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
3
7
~1
4
4
5
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1437-1445
1437
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
Transm
ission system
regularization with 5-level cascad
e
d IPFC
Sri
d
ha
r Ba
bu
Guri
j
a
la
,
K S
S
r
ik
a
n
th,
R
a
mch
a
ndra
Nitt
a
l
a
,
G.
Ro
h
it
Reddy
Kon
e
ru L
aks
h
maiah
Ed
ucat
io
n
Fo
und
ati
o
n
,
India
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
8
,
2
018
Re
vise
d Jan
1
1
, 2019
Ac
ce
p
t
ed
M
ar 2
9
,
2
019
I
n
r
e
c
e
n
t
y
e
a
r
s
,
t
h
e
r
e
i
s
a
n
i
m
m
e
n
s
e
l
y
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u
g
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d
e
m
a
n
d
t
o
p
o
w
e
r
d
u
e
t
o
in
du
st
ria
l
i
zati
on
an
d
m
o
derni
zati
on,
b
u
t
corres
pon
di
ng
ly
t
he
a
m
p
lifi
cati
on
of
gen
e
ratio
n
an
d
t
r
an
sm
ission
h
as
n
o
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b
een
d
o
n
e
d
u
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t
o
co
ns
trai
ne
d
res
o
u
r
ces
and
env
i
ro
nm
ent
a
l
l
i
mi
ta
t
i
ons.
Th
e
hu
ge
g
row
t
h
in
d
em
an
d
l
ead
t
o
vario
u
s
pro
b
l
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ms
i
n
power
s
y
s
tem
s
.
Heavy
g
r
ow
th
i
n
s
e
mico
ndu
cto
r
t
echn
o
log
y
m
a
de
p
ow
er
e
lectro
ni
cs
p
lay
a
key
rol
e
i
n
solv
ing
th
ese
p
r
ob
le
m
s.
F
l
e
x
i
bl
e
AC
t
ransmis
s
i
o
n
sy
s
t
em
(
F
A
CT
S
)
d
evices
a
re
u
sed
f
o
r
fixin
g
v
ari
ou
s
pro
b
l
e
ms
i
n
power
s
y
s
t
e
m.
T
hey
are
u
s
ed
f
o
r
e
n
h
anci
ng
t
he
e
xi
st
in
g
tran
smissi
on
cap
abi
l
i
t
ies
and
i
m
p
r
ov
in
g
th
e
sys
t
e
m
d
y
n
am
i
c
p
erf
orm
a
nce
so
th
at
t
o
mak
e
transmi
ssion
s
ystem
fl
e
x
ible
a
nd efficient
i
n
o
per
ation.
I
nter
line
power
flow
c
ont
r
oll
e
r
(IPFC)
i
s
a
l
ates
t
generation
s
e
ries
c
onn
ect
ed
F
ACT
S
dev
i
ce,
h
av
in
g
capabi
l
i
t
y
of
c
o
n
tro
l
lin
g
po
wer
fl
ow
a
m
o
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m
u
l
t
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line
i
n
a
t
r
a
n
s
m
i
s
s
i
o
n
n
e
t
w
o
r
k
.
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n
t
h
i
s
p
a
p
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c
a
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d
5
l
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r
i
s
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s
e
d
a
s
the
in
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m
od
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l
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f
o
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C
.
Control
techn
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q
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es
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a
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rol
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p
o
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r
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minimizat
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ta
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his
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scu
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s
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p
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w
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verter us
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SP
W
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a
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Lev
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Inter
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F
l
o
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C
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P
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m
o
dule
SP
W
M
SVM
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:
S
r
i
dha
r Bab
u
G
urija
la,
K
oner
u
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ak
sh
m
a
iah
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u
c
at
i
on F
o
u
n
d
a
t
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on,
G
r
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e
nfie
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s,
V
adde
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u
n
t
ûr (
dt
)
,
A
nd
hra
P
r
a
d
esh,
I
ndia.
5
22
502
Em
ail:
sr
i
d
ha
rbab
u
1
6
@
gm
ai
l.com
1.
I
N
TR
OD
U
C
TI
O
N
M
o
d
e
rn
bul
k
po
wer
sy
st
e
m
s,
i
ndu
st
ri
e
s
a
nd
t
e
c
h
nol
ogy
a
re
i
n
c
re
a
s
i
n
g
r
a
p
i
d
l
y
da
y
by da
y
,
so
t
h
er
e is
a
hu
ge
d
e
m
a
n
d
to
e
l
e
c
t
ric
i
ty.
To
m
eet
t
he
l
oad
a
n
d
i
n
cr
easi
ng
m
a
r
ket
de
m
a
nd
e
i
t
h
e
r
t
he
g
ener
at
i
o
n
c
a
pac
i
ty
sho
u
l
d
b
e
incr
ease
d
o
r
new
transm
iss
i
on
line
s
a
re
t
o
be
i
n
s
ta
l
l
ed
o
r
u
s
e
th
e
exi
s
t
i
ng
t
ra
n
s
mi
s
s
io
n
sy
st
em
efficie
n
t
l
y.
B
ut
i
nsta
l
l
a
t
io
n
of
n
ew
s
ystem
d
e
als
w
ith
h
u
g
e
in
v
es
tme
n
t
a
n
d
t
a
kes
tim
e.
H
ence
t
he
u
t
i
l
itie
s
ar
e
forc
ed
t
o
de
pe
nd
o
na
lrea
d
y
e
x
i
st
ing
s
y
st
e
m
.
I
n
orde
r
to
i
m
pro
v
e
the
effic
i
e
n
cy
of
t
h
e system
the
y
a
r
e ma
de
to
w
o
rk
a
t
t
h
eir
ma
x
i
m
u
m
lim
it,
t
his
re
s
u
lts
i
n
o
u
ta
ge
s
o
f
l
i
n
es
o
r
o
t
her
e
q
uipm
en
t
or
c
o
u
ld
r
esu
l
t
in
f
a
ilur
e
o
f
ent
i
re
s
yste
m.
F
lex
i
b
l
e
A
C
T
ransm
i
ss
io
n
S
y
st
e
m
s
(F
A
C
TS
)
devi
ces
b
ecom
e
a
n
imp
o
r
t
a
n
t
an
d
e
f
f
ect
i
v
e
op
tio
n
for
suc
h
i
ncre
as
ing
de
m
a
nd
an
d
s
t
res
s
o
n
t
h
e
s
y
st
e
m
.
F
A
C
T
S
d
e
v
i
c
e
s
a
r
e
u
s
e
d
i
n
s
o
l
v
i
n
g
m
a
n
y
i
s
s
u
e
s
rela
t
e
d
to
t
r
a
n
s
missi
on
s
y
st
e
m
s.
T
he
m
ain
fu
nc
ti
on
is
t
o
c
o
n
t
ro
l
pow
er
f
low
i
n
t
ra
nsm
i
ssio
n
lines,
a
n
d
t
h
e
ot
her
fu
nc
tio
n
s
a
re
volta
ge
c
ontr
o
l,
t
rans
i
e
nt
s
ta
bi
l
i
t
y
i
m
p
rov
em
en
t
a
nd
osc
i
l
l
a
t
i
o
n
da
mpi
n
g
[1]
.
F
A
C
TS
t
e
c
h
n
o
l
o
g
i
e
s
o
f
f
e
r
b
e
t
t
e
r
s
o
l
u
t
i
o
n
s
i
n
t
o
d
a
y
’
s
p
o
w
e
r
s
y
s
t
e
m
s
l
i
ke
i
n
c
re
asin
gp
ow
er
t
rans
fer
ca
p
a
bi
lit
y,
ma
int
a
in
in
g c
o
nti
n
u
o
u
s c
ontr
o
l
ove
r
v
o
l
t
age
profi
l
e,
im
p
ro
ve
s
y
s
t
em
dam
ping,
m
i
nim
i
z
i
n
g
s
y
s
t
em
losses,
e
tc.
