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y
s
tem
s
f
o
r
th
e
p
r
o
d
u
ctio
n
,
d
is
tr
ib
u
tio
n
,
tr
a
n
s
m
is
s
io
n
,
an
d
tr
an
s
p
o
r
t o
f
elec
t
r
ic
p
o
wer
[
1
]
-
[
6
]
.
T
h
e
p
r
im
ar
y
ex
p
lan
atio
n
s
ar
e:
˗
R
ec
en
t
an
d
o
n
g
o
in
g
ad
v
an
ce
s
in
tech
n
o
lo
g
y
f
o
r
elec
tr
ical
s
y
s
tem
s
,
as
well
as
th
e
ac
ce
s
s
i
b
ilit
y
o
f
a
wid
e
v
ar
iety
o
f
s
witch
es c
r
ea
ted
f
r
o
m
s
em
ico
n
d
u
cto
r
s
s
u
ited
f
o
r
u
s
e
in
ap
p
licatio
n
s
o
f
h
ig
h
p
o
w
er
.
˗
T
h
e
m
o
v
in
g
f
o
r
war
d
d
ev
elo
p
m
en
t
o
f
tech
n
o
l
o
g
y
f
o
r
m
icr
o
elec
tr
o
n
ics
h
as
m
ad
e
it
p
o
s
s
ib
le
to
im
p
lem
en
t
co
m
p
lex
s
ig
n
al
p
r
o
ce
s
s
in
g
an
d
co
n
tr
o
l
tech
n
i
q
u
es,
as
well
a
s
th
e
alg
o
r
ith
m
s
n
ec
ess
ar
y
f
o
r
s
u
ch
s
tr
ateg
ies,
in
a
v
ar
iety
o
f
co
n
tex
ts
an
d
c
o
n
tex
t
-
s
p
ec
if
ic
ap
p
licatio
n
s
.
˗
T
h
e
elec
tr
ic
u
tili
ty
s
ec
to
r
is
u
n
d
er
g
o
in
g
r
estru
ctu
r
i
n
g
,
wh
i
ch
n
ec
ess
itates
th
e
u
s
e
o
f
p
o
wer
elec
tr
o
n
ics
-
b
ased
tech
n
o
lo
g
y
to
s
o
lv
e
is
s
u
es lik
e
p
o
wer
lin
e
co
n
g
esti
o
n
.
˗
T
h
e
o
n
g
o
in
g
ex
p
a
n
s
io
n
o
f
e
n
e
r
g
y
d
e
m
an
d
h
as led
to
th
e
u
s
e
o
f
th
e
elec
tr
ic
p
o
wer
u
tili
ty
in
f
r
astru
ctu
r
e
th
at
is
v
er
y
n
ea
r
to
r
ea
ch
in
g
its
m
ax
im
u
m
ca
p
ac
ity
,
wh
ic
h
n
ec
e
s
s
itate
s
th
e
u
s
e
o
f
elec
tr
o
n
ic
p
o
wer
eq
u
ip
m
e
n
t
in
o
r
d
e
r
to
im
p
r
o
v
e
t
h
e
s
y
s
tem
'
s
s
tab
ilit
y
.
˗
T
h
e
tr
en
d
to
war
d
in
cr
ea
s
ed
u
s
ag
e
o
f
g
r
ee
n
en
er
g
y
is
a
r
esp
o
n
s
e
to
th
e
p
h
en
o
m
en
a
o
f
g
lo
b
al
war
m
in
g
as
well
as
en
v
ir
o
n
m
en
tal
p
r
o
b
lem
s
lin
k
ed
with
ce
n
tr
ali
ze
d
p
o
wer
g
en
er
atio
n
.
B
ec
au
s
e
o
f
r
ec
en
t
d
ev
elo
p
m
e
n
ts
in
tech
n
o
lo
g
y
,
th
is
m
o
v
em
en
t
h
as
g
ain
e
d
tr
a
ctio
n
,
wh
ich
h
as
led
to
t
h
e
c
o
m
m
er
cial
an
d
tech
n
o
lo
g
ical
f
ea
s
ib
ilit
y
o
f
alter
n
ativ
e
s
o
u
r
ce
s
o
f
en
er
g
y
,
esp
ec
ially
th
o
s
e
th
at
ar
e
r
en
ewa
b
le.
Sp
ec
if
ically
,
th
is
v
iab
ilit
y
h
as
r
esu
lted
in
t
h
e
v
iab
ilit
y
o
f
r
en
ewa
b
le
e
n
er
g
y
r
eso
u
r
ce
s
.
Po
wer
elec
tr
o
n
i
c
co
n
v
er
te
r
s
ar
e
f
r
eq
u
e
n
tly
u
s
ed
to
estab
lis
h
a
co
n
n
ec
tio
n
b
etwe
en
th
ese
ty
p
es
o
f
en
er
g
y
r
eso
u
r
ce
s
an
d
th
e
elec
tr
ic
p
o
wer
s
y
s
tem
[
8
]
-
[
1
0
]
.
T
h
e
d
ir
ec
t
cu
r
r
en
t
s
id
e
o
f
t
h
e
v
o
ltag
e
s
o
u
r
ce
c
o
n
v
e
r
ter
(
V
SC
)
is
lin
k
ed
to
an
id
ea
l
d
ir
e
ct
cu
r
r
en
t
v
o
ltag
e
s
o
u
r
ce
,
wh
ich
is
r
esp
o
n
s
ib
le
f
o
r
d
ictatin
g
th
e
v
o
ltag
e
o
f
th
e
d
ir
ec
t
cu
r
r
en
t
b
u
s
.
As
a
r
esu
lt,
th
e
s
y
s
tem
o
f
VSC
s
er
v
es
as
a
ch
an
n
el
f
o
r
th
e
f
lo
w
o
f
p
o
wer
in
b
o
th
d
ir
ec
tio
n
s
,
co
n
n
ec
tin
g
th
e
AC
s
y
s
tem
an
d
t
h
e
DC
v
o
ltag
e
s
o
u
r
ce
.
B
u
t
in
a
lo
t
o
f
s
itu
atio
n
s
,
s
u
ch
as
f
u
el
-
ce
ll
an
d
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
,
t
h
is
is
n
o
t
t
h
e
ca
s
e.
T
h
e
DC
s
id
e
o
f
th
e
VSC
is
n
o
t
in
ter
f
ac
ed
with
a
v
o
ltag
e
s
o
u
r
ce
;
r
at
h
er
,
it
is
co
u
p
le
d
to
a
DC
p
o
wer
s
o
u
r
ce
.
