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l J
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ro
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a
nd
Driv
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y
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t
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s
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I
J
P
E
DS
)
Vo
l.
1
2
,
No
.
3
,
Sep
tem
b
er
202
1
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p
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1
5
8
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~
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I
SS
N:
2088
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1
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v
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1
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1586
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:
h
ttp
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Im
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ACE 1
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d
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sy
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se
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tr
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ase
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s
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rticle
u
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d
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r th
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CC B
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.
C
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r
r
e
s
p
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A
uth
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r
:
J
awa
d
L
am
ter
k
ati
Dep
ar
tem
en
t
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f
E
lectr
ical
E
n
g
in
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r
in
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Hass
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I
I
,
Un
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s
ity
Hig
h
er
Sch
o
o
l
o
f
T
ec
h
n
o
lo
g
y
(
E
STC),
C
asab
lan
ca
,
Mo
r
o
co
o
E
m
ail: ja
wad
.
lam
ter
k
ati@
g
m
ai
l
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
u
s
e
o
f
h
ig
h
-
p
o
wer
elec
tr
o
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ics
is
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ein
g
ex
ten
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ed
to
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if
f
e
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en
t
s
y
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tem
r
elate
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s
tr
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ip
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b
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p
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t
s
id
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ca
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s
e
s
ev
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al
p
r
o
b
l
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s
as:
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wer
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ac
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h
ig
h
v
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o
f
h
ar
m
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ti
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n
o
f
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c
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t
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m
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p
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g
r
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,
u
n
c
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n
tr
o
lled
DC
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k
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tp
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t
v
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e
an
d
th
e
p
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f
l
o
w
u
n
id
ir
ec
tio
n
n
el.
So
,
n
ew
g
e
n
er
atio
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o
f
c
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n
tr
o
lled
r
ec
tifie
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s
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as
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in
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ated
k
n
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w
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th
r
ee
-
p
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ase
v
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ce
PW
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tifie
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s
.
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h
e
PW
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tifie
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i
s
a
p
r
ef
er
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ed
c
h
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is
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f
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r
p
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DC
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v
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s
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ce
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ed
d
r
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d
u
e
to
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ca
p
ab
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o
f
DC
v
o
lta
g
e
co
n
tr
o
l
an
d
b
i
-
d
ir
ec
tio
n
al
p
o
wer
f
lo
w,
in
p
u
t
p
o
wer
f
ac
to
r
r
eg
u
latio
n
,
lin
e
cu
r
r
en
t
h
ar
m
o
n
ic
r
ed
u
ctio
n
[
1
]
,
[
2
]
.
Fo
r
im
p
r
o
v
i
n
g
th
e
in
p
u
t
p
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f
ac
to
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an
d
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n
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t
cu
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in
to
s
in
u
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wav
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r
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ith
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p
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co
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tr
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lo
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p
[
3
]
-
[
9
]
:
T
h
e
v
o
ltag
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-
o
r
ie
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ted
co
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b
ased
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ased
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.
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an
s
f
o
r
m
in
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th
e
th
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ase
q
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titi
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to
ap
p
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o
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iate
DC
co
m
p
o
n
en
ts
,
th
e
p
r
o
p
o
r
tio
n
al
an
d
in
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r
al
(
PI)
co
n
t
r
o
ller
s
ar
e
ab
le
to
lead
to
esti
m
ated
dq
co
m
p
o
n
en
ts
to
th
e
d
esire
d
r
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e
r
en
ce
v
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es
with
ze
r
o
s
tead
y
s
tate
er
r
o
r
[
8
]
-
[
1
2
]
.
T
h
e
d
-
ax
is
r
e
f
er
en
ce
cu
r
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en
t
is
co
n
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o
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led
to
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m
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e
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k
v
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ile
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t
in
q
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n
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o
lled
to
o
b
tain
a
u
n
ity
p
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wer
f
ac
to
r
[
1
3
]
.
Ma
n
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d
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f
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t
PW
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m
o
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latio
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s
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e
b
ein
g
u
s
ed
,
s
u
ch
as
s
in
u
s
o
id
al
PW
M,
d
elta
m
o
d
u
latio
n
tech
n
iq
u
es
an
d
th
e
s
p
ac
e
v
ec
teu
r
tech
n
iq
u
e.
I
t
h
as
b
ee
n
an
aly
ze
d
th
eo
r
ically
an
d
p
r
o
v
ed
th
at
th
e
SVM
tech
n
iq
u
e
is
th
e
b
est
m
o
d
u
latio
n
s
o
l
u
tio
n
o
n
th
e
w
h
o
le.
SVM
is
th
e
b
est
way
to
s
u
p
p
r
ess
th
e
in
p
u
t
h
ar
m
o
n
ic
as
well
f
o
r
s
p
ec
if
ic
ap
p
licatio
n
s
s
u
ch
as
m
o
to
r
s
p
ee
d
co
n
tr
o
l.
An
o
th
e
r
ad
v
a
n
tag
e
o
f
u
s
in
g
SVM
tech
n
iq
u
e
in
in
v
e
r
ter
ca
n
ac
h
i
ev
e
1
5
%
m
o
r
e
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
t
in
th
e
o
u
tp
u
t
v
o
ltag
e
an
d
p
r
o
v
id
es
3
3
%
r
ed
u
ctio
n
o
f
ef
f
ec
tiv
e
s
witch
in
g
f
r
eq
u
en
cy
.
Ho
we
v
er
,
s
witch
in
g
lo
s
s
es
also
s
tr
o
n
g
ly
d
ep
e
n
d
o
n
a
lo
ad
p
o
wer
f
ac
to
r
.
