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K
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w
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r
d
s
:
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-
b
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g
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ce
lls
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C
L
h
y
b
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id
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ter
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lam
p
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Ser
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Vo
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s
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c
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CC B
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C
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s
p
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A
uth
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r
:
Ma
h
m
o
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d
Saad
eh
Dep
ar
tm
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t o
f
E
lectr
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g
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Facu
lty
o
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g
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T
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Hash
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Un
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P.O.
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@
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.
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u
.
jo
1.
I
NT
RO
D
UCT
I
O
N
An
ef
f
icien
t
p
o
wer
tr
an
s
m
is
s
io
n
an
d
d
is
tr
ib
u
tio
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y
s
tem
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s
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n
d
am
en
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r
eq
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en
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ill
cu
s
to
m
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s
with
es
s
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tial
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s
.
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a
d
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tr
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etwo
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s
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e
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s
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d
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with
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[
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s
tr
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Gr
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t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
2
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8
8
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I
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t J E
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&
C
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m
p
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g
,
Vo
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15
,
No
.
2
,
Ap
r
il
20
25
:
1
2
9
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3
2
1
1298
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tio
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as
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ased
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e
d
ir
ec
t
cu
r
r
en
t
(
HVDC)
tr
an
s
m
is
s
io
n
was
s
u
g
g
ested
.
HVDC
is
n
o
n
ew
s
o
lu
tio
n
,
b
u
t
th
e
ad
o
p
tio
n
o
f
d
ir
ec
t
cu
r
r
en
t
(
DC
)
tr
an
s
m
is
s
io
n
wa
s
lim
ited
d
u
e
to
th
e
lack
o
f
r
e
liab
le
h
ig
h
v
o
ltag
e
p
o
wer
co
n
v
er
s
io
n
eq
u
ip
m
e
n
t.
T
h
e
r
ev
o
lu
tio
n
in
th
e
p
o
wer
s
em
ico
n
d
u
ct
o
r
in
d
u
s
tr
y
m
an
a
g
ed
to
r
ed
u
ce
th
e
co
m
p
lex
ity
a
n
d
s
ize
o
f
th
e
p
o
wer
co
n
v
er
ter
s
.
HVDC
g
r
ew
i
n
a
r
em
ar
k
ab
le
m
an
n
er
m
ak
in
g
it
an
attr
ac
tiv
e
alter
n
ativ
e
to
c
o
n
v
en
tio
n
al
HVAC
tr
an
s
m
is
s
io
n
[
3
]
.
R
ec
en
t
ad
v
an
ce
m
e
n
ts
in
H
VDC
s
y
s
tem
s
h
av
e
r
ev
o
lu
t
io
n
ized
p
o
wer
tr
a
n
s
m
is
s
io
n
,
o
f
f
e
r
in
g
s
ig
n
if
ican
t
b
en
e
f
its
o
v
er
t
r
ad
it
io
n
al
HVAC
s
y
s
tem
s
,
esp
ec
ia
lly
in
lo
n
g
-
d
is
tan
ce
a
n
d
h
ig
h
-
p
o
wer
ap
p
licatio
n
s
.
HVDC
s
y
s
tem
s
,
p
ar
ticu
lar
ly
t
h
o
s
e
em
p
lo
y
in
g
v
o
ltag
e
s
o
u
r
c
e
co
n
v
e
r
ter
s
(
VSC
s
)
,
h
av
e
em
er
g
ed
as
a
s
u
p
er
io
r
alter
n
ativ
e
d
u
e
to
th
eir
e
f
f
icien
cy
,
s
tab
ilit
y
,
an
d
ab
ilit
y
to
in
teg
r
ate
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
.
T
h
ese
s
y
s
tem
s
en
ab
le
th
e
s
ea
m
less
in
teg
r
ati
o
n
o
f
o
f
f
s
h
o
r
e
win
d
f
ar
m
s
a
n
d
o
th
er
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
in
to
ex
is
tin
g
g
r
id
s
,
f
ac
ilit
atin
g
t
h
e
tr
a
n
s
itio
n
to
war
d
s
m
o
r
e
s
u
s
tain
ab
le
e
n
er
g
y
s
y
s
tem
s
.
Ho
wev
er
,
th
e
co
m
p
lex
ity
o
f
m
u
lti
ter
m
in
al
d
ir
ec
t
c
u
r
r
e
n
t
(
MT
DC
)
s
y
s
tem
s
in
tr
o
d
u
ce
s
n
ew
ch
allen
g
es
in
co
n
t
r
o
l
an
d
p
r
o
tectio
n
,
w
h
ich
ar
e
cr
itical
r
esear
ch
ar
ea
s
[
4
]
.
I
n
th
e
co
n
tex
t
o
f
MT
DC
s
y
s
tem
s
,
th
e
r
o
le
o
f
a
d
v
an
ce
d
co
n
v
e
r
ter
s
s
u
ch
as
VSC
s
h
as
b
ee
n
h
ig
h
lig
h
ted
in
s
tu
d
y
[
5
]
e
m
p
h
asizin
g
th
e
im
p
o
r
ta
n
ce
o
f
r
o
b
u
s
t
co
n
tr
o
l
s
tr
ateg
ies
in
en
s
u
r
i
n
g
v
o
lta
g
e
s
tab
ilit
y
ac
r
o
s
s
in
ter
co
n
n
ec
te
d
g
r
id
s
.
T
h
e
in
tr
o
d
u
ctio
n
o
f
f
r
ac
tio
n
al
o
r
d
er
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
al
c
o
n
t
r
o
ller
s
r
ep
r
esen
ts
a
s
ig
n
if
ican
t
im
p
r
o
v
em
en
t
o
v
er
tr
ad
itio
n
al
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI
)
co
n
t
r
o
ller
s
,
o
f
f
er
in
g
en
h
an
ce
d
s
tab
ilit
y
an
d
ad
a
p
tab
ilit
y
in
m
u
lti
-
in
f
e
ed
v
o
lta
g
e
s
o
u
r
ce
co
n
v
er
ter
-
h
ig
h
v
o
ltag
e
d
i
r
ec
t
cu
r
r
en
t
(
VSC
-
HVDC
)
s
y
s
tem
s
.
T
h
is
in
n
o
v
atio
n
a
d
d
r
ess
es
th
e
lim
itatio
n
s
o
f
co
n
v
en
tio
n
al
co
n
tr
o
l
m
eth
o
d
s
,
p
ar
tic
u
lar
ly
in
h
an
d
lin
g
n
o
n
lin
ea
r
ities
an
d
d
y
n
am
ic
c
h
an
g
es
in
p
o
wer
s
y
s
tem
s
,
th
er
eb
y
im
p
r
o
v
in
g
th
e
o
v
er
all
r
e
liab
ilit
y
o
f
HVDC
n
etwo
r
k
s
.
Fu
r
th
er
m
o
r
e
,
th
e
in
teg
r
atio
n
o
f
o
f
f
s
h
o
r
e
win
d
p
o
wer
in
to
w
ea
k
g
r
i
d
s
v
ia
VSC
-
HVDC
tr
an
s
m
is
s
io
n
s
y
s
tem
s
h
as
b
ee
n
th
o
r
o
u
g
h
l
y
ex
p
lo
r
e
d
in
s
tu
d
y
[
6
]
.
T
h
is
s
tu
d
y
h
ig
h
lig
h
ts
th
e
ef
f
ec
tiv
en
ess
o
f
VSC
s
in
m
ain
tain
in
g
v
o
ltag
e
s
tab
ilit
y
a
n
d
s
u
p
p
o
r
tin
g
g
r
id
o
p
e
r
atio
n
s
u
n
d
er
f
lu
ctu
atin
g
l
o
ad
c
o
n
d
iti
o
n
s
.
T
h
e
ab
ilit
y
o
f
VSC
-
HVD
C
s
y
s
tem
s
to
p
r
o
v
i
d
e
d
y
n
am
ic
r
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t
is
cr
u
cial
f
o
r
en
h
a
n
cin
g
th
e
r
esil
ien
ce
o
f
wea
k
g
r
id
s
,
wh
ich
is
in
cr
e
asin
g
ly
co
m
m
o
n
in
r
em
o
te
a
n
d
o
f
f
s
h
o
r
e
lo
ca
tio
n
s
.
T
h
e
em
er
g
en
ce
o
f
ad
v
an
ce
d
p
r
o
tectio
n
m
eth
o
d
s
f
o
r
DC
f
au
lts
in
HV
DC
s
y
s
tem
s
is
an
o
th
er
cr
itical
ar
ea
o
f
r
esear
ch
,
as
i
n
[
7
]
.
I
n
wh
ich
,
a
co
m
p
r
e
h
en
s
iv
e
r
e
v
iew
o
f
DC
f
au
lt
p
r
o
tectio
n
tech
n
iq
u
es
u
n
d
er
s
co
r
es
th
e
im
p
o
r
tan
ce
o
f
f
ast
an
d
r
eli
ab
le
f
au
lt
d
etec
tio
n
a
n
d
is
o
lati
o
n
m
ec
h
a
n
is
m
s
in
p
r
ev
e
n
tin
g
ca
s
ca
d
in
g
f
ailu
r
es
in
HVDC
n
etwo
r
k
s
.
T
h
ese
a
d
v
an
ce
m
en
ts
a
r
e
ess
en
tial
f
o
r
t
h
e
s
af
e
an
d
ef
f
icien
t
o
p
er
atio
n
o
f
f
u
tu
r
e
DC
g
r
id
s
,
p
ar
ticu
lar
ly
as th
e
d
e
p
lo
y
m
en
t
o
f
HVDC sy
s
tem
s
co
n
tin
u
es to
ex
p
a
n
d
g
l
o
b
ally
.
T
h
e
d
ev
elo
p
m
e
n
t
o
f
h
y
b
r
id
f
ee
d
f
o
r
war
d
co
n
tr
o
l
s
ch
em
es
f
o
r
in
d
u
cto
r
-
ca
p
ac
ito
r
-
in
d
u
c
to
r
(
L
C
L
)
g
r
id
-
co
n
n
ec
ted
in
v
e
r
ter
s
,
as
d
em
o
n
s
tr
ated
in
[
8
]
,
f
u
r
t
h
er
co
n
tr
ib
u
tes
to
th
e
en
h
a
n
ce
m
en
t
o
f
HVDC
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
eir
wo
r
k
f
o
c
u
s
es
o
n
m
itig
atin
g
th
e
ch
allen
g
es
ass
o
ciate
d
with
L
C
L
f
ilter
s
,
s
u
ch
as
r
eso
n
an
ce
an
d
s
tab
ilit
y
is
s
u
es,
b
y
em
p
lo
y
in
g
a
d
v
an
ce
d
c
o
n
tr
o
l
tec
h
n
iq
u
es
th
at
im
p
r
o
v
e
th
e
d
y
n
am
ic
r
esp
o
n
s
e
an
d
r
ed
u
ce
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
T
h
is
is
p
ar
ticu
lar
ly
r
elev
an
t
in
th
e
co
n
tex
t
o
f
HVDC
s
y
s
tem
s
,
wh
er
e
m
ain
tain
in
g
p
o
wer
q
u
ality
an
d
s
tab
ilit
y
is
p
ar
am
o
u
n
t.
I
n
co
n
clu
s
io
n
,
th
e
o
n
g
o
in
g
r
esear
ch
,
an
d
tech
n
o
lo
g
ical
ad
v
an
ce
m
e
n
ts
in
HVDC
s
y
s
tem
s
ar
e
ad
d
r
ess
in
g
th
e
co
m
p
lex
ch
all
en
g
es
ass
o
ciate
d
with
m
o
d
e
r
n
p
o
wer
tr
a
n
s
m
is
s
io
n
.
T
h
e
i
n
teg
r
atio
n
o
f
n
o
v
el
co
n
tr
o
l
s
tr
ateg
ies,
im
p
r
o
v
e
d
co
n
v
er
ter
tech
n
o
lo
g
ies,
an
d
ad
v
an
ce
d
p
r
o
tectio
n
m
ec
h
an
i
s
m
s
ar
e
cr
u
cial
f
o
r
r
ea
lizin
g
th
e
f
u
ll
p
o
ten
tial
o
f
HVDC
s
y
s
tem
s
.
T
h
ese
d
ev
elo
p
m
en
ts
n
o
t
o
n
ly
en
h
an
ce
th
e
p
er
f
o
r
m
a
n
ce
an
d
r
eliab
ilit
y
o
f
HVDC n
etwo
r
k
s
b
u
t a
ls
o
p
av
e
t
h
e
way
f
o
r
m
o
r
e
r
esil
ien
t a
n
d
s
u
s
tain
ab
le
en
er
g
y
in
f
r
astru
ctu
r
es.
I
n
th
is
r
esear
c
h
,
th
e
p
e
r
f
o
r
m
an
ce
o
f
an
L
C
L
h
y
b
r
id
v
o
lt
ag
e
s
o
u
r
ce
co
n
v
er
ter
is
in
v
e
s
tig
ated
.
