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I
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w
h
ic
h
in
s
ta
lled
at
co
n
v
er
ter
s
tatio
n
s
o
r
b
y
g
r
id
[
3
]
.
On
th
e
o
th
er
h
an
d
th
e
co
n
v
er
ter
o
f
VSC
-
H
VDC
h
a
s
ab
ilit
y
to
s
u
p
p
l
y
o
r
ab
s
o
r
b
r
ea
ctiv
e
p
o
w
er
in
to
o
r
f
r
o
m
t
h
e
g
r
id
s
o
t
h
i
s
s
y
s
te
m
ca
n
co
n
tr
o
l
th
e
r
ea
cti
v
e
p
o
w
er
o
f
t
h
e
A
C
s
y
s
te
m
s
at
b
o
th
en
d
s
in
d
ep
en
d
en
tl
y
w
h
i
le
th
e
f
lo
w
o
f
a
cti
v
e
p
o
w
er
is
b
alan
ce
d
b
et
w
ee
n
t
h
e
s
e
en
d
s
[
4
]
.
T
h
e
ai
m
o
f
t
h
i
s
p
ap
er
is
f
i
n
d
i
n
g
o
p
ti
m
al
p
ar
a
m
eter
s
o
f
P
I
u
s
in
g
o
p
ti
m
izatio
n
m
et
h
o
d
s
to
co
n
tr
o
l
th
e
r
ea
ctiv
e
p
o
w
er
in
t
h
e
s
y
s
te
m
d
u
r
in
g
an
y
d
i
s
t
u
r
b
an
ce
in
o
r
d
er
to
g
et
b
etter
an
d
f
aster
d
y
n
a
m
ic
r
esp
o
n
s
e.
T
h
e
d
is
tu
r
b
an
ce
s
u
s
ed
i
n
th
i
s
p
ap
er
ar
e
th
r
ee
p
h
ase
f
au
lt,
AC
v
o
ltag
e
s
a
g
an
d
s
tep
ch
a
n
g
e
i
n
r
eg
u
la
to
r
s
r
ef
er
en
ce
v
alu
e
s
.
C
o
n
v
e
n
tio
n
al
m
et
h
o
d
s
s
u
c
h
as
S
m
ith
a
n
d
p
o
le
ass
i
g
n
m
e
n
t
m
et
h
o
d
s
ar
e
u
s
ed
to
s
et
P
I
p
ar
am
eter
s
[
5
]
.
Du
e
to
t
h
e
d
if
f
ic
u
lt
y
o
f
g
etti
n
g
t
h
e
tr
a
n
s
f
er
f
u
n
ct
io
n
o
f
VS
C
HVD
C
s
y
s
te
m
,
t
h
e
s
e
m
e
th
o
d
s
w
ill
n
o
t
u
s
e
f
u
l.
J
in
g
Yo
n
g
u
s
e
es
ti
m
a
tio
n
m
eth
o
d
to
s
et
g
ain
s
o
f
P
I
co
n
tr
o
ller
u
s
in
g
P
SC
A
D/E
MT
DC
s
o
f
t
w
ar
e,
b
u
t
th
e
esti
m
atio
n
m
et
h
o
d
h
a
s
n
o
s
c
ie
n
ti
f
ic
f
o
u
n
d
atio
n
[
6
]
.
A
s
i
m
p
le
x
al
g
o
r
ith
m
i
s
p
r
ese
n
ted
f
o
r
opt
i
m
izi
n
g
t
h
e
p
ar
am
eter
s
o
f
P
I
co
n
tr
o
ller
s
[
7
]
.
Mo
d
elin
g
o
f
th
e
VS
C
-
HV
DC
s
y
s
te
m
f
o
r
o
p
tim
al
p
o
w
er
f
lo
w
(
OP
F
)
s
o
lu
tio
n
u
s
i
n
g
Ne
w
to
n
-
R
a
p
h
s
o
n
m
eth
o
d
[
8
]
.
R
ec
en
t
l
y
t
h
er
e
ar
e
n
e
w
m
et
h
o
d
s
f
o
r
o
p
ti
m
izatio
n
ca
lled
m
e
ta
h
eu
r
i
s
tic
m
et
h
o
d
s
w
h
ic
h
h
a
s
ab
ilit
y
to
g
et
t
h
e
o
p
tim
a
l
v
al
u
e
o
f
an
y
p
ar
a
m
et
er
n
ea
r
g
lo
b
al
v
alu
e
f
ast.
Ge
n
etic
alg
o
r
it
h
m
i
s
u
s
ed
to
g
et
th
e
p
ar
am
eter
s
o
f
co
n
tr
o
ller
[
9
]
.
A
r
ti
f
icial
b
ee
c
o
lo
n
y
a
n
d
m
i
n
e
b
last
al
g
o
r
ith
m
s
ar
e
ap
p
lied
to
g
e
t o
p
ti
m
a
l
g
ain
o
f
VS
C
-
HV
DC
s
y
s
te
m
w
it
h
s
lid
i
n
g
m
o
d
e
co
n
tr
o
l
[
1
0
]
.
I
n
th
is
p
ap
er
th
e
m
e
ta
h
eu
r
i
s
tic
m
eth
o
d
s
u
s
ed
ar
e
(
GSA
&
S
C
A
)
f
o
r
g
etti
n
g
o
p
ti
m
al
v
a
lu
e
s
o
f
t
h
e
g
ain
s
.