I
P
F
C
i
s
o
n
e
o
f
t
he
l
a
t
est
ge
ne
r
a
ti
on
F
A
CTS
con
t
ro
l
l
er
u
se
d
to
c
on
tro
l
p
o
w
er
f
low
s
a
mo
ng
m
u
l
t
i
p
le
transm
i
s
s
i
on
l
i
ne
s.
T
h
i
s
de
v
i
c
e
u
ses
co
nt
rol
l
ers
i
n
o
rd
er
t
o
c
o
n
t
r
o
l
p
o
w
e
r
a
mong
th
e
line
s
.
A
n
y
type
o
f
con
v
er
t
e
r
ca
n
be
u
se
d
he
re
c
asca
de
d
H
bri
d
ge
i
n
v
e
r
ter
w
a
s
im
p
l
e
me
n
t
ed.
Th
es
e
c
o
n
t
ro
ll
ers
a
r
e
co
nt
rol
l
e
d
by
u
s
i
n
g
c
ont
rol
te
ch
ni
q
u
e
s,
t
h
e
r
e
a
re
se
v
era
l
c
o
n
t
r
ol
t
e
c
hni
que
s,
am
ong t
h
e
m
sinu
s
o
i
da
l p
u
l
s
e
w
i
d
t
h m
o
du
l
a
tio
n
(S
P
W
M)
a
n
d
s
pa
ce
vec
t
or
m
od
u
l
a
t
i
o
n
(
S
V
M
)
are
ch
os
en.
D
e
ta
il
s
a
n
d
i
m
pl
emen
t
a
ti
on
of
c
on
t
r
o
lle
r
a
nd
c
o
nt
rol
t
e
c
h
ni
qu
es
a
re d
i
s
c
u
sse
d
i
n
fol
l
o
w
i
ng sec
t
io
n
s
.
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
3
7
–
1
445
1
438
2.
IPFC
The
la
t
e
s
t
g
e
n
e
r
ati
on
F
A
CT
S
de
vi
c
e
s
p
er
f
o
r
m
m
ult
i
p
l
e
oper
a
ti
o
n
s
w
h
i
ch
m
ade
t
h
em
power
ful
i
n
c
o
n
t
r
o
lli
n
g
t
ransm
i
ss
i
on
syst
e
m
s.
U
PF
C
is
one
o
f
the
ver
s
atile
too
l
,
b
u
t
U
P
F
C
c
ontr
o
ls
o
nl
y
s
i
ng
le
l
i
n
e
a
t
a
time
.
T
he
l
at
es
t
ge
ner
a
ti
on
F
A
C
T
S
dev
i
c
e
I
P
F
C
,
has
t
h
e
a
dva
n
t
ag
e
o
f
U
PFC
a
nd
a
ls
oit
c
a
n
s
imul
ta
ne
o
u
sl
y
m
a
na
ge
a
nd
c
o
n
t
r
o
l
pow
er
f
l
o
w
of
m
u
l
tip
l
e
l
ines.
I
P
F
C
h
el
ps
i
n
in
c
r
easin
g
th
e
po
we
r
t
r
a
n
sf
er
c
ap
a
b
i
l
i
t
y
,
r
e
gu
lat
i
ng
a
n
d
m
a
nag
i
n
g
t
he
pow
er
f
low
,
c
ompe
n
s
a
t
i
o
n
o
f
r
ea
ct
iv
e
p
o
w
e
r
,
p
r
e
ve
nti
n
g
the
l
o
op
c
ur
r
e
nt,
a
n
d
a
v
o
i
d
t
h
e
ove
r
l
oa
d
i
ng
o
f
t
he
n
e
t
w
o
r
k
.
I
n
a
d
d
it
io
n
to
t
he
se
capa
b
i
l
i
t
i
e
s
i
t
i
m
pr
oves
vo
lta
ge
s
ta
b
ili
t
y
,
dy
nam
i
c
a
n
d
tra
n
sie
n
t st
abi
l
ity a
l
l
the
se
ca
p
a
b
i
lit
ies
ha
ve m
ade
t
h
i
s
t
oo
l as a
m
ult
i
fun
c
tio
n
d
evice
[4
-6
]
.
In
o
th
er
w
o
r
d
s
,
I
P
F
C
p
r
o
v
i
de
s
hi
g
h
ly
e
ff
ec
t
i
v
e
schem
e
f
or
pow
er
t
r
a
nsm
i
ss
io
n
m
a
n
a
g
e
men
t
th
r
oug
h
mu
lt
ilin
e
[
7
]-[8
]
2.
1.
M
a
t
h
e
m
at
ica
l
m
od
ell
i
n
g
o
f
IPFC
Ra
ti
n
g
o
f
IP
FC
i
s
s
p
ec
if
i
e
d
m
a
inl
y
by
two
qua
n
t
i
t
i
es
:
pri
m
arily
o
n
the
a
m
oun
t
of
m
ax
i
m
um
i
nje
c
t
e
d
vo
l
t
age
a
nd
se
con
d
l
y
on
t
h
e
vo
l
t
-am
p
ere
r
a
ti
ng.
I
PF
C
reache
s
i
t
s
r
a
te
d
pow
er
o
n
l
y
w
h
e
n
b
o
t
h
t
h
e
i
n
j
e
c
t
e
d
v
o
ltag
e and
line cu
rr
en
t
are at
r
ated
v
alues. Po
wer
injec
tion
i
n
t
o
li
nes
de
pe
nds
o
n
the
a
c
t
u
a
l
pow
e
r
f
low
i
n
t
h
e
li
ne
(
witho
u
t
a
ny i
n
ject
i
o
n). Wh
i
c
h
w
ill
be se
e
n c
l
ear
ly
i
n
the
a
na
l
y
s
i
s
of
I
PF
C
design.
2
.
2
.
Pow
e
r
i
n
jectio
n
mo
del o
f
I
PFC
P
o
w
e
r
in
jec
t
i
o
n
m
ode
l
is
t
he
M
a
t
hem
a
tica
l
m
ode
l
for
I
P
F
C
(
F
i
gur
e
1)
.
W
h
ic
h
hel
p
s
i
n
un
de
r
s
t
a
n
d
in
g
t
h
e
impa
c
t
o
f
I
P
F
C
o
n
pow
er
s
yste
m.
F
ur
ther
m
o
r
e
b
y
m
a
them
at
ical
m
odel
l
i
ng,
I
P
F
C
c
a
n
ea
sil
y
b
e
i
n
c
o
rp
o
r
at
ed
in
th
e
s
y
st
e
m
.
I
P
F
C
p
r
o
v
i
de
r
e
a
c
t
i
v
e
c
o
mp
e
n
sa
tio
n
of
e
a
c
h
li
ne
i
n
d
epe
nde
n
t
l
y
,
f
o
r
ef
f
e
ctiv
e
o
p
e
ratio
n
o
f
IP
FC,
Ma
the
m
a
tica
l
m
odel
i
ng
o
f
i
m
por
ta
nt
c
omp
one
nts
of
I
P
F
C
i
s
ver
y
e
ssential.
F
i
gur
e
1.
I
P
F
C
P
o
w
e
r
inj
e
c
t
i
on
mode
l
S
i
mple
d
es
ig
n
of
I
P
F
C
base
on
our
s
ys
t
e
m
m
s
in
V
V
V
im
(
1
)
The
am
o
unt
o
f
ac
tive
p
o
w
e
r
and
r
e
ac
ti
ve
p
ow
e
r
i
n
j
e
c
t
ed
i
n
t
o
the
s
y
s
te
m
is
calc
u
l
a
te
d
b
y
t
he
fo
llow
i
n
g
;
cos
3
l
in
in
I
V
P
im
(
2
)
sin
3
l
in
in
I
V
Q
im
(
3
)
3.
CASCADE 5
LEVEL
I
NVER
T
ER
Th
is
t
op
olo
g
y
o
f i
n
ver
t
e
r
use
s
less n
u
m
b
er
o
f
sw
itc
hes w
h
e
n
com
par
e
d
to
o
t
h
e
r
a
n
d
so
f
t
sw
i
t
ch
i
ng
is
pos
si
b
l
e
by
n
e
w
s
w
itc
h
i
n
g
m
eth
o
d
s.
