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.
4, D
e
c
e
m
ber
201
9,
pp.
1944~
19
50
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1944-1950
1944
Jou
rn
a
l
h
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me
pa
ge
:
ht
tp:
//i
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e
score
.
com
/
j
o
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s
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i
n
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x
.
p
hp/IJ
PED
S
Performan
ce analysis of LMS
base
d contr
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po
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p
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ovement i
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system for linear
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mma
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A
h
ma
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heera
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i
r
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ni
D
e
partm
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n
t
o
f El
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ngineer
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g
,
Jami
a
Mil
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Art
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fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Mar
6
,
201
9
Re
vise
d A
p
r
20,
201
9
A
c
c
e
pte
d
J
u
l
8
,
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Th
is
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e
nt
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apt
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ve
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ased
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ta
t
i
c
c
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mpe
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sa
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r
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STATCO
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o
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l
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oad
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o
s
o
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uality
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ms
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o
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f
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om
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h
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it
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l
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h
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c
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ted
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eyw
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s
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DSTA
TC
OM,
LMS
P
o
w
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lit
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TH
VSC
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:
Mo
hmm
a
d
A
h
ma
d,
R
e
sear
ch S
cho
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ar
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D
e
pa
rtme
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o
f
El
e
c
t
rica
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eri
ng,
Jam
i
a
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llia
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slam
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e
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11
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Em
ail:
ahm
a
db
tech
@
g
m
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il.c
o
m
1.
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N
TR
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C
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The
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[
1]
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Int J
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2088-
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Perf
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dali
ne
b
ase
d
N
eura
l
ne
tw
ork,
sin
gle
D
Q
t
h
e
o
ry e
tc.
A
d
a
p
t
i
ve
f
il
t
e
r
t
h
eor
y
s
how
s
its
p
ow
e
r
t
o
tra
c
k
the
cha
n
ge
s
o
f
the
un
kn
o
w
n
sy
stem
s’
e
nv
i
r
o
n
m
e
n
t
and
c
h
ar
acter
i
s
tic
s.
T
he
f
i
l
te
r
par
a
m
e
ter
s
w
il
l
be
s
e
l
f-a
dj
us
te
d
du
rin
g
th
e
e
n
vi
ron
m
e
n
t
ch
angi
ng
s
o
t
h
at
t
h
e
f
ilt
er
b
eh
a
v
io
ur
a
n
d
env
i
ro
nme
n
t
w
i
ll
b
e
ord
e
r
t
o
f
u
l
fi
l
it
s
pu
rp
ose.
T
he
re
e
xis
t
s
va
rio
u
s
a
d
a
p
ti
ve
c
o
n
tr
ol-
base
d
a
l
g
o
ri
th
m
a
v
ai
la
ble
i
n
t
he
liter
a
ture
s
uc
h
as
r
ec
ursive
l
ea
st
s
q
u
a
r
e
(RLS),
L
ea
st
M
ea
n
Sq
uar
e
(
LM
S
)
etc.
[
1
3
-1
4].
Am
ong
t
h
ese
a
l
g
o
ri
thm
s
,
LMS
a
nd
i
t
s
var
i
a
n
ts
b
ec
o
me
p
op
u
l
ar
f
or
t
he
ir
b
es
t
c
o
nve
rgenc
e
spee
d
and
s
t
a
b
il
it
y
[
1
5-
18].
The
fu
nc
ti
on
o
f
L
MS
a
lgor
ithm
is
t
o
ex
tr
a
c
t
acc
ur
ate
p
u
l
s
e
an
d
minimi
ze
s
t
h
e
er
ror
appr
opr
i
a
t
e
ly
f
or
t
he pr
o
p
e
r
op
e
r
a
tio
n of D
S
T
A
T
CO
M.
I
n
t
h
i
s pape
r, con
t
i
n
uou
s tim
e LMS
based a
d
apt
i
v
e co
n
t
rol alg
o
r
i
t
hm w
ith
D
S
T
A
T
C
O
M syste
m
w
ill
be
d
isc
u
ss
t
o
i
m
p
ro
ve
c
urr
e
nt
r
e
l
a
t
e
d
p
ow
er
q
ua
lit
y
pro
b
lem
s
,
h
a
r
m
onic
s
’
el
imi
n
at
i
o
n,
l
o
a
d
ba
lanc
in
g
o
f
no
n
l
i
n
ea
r
loa
d
s
etc.
M
ore
ove
r
,
t
his
fi
lter
s
t
r
u
c
t
ur
e
is
s
imp
l
e,
a
nd
to
g
e
t
d
esired
r
es
po
ns
e,
o
n
l
y
o
n
e
c
o
nstan
t
i
s
r
eq
ui
r
e
d
.
2.
S
Y
S
T
EM
C
O
N
F
I
GU
R
A
TI
O
N
The
bl
oc
k
d
i
a
g
ram
of
t
he
D
S
T
A
T
CO
M
sy
st
e
m
w
it
h
thre
e
p
h
a
s
e
sys
t
e
m
havi
ng
a
n
o
n
-l
inear
l
oa
d
c
o
nn
e
c
t
e
d
a
t
a
PCC
i
s
sho
w
n i
n
F
i
g
u
r
e
1
.
