In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
4
1
0
~1
4
1
8
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1410-1418
1410
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
A high voltage direct curre
nt transmission system:
natur
a
l and selective
harmonic cancellation
Azi
z
a
Ben
a
boud
1
, Alfre
d R
u
fer
2
1
E
RN,
Roy
a
l Navy
S
cho
o
l
,
B
oulev
ard
S
o
ur
J
d
i
d,
C
as
abl
a
nca,
M
oroc
co
2
EP
F
L
, Swiss Federal
Ins
t
it
u
t
e o
f
Techn
o
l
o
g
y
L
a
u
s
a
n
n
e,
Lau
sanne,
S
witzerl
a
nd
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Oct
2
3
,
2
018
Re
vise
d Jan
2,
201
9
Ac
ce
p
t
ed
M
ar 2
4
,
2
019
Th
is
s
t
u
d
y
f
o
c
u
s
ed
o
n
t
h
e
s
p
eci
a
l
H
igh
Volt
age
D
i
rect
C
urrent
t
e
c
hn
olog
y.
Th
e
cont
ext
is
g
iv
en
b
y
com
b
inin
g
t
w
o
o
r
i
g
i
n
a
l
s
o
l
ut
i
o
ns
;
t
h
e
f
ir
st
s
olu
t
io
n,
us
in
g
a
n
a
tu
ral
harm
on
ic
can
c
e
ll
ati
o
n
,
c
o
n
s
i
sts
t
o
c
on
nect
i
n
s
eries
two
clas
si
ca
l
f
r
eq
uen
c
y
i
n
v
e
rters
which
are
coup
led
t
o
t
he
g
ri
d
thr
o
ugh
a
s
p
ecifi
c
tran
s
f
o
r
m
e
r
co
nnect
io
n.
O
n
th
e
ot
her
h
a
n
d
,
t
h
e
s
econ
d
s
o
l
u
t
i
o
n
i
s
ach
ieved
by
u
s
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n
g
t
h
r
ee,
f
iv
e
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m
ore
l
e
ve
l
conv
erters
i
n
s
q
u
a
re
w
av
e
m
o
du
la
t
i
o
n
,
in
order
to
e
liminat
e
some
s
e
l
ect
ive
h
a
rmon
ic
s
by
o
p
t
i
m
iz
in
g
a
sw
i
t
c
hing
a
ng
le
.
Th
e
s
i
m
u
l
a
ti
on
a
nd
e
x
p
e
rim
e
n
t
al
r
esu
lts
i
ndicat
e
t
h
at
t
h
e
p
ro
p
o
sed
Hi
gh
Vo
lt
age
Direct
C
u
rrent
t
ran
s
m
i
ssi
on
s
y
stems
off
e
r
hi
gh
effi
c
i
e
n
cy,
unity
po
wer
f
act
or
a
n
d
b
etter
current
a
nd
v
o
l
t
a
ge
q
ual
i
t
y
w
it
h
f
e
w
e
r
harm
on
ic.
K
eyw
ord
s
:
HV
DC
T
ra
ns
m
i
s
s
ion
Square
W
ave
M
odulation
NP
C t
h
ree l
e
vel con
v
erters
NP
C fi
ve l
evel
c
on
verters
Tran
sf
orm
e
r co
n
n
ectio
n
S
w
itchi
ng
ang
l
e.
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
A
z
iza
Bena
bou
d
Roya
l
N
a
vy
S
c
hoo
l,
Bou
l
e
v
a
r
d S
o
u
r
Jdid,
C
a
s
ab
la
nca
,
M
or
occ
o
A
z
iza
.
be
na
bo
u
d
@
g
ma
il.
com
1.
I
N
TR
OD
U
C
TI
O
N
P
o
w
e
r
e
l
e
c
tro
n
ic
t
e
c
h
n
o
lo
g
y
i
s
f
unda
me
nta
l
t
o
rene
w
a
ble
e
n
erg
y
sys
t
em
s.
M
a
ny
rene
w
a
ble
resour
ces
a
re
i
n
t
erm
itte
nt,
a
nd
w
ith
ou
t
po
w
e
r
electr
o
n
i
c
s
w
e
co
u
l
d
n
o
t
r
e
gu
la
te
v
olta
ge
,
fre
que
n
c
y,
a
n
d
pow
er
out
pu
t
c
h
a
r
ac
t
e
ris
tics.
R
e
n
ew
a
b
l
e
s
our
ces,
such
a
s
sun
l
i
g
ht,
hy
dro
g
en,
an
d
w
i
n
d
e
ner
g
y,
r
e
qui
r
e
A
C-
D
C
con
ve
rsio
n
fol
l
ow
e
d
b
y
t
h
e
D
C
-A
C inver
t
e
r
to i
n
te
gr
ate
the
A
C gri
d
[
1].
In
t
hi
s
pa
pe
r
w
e
p
rese
n
t
a
s
p
e
c
i
a
l
H
igh
V
o
l
t
a
ge
D
i
r
ec
t
C
u
rr
en
t
tec
h
n
o
logy
.
It
c
onsist
s
on
the
flexible
exc
h
a
n
ge
o
f
p
o
w
e
r
be
tw
ee
n
tw
o
no
des
of
a
n
etw
o
rk
t
hro
u
gh
a
D
C
l
i
nk.
T
he
c
onve
rsi
on
from
A
C
t
o
D
C
a
n
d
vice
v
e
r
sa
i
s
a
c
hie
v
e
d
by
tw
o
c
l
ass
i
cal
f
r
e
q
u
enc
y
i
nver
t
e
r
s
in
a
se
ries
c
o
nnec
t
i
o
n.
I
n
order
t
o
t
ake
a
d
v
a
nta
g
e
o
f
n
a
t
u
r
al
h
a
r
mo
n
i
c
c
a
n
c
e
l
l
a
t
i
on
,
th
e
s
e
i
nvert
e
r
s
are
co
upl
ed
t
h
r
ou
gh
a
s
p
e
ci
fi
c
t
r
an
sforme
r
c
o
nn
ec
ti
on
,
a
n
d
t
h
ei
r cont
rol
si
g
n
al
s a
r
e
shi
f
te
d b
y
3
0
°
[
2]
.
In
a
ddition
t
he
t
ransform
ation
ra
ti
o
m
u
s
t
b
e
equal
f
o
r
the
firs
t
t
r
a
n
s
f
o
r
m
e
r
t
o
1
a
n
d
f
o
r
t
h
e
s
e
c
o
n
d
tra
n
sf
or
m
e
r t
o
√
3 [
3
]
.
On
t
he
o
t
h
e
r
h
a
nd,
a
c
ont
ro
l
m
e
th
od
i
s a
l
so
p
rop
o
s
ed
to
be
ne
f
i
t
fr
o
m
sel
e
ct
iv
e
h
a
rmo
n
i
c
c
a
n
cel
la
tio
n
by
us
ing
three,
f
ive
or
m
ulti-le
vel
c
onve
r
t
ers in
s
qu
are wave
m
odu
lat
i
o
n
[
4,
5
].
Th
i
s
p
ap
er
i
s
or
ga
niz
e
d
a
s
f
o
l
l
o
w
s
.
