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lcu
latio
n
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
we
r
with
o
u
t
em
p
lo
y
in
g
v
o
ltag
e
s
en
s
o
r
s
[
5
]
,
[
6
]
.
T
h
i
s
n
o
t
o
n
ly
r
ed
u
ce
s
th
e
d
ev
el
o
p
m
en
t
o
f
h
a
r
d
war
e
b
u
t
also
en
h
an
ce
s
s
y
s
tem
r
eliab
ilit
y
.
T
h
e
in
teg
r
atio
n
o
f
a
v
o
ltag
e
v
ec
to
r
s
elec
tio
n
l
o
o
k
u
p
tab
le
allo
ws
VFDPC
to
o
p
er
ate
with
l
o
w
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
w
h
ile
p
r
o
v
id
i
n
g
a
r
a
p
id
an
d
s
tea
d
y
r
esp
o
n
s
e
d
u
r
in
g
d
y
n
a
m
ic
o
p
er
atin
g
s
itu
atio
n
s
,
s
u
ch
as a
b
r
u
p
t l
o
ad
ch
a
n
g
es a
n
d
g
r
i
d
d
is
tu
r
b
a
n
ce
s
[
7
]
–
[
9
]
.
Desp
ite
th
e
ad
v
an
ce
m
e
n
ts
in
th
e
VFDPC
co
n
tr
o
l
s
y
s
tem
,
a
s
ig
n
if
ican
t
is
s
u
e
co
n
tin
u
es
t
o
ex
is
t:
th
e
ab
s
en
ce
o
f
r
o
b
u
s
t
r
ea
l
-
tim
e
v
a
lid
atio
n
p
r
o
ce
s
s
es
f
o
r
v
ir
tu
al
f
lu
x
esti
m
atio
n
.
T
h
e
ac
cu
r
ac
y
an
d
r
esp
o
n
s
iv
en
ess
o
f
f
lu
x
p
r
ed
ictio
n
a
r
e
cr
u
cial
f
o
r
th
e
ef
f
ec
tiv
e
o
p
er
atio
n
o
f
VFDP
C
,
p
ar
ticu
lar
ly
in
en
v
ir
o
n
m
en
ts
wh
er
e
th
e
g
r
id
e
x
h
ib
its
u
n
p
r
ed
ictab
le
b
e
h
av
io
r
an
d
lo
ad
r
eq
u
ir
em
en
ts
f
lu
ctu
ate
[
1
0
]
,
[
1
1
]
.
I
n
a
d
eq
u
ate
v
alid
atio
n
m
ay
lead
to
e
r
r
o
r
s
i
n
p
o
wer
ca
lcu
l
atio
n
s
,
r
ed
u
c
e
s
tab
ilit
y
,
an
d
d
eg
r
ad
e
c
o
n
tr
o
l
p
er
f
o
r
m
a
n
ce
,
p
ar
ticu
lar
ly
d
u
r
in
g
s
u
d
d
en
o
cc
u
r
r
e
n
ce
s
.
T
h
is
s
tu
d
y
ad
d
r
ess
es
th
e
g
a
p
b
y
lo
o
k
in
g
in
to
p
r
ac
tical
r
ea
l
-
tim
e
v
ali
d
atio
n
m
eth
o
d
s
f
o
r
v
ir
tu
al
f
lu
x
i
n
d
i
r
ec
t
p
o
wer
c
o
n
tr
o
l
s
y
s
tem
s
.
T
h
e
s
u
g
g
ested
m
eth
o
d
m
a
k
es
VFDPC
m
o
r
e
s
tab
le
an
d
f
lex
i
b
le
in
less
-
th
an
-
id
ea
l
s
ettin
g
s
b
y
c
o
n
s
tan
tly
ch
ec
k
in
g
f
l
u
x
esti
m
atio
n
ag
ain
s
t
ch
an
g
in
g
g
r
id
p
a
r
am
eter
s
[
1
2
]
–
[
1
4
]
.
T
h
e
ap
p
r
o
ac
h
in
ten
d
s
to
m
a
k
e
it
ea
s
ier
to
q
u
ick
ly
ch
an
g
e
co
n
tr
o
l
ac
tio
n
s
i
n
r
ea
l
tim
e,
wh
i
ch
will
lo
wer
T
HD
an
d
im
p
r
o
v
e
th
e
o
v
e
r
all
ac
cu
r
ac
y
o
f
c
o
n
tr
o
l.
T
h
is
m
ain
co
n
tr
ib
u
tio
n
is
th
e
d
ev
elo
p
m
en
t
an
d
ev
alu
atio
n
o
f
a
r
ea
l
-
tim
e
v
alid
atio
n
f
r
am
ewo
r
k
f
o
r
VFDP
C
,
s
p
ec
if
ically
d
esig
n
ed
f
o
r
h
ig
h
-
p
er
f
o
r
m
a
n
ce
g
r
i
d
-
co
n
n
ec
ted
c
o
n
v
e
r
ter
s
.
T
h
e
s
u
g
g
ested
s
o
lu
tio
n
is
ev
alu
ated
u
n
d
e
r
v
ar
io
u
s
d
y
n
am
ic
s
ce
n
ar
io
s
,
s
u
ch
as
v
o
lt
ag
e
s
ag
s
an
d
s
u
d
d
en
lo
ad
c
h
an
g
es,
in
o
r
d
er
to
d
eter
m
in
e
its
ab
ilit
y
t
o
m
ai
n
tain
s
y
s
tem
s
tab
ilit
y
an
d
p
er
f
o
r
m
a
n
ce
.