A
h
y
b
r
id
L
C
L
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
b
ased
m
u
lti
-
ter
m
in
al
d
ir
ec
t
cu
r
r
en
t
(
VSC
-
MT
DC
)
tr
an
s
m
is
s
io
n
s
y
s
tem
was
m
o
d
eled
an
d
s
im
u
lated
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
L
C
L
h
y
b
r
id
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
s
was
th
en
co
m
p
a
r
ed
to
tr
ad
itio
n
al
v
o
ltag
e
s
o
u
r
ce
s
co
n
v
er
ter
s
d
u
r
in
g
n
o
r
m
al
a
n
d
ab
n
o
r
m
al
c
o
n
d
itio
n
s
.
T
h
e
L
C
L
cir
cu
it
was
al
s
o
co
m
p
ar
ed
to
th
e
H
-
b
r
id
g
e
ce
lls
in
th
eir
r
esp
ec
tiv
e
ef
f
ec
tiv
e
n
ess
in
im
p
r
o
v
in
g
a
th
r
ee
-
lev
el
n
eu
tr
al
clam
p
ed
co
n
v
er
ter
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Mo
d
ellin
g
a
n
d
co
n
tr
o
l o
f LC
L v
o
lta
g
e
s
o
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r
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co
n
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r
ter
-
b
a
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(
Ma
h
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1299
I
n
th
is
r
esear
ch
,
a
co
m
p
r
eh
en
s
iv
e
co
m
p
a
r
ativ
e
a
n
aly
s
is
o
f
ad
v
a
n
ce
d
HVDC
co
n
v
e
r
ter
s
was
co
n
d
u
cte
d
.
T
h
e
c
o
m
p
r
eh
en
s
i
v
e
an
aly
s
is
co
n
d
u
cted
f
o
c
u
s
es
o
n
th
e
p
er
f
o
r
m
a
n
ce
o
f
a
n
o
v
el
L
C
L
h
y
b
r
id
co
n
v
er
ter
in
c
o
m
p
a
r
is
o
n
to
tr
ad
itio
n
al
co
n
v
e
r
ter
s
s
u
ch
a
s
th
e
th
r
ee
-
lev
el
n
eu
tr
al
-
p
o
i
n
t
clam
p
ed
(
NPC
)
co
n
v
er
ter
an
d
th
e
h
y
b
r
id
c
o
n
v
er
ter
with
H
-
b
r
id
g
e
ce
lls
.
W
h
ile
th
e
L
C
L
h
y
b
r
id
co
n
v
e
r
ter
ap
p
r
o
ac
h
is
n
o
t
en
tire
ly
n
ew,
o
u
r
s
tu
d
y
p
r
o
v
id
es
a
d
etailed
ev
alu
atio
n
o
f
its
p
er
f
o
r
m
an
ce
u
n
d
er
v
ar
io
u
s
o
p
er
atin
g
co
n
d
itio
n
s
,
wh
ich
h
as n
o
t
b
ee
n
th
o
r
o
u
g
h
l
y
ex
p
lo
r
ed
in
p
r
ev
i
o
u
s
s
tu
d
ies.
T
h
e
co
m
p
ar
ativ
e
an
aly
s
is
r
ev
ea
led
th
at
th
e
L
C
L
h
y
b
r
id
co
n
v
er
ter
o
f
f
e
r
s
d
is
tin
ct
ad
v
an
tag
es
in
f
au
lt
s
u
p
p
r
ess
io
n
an
d
DC
o
u
tp
u
t
v
o
ltag
e
q
u
ality
,
p
ar
ticu
lar
ly
wh
e
n
in
teg
r
ated
in
to
m
u
lti
-
ter
m
in
al
HVD
C
s
y
s
tem
s
.
B
y
s
y
s
tem
atica
lly
co
m
p
ar
in
g
d
if
f
er
en
t
to
p
o
lo
g
ies,
we
wer
e
ab
le
to
id
en
tify
th
e
s
tr
en
g
th
s
an
d
lim
itatio
n
s
o
f
ea
ch
ap
p
r
o
ac
h
,
p
r
o
v
id
i
n
g
v
al
u
ab
le
in
s
ig
h
ts
f
o
r
th
e
d
esig
n
an
d
im
p
lem
en
tatio
n
o
f
HVDC
s
y
s
tem
s
.
Alth
o
u
g
h
th
e
co
n
ce
p
t
o
f
th
e
L
C
L
h
y
b
r
id
co
n
v
er
te
r
h
as
b
ee
n
p
r
o
p
o
s
ed
b
ef
o
r
e,
o
u
r
wo
r
k
co
n
tr
ib
u
tes
to
th
e
f
ield
b
y
v
alid
atin
g
its
ef
f
ec
tiv
en
ess
th
r
o
u
g
h
r
i
g
o
r
o
u
s
s
im
u
latio
n
an
d
an
aly
s
is
.
Mo
r
eo
v
er
,
o
u
r
f
in
d
in
g
s
h
ig
h
lig
h
t
p
r
ac
tical
co
n
s
id
er
atio
n
s
f
o
r
d
ep
lo
y
in
g
s
u
ch
co
n
v
er
te
r
s
in
r
ea
l
-
wo
r
ld
ap
p
licatio
n
s
,
ad
d
r
ess
in
g
k
ey
ch
allen
g
es
s
u
ch
as
co
s
t,
co
m
p
lex
ity
,
an
d
s
ca
lab
ilit
y
.
T
h
is
s
tu
d
y
n
o
t
o
n
l
y
en
h
a
n
ce
s
th
e
u
n
d
er
s
tan
d
in
g
o
f
th
e
L
C
L
h
y
b
r
id
co
n
v
er
ter
'
s
ca
p
ab
ilit
ies
b
u
t
also
o
f
f
er
s
p
r
ac
tical
r
ec
o
m
m
e
n
d
atio
n
s
f
o
r
its
in
teg
r
atio
n
in
to
f
u
tu
r
e
HVDC
s
y
s
tem
s
.
B
y
p
r
o
v
id
in
g
a
b
alan
ce
d
ass
es
s
m
en
t
o
f
d
if
f
er
en
t
co
n
v
er
ter
tech
n
o
lo
g
ies,
o
u
r
r
ese
ar
ch
co
n
tr
ib
u
tes
to
th
e
o
n
g
o
in
g
d
ev
elo
p
m
en
t o
f
m
o
r
e
r
esil
ien
t a
n
d
e
f
f
icien
t p
o
wer
tr
an
s
m
is
s
io
n
s
o
lu
tio
n
s
.
T
h
e
L
C
L
h
y
b
r
id
c
o
n
v
e
r
ter
s
h
o
wed
s
ig
n
if
ican
t
im
p
r
o
v
em
e
n
t
o
v
er
th
e
tr
ad
itio
n
al
th
r
ee
-
le
v
el
n
e
u
tr
al
clam
p
ed
co
n
v
er
ter
in
n
o
r
m
al
an
d
ab
n
o
r
m
al
co
n
d
itio
n
s
.
T
h
e
H
-
b
r
id
g
e
ce
lls
h
av
e
a
b
etter
ef
f
ec
t
th
an
th
e
L
C
L
cir
cu
it
in
im
p
r
o
v
in
g
th
e
th
r
ee
-
lev
el
n
eu
tr
al
clam
p
ed
r
esp
o
n
s
e.
Ad
d
in
g
th
e
L
C
L
cir
cu
it
to
th
e
h
y
b
r
i
d
co
n
v
er
te
r
h
as
a
m
i
n
o
r
ef
f
ec
t
in
im
p
r
o
v
i
n
g
th
e
h
y
b
r
i
d
co
n
v
er
te
r
p
e
r
f
o
r
m
an
ce
.
I
t
was
d
e
m
o
n
s
tr
ated
t
h
at
th
e
L
C
L
h
y
b
r
id
co
n
v
er
ter
h
as
th
e
a
b
ilit
y
to
s
u
p
p
r
ess
DC
as
well
as
AC
f
au
lts
.
I
n
two
ter
m
i
n
al
an
d
m
u
lti
-
ter
m
in
al
HVDC
s
y
s
tem
s
,
th
e
L
C
L
h
y
b
r
id
co
n
v
er
ter
p
r
o
v
ed
to
h
av
e
a
s
u
p
er
io
r
o
p
er
atio
n
b
eh
a
v
io
r
.
Fo
llo
win
g
th
is
in
tr
o
d
u
ctio
n
,
s
ec
tio
n
2
p
r
esen
ts
a
r
e
v
iew
o
f
th
e
r
elev
an
t
liter
atu
r
e,
estab
lis
h
in
g
th
e
th
eo
r
etica
l
an
d
p
r
ac
tical
co
n
te
x
t
f
o
r
th
is
s
tu
d
y
.
Af
ter
th
at
s
ec
tio
n
3
d
is
cu
s
s
es
th
e
co
n
v
er
ter
to
p
o
lo
g
ies
a
d
o
p
ted
in
th
is
r
esear
ch
.
I
t
p
r
o
v
i
d
es
an
o
v
e
r
v
iew
o
f
VSC
s
an
d
ju
s
tifie
s
th
e
ad
o
p
tio
n
o
f
V
SC
o
p
p
o
s
ed
to
lin
e
co
m
m
u
tated
co
n
v
er
ter
s
(
L
C
C
)
.
T
h
en
s
ec
tio
n
4
d
escr
ib
es
th
e
m
et
h
o
d
o
lo
g
y
o
f
th
is
r
esear
ch
.
Sectio
n
f
o
u
r
p
r
esen
ts
th
e
m
eth
o
d
o
l
o
g
y
ad
o
p
ted
f
o
r
th
e
s
im
u
latio
n
an
d
an
aly
s
is
o
f
th
e
VSC
to
p
o
lo
g
ies.
I
t
d
etails
s
y
s
tem
lay
o
u
t,
co
n
v
er
ter
m
o
d
elin
g
,
d
esig
n
,
an
d
co
n
tr
o
l.
I
t
also
p
r
e
s
en
ts
th
e
cr
iter
ia
f
o
r
co
m
p
ar
is
o
n
an
d
ev
alu
atio
n
.
Sectio
n
4
p
r
esen
ts
th
e
s
im
u
latio
n
an
d
r
esu
lts
o
f
th
e
co
m
p
ar
ativ
e
an
al
y
s
is
,
d
is
cu
s
s
in
g
th
e
p
e
r
f
o
r
m
an
ce
,
ad
v
an
tag
es,
an
d
lim
itatio
n
s
o
f
ea
ch
to
p
o
lo
g
y
.
Sectio
n
5
co
n
clu
d
es
th
e
p
ap
er
,
s
u
m
m
ar
izin
g
th
e
k
ey
f
i
n
d
in
g
s
an
d
p
r
o
p
o
s
in
g
d
ir
ec
tio
n
s
f
o
r
f
u
tu
r
e
r
esear
ch
.
2.
L
I
T
E
R
AT
U
RE
R
E
VI
E
W
I
n
HVDC
s
y
s
tem
s
,
p
o
wer
is
co
n
v
er
ted
f
r
o
m
AC
to
DC
an
d
th
en
tr
an
s
m
itted
v
ia
o
v
er
h
ea
d
lin
es,
ca
b
les,
o
r
a
co
m
b
in
atio
n
o
f
b
o
th
,
b
e
f
o
r
e
b
ei
n
g
co
n
v
er
ted
b
ac
k
to
AC
at
th
e
d
esti
n
atio
n
.
T
h
is
co
n
v
er
s
io
n
p
r
o
ce
s
s
is
f
ac
ilit
ated
b
y
p
o
wer
co
n
v
er
ter
s
,
ty
p
ically
o
p
er
a
tin
g
as
in
v
er
ter
s
o
r
r
ec
tifie
r
s
,
d
ep
en
d
in
g
o
n
th
e
p
o
wer
f
lo
w
d
ir
ec
tio
n
.
Key
c
o
m
p
o
n
en
ts
o
f
an
HVDC
s
tat
io
n
in
clu
d
e
th
e
AC
s
witch
y
ar
d
,
eq
u
i
p
p
ed
with
h
ar
m
o
n
ic
f
ilter
s
an
d
r
ea
ctiv
e
p
o
wer
c
o
m
p
e
n
s
atio
n
d
ev
ice
s
;
co
n
v
er
ter
tr
a
n
s
f
o
r
m
e
r
s
,
d
e
s
ig
n
ed
to
c
o
n
n
ec
t
co
n
v
er
ter
s
t
o
th
e
AC
s
y
s
tem
wh
ile
p
r
o
v
i
d
in
g
is
o
latio
n
an
d
v
o
ltag
e
tr
a
n
s
f
o
r
m
atio
n
;
HVDC
co
n
v
er
ter
s
,
co
m
p
o
s
ed
o
f
th
y
r
is
to
r
s
o
r
tr
an
s
is
to
r
s
;
an
d
tr
an
s
m
is
s
io
n
m
ed
iu
m
s
ac
co
m
p
an
ied
b
y
D
C
f
ilter
s
to
m
itig
ate
h
ar
m
o
n
ic
d
is
tu
r
b
a
n
ce
s
.