I
t
is
v
er
y
im
p
o
r
tan
t
c
r
iter
io
n
,
wh
ic
h
allo
ws
f
ar
th
e
r
r
ed
u
ctio
n
o
f
s
witch
in
g
l
o
s
s
es
u
p
to
5
0
%
[
1
4
]
.
Fin
ally
,
th
e
p
r
o
p
o
s
ed
VOC
-
SVM
tech
n
iq
u
e
was
test
ed
b
o
th
in
s
im
u
latio
n
a
n
d
ex
p
er
im
e
n
t
ally
,
u
s
in
g
d
SP
AC
E
1104
-
b
ased
ex
p
e
r
im
en
tal
p
r
o
t
o
ty
p
e,
an
d
illu
s
tr
ativ
e
r
esu
lts
ar
e
p
r
esen
ted
.
R
esu
lts
co
n
f
ir
m
th
e
ef
f
ec
tiv
en
ess
an
d
th
e
h
ig
h
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
VOC.
2.
WO
RK
I
NG
P
RINC
I
P
L
E
S
AND
M
O
D
E
L
I
NG
O
F
T
H
R
E
E
-
P
H
AS
E
P
W
M
RE
C
T
I
F
I
E
R
T
h
e
cir
c
u
it
d
iag
r
am
o
f
th
e
t
h
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
r
ec
t
if
ier
s
tr
u
ctu
r
e
is
s
h
o
wn
in
Fig
u
r
e
1
.
I
n
o
r
d
er
to
s
et
u
p
m
ath
m
o
d
el,
it
is
a
s
s
u
m
ed
th
at
th
e
AC
v
o
ltag
e
is
a
b
alan
ce
d
th
r
ee
-
p
h
as
e
s
u
p
p
ly
,
th
e
f
ilter
r
ea
cto
r
is
lin
ea
r
,
I
GB
T
is
id
ea
l
s
witch
an
d
lo
s
s
less
[
1
5
]
,
[
1
6
]
.
T
h
e
co
n
v
er
ter
is
c
o
n
n
ec
ted
to
th
e
th
r
ee
-
p
h
ase
p
o
wer
s
u
p
p
l
y
v
ia
an
in
d
u
cto
r
L
an
d
in
t
er
n
al
r
esis
tan
ce
R
f
o
r
ea
ch
p
h
ase.
T
h
e
th
r
ee
-
p
h
as
e
v
o
ltag
e
s
u
p
p
l
y
is
d
en
o
ted
e
a
,
e
b
an
d
e
c
.
T
h
r
ee
id
en
tical
lin
e
in
d
u
cto
r
s
in
d
icate
d
b
y
L
a
,
L
b
an
d
L
c
ac
t
as
lin
e
f
ilter
s
f
o
r
s
m
o
o
th
in
g
th
e
lin
e
cu
r
r
en
t
with
m
in
im
u
m
r
ip
p
les.
E
ac
h
in
d
u
cto
r
h
as
an
in
ter
n
al
r
es
is
tan
ce
wh
ich
is
d
en
o
ted
b
y
R
a
,
R
b
an
d
R
c
.
A
p
ar
t
o
f
r
ed
u
cin
g
t
h
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD
)
o
f
th
e
lin
e
cu
r
r
en
ts
,
t
h
e
in
d
u
ctio
n
s
also
p
r
o
v
id
e
th
e
b
o
o
s
t
th
e
f
ea
tu
r
e
o
f
th
e
co
n
v
er
ter
.
Six
p
o
wer
tr
a
n
s
is
to
r
s
(
I
GB
T
s
)
with
an
ti
-
p
ar
allel
d
io
d
e
ar
e
u
s
ed
as
t
h
e
SVR
p
o
wer
s
wi
tch
es,
s
in
ce
,
I
GB
T
s
h
av
e
f
ea
tu
r
es
o
f
h
ig
h
-
p
o
wer
r
atin
g
w
h
ich
is
u
s
ed
to
ca
r
r
y
o
u
t
th
e
PW
M
g
en
er
atio
n
as
well
a
s
th
e
p
o
wer
b
id
i
r
ec
tio
n
al
c
o
n
v
er
s
io
n
,
a
l
o
ad
an
d
ca
p
a
city
ar
e
c
o
n
n
ec
ted
s
im
u
ltan
eo
u
s
ly
at
t
h
e
o
u
tp
u
t
o
f
th
e
co
n
v
er
ter
.
T
h
e
ca
p
ac
it
y
is
u
s
ed
as
a
v
o
ltag
e
s
o
u
r
ce
an
d
f
o
llo
ws
t
h
e
r
ec
tifie
r
to
also
o
p
e
r
ate
as a
n
i
n
v
er
ter
[
1
7
]
.
T
h
e
s
tate
o
f
s
witch
es in
ea
ch
o
f
th
e
leg
ca
n
b
e
d
escr
ib
e
d
u
s
in
g
s
witch
in
g
f
u
n
cti
o
n
d
e
f
in
ed
i
n
(
1
)
.
(
)
=
{
0
,
1
}
,
=
,
,
(
1
)
T
h
er
e
ar
e
s
ix
ac
tiv
es’
s
tates
o
f
co
n
v
er
ter
f
o
r
+
+
=
{
1
,
2
}
an
d
two
p
ass
iv
e
s
tates
f
o
r
+
+
=
{
0
,
3
}
.
I
n
ea
ch
o
f
th
e
ac
tiv
e
s
tate
th
er
e
ex
is
ts
a
cir
cu
it
f
o
r
en
e
r
g
y
tr
an
s
f
er
b
etwe
en
th
e
DC
an
d
AC
s
id
e.