T
he
d
i
s
t
r
i
but
ion
sy
st
e
m co
nsi
s
t
s
o
f a
three
pha
se
gri
d
o
f
4
1
5
V
(li
ne
to
l
i
n
e),
50
H
z
,
ha
vin
g
R
s
a
n
d
L
s
a
s
ser
i
e
s
r
e
s
i
s
ta
nc
e
a
n
d
in
d
u
cta
n
c
e
r
es
pe
ct
ive
l
y
,
a
l
o
ng
w
i
t
h
I
GBT
b
a
sed
Vol
t
a
g
e
S
o
urc
e
Con
v
e
r
ter
(VSC),
d
c
l
i
n
k
c
apac
ita
nce
(C
dc
)
,
a
n
int
e
rfa
c
i
ng
i
n
d
u
c
t
ance
L
f
b
e
t
w
e
e
n
V
S
C
a
n
d
P
CC
to
r
e
d
uce
the
r
i
p
p
l
es
i
n
c
o
mpe
n
sa
t
i
ng
cur
r
ent,
a
n
d
r
i
pple
f
il
ter
R
f
a
nd
C
f
to
s
up
pr
e
ss
t
h
e
h
i
gh
sw
itc
h
i
ng
fre
que
nc
y
no
is
e
[
19].
V
S
C
i
s
a
t
hree
-le
g
v
o
l
t
a
ge
s
o
u
rc
e
in
verte
r
ha
vin
g
s
i
x
I
GB
T
s
w
i
t
ch
es
w
i
t
h
a
n
i
np
ut
a
s
dc
v
o
ltage
s
o
u
r
c
e
a
nd
t
h
e
ou
tpu
t
a
s
t
h
re
e
p
h
ase
ac
s
u
pp
ly
f
ee
d
i
ng
t
o
t
h
e
gri
d
a
s
w
e
ll
a
s
t
o
t
he
l
ine
a
r/
no
n-
line
a
r l
o
a
d
c
on
necte
d
a
t P
C
C.
T
he
s
ys
t
e
m is a
n
a
l
y
ze
d for b
o
th t
he
l
oa
d,
l
i
n
ea
r
a
n
d no
n-l
i
near
l
oad
s
. Ind
u
ct
i
v
e
R
L
l
oa
d
i
s
e
m
p
l
o
yed
a
s
line
a
r
loa
d
a
t
P
C
C
,
w
hi
le
a
s
a
n
o
n
-l
inea
r
l
o
a
d
,
a
thre
e-p
h
a
s
e
di
o
d
e
br
id
ge
r
e
c
tif
i
e
r
w
ith
i
n
duc
t
i
ve
bra
nc
h a
t
d
c
side
, is use
d
.
F
i
gure
1.
B
l
o
c
k
d
i
a
gram
of DC b
us ba
s
e
d
D
S
T
A
T
CO
M w
ith t
hree
pha
se
s
ys
t
e
m
3.
CONT
ROL ALGO
RITH
M
Th
e
sch
e
mat
i
c
d
i
a
g
r
am
o
f
DSTATC
OM
b
ased
o
n
Le
a
s
t
M
e
a
n
S
qu
a
r
e
(L
MS
)
cont
r
o
l
algorithm
i
s
show
n i
n
F
igur
e 2. The
m
ain func
t
i
on o
f
th
i
s a
l
gor
it
hm
is to de
ri
ve u
nit t
e
m
p
la
tes for ea
ch of t
h
e thr
ee p
h
a
ses
(x
aa
,
x
ab
a
nd
x
ac
) extrac
t
e
d
fro
m the o
b
se
rved
g
rid
voltages
(
v
sa
,
v
sb
a
n
d
v
sc
)
,
require
d
gr
id refe
r
enc
e
curr
e
nt by
sens
in
g t
h
e thre
e p
h
ase
loa
d
c
urrent
(i
La
,
i
Lb
and i
Lc
),
g
ri
d
vo
l
t
a
g
e
m
a
gni
tud
e
(
V
t
)
and
V
dc
across
the
VSC.
T
he
sw
it
c
h
i
n
g
p
u
ls
es
f
or
D
S
T
A
T
CO
M
are
ge
ne
rated
a
f
t
e
r
m
a
ki
n
g
a
c
om
p
ar
is
on
b
e
t
w
e
e
n
t
he
t
w
o
g
r
i
d
c
u
rre
nts:
refere
nce
cur
r
e
n
t o
b
t
ai
ne
d
fro
m
a
lg
or
ithm
a
n
d
the o
b
se
rve
d
c
urr
e
n
t from
t
h
e
syst
e
m.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
9
4
4
– 1
950
1
946
F
i
gur
e 2.
S
chem
atic
d
i
a
gram
for LMS
ba
s
e
d
contr
o
l
al
g
o
ri
thm
I
n
itia
l
l
y
t
h
e
ac
t
i
ve
o
r
i
n
-p
has
e
v
o
l
t
a
ge
u
n
i
t
tem
p
l
a
tes
of
e
a
c
h
o
f
t
h
ree
ph
as
es
x
aa
,
x
ab
a
nd
x
ac
can
b
e
ca
l
c
u
l
a
t
e
d
w
i
t
h
t
h
e
he
lp
o
f
gr
i
d
vol
ta
ge
m
ag
ni
t
ude
(
V
t
)
[
2
0].
