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)
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2
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783
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I
SS
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1
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v
1
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.
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792
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ly
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In
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it
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th
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p
a
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e
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sta
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f
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h
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m
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c
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is
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e
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o
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th
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ste
m
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d
s
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n
g
r
id
imp
e
d
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n
c
e
.
It
is
v
e
rifi
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d
with
M
ATLAB
S
imu
lati
o
n
s.
K
ey
w
o
r
d
s
:
Dis
tr
ib
u
tio
n
g
en
er
atio
n
Gr
id
im
p
ed
an
ce
I
m
p
ed
an
ce
b
ased
s
tab
ilit
y
cr
iter
io
n
I
n
v
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ter
o
u
tp
u
t im
p
ed
a
n
ce
Ma
x
im
u
m
p
o
wer
p
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n
t tr
ac
k
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g
Min
o
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p
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ain
Pro
p
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al
-
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an
t
c
u
r
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e
n
t
co
n
tr
o
ller
PV a
r
r
ay
T
h
is i
s
a
n
o
p
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n
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c
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rticle
u
n
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r th
e
CC B
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SA
li
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se
.
C
o
r
r
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s
p
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nd
ing
A
uth
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r
:
R
.
S.
R
av
i San
k
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Dep
ar
tm
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lectr
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Vig
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I
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titu
te
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T
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Vis
ak
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ap
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am
,
An
d
h
r
a
Pra
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h
,
I
n
d
ia
E
m
ail:
s
aty
a_
r
av
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0
0
1
@
y
ah
o
o
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Pro
life
r
atio
n
o
f
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
is
th
e
cu
r
r
en
t
s
ce
n
ar
io
to
th
e
m
ee
t
th
e
in
cr
e
asin
g
lo
ad
d
em
an
d
.
W
h
en
th
ese
s
o
u
r
ce
s
ar
e
c
o
n
n
ec
ted
to
th
e
g
r
id
t
h
er
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is
in
ter
ac
tio
n
b
etwe
en
t
h
e
L
C
L
f
ilter
,
g
r
id
im
p
ed
an
ce
,
a
n
d
in
n
er
cu
r
r
en
t
l
o
o
p
o
f
th
e
in
v
er
t
er
s
.
T
h
er
e
b
y
,
it
ca
u
s
es
th
e
h
ar
m
o
n
ic
in
s
tab
il
ity
[
1
]
,
[
2]
.
W
h
ich
f
u
r
th
er
lead
s
to
am
p
lific
atio
n
o
f
r
e
s
o
n
an
ce
o
v
er
th
e
r
an
g
e
o
f
f
r
eq
u
e
n
cies.
T
h
is
s
o
m
etim
es
lead
s
to
u
n
wan
ted
with
d
r
awa
l
o
f
th
e
PV
in
v
er
ter
s
f
r
o
m
th
e
g
r
id
[3
]
,
[
4
]
.
T
h
e
i
n
ter
ac
tio
n
o
f
th
e
a
d
m
ittan
ce
s
o
f
m
u
ltip
le
in
v
er
ter
s
ca
u
s
es
two
is
s
u
es
o
n
e
is
am
p
l
if
icatio
n
o
f
R
eso
n
an
ce
a
n
d
s
e
co
n
ed
o
n
e
h
ar
m
o
n
ic
in
s
tab
ilit
y
.
T
h
e
se
two
is
s
u
es
ar
e
an
aly
ze
d
an
d
an
s
wer
ed
b
y
m
ea
n
s
o
f
I
B
SC
an
aly
s
is
.
I
B
S
C
was
ap
p
li
ed
to
d
esig
n
t
h
e
o
u
t
p
u
t
f
ilter
in
ch
o
p
p
e
r
cir
c
u
its
[5
]
,
[
6
]
.
T
h
e
co
n
v
er
s
io
n
m
eth
o
d
f
o
r
h
ar
m
o
n
ic
tr
an
s
f
er
f
u
n
ctio
n
-
b
ased
m
o
d
el
f
o
r
a
Vo
ltag
e
s
o
u
r
ce
co
n
v
er
te
r
in
to
a
s
im
p
le
an
d
ef
f
icien
t
Sin
g
le
I
n
p
u
t
Sin
g
le
Ou
tp
u
t
m
o
d
el
[
7
]
.
Stab
ilit
y
ch
ar
ac
ter
is
tics
wer
e
o
b
tain
e
d
with
th
e
f
r
eq
u
en
cy
c
o
u
p
lin
g
ef
f
ec
t.
I
n
[
8
]
,
I
m
p
ed
an
ce
m
o
d
el
in
d
q
-
f
r
am
e
was
d
ev
elo
p
ed
f
o
r
o
f
f
s
h
o
r
e
win
d
p
o
wer
p
la
n
t
to
s
tu
d
y
th
e
ef
f
ec
t
o
f
i
n
v
e
r
t
er
s
an
d
tr
an
s
m
is
s
io
n
ca
b
les.