T
h
is
s
tu
d
y
e
n
h
an
ce
s
th
e
ex
is
tin
g
k
n
o
wled
g
e
b
y
illu
s
tr
atin
g
h
o
w
r
ea
l
-
tim
e
f
lu
x
v
alid
ati
o
n
ca
n
m
a
r
k
ed
l
y
im
p
r
o
v
e
co
n
tr
o
l
p
r
ec
is
io
n
,
d
ep
en
d
a
b
ilit
y
,
an
d
r
o
b
u
s
tn
ess
in
co
n
tem
p
o
r
ar
y
p
o
wer
s
y
s
tem
s
[
1
5
]
–
[
1
7
]
.
Mo
r
eo
v
er
,
it
e
n
ab
les
th
e
p
o
ten
tial
im
p
lem
en
tatio
n
o
f
s
en
s
o
r
less
co
n
tr
o
l m
eth
o
d
o
l
o
g
ies in
n
e
x
t
-
g
en
er
atio
n
g
r
id
s
y
s
tem
s
[
1
8
]
,
[
1
9
]
.
2.
M
E
T
H
O
D
T
h
is
s
tu
d
y
ex
a
m
in
es
th
e
r
ea
l
-
t
im
e
v
alid
atio
n
o
f
th
e
v
ir
tu
al
f
lu
x
id
ea
in
d
ir
ec
t
p
o
wer
co
n
tr
o
l
(
DPC
)
,
p
r
io
r
itizin
g
t
h
e
im
p
r
o
v
em
e
n
t
o
f
d
y
n
am
ic
p
er
f
o
r
m
an
ce
d
esp
i
te
v
ar
iab
le
g
r
id
s
ettin
g
s
[
2
0
]
–
[
2
2
]
.
T
h
e
s
u
g
g
ested
m
eth
o
d
o
l
o
g
y
en
c
o
m
p
ass
es n
u
m
er
o
u
s
ess
en
tial e
lem
en
ts
d
es
ig
n
ed
to
ad
d
r
ess
th
e
is
s
u
es a
s
s
o
ciate
d
with
v
ir
tu
al
f
lu
x
esti
m
atio
n
,
r
ea
l
-
tim
e
co
n
tr
o
l,
an
d
d
y
n
a
m
ic
s
y
s
tem
b
eh
av
io
r
.
Fig
u
r
e
1
d
e
p
icts
th
e
th
r
ee
-
p
h
ase
g
r
i
d
-
co
n
n
ec
ted
c
o
n
v
er
te
r
to
p
o
l
o
g
y
em
p
lo
y
e
d
in
th
is
p
ap
er
,
wh
ich
p
r
o
v
id
es
th
e
f
u
n
d
am
en
t
al
s
tr
u
ctu
r
e
f
o
r
th
e
im
p
lem
en
tatio
n
o
f
th
e
VFDPC
ap
p
r
o
ac
h
.
T
h
e
illu
s
tr
atio
n
d
ep
icts
th
e
in
ter
f
ac
e
b
etwe
en
th
e
g
r
id
a
n
d
th
e
co
n
v
er
ter
v
ia
in
d
u
ctiv
e
-
r
esis
tiv
e
b
r
an
c
h
es
(
L
a,
L
b
,
L
c)
,
an
d
(
R
a,
R
b
,
R
c)
to
g
eth
er
with
th
e
s
witch
in
g
n
etwo
r
k
th
at
g
en
er
ates
th
e
n
ec
ess
ar
y
c
o
n
v
er
ter
v
o
ltag
e
v
ec
to
r
s
(
Vco
n
v
,
a)
,
(
Vco
n
v
,
b
)
,
an
d
(
Vco
n
v
,
c)
.
T
h
is
h
a
r
d
war
e
ar
r
an
g
em
e
n
t
f
ac
ilit
ates
th
e
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
o
f
v
ir
tu
al
f
lu
x
esti
m
atio
n
an
d
co
n
tr
o
l
lo
g
ic,
as
ex
am
in
ed
in
th
e
f
o
llo
win
g
s
ec
tio
n
s
.
T
h
i
s
p
a
p
e
r
i
s
o
r
g
a
n
i
z
e
d
i
n
t
o
f
o
u
r
s
e
c
ti
o
n
s
,
s
t
a
r
t
i
n
g
w
it
h
a
n
i
n
tr
o
d
u
c
t
i
o
n
:
i
)
S
e
c
ti
o
n
1
p
r
o
v
i
d
e
s
a
d
et
a
i
le
d
r
e
v
i
e
w
o
f
t
h
e
e
x
i
s
t
i
n
g
r
e
s
e
a
r
c
h
,
o
f
f
e
r
i
n
g
a
n
o
v
e
r
v
i
e
w
o
f
D
P
C
a
n
d
t
h
e
l
a
t
e
s
t
d
e
v
e
l
o
p
m
e
n
t
s
i
n
V
F
DP
C
;
i
i
)
S
e
ct
i
o
n
2
c
o
v
e
r
s
t
h
e
m
e
t
h
o
d
o
l
o
g
y
,
e
x
p
l
a
i
n
i
n
g
k
e
y
c
o
n
c
e
p
t
s
b
e
h
i
n
d
V
F
DP
C
,
s
u
c
h
a
s
h
o
w
g
r
i
d
v
o
l
t
a
g
e
a
n
d
p
o
w
e
r
a
r
e
e
s
t
i
m
a
t
e
d
,
a
n
d
i
n
t
r
o
d
u
c
e
s
a
n
e
w
l
y
d
e
v
e
l
o
p
e
d
s
w
it
c
h
i
n
g
l
o
o
k
u
p
t
a
b
l
e
;
i
i
i
)
S
e
ct
i
o
n
3
p
r
e
s
en
t
s
t
h
e
r
e
s
u
lt
s
a
n
d
a
n
a
l
y
s
is
,
f
o
c
u
s
i
n
g
o
n
s
y
s
t
e
m
p
e
r
f
o
r
m
a
n
c
e
u
n
d
e
r
b
a
l
a
n
c
e
d
v
o
l
t
a
g
e
c
o
n
d
i
t
i
o
n
s
,
i
ts
i
m
p
a
c
t
o
n
t
o
t
a
l
h
a
r
m
o
n
i
c
d
i
s
t
o
r
t
i
o
n
(
T
HD
)
,
a
n
d
c
o
m
p
a
r
i
s
o
n
s
wi
t
h
t
r
a
d
i
ti
o
n
a
l
c
o
n
t
r
o
l
m
e
t
h
o
d
s
;
a
n
d
i
v
)
S
e
ct
i
o
n
4
c
o
n
c
l
u
d
e
s
w
i
t
h
a
s
u
m
m
a
r
y
o
f
t
h
e
m
a
i
n
f
i
n
d
i
n
g
s
,
p
r
a
c
t
i
c
a
l
i
m
p
l
i
c
at
i
o
n
s
,
a
n
d
r
e
c
o
m
m
e
n
d
a
t
i
o
n
s
f
o
r
f
u
t
u
r
e
s
t
u
d
ie
s
.
