ef
o
r
e,
a
c
o
n
tr
o
l
s
y
s
tem
is
n
ee
d
ed
to
ch
o
o
s
e
th
e
o
p
tim
al
v
o
ltag
e
v
ec
to
r
s
f
o
r
D
T
C
d
r
iv
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
.
T
o
d
eter
m
in
e
th
e
o
p
tim
al
v
ec
to
r
,
th
e
f
lu
x
an
d
to
r
q
u
e
h
y
s
ter
esis
co
m
p
ar
ato
r
s
m
u
s
t
h
av
e
m
o
r
e
lev
els th
an
th
e
s
tan
d
ar
d
2
-
lev
e
l in
v
er
ter
-
b
ased
DT
C
[
2
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
To
r
g
u
e
a
n
d
flu
x
r
ip
p
le
mitig
a
t
io
n
tech
n
iq
u
e
u
s
in
g
m
u
lti
-
leve
l in
ve
r
ter fo
r
…
(
A
b
o
b
a
ke
r
K
ikki
A
b
o
b
a
ke
r
)
293
Fig
u
r
e
4
.
B
lo
ck
d
iag
r
am
o
f
D
T
C
-
5
L
C
HB
I
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
co
n
tr
o
l
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
s
eq
u
en
tial
m
o
d
el
p
r
ed
ictiv
e
co
n
t
r
o
l
(
SMPC
)
.
T
h
e
s
im
u
latio
n
is
p
e
r
f
o
r
m
ed
with
MA
T
L
AB
/Si
m
u
lin
k
s
im
u
latio
n
s
o
f
twar
e.
T
h
e
tar
g
et
s
y
s
tem
f
o
r
th
e
im
p
l
em
en
ted
c
o
n
tr
o
l
s
ch
em
e
i
s
a
n
in
d
u
ctio
n
m
o
to
r
d
er
iv
ed
b
y
5
-
l
ev
el
C
HB
in
v
er
ter
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
r
esu
lts
ar
e
co
m
p
ar
e
d
with
th
e
co
n
v
en
tio
n
al
DT
C
-
5
L
C
HB
I
r
esu
lts
.
Deta
il
s
o
f
th
e
p
ar
am
eter
s
u
s
ed
f
o
r
th
e
s
im
u
la
tio
n
ar
e
p
r
esen
ted
in
T
a
b
le
1
.
T
ab
le
1.
Sy
s
tem
p
ar
a
m
eter
s
P
a
r
a
me
t
e
r
V
a
l
u
e
P
a
r
a
me
t
e
r
V
a
l
u
e
S
t
a
t
o
r
r
e
s
i
st
a
n
c
e
, R
s
3
Ω
N
u
mb
e
r
o
f
p
o
l
e
s,
P
4
R
o
t
o
r
r
e
si
s
t
a
n
c
e
.
R
r
3
.
7
9
3
Ω
C
o
m
b
i
n
e
d
i
n
e
r
t
i
a
,
J
0
.
0
2
7
9
9
k
g
-
m
2
S
t
a
t
o
r
s
e
l
f
-
i
n
d
u
c
t
a
n
c
e
,
L
S
0
.
3
3
0
8
H
C
o
m
b
i
n
e
d
v
i
sc
o
u
s fr
i
c
t
i
o
n
,
B
0
.
0
1
0
2
5
N
.
m.s
R
o
t
o
r
sel
f
-
i
n
d
u
c
t
a
n
c
e
,
L
r
0
.
3
3
0
8
H
D
C
l
i
n
k
v
o
l
t
a
g
e
(
p
e
r
p
h
a
s
e
)
,
V
D
C
1
6
5
V
M
u
t
u
a
l
i
n
d
u
c
t
a
n
c
e
,
L
m
0
.
3
0
4
9
H
S
t
a
t
o
r
f
l
u
x
r
e
f
e
r
e
n
c
e
,
0
.
8
9
6
W
b
R
e
f
e
r
e
n
c
e
s
p
e
e
d
ω*
1
4
9
.
6
r
a
d
/
s
Lo
a
d
t
o
r
q
u
e
1
0
N
m
T
o
v
alid
ate
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
ch
em
e,
v
ar
io
u
s
p
ar
am
eter
s
v
ar
iatio
n
s
with
tim
e
ar
e
test
ed
as
s
h
o
wn
in
Fig
u
r
es
5
-
8
.
I
n
Fig
u
r
e
5
s
h
o
ws
th
at
co
m
p
ar
ativ
e
r
esu
lts
o
f
th
e
r
o
to
r
s
p
ee
d
o
f
b
o
th
co
n
tr
o
l
alg
o
r
ith
m
s
.