S
e
c
t
i
o
n
2
ci
te
s
s
o
m
e
r
ela
t
e
d
work;
sess
ion
3
l
i
s
t
s
the
advantage
s
of
HVD
C
tra
n
smi
s
sio
n
.
S
e
c
t
ion
4
d
e
sc
ri
be
s
the
p
r
opo
se
d
HV
DC
s
ys
te
m
an
d
show
s
ho
w
to
b
ene
f
i
t
f
r
o
m
n
a
t
u
ra
l
h
a
rmon
i
c
c
a
n
ce
l
l
a
ti
on
.
Se
ctio
n
5
p
r
o
poses
a
c
on
tr
ol
m
et
hod
t
o
be
ne
fi
t
f
r
o
m
s
e
l
e
c
tive
h
a
rmo
n
ic
ca
ncel
la
t
i
o
n
b
y
us
in
g
Mu
l
t
i
l
ev
e
l
N
P
C
i
nv
er
t
e
r
in
S
WM
,
an
d
Sect
i
on
6
p
ro
po
s
e
s
t
h
e
de
dic
a
t
e
d
c
o
n
t
r
o
l
stra
te
g
y
.
La
t
e
r
in
S
ec
t
i
on
7
,
si
m
u
la
ti
on
a
nd
e
x
p
e
ri
ment
al
r
es
ul
ts
a
re
p
re
se
nte
d
t
o
h
i
g
h
li
g
h
t
t
he
c
a
p
a
b
i
l
i
t
i
e
s
of
th
e
p
r
op
ose
d
HVDC
s
yste
ms.
Final
l
y
i
n
se
ct
i
o
n
8,
t
he
m
ai
n
conc
l
us
i
ons
o
f
ou
r
res
earch
w
or
k
as
w
e
l
l
a
s
a
d
i
s
c
u
s
si
o
n
o
f
th
ei
r
pot
e
n
ti
al
i
m
p
lica
t
i
o
ns
a
re h
ig
h
lig
ht
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
A
high
vo
l
t
a
g
e
di
rect
cur
r
en
t t
r
an
sm
i
s
s
i
on sy
stem
:
Na
t
u
r
a
l an
d
selec
t
ive
h
a
rm
o
n
i
c
…
(
A
ziza
Bena
b
o
u
d
)
1
411
2.
RELA
TED WORK
S
u
st
a
i
na
b
l
e
e
n
er
gy
ge
ner
a
ti
o
n
l
i
k
e
hydr
o,
w
i
n
d
a
n
d
su
n
w
i
l
l
b
e
in
t
e
gr
ate
d
i
n
t
o
p
o
w
e
r
ne
t
w
o
r
k
a
l
l
o
v
e
r
th
e
wo
r
l
d
a
s
p
res
e
nt
e
d
i
n
Fi
gu
re
1
.
Th
ey
a
r
e
n
o
r
ma
lly
not
l
o
ca
ted
c
l
o
s
e
t
o
t
he
c
onsum
p
tio
n.
I
t
wil
l
b
e
ve
r
y
i
mp
or
ta
nt
t
o
f
i
nd
ef
f
i
cie
n
t
w
a
y
s
t
o
tr
an
spor
t
lar
g
e
am
ou
n
t
s
of
e
l
e
ct
ri
ci
ty
l
on
g
di
st
an
ce
s.
T
o
d
a
y
,
HVDC
t
r
an
smi
s
si
o
n
see
m
s t
o
b
e t
h
e
be
st
sol
ut
i
o
n
of t
hi
s
p
r
obl
e
m
[
6]
.
F
i
gur
e
1.
P
ow
er
n
e
t
w
o
r
k
a
l
l
o
ver
t
h
e
w
o
r
l
d.
I
t
h
as
b
e
e
n
w
ide
l
y
d
o
cum
e
n
t
ed
i
n
t
h
e
his
t
o
r
y
o
f
t
he
i
nd
us
tr
ia
l
e
l
e
c
tric
i
t
y
t
hat
the
firs
t
c
o
mm
er
cial
el
ec
t
r
i
c
ity
g
ene
r
a
t
e
d
b
y
T
homas
A
l
v
a
E
d
i
s
o
n
was
di
rec
t
c
u
r
re
n
t
elec
t
r
ic
al
p
ow
er
.
A
l
so
i
n
18
8
2
w
he
n
t
h
e
tr
a
n
smiss
i
on
o
f
e
l
ec
t
r
ic
e
ner
gy
beg
a
n,
it
w
a
s
base
d
o
n
d
ir
ec
t
c
ur
r
e
nt
s
yste
m
s
[
7]
.
H
o
w
e
v
e
r
,
D
C
p
o
w
e
r
a
t
l
ow
vo
l
t
age
co
u
l
d no
t be
tra
n
s
m
itte
d o
v
er
lo
n
g
d
ista
nces.
I
n
1
8
8
7
,
N
i
ko
l
a
T
e
s
la
i
ntr
oduc
ed
a
s
yste
m
f
o
r
a
lte
r
n
a
t
i
ng
cur
r
e
nt
g
ener
at
or
s,
t
r
a
nsf
o
r
m
e
r
s,
m
otor
s,
wi
res
an
d
lig
ht
.
T
h
e
a
d
v
a
nt
ag
e
s
o
f
t
r
a
n
smit
ti
n
g
A
C
e
l
ectri
c
a
l
e
ne
r
g
y
o
v
e
r
l
on
g
dista
n
c
e
s
c
o
m
p
ar
e
d
t
o
D
C
tr
a
n
smiss
i
on
w
e
r
e
m
ade
c
l
e
a
r
in
t
hese
v
er
y
e
a
r
l
y
be
gi
n
n
i
n
g
s
.
D
u
r
i
n
g
t
he
d
e
c
a
de
o
f
1
9
30s,
m
e
r
c
ur
y
ar
c
r
ecti
f
ier
s
w
e
r
e
in
ven
t
e
d
a
n
d
D
C
t
r
a
nsmiss
ion
be
ga
n
to
b
e
c
o
n
s
i
d
er
ed
a
ga
in
a
s
an
o
pt
ion
of
t
r
a
nsmi
t
tin
g
e
l
e
c
t
r
i
ca
l
e
n
er
gy
,
bu
t
th
i
s
t
i
m
e
at
h
igh
vol
t
a
g
e
l
ev
el
s.
I
n
1
954
,
the
f
i
r
s
t
H
V
D
C
(
1
0
M
W)
t
r
a
nsmiss
i
on
sys
t
e
m
w
as
c
ommissi
o
n
e
d
i
n
G
ot
l
a
nd
[
8
]
.
S
i
n
c
e
t
h
e
19
60
s,
H
V
D
C
t
r
a
n
s
m
i
ssi
o
n
s
y
ste
m
i
s
now
a
m
atur
e
tec
h
n
ol
ogy
a
n
d
h
a
s
p
l
a
yed
a
v
i
t
a
l
pa
r
t
in
b
o
t
h
lo
n
g
d
i
s
ta
nc
e
tr
a
n
sm
i
s
si
on
a
nd
i
n
t
he
i
nte
r
con
n
ec
t
i
on
o
f
sy
stems.