T
h
e
an
aly
ze
d
th
e
h
ar
m
o
n
ic
s
tab
ilit
y
in
m
o
d
u
lar
m
u
ltil
ev
el
b
ased
DC
s
y
s
tem
s
.
I
t
was
v
er
if
ie
d
with
h
ar
d
war
e
ex
p
er
im
en
tatio
n
as
well
as
s
im
u
latio
n
.
DC
im
p
ed
an
ce
m
o
d
el
o
f
th
e
s
y
s
tem
wa
s
d
ev
elo
p
ed
b
y
co
n
s
id
er
in
g
th
e
ca
p
ac
ito
r
v
o
lt
ag
e
f
lu
ctu
atio
n
,
h
ar
m
o
n
ic
r
esp
o
n
s
es
[
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
2
,
J
u
n
e
2
0
2
1
:
783
–
792
784
I
n
th
is
wo
r
k
,
I
B
SC
to
o
l
is
u
s
ed
in
t
h
e
m
u
lti
-
in
v
er
ter
s
tied
to
g
r
id
to
e
x
am
in
e
t
h
e
h
a
r
m
o
n
ic
s
tab
ili
ty
.
T
h
e
s
y
s
tem
s
tab
ilit
y
i
s
ev
alu
ated
b
y
g
r
a
p
h
ical
an
aly
s
is
u
s
in
g
m
in
o
r
lo
o
p
g
ain
o
f
th
e
o
v
e
r
all
s
y
s
tem
.
I
f
th
e
s
y
s
tem
o
b
ey
s
th
e
n
y
q
u
iest
s
tab
ilit
y
cr
iter
ia
th
an
t
h
e
s
y
s
tem
is
s
tab
le
o
th
er
wis
e
it
is
u
n
s
tab
le.
T
h
e
co
n
ce
p
t
o
f
p
ass
iv
ity
-
b
ased
s
tab
ilit
y
an
aly
s
is
h
as
r
ec
en
tl
y
g
ain
ed
atten
ti
o
n
in
c
o
n
tr
o
l
s
y
s
tem
[
10
]
a
n
d
f
r
o
m
t
h
is
s
tab
ilit
y
an
aly
s
is
ea
ch
s
u
b
s
y
s
tem
h
as
a
p
h
ase
m
ar
g
in
lies
b
etwe
en
-
90
to
90
.
T
h
e
n
th
e
s
y
s
tem
is
s
tab
le
o
th
er
wis
e
s
y
s
tem
is
u
n
s
tab
le
.
I
n
t
h
is
p
ap
er
,
S
ec
tio
n
2
d
ea
l
s
with
th
e
Ma
th
e
m
atica
ll
m
o
d
el
in
g
o
f
t
h
e
PV
s
y
s
tem
,
i
n
S
ec
t
io
n
3
,
th
e
c
al
cu
lat
io
n
o
f
th
e
Ou
tp
u
t
I
m
p
ed
an
ce
o
f
in
v
er
ter
an
d
t
h
e
m
o
d
elin
g
o
f
th
e
PR
cu
r
r
en
t
co
n
tr
o
ller
.
I
n
S
ec
tio
n
.
4
.
s
im
u
latio
n
r
esu
lts
o
f
th
e
two
c
ase
s
tu
d
ies ar
e
d
is
cu
s
s
ed
.
2.
M
AT
H
E
M
AT
I
CA
L
L
M
O
D
E
L
I
NG
O
F
P
V
SYST
E
M
2
.
1
.
M
o
delin
g
o
f
P
V
a
rr
a
y
I
n
th
is
s
tu
d
y
PV
ar
r
ay
p
r
o
v
id
e
s
th
e
DC
v
o
ltag
e
to
b
o
o
s
t
co
n
v
er
ter
.
Sin
g
le
d
io
d
e
m
o
d
el
o
f
a
PV
C
ell
is
d
ep
icate
d
in
Fig
u
r
e
1
.
I
t
r
ep
r
esen
ts
s
im
p
le
m
o
d
eli
n
g
wh
er
e
r
esis
tan
ce
s
ar
e
n
eg
lecte
d
[
11
]
-
[
1
6
].
T
h
e
p
ar
am
eter
s
o
f
th
e
P
V
m
o
d
u
l
e
ar
e
s
h
o
w
n
in
T
ab
le.
1
.
T
h
e
s
e
ar
e
u
s
ed
t
o
s
im
u
late
th
e
PV
ar
r
ay
in
m
atlab
s
im
u
latio
n
.
t
wo
m
o
d
u
les
ar
e
c
o
n
n
ec
ted
in
s
er
ies
to
g
iv
e
th
e
v
o
ltag
e
o
f
7
0
0
V
an
d
th
e
PV
cu
r
r
en
t
s
u
p
p
lied
is
4
0
A.