Th
es
e
x
pa
,
x
pb
a
nd
x
pc
a
r
e
in
pha
se
w
it
h
the
thre
e
pha
se
g
rid v
o
lta
ges v
sa
,
v
sb
a
nd
v
sc
a
n
d m
a
the
m
atica
l
l
y
t
hese
ar
e
r
epresented as:
,
,
,
(
1
)
V
t
is t
he
m
agn
i
t
u
de
o
f
t
h
e
t
h
re
e pha
s
e
in
s
t
a
nta
n
e
o
u
s
supp
ly
v
olt
a
g
es g
iv
en
a
s:
(
2
)
wher
e insta
n
ta
neo
u
s
thre
e
ph
ase
volta
ge
s ar
e:
v
sa
(t) =
V
m
Sin
ω
t
v
sb
(t) =
V
m
Sin
(
ω
t - 120º)
(3
)
v
sc
(t) = V
m
Si
n
(
ω
t -
240º)
Th
re
e
blo
c
ks
a
re
u
se
d
to
e
st
ima
t
e
a
c
t
i
v
e
w
e
i
ght
c
o
m
p
o
n
e
nt
r
e
l
at
ed
t
o
ea
ch
o
f
th
e
t
h
ree
p
h
a
se
s.
E
ac
h
bl
oc
k
re
ce
i
v
e
s
t
he
i
n
p
u
t
s
i
g
n
a
l
as
a
l
oa
d
cu
rre
nt.
The
di
ffe
r
en
ce
b
e
t
we
e
n
t
h
e
i
n
put
a
nd
o
u
t
pu
t
i
s
t
e
r
med
a
s
err
o
r
sig
n
al
w
hi
l
e
t
he
o
u
t
put
i
s
o
b
ta
i
n
ed
a
ft
er
t
he
m
u
l
tip
li
cat
i
o
n
of
u
ni
t
in
p
ha
se
t
em
p
l
a
t
e
(x
pa
for
phase
‘a’)
w
ith
i
ts
c
or
respo
n
d
i
ng
w
e
i
g
h
t
c
omp
one
n
t
.
More
over,
t
he
i
nt
egra
t
e
d
o
u
t
pu
t
o
f
t
he
p
ro
duc
t
o
f
u
n
i
t
te
m
p
late
and
er
ror
al
on
g
wit
h
g
ai
n
i
s
k
n
o
wn
a
s
a
c
t
iv
e
com
p
one
n
t
o
f
loa
d
c
u
r
r
ent
for
a
par
tic
ula
r
pha
se.
The
e
q
u
a
tio
ns
for
pha
se
‘
a’ represe
n
t
i
n
g th
e
ab
o
v
e
i
n
time
dom
ai
n ar
e writ
te
n
in (4)
.
Whe
r
e
o
u
t
p
ut
.
(
4
)
.
0
S
i
milarl
y,
f
or
pha
se
‘
b’
a
nd
pha
se
‘
c
’
,
the
a
c
ti
ve
w
ei
g
h
t
com
p
o
ne
nts
(w
b
a
nd
w
c
)
ca
n
be
c
a
l
c
u
l
a
te
d
.
The
a
v
e
r
age
o
f
a
c
t
i
v
e
we
i
ght
s
for
a
ll
t
h
e
t
h
ree
p
h
ases
w
i
ll
b
e
t
a
ke
n
to
e
n
s
ur
e
bala
n
c
e
so
u
r
ce
c
urr
e
nt.
T
h
is
i
s
st
a
t
ed as w
pA
a
nd va
l
u
e
w
i
l
l
b
e:
3
(5
)
The
dc
l
i
n
k
v
o
l
t
age of
V
S
C
i
s
sensed
w
i
t
h
refere
nce
dc vo
l
ta
ge
to
g
e
t
e
rror
.
C
onse
que
n
tly
,
this
e
r
r
or
is
f
ee
d
to
P
rop
o
rt
io
na
l
pl
us
I
nte
g
ra
l
co
n
t
r
o
lle
r
(P
I)
of
d
c
bus
v
o
l
tage
t
o
ge
t
dc
l
o
s
s
w
e
i
ght
c
omp
o
n
e
n
t
(
w
cd
)
and
the
eq
ua
t
i
o
n
is
w
r
it
te
n as
[
2
1
-2
2]:
1
1
.
1
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
Perf
orm
a
nce
a
n
a
l
ys
is o
f
L
M
S
base
d
c
o
n
t
rol al
g
o
r
ithm
for p
o
w
e
r
qu
a
l
i
t
y …
(Mohm
m
ad Ahm
a
d)
1
947
wher
e
1
∗
1
1
(
6
)
k
p
a
n
d
k
d
ar
e
the
pro
port
i
o
n
a
l
an
d
i
n
tegra
l
g
a
i
n
for
the
dc
v
olta
ge
c
o
n
tr
ol
ler,
w
hil
e
v
dd
(n+1)
is
t
he
e
r
r
or
betw
ee
n dc
re
f
er
ence
val
ue
a
nd
the
sense
d
v
alue
o
f dc
b
us.
The
r
ef
ore,
one
can
o
b
t
ai
n
th
e
to
ta
l
act
i
v
e
w
e
ig
ht
c
om
p
one
n
t
by
add
i
ng
a
v
e
ra
ge
a
ct
iv
e
weig
ht
com
p
o
n
e
n
t a
n
d
dc
l
oss c
o
mp
o
n
e
n
t
w
h
ic
h is s
tate
d
as:
(
7
)
The
re
fer
e
nce
gri
d
c
urre
nt
s
o
f
t
he
t
hr
ee
pha
ses
can
b
e
o
b
t
aine
d
b
y
m
u
lti
pl
yin
g
t
ot
al
a
c
t
i
v
e
w
e
igh
t
c
o
mp
on
en
ts wi
t
h
c
o
r
re
spon
din
g
uni
t
t
e
mp
l
a
tes
f
o
r e
a
c
h
p
h
a
se
. Th
ese
are repre
s
e
n
t
i
n
g
a
s:
∗
.