I
n
1
9
7
0
HVDC
t
r
a
n
s
mission
h
a
d
a
r
e
vo
lu
tio
nar
y
c
ha
n
g
e
w
h
en
t
h
y
r
i
s
t
or
s
w
e
r
e
u
se
d
in
a
c
on
ver
t
e
r
f
or
t
he
f
ir
st
t
im
e,
t
her
e
a
r
e
u
se
d
f
o
r
dc
tr
a
n
smiss
i
on
a
nd
i
t
i
s
k
n
o
w
n
a
s
Cur
r
ent
S
our
ce
Co
n
v
e
r
ter
(CS
C
-
H
VDC)
[
9
],
[
1
0
]
.
A
ne
w
r
e
le
va
nt
s
tep
in
D
C
t
r
ansmiss
i
o
n
h
a
p
pe
ned
in
1
99
0s
w
he
n
t
h
e
I
n
s
u
l
at
ed
G
a
t
e
Bi
pol
ar
Tr
ansist
or
(
I
G
B
T
)
w
a
s
in
tr
o
duce
d
,
th
us
g
ivi
n
g
r
i
se
t
o
V
o
l
t
a
g
e
S
ou
rce
Co
nv
erter
(VS
C
-HVDC)
at
h
igh
vo
l
t
age
l
e
v
e
ls
[
1
1
]
.
T
his
la
st
v
er
si
on
c
o
u
l
d
b
e
r
e
a
lize
d
t
ha
nks
t
o
t
h
e
r
e
solu
t
i
o
n
o
f
t
h
e
p
r
ob
l
e
m
of
t
he
s
er
ie
s
c
o
n
n
ec
ti
o
n
o
f
I
G
BT’
s
,
a
l
so
d
ue
t
o
t
h
e
deve
lopm
en
t
of
t
he
i
r
s
o
c
a
lle
d
pr
ess-pac
k
v
ersi
o
n
,
ea
sily
i
nsert
a
ble
i
n
lar
g
e
c
o
nver
t
er
s
tac
k
s
[
12,
13]
.
V
S
C
t
e
ch
no
l
o
gy
a
l
low
s
c
o
n
t
r
o
l
l
i
n
g
a
c
t
i
ve
a
nd
r
e
a
c
t
i
ve
p
ow
er
i
n
d
epe
n
d
e
nt
l
y
w
i
t
h
out
a
ny
nee
d
s
f
o
r
e
x
t
r
a
c
o
m
p
e
n
s
a
ti
n
g
e
q
u
ipm
e
nt
;
an
d
br
i
n
gs
t
he
a
d
v
a
n
ta
ge
o
f
dec
o
u
p
l
ing
of
h
a
r
mo
ni
c
s
b
et
we
en
g
e
n
erat
o
r
s.
Ho
wev
e
r
k
nown
sy
st
ems
o
f
HVDC
u
se
t
wo
l
e
v
el
i
nv
er
t
e
r
techn
o
lo
gy
,
th
at
i
ntr
o
d
u
c
e
s
r
e
lat
i
v
e
l
y
hig
h
c
on
te
n
t
of har
mon
i
c
v
o
l
ta
ge
s an
d
curr
ent
s
[1
4
,
15].
I
m
por
ta
nt
r
ese
a
r
c
h ef
f
o
r
t
s w
e
r
e
d
o
n
e
to
c
a
n
c
e
l
som
e
h
ar
m
onic
s
o
r
t
o
r
ed
uc
e
th
e
h
a
rmon
i
c
s
di
st
o
r
t
i
on
of
o
u
t
pu
t
i
n
ver
t
e
r
v
o
l
t
a
ge
a
n
d
c
ur
r
e
nts,
t
h
i
s
sys
t
em
c
a
n
f
u
l
fi
l
l
t
h
e
r
e
qu
ir
e
m
e
n
t
s
o
f
t
h
e
o
u
t
p
ut
pow
e
r
q
ua
li
ty
,
bu
t
wi
t
h
a
l
imi
t
ed
v
a
l
ue
o
f
th
e
con
v
e
r
ters
e
ffi
c
i
e
n
cy
b
e
c
a
u
se
o
f
ver
y
h
ig
h
sw
itch
i
ng
l
o
sses
d
ue
t
o
t
h
e
hi
g
h
f
r
e
que
n
c
y
of
t
h
e
P
WM
t
e
c
h
n
i
que
n
or
ma
l
l
y
u
s
e
d
f
or
i
ts
c
on
t
r
ol
[
1
6
]
.
I
n
o
r
d
er
t
o
ta
k
e
a
dva
nta
g
e
o
f
n
at
ur
al
a
n
d
s
elec
ti
ve
h
a
r
mo
nic
c
a
nce
lla
tio
n
a
spec
i
a
l
H
i
gh
V
o
l
t
a
g
e
D
i
r
e
ct
C
ur
r
e
n
t
t
ec
hn
olo
gy
is
p
r
e
se
n
t
e
d
i
n
thi
s
p
ap
er
.
Th
e
c
o
n
t
e
xt
o
f
thi
s
c
on
tr
ibut
io
n
is
g
i
v
e
n
b
y
c
o
mbi
n
ing
t
w
o
or
ig
in
al
s
olu
t
io
ns
[
3,
4
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
4
1
0
–
1
418
1
412
3.
HVDC
O
R
H
VAC
T
RANS
MISSION
HVD
C
syste
m
a
llows
t
r
a
nsm
itt
ing
e
l
ec
trica
l
p
ower
f
rom
one
p
o
i
n
t
t
o
a
n
o
t
h
e
r
t
h
a
t
a
r
e
n
o
t
syn
c
hr
o
n
iz
ed
o
r
d
o
es
n
o
t
e
v
e
n
ha
ve
t
he
s
a
m
e
fr
eque
nc
y.
F
igur
e
2
r
epr
e
sen
t
s
a
sc
he
ma
t
i
c
dia
g
r
a
m
of
t
he
HVD
C
t
r
ansm
i
ssion system
.
Figu
re
2. Sc
h
e
m
a
tic
diagram
o
f
the
HVDC
t
ra
nsm
i
s
s
i
o
n s
y
s
t
em
S
o
m
e
a
d
v
a
n
t
a
g
e
s
o
f
H
D
V
C
t
r
a
n
s
m
i
s
s
i
o
n
s
y
s
t
e
m
a
r
e
:
N
o
l
i
m
i
t
s
i
n
t
ra
nsm
i
tte
d
d
i
st
an
c
e
,
t
h
is
i
s
v
a
li
d
for
sea
o
r
und
er
gr
oun
d
ca
ble
s
.
V
e
r
y
f
a
s
t
co
ntro
l
of
p
o
w
e
r
f
low
,
w
h
i
c
h
i
m
p
l
i
e
s
s
t
a
b
i
l
i
t
y
i
m
p
r
o
v
e
m
e
n
t
s
,
n
o
t
only
fo
r
t
h
e
H
V
D
C
l
i
n
k
b
ut
a
l
s
o
for
the
su
rro
und
in
g
AC
s
y
s
te
m.
