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
(
I
J
P
E
DS
)
Vo
l.
9
,
No
.
1
,
Ma
r
c
h
2
0
1
8
,
p
p
.
323
~
335
I
SS
N:
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0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
ijp
ed
s
.
v
9
.
i1
.
pp
3
2
3
-
3
3
5
323
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e.
co
m/jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JP
E
DS
Rev
iew
o
f
t
he
Mo
st Ap
pli
ca
ble Reg
ula
tor Col
lections
t
o
Contro
l
t
he
Para
llel Ac
tive Power
F
il
ter
B
elk
a
ce
m
G
a
s
m
i
1
,
O
t
hm
a
ne
Abdelk
ha
la
k
2
S
m
a
rt
G
rid
s a
n
d
Re
n
e
wa
b
le E
n
e
r
g
ies
Lab
,
De
p
a
rtme
n
t
o
f
E
lec
tri
c
a
l
En
g
in
e
e
rin
g
,
TAHRI M
o
h
a
m
m
e
d
Un
i
v
e
rsity
,
Be
c
h
a
r,
Alg
e
ria
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Oct
1
7
,
2
0
1
7
R
ev
is
ed
Dec
1
4
,
2
0
1
7
Acc
ep
ted
Dec
28
,
2
0
1
7
T
h
is
wo
r
k
p
r
esen
ts
a
s
tu
d
y
o
f
th
e
th
r
ee
-
p
h
ase
p
ar
allel
ac
tiv
e
p
o
wer
f
ilter
an
d
th
e
v
ar
io
u
s
co
n
tr
o
l
ler
s
u
s
ed
in
its
co
n
tr
o
l.
Mo
r
eo
v
er
,
in
o
r
d
er
t
o
im
p
r
o
v
e
th
e
q
u
alit
y
o
f
elec
tr
ical
en
e
r
g
y
,
b
y
m
ak
in
g
it
co
n
f
o
r
m
to
th
e
n
ew
n
o
r
m
ativ
e
co
n
s
tr
ain
ts
,
we
h
av
e
also
b
ee
n
led
to
d
ev
elo
p
an
d
ap
p
ly
ad
v
an
ce
d
au
to
m
atio
n
m
eth
o
d
s
.
I
n
th
is
f
r
a
m
ewo
r
k
,
th
is
p
ap
er
r
ep
o
r
ts
o
f
s
ev
er
al
r
e
g
u
lat
o
r
y
s
tr
u
ctu
r
es
:
f
u
zz
y
lo
g
i
c,
PW
M,
n
ew
s
p
ac
e
v
ec
to
r
PW
M
(
NSV
PW
M)
,
s
p
ac
e
v
ec
to
r
PW
M
(
S
VPW
M)
,
HYST
E
R
E
SIS
m
o
r
eo
v
er
,
in
o
r
d
er
to
p
r
o
d
u
ce
a
p
a
r
allel
ac
tiv
e
f
ilter
,
a
th
o
r
o
u
g
h
s
tu
d
y
o
f
ex
p
er
im
e
n
tal
f
ea
s
ib
ilit
y
was
ca
r
r
ied
o
u
t,
tak
in
g
in
to
ac
co
u
n
t t
h
e
in
d
u
s
tr
ial
c
o
n
s
tr
ain
ts
o
f
th
e
p
r
o
d
u
ct
b
o
t
h
in
its
d
esig
n
an
d
its
ap
p
licatio
n
.
K
ey
w
o
r
d
:
Fu
zz
y
lo
g
ic
HYST
E
R
E
SIS
NSVP
W
M
Par
allel
Activ
e
Po
wer
Fil
ter
(
PAPF
)
PW
M
R
eg
u
lato
r
co
llectio
n
s
SVP
WM
Co
p
y
rig
h
t
©
2
0
1
8
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
All
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
B
elk
ac
em
Gasm
i,
Sm
ar
t G
r
id
s
an
d
R
en
ewa
b
le
E
n
er
g
ies L
ab
,
Dep
ar
tem
en
t o
f
E
lectr
ical
an
d
E
n
g
in
ee
r
in
g
,
Un
iv
er
s
ity
T
ah
r
i
Mo
h
am
m
ed
,
Stre
et
o
f
I
n
d
e
p
en
d
e
n
ce
B
ec
h
a
r
Alg
er
ia
B
p
4
1
7
.
E
m
ail:
b
elk
ac
em
tu
b
e@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Pro
g
r
ess
iv
ely
,
an
d
in
o
r
d
er
to
s
tem
th
e
in
cr
ea
s
e
i
n
d
is
tu
r
b
an
ce
p
r
o
b
lem
s
o
n
p
o
wer
g
r
id
s
,
in
cr
ea
s
in
g
ly
s
tr
in
g
en
t
elec
tr
ic
al
q
u
ality
s
tan
d
ar
d
s
will
b
e
im
p
o
s
ed
o
n
s
u
p
p
lier
s
a
n
d
in
d
u
s
tr
ial
co
n
s
u
m
er
s
.