Ad
d
it
io
n
ally
,
a
u
x
iliar
y
s
y
s
tem
s
s
u
p
p
o
r
t
th
e
c
o
o
lin
g
,
co
n
tr
o
l,
a
n
d
in
ter
n
al
p
o
wer
s
u
p
p
ly
r
eq
u
ir
em
en
ts
o
f
th
e
s
ta
tio
n
.
HVDC
tr
an
s
m
is
s
io
n
s
y
s
tem
s
o
f
f
er
s
ig
n
if
ica
n
t
ad
v
a
n
tag
es
o
v
er
HVAC
s
y
s
tem
s
,
in
clu
d
in
g
ef
f
icien
cy
,
lo
wer
en
v
ir
o
n
m
en
tal
f
o
o
tp
r
in
t,
an
d
im
p
r
o
v
e
d
p
o
wer
s
y
s
tem
s
tab
ilit
y
.
W
i
th
th
e
ca
p
ac
it
y
f
o
r
h
ig
h
er
p
o
we
r
d
eliv
er
y
p
e
r
co
n
d
u
cto
r
an
d
l
o
n
g
er
t
r
an
s
m
is
s
io
n
d
is
tan
ce
s
,
HVDC
d
ec
r
ea
s
es
o
v
er
all
co
s
ts
an
d
lo
s
s
es.
I
ts
ad
v
an
tag
es
e
x
ten
d
to
elim
in
a
tin
g
th
e
n
ec
ess
ity
f
o
r
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
,
r
ed
u
ci
n
g
lin
e
lo
s
s
es,
an
d
allo
win
g
f
o
r
asy
n
c
h
r
o
n
o
u
s
c
o
n
n
ec
tio
n
s
an
d
g
r
o
u
n
d
r
etu
r
n
u
s
ag
e.
HVDC
tech
n
o
lo
g
y
al
s
o
en
h
an
ce
s
p
o
wer
q
u
ality
with
in
AC
s
y
s
tem
s
b
y
co
n
tr
o
llin
g
p
o
wer
f
lo
w
a
n
d
p
r
o
v
id
in
g
a
d
am
p
i
n
g
to
r
q
u
e,
w
h
ich
co
n
tr
ib
u
tes
to
s
y
s
tem
s
tab
ilit
y
.
T
h
ese
s
y
s
tem
s
ar
e
ch
ar
ac
ter
ized
b
y
s
m
aller
tr
an
s
m
is
s
io
n
to
wer
s
an
d
th
e
ab
s
en
ce
o
f
is
s
u
es
lik
e
ch
ar
g
in
g
cu
r
r
en
t a
t stead
y
s
tate,
s
k
in
ef
f
ec
t,
co
r
o
n
a,
a
n
d
r
ad
io
in
ter
f
e
r
en
ce
[
9
]
.
H
V
DC
s
y
s
t
e
m
s
o
f
f
e
r
f
u
r
t
h
e
r
i
m
p
r
o
v
e
d
p
e
r
f
o
r
m
a
n
c
e
i
n
t
e
r
m
s
o
f
p
o
w
e
r
f
l
o
w
m
a
n
a
g
em
e
n
t
,
l
o
s
s
r
e
d
u
c
t
i
o
n
,
a
n
d
i
n
te
g
r
a
t
i
o
n
o
f
d
i
s
t
r
i
b
u
t
e
d
g
e
n
e
r
a
t
i
o
n
c
o
m
p
a
r
e
d
t
o
AC
s
y
s
t
e
m
s
.
L
o
s
s
es
i
n
H
V
DC
s
y
s
t
e
m
s
a
r
e
r
e
d
u
c
e
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[
1
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.
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DG
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[
1
1
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
2
9
7
-
1
3
2
1
1300
I
n
HVAC
s
y
s
tem
s
,
ex
ten
s
iv
e
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
an
d
h
ar
m
o
n
ic
f
ilter
in
g
ar
e
r
eq
u
ir
ed
t
o
m
ain
tain
s
tab
ilit
y
an
d
p
o
we
r
q
u
ality
.
Mu
lti
-
o
b
jectiv
e
o
p
tim
i
za
tio
n
tech
n
iq
u
es f
o
r
r
ea
ctiv
e
p
o
wer
m
an
ag
em
en
t
in
AC
s
y
s
tem
s
h
ig
h
lig
h
t
th
e
n
ee
d
f
o
r
s
u
ch
co
m
p
e
n
s
atio
n
s
to
ad
d
r
ess
is
s
u
es
lik
e
v
o
ltag
e
d
e
v
iatio
n
an
d
p
o
we
r
lo
s
s
[
1
2
]
.
I
n
co
n
tr
ast,
DC
s
y
s
t
em
s
in
h
er
en
tly
av
o
id
th
ese
is
s
u
es
d
u
e
to
th
e
u
n
id
ir
ec
tio
n
al
n
atu
r
e
o
f
DC
p
o
wer
f
lo
w,
wh
ich
o
f
f
er
s
ef
f
icien
c
y
an
d
s
tab
ilit
y
ad
v
an
ta
g
es,
p
ar
ti
cu
lar
ly
with
h
ig
h
in
teg
r
atio
n
o
f
r
en
ewa
b
le
en
e
r
g
y
s
o
u
r
ce
s
[
1
3
]
.
Ad
v
an
ce
d
o
p
tim
izatio
n
tech
n
i
q
u
es
an
d
alg
o
r
ith
m
s
ca
n
b
e
e
f
f
ec
tiv
ely
ap
p
lied
to
HVDC
s
y
s
tem
s
to
im
p
r
o
v
e
th
eir
p
er
f
o
r
m
an
ce
.
T
h
ese
m
eth
o
d
s
h
av
e
th
e
p
o
ten
ti
al
to
en
h
an
ce
v
o
ltag
e
s
tab
ilit
y
an
d
r
ed
u
ce
lo
s
s
es,
co
n
tr
ib
u
tin
g
to
b
etter
o
v
er
all
s
y
s
tem
ef
f
icien
cy
.
I
n
te
g
r
atin
g
d
is
tr
ib
u
ted
g
en
e
r
ato
r
s
in
DC
s
y
s
tem
s
u
s
in
g
s
u
ch
o
p
tim
izatio
n
alg
o
r
ith
m
s
f
u
r
th
er
im
p
r
o
v
es
s
y
s
tem
p
er
f
o
r
m
an
ce
,
in
clu
d
in
g
en
h
a
n
ce
d
v
o
ltag
e
s
tab
ilit
y
an
d
r
ed
u
ce
d
p
o
wer
l
o
s
s
es
[
1
4
]
.
Desp
ite
th
ese
b
en
ef
its
,
HVD
C
s
y
s
tem
s
in
tr
o
d
u
ce
s
s
o
m
e
ch
allen
g
es
s
u
ch
as
th
e
h
ig
h
co
s
t
o
f
p
o
wer
co
n
v
er
ter
s
.
So
m
e
co
n
v
er
ter
s
r
eq
u
ir
e
r
ea
ctiv
e
p
o
wer
an
d
h
av
e
lim
ited
o
v
er
lo
ad
ca
p
ac
ity
.
A
d
d
itio
n
ally
,
HVDC
co
n
v
er
ter
s
in
tr
o
d
u
ce
h
a
r
m
o
n
i
cs,
n
ec
ess
itat
in
g
th
e
u
s
e
o
f
f
ilter
s
.
T
h
e
co
m
p
lex
ity
o
f
m
u
lti
-
ter
m
in
al
o
p
er
atio
n
s
also
p
r
esen
ts
o
p
er
atio
n
al
ch
all
en
g
es.
No
n
eth
eless
,
th
e
b
en
e
f
its
o
f
HVDC
o
u
tweig
h
th
ese
d
r
awb
ac
k
s
,
m
ak
i
n
g
it a
p
r
ef
er
r
e
d
ch
o
ice
f
o
r
lo
n
g
-
d
is
tan
ce
p
o
wer
tr
an
s
m
is
s
io
n
.
Sin
ce
its
in
itial c
o
m
m
er
cial
i
m
p
lem
en
tatio
n
in
1
9
5
4
,
HVDC tec
h
n
o
lo
g
y
h
as si
g
n
if
ican
tly
m
atu
r
ed
.
I
t
is
b
ec
o
m
in
g
in
d
is
p
en
s
ab
le
f
o
r
a
v
ar
iety
o
f
tr
a
n
s
m
is
s
io
n
ch
allen
g
es,
n
o
tab
ly
i
n
in
teg
r
atin
g
o
f
f
s
h
o
r
e
win
d
f
ar
m
s
,
en
h
a
n
cin
g
lo
n
g
-
d
is
tan
ce
b
u
lk
p
o
wer
t
r
an
s
m
is
s
io
n
,
f
ac
ilit
atin
g
co
n
n
ec
tio
n
s
b
et
wee
n
asy
n
ch
r
o
n
o
u
s
g
r
id
s
,
an
d
s
u
p
p
ly
in
g
p
o
wer
t
o
d
en
s
ely
p
o
p
u
lated
u
r
b
a
n
ar
ea
s
.
HVDC
's
s
u
p
er
io
r
ity
s
tem
s
f
r
o
m
its
ab
ilit
y
to
tr
an
s
m
it
p
o
wer
o
v
e
r
v
ast
d
is
tan
ce
s
with
s
ig
n
if
ican
tly
lo
wer
lo
s
s
es
co
m
p
ar
ed
to
AC
tr
an
s
m
is
s
io
n
,
m
ak
in
g
it
ec
o
n
o
m
ically
v
iab
le
f
o
r
co
n
n
ec
tin
g
r
em
o
te
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
—
s
u
ch
as
h
y
d
r
o
,
win
d
,
an
d
s
o
lar
—
to
d
is
tan
t lo
ad
ce
n
ter
s
.
I
n
u
r
b
a
n
s
ettin
g
s
,
u
tili
za
tio
n
o
f
o
ld
er
less
ef
f
icien
t
g
en
er
atio
n
u
n
its
is
co
n
s
tr
ain
ed
b
y
en
v
i
r
o
n
m
en
tal
r
eg
u
latio
n
s
.
I
n
s
u
ch
s
itu
atio
n
s
,
HVDC
p
r
o
v
es
ad
v
an
tag
e
o
u
s
b
y
en
ab
lin
g
th
e
in
teg
r
atio
n
o
f
n
ew,
m
o
r
e
ef
f
icien
t
g
en
er
atio
n
u
n
its
lo
ca
ted
f
ar
f
r
o
m
cities.
C
o
m
p
ac
t
HVDC
s
tatio
n
s
,
u
til
izin
g
u
n
d
er
g
r
o
u
n
d
tr
an
s
m
is
s
io
n
cir
cu
its
,
ad
d
r
ess
th
e
ch
allen
g
es
p
o
s
ed
b
y
r
ig
h
t
-
of
-
way
an
d
lan
d
u
s
e
lim
itatio
n
s
,
en
s
u
r
in
g
r
eliab
le
p
o
wer
d
eliv
e
r
y
with
o
u
t
co
m
p
r
o
m
is
in
g
s
y
s
tem
s
tab
ilit
y
.
Fo
r
ca
b
le
tr
an
s
m
is
s
io
n
s
,
HVDC
elim
in
ates
th
e
n
ee
d
f
o
r
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
,
allo
win
g
f
o
r
lo
n
g
er
tr
a
n
s
m
is
s
io
n
d
is
tan
ce
s
with
o
u
t
th
e
p
h
y
s
ical
r
estrictio
n
s
im
p
o
s
ed
b
y
AC
s
y
s
tem
s
'
h
ig
h
er
ca
p
ac
itan
ce
an
d
in
d
u
cta
n
ce
.
T
h
is
attr
ib
u
te
is
also
o
f
p
ar
ticu
lar
in
ter
est
f
o
r
s
u
b
m
ar
in
e
ca
b
les,
wh
er
e
HVDC
'
s
ab
s
en
ce
o
f
ca
p
ac
itiv
e
ch
ar
g
in
g
cu
r
r
e
n
t
a
n
d
h
ig
h
e
r
r
atin
g
m
ak
e
it
a
p
r
ac
tica
l
an
d
co
s
t
-
ef
f
ec
tiv
e
o
p
tio
n
.
Mo
r
eo
v
er
,
HVDC lin
k
s
s
er
v
e
as a
r
o
b
u
s
t so
lu
tio
n
f
o
r
co
n
n
ec
tin
g
asy
n
ch
r
o
n
o
u
s
AC
g
r
id
s
,
s
u
p
p
o
r
tin
g
en
er
g
y
tr
ad
in
g
an
d
s
y
s
tem
s
tab
ilizatio
n
.