D
i
re
ct
i
o
n
of
p
o
w
e
r
f
l
o
w
c
a
n
b
e
ch
ange
d
very
q
u
i
c
k
ly
;
an
d
o
n
ly
t
wo
c
on
duc
t
o
rs
a
re
n
e
e
de
d
(
o
r
e
v
e
n
one
c
on
duc
t
o
r
if
t
he
g
rou
nd
o
r
s
ea
i
s
used
a
s
r
e
tur
n
)
for
H
V
D
C
c
om
par
e
d
t
o
t
hr
ee
co
nd
uc
tor
s
f
or
a
lt
e
r
na
ti
n
g
c
u
rren
t
[
17
].
4.
S
Y
STEM AND METH
OD
D
E
S
CRIPTI
O
N
F
i
g
u
r
e
3
ill
us
trates
t
he
s
c
h
e
m
a
t
ic
d
iagra
m
o
f
t
h
e
pro
p
o
sed
HVD
C
s
yste
m
s
.
I
t
i
s
a
cch
i
e
ve
d
by
tw
o
f
r
e
que
n
c
y
inve
r
t
er
s
i
n
s
er
ie
s
con
n
e
c
tio
ns.
T
h
e
s
e
fr
eq
uenc
y
in
ve
r
t
e
r
s
ca
n
be
c
o
n
f
i
g
u
r
e
d
a
s
a
t
hr
ee,
f
ive
o
r
m
o
r
e
l
eve
l
i
n
v
e
r
t
er
s.
T
hey
ar
e
c
o
u
p
l
e
d
t
h
r
o
ug
h
a
spec
i
f
i
c
t
r
a
ns
f
o
r
m
er
c
onnec
tio
n,
a
n
d
t
he
ir
c
o
n
tr
o
l
s
i
g
n
a
l
s
are
sh
i
f
t
e
d
b
y
30°.
Fi
gure
3
.
Sc
h
em
a
t
ic
d
i
a
gram
of
th
e
pr
o
p
os
e
d
HVDC s
y
s
tem
with t
h
r
e
e
le
vel
inve
rter
s
F
i
gure
4
.
S
c
h
em
a
t
ic
d
i
a
gram
o
f
th
e
pro
p
o
s
e
d
t
ra
nsf
o
rm
er’s
c
o
n
ne
cti
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
A
high
vo
l
t
a
g
e
di
rect
cur
r
en
t t
r
an
sm
i
s
s
i
on sy
stem
:
Na
t
u
r
a
l an
d
selec
t
ive
h
a
rm
o
n
i
c
…
(
A
ziza
Bena
b
o
u
d
)
1
413
F
i
g
u
r
e
4
s
h
o
w
s
t
he
t
r
a
ns
for
m
er
’
s
c
on
nec
t
i
on.
V
’
p1
r
epr
e
sen
t
s
the
f
i
r
s
t
ou
tpu
t
i
nve
r
t
er
v
ol
t
a
ge
a
n
d
u’
p1
r
epr
e
sents
t
h
e
se
co
n
d
p
ha
se
t
o
p
h
a
s
e
out
pu
t
i
n
ve
r
t
er
v
o
lta
ge.
V
s1
a
nd
V
’
s1
a
r
e
r
espe
ctive
l
y
t
h
e
sec
o
ndar
y
vo
l
t
age
s
o
f
tr
a
n
sf
or
m
e
r
s
(
I)
a
nd
(
I
I
).
T
h
e
t
r
an
sf
o
r
ma
t
i
on
r
at
i
o
i
s
c
h
o
s
e
n
e
qual
fo
r
t
h
e
f
i
r
s
t
t
r
a
n
sf
or
m
e
r
to
1
a
nd
fo
r
th
e
s
econd
t
r
a
ns
fo
r
m
e
r
to
√
3
. Th
e
o
utp
u
t vo
ltag
e
is
g
i
v
e
n
acco
r
d
in
g
t
o
(
1
)
:
V
V
V
′
V
V
a
nd
V
′
′
√
wi
t
h
u
′
V
′
V
′
(
1
)
I
n
t
he
o
the
r
h
a
nd,
b
o
t
h
in
ver
t
e
r
s
ha
ve
t
he
s
a
m
e
sw
i
t
c
h
in
g
ang
l
e
δ
n
.
The
ou
tp
u
t
v
o
lta
ge
i
s
gi
ve
n
by
(
2
)
:
V
√
∑
U
co
s
co
s
1
15
°
cos
1
15
°
s
i
n
ωt
(
2
)
V
i
s
r
e
pr
esente
d
by
m
u
lti
p
lic
at
i
o
n
of
t
w
o
t
er
m
s
w
hi
c
h
d
e
p
end
o
n
the
ha
r
m
onic
υ
a
nd
on
the
sw
i
t
c
h
i
n
g
an
gl
e
δ
n
.
It will be
e
qua
l
ze
ro whe
n o
n
e
of t
h
e
se
ter
ms is
nul
l
:
co
s
1
15
°
co
s
1
15
°
0
or
c
o
s
0
(
3
)
The
f
i
r
s
t t
e
r
m
o
f
(
3
)
is
v
e
r
i
f
ie
d an
d
c
a
n be equa
l to ze
r
o
w
h
en
: ν
6
12
n
∓1
and n
mus
t
be an
in
te
ger
,
o
t
h
e
r
w
i
se
calcu
la
t
e
d
if
υ
=
5
,
7,
17,
19,
29,
31,
…
.
.
T
h
e
s
e
harm
onics
a
re
n
atura
l
l
y
c
ance
l
l
e
d
.
V
c
o
n
t
a
i
n
s
t
he
f
u
nda
me
n
t
a
l
(
υ
=
1)
a
n
d
h
a
r
m
onic
s
num
ber
11,
1
3,
2
3,
.
.
.
O
n
e
or
t
w
o
o
f
th
ese
har
m
on
ics
c
a
n
b
e
c
a
nce
l
l
e
d
w
h
e
n
t
he
s
e
c
o
n
d
t
e
r
m
of
(
3)
i
s
ve
rif
i
e
d
.
This
p
oi
n
t
w
il
l
be
d
escr
i
b
ed
i
n
t
h
e
ne
xt
s
ec
t
i
on.
5.
M
U
L
T
I
LEVE
L
N
E
U
T
RAL
P
OINT CLA
MPED
I
NV
E
R
TER IN
SWM
5
.
1
.
T
h
ree lev
el
N
PC
i
n
v
ert
e
r in SWM
A
three
Leve
l
Neutra
l
P
o
in
t
C
l
am
pe
d
in
ve
rter
i
s
mos
t
ly
u
se
d
for
m
ed
i
u
m
and
h
i
gh
vol
t
a
ge
a
p
p
lica
tio
ns.
(a
)
(b
)
F
i
gur
e
5.
(
a): P
h
as
e
circu
i
t
di
a
g
ram o
f
a
3
lev
el
NP
C
in
v
e
rter
.