Face
d
with
th
ese
n
ew
r
eg
u
latio
n
s
b
u
t
also
in
r
esp
o
n
s
e
to
th
e
in
cr
ea
s
in
g
ly
s
p
ec
if
ic
d
em
an
d
o
f
elec
tr
ic
p
o
wer
u
s
er
s
,
ac
tiv
e
co
m
p
en
s
ato
r
s
m
u
s
t
ad
ap
t
b
y
m
ak
in
g
th
eir
s
tr
u
ctu
r
es
an
d
m
eth
o
d
s
o
f
r
eg
u
latio
n
m
o
r
e
c
o
m
p
lex
.
E
s
p
ec
ially
s
in
ce
th
ese
s
o
lu
tio
n
s
m
u
s
t
b
e
s
u
b
ject
to
th
e
p
h
y
s
ical
an
d
tech
n
o
lo
g
ical
lim
its
in
h
er
en
t
in
ac
tiv
e
f
ilter
in
g
d
ev
ices[
1
,
2
]
.
W
ith
in
th
e
f
r
am
ewo
r
k
o
f
th
is
r
esear
ch
p
r
o
b
lem
,
a
p
ap
er
h
as
b
ee
n
in
itiated
with
in
Simu
lin
k
in
o
r
d
er
to
o
p
tim
ize
th
e
co
n
t
r
o
l
p
er
f
o
r
m
an
ce
o
f
th
e
ac
tiv
e
c
o
m
p
e
n
s
ato
r
s
wh
ile
tak
in
g
in
to
ac
c
o
u
n
t
all
th
e
co
n
s
tr
ain
ts
an
d
m
ater
ial
lim
itatio
n
s
in
h
er
en
t
in
th
eir
s
tr
u
ctu
r
es.
T
h
u
s
,
ad
v
an
ce
d
s
tu
d
ies
h
av
e
b
ee
n
ca
r
r
ied
o
u
t
o
n
th
e
d
if
f
er
en
t ty
p
es o
f
r
eg
u
lato
r
ex
i
s
tin
g
an
d
o
n
th
eir
f
ea
s
ib
ilit
y
in
ter
m
s
o
f
d
ig
ital im
p
la
n
tatio
n
[
3
].
An
in
d
u
s
tr
ial
p
ar
tn
er
s
h
i
p
h
as
b
ee
n
ad
d
ed
to
th
is
r
esear
ch
in
o
r
d
er
to
v
alid
ate
th
e
ex
p
er
im
en
tal
f
ea
s
ib
ilit
y
o
f
o
u
r
in
v
esti
g
atio
n
s
.
I
t
was
a
r
esear
ch
lab
o
r
at
o
r
y
:
Sm
ar
t
Gr
id
s
&
R
en
ewa
b
le
E
n
er
g
ies
L
a
b
.
(
SGR
E
L
)
,
Un
iv
er
s
ity
o
f
B
e
ch
ar
Alg
er
ia,
wh
ich
wan
ted
to
d
ev
elo
p
an
in
d
u
s
tr
ial
p
r
o
t
o
ty
p
e
o
f
p
a
r
allel
u
n
iv
er
s
al
ac
tiv
e
f
ilter
ca
p
ab
le
o
f
ad
a
p
tin
g
a
n
d
c
o
m
p
en
s
atin
g
as
wid
ely
as
p
o
s
s
ib
le
all
th
e
c
u
r
r
en
t d
is
tu
r
b
an
ce
s
th
at
co
u
ld
a
p
p
ea
r
o
n
th
e
elec
tr
ical
n
etwo
r
k
[
4
].
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
wer
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
c
h
2
0
1
8
:
323
–
3
3
5
324
2.
ST
RUC
T
UR
E
O
F
P
AP
F
SY
ST
E
M
T
h
e
ac
tiv
e
f
ilter
co
n
n
ec
ted
i
n
p
ar
allel
to
th
e
n
etwo
r
k
,
as
s
h
o
wn
in
f
ig
u
r
e
(
1
)
,
is
m
o
s
t
o
f
ten
co
n
tr
o
lled
as
a
cu
r
r
en
t
g
en
er
ato
r
.
I
t
in
jec
ts
in
to
th
e
n
etwo
r
k
d
is
tu
r
b
in
g
cu
r
r
en
ts
eq
u
al
to
th
o
s
e
ab
s
o
r
b
ed
b
y
th
e
p
o
llu
tin
g
ch
ar
g
e,
b
u
t
in
p
h
ase
o
p
p
o
s
itio
n
with
t
h
em
.
T
h
e
m
ain
s
-
s
id
e
cu
r
r
en
t
is
th
en
s
in
u
s
o
id
al.
T
h
u
s
,
th
e
o
b
jectiv
e
o
f
(
PAPF
)
is
to
p
r
ev
en
t
d
is
tu
r
b
i
n
g
(
h
ar
m
o
n
ic,
r
ea
cti
v
e
an
d
u
n
b
alan
ce
d
)
cu
r
r
en
ts
p
r
o
d
u
c
ed
b
y
p
o
llu
tan
t
lo
ad
s
f
r
o
m
cir
cu
latin
g
th
r
o
u
g
h
th
e
n
etwo
r
k
im
p
ed
a
n
ce
s
itu
ated
u
p
s
tr
ea
m
o
f
th
e
co
n
n
ec
tio
n
p
o
in
t
o
f
th
e
ac
tiv
e
f
ilter
[
5
-
6
].
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
B
a
s
ic
Par
allel
Activ
e
Po
wer
Fil
te
r
Fro
m
f
ig
u
r
e
1
th
e
in
s
tan
tan
eo
u
s
cu
r
r
en
ts
ca
n
b
e
wr
itten
as e
q
u
atio
n
1
.