L
o
a
d
Eg
,
a
Eg
,
b
Eg
,
c
Ra
Rb
Rc
La
Lb
Lc
Sa
Sb
Sc
Sa
Sb
Sc
C
V
d
c
V
c
o
n
v
,
b
V
c
o
n
v
,
c
V
c
o
n
v
,
a
n
Fig
u
r
e
1
.
T
h
r
ee
-
p
h
ase
g
r
id
-
co
n
n
ec
ted
co
n
v
er
ter
to
p
o
l
o
g
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
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lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
xp
erimen
ta
l v
a
lid
a
tio
n
o
f v
ir
tu
a
l flu
x
co
n
ce
p
t in
…
(
Mu
h
a
mma
d
Ha
feez Mo
h
a
med
Ha
r
ir
i
)
2511
2
.
1
.
P
r
o
blem
f
o
rm
ula
t
io
n
T
h
e
VFDPC
ap
p
r
o
ac
h
wo
r
k
s
b
y
esti
m
atin
g
two
k
ey
th
in
g
s
:
th
e
in
s
tan
tan
eo
u
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
in
p
u
ts
,
an
d
th
e
v
ir
tu
al
f
lu
x
o
f
th
e
th
r
ee
-
p
h
ase
g
r
id
[
2
3
]
,
[
2
4
]
.
E
s
s
en
tially
,
VFDPC
co
m
b
in
es
a
m
eth
o
d
f
o
r
d
ir
ec
tly
co
n
tr
o
llin
g
p
o
wer
with
a
tech
n
iq
u
e
f
o
r
esti
m
ati
n
g
in
p
u
t
v
o
ltag
e
s
o
u
r
ce
s
to
m
an
ag
e
an
AC
-
DC
co
n
v
er
ter
ef
f
icien
tly
.
I
n
VFD
PC
,
ac
cu
r
ately
esti
m
atin
g
th
e
g
r
id
'
s
v
ir
tu
al
f
lu
x
an
d
ch
o
o
s
in
g
th
e
r
ig
h
t switch
in
g
s
tates
f
o
r
th
e
co
n
v
er
te
r
ar
e
b
o
th
ess
en
tial
f
o
r
s
m
o
o
th
o
p
er
atio
n
.
T
o
im
p
r
o
v
e
ac
cu
r
ac
y
,
a
lo
w
-
p
ass
f
ilter
is
ad
d
ed
to
th
e
s
y
s
tem
,
wh
ich
h
elp
s
co
r
r
ec
t
a
n
y
p
h
ase
o
r
m
a
g
n
itu
d
e
er
r
o
r
s
th
at
m
a
y
o
cc
u
r
d
u
r
i
n
g
v
ir
tu
al
f
lu
x
esti
m
atio
n
.
B
y
ca
r
ef
u
lly
m
an
ag
in
g
th
ese
p
o
wer
i
n
p
u
ts
,
VFDPC
ca
n
r
eg
u
late
b
o
th
th
e
li
n
e
cu
r
r
e
n
ts
an
d
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
t
h
e
DC
lin
k
.
As
s
h
o
wn
in
Fig
u
r
e
2
,
th
e
co
n
tr
o
l
s
tr
u
ctu
r
e
o
f
VFDPC
tr
ea
ts
th
e
u
tili
ty
g
r
id
’
s
s
o
u
r
ce
v
o
ltag
e
as
t
h
o
u
g
h
it
wer
e
a
v
i
r
tu
al
AC
m
ac
h
i
n
e.
T
h
is
ap
p
r
o
ac
h
allo
ws
f
o
r
p
r
e
cise
an
d
r
esp
o
n
s
iv
e
p
o
wer
co
n
tr
o
l in
t
h
e
co
n
v
er
ter
s
y
s
tem
.
L
L
L
Ig
,
a
Ig
,
b
Ig
,
c
S
w
i
t
c
h
i
n
g
T
a
b
l
e
V
D
C
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I
G
B
T
V
d
c
r
e
f
PI
X
dP
dQ
ϴ
n
Q
r
e
f
=
0
C
u
r
r
e
n
t
m
e
a
s
u
r
e
m
e
n
t
,
I
n
s
t
a
n
t
a
n
e
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s
p
o
w
e
r
a
n
d
G
r
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v
i
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t
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l
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f
l
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t
i
m
a
t
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o
n
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,
a
Eg
,
b
Eg
,
c
Sa
Sb
Sc
Sa
Sb
Sc
ϴ
Q
P
P
Q
N
Fig
u
r
e
2
.
VFDPC
co
n
tr
o
l d
iag
r
am
T
h
e
(
1
)
ex
p
r
ess
es
th
e
r
elatio
n
s
h
ip
b
etwe
en
p
ar
am
eter
s
th
at
h
av
e
b
ee
n
c
o
n
tr
o
lled
in
th
e
r
e
ctif
ier
b
y
Pu
ls
e
W
id
th
Mo
d
u
latio
n
(
PW
M)
.