I
n
a
c
a
s
ca
de
d
H
br
idg
e
i
nve
r
t
e
r
wh
en
L
n
u
m
b
e
r
of
b
rid
g
e
s
a
r
e
ca
sc
ad
ed
in
a
p
ha
se
t
he
n
the
num
ber
of
o
u
t
p
u
t
v
ol
t
a
ge
l
eve
l
s
is
g
i
v
e
n
b
y
2
L+1
and
v
o
lt
a
g
e
st
ep
o
f
ea
ch
l
ev
el
i
s
gi
v
e
n
by
Vs/2L.
The
fo
l
low
i
n
g
t
a
b
le
r
epre
sents the
sw
i
t
c
h
in
g m
e
c
h
an
is
m
f
o
r
cas
c
ad
ed
5
lev
e
l
in
v
e
r
t
er
(
F
i
g
u
r
e
2
)
.
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
T
r
ansm
i
s
s
i
o
n sy
ste
m
regu
l
a
r
i
za
ti
o
n
wit
h
5-
l
eve
l casc
ade
d I
PFC
(
S
ridh
ar
Ba
bu
G
u
r
i
j
a
la)
1
439
F
i
gur
e
2.
Casc
a
d
e
H
br
idge
Ea
ch
i
n
v
e
r
ter
l
e
ve
l
c
a
n
ge
ne
ra
te
f
ive
d
i
ffe
r
ent
v
o
lta
ge
o
ut
p
u
ts
,
+2V
s
,
+
V
s
,
0
and
–V
s,
-
2V
s
by
c
o
n
n
ec
ti
n
g
t
he
D
C
sour
c
e
t
o
the
A
C
o
u
t
pu
t
b
y
d
if
fe
r
e
n
t
c
om
bina
t
io
ns
o
f
the
fo
ur
s
w
itc
hes
as
a
s
h
o
w
n
i
n
Tabl
e
1
.
S
witch
e
s
S
1
,
S2
,
S
3
,
S4
,
S5
,
S
6
,
S7
,
an
d
S
8
a
re
s
witch
e
d
i
n
d
i
f
f
er
ent
m
ode
s
of
s
w
i
t
c
hin
g
s
eq
ue
nce
s
t
o
g
e
n
erat
e
out
put
v
o
l
t
a
g
e
s
ac
ro
ss
o
u
tpu
t
t
ermi
n
a
l
s
o
f
t
h
e
H
b
r
id
ge
m
odu
le.
Tab
l
e
1
show
s
the
possi
b
l
e
sw
itc
h
i
n
g
s
ta
te
t
o
pr
o
duce
a
5
-
leve
l
ou
tpu
t
v
ol
ta
ge
.
Th
e
ma
j
o
r
a
ppl
i
c
atio
n
s
o
f
thi
s
i
nv
ert
e
r
i
nvol
v
e
m
ot
o
r
d
r
i
ves
,
e
l
e
c
t
ri
c
v
e
h
i
c
l
e
d
r
i
v
es
,
ac
t
i
v
e
f
il
t
e
rs,
pow
e
r
f
act
or
c
om
pen
s
at
or
s,
i
nter
f
a
c
i
ng
w
i
t
h
r
enew
a
b
le
e
ne
r
gy
so
ur
ces
Ta
b
l
e
1.
S
w
it
c
h
in
g
seq
u
enc
e
o
f
ca
scade
5
le
vel
i
n
ver
t
e
r
output
S
w
i
t
c
h
i
n
g
s
t
at
es
S
1
S
2
S
3
S
4
S
5
S
6
S
7
S
8
+V
s
1
0
0
1
1
1
0
0
-V
s
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
+2
V
s
1
0
0
1
1
0
0
1
-2
V
s
0
1
1
0
0
1
1
0
4.
PV
M
ODULE
So
l
a
r
el
ect
ri
c
p
o
w
er
g
e
n
erati
o
n
s
y
st
e
m
g
en
era
t
e
s
e
l
ect
ric
i
ty
w
h
e
n
s
o
l
ar
r
a
d
iatio
n
is
p
ene
t
r
a
te
d
t
h
r
o
u
g
h
s
o
l
a
r
m
o
d
u
l
e
.
A
n
u
m
b
e
r
o
f
s
o
l
a
r
c
e
l
l
s
c
o
n
n
e
c
t
e
d
i
n
s
e
r
i
es
b
as
ed
o
n
r
e
qu
ir
e
d
s
ta
nda
r
d
o
u
t
put
v
o
l
t
a
ge
an
d
po
wer.
T
he
r
at
ing
o
f
P
V
mo
d
u
l
e
s
i
s
done
w
i
t
h
th
e
i
r
ou
t
p
ut
o
pen
cir
c
ui
t
vo
l
t
age
OC
V
,
sho
r
t
ci
rc
uit
cu
rre
n
t
SC
I
, p
eak
po
wer
P
W
.
In
this p
a
p
e
r
we
a
re u
s
i
ng
PV m
odu
le
a
s
a
D
C
l
i
n
k,
t
o m
a
i
n
tai
n
t
h
e
vol
tag
e
o
n
D
C
s
ide
.
The
l
i
ne
d
ia
gr
am
o
f
PV
m
odule
is
s
h
o
w
n
i
n
f
i
gur
e.
F
i
gur
e
3.
P
V
m
odule
l
i
ne
d
i
a
gr
am
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
3
7
–
1
445
1
440
5.
CONTROL
TECHNIQ
UES
C
o
n
t
r
o
l
s
y
s
t
e
m
p
l
a
y
s
a
v
i
t
a
l
r
o
l
e
i
n
c
o
n
t
r
o
l
l
i
n
g
t
h
e
i
n
j
e
c
t
e
d
v
o
lta
ge
o
r
pow
er
f
r
o
m
I
P
F
C
.
C
o
ntr
o
l
tec
h
n
i
q
u
e
s
a
r
e
i
mpor
ta
n
t
b
ec
a
u
se
c
on
ver
t
e
r
s
out
pu
t
c
o
nsists
o
f
f
undamental
frequenc
y
compone
nt
a
long
wi
th
d
i
f
f
e
r
e
n
t
f
r
equ
e
n
c
y
co
mpon
e
n
t
s
,
su
ch
fre
qu
en
cy
c
o
m
po
ne
n
t
s
are
u
nde
s
i
r
a
b
l
e
to
t
he
s
ys
tem
and
the
y
a
r
e
r
e
spo
n
sib
l
e
for
oper
a
tio
na
l
i
m
per
f
ec
ti
on
s
a
t
v
ar
ious
l
e
v
e
l
s.
H
e
nce
em
plo
y
i
n
g
o
f
sui
t
a
b
le
c
o
n
t
r
ol
t
e
c
h
ni
que
s
f
o
r
mu
lt
i-
leve
l
i
n
v
e
r
t
e
r
t
o
oper
a
te
over
w
i
de
r
a
n
g
e
of
l
oa
d
i
ng
c
o
n
d
it
io
ns
w
i
t
h
l
es
s
TH
D
per
c
ent
a
ge
a
n
d
ob
t
a
i
ni
ng of
hig
he
r
c
o
nver
t
er
e
ff
icie
nc
y
ha
s
bee
n
a
t
o
p
i
c
o
f
int
en
s
i
v
e
resear
ch
.
The
m
a
in
o
bje
c
t
i
v
e
s
o
f
modu
lat
i
on
s
t
r
a
te
gie
s
a
r
e
:
a.
Ca
pa
b
l
e
of
o
p
e
r
a
ti
ng
o
v
er
w
ide
r
a
nges
of
m
odu
l
a
tio
n
i
n
dex,
L
e
s
s
T
H
D
o
ut
put
vol
t
a
g
e
,
l
e
ss
s
wi
t
c
h
i
ng
lo
sses,
E
asy fo
r im
plem
enta
ti
on,
t
i
m
e
and
c
o
mp
ut
at
ion
a
l
bu
rd
en
sh
oul
d
be
l
es
s.
b.