T
h
e
PV
p
o
wer
s
u
p
p
lied
b
y
th
e
i
n
v
er
ter
is
2
KW
ev
en
t
h
o
u
g
h
it
is
d
esig
n
ed
f
o
r
th
e
1
4
KW
.
T
h
e
PV
ar
r
ay
v
o
ltag
e,
cu
r
r
en
t a
n
d
p
o
wer
wa
v
e
f
o
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m
s
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e
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ep
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r
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2
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r
e
4
.
2
.
2
.
M
a
x
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um
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wer
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ra
c
k
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(
M
P
P
T
)
PV
p
an
el
o
u
tp
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t
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h
ig
h
ly
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e
p
en
d
in
g
o
n
clim
atic
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n
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itio
n
s
,
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tr
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ed
m
ax
im
u
m
p
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wer
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r
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m
PV
p
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els
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Dif
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er
en
t
MPPT
tech
n
iq
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es
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e
p
r
o
p
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ed
i
n
liter
atu
r
e.
Fo
r
s
im
p
le
im
p
lem
e
n
tatio
n
,
P
&O
tech
n
iq
u
e
is
im
p
lem
en
ted
in
t
h
is
p
a
p
er
[1
7
]
,
[
1
8
]
.
T
ab
le
1
.
Sp
ec
if
icatio
n
s
o
f
th
e
PV
m
o
d
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le
P
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r
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r
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r
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a
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t
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2
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r
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in
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Fig
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r
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3
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PV
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t
(
in
am
p
s
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Fig
u
r
e
4
.
PV
p
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wer
(
in
watts)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
Ha
r
mo
n
ic
s
ta
b
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y
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n
a
lysi
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f m
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M
O
DE
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F
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DM
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3
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h
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n
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ec
te
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ter
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s
h
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wn
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Fig
u
r
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5
.
in
th
at
PV in
v
e
r
ter
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o
r
f
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n
g
p
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r
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L
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s
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ed
.
T
h
e
o
v
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all
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y
s
tem
is
r
ep
r
esen
ted
in
b
lo
ck
d
iag
r
a
m
e
in
Fi
g
u
r
e
6
.
I
n
th
is
wo
r
k
PR
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r
r
en
t c
o
n
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as c
u
r
r
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t c
o
n
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[
1
9
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,
[
2
0
].
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+
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u
r
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5
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1
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Ph
.
d
e
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icatio
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u
r
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6
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lo
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d
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e
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f
t
h
e
s
y
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tem
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c
G
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u
r
r
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t c
o
n
tr
o
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d
G
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d
elay
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ain
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d
(
P
W
M
K
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PW
M
g
ain
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e
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2
1
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T
d
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1
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h
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ef
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ed
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m
ittan
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o
f
L
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L
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Fin
ally
,
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co
n
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ter
ad
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ittan
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is
g
iv
en
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
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Sy
s
t
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Vo
l.
12
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No
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2
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u
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2
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1
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–
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786
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g
f
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d
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s
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id
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2
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P
ro
po
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re
s
o
na
nt
curr
ent
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o
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:
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p
r
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p
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tio
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r
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n
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n
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(
PR
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co
n
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ex
h
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its
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b
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y
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ic
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ce
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n
p
u
t
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tp
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t r
elatio
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o
f
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n
id
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l
PR
co
n
tr
o
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ex
p
r
ess
ed
by
(
6
)
[
2
2
]
,
[
2
3
]
.
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n
th
e
s
am
e
way
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o
r
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n
o
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i
d
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l
PR
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o
n
tr
o
ller
it is
g
iv
en
b
y
(
7
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[2
4
]
:
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d
ea
l
p
r
o
p
o
r
tio
n
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r
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n
a
n
t
co
n
tr
o
ller
:
2
2
2
)
(
+
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=
s
s
K
K
s
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r
P
PR
(
6
)
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n
-
i
d
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l PR
c
o
n
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o
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c
2
c
r
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PR
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2
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3
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3
.
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a
rm
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t
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is
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ied t
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t
he
g
rid
T
h
e
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lo
c
k
d
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r
am
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e
r
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s
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Fig
u
r
e
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d
its
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r
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r
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u
r
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9
.
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c
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is
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r
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id
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ar
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+
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.
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PR
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e
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v
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ter
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an
L
C
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f
ilter
is
u
s
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to
im
p
r
o
v
e
t
h
e
q
u
ality
o
f
g
r
id
c
u
r
r
en
t
[
2
5
]
-
[
2
8
].
PW
M
tech
n
iq
u
e
is
im
p
lem
en
t
ed
to
p
r
o
d
u
ce
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witch
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ter
.
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icatio
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ar
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eter
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o
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th
e
f
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ter
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tated
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T
ab
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2.
P
V
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W
i
t
h
M
P
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3
-
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In
v
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e
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r
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u
r
e
8
.