T
h
e
r
est
o
f
p
ap
er
is
o
r
g
a
n
ize
d
as
f
o
llo
w
s
:
I
n
Sectio
n
2
,
Mo
d
elin
g
a
n
d
d
escr
ip
tio
n
o
f
th
e
s
y
s
te
m
.
C
o
n
tr
o
l
S
y
s
te
m
is
i
n
tr
o
d
u
ce
d
in
s
ec
tio
n
3
.
Op
ti
m
iza
tio
n
m
et
h
o
d
s
ar
e
p
r
esen
ted
in
Se
ctio
n
4
.
Si
m
u
latio
n
r
esu
lt
s
ar
e
p
r
o
v
id
ed
in
Sectio
n
5
an
d
Sectio
n
6
in
clu
d
e
s
co
n
c
lu
s
io
n
.
2.
M
O
DE
L
I
N
G
AN
D
DE
SCRI
P
T
I
O
N
O
F
SYS
T
E
M
T
h
e
VSC
b
ased
HVDC
tr
a
n
s
m
is
s
io
n
s
y
s
te
m
b
et
w
ee
n
t
w
o
AC
s
y
s
te
m
s
co
n
s
i
s
ts
o
f
t
w
o
co
n
v
er
ter
s
tatio
n
s
(
o
n
e
is
a
s
a
r
ec
tif
ier
an
d
th
e
o
th
er
i
s
i
n
v
er
ter
)
co
n
n
ec
ted
b
y
a
DC
ca
b
le.
Fi
g
u
r
e
1
s
h
o
w
s
t
h
e
s
i
n
g
le
lin
e
d
iag
r
a
m
o
f
V
SC
-
HV
DC
.
I
n
th
i
s
p
ap
er
VSC
-
HVDC
s
y
s
te
m
m
o
d
el
w
h
ic
h
is
e
s
tab
li
s
h
ed
in
M
A
T
L
A
B
Si
m
u
li
n
k
i
s
u
s
ed
.
T
h
is
s
y
s
te
m
is
d
es
ig
n
ed
to
tr
a
n
s
m
it
2
0
0
MW
at
1
0
0
K
V
DC
.
Fi
g
u
r
e
2
s
h
o
w
s
t
h
e
Si
m
u
l
in
k
m
o
d
el
o
f
th
e
s
y
s
te
m
.
Fig
u
r
e
1
.
SL
G
f
o
r
VSC
-
HVD
C
Fig
u
r
e
2
.
Si
m
u
li
n
k
m
o
d
el
o
f
VSC
-
HVD
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
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E
n
g
I
SS
N:
2252
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8792
R
ea
ctive
p
o
w
er c
o
n
tr
o
l to
en
h
a
n
ce
th
e
V
S
C
-
HV
DC
s
yste
m
p
erfo
r
ma
n
ce
u
n
d
er …
(
Mo
h
a
med
S
.
Gh
a
ya
d
)
147
T
h
is
m
o
d
el
co
n
s
is
ts
o
f
:
a.
T
w
o
id
en
tica
l
A
C
S
y
s
te
m
(
1
&
2
)
an
d
th
eir
r
ati
n
g
s
ar
e
2
0
0
0
MV
A
,
2
3
0
k
V
an
d
5
0
Hz.
b.
T
r
an
s
f
o
r
m
er
s
:
t
h
e
f
u
n
ctio
n
o
f
th
e
tr
an
s
f
o
r
m
is
s
tep
p
in
g
d
o
w
n
t
h
e
ac
s
y
s
te
m
v
o
lta
g
e
f
r
o
m
2
3
0
k
V
to
1
0
0
kV
to
b
e
p
r
o
p
e
r
f
o
r
ea
ch
co
n
v
er
ter
.
c.
AC
Fil
ter
s
:
Sh
u
n
t
h
i
g
h
p
ass
f
i
lter
s
w
ith
4
0
MV
A
R
ar
e
in
s
ta
lled
af
ter
th
e
tr
an
s
f
o
r
m
er
s
o
n
th
e
A
C
s
y
s
te
m
s
id
e
to
eli
m
i
n
ate
h
i
g
h
o
r
d
er
h
ar
m
o
n
ics.
d.
P
h
ase
R
ea
cto
r
s
:
T
h
ese
r
ea
cto
r
s
ar
e
co
n
n
ec
ted
i
n
s
er
ie
s
b
et
wee
n
t
h
e
tr
an
s
f
o
r
m
er
an
d
th
e
s
t
atio
n
co
n
v
er
ter
an
d
th
ei
r
v
al
u
e
s
ar
e
0
.
1
5
p
u
.
T
h
ey
ar
e
u
s
ed
f
o
r
co
n
tr
o
llin
g
r
ea
cti
v
e
an
d
ac
ti
v
e
p
o
w
e
r
b
y
r
eg
u
lati
n
g
cu
r
r
en
ts
w
h
ic
h
p
ass
e
s
th
r
o
u
g
h
th
e
m
a
n
d
u
s
ed
to
r
ed
u
ce
th
e
h
ig
h
f
r
eq
u
e
n
c
y
h
ar
m
o
n
ics.
e.
C
o
n
v
er
ter
s
s
ta
tio
n
s
:
T
h
er
e
ar
e
t
w
o
co
n
v
er
ter
s
o
n
e
ac
t
s
as
a
r
ec
tif
ier
a
n
d
th
e
o
t
h
er
as
a
n
i
n
v
er
ter
a
n
d
th
e
s
e
m
ico
n
d
u
cto
r
u
s
ed
is
I
GB
T
w
it
h
a
n
tip
ar
allel
d
io
d
e.