Fig
u
r
e
5
(
a)
s
h
o
w
s
d
y
n
am
ic
d
r
iv
e
s
p
ee
d
r
esp
o
n
s
e
f
r
o
m
r
est
to
1
4
9
.
6
r
a
d
/s
ec
an
d
co
m
p
ar
es
it
to
ω
-
r
ef
.
At
0
.
2
8
s
ec
o
n
d
s
,
th
e
r
o
t
o
r
s
p
ee
d
m
atc
h
es
th
e
r
ef
er
e
n
ce
s
p
ee
d
an
d
r
em
ain
s
th
e
s
am
e.
R
esu
lts
in
d
icate
th
at
th
e
co
n
t
r
o
l
m
ec
h
an
is
m
p
er
f
o
r
m
s
.
Fig
u
r
e
5
(
b
)
.
th
is
is
r
o
to
r
s
p
ee
d
v
a
r
iatio
n
.
B
o
th
co
n
tr
o
l
alg
o
r
ith
m
s
ac
h
ie
v
e
an
d
m
ain
tain
th
e
r
ef
e
r
en
ce
s
p
ee
d
with
m
in
im
al
v
ar
iatio
n
.
T
h
e
r
esear
ch
f
in
d
in
g
s
d
em
o
n
s
tr
ate
th
ei
r
s
p
ee
d
m
o
n
ito
r
in
g
ef
f
ec
tiv
en
ess
.
B
o
th
co
n
tr
o
l m
e
th
o
d
s
r
eg
u
late
s
p
ee
d
s
im
ilar
ly
in
th
e
s
y
s
tem
s
et
tin
g
s
an
d
p
ar
a
m
eter
s
ev
alu
ated
.
Fig
u
r
e
6
s
h
o
ws
th
e
v
ar
iatio
n
m
ag
n
etic
f
lu
x
.
Fig
u
r
e
6
(
a
)
s
h
o
ws
th
e
v
ar
iatio
n
m
a
g
n
etic
f
lu
x
(
f
lu
x
-
SMPC
)
an
d
th
e
r
ef
er
en
ce
f
lu
x
(
f
l
u
x
-
r
e
f
)
with
tim
e
f
o
r
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
m
ag
n
etic
f
lu
x
o
f
t
h
e
I
M
an
d
f
o
llo
ws th
e
r
ef
er
en
ce
f
lu
x
at
0
.
8
7
W
b
im
m
ed
iately
f
r
o
m
t
h
e
s
tar
tin
g
p
o
in
t
(
t
=
0
)
.
Fig
u
r
e
6
(
b
)
s
h
o
ws
th
e
v
ar
iati
o
n
in
f
lu
x
lin
k
ag
e
f
o
r
b
o
t
h
c
o
n
tr
o
l
m
eth
o
d
s
.
I
t
a
p
p
ea
r
s
t
h
at
th
er
e
a
r
e
v
is
ib
le
r
ip
p
les
in
th
e
f
lu
x
lin
k
ag
e
f
o
r
b
o
th
co
n
t
r
o
l
m
eth
o
d
s
.
Ho
wev
er
,
th
e
r
ip
p
les
ar
e
d
o
m
in
an
t
in
th
e
DT
C
m
eth
o
d
co
m
p
a
r
ed
to
SMPC
m
eth
o
d
.
T
h
e
DT
C
m
eth
o
d
ex
h
ib
its
lar
g
er
f
lu
x
o
s
cillatio
n
s
d
u
r
in
g
s
tead
y
-
s
tate
o
p
er
atio
n
,
in
d
icatin
g
a
h
ig
h
e
r
lev
el
o
f
r
ip
p
le
c
o
m
p
a
r
ed
t
o
th
e
SMPC
m
eth
o
d
,
wh
ic
h
s
h
o
ws
m
o
r
e
s
tab
le
b
eh
av
io
r
.
T
h
e
SMPC
co
n
tr
o
l
ap
p
ea
r
s
to
t
r
ac
k
th
e
r
ef
er
e
n
ce
f
lu
x
m
o
r
e
clo
s
ely
with
f
ewe
r
f
lu
ctu
atio
n
s
,
s
u
g
g
esti
n
g
s
u
p
e
r
io
r
p
er
f
o
r
m
a
n
ce
in
m
ain
tain
in
g
f
lu
x
s
tab
ilit
y
.
Ho
wev
er
,
b
o
th
s
tr
ateg
ies
g
en
er
ally
m
ain
tain
th
e
f
lu
x
at
th
e
d
esire
d
lev
el
af
te
r
th
e
in
itial
r
is
e,
en
s
u
r
in
g
ef
f
ec
ti
v
e
co
n
tr
o
l
a
f
ter
tr
an
s
ien
t
co
n
d
itio
n
s
.