Fiv
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PV a
r
r
a
y
s
tied
to
g
r
id
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
Ha
r
mo
n
ic
s
ta
b
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a
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a
lysi
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f m
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2
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8
8
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I
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Po
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12
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2
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783
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4.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
Ha
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I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
2
,
J
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
694
Ha
r
mo
n
ic
s
ta
b
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a
n
a
lysi
s
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f m
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ka
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in
g
th
e
g
r
id
i
n
d
u
ctan
ce
with
co
n
s
tan
t
g
r
id
r
esis
tan
ce
an
d
also
b
y
v
ar
y
in
g
lo
a
d
i
m
p
ed
an
ce
an
d
m
ain
tain
in
g
g
r
id
i
n
d
u
ctan
ce
c
o
n
s
tan
t.
I
t
was
o
b
s
er
v
ed
th
at
o
v
er
all
s
y
s
tem
is
s
tab
le
u
p
to
g
r
id
in
d
u
ct
an
ce
o
f
5
m
H
an
d
ab
o
v
e
th
is
v
alu
e,
th
e
s
y
s
tem
b
ec
o
m
es
u
n
s
tab
le.
I
t
is
also
d
em
o
n
s
tr
ated
th
at
s
ta
b
ilit
y
o
f
th
e
s
y
s
tem
d
ep
en
d
s
o
n
g
r
id
i
m
p
ed
a
n
ce
o
n
ly
an
d
d
o
es
n
o
t
d
e
p
en
d
o
n
l
o
ad
im
p
ed
a
n
ce
.
I
t
is
s
u
b
s
tan
tiated
b
y
m
ea
n
s
o
f
g
r
ap
h
ical
an
al
y
s
is
a
n
d
Ma
tlab
Simu
latio
n
s
.
RE
F
E
R
E
NC
E
S
[1
]
X.
Wan
g
,
F
.
B
laa
b
jerg
a
n
d
W.
Wu
,
“
M
o
d
e
li
n
g
a
n
d
A
n
a
ly
sis
o
f
Ha
rm
o
n
ic
S
tab
il
i
ty
i
n
a
n
AC
P
o
we
r
-
El
e
c
tro
n
ics
-
Ba
se
d
P
o
we
r
S
y
ste
m
,”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
i
c
s
,
v
o
l.
2
9
,
n
o
.
1
2
,
p
p
.
6
4
2
1
-
6
4
3
2
,
De
c
.
2
0
1
4
,
DO
I:
1
0
.
1
1
0
9
/
TP
EL
.
2
0
1
4
.
2
3
0
6
4
3
2
.
[2
]
X.
Wan
g
,
F
.
Blaa
b
jer
g
,
M
.
Li
s
e
rre
,
Z.
C
h
e
n
,
J
.
He
a
n
d
Y.
Li
,
“
An
Ac
ti
v
e
Da
m
p
e
r
fo
r
S
tab
i
li
z
in
g
P
o
we
r
-
El
e
c
tro
n
ics
-
Ba
se
d
AC
S
y
ste
m
s
,”
in
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l
.
2
9
,
n
o
.
7
,
p
p
.
3
3
1
8
-
3
3
2
9
,
Ju
l
y
2
0
1
4
,
DO
I:
1
0
.
1
1
0
9
/T
P
EL
.
2
0
1
3
.
2
2
7
8
7
1
6
.
[3
]
J.
H.
R.
E
n
slin
a
n
d
P
.
J.
M
.
He
sk
e
s
,
“
Ha
rm
o
n
ic
in
tera
c
ti
o
n
b
e
twe
e
n
a
lar
g
e
n
u
m
b
e
r
o
f
d
istri
b
u
ted
p
o
we
r
in
v
e
rters
a
n
d
th
e
d
istr
ib
u
ti
o
n
n
e
two
r
k
,”
IE
EE
3
4
t
h
An
n
u
a
l
Co
n
fer
e
n
c
e
o
n
Po
we
r
El
e
c
tro
n
ics
S
p
e
c
ia
l
ist
,
2
0
0
3
.
P
ES
C
'
0
3
.
,
2
0
0
3
,
p
p
.
1
7
4
2
-
1
7
4
7
v
o
l
.
4
,
DO
I:
1
0
.
1
1
0
9
/
P
ES
C.
2
0
0
3
.
1
2
1
7
7
1
9
.
[4
]
“
IEE
E
Re
c
o
m
m
e
n
d
e
d
P
ra
c
ti
c
e
a
n
d
Re
q
u
irem
e
n
ts
fo
r
Ha
rm
o
n
ic
Co
n
tr
o
l
i
n
El
e
c
tri
c
P
o
we
r
S
y
ste
m
s
,”
in
IEE
E
S
td
519
-
2
0
1
4
(Rev
isio
n
o
f
IEE
E
S
t
d
5
1
9
-
1
9
9
2
)
,
p
p
.