T
h
er
e
is
a
co
n
tr
o
ller
cir
cu
it
in
ea
c
h
s
tatio
n
to
r
ea
ch
co
n
tr
o
lled
p
u
ls
es to
I
GB
T
.
f.
DC
C
ap
ac
ito
r
s
: T
h
ese
ca
p
ac
it
o
r
s
ar
e
in
s
tal
led
o
n
t
h
e
DC
s
id
e
an
d
th
e
s
ize
o
f
th
e
m
d
ep
en
d
o
n
th
e
r
eq
u
ir
ed
DC
v
o
ltag
e
.
T
h
e
f
u
n
ctio
n
o
f
t
h
ese
ca
p
ac
ito
r
s
i
s
r
ed
u
ci
n
g
th
e
v
o
ltag
e
r
ip
p
les
o
n
t
h
e
D
C
s
i
d
e
an
d
u
s
ed
a
s
en
er
g
y
s
to
r
ag
e
to
co
n
tr
o
l th
e
t
h
e
p
o
w
er
f
lo
w
a
n
d
th
e
y
h
a
v
e
v
alu
e
o
f
7
0
m
icr
o
f
ar
ad
.
g.
DC
C
ab
les:
T
h
e
t
w
o
co
n
v
er
t
er
s
s
tatio
n
s
ar
e
co
n
n
ec
ted
t
h
r
o
u
g
h
D
C
ca
b
les
.
T
h
e
p
o
w
er
is
tr
an
s
m
i
tted
th
r
o
u
g
h
t
w
o
p
i
s
ec
tio
n
s
o
f
le
n
g
th
7
5
k
m
.
T
h
e
co
n
s
tr
u
ct
io
n
o
f
s
ta
tio
n
1
is
s
h
o
w
n
i
n
Fi
g
3
a
n
d
it
is
id
e
n
tical
f
o
r
s
tatio
n
2
.
T
h
e
co
n
s
tr
u
ctio
n
o
f
s
tatio
n
1
is
s
h
o
w
n
i
n
Fi
g
u
r
e
3
an
d
it is
i
d
en
tical
f
o
r
s
tat
io
n
2
Fig
u
r
e
3
.
C
o
n
s
tr
u
ctio
n
o
f
s
tati
o
n
1
3.
CO
NT
RO
L
SYS
T
E
M
T
h
e
co
n
tr
o
ller
d
esig
n
o
f
co
n
v
er
ter
1
an
d
co
n
v
er
ter
2
ar
e
id
en
tical.
T
h
e
tw
o
co
n
t
r
o
ller
s
ar
e
in
d
ep
en
d
en
t
w
i
th
n
o
co
m
m
u
n
icatio
n
b
et
w
ee
n
th
e
m
.
T
h
es
e
ar
e
u
s
ed
to
co
n
tr
o
l
ac
tiv
e
p
o
w
er
(
P
)
,
r
ea
ctiv
e
p
o
w
er
(
Q)
an
d
DC
v
o
ltag
e(
U
d
)
in
t
h
e
s
y
s
te
m
.
Fi
g
u
r
e
4
s
h
o
w
s
a
n
o
v
er
v
ie
w
d
iag
r
a
m
o
f
th
e
co
n
tr
o
l
s
y
s
te
m
a
n
d
its
co
n
n
ec
tio
n
w
i
th
t
h
e
m
ain
c
ir
cu
it.
Fig
u
r
e
4
.
Ov
er
v
ie
w
d
ia
g
r
a
m
b
lo
ck
s
o
f
t
h
e
VS
C
co
n
tr
o
l s
y
s
te
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
u
g
u
s
t 2
0
1
9
:
1
4
5
–
1
5
8
148
T
h
e
co
n
tr
o
l c
ir
cu
it c
o
n
s
is
ts
o
f
m
ai
n
b
lo
ck
s
as
f
o
llo
w
:
3
.
1
.
T
he
ph
a
s
e
lo
ck
e
d lo
o
p (
P
L
L
)
blo
c
k
T
h
e
f
u
n
ctio
n
o
f
th
is
b
lo
ck
i
s
to
ca
lc
u
late
t
h
e
tr
a
n
s
f
o
r
m
a
tio
n
a
n
g
le
(
Ө)
w
h
ich
u
s
ed
i
n
t
h
e
(
d
-
q
tr
an
s
f
o
r
m
atio
n
)
.
T
h
is
is
d
o
n
e
b
y
m
ea
s
u
r
in
g
t
h
e
f
r
eq
u
e
n
c
y
o
f
th
e
s
y
s
te
m
a
n
d
p
r
o
v
id
es
th
is
a
n
g
le.
I
n
s
tead
y
s
tate,
s
i
n
(
Ө)
is
in
p
h
ase
w
it
h
t
h
e
f
u
n
d
a
m
e
n
tal
p
o
s
iti
v
e
s
eq
u
e
n
ce
o
f
(
-
co
m
p
o
n
e
n
t)
an
d
p
h
ase
A
o
f
t
h
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
li
n
g
v
o
lta
g
e
(
Uab
c)
.
3
.
2
.