B
ef
o
r
e
th
e
AC
s
y
s
tem
ca
n
u
tili
ze
th
is
p
o
wer
,
a
co
n
tr
o
lled
en
er
g
y
e
x
ch
an
g
e
an
d
p
r
ec
is
e
r
eg
u
latio
n
m
u
s
t
b
e
im
p
lem
en
ted
to
e
n
s
u
r
e
s
ea
m
le
s
s
in
teg
r
atio
n
an
d
o
p
er
atio
n
al
s
tab
ilit
y
[
1
1
]
-
[
1
6
]
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
s
tu
d
y
is
to
en
h
an
ce
th
e
s
tab
ilit
y
o
f
th
e
r
eg
u
lated
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t u
s
in
g
an
o
p
tim
ized
f
ee
d
-
f
o
r
war
d
co
m
p
en
s
atio
n
ap
p
r
o
ac
h
.
T
h
e
in
t
r
o
d
u
ctio
n
o
f
th
is
wo
r
k
o
u
tlin
es
th
e
s
ig
n
i
f
ican
ce
o
f
p
o
wer
elec
tr
o
n
ic
c
o
n
v
e
r
ter
s
an
d
th
e
ch
allen
g
es
in
DC
b
u
s
v
o
ltag
e
r
eg
u
latio
n
.
T
h
e
p
ap
er
is
s
tr
u
ctu
r
e
d
s
y
s
tem
atica
lly
:
i)
S
ec
tio
n
1
p
r
o
v
id
es
an
in
t
r
o
d
u
ctio
n
;
ii)
S
ec
tio
n
2
p
r
esen
ts
th
e
s
y
s
tem
s
tr
u
ctu
r
e
;
iii)
S
ec
tio
n
3
d
etails
th
e
m
ath
em
atica
l
m
o
d
ellin
g
;
iv
)
S
ec
tio
n
4
d
is
cu
s
s
es
t
h
e
co
n
tr
o
l
s
tr
ateg
y
;
v
)
S
ec
tio
n
5
in
tr
o
d
u
ce
s
th
ir
d
h
ar
m
o
n
ic
in
jectio
n
f
o
r
im
p
r
o
v
ed
PW
M
p
er
f
o
r
m
a
n
ce
;
an
d
v
i)
S
ec
tio
n
6
v
alid
ates
th
e
ap
p
r
o
ac
h
th
r
o
u
g
h
s
im
u
latio
n
r
esu
lts
.
2.
SYST
E
M
ST
RUC
T
UR
E
Fig
u
r
e
1
illu
s
tr
ates
th
e
VSC
s
y
s
tem
,
an
d
th
e
s
o
u
r
ce
o
f
DC
v
o
ltag
e
is
r
ep
r
esen
ted
as
a
(
v
a
r
y
in
g
)
DC
p
o
wer
s
o
u
r
ce
i
n
th
is
in
s
tan
ce
.
T
y
p
ically
,
th
e
s
o
u
r
ce
o
f
p
o
w
er
is
r
ep
r
esen
ted
b
y
a
u
n
it
o
f
p
o
wer
elec
tr
o
n
ics
th
at
h
as
th
e
m
ain
en
er
g
y
s
o
u
r
ce
th
at
p
o
wer
s
it.
I
n
p
ar
ticu
lar
,
th
is
m
ay
b
e
a
f
u
el
ce
ll
u
n
it,
a
g
as
tu
r
b
in
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
DC
b
u
s
co
n
tr
o
l str
a
teg
y
a
n
d
i
mp
lica
tio
n
s
fo
r
vo
lta
g
e
s
o
u
r
ce
co
n
ve
r
ter s
ystem
(
Ha
id
er F
a
d
el
)
1507
g
en
er
ato
r
s
y
s
tem
,
a
v
a
r
iab
le
-
s
p
ee
d
win
d
tu
r
b
i
n
e
-
g
en
er
ato
r
s
y
s
tem
,
o
r
a
n
ar
r
a
y
o
f
s
o
lar
p
a
n
els.
W
e
tack
le
th
is
as
a
b
lack
b
o
x
an
d
m
ak
e
t
h
e
a
s
s
u
m
p
tio
n
th
at
it
tr
ad
es
a
p
o
w
er
s
u
p
p
l
y
with
t
h
e
DC
s
id
e
o
f
th
e
VSC
th
at
v
ar
ies
o
v
er
tim
e.
B
ec
au
s
e
o
f
th
is
,
th
e
VSC
s
y
s
tem
s
h
o
wn
in
Fig
u
r
e
1
p
er
m
its
a
p
o
wer
e
x
ch
an
g
e
in
b
o
th
d
ir
ec
ti
o
n
s
b
etwe
en
th
e
p
o
we
r
s
u
p
p
ly
an
d
th
e
alter
n
atin
g
cu
r
r
en
t
AC
s
y
s
tem
.
Fo
r
th
e
r
est
o
f
th
is
d
is
cu
s
s
io
n
,
we
a
r
e
g
o
in
g
to
talk
ab
o
u
t th
e
VSC
s
y
s
tem
s
h
o
wn
in
Fig
u
r
e
1
as th
e
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t w
h
ich
r
eg
u
lates.
T
h
e
r
eg
u
lated
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t
is
cr
u
cial
in
th
e
STAT
C
OM
,
th
e
co
m
p
o
n
e
n
ts
o
f
v
ar
iab
le
-
s
p
ee
d
win
d
p
o
wer
,
an
d
th
e
b
ac
k
-
to
-
b
ac
k
HVDC
co
n
v
er
te
r
s
y
s
tem
[
1
7
]
-
[
1
9
]
.
As
s
ee
n
in
Fig
u
r
e
1
,
th
e
VS
C
is
ap
p
r
o
x
im
ated
b
y
a
C
PU
with
lo
s
s
less
p
o
wer
th
at
co
n
tain
s
an
an
alo
g
o
u
s
DC
-
b
u
s
ca
p
ac
ito
r
,
a
cu
r
r
en
t
s
o
u
r
ce
th
at
r
ep
r
esen
ts
th
e
lo
s
s
o
f
VSC
s
witch
in
g
p
o
wer
,
an
d
th
e
AC
s
id
e's
s
er
ies
o
n
-
s
tate
r
esis
tan
c
e
th
at
r
ep
r
esen
ts
th
e
VSC
co
n
d
u
ctio
n
p
o
wer
lo
s
s
.
T
h
e
VS
C
'
s
DC
s
id
e
ca
n
b
e
co
n
n
ec
ted
t
o
eith
er
a
DC
v
o
lt
ag
e
o
r
a
DC
p
o
we
r
s
o
u
r
ce
.
A
s
er
ies
R
L
b
r
an
ch
co
n
n
e
cts
ea
ch
VSC
p
h
ase
to
th
e
AC
s
y
s
tem
.
In
th
is
p
ap
er
,
we
will
b
e
ap
p
r
o
x
im
atin
g
an
en
d
less
ly
s
tiff
A
C
s
y
s
tem
in
o
r
d
er
to
b
etter
u
n
d
er
s
tan
d
it.
