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ted
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r
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en
ts
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a
r
m
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t,
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n
d
r
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s
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h
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p
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s
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es
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lo
w
p
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f
ac
to
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d
h
ig
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c
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r
r
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t
to
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ar
m
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ic
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is
to
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(
T
HD)
.
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ch
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o
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ca
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am
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g
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id
eq
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i
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en
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o
d
u
ce
th
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m
al
s
tr
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s
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in
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ac
h
in
es,
an
d
d
estr
o
y
f
ilter
in
g
ca
p
ac
ito
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s
[
1
]
.
T
o
m
itig
ate
th
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d
r
awb
ac
k
s
,
we
tu
r
n
to
th
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PW
M
r
ec
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with
r
o
b
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co
n
tr
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s
tr
ateg
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PW
M
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Activ
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ca
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licatio
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as p
o
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p
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r
p
o
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f
ac
to
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co
r
r
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tio
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its
[
2
]
.
T
h
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ac
ti
v
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AC
-
DC
co
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v
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s
ex
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d
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ti
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bi
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ct
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n
d
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ab
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b
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co
m
p
a
ct
p
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v
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f
ilte
r
s
[
1
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-
[
4
]
.
Va
r
i
o
u
s
c
o
n
t
r
o
l
s
t
r
a
te
g
ies
h
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est
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b
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t
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ta
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(
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v
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o
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d
c
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(
VO
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[
1
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,
a
lt
h
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g
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t
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c
o
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tr
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l
m
e
th
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ca
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ac
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th
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m
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m
a
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n
g
o
als
,
t
h
ei
r
ap
p
r
o
ac
h
d
if
f
e
r
[
5
]
.
O
v
e
r
r
ec
e
n
t
y
ea
r
s
,
d
i
r
e
ct
p
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w
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t
r
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l
(
D
PC
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h
as
att
r
a
ct
ed
s
u
b
s
ta
n
ti
al
r
es
ea
r
c
h
i
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te
r
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t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
6
9
4
DP
C
b
a
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s
tep
p
in
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co
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tr
o
l a
p
p
lied
to
a
n
a
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r
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tifi
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a
n
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lysi
s
a
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d
co
mp
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…
(
S
lima
n
e
C
h
ib
o
u
b
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1809
[
6
]
-
[
7
]
.
M
o
d
el
e
d
af
te
r
d
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r
e
ct
t
o
r
q
u
e
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e
m
p
lo
y
ed
i
n
m
o
t
o
r
d
r
i
v
e
[
5
]
,
DPC
ex
p
l
ici
tl
y
m
a
n
a
g
es
i
n
s
t
an
ta
n
e
o
u
s
ac
t
iv
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an
d
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ea
c
ti
v
e
p
o
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co
m
p
o
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en
t
s
t
h
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o
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g
h
d
ec
o
u
p
le
d
c
o
n
t
r
o
l l
o
o
p
s
.
U
n
lik
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ca
s
ca
d
e
ar
ch
itectu
r
es,
co
n
v
en
tio
n
al
DPC
elim
in
at
es
in
n
er
cu
r
r
en
t
lo
o
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d
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PW
M
m
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u
lato
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b
lo
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as
th
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co
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v
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ter
s
witch
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tates
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v
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a
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witch
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S
witch
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tates
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ased
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th
e
in
s
tan
tan
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s
p
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we
r
er
r
o
r
s
alo
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la
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p
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n
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f
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e
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r
i
d
v
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ltag
e
[
6
]
,
[
8
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o
r
v
ir
tu
al
-
f
lu
x
v
ec
to
r
s
[
8
]
,
[
1
]
.
D
esp
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s
im
p
licity
,
class
ical
DPC
ex
h
ib
its
s
o
m
e
d
r
awb
ac
k
s
,
s
u
ch
as
r
ip
p
les
in
cu
r
r
en
t
an
d
p
o
wer
,
alo
n
g
with
v
ar
iab
le
s
witch
in
g
f
r
eq
u
en
c
y
,
wh
ich
m
ay
d
ir
ec
tly
af
f
ec
t
s
y
s
te
m
p
er
f
o
r
m
a
n
ce
an
d
co
m
p
r
o
m
is
e
s
tab
ilit
y
[
9
]
.
Var
io
u
s
co
n
tr
o
l
s
tr
ateg
ies
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
im
p
r
o
v
e
DPC
tech
n
iq
u
es
an
d
o
v
e
r
co
m
e
its
lim
itatio
n
s
;
am
o
n
g
th
ese,
th
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
(
B
S)
tech
n
iq
u
e,
wh
ic
h
we
will
co
m
b
in
e
with
DPC
to
d
ev
elo
p
a
r
o
b
u
s
t
an
d
s
tab
le
co
n
tr
o
l
tech
n
iq
u
e
ag
ain
s
t
p
er
tu
r
b
atio
n
s
o
r
p
ar
am
eter
v
ar
iatio
n
.
T
h
e
s
y
s
tem
atic,
s
tep
-
by
-
s
tep
s
y
n
th
esis
o
f
f
e
r
ed
b
y
B
ac
k
s
tep
p
in
g
co
n
tr
o
l
(
B
S)
h
as
m
ad
e
it
a
wid
el
y
ad
o
p
te
d
ap
p
r
o
ac
h
f
o
r
n
o
n
-
lin
ea
r
co
n
tr
o
l
ap
p
licatio
n
s
[
1
0
]
,
[
1
1
]
.
I
n
th
is
ap
p
r
o
ac
h
,
v
ir
tu
a
l
co
n
tr
o
l
laws
ar
e
d
ef
in
ed
f
o
r
lo
wer
-
o
r
d
e
r
s
u
b
s
y
s
tem
s
,
wh
ile
th
e
o
v
er
all
s
y
s
tem
s
tab
ilit
y
i
s
en
s
u
r
ed
b
y
co
n
s
tr
u
ctin
g
a
ca
n
d
id
ate
L
y
a
p
u
n
o
v
f
u
n
ctio
n
th
at
ag
g
r
eg
ates
th
e
f
u
n
ctio
n
s
d
er
iv
ed
at
ea
ch
d
esig
n
s
tep
[
1
2
]
.
T
h
e
b
ac
k
s
tep
p
i
n
g
co
n
tr
o
l
f
o
r
D
PC
o
f
a
th
r
ee
-
p
h
ase
PW
M
r
ec
tifie
r
was
p
r
o
p
o
s
ed
b
y
R
o
n
g
et
al
i
n
2
0
1
8
[
1
2
]
;
it
was
u
s
ed
to
r
eg
u
late
th
e
r
ea
ct
iv
e
p
o
wer
a
n
d
DC
-
b
u
s
v
o
ltag
e
o
f
th
e
r
ec
tifie
r
.