O
ute
r
a
ct
iv
e
a
nd
re
a
ct
i
v
e
po
w
er
a
nd
v
o
lt
a
g
e
lo
o
p
T
h
e
DC
v
o
lta
g
e
a
n
d
ac
tiv
e
p
o
w
er
ar
e
co
n
tr
o
lled
b
y
t
h
e
c
o
n
tr
o
llin
g
t
h
e
p
o
w
er
a
n
g
le
(
δ
)
an
d
th
e
r
ea
ctiv
e
p
o
w
er
co
n
tr
o
l
is
d
o
n
e
b
y
co
n
tr
o
lli
n
g
th
e
m
o
d
u
latio
n
i
n
d
ex
(
w
h
ich
i
s
th
e
r
atio
b
etw
ee
n
th
e
f
u
n
d
a
m
en
ta
l
o
u
tp
u
t
v
o
ltag
e
o
f
co
n
v
er
ter
an
d
th
e
D
C
v
o
lta
g
e
)
.
T
h
e
in
s
ta
n
ta
n
eo
u
s
ac
t
iv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
o
f
th
e
in
v
er
ter
ca
n
b
e
w
r
itte
n
in
t
er
m
s
o
f
t
h
e
d
-
q
co
m
p
o
n
e
n
ts
o
f
th
e
v
o
lta
g
e
an
d
t
h
e
cu
r
r
en
t a
s
f
o
llo
w
s
:
(
1
)
(
2
)
I
f
th
e
r
ef
er
en
ce
o
f
t
h
e
d
q
-
f
r
a
m
e
is
ch
o
s
e
n
s
u
ch
t
h
at
th
e
(
q
-
co
m
p
o
n
e
n
t)
o
f
th
e
v
o
lta
g
e
is
b
ein
g
v
er
y
s
m
al
l
an
d
ca
n
b
e
n
e
g
lecte
d
(
UL
q
≈
0
)
th
en
in
(
1
)
an
d
(
2
)
i
n
d
icate
th
at
th
e
r
ea
cti
v
e
an
d
t
h
e
ac
tiv
e
p
o
w
er
ar
e
p
r
o
p
o
r
tio
n
al
to
th
e
q
a
n
d
d
co
m
p
o
n
en
t
o
f
th
e
cu
r
r
en
t
r
esp
ec
tiv
el
y
.
T
h
er
ef
o
r
e,
it
is
p
o
s
s
ib
l
e
to
co
n
tr
o
l
th
e
DC
v
o
ltag
e,
th
e
ac
ti
v
e
p
o
w
er
an
d
th
e
r
ea
ctiv
e
p
o
w
er
b
y
co
n
tr
o
llin
g
th
e
cu
r
r
en
t
co
m
p
o
n
en
t
s
i
vd
a
n
d
i
vq
r
esp
ec
tiv
el
y
.
T
h
e
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
a
n
d
v
o
lta
g
e
lo
o
p
co
n
tain
s
th
e
o
u
ter
lo
o
p
r
eg
u
lato
r
s
th
at
co
m
p
u
te
th
e
r
ef
er
e
n
ce
v
al
u
e
o
f
t
h
e
c
u
r
r
en
t
v
ec
to
r
(
I
ref_dq
)
w
h
ic
h
i
s
th
e
in
p
u
t
to
t
h
e
in
n
er
cu
r
r
en
t
lo
o
p
.
A
ls
o
it
co
n
ta
in
s
P
I
co
n
tr
o
ller
w
it
h
a
f
ee
d
f
o
r
w
ar
d
co
n
tr
o
l to
in
cr
ea
s
e
th
e
s
p
ee
d
r
esp
o
n
s
e.
3.
3
.
I
nn
er
curr
ent
lo
o
p
T
h
is
lo
o
p
is
u
s
ed
to
tr
ac
k
th
e
r
ef
er
en
ce
cu
r
r
en
t
v
ec
to
r
w
it
h
a
f
ee
d
f
o
r
w
ar
d
s
ch
e
m
e
to
ac
h
iev
e
f
as
t
co
n
tr
o
l o
f
th
e
co
n
tr
o
ller
at
d
is
t
u
r
b
an
ce
s
a
n
d
lo
ad
ch
an
g
e
s
.
T
h
e
eq
u
atio
n
af
ter
ap
p
ly
i
n
g
KV
L
f
o
r
ea
ch
p
h
ase
is
:
(
3
)
Du
r
in
g
u
n
b
alan
ce
d
o
p
er
atio
n
o
f
eq
u
atio
n
[
3
]
,
th
e
v
o
lta
g
e
d
r
o
p
eq
u
atio
n
s
o
v
er
th
e
i
m
p
ed
an
ce
(
R
+
j
ω
L
)
h
o
ld
s
f
o
r
p
o
s
iti
v
e
an
d
n
e
g
ati
v
e
s
eq
u
e
n
ce
v
o
lta
g
es
a
n
d
cu
r
r
en
ts
.
T
h
e
v
o
ltag
e
s
d
r
o
p
s
ar
e
d
escr
ib
ed
b
y
t
h
e
d
if
f
er
e
n
tial i
n
(
4
)
as f
o
llo
w
:
(
4
)
W
h
er
e
Z
=
(
p
)
f
o
r
p
o
s
itiv
e
s
eq
u
en
ce
a
n
d
(
n
)
f
o
r
n
eg
ativ
e
s
eq
u
en
ce
.