(
t
)
i
c
(
t
)
i
L
(
t
)
i
s
−
=
(
1
)
wh
er
e:
)
(
t
i
S
: so
u
r
ce
cu
r
r
en
t,
)
(
t
i
L
: c
u
r
r
e
n
t o
f
lo
a
d
,
)
(
t
i
C
: c
u
r
r
en
t o
f
PAPF
.
T
h
e
s
o
u
r
ce
v
o
ltag
e
is
g
iv
e
n
b
y
(
w
t
)
s
i
n
(
t
)
v
s
v
m
=
(
2
)
wh
er
e:
)
(
t
v
S
: th
e
s
o
u
r
ce
v
o
ltag
e,
: th
e
p
u
ls
atio
n
.
if
a
n
o
n
lin
ea
r
lo
a
d
is
ap
p
lied
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th
en
th
e
lo
ad
c
u
r
r
e
n
t
will
h
a
v
e
a
f
u
n
d
am
en
tal
c
o
m
p
o
n
en
t,
an
d
th
e
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
ca
n
b
e
r
ep
r
esen
te
d
as;
=
+
=
1
n
)
n
(
n
w
t
s
i
n
I
n
(
t
)
i
L
(
3
)
=
+
=
+
1
n
)
n
(
n
w
t
s
i
n
I
n
(
t
)
i
L
)
(
w
t
s
i
n
I
1
1
(
4
)
wh
er
e:
: th
e
p
h
ase
d
if
f
er
en
ce
b
etwe
en
)
(
t
V
S
an
d
)
(
t
i
L
.
I
n
s
tan
tan
eo
u
s
lo
ad
p
o
wer
ca
n
b
e
g
iv
en
as
(
t
)
i
L
(
t
)
s
(
t
)
L
v
P
−
=
(
5
)
(t
)
i
L
(t
)
2
n
)
n
(n
wt
s
i
n
I
n
*
(wt
)
s
i
n
)
1
s
i
n
(
*
(wt
)
c
o
s
*
(wt
)
s
i
n
1
c
o
s
(
*
(wt
)
s
i
n
2
(t
)
L
P
−
=
+
+
+
=
V
s
*
V
m
I
1
V
m
)
I
1
V
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
wer
E
lectr
o
n
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
R
ev
iew
o
f th
e
Mo
s
t A
p
p
lica
b
le
R
eg
u
la
to
r
C
o
llectio
n
s
to
C
o
n
t
r
o
l th
e.
.
.
(
B
elka
ce
m
Ga
s
mi
)
325
(
t
)
(
t
)
r
(
t
)
f
(
t
)
L
P
h
P
P
P
+
+
=
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6
)
wh
er
e:
)
(
t
P
L
:
th
e
p
o
wer
o
f
th
e
lo
a
d
,
)
(
t
P
f
:
ac
tiv
e
p
o
wer
,
)
(
t
P
r
:
r
ea
ctiv
e
p
o
wer
,
)
(
t
P
h
:
th
e
d
ef
o
r
m
in
g
p
o
wer
.
f
r
o
m
e
q
u
atio
n
(
6
)
r
ea
l (
Fu
n
d
a
m
en
tal)
p
o
wer
is
d
r
awn
b
y
th
e
lo
ad
(t
)
s
*
(t
)
s
)
1
c
o
s
(
*
(w
t
)
s
i
n
2
I
1
V
m
(t
)
f
i
v
P
=
=
(
7
)
f
r
o
m
e
q
u
atio
n
(
7
)
t
h
e
s
o
u
r
ce
c
u
r
r
en
t su
p
p
lied
b
y
th
e
s
o
u
r
ce
,
af
ter
co
m
p
e
n
s
atio
n
s
i
n
(w
t
)
)s
i
n
(w
t
)
1
(
c
o
s
1
(t
)
v
s
(t
)
P
f
(t
)
s
I
sm
I
i
=
+
=
=
(
8
)
Hen
ce
,
to
tal
p
ea
k
c
u
r
r
e
n
t su
p
p
lied
b
y
th
e
s
o
u
r
ce
I
I
I
sp
sL
sm
(
t
)
+
=
(
9
)
wh
er
e:
)
(
t
I
p
S
: to
tal
p
ea
k
c
u
r
r
en
t
s
u
p
p
lied
b
y
t
h
e
s
o
u
r
ce
,
)
(
t
I
L
S
:
th
e
p
ea
k
cu
r
r
en
t a
b
s
o
r
b
ed
b
y
t
h
e
lo
ad
.
T
h
e
ac
tiv
e
f
ilter
m
u
s
t p
r
o
v
i
d
e
th
e
f
o
llo
win
g
c
o
m
p
e
n
s
atio
n
c
u
r
r
en
t,
as sh
o
wn
in
eq
u
atio
n
(
9
)
.
I
t
(t
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i
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(t
)
s
i
L
i
c
−
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is
n
ec
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s
ar
y
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ca
lcu
late
i
s
(
t)
,
T
h
e
p
u
r
p
o
s
e
o
f
ac
tiv
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f
ilter
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g
is
th
e
g
en
er
atio
n
o
f
h
ar
m
o
n
ic
c
u
r
r
en
ts
o
f
th
e
s
am
e
am
p
litu
d
e
b
u
t
in
p
h
ase
o
p
p
o
s
itio
n
with
th
o
s
e
ab
s
o
r
b
ed
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y
th
e
lo
ad
.