T
h
ese
lin
k
s
ac
t
as
b
u
f
f
er
s
to
p
r
ev
e
n
t
th
e
p
r
o
p
ag
ati
o
n
o
f
d
is
tu
r
b
a
n
ce
s
an
d
aid
in
d
am
p
in
g
p
o
wer
o
s
cillatio
n
s
f
o
llo
win
g
d
is
tu
r
b
an
ce
s
,
en
h
an
cin
g
th
e
o
v
er
all
r
eliab
ilit
y
an
d
ec
o
n
o
m
ic
o
p
er
atio
n
o
f
i
n
ter
co
n
n
ec
ted
p
o
wer
s
y
s
tem
s
.
T
h
er
e
ar
e
v
ar
i
o
u
s
co
n
f
i
g
u
r
atio
n
s
o
f
HVDC
s
y
s
tem
s
.
T
h
e
f
o
u
r
m
ain
co
n
f
i
g
u
r
atio
n
s
in
v
esti
g
ated
in
th
is
r
esear
ch
ar
e
b
ac
k
-
to
-
b
ac
k
,
m
o
n
o
p
o
lar
,
b
ip
o
la
r
,
an
d
m
u
lti
-
ter
m
i
n
al
HVDC sy
s
tem
co
n
f
ig
u
r
atio
n
s
.
T
h
e
s
im
p
lest
co
n
f
ig
u
r
atio
n
is
th
e
b
ac
k
-
to
-
b
ac
k
HVDC
s
y
s
te
m
.
I
n
th
is
co
n
f
ig
u
r
atio
n
b
o
th
co
n
v
er
ter
s
ar
e
p
lace
d
in
th
e
s
am
e
s
tatio
n
th
er
ef
o
r
e
n
o
tr
an
s
m
is
s
io
n
li
n
e
is
n
ee
d
ed
.
A
b
ac
k
-
to
-
b
ac
k
s
y
s
tem
is
u
s
ed
to
co
n
n
ec
t
two
ad
jace
n
t
AC
g
r
i
d
s
with
s
am
e
o
r
d
if
f
er
en
t
f
r
e
q
u
en
cies.
Mo
r
eo
v
er
,
to
ac
h
ie
v
e
a
d
ef
in
ed
p
o
we
r
f
lo
w
th
is
to
p
o
lo
g
y
is
u
s
ed
with
in
a
m
esh
ed
g
r
id
.
A
m
o
n
o
p
o
l
ar
HVDC
s
y
s
t
em
i
s
a
c
o
n
f
i
g
u
r
a
ti
o
n
w
h
e
r
e
th
e
t
w
o
c
o
n
v
e
r
te
r
s
tat
io
n
s
ar
e
co
n
n
e
cte
d
w
it
h
a
s
in
g
le
p
o
l
e
li
n
e
.
T
h
e
v
o
l
ta
g
e
p
o
la
r
i
ty
ca
n
b
e
eit
h
e
r
p
o
s
iti
v
e
o
r
n
e
g
at
iv
e.
T
h
e
g
r
o
u
n
d
s
e
r
v
es
as
th
e
r
et
u
r
n
p
at
h
.
T
h
is
co
n
f
i
g
u
r
ati
o
n
is
wi
d
el
y
u
s
ed
i
n
u
n
d
e
r
s
e
a
t
r
a
n
s
m
is
s
i
o
n
e
s
p
e
cia
ll
y
f
o
r
v
e
r
y
l
o
n
g
s
e
a
ca
b
le
tr
an
s
m
is
s
i
o
n
.
I
n
a
b
ip
o
la
r
HVDC
s
y
s
tem
t
h
e
two
co
n
v
e
r
ter
s
tatio
n
s
ar
e
co
n
n
ec
ted
with
two
co
n
d
u
ct
o
r
s
.
On
e
co
n
d
u
ct
o
r
is
p
o
s
itiv
e
wh
ile
th
e
o
th
er
is
n
eg
ativ
e.
A
m
id
-
p
o
in
t
is
co
n
n
ec
ted
to
g
r
o
u
n
d
.
I
t
is
m
ain
ly
u
s
ed
in
ap
p
licatio
n
s
wh
er
e
o
v
er
h
ea
d
lin
es
ar
e
u
s
ed
to
tr
an
s
m
it
p
o
wer
.
B
ip
o
lar
s
y
s
tem
s
ca
n
b
e
co
n
s
id
er
ed
as
two
m
o
n
o
p
o
lar
s
y
s
tem
s
.
T
h
e
m
ain
ad
v
an
ta
g
e
o
f
s
u
ch
to
p
o
l
o
g
y
is
th
at
if
o
n
e
p
o
le
is
o
u
t
o
f
s
er
v
ice,
th
e
o
th
er
o
n
e
ca
n
s
till
h
av
e
th
e
ab
ilit
y
to
tr
a
n
s
m
it
p
o
wer
m
ea
n
in
g
th
at
ea
c
h
s
id
e
o
f
th
is
to
p
o
lo
g
y
ca
n
o
p
er
ate
in
d
ep
e
n
d
en
tly
if
th
e
n
eu
tr
al
p
o
in
t is g
r
o
u
n
d
e
d
at
b
o
th
s
tatio
n
s
.
I
n
m
u
lti
-
ter
m
in
al
HVDC
s
y
s
t
em
s
th
er
e
ar
e
m
o
r
e
th
a
n
two
s
ets
o
f
co
n
v
er
ts
.
C
o
n
n
ec
tin
g
m
o
r
e
th
an
two
co
n
v
er
ter
s
tatio
n
s
ca
n
b
e
d
o
n
e
with
p
ar
allel
m
u
lti
-
ter
m
i
n
al
HVDC
s
tatio
n
s
,
s
er
ies
m
u
lti
-
ter
m
in
al
HVDC
s
tatio
n
s
o
r
h
y
b
r
id
m
u
lti
-
ter
m
i
n
al
HVDC
s
y
s
tem
.
Sin
ce
th
e
co
n
v
er
ter
s
tatio
n
s
ar
e
p
h
y
s
ically
s
ep
ar
ated
in
th
e
m
u
lti
-
ter
m
in
al
HVDC
tr
an
s
m
is
s
io
n
a
DC
cir
cu
it
i
s
n
ee
d
ed
to
co
n
n
ec
t
th
em
.
T
h
e
in
h
er
e
n
t
f
au
lt
s
u
p
p
r
ess
io
n
ca
p
ab
ilit
ies
o
f
m
o
d
u
lar
m
u
ltil
ev
el
co
n
v
er
ter
s
(
MM
C
s
)
h
av
e
s
p
u
r
r
ed
th
e
d
ev
elo
p
m
en
t
o
f
in
n
o
v
ati
v
e
h
y
b
r
id
co
n
v
er
ter
to
p
o
lo
g
ies
f
o
r
HVDC
ap
p
licatio
n
s
.
T
h
ese
to
p
o
lo
g
ies
aim
t
o
c
o
m
b
in
e
th
e
f
au
lt
-
r
i
d
e
-
th
r
o
u
g
h
ad
v
an
tag
es
o
f
MM
C
-
b
ased
d
esig
n
s
with
th
e
o
p
er
atio
n
al
s
im
p
licity
an
d
r
ed
u
ce
d
co
m
p
o
n
e
n
t
co
u
n
t
o
f
tr
ad
itio
n
al
two
-
lev
el
VSC
s
[
1
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Mo
d
ellin
g
a
n
d
co
n
tr
o
l o
f LC
L v
o
lta
g
e
s
o
u
r
ce
co
n
ve
r
ter
-
b
a
s
ed
h
yb
r
id
…
(
Ma
h
mo
o
d
S
a
a
d
eh
)
1301
A
n
o
tab
le
s
tr
ateg
y
in
v
o
l
v
es
in
co
r
p
o
r
atin
g
H
-
b
r
id
g
e
ce
lls
o
n
th
e
AC
s
id
e
o
f
a
two
-
lev
el
co
n
v
er
ter
.
T
h
ese
ce
lls
h
av
e
b
ee
n
s
h
o
wn
to
f
u
n
ctio
n
ef
f
ec
tiv
ely
as
ac
tiv
e
f
ilter
s
,
th
er
eb
y
im
p
r
o
v
in
g
o
u
tp
u
t
v
o
ltag
e
q
u
ality
,
a
n
d
e
n
h
an
cin
g
th
e
co
n
v
er
ter
’
s
ab
ilit
y
to
m
an
a
g
e
DC
f
au
lts
.
Ho
wev
er
,
th
e
H
-
b
r
id
g
e
ce
lls
ad
d
co
m
p
lex
ity
a
n
d
in
cr
e
ase
s
witc
h
in
g
lo
s
s
es with
in
th
e
s
y
s
tem
[
1
6
]
,
[
1
7
]
.
Alter
n
ativ
ely
,
th
e
L
C
L
cir
cu
i
t
o
f
f
er
s
a
d
if
f
e
r
en
t
ap
p
r
o
ac
h
to
f
au
lt
m
an
ag
e
m
en
t
an
d
p
o
wer
q
u
ality
im
p
r
o
v
em
e
n
t
in
HVDC
co
n
v
er
ter
s
.
T
r
ad
itio
n
ally
em
p
lo
y
e
d
in
g
r
i
d
-
co
n
n
ec
ted
c
o
n
v
er
te
r
s
f
o
r
th
eir
s
u
p
e
r
io
r
h
ig
h
-
f
r
eq
u
e
n
cy
h
ar
m
o
n
ic
atte
n
u
atio
n
,
L
C
L
f
ilter
s
ar
e
n
o
w
b
ein
g
ex
p
lo
r
ed
f
o
r
t
h
eir
p
o
t
en
tial
in
en
h
a
n
cin
g
b
o
th
AC
an
d
DC
f
au
lt
s
u
p
p
r
ess
io
n
wh
en
i
n
teg
r
ated
with
co
n
v
en
tio
n
al
VSC
s
[
1
8
]
–
[
2
1
]
.
Desp
ite
th
e
r
ec
o
g
n
ized
b
e
n
ef
its
o
f
b
o
th
H
-
b
r
id
g
e
ce
lls
an
d
L
C
L
cir
cu
its
,
co
m
p
r
eh
e
n
s
iv
e
co
m
p
ar
ati
v
e
an
aly
s
es
o
f
th
eir
p
er
f
o
r
m
an
ce
with
in
a
u
n
if
ied
s
y
s
tem
ar
e
lack
in
g
.
T
h
is
r
esear
ch
s
ee
k
s
to
f
ill
th
is
g
a
p
b
y
d
ir
ec
tly
s
im
u
latin
g
an
d
e
v
alu
atin
g
th
e
ef
f
ec
ts
o
f
L
C
L
cir
cu
its
alo
n
g
s
id
e
a
tr
a
d
itio
n
al
th
r
ee
-
lev
el
NPC
an
d
an
ex
is
tin
g
h
y
b
r
id
co
n
f
ig
u
r
atio
n
e
m
p
lo
y
i
n
g
H
-
b
r
id
g
e
ce
lls
.
Ou
r
f
in
d
i
n
g
s
co
n
tr
ib
u
te
to
o
p
tim
izin
g
h
y
b
r
i
d
HVDC
co
n
v
er
ter
d
esig
n
s
,
b
alan
cin
g
s
p
ec
if
ic
p
er
f
o
r
m
an
ce
m
etr
ics ag
ain
s
t c
o
s
t c
o
n
s
id
er
atio
n
s
.
3.
VO
L
T
AG
E
SO
URC
E
CO
N
VE
R
T
E
R
S VS
L
I
N
E
CO
M
M
UT
AT
E
D
CO
NV
E
R
T
E
R
S
T
h
e
co
n
v
er
ter
s
tatio
n
is
co
n
s
i
d
er
ed
th
e
m
o
s
t
im
p
o
r
tan
t
ele
m
en
t
o
f
a
n
HVDC
s
y
s
tem
.
B
ased
o
n
th
e
ty
p
e
o
f
p
o
wer
co
n
v
er
s
io
n
p
r
o
ce
s
s
u
s
ed
in
th
e
s
tatio
n
,
th
e
HVDC
s
y
s
tem
is
id
en
tifie
d
.
T
wo
m
ain
p
o
wer
co
n
v
er
ter
tech
n
o
l
o
g
ies
h
av
e
b
ee
n
u
tili
ze
d
in
th
e
co
n
v
er
s
i
o
n
s
tatio
n
s
,
cu
r
r
e
n
t
s
o
u
r
ce
c
o
n
v
er
ter
(
C
SC
)
an
d
VSC
.
Fig
u
r
e
1
s
h
o
ws
th
e
cl
ass
if
icatio
n
o
f
p
o
wer
co
n
v
er
t
er
s
.
T
h
y
r
is
to
r
b
ased
C
SC
HVDC
(
co
n
v
en
tio
n
al
HVDC)
cir
cu
its
ar
e
ter
m
ed
as
L
C
C
s
in
ce
th
e
co
n
v
er
ter
v
al
v
es
r
ely
o
n
t
h
e
s
y
s
tem
lin
e
AC
v
o
ltag
e
to
p
e
r
f
o
r
m
th
e
co
m
m
u
tatio
n
ac
tio
n
.
