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[
1
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2
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[
3
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.
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[
4
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[
5
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6
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7
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s
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in
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s
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[
8
]
,
[
9
]
.
Am
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I
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ice
[
1
5
]
–
[
1
8
]
.
T
h
e
aim
o
f
o
u
r
p
r
o
p
o
s
ed
wo
r
k
is
to
f
o
r
m
u
late
a
tech
n
iq
u
e
wh
ich
ca
n
e
lim
in
ate
h
ar
m
o
n
ics
in
lo
ad
v
o
ltag
e
an
d
also
in
s
o
u
r
ce
cu
r
r
e
n
t.
I
n
th
is
p
ap
er
,
th
e
h
y
b
r
id
s
er
ies
ac
tiv
e
p
o
wer
f
ilter
(
HSAPF
)
i
s
d
esig
n
ed
u
s
in
g
o
p
tim
ized
p
r
o
p
o
r
tio
n
al
in
teg
r
al
(
PI)
co
n
tr
o
ller
g
ain
.
I
n
g
en
e
r
al,
th
e
c
o
n
tr
o
ller
d
o
es
two
o
p
e
r
atio
n
s
i.e
.
,
in
itiate
th
e
s
witch
in
g
p
u
ls
es
wh
ich
is
r
eq
u
ir
e
d
f
o
r
th
e
in
v
e
r
ter
an
d
g
en
e
r
ate
r
ef
er
e
n
ce
cu
r
r
en
t
[
1
9
]
–
[
2
1
]
.
T
h
e
s
elec
tio
n
o
f
p
r
o
p
er
r
ef
er
e
n
ce
co
n
tr
o
l
v
o
ltag
e
alg
o
r
ith
m
is
im
p
o
r
tan
t
to
r
ed
u
ce
h
ar
m
o
n
ics
an
d
g
et
im
p
r
o
v
e
d
r
esu
l
ts
.
T
o
g
en
er
ate
th
e
r
ef
er
en
ce
c
o
m
p
en
s
atin
g
v
o
ltag
e
m
an
y
m
eth
o
d
s
ca
n
b
e
f
o
u
n
d
in
th
e
liter
atu
r
e
an
d
o
n
e
o
f
th
e
m
is
in
s
tan
tan
eo
u
s
p
o
wer
th
eo
r
y
(
p
-
q
)
wh
ich
is
al
s
o
k
n
o
wn
as sy
n
c
h
r
o
n
o
u
s
r
ef
e
r
en
ce
f
r
am
e
th
eo
r
y
[
2
2
]
.
T
ill
n
o
w,
th
e
DC
lin
k
ca
p
ac
ito
r
v
o
ltag
e
was
co
n
tr
o
lled
u
s
in
g
th
e
co
n
v
e
n
tio
n
al
PI
co
n
tr
o
ller
b
ec
au
s
e
o
f
its
s
im
p
le
d
esig
n
an
d
also
it
ca
n
b
e
ea
s
ily
ap
p
lied
[
2
3
]
.
E
v
en
th
o
u
g
h
with
th
e
m
an
y
ad
v
an
ta
g
es
o
f
th
e
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
it
f
ails
to
g
iv
e
th
e
d
esire
d
r
esu
lts
an
d
h
en
ce
PI
c
o
n
tr
o
ller
tu
n
e
d
with
th
e
g
r
ey
wo
lf
o
p
tim
izatio
n
(
GW
O)
an
d
p
a
r
t
icle
s
war
m
o
p
tim
izatio
n
tech
n
iq
u
e
(
PS
O)
is
test
ed
in
th
is
r
esear
ch
wo
r
k
.
I
t
is
f
o
u
n
d
to
b
e
m
o
r
e
ef
f
ec
tiv
e,
an
d
it
g
iv
es
b
etter
p
er
f
o
r
m
an
ce
wh
en
co
m
p
ar
ed
with
t
h
e
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
.
T
h
e
m
ain
aim
o
f
u
s
in
g
th
e
o
p
tim
izatio
n
tech
n
iq
u
e
is
to
f
in
d
th
e
PI
c
o
n
tr
o
ller
g
ain
p
ar
am
ete
r
s
as
p
er
o
u
r
r
eq
u
ir
em
en
t
.