As
a
r
esu
lt,
th
e
AC
s
y
s
tem
m
ay
b
e
co
n
ce
p
tu
alize
d
as
a
r
ep
r
esen
tatio
n
o
f
th
e
o
p
tim
al
th
r
ee
-
p
h
ase
p
o
wer
s
u
p
p
ly
,
d
en
o
ted
b
y
.
I
n
a
d
d
itio
n
to
th
is
,
it
is
p
r
esu
m
ed
t
h
at
is
s
y
m
m
etr
ical,
s
in
u
s
o
id
al,
an
d
h
as
a
f
r
eq
u
e
n
cy
th
at
is
g
en
er
ally
s
tab
le.
At
th
e
p
o
in
t
o
f
co
m
m
o
n
c
o
n
n
ec
tio
n
,
th
e
r
ea
l
a
n
d
r
ea
ctiv
e
p
o
wer
co
m
p
o
n
en
ts
(
)
an
d
(
)
ar
e
tr
ad
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b
etwe
en
th
e
AC
s
y
s
tem
an
d
th
e
VSC
s
y
s
tem
.
Fig
u
r
e
1
s
h
o
ws
th
is
p
r
o
ce
s
s
p
o
in
t o
f
co
m
m
o
n
c
o
u
p
lin
g
(
PC
C
)
[
1
6
]
.
W
h
er
e
,
,
an
d
ar
e
th
e
AC
v
o
ltag
es a
t th
e
in
v
er
ter
ter
m
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al.
,
,
an
d
ar
e
th
e
AC
-
s
id
e
v
o
ltag
es so
u
r
ce
.
is
th
e
in
s
tan
t
an
eo
u
s
p
o
wer
at
th
e
DC
s
id
e,
is
th
e
elec
tr
ical
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wer
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th
e
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id
e
o
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in
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er
ter
,
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o
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p
p
lied
to
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e
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o
ltag
e
s
o
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r
ce
o
n
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e
AC
s
id
e.
is
th
e
v
ar
y
in
g
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tim
e
p
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wer
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ch
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g
e
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th
e
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o
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r
ce
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id
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d
=
×
.
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u
r
e
1
.
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d
iag
r
am
m
atic
r
e
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r
esen
tatio
n
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th
e
r
eg
u
lated
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v
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r
t
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h
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d
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)
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e
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e
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v
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Fi
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(.
)^
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(.
)^
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K
v
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s
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Com
p
e
n
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in
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f
r
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e
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f.
S
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ator
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e
e
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p
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t
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P
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r
e
f
−
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r
e
f
−
V
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C
r
e
f
−
V
DC
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
.
3
,
Sep
tem
b
er
20
25
:
1505
-
1
5
1
5
1508
c
o
m
m
a
n
d
i
n
o
r
d
e
r
t
o
c
o
n
t
r
o
l
t
h
e
v
o
l
t
a
g
e
o
f
t
h
e
D
C
b
u
s
.
Ac
c
o
r
d
i
n
g
t
o
t
h
e
r
e
s
u
l
t
s
o
f
t
h
is
c
o
m
p
a
r
i
s
o
n
,
i
s
a
d
j
u
s
t
e
d
i
n
s
u
c
h
a
wa
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h
a
t t
h
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p
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t
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a
t
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c
h
a
n
g
e
d
wi
t
h
t
h
e
DC
-
b
u
s
c
a
p
a
ci
t
o
r
is
m
a
in
t
a
i
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d
a
t z
e
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o
.
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n
t
h
e
o
t
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h
a
n
d
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t
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ea
c
t
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p
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w
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c
a
n
b
e
m
o
d
i
f
i
e
d
o
n
a
n
i
n
d
i
v
i
d
u
a
l
b
as
is
.
I
n
a
g
r
e
a
t n
u
m
b
er
o
f
a
p
p
l
i
c
at
i
o
n
s
,
i
s
c
o
n
t
r
o
l
le
d
t
o
r
e
m
a
i
n
a
t
z
er
o
;
i
n
t
h
e
s
e
ca
s
es
,
t
h
e
V
SC
s
y
s
t
e
m
m
a
i
n
t
a
i
n
s
a
p
o
w
e
r
f
a
c
to
r
o
f
u
n
i
t
y
.
I
t
i
s
p
o
s
s
i
b
le
t
o
c
o
n
t
r
o
l
PC
C
v
o
l
t
a
g
e
b
y
b
e
i
n
g
a
d
j
u
s
t
e
d
i
n
a
cl
o
s
e
d
-
l
o
o
p
m
a
n
n
e
r
[
1
4
]
-
[
1
8
]
.
3.
M
O
DE
L
L
I
NG
O
F
CO
NT
R
O
L
L
E
D
P
O
WE
R
P
O
R
T
WI
T
H
RE
G
U
L
AT
E
D
DC
-
VO
L
T
AG
E
T
h
e
m
ain
co
n
tr
o
l
n
ee
d
s
f
o
r
th
e
r
eg
u
lated
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t
s
h
o
wn
in
Fig
u
r
e
1
is
to
r
eg
u
late
th
e
v
o
ltag
e
o
f
th
e
DC
b
u
s
,
w
h
ich
is
d
en
o
te
d
b
y
.
T
o
p
u
t
it
an
o
t
h
er
way
,
it
is
p
r
e
f
er
r
e
d
to
r
eg
u
late
2
as
o
p
p
o
s
ed
t
o
.
Usi
n
g
(
1
)
as a
s
tar
tin
g
p
o
i
n
t,
th
e
d
y
n
am
ics o
f
2
ar
e
ch
ar
ac
ter
ized
as
(
1
)
.
2
=
2
−
2
−
2
[
+
(
2
3
̂
2
)
]
+
2
[
(
2
3
̂
2
)
]
(
1
)
Acc
o
r
d
in
g
to
th
e
co
m
b
in
ed
d
y
n
am
ic
m
o
d
el
o
f
th
e
two
-
le
v
e
l
VS
C
in
(
1
)
,
2
is
th
e
o
u
tp
u
t;
is
th
e
co
n
tr
o
l
in
p
u
t;
,
,
an
d
ar
e
t
h
e
d
is
tu
r
b
an
ce
in
p
u
ts
;
an
d
is
t
h
e
in
p
u
t
th
at
co
n
tr
o
ls
th
e
g
ain
.
I
n
ac
co
r
d
an
ce
with
wh
at
is
d
ep
icted
in
Fig
u
r
e
1
,
2
is
co
m
p
ar
ed
t
o
2
,
T
h
e
s
ig
n
al
o
f
er
r
o
r
is
d
ea
lt
with
b
y
th
e
co
m
p
en
s
ato
r
(
)
,
an
d
th
e
o
r
d
er
−
is
s
en
t
to
t
h
e
co
n
tr
o
ll
er
o
f
th
e
r
ea
l
p
o
wer
.