1
-
2
9
,
1
1
J
u
n
e
2
0
1
4
,
DO
I:
1
0
.
1
1
0
9
/
IEE
ES
TD.
2
0
1
4
.
6
8
2
6
4
5
9
.
.
[5
]
R.
D.
M
id
d
leb
r
o
o
k
,
“
I
n
p
u
t
fi
lt
e
r
c
o
n
sid
e
ra
ti
o
n
s
i
n
d
e
sig
n
a
n
d
a
p
p
li
c
a
ti
o
n
o
f
sw
it
c
h
in
g
re
g
u
lat
o
rs
,”
in
Pr
o
c
.
IEE
E
IAS
A
n
n
u
.
M
e
e
ti
n
g
,
1
9
7
6
,
p
p
.
3
6
6
–
3
8
2
.
[6
]
Xia
o
g
a
n
g
F
e
n
g
,
Ji
n
ju
n
Li
u
a
n
d
F
.
C.
Lee
,
“
Im
p
e
d
a
n
c
e
sp
e
c
ifi
c
a
ti
o
n
s
fo
r
sta
b
le
DC
d
istri
b
u
ted
p
o
we
r
sy
ste
m
s
,”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
le
c
tro
n
ics
,
v
o
l.
1
7
,
n
o
.
2
,
p
p
.
1
5
7
-
1
6
2
,
M
a
rc
h
2
0
0
2
,
DO
I:
1
0
.
1
1
0
9
/6
3
.
9
8
8
8
2
5
.
.
[7
]
C.
Zh
a
n
g
,
M
.
M
o
li
n
a
s,
S
.
F
ø
y
e
n
,
J.
A.
S
u
u
l
a
n
d
T
.
Iso
b
e
,
“
H
a
rm
o
n
ic
-
Do
m
a
in
S
IS
O
Eq
u
i
v
a
len
t
Im
p
e
d
a
n
c
e
M
o
d
e
li
n
g
a
n
d
S
ta
b
il
it
y
An
a
ly
si
s
o
f
a
S
in
g
le
-
P
h
a
se
G
rid
-
Co
n
n
e
c
ted
VSC
,”
in
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
3
5
,
n
o
.
9
,
p
p
.
9
7
7
0
-
9
7
8
3
,
S
e
p
t.
2
0
2
0
,
DO
I:
1
0
.
1
1
0
9
/T
P
EL
.
2
0
2
0
.
2
9
7
0
3
9
0
.
[8
]
W.
Zh
o
u
,
Y.
Wa
n
g
,
R.
E
.
To
rre
s
-
Olg
u
i
n
a
n
d
Z
.
Ch
e
n
,
“
Eff
e
c
t
o
f
R
e
a
c
ti
v
e
P
o
we
r
Ch
a
ra
c
teristic
o
f
O
ffsh
o
re
Wi
n
d
P
o
we
r
P
lan
t
o
n
L
o
w
-
F
re
q
u
e
n
c
y
S
tab
il
it
y
,”
in
IEE
E
T
r
a
n
s
a
c
ti
o
n
s
o
n
En
e
rg
y
Co
n
v
e
rs
io
n
,
v
o
l.
3
5
,
n
o
.
2
,
p
p
.
8
3
7
-
8
5
3
,
Ju
n
e
2
0
2
0
,
DO
I:
1
0
.
1
1
0
9
/T
E
C.
2
0
2
0
.
2
9
6
5
0
1
7
.
[9
]
K
.
Ji,
G
.
Ta
n
g
,
J.
Ya
n
g
,
Y.
Li
a
n
d
D.
Li
u
,
“
Ha
rm
o
n
ic
S
tab
il
it
y
A
n
a
ly
sis
o
f
M
M
C
-
Ba
se
d
DC
S
y
st
e
m
Us
in
g
DC
Im
p
e
d
a
n
c
e
M
o
d
e
l
,”
i
n
IEE
E
J
o
u
rn
a
l
o
f
Eme
rg
in
g
a
n
d
S
e
lec
ted
T
o
p
ics
in
P
o
we
r
El
e
c
tro
n
ics
,
v
o
l.
8
,
n
o
.
2
,
p
p
.
1
1
5
2
-
1
1
6
3
,
J
u
n
e
2
0
2
0
,
DO
I:
1
0
.
1
1
0
9
/JES
TP
E.
2
0
1
9
.
2
9
2
3
2
7
2
.
[1
0
]
J.W
y
a
tt
,
L.
C
h
u
a
,
J.
G
a
n
n
e
tt
,
I.
G
o
k
n
a
r
a
n
d
D.
G
re
e
n
,
“
En
e
rg
y
c
o
n
c
e
p
ts
in
t
h
e
sta
te
-
sp
a
c
e
th
e
o
ry
o
f
n
o
n
li
n
e
a
r
n
-
p
o
rts:P
a
rtI
-
p
a
ss
iv
it
y
,”
IEE
E
T
ra
n
s.Circ
u
it
s S
y
st
.