Fro
m
th
e
eq
u
atio
n
s
,
th
e
g
r
id
v
o
ltag
e
f
r
o
m
th
e
th
r
ee
-
p
h
a
s
e
s
y
s
tem
is
eq
u
al
to
th
e
s
u
m
m
atio
n
v
o
ltag
e
f
r
o
m
th
e
in
te
r
n
al
r
esis
tan
ce
,
in
d
u
ctan
ce
,
an
d
co
n
v
er
ter
p
o
le
v
o
l
tag
e.
Fo
llo
win
g
th
is
,
in
(
2
)
-
(
4
)
d
eter
m
i
n
es
th
e
p
h
ase
v
o
ltag
e
at
th
e
p
o
le’
s
co
n
v
er
ter
.
T
h
is
p
ar
a
m
eter
v
alu
e
is
c
o
o
p
er
atin
g
with
th
e
DC
-
lin
k
o
u
tp
u
t v
o
ltag
e
an
d
th
e
co
n
v
er
te
r
’
s
s
witch
in
g
s
tates f
r
o
m
ea
c
h
p
h
ase
.
[
,
,
,
]
=
R
[
,
,
,
]
+
[
,
,
,
]
+
[
,
,
,
]
(
1
)
,
=
3
(
2
′
−
(
′
+
′
)
)
(
2
)
,
=
3
(
2
′
−
(
′
+
′
)
)
(
3
)
,
=
3
(
2
′
−
(
′
+
′
)
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(
4
)
Nex
t,
as
in
d
ir
ec
t
p
o
wer
c
o
n
t
r
o
l
s
tr
ateg
y
,
th
e
v
o
ltag
e
m
u
s
t
b
e
co
n
v
er
ted
f
r
o
m
a
b
c
-
co
o
r
d
in
ates
in
to
alp
h
a
an
d
b
eta
c
o
o
r
d
i
n
ates
,
o
r
k
n
o
wn
as
th
e
s
tatio
n
ar
y
r
ef
er
en
ce
f
r
am
e
.
Ma
tr
ix
f
o
r
m
u
latio
n
h
as
b
ee
n
im
p
lem
en
ted
to
d
o
th
is
tr
an
s
f
o
r
m
atio
n
,
as sh
o
wn
i
n
(
5
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2509
-
2
5
2
0
2512
[
]
=
2
3
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
]
[
]
(
5
)
Gr
id
v
ir
tu
al
f
lu
x
ca
n
b
e
o
b
ta
in
ed
b
y
in
te
g
r
atin
g
th
e
v
ec
to
r
o
f
g
r
i
d
v
o
ltag
e
,
as
s
h
o
wn
i
n
(
6
)
,
a
n
d
th
e
f
in
al
e
q
u
atio
n
s
ca
n
b
e
s
ee
n
in
(
7
)
.
,
=
∫
(
,
(
)
)
(
6
)
=
∫
(
,
+
,
+
,
)
(
7
)
Pra
ctica
lly
,
th
e
v
alu
e
o
f
r
esis
tan
ce
ca
n
b
e
n
eg
lecte
d
d
u
e
t
o
its
s
m
all
v
alu
e
co
m
p
ar
ed
to
th
e
v
alu
e
o
f
lin
e
in
d
u
ctan
ce
.
T
h
e
r
ef
o
r
e,
th
e
f
in
al
eq
u
atio
n
s
with
o
u
t c
o
n
s
id
er
i
n
g
th
e
v
alu
e
o
f
r
esis
tan
ce
ca
n
b
e
s
ee
n
as sh
o
wn
in
(
8
)
an
d
(
9
)
f
o
r
r
ea
l a
n
d
im
ag
in
ar
y
ax
es.
,
=
∫
,
+
,
=
,
+
,
(
8
)
,
=
∫
,
+
,
=
,
+
,
(
9
)
I
n
(
1
0
)
an
d
(
1
1
)
ar
e
a
d
d
ed
to
t
h
e
esti
m
atio
n
m
eth
o
d
to
co
m
p
en
s
ate
f
o
r
th
ese
er
r
o
r
s
.
T
h
ese
eq
u
atio
n
s
ar
e
in
ten
d
ed
to
ta
k
e
in
to
ac
c
o
u
n
t
h
o
w
th
e
L
PF
b
eh
av
es
d
if
f
er
en
tly
at
d
if
f
e
r
en
t
f
r
e
q
u
en
cies.
T
h
is
m
ak
es
it
p
o
s
s
ib
le
to
ac
cu
r
ately
r
ec
o
n
s
tr
u
ct
th
e
f
lu
x
at
all
f
r
eq
u
en
cies
ex
ce
p
t
th
e
f
u
n
d
a
m
en
tal
g
r
id
f
r
eq
u
en
cy
,
wh
ich
is
k
ep
t
co
n
s
tan
t.
T
h
en
,
t
h
e
r
ec
tif
ied
f
lu
x
c
o
m
p
o
n
en
ts
ar
e
r
ec
al
cu
lated
u
s
in
g
im
p
o
r
tan
t
f
a
cto
r
s
s
u
ch
as
th
e
g
r
id
an
g
u
lar
f
r
eq
u
e
n
cy
,
t
h
e
f
ilter
c
u
t
-
o
f
f
f
r
eq
u
en
cy
,
an
d
t
h
e
ch
ar
ac
ter
is
tics
o
f
th
e
co
n
v
er
ter
'
s
s
witch
in
g
.
Fig
u
r
e
3
s
h
o
ws
th
at
th
is
m
o
d
if
icatio
n
ap
p
r
o
ac
h
is
b
u
ilt
in
to
th
e
f
lu
x
esti
m
atio
n
lo
o
p
.
T
h
e
p
ictu
r
e
s
h
o
ws
th
e
wh
o
le
v
ir
tu
al
f
lu
x
e
s
tim
ate
b
lo
ck
,
wh
ich
u
s
es
tr
an
s
f
er
f
u
n
ctio
n
s
th
at
r
ep
r
esen
t
th
e
L
PF
b
eh
av
io
r
to
p
r
o
ce
s
s
th
e
co
n
v
er
te
r
v
o
ltag
e
in
p
u
ts
.