I
n
its
t
u
r
n
,
t
h
e
r
ea
l
-
p
o
wer
c
o
n
tr
o
ller
is
r
esp
o
n
s
ib
le
f
o
r
r
eg
u
latin
g
at
−
,
wh
er
ea
s
is
o
p
en
to
i
n
d
ep
en
d
en
t
r
eg
u
latio
n
.
I
f
t
h
er
e
is
a
r
eq
u
i
r
em
en
t
f
o
r
a
c
o
n
tr
o
lled
b
id
i
r
ec
tio
n
al
r
eg
u
latio
n
o
f
r
ea
ctiv
e
p
o
wer
i
n
ter
ac
tio
n
with
th
e
AC
s
y
s
tem
,
−
ca
n
b
e
a
d
ju
s
ted
to
a
v
alu
e
th
at
is
n
o
t
ze
r
o
.
I
n
an
alter
n
atin
g
cu
r
r
en
t
(
AC
)
s
y
s
te
m
with
a
h
ig
h
im
p
ed
an
ce
,
th
e
P
C
C
v
o
ltag
e
is
p
r
o
n
e
to
f
lu
ctu
a
tio
n
s
d
u
e
to
th
e
tim
e
-
d
e
p
en
d
e
n
t
s
h
if
ts
in
(
i.e
.
,
d
u
e
to
th
e
ch
a
n
g
es
o
f
)
.
I
n
a
c
lo
s
ed
-
lo
o
p
s
y
s
tem
th
at
s
u
p
p
lie
s
th
e
PC
C
v
o
ltag
e
b
ac
k
,
is
co
n
tr
o
lled
an
d
co
m
m
an
d
s
−
is
o
n
e
way
in
wh
i
ch
th
e
v
o
ltag
e
o
f
t
h
e
PC
C
m
ay
b
e
m
an
a
g
ed
in
t
h
is
in
s
tan
ce
[
1
7
]
-
[
2
5
]
.
I
n
o
r
d
er
to
o
b
tain
th
e
tr
an
s
f
er
f
u
n
ctio
n
(
)
=
(
)
/
−
(
)
,
we
f
ir
s
t
n
ee
d
t
o
m
ak
e
th
e
o
b
s
er
v
atio
n
t
h
at
as (
2
)
.
(
)
=
(
)
(
)
(
2
)
I
n
wh
ich
(
)
is
p
r
o
v
id
e
d
b
y
(
3
)
.
(
)
=
1
+
1
(
3
)
W
h
er
e
r
ep
r
esen
ts
th
e
f
in
al
clo
s
ed
-
lo
o
p
s
y
s
tem
'
s
tim
e
co
n
s
tan
t.
W
h
en
we
ass
u
m
e
t
h
at
r
em
ain
s
u
n
ch
an
g
ed
,
a
n
d
m
u
ltip
ly
b
o
th
s
id
es o
f
(
2
)
b
y
(
3
/
2
)
,
we
g
et
th
e
r
es
u
lt
as (
4
)
.
(
)
=
(
)
−
(
)
(
4
)
As a
r
esu
lt,
(
)
=
(
)
,
an
d
tak
in
g
in
to
ac
co
u
n
t (
3
)
,
it o
b
tain
s
(
5
)
.
(
)
−
(
)
=
(
)
=
1
+
1
(
5
)
B
ec
au
s
e
in
-
f
r
am
e,
ac
tu
al
p
o
wer
is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
,
th
e
f
o
r
m
(
5
)
is
th
e
o
n
e
t
h
at
o
n
e
wo
u
ld
in
tu
itiv
ely
ex
p
ec
t
to
s
ee
.
B
e
ca
u
s
e
o
f
th
e
/
an
d
/
f
ac
to
r
s
,
th
e
co
n
tr
o
l
p
lan
t
th
at
is
d
escr
ib
ed
b
y
(
1
)
is
a
n
o
n
lin
ea
r
s
y
s
tem
.
T
h
e
p
lan
t th
at
h
as b
e
en
lin
ea
r
ized
is
g
iv
e
n
b
y
(
6
)
.
W
h
er
e
th
e
s
u
p
er
s
cr
ip
ts
~
an
d
0
r
e
f
er
,
r
esp
ec
tiv
ely
,
to
th
e
v
alu
es
o
f
th
e
v
ar
iab
les
d
u
r
in
g
s
tead
y
-
s
tate
cir
cu
m
s
tan
ce
s
an
d
s
m
all
-
s
ig
n
al
d
is
tu
r
b
an
ce
s
.
Af
ter
ap
p
ly
in
g
th
e
L
ap
lace
tr
an
s
f
o
r
m
to
(
6
)
,
we
wer
e
ab
le
to
d
er
iv
e
th
e
tr
a
n
s
f
er
f
u
n
ctio
n
(
)
as
̃
2
/
̃
u
s
in
g
(
7
)
.
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
DC
b
u
s
co
n
tr
o
l str
a
teg
y
a
n
d
i
mp
lica
tio
n
s
fo
r
vo
lta
g
e
s
o
u
r
ce
co
n
ve
r
ter s
ystem
(
Ha
id
er F
a
d
el
)
1509
W
h
er
e
th
e
co
n
s
tan
t o
f
th
e
tim
e
τ
is
as (
8
)
.
=
2
0
3
2
=
2
0
3
2
(
8
)
Acc
o
r
d
in
g
t
o
th
e
s
o
lu
tio
n
o
f
(
8
)
,
th
e
v
alu
e
o
f
th
e
tim
e
c
o
n
s
tan
t
is
p
r
o
p
o
r
tio
n
al
to
th
e
r
e
al
p
o
wer
f
lo
w
in
a
s
tead
y
c
o
n
d
itio
n
0
(
o
r
0
)
.
T
h
e
r
ef
o
r
e,
if
0
is
lo
w,
th
en
it
will
b
e
n
eg
lig
ib
le,
a
n
d
th
is
will
in
d
icate
th
at
th
e
p
lan
t
is
m
o
s
tly
an
in
teg
r
ato
r
.
As
th
e
v
alu
e
o
f
g
o
es
u
p
,
th
e
v
alu
e
o
f
t
h
e
tim
e
co
n
s
tan
t
g
o
es
u
p
as
well,
wh
ich
in
d
u
ce
s
a
p
h
ase
ch
an
g
e
in
(
)
.
W
h
en
th
e
d
ev
ice
is
o
p
er
atin
g
in
its
in
v
er
tin
g
m
o
d
e
,
0
h
as
a
p
o
s
itiv
e
v
alu
e,
t
h
u
s
also
h
as
a
p
o
s
itiv
e
v
alu
e
an
d
c
o
n
tr
ib
u
tes
to
th
e
p
h
ase
o
f
(
)
.