I
n
s
tead
y
-
s
tate
o
p
er
atio
n
,
th
e
DT
C
m
eth
o
d
h
a
s
m
o
r
e
f
lu
x
o
s
cillatio
n
s
an
d
r
i
p
p
le
th
an
th
e
SMPC
m
eth
o
d
,
w
h
ich
is
m
o
r
e
s
tab
le.
T
h
e
SMPC
co
n
tr
o
l
tr
ac
k
s
t
h
e
r
ef
er
en
ce
f
lu
x
m
o
r
e
p
r
ec
is
ely
an
d
with
f
ewe
r
d
e
v
iatio
n
s
,
en
s
u
r
in
g
f
lu
x
s
tab
ilit
y
.
B
o
th
s
y
s
tem
s
u
s
u
ally
m
ain
tai
n
th
e
f
lo
w
at
th
e
in
ten
d
ed
lev
el
af
te
r
th
e
in
itial
in
cr
ea
s
e,
en
s
u
r
in
g
ef
f
icien
t
m
an
ag
em
en
t
d
u
r
in
g
ch
a
n
g
es i
n
co
n
d
itio
n
s
.
5
-
LEV
EL O
F
H
Y
S
TE
R
ES
I
S
C
O
N
TR
O
LLER
S
WI
T
C
H
I
N
G
S
E
L
E
C
T
I
O
N
T
A
B
L
E
IM
8
-
LEV
EL O
F
H
Y
S
TER
ES
I
S
C
O
N
TR
O
LLER
S
e
c
to
r
d
e
c
i
s
i
o
n
Es
ti
m
a
ti
o
n
o
f
To
r
q
u
a
n
d
F
l
u
x
5
-
l
e
ve
l
C
H
B
i
n
ve
r
t
e
r
+
+
-
-
T*
Te
y*
y
T
Y
ₑ
N
Vc
Va
Vb
S
b
22
CE
LL
1
CE
LL
2
CE
LL
2
CE
LL
1
CE
LL
1
CE
LL
1
Vd
c
1
Vd
c
2
Vd
c
1
Vdc
1
S
c
11
S
c
12
S
c
41
S
c
22
S
c
41
S
c
21
S
c
31
S
b
41
S
b
11
S
b
31
S
a
41
S
a
21
S
a
11
S
a
31
S
b
21
Vd
c
2
S
b
12
S
b
32
S
b
42
S
c
32
Vdc
2
S
a
12
S
a
22
S
a
32
S
a
42
PI
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
287
-
297
294
(
a)
(
b
)
Fig
u
r
e
5
.
Re
f
er
e
n
ce
s
p
ee
d
an
d
r
o
to
r
s
p
ee
d
: (
a)
r
ef
er
en
ce
s
p
ee
d
an
d
r
o
to
r
s
p
ee
d
o
f
SMPC
a
n
d
(
b
)
co
m
p
ar
is
o
n
r
esu
lts
b
etwe
en
SMPC
an
d
DT
C
(
a)
(
b
)
Fig
u
r
e
6
.
R
ef
er
e
n
ce
f
lu
x
an
d
f
lu
x
: (
a)
r
e
f
er
en
ce
s
tato
r
f
lu
x
a
n
d
s
tato
r
f
lu
x
o
f
SMPC
an
d
(
b
)
co
m
p
ar
is
o
n
r
esu
lts
b
etwe
en
SMPC
an
d
DT
C
Fu
r
th
er
m
o
r
e
,
Fig
u
r
e
7
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
r
esp
o
n
s
e,
F
ig
u
r
e
7
(
a)
illu
s
tr
ates
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
v
ar
iatio
n
with
tim
e.
As
s
ee
n
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
s
h
o
ws
a
d
y
n
am
ic
r
esp
o
n
s
e
at
th
e
in
itial
s
tag
e,
with
r
ap
id
ch
an
g
e
in
lev
els
th
at
in
clu
d
e
p
o
s
itiv
e
an
d
n
e
g
ati
v
e
v
alu
es,
in
a
tr
an
s
ien
t
r
esp
o
n
s
e
b
etwe
en
0
s
ec
t
o
0
.
2
8
s
ec
,
af
te
r
wh
ic
h
th
e
to
r
q
u
e
r
em
ain
s
s
tab
le.
At
1
s
ec
w
h
e
n
th
e
lo
ad
to
r
q
u
e
is
1
0
Nm
,
th
e
r
e
is
a
n
o
tab
le
s
p
ik
e
in
th
e
to
r
q
u
e
f
o
r
a
s
h
o
r
t d
u
r
atio
n
,
af
ter
wh
ich
th
e
t
o
r
q
u
e
r
etu
r
n
s
to
r
el
ativ
ely
s
tead
y
s
tate
w
ith
m
in
o
r
r
ip
p
les.