(b)
:
O
u
t
p
ut
v
o
l
ta
g
e
’s
w
av
e
f
o
r
m o
f
3
lev
el N
PC
i
n
v
e
r
t
e
r
F
i
g
u
r
e
5
(
a
)
s
h
o
w
s
t
h
e
c
i
r
c
u
i
t
o
f
t
h
e
N
e
u
t
r
a
l
P
o
i
n
t
C
l
a
m
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e
d
i
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t
er,
t
h
e
DC
s
id
e
i
s
c
o
n
n
e
ct
e
d
t
o
t
h
e
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e
ut
ra
l
poi
nt
b
e
t
ween
c
ap
a
c
i
t
o
rs
v
i
a
d
i
o
d
e
s
to
r
ea
ch
t
h
e
t
hi
rd
le
ve
l
in
t
he
o
u
t
p
u
t
v
o
l
tage.
[
18,
1
9]
.
F
i
g
u
r
e
5
(
b
)
show
s
an ou
t
put-
v
o
l
tage
’
s
w
a
v
e
f
or
m
of
a
thr
ee
-
l
eve
l
c
o
n
v
er
te
r
ope
r
a
te
d
i
n
s
quar
e
-
w
ave
m
o
de
.
I
n
th
is o
u
t
p
u
t
vo
lt
age
’
s wa
vefor
m
, δ
n
i
s
t
h
e
op
t
i
mize
d
sw
i
t
c
h
i
ng
an
g
l
e,
it
c
a
n
be
g
ive
n
b
y
(
4
)
:
U
νπ
U
cos
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
4
1
0
–
1
418
1
414
T
h
e
swit
ch
ing
an
g
l
e
δ
n
ca
n
be
s
elec
ted
to
e
l
i
m
inate
som
e
h
a
r
m
oni
c
s
.
F
o
r
exa
m
ple
,
t
he
1
1
th
har
m
on
ic
d
i
sa
pp
e
a
rs
w
hen
δ
n
=
8.
18
°,
o
r
the
1
3
th
h
ar
monic
d
i
sa
ppe
ar
s
w
h
e
n
δ
n
=
6
.
9
2
°
.
M
o
r
e
h
a
r
m
o
n
i
c
s
c
o
u
l
d
b
e
e
l
im
i
n
a
t
e
d
t
o
g
e
the
r
w
he
n
us
i
ng
f
i
ve
o
r
m
o
re
l
eve
l
i
n
v
er
ter
.
5.
2.
F
i
v
e
le
ve
l
N
P
C
in
vert
er
i
n
S
W
M
A
F
i
ve
L
e
v
el
N
e
u
tr
a
l
P
oint
C
l
a
mpe
d
i
n
v
e
r
ter
is
c
om
pose
d
by
8
sw
i
t
c
h
e
s
a
nd
con
n
ecte
d
t
o
neu
t
r
a
l
po
in
t
v
i
a
diode
s
as
i
l
l
u
str
a
t
e
d
in
f
i
g
ur
e
(
6
.
a
)
.
T
h
e
o
u
t
pu
t
v
o
l
t
a
ge’
s
w
ave
f
o
r
m
i
s
dr
ow
n
in
F
i
g
ur
e
(
6
.
b
)
.
I
n
this
w
a
ve
f
or
m,
δ
n1
a
nd
δ
n2
pr
e
s
e
n
t
sw
it
c
h
ing
a
n
g
l
e
s
w
h
i
c
h
c
a
n
b
e
c
h
osen
a
c
c
o
r
d
ing
to
(
5)
i
n
or
der
to
e
l
i
m
i
nate
f
o
r
e
x
am
pl
e
th
e
11th
an
d
th
e
13
t
h
h
ar
mon
i
c
s
t
o
g
e
t
h
e
r
.
U
co
s
1
1
c
o
s
1
1
0
U
co
s
1
3
c
o
s
1
3
0
(
5
)
Bo
t
h
1
1
th
a
n
d
1
3
th
h
arm
o
n
i
cs
c
an
b
e
el
imi
n
ate
d
w
he
n
δ
n1
a
n
d
δ
n2
a
re
s
e
l
ected
to
v
erify
(5
).
It
m
ean
s
δ
n1
=
1.
2
6
°
an
d
δ
n2
= 1
3
.8
5°.
O
t
her
o
p
ti
m
i
z
a
t
i
o
n
te
ch
n
i
q
u
e
ca
n
be
u
se
d
to
f
i
nd
t
h
e
bes
t
c
ombi
n
a
t
i
on
o
f
swi
t
c
hi
ng
a
ngl
es
t
o
re
du
ce
th
e
THD
[
6
].
(a
)
(b
)
Fig
u
re 6
.
(a)
:
P
has
e
c
ir
c
u
it d
ia
gr
a
m
of
a 5
lev
e
l
N
P
C in
verter
.
(
b
)
:
O
u
tp
ut
v
ol
t
a
ge
’s wa
v
ef
or
m of
5
lev
el
N
P
C
in
ver
t
e
r
6.
TH
E
PROP
OS
E
D
M
ET
HO
DE
T
O
CON
T
RO
L MULT
IL
EVEL N
P
C INVERTE
R
I
n
t
hi
s
sect
io
n
a
contr
o
l
s
t
r
a
t
e
gy
is
p
r
o
p
o
sed
for
t
h
r
e
e
,
f
ive
or
m
or
e
le
vel
N
e
u
t
r
a
l
P
o
i
n
t
Clam
ped
c
o
n
v
e
r
ter
,
c
ha
racte
r
i
z
ed
b
y
its
h
i
gh
e
f
fic
i
en
cy
due
t
o
the
use
of
s
quar
e
-
w
ave
oper
a
t
i
o
n
m
ode.
The
main
a
d
v
a
n
t
a
g
e of
t
his
m
ode
i
s
t
h
e
quasi
a
bsenc
e
of
s
w
i
t
c
hin
g
lo
sses
.
I
n
t
hi
s mo
de,
onl
y the
fr
equenc
y
ca
n
be
v
ar
ied
be
t
w
e
e
n
t
h
e
i
nput
a
nd
the
ou
tp
ut
v
o
lta
ge
s,
but
t
h
e
i
r
m
a
gnitu
des
a
re
n
ot
freel
y
c
o
ntro
llab
l
e.
A
v
o
l
tage
m
a
gnitude
a
da
ptat
io
n
ca
n
be
d
o
n
e
b
y
v
ar
y
i
n
g
t
he
D
C
lin
k
vo
lt
a
g
e
.
The
p
r
oduc
ed
a
c
tive
and
r
eac
t
i
ve
pow
e
r
c
a
n
b
e
c
ontr
o
l
l
e
d
by
the
ge
ner
a
tor
exc
itat
i
o
n
a
s
w
e
ll
a
s
b
o
t
h
t
he
a
ng
l
e
s
hi
ft
b
e
t
w
e
en
t
he
g
ene
r
ator
a
nd
r
e
ctif
ier
vo
ltages
a
nd
b
e
tw
e
e
n
the
in
v
e
r
t
er
a
nd
netw
or
k
vo
lt
a
g
es,
F
i
g
u
r
e
3.
T
he
capa
c
itive
in
term
ediary
c
ircuit
b
r
i
ngs
the
advan
t
age
of
d
ec
oupl
in
g
of
h
a
r
m
o
nics
b
e
t
w
een
t
he
g
ener
ato
r
and
t
h
e
netw
or
k
c
u
r
r
e
n
t
s
[20]
.
B
o
th
i
np
ut
a
nd
out
put
c
on
ver
t
er
s
ar
e
contr
o
lle
d
in
t
he
s
am
e
m
a
n
ner.