,
v
o
l.
2
8
,
n
o
.
1
,
p
p
.
48
–
6
1
,
Ja
n
.
1
9
8
1
.
[1
1
]
Zah
e
d
i
,
“
A
re
v
iew
o
f
d
ri
v
e
rs,
b
e
n
e
fit
s,
a
n
d
c
h
a
ll
e
n
g
e
s
in
in
teg
r
a
ti
n
g
re
n
e
wa
b
le
e
n
e
r
g
y
so
u
rc
e
s
in
to
e
lec
tri
c
it
y
g
rid
,”
Ren
e
w
a
b
le
a
n
d
S
u
st
a
i
n
a
b
le
En
e
rg
y
Rev
iews
,
v
o
l.
15,
n
o
.
9
,
p
p
.
4
7
7
5
-
4
7
7
9
,
2
0
1
1
,
DO
I:
1
0
.
1
0
1
6
/
j.
rse
r.
2
0
1
1
.
0
7
.
0
7
4
.
[1
2
]
M
.
Ca
stil
la,
J.
M
iret,
J.
M
a
tas
,
L
.
G
a
r
c
ia
d
e
Vic
u
n
a
a
n
d
J.
M
.
G
u
e
rre
ro
,
“
Co
n
tr
o
l
De
sig
n
G
u
id
e
li
n
e
s
fo
r
S
in
g
le
-
P
h
a
se
G
rid
-
Co
n
n
e
c
ted
P
h
o
to
v
o
l
taic
In
v
e
rters
Wi
t
h
Da
m
p
e
d
R
e
so
n
a
n
t
Ha
rm
o
n
ic
C
o
m
p
e
n
sa
to
r
s
,”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
5
6
,
n
o
.
1
1
,
p
p
.
4
4
9
2
-
4
5
0
1
,
N
o
v
.
2
0
0
9
,
DO
I:
1
0
.
1
1
0
9
/
TIE
.
2
0
0
9
.
2
0
1
7
8
2
0
.
[1
3
]
S
.
Eren
,
M
.
P
a
h
lev
a
n
i
M
.
Ca
stil
l
a
,
J.
M
iret,
J.
M
a
tas
,
L.
G
a
rc
i
a
d
e
Vic
u
n
a
a
n
d
J.
M
.
G
u
e
rre
ro
,
“
Co
n
tr
o
l
De
sig
n
G
u
id
e
li
n
e
s
fo
r
S
i
n
g
le
-
P
h
a
se
G
rid
-
Co
n
n
e
c
ted
P
h
o
t
o
v
o
lt
a
ic
I
n
v
e
rters
Wi
t
h
Da
m
p
e
d
Re
so
n
a
n
t
Ha
rm
o
n
ic
Co
m
p
e
n
sa
to
rs
,”
i
n
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
v
o
l.
5
6
,
n
o
.
1
1
,
p
p
.
4
4
9
2
-
4
5
0
1
,
No
v
.
2
0
0
9
,
DO
I:
1
0
.
1
1
0
9
/
TIE
.
2
0
0
9
.
2
0
1
7
8
2
0
.
[1
4
]
S
.
Eren
,
M
.
P
a
h
lev
a
n
i
n
e
z
h
a
d
,
A.
Ba
k
h
sh
a
i
a
n
d
P
.
K.
Ja
in
,
“
Co
m
p
o
site
No
n
li
n
e
a
r
F
e
e
d
b
a
c
k
Co
n
tro
l
a
n
d
S
tab
il
it
y
An
a
ly
sis
o
f
a
G
rid
-
Co
n
n
e
c
ted
V
o
lt
a
g
e
S
o
u
rc
e
In
v
e
rter
Wi
t
h
LCL
F
il
ter
,”
in
IEE
E
T
r
a
n
sa
c
t
io
n
s
o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
6
0
,
n
o
.
1
1
,
p
p
.
5
0
5
9
-
5
0
7
4
,
No
v
.
2
0
1
3
,
DO
I:
1
0
.
1
1
0
9
/T
I
E.
2
0
1
2
.
2
2
2
5
3
9
9
.
[1
5
]
S
a
n
k
a
r,
R.
R.
S
.
&
Ku
m
a
r,
J.S
.
V.
a
n
d
Ra
o
,
M
.
G
.
,
“
Ad
a
p
ti
v
e
F
u
z
z
y
P
I
Cu
rre
n
t
Co
n
tro
l
o
f
G
rid
In
tera
c
t
P
V
In
v
e
rter
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
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6
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a
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S
.
,
Ku
m
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r,
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.
V.
a
n
d
De
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ik
a
,
K.K.