E
q
u
atio
n
(
4
)
ca
n
b
e
tr
a
n
s
f
o
r
m
e
d
to
th
e
α
β
-
f
r
a
m
e
a
s
f
o
llo
w
i
n
(
5
)
:
(
5
)
E
q
u
atio
n
(
5
)
ca
n
b
e
f
u
r
t
h
er
tr
an
s
f
o
r
m
ed
to
th
e
r
o
tatin
g
d
q
-
f
r
a
m
e
as
f
o
llo
w
i
n
(
6
)
&
(
7
)
.
(
6
)
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
R
ea
ctive
p
o
w
er c
o
n
tr
o
l to
en
h
a
n
ce
th
e
V
S
C
-
HV
DC
s
yste
m
p
erfo
r
ma
n
ce
u
n
d
er …
(
Mo
h
a
med
S
.
Gh
a
ya
d
)
1
49
T
h
e
p
o
s
itiv
e
a
n
d
n
eg
at
iv
e
s
eq
u
en
ce
v
o
lta
g
es
o
f
th
e
VS
C
s
id
e
ar
e
o
b
tain
ed
f
r
o
m
t
h
e
last
eq
u
atio
n
s
a
s
f
o
llo
w
:
(
8
)
(
9
)
(
1
0
)
(
1
1
)
T
h
e
m
ea
n
v
o
ltag
e
s
o
v
er
t
h
e
s
a
m
p
le
p
er
io
d
k
to
k
+1
ar
e
o
b
tain
ed
b
y
i
n
te
g
r
atin
g
(
8
)
,
(
9
)
,
(
1
0
)
an
d
(
1
1
)
f
r
o
m
(
k)
T
s
to
(
k+1
)
Ts
a
n
d
d
iv
id
in
g
b
y
T
s
(
w
h
er
e
T
s
is
th
e
s
a
m
p
lin
g
ti
m
e)
.
(
1
2
)
(
1
3
)
(
1
4
)
(
1
5
)
E
q
u
atio
n
s
(
1
6
-
1
9
)
ar
e
o
b
tain
ed
b
y
as
s
u
m
i
n
g
co
n
s
tan
t
n
et
w
o
r
k
v
o
lta
g
e
an
d
li
n
ea
r
cu
r
r
e
n
t
d
u
r
in
g
o
n
e
s
a
m
p
le
p
er
io
d
T
s
.
(
16
)
(
17
)
(
18
)
(
19
)
T
h
e
co
n
tr
o
l
is
b
ased
o
n
(
1
6
-
1
9
)
,
w
h
er
e
th
e
v
o
lta
g
es
a
n
d
cu
r
r
en
ts
at
ti
m
e
(
k
+1
)
ar
e
th
u
s
eq
u
al
to
th
e
r
ef
er
en
ce
v
a
lu
e
s
at
ti
m
e
(
k
)
.
3.
4
.
DC
v
o
lt
a
g
e
ba
la
nce
co
n
t
ro
l
T
h
is
b
lo
ck
is
u
s
ed
to
k
ee
p
t
h
e
v
o
ltag
e
D
C
s
id
e
o
f
t
h
e
th
r
e
e
-
le
v
el
b
r
id
g
e
b
alan
ce
d
(
i.e
.
,
eq
u
al
p
o
le
v
o
ltag
e
s
)
in
s
tead
y
-
s
tate.
I
t
is
p
o
s
s
ib
le
to
f
in
d
s
m
all
d
ev
iati
o
n
s
b
et
w
ee
n
th
e
p
o
le
v
o
ltag
e
s
d
u
e
to
ch
an
g
es
o
f
co
n
v
er
ter
cu
r
r
en
t
o
r
d
u
e
to
n
o
n
li
n
ea
r
it
y
o
n
s
h
o
r
tag
e
o
f
p
r
ec
is
io
n
in
t
h
e
ex
e
c
u
tio
n
o
f
th
e
p
u
ls
e
w
id
t
h
m
o
d
u
lated
b
r
id
g
e
v
o
lta
g
e.
Fi
g
u
r
e
5
s
h
o
w
s
a
h
ig
h
-
le
v
el
d
iag
r
a
m
o
f
t
h
e
s
i
m
u
li
n
k
m
o
d
el
f
o
r
VSC
co
n
tr
o
ller
.
4.
O
P
T
I
M
I
Z
AT
I
O
N
M
E
T
H
O
DS
T
h
e
w
o
r
d
o
f
o
p
ti
m
izatio
n
s
ta
n
d
s
f
o
r
t
h
e
p
r
o
ce
s
s
o
f
g
etti
n
g
o
p
ti
m
al
v
al
u
e
f
o
r
t
h
e
p
ar
a
m
e
ter
s
o
f
an
y
s
y
s
t
e
m
to
m
i
n
i
m
ize
o
r
m
ax
i
m
i
ze
its
o
b
j
ec
tiv
e
f
u
n
ctio
n
.
T
h
e
o
p
tim
izatio
n
p
r
o
b
lem
s
ca
n
b
e
cla
s
s
i
f
ied
in
to
m
a
n
y
ca
t
eg
o
r
ies
b
ased
o
n
i
f
th
e
y
ar
e
d
is
cr
ete
o
r
co
n
tin
u
o
u
s
,
m
o
n
o
o
r
m
u
lti
-
o
b
j
ec
tiv
e,
co
n
s
tr
ain
ed
o
r
u
n
co
n
s
tr
ai
n
ed
an
d
d
y
n
a
m
ic
o
r
s
tatic.