H
o
wev
er
,
th
is
m
eth
o
d
b
r
ea
k
s
d
o
wn
u
n
d
e
r
v
ar
y
in
g
lo
ad
co
n
d
i
tio
n
s
[
1
3
]
an
d
r
elies
on
th
e
s
ig
n
f
u
n
ctio
n
(
1
3
)
an
d
(
1
5
)
,
w
h
ich
in
tr
o
d
u
ce
s
th
e
we
ll
-
k
n
o
wn
c
h
atter
in
g
an
d
h
ig
h
-
f
r
eq
u
e
n
cy
r
ip
p
le.
I
n
co
n
tr
ast,
th
e
co
n
t
r
o
l
law
d
ev
e
lo
p
ed
i
n
th
is
p
ap
er
av
o
id
s
th
e
s
ig
n
f
u
n
ctio
n
,
lea
d
in
g
to
s
m
o
o
th
c
o
n
tr
o
l
ac
ti
o
n
with
o
u
t
ch
atter
in
g
,
wh
ile
m
ain
tain
in
g
h
ig
h
p
er
f
o
r
m
an
ce
u
n
d
er
n
o
r
m
al,
u
n
b
alan
ce
d
,
an
d
d
is
to
r
ted
g
r
id
co
n
d
itio
n
s
,
as
well
as
u
n
d
er
p
ar
am
eter
v
a
r
iatio
n
s
.
I
n
th
is
p
ap
er
,
we
ta
k
e
a
s
tep
f
u
r
th
er
b
y
p
r
o
p
o
s
in
g
a
B
S
co
n
tr
o
ller
f
o
r
DC
v
o
ltag
e
,
ac
tiv
e
p
o
wer
,
an
d
r
ea
ctiv
e
p
o
wer
to
o
v
er
co
m
e
th
e
p
r
e
v
io
u
s
lim
itatio
n
.
T
h
e
co
n
tr
o
l
law
is
v
alid
ated
b
y
a
p
r
o
ce
s
s
o
r
-
in
-
th
e
-
l
o
o
p
(
PIL
)
im
p
lem
e
n
t
atio
n
.
T
h
is
p
ap
er
p
r
esen
ts
an
im
p
r
o
v
ed
DPC
-
b
ac
k
s
tep
p
in
g
s
tr
ateg
y
f
o
r
a
t
h
r
ee
-
p
h
ase
PW
M
r
ec
tifie
r
.
T
h
e
m
ain
o
b
jectiv
es
ar
e
to
m
ain
tain
g
o
o
d
p
er
f
o
r
m
a
n
ce
u
n
d
er
v
ar
io
u
s
d
is
tu
r
b
an
ce
s
,
en
s
u
r
e
u
n
it
y
p
o
wer
f
ac
to
r
,
a
n
d
ac
h
iev
e
lo
w
cu
r
r
en
t
T
HD
(
u
n
d
er
5
%).
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
eth
o
d
aim
s
to
elim
in
ate
t
h
e
class
ical
s
witch
in
g
tab
le
o
f
DPC
co
n
tr
o
l
[
1
4
]
-
[
1
7
]
an
d
th
e
lim
itatio
n
s
o
f
t
h
e
p
r
ev
i
o
u
s
DPC
-
BS
ap
p
r
o
ac
h
.
T
h
is
s
tu
d
y
will
co
m
p
ar
e
DPC
an
d
DPC
-
B
S
,
d
em
o
n
s
tr
ate
th
e
tr
ad
e
-
o
f
f
s
b
etwe
en
t
h
e
two
co
n
tr
o
ls
,
an
d
h
ig
h
lig
h
t
th
e
ad
v
an
tag
es o
f
th
e
p
r
o
p
o
s
ed
DPC
-
b
ac
k
s
tep
p
in
g
co
n
t
r
o
l.
2.
T
H
E
P
W
M
RE
CT
I
F
I
E
R
T
h
e
ac
tiv
e
r
ec
tifie
r
s
tu
d
ie
d
in
th
is
p
ap
er
is
b
ased
o
n
th
r
ee
le
g
s
,
ea
ch
o
n
e
co
n
s
is
tin
g
o
f
two
s
witch
es
th
at
co
n
tain
an
I
GB
T
tr
a
n
s
is
t
o
r
with
an
an
tip
ar
allel
d
io
d
e
[
1
8
]
-
[
2
1
]
.
F
ig
u
r
e
1
illu
s
tr
ates
an
ac
tiv
e
r
e
ctif
ier
s
ch
em
e
,
wh
er
e
e
a
,
e
b
,
e
c
ar
e
A
C
g
r
id
v
o
ltag
es;
R
,
L
ar
e
th
e
eq
u
iv
alen
t
r
esis
tan
ce
an
d
in
d
u
c
tan
ce
o
f
th
e
g
r
i
d
;
C
is
th
e
DC
b
u
s
ca
p
ac
ito
r
;
R
L
is
th
e
lo
a
d
r
esis
tan
ce
;
i
a
,
i
b
,
i
c
a
r
e
AC
g
r
id
cu
r
r
en
ts
;
I
dc
is
DC
lo
ad
cu
r
r
e
n
t;
an
d
V
d
c
is
DC
lo
ad
v
o
ltag
e.
T
h
e
co
u
p
lin
g
g
r
id
r
esis
tan
ce
s
(
R
)
an
d
g
r
id
r
e
ac
tan
ce
(
L
)
ar
e
e
q
u
al.
Switch
in
g
lo
s
s
an
d
o
n
-
s
tate
v
o
ltag
e
a
r
e
n
eg
li
g
ib
le,
a
n
d
t
h
e
s
witch
in
g
f
r
e
q
u
en
cy
is
ass
u
m
ed
to
b
e
h
ig
h
e
n
o
u
g
h
.
Ass
u
m
in
g
a
u
n
ity
p
o
wer
f
ac
to
r
,
g
r
i
d
v
o
ltag
e
an
d
cu
r
r
en
t a
r
e
(
1
)
.
{
(
)
=
.
(
)
(
)
=
.
(
−
2
3
)
(
)
=
.
s
in
(
−
4
3
)
{
(
)
=
.
(
)
(
)
=
.
(
−
2
3
)
(
)
=
.
s
in
(
−
4
3
)
(
1
)
W
h
er
e
,
,
,
r
esp
ec
tiv
ely
,
a
r
e
th
e
m
ax
im
u
m
s
im
p
le
v
o
ltag
e
(
V
)
,
th
e
m
a
x
im
u
m
g
r
id
c
u
r
r
e
n
t
(
A
)
,
an
d
th
e
an
g
u
lar
f
r
eq
u
e
n
cy
(
r
ad
/s
)
.
Fro
m
Fig
u
r
e
1
,
we
ca
n
f
in
d
:
[
]
=
.
[
]
+
.
[
]
+
[
]
(
2
)
B
y
tr
an
s
f
o
r
m
in
g
(
2
)
to
th
e
α
β r
ef
er
en
ce
f
r
am
e,
we
o
b
tain
:
=
+
.
+
(
3
)
=
+
.
+
(
4
)
I
n
th
is
r
ef
er
e
n
ce
,
ac
tiv
e
a
n
d
r
e
ac
tiv
e
p
o
wer
(
P a
n
d
Q)
ca
n
b
e
ex
p
r
ess
ed
as (
5
)
a
n
d
(
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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
180
8
-
1
8
2
1
1810
=
.