T
h
e
v
o
ltag
e
e
q
u
atio
n
s
ar
e
g
iv
e
n
b
y
:
{
=
+
+
=
+
+
=
+
+
(2
)
T
h
e
cu
r
r
e
n
t a
cr
o
s
s
C
is
:
=
+
+
−
(
3
)
T
h
e
(
2
)
ca
n
b
e
r
ewr
itten
as f
o
l
lo
win
g
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
158
6
–
159
7
1588
{
=
−
+
−
=
−
−
−
=
3
2
(
+
)
−
(
4
)
3.
VO
L
T
AG
E
O
RI
E
NT
E
D
C
O
NT
RO
L
T
E
CH
N
I
Q
UE
(
V
O
C)
T
h
e
v
o
ltag
e
-
o
r
ien
ted
co
n
tr
o
l
(
VOC)
s
tr
ateg
y
is
b
a
s
ed
o
n
th
e
k
n
o
wled
g
e
o
f
th
e
p
o
s
itio
n
o
f
th
e
lin
e
v
o
ltag
e
v
ec
to
r
an
d
th
e
r
elativ
e
s
p
atial
o
r
ien
tatio
n
o
f
th
e
cu
r
r
en
t
v
ec
to
r
.
T
y
p
ically
,
g
r
id
c
o
n
n
ec
ted
co
n
v
er
ter
s
co
n
tr
o
l
-
s
tr
u
ctu
r
es
ar
e
b
ased
o
n
Pa
r
k
’
s
tr
an
s
f
o
r
m
atio
n
to
a
r
o
tatin
g
(
d
-
q
)
r
e
f
er
en
ce
f
r
a
m
e
(
alig
n
ed
with
th
e
lin
e
-
v
o
ltag
e)
.
I
n
f
ac
t,
it
is
u
s
u
ally
b
u
ilt
b
y
two
ca
s
ca
d
ed
co
n
tr
o
l
lo
o
p
s
s
o
th
at
a
f
ast
-
in
n
e
r
lo
o
p
co
n
tr
o
ls
th
e
g
r
id
cu
r
r
e
n
t
an
d
an
ex
ter
n
al
lo
o
p
th
e
DC
-
lin
k
v
o
ltag
e.
T
h
e
c
o
n
tr
o
l
s
t
r
u
ctu
r
e
o
f
th
e
p
r
o
p
o
s
ed
s
ch
em
e
is
s
h
o
wn
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
Stru
ctu
r
e
o
f
v
o
ltag
e
o
r
ien
ted
co
n
tr
o
l in
a
r
o
tatin
g
s
y
n
ch
r
o
n
o
u
s
r
ef
er
en
ce
f
r
am
e
I
t g
iv
en
in
th
e
s
y
n
c
h
r
o
n
o
u
s
(
d
-
q
)
co
o
r
d
in
ates:
=
(
+
)
=
3
2
=
(
−
)
(
5
)
Dif
f
er
en
t
co
n
t
r
o
l
s
tr
ateg
ies
h
av
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
th
is
th
r
ee
-
p
h
ase
b
o
o
s
t
o
p
er
atio
n
[
1
7
]
,
[
1
8
]
.
I
f
i
q
=0
an
d
e
q
=0
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
eq
u
atio
n
s
will
b
e
s
im
p
lifie
d
to
=
3
2
an
d
q=
0
.
B
ased
o
n
th
ese
eq
u
atio
n
s
,
th
e
f
ee
d
f
o
r
wa
r
d
cu
r
r
en
t
co
n
tr
o
l
m
et
h
o
d
is
o
n
e
o
f
t
h
e
wid
ely
u
s
ed
s
ch
em
es
f
o
r
p
o
wer
c
o
n
tr
o
l.
Fig
u
r
e
3
s
h
o
ws
th
e
b
asic
d
iag
r
am
o
f
th
e
co
n
tr
o
ller
.
T
h
e
dq
c
u
r
r
en
t
co
n
t
r
o
l
an
d
f
ee
d
f
o
r
wa
r
d
co
m
p
en
s
atio
n
ar
e
th
e
m
ain
p
ar
ts
o
f
t
h
is
d
ec
o
u
p
led
co
n
tr
o
l
s
ch
em
e.
T
h
e
co
n
t
r
o
ller
h
as
an
o
u
ter
lo
o
p
f
o
r
th
e
DC
-
b
u
s
v
o
ltag
e
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
694
I
mp
leme
n
ta
tio
n
o
n
th
e
d
S
P
A
C
E
1
1
0
4
o
f V
OC
-
S
V
M b
a
s
ed
a
n
ti
-
w
in
d
u
p
P
I
… (
J.
La
mterka
ti
)
1589
r
eg
u
latio
n
.
T
h
is
co
n
tr
o
ller
o
u
t
p
u
t
s
ets
th
e
r
ef
er
en
ce
v
alu
e
f
o
r
th
e
d
c
o
m
p
o
n
en
t
o
f
th
e
c
u
r
r
e
n
t
th
at
co
n
tr
o
ls
th
e
p
o
wer
[
1
9
]
.
−
C
u
r
r
en
t
d
ec
o
u
p
lin
g
c
o
n
tr
o
l o
f
th
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
PW
M
r
ec
tifie
r
I
t
is
clea
r
f
r
o
m
(
9
)
th
at
t
h
e
co
n
v
er
ter
eq
u
atio
n
s
in
th
e
(
d
-
q
)
ax
is
ar
e
co
u
p
led
to
t
o
ea
ch
o
t
h
er
th
r
o
u
g
h
Lw
i
q
an
d
Lw
i
d
ter
m
s
,
wh
ich
m
ea
n
s
th
at
if
we
c
o
n
tr
o
l
o
n
e
o
f
th
em
,
th
e
o
th
er
o
n
e
will
b
e
ch
a
n
g
ed
co
r
r
esp
o
n
d
in
g
ly
,
th
u
s
we
ca
n
n
o
t
co
n
t
r
o
l
th
em
in
d
ep
en
d
en
tl
y
.