T
h
u
s
,
th
e
cu
r
r
en
t
a
b
s
o
r
b
e
d
to
t
h
e
n
etwo
r
k
will
b
e
s
in
u
s
o
i
d
al.
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t
is
n
ec
ess
ar
y
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p
r
ec
is
el
y
id
e
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tify
t
h
e
h
ar
m
o
n
ic
cu
r
r
en
ts
o
f
th
e
p
o
llu
tan
t lo
ad
.
T
h
e
r
ef
er
en
ce
s
o
u
r
ce
c
u
r
r
en
ts
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s
p
af
ter
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o
m
p
en
s
atio
n
ca
n
b
e
g
iv
en
as
(
w
t
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si
n
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sp
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*
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(
1
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2
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(
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t
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n
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sp
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(
1
1
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)
120
(
w
t
si
n
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sp
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sb
(
1
2
)
wh
er
e
:
i
Sb
*
: th
e
r
ef
e
r
en
ce
s
o
u
r
ce
c
u
r
r
en
ts
af
ter
c
o
m
p
en
s
atio
n
.
T
h
e
en
er
g
y
s
to
r
ag
e
o
n
th
e
D
C
s
id
e
is
o
f
ten
d
o
n
e
b
y
a
ca
p
ac
itiv
e
s
to
r
ag
e
s
y
s
tem
r
ep
r
es
en
ted
b
y
a
ca
p
ac
ito
r
C
d
c
wh
ich
p
lay
s
th
e
r
o
le
o
f
a
DC
v
o
ltag
e
s
o
u
r
ce
Vd
c.
T
h
e
ch
o
ice
o
f
th
e
s
to
r
ag
e
s
y
s
tem
p
ar
am
eter
s
(
Vd
c
et
C
d
c)
af
f
ec
ts
th
e
d
y
n
am
ics
an
d
co
m
p
en
s
atio
n
q
u
a
lity
o
f
th
e
ac
tiv
e
p
ar
allel
f
ilt
er
.
I
n
d
ee
d
,
a
h
ig
h
v
o
ltag
e
Vd
cim
p
r
o
v
es
th
e
d
y
n
am
ics
o
f
th
e
ac
tiv
e
f
ilter
.
Mo
r
eo
v
er
,
th
e
u
n
d
u
latio
n
s
o
f
th
e
DC
v
o
ltag
e
Vd
c,
ca
u
s
ed
b
y
th
e
c
u
r
r
en
ts
g
e
n
e
r
ated
b
y
th
e
ac
tiv
e
f
ilter
an
d
lim
ited
b
y
th
e
ch
o
ice
o
f
C
d
c
,
ca
n
d
eg
r
ad
e
th
e
co
m
p
en
s
atio
n
q
u
ality
o
f
th
e
p
ar
allel
ac
tiv
e
f
ilter
.
T
h
ese
f
lu
ctu
atio
n
s
ar
e
all
th
e
m
o
r
e
im
p
o
r
tan
t
as
th
e
am
p
litu
d
e
o
f
th
e
f
ilter
cu
r
r
e
n
t
is
lar
g
e
an
d
its
f
r
e
q
u
en
c
y
is
lo
w.
T
h
e
DC
v
o
ltag
e
Vd
c
m
u
s
t
b
e
h
ig
h
en
o
u
g
h
to
im
p
r
o
v
e
th
e
co
n
tr
o
llab
ilit
y
o
f
th
e
ac
tiv
e
f
ilter
wh
ile
r
esp
ec
tin
g
th
e
th
r
esh
o
ld
v
o
lta
g
e
o
f
s
witch
es.
B
y
r
esp
ec
tin
g
th
is
co
m
p
r
o
m
is
e,
a
DC
v
o
ltag
e
is
ch
o
s
en
: V
d
c
=
8
0
0
V.
2
.
1
.
H
a
rmo
nic c
urre
nts c
o
ntr
o
l
u
s
in
g
f
uzzy
l
o
g
ic
On
e
o
f
t
h
e
m
ain
ap
p
licatio
n
s
is
th
e
co
n
tr
o
l
o
f
s
y
s
tem
s
f
o
r
wh
i
ch
th
er
e
is
n
o
s
p
ec
if
ic
m
o
d
el
(
F
ig
u
r
e
2
)
.
T
h
e
f
u
zz
y
co
n
tr
o
ller
r
ec
ei
v
es
as
in
p
u
t
an
o
b
s
er
v
atio
n
o
f
th
e
s
y
s
tem
(
f
o
r
e
x
am
p
le
th
e
e
r
r
o
r
with
r
esp
ec
t
t
o
th
e
s
et
p
o
in
t)
an
d
d
ed
u
ce
s
a
c
o
m
m
an
d
to
b
e
ap
p
lied
to
t
h
e
s
y
s
tem
,
ac
co
r
d
in
g
to
a
d
ec
is
io
n
tab
le
(
r
u
les).