T
he
r
e
f
o
r
e
,
only
one
s
id
e
c
o
n
t
r
o
l
of
t
h
e
ou
t
p
u
t
con
v
erter
i
s
d
escr
ibed in th
is paper
, F
ig
ur
e 4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
A
high
vo
l
t
a
g
e
di
rect
cur
r
en
t t
r
an
sm
i
s
s
i
on sy
stem
:
Na
t
u
r
a
l an
d
selec
t
ive
h
a
rm
o
n
i
c
…
(
A
ziza
Bena
b
o
u
d
)
1
415
D
C
v
o
l
ta
ge
a
nd
the
a
ngle
s
h
i
f
t
b
e
tw
een
t
he
i
n
v
e
r
ter
and
n
e
t
w
or
k
v
o
l
ta
ge
s
ar
e
given
a
s
f
unc
ti
on
o
f
a
c
ti
ve
a
n
d
r
ea
cti
v
e
po
w
e
rs
r
efere
n
c
e
s
and
they
d
epen
d
on
t
h
e
i
n
duc
t
a
nce’
s
va
l
u
e
and
the
gr
id
v
ol
tage
m
a
gnitude
a
c
c
or
din
g
t
o
(
6
)
a
nd
(
7
)
:
U
V
Q
P
(
6
)
θ
t
a
n
(
7
)
X
X
X
W
i
t
h
X
a
nd
X
ar
e r
e
spec
tive
l
y
th
e
tr
ansf
or
me
r
a
nd
t
h
e
ne
tw
or
k
i
n
d
u
c
t
a
n
c
e
s.
St
a
r
t
i
n
g
fro
m
t
h
e
a
c
t
i
v
e
a
n
d
rea
c
t
iv
e
po
wers
r
ef
ere
n
ce
s
equ
a
l
t
o
z
e
r
o
(
F
i
gur
e
7-
a)
,
the
sys
t
em
r
uns
in
i
t
ia
ll
y
in
no
loa
d
o
per
a
t
i
o
n
,
bo
th
i
n
v
er
ter
a
nd
ne
tw
or
k
v
o
l
t
a
ge
s
ha
ve
t
he
s
am
e
phase
w
h
e
r
e
t
he
a
mp
li
t
u
de
i
s
e
qua
l
t
o
nom
in
al.
Ther
e
f
or
e
t
h
e
li
ne
c
ur
r
e
n
t
i
s
z
e
r
o
.
F
i
gur
e
7.
D
iagr
am
o
f
vol
t
a
ge
a
nd
c
u
r
r
e
n
t
I
n
t
he
f
ir
st
t
r
a
n
s
iti
o
n
,
the
ne
t
w
or
k
ac
ti
ve
a
nd
r
eac
tive
p
o
w
e
r
s
a
re
d
ifferent
f
r
o
m
zero
.
Co
n
s
equ
e
n
tly
,
the
a
n
gle
s
h
i
f
t
and
t
h
e
D
C
v
o
l
ta
ge
c
ha
n
g
e
fr
om
(
θn0,
U
d0)
t
o
(
θ
nc,
U
d
c)
(
F
i
gur
e
7-
b)
.
Their
va
lue
s
d
e
p
en
d
o
n
th
e activ
e
an
d
reactiv
e
po
w
e
r-ref
e
ren
c
es
acco
r
d
i
n
g
to
(6
)
an
d
(7
).
In
t
h
e
s
ec
ond
t
r
a
n
sit
i
o
n
,
t
he
r
ea
ct
iv
e
powe
r
r
a
m
p
s
down
t
o
z
e
r
o
,
a
s
s
h
o
w
n
i
n
(
F
igur
e
7-
c)
.
C
onse
q
uen
t
ly,
t
h
e
a
n
gle
sh
if
t
and
the
D
C
v
olta
ge
m
us
t
c
h
ange
f
r
om
(
θn
c,
U
dc
)
t
o
(
θ’
nc
,
U
’
dc
)
.
T
hen
t
h
e
r
eac
t
i
ve
power
ca
n
be
com
p
ensa
t
e
d an
d
t
h
e
sys
t
em
c
an be
oper
a
te
d
usi
ng
a
uni
t
y
pow
e
r
f
actor
.
7.
EX
PERIMENT
AL R
E
S
ULTS
A
N
D
DIS
CUSSION
S
The
s
y
stem
d
epic
te
d
i
n
F
i
g
ur
e
4
ha
s
be
e
n
s
imu
l
a
t
e
d
i
n
Ma
t
l
ab
S
i
m
u
l
i
nk
us
in
g
t
h
e
fo
llow
i
n
g
ch
a
r
ac
t
e
ri
sti
c
s:
V
n
=
1
p
u
i
s
t
h
e
ne
tw
or
k
v
o
l
ta
ge.
X
n
=
0
.
2
p
u
:
i
n
du
cta
n
c
e
b
etw
e
e
n
t
r
a
ns
f
o
r
m
e
r
s
a
nd
ne
t
w
or
k.
Tr
ansform
e
r
s
c
hara
cteris
t
i
cs
:
L=
1
e-3
p
u
i
s
L
e
aka
g
e
in
duc
t
a
nce,
R=
1
e-3
p
u
i
s
wi
n
d
i
n
g
re
sis
t
a
n
ce.
S
im
u
l
a
t
i
o
n
r
e
sults
f
or
d
if
f
e
r
e
nt
s
w
i
t
c
h
i
ng
a
ngle
δ
n
a
r
e
presen
te
d;
F
i
g
u
r
e
8
.
T
r
a
nsfor
m
er
out
pu
t
vo
l
t
a
g
e
w
h
e
n
δ
n
=
8.
18
F
igur
e
9.
T
r
a
nsfor
m
e
r
out
pu
t
vo
l
t
age
w
h
e
n
δ
n
= 6.
9
2
°
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
4
1
0
–
1
418
1
416
F
i
gur
e
8
a
nd
F
i
gur
e
9
s
h
ow
r
espe
ct
ive
l
y
t
h
e
tr
a
n
s
f
or
me
r
ou
tpu
t
vol
t
a
ge
w
h
e
n
δ
n
=
8.
18
°,
t
he
1
1
th
ha
r
m
onic
d
i
sa
ppea
r
s
an
d
the
c
a
se
w
hen
δ
n
=
6
.
92°
t
he
1
3
th
h
ar
mon
i
c
d
i
sa
ppea
r
s.
H
ar
mo
nic
s
num
be
r
υ
=
5,
7
,
17,
19,
29,
31,
…
.
.
a
r
e
n
a
t
ur
a
l
l
y
c
a
n
ce
l
l
e
d
.
S
im
ulat
io
n
r
e
su
lt
s
c
onf
ir
m
t
h
e
ana
l
yt
i
c
s
calc
u
l
a
ti
ons
d
o
n
e
a
ccor
d
i
n
g
to
(
2)
i
n
the pr
ev
i
o
u
s
s
ec
t
i
on
s.