+
.
(
5
)
=
.
−
.
(
6
)
T
h
ese
eq
u
atio
n
s
ar
e
v
er
y
im
p
o
r
tan
t a
n
d
f
o
r
m
t
h
e
f
o
u
n
d
atio
n
o
f
th
e
co
n
tr
o
l th
e
o
r
y
b
ein
g
s
tu
d
ied
.
Fig
u
r
e
1
.
Activ
e
r
ec
tifie
r
s
ch
e
m
e
3.
DE
S
I
G
N
O
F
B
ACK
S
T
E
P
P
I
NG
CO
NT
RO
L
T
h
e
b
ac
k
s
tep
p
in
g
tec
h
n
iq
u
e
p
r
o
v
id
es
a
s
y
s
tem
atic
an
d
r
e
cu
r
s
iv
e
m
eth
o
d
f
o
r
d
esig
n
in
g
n
o
n
lin
ea
r
co
n
tr
o
l
laws,
r
el
y
in
g
o
n
L
y
ap
u
n
o
v
f
u
n
ctio
n
s
to
en
s
u
r
e
th
e
s
tep
-
by
-
s
tep
s
tab
ilit
y
o
f
ea
ch
s
y
n
th
esis
s
tep
.
At
ea
ch
s
tag
e
o
f
th
e
p
r
o
ce
s
s
,
v
ir
tu
al
co
n
tr
o
l
in
p
u
ts
ar
e
g
en
er
ated
to
d
r
iv
e
th
e
s
y
s
tem
s
tates
to
war
d
s
th
eir
eq
u
ilib
r
iu
m
s
tate.
T
h
is
tech
n
iq
u
e
allo
ws
th
e
s
y
n
th
esis
o
f
co
n
tr
o
l
laws
wh
ile
p
o
ten
tially
co
n
s
id
er
in
g
d
is
tu
r
b
an
ce
s
o
r
u
n
f
am
iliar
ity
with
th
e
s
y
s
tem
’
s
p
ar
am
eter
s
.
3
.
1
.
B
a
c
k
s
t
eppin
g
co
ntr
o
l f
o
r
t
he
DC
B
us
Ou
r
o
b
jectiv
e
is
t
o
d
ef
in
e
th
e
ac
tiv
e
p
o
wer
ex
p
r
ess
io
n
f
r
o
m
th
e
v
o
ltag
e
r
e
f
er
en
ce
.
B
ased
o
n
Fig
u
r
e
1
,
u
s
in
g
Kir
ch
h
o
f
f
'
s
laws,
we
ca
n
f
in
d
:
=
+
(
7
)
W
ith
:
{
=
.
=
(
8)
T
h
en
,
f
r
o
m
(
7
)
a
n
d
(
8
)
,
we
ca
n
wr
ite:
=
1
.
(
−
)
(
9)
T
h
e
s
tead
y
-
s
tate
er
r
o
r
o
f
t
h
e
D
C
v
o
ltag
e
is
d
ef
in
ed
as
(
1
0
)
.
1
=
−
(
1
0
)
No
w,
a
p
o
s
itiv
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
with
a
n
eg
ativ
e
d
er
iv
ativ
e
m
u
s
t b
e
s
elec
ted
.
T
h
is
f
u
n
ctio
n
,
u
n
d
er
th
ese
cr
iter
ia,
will
en
s
u
r
e
th
e
s
y
s
tem
’
s
s
tab
ilit
y
with
o
u
t
d
i
v
er
g
en
ce
;
T
h
e
L
y
ap
u
n
o
v
th
e
o
r
y
is
ac
tu
ally
q
u
ite
lo
g
ical.
I
f
y
o
u
h
av
e
s
o
m
e
f
u
n
c
tio
n
th
at
is
alwa
y
s
d
ec
r
ea
s
in
g
,
th
en
it
will
r
ea
ch
ze
r
o
ev
e
n
tu
ally
.
So
,
t
h
er
e
is
n
o
way
th
at
th
e
s
y
s
tem
d
iv
er
g
es: it m
u
s
t b
e
s
tab
le.
T
h
e
ch
o
s
en
ca
n
d
id
ate
f
o
r
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
:
1
=
1
2
.
θ
1
2
(
1
1
)
1
=
1
.
1
(
1
2
)
T
o
en
s
u
r
e
s
y
s
tem
s
tab
ilit
y
,
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
d
er
i
v
ativ
e
m
u
s
t b
e
n
eg
ativ
e
;
c
h
o
o
s
in
g
1
=
−
1
·
1
(
wh
er
e
K
1
>
0
)
g
u
a
r
an
tees th
is
s
y
s
tem
's
co
n
v
er
g
en
ce
a
n
d
s
ta
b
ilit
y
.
Fro
m
(
9
)
an
d
(
1
0
)
,
we
h
av
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
6
9
4
DP
C
b
a
ck
s
tep
p
in
g
co
n
tr
o
l a
p
p
lied
to
a
n
a
ctive
r
ec
tifi
er:
a
n
a
lysi
s
a
n
d
co
mp
a
r
is
o
n
…
(
S
lima
n
e
C
h
ib
o
u
b
)
1811
1
̇
=
̇
−
̇
(
1
3
)
1
̇
=
̇
−
1
.
(
−
)
=
−
1
.
1
(
1
4
)
W
ith
̇
=
0
we
ca
n
ea
s
ily
f
in
d
th
e
a
ctiv
e
p
o
wer
ex
p
r
ess
io
n
.
T
h
is
b
lo
ck
will g
en
er
ate
o
u
r
p
o
wer
r
ef
er
en
ce
;
th
e
r
ea
ctiv
e
p
o
we
r
r
ef
er
e
n
ce
is
n
u
ll.
=
.
(
1
1
.
+
)
(
1
5
)
3
.
2
.
B
a
c
k
s
t
eppin
g
f
o
r
a
ct
iv
e
a
nd
re
a
ct
iv
e
po
wer
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
tead
y
-
s
tate
er
r
o
r
s
ar
e:
2
=
−
(
1
6
)
3
=
−
(
1
7
)
I
n
B
S th
eo
r
y
,
t
h
e
s
ec
o
n
d
L
y
ap
u
n
o
v
f
u
n
ctio
n
m
u
s
t
b
e
wr
itten
as
(
1
8
)
-
(
2
0
)
.
2
=
1
+
1
2
.
(
2
2
+
3
2
)
(
1
8
)
̇
2
=
1
̇
+
2
.
2
+
3
.
3
(
1
9
)
̇
2
=
−
1
1
2
−
2
2
2
−
3
3
2
<
0
;
∀
≠
0
∀
>
0
(
2
0
)
T
h
e
d
er
iv
ativ
es o
f
th
e
s
tead
y
-
s
tate
er
r
o
r
s
ar
e
(
2
1
)
a
n
d
(
2
2
)
.