I
n
co
n
tr
ast,
wh
en
th
e
r
ec
tific
atio
n
o
p
er
ati
n
g
m
o
d
e
is
en
g
a
g
ed
—
th
at
is
,
wh
en
0
is
less
th
an
ze
r
o
—
th
e
v
alu
e
o
f
is
also
less
th
an
ze
r
o
,
wh
ich
ca
u
s
es
a
d
ec
r
em
en
t
in
th
e
p
h
ase
o
f
(
)
.
T
h
e
p
h
ase
d
ec
r
ea
s
es
ev
en
f
u
r
th
er
as
th
e
ab
s
o
lu
te
v
alu
e
o
f
0
in
cr
ea
s
es.
T
h
e
p
lan
t
ze
r
o
m
ay
b
e
ca
lcu
la
ted
u
s
in
g
th
e
f
o
r
m
u
la
=
−
1
/
,
wh
ich
ca
n
b
e
f
o
u
n
d
in
(
7
)
.
As
a
r
esu
lt,
a
n
eg
ativ
e
v
alu
e
o
f
is
eq
u
iv
alen
t
to
th
e
v
alu
e
ze
r
o
o
n
th
e
r
ig
h
t
-
h
alf
p
lan
e
(
R
HP)
.
As
a
d
ir
ec
t
co
n
s
eq
u
en
ce
o
f
th
i
s
,
th
e
r
eg
u
lated
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t
is
a
n
o
n
-
m
in
im
u
m
-
p
h
ase
s
y
s
tem
wh
ile
it is
o
p
er
atin
g
in
th
e
r
ec
tify
in
g
m
o
d
e
[
2
4
]
-
[
2
7
]
.
4.
CO
NT
RO
L
O
F
A
P
O
WE
R
P
O
RT
WI
T
H
A
CO
NT
RO
L
L
E
D
D
C
VO
L
T
AG
E
Fig
u
r
e
2
s
h
o
ws
a
b
l
o
ck
lay
o
u
t
o
f
th
e
DC
-
b
u
s
v
o
ltag
e
co
n
tr
o
ller
u
s
ed
f
o
r
th
e
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t
th
at
is
r
eg
u
lated
in
Fig
u
r
e
1
.
T
h
e
co
m
p
en
s
ato
r
(
)
,
co
n
tr
o
ller
p
f
th
e
r
ea
l
p
o
wer
(
)
,
an
d
co
n
tr
o
l
p
lan
t
(
)
co
m
p
r
is
e
th
e
cl
o
s
ed
-
lo
o
p
s
y
s
tem
,
as
d
ef
in
ed
b
y
(
7
)
.
Fig
u
r
es
1
an
d
2
s
h
o
w
th
at
i
n
o
r
d
er
to
o
f
f
s
et
th
e
n
eg
ativ
e
s
ig
n
o
f
(
)
,
(
)
is
m
u
ltip
lied
b
y
1
.
(
)
s
h
o
u
ld
c
o
m
p
r
is
e
a
l
ea
d
f
u
n
cti
o
n
o
f
tr
an
s
f
er
with
an
in
teg
r
al
ter
m
.
T
h
e
lead
tr
a
n
s
f
er
f
u
n
ctio
n
a
d
ju
s
ts
f
o
r
p
lan
t
p
h
ase
lag
an
d
m
ain
tain
s
an
ad
e
q
u
ate
p
h
ase
m
ar
g
i
n
at
th
e
f
r
eq
u
en
cy
o
f
th
e
g
ain
cr
o
s
s
o
v
er
.
(
)
h
as
th
e
g
r
ea
test
p
h
ase
lag
wh
en
is
at
o
n
r
ated
n
eg
ativ
e
v
alu
e,
ac
co
r
d
in
g
to
(
7
)
an
d
(
8
)
.
T
h
e
clo
s
ed
-
lo
o
p
s
y
s
tem
r
em
ain
s
s
tab
le
at
all
o
th
e
r
w
o
r
k
in
g
p
o
i
n
ts
if
a
s
ig
n
if
ican
t p
h
ase
m
ar
g
in
is
s
u
p
p
lied
at
th
is
p
ar
ticu
lar
p
o
in
t
[
2
8
]
-
[
3
2
]
.
I
n
o
r
d
e
r
to
d
esig
n
(
)
,
ch
o
o
s
in
g
th
e
g
ain
cr
o
s
s
o
v
er
o
f
to
b
e
s
u
f
f
icien
tly
less
th
an
th
e
am
o
u
n
t
o
f
b
an
d
wid
t
h
o
f
(
)
,
s
u
ch
th
at
(
)
=
1
+
0
.
T
h
en
,
(
)
is
ca
lcu
lated
to
h
av
e
a
s
u
f
f
icien
tly
wid
e
p
h
ase
m
ar
g
in
i
n
th
e
m
o
s
t
s
ev
er
e
o
p
e
r
atio
n
al
co
n
d
itio
n
s
.
T
h
e
f
r
eq
u
en
cy
r
esp
o
n
s
e
d
e
s
ig
n
ap
p
r
o
ac
h
was
em
p
lo
y
ed
.
T
h
e
r
ea
s
o
n
f
o
r
th
is
,
ac
co
r
d
in
g
to
th
e
−
f
r
am
e
co
n
tr
o
l,
(
)
is
o
f
ten
a
h
ig
h
-
o
r
d
er
tr
an
s
f
er
f
u
n
ctio
n
th
at
is
m
o
s
tly
d
eter
m
in
ed
b
y
its
b
an
d
wid
th
in
co
n
tr
ast
to
its
p
o
le/ze
r
o
m
ap
.
(
)
(
as
p
r
o
v
i
d
ed
b
y
(
5
)
)
is
a
f
ir
s
t
-
o
r
d
e
r
tr
a
n
s
f
er
f
u
n
ctio
n
in
th
is
ca
s
e,
an
d
th
e
r
o
o
t
-
lo
cu
s
d
esig
n
tech
n
iq
u
e
is
a
ls
o
an
alter
n
ativ
e.
T
h
e
b
en
e
f
it
o
f
th
e
r
o
o
t
-
lo
cu
s
tech
n
iq
u
e
is
th
at
p
e
r
f
o
r
m
an
ce
m
etr
ics
s
u
ch
as
th
e
s
ettlin
g
tim
e
an
d
m
a
x
im
u
m
o
v
er
s
h
o
o
t
a
r
e
m
o
r
e
ea
s
ily
tie
d
to
th
e
p
o
le/ze
r
o
lo
ci
an
d
m
a
y
b
e
ea
s
ily
co
n
s
id
er
ed
in
t
o
ac
co
u
n
t
in
th
e
d
esig
n
p
r
o
ce
s
s
[
2
5
]
-
[
3
3
]
.
Fig
u
r
e
2
.