T
o
g
et
th
e
v
ir
t
u
al
f
lu
x
co
m
p
o
n
en
ts
r
ig
h
t,
m
o
r
e
co
m
p
en
s
atio
n
ter
m
s
ar
e
u
s
ed
.
T
h
is
b
etter
esti
m
atio
n
m
eth
o
d
m
a
k
es
th
e
s
y
s
tem
m
o
r
e
r
esis
tan
t
to
m
ea
s
u
r
em
en
t
er
r
o
r
s
an
d
k
ee
p
s
co
n
tr
o
l c
o
n
s
is
ten
cy
in
r
ea
l
-
wo
r
ld
s
itu
atio
n
s
.
,
=
,
,
+
,
,
(
)
(
1
0
)
,
=
,
,
=
,
,
−
,
,
(
)
(
1
1
)
Fig
u
r
e
3
.
T
h
e
d
iag
r
am
o
f
a
lo
w
-
p
ass
f
ilter
in
v
ir
tu
al
f
lu
x
f
o
r
th
e
f
ilter
in
g
p
r
o
ce
s
s
2
.
2
.
L
o
o
k
up
t
a
ble
T
h
e
(
1
2
)
an
d
(
1
3
)
p
r
o
v
id
e
th
e
esti
m
ates
f
o
r
in
p
u
t
ac
tiv
e
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
in
a
s
tatio
n
ar
y
r
ef
er
en
ce
f
r
am
e.
=
(
3
2
)
(
,
,
−
,
,
)
(
1
2
)
=
(
3
2
)
(
,
,
+
,
,
)
(
1
3
)
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
E
xp
erimen
ta
l v
a
lid
a
tio
n
o
f v
ir
tu
a
l flu
x
co
n
ce
p
t in
…
(
Mu
h
a
mma
d
Ha
feez Mo
h
a
med
Ha
r
ir
i
)
2513
As a
r
esu
lt,
th
e
d
if
f
er
e
n
tiatio
n
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
c
an
b
e
ex
p
r
ess
ed
as (
1
4
)
an
d
(
1
5
)
,
r
esp
ec
tiv
ely
.
=
3
2
(
,
,
+
,
,
−
,
,
−
,
,
)
(
1
4
)
=
3
2
(
,
,
+
,
,
+
,
,
+
,
,
)
(
1
5
)
T
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
v
o
ltag
e
v
ec
to
r
s
elec
tio
n
m
ec
h
an
is
m
in
VFDPC
was
d
eter
m
in
ed
b
y
an
aly
zin
g
th
e
s
y
s
tem
'
s
b
eh
av
i
o
r
th
r
o
u
g
h
s
im
u
latio
n
s
o
f
i
n
s
tan
tan
eo
u
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
r
esp
o
n
s
es
to
d
esig
n
ated
c
o
n
v
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te
r
v
o
ltag
e
v
ec
to
r
s
.
T
h
e
r
esu
lts
ar
is
e
f
r
o
m
th
e
m
ath
em
atica
l
eq
u
atio
n
s
o
f
p
o
wer
d
er
iv
ativ
es
r
eg
ar
d
in
g
v
o
ltag
e
v
ec
to
r
o
r
ie
n
tatio
n
.
Fig
u
r
es
4
a
n
d
5
e
x
h
i
b
it
th
e
d
e
r
iv
ativ
es
o
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tiv
e
a
n
d
r
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e
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o
wer
,
r
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r
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to
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ar
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ter
v
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ltag
e
v
e
cto
r
s
.
T
h
ese
wav
ef
o
r
m
s
illu
s
tr
ate
h
o
w
v
a
r
io
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s
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to
r
s
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th
e
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ate
o
f
p
o
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r
ch
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e,
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ch
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o
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l v
o
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e
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ec
t
o
r
to
m
in
im
i
ze
p
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wer
er
r
o
r
.
0
3
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0
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0
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2
0
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5
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8
0
2
1
0
2
4
0
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0
3
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3
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A
c
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3
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4
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A
n
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Fig
u
r
e
4
.
Activ
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p
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tiv
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0
30
60
90
1
2
0
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5
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4
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0
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3
0
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0
A
n
g
l
e
(
d
e
g
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0
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6
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1
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2
V
3
V
4
V
5
R
e
a
c
t
i
v
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P
o
w
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r
D
e
r
i
v
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t
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e
(
dQ
/
dt
)
V
0
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7
Fig
u
r
e
5
.
R
ea
ctiv
e
p
o
wer
d
er
i
v
ativ
e
T
h
e
d
ec
is
io
n
lo
g
ic
is
in
teg
r
a
ted
in
to
a
lo
o
k
u
p
ta
b
le,
illu
s
tr
ated
in
T
ab
le
1
,
wh
ich
co
r
r
elate
s
th
e
in
s
tan
tan
eo
u
s
p
o
wer
e
r
r
o
r
s
ta
tes
(
d
P,
d
Q)
an
d
th
e
s
ec
to
r
p
o
s
itio
n
with
th
e
ap
p
r
o
p
r
iate
v
o
ltag
e
v
ec
to
r
.
T
h
e
tab
le
class
if
ies
th
e
1
2
p
o
ten
tia
l
v
o
ltag
e
v
ec
to
r
s
ec
to
r
s
an
d
d
e
s
ig
n
ates
co
n
tr
o
l
ac
tio
n
s
ac
co
r
d
in
g
to
wh
eth
e
r
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
er
r
o
r
s
ar
e
r
is
in
g
(
1
)
o
r
d
ec
r
ea
s
i
n
g
(
0
)
.