Vari
o
u
s
m
et
ho
d
s
h
av
e
b
een
d
ev
e
l
op
e
d
,
a
su
rv
e
y
o
f
mo
d
u
l
a
t
i
on
m
et
hod
s
is
g
i
v
en
i
n
[9
].
V
a
r
i
ous
a
l
g
o
r
i
t
h
m
s
a
nd
a
ppr
oa
c
h
es
o
f
t
r
i
a
n
g
u
l
a
r
c
o
m
par
i
si
on
(
T
C
)
a
nd
sp
a
ce
v
e
ctor
(
S
V
)
were
d
isc
u
ssed
i
n
[
1
0
]
,
[13]
.
6.
SP
W
M
S
P
WM
s
ta
nds
f
or
S
inus
oi
da
l
pu
lse
w
i
dth
m
o
d
u
la
ti
on.
I
t
i
s
a
dap
t
e
d
f
o
r
re
d
u
c
t
i
oni
nh
a
r
mo
ni
c
co
nt
en
t
in
o
u
t
pu
t
v
o
lta
ge
a
nd
o
b
ta
i
n
ings
i
n
uso
i
da
l
o
u
t
p
ut.
I
m
plem
enta
t
i
o
n
of
t
h
i
s
i
s
e
a
s
y
a
n
d
se
ver
a
l
s
t
ud
ies
w
e
r
e
do
ne
[
2
4
]
.
T
h
e
g
a
t
e
p
u
l
ses
a
r
e
ge
ner
a
te
d
w
h
e
n
s
inus
o
i
d
a
l
r
e
fer
e
nce
s
i
gna
l
is
c
om
pa
r
e
d
w
i
t
h
r
ec
ta
ng
u
l
a
r
carr
i
e
r
w
a
v
e
.
The
out
pu
t
fr
e
que
nc
y
o
f
t
he
i
n
v
e
r
ter
c
a
n
b
e
ca
lcu
l
a
t
ed
w
he
n
f
r
e
que
nc
y
o
f
t
he
r
e
f
er
e
n
ce
w
ave
is
kn
ow
n.
I
n
or
d
e
r
to
c
a
l
c
u
la
te
t
he
o
ut
p
u
t
v
o
lt
age
o
f
t
he
i
nve
r
t
e
r
m
odu
l
a
tio
n
in
de
x
i
s
u
se
d
a
nd
thi
s
m
od
u
l
a
t
i
o
n
in
de
x
i
s
c
o
n
tr
o
lle
d
b
y
p
eak
a
m
p
l
i
t
ude.
So
m
e
o
f
t
h
e
ad
v
a
n
t
ag
e
s
o
f
SP
WM
a
re
;
a.
The
o
u
t
p
ut
v
o
lta
ge
i
s
ne
ar
s
i
n
uso
i
da
l.
b.
Re
duc
tio
n
i
n
h
a
r
m
oni
c
c
o
n
t
e
n
t
i
n
t
he
o
u
t
p
u
t
vol
ta
ge.
F
i
g
u
r
e
4
.
G
e
ner
a
tion
o
f
p
u
l
se
s
by
S
P
WM
7.
SV
W
The
de
ve
lo
pm
ent
in
d
ig
ital
s
i
g
n
a
l
p
roc
e
s
s
o
r
s
lea
d
t
o
the
i
m
plem
en
t
a
t
i
o
n
o
f
v
a
riou
s
PWM
met
hods
ha
ve
b
ec
om
e
p
o
p
u
l
ar
,
of
t
hes
e
m
etho
ds
S
V
P
WM
h
a
v
e
be
c
o
me
one
o
f
the
mo
s
t
pop
ul
ar
P
WM
m
e
t
hods
[
1
1
]
-
[
1
2
]
.
D
u
ty
c
yc
les
a
r
e
im
por
ta
nt
i
n
o
b
t
a
i
ni
ng
r
e
quir
e
d
ou
t
p
ut,
i
t
uses
s
pac
e
vec
t
or
(
S
V
)
a
ppr
oach
i
n
or
der
to
c
o
mpu
t
e
d
u
t
y
cycle
s
f
or
s
w
itc
hes.
A
s
im
pl
if
ie
d
ap
pr
oa
c
h
o
f
S
V
P
W
M
w
a
s
pr
op
osed
i
n
[
1
4]
-
[
16]
.
A
thr
e
e
phase
i
n
v
er
t
e
r
ge
ne
r
a
tes
8
sw
i
t
c
h
i
n
g
state
s
o
f
these
6
are
ac
t
i
v
e
st
at
e
s
a
nd
2
a
re
z
ero
st
at
e
s
.
S
i
x
se
c
t
or
s
s
p
a
n
n
i
ng
6
00
ea
c
h
f
or
m
a
hexa
gon.
A
c
ombi
n
a
ti
o
n
o
f
swi
t
c
h
in
g
s
t
a
t
e
s
a
n
d
by
m
a
i
n
ta
in
ing
vo
l
t
-
se
co
nd
ba
la
nce
gener
a
tes
r
e
fe
r
e
nc
e
vo
l
t
a
g
e
s
p
ac
e
vec
t
or
re
f
V
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
T
r
a
n
sm
is
si
on
system
re
gu
lar
i
za
t
i
o
n
wi
t
h
5-l
e
v
e
l c
a
sc
ade
d I
PFC
(Sri
dhar
Ba
bu G
u
r
ija
la)
1
441
F
i
gure
5.
S
V
M
s
ectors
I
t
i
s
p
r
o
d
u
c
e
d
i
n
a
v
e
r
a
g
e
s
e
n
s
e
a
s
t
h
e
r
e
i
s
n
o
d
i
r
e
c
t
w
a
y
t
o
g
e
ne
rate
t
h
i
s.In
o
r
d
e
r
t
o
ob
t
a
i
n
s
a
m
p
l
e
d
refere
nce
ve
c
t
or
i
n
term
s
o
f
m
agn
i
t
u
de
a
n
d
a
n
g
le,
the
p
r
o
d
uc
ed
v
o
lta
ge
v
ec
t
o
r
s
a
re
a
p
p
lie
d
a
t
d
iffe
ren
t
dura
t
i
o
ns
w
i
t
h
i
n
a
sam
p
li
n
g
t
i
me
p
eri
od
s
u
ch
t
ha
t
a
v
era
g
e
v
e
ct
o
r
p
r
odu
c
e
d
ov
e
r
a
s
u
b
cy
c
l
e
i
s
e
qu
a
l
t
o
sam
p
l
e
d re
fer
e
nce
ve
ct
or.
7.1.
Calcu
l
ati
o
n
of
ref
erenc
e
v
ec
t
o
r
ref
V
cn
bn
an
d
V
V
V
V
2
1
2
1
(4
)
cn
bn
q
V
V
V
2
3
`
(5
)
2
3
2
3
0
2
1
2
1
1
3
2
q
d
V
V
(6
)
2
2
q
d
ref
V
V
V
(7
)
A
nd
d
q
V
V
1
tan
(8
)
7.2.
D
e
t
erm
i
n
atio
n
of switc
h
i
n
g
t
ime d
u
ration
3
sin
.
.
3
1
n
V
V
T
T
dc
ref
z
(9
)
3
1
sin
.
.
3
2
n
V
V
T
T
dc
ref
z
(1
0
)
2
1
0
T
T
T
T
z
Where
z
z
f
T
1
(1
1
)
A
c
i
r
c
ular
t
raj
e
c
t
or
y
is
f
orm
e
d
insi
de
h
e
x
a
g
o
n
i
n
si
n
u
soi
d
al
r
e
fere
nce
spa
ce
vec
t
or
f
o
r
m.