So
,
we
n
ee
d
to
ca
r
r
y
o
n
th
e
d
ec
o
u
p
lin
g
co
n
tr
o
l
in
th
e
o
r
d
er
to
c
o
n
tr
o
l t
h
em
in
d
ep
en
d
e
n
tly
.
W
e
u
s
e
th
e
s
tr
ateg
y
o
f
f
ee
d
-
f
o
r
war
d
d
ec
o
u
p
lin
g
co
n
tr
o
l,
m
ak
e:
{
+
=
(
+
)
∗
(
−
)
+
=
(
+
)
∗
(
−
)
(
6
)
Su
b
s
titu
te
(
6
)
in
to
(
5
)
:
{
=
(
+
)
∗
(
−
)
−
+
=
(
+
)
∗
(
−
)
+
+
(
7
)
Su
b
s
titu
te
(
7
)
in
(
4
)
:
{
=
1
(
+
)
∗
−
1
[
+
(
+
)
]
∗
=
1
(
+
)
∗
−
1
[
+
(
+
)
]
∗
(
8
)
Af
ter
d
ec
o
u
p
lin
g
co
n
tr
o
l
(
8
)
we
ca
n
co
n
tr
o
l
i
d
an
d
i
q
i
n
d
ep
en
d
e
n
tly
,
t
h
u
s
we
ca
n
r
e
s
p
er
ctiv
ely
co
n
tr
o
l
th
e
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
wer
s
in
d
ep
e
n
d
en
tly
a
n
d
th
is
ca
n
m
ak
e
d
e
d
esig
n
o
f
cu
r
r
en
t
lo
o
p
m
u
s
h
ea
s
i
er
.
C
u
r
r
en
t
lo
o
p
d
esig
n
b
lo
ck
d
iag
r
am
is
s
h
o
wn
in
Fi
g
u
r
e
3
.
I
n
o
r
d
er
to
d
esig
n
th
e
v
o
ltag
e
lo
o
p
,
th
e
r
ea
ctiv
e
co
m
p
o
m
en
t
b
e
ze
r
o
t
o
in
s
u
r
e
th
e
PW
M
r
ec
tifie
r
u
i
n
ity
p
o
wer
f
ac
to
r
[
2
0
]
-
[
2
2
]
.
T
h
e
g
iv
en
v
alu
e
o
f
ac
tiv
e
co
m
p
en
en
t
i
d
is
p
r
o
d
u
c
ed
b
y
an
ti
-
win
d
u
p
PI
co
n
tr
o
ller
,
wh
ich
s
h
o
n
w
in
(
9
)
,
th
e
k
p
is
th
e
p
r
o
p
o
r
tio
n
ly
f
ac
to
r
,
th
e
k
i
is
th
e
in
teg
r
al
co
e
f
f
icien
t.
=
(
+
)
(
,
−
)
(
9
)
Fig
u
r
e
2
.
Stru
ctu
r
e
d
iag
r
am
o
f
cu
r
r
en
ts
d
ec
o
u
p
lin
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
158
6
–
159
7
1590
4.
SYNT
E
S
I
S
O
F
CO
NT
RO
L
L
E
R
S
4
.
1
.
Desig
n o
f
curr
ent
co
ntr
o
ller
T
h
e
b
lo
ck
d
iag
r
am
o
f
cu
r
r
en
t
co
n
tr
o
l
lo
o
p
is
s
h
o
wn
in
Fig
u
r
e
4
;
b
asically
,
th
ey
ten
d
t
o
r
e
g
u
late
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
e
n
t
r
es
p
ec
tiv
ely
.
T
h
e
d
-
ax
is
cu
r
r
en
t
l
o
o
p
attem
p
ts
to
m
ai
n
tain
a
co
n
s
tan
t
DC
v
o
ltag
e
b
y
tr
ac
in
g
t
h
e
r
ef
e
r
en
ce
cu
r
r
e
n
t
v
alu
e
i
d,
ref
p
r
o
d
u
ce
d
b
y
th
e
o
u
th
er
v
o
ltag
e
lo
o
p
.
I
n
o
r
d
er
to
ac
h
iev
e
th
e
u
n
ity
p
o
wer
co
n
d
itio
n
,
t
h
e
q
-
a
x
is
cu
r
r
en
t c
o
m
p
o
n
e
n
t
i
q,
ref
h
as to
b
e
s
et
to
ze
r
o
[
1
4
]
.
Fig
u
r
e
3
.
C
u
r
r
e
n
t c
o
n
t
r
o
l lo
o
p
d
iag
r
am
T
h
e
lin
e
v
o
ltag
e
is
s
ee
n
as a
co
n
s
tan
t p
er
tu
r
b
atio
n
,
a
n
d
is
co
m
p
en
s
ated
b
y
th
e
in
teg
r
al
p
ar
t
o
f
PI
co
n
tr
o
ller
.
I
n
th
is
way
,
th
e
ze
r
o
o
f
th
e
PI
co
n
tr
o
ller
s
is
p
lace
d
o
v
er
th
e
p
o
le
o
f
t
h
e
s
y
s
tem
.
So
:
=
(
1
0
)
W
ith
th
is
s
y
n
th
esis
,
in
clo
s
ed
-
lo
o
p
,
th
e
s
y
s
tem
will b
e
s
im
p
lifie
d
an
d
its
clo
s
ed
lo
o
p
tr
a
n
s
f
er
f
u
n
ct
io
n
is
:
(
)
=
1
1
+
(
1
1
)
T
h
e
clo
s
e
-
lo
o
p
tim
e
co
n
s
tan
t
=
ca
n
b
e
a
s
p
ec
if
icatio
n
o
f
t
h
e
c
o
n
tr
o
ller
d
esig
n
.