T
h
e
DC
v
o
ltag
e
co
n
t
r
o
ller
b
lo
c
k
d
iag
r
a
m
5.
T
H
I
RD
H
AR
M
O
NI
C
I
NJ
E
CT
I
O
N
F
O
R
P
W
M
T
h
e
th
ir
d
-
h
a
r
m
o
n
ic
in
jecte
d
P
W
M
tech
n
iq
u
e
was
u
tili
ze
d
to
in
cr
ea
s
e
th
e
allo
wab
le
v
o
ltag
e
r
an
g
e
o
f
th
e
VSC
.
T
h
e
th
ir
d
-
h
ar
m
o
n
ic
was
d
ev
elo
p
ed
a
n
d
im
p
lem
en
t
ed
in
α
β
-
f
r
am
e
as
d
e
p
icted
in
th
e
b
lo
ck
d
iag
r
a
m
s
h
o
wn
in
Fig
u
r
e
3
,
th
at
r
e
p
r
e
s
en
ts
a
b
lo
ck
d
iag
r
am
f
o
r
th
ir
d
-
h
ar
m
o
n
ic
in
jecte
d
PW
M
in
−
f
r
am
e,
wh
er
e
g
en
er
ates
th
e
th
ir
d
-
h
ar
m
o
n
ic
in
jecte
d
b
ased
o
n
(
9
)
-
(
1
1
)
.
T
h
e
b
lo
ck
d
iag
r
am
clea
r
ly
illu
s
tr
ates
h
o
w
th
e
to
f
r
am
e
tr
an
s
f
o
r
m
atio
n
o
f
an
d
r
esu
lts
in
.
T
h
e
th
ir
d
-
h
ar
m
o
n
ic
in
jecte
d
PW
M
also
d
em
an
d
s
2
.
C
o
n
s
eq
u
en
tly
,
we
wr
ite
2
in
ter
m
s
o
f
an
d
as
=
√
2
+
2
[
3
4
]
-
[
3
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
1505
-
1
5
1
5
1510
−
(
)
=
3
2
(
)
−
2
3
3
(
)
2
+
2
(
9
)
−
(
)
=
3
2
(
)
−
2
3
3
(
)
2
+
2
(
1
0
)
−
(
)
=
3
2
(
)
−
2
3
3
(
)
2
+
2
(
1
1
)
PLL
s
ch
em
atic
d
iag
r
am
b
ase
d
o
n
(
1
2
)
-
(
1
4
)
is
s
h
o
wn
in
Fig
u
r
e
4
,
wh
ich
illu
s
tr
ates
h
o
w
th
e
PLL
tr
an
s
f
o
r
m
s
to
an
d
ch
an
g
es
th
e
f
r
am
e
s
p
ee
d
o
f
r
o
tatio
n
(
)
to
eq
u
ate
to
ze
r
o
as
in
th
e
s
tead
y
s
tate,
wh
er
e
=
⁄
.
C
o
n
s
eq
u
en
tly
,
=
0
+
0
,
an
d
=
̂
[
2
6
]
-
[
3
7
]
.
T
h
e
in
teg
r
ato
r
,
d
escr
ib
e
d
in
(
1
3
)
,
ca
n
b
e
r
ec
o
g
n
ized
f
r
o
m
Fig
u
r
e
4
h
aw
it
is
im
p
lem
en
ted
u
s
in
g
VC
O
(
v
o
ltag
e
-
co
n
tr
o
lled
o
s
cillato
r
)
.
T
h
e
VC
O
is
f
u
n
ctio
n
in
g
as
a
r
esettin
g
in
teg
r
at
o
r
,
r
esettin
g
its
o
u
tp
u
t
(
ρ
)
to
ze
r
o
as
it
ap
p
r
o
ac
h
es
2
π.
T
h
e
co
m
p
e
n
s
ato
r
H(
s
)
in
f
lu
e
n
ce
s
th
e
PLL
d
y
n
am
ic
p
er
f
o
r
m
an
ce
s
ig
n
if
ican
tly
.
Fig
u
r
e
5
ex
p
lain
s
clea
r
ly
h
o
w
th
e
clo
s
ed
lo
o
p
co
n
tr
o
l
o
f
PLL
is
b
u
ilt.
T
h
e
r
ef
er
e
n
ce
s
ig
n
al,
0
+
,
co
n
s
is
ts
o
f
a
co
n
s
tan
t
co
m
p
o
n
en
t,
,
an
d
a
r
am
p
f
u
n
ctio
n
,
0
.
W
ith
th
e
in
clu
s
io
n
o
f
an
in
teg
r
al
ter
m
with
in
th
e
lo
o
p
g
ain
,
th
e
PLL
ca
n
tr
a
ck
th
e
s
tead
y
s
tate
ze
r
o
er
r
o
r
o
f
th
e
co
n
s
tan
t
co
m
p
o
n
en
t
o
f
t
h
e
r
ef
er
en
ce
s
ig
n
al.
I
n
o
r
d
er
to
ac
h
iev
e
ze
r
o
s
tead
y
-
s
tate
er
r
o
r
f
o
r
t
h
e
r
am
p
co
m
p
o
n
e
n
t,
th
e
lo
o
p
g
ain
m
u
s
t
in
co
r
p
o
r
ate
at
least
two
in
teg
r
ato
r
s
.
Hen
ce
,
H(
s
)
m
u
s
t
in
co
r
p
o
r
ate
a
m
in
im
u
m
o
f
o
n
e
in
teg
r
al
ter
m
,
co
r
r
esp
o
n
d
in
g
to
s
=
0
p
o
le.
T
h
e
o
th
er
to
o
ts
o
f
H(
s
)
,
ze
r
o
s
an
d
p
o
les,
ar
e
d
eter
m
in
ed
b
y
clo
s
ed
-
lo
o
p
th
e
o
f
PLL
b
an
d
wid
th
an
d
s
tab
ilit
y
cr
iter
ia
(
g
ain
an
d
p
h
ase
m
ar
g
i
n
s
)
[
3
8
]
-
[
4
9
]
.
=
̂
s
in
(
0
+
−
)
(
1
2
)
=
(
)
(
1
3
)
(
)
=
(
)
(
)
(
1
4
)
Fig
u
r
e
3
.
T
h
e
b
lo
c
k
d
iag
r
am
o
f
th
ir
d
h
ar
m
o
n
ic
in
jectio
n
f
o
r
g
en
er
atin
g
t
h
e
m
o
d
u
latin
g
s
ig
n
al
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
DC
b
u
s
co
n
tr
o
l str
a
teg
y
a
n
d
i
mp
lica
tio
n
s
fo
r
vo
lta
g
e
s
o
u
r
ce
co
n
ve
r
ter s
ystem
(
Ha
id
er F
a
d
el
)
1511
Fig
u
r
e
4
.