Fo
r
e
x
am
p
le,
wh
en
b
o
th
d
P
an
d
d
Q
a
r
e
m
in
im
al,
th
e
d
atab
ase
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r
o
m
o
t
es
v
o
ltag
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ec
to
r
s
th
at
m
ai
n
tain
th
e
cu
r
r
en
t
p
o
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lev
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co
n
v
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s
ely
,
wh
en
b
o
t
h
er
r
o
r
s
ar
e
s
ig
n
if
ica
n
t,
th
e
lo
o
k
u
p
tab
le
p
r
io
r
itizes v
ec
to
r
s
th
a
t r
ap
id
ly
r
ec
tif
y
th
e
d
i
f
f
er
en
ce
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2509
-
2
5
2
0
2514
Fig
u
r
es
4
,
5
,
a
n
d
T
a
b
le
1
c
o
llectiv
ely
p
r
esen
t
an
in
-
d
ep
th
ex
p
lan
atio
n
o
f
th
e
p
o
wer
er
r
o
r
-
b
ased
v
ec
to
r
s
elec
tio
n
tech
n
iq
u
e
th
at
s
u
p
p
o
r
ts
th
e
VFDPC
alg
o
r
ith
m
.
T
h
is
in
teg
r
ated
co
n
tr
o
l
lo
g
ic
f
ac
ilit
ates
p
r
ec
is
e
an
d
ad
ap
tiv
e
v
o
ltag
e
v
ec
to
r
ap
p
licatio
n
,
en
s
u
r
in
g
p
er
f
ec
t
co
n
tr
o
l
o
f
ac
tiv
e
an
d
r
e
ac
tiv
e
p
o
wer
wh
ile
im
p
r
o
v
in
g
th
e
s
y
s
tem
'
s
r
esp
o
n
s
iv
en
ess
to
d
y
n
am
ic
co
n
d
itio
n
s
.
T
ab
le
1
.
VFDPC
lo
o
k
u
p
tab
le
P
o
w
e
r
e
r
r
o
r
st
a
t
u
s
S
e
c
t
o
r
p
o
s
i
t
i
o
n
(
θ
n
)
a
n
d
c
o
n
v
e
r
t
e
r
v
o
l
t
a
g
e
v
e
c
t
o
r
(
V
n
)
dP
dQ
θ
1
θ
2
θ
3
θ
4
θ
5
θ
6
θ
7
θ
8
θ
9
θ
10
θ
11
θ
12
0
0
V
1
V
1
V
2
V
2
V
3
V
3
V
4
V
4
V
5
V
5
V
6
V
6
0
1
V
2
V
2
V
3
V
3
V
4
V
4
V
5
V
5
V
6
V
6
V
1
V
1
1
0
V
6
V
6
V
1
V
1
V
2
V
2
V
3
V
3
V
4
V
4
V
5
V
5
1
1
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4
V
4
V
5
V
5
V
6
V
6
V
1
V
1
V
2
V
2
V
3
V
3
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Fig
u
r
e
6
p
r
esen
ts
th
e
s
im
u
latio
n
r
esu
lts
o
f
t
h
e
VFDPC
co
n
tr
o
l
s
tr
ateg
y
.
T
h
e
r
esu
lts
d
em
o
n
s
tr
ate
th
at
th
e
v
o
ltag
e
v
ec
to
r
s
elec
tio
n
in
th
e
lo
o
k
-
u
p
tab
le
is
ap
p
r
o
p
r
ia
te,
en
s
u
r
in
g
s
m
o
o
th
in
p
u
t
v
o
lt
ag
e
an
d
cu
r
r
e
n
t,
as
s
h
o
wn
in
Fig
u
r
es 6
(
a)
an
d
6
(
b
)
.
Ad
d
itio
n
ally
,
th
is
co
n
tr
o
l stra
teg
y
ef
f
ec
tiv
ely
co
n
v
er
ts
th
e
AC
s
o
u
r
ce
to
a
D
C
o
u
tp
u
t,
f
o
llo
win
g
th
e
r
ef
er
e
n
ce
v
alu
e,
as
o
b
s
er
v
e
d
in
Fig
u
r
e
6
(
c)
.
Fig
u
r
e
6
(
d
)
illu
s
tr
ates
th
e
in
s
tan
tan
eo
u
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
,
w
h
ile
Fig
u
r
e
6
(
e)
co
n
f
ir
m
s
u
n
i
ty
p
o
wer
f
ac
to
r
o
p
er
atio
n
,
wh
er
e
p
h
ase
v
o
ltag
es
alig
n
with
t
h
eir
c
o
r
r
esp
o
n
d
in
g
cu
r
r
en
ts
.
Fin
ally
,
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
m
ea
s
u
r
ed
in
6
(
f
)
is
s
ig
n
if
ican
tly
r
ed
u
ce
d
,
m
ee
tin
g
I
E
E
E
s
tan
d
ar
d
r
eq
u
ir
em
en
ts
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
6
.
Simu
latio
n
r
esu
lts
f
r
o
m
VFDPC
co
n
tr
o
l stra
teg
y
:
(
a)
p
h
ase
v
o
lta
g
e
,
(
b
)
l
in
e
cu
r
r
e
n
t
,
(
c)
DC
-
lin
k
v
o
ltag
e
,
(
d
)
a
ctiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
,
(
e
)
u
n
ity
p
o
wer
f
ac
t
o
r
,
an
d
(
f
)
h
ar
m
o
n
i
c
s
p
ec
tr
u
m
3
.
1
.
E
x
perim
ent
a
l
v
a
lid
a
t
io
n f
o
r
VF
DP
C
co
ntr
o
l st
ra
t
e
g
y
T
h
e
d
ev
elo
p
m
en
t
o
f
t
h
e
co
n
t
r
o
l
alg
o
r
ith
m
is
p
er
f
o
r
m
e
d
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
an
d
r
ea
l
-
tim
e
im
p
lem
en
tatio
n
with
th
e
d
SP
AC
E
DS1
1
0
4
Dig
ital
Sig
n
al
Pro
ce
s
s
in
g
(
DSP)
b
o
ar
d
in
s
er
ted
in
a
d
esk
to
p
co
m
p
u
ter
[
2
5
]
.