T
h
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
v
ar
iatio
n
f
o
r
th
e
two
co
n
tr
o
l
m
eth
o
d
s
is
s
h
o
wn
Fig
u
r
e
7
(
b
)
with
b
o
th
s
tr
ateg
ies
s
h
o
w
a
r
ap
i
d
in
c
r
e
ase
in
to
r
q
u
e
b
etwe
en
0
s
ec
an
d
0
.
3
s
ec
.
Af
ter
t
h
e
in
itial
tr
an
s
ien
t
p
e
r
io
d
at
(0
.
3
s
ec
to
1
s
ec
)
,
th
e
to
r
q
u
e
i
n
th
e
DT
C
s
h
o
ws
s
ig
n
if
ican
t
r
ip
p
les,
wh
ile
th
e
t
o
r
q
u
e
in
t
h
e
SMPC
i
s
s
m
o
o
th
er
an
d
h
as a
s
m
aller
s
tead
y
-
s
tate
r
ip
p
le.
I
n
th
e
tr
an
s
it st
ate
(
lo
ad
=
1
0
Nm
,
t =
1
s
ec
)
,
th
e
to
r
q
u
e
in
cr
ea
s
e
f
o
r
b
o
th
co
n
tr
o
l stra
teg
ies with
h
ig
h
e
r
t
o
r
q
u
e
r
ip
p
le
in
SMPC
th
an
in
DT
C
m
eth
o
d
.
T
h
e
s
im
u
latio
n
wav
ef
o
r
m
f
o
r
th
e
v
ar
iatio
n
o
f
s
tato
r
cu
r
r
en
t
with
tim
e
is
d
ep
icted
in
Fig
u
r
e
8
(
a)
.
At
s
tar
tin
g
,
th
er
e
is
a
n
o
ticea
b
le
s
p
ik
e
o
f
m
a
g
n
itu
d
e
2
0
A,
wh
ic
h
r
ap
i
d
ly
d
ec
r
ea
s
es
in
am
p
litu
d
e
o
f
2
.
8
A
f
r
o
m
0
.
3
s
ec
to
1
s
ec
.
af
ter
wh
ich
th
e
cu
r
r
en
t
in
cr
ea
s
ed
d
u
r
in
g
a
lo
a
d
s
tep
to
ar
o
u
n
d
6
A.
I
n
Fig
u
r
e
8
(
b
)
,
d
ep
icts
th
e
co
m
p
ar
ativ
e
wa
v
ef
o
r
m
o
f
p
ar
am
eter
s
f
o
r
th
e
p
r
o
p
o
s
ed
SMPC
-
5
L
C
H
B
an
d
DT
C
-
5
L
C
HB
.
T
h
e
s
tato
r
cu
r
r
en
t
v
ar
iatio
n
with
tim
e
f
o
r
th
e
two
-
co
n
tr
o
l
m
et
h
o
d
s
DT
C
a
n
d
SMPC
is
illu
s
tr
ated
in
Fig
u
r
e
8
(
b
)
.
At
o
b
s
er
v
ed
,
b
etwe
en
0
s
ec
to
0
.
3
s
ec
th
e
DT
C
an
d
SMPC
cu
r
r
en
t
s
h
o
w
a
lar
g
e
tr
an
s
ien
t
r
esp
o
n
s
e
with
h
ig
h
p
ea
k
s
,
a
f
ter
th
is
th
e
SMPC
cu
r
r
en
t
ap
p
ea
r
s
to
s
tab
ilize
m
o
r
e
r
ap
i
d
ly
in
to
a
s
tead
y
s
tate
with
f
ewe
r
r
ip
p
les
co
m
p
ar
ed
to
th
e
DT
C
cu
r
r
en
t.
SMPC
h
as
a
m
o
r
e
c
o
n
s
tan
t
cu
r
r
en
t
r
esp
o
n
s
e
an
d
lo
wer
r
ip
p
le
d
u
r
in
g
s
tead
y
s
tate,
s
u
g
g
esti
n
g
b
etter
cu
r
r
en
t c
o
n
tr
o
l th
a
n
DT
C
.
T
h
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
f
o
r
th
e
DT
C
-
5
L
C
HB
is
s
h
o
wn
in
Fig
u
r
e
9
.
As n
o
ted
,
th
e
DT
C
-
5
L
C
HB
h
as
a
T
HD
o
f
9
.
8
6
%,
wh
ich
is
m
o
r
e
wh
en
co
m
p
ar
ed
to
th
e
T
HD
o
f
th
e
p
r
o
p
o
s
ed
s
tr
ateg
y
5
.
6
8
%
.
I
n
s
u
m
m
ar
y
,
SMPC
im
p
r
o
v
es
s
p
ee
d
,
f
lu
x
co
n
tr
o
l,
h
ar
m
o
n
ic
d
is
to
r
tio
n
r
ed
u
ctio
n
,
a
n
d
s
m
o
o
th
er
s
tato
r
cu
r
r
en
t
b
eh
av
i
o
r
.