T
h
e
p
h
ase
-
lo
ck
ed
l
o
o
p
b
lo
c
k
d
iag
r
am
Fig
u
r
e
5
.
T
h
e
clo
s
ed
-
lo
o
p
c
o
n
tr
o
l
o
f
th
e
p
h
ase
-
lo
c
k
ed
lo
o
p
6.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
h
e
s
y
s
tem
is
s
im
u
lated
b
as
ed
o
n
th
e
p
ar
am
eter
s
s
h
o
wn
in
T
ab
le
1
.
T
h
e
r
eg
u
lated
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t,
s
h
o
w
n
in
Fig
u
r
e
1
,
is
s
im
u
lated
in
MA
T
L
A
B
Si
m
u
lin
k
.
I
ts
r
esp
o
n
s
e
to
a
s
tar
t
-
u
p
an
d
p
r
o
g
r
ess
iv
e
ad
ju
s
tm
en
ts
in
is
illu
s
tr
ated
i
n
Fig
u
r
e
6
,
wh
ich
p
r
esen
ts
th
e
o
b
tain
e
d
r
esu
lts
wh
e
n
th
e
DC
-
b
u
s
v
o
ltag
e
co
n
tr
o
l
l
o
o
p
'
s
f
ee
d
-
f
o
r
war
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ad
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s
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en
t
is
tu
r
n
ed
o
f
f
,
th
e
VSC
s
y
s
tem
u
n
d
er
g
o
es
th
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s
u
b
s
e
q
u
en
t
s
eq
u
en
ce
o
f
o
cc
u
r
r
e
n
ce
s
.
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wh
en
=
0
,
T
h
e
VSC
'
s
g
atin
g
s
ig
n
als
ar
e
s
u
p
p
r
ess
ed
,
wh
ich
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ak
es
th
e
co
n
tr
o
ller
s
id
le
;
h
en
ce
,
th
e
VSC
'
s
D
C
-
s
id
e
ca
p
ac
ito
r
s
ar
e
ch
ar
g
ed
v
ia
th
e
an
tip
ar
allel
d
i
o
d
es
in
th
e
s
w
itch
ce
lls
,
r
esu
ltin
g
in
a
v
o
ltag
e
o
f
ap
p
r
o
x
im
ately
7
0
0
V
.
T
h
en
,
wh
en
=
0
.
20
,
th
e
g
ati
n
g
s
ig
n
als
ar
e
u
n
b
lo
ck
e
d
,
co
n
tr
o
ller
s
ar
e
in
v
o
lv
e
d
,
an
d
VDCre
f
is
g
r
ad
u
ally
in
cr
ea
s
ed
f
r
o
m
7
0
0
t
o
1
4
5
0
V.
C
o
n
s
eq
u
en
tly
,
to
r
a
is
e
th
e
VD
C
,
(
)
co
m
m
an
d
s
a
n
e
g
ativ
e
−
to
b
r
in
g
in
a
r
ea
l
p
o
wer
f
r
o
m
th
e
AC
s
y
s
tem
to
th
e
VSC
DC
ter
m
in
al;
−
is
m
o
m
en
tar
ily
ca
p
p
e
d
t
o
its
n
e
g
ativ
e
th
r
esh
o
ld
.
W
h
en
th
e
s
im
u
latio
n
tim
e
=
0
.
30
,
VDC
is
co
n
tr
o
lled
at
=
1450
,
an
d
−
r
em
ain
at
th
eir
m
o
d
est
v
alu
es
co
r
r
esp
o
n
d
s
to
th
e
VSC
p
o
wer
lo
s
s
.
Fig
u
r
e
6
e
x
p
lain
s
a
g
r
ad
u
al
in
cr
ea
s
e
in
,
f
r
o
m
0
to
1
0
0
0
KW
,
wh
en
=
0
.
35
,
ca
u
s
in
g
an
o
v
er
s
h
o
o
t in
VDC.
T
o
r
etain
VD
C
to
1
4
5
0
V,
th
e
co
m
p
en
s
ato
r
h
as
to
in
cr
ea
s
e
−
as
well
a
s
in
r
esp
o
n
s
e
to
th
e
d
is
tu
r
b
an
ce
.
As
=
0
.
50
,
s
tead
ily
d
ec
r
ea
s
es
f
r
o
m
1000
to
−
1000
MW.
Un
d
er
s
h
o
o
ts
in
VDC
wil
l
ap
p
ea
r
u
n
til
th
e
co
m
p
e
n
s
ato
r
s
tar
ts
to
r
ed
u
ce
−
.
T
h
e
ex
ce
ed
e
d
p
atter
n
at
=
0
.
50
is
s
lig
h
tly
d
if
f
er
e
n
t
f
r
o
m
th
e
o
v
er
s
h
o
o
t
at
=
0
.
35
.
Af
ter
th
at,
wh
en
=
0
.
65
,
Qsre
f
witn
ess
es
a
tr
an
s
itio
n
f
r
o
m
0
to
500
.
T
h
is
d
is
tu
r
b
a
n
ce
d
o
es
n
o
t
s
ig
n
if
ican
tly
im
p
ac
t
VDC
s
in
ce
th
e
co
n
tr
ib
u
tio
n
o
f
to
2
⁄
is
p
o
n
d
e
r
ed
b
y
th
e
ter
m
2
/
(
3
2
)
,
wh
ich
is
u
s
u
ally
a
s
m
all
am
o
u
n
t.
T
h
e
r
esp
o
n
s
e
o
f
th
e
r
eg
u
late
d
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t,
d
ep
icted
in
Fig
u
r
e
1
,
to
d
is
tu
r
b
an
ce
s
is
illu
s
tr
ated
in
Fig
u
r
e
6
.
W
h
en
f
ee
d
-
f
o
r
war
d
ad
ju
s
tm
en
t is ac
ti
v
ated
with
in
th
e
DC
-
b
u
s
v
o
ltag
e
co
n
tr
o
l lo
o
p
(
b
y
in
co
r
p
o
r
atin
g
a
m
ea
s
u
r
e
o
f
in
to
th
e
o
u
t
p
u
t
o
f
(
)
)
.
C
o
m
p
a
r
is
o
n
o
f
Fig
u
r
es
6
an
d
7
d
em
o
n
s
tr
ates
th
at
em
p
lo
y
in
g
f
ee
d
-
f
o
r
war
d
c
o
r
r
e
ctio
n
clea
r
ly
m
in
im
izes
d
ev
iat
io
n
s
o
f
VDC
f
r
o
m
.
Var
iatio
n
s
in
ar
e
p
r
o
m
p
tly
co
m
m
u
n
icate
d
to
−
,
allo
win
g
s
wif
t p
o
wer
r
eb
ala
n
ci
n
g
.
T
h
e
o
b
tain
ed
s
im
u
latio
n
r
esu
lts
ex
p
lain
th
e
f
u
n
ctio
n
ality
o
f
th
e
DC
-
b
u
s
v
o
ltag
e
co
n
tr
o
ller
in
th
e
−
Fra
m
e.