T
h
e
ex
p
er
im
en
tal
p
r
o
to
ty
p
e
o
f
th
e
AC
-
DC
co
n
v
er
ter
s
y
s
tem
h
as
b
ee
n
d
ev
elo
p
e
d
in
th
e
Un
iv
er
s
iti
T
ek
n
ik
al
Ma
lay
s
ia
Me
lak
a
(
UT
eM
)
lab
o
r
at
o
r
y
to
s
tu
d
y
an
d
ex
a
m
in
e
t
h
e
p
r
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p
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ed
DPC
s
ch
em
e.
T
h
e
m
ain
h
ar
d
war
e
co
n
f
ig
u
r
at
io
n
f
o
r
th
e
e
x
p
er
im
e
n
tal
s
etu
p
is
s
h
o
wn
in
th
e
b
lo
c
k
d
iag
r
a
m
o
f
Fig
u
r
e
7
.
T
h
e
s
etu
p
co
n
s
is
ts
o
f
a
th
r
ee
-
p
h
as
e
g
r
id
s
u
p
p
ly
,
a
th
r
ee
-
p
h
ase
t
r
an
s
f
o
r
m
er
,
lin
e
in
d
u
cto
r
s
,
an
AC
-
DC
co
n
v
er
ter
p
o
wer
cir
cu
it,
g
ate
d
r
iv
er
s
an
d
is
o
latio
n
,
DC
-
lin
k
ca
p
ac
ito
r
s
,
a
v
ar
iab
le
r
esis
tiv
e
lo
ad
,
v
o
ltag
e,
an
d
c
u
r
r
en
t
s
en
s
o
r
s
,
an
d
a
DSP
co
n
tr
o
ller
b
o
ar
d
.
T
h
e
s
am
p
lin
g
tim
e,
T
s
,
f
o
r
r
ea
l
im
p
lem
en
tatio
n
h
as
b
ee
n
in
cr
ea
s
ed
to
6
6
.
6
6
7
µs
o
r
1
5
k
Hz
s
am
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lin
g
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r
eq
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en
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y
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ec
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s
e
o
f
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e
s
p
e
ed
lim
it
o
f
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e
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b
o
ar
d
.
A
lar
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e
ca
p
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itan
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80
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[
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V
a
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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
6
9
4
E
xp
erimen
ta
l v
a
lid
a
tio
n
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f v
ir
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a
l flu
x
co
n
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p
t in
…
(
Mu
h
a
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d
Ha
feez Mo
h
a
med
Ha
r
ir
i
)
2515
th
e
DC
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ca
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ito
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th
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u
tp
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t
o
f
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ase
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u
p
th
e
AC
-
DC
co
n
v
er
ter
s
y
s
tem
u
n
it
is
n
ec
ess
ar
y
.
I
n
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
eth
o
d
,
th
e
f
o
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g
wa
y
o
f
ch
ar
g
in
g
u
p
th
e
u
n
it
is
estab
lis
h
ed
.
T
h
e
ca
p
ac
ito
r
is
p
r
e
-
c
h
ar
g
ed
to
a
ce
r
tain
DC
v
o
ltag
e
v
alu
e
Vd
c
,
t
h
r
o
u
g
h
th
e
an
ti
-
p
a
r
allel
d
io
d
e
o
f
th
e
I
GB
T
s
witch
es.
Fig
u
r
e
7
.
d
SP
AC
E
DS1
1
0
4
d
ig
ital sig
n
al
p
r
o
ce
s
s
in
g
(
DSP)
Fig
u
r
e
8
r
ep
r
esen
ts
th
e
b
ala
n
ce
d
in
p
u
t
th
r
ee
-
p
h
ase
g
r
id
s
id
e
v
o
ltag
e
wav
ef
o
r
m
s
o
n
ce
t
h
e
VFDPC
h
as
b
ee
n
ac
tiv
ated
.
I
n
Fig
u
r
e
8
(
a)
,
th
e
b
ala
n
ce
d
v
o
ltag
e
wav
ef
o
r
m
s
o
f
t
h
e
th
r
ee
-
p
h
ase
g
r
i
d
ar
e
s
h
o
wn
.
Fig
u
r
e
8
(
b
)
th
en
illu
s
tr
ates
th
e
VFD
PC
in
ac
tio
n
,
u
s
in
g
th
e
n
ew
s
witch
in
g
tab
le
to
g
en
er
ate
n
e
ar
ly
s
in
u
s
o
id
al
lin
e
cu
r
r
en
ts
o
p
er
atin
g
at
a
u
n
ity
p
o
wer
f
ac
to
r
,
as
illu
s
tr
ated
in
Fig
u
r
e
8
(
c)
.
T
h
e
r
ea
ctiv
e
p
o
wer
r
ef
er
en
ce
Qr
ef
is
s
et
to
0
Var
to
o
b
tain
u
n
it
y
p
o
wer
f
ac
to
r
o
p
er
atio
n
s
o
t
h
at
th
e
p
h
ase
v
o
ltag
es
ar
e
in
p
h
ase
with
th
eir
ass
o
ciate
d
cu
r
r
en
ts
.
T
h
e
m
o
s
t
u
p
p
er
wav
ef
o
r
m
in
Fig
u
r
e
8
(
d
)
s
h
o
ws
th
e
DC
o
u
tp
u
t
v
o
ltag
e,
Vd
c
is
well
r
eg
u
lated
at
a
r
ef
er
en
c
e
v
o
ltag
e,
Vd
c,
r
ef
o
f
1
5
0
V
,
wh
ile
m
ain
tain
in
g
th
e
s
in
u
s
o
id
al
t
h
r
ee
-
p
h
ase
cu
r
r
e
n
t.