,
∗
.
,
∗
.
(
8
)
The
n
,
the
a
c
t
u
al
g
rid
curr
en
t
s
a
re
c
om
pare
d
wi
th
t
he
r
efe
r
enc
e
gri
d
c
ur
rent
f
or
eac
h
pha
se.
Th
e
di
ffe
re
nce
s
o
f
t
h
ese
tw
o
c
u
r
r
ent
s
a
re
a
ga
i
n
c
ompa
red
i
n
d
i
vi
dua
l
ly
w
ith
a
r
e
f
er
ence
s
i
gna
l
,
a
t
ria
n
g
u
lar
c
a
rr
ier
wa
v
e
o
f
10
k
Hz.
B
y
t
hi
s
comp
a
r
i
s
on
,
t
h
e
six
pul
se
s
a
r
e
e
x
t
r
act
e
d
(S
1
t
o
S
6
)
w
h
ich
ar
e
ut
i
lize
d
a
s
t
h
e
ga
te
signa
l
of
s
ix
s
w
itc
he
s of
t
he
t
hree
-ar
m
vol
t
a
ge so
u
rc
e
conv
erte
r.
4.
RESULT
S
A
N
D
DISCU
SSIO
N
The
perfor
m
a
n
ce
of
a
c
on
tro
l
c
ircui
t
w
it
h
a
li
nea
r
R
-
L
l
oa
d
is
s
h
ow
n
i
n
F
i
gur
e
3,
w
he
re
t
he
l
oad
o
f
pha
se
‘
a’
i
s
disc
o
n
n
e
c
t
e
d
fro
m
tim
e
0.5
t
o
0
.6
s
ec
o
n
d
.
The
va
ri
a
t
ion
of
g
r
i
d
v
o
l
t
a
g
e
a
t
P
CC
(v
s
),
s
ourc
e
curr
ents
o
f
the
three
phases
(i
s
),
l
oa
d
c
u
rre
nt
f
or
t
hre
e
phase
s
(i
L
)
and
t
h
e
compensator
current
(
i
C
)
are
show
n
in
t
he
f
ig
ure
.
M
ore
ove
r,
t
he
a
c
t
i
v
e
a
nd
re
ac
ti
ve
p
ow
er
o
f
l
o
a
d
,
s
our
ce
a
nd
c
o
m
p
en
sa
tor
is
a
ls
o
r
e
pre
s
e
n
te
d
i
n
F
i
gure
4.
F
i
gure
3.
V
ar
i
a
tio
n
of d
iffere
nt
c
urre
nts
for
line
a
r
lo
a
d
w
it
h
l
o
ad
di
s
c
o
n
n
ect
io
n
o
f
ph
a
se
a
b
et
we
en
0.5
t
o
0
.6 s
-50
0
0
50
0
Vs
(
V
)
-3
0
0
30
Is
(
A
)
-3
5
35
IL
a
(
A
)
-35
35
I
Lb (
A
)
-3
5
35
IL
c (
A
)
-2
0
2
Ica
(
A
)
-2
0
2
Ic
b
(
A
)
0.
45
0.
5
0.
5
5
0.
6
0.
65
-2
0
2
Ti
m
e
(
s
)
I
cc (
A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
9
4
4
– 1
950
1
948
F
u
rther,
t
he
c
ontro
l
c
i
r
c
u
it
is
a
na
lyze
d
for
a
non-
li
ne
ar
l
oad
o
f
a
d
i
o
d
e
b
r
i
d
g
e
w
i
t
h
R
-
L
b
r
a
n
c
h
con
n
ec
ted
a
t
i
t
s
d
c
si
de
.
The
perform
ance
o
f
th
is
s
ys
t
e
m
i
s
d
ep
ic
ted
in
F
igur
e
5
w
h
en
t
he
p
ha
se
‘
a
’
l
oad
is
di
sc
o
n
n
ecte
d
f
r
o
m
0.5
t
o
0
.
6
s
e
c
o
nd.
T
h
i
s
figur
e
c
ons
i
s
ts
o
f
so
urc
e
/
g
ri
d
vol
ta
ge
a
t
P
C
C
(v
s
)
,
g
rid
c
u
rrent
(
i
s
),
ou
tpu
t
(
y
a
),
e
rror
signal
(
e
a
),
a
c
t
i
v
e
c
o
mpo
n
en
t
s
’
av
e
r
ag
e
we
i
g
h
t
(
w
avg
),
w
eig
h
t
c
o
m
pone
n
t
c
orre
sp
on
ds
t
o
P
I
controller’s
o
utput
(w
cd
),
a
c
t
i
v
e
c
o
mpon
en
ts
t
ot
al
w
ei
g
h
t
(w
pt
)
and
dc
bus
v
o
lta
ge
(
V
dc
).
M
or
e
o
ve
r
,
t
h
e
w
a
ve
form
s
of
l
oa
d
c
u
rre
nt
a
s
w
e
ll
a
s
c
o
m
p
en
sa
tor
c
u
rre
nt
a
lon
g
w
i
th
g
r
i
d
v
o
l
t
a
g
e,
c
urre
nt
i
s
repr
esen
ted
in Fig
ure
6.