Ap
ar
t
f
r
o
m
th
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
s
u
ch
as
g
en
etic
alg
o
r
ith
m
[
2
4
]
,
b
ac
ter
ial
f
o
r
g
in
g
[
2
5
]
,
p
ar
ticle
s
war
m
o
p
tim
izatio
n
[
2
6
]
,
f
ir
ef
l
y
alg
o
r
ith
m
[
2
7
]
,
tea
ch
in
g
lear
n
in
g
-
b
ased
o
p
tim
izatio
n
[
2
8
]
th
e
u
s
e
o
f
n
eu
r
al
n
etwo
r
k
s
[
2
9
]
,
n
eu
r
al
n
etwo
r
k
with
f
u
zz
y
in
ter
f
ac
e
s
y
s
tem
[
3
0
]
an
d
th
e
h
y
b
r
id
co
m
b
in
atio
n
o
f
th
e
d
if
f
er
en
t
o
p
tim
izatio
n
tech
n
iq
u
es
s
u
ch
as
PS
O
-
GW
O
[
3
1
]
a
n
d
GA
-
PS
O
ar
e
also
f
o
u
n
d
i
n
liter
atu
r
e
th
at
ca
n
o
p
tim
ize
th
e
co
n
tr
o
ller
g
ain
s
to
g
iv
e
th
e
r
eq
u
i
r
ed
r
esu
lt.
T
h
e
b
asic
id
ea
b
eh
in
d
u
s
in
g
th
is
o
p
tim
izatio
n
tech
n
iq
u
es
is
to
esti
m
ate
th
e
PI
co
n
tr
o
ller
g
ain
s
as
p
e
r
m
in
im
u
m
o
b
jectiv
e
f
u
n
ctio
n
.
So
,
th
e
GW
O
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
h
er
e
t
o
tu
n
e
t
h
e
c
o
n
tr
o
ller
p
ar
am
ete
r
s
an
d
to
im
p
r
o
v
e
th
e
DC
lin
k
ca
p
ac
ito
r
a
cc
u
r
ac
y
.
T
h
e
GW
O
tech
n
iq
u
e
m
a
k
es
th
e
DC
-
lin
k
v
o
ltag
e
m
o
r
e
s
tab
le
an
d
f
aster
as
co
m
p
ar
ed
to
o
th
er
tech
n
iq
u
es.
T
h
e
o
p
tim
ized
v
alu
e
o
f
PI
co
n
tr
o
ller
g
ai
n
s
o
b
tain
ed
f
r
o
m
GW
O
tech
n
iq
u
e
is
u
s
ed
in
th
e
HSAPF
co
n
tr
o
l
s
ch
em
e
to
m
itig
ate
p
o
wer
q
u
ality
is
s
u
es.
T
h
e
HS
APF
with
co
n
tr
o
l
alg
o
r
ith
m
is
b
u
ilt
in
MA
T
L
AB
Simu
lin
k
an
d
its
p
er
f
o
r
m
a
n
ce
is
an
aly
s
ed
f
o
r
d
if
f
er
e
n
t
ty
p
es
o
f
n
o
n
-
lin
ea
r
lo
ad
s
.
T
o
v
er
if
y
th
e
s
im
u
latio
n
r
esu
lts
,
th
e
ex
p
er
im
en
tal
s
et
u
p
h
as
b
ee
n
d
o
n
e
an
d
th
e
OPAL
-
R
T
4
5
1
0
s
im
u
lato
r
is
u
s
ed
to
v
alid
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
d
esig
n
ed
s
y
s
tem
.
T
h
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD
)
in
s
o
u
r
ce
c
u
r
r
e
n
t
an
d
lo
ad
v
o
lta
g
e
ar
e
s
h
o
wn
an
d
co
m
p
ar
ed
with
th
e
r
esu
lts
o
b
tain
ed
f
r
o
m
th
e
ex
i
s
tin
g
tech
n
iq
u
e
.
T
h
e
h
a
r
m
o
n
ic
s
p
ec
tr
u
m
s
ju
s
tify
th
at
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
r
estricts
th
e
h
ar
m
o
n
ics
lev
el
well
u
n
d
er
5
%
f
o
r
m
e
d
iu
m
v
o
ltag
e
ap
p
licatio
n
as
p
er
I
E
E
E
5
1
9
-
2
0
1
4
Stan
d
a
r
d
s
.
T
h
e
n
o
n
lin
e
ar
lo
ad
wh
ic
h
co
n
s
u
m
es
s
o
m
e
r
ea
ctiv
e
p
o
wer
is
also
m
itig
ated
to
en
s
u
r
e
th
e
u
n
ity
p
o
wer
f
ac
to
r
o
p
er
atio
n
o
f
th
e
s
y
s
tem
.