T
h
e
q
u
an
titi
es
m
an
ip
u
lated
b
y
th
e
co
n
tr
o
ller
ar
e
f
u
zz
y
s
ets
(
eg
lar
g
e,
m
ed
iu
m
,
s
m
all)
,
wh
ich
n
ec
ess
itates
a
co
n
v
er
s
io
n
o
f
th
e
n
u
m
er
ical
v
alu
es
as in
p
u
t,
th
is
is
th
e
'
f
u
zz
if
icatio
n
'
.
Dep
en
d
in
g
o
n
th
ese
f
u
zz
y
v
ar
iab
les an
d
d
ec
is
io
n
r
u
les,
t
h
e
co
n
tr
o
ller
ca
lcu
lates
th
e
f
u
zz
y
v
alu
e
o
f
th
e
co
m
m
a
n
d
,
th
is
is
th
e
in
f
er
en
ce
.
I
t
is
th
e
n
n
ec
ess
ar
y
to
co
n
v
e
r
t
th
is
v
a
r
iab
le
in
to
a
n
u
m
er
ical
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alu
e,
th
at
is
d
ef
u
zz
if
icatio
n
,
t
h
e
r
u
les
m
o
d
el
th
e
k
n
o
wled
g
e
o
f
an
ex
p
e
r
t
o
r
th
e
b
eh
av
i
o
r
o
f
a
n
o
th
e
r
co
n
tr
o
ll
er
ca
p
ab
le
o
f
r
eg
u
latin
g
t
h
e
s
y
s
tem
.
T
h
e
d
etailed
s
tu
d
y
o
f
th
ese
th
r
ee
p
ar
ts
is
n
ec
ess
ar
y
to
d
eter
m
in
e
th
e
s
tr
u
ctu
r
e
o
f
th
e
co
n
tr
o
ller
th
at
wi
ll
b
est
an
s
wer
th
e
p
r
o
b
lem
p
o
s
ed
[
7
].
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
wer
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
c
h
2
0
1
8
:
323
–
3
3
5
326
Fig
u
r
e
2
.
MA
T
L
AB
Simu
lin
k
m
o
d
el
o
f
f
u
zz
y
lo
g
ic
c
o
n
tr
o
lle
r
Fig
u
r
e
3
.
T
h
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
o
f
in
p
u
t a
n
d
o
u
tp
u
t
Fig
u
r
e
4
.
R
u
les o
f
f
u
zz
y
l
o
g
ic
co
n
tr
o
ller
2
.
2
.
H
a
rmo
nic c
urre
nts c
o
ntr
o
l us
ing
P
WM
T
h
e
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
co
n
tr
o
l
tec
h
n
iq
u
e
s
o
lv
es
th
e
p
r
o
b
lem
o
f
c
o
n
tr
o
llin
g
th
e
s
witch
in
g
f
r
eq
u
en
cy
b
y
o
p
er
a
tin
g
with
a
f
ix
e
d
f
r
eq
u
e
n
cy
e
asy
to
f
ilter
d
o
w
n
s
tr
ea
m
o
f
t
h
e
in
v
e
r
ter
[
8
]
.
T
h
e
s
im
p
lest
an
d
b
est
k
n
o
wn
p
u
l
s
e
wid
th
m
o
d
u
latio
n
is
u
n
d
o
u
b
ted
ly
th
e
n
atu
r
al
s
am
p
lin
g
ML
I
.
T
h
is
co
n
tr
o
l
tech
n
iq
u
e
f
ir
s
t
u
s
es
a
r
eg
u
lat
o
r
wh
ich
d
eter
m
in
es
th
e
r
ef
er
en
ce
v
o
ltag
e
o
f
th
e
in
v
er
ter
f
r
o
m
th
e
d
if
f
er
en
c
e
b
etwe
en
th
e
m
ea
s
u
r
ed
cu
r
r
en
t
an
d
its
r
ef
er
e
n
ce
.
T
h
is
v
o
ltag
e
is
th
en
co
m
p
ar
ed
with
a
s
aw
to
o
th
s
ig
n
al
(
h
ig
h
f
r
eq
u
e
n
cy
ca
r
r
ier
f
i
x
in
g
th
e
s
witch
in
g
f
r
eq
u
en
cy
)
.
T
h
e
o
u
tp
u
t
o
f
th
e
c
o
m
p
ar
at
o
r
s
u
p
p
lies
th
e
co
n
tr
o
l
co
m
m
an
d
o
f
th
e
s
witch
es.T
h
e
g
en
er
al
b
lo
c
k
d
iag
r
am
o
f
co
n
t
r
o
l c
u
r
r
e
n
ts
is
illu
s
tr
ated
in
Fig
u
r
e
2
[
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
wer
E
lectr
o
n
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
R
ev
iew
o
f th
e
Mo
s
t A
p
p
lica
b
le
R
eg
u
la
to
r
C
o
llectio
n
s
to
C
o
n
t
r
o
l th
e.
.
.
(
B
elka
ce
m
Ga
s
mi
)
327
Fig
u
r
e
5
.
PW
M
s
y
n
o
p
tic
b
l
o
c
k
d
iag
r
am
o
f
c
u
r
r
e
n
ts
co
n
tr
o
l
2
.
3
.