Ho
wev
er
,
DT
C
ex
ce
ls
at
p
r
o
v
id
in
g
a
m
o
r
e
co
n
s
tan
t
to
r
q
u
e
r
esp
o
n
s
e
with
f
ewe
r
f
lu
ctu
atio
n
s
.
SMP
C
p
er
f
o
r
m
s
b
etter
with
less
o
s
cillatio
n
an
d
b
et
ter
ef
f
icien
c
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
To
r
g
u
e
a
n
d
flu
x
r
ip
p
le
mitig
a
t
io
n
tech
n
iq
u
e
u
s
in
g
m
u
lti
-
leve
l in
ve
r
ter fo
r
…
(
A
b
o
b
a
ke
r
K
ikki
A
b
o
b
a
ke
r
)
295
(
a)
(
b
)
Fig
u
r
e
7
.
E
lectr
o
m
ag
n
etic
t
o
r
q
u
e
r
esp
o
n
s
e:
(
a)
to
r
q
u
e
o
f
SMPC
an
d
(
b
)
co
m
p
ar
is
o
n
r
esu
lts
b
etwe
en
SMPC
an
d
DT
C
(
a)
(
b
)
Fig
u
r
e
8
.
Stato
r
c
u
r
r
e
n
t: (
a)
s
tato
r
cu
r
r
e
n
t o
f
SMPC
an
d
(
b
)
co
m
p
ar
is
o
n
r
esu
lts
b
etwe
en
SMPC
an
d
DT
C
Fig
u
r
e
9
.
S
tato
r
c
u
r
r
e
n
t T
HD:
C
o
m
p
ar
ativ
e
r
esu
lts
b
etwe
en
SMPC
-
5
L
C
H
B
an
d
DT
C
-
5
L
C
HB
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
i
n
tr
o
d
u
ce
s
a
n
o
v
e
l
ap
p
r
o
ac
h
f
o
r
h
ig
h
-
p
er
f
o
r
m
a
n
ce
co
n
tr
o
l
o
f
an
in
d
u
ctio
n
m
o
to
r
.
T
h
e
ap
p
r
o
ac
h
u
s
es a
m
o
d
el
p
r
ed
ict
iv
e
co
n
t
r
o
l,
u
tili
zin
g
th
e
f
u
n
d
a
m
en
tal
eq
u
atio
n
s
o
f
th
e
m
ac
h
i
n
e
an
d
th
e
in
v
e
r
ter
.
Simu
latio
n
o
u
tco
m
es
v
alid
ate
th
at
th
is
s
tr
ateg
y
ef
f
ec
tiv
ely
r
ed
u
ce
s
co
n
tr
o
ls
to
r
q
u
e,
f
lu
x
a
n
d
th
e
T
HD
c
u
r
r
e
n
t
ar
o
u
n
d
5
.
6
8
%
co
m
p
ar
ed
with
DT
C
ar
o
u
n
d
9
.
8
6
%.
Fu
r
t
h
er
m
o
r
e,
t
h
e
u
s
e
o
f
weig
h
tin
g
f
ac
to
r
s
h
as
b
ee
n
elim
in
ated
in
th
e
r
eg
u
latio
n
o
f
f
lu
x
an
d
to
r
q
u
e
in
p
r
ed
ict
iv
e
co
n
tr
o
l.
A
n
o
v
el
SMPC
alg
o
r
ith
m
h
as
b
ee
n
d
ev
elo
p
e
d
f
o
r
5
L
-
C
HB
MI
3
p
h
ase
in
v
er
ter
.
T
h
e
p
r
o
p
o
s
ed
tec
h
n
iq
u
e
tak
es in
to
ac
co
u
n
t a
s
u
b
s
et
o
f
all
p
o
ten
tial
v
o
ltag
e
v
ec
to
r
s
,
with
th
e
aim
o
f
m
in
im
izin
g
th
e
n
u
m
b
er
o
f
co
m
p
u
tatio
n
s
r
eq
u
ir
e
d
an
d
en
s
u
r
i
n
g
its
co
m
p
atib
ilit
y
with
s
tan
d
ar
d
c
o
n
tr
o
l
p
latf
o
r
m
.
Ultim
ately
,
th
e
SMPC
-
5
L
C
HB
MI
's
f
in
d
in
g
s
af
f
ir
m
th
e
p
o
te
n
tial
o
f
th
is
s
tr
ateg
y
as a
n
ap
p
ea
lin
g
a
n
d
p
r
o
m
is
in
g
o
p
tio
n
f
o
r
h
ig
h
-
p
er
f
o
r
m
an
ce
AC
d
r
iv
es
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
287
-
297
296
AP
P
E
NDI
X
Fig
u
r
e
3
.