The
ac
ti
ve
a
nd
r
ea
cti
v
e
p
o
w
e
r
for
so
urc
e
/
g
ri
d,
l
oa
d
a
nd
c
o
m
p
ens
a
t
or
i
s
a
l
so
s
how
n
in
F
igur
e
7.
I
t
i
s
conc
l
ude
d
fro
m
t
he
f
i
gure
tha
t
t
he
a
c
tive
pow
e
r
t
o
the
loa
d
(
P
L
)
is
m
ain
l
y
s
u
p
p
l
ie
d
from
the
grid
a
s
act
iv
e
pow
er
(P
S
), w
here
as the
r
ea
cti
v
e pow
e
r
i
n
t
o t
h
e
loa
d
is m
a
jo
rly
su
pp
l
i
ed
b
y
com
p
ensa
tor
as re
a
c
t
ive
p
o
wer
.
A
com
p
ariso
n
of
d
iffe
rent
p
ara
m
e
t
e
r
s
is
m
ade
be
twee
n
l
i
n
ea
r
as
w
e
ll
a
s
n
o
n
-l
ine
a
r
l
o
ad
a
nd
is
s
how
n
i
n
Tab
l
e
1
.
I
t
i
s
c
l
e
ar
f
rom
the
t
a
ble
tha
t
,
for
l
i
ne
ar
l
oa
d,
t
he
harm
on
i
c
s
ar
e
less
i
n
g
ri
d/s
our
ce
v
o
l
ta
ge
,
s
ourc
e
curr
ent
a
n
d
l
o
a
d
c
urre
nt
a
s
c
o
mpa
r
e
to
t
he
h
a
r
m
oni
c
s
o
bta
i
ned
i
n
the
case
of
n
o
n
-l
inea
r
loa
d
.
T
h
e
har
m
on
ics
prese
n
t
i
n
s
o
u
r
ce
c
u
r
r
ent
ar
e
5
%
and
6.9
%
for
li
n
e
ar
a
nd
no
n-
l
i
n
ea
r
l
o
a
d
r
espec
t
i
v
e
l
y.
W
h
ile
t
he
h
a
r
monic
s
in
l
oa
d
cur
r
en
t
a
r
e
0.1
%
and
29.5
%
for
li
n
e
ar
a
nd
no
n-l
i
n
e
a
r
load
o
f
bri
d
ge
r
ec
tifi
e
r
respec
t
i
ve
l
y
.
F
u
rther,
i
t
ca
n
a
l
so
b
e
see
n
f
r
o
m
the
ta
bl
e
t
h
a
t
,
as
t
he
l
o
a
d
cha
n
ges
fro
m
l
i
n
e
ar
t
o
non
-li
n
e
a
r
,
t
h
e
loa
d
p
o
w
er
a
nd
s
o
u
r
ce
pow
er
cha
n
g
es
sligh
t
ly,
w
h
ile
the
c
om
pen
s
at
or pow
e
r
r
e
m
ains a
p
p
r
o
x
i
m
a
te
l
y
t
he
sam
e.
Tab
l
e
1
.
Com
pa
riso
n of
d
i
f
fer
e
nt par
am
eter
s
for
line
a
r
and n
on-
li
nea
r
loa
d
Lo
ad
T
yp
e
Sourc
e
V
olt
a
g
e
(Vs)
S
our
c
e
c
ur
re
nt
(A)
L
o
a
d
C
urr
e
nt
(A
)
S
o
urc
e
P
owe
r
L
oa
d
P
o
we
r
Co
m
p
en
s
a
to
r
Po
w
e
r
RM
S
va
lu
e
(V
)
THD
(%)
RM
S
va
lu
e
T
HD
(%
)
RM
S
va
lu
e
TH
D
(%)
P
S
(W)
Q
S
(
VAr
)
P
L
(W)
Q
L
(VA
r)
P
C
(W)
Q
C
(VA
r)
L
i
nea
r
413.
3
3.
5
26.
0
5.
0
31.
1
0.
1
1
823
0
171
2070
0
4064
5
4
-
5
3
9
N
on
line
a
r
413.
4
3.
8
26.
4
6.
9
31.
2
29.
5
1
820
0
255
2090
0
447
5
4
-
5
40
F
i
gure
4.
A
ctiv
e
P
o
w
e
r a
nd reac
t
i
ve
p
ow
er
v
a
ri
at
i
on
F
i
gure
5.
V
ariat
i
o
n
of d
i
ffe
r
en
t
para
me
t
e
rs for
non-
li
near
loa
d
0
1.
5
x
1
0
4
Ps
(
W
)
0
10
0
20
0
Qs
(
V
A
r
)
0
2
x
1
0
4
PL
(
W
)
0
20
00
QL
(
V
A
r
)
0
60
Pc
(
W
)
0.
45
0.
5
0.
55
0.
6
0.
6
5
-5
0
0
0
Ti
m
e
(
s
)
Qc
(
V
A
r
)
-5
0
0
0
50
0
Vs
(
V
)
-3
0
30
Is
(
A
)
-3
0
30
ya
-4
0
0
40
ea
10
30
Wa
v
g
0
1
Wc
d
20
30
35
Wp
t
0.
4
5
0.
5
0.
55
0.
6
0.