H
a
rmo
nic c
urre
nts c
o
ntr
o
l us
ing
SVPW
M
Th
e
SVPW
M
m
eth
o
d
is
wid
ely
u
s
ed
in
in
v
er
ter
co
n
tr
o
l,
it
ca
n
in
cr
ea
s
e
th
e
m
ax
im
u
m
v
a
lu
e
o
f
th
e
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
with
a
r
ed
u
ce
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
r
ate
co
m
p
ar
ed
to
th
o
s
e
o
b
tain
e
d
b
y
t
h
e
s
in
u
s
o
id
al
PW
M
m
eth
o
d
[
1
0
]
.
T
h
e
g
o
al
o
f
all
m
o
d
u
latio
n
s
tr
ateg
ies
i
s
t
o
r
ed
u
ce
s
witch
in
g
l
o
s
s
es
an
d
h
ar
m
o
n
ics,
an
d
to
p
r
o
v
id
e
ac
c
u
r
ate
co
n
tr
o
l.
T
h
e
SVP
W
M
co
m
m
an
d
co
n
s
is
ts
o
f
p
lacin
g
th
e
co
n
tr
o
l v
ec
t
o
r
in
th
e
two
-
u
s
e
o
f
th
e
C
lar
ck
tr
an
s
f
o
r
m
atio
n
.
T
h
e
co
d
in
g
o
f
th
e
p
o
s
s
ib
le
s
witch
es
o
f
th
e
s
witch
es
ca
n
b
e
ca
r
r
ied
o
u
t
o
n
t
h
r
ee
s
tates
eig
h
t
p
o
s
s
ib
le
v
ec
to
r
s
o
f
wh
ich
two
ar
e
ze
r
o
(
V0
an
d
V7
)
[
1
1
]
.
T
h
e
r
elatio
n
s
h
ip
b
et
wee
n
th
e
s
witch
in
g
v
ar
iab
le
v
ec
to
r
[
a,
b
,
c]
t a
n
d
lin
e
-
to
-
lin
e
v
o
ltag
e
v
ec
to
r
[
Vab
,
Vb
c,
Vca
]
is
g
iv
en
b
y
(
1
3
)
i
n
t
h
e
f
o
llo
win
g
:
−
−
−
=
c
b
a
1
0
1
1
1
0
0
1
1
V
dc
V
ca
V
bc
V
ab
(
1
3
)
Als
o
,
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
s
witch
in
g
v
ar
iab
le
v
ec
to
r
[
a,
b
,
c]
t a
n
d
th
e
p
h
ase
v
o
ltag
e
v
ec
to
r
[
Vab
,
Vb
c,
Vca
]
ca
n
b
e
e
x
p
r
ess
ed
b
elo
w.
−
−
−
=
c
b
a
1
1
1
V
dc
V
cn
V
bn
V
an
2
1
-
2
1
-
1
-
2
3
(
1
4
)
wh
er
e
:
V
an
,
V
bn
,
V
cn
:
s
im
p
le
v
o
ltag
es.
th
e
d
etail
o
f
eig
h
t v
o
ltag
e
v
ec
t
o
r
s
is
p
r
esen
ted
in
T
a
b
le
1
T
ab
le
1
.
Switch
in
g
v
ec
to
r
s
,
p
h
ase
v
o
ltag
es a
n
d
o
u
tp
u
t lin
e
t
o
lin
e
v
o
ltag
es
V
o
l
t
a
g
e
v
e
c
t
o
r
s
S
w
i
t
c
h
i
n
g
v
e
c
t
o
r
s
Li
n
e
t
o
n
e
u
t
r
a
l
v
o
l
t
a
g
e
Li
n
e
t
o
l
i
n
e
v
o
l
t
a
g
e
a
b
c
V
an
V
bn
V
cn
V
ab
V
bc
V
ca
V0
0
0
0
0
0
0
0
0
0
V1
1
0
0
3
2
3
1
−
3
1
−
1
0
-
1
V2
1
1
0
3
1
3
1
−
3
2
−
0
1
-
1
V3
0
1
0
3
1
−
3
2
3
1
−
-
1
1
0
V4
0
1
1
3
2
−
3
1
3
1
-
1
0
1
V5
0
0
1
3
1
−
3
1
−
3
2
0
-
1
1
V6
1
0
1
3
1
3
2
−
3
1
1
-
1
0
V7
1
1
1
0
0
0
0
0
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
wer
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
c
h
2
0
1
8
:
323
–
3
3
5
328
Fig
u
r
e
6
s
h
o
ws th
e
b
lo
ck
d
iag
r
am
o
f
p
r
o
p
o
s
ed
ac
tiv
e
f
ilter
c
o
n
tr
o
l m
eth
o
d
im
p
lem
en
ted
u
s
in
g
SVPW
M
in
MA
T
L
AB
/Si
m
u
lin
k
.
Fig
u
r
e
6
.
SVPW
M
s
y
n
o
p
tic
b
l
o
ck
d
iag
r
am
o
f
cu
r
r
en
ts
co
n
tr
o
l
2
.
4
.
H
a
rmo
nic c
urre
nts c
o
ntr
o
l us
ing
hy
s
t
er
esi
s
C
o
n
v
en
tio
n
al
h
y
s
ter
esis
co
n
tr
o
l
is
v
er
y
co
m
m
o
n
l
y
u
s
ed
d
u
e
to
its
ea
s
e
o
f
u
s
e
an
d
r
o
b
u
s
tn
ess
.