2
̇
=
̇
−
̇
(
2
1
)
̇
3
=
̇
−
̇
(
2
2
)
Acc
o
r
d
in
g
t
o
(
3
)
-
(
6
)
,
an
d
b
y
n
eg
lectin
g
th
e
g
r
id
r
esis
tan
ce
,
t
h
e
d
er
iv
ativ
es o
f
th
e
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
s
ar
e
(
2
3
)
an
d
(
2
4
)
.
̇
=
̇
.
+
.
̇
+
̇
.
+
.
̇
̇
=
−
·
·
+
(
−
)
·
+
·
·
+
(
−
)
·
(
2
3
)
̇
=
̇
.
+
.
̇
−
̇
.
−
.
̇
=
·
·
+
(
−
)
·
+
·
·
−
(
−
)
·
(
2
4
)
B
y
r
ea
r
r
an
g
i
n
g
th
ese
two
eq
u
a
tio
n
s
,
we
will f
in
d
:
̇
=
·
(
·
−
·
)
+
(
−
)
·
+
(
−
)
·
=
−
·
+
(
2
+
2
−
·
−
·
)
(
2
5
)
̇
=
·
(
·
+
·
)
+
(
−
)
·
−
(
−
)
·
=
·
+
(
·
−
·
)
(
2
6
)
Su
b
s
titu
tin
g
(
2
5
)
an
d
(
2
6
)
in
to
(
2
1
)
a
n
d
(
2
2
)
,
we
will h
av
e:
̇
₂
=
̇
+
·
−
(
2
−
(
·
+
·
)
)
=
−
₂
·
₂
(
2
7
)
̇
₃
=
0
−
·
−
(
·
−
·
)
=
−
₃
·
₃
(
2
8
)
W
ith
2
=
2
+
2
.
Fin
ally
,
f
r
o
m
t
h
e
p
r
e
v
io
u
s
eq
u
ati
ons
,
we
ca
n
f
in
d
th
a
t o
u
r
co
n
tr
o
l sig
n
als ar
e:
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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
180
8
-
1
8
2
1
1812
=
2
.
[
−
2
⋅
2
⋅
−
3
⋅
3
⋅
+
⋅
⋅
−
⋅
(
̇
−
2
+
⋅
)
]
(
2
9
)
=
2
⋅
[
−
2
⋅
2
⋅
+
3
⋅
3
⋅
−
⋅
⋅
−
⋅
(
̇
−
2
+
⋅
)
]
(
3
0
)
T
h
e
(
2
0
)
en
s
u
r
es
s
y
s
tem
s
tab
ilit
y
if
K
1
, K
2
,
an
d
K
3
a
r
e
all
p
o
s
itiv
e
g
ain
s
.
3
.
3
.
DP
C
-
B
a
c
k
s
t
eppin
g
co
ntr
o
l schem
e
T
o
u
n
d
e
r
s
tan
d
th
e
im
p
lem
e
n
tatio
n
o
f
th
e
co
n
tr
o
ller
,
Fig
u
r
e
2
illu
s
tr
ates
th
e
b
lo
ck
d
iag
r
am
o
f
th
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
l.
T
h
is
d
iag
r
am
h
ig
h
lig
h
ts
th
e
i
n
teg
r
a
tio
n
o
f
th
e
b
ac
k
s
tep
p
in
g
law
with
in
th
e
ac
tiv
e
r
ec
tifie
r
s
y
s
tem
.
T
h
e
PW
M
g
en
er
ato
r
p
r
o
d
u
ce
s
th
e
s
ix
p
u
ls
es
r
eq
u
ir
ed
t
o
co
n
tr
o
l
th
e
s
ix
elec
tr
o
n
ic
s
witch
es
o
f
th
e
ac
tiv
e
r
ec
tifie
r
.
Fig
u
r
e
2
.
DPC
-
b
ac
k
s
tep
p
in
g
b
lo
ck
d
iag
r
a
m
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
o
d
em
o
n
s
tr
ate
th
e
ef
f
ec
ti
v
en
ess
o
f
o
u
r
DPC
-
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
s
tr
ateg
y
,
w
e
u
s
e
th
e
MA
T
L
AB
/S
im
u
lin
k
en
v
ir
o
n
m
en
t.
T
h
is
r
o
b
u
s
t
an
d
r
elia
b
le
s
im
u
latio
n
to
o
l
will
d
e
m
o
n
s
tr
ate,
th
r
o
u
g
h
s
im
u
latio
n
,
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l.
T
h
e
s
im
u
latio
n
s
ce
n
ar
io
b
e
g
in
s
with
a
r
ef
er
e
n
ce
DC
v
o
ltag
e
o
f
7
0
0
V
;
af
ter
o
n
e
s
e
co
n
d
,
th
e
r
ef
er
e
n
ce
is
s
tep
p
ed
u
p
to
8
0
0
V;
f
in
ally
,
it
is
s
tep
p
ed
d
o
w
n
to
6
0
0
V
with
a
s
witch
in
g
f
r
eq
u
en
cy
o
f
5
0
k
Hz.
T
h
e
m
ain
o
b
jectiv
e
o
f
th
ese
tr
an
s
itio
n
s
is
to
an
aly
ze
th
e
s
y
s
tem
's
b
eh
av
io
r
d
u
r
i
n
g
tr
a
n
s
ien
t
ch
a
n
g
e
an
d
ex
am
i
n
e
th
e
e
v
o
lu
tio
n
o
f
t
h
e
g
r
i
d
cu
r
r
en
t
an
d
its
c
o
r
r
esp
o
n
d
in
g
T
HD,
th
e
p
o
wer
f
ac
to
r
,
an
d
th
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
wer
.
T
o
c
o
m
p
ar
e,
th
r
o
u
g
h
s
im
u
latio
n
,
th
e
co
n
v
en
tio
n
al
DPC
co
n
tr
o
l
with
th
e
DPC
-
b
ac
k
s
tep
p
in
g
c
o
n
tr
o
l
an
d
i
d
en
tify
t
h
e
ad
v
an
tag
es
th
at
t
h
e
p
r
o
p
o
s
e
d
co
n
tr
o
ller
o
f
f
er
s
,
an
d
d
eter
m
in
e
a
n
y
p
o
te
n
tial
lim
itatio
n
s
it
m
ay
h
av
e
co
m
p
ar
ed
to
co
n
v
e
n
tio
n
al
DPC
,
we
will
im
p
o
s
e
d
if
f
er
en
t
s
ce
n
ar
io
s
in
wh
ich
we
wan
t to
ev
alu
ate
th
e
o
p
tim
al
p
er
f
o
r
m
a
n
ce
of
ea
c
h
co
n
t
r
o
l stra
teg
y
.
4
.
1
.
T
he
s
y
s
t
em
's
pa
ra
m
e
t
er
s
T
h
e
s
y
s
tem
is
s
im
u
lated
u
s
in
g
th
e
p
ar
am
eter
s
lis
ted
in
T
ab
le
1
.