Flo
wch
ar
t
o
f
p
r
o
p
o
s
ed
co
n
tr
o
l sch
em
e
RE
F
E
R
E
NC
E
S
[
1
]
Y
.
Zh
a
n
g
,
B
.
Z
h
a
n
g
,
H
.
Y
a
n
g
,
M
.
N
o
r
a
mb
u
e
n
a
,
a
n
d
J.
R
o
d
r
i
g
u
e
z
,
“
G
e
n
e
r
a
l
i
z
e
d
s
e
q
u
e
n
t
i
a
l
m
o
d
e
l
p
r
e
d
i
c
t
i
v
e
c
o
n
t
r
o
l
o
f
I
M
d
r
i
v
e
s
w
i
t
h
f
i
e
l
d
-
w
e
a
k
e
n
i
n
g
a
b
i
l
i
t
y
,
”
I
E
EE
T
ra
n
sa
c
t
i
o
n
s
o
n
P
o
w
e
r
El
e
c
t
ro
n
i
c
s
,
v
o
l
.
3
4
,
n
o
.
9
,
p
p
.
8
9
4
4
–
8
9
5
5
,
S
e
p
.
2
0
1
9
,
d
o
i
:
1
0
.
1
1
0
9
/
TPE
L.
2
0
1
8
.
2
8
8
6
2
0
6
.
[
2
]
F
.
W
a
n
g
,
Z.
Z
h
a
n
g
,
X
.
M
e
i
,
J.
R
o
d
r
í
g
u
e
z
,
a
n
d
R
.
K
e
n
n
e
l
,
“
A
d
v
a
n
c
e
d
c
o
n
t
r
o
l
st
r
a
t
e
g
i
e
s
o
f
i
n
d
u
c
t
i
o
n
m
a
c
h
i
n
e
:
F
i
e
l
d
o
r
i
e
n
t
e
d
c
o
n
t
r
o
l
,
d
i
r
e
c
t
t
o
r
q
u
e
c
o
n
t
r
o
l
a
n
d
m
o
d
e
l
p
r
e
d
i
c
t
i
v
e
c
o
n
t
r
o
l
,
”
E
n
e
r
g
i
e
s
,
v
o
l
.
1
1
,
n
o
.
1
,
p
.
1
2
0
,
Ja
n
.
2
0
1
8
,
d
o
i
:
1
0
.
3
3
9
0
/
e
n
1
1
0
1
0
1
2
0
.
[
3
]
J.
H
o
l
t
z
,
“
A
d
v
a
n
c
e
d
P
W
M
a
n
d
p
r
e
d
i
c
t
i
v
e
c
o
n
t
r
o
l
—
a
n
o
v
e
r
v
i
e
w
,
”
I
EEE
T
r
a
n
s
a
c
t
i
o
n
s o
n
I
n
d
u
st
r
i
a
l
El
e
c
t
ro
n
i
c
s
,
v
o
l
.
6
3
,
n
o
.
6
,
p
p
.
3
8
3
7
–
3
8
4
4
,
Ju
n
.
2
0
1
6
,
d
o
i
:
1
0
.
1
1
0
9
/
T
I
E.
2
0
1
5
.
2
5
0
4
3
4
7
.
[
4
]
P
.
K
a
r
a
m
a
n
a
k
o
s
a
n
d
T.
G
e
y
e
r
,
“
M
o
d
e
l
p
r
e
d
i
c
t
i
v
e
t
o
r
q
u
e
a
n
d
f
l
u
x
c
o
n
t
r
o
l
mi
n
i
mi
z
i
n
g
c
u
r
r
e
n
t
d
i
st
o
r
t
i
o
n
s,
”
I
EE
E
T
ra
n
s
a
c
t
i
o
n
s
o
n
Po
w
e
r
El
e
c
t
r
o
n
i
c
s
,
v
o
l
.
3
4
,
n
o
.
3
,
p
p
.
2
0
0
7
–
2
0
1
2
,
M
a
r
.
2
0
1
9
,
d
o
i
:
1
0
.
1
1
0
9
/
TPEL.
2
0
1
8
.
2
8
6
2
2
5
3
.
[
5
]
H
.
T.
,
A
.
V
.
R
.
Te
j
a
,
G
.
B
h
u
v
a
n
e
sw
a
r
i
,
a
n
d
B
.