I
n
f
ac
t,
th
is
s
tr
ateg
y
en
s
u
r
es
s
atis
f
ac
to
r
y
co
n
t
r
o
l
o
f
th
e
cu
r
r
en
t
with
o
u
t
r
eq
u
ir
i
n
g
a
th
o
r
o
u
g
h
k
n
o
wled
g
e
o
f
th
e
m
o
d
el
o
f
th
e
s
y
s
tem
to
b
e
co
n
tr
o
lle
d
o
r
o
f
its
p
ar
am
eter
s
.
T
h
e
p
r
in
cip
le
o
f
f
ir
s
t
estab
lis
h
in
g
th
e
er
r
o
r
s
ig
n
al,
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
r
e
f
er
e
n
ce
cu
r
r
en
t
if
r
ef
a
n
d
t
h
e
cu
r
r
e
n
t
p
r
o
d
u
ce
d
b
y
th
e
in
v
e
r
t
er
if
,
is
s
h
o
wn
in
f
ig
u
r
e
(
7
)
.
T
h
is
er
r
o
r
is
th
en
co
m
p
ar
e
d
with
a
tem
p
late
ca
lled
a
h
y
s
t
er
esis
b
an
d
in
o
r
d
er
to
f
ix
th
e
co
n
tr
o
l
c
o
m
m
an
d
s
o
f
th
e
s
witch
es.
Ho
wev
er
,
th
i
s
co
n
tr
o
l
h
as
a
m
ajo
r
d
is
ad
v
an
tag
e:
it
d
o
es
n
o
t
m
ak
e
it
p
o
s
s
ib
le
to
co
n
tr
o
l
th
e
s
witch
in
g
f
r
eq
u
en
cy
o
f
th
e
s
em
ico
n
d
u
ct
o
r
s
,
h
e
n
ce
t
h
e
p
r
esen
ce
o
f
a
lar
g
e
n
u
m
b
e
r
o
f
h
ar
m
o
n
ics
in
th
e
g
en
er
ated
c
u
r
r
en
ts
[
1
2
,
1
3
].
Fig
u
r
e
7
.
Hy
s
ter
esis
s
y
n
o
p
tic
b
lo
ck
d
ia
g
r
am
o
f
cu
r
r
en
ts
co
n
t
r
o
l
T
h
e
s
witch
in
g
lo
g
ic
is
f
o
r
m
u
la
ted
as f
o
llo
ws:
If
ica
<
(i
*
ca
−H
B
)
u
p
p
er
s
witch
is
OFF an
d
lo
wer
s
witch
is
ON
f
o
r
leg
"a
"
(
SA =
1
)
.
If
ica
>
(i
*
ca
+
HB
)
u
p
p
er
s
witch
is
ON
an
d
lo
wer
s
witch
is
OFF f
o
r
leg
"a
"(
SA =
0
)
.
2
.
5
.
H
a
rmo
nic c
urre
nts c
o
ntr
o
l us
ing
NSVP
W
M
(
pro
po
s
ed
m
et
ho
d)
T
h
e
s
tr
ateg
y
p
r
o
p
o
s
ed
in
th
is
p
ap
er
is
an
NSVPW
M
with
h
y
s
ter
esis
th
at
ca
n
b
e
im
p
lem
e
n
ted
b
y
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
wer
E
lectr
o
n
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
R
ev
iew
o
f th
e
Mo
s
t A
p
p
lica
b
le
R
eg
u
la
to
r
C
o
llectio
n
s
to
C
o
n
t
r
o
l th
e.
.
.
(
B
elka
ce
m
Ga
s
mi
)
329
f
o
llo
win
g
f
i
g
u
r
e:
Fig
u
r
e
8
.
NVPW
M
s
y
n
o
p
tic
b
lo
ck
d
iag
r
a
m
o
f
cu
r
r
e
n
ts
co
n
tr
o
l
Fro
m
Fig
u
r
e
8
,
V
*
ca
n
b
e
ca
lc
u
lated
as f
o
llo
ws:
f
I
dt
du
f
L
f
U
f
U
s
U
*
c
V
*
b
V
*
a
V
*
V
=
+
=
=
(
1
5
)
wh
er
e
:
V
*
:
th
e
r
ef
e
r
en
ce
v
o
ltag
e
,
U
f
:
s
o
u
r
ce
v
o
ltag
e,
U
f
,
L
f
,
I
f
:
r
esp
ec
tiv
ely
th
e
v
o
ltag
e,
in
d
u
ctan
ce
,
cu
r
r
en
t
o
f
PAPF
.
Fig
u
r
e
9
.
T
h
e
o
u
t
p
u
t v
o
ltag
e
V*
.
Dete
r
m
in
e
Vab
,
Vb
c,
Vca
an
d
Xab
,
Xb
c,
Xca
(
1
6
)
−
=
−
=
−
=
0
ca
V
1
ca
X
0
bc
V
1
bc
X
0
ab
V
1
ab
X
V
*
c
V
ca
V
*
c
V
*
b
V
bc
V
*
b
V
*
a
V
ab
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
wer
E
lectr
o
n
&
Dr
i S
y
s
t
,
Vo
l.
9
,
No
.
1
,
Ma
r
c
h
2
0
1
8
:
323
–
3
3
5
330
Fig
u
r
e
1
0
.