I
t
is
o
b
s
er
v
ed
th
at
s
ig
n
if
ican
t
o
s
cillatio
n
s
o
cc
u
r
wh
en
alter
in
g
f
r
o
m
1000
to
−
1000
u
tili
zin
g
u
n
co
m
p
en
s
ated
lo
o
p
g
ain
.
Desp
ite
co
r
r
ec
tin
g
th
e
lo
o
p
g
ain
,
r
em
ain
s
s
o
m
e
h
o
w
d
ep
en
d
e
n
t
o
n
;
h
o
wev
er
,
VD
C
ex
h
ib
its
h
ig
h
er
s
tab
ilit
y
.
W
h
en
t
=
0
.
2
0
s
,
a
g
r
a
d
u
al
in
cr
ea
s
e
in
f
r
o
m
7
0
0
to
1
4
5
0
V
as
il
lu
s
tr
ated
F
ig
u
r
e
6
.
T
o
ac
h
iev
e
th
is
in
cr
ea
s
e,
(
)
f
ac
ilit
ate
s
th
e
tr
an
s
f
er
o
f
ac
tu
al
p
o
wer
f
r
o
m
th
e
AC
to
th
e
D
C
s
id
es
o
f
VSC
u
s
in
g
a
n
eg
ativ
e
−
.
At
t
=
0
.
3
5
s
,
g
r
ad
u
ally
in
cr
ea
s
es
f
r
o
m
0
to
1
0
0
0
k
W
,
ca
u
s
in
g
an
o
v
er
s
h
o
o
t
in
VDC.
T
h
e
co
m
p
en
s
ato
r
ad
ju
s
ts
−
to
r
etain
VDC
to
1
4
5
0
V.
Af
ter
war
d
,
at
t =
0
.
5
0
s
,
−
tr
an
s
itio
n
s
s
eq
u
en
tially
f
r
o
m
1
0
0
0
to
-
1
0
0
0
k
W
,
r
esu
ltin
g
in
u
n
d
er
s
h
o
o
tin
g
in
VDC
u
n
til
th
e
co
m
p
en
s
ato
r
r
ed
u
ce
s
−
.
At
t
=
0
.
6
5
s
,
−
ch
an
g
es
f
r
o
m
0
to
5
0
0
k
VAr
,
wh
ich
m
in
im
ally
im
p
ac
ts
VDC,
as
ex
p
lain
ed
in
Fig
u
r
e
6
.
T
h
is
p
h
en
o
m
en
o
n
is
elab
o
r
ated
in
(
6
)
.
Fu
r
t
h
er
m
o
r
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.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
1505
-
1
5
1
5
1512
Fig
u
r
e
7
d
em
o
n
s
tr
ates
h
o
w
t
h
e
p
o
we
r
p
o
r
t
c
o
n
tr
o
lled
b
y
th
e
DC
v
o
ltag
e
r
esp
o
n
d
s
to
d
is
tu
r
b
an
ce
s
wh
en
f
ee
d
f
o
r
war
d
co
m
p
en
s
atio
n
is
ac
tiv
ated
f
o
r
th
e
v
o
ltag
e
c
o
n
tr
o
l
lo
o
p
o
f
DC
-
b
u
s
.
Utilizin
g
f
ee
d
f
o
r
war
d
co
r
r
ec
tio
n
s
u
b
s
tan
tially
m
itig
ates d
ev
iatio
n
s
o
f
VDC f
r
o
m
,
as c
lar
if
ied
in
Fig
u
r
es 6
a
n
d
7
.
T
ab
le
1
.
Sy
s
tem
p
ar
a
m
eter
s
P
a
r
a
me
t
e
r
s
V
a
l
u
e
391
1500
50
1700
0
314
/
9625
100
0
.
75
Ω
0
.
85
Ω
Fig
u
r
e
6
.
T
h
e
d
y
n
am
ic
b
e
h
av
i
o
r
o
f
a
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t
with
co
n
tr
o
l
o
f
n
o
f
ee
d
-
f
o
r
war
d
co
m
p
en
s
atio
n
Fig
u
r
e
7
.
T
h
e
d
y
n
am
ic
b
e
h
av
i
o
r
o
f
DC
-
v
o
ltag
e
p
o
we
r
p
o
r
t
with
co
n
tr
o
l o
f
f
ee
d
-
f
o
r
war
d
c
o
m
p
en
s
atio
n
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
DC
b
u
s
co
n
tr
o
l str
a
teg
y
a
n
d
i
mp
lica
tio
n
s
fo
r
vo
lta
g
e
s
o
u
r
ce
co
n
ve
r
ter s
ystem
(
Ha
id
er F
a
d
el
)
1513
7.
CO
NCLU
SI
O
N
T
h
e
m
o
d
el
t
h
at
was
s
im
u
lated
o
f
th
e
r
eg
u
lated
DC
-
v
o
ltag
e
p
o
wer
p
o
r
t
im
p
lies
th
at
u
s
in
g
a
f
ee
d
-
f
o
r
war
d
co
m
p
en
s
atio
n
(
)
en
h
an
ce
s
th
e
s
tab
ilit
y
o
f
th
e
VD
C
r
esp
o
n
s
e.
T
h
is
en
h
an
ce
m
en
t
is
as
s
o
ciate
d
with
th
e
p
r
o
m
p
t
tr
a
n
s
m
is
s
io
n
o
f
an
y
ch
a
n
g
es
to
−
,
en
s
u
r
in
g
f
ast
tr
ac
k
in
g
o
f
VDC
to
VDC
an
d
s
wif
t
r
ec
o
v
er
y
o
f
p
o
wer
b
ala
n
ce
with
o
u
t
a
m
ajo
r
d
ev
iatio
n
in
th
e
r
esp
o
n
s
e.
I
t
is
wo
r
t
h
n
o
ticin
g
th
at
th
e
u
n
d
er
s
h
o
o
t
p
atter
n
at
t
=
0
.
5
0
s
d
if
f
er
s
f
r
o
m
t
h
e
p
atter
n
o
f
th
e
o
v
er
s
h
o
o
t
at
t
=
0
.
3
5
s
d
u
e
to
th
e
s
u
b
s
tan
tial
ch
an
g
es
in
p
h
ase
m
ar
g
in
an
d
f
r
eq
u
en
cy
r
esp
o
n
s
e
b
etwe
en
th
ese
o
p
er
atio
n
al
co
n
d
itio
n
s
.
As
a
r
esu
lt,
th
e
s
y
s
tem
'
s
r
esp
o
n
s
e
to
d
is
tu
r
b
an
ce
s
v
ar
ies b
ased
o
n
th
e
o
p
er
ati
n
g
co
n
d
itio
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