I
n
S
V
M,
the
r
a
d
i
us
o
f
la
rgest
c
i
r
c
le
t
h
a
t
ca
n
be
i
nsc
r
ibe
d
w
i
t
h
i
n
h
e
x
a
g
on
is
t
he
h
ig
hes
t
p
oss
i
bl
e
vo
l
t
a
g
e
t
h
a
t
c
an
b
e
ac
hi
e
v
e
d
.
The
ma
xi
m
u
m
ob
ta
ina
b
le
f
u
n
d
am
enta
l o
u
t
p
u
t
vo
l
t
a
ge
i
s.
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
3
7
–
1
445
1
442
dc
dc
ref
V
V
V
3
1
6
co
s
3
2
Whe
n
c
ompa
r
e
d
t
o
S
P
W
M
,
S
V
M
i
s
hav
i
n
g
m
axim
um
D
C
b
u
s
u
t
i
liza
t
i
o
n
.
There
a
r
e
a
num
ber
o
f
pu
b
lica
t
i
ons
d
e
s
c
r
ib
i
n
g
the
va
r
i
o
u
s
aspec
t
s
o
f
S
V
M
f
or
h
ig
h
lev
e
l
i
nve
r
t
er
s
[19]
-
[
2
3
]
.
8.
CAS
E
S
T
UDI
ES
The
system
i
s
des
i
g
n
e
d
b
yco
n
s
i
der
i
n
g
a
s
o
u
r
c
e
po
i
n
t
(
s
en
di
ng
e
n
d)
a
t
3
3
k
v
.
R
1
,
R2
a
nd
X
L
1,
X
L2
a
r
e
t
h
e
trans
m
issi
on
l
i
n
e
pa
ram
e
ter
s
.
S
i
nc
e
m
o
s
t
o
f
t
h
e
i
n
d
u
str
ies
take
1
1
kv,
T
1
and
T2,
s
t
ep
dow
n
transform
e
rs
a
r
e
u
sed
which
step
s
d
o
w
n
3
3k
v
t
o
1
1
kv.
A
s
I
P
F
C
i
s
a
b
ac
k
to
b
a
c
k
c
on
nec
t
i
o
n
of
v
o
l
t
a
ge
sourc
e
co
n
v
ert
e
rs.
VSC
1 and
VSC
2
ar
e t
h
e
tw
o v
o
lta
ge
s
o
u
r
c
e c
on
ver
t
e
r
s.
The D
C
si
de
s
of
t
hese c
on
v
e
r
t
er
s
a
r
e
con
n
e
c
te
d
w
i
t
h
a
c
omm
o
n
D
C
l
in
k.
H
er
e
P
V
m
odu
le
i
s
use
d
a
s
a
D
C
l
i
n
k.
L
oa
d
1,
2
,
3,
4
a
r
e
c
o
n
s
i
d
er
ed
a
s
i
n
d
u
s
t
r
i
a
l
l
o
a
d
s
.
I
n
o
r
d
e
r
t
o
t
e
s
t
t
h
e
e
f
f
i
c
i
e
n
c
y
o
f
c
o
n
t
r
o
l
t
e
c
h
n
i
ques
i
n
cor
por
ate
d
,
in
I
PF
C
,
t
her
e
a
r
e
t
w
o
c
a
se
s
t
u
die
s
c
o
n
s
i
de
r
e
d.
a.
V
o
l
t
age
dr
op
a
t
t
he
r
ec
ei
vi
ng
end
o
f
t
r
a
nsmi
ssion
li
ne
b.
S
udde
n
l
o
ad
o
n
bo
t
h
t
he
t
r
a
n
s
m
i
ssi
o
n
l
i
n
es
In
b
ot
h
t
h
e
ca
se
s,
I
P
F
C
i
s
c
on
n
e
ct
ed
t
o
t
h
e
t
e
st
syst
e
m
w
i
t
h
t
w
o
c
o
n
tr
o
l
t
echn
i
que
s
i
ndi
vi
d
u
al
l
y
.
The
pu
lses
a
r
e
g
ive
n
t
o
c
a
s
ca
de
d
h
br
id
ge
i
nver
t
er
t
hr
o
u
gh
tw
o
c
o
nt
r
o
l
tec
h
n
i
que
s.
F
i
n
a
l
ly
a
c
om
par
a
t
i
ve
a
nal
y
s
i
s
is
d
r
a
w
n
betw
e
e
n
t
he
c
o
n
t
r
o
l
te
chn
i
que
s
i
n
co
r
por
ate
d
i
n
I
P
FC
w
i
t
h
c
a
s
ca
de
d
i
nver
t
e
r
.
The
abo
v
e
ca
se
s
tu
die
s
a
r
e
per
f
o
r
m
ed a
nd
t
h
e
bes
t
p
o
ssible
co
n
t
r
o
l
t
e
c
h
n
i
que
i
s
in
v
e
st
ig
a
t
e
d
.
F
i
gur
e
6.
L
ine
dia
g
r
a
m
of
I
P
F
C
8.
1.
V
o
lt
a
g
e
d
r
op
a
t
th
e
re
ce
i
v
in
g
en
d
volt
a
ge
o
f
t
r
an
smissi
on
line
Whe
n
1
1
kv
i
s
b
ei
n
g
t
r
a
nsm
i
t
t
e
d
t
h
r
o
u
g
h
l
ine
,
due
t
o
he
a
v
y
ind
u
c
ti
ve
n
a
t
ur
e
of
l
oad
i
n
t
h
e
r
ece
i
v
i
n
g
e
n
d
w
e
h
ave
a
b
so
r
b
ed
a
h
uge
d
r
o
p
i
n
t
he
r
e
c
e
iv
ing
e
nd
v
o
lta
ge.
Th
e
vo
lt
ag
e
h
a
s
b
e
e
n
d
r
o
pp
ed
f
ro
m
11
kv
t
o
5k
v
i
n
b
o
t
h
t
h
e
tr
a
n
sm
iss
i
on
l
i
n
es.
Th
i
s
d
r
op
a
f
f
e
c
t
s
t
h
e
g
e
ner
a
tio
n
si
d
e
a
nd
in
t
ur
n
t
h
e
ge
ner
a
tio
n
ca
pac
i
t
y
sho
u
l
d
be
i
nc
r
e
a
s
e
d
i
n
or
de
r
t
o
c
om
pe
nsa
t
e
the
dr
op.
I
n
or
der
t
o
im
pr
o
v
e
t
h
i
s
s
ce
nar
i
o
w
e
h
ave
i
m
p
l
e
m
ented
I
P
F
C
i
n
the
s
y
s
t
em
.
We
h
ave
incor
por
a
t
e
d
I
PF
C
as
s
how
n
in
F
igur
e
6.
F
i
g
u
r
e
8
r
epr
e
sen
t
s
v
o
lta
ge
a
t
r
e
c
e
iv
i
n
ge
nd
of
l
i
n
e
1
w
it
h
I
P
F
C
-
S
P
W
M
,
wh
en
I
PFC
-S
PWM
is
inc
o
r
p
o
r
ate
d
i
t
i
s
obser
ved
t
h
a
t
t
he
v
o
lta
ge
h
a
s
b
ee
n impr
ov
ed
to
1
1kv
.
The
sa
me
i
s
ob
se
r
v
ed
in
lin
e
2
.
Figu
r
e
9
repr
esen
ts
v
o
lta
ge
a
t
re
ceiv
i
nge
n
d
o
f
l
i
n
e1 with
I
P
F
C-SVM
.
O
n
c
o
m
par
i
son of bo
t
h
t
h
ese
fi
g
u
r
e
s,
it
i
s
s
e
e
n
tha
t
i
n
i
tia
ll
y
t
h
e
vo
l
t
age
w
ith
S
PWM
is
b
ei
n
g
acc
umu
l
a
t
e
d
w
ith
h
a
r
m
o
n
i
c
s
.
T
h
e
T
H
D
w
i
t
h
I
P
F
C
-
S
P
W
M
i
s
6.
20
%
w
h
e
r
e
the
TH
D
w
i
t
h
I
P
F
C-S
V
M
is
0
.