T
h
e
o
u
tp
u
ts
: X
ab
,
Xb
c
an
d
Xca
Dete
r
m
in
e
R
V(
1
)
,
R
V(
2
)
,
R
V(
3
)
,
R
V(
4
)
,
R
V(
5
)
an
d
R
V
(
6
)
Fro
m
Fig
u
r
e
6
,
R
V(
1
)
,
R
V(
2
)
,
R
V(
3
)
,
R
V(
4
)
,
R
V(
5
)
an
d
R
V(
6
)
ca
n
b
e
d
eter
m
in
ed
as f
o
llo
ws:
(
1
7
)
Fig
u
r
e
1
1
.
T
h
e
o
u
tp
u
ts
: RV(
1
)
,
R
V(
2
)
,
R
V(
3
)
,
R
V(
4
)
,
R
V(
5
)
an
d
R
V(
6
)
g
en
er
atin
g
o
f
t
h
e
i
n
v
er
ter
s
witch
in
g
p
u
ls
es
Fig
u
r
e
1
2
s
h
o
ws th
e
N
SVP
W
M
p
u
ls
es to
attac
k
th
e
g
ates o
f
AP
Fig
u
r
e
1
2
.
T
h
e
o
u
tp
u
t
p
u
ls
es to
attac
k
th
e
g
ates o
f
m
u
ltil
ev
e
l in
v
er
ter
s
3.
M
AT
L
A
B
B
A
SE
D
SI
M
U
L
A
T
I
O
N
T
h
e
s
im
u
lated
s
y
s
tem
is
s
h
o
wn
in
f
ig
u
r
e
1
3
.
I
t
is
co
m
p
o
s
ed
o
f
a
p
o
wer
s
u
p
p
l
y
n
etwo
r
k
,
a
r
ec
t
if
ier
b
r
id
g
e
an
d
an
ac
tiv
e
cu
r
r
e
n
t stru
ctu
r
e
f
ilter
.
T
h
e
r
ec
tifie
r
f
lo
win
g
o
n
an
R
-
L
lo
ad
p
lay
s
th
e
r
o
le
o
f
th
e
p
o
llu
tin
g
lo
ad
.
T
h
e
ac
tiv
e
f
ilter
co
n
s
is
ts
o
f
an
in
v
er
ter
with
s
ix
s
wit
ch
es
an
d
a
p
er
f
ec
t
cu
r
r
en
t
s
o
u
r
ce
.
T
h
e
in
v
e
r
ter
b
r
id
g
e
s
witch
es a
r
e
f
o
r
m
ed
b
y
I
GB
T
s
(
with
an
tip
ar
allel
d
io
d
es)
in
s
er
ies with
d
io
d
es.
T
h
e
s
im
u
latio
n
r
esu
lts
f
o
r
th
e
f
iv
e
c
o
n
tr
o
l
tech
n
iq
u
es
m
ak
e
it
p
o
s
s
ib
le
to
d
em
o
n
s
tr
ate
th
e
p
er
f
o
r
m
an
ce
o
f
ea
ch
o
f
th
e
f
iv
e
co
n
tr
o
ller
s
.
Fig
u
r
es
1
3
to
1
7
illu
s
tr
ate
th
e
r
esp
o
n
s
e
o
f
t
h
e
th
r
ee
-
p
h
ase
s
h
u
n
t
ca
X
bc
X
ab
X
(6)
V
R
ca
X
bc
X
ab
X
(5)
V
R
ca
X
bc
X
ab
X
(4)
V
R
ca
X
bc
X
ab
X
(3)
V
R
ca
X
bc
X
ab
X
(2)
V
R
ca
X
bc
X
ab
X
(1)
V
R
+
+
=
+
+
=
+
+
=
+
+
=
+
+
=
+
+
=
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
wer
E
lectr
o
n
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
R
ev
iew
o
f th
e
Mo
s
t A
p
p
lica
b
le
R
eg
u
la
to
r
C
o
llectio
n
s
to
C
o
n
t
r
o
l th
e.
.
.
(
B
elka
ce
m
Ga
s
mi
)
331
f
ilter
in
s
tead
y
-
s
tate
a
n
d
tr
a
n
s
ien
t
co
n
d
itio
n
s
:
we
p
r
esen
t
in
p
ar
ticu
lar
th
e
v
o
lta
g
e
o
f
th
e
s
o
u
r
ce
Vs,
th
e
cu
r
r
en
t
o
f
th
e
s
o
u
r
ce
is
,
th
e
r
ef
er
e
n
ce
cu
r
r
en
t
ir
ef
,
th
e
cu
r
r
e
n
t
co
n
s
u
m
ed
b
y
th
e
lo
ad
iL,
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
ter
m
in
als
o
f
ca
p
ac
ito
r
Vd
c,
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
r
ate
T
HD
o
f
th
e
lin
e
cu
r
r
en
t
an
d
th
e
cu
r
r
en
t
o
f
th
e
l
o
ad
.
T
h
e
s
im
u
latio
n
p
ar
a
m
eter
s
u
s
ed
in
th
e
d
if
f
er
en
t c
o
n
tr
o
l te
ch
n
iq
u
es a
r
e
p
r
esen
ted
in
T
ab
le
2
.
T
ab
le
2
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ased
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r
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Fig
u
r
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in
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lo
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co
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er
MA
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