Vo
lta
g
e
s
o
u
r
ce
co
n
v
er
ter
s
th
at
em
p
lo
y
tu
r
n
o
f
f
s
em
ico
n
d
u
cto
r
d
e
v
ices
ar
e
k
n
o
wn
as
s
elf
o
r
f
o
r
ce
d
c
o
m
m
u
tate
d
co
n
v
er
ter
s
.
L
C
C
b
ased
HVDC
is
a
m
atu
r
e
tech
n
o
lo
g
y
with
D
C
p
o
wer
lev
els
an
d
v
o
ltag
es
h
ig
h
e
r
th
an
VSC
b
ased
s
y
s
tem
s
.
On
th
e
o
t
h
er
h
a
n
d
,
VSC
b
ased
s
y
s
tem
s
wh
ich
o
r
ig
in
ally
co
m
e
f
r
o
m
m
o
to
r
d
r
iv
e
ap
p
licatio
n
s
ar
e
p
r
esen
ted
with
a
p
o
wer
r
ate
o
f
4
0
0
MW.
T
h
e
th
r
ee
-
p
h
ase
f
u
ll
wav
e
b
r
id
g
e,
also
k
n
o
wn
as
th
e
6
-
p
u
ls
e
o
r
Gr
ae
tz
B
r
id
g
e
is
th
e
b
as
i
c
b
u
ild
in
g
b
lo
ck
u
s
ed
f
o
r
HVDC
co
n
v
er
s
io
n
[
2
2
]
,
[
2
3
]
.
I
t
is
ca
lled
s
ix
-
p
u
ls
e,
s
in
ce
th
e
DC
o
u
tp
u
t
v
o
ltag
e
will
h
av
e
a
h
ar
m
o
n
ic
r
ip
p
le
o
f
s
ix
tim
es
th
e
f
u
n
d
am
e
n
tal
f
r
e
q
u
en
c
y
,
d
u
e
to
t
h
e
s
ix
c
o
m
m
u
tatio
n
s
o
r
s
witch
in
g
o
p
er
atio
n
s
p
er
p
er
io
d
.
T
h
e
s
ix
-
p
u
ls
e
b
r
i
d
g
e
co
n
s
is
ts
o
f
s
ix
s
em
ico
n
d
u
cto
r
s
witch
es
o
r
th
y
r
is
to
r
v
alv
es.
I
n
o
r
d
er
to
ac
h
iev
e
th
e
r
eq
u
ir
e
d
DC
v
o
ltag
e
r
atin
g
,
th
e
v
alv
es
ar
e
co
m
p
o
s
ed
o
f
a
n
u
m
b
e
r
o
f
s
er
ies
co
n
n
ec
ted
th
y
r
is
to
r
s
.
C
o
n
n
ec
tin
g
th
e
DC
ter
m
in
als
o
f
two
s
ix
-
p
u
ls
e
b
r
id
g
es
in
s
er
ies
wh
ile
th
e
AC
v
o
ltag
e
s
o
u
r
ce
s
p
h
ase
d
is
p
lace
d
b
y
3
0
o
,
will
in
cr
ea
s
e
th
e
DC
v
o
ltag
e
an
d
s
o
m
e
o
f
AC
cu
r
r
en
t
an
d
DC
v
o
ltag
e
h
ar
m
o
n
ic
s
will
b
e
elim
in
ated
.
T
h
is
co
n
f
ig
u
r
atio
n
is
r
ef
e
r
r
ed
to
as
1
2
-
p
u
ls
e
co
n
v
er
ter
.
I
t
is
th
e
m
o
s
t
class
ical
an
d
m
o
s
t
u
s
ed
s
ch
em
e
in
HVDC.
I
n
th
e
1
2
-
p
u
ls
e
co
n
v
er
ter
s
th
e
f
if
th
a
n
d
s
ev
en
t
h
h
ar
m
o
n
ics
ar
e
ca
n
ce
lled
o
u
t
in
th
e
co
n
v
er
ter
tr
an
s
f
o
r
m
er
[
2
2
]
,
[
2
3
]
.
T
r
an
s
f
er
r
in
g
o
f
DC
cu
r
r
en
t
f
r
o
m
o
n
e
v
alv
e
to
an
o
th
er
in
th
e
s
am
e
r
o
w
in
a
s
y
n
ch
r
o
n
i
ze
d
f
ir
in
g
s
eq
u
en
ce
o
f
th
e
th
y
r
is
to
r
v
al
v
es
is
ca
l
led
co
m
m
u
tatio
n
.
T
o
co
m
m
u
tate
f
r
o
m
o
n
e
s
witch
in
g
d
ev
ice
to
its
n
eig
h
b
o
r
,
lin
e
c
o
m
m
u
tated
c
o
n
v
er
ter
s
d
ep
e
n
d
o
n
th
e
lin
e
v
o
ltag
e
o
f
th
e
AC
s
y
s
tem
to
wh
ich
th
e
co
n
v
er
ter
is
co
n
n
ec
ted
.
I
n
L
C
C
,
th
e
f
lo
w
o
f
th
e
DC
cu
r
r
en
t
is
u
n
id
ir
ec
t
io
n
al,
an
d
it
is
co
n
s
id
er
ed
co
n
s
tan
t
s
in
ce
it
f
lo
w
s
th
r
o
u
g
h
a
lar
g
e
in
d
u
ctan
ce
.
A
s
a
r
esu
lt,
to
r
ev
er
s
e
th
e
d
ir
ec
t
io
n
o
f
p
o
wer
f
lo
w,
th
e
p
o
lar
it
y
o
f
DC
v
o
ltag
e
at
b
o
th
s
tatio
n
s
is
r
ev
er
s
ed
.
B
eh
av
in
g
lik
e
a
cu
r
r
e
n
t
s
o
u
r
ce
,
th
e
co
n
v
e
r
ter
o
n
th
e
AC
s
id
e
in
jects
b
o
th
g
r
id
f
r
eq
u
e
n
cy
an
d
h
ar
m
o
n
ic
c
u
r
r
e
n
ts
in
to
th
e
AC
n
etwo
r
k
[
2
4
]
.
Fig
u
r
e
1
.
C
lass
if
icatio
n
o
f
p
o
wer
co
n
v
er
te
r
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
2
9
7
-
1
3
2
1
1302
On
e
im
p
o
r
ta
n
t
p
r
o
p
er
ty
o
f
a
n
L
C
C
is
th
at
it
ca
n
o
n
l
y
o
p
er
ate
if
th
e
ac
cu
r
r
en
t
lag
s
t
h
e
v
o
ltag
e
.
C
o
n
s
eq
u
en
tly
,
r
ea
ctiv
e
p
o
we
r
is
n
ee
d
ed
to
co
m
p
lete
th
e
co
n
v
er
s
io
n
p
r
o
ce
s
s
.
As
th
e
tr
an
s
m
itted
p
o
wer
in
cr
ea
s
es,
th
e
r
ea
ctiv
e
p
o
wer
r
eq
u
ir
ed
in
cr
ea
s
es in
a
n
o
n
lin
e
ar
m
an
n
er
.
I
t is estima
ted
th
at
th
e
co
n
s
u
m
p
tio
n
o
f
r
ea
ctiv
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p
o
wer
in
a
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HVDC
co
n
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ter
is
ar
o
u
n
d
0
.
5
p
.
u
.
o
f
th
e
ac
tiv
e
p
o
we
r
[
2
5
]
.
On
th
e
AC
s
id
e,
AC
f
ilter
s
ar
e
in
s
talled
to
f
u
lf
ill
two
r
eq
u
ir
em
en
ts
;
t
o
f
ilter
th
e
cu
r
r
en
t
h
ar
m
o
n
ics
an
d
to
s
u
p
p
ly
th
e
r
ea
ctiv
e
p
o
wer
r
eq
u
i
r
ed
.
T
h
e
n
ee
d
f
o
r
f
ilter
in
g
in
c
r
ea
s
es
n
o
n
lin
ea
r
ly
in
th
e
s
am
e
m
an
n
er
as
f
o
r
r
ea
ctiv
e
p
o
wer
ab
s
o
r
p
tio
n
,
b
u
t
in
th
e
o
p
p
o
s
ite
way
.
An
y
ex
ce
s
s
o
r
s
h
o
r
tag
e
in
r
ea
ctiv
e
p
o
wer
f
r
o
m
th
e
lo
ca
l
s
o
u
r
ce
s
s
h
o
u
ld
b
e
a
d
ju
s
ted
b
y
th
e
ac
s
y
s
tem
[
2
6
]
.
On
th
e
DC
s
id
e,
f
ilter
s
ar
e
n
ee
d
ed
to
m
in
im
ize
h
ar
m
o
n
ic
v
o
ltag
es;
also
,
r
ea
cto
r
s
ar
e
p
r
esen
t,
s
o
t
h
e
r
ip
p
le
o
f
t
h
e
DC
v
o
ltag
e
is
r
ed
u
ce
d
.
Mo
r
e
o
v
er
,
r
ea
cto
r
s
ca
n
r
ed
u
ce
th
e
p
ea
k
cu
r
r
en
t in
ca
s
e
o
f
a
f
a
u
lt o
n
t
h
e
DC
co
n
n
ec
tio
n
[
2
7
]
.
L
C
C
-
b
ased
s
y
s
tem
s
ar
e
well
-
estab
lis
h
ed
an
d
r
eliab
le
tech
n
o
lo
g
y
with
th
e
lo
west
lo
s
s
es
am
o
n
g
co
n
v
er
ter
s
s
ch
e
m
es
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ailab
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T
h
ese
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ter
s
h
av
e
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ec
o
n
o
m
ic
ad
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n
tag
e,
s
in
ce
th
ey
ar
e
th
y
r
is
to
r
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ased
co
n
v
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ter
s
a
n
d
t
h
y
r
is
to
r
s
ca
n
h
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d
le
two
to
th
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ee
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es
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h
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p
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th
an
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y
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th
e
r
s
e
m
ico
n
d
u
ct
o
r
d
ev
ices
wh
ich
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m
ea
n
s
th
at
L
C
C
h
as
g
o
o
d
o
v
er
lo
a
d
ca
p
a
b
ilit
y
.
U
p
to
n
o
w
L
C
C
tech
n
o
lo
g
y
h
as th
e
h
ig
h
est
v
o
ltag
e
an
d
p
o
wer
lev
els
a
n
d
t
h
er
e
is
a
s
ig
n
if
ican
t
r
esear
ch
ef
f
o
r
t
to
in
cr
ea
s
e
it
f
u
r
th
er
m
o
r
e.
Ho
wev
er
,
L
C
C
tech
n
o
lo
g
y
s
u
f
f
er
s
f
r
o
m
d
r
awb
ac
k
s
,
lik
e
its
d
ep
en
d
en
ce
o
n
th
e
co
n
n
ec
ted
n
etwo
r
k
v
o
ltag
e
,
s
p
ec
ial
tr
an
s
f
o
r
m
er
s
a
r
e
r
eq
u
ir
e
d
t
o
w
ith
s
tan
d
DC
s
tr
ess
es
an
d
ex
tr
a
s
h
u
n
t
r
ea
ctiv
e
p
o
wer
s
o
u
r
ce
s
ar
e
n
ee
d
e
d
d
u
e
t
o
lar
g
e
co
n
s
u
m
p
tio
n
o
f
r
ea
ctiv
e
p
o
wer
also
th
e
a
b
ilit
y
to
co
n
tr
o
l r
ea
ctiv
e
p
o
we
r
is
lim
ited
.
I
n
an
attem
p
t
to
ad
d
r
ess
s
o
m
e
o
f
L
C
C
d
is
ad
v
an
tag
es,
ca
p
ac
ito
r
co
m
m
u
tated
co
n
v
er
ter
s
(
C
C
C
)
an
d
co
n
tr
o
lled
s
er
ies ca
p
ac
ito
r
co
n
v
er
ter
s
(
C
SC
C
)
wer
e
p
r
o
p
o
s
ed
[
2
2
]
,
[
2
8
]
,
[
2
9
]
.
B
y
co
n
n
ec
tin
g
s
er
ies ca
p
ac
ito
r
s
b
etwe
en
th
e
v
alv
es
an
d
th
e
t
r
an
s
f
o
r
m
er
s
,
th
e
d
e
m
an
d
o
f
s
h
u
n
t
r
ea
ctiv
e
co
m
p
en
s
atio
n
a
s
well
a
s
s
tr
en
g
th
r
eq
u
ir
em
e
n
ts
o
f
th
e
co
n
n
ec
ted
ac
s
y
s
tem
ca
n
b
e
r
ed
u
ce
d
.