,
“
F
lex
i
b
le
P
o
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r
Re
g
u
latio
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o
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rid
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n
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ted
I
n
v
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y
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re
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Dir
e
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t
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o
we
r
Co
n
tro
l
,”
In
d
o
n
e
sia
n
J
o
u
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a
l
o
f
El
e
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trica
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En
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7
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RS
Ra
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k
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S
V
Ja
y
a
Ku
m
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o
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Cu
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tro
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f
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rid
C
o
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te
d
P
V
S
y
ste
m
,”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
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c
trica
l
En
g
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n
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ter
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8
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S
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.
K.
Ko
ll
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B.
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m
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2
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In
ter
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C
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Circ
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Po
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C
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(ICCPCT
)
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792
[1
9
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G
.
P
e
tro
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e
,
G
.
S
p
a
g
n
u
o
lo
a
n
d
M
.
Vitelli
,
“
A
M
u
lt
i
v
a
riab
le
P
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rtu
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-
a
n
d
-
Ob
se
rv
e
M
a
x
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m
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o
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T
ra
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k
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g
Tec
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Ap
p
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h
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lt
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ic
I
n
v
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rter
,”
in
IE
EE
T
r
a
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tro
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ics
,
v
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l.
5
8
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.
1
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7
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0
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2
0
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0
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2
0
4
4
7
3
4
.
[2
0
]
C.
Yo
o
n
,
X.
Wan
g
,
F
.
M
.
F
a
ria
d
a
S
il
v
a
,
C.
L.
Ba
k
a
n
d
F
.
Blaa
b
jerg
,
“
Ha
rm
o
n
ic
sta
b
il
it
y
a
ss
e
ss
m
e
n
t
fo
r
m
u
lt
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-
p
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ll
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led
,
g
rid
-
c
o
n
n
e
c
ted
i
n
v
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rt
e
rs,
”
2
0
1
4
In
ter
n
a
ti
o
n
a
l
Po
we
r
El
e
c
tro
n
ics
a
n
d
A
p
p
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Co
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fer
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4
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.
[2
1
]
J.
L.
Ag
o
rre
ta,
M
.
B
o
rre
g
a
,
J.
Ló
p
e
z
a
n
d
L
.
M
a
rr
o
y
o
,
“
M
o
d
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li
n
g
a
n
d
C
o
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tr
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o
f
NN
-
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a
ra
ll
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led
Grid
-
Co
n
n
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c
ted
In
v
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Wi
t
h
LCL
F
il
ter
C
o
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p
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Du
e
t
o
G
rid
Im
p
e
d
a
n
c
e
i
n
P
V
P
lan
ts
,”
i
n
IE
EE
T
r
a
n
s
a
c
ti
o
n
s
o
n
P
o
we
r
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,
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l.
2
6
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5
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9
/T
P
EL
.
2
0
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0
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.
[2
2
]
H.
Ko
m
u
rc
u
g
il
,
N.
Alti
n
,
S
.
Oz
d
e
m
ir
a
n
d
I.
S
e
fa
,
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L
y
a
p
u
n
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F
u
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ti
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d
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se
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trate
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y
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r
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in
g
le
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P
h
a
se
G
rid
-
Co
n
n
e
c
ted
VSI
Wi
th
LCL
F
il
ter,
”
i
n
IEE
E
T
r
a
n
sa
c
ti
o
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o
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I
n
d
u
stria
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El
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tro
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l.
6
3
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p
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8
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a
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I:
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9
/T
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2
0
1
5
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4
.
[2
3
]
G
.
S
h
e
n
,
X.
Z
h
u
,
J.
Z
h
a
n
g
a
n
d
D.
Xu
,
“
A
Ne
w
F
e
e
d
b
a
c
k
M
e
th
o
d
f
o
r
P
R
C
u
rre
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t
C
o
n
tro
l
o
f
L
CL
-
F
il
ter
-
Ba
se
d
G
rid
-
Co
n
n
e
c
ted
I
n
v
e
rter,
”
i
n
IE
EE
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
E
lec
tro
n
ics
,
v
o
l.
5
7
,
n
o
.
6
,
p
p
.
2
0
3
3
-
2
0
4
1
,
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n
e
2
0
1
0
,
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I:
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1
1
0
9
/T
IE
.
2
0
1
0
.
2
0
4
0
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5
2
.
[2
4
]
M
.
Ve
n
k
a
tes
a
n
,
R.
Ra
jes
h
wa
ri,
N.
De
v
e
ra
jan
a
n
d
M
.
Ka
li
y
a
m
o
o
rth
y
,
“
C
o
m
p
a
ra
ti
v
e
S
t
u
d
y
o
f
T
h
r
e
e
P
h
a
se
G
rid
Co
n
n
e
c
ted
P
h
o
t
o
v
o
lt
a
ic
In
v
e
rter
Us
in
g
P
I
a
n
d
F
u
z
z
y
Lo
g
ic
Co
n
tro
ll
e
r
with
S
witch
i
n
g
L
o
ss
e
s
Ca
lcu
latio
n
,”
In
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r
E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(IJ
PE
DS
)
,
v
o
l.