T
h
e
s
eq
u
en
ce
o
f
th
e
r
em
ain
i
n
g
p
ar
t
o
f
th
e
p
ap
er
is
alig
n
ed
as
f
o
llo
ws:
th
e
o
p
tim
izatio
n
t
ec
h
n
iq
u
es
an
d
th
e
o
b
jectiv
e
f
u
n
ctio
n
is
g
iv
en
in
Sectio
n
2
.
T
h
e
o
v
er
v
ie
w
o
f
s
y
s
tem
to
p
o
lo
g
y
an
d
s
y
n
ch
r
o
n
o
u
s
r
ef
er
e
n
ce
m
eth
o
d
is
ex
p
lain
ed
in
s
ec
tio
n
3
.
I
n
Sectio
n
4
all
th
e
s
im
u
latio
n
r
esu
lts
ar
e
d
is
cu
s
s
ed
in
d
etail
wh
er
ea
s
th
e
Sectio
n
5
in
clu
d
es
th
e
ex
p
er
i
m
en
tal
r
esu
lts
o
b
tain
ed
u
s
in
g
OPAL
-
R
T
4
5
1
0
s
im
u
lato
r
.
Sectio
n
6
g
iv
es
th
e
co
n
clu
s
io
n
.
2.
O
P
T
I
M
I
Z
AT
I
O
N
T
E
CH
NI
Q
UE
S
T
h
is
s
ec
tio
n
p
r
esen
ts
a
b
r
ief
a
lg
o
r
ith
m
o
f
PS
O
,
GW
O
an
d
t
h
e
o
b
jectiv
e
f
u
n
ctio
n
wh
ich
is
d
esig
n
ed
as th
e
m
in
im
u
m
f
u
n
ctio
n
f
o
r
o
b
tain
in
g
PI
co
n
tr
o
ller
g
ain
s
.
2
.
1
.
P
a
rt
icle
s
wa
rm
o
ptim
iz
a
t
io
n
I
n
th
is
tech
n
iq
u
e
all
in
d
iv
i
d
u
als
ar
e
g
iv
en
a
p
o
s
itio
n
in
t
h
e
s
o
lu
tio
n
s
p
ac
e
wh
ich
is
co
n
tin
u
o
u
s
ly
u
p
d
ated
till
th
e
d
esire
d
o
b
ject
iv
e
is
r
ea
ch
ed
[
3
2
]
.
T
h
e
b
est
p
o
s
itio
n
is
o
b
tain
ed
as
p
er
th
e
d
ef
in
ed
o
b
jectiv
e
f
u
n
ctio
n
f
o
r
wh
ic
h
th
e
co
n
tr
o
l
ler
g
ain
s
ar
e
o
p
tim
ized
a
n
d
th
e
er
r
o
r
b
etwe
en
th
e
d
esire
d
r
e
f
er
en
ce
v
o
ltag
e
an
d
th
e
v
o
ltag
e
o
b
tain
ed
ac
r
o
s
s
th
e
DC
lin
k
ca
p
ac
ito
r
r
ea
ch
es to
a
m
in
im
u
m
v
alu
e.
T
h
e
er
r
o
r
c
an
b
e
d
escr
ib
e
d
as:
(
)
=
R
ef
er
en
ce
v
o
ltag
e
−
(
1
)
wh
er
e
V
dc
is
ca
p
ac
ito
r
v
o
ltag
e
.
T
h
e
co
n
t
r
o
ller
o
u
tp
u
t is as g
iv
en
in
(
2
):
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
2
7
4
-
1
2
8
8
1276
=
(
)
+
∫
(
)
0
(
2
)
T
h
e
tu
n
in
g
o
f
PI
p
a
r
am
eter
s
i
s
a
m
ajo
r
is
s
u
e
s
in
ce
th
e
lo
a
d
is
v
ar
iab
le
in
n
at
u
r
e
an
d
in
s
u
ch
v
ar
y
in
g
lo
ad
co
n
d
itio
n
s
t
h
e
DC
lin
k
v
o
ltag
e
s
h
o
u
l
d
r
e
m
ain
c
o
n
s
tan
t
.
T
h
e
ap
p
licatio
n
o
f
PS
O
in
o
u
r
p
r
o
p
o
s
ed
s
y
s
tem
is
ex
p
lain
ed
in
s
ec
tio
n
2
.
3
.