An
o
v
er
v
ie
w
o
f
s
o
m
e
co
n
v
e
n
tio
n
a
l
m
eth
o
d
s
a
n
d
m
e
ta
h
e
u
r
is
tic
tec
h
n
iq
u
es
w
h
ic
h
ca
n
b
e
u
s
ed
in
elec
tr
ica
l p
o
w
er
o
p
ti
m
iza
tio
n
p
r
o
b
lem
s
i
s
p
r
esen
ted
in
[
1
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
u
g
u
s
t 2
0
1
9
:
1
4
5
–
1
5
8
150
Fig
u
r
e
5
.
Si
m
u
li
n
k
m
o
d
el
o
f
c
o
n
tr
o
l c
ir
cu
it
T
h
e
co
n
v
en
tio
n
al
o
p
ti
m
iza
tio
n
alg
o
r
it
h
m
s
d
o
n
o
t
g
i
v
e
a
s
u
itab
le
s
o
lu
tio
n
b
ec
au
s
e
t
h
e
s
e
ar
ch
s
p
ac
e
in
cr
ea
s
es
ex
p
o
n
e
n
tial
l
y
w
it
h
th
e
p
r
o
b
le
m
s
ize.
Me
ta
h
eu
r
i
s
tic
o
p
ti
m
izatio
n
alg
o
r
i
th
m
s
lo
o
k
to
th
e
o
p
tim
izatio
n
p
r
o
b
le
m
s
as
b
lac
k
b
o
x
es
[
1
2
]
.
T
h
is
m
ea
n
s
th
at
g
etti
n
g
th
e
m
at
h
e
m
atica
l
m
o
d
els
is
n
o
t
n
ec
ess
ar
y
b
ec
au
s
e
s
u
ch
o
p
ti
m
izatio
n
m
e
th
o
d
s
o
n
l
y
v
ar
y
t
h
e
in
p
u
ts
(
p
a
r
a
m
eter
s
)
an
d
n
o
tice
t
h
e
o
u
tp
u
ts
o
f
th
e
s
y
s
te
m
f
o
r
m
i
n
i
m
izi
n
g
a
n
d
m
a
x
i
m
izi
n
g
its
o
u
tp
u
ts
.
T
h
ese
m
e
th
o
d
s
t
r
y
to
s
ee
k
g
o
o
d
s
o
lu
tio
n
s
(
n
ea
r
g
lo
b
al)
f
o
r
th
e
p
r
o
b
lem
s
ea
r
ch
s
p
ac
e
.
T
h
ese
m
et
h
o
d
s
ar
e
m
o
ti
v
ated
f
r
o
m
ev
o
lu
tio
n
ar
y
p
h
e
n
o
m
e
n
a
,
b
eh
av
io
r
o
f
cr
ea
tu
r
es,
p
h
y
s
ical
la
w
s
a
n
d
h
u
m
a
n
-
r
ela
ted
co
n
ce
p
ts
.
So
m
e
o
f
t
h
e
f
a
m
o
u
s
alg
o
r
it
h
m
s
i
n
ea
ch
o
f
t
h
ese
s
u
b
clas
s
es
ar
e
p
r
esen
ted
as f
o
llo
w
s
:
a)
B
eh
av
io
r
o
f
cr
ea
t
u
r
es
-
b
ased
tech
n
iq
u
e
s
:
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
P
SO)
[
1
3
]
,
An
t
C
o
lo
n
y
Op
ti
m
izatio
n
[
1
4
]
(
A
C
O)
an
d
A
r
ti
f
icial
B
ee
C
o
lo
n
y
(
A
B
C
)
alg
o
r
ith
m
[
1
5
]
.
b)
E
v
o
lu
tio
n
ar
y
tec
h
n
iq
u
es
:
Dif
f
er
en
tial E
v
o
l
u
tio
n
(
DE
)
[
1
6
]
a
n
d
Gen
etic
A
l
g
o
r
it
h
m
s
(
G
A
)
[
1
7
]
.
c)
P
h
y
s
ic
s
r
u
le
s
-
b
ased
tech
n
i
q
u
es:
C
o
llid
in
g
B
o
d
ies
Op
ti
m
izatio
n
(
C
B
O)
[
1
8
]
,
Gr
av
itatio
n
al
Sear
c
h
A
l
g
o
r
ith
m
(
GS
A
)
[
1
9
]
an
d
B
lack
Ho
le
(
B
H)
[
2
0
]
.
d)
Hu
m
an
-
r
elate
d
tec
h
n
iq
u
e
s
:
M
in
e
B
las
t
A
l
g
o
r
ith
m
(
MB
A
)
[
2
1
]
,
L
ea
g
u
e
C
h
a
m
p
io
n
s
h
ip
A
lg
o
r
ith
m
(
L
C
A
)
[
2
2
]
an
d
T
ea
ch
in
g
-
L
ea
r
n
i
n
g
-
B
ased
Op
ti
m
izatio
n
(
T
L
B
O)
[
2
3
]
.
I
n
th
i
s
p
ap
er
a
tw
o
m
eta
he
u
r
i
s
tic
s
ea
r
ch
al
g
o
r
ith
m
s
w
ill
b
e
u
s
ed
w
h
ich
h
as
le
s
s
co
m
p
u
tati
o
n
al
ti
m
e
,
r
elativ
e
h
ig
h
ac
cu
r
ac
y
an
d
le
s
s
p
ar
a
m
eter
s
r
eq
u
ir
e
m
e
n
ts
.