T
h
ese
ad
d
ed
ca
p
ac
ito
r
s
p
r
o
v
id
e
s
o
m
e
o
f
th
e
v
o
ltag
e
r
eq
u
ir
ed
to
co
m
m
u
tate,
th
u
s
im
p
r
o
v
i
n
g
v
o
ltag
e
s
tab
ilit
y
an
d
r
ed
u
ci
n
g
th
e
p
r
o
b
ab
ilit
y
o
f
co
m
m
u
tatio
n
f
ailu
r
e
in
ca
s
e
o
f
a
f
a
u
lt.
Nev
er
th
ele
s
s
,
th
e
h
ig
h
er
co
s
t
o
f
th
e
c
o
n
v
er
ter
,
th
e
p
r
o
tectio
n
n
ee
d
ed
f
o
r
th
e
ca
p
ac
ito
r
s
ag
ain
s
t
o
v
er
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v
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es
a
n
d
th
e
n
eg
ativ
e
im
p
ac
t
o
f
th
e
en
er
g
y
s
to
r
ed
i
n
th
e
s
er
ies
ca
p
ac
ito
r
o
n
th
e
d
y
n
am
ic
r
esp
o
n
s
e
in
u
n
b
alan
ce
d
co
n
d
itio
n
s
ar
e
s
o
m
e
o
f
C
C
C
co
n
f
ig
u
r
atio
n
d
is
ad
v
a
n
tag
es.
Dev
elo
p
m
en
ts
in
s
em
ico
n
d
u
ct
o
r
d
ev
ice
r
atin
g
s
m
ad
e
it
p
o
s
s
ib
le
to
b
u
ild
h
ig
h
v
o
ltag
e
v
al
v
es
h
en
ce
,
m
ak
in
g
VSC
ap
p
licab
le
to
HVDC.
B
a
s
ed
o
n
s
elf
-
co
m
m
u
t
atin
g
,
f
u
lly
co
n
tr
o
lled
v
al
v
es
(
i.e
.
in
s
u
lated
-
g
ate
b
ip
o
lar
tr
an
s
is
to
r
(
I
GB
T
)
)
V
SC
’
s
o
f
f
er
a
m
o
r
e
f
lex
i
b
le
s
o
lu
tio
n
f
o
r
HVDC
tr
an
s
m
is
s
io
n
.
Ab
s
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o
f
co
m
m
u
tatio
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f
ail
u
r
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f
ast
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d
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u
p
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d
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o
l
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an
d
r
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p
o
w
er
an
d
s
m
all
f
ilter
r
eq
u
ir
em
e
n
ts
ar
e
s
o
m
e
o
f
VSC
attr
ac
tiv
e
f
ea
tu
r
es
[
3
0
]
.
W
it
h
VSC
,
co
m
p
ac
t
s
ite
ar
ea
i
s
a
ch
iev
ed
,
th
e
s
tr
en
g
th
o
f
AC
n
etwo
r
k
is
n
o
t
cr
itical,
v
o
ltag
e
a
n
d
tr
an
s
ien
t
s
tab
ilit
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ar
e
im
p
r
o
v
ed
,
a
n
d
p
o
wer
d
ir
e
ctio
n
is
r
e
v
er
s
ed
b
y
ch
an
g
in
g
th
e
d
ir
ec
tio
n
o
f
c
u
r
r
en
t.
On
e
im
p
o
r
tan
t
f
ea
t
u
r
e
alt
h
o
u
g
h
is
m
is
s
in
g
,
th
e
a
b
ilit
y
t
o
clea
r
f
au
lts
o
n
th
e
DC
s
id
e.
A
co
m
p
ar
is
o
n
o
f
L
C
C
an
d
VSC
tech
n
o
lo
g
ies is
p
r
o
v
id
ed
i
n
T
ab
le
1
.
T
ab
le
1
.
C
o
m
p
a
r
is
o
n
o
f
L
C
C
an
d
VSC
tech
n
o
lo
g
y
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t
e
m
C
S
C
-
L
C
C
t
e
c
h
n
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g
y
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t
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3
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ased
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[
1
6
]
,
[
3
2
]
.
A
h
y
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r
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ased
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with
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b
in
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ar
d
s
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ad
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e
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ig
h
v
o
ltag
e
s
p
ik
es
s
h
o
win
g
in
th
e
o
u
t
p
u
t
v
o
ltag
e,
ca
r
ef
u
l
s
y
n
c
h
r
o
n
izatio
n
is
r
eq
u
ir
ed
b
etwe
en
th
e
two
-
le
v
el
c
o
n
v
er
ter
an
d
wav
e
-
s
h
ap
in
g
cir
cu
it.
On
th
e
o
t
h
er
h
a
n
d
,
p
u
ttin
g
th
e
wav
e
-
s
h
ap
in
g
cir
cu
it
o
n
th
e
DC
s
id
e
will
r
ed
u
ce
th
e
s
witch
in
g
lo
s
s
es
an
d
will
s
im
p
lify
th
e
d
esig
n
o
f
th
e
v
alv
e
s
in
ce
th
e
r
e
q
u
ir
e
m
en
ts
f
o
r
d
y
n
am
ic
v
o
ltag
e
s
h
ar
in
g
b
ec
o
m
e
less
ef
f
ec
tiv
e.
B
o
th
s
er
ies
ar
r
an
g
e
m
en
ts
s
h
ar
e
s
o
m
e
ad
v
an
tag
e
s
s
u
ch
as
th
e
f
ac
t
th
at
it
n
ee
d
s
n
ea
r
ly
h
alf
th
e
n
u
m
b
er
o
f
ce
lls
r
e
q
u
ir
e
d
f
o
r
th
e
e
q
u
iv
alen
t
MM
C
.
T
h
is
is
b
ec
au
s
e
th
e
n
ec
ess
ar
y
v
o
lt
ag
e
r
atin
g
o
f
ea
c
h
co
n
v
er
ter
b
r
an
ch
is
s
h
ar
ed
b
e
twee
n
th
e
s
witch
an
d
wav
e
-
s
h
ap
in
g
cir
cu
it.
I
n
ad
d
itio
n
,
s
i
n
ce
th
e
f
u
ll
b
r
id
g
e
ce
lls
ar
e
u
s
ed
in
th
is
to
p
o
lo
g
y
it c
an
s
u
p
p
r
ess
th
e
f
au
lt c
u
r
r
en
ts
.
A
p
ar
allel
to
p
o
lo
g
y
u
s
es a
n
H
-
b
r
id
g
e
in
ea
ch
p
h
ase
co
n
n
ec
te
d
in
p
ar
allel
with
a
wav
e
s
h
ap
i
n
g
cir
cu
it
th
at
co
n
s
is
ts
o
f
h
alf
b
r
id
g
e
s
u
b
m
o
d
u
les.
Un
lik
e
th
e
n
o
r
m
al
m
u
lti
-
lev
el
co
n
v
er
te
r
,
in
th
e
p
ar
allel
co
n
f
ig
u
r
atio
n
t
h
er
e
is
n
o
b
ala
n
cin
g
c
u
r
r
en
t
f
lo
w
s
in
ce
f
r
o
m
th
e
DC
s
id
e
it
is
s
ee
n
th
at
th
e
th
r
ee
p
h
ases
ar
e
co
n
n
ec
ted
in
s
er
ies.
Mo
r
e
o
v
e
r
,
th
e
n
u
m
b
er
o
f
s
u
b
m
o
d
u
le
s
is
r
ed
u
ce
d
b
y
alm
o
s
t
2
5
%
i
n
co
m
p
ar
is
o
n
with
n
o
r
m
al
m
u
lti
-
lev
el
b
ec
a
u
s
e
th
e
wav
e
s
h
ap
in
g
cir
cu
it
is
p
lac
ed
o
u
ts
id
e
th
e
m
ain
cir
c
u
it
p
at
h
.
As
th
e
n
u
m
b
er
o
f
ce
lls
in
th
e
wav
e
s
h
ap
in
g
cir
c
u
it
in
cr
ea
s
es
th
e
h
ar
m
o
n
ic
co
n
ten
t
in
t
h
e
AC
v
o
lta
g
e
is
m
i
n
im
ized
.
Ho
wev
e
r
,
th
e
DC
o
u
tp
u
t
v
o
ltag
e
h
as
a
s
i
g
n
if
ican
t
co
m
p
o
n
en
t
o
f
6
th
h
ar
m
o
n
ic
an
d
th
at
ca
n
b
e
r
em
o
v
e
d
b
y
u
s
in
g
p
ass
iv
e
f
ilter
s
.
3
.
1
.
Co
ntr
o
l o
f
H
VDC
co
nv
er
t
er
s
T
h
e
co
n
tr
o
l
s
y
s
tem
o
f
t
h
e
h
y
b
r
id
L
C
C
HVDC
s
y
s
tem
is
m
eticu
lo
u
s
ly
d
esig
n
e
d
to
m
ai
n
tain
s
tab
le
DC
cu
r
r
en
t
an
d
v
o
ltag
e
.
T
h
is
i
s
ac
h
iev
ed
th
r
o
u
g
h
a
p
o
le
-
co
n
tr
o
l
s
tr
ateg
y
th
at
d
y
n
am
ically
s
elec
ts
th
e
o
p
tim
al
co
n
tr
o
l
m
o
d
e
b
ased
o
n
th
e
lo
west
o
u
tp
u
t
f
r
o
m
th
e
co
n
s
tan
t
cu
r
r
en
t,
co
n
s
tan
t
v
o
ltag
e,
an
d
co
n
s
tan
t
ex
tin
ctio
n
an
g
le
co
n
tr
o
ls
,
as illu
s
tr
ated
in
Fig
u
r
e
2
.
Fig
u
r
e
2
p
r
esen
ts
tw
o
ess
en
tial PI
co
n
tr
o
l b
lo
ck
d
i
ag
r
am
s
.
T
h
e
u
p
p
er
d
iag
r
am
m
an
ag
es
DC
cu
r
r
en
t
co
n
tr
o
l,
wh
ile
th
e
l
o
wer
o
n
e
g
o
v
er
n
s
th
e
ex
ti
n
ctio
n
a
n
g
le
c
o
n
tr
o
l.
A
s
elec
tio
n
m
ec
h
an
is
m
,
n
o
t
d
e
p
icted
in
th
e
f
ig
u
r
e,
d
eter
m
in
es
wh
ich
o
f
t
h
e
two
f
ir
in
g
an
g
le
co
m
m
an
d
s
s
h
o
u
ld
b
e
im
p
lem
en
ted
,
c
h
o
o
s
in
g
t
h
e
o
n
e
with
th
e
s
m
aller
an
g
le.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
2
9
7
-
1
3
2
1
1304
Ad
d
itio
n
ally
,
a
v
o
ltag
e
d
ep
en
d
en
t
cu
r
r
e
n
t
lim
it
b
lo
ck
is
in
co
r
p
o
r
ate
d
to
r
ed
u
ce
th
e
cu
r
r
e
n
t
o
u
tp
u
t
if
th
e
DC
v
o
ltag
e
d
r
o
p
s
b
elo
w
a
ce
r
tain
th
r
esh
o
ld
.
T
y
p
ically
,
t
h
e
in
v
e
r
ter
o
p
er
ates
i
n
c
o
n
s
tan
t
ex
tin
ctio
n
a
n
g
le
m
o
d
e,
wh
ile
t
h
e
r
ec
tifie
r
f
u
n
ct
io
n
s
in
co
n
s
tan
t
cu
r
r
e
n
t
m
o
d
e.
Du
r
in
g
t
r
an
s
itio
n
s
b
etwe
en
th
ese
co
n
tr
o
l
m
o
d
es,
a
cu
r
r
en
t
e
r
r
o
r
s
ig
n
al
ad
ju
s
t
s
th
e
ex
tin
ctio
n
a
n
g
le
r
ef
er
e
n
ce
.
T
h
is
cu
r
r
en
t
s
ig
n
al,
wh
ich
f
ee
d
s
in
to
th
e
ex
tin
ctio
n
an
g
le
c
o
n
tr
o
l
d
iag
r
am
,
o
r
ig
i
n
ates
f
r
o
m
th
e
p
o
wer
er
r
o
r
s
ig
n
al
p
r
o
d
u
ce
d
b
y
th
e
cu
r
r
en
t
c
o
n
tr
o
l
b
lo
ck
.
T
h
e
p
r
ec
is
e
co
n
tr
o
l
o
f
th
e
ex
ti
n
ctio
n
an
g
le
is
cr
u
cial
to
p
r
e
v
en
t
co
m
m
u
tatio
n
f
ail
u
r
es.
Su
ch
f
ailu
r
es
o
cc
u
r
w
h
en
t
h
e
c
o
m
m
u
tatio
n
p
r
o
ce
s
s
is
n
o
t
co
m
p
leted
with
in
th
e
r
eq
u
ir
e
d
tim
e
f
r
am
e
.
I
t
is
p
o
ten
tiall
y
lead
in
g
to
th
y
r
is
to
r
m
alf
u
n
ctio
n
s
b
y
r
etu
r
n
in
g
to
a
f
o
r
war
d
-
b
iased
s
tate
p
r
em
atu
r
ely
d
u
r
in
g
in
v
er
ter
o
p
er
atio
n
.