In
o
rder
t
o
va
li
date
t
he de
d
ica
t
e
d
c
o
n
t
r
o
l
s
t
r
a
teg
y
,
a
thre
e
le
vel
freq
u
e
n
c
y
c
on
v
e
rter
c
on
n
e
cted
t
o t
h
e
gr
id
v
i
a
i
n
d
u
c
t
anc
e
s
has
bee
n
s
im
ula
t
e
d
.
F
i
gur
e
10
s
how
s
sim
u
la
te
d
ac
t
i
v
e
a
nd
r
e
a
c
t
i
ve
pow
er
s
for
d
i
f
f
e
r
e
nt
ope
ra
ti
o
n
m
od
es.
The
l
i
n
e
cu
rr
ent
is
i
n
p
h
as
e
wit
h
t
he
n
e
t
work
v
o
lta
ge
w
he
n
t
h
e
r
e
a
c
t
iv
e
p
o
w
e
r
is
n
ul
l
.
T
h
e
sy
s
t
em o
p
e
r
a
tes w
i
th
u
nity
power facto
r
.
Fig
u
r
e
10
.
Simu
l
a
tion
r
e
sult
s
:
(
co
sφ = 0
.8
)
an
d
(co
s
φ
=
1
).
The
sam
e
s
yste
m
has
be
en
b
u
i
lt
an
d
tes
t
e
d
u
s
i
n
g
a
l
ow
v
o
l
ta
ge
l
a
b
or
at
or
y
p
r
ot
oty
p
e
F
i
gur
e
11.
F
i
gur
e
1
1
.
Labor
a
t
or
y
pr
o
t
o
t
ype
u
s
i
n
g
3
L
3
P
N
P
C
i
nver
t
e
r
Ac
tive
a
n
d
r
e
ac
tive
p
o
we
rs
a
re
m
e
a
sured
an
d
pre
s
en
te
d
in
F
igur
e
1
2
a
n
d
F
i
gur
e
13
t
o
g
e
t
he
r
w
ith
t
he
a
l
te
r
n
at
i
v
e
li
n
e
c
ur
r
e
nt,
in
ver
t
e
r
a
nd
ne
tw
or
k
v
o
l
t
a
g
es.
W
h
e
n
t
h
e
r
ea
ct
i
v
e
p
o
w
er
i
s
n
e
a
r
z
ero
,
t
h
e
a
lt
erna
t
i
ve
li
ne
c
ur
r
e
n
t
i
s
i
n
pha
se
w
it
h
th
e
netw
or
k
vo
lt
age
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
A
high
vo
l
t
a
g
e
di
rect
cur
r
en
t t
r
an
sm
i
s
s
i
on sy
stem
:
Na
t
u
r
a
l an
d
selec
t
ive
h
a
rm
o
n
i
c
…
(
A
ziza
Bena
b
o
u
d
)
1
417
F
i
gur
e
1
2
.
P
r
acti
c
a
l
v
e
r
i
f
icat
i
o
n
r
e
sults
:
(
c
osφ
=
1)
F
i
g
u
r
e
13.
P
r
acti
c
a
l
v
e
r
i
f
ica
t
i
o
n
r
e
sults
:
(
c
osφ
≠
1)
8.
CONCLUSION
Su
s
t
ai
n
a
b
l
e
e
n
ergy
g
e
n
er
ati
on
is
o
f
t
e
n
l
oca
t
e
d
v
e
r
y
fa
r
fr
om
t
he
p
lace
w
her
e
t
he
ene
r
gy
w
ill
be
c
o
n
s
um
ed.
I
t
w
il
l
be
v
e
r
y
i
m
por
ta
nt
t
o
f
i
nd
e
f
f
i
cie
n
t
w
a
ys
t
o
t
ra
n
s
port
l
a
rg
e
a
m
o
u
n
t
s
o
f
e
l
e
ct
r
i
c
i
t
y
l
ong
d
i
stan
ces.
T
o
d
ay
,
HVDC
t
r
a
n
s
missio
n
s
e
ems
to
b
e
the
b
e
st
s
ol
uti
on
o
f
this
p
rob
l
em.
I
n
d
e
ed
,
HVDC
tra
n
smiss
i
on
s
ys
tem
s
m
ake
it
po
ssi
b
l
e
to
e
a
s
ily
i
n
t
er
co
nn
ect
n
e
tw
or
ks
w
her
e
v
ol
ta
ge
a
nd
f
r
e
q
u
e
n
cy
a
r
e
n
o
t
c
o
mpa
t
i
b
le,
to
t
r
a
nsmi
t
ener
gy
o
v
er
l
o
n
g
d
i
s
ta
nce
s
a
nd
t
h
ey
a
ls
o
c
o
n
t
r
i
bu
te
t
o
t
h
e
st
a
b
il
it
y
of
t
he
n
etw
o
r
k
tha
n
ks
t
o
the
i
r
contr
o
l
l
a
b
il
it
y
i
n
t
he
4
Q
u
a
dr
an
ts
P
Q
.
T
he
c
o
n
t
r
i
bu
tio
n
pr
o
p
o
se
d
i
n
t
his
paper
i
n
clu
d
e
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
141
0
– 1
418
1
418
ori
g
ina
l
e
l
e
me
nts
base
d
o
n
t
h
e
c
omb
i
na
t
i
o
n
o
f
tw
o
so
l
u
t
i
on
s,
t
o
r
ed
uc
e
the
ha
rmon
ics
di
stor
ti
o
n
o
f
the
o
u
t
p
u
t
in
verter
v
o
l
t
a
g
e
,
a
nd
to
o
pe
rate
w
i
t
h
u
n
ity
pow
er
f
ac
t
o
r
and
be
t
t
er
c
u
r
r
e
nt
q
ua
l
i
t
y
.
The
s
i
m
u
lat
i
on
a
n
d
expe
r
i
me
n
t
a
l
r
esu
l
t
s
i
n
d
i
c
a
te
t
ha
t
the
pr
op
ose
d
H
V
D
C
t
r
a
n
sm
issi
on
s
ys
t
e
m
s
o
ff
er
h
igh
efficienc
y
,
and
show
e
d
t
ha
t
w
i
t
h
t
he
c
ontro
l
of
t
he
t
w
o
i
n
v
erter
s
a
n
d
t
h
e
s
pe
ci
al
c
o
upl
ing
of
t
h
e
t
wo
t
ra
nsfo
rme
r
s
,
t
hi
s
con
t
ri
b
u
t
i
on
ma
kes i
t
pos
sib
l
e
to take
ad
va
nt
a
g
e of na
t
ura
l
a
nd
s
e
l
ect
i
v
e
ha
rm
oni
c
c
a
nce
lla
ti
on.
REFE
RENCES
[1]
P
r
asad
a
r
ao
V
S
,
J
o
s
hi
M
an
oh
ar
K
V.
A
n
a
ly
s
i
s
Grid
I
nterco
nn
ectio
n
o
f
P
V
S
y
s
t
e
m
U
s
i
n
g
S
y
m
m
e
t
r
i
c
a
n
d
As
ymm
e
tri
c
M
LI
T
op
o
l
ogy
.
In
te
r
natio
na
l Jo
ur
nal of
P
o
wer
El
ectro
ni
cs a
nd Dr
ive S
y
st
em.
2
0
18;
9
(4):
161
6-1
6
2
3
,
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Ruf
e
r
A,
K
nap
p
P
.