T
h
e
f
ir
s
t
m
e
th
o
d
is
ca
lled
G
r
av
itatio
n
a
l
Sear
ch
A
l
g
o
r
ith
m
(
GS
A
)
a
n
d
t
h
e
s
ec
o
n
d
is
ca
lled
Si
n
e
C
o
s
i
n
e
Al
g
o
r
ith
m
(
S
C
A
)
.
T
h
e
t
w
o
m
e
t
h
o
d
s
ar
e
e
x
p
lain
ed
b
r
ief
l
y
i
n
th
e
f
o
llo
w
i
n
g
s
ec
tio
n
s
:
4
.
1
.
G
ra
v
it
a
t
io
na
l sea
rc
h a
l
g
o
rit
h
m
(
G
SA)
T
h
is
alg
o
r
it
h
m
is
d
ep
en
d
i
n
g
o
n
g
r
a
v
it
y
la
w
f
o
r
Ne
w
to
n
wh
ich
s
a
y
s
‘
‘
T
h
e
attr
ac
tio
n
f
o
r
ce
b
et
w
ee
n
th
e
p
ar
ticles
is
i
n
v
er
s
el
y
p
r
o
p
o
r
tio
n
al
to
th
e
s
q
u
ar
e
o
f
th
e
d
i
s
tan
ce
b
et
w
ee
n
th
e
m
a
n
d
d
ir
ec
tl
y
p
r
o
p
o
r
tio
n
al
to
th
e
p
r
o
d
u
ct
o
f
th
eir
m
as
s
es”
.
I
n
th
i
s
alg
o
r
ith
m
,
ag
e
n
t
s
ar
e
co
n
s
id
er
ed
as
p
ar
ticles
an
d
th
eir
p
er
f
o
r
m
an
ce
i
s
m
ea
s
u
r
e
d
b
y
th
ei
r
m
as
s
es
i.e
.
th
e
b
etter
s
o
lu
tio
n
is
co
r
r
esp
o
n
d
in
g
to
th
e
h
ea
v
y
m
as
s
es.
A
ll
th
e
s
e
p
ar
ticles
attr
ac
t
ea
ch
o
th
er
b
y
th
e
attr
ac
tio
n
f
o
r
ce
an
d
t
h
is
f
o
r
ce
ca
u
s
e
s
a
m
o
v
e
m
e
n
t
o
f
all
p
ar
ticles
to
w
ar
d
s
th
e
p
ar
ticles
w
i
th
h
ea
v
ier
m
as
s
es
w
h
ile
h
ea
v
y
m
as
s
es
m
o
v
e
m
o
r
e
s
lo
w
l
y
th
a
n
li
g
h
t
er
o
n
es.
A
s
t
h
e
ti
m
e
p
ass
e
s
,
all
m
as
s
es
w
ill
b
e
attr
ac
ted
b
y
th
e
h
ea
v
ie
s
t
m
a
s
s
.
T
h
is
m
a
s
s
w
ill
p
r
ese
n
t
an
o
p
ti
m
u
m
s
o
lu
tio
n
in
t
h
e
s
ea
r
ch
s
p
ac
e.
T
h
e
p
r
in
cip
le
o
f
GS
A
is
e
x
p
lai
n
ed
in
d
etails
in
[
1
9
]
.
Fig
u
r
e
6
s
h
o
w
s
t
h
e
s
te
p
s
o
f
o
p
er
atio
n
in
ea
ch
iter
atio
n
as a
f
lo
w
c
h
ar
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
p
p
l P
o
w
er
E
n
g
I
SS
N:
2252
-
8792
R
ea
ctive
p
o
w
er c
o
n
tr
o
l to
en
h
a
n
ce
th
e
V
S
C
-
HV
DC
s
yste
m
p
erfo
r
ma
n
ce
u
n
d
er …
(
Mo
h
a
med
S
.
Gh
a
ya
d
)
151
Fig
u
r
e
6
.
Flo
w
c
h
ar
t o
f
GS
A
4
.
2
.
Sin
e
co
s
ine a
lg
o
rit
h
m
:
T
h
e
o
pti
m
iza
t
io
n
p
r
o
ce
s
s
in
th
is
al
g
o
r
ith
m
s
tar
ts
th
e
b
y
a
s
et
o
f
r
an
d
o
m
s
o
l
u
tio
n
t
h
e
n
it
b
eg
an
s
to
u
p
d
ate
th
e
p
o
s
itio
n
o
f
t
h
i
s
s
o
l
u
tio
n
.
T
h
e
u
p
d
atin
g
p
o
s
itio
n
i
s
d
o
n
e
ac
co
r
d
in
g
to
:
(
2
0
)
(
2
1
)
W
h
er
e
X
i
t+
1
is
t
h
e
p
o
s
itio
n
o
f
n
e
w
s
o
l
u
tio
n
,
X
i
t
i
s
th
e
p
o
s
itio
n
o
f
c
u
r
r
en
t
s
o
lu
tio
n
i
n
t
-
iter
at
io
n
an
d
r
1
,
r
2
,
r
3
ar
e
r
an
d
o
m
n
u
m
b
er
s
[
2
4
]
.
T
h
e
s
w
i
tch
i
n
g
b
et
w
ee
n
t
h
e
t
w
o
eq
u
atio
n
s
i
s
b
ased
o
n
r
an
d
o
m
v
ar
iab
le
(
r
4
)
.