7
.
No
.
2
,
p
p
.
5
4
3
-
5
5
0
,
2
0
1
6
.
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I:
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0
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5
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p
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d
s.v
7
.
i
2
.
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p
5
4
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-
5
5
0
.
[
25]
Ca
o
,
Wen
c
h
a
o
,
“
Im
p
e
d
a
n
c
e
-
Ba
se
d
S
tab
il
it
y
An
a
l
y
sis
a
n
d
Co
n
tr
o
ll
e
r
De
sig
n
o
f
T
h
re
e
-
P
h
a
se
In
v
e
r
ter
-
Ba
se
d
A
c
S
y
ste
m
s.
”
P
h
D d
iss.,
Un
iv
e
rsity
o
f
Ten
n
e
ss
e
e
,
2
0
1
7
.
h
tt
p
s://
trac
e
.
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n
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e
e
.
e
d
u
/u
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_
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ra
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4
4
9
[2
6
]
J.
S
u
n
,
“
Im
p
e
d
a
n
c
e
-
Ba
se
d
S
tab
i
li
ty
Crit
e
ri
o
n
fo
r
G
rid
-
Co
n
n
e
c
te
d
In
v
e
rters
,
”
in
IE
EE
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
ics
,
v
o
l.
2
6
,
n
o
.
1
1
,
p
p
.
3
0
7
5
-
3
0
7
8
,
No
v
.
2
0
1
1
,
DO
I:
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0
.
1
1
0
9
/T
P
EL
.
2
0
1
1
.
2
1
3
6
4
3
9
.
[2
7
]
X.
Wan
g
,
F
.
B
laa
b
jerg
a
n
d
W.
Wu
,
“
M
o
d
e
li
n
g
a
n
d
A
n
a
ly
sis
o
f
Ha
rm
o
n
ic
S
tab
il
i
ty
i
n
a
n
AC
P
o
we
r
-
El
e
c
tro
n
ics
-
Ba
se
d
P
o
we
r
S
y
ste
m
,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
El
e
c
tro
n
i
c
s
,
v
o
l.
2
9
,
n
o
.
1
2
,
p
p
.
6
4
2
1
-
6
4
3
2
,
De
c
.
2
0
1
4
,
DO
I:
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0
.
1
1
0
9
/
TP
EL
.
2
0
1
4
.
2
3
0
6
4
3
2
.
[2
8
]
KK
De
e
p
ik
a
,
G
K
Ra
o
,
J Vijay
a
Ku
m
a
r,
a
n
d
RS
Ra
v
i
S
a
n
k
a
r
,
“
En
h
a
n
c
e
m
e
n
t
o
f
Vo
lt
a
g
e
Re
g
u
lati
o
n
u
sin
g
a
7
-
Lev
e
l
In
v
e
rter
b
a
se
d
El
e
c
tri
c
S
p
rin
g
wit
h
Re
d
u
c
e
d
Nu
m
b
e
r
o
f
S
witc
h
e
s,
”
In
d
o
n
e
sia
n
J
o
u
r
n
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(IJ
PE
DS
)
,
Vo
l.
1
1
,
n
o
.
2
,
p
p
.
5
5
5
-
5
6
5
,
2
0
2
0
,
DO
I:
1
0
.
1
1
5
9
1
/
ij
p
e
d
s.
v
1
1
.
i
2
.
p
p
5
5
5
-
5
6
5
.
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
Dr
.
R.S
.
Ra
v
i
S
a
n
k
a
r
C
u
rre
n
tl
y
wo
rk
i
n
g
a
s
As
so
c
iate
P
ro
fe
ss
o
r
in
th
e
d
e
p
a
rtme
n
t
o
f
E
EE
i
n
Vig
n
a
n
’s
I
n
stit
u
te
o
f
In
f
o
rm
a
ti
o
n
Tec
h
n
o
l
o
g
y
,
Visa
k
h
a
p
a
tn
a
m
,
An
d
h
ra
P
ra
d
e
sh
,
I
n
d
ia
.
Re
c
e
iv
e
d
h
is
Ba
c
h
e
lo
rs,
M
a
ste
rs
a
n
d
D
o
c
to
ra
l
d
e
g
re
e
fro
m
In
st
it
u
t
io
n
o
f
En
g
i
n
e
e
rs,
JN
TU
Hy
d
e
ra
b
a
d
,
JN
TUA
An
a
n
th
a
p
u
ra
m
.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
p
o
we
r
q
u
a
li
ty
in
d
istri
b
u
ti
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p
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sh
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fr
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Ka
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se
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ter
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o
p
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t
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c
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n
iq
u
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s.
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