So
:
=
(
1
2
)
T
h
e
p
ar
am
eter
s
o
f
th
e
c
u
r
r
en
t
lo
o
p
PI
co
n
tr
o
ller
ca
n
b
e
g
iv
e
n
b
y
:
=
=
a
n
d
=
1
=
(
1
3
)
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
en
t c
o
n
tr
o
l lo
o
p
s
ar
e
s
im
ilar
; th
e
r
e
-
f
o
r
e
,
th
e
(
1
3
)
is
v
alid
f
o
r
b
o
th
co
n
tr
o
ller
s
.
4
.
2
.
Desig
n o
f
v
o
lt
a
g
e
co
ntr
o
ller
Af
ter
co
r
r
ec
tio
n
,
th
e
cu
r
r
en
t
lo
o
p
is
co
n
s
id
er
ed
t
o
b
e
eq
u
al
to
u
n
ity
.
T
h
u
s
,
th
e
b
lo
c
k
d
iag
r
am
o
f
v
o
ltag
e
co
n
tr
o
l
lo
o
p
is
g
iv
en
in
Fig
u
r
e
5
.
I
n
o
r
d
er
to
lim
it
DC
b
u
s
v
o
ltag
e
f
lu
ctu
atio
n
s
a
p
r
o
p
o
r
ti
o
n
al
-
in
teg
r
al
(
PI)
co
n
t
r
o
ller
with
a
n
ti
-
win
d
u
p
c
o
m
p
e
n
s
atio
n
is
p
r
o
p
o
s
e
d
f
o
r
th
e
DC
b
u
s
r
eg
u
latio
n
.
T
h
e
r
eg
u
lato
r
ac
ts
u
s
in
g
a
p
r
o
p
o
r
tio
n
al
g
ain
K
p
,
i
m
p
r
o
v
i
n
g
th
e
d
y
n
am
ic
a
n
d
th
e
q
u
an
tity
o
f
in
ter
g
r
ato
r
v
ia
t
h
e
g
ain
K
i
,
f
o
r
g
o
o
d
o
p
er
atio
n
i
n
s
tead
y
s
ate
[
2
3
]
.
T
o
lim
it
th
e
s
atu
r
atio
n
o
f
t
h
e
o
u
tp
u
t
o
f
t
h
e
co
n
tr
o
ller
,
ca
u
s
ed
b
y
n
o
is
e
d
etec
tio
n
am
p
lif
icatio
n
,
an
an
ti
-
win
d
u
p
lo
o
p
is
ad
d
ed
b
y
a
s
ec
o
n
d
in
teg
r
ato
r
t
er
m
,
with
a
lo
o
p
g
ain
(
1
/
T
u
)
ch
o
s
en
to
h
ig
h
,
with
o
u
t
af
f
ec
tin
g
th
e
d
esire
d
p
er
f
o
r
m
a
n
ce
s
[
2
4
]
,
[
2
5
]
.
T
ak
in
g
in
t
o
ac
co
u
n
t
th
e
PI
r
e
g
u
lateu
r
f
u
n
ctio
n
tr
an
s
f
er
f
u
n
ctio
n
an
d
th
at
o
f
th
e
DC
s
id
e,
th
e
s
y
n
th
esis
o
f
t
h
e
K
p
an
d
K
i
g
ai
n
s
o
f
th
e
PI
c
o
n
tr
o
ller
p
ass
es
th
r
o
u
g
h
p
lace
m
e
n
t
o
f
th
e
p
o
les o
f
d
ir
ec
t c
lo
s
ed
lo
o
p
,
is
g
iv
en
b
y
th
e
f
o
llo
win
g
tr
an
s
f
er
f
u
n
ctio
n
:
,
=
.
+
.
2
+
.
+
=
/
(
+
/
)
2
+
/
.
+
/
(
1
4
)
Fro
m
(
1
1
)
,
we
n
o
te
th
at
th
e
cl
o
s
ed
lo
o
p
is
a
ca
n
o
n
ical
tr
an
s
f
er
f
u
n
ctio
n
o
f
s
ec
o
n
d
o
r
d
e
r
:
,
=
2
2
+
2
.
.
.
+
(
1
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
694
I
mp
leme
n
ta
tio
n
o
n
th
e
d
S
P
A
C
E
1
1
0
4
o
f V
OC
-
S
V
M b
a
s
ed
a
n
ti
-
w
in
d
u
p
P
I
… (
J.
La
mterka
ti
)
1591
B
y
eq
u
alizin
g
(
1
4
)
an
d
(
1
5
)
,
an
d
a
d
o
p
tin
g
a
n
o
p
tim
al
d
am
p
in
g
c
o
ef
f
icien
t;
th
e
g
ain
s
o
f
co
n
tr
o
ller
ar
e
q
u
an
tifie
d
as f
o
llo
ws:
=
2
.
.
.
a
n
d
=
.
2
(
1
6
)
Fig
u
r
e
4
.
An
ti
-
win
d
u
p
PI
co
n
t
r
o
ller
f
o
r
DC
-
lin
k
v
o
ltag
e
co
n
t
r
o
l
5.
SPAC
E
V
E
C
T
O
R
M
O
DU
L
AT
I
O
N
T
E
CH
N
I
Q
UE
T
h
e
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
(
SVM)
is
an
alter
n
ativ
e
in
v
e
r
ter
s
witch
co
n
tr
o
l
m
et
h
o
d
to
c
o
n
v
en
tio
n
al
s
in
u
s
o
id
al
PW
M,
it
is
ch
ar
ac
t
er
ized
b
y
a
f
ast
-
tr
an
s
ien
t
r
esp
o
n
s
e
an
d
a
less
h
ar
m
o
n
ic
d
is
to
r
tio
n
[
2
6
]
.