T
h
e
ch
o
s
en
p
ar
am
eter
s
ar
e
wid
ely
ad
o
p
ted
in
t
h
e
liter
atu
r
e
[
2
2
]
-
[
2
5
]
to
r
ef
lect
r
ea
lis
tic
o
p
e
r
atin
g
co
n
d
itio
n
s
.
T
h
ese
p
a
r
am
eter
s
d
ef
in
e
th
e
elec
tr
ical
an
d
co
n
tr
o
l
co
n
d
itio
n
s
o
f
th
e
ac
tiv
e
r
ec
tifie
r
.
T
ab
le
1
.
Sy
s
tem
'
s
p
ar
am
eter
s
P
a
r
a
me
t
e
r
S
y
mb
o
l
V
a
l
u
e
P
a
r
a
me
t
e
r
S
y
mb
o
l
V
a
l
u
e
D
C
v
o
l
t
a
g
e
V
dc
6
0
0
t
o
8
0
0
V
G
r
i
d
r
e
s
i
st
a
n
c
e
R
0
.
1
Ω
G
r
i
d
v
o
l
t
a
g
e
(
R
M
S
)
e
g
2
3
0
V
D
C
b
u
s
c
a
p
a
c
i
t
y
C
2
mF
G
r
i
d
f
r
e
q
u
e
n
c
y
f
5
0
H
z
Lo
a
d
r
e
si
s
t
a
n
c
e
R
L
5
0
Ω
G
r
i
d
i
n
d
u
c
t
a
n
c
e
L
5
a
n
d
1
0
mH
S
a
mp
l
i
n
g
f
r
e
q
u
e
n
c
y
fs
5
0
k
H
z
4
.
2
.
Sim
ula
t
i
o
n r
esu
lt
s
o
f
DP
C
a
nd
DP
C
-
B
S u
nd
er
ba
la
nced
G
rid w
it
h
L
=
5
m
H
I
n
th
is
s
im
u
latio
n
,
we
will
an
aly
ze
th
e
b
eh
a
v
io
r
o
f
th
e
co
n
t
r
o
l
s
tr
ateg
ies
u
n
d
er
o
p
tim
al
a
n
d
n
o
r
m
al
g
r
id
co
n
d
itio
n
s
.
T
h
e
s
y
s
tem
p
er
f
o
r
m
s
o
p
tim
ally
with
a
g
r
id
in
d
u
ctan
ce
(
L
)
o
f
5
m
H,
w
h
ich
r
ep
r
esen
ts
th
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
6
9
4
DP
C
b
a
ck
s
tep
p
in
g
co
n
tr
o
l a
p
p
lied
to
a
n
a
ctive
r
ec
tifi
er:
a
n
a
lysi
s
a
n
d
co
mp
a
r
is
o
n
…
(
S
lima
n
e
C
h
ib
o
u
b
)
1813
o
p
tim
al
o
p
er
ati
n
g
co
n
d
itio
n
co
n
s
id
er
ed
in
th
is
s
tu
d
y
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
o
u
r
s
y
s
tem
u
n
d
er
th
e
MA
T
L
AB
/S
im
u
lin
k
en
v
ir
o
n
m
en
t a
r
e
p
r
esen
ted
in
Fig
u
r
es 3
–
6
.
B
ased
o
n
th
e
p
r
esen
ted
s
im
u
l
atio
n
r
esu
lts
,
b
o
th
co
n
t
r
o
l
s
tr
ateg
ies
d
em
o
n
s
tr
ate
g
o
o
d
p
er
f
o
r
m
an
ce
as
s
h
o
wn
in
Fig
u
r
e
3
;
th
e
DC
-
B
u
s
v
o
ltag
e
tr
ac
k
s
its
r
ef
er
en
ce
ac
cu
r
ately
with
a
n
eg
lig
ib
le
s
tead
y
-
s
tat
e
er
r
o
r
.
Ov
er
all,
DPC
-
B
S
co
n
tr
o
l
ex
h
ib
its
a
f
aster
d
y
n
am
ic
r
esp
o
n
s
e,
lo
wer
o
v
er
s
h
o
o
t,
less
n
o
is
y
cu
r
r
en
t
(
1
.
7
6
%
v
s
3
.
3
7
%)
,
an
d
n
ea
r
-
ze
r
o
r
ea
cti
v
e
p
o
wer
ab
s
o
r
p
tio
n
.
C
o
n
v
e
r
s
ely
,
DPC
co
n
tr
o
l
p
r
o
v
id
es
a
s
m
o
o
th
er
cu
r
r
en
t
r
esp
o
n
s
e
,
wh
ile
DPC
-
B
S
g
en
er
ates
s
p
ik
es
d
u
r
in
g
tr
an
s
ien
t
ch
an
g
es
(
Fig
u
r
e
4
)
d
u
e
to
th
e
p
o
wer
d
er
i
v
ativ
e
ter
m
in
th
e
co
n
tr
o
l
law.
H
o
wev
er
,
th
ese
s
p
ik
es
a
r
e
r
a
p
id
ly
d
am
p
ed
b
y
th
e
p
r
o
p
o
s
ed
co
n
t
r
o
ller
.
B
o
th
s
tr
ateg
ies
m
ee
t o
u
r
k
ey
o
b
jectiv
e
;
h
o
we
v
er
,
DPC
-
B
S c
o
n
tr
o
l
p
r
o
v
i
d
es
s
u
p
er
io
r
T
HD
p
e
r
f
o
r
m
an
ce
b
ec
au
s
e
DPC
ab
s
o
r
b
s
a
s
m
all
am
o
u
n
t
o
f
r
ea
ctiv
e
p
o
wer
(
Fig
u
r
e
5
)
.
Fu
r
th
er
m
o
r
e,
u
n
d
er
n
o
r
m
al
c
o
n
d
itio
n
s
,
th
e
g
r
id
c
u
r
r
e
n
ts
ex
h
ib
it
ex
ce
llen
t sin
u
s
o
id
al
b
eh
a
v
io
r
an
d
ar
e
in
p
h
ase
with
th
eir
c
o
r
r
esp
o
n
d
in
g
g
r
i
d
v
o
ltag
e
(
Fig
u
r
e
6
)
.
(
a)
(
b
)
Fig
u
r
e
3
.
DC
-
B
u
s
v
o
ltag
e
r
es
p
o
n
s
e:
(
a)
o
v
er
all
r
esp
o
n
s
e
an
d
(
b
)
t
r
an
s
ien
t step
o
f
Vd
c
v
o
lt
ag
e
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
4
.
Gr
id
cu
r
r
e
n
t a
n
d
T
H
D
co
m
p
ar
is
o
n
o
f
DPC
-
B
S a
n
d
DPC
co
n
tr
o
ls
: (
a)
DPC
-
B
S g
r
id
cu
r
r
e
n
t,
(
b
)
DPC
g
r
id
cu
r
r
en
t,
(
c)
zo
o
m
ed
-
in
DPC
-
B
S g
r
id
cu
r
r
e
n
t a
t 8
0
0
V
Vd
c,
(
d
)
zo
o
m
e
d
-
in
D
PC
g
r
id
cu
r
r
en
t a
t
8
0
0
V
Vd
c,
(
e)
DPC
-
B
S c
u
r
r
en
t T
HD
(
1
.