15%.
F
i
g
u
r
e
1
0(
a)
r
epr
e
sen
t
s
R
M
S
c
ur
r
e
nt
a
t
the
end
of
t
r
a
nsm
i
ssio
n
l
in
e1
w
ith
I
PFC-SPWM
and
f
i
g
u
r
e
10(
b)
r
epr
e
sent
s
curr
ent
w
ith
I
PFC-SVM.
I
n
com
p
aris
o
n
t
h
e
R
MS
c
ur
r
e
nt
w
i
t
h
I
P
F
C
S
P
W
M
is
5
A
w
h
er
e
a
s
wit
h
S
V
M
i
t
is
9
A.
W
ith
S
PW
M
in
i
t
i
a
ll
y
ti
ll
0.
04s
h
arm
o
nic
s
a
r
e
s
ee
n
b
u
t
in
c
ase
of
S
V
M
t
he
y
a
r
e
a
b
se
nt
.
TH
D
w
i
t
h
S
P
WM
i
s
8.
68
%
and
w
ith
S
V
M
it
i
s
0
.
14%.
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
T
r
ansm
i
s
s
i
o
n sy
ste
m
regu
l
a
r
i
za
ti
o
n
wit
h
5-
l
eve
l casc
ade
d I
PFC
(
S
ridh
ar
Ba
bu
G
u
r
i
j
a
la)
1
443
F
i
gur
e
7.
V
olta
ge
a
t
tr
a
n
smiss
i
o
n
l
i
n
e
1
i
n
t
h
e
a
bse
n
ce
of
I
P
F
C
F
i
gur
e
8.
V
olta
ge
i
n
t
h
e
pr
ese
n
ce
of
I
P
F
C
-
SP
WM
F
i
gur
e
9.
V
olta
ge
i
n
t
h
e
pr
ese
n
c
e
o
f
I
P
F
C
-S
V
M
(a
)
(b
)
F
i
g
u
r
e
1
0
.
(
a
)
RMS
cu
r
ren
t
o
f lin
e
1
in
p
resen
c
e
o
f
I
PFC-
SPWM (b
)
RMS
c
u
rrent
i
n
p
r
e
se
nce
of
I
PF
C
-
SVM
8.
2.
S
u
d
d
e
n
i
n
cr
ease
i
n
load
o
n
b
ot
h
t
r
an
sm
i
ssi
on
l
in
es
I
n
t
his
ca
se
b
oth
the
l
i
ne
s
a
t
t
he
r
e
cei
v
i
n
g
end
has
un
de
r
g
o
n
e
w
i
t
h
a
s
ud
de
n
ad
d
iti
on
o
f
lo
ad
a
t
0.
1sec
a
t
s
am
e
in
sta
n
c
e
o
f
ti
m
e
.
Figure
11
re
pr
esen
ts
r
ece
i
v
in
g
e
nd
v
o
lta
ge
o
f
b
o
t
h
t
r
a
ns
m
i
ssi
on
l
i
ne.
I
n
b
o
t
h
the
l
i
ne
s
it
i
s
obs
e
r
ved
tha
t
v
o
ltage
h
as
d
rop
p
e
d
from
5
5
0
0
V
to
a
lm
o
s
t
2
8
0
0
V
w
h
e
n
t
he
l
oa
d
i
s
a
dde
d
sud
d
e
n
ly t
he
v
ol
t
a
ge is
com
p
l
e
t
e
ly
d
istor
t
ed.
F
r
o
m
F
i
g
u
r
e
12
i
t
i
s
o
b
s
erve
d
th
a
t
vol
t
a
g
e
w
i
t
h
bo
th
c
on
t
r
ol
t
e
c
h
niq
u
e
s
i
s
ve
r
y
w
e
ll
com
p
en
sate
d
b
y
I
P
FC.
Sim
i
la
r
to
case
1
t
h
e
m
a
jor
di
ffe
re
n
c
e
in
t
he
c
on
tr
ol
t
ec
hni
ques
i
s
obser
ve
d
in
t
e
r
m
s
o
f
r
e
c
e
ivi
ng
e
nd
cu
rren
t
a
nd
TH
D
v
alu
e
s
.
THD o
f
I
PFC-S
P
W
M is
6
.19
%
and
th
a
t of I
PFC-
S
VM is 0
.
1
5
%
.
F
i
g
u
r
e
1
3
(
a
)
r
e
pr
esen
ts
R
MS
c
ur
r
e
n
t
o
f
l
i
ne
1
in
p
r
e
sence
of
S
P
W
M
a
n
d
(
b
)
r
e
p
r
e
s
e
n
t
s
i
n
p
r
e
s
e
n
c
e
of
S
VM.
In
t
his
case
s
ince
t
here
i
s
a
sud
d
e
n
i
ncr
ease
in
l
oa
d
a
t
0
.
1s
t
he
r
e
i
s
a
sm
al
l
dist
u
r
banc
e
seen.
A
n
d
i
n
SP
W
M
R
M
S
c
u
r
r
e
n
t
h
a
s
h
arm
o
n
i
cs
i
n
th
e
b
e
g
i
n
n
in
g
.
I
n
I
P
F
C
-
S
P
W
M
T
H
D
i
s
8
.
6
6
%
a
n
d
w
i
t
h
S
V
M
i
t
i
s
s
e
e
n
a
s
0
.
1
4
%
.
H
e
n
ce
o
b
ser
v
ing
t
h
ese
two
c
a
s
e
s
S
V
M
is
p
r
o
ve
n
as
o
pt
i
m
um
s
o
l
u
t
ion
i
n
t
e
r
m
s
o
f
v
o
l
t
a
g
e
c
o
mpe
n
sa
t
i
on.
T
he
r
e
f
o
r
e
f
or
a
n
I
P
F
C
w
ith
c
a
s
ca
de
d
H
br
idge
i
n
v
e
r
t
e
r
S
V
M
contr
o
l
tec
h
n
i
q
u
e
is
t
he
o
p
t
ima
l
s
o
l
uti
o
n
f
or
t
r
a
ns
mission
li
ne
p
r
o
b
l
em
s.
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
3
7
–
1
445
1
444
(a)
(b
)
F
i
gur
e
1
1
.
(
a
)
&
(
b
)
V
o
l
t
a
g
e
a
t
line
1
an
d
l
i
n
e
2
w
h
en
t
her
e
i
s
a
s
udde
n
i
n
cr
ease
in
l
oa
d
(a)
(b
)
Fig
u
r
e
12
.
(a
)
Vo
ltag
e
at
t
h
e
o
f
lin
e
1
in
p
r
esen
ce o
f IP
FC-
S
PW
M
,
(
b
)
in
p
r
esen
ce of IPFC-S
VM
(a)
(b
)
F
i
gur
e
1
3
.
(
a
)
RMS
cur
r
ent
of
line
1
in
p
r
e
se
nce
of
I
P
F
C
-
S
P
W
M
(
b)
R
MS
c
ur
r
e
nt
i
n
pr
e
s
e
n
ce
o
f
I
P
F
C
-
S
V
M
Tab
l
e
2. THD va
lue
s
o
f
all
ca
se
stu
die
s
ca
s
e
s
Volta
g
e
THD
with
IP
F
C
-
S
P
W
M
V
o
l
t
a
g
e
T
HD
w
ith
IPF
C
-SVM
Curr
e
n
t THD with
IPFC
-S
PWM
Cu
r
r
e
n
t
T
H
D
w
i
t
h
IPF
C
-SVM
D
r
oppi
ng
o
f
t
he
r
ec
e
i
ving e
nd
volta
ge
of
Tr.line
1
6.
20%
0.
15%
8.
68%
0.
14%
Sudde
n
inc
r
ea
s
e
i
n
loa
d
on
tw
o
Tr
.lin
es
6.
19%
0.
15%
8.
66%
0.
14%
9.