Fig
u
r
e
2
.
C
o
n
tr
o
l b
lo
c
k
s
f
o
r
L
C
C
c
o
n
v
er
ter
s
On
th
e
o
th
er
h
a
n
d
,
th
e
c
o
n
tr
o
l
o
f
a
VSC
HVDC
s
h
o
u
ld
f
u
lf
ill
th
e
p
u
r
p
o
s
es
o
f
co
n
tr
o
llin
g
th
e
tr
an
s
f
er
r
ed
p
o
wer
an
d
th
e
in
d
ep
en
d
e
n
t
co
n
tr
o
l
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
.
I
n
th
e
l
iter
atu
r
e,
th
er
e
ar
e
d
if
f
er
en
t
c
o
n
tr
o
l
m
eth
o
d
s
f
o
r
th
e
co
n
tr
o
l
o
f
VSC
-
HVDC.
T
wo
k
n
o
w
n
s
tr
ateg
ies
f
o
r
co
n
tr
o
l
o
f
VSC
ar
e
th
e
d
ir
ec
t
p
o
wer
c
o
n
tr
o
l
(
DPC
)
m
eth
o
d
an
d
th
e
v
ec
to
r
co
n
tr
o
l
m
eth
o
d
.
T
h
e
b
asic
co
n
tr
o
l
p
r
in
cip
le
o
f
DPC
is
b
ased
o
n
th
e
i
n
s
tan
tan
eo
u
s
a
ctiv
e
an
d
r
ea
ctiv
e
p
o
wer
co
n
tr
o
l
lo
o
p
s
.
I
n
DPC
,
b
ased
o
n
th
e
in
s
tan
tan
eo
u
s
d
if
f
er
en
ce
s
b
etwe
en
co
m
m
a
n
d
ed
an
d
r
ea
ctiv
e
p
o
wer
,
a
s
wi
tch
in
g
tab
le
s
elec
ts
th
e
co
n
v
e
r
ter
s
witch
in
g
s
tate
s
as
a
r
esu
lt,
th
e
in
ter
n
al
c
u
r
r
en
t
lo
o
p
s
an
d
PW
M
m
o
d
u
la
to
r
b
lo
ck
ar
e
n
o
t
r
eq
u
ir
ed
.
Var
iab
le
s
witch
in
g
f
r
eq
u
e
n
cy
a
n
d
t
h
e
n
ee
d
f
o
r
f
a
s
t
co
n
v
er
s
io
n
an
d
co
m
p
u
tatio
n
ar
e
s
o
m
e
th
is
m
eth
o
d
'
s
d
is
ad
v
an
tag
es
th
at
lim
it
its
u
s
e
[
3
3
]
,
[
3
4
]
.
T
h
e
co
n
t
r
o
l
s
tr
ateg
y
u
tili
ze
s
f
ield
-
o
r
ien
ted
v
ec
to
r
co
n
t
r
o
l,
e
n
ab
lin
g
t
h
e
in
d
e
p
en
d
e
n
t
m
a
n
a
g
em
en
t
o
f
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
wer
.
T
h
is
s
ep
ar
atio
n
is
ess
en
tial
f
o
r
th
e
p
r
ec
is
e
r
eg
u
latio
n
o
f
th
ese
p
o
wer
co
m
p
o
n
e
n
ts
,
en
s
u
r
in
g
ef
f
icien
t
an
d
ad
ap
ta
b
le
o
p
e
r
atio
n
o
f
th
e
VSC
.
T
h
e
co
n
tr
o
l
s
y
s
tem
tr
a
n
s
f
o
r
m
s
t
h
r
ee
-
p
h
ase
cu
r
r
e
n
ts
an
d
v
o
ltag
es
in
t
o
a
two
-
ax
is
d
-
q
r
ef
er
e
n
ce
f
r
am
e
th
at
r
o
tat
es
s
y
n
ch
r
o
n
o
u
s
ly
with
th
e
A
C
s
y
s
tem
f
r
eq
u
e
n
cy
,
s
im
p
lify
in
g
th
e
co
n
tr
o
l
o
f
A
C
q
u
an
titi
es
as
th
ey
b
ec
o
m
e
DC
q
u
an
titi
es
in
th
is
f
r
am
e.
T
h
e
co
n
tr
o
l
s
ch
em
e
co
m
p
r
is
es two
p
r
im
ar
y
co
n
t
r
o
ller
s
: th
e
cu
r
r
en
t c
o
n
tr
o
ller
a
n
d
th
e
DC
-
lin
k
v
o
lta
g
e
co
n
tr
o
ller
.
C
u
r
r
en
t
co
n
tr
o
l lo
o
p
:
T
h
is
in
n
er
lo
o
p
f
u
n
ctio
n
s
in
th
e
s
y
n
ch
r
o
n
o
u
s
r
ef
er
e
n
ce
f
r
am
e,
tr
an
s
f
o
r
m
in
g
th
e
th
r
ee
-
p
h
ase
AC
cu
r
r
en
ts
in
to
two
o
r
th
o
g
o
n
al
co
m
p
o
n
en
ts
(
d
an
d
q
ax
es).
T
h
is
co
n
v
er
s
io
n
s
im
p
lifie
s
co
n
tr
o
l
b
y
m
a
k
in
g
th
ese
c
o
m
p
o
n
en
ts
DC
s
ig
n
als
u
n
d
er
b
alan
ce
d
c
o
n
d
itio
n
s
.
T
h
e
PI
co
n
tr
o
ller
s
in
th
is
lo
o
p
g
u
ar
an
tee
ze
r
o
s
tead
y
-
s
tate
er
r
o
r
a
n
d
r
o
b
u
s
t
p
er
f
o
r
m
an
ce
.
T
h
e
y
m
an
a
g
e
th
e
d
-
ax
is
cu
r
r
en
t,
r
ep
r
ese
n
tin
g
ac
tiv
e
p
o
wer
,
an
d
th
e
q
-
a
x
is
cu
r
r
en
t,
r
e
p
r
esen
tin
g
r
ea
ctiv
e
p
o
wer
.
T
o
ac
h
iev
e
d
ec
o
u
p
led
c
o
n
tr
o
l,
f
ee
d
-
f
o
r
war
d
co
m
p
en
s
atio
n
is
u
s
ed
to
co
u
n
ter
ac
t
th
e
c
r
o
s
s
-
co
u
p
lin
g
ter
m
s
r
esu
ltin
g
f
r
o
m
th
e
in
d
u
ctiv
e
n
atu
r
e
o
f
th
e
AC
s
y
s
tem
,
allo
win
g
in
d
ep
e
n
d
en
t
co
n
tr
o
l o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
.
T
h
e
m
ath
em
atica
l
r
ep
r
esen
tatio
n
o
f
t
h
e
co
n
v
er
ter
'
s
th
r
ee
-
p
h
ase
cu
r
r
en
ts
an
d
v
o
ltag
es
in
a
2
-
ax
is
d
-
q
r
ef
er
en
ce
f
r
am
e,
r
o
tatin
g
at
th
e
AC
f
r
eq
u
en
cy
,
ω
,
ca
n
b
e
d
escr
ib
ed
as
(
1
)
an
d
(
2
)
:
=
−
+
−
,
(
1
)
=
−
+
−
,
(
2
)
h
er
e,
an
d
ar
e
th
e
d
-
ax
is
an
d
q
-
ax
is
v
o
ltag
es,
an
d
ar
e
th
e
cu
r
r
e
n
ts
in
th
e
an
d
ax
es,
an
d
r
ep
r
esen
t r
esis
tan
ce
an
d
in
d
u
c
tan
ce
,
an
d
,
an
d
,
ar
e
th
e
c
o
n
v
e
r
ter
v
o
ltag
es in
th
e
-
f
r
am
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Mo
d
ellin
g
a
n
d
co
n
tr
o
l o
f LC
L v
o
lta
g
e
s
o
u
r
ce
co
n
ve
r
ter
-
b
a
s
ed
h
yb
r
id
…
(
Ma
h
mo
o
d
S
a
a
d
eh
)
1305
T
h
e
p
o
wer
b
alan
ce
b
etwe
en
th
e
AC
in
p
u
t a
n
d
DC
o
u
tp
u
t is g
iv
en
b
y
(
3
)
:
=
3
2
(
+
)
=
(
3
)
wh
er
e
an
d
ar
e
th
e
DC
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
e
n
t,
r
esp
ec
ti
v
ely
.
T
h
e
co
n
tr
o
l
s
y
s
tem
d
ec
o
u
p
les
an
d
b
y
co
m
p
en
s
atin
g
f
o
r
th
e
ter
m
s
an
d
th
r
o
u
g
h
f
ee
d
-
f
o
r
wa
r
d
c
o
n
tr
o
l.
DC
v
o
ltag
e
co
n
tr
o
l
lo
o
p
:
T
h
is
o
u
ter
lo
o
p
r
eg
u
lates
th
e
DC
lin
k
v
o
ltag
e
to
b
alan
ce
th
e
p
o
wer
b
etwe
en
th
e
DC
an
d
A
C
s
id
e
s
.
I
t
g
en
er
ates
r
ef
er
en
ce
s
ig
n
als
f
o
r
th
e
cu
r
r
en
t
co
n
t
r
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l
lo
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p
b
ased
o
n
th
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d
esire
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DC
v
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ltag
e
an
d
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ates
at
a
s
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wer
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y
n
am
ic
r
esp
o
n
s
e
th
an
th
e
cu
r
r
e
n
t
co
n
tr
o
l
lo
o
p
.
T
h
e
DC
v
o
ltag
e
co
n
tr
o
ller
e
n
s
u
r
es st
ab
le
p
o
we
r
f
lo
w
b
etwe
en
t
h
e
VSC
an
d
th
e
co
n
n
ec
ted
g
r
i
d
o
r
lo
ad
.
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h
e
DC
lin
k
v
o
ltag
e
d
y
n
a
m
ics ca
n
b
e
e
x
p
r
ess
ed
as:
=
−
(
4
)
wh
er
e
is
th
e
c
u
r
r
en
t
o
n
th
e
D
C
s
id
e
an
d
is
th
e
lo
ad
cu
r
r
en
t.
T
h
e
m
in
im
u
m
r
e
q
u
ir
ed
DC
-
s
id
e
v
o
ltag
e
is
d
eter
m
in
ed
b
y
(
5
)
:
,
=
2
∗
√
2
3
,
=
2
∗
,
ℎ
(
5
)
wh
er
e
,
is
th
e
lin
e
-
to
-
lin
e
R
M
S
v
o
ltag
e
an
d
,
ℎ
is
th
e
AC
s
id
e
v
o
ltag
e
p
ea
k
.
T
h
e
r
ef
er
en
ce
v
alu
e
f
o
r
I
d
is
ca
lcu
lated
u
s
in
g
f
ee
d
-
f
o
r
war
d
ter
m
s
to
ac
cu
r
ately
co
m
p
en
s
ate
f
o
r
l
o
ad
v
a
r
iatio
n
s
.
,
=
3
2
∗
+
(
6
)
T
h
is
h
ier
ar
ch
ical
co
n
tr
o
l
s
tr
ateg
y
,
with
f
aster
in
n
er
c
u
r
r
en
t
co
n
tr
o
l
an
d
s
lo
wer
o
u
ter
v
o
ltag
e
co
n
tr
o
l,
o
p
tim
izes th
e
s
y
s
tem
'
s
d
y
n
am
ic
r
esp
o
n
s
e
an
d
s
tab
ilit
y
.
Dis
cr
ep
an
cies
in
th
e
VSC
's
c
ap
ac
ito
r
v
o
ltag
e
(
)
,
ter
m
in
al
v
o
ltag
e
m
is
m
atch
,
an
d
th
e
d
ir
ec
t
an
d
q
u
ad
r
atu
r
e
ax
is
co
m
p
o
n
en
ts
o
f
v
o
ltag
e
g
e
n
er
ate
th
e
VSC
's
m
ag
n
itu
d
e
an
d
an
g
le
c
o
n
tr
o
lli
n
g
s
ig
n
als.
T
h
e
-
tr
an
s
f
o
r
m
atio
n
s
im
p
lifie
s
th
e
th
r
ee
AC
q
u
an
titi
es
to
two
DC
q
u
an
titi
es.
Vo
ltag
es
an
d
ar
e
d
eter
m
in
ed
u
s
in
g
d
an
d
q
er
r
o
r
s
t
h
r
o
u
g
h
a
d
ec
o
u
p
led
co
n
t
r
o
ller
b
lo
ck
.
T
h
e
m
o
d
u
latio
n
in
d
ex
m
ag
n
it
u
d
e
(
m
)
an
d
p
h
ase
(
θ)
s
ig
n
al
ar
e
th
en
ca
lcu
lated
.
A
p
h
ase
-
lo
ck
ed
lo
o
p
(
PLL
)
s
y
n
ch
r
o
n
izes
with
th
e
AC
n
et
wo
r
k
to
p
r
o
d
u
ce
th
e
f
ir
in
g
p
u
ls
es f
o
r
th
e
I
GB
T
s
in
th
e
VSC
.