7
6
%),
an
d
(
f
)
DPC
c
u
r
r
en
t T
HD
(
3
.
3
7
%)
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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
180
8
-
1
8
2
1
1814
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
5
.
Activ
e
a
n
d
r
ea
ctiv
e
p
o
wer
r
esp
o
n
s
e:
(
a)
o
v
er
all
r
e
s
p
o
n
s
e
(
DPC
-
B
S),
(
b
)
z
o
o
m
o
f
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
(
DPC
-
B
S),
(
c)
o
v
er
all
r
esp
o
n
s
e
(
DPC
)
,
an
d
(
d
)
z
o
o
m
o
f
t
h
e
ac
tiv
e
an
d
r
ea
c
tiv
e
p
o
wer
(
DPC
)
(
a)
(
b
)
F
i
g
u
r
e
6
.
G
r
i
d
c
u
r
r
e
n
t
a
n
d
v
o
l
ta
g
e
:
(
a
)
D
PC
-
B
S
g
r
i
d
c
u
r
r
e
n
t
an
d
v
o
l
t
a
g
e
a
n
d
(
b
)
D
P
C
g
r
i
d
c
u
r
r
e
n
t
a
n
d
v
o
l
t
a
g
e
4
.
3
.
Sim
ula
t
i
o
n r
esu
lt
s
o
f
DP
C
a
nd
DP
C
-
B
S u
nd
er
un
b
a
la
nced
G
rid w
it
h L
=
5
m
H
T
o
ev
alu
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
ller
u
n
d
er
u
n
b
alan
ce
d
g
r
id
co
n
d
i
tio
n
s
,
th
e
s
ec
o
n
d
p
h
ase
v
o
ltag
e
(
eb
)
is
d
ec
r
ea
s
ed
b
y
1
0
%
,
an
d
th
e
th
ir
d
p
h
ase
v
o
ltag
e
(
ec
)
is
in
cr
ea
s
ed
b
y
5
%.
C
o
n
s
eq
u
en
tly
,
as
illu
s
tr
ated
in
Fig
u
r
e
6
,
th
e
th
r
ee
-
p
h
ase
R
MS
v
o
ltag
es
ar
e
s
et
to
[
ea
,
eb
,
ec
]
=
[
2
3
0
,
2
0
7
,
2
4
1
]
V.
T
h
e
s
im
u
latio
n
r
esu
lts
ar
e
p
r
esen
ted
b
elo
w.
Un
d
er
u
n
b
alan
ce
d
g
r
id
co
n
d
itio
n
s
,
b
o
th
co
n
t
r
o
l
s
tr
ate
g
ies'
p
er
f
o
r
m
an
ce
d
eg
r
a
d
es
;
h
o
wev
er
,
co
m
p
ar
ed
t
o
DPC
,
th
e
p
r
o
p
o
s
ed
DPC
-
B
S
co
n
tr
o
ller
d
em
o
n
s
tr
ates
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
,
with
a
m
ax
im
u
m
cu
r
r
en
t
T
HD
o
f
4
.
9
1
%
as
s
h
o
wn
in
Fig
u
r
es
7
an
d
8
,
s
ati
s
f
y
in
g
o
u
r
o
b
jectiv
e
(
T
HD
<5
%).
W
h
ile
DP
C
ex
h
ib
its
b
etter
Vd
c
v
o
ltag
e
tr
ac
k
in
g
b
y
m
ain
tain
i
n
g
a
s
m
all
s
tead
y
-
s
tate
er
r
o
r
,
as
Fig
u
r
e
9
s
h
o
ws
(
0
.
3
V
v
s
.
1
.
5
V
f
o
r
th
e
DPC
-
B
S),
it
u
n
d
er
p
er
f
o
r
m
s
in
ev
er
y
o
th
er
asp
ec
t.
I
n
f
ac
t,
DPC
f
ails
to
m
ain
tain
a
cu
r
r
en
t
T
HD
u
n
d
er
5
%
o
r
a
u
n
ity
p
o
wer
f
ac
to
r
,
as
d
ep
icted
i
n
Fig
u
r
e
1
0
;
th
e
DPC
co
n
tr
o
l
s
tr
ateg
y
co
n
s
u
m
es
a
s
m
all
am
o
u
n
t
o
f
r
ea
ctiv
e
p
o
wer
,
w
h
ile
th
e
DPC
-
B
S
r
ea
ctiv
e
p
o
wer
r
em
ain
s
ze
r
o
.
O
v
er
all,
e
v
en
with
a
s
lig
h
tly
h
ig
h
er
s
tead
y
-
s
tate
er
r
o
r
,
t
h
e
DPC
-
B
S st
r
ateg
y
o
u
tp
er
f
o
r
m
s
co
n
v
e
n
tio
n
al
DPC
b
y
m
ee
tin
g
o
u
r
k
ey
o
b
jectiv
es.
4
.
4
.
P
e
r
f
o
rm
a
n
c
e
o
f
D
P
C
v
s
.
D
P
C
-
B
S
u
n
d
e
r
d
i
s
t
o
r
t
e
d
g
r
i
d
co
n
d
i
t
i
o
n
s
a
n
d
u
n
f
a
v
o
ra
b
l
e
i
n
d
u
c
t
a
n
ce
L
=
1
0
m
H
T
o
ev
alu
ate
t
h
e
r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
ed
DPC
-
B
S
co
n
tr
o
ller
,
two
u
n
f
av
o
r
ab
le
co
n
d
itio
n
s
ar
e
im
p
o
s
ed
.
First,
th
e
g
r
id
in
d
u
c
tan
ce
is
in
cr
ea
s
ed
to
L
=
1
0
m
H,
wh
ich
is
twice
th
e
n
o
m
i
n
al
d
esig
n
v
alu
e
o
f
5
m
H.
Seco
n
d
,
a
5
th
h
ar
m
o
n
i
c
co
m
p
o
n
en
t
with
an
a
m
p
litu
d
e
o
f
5
%
o
f
th
e
f
u
n
d
am
en
tal
v
o
ltag
e
is
in
jecte
d
in
to
all
th
r
ee
p
h
ases
.
T
h
ese
ex
tr
em
e,
y
et
u
n
f
av
o
r
ab
le
co
n
d
itio
n
s
s
tr
ess
-
tes
t
o
u
r
co
n
tr
o
l
ler
'
s
ad
ap
tatio
n
to
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
DP
C
b
a
ck
s
tep
p
in
g
co
n
tr
o
l a
p
p
lied
to
a
n
a
ctive
r
ec
tifi
er:
a
n
a
lysi
s
a
n
d
co
mp
a
r
is
o
n
…
(
S
lima
n
e
C
h
ib
o
u
b
)
1815
pa
r
am
eter
v
ar
iatio
n
s
a
n
d
d
is
tu
r
b
an
ce
r
ejec
tio
n
ca
p
ab
ilit
ies.