CONCLUS
I
O
N
In
t
h
i
s
pa
per
a
com
p
ara
t
i
v
e
a
n
al
ys
is
i
s
pe
rfor
m
e
d
o
n
t
h
e
con
t
ro
l
tec
h
niq
u
e
s
o
f
IP
FC
w
it
h
d
i
ffe
r
en
t
c
a
se
s
tud
i
e
s
.
Con
t
r
o
l
te
c
h
ni
qu
e
is
t
he
b
a
s
i
c
b
ui
l
d
in
g
b
l
ock
of
I
P
F
C
,
so
c
ho
os
in
g
a
pr
ope
r
con
t
r
o
l
te
c
h
ni
que
i
s
a
c
h
a
l
l
e
ngi
ng
t
ask
.
F
ro
m
t
h
e
re
su
lt
s
ob
t
a
in
ed
i
n
t
h
e
ab
ov
e
ca
se
s
tu
d
i
es
i
t
is
e
v
i
de
n
t
t
hat
the
best
s
olu
t
i
on
f
o
r
p
o
w
e
r
f
l
o
w
c
o
n
t
r
o
l
i
f
I
P
F
C
,
i
n
c
a
s
e
w
h
e
r
e
m
o
r
e
t
h
a
n
t
w
o
l
i
n
e
s
a
re
e
merg
ing
.
F
ro
m
t
h
e
cas
e
s
tu
dies
pe
r
f
or
m
e
d
a
b
o
v
e
i
t
i
s
ob
ser
v
e
d
t
ha
t
t
h
o
ugh
I
P
F
C
w
it
h
S
P
WM
i
s
m
a
i
n
t
a
in
ing
g
o
o
d
v
o
l
ta
ge
p
r
o
fil
e
,
IPFC-
S
V
M
is
m
a
i
nt
a
i
n
i
ng
g
o
o
d
f
u
nda
me
n
t
a
l
c
o
m
pone
n
t
a
l
o
n
g
w
i
t
h
g
oo
d
v
o
l
t
a
g
e
p
r
o
f
i
l
e
a
n
d
l
e
s
s
T
H
D
,
w
h
i
c
h
i
s
sa
tisfy
in
g t
h
e
o
b
j
e
c
t
ive
of a
c
ontr
o
l tec
h
niq
u
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
T
r
a
n
sm
is
si
on
system
re
gu
lar
i
za
t
i
o
n
wi
t
h
5-l
e
v
e
l c
a
sc
ade
d I
PFC
(Sri
dhar
Ba
bu G
u
r
ija
la)
1
445
REFE
RENCES
[1]
J
.
G
uo,
M
.
L.
C
ro
w
and
J
a
gann
ath
a
nS
arang
a
p
a
n
i
,
“
A
n
Im
pro
v
ed
U
P
F
C
Contro
l
for
Oscillation
D
a
mpi
n
g”,
Jo
ur
nal
o
f
IEEE
T
r
a
n
s
a
ct
ions on
Power
Sy
s
t
em
s
,
Vo
l
.
24,
N
o.
1
,
p
p.
2
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eb
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20
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9
.
[2]
N
.
A
b
i
-S
a
m
ra,
D
.
C
am
o
v
a
l
e,
A
.
S
u
nd
aram,
W
.
M
al
colm,
“T
he
r
o
l
e
o
f
the
d
i
st
ribu
tion
sy
s
t
e
m
d
yn
a
m
ic
v
ol
ta
g
e
restorer in enhancing
the
pow
er at sensi
tive
f
acilities,
”
WE
SCON/96
, Pa
g
e
(
s)
: 16
7
-1
81
,
1
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[3]
R.
B
uxto
n
,
“P
rot
ectio
n
f
r
om
vol
ta
ge
d
ip
s
wi
th
t
h
e
d
yn
a
m
ic
v
olta
ge
r
es
torer,
”
IE
E H
a
l
f
Day Col
l
o
quium on
D
y
na
mi
c
Vo
lta
g
e
Rest
o
r
ers -
Rep
l
a
c
ing
T
h
o
s
e Mis
s
i
ng Cycles
,
Glas
go
w
,
19
98,
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3
/
1
-
3/6.
(
Di
ges
t
N
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1
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[4]
A
.
B
u
r
den
,
“
Ca
led
o
n
i
an
P
aper
DVR-t
he
u
tili
t
y
pers
pect
ive,
”
I
E
E
Ha
l
f
Da
y
C
o
llo
q
u
i
um
o
n
D
y
na
mic
Vo
ltag
e
R
e
st
o
r
ers
-
Replacing Those
M
i
ssi
ng Cycles
,
Gl
a
s
g
o
w,
1
9
9
8
,
p
p. 2
/1
-2/
2
.
(
D
i
g
e
st
No
.
1
998/1
8
9
)
.
[5]
J
Ch
en,
TT
Lie
“
E
n
h
a
ncem
ent
of
p
o
w
er
s
yst
e
m
dam
p
in
g
u
s
i
n
g
V
S
C
b
a
sed
s
e
ries
c
on
nected
F
A
C
TS
c
o
n
t
r
o
llers
”
_
D
i
stribu
ti
on, I
E
E
,
20
03
[6]
R
St
rzelecki
,
J
B
ojars
k
i
-
“
Probabilistic
m
e
t
hod
f
o
r
parall
el
f
i
lter's
power
select
ion
i
n
i
nterlin
e
po
wer
f
l
ow
cont
roller
”
E
PE-P
E
M
C
Conf
ere
n
ce
, Cit
eseer,
20
0
2
.
[7]
MR
B
ANAEI
“Improvem
e
nt
o
f
Dynam
i
cal
S
ta
bilit
y
U
s
i
ng
I
n
terline
Pow
e
r
Flow
C
on
t
r
oller”
-
Ad
van
c
es
i
n
E
l
ect
r
i
cal an
d
Co
mpu
t
er
, 20
1
0
[8]
L.
G
yu
gy
i
,
K
.
K
.
S
e
n
,
a
n
d
C
.
D
.
Sc
h
a
ud
e
r
,
“The
i
n
t
e
r
lin
e
p
owe
r
fl
o
w
co
nt
ro
ll
er
c
oncep
t
a
new
ap
p
r
oach
t
o
po
wer
flow m
a
nagem
e
nt
in t
r
a
n
s
m
ission s
y
stems,
”
I
E
EE Trans. P
o
wer
Del
., vo
l
. 1
4,
no
.
3
, pp
.
1
11
5
–
1
1
2
3
, Ju
l
.
1
9
9
9
.
[9]
N
.
G.
H
ing
o
rani
a
n
d
L
.
Gy
ug
yi.
Un
id
erst
andi
ng
F
ACTS
-Con
c
e
p
t
s
an
d
T
echn
o
l
ogy
o
f
Flex
ib
le
A
C
T
r
ans
m
i
s
s
i
on
Syst
e
m
s
. I
E
E
E
p
r
ess, F
i
r
st Indian Edition
, 2001
.
[10]
R.
P
a
l
ani
s
a
m
y,
K
.
V
i
j
a
yaku
m
a
r,
D
.
Sel
v
ab
harath
i
“
M
S
P
WM
b
ased
I
m
p
l
em
ent
a
ti
on
o
f
No
vel
5-levelIn
v
ert
e
r
w
ith
P
h
ot
ov
o
l
t
a
ic
S
ys
t
e
m
”
IJ
P
EDS v
o
l
u
m
e
8
,
No
4
,
D
ecem
ber
201
7.
[11]
G
r
aham
m
e
Holm
e
s
and
T.A. Lip
o, “
Puls
e w
i
d
t
h
m
o
dulation
f
o
r po
we
r
co
nvert
ers”
I
EEE
press,
200
4.
[12]
De
b
a
nja
n
R
oy
,
Ma
d
h
u
S
i
ng
h,
T
a
p
a
s
R
oy
“
A
No
v
e
l
Ap
pro
a
c
h
f
o
r
S
pa
c
e
V
ecto
r
B
as
ed
P
W
M
A
lgori
t
hm
f
o
r
D
iode
Cl
am
ped
T
h
ree
lev
e
l
VS
I
F
e
d
Ind
u
ct
ion
Mo
to
r
Driv
e”.