S
i
n
g
h
,
“
P
e
r
f
o
r
ma
n
c
e
e
n
h
a
n
c
e
me
n
t
i
n
a
mu
l
t
i
l
e
v
e
l
i
n
v
e
r
t
e
r
f
e
d
P
T
C
i
n
d
u
c
t
i
o
n
m
o
t
o
r
d
r
i
v
e
b
y
o
p
t
i
m
a
l
v
o
l
t
a
g
e
v
e
c
t
o
r
se
l
e
c
t
i
o
n
,
”
I
n
t
e
rn
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
P
o
w
e
r
E
l
e
c
t
ro
n
i
c
s
a
n
d
D
r
i
v
e
S
y
st
e
m
s
(
I
J
PED
S
)
,
v
o
l
.
1
0
,
n
o
.
2
,
p
p
.
8
0
1
–
8
1
2
,
J
u
n
.
2
0
1
9
,
d
o
i
:
1
0
.
1
1
5
9
1
/
i
j
p
e
d
s.
v
1
0
.
i
2
.
p
p
8
0
1
-
8
1
2
.
[
6
]
M
.
M
a
m
d
o
u
h
,
M
.
A
.
A
b
i
d
o
,
a
n
d
Z.
H
a
mo
u
z
,
“
W
e
i
g
h
t
i
n
g
f
a
c
t
o
r
se
l
e
c
t
i
o
n
t
e
c
h
n
i
q
u
e
s
f
o
r
p
r
e
d
i
c
t
i
v
e
t
o
r
q
u
e
c
o
n
t
r
o
l
o
f
i
n
d
u
c
t
i
o
n
mo
t
o
r
d
r
i
v
e
s
:
A
c
o
m
p
a
r
i
s
o
n
s
t
u
d
y
,
”
Ar
a
b
i
a
n
J
o
u
r
n
a
l
f
o
r
S
c
i
e
n
c
e
a
n
d
En
g
i
n
e
e
ri
n
g
,
v
o
l
.
4
3
,
p
p
.
4
3
3
–
4
4
5
,
F
e
b
.
2
0
1
8
,
d
o
i
:
1
0
.
1
0
0
7
/
s
1
3
3
6
9
-
0
1
7
-
2
8
4
2
-
2.
[
7
]
C
.
A
.
R
o
j
a
s
,
J
.
R
.
R
o
d
r
i
g
u
e
z
,
S
.
K
o
u
r
o
,
a
n
d
F
.
V
i
l
l
a
r
r
o
e
l
,
“
M
u
l
t
i
o
b
j
e
c
t
i
v
e
f
u
z
z
y
-
d
e
c
i
s
i
o
n
-
m
a
k
i
n
g
p
r
e
d
i
c
t
i
v
e
t
o
r
q
u
e
c
o
n
t
r
o
l
f
o
r
a
n
i
n
d
u
c
t
i
o
n
m
o
t
o
r
d
r
i
v
e
,
”
I
E
E
E
T
r
a
n
s
a
c
t
i
o
n
s
o
n
P
o
w
e
r
E
l
e
c
t
r
o
n
i
c
s
,
v
o
l
.
3
2
,
n
o
.
8
,
p
p
.
6
2
4
5
–
6
2
6
0
,
A
u
g
.
2
0
1
7
,
d
o
i
:
1
0
.
1
1
0
9
/
T
P
E
L
.
2
0
1
6
.
2
6
1
9
3
7
8
.
[
8
]
C
.
A
.
R
o
j
a
s
,
J
.
R
o
d
r
i
g
u
e
z
,
F
.
V
i
l
l
a
r
r
o
e
l
,
J
.
R
.
E
s
p
i
n
o
z
a
,
C
.
A
.
S
i
l
v
a
,
a
n
d
M
.
T
r
i
n
c
a
d
o
,
“
P
r
e
d
i
c
t
i
v
e
t
o
r
q
u
e
a
n
d
f
l
u
x
c
o
n
t
r
o
l
w
i
t
h
o
u
t
w
e
i
g
h
t
i
n
g
f
a
c
t
o
r
s
,
”
I
E
E
E
T
r
a
n
s
a
c
t
i
o
n
s
o
n
I
n
d
u
s
t
r
i
a
l
E
l
e
c
t
r
o
n
i
c
s
,
v
o
l
.
6
0
,
n
o
.
2
,
p
p
.
6
8
1
–
6
9
0
,
F
e
b
.
2
0
1
3
,
d
o
i
:
1
0
.
1
1
0
9
/
T
I
E
.
2
0
1
2
.
2
2
0
6
3
4
4
.
[
9
]
Y
.
Zh
a
n
g
,
Y
.
B
a
i
,
a
n
d
H
.
Y
a
n
g
,
“
A
u
n
i
v
e
r
sa
l
m
u
l
t
i
p
l
e
-
v
e
c
t
o
r
-
b
a
se
d
m
o
d
e
l
p
r
e
d
i
c
t
i
v
e
c
o
n
t
r
o
l
o
f
i
n
d
u
c
t
i
o
n
m
o
t
o
r
d
r
i
v
e
s,
”
I
EEE
T
ra
n
s
a
c
t
i
o
n
s
o
n
P
o
w
e
r E
l
e
c
t
r
o
n
i
c
s
,
v
o
l
.