T
h
e
r
ec
en
t
eq
u
atio
n
s
ar
e
t
h
e
r
ea
s
o
n
b
eh
i
n
d
t
h
e
n
a
m
e
o
f
t
h
i
s
alg
o
r
ith
m
.
As
t
h
e
iter
atio
n
co
u
n
ter
in
cr
ea
s
e
s
,
t
h
e
r
an
g
e
s
o
f
co
s
i
n
e
a
n
d
s
i
n
e
f
u
n
c
tio
n
s
ar
e
u
p
d
ated
to
e
m
p
h
as
iz
e
ex
p
lo
itatio
n
o
f
th
e
s
ea
r
c
h
s
p
ac
e.
T
h
e
alg
o
r
ith
m
s
to
p
s
t
h
e
o
p
ti
m
izatio
n
p
r
o
ce
s
s
w
h
en
t
h
e
iter
atio
n
co
u
n
ter
b
ec
o
m
e
s
h
ig
h
er
t
h
a
n
t
h
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
.
Fi
g
u
r
e
7
s
h
o
w
s
t
h
e
f
lo
w
ch
ar
t o
f
t
h
e
al
g
o
r
ith
m
.
Fig
u
r
e
7
.
Flo
w
c
h
ar
t
o
f
S
C
A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
u
g
u
s
t 2
0
1
9
:
1
4
5
–
1
5
8
152
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
T
h
e
o
b
j
ec
tiv
e
o
f
th
is
s
ec
tio
n
i
s
ch
ec
k
i
n
g
th
e
d
y
n
a
m
ic
r
ea
ctiv
e
p
o
w
er
r
esp
o
n
s
e
o
f
th
e
HV
DC
s
y
s
te
m
an
d
tr
y
i
n
g
to
i
m
p
r
o
v
e
t
h
i
s
r
es
p
o
n
s
e
v
ia
t
u
n
in
g
t
h
e
P
I
co
n
tr
o
ller
p
ar
am
eter
s
u
s
i
n
g
o
p
ti
m
i
za
tio
n
m
et
h
o
d
s
.
T
o
ch
ec
k
t
h
e
d
y
n
a
m
ic
r
esp
o
n
s
e
t
h
e
s
y
s
te
m
i
s
ex
p
o
s
ed
to
d
if
f
e
r
en
t
d
is
tu
r
b
an
ce
s
s
u
c
h
as
th
r
e
e
p
h
ase
f
au
l
t,
AC
v
o
ltag
e
s
a
g
an
d
s
tep
ch
an
g
e
i
n
r
ef
er
en
ce
v
al
u
es.
T
h
en
o
b
s
er
v
in
g
th
e
r
ea
ctiv
e
p
o
w
er
r
esp
o
n
s
e
w
ith
r
esp
ec
t
to
th
e
r
e
f
er
en
ce
i
n
ea
c
h
ca
s
e.
T
h
is
s
ec
tio
n
co
n
s
is
ts
o
f
t
w
o
p
ar
ts
,
T
h
e
f
ir
s
t
p
ar
t e
x
p
lai
n
t
y
p
e
o
f
p
ar
am
eter
s
an
d
th
e
v
alu
e
s
o
f
t
h
e
d
ef
a
u
lt
a
n
d
o
p
ti
m
al
p
ar
a
m
eter
s
af
ter
ap
p
l
y
i
n
g
o
p
ti
m
izat
io
n
m
eth
o
d
s
,
w
h
il
e
th
e
s
ec
o
n
d
p
ar
t
co
n
clu
d
e
t
h
e
co
m
p
ar
is
o
n
b
et
w
ee
n
t
h
e
r
ea
ctiv
e
p
o
w
er
d
y
n
a
m
ic
r
esp
o
n
s
e
o
f
d
ef
a
u
lt
s
y
s
te
m
a
n
d
o
p
ti
m
ized
s
y
s
te
m
.
P
a
rt
1
:
G
et
t
ing
o
pti
m
a
l pa
ra
m
et
er
s
us
i
ng
G
S
A
a
nd
SCA
m
et
ho
d
I
n
th
is
p
ar
t
th
e
GS
A
a
n
d
SC
A
ar
e
u
s
ed
to
tu
n
e
th
e
r
ea
ctiv
e
p
o
w
er
P
I
co
n
tr
o
ller
w
h
en
t
h
e
s
y
s
te
m
i
s
ex
p
o
s
ed
to
s
ev
er
e
th
r
ee
p
h
ase
f
au
lt
at
s
y
s
te
m
.
T
h
er
e
ar
e
s
ix
co
n
tr
o
l
p
ar
am
eter
s
(
K
I
_
r
eg
u
l
ato
r
,
k
P
_
co
n
tr
o
l
an
d
k
I
_
co
n
to
l
f
o
r
s
tatio
n
1
an
d
K
I
_
r
eg
u
lato
r
,
k
P
_
co
n
tr
o
l a
n
d
k
I
_
c
o
n
to
l f
o
r
s
tatio
n
2
)
w
h
ic
h
u
s
ed
to
co
n
tr
o
l r
ea
ctiv
e
p
o
w
er
.
K
I
_
r
eg
u
lato
r
u
s
ed
to
k
ee
p
th
e
v
alu
e
o
f
m
ea
s
u
r
ed
r
ea
ctiv
e
p
o
w
er
w
it
h
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