Inter
n
a
t
i
onal Jo
urn
a
l
o
f
p
o
wer E
l
ectr
o
n
i
cs
a
n
d
D
r
i
ves
(I
J
P
E
D
S
)
,
,
Vo
l
u
m
e 8,
No
4,
Dec
2
0
1
7
.
[13]
P
.
G.
H
an
dl
e
y
a
n
d
T
.J.
Boys,
“
S
pac
e
v
e
c
t
o
r
m
o
d
u
l
a
tio
n:
A
n
eng
i
ne
ering
rev
i
ew
”
IE
E 4
t
h In
t
e
rna
t
ion
a
l
Co
nfer
ence
o
n
Power El
ectron
i
cs
and Vari
a
b
le S
p
eed
Drives
,
Conf
Pu
b
3
2
4
,
pp.
8
7
-
91
,
19
90
.
[14]
G
.
N
arayan
a
n
a
n
d
V
.T.
Rang
anath
a
n,
“
Tri
a
n
g
l
e
c
o
m
p
a
ris
on
and
sp
a
ce
v
ect
or
a
ppr
o
aches
t
o
p
u
ls
e
w
i
d
t
h
m
odulat
ion
i
n
inv
erter f
e
d
dri
v
e”,
Jo
ur
na
l of
In
di
an
Insti
t
ute
o
f
S
c
ience
,
S
e
pt
/Oct
,
p
p
.
409
-42
7
,
200
0.
[15]
Jo
oh
n-Sh
e
o
k
Kim
a
n
d
Se
un
g-Ki
S
ul,
“
A
n
ov
e
l
v
o
l
ta
ge
m
od
ula
t
i
o
n
t
e
c
h
n
i
q
u
e
of
t
he
s
pa
c
e
v
e
c
t
or
P
WM”
in
Pro
c
.
IP
EC
, Yo
k
o
h
ama, Japan
,
p
p
.
7
4
2
-
74
7, 1
99
5.
[16]
D
ae-W
o
o
n
g
Ch
u
ng,
J
oo
hn
-S
he
ok
K
im
a
n
d
S
e
u
ng-K
i
S
ul,
“Un
i
f
i
ed
vol
t
a
ge
m
od
ul
a
t
i
on
t
echn
i
q
u
e
f
o
r
real-tim
e
t
h
ree-p
h
ase
pow
er con
vers
ion
”
IEEE T
r
ans.
Ind.
Ap
plicat
.
,
vol.
34,
no.
2
,
M
ar/Apr,
p
p.
374
-38
0
,
1
9
98.
[17]
T
.
B
rah
m
anand
a
R
edd
y
,
J.
A
m
a
rn
a
t
h
and
D.
S
u
b
barayu
du
,
“
I
mpro
vem
ent
of
D
T
C
p
erf
o
rm
ance
b
y
u
si
ng
h
y
b
rid
s
p
ace
ve
cto
r
P
ulsew
i
dth
m
odulatio
n
al
go
rit
h
m
”
In
tern
atio
nal R
eview o
f
E
l
ectri
ca
l
En
g
i
neeri
n
g
,
V
o
l
.
4
,
no.
2,
J
u
l
-
Au
g, pp
. 59
3
-6
0
0
, 20
0
7
.
[18]
S
t
eph
e
n
W
.
M
idd
l
ek
a
u
ff
,
E.
R
an
do
lp
h
Co
llin
s
,
J
r.,
“S
ystem
an
d
C
u
s
t
o
m
e
r
Im
p
act:
Con
s
i
d
erati
o
n
s
f
or
S
eries
Cu
st
o
m
P
o
w
er D
evices
,”
I
E
EE
T
r
a
n
s
.
O
n
P
o
w
e
r De
liv
e
r
y
,
Vo
1
.
1
3
, No
.
1
, Jan,
pp
. 27
8
-2
82
,
19
98
.
[19]
A
m
it
K
um
ar
G
up
ta
a
n
d
A
s
h
win
M
.
K
ha
m
b
adko
ne,
“
A
G
en
era
l
S
p
ace
V
e
c
t
or
P
W
M
A
lgor
ithm
f
o
r
Mu
lti
Level
In
vert
ers,
I
nclu
d
i
ng
O
p
e
rati
on
i
n
O
v
erm
o
d
u
l
a
ti
o
n
R
ang
e”,
IE
EE Transacti
o
ns
on Power Elect
ron
i
c
s
,
vol.
2
2
,
no
.
2,
M
a
rch
20
07
.
[20]
B.
S
i
r
ish
a
,
P
.
S
at
is
h
Kumar,
N
.Sus
heela,
“
Th
ree
P
h
ase
Two
L
e
g
N
e
u
t
r
a
l
P
o
i
n
t
C
l
a
m
p
e
d
C
o
n
v
e
r
t
e
r
w
i
t
h
o
u
t
p
u
t
D
C
V
o
ltag
e
R
egu
l
atio
n
and
In
pu
t
P
o
wer
F
acto
r
C
orrect
io
n”,
Int
e
rnati
o
n
a
l
Jo
ur
na
l
of Po
wer El
ectroni
cs
an
d Drive
S
y
st
em (
I
JPEDS)
,
v
o
l
.
2
,
n
o
.
2
,
June
201
2.
[21]
B.
Sirish
a
,
P.
S
atis
h
K
u
m
a
r,
“
A
Space Ve
cto
r
P
uls
e
W
idth
M
od
u
l
a
t
i
o
n
Techn
i
q
u
e
fo
r F
i
v
e
L
ev
el Cas
caded HBrid
ge
Inv
e
rte
r
I
nc
lu
di
ng
O
ve
r
Mod
u
la
t
i
on
R
egion
with
F
P
G
A
I
m
plementat
io
n”
,
Inter
n
a
t
i
onal Jou
r
n
a
l
of po
wer
E
l
ect
ro
n
i
cs a
nd Dri
ves
(
I
JPED
S
)
, vo
l
.
8,
n
o.
3,
Se
pte
m
b
e
r 20
17
.
[22]
B.
S
i
r
ish
a
,
P.
S
at
ish
K
u
m
a
r,
“
Impl
emen
tatio
n
of
F
P
G
A
based
S
p
ac
e
V
e
ctor
P
WM
M
et
ho
d
f
o
r
F
ive
L
e
vel
Cascad
ed
Invert
er”,
IE
E
E
7th Power
Ind
i
a
Int
e
rna
tio
na
l
Con
f
eren
ce
(
P
IICON 20
16)
a
t
Bikan
e
r
Raj
a
sth
a
n,
N
ov
e
m
b
e
r
25-2
7
20
16
.
[23]
B.
S
iri
s
ha,
P
.
S
at
ish
K
u
m
a
r,
“
A
S
i
m
p
lifi
ed
S
p
a
ce
Vect
or
P
W
M
f
or
C
as
c
a
d
e
d
H
-
B
rid
g
e
In
vert
e
r
i
n
c
ludin
g
O
ve
r
Modulation
Operati
on”,
13th
In
t
e
rna
t
i
o
n
a
l
IEEE India
Confer
ence INDICO
N 20
16
a
t
IISC,
B
engaluru,
India.
D
ecem
ber 1
6
-18
, 2
01
6
[24]
N
a
bi
l
F
a
rah,
J
u
r
if
a
Bt.
M
a
t
L
a
zi
,
M
H
N
T
a
lib
”
Com
p
arat
iv
e
S
t
ud
y
o
f
Th
ree
Diff
erent
T
o
p
o
l
ogies
o
f
F
i
ve-Lev
el
In
vert
er
w
it
hSPWM
M
o
du
la
ti
o
n
T
echn
i
q
u
e”
Int
e
rn
ation
a
l
Jo
u
r
na
l o
f
p
o
wer
E
l
ectr
onics and Drives
(
I
JPEDS)
,
V
o
l
u
m
e
8
,
N
o
4
,
Dec
201
7.
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