Owin
g
to
p
r
ec
is
e
v
ir
tu
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f
lu
x
e
s
tim
atio
n
,
b
o
th
ac
tiv
e
an
d
r
ea
c
tiv
e
p
o
wer
ar
e
ac
cu
r
ately
ca
lc
u
lated
,
as d
ep
icted
in
Fig
u
r
e
8
(
e)
.
Fin
ally
,
th
e
AC
-
DC
co
n
v
er
ter
u
tili
zin
g
VFDPC
with
a
n
ew
s
witch
in
g
tab
le
g
en
er
ates
a
cu
r
r
en
t
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
H
D)
o
f
4
.
5
%
as
s
h
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wn
in
8
(
f
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.
T
h
is
T
HD
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alu
e
co
m
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s
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ar
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o
a
r
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2509
-
2
5
2
0
2516
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
8
.
Simu
latio
n
r
esu
lts
f
r
o
m
VFDPC
co
n
tr
o
l stra
teg
y
:
(
a)
p
h
ase
v
o
lta
g
e
,
(
b
)
lin
e
cu
r
r
e
n
t
,
(
c)
DC
-
lin
k
v
o
ltag
e
,
(
d
)
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
,
(
e
)
u
n
ity
p
o
wer
f
ac
t
o
r
,
an
d
(
f
)
h
ar
m
o
n
i
c
s
p
ec
tr
u
m
3
.
2
.
L
o
a
d
v
a
ria
t
io
n
E
x
p
er
im
en
t
test
s
ar
e
also
co
n
d
u
cted
to
v
er
if
y
th
e
d
y
n
am
ic
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
VFDPC
.
Fig
u
r
e
9
s
h
o
ws
tr
an
s
ien
t
r
esp
o
n
s
es
f
o
r
th
e
r
ap
id
ch
a
n
g
e
o
f
lo
ad
p
o
wer
u
n
d
er
u
n
ity
p
o
wer
f
a
cto
r
o
p
er
atio
n
.
T
h
e
ad
d
itio
n
al
r
esis
to
r
is
ab
r
u
p
tly
co
n
n
ec
ted
in
p
ar
allel
with
th
e
ex
is
tin
g
r
esis
to
r
at
th
e
o
u
tp
u
t
o
f
th
e
PW
M
r
ec
tifie
r
to
ca
u
s
e
a
s
u
d
d
e
n
in
cr
ea
s
e
in
th
e
lo
ad
p
o
wer
.
As a
r
e
s
u
lt,
th
e
esti
m
ated
in
p
u
t a
ctiv
e
p
o
wer
,
P,
an
d
th
e
p
h
ase
cu
r
r
en
ts
in
cr
ea
s
e
s
im
u
ltan
eo
u
s
ly
to
f
u
lf
ill
th
e
lo
ad
p
o
wer
d
em
an
d
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
eth
o
d
ca
n
m
ain
tain
th
e
DC
-
lin
k
o
u
tp
u
t
v
o
ltag
e
at
th
e
r
ef
er
en
ce
v
alu
e
o
f
1
5
0
V
an
d
th
e
s
in
u
s
o
id
al
lin
e
cu
r
r
en
ts
with
a
u
n
ity
p
o
wer
f
a
cto
r
.
T
h
e
esti
m
ated
r
ea
ctiv
e
p
o
wer
,
Q
,
is
k
ep
t
at
0
Var
t
o
m
ain
tain
th
e
u
n
ity
p
o
wer
f
ac
to
r
o
p
er
atio
n
o
f
th
e
PW
M
r
ec
tifie
r
.
Fig
u
r
e
9
.
T
r
an
s
ien
t r
esp
o
n
s
e
f
o
r
lo
ad
i
n
cr
ea
s
in
g
in
VFDPC
f
r
o
m
ex
p
er
im
en
tal
r
esu
lts
u
n
d
e
r
b
alan
ce
d
v
o
ltag
e
s
u
p
p
ly
co
n
d
itio
n
s
.
Fro
m
to
p
:
DC
-
lin
k
o
u
tp
u
t v
o
ltag
e
(
1
0
7
V/d
iv
)
,
esti
m
ated
in
p
u
t a
ctiv
e
p
o
wer
(
1
5
0
W
/d
iv
)
,
esti
m
ated
in
p
u
t r
ea
ctiv
e
p
o
we
r
(
7
5
Va
r
/d
iv
)
,
a
n
d
p
h
ase
a
-
c
u
r
r
en
t (
2
.
5
A/d
iv
)
E
v
alu
atio
n
o
f
t
h
e
d
y
n
am
ic
r
esp
o
n
s
e
u
n
d
er
th
e
ch
an
g
e
o
f
lo
ad
p
o
wer
f
r
o
m
h
ig
h
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w
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em
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er
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r
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ed
b
y
in
s
tan
tly
d
is
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n
n
ec
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g
th
e
a
d
d
iti
o
n
al
r
esis
to
r
s
in
p
ar
allel
with
th
e
ex
is
tin
g
lo
ad
r
esis
to
r
o
f
1
4
0
Ω
.
Fig
u
r
e
1
0
s
h
o
ws
th
e
tr
an
s
ien
t
r
esp
o
n
s
e
d
u
r
in
g
th
is
co
n
d
itio
n
.
T
h
e
in
p
u
t
esti
m
ated
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,
P
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d
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e
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ase
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r
r
en
t
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e
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ec
r
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g
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r
r
en
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ly
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h
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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
E
xp
erimen
ta
l v
a
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h
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cu
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f
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g
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r
o
u
g
h
t
h
e
AC
-
DC
co
n
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ter
s
y
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.
Fig
u
r
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1
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.
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r
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esp
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ated
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n
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ase
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g
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h
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u
r
e
1
1
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e
f
ig
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r
e,
th
e
DC
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u
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u
t
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o
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e
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[
1
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T.
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