Fig
u
r
e
1
1
b
elo
w
s
h
o
ws
th
e
d
i
s
to
r
ted
g
r
id
v
o
ltag
e
u
s
ed
in
th
is
s
im
u
latio
n
.
T
h
e
s
im
u
latio
n
r
esu
lts
ar
e
p
r
esen
te
d
in
th
e
n
ex
t
f
ig
u
r
es.
I
n
th
is
s
im
u
latio
n
,
t
h
e
in
tr
o
d
u
ctio
n
o
f
th
e
5
th
h
ar
m
o
n
ic
(
F
ig
u
r
e
1
1
)
c
o
m
b
in
e
d
with
in
c
r
ea
s
ed
g
r
id
in
d
u
ctan
ce
L
im
p
o
s
es
u
n
f
a
v
o
r
ab
le
an
d
ch
alle
n
g
in
g
c
o
n
d
itio
n
s
.
B
o
th
s
tr
ateg
ies
m
ain
tain
s
tab
ilit
y
at
th
e
p
r
ice
o
f
p
er
f
o
r
m
a
n
ce
;
th
e
g
r
id
c
u
r
r
en
t
(
Fig
u
r
e
1
2
)
s
u
f
f
er
s
f
r
o
m
i
n
ten
s
e
d
is
to
r
tio
n
as
its
T
HD
i
n
cr
ea
s
es
wh
ile
th
e
d
y
n
am
i
c
r
esp
o
n
s
e
d
ec
r
ea
s
es.
I
n
ad
d
itio
n
,
we
r
ea
ch
o
u
r
T
HD
lim
it o
f
5
.
8
2
% v
s
.
9
.
6
3
% a
s
F
ig
u
r
e
1
3
s
h
o
ws,
in
f
av
o
r
o
f
th
e
DPC
-
B
S,
wh
ich
co
n
f
ir
m
s
th
e
e
f
f
icac
y
an
d
r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l.
(
a)
(
b
)
(
c)
Fig
u
r
e
7
.
R
esp
o
n
s
e
u
n
d
er
u
n
b
alan
ce
d
g
r
id
v
o
ltag
e:
(
a)
u
n
b
al
an
ce
d
g
r
i
d
v
o
ltag
e
,
(
b
)
DPC
-
B
S c
u
r
r
en
t r
esp
o
n
s
e
u
n
d
er
u
n
b
ala
n
ce
d
g
r
id
,
a
n
d
(
c
)
DPC
cu
r
r
en
t r
esp
o
n
s
e
u
n
d
er
u
n
b
alan
ce
d
g
r
id
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
8
.
C
u
r
r
e
n
t T
HD
ch
ar
ac
ter
is
tics
o
f
th
e
DPC
an
d
DPC
-
B
S c
o
n
tr
o
ls
: (
a)
m
in
im
u
m
c
u
r
r
en
t T
HD
o
f
DPC
,
(
b
)
m
a
x
im
u
m
c
u
r
r
en
t T
HD
o
f
DPC
,
(
c)
m
in
im
u
m
cu
r
r
en
t T
HD
o
f
DPC
-
B
S,
an
d
(
d
)
m
a
x
im
u
m
c
u
r
r
en
t T
HD
o
f
DPC
-
BS
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.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
180
8
-
1
8
2
1
1816
(
a)
(
b
)
Fig
u
r
e
9
.
B
C
-
B
u
s
v
o
ltag
e
r
esp
o
n
s
e:
(
a)
o
v
er
all
r
esp
o
n
s
e
an
d
(
b
)
z
o
o
m
o
f
VDC v
o
ltag
e
u
n
d
er
8
0
0
V
(
a)
(
b
)
Fig
u
r
e
1
0
.
Activ
e
an
d
r
ea
ctiv
e
p
o
wer
r
esp
o
n
s
e:
(
a)
a
ctiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
o
f
DPC
co
n
tr
o
l
an
d
(
b
)
a
ctiv
e
a
n
d
r
ea
ctiv
e
p
o
wer
o
f
DPC
-
B
S
co
n
tr
o
l
(
a)
(
b
)
Fig
u
r
e
1
1
.
Dis
to
r
ted
g
r
id
v
o
lta
g
e:
(
a)
d
is
to
r
ted
g
r
id
v
o
ltag
e
e
v
o
lu
tio
n
a
n
d
(
b
)
T
HD
o
f
th
e
g
r
id
v
o
ltag
e
(
a)
(
b
)
Fig
u
r
e
1
2
.
Dis
to
r
ted
g
r
id
c
u
r
r
e
n
t o
f
: (
a)
DPC
-
B
S c
o
n
tr
o
l a
n
d
(
b
)
DPC
co
n
tr
o
l
As
DP
C
ex
h
ib
its
u
n
s
atis
f
ac
to
r
y
r
esu
lts
in
cu
r
r
en
t
T
HD,
it
also
f
ails
to
m
ain
tain
an
ac
ce
p
tab
le
Vd
c
r
esp
o
n
s
e
(
Fig
u
r
e
1
4
)
.
Desp
it
e
th
e
n
e
g
lig
ib
le
s
tead
y
-
s
tate
er
r
o
r
(
wh
ic
h
was
alwa
y
s
a
n
ad
v
a
n
tag
e
o
f
t
h
e
co
n
v
en
tio
n
al
DPC
)
,
th
e
f
ir
s
t
o
v
er
s
h
o
o
t
in
cr
ea
s
ed
d
r
am
at
ic
ally
,
lead
in
g
to
a
lo
n
g
er
r
esp
o
n
s
e
tim
e.
Vo
ltag
e
s
p
ik
es
ap
p
ea
r
f
o
r
th
e
f
ir
s
t
tim
e
in
s
tead
y
s
tate
at
8
0
0
V
Vd
c,
in
d
icatin
g
th
e
lim
itatio
n
o
f
DPC
in
ad
ap
tin
g
to
p
er
tu
r
b
atio
n
o
r
p
ar
am
eter
v
ar
iatio
n
.
I
n
co
n
cl
u
s
io
n
,
t
h
e
DPC
-
B
S
d
em
o
n
s
tr
ates
s
ig
n
if
ican
tly
b
ett
er
p
er
f
o
r
m
an
ce
th
a
n
DPC
co
n
tr
o
l
u
n
d
er
u
n
f
av
o
r
a
b
le
co
n
d
itio
n
s
;
h
o
wev
er
,
th
e
cu
r
r
e
n
t
T
HD
s
lig
h
tly
ex
ce
ed
s
th
e
5
% th
r
esh
o
ld
.
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
DP
C
b
a
ck
s
tep
p
in
g
co
n
tr
o
l a
p
p
lied
to
a
n
a
ctive
r
ec
tifi
er:
a
n
a
lysi
s
a
n
d
co
mp
a
r
is
o
n
…
(
S
lima
n
e
C
h
ib
o
u
b
)
1817
(
a)
(
b
)
Fig
u
r
e
1
3
.