C
o
n
tr
o
l
s
tr
u
ctu
r
e
is
g
r
ea
tly
s
im
p
lifie
d
an
d
p
o
we
r
elec
t
r
o
n
ic
h
ar
d
war
e
is
ex
p
lo
ited
to
th
e
m
ax
im
u
m
.
T
h
e
v
o
ltag
e
v
ec
to
r
s
wh
ich
ar
e
g
en
er
ated
b
y
th
e
in
v
e
r
ter
f
o
r
ea
ch
s
am
p
lin
g
p
er
io
d
ar
e
p
lo
tted
in
Fig
u
r
e
5
.
T
h
er
e
ar
e
eig
h
t
p
o
s
s
ib
le
o
u
p
u
t v
o
ltag
e
v
ec
to
r
s
,
s
ix
ac
tiv
e
v
ec
to
r
s
V
1
-
V
6
,
an
d
two
ze
r
o
v
ec
to
r
s
V
0
-
V
7
co
r
r
e
s
p
o
n
d
to
t
h
e
in
v
er
ter
s
witch
es st
a
tes
S
0
(
0
0
0
)
,
S
1
(
1
0
0
)
,
…,
S
7
(
1
1
1
)
,
r
esp
ec
tiv
ely
.
T
h
e
p
r
in
cip
le
o
f
SVM
is
th
e
p
r
ed
ictio
n
o
f
in
v
er
ter
v
o
ltag
e
v
ec
to
r
b
y
th
e
p
r
o
jectio
n
o
f
th
e
r
ef
er
en
ce
b
etwe
en
ad
jace
n
t
v
ec
to
r
s
in
e
ac
h
s
ec
to
r
N
i
:
(
−
1
)
3
<
≤
3
.
T
h
e
d
ete
r
m
i
n
atio
n
o
f
t
h
e
s
ec
to
r
is
b
ased
o
n
th
e
f
o
llo
win
g
e
x
p
r
ess
io
n
:
=
(
)
(
1
7
)
wh
er
e
an
d
d
en
o
te
th
e
v
o
ltag
e
v
ec
to
r
co
m
p
o
n
en
ts
in
th
e
C
o
n
co
r
d
ia
r
ef
e
r
en
ce
.
T
h
e
p
r
in
cip
le
o
f
th
e
SVM’
s
is
to
p
r
o
ject
th
e
d
esire
d
v
o
lta
g
e
v
ec
t
o
r
Vs
ref
o
n
two
ad
jace
n
t
v
o
lta
g
e
v
ec
to
r
s
V
i
an
d
V
i+
1
co
r
r
esp
o
n
d
in
g
to
two
s
witch
in
g
s
tates
o
f
th
e
in
v
er
ter
.
T
h
e
v
alu
es
o
f
th
is
p
r
o
jectio
n
p
r
o
v
id
e
th
e
d
eter
m
in
atio
n
o
f
d
esire
d
co
m
m
u
tatio
n
tim
es
T
i
a
n
d
T
i+
1
an
d
co
r
r
esp
o
n
d
to
two
n
o
n
ze
r
o
s
witch
in
g
s
tates
o
f
th
e
in
v
er
ter
.
T
o
m
ain
tain
th
e
co
n
s
tan
t
co
m
m
u
tati
o
n
f
r
eq
u
en
cy
,
in
th
e
ca
s
e
wh
er
e
T
i
+T
i
+
1
≤
T
PWM
,
a
ze
r
o
s
tate
o
f
th
e
in
v
er
ter
is
ap
p
lied
d
u
r
i
n
g
a
c
o
m
p
lem
en
ta
r
y
d
u
r
atio
n
t
o
th
e
p
e
r
io
d
T
PWM
.
W
h
en
th
e
r
e
f
er
en
ce
v
o
ltag
e
v
e
cto
r
V
sref
is
in
s
ec
to
r
1
(
Fig
u
r
e
5
)
,
it
ca
n
co
m
p
o
s
e
b
y
th
e
ac
ti
v
e
v
o
ltag
e
v
ec
to
r
s
V
1
,
V
2
an
d
V
0
[
2
7
]
,
[
2
8
]
.
Fo
r
a
cy
cle
s
witch
in
g
,
we
h
a
v
e:
⃗
=
+
=
1
⃗
1
+
2
⃗
2
(
1
8
)
W
h
er
e:
=
1
+
2
+
0
(
1
9
)
T
h
e
in
clu
s
io
n
o
f
ze
r
o
b
asic
v
e
cto
r
s
d
o
es’n
t
af
f
ec
t
th
e
v
ec
t
o
r
s
u
m
V
sref
,
it
o
n
ly
h
elp
s
to
b
ala
n
ce
th
e
tu
r
n
o
n
an
d
o
f
f
p
e
r
io
d
s
o
f
th
e
tr
an
s
is
to
r
s
,
a
n
d
th
u
s
th
eir
p
o
wer
d
is
s
ip
atio
n
.
T
h
e
e
x
p
r
ess
io
n
s
o
f
th
e
v
o
lta
g
e
v
ec
to
r
a
r
e:
{
⃗
1
=
√
2
3
(
0
+
0
)
⃗
2
=
√
2
3
(
3
+
3
)
(
2
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
158
6
–
159
7
1592
T
h
e
ex
p
r
ess
io
n
o
f
T
1
an
d
T
2
ar
e
as:
{
1
=
(
√
3
2
−
1
√
2
)
.
2
=
√
2
(
2
1
)
Fig
u
r
e
5
.
Prin
cip
le
o
f
s
p
ac
e
v
e
cto
r
m
o
d
u
latio
n
Fig
u
r
e
6
.