N
e
t
zein
s
p
e
isung
m
it
v
erlu
st
armem
p
u
ls
wechsel
r
icht
er
.
St
euer
ung
s el
ek
t
r
o
n
i
k
, pr
ecision
.
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9
1
:
25-29.
[3]
Buhler
H
.
Converti
s
seurs
stat
iq
ues.
Co
ll
ecti
on
E
l
ect
ricité,
Presses
Po
l
y
tech
ni
q
u
es
et U
n
iver
si
ta
ires
Ro
ma
ndes,
L
a
u
s
an
ne,
1
9
91:
2
63
-2
67
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[4]
Benab
oud
A
.
Con
v
erti
s
s
eur
de
f
réqu
ence
in
di
rect
à
r
ap
po
rt
d
e
te
n
s
io
n
fix
e
:
i
n
terf
ace
ent
r
e
t
u
rb
o-alt
e
rnat
eurs
à
hau
t
e v
i
t
e
sse
e
t rés
eau él
ectriq
u
e.
Do
c
t
or
a
l
t
h
esis
n
3
733
EPFL
,
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s
an
ne
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Das
h
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S
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o
n
i
c
E
liminatio
n
of
a
n
El
even
L
evel
I
n
v
erte
r
Usin
g
W
h
a
le
Op
ti
mizati
o
n
Tech
ni
que.
Int
e
rnati
o
n
a
l Jou
r
n
a
l
of Po
we
r Electr
onics
an
d
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r
i
ve Sys
t
em
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Tan
g
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.
Hi
gh
P
o
w
er
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o
n
v
e
rsi
on
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no
lo
gy
f
o
r
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gh
V
o
l
tage
D
C
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an
smissi
o
n
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pp
li
catio
n
.
2016
ECCE- I
E
EE.
Mi
lwau
kee,
W
I
,
US
A, En
e
r
gy
Conver
si
on
Cong
re
s
s
a
nd Exp
o
sit
i
o
n
:
18
-2
2.
[7]
Lat
o
rre
H
.
Mod
e
l
i
ng
a
nd
C
ont
rol
of
V
SC-HV
D
C
Trans
m
i
s
s
i
on
s
.
Doct
ora
l
thes
i
s
, Royal In
stitute of
Technology
Sch
o
o
l
o
f
E
l
ect
r
i
ca
l
Engin
eerin
g
,
El
ectric p
o
wer s
y
st
ems
S
t
ockh
olm, S
w
eden,
2
01
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[8]
Kim
C
,
So
od
V
,
Ja
n
g
G
,
Lim
S,
L
e
e
S.
H
V
D
C
T
R
ANS
MI
SSION
P
o
w
e
r
C
o
n
v
e
rsi
on
A
pplicatio
ns
i
n
P
o
wer
Sy
ste
m
s
.
I
EEE P
R
E
SS,
John Wi
l
ey
&
S
ons
(
A
si
a
)
P
t
e
L
t
d
.
200
9
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[9]
Hoffmann M,
Le
o
wald K.
A th
yris
to
r va
l
v
e f
o
r a pe
ak
b
lock
in
g v
o
lta
ge
o
f 12
0 k
v
.
Siemen
s-Z
e
it
sch
r
ift
.
1
9
68;
42(4
)
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[10]
Anwan
d
er E, E
tt
er P. Thy
r
i
stor c
o
n
v
e
rt
er v
al
v
e
for
1
00
kv
dc b
r
id
ge
v
olta
ge
.
Brown B
o
veri
M
itt
.
1
96
9;
5
6
(
2).
[11]
Co
l
e
S
, Bel
mans
R. Trans
mi
ss
i
o
n
o
f
bu
l
k
po
wer,
I
n
dustrial Elect
ronics Magaz
i
n
e
I
E
E
E
. 2
00
9
;
3(3
)
:
1
9-2
4
.
[12]
Ei
cher
S
, Rah
i
mo
M
,
Tsy
p
l
a
ko
v
E
,
S
ch
neid
er
D
,
Ko
pt
a
A,
S
chl
a
p
b
a
ch
U
,
Carrol
l
E
.
4.
5
kv pres
s
pack
i
gb
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gn
e
d
f
o
r
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a
nd
r
eli
a
bilit
y
.
IEEE, Industry
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pplicat
i
o
ns Co
nf
erence,
39t
h
I
A
S Annual
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eet
ing.
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t
l
e,
WA,
USA,
200
4
;
3
:
1534
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39.
[13]
As
pl
und
G
.
A
ppli
cati
on
of
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li
ght
t
o
p
o
wer
s
y
s
t
e
m
e
nh
ance
m
e
nt
.
P
o
wer en
gi
neeri
n
g
so
cie
t
y wi
nt
er meet
ing
IEEE.
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00
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4
:
2498
-25
0
3
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[14]
Gy
ug
yi
L
.
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e
p
o
wer
gen
e
rat
i
o
n
a
n
d
c
ont
rol
by
t
hy
ristor
c
i
rcuits.
IEEE
Tra
n
s
a
cti
on In
dustr
y Ap
p
l
ica
t
i
ons.
19
79
;
1
5
(5):
5
21-5
3
2
.
[15]
S
h
al
chi
Alis
hah
R,
N
aza
rp
ou
r
D
,
H
os
sei
n
i
S
H
,
Sabahi
M
.
D
e
sig
n
o
f
N
e
w
Sing
le-p
hase
M
ul
tilev
e
l
Vo
ltag
e
So
urce
Inverter.
In
ter
n
a
t
io
nal Jo
ur
na
l o
f
P
o
wer El
ectro
n
i
cs a
nd Drive S
y
st
em
.
20
14
; 5
(
1)
:
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[16]
Lak
s
hm
an
a
B,
V
enk
a
taratn
am
G
.
TH
D
an
d
Sw
it
chi
ng
lo
s
s
es
A
naly
s
i
s
o
f
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t
i
-
Level
Inverter
F
ed
3
φ
Induct
i
o
n
Mot
o
r
D
r
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ternati
o
na
l
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f
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i
e
ntific
&
E
ngineering
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As
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und
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S
u
s
tai
n
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le
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rgy
sy
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with
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VDC
t
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i
ssi
on.
I
EEE Po
wer
Eng
i
neer
in
g Societ
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M
eet
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v
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0
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Baker
Ri
chard
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B
ri
dg
e con
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erter ci
rcui
t.
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a
t
es
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a
t
e
nt,
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63.
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a
y
1
9
8
1
.
[19]
Nab
ae
A,
T
akah
ash
i
I
,
Ak
agi
H.
A
n
eut
r
a
l
-p
oin
t
-c
l
a
mp
ed
P
W
M
i
nve
rt
er
.
IEEE Tran
sacti
ons on
I
n
dustry
Applications
. 19
8
1;
I
A(1
7
)
:
51
8
-5
23
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[20]
Benab
oud
A
,
Ruf
e
r
A
.
A
F
lex
i
b
l
e,
H
ig
h
effi
cien
cy,
V
S
I-Based
HVD
C
tr
ansm
ission
s
ystem
with
r
educ
ed
harm
onics
.
P
o
wer
Elect
ro
n
i
cs Specia
lists Co
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