3
3
,
n
o
.
8
,
p
p
.
6
9
5
7
–
6
9
6
9
,
A
u
g
.
2
0
1
8
,
d
o
i
:
1
0
.
1
1
0
9
/
TPEL.
2
0
1
7
.
2
7
5
4
3
2
4
.
[
1
0
]
T.
G
e
y
e
r
,
“
A
l
g
e
b
r
a
i
c
w
e
i
g
h
t
i
n
g
f
a
c
t
o
r
se
l
e
c
t
i
o
n
f
o
r
p
r
e
d
i
c
t
i
v
e
t
o
r
q
u
e
a
n
d
f
l
u
x
c
o
n
t
r
o
l
,
”
i
n
2
0
1
7
I
EE
E
E
n
e
rg
y
C
o
n
v
e
rsi
o
n
C
o
n
g
ress
a
n
d
Ex
p
o
s
i
t
i
o
n
(
EC
C
E)
,
I
EEE,
O
c
t
.
2
0
1
7
,
p
p
.
3
5
7
–
3
6
4
.
d
o
i
:
1
0
.
1
1
0
9
/
EC
C
E.
2
0
1
7
.
8
0
9
5
8
0
4
.
[
1
1
]
V
.
V
o
d
o
l
a
e
t
a
l
.
,
“
S
e
q
u
e
n
t
i
a
l
M
P
C
s
t
r
a
t
e
g
y
f
o
r
h
i
g
h
p
e
r
f
o
r
ma
n
c
e
i
n
d
u
c
t
i
o
n
mo
t
o
r
d
r
i
v
e
s
:
a
d
e
t
a
i
l
e
d
a
n
a
l
y
si
s
,
”
i
n
2
0
1
9
I
E
EE
En
e
rg
y
C
o
n
v
e
rsi
o
n
C
o
n
g
r
e
ss
a
n
d
Ex
p
o
si
t
i
o
n
(
EC
C
E)
,
I
EEE,
S
e
p
.
2
0
1
9
,
p
p
.
6
5
9
5
–
6
6
0
0
.
d
o
i
:
1
0
.
1
1
0
9
/
E
C
C
E
.
2
0
1
9
.
8
9
1
2
7
0
8
.
[
1
2
]
M
.
N
o
r
a
mb
u
e
n
a
,
J.
R
o
d
r
i
g
u
e
z
,
Z
.
Z
h
a
n
g
,
F
.
W
a
n
g
,
C
.
G
a
r
c
i
a
,
a
n
d
R
.
K
e
n
n
e
l
,
“
A
v
e
r
y
s
i
mp
l
e
s
t
r
a
t
e
g
y
f
o
r
h
i
g
h
-
q
u
a
l
i
t
y
p
e
r
f
o
r
ma
n
c
e
o
f
a
c
m
a
c
h
i
n
e
s u
si
n
g
mo
d
e
l
p
r
e
d
i
c
t
i
v
e
c
o
n
t
r
o
l
,
”
I
EE
E
T
ra
n
s
a
c
t
i
o
n
s o
n
Po
w
e
r
E
l
e
c
t
r
o
n
i
c
s
,
v
o
l
.
3
4
,
n
o
.
1
,
p
p
.
7
9
4
–
8
0
0
,
Ja
n
.
2
0
1
9
,
d
o
i
:
1
0
.
1
1
0
9
/
TPEL.
2
0
1
8
.
2
8
1
2
8
3
3
.
M
e
a
s
u
r
m
e
n
ts
:
I
s
,
w
S
T
E
P
1
fo
r
j
=
0
.
.
6
1
P
r
e
d
i
c
t:
T
K
+
2
(
v
s
k
+1
)
A
p
p
l
y
s
k+
1
Es
ti
m
a
te
:
Ψ
s
k
,
Ψ
r
k
Ev
a
l
u
a
te
:
g
1
=
(
T
*
-
T
K
+2
)
2
j
61
F
o
r
j=1
.
.
.
1
0
j
S
T
E
P
2
S
T
E
P
3
S
TEP
5
S
TEP
6
S
TEP
7
S
TEP
4
P
r
e
-
s
e
l
e
c
t:
v
s
k
+1
(1
),
v
s
k
+1
(2
)
P
r
e
d
i
c
t:
Ψ
s
k
+2
[v
s
k
+1
(
j
)
]
Ev
a
l
u
a
t:
g
2
=
(
Ψ
s
*
-
Ψ
s
k
+2
)
2
S
e
l
e
c
t:
s
k
+
1
Evaluation Warning : The document was created with Spire.PDF for Python.