T
HD
o
f
d
is
to
r
ted
g
r
id
cu
r
r
e
n
t
: (
a)
DPC
-
B
S (
5
.
8
2
%)
an
d
(
b
)
DPC
(
9
.
6
3
%)
(
a)
(
b
)
Fig
u
r
e
1
4
.
DC
-
b
u
s
v
o
ltag
e:
(
a
)
f
ir
s
t o
v
er
s
h
o
o
t o
f
Vd
c
v
o
ltag
e
an
d
(
b
)
z
o
o
m
o
f
Vd
c
r
esp
o
n
s
e
at
8
0
0
V
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
s
u
m
m
ar
ize
th
e
co
m
p
ar
at
iv
e
an
aly
s
is
o
f
th
e
DPC
an
d
DPC
-
B
S
co
n
tr
o
l
s
tr
ateg
ies,
T
ab
le
2
p
r
o
v
id
es
th
e
k
ey
d
if
f
er
en
ce
s
u
n
d
er
b
ala
n
ce
d
,
u
n
b
alan
c
ed
,
a
n
d
d
is
to
r
ted
g
r
i
d
co
n
d
itio
n
s
.
T
h
e
m
etr
ics
ev
alu
ated
in
cl
u
d
e
t
h
e
m
a
x
im
u
m
an
d
m
in
im
u
m
c
u
r
r
en
t
T
H
D,
s
tead
y
-
s
tate
er
r
o
r
o
f
th
e
D
C
-
B
US
v
o
ltag
e,
th
e
s
ettlin
g
tim
e
at
9
5
%,
a
n
d
t
h
e
f
ir
s
t
o
v
er
s
h
o
o
t.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
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ased
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n
th
e
DPC
-
B
S
s
tr
ateg
y
d
em
o
n
s
tr
ates
s
u
p
er
io
r
d
y
n
am
ic
r
esp
o
n
s
e,
r
o
b
u
s
tn
ess
ag
ain
s
t
p
ar
am
eter
v
ar
iatio
n
,
an
d
d
i
s
tu
r
b
an
ce
r
ejec
tio
n
ac
r
o
s
s
all
test
ed
s
ce
n
ar
io
s
.
T
h
e
co
n
v
en
tio
n
al
DPC
ac
h
iev
ed
a
lo
wer
s
tead
y
-
s
tate
er
r
o
r
,
b
u
t
it
u
n
d
er
p
e
r
f
o
r
m
s
in
cr
itic
al
m
etr
ics
s
u
ch
as
cu
r
r
en
t
T
HD
an
d
r
es
p
o
n
s
e
ti
m
e.
T
h
e
f
aster
tr
a
n
s
ien
t
p
er
f
o
r
m
a
n
ce
o
f
th
e
b
ac
k
s
tep
p
in
g
ap
p
r
o
ac
h
is
m
ain
ly
attr
ib
u
ted
to
th
e
p
r
esen
ce
o
f
th
e
d
er
iv
ati
v
e
ter
m
in
th
e
co
n
tr
o
l
law,
wh
ich
en
h
an
ce
s
th
e
s
y
s
tem
'
s
ab
ilit
y
to
tr
ac
k
r
ap
id
v
a
r
iatio
n
s
.
Ho
wev
er
,
th
e
s
am
e
d
e
r
iv
ativ
e
ac
tio
n
is
also
r
es
p
o
n
s
ib
le
f
o
r
lar
g
er
o
v
er
s
h
o
o
t.
Ov
er
all,
th
e
r
esu
lts
o
f
th
is
co
m
p
ar
ativ
e
s
tu
d
y
c
o
n
f
ir
m
t
h
e
ef
f
icien
c
y
o
f
th
e
b
ac
k
s
te
p
p
in
g
ap
p
r
o
ac
h
in
m
ain
tain
in
g
s
y
s
tem
s
tab
ilit
y
ev
en
u
n
d
er
u
n
f
av
o
r
ab
le
g
r
id
c
o
n
d
itio
n
s
.
T
ab
le
2
.
Su
m
m
a
r
y
o
f
co
m
p
ar
a
tiv
e
p
er
f
o
r
m
an
ce
o
f
DPC
an
d
DPC
-
BS
O
p
e
r
a
t
i
n
g
c
o
n
d
i
t
i
o
n
M
e
t
r
i
c
D
P
C
D
P
C
-
BS
C
o
m
p
a
r
i
so
n
w
i
n
n
e
r
B
a
l
a
n
c
e
d
g
r
i
d
M
a
x
c
u
r
r
e
n
t
TH
D
2
.
5
1
%
1
.
9
8
%
D
P
C
-
BS
M
i
n
c
u
r
r
e
n
t
TH
D
3
.
3
4
%
1
.
7
6
%
D
P
C
-
BS
V
d
c
s
t
e
a
d
y
-
st
a
t
e
e
r
r
o
r
<
0
.
1
V
1
.
2
V
t
o
1
.
3
V
D
P
C
R
e
s
p
o
n
se
t
i
me
(
9
5
%)
5
4
.
3
4
mS
1
6
.
3
mS
D
P
C
-
BS
F
i
r
st
o
v
e
r
sh
o
o
t
5
.
9
7
%
1
3
.
3
1
%
D
P
C
P
o
w
e
r
f
a
c
t
o
r
≈ 1
≈ 1
B
o
t
h
U
n
b
a
l
a
n
c
e
d
g
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d
M
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r
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D
5
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1
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6
%
D
P
C
-
BS
M
i
n
c
u
r
r
e
n
t
TH
D
5
.
2
1
%
4
.
8
1
%
D
P
C
-
BS
V
d
c
s
t
e
a
d
y
-
st
a
t
e
e
r
r
o
r
0
.
1
V
1
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2
V
t
o
1
.
5
V
D
P
C
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e
s
p
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n
se
t
i
me
(
9
5
%)
6
3
.
8
4
mS
1
6
.
4
7
mS
D
P
C
-
BS
F
i
r
st
o
v
e
r
sh
o
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t
7
%
1
3
.
3
7
%
D
P
C
P
o
w
e
r
f
a
c
t
o
r
≈ 1
≈ 1
b
o
t
h
D
i
st
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r
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e
d
g
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d
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P
C
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BS
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u
r
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n
t
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D
6
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4
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5
.
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2
%
D
P
C
-
BS
V
d
c
s
t
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a
d
y
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st
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t
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r
r
o
r
0
.
1
V
t
o
0
.
4
V
1
.
5
V
D
P
C
R
e
s
p
o
n
se
t
i
me
(
9
5
%)
1
6
0
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2
1
.
9
6
mS
D
P
C
-
BS
F
i
r
st
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v
e
r
sh
o
o
t
5
2
.
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%
7
.
6
%
D
P
C
-
BS
P
o
w
e
r
f
a
c
t
o
r
≈ 1
≈
0
.
9
9
9
8
D
P
C
-
BS
Evaluation Warning : The document was created with Spire.PDF for Python.