6
5
70
0
Ti
m
e
(
s
)
Vd
c
(
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
Perf
orm
a
nce
a
n
a
l
ys
is o
f
L
M
S
base
d
c
o
n
t
rol al
g
o
r
ithm
for p
o
w
e
r
qu
a
l
i
t
y …
(Mohm
m
ad Ahm
a
d)
1
949
F
i
gure
6.
L
oad
a
nd c
o
mpe
n
sa
t
o
r
cur
r
ent f
o
r a
non-
l
i
nea
r
l
oa
d
F
i
gure
7.
A
ctiv
e
and r
eac
t
i
ve
pow
er
var
i
a
t
i
o
n
f
or
no
n-
li
nea
r
loa
d
5.
CONCL
U
S
ION
A
thre
e-pha
se
a
da
p
tive
fil
t
e
rin
g
b
ase
d
D
STATCOM
system
i
s
i
m
ple
m
e
n
t
e
d
t
o
miti
ga
te
t
he
harm
on
ics cau
sed b
y
no
n
-l
i
n
ea
r
loa
d
.
The
a
c
tive
w
e
i
ght c
o
m
pone
n
t
ex
tra
c
ted from
l
oad cu
r
r
ent is uti
liz
ed for
the
ga
te
p
ulse
g
ene
r
a
t
i
o
n.
T
h
e
s
yste
m
is
a
na
l
y
z
e
d
f
or
b
o
t
h
line
a
r
a
s
we
ll
a
s
non
-l
in
e
a
r
l
o
ad
c
o
n
n
ect
ed
a
t
PCC
w
ith
a
l
oa
d
dis
c
on
nec
t
i
o
n
of
p
ha
se
‘
a’
f
or
a
s
hor
t
pe
ri
od
o
f
t
i
me.
The
res
u
lts
for
both
t
he
c
a
s
es
a
re
c
ompa
red
and
e
x
p
l
a
i
ne
d.
T
he
o
bta
i
ned
r
e
sults
s
h
o
w
tha
t
t
he
c
on
tro
l
s
ys
t
e
m
is
c
a
p
ab
le
t
o
improve
s
ma
ny
pr
ob
l
e
ms
rela
t
e
d
t
o
p
ow
er
qual
i
ty
like
loa
d
u
n
b
a
l
anc
i
ng
pro
b
lem
,
h
a
r
m
o
n
i
c
s
i
n
s
our
ce
curr
ent
a
nd
i
n
s
o
u
r
ce
v
o
lta
ge
.
The
a
c
t
ive
a
n
d
rea
c
ti
ve
p
ow
er
f
or
l
oa
d,
g
r
i
d
an
d
c
o
m
p
e
n
sa
tor
i
s
a
lso
e
x
pl
aine
d
w
i
th
t
he
h
e
l
p
o
f
a
d
ia
g
r
am,
conc
l
u
d
i
ng t
h
a
t
t
he
ac
t
i
v
e
p
o
w
er
to the
l
o
ad
is m
a
in
ly fed f
rom
the gri
d, w
hile t
he r
eac
t
i
ve
pow
e
r
c
ome
s
fr
o
m
the c
o
mpe
n
sa
t
o
r
.
APPENDIX
Thr
ee
p
h
ase
A
C
s
upp
l
y
:
5
0
H
z
,
L
i
n
e
t
o
l
i
n
e
V
o
lta
ge
:
41
5
V
,
N
on-
l
i
n
e
a
r
l
o
a
d
:
A
d
i
o
d
e
b
r
i
d
g
e
r
e
c
t
if
ie
r
w
i
t
h
R
=
1
5
Ω
,
L
=
1
0
mH,
In
t
e
rfa
c
i
ng
i
ndu
c
t
o
r
s:
L
i
=
1.5
m
H,
R
ippl
e
F
i
lter
:
R
f
= 20
Ω
,
C
f
= 1
0
µ
F
,
d
c
lin
k
Ca
pac
i
t
o
r:
C
dc
=
4
0
00
µF
,
D
C
P
I
contro
ller
G
a
i
n
:
K
P
=
0
.25
an
d
K
I
=
0
.1,
Refere
nce
vo
l
t
age
of
D
C
li
n
k
:
70
0 V
,
Carr
i
e
r
w
ave
fre
que
nc
y: 1
0
kH
z.
REFE
RENCES
[1]
A
.
G
h
o
s
h
a
n
d
G
.
L
e
d
w
i
c
h
,
"
P
o
w
e
r
Q
u
ali
t
y
Enhan
cem
ent
Us
ing
Cu
sto
m
P
o
w
e
r
D
e
v
i
c
e
s
,
"
N
e
w
Y
o
r
k
,
N
Y
,
U
S
A
:
Spr
in
ger
,
20
09
.
[2]
R.
M
a
j
um
d
e
r,
“
React
iv
e
p
o
w
e
r
c
o
m
p
en
sati
on
in
s
in
g
l
e-phas
e
opera
ti
on
o
f
m
i
c
r
o
g
r
id
,
”
IE
EE
T
r
an
s
.
I
n
d.
E
l
e
c
t
r
o
n
.
,
vol
.
6
0
,
no
.
4,
pp.
1
403
–1
41
6,
2
0
1
3.
[3]
C.
S
.
C
hen
,
C
.H.
Lin
,
W
.
L
.
Hsi
e
h
,
C.
T.
H
s
u
,
and
T
.
T.