Pro
jectio
n
o
f
th
e
r
ef
er
en
ce
v
o
ltag
e
v
ec
to
r
on
V
1
an
d
V
2
T
h
e
eq
u
atio
n
s
f
o
r
T
1
a
n
d
T
2
ar
e
id
en
tically
f
o
r
all
s
p
ac
e
v
ec
t
o
r
m
o
d
u
latio
n
m
et
h
o
d
s
.
T
h
e
o
n
ly
d
if
f
er
e
n
ce
b
etwe
en
th
e
o
th
er
ty
p
es
o
f
SVM
is
th
e
p
lace
m
en
t
o
f
ze
r
o
v
ec
t
o
r
s
at
th
e
s
am
p
lin
g
tim
e.
T
h
e
b
asic
SV
M
m
eth
o
d
is
th
e
m
o
d
u
latio
n
m
eth
o
d
with
s
y
m
m
etr
ical
s
p
ac
in
g
ze
r
o
v
ec
to
r
s
(
SVPW
M)
.
I
n
th
is
m
eth
o
d
tim
es
T
0
an
d
T
7
ar
e
eq
u
al
[
2
9
]
:
0
=
7
=
(
−
1
−
2
)
/
2
(
2
2
)
Fo
r
th
e
f
ir
s
t secto
r
s
witch
in
g
s
eq
u
en
ce
ca
n
b
e
wr
itten
as:
0
→
1
→
2
→
7
→
2
→
1
→
0
(
2
3
)
6.
SI
M
UL
A
T
I
O
N
A
ND
E
XP
E
RIM
E
N
T
AL
R
E
S
UL
T
S
I
n
o
r
d
er
t
o
v
er
if
y
th
e
ef
f
ec
ti
v
en
ess
an
d
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
tr
ate
g
is
es,
b
o
th
s
im
u
latio
n
an
d
ex
p
er
im
en
tal
test
s
ar
e
ca
r
r
ied
o
u
t.
T
h
e
n
a
lo
r
ato
r
y
s
etu
p
was
estab
lis
h
ed
u
s
in
g
d
SP
AC
E
s
y
s
tem
with
DS1
1
0
4
c
o
n
tr
o
ll
er
b
o
a
r
d
a
n
d
I
GB
T
s
v
o
ltag
e
i
n
v
er
ter
.
T
h
e
elec
tr
ical
p
ar
am
eter
s
o
f
th
e
p
o
wer
cir
cu
it a
n
d
co
n
tr
o
l
d
ata
ar
e
lis
ted
in
T
ab
le
1.
T
ab
le
1
.
Sy
s
tem
an
d
co
n
tr
o
l p
ar
am
eter
s
P
r
a
met
e
r
S
y
m
b
o
l
V
a
l
u
e
A
C
l
i
n
e
v
o
l
t
a
g
e
(
R
M
S
)
F
r
e
q
u
e
n
c
y
Li
n
e
r
e
s
i
st
a
n
c
e
Lo
a
d
r
e
si
s
t
a
n
c
e
AC
-
si
d
e
i
n
d
u
c
t
a
n
c
e
DC
-
b
u
s
c
a
p
a
c
i
t
o
r
DC
-
b
u
s
v
o
l
t
a
g
e
e
[V]
f
[
H
z
]
R
[
Ω
]
R
L
[
Ω
]
L
[
mH
]
C
[
mF
]
V
DC
[V]
50
50
0
.
2
64
10
1
.
1
1
2
5
S
w
i
t
c
h
i
n
g
f
r
e
q
e
n
c
y
f
s
[
K
H
z
]
10
6
.
1
.
Sim
ula
t
io
n
re
s
ults
Var
io
u
s
test
s
,
in
s
im
u
latio
n
s
tad
ies,
wer
e
co
n
d
u
cted
to
v
er
if
y
p
er
f
o
r
m
an
ce
o
f
t
h
e
p
r
o
p
o
s
ed
VOC
s
ch
em
e.
T
h
e
r
esu
lts
s
h
o
ws th
e
s
im
u
lated
wav
ef
o
r
m
s
u
n
d
er
u
n
ity
p
o
wer
f
ac
to
r
(
UPF)
o
p
er
a
tio
n
(
i
q,
ref
=0
)
in
th
e
s
tad
y
s
tate
f
o
r
p
u
r
ely
s
in
u
s
o
i
d
al
s
u
p
p
ly
v
o
ltag
e
s
o
u
r
ce
.
Fig
u
r
e
s
7
(
a
)
-
(
e)
s
h
o
ws
th
e
d
y
n
am
ic
b
eh
av
i
o
r
u
n
d
e
r
a
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
694
I
mp
leme
n
ta
tio
n
o
n
th
e
d
S
P
A
C
E
1
1
0
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o
f V
OC
-
S
V
M b
a
s
ed
a
n
ti
-
w
in
d
u
p
P
I
… (
J.
La
mterka
ti
)
1593
s
tep
ch
an
g
e
o
f
V
DC
,
ref
,
af
te
r
a
s
h
o
r
t
tr
an
s
ien
t,
th
e
o
u
tp
u
t
v
o
ltag
e
is
m
ain
tain
ed
clo
s
e
to
its
n
ew
r
ef
er
en
ce
.
W
e
r
em
ar
k
th
at
t
h
e
an
ti
-
win
d
u
p
PI
DC
-
b
u
s
co
n
tr
o
ller
h
as
ac
h
iv
ed
th
e
test
g
o
als:
n
o
o
v
er
s
h
o
o
ts
an
d
b
etter
co
n
s
tan
cy
i
n
s
tead
y
s
tate.
T
h
e
lin
e
c
u
r
r
en
ts
a
r
e
v
er
y
clo
s
e
t
o
s
in
e
wav
e
f
r
o
m
with
a
s
p
ec
t
r
al
an
aly
s
is
d
e
v
o
id
o
f
lo
w
-
o
r
d
er
h
ar
m
o
n
ics
(
THD
=1
.