Fig
u
r
e
3
illu
s
tr
ates th
e
v
ec
to
r
c
o
n
tr
o
l p
r
in
cip
le
[
3
3
]
.
Fig
u
r
e
3
.
Vec
to
r
co
n
tr
o
l p
r
i
n
cip
le
[
3
3
]
4.
M
E
T
H
O
D
I
n
th
is
s
ec
tio
n
,
s
y
s
tem
lay
o
u
t
an
d
m
o
d
els
ar
e
p
r
esen
ted
.
Deta
ils
o
f
im
p
lem
en
ted
VSC
co
n
tr
o
l
is
d
is
cu
s
s
ed
as
well.
Af
ter
th
at
m
o
r
e
d
etails
ar
e
p
r
esen
ted
a
b
o
u
t
co
n
v
er
ter
m
o
d
elin
g
an
d
d
esig
n
.
T
h
r
ee
-
lev
el
n
eu
tr
al
p
o
in
t
clam
p
e
d
co
n
v
er
t
er
,
h
y
b
r
id
th
r
ee
-
lev
el
b
r
id
g
e
c
o
n
v
er
ter
,
an
d
L
C
L
h
y
b
r
id
th
r
ee
-
lev
el
b
r
id
g
e
ar
e
in
clu
d
ed
in
th
e
co
n
v
er
ter
m
o
d
elin
g
an
d
d
esig
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
2
9
7
-
1
3
2
1
1306
T
h
e
co
m
p
u
tatio
n
al
co
m
p
lex
i
ty
o
f
th
e
MA
T
L
AB
/Si
m
u
lin
k
s
im
u
latio
n
s
u
s
ed
in
t
h
is
s
tu
d
y
is
s
tr
aig
h
tf
o
r
war
d
a
n
d
m
a
n
ag
ea
b
le.
Giv
en
th
e
s
tan
d
ar
d
n
atu
r
e
o
f
th
e
s
im
u
latio
n
s
,
wh
ich
f
o
cu
s
o
n
ev
alu
atin
g
t
h
e
p
er
f
o
r
m
an
ce
o
f
d
if
f
e
r
en
t
co
n
v
er
ter
to
p
o
lo
g
ies u
n
d
e
r
v
ar
io
u
s
o
p
er
atin
g
c
o
n
d
itio
n
s
,
th
e
co
m
p
u
tatio
n
al
d
em
an
d
s
r
em
ain
with
in
th
e
ca
p
ab
ilit
ies
o
f
ty
p
ical
MA
T
L
AB
/Si
m
u
lin
k
en
v
ir
o
n
m
e
n
ts
.
All
s
im
u
lated
to
p
o
lo
g
ies
th
e
th
r
ee
-
lev
el
n
eu
tr
al
p
o
in
t
clam
p
ed
co
n
v
er
ter
,
h
y
b
r
i
d
co
n
v
er
t
er
with
AC
s
id
e
ca
s
ca
d
ed
H
-
b
r
id
g
e
ce
lls
,
an
d
th
e
L
C
L
h
y
b
r
i
d
co
n
v
er
ter
s
im
u
la
tio
n
s
wer
e
all
e
f
f
icien
tly
e
x
e
cu
ted
o
n
s
tan
d
a
r
d
co
m
p
u
tatio
n
al
h
ar
d
war
e.
T
h
e
co
m
p
lex
ity
p
r
im
ar
ily
in
v
o
lv
e
s
b
asic
co
n
tr
o
l
alg
o
r
ith
m
s
a
n
d
s
tan
d
ar
d
s
im
u
latio
n
p
r
ac
tices,
wh
ich
d
o
n
o
t
n
ec
ess
itate
ad
v
an
ce
d
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
.
T
h
is
alig
n
s
with
co
m
m
o
n
p
r
ac
tices
in
p
o
wer
s
y
s
tem
s
im
u
latio
n
s
,
wh
er
e
MA
T
L
A
B
/Si
m
u
lin
k
is
wid
ely
u
s
ed
d
u
e
to
its
r
o
b
u
s
t
an
d
u
s
er
-
f
r
i
en
d
ly
i
n
ter
f
ac
e
f
o
r
m
o
d
elin
g
a
n
d
s
im
u
latio
n
o
f
elec
tr
ical
s
y
s
tem
s
.
4
.
1
.
Sy
s
t
e
m
la
y
o
ut
a
nd
m
o
d
el
A
two
ter
m
in
al
HVDC
lin
k
i
s
u
s
ed
to
in
ter
c
o
n
n
ec
t
two
H
VAC
s
y
s
tem
s
.
T
h
e
s
y
s
tem
is
m
o
d
el
is
p
r
esen
ted
Fig
u
r
e
4
.
I
n
th
is
s
y
s
tem
,
th
e
HVDC
lin
k
is
r
ep
r
esen
ted
b
y
a
2
0
0
MV
A
+/
-
1
0
0
k
V
VSC
-
HVDC
tr
an
s
m
is
s
io
n
lin
k
.
T
h
e
AC
s
y
s
tem
s
,
1
an
d
2
,
in
th
e
m
o
d
el
ar
e
4
0
0
k
V,
2
0
0
0
MV
A
AC
s
y
s
tem
s
.
T
h
ese
two
AC
s
y
s
tem
s
ar
e
d
em
o
n
s
tr
ated
b
y
L
-
R
eq
u
iv
alen
ts
at
f
u
n
d
a
m
en
tal
f
r
eq
u
e
n
cy
5
0
Hz.
I
n
o
r
d
er
to
tr
an
s
f
o
r
m
th
e
v
o
ltag
e
lev
el
to
a
s
u
itab
le
lev
el
f
o
r
th
e
co
n
v
er
ter
a
wy
e
g
r
o
u
n
d
ed
/
d
elta
tr
an
s
f
o
r
m
er
is
u
tili
ze
d
.
I
n
th
is
m
o
d
el
th
e
VSC
co
n
v
er
ter
s
u
s
ed
ar
e
t
h
r
ee
-
lev
el
n
eu
tr
al
p
o
in
t
clam
p
ed
co
n
v
er
ter
s
u
s
in
g
I
GB
T
/d
io
d
es.
T
h
e
co
n
v
er
te
r
s
ar
e
co
n
n
ec
te
d
th
r
o
u
g
h
a
1
0
0
k
m
ca
b
le
(
2
p
i sectio
n
s
)
.
Fig
u
r
e
4
.
VSC
-
HVDC tr
an
s
m
i
s
s
io
n
s
y
s
tem
m
o
d
el
T
h
e
two
m
ain
tr
a
n
s
m
is
s
io
n
lin
e
m
o
d
els
u
tili
ze
d
in
tim
e
d
o
m
ain
s
im
u
latio
n
s
ar
e
PI
s
ec
tio
n
s
lin
e
m
o
d
el
a
n
d
d
is
tr
ib
u
ted
p
ar
a
m
eter
s
lin
e
m
o
d
el.
I
n
a
PI
s
ec
tio
n
s
lin
e
m
o
d
el,
th
e
r
esis
tan
ce
,
in
d
u
ctan
ce
,
an
d
ca
p
ac
itan
ce
ar
e
u
n
if
o
r
m
ly
d
is
tr
ib
u
ted
alo
n
g
t
h
e
lin
e.
An
ap
p
r
o
x
im
ate
m
o
d
el
o
f
th
e
d
is
tr
ib
u
ted
p
ar
am
eter
s
lin
e
is
o
b
tain
ed
b
y
ca
s
ca
d
in
g
s
ev
er
al
id
en
tical
PI
s
ec
tio
n
s
.
T
h
e
PI
s
ec
tio
n
s
lin
e
m
o
d
el
h
as
a
f
i
n
ite
n
u
m
b
er
o
f
s
ec
tio
n
s
.
T
h
e
n
u
m
b
er
o
f
s
ec
tio
n
s
to
b
e
u
s
ed
d
ep
en
d
s
o
n
th
e
f
r
eq
u
en
c
y
r
an
g
e
to
b
e
r
ep
r
esen
ted
.
Alth
o
u
g
h
f
o
r
f
r
e
q
u
en
c
y
d
o
m
a
in
s
tu
d
ies
PI
s
ec
tio
n
s
lin
e
m
o
d
els
ca
n
b
e
p
r
ec
is
e,
in
th
e
tim
e
d
o
m
ain
,
p
ar
ticu
lar
ly
f
o
r
lo
n
g
lin
es
(
wh
er
e
p
r
o
p
ag
atio
n
t
r
av
el
tim
e
s
p
an
s
m
an
y
tim
e
s
tep
s
)
,
ac
cu
r
ac
y
is
co
m
p
r
o
m
is
ed
.
T
h
e
ca
lcu
latio
n
s
tep
tim
e
o
f
an
y
s
im
u
latio
n
s
h
o
u
l
d
b
e
less
th
an
th
e
p
r
o
p
ag
atio
n
tim
e.
PI
lin
e
s
ec
tio
n
s
ar
e
m
o
r
e
u
s
ef
u
l
f
o
r
v
er
y
s
h
o
r
t
tr
a
n
s
m
is
s
io
n
lin
es
wh
er
e
th
e
p
r
o
p
ag
atio
n
tr
a
v
el
tim
e
is
less
th
an
s
im
u
latio
n
s
tep
tim
e.
Fo
r
s
tu
d
y
in
g
in
ter
ac
tio
n
s
b
etwe
en
HVA
C
an
d
HVD
C
s
y
s
tem
,
a
s
im
p
le
PI
s
ec
t
io
n
s
li
n
e
m
o
d
el
wo
u
ld
b
e
in
s
u
f
f
icien
t
[
3
5
]
.
Un
lik
e
th
e
PI
s
ec
tio
n
s
lin
e
m
o
d
el,
th
e
d
is
tr
ib
u
ted
p
ar
am
ete
r
s
lin
e
m
o
d
el
ef
f
ec
tiv
ely
h
as
an
in
f
in
ite
n
u
m
b
er
o
f
s
ec
tio
n
s
.
T
h
e
d
is
tr
ib
u
ted
tr
an
s
m
is
s
io
n
lin
e
m
o
d
el
o
p
er
ates
o
n
th
e
p
r
in
cip
le
o
f
t
r
av
elin
g
wav
es.
A
v
o
ltag
e
d
is
tu
r
b
an
ce
p
r
o
g
r
ess
es
alo
n
g
a
co
n
d
u
cto
r
at
its
p
r
o
p
ag
atio
n
s
p
ee
d
(
clo
s
e
to
th
e
s
p
ee
d
o
f
lig
h
t)
u
n
til
it
r
ef
lects
b
ac
k
at
th
e
lin
e'
s
en
d
.
An
y
s
ig
n
al
i
n
tr
o
d
u
ce
d
at
t
h
e
s
en
d
in
g
e
n
d
will
ar
r
iv
e
at
th
e
r
ec
eiv
in
g
en
d
f
o
llo
win
g
a
d
elay
,
p
o
s
s
ib
ly
with
s
o
m
e
m
in
o
r
alter
atio
n
s
.
T
h
e
d
is
tr
ib
u
ted
p
ar
am
eter
s
li
n
e
m
o
d
el
u
tili
ze
s
B
er
g
er
o
n
'
s
tr
av
elin
g
wav
e
m
eth
o
d
.
T
h
is
ap
p
r
o
ac
h
em
p
lo
y
s
a
tr
a
v
elin
g
wav
e
lin
e
m
o
d
el
ch
ar
ac
ter
ized
b
y
d
is
tr
ib
u
ted
L
C
p
ar
am
eter
s
an
d
in
teg
r
ated
lu
m
p
ed
r
esis
tan
ce
.
I
t
g
en
er
ates
a
co
n
s
t
an
t
s
u
r
g
e
im
p
ed
a
n
ce
an
d
ess
en
tially
o
p
er
ates
as
a
s
in
g
le
-
f
r
e
q
u
en
cy
m
o
d
el.
T
h
e
B
er
g
er
o
n
m
eth
o
d
is
s
u
itab
le
f
o
r
f
u
n
d
am
en
tal
f
r
e
q
u
en
c
y
im
p
ed
an
ce
s
tu
d
ies
ac
r
o
s
s
v
ar
io
u
s
ap
p
licatio
n
s
.
I
n
th
e
B
er
g
er
o
n
Mo
d
el,
th
e
in
d
u
cta
n
ce
an
d
ca
p
ac
itan
ce
co
m
p
o
n
en
ts
ar
e
d
is
tr
ib
u
ted
,
u
n
lik
e
in
PI
s
ec
tio
n
s
wh
er
e
th
ese
p
ar
am
eter
s
ar
e
lu
m
p
ed
.
E
f
f
ec
tiv
ely
,
it si
m
u
lates h
av
in
g
an
in
f
i
n
ite
n
u
m
b
er
o
f
PI
s
ec
tio
n
s
[
3
6
]
.
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