K
u,
“
Enhanc
em
en
t
of
P
V
pen
e
trati
o
n
with
D
S
T
ATCO
M
i
n
Taip
ow
er
d
i
s
t
r
ibuti
on
syst
em
,
”
IEEE
T
r
ans.
Power
Sys
t
., vol
.
28, no. 2, pp
. 1560–1567,
2013.
[4]
B.
S
i
n
g
h
a
nd
J
.
S
o
lank
i,
“
A
co
mparis
on
o
f
con
t
rol
algo
rit
h
m
s
f
o
r
DSTA
TC
OM,”
IE
EE
T
r
ansactio
ns
o
n
Ind
u
s
t
r
i
a
l
Elect
ro
n
i
cs
,
v
o
l
.
5
6
,
n
o
.
7
,
pp.
2738
-27
45,
2
0
0
9
.
[5]
S
a
b
h
a
Raj
Arya,
Ram
N
i
w
a
s
,
K
ri
sh
an
K
ant
Bh
alla,
Bh
im
S
in
gh
,
A
m
b
r
i
sh
C
h
a
nd
r
a
,
a
n
d
Ka
ma
l
Al
-Ha
d
d
a
d,
“
Po
we
r
Qual
it
y
Im
p
r
ov
e
m
en
t
i
n
I
s
o
l
a
ted
Di
st
ribu
ted
P
o
w
e
r
Gen
e
ra
t
i
n
g
S
y
st
e
m
Using
D
STA
T
CO
M
,
”
I
E
E
E
T
r
an
sac
t
io
ns
on Indu
stry
A
p
p
l
i
c
ation
s
, v
o
l
.
5
1
, n
o. 6
, 2
01
5
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(
V
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
9
4
4
– 1
950
1
950
[6]
Bhim
S
in
gh
a
nd
S
a
bh
a
Raj
A
r
ya,
“
B
ack-P
rop
a
gat
i
on
C
o
n
t
r
o
l
A
lg
ori
th
m
fo
r
P
o
we
r
Qu
a
l
i
t
y
I
m
pro
v
e
m
e
n
t
U
s
ing
DSTA
TC
OM,
”
IEEE
T
r
ansact
i
ons
on
Ind
u
s
t
r
i
a
l
E
l
ectr
onics
, v
o
l
. 6
1, n
o
. 3
, 20
1
4
[7]
Sa
bh
a
Ra
j
Arya
,
B
him
S
i
ng
h
,
Ra
m
N
i
wa
s,
A
m
b
r
i
sh
C
h
a
nd
ra
a
nd
K
a
m
a
l
A
l-Ha
dd
a
d
,
“Powe
r
Q
u
a
lity
En
han
c
em
en
t
Usi
ng
D
S
T
A
T
CO
M
i
n
D
i
s
t
r
ib
u
t
ed
P
ower
G
enerati
o
n
Sy
s
t
em
,”
IEEE
Tran
sacti
o
n
s
on
In
du
st
ry Ap
p
l
icatio
n
s
,
vol
.
5
2
,
no
.
6,
2016
[8]
N.
G
.
Hi
ng
oran
i,
a
n
d
L
.
Gy
ug
yi,
Un
ders
tand
in
g
F
A
CTS:
C
o
n
cep
ts
a
n
d
T
e
c
h
no
lo
gy
o
f
F
l
e
x
ib
le
A
C
Tr
a
n
s
m
is
si
o
n
Sy
st
e
m
s
,
IE
EE
P
r
es
s
, N
e
w Y
o
r
k
(
USA),
2000
.
[9]
B
.
S
i
n
g
h
,
A
.
C
h
a
n
d
r
a
,
a
n
d
K
.
A
l
-
H
a
d
d
a
d
,
“
P
o
w
e
r
Q
u
a
l
i
t
y
:
P
r
o
b
l
e
m
s
and
M
itiga
t
i
on
Techni
ques,
”
Ho
bo
ken, NJ,
USA
:
W
ile
y,
20
1
5.
[10]
M
o
hammed
A
s
i
m
,
M
o
hd
T
ari
q
,
M.A
.
M
a
llick
and
Imt
i
az
Ashra
f
,
“An
Im
prov
e
d
C
ons
tant
V
o
l
tag
e
B
ased
M
P
P
T
Te
c
h
niqu
e
for
P
M
DC
M
otor
,”
In
te
rna
tio
na
l J
o
ur
na
l o
f
Po
we
r Ele
c
t
ron
i
c
s
an
d D
r
i
v
e
Sy
ste
m
(
I
J
P
E
D
S)
,
v
o
l
. 7,
no
.
4
,
pp.
1
3
3
0
-
133
6,
2
0
1
6
.
[11]
B.
S
ing
h
,
P
.
Ja
y
a
pra
k
a
s
h
,
D
.
P
.
K
otha
ri
,
A.
C
ha
n
d
ra
,
a
n
d
K.
A
l
Ha
d
d
a
d
“Co
m
pre
h
e
n
sive
s
tu
dy
o
f
DS
TA
TCO
M
conf
i
g
u
r
atio
ns,
”
IE
EE T
r
an
s.
Ind.
Infor
m
at
.,
vol.
10,
n
o
.
2
,
pp
.
8
5
4
–
8
70,
2
0
1
4
.
[12]
B.
S
in
gh,
G
.
Bhu
v
an
eswari
,
an
d
S
.
R
.