7
5
%)
an
d
in
p
h
ase
with
th
e
p
o
wer
s
o
u
r
ce
v
o
ltag
e
b
ec
au
s
e
th
e
r
ea
ctiv
e
cu
r
r
en
t r
e
f
er
en
ce
c
o
m
p
o
n
en
t
i
q,
ref
was im
p
o
s
ed
0
A.
T
h
e
r
ea
c
tiv
e
cu
r
r
en
t
(
i
d
)
is
m
ain
tain
ed
t
o
ze
r
o
.
(
a
)
(
b
)
(
c
)
(
d
)
(
e
)
Fig
u
r
e
7
.
Dy
n
am
ic
r
esp
o
n
s
e
ch
ar
ac
ter
is
tics
f
o
r
s
tep
ch
an
g
e
o
f
th
e
V
DC
ref
,
f
r
o
m
1
2
5
V
to
1
4
0
V
an
d
in
v
er
s
ely
,
u
s
in
g
an
ti
-
win
d
u
p
PI
co
n
tr
o
lle
r
,
(
a)
DC
-
lin
k
v
o
ltag
e,
(
b
)
v
o
lt
ag
e
e
a
an
d
c
u
r
r
e
n
ts
p
h
ases
,
(
c)
zo
o
m
o
n
v
o
ltag
e
e
a
an
d
lin
e
cu
r
r
en
ts
,
(
d
)
d
q
-
cu
r
r
en
ts
,
(
e)
h
a
r
m
o
n
ic
s
p
ec
tr
u
m
o
f
lin
e
cu
r
r
e
n
t
T
o
s
h
o
w
th
e
g
o
o
d
p
er
f
o
r
m
a
n
c
e
o
f
th
e
p
r
o
p
o
s
ed
VOC
-
SVM
co
n
tr
o
l
b
ased
an
ti
-
win
d
u
p
PI
co
n
tr
o
ller
d
u
r
in
g
a
tr
a
n
s
ien
t,
th
e
lo
ad
is
ch
an
g
ed
in
t
1
=1
s
,
f
r
o
m
6
4
Ω
to
32Ω
.
I
t
is
clea
r
ly
s
h
o
wn
in
Fig
u
r
e
s
8
(
a)
-
(
d
)
th
at
th
e
s
y
s
tem
h
as
a
g
o
o
d
d
y
n
am
ic
r
esp
o
n
s
e
to
v
ar
iatio
n
l
o
ad
at
1s
.
T
h
e
cu
r
r
en
t
wa
v
ef
o
r
m
is
p
e
r
f
ec
tely
s
in
u
s
o
id
al
an
d
h
as
s
o
m
e
p
h
a
s
e
as
th
e
v
o
ltag
e
wav
ef
o
r
m
s
.
T
h
e
r
ea
ctiv
e
cu
r
r
en
t
co
n
tin
u
ed
ze
r
o
ev
en
with
v
ar
iatio
n
lo
ad
.
W
ith
an
ti
-
win
d
u
p
PI
co
n
tr
o
ller
,
th
e
o
u
tp
u
t v
o
ltag
e
is
r
ec
o
u
v
r
e
d
in
less
th
an
0
.
0
5
s
.
1
1
.
5
2
120
125
130
135
140
145
t
i
m
e
(
s
)
V
d
c
(
V
)
V
d
c
V
d
c
r
e
f
1
1
.
5
2
-5
0
5
t
i
m
e
(
s
)
e
a
/
1
0
(
V
)
a
n
d
i
a
b
c
(
A
)
1
.
2
1
.
2
2
1
.
2
4
1
.
2
6
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0
5
t
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m
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(
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a
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(
V
)
a
n
d
i
a
b
c
(
A
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1
1
.
5
2
-2
0
2
4
6
t
i
m
e
(
s
)
i
d
a
n
d
i
q
(
V
)
i
d
(
V
)
i
q
(
V
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
158
6
–
159
7
1594
(
a
)
(
b
)
(
c
)
(
d
)
Fig
u
r
e
8
.
(
a
)
DC
-
lin
k
v
o
ltag
e,
(
b
)
Vo
ltag
e
e
a
a
n
d
lin
e
c
u
r
r
en
ts
,
(
c)
zo
o
m
o
n
v
o
lta
g
e
e
a
an
d
li
n
e
cu
r
r
e
n
ts
,
(
d
)
d
q
-
cu
r
r
en
ts
6
.
2
.
E
x
perim
ent
a
l
re
s
ults
T
o
v
alid
ate
th
e
s
im
u
latio
n
r
es
u
lts
o
f
th
e
p
r
o
p
o
s
ed
VOC
-
SV
M
with
an
ti
-
win
d
u
p
PI
co
n
tr
o
l
ler
s
tu
d
ied
o
n
th
e
ab
o
v
e
s
ec
tio
n
,
d
if
f
e
r
e
n
t
p
r
atica
l
test
s
wer
e
ca
r
r
ied
o
u
t.
An
ex
p
e
r
im
en
tal
test
b
en
ch
is
d
esig
n
ed
b
y
u
s
in
g
a
d
SP
AC
E
1
1
0
4
b
o
ar
d
as
illu
s
tr
ated
in
Fig
u
r
e
9
.
T
h
e
d
SP
AC
E
1
1
0
4
b
o
ar
d
is
b
ased
o
n
a
2
5
0
MH
z
6
0
3
-
Po
wer
PC
-
6
4
b
its
p
r
o
ce
s
s
o
r
an
d
a
s
lav
e
d
ig
ital
s
ig
n
al
p
r
o
ce
s
s
in
g
(
DSP)
ca
r
d
b
as
ed
o
n
a
2
0
MH
z,
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