PS
O
s
ea
r
ch
es
f
o
r
b
est
p
o
s
itio
n
in
th
e
e
n
tire
s
ea
r
ch
s
p
ac
e
an
d
r
e
ly
o
n
m
ath
e
m
atica
l
ex
p
r
ess
io
n
as g
iv
en
i
n
(
4
)
.
(
+
1
)
=
∗
(
)
+
1
∗
1
∗
[
(
)
−
(
)
]
+
2
∗
2
∗
[
(
)
−
(
)
]
(
3
)
an
d
(
+
1
)
=
(
)
+
(
+
1
)
(
4
)
T
h
e
n
o
tatio
n
s
m
an
d
q
d
en
o
te
n
u
m
b
er
o
f
iter
atio
n
s
an
d
q
is
t
h
e
p
ar
ticle
n
u
m
b
er
.
T
h
e
ter
m
(
)
an
d
(
)
d
ef
in
es
th
e
v
elo
city
an
d
p
o
s
it
io
n
o
f
th
e
p
ar
ticle
at
m
th
iter
at
io
n
.
T
h
e
o
th
e
r
co
n
s
tan
ts
s
u
ch
as
c
1
an
d
c
2
ar
e
b
asically
th
e
co
g
n
itiv
e
p
a
r
t
an
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r
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5)
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(
6
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I
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u
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2
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3
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As
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eq
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ir
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t,
(
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s
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r
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ter
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tim
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k
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ith
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s
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f
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e
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in
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ce
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{
(
,
)
}
(
8)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
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8
8
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I
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2
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20
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1278
3.
O
VE
RVI
E
W
O
F
SY
ST
E
M
T
O
P
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L
O
G
Y
HSAPF
co
n
s
i
s
ts
o
f
two
ty
p
es
o
f
f
ilter
s
co
n
n
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ted
to
th
e
lo
ad
:
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n
e
t
y
p
e
is
co
n
n
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ted
in
s
er
ies
wh
er
ea
s
th
e
o
t
h
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in
p
a
r
allel.
Fig
u
r
e
3
s
h
o
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th
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lo
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d
iag
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o
f
HSAPF
.
Ser
ies
co
n
n
ec
ted
f
ilter
is
k
n
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ac
tiv
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ilter
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d
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as
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n
am
el
y
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f
u
ll
b
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ter
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ii)
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d
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s
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et
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11
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d
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ased
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d
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u
latio
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ed
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MA
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L
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.
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h
e
Simu
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k
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o
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f
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d
esig
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y
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as
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wn
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Fig
u
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e
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T
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as 8
5
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u
r
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4
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I
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e
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id
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o
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s
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ca
s
e
1
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d
2
d
eb
ates
ab
o
u
t
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
HSAPF
with
PI
co
n
tr
o
ller
tu
n
ed
u
s
in
g
PS
O
an
d
GW
O
tech
n
iq
u
e
r
esp
ec
tiv
el
y
f
o
r
R
L
C
lo
ad
.
C
ase
3
an
d
4
is
d
ev
o
ted
f
o
r
ass
ess
in
g
th
e
ef
f
ec
tiv
en
ess
o
f
PS
O
an
d
GW
O
tu
n
ed
HSAPF
with
PI
co
n
tr
o
l
ler
r
esp
ec
tiv
ely
f
o
r
R
L
lo
ad
.
T
h
e
p
er
f
o
r
m
a
n
ce
ch
ar
ac
ter
is
tics
o
f
DC
lin
k
v
o
ltag
e
is
also
ev
alu
ated
in
tim
e
d
o
m
ain
f
o
r
R
L
C
lo
ad
.
Fo
r
th
e
p
u
r
p
o
s
e
o
f
co
m
p
a
r
is
o
n
,
%THD
o
f
s
o
u
r
ce
cu
r
r
e
n
t
an
d
lo
ad
v
o
ltag
e
is
ca
lc
u
lated
b
e
f
o
r
e
ap
p
l
y
in
g
co
m
p
en
s
atio
n
f
o
r
b
o
th
t
h
e
ty
p
es
o
f
lo
ad
co
n
d
itio
n
s
.
Als
o
,
to
s
h
o
w
th
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
o
p
tim
izatio
n
tech
n
iq
u
e
%THD
is
ca
lcu
lated
f
o
r
th
e
s
y
s
tem
with
HSAPF
t
u
n
ed
with
c
o
n
v
e
n
tio
n
al
PI
co
n
tr
o
ller
.
4
.
1
.
Ca
s
e
1
:
P
I
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