Arya,
“
R
evi
e
w
on
Power
Qua
li
ty
S
o
l
ut
io
n
T
e
c
h
no
lo
gy
,
”
Asi
a
n Power
Elect
ro
n
i
cs
Jo
urnal
,
vo
l
. 6
, n
o
. 2
,
pp
. 19
-
27
,
2
0
1
2
[13]
S.
O
. Haykin,
“
Adaptive
Fi
lter Theory,”
3rd ed.
En
g
l
ewood
Cliffs
,
NJ, U
S
A
: Pren
ti
ce-Hall
, 1
9
9
6
.
[14]
Bhim
S
i
ngh,
S
abh
a
R
aj
A
rya,
A
m
b
ris
h
C
h
a
ndra
an
d
Kam
a
l
A
l
-Had
dad
,
“I
mplementation
o
f
A
dapt
ive
Filt
e
r
i
n
Distri
bu
ti
on
Static
C
om
p
e
ns
a
t
or,
”
IEEE
T
r
ansactio
ns on
Ind
u
str
y
Ap
pli
c
atio
ns
, v
o
l
. 5
0,
no
.
5,
20
14
[15]
T.
A
bo
u
l
n
a
sr,
a
n
d
K
.
M
ayy
a
s,
“
A
rob
u
s
t
v
ari
a
bl
e
s
t
ep-si
ze
LM
S
-
t
yp
e
a
l
g
o
ri
th
m:
a
na
lys
i
s
a
n
d
s
i
mu
la
t
i
on
s
,”
IEEE
T
r
an
sa
cti
ons o
n
S
i
g
nal Proces
si
n
g
,
vol.
4
5
,
n
o.
3
, p
p.
631
-63
9
,
1997.
[16]
Sa
bh
a
Ra
j
Arya
a
nd
B
h
i
m
S
i
ng
h,
“
Pe
rfor
ma
nc
e
of
D
S
T
ATCO
M
Using
L
eaky
LMS
Co
n
t
rol
A
l
go
rit
h
m
”,
IEE
E
Jour
na
l of Emergi
ng
an
d
S
e
lected
T
opics
in
Po
wer Elect
ro
n
i
cs
,
vol
.
1
,
n
o
.
2
,
2
013.
[17]
Y.
A
varg
el
a
n
d
I
.
Co
hen,
“
Ad
apt
i
v
e
n
o
n
l
i
n
e
ar
s
y
s
t
e
m
id
entificat
ion
in
t
he
s
ho
r
t
-
time
fo
ur
ie
r
tr
a
n
sfo
r
m
do
ma
in
,”
IEEE
T
r
a
n
s
a
c
t
io
n
s
on S
i
gnal
Process
i
n
g
,
vo
l. 57
, n
o
.
1
0,
pp
.
38
9
1
-
39
0
4
, 20
0
9
.
[18]
E.
A
.
H
e
rman
de,
D.
B
l
a
nce,
D
.
P
.
R
ui
z,
a
nd
M
.
C
.
Carri
o
n
,
“
The
averag
ed,
ov
erdet
e
rmi
n
ed
,
and
g
e
ner
a
l
LM
S
algo
rit
h
m,”
IEEE
T
r
a
n
s.
Sign
a
l
Pr
oces
s
.
,
v
o
l
. 55
,
n
o.
12
,
pp
. 5
59
3–
5
6
0
3
, 20
0
7
.
[19]
N.
M
ohan
,
T
.
M.
U
nd
eland,
a
nd
W.
P
.
Robbin
s
,
“
P
ow
er
E
lectro
ni
cs
:
Con
v
ert
e
rs,
Ap
plicati
ons
a
n
d
D
es
ig
n
,
”
3r
d
ed.
Hob
o
ken
, NJ, USA:
Wiley
,
2
00
9
.
[20]
S.K
.
P
a
t
el,
S.
R
.
Arya
a
nd
R
.
M
a
urya,
“Harmonic
Mitigation
Tech
ni
qu
e
f
o
r
DSTA
TCOM
u
si
ng
C
ont
in
uo
u
s
T
ime
LMS
Adaptive
F
ilter,”
IE
EE
Conferen
ce on
UP
CON
,
I
IT
BHU
Va
ran
a
si,
India,
D
ec
9-1
1
,
20
16
[21]
M.
S
ri
ni
vas,
I
.
Hu
ss
ain
an
d
B.
S
i
n
g
h
,
“
C
om
bined
LM
S
–
LM
F
Bas
e
d
C
ont
rol
A
l
gori
th
m
o
f
D
STAT
C
O
M
f
o
r
Power
Qual
it
y E
n
h
a
ncem
ent
in D
i
s
t
r
ib
u
t
ion S
y
ste
m
,”
I
E
EE
tra
n
sac
t
io
ns
on
Ind
u
str
i
al
E
l
e
c
tron
ic
s
,
v
o
l
.
6
3
,
no.
7
,
J
uly
20
16
[22]
R.K.
A
ga
rwa
l
,
I.
H
us
sa
in
a
nd
B
.
S
i
n
g
h
,
“
LM
F-Ba
se
d
Con
t
ro
l
A
l
g
o
r
ithm
f
o
r
S
i
ngle
Stage
Th
ree-P
h
ase
Gri
d
Integ
r
ated
S
o
l
ar P
V S
y
st
em,
”
IEE
E
Tr
an
sactio
ns on
Su
st
a
i
nab
le Ener
gy
,
vo
l
.
7
,
no.
4
,
O
c
to
ber
2
0
1
6
Evaluation Warning : The document was created with Spire.PDF for Python.