I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
,
p
p
.
3
6
4
~
3
7
2
I
SS
N:
2252
-
8
7
9
2
,
DOI
:
1
0
.
1
1
5
9
1
/ijap
e.
v
1
0
.
i4
.
p
p
3
6
4
-
372
364
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
p
e.
ia
esco
r
e.
co
m
A
g
rid in
terc
o
nne
cted
n
ested
neut
r
a
l poin
t
cla
mped
i
nv
erte
r
with
v
o
ltag
e sy
nc
hro
niza
tion usin
g
sy
nchro
no
us refe
rence
frame
co
ntrolle
r
B
o
g
im
i
Siris
ha
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
Un
i
v
e
rsity
C
o
ll
e
g
e
o
f
E
n
g
i
n
e
e
rin
g
(A),
Os
m
a
n
ia Un
i
v
e
rsity
,
Hy
d
e
ra
b
a
d
,
I
n
d
ia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Au
g
30
,
2
0
21
R
ev
is
ed
Oct
29
,
2
0
21
Acc
ep
ted
No
v
1
9
,
2
0
21
Ne
ste
d
n
e
u
tral
p
o
i
n
t
c
lam
p
e
d
m
u
lt
i
lev
e
l
i
n
v
e
rter
with
i
n
ter
c
o
n
n
e
c
ti
o
n
t
o
g
rid
th
ro
u
g
h
t
h
e
s
y
n
c
h
r
o
n
o
u
s
re
fe
re
n
c
e
fra
m
e
(
S
RF
)
c
o
n
t
ro
ll
e
r
f
o
r
sy
n
c
h
r
o
n
iza
ti
o
n
o
f
v
o
lt
a
g
e
t
o
t
h
e
g
rid
is
d
e
m
o
n
stra
ted
.
Th
e
s
y
st
e
m
'
s
m
a
in
fe
a
tu
re
is
th
a
t
v
o
lt
a
g
e
stre
ss
in
e
a
c
h
in
v
e
rter
sw
it
c
h
i
n
g
d
e
v
ice
i
s
k
e
p
t
t
o
a
m
in
imu
m
,
a
n
d
re
d
u
n
d
a
n
t
in
v
e
rt
e
r
sw
it
c
h
in
g
sta
tes
a
re
u
ti
l
ise
d
fo
r
n
e
u
tral
p
o
i
n
t
a
n
d
fly
i
n
g
c
a
p
a
c
it
o
r
v
o
lt
a
g
e
b
a
lan
c
in
g
with
sin
u
so
id
a
l
p
u
lse
-
wid
th
m
o
d
u
lati
o
n
(
P
WM
)
tec
h
n
iq
u
e
,
s
y
n
c
h
r
o
n
isa
ti
o
n
t
o
g
r
id
v
o
lt
a
g
e
s,
a
n
d
p
o
we
r
in
jec
ti
o
n
with
lo
w
h
a
rm
o
n
ic
g
e
n
e
ra
ti
o
n
.
T
h
e
in
v
e
rter
re
c
e
iv
e
s
it
s
in
p
u
t
fro
m
a
p
h
o
t
o
v
o
lt
a
ic
(
PV
)
so
u
rc
e
th
a
t
i
s
c
o
u
p
led
t
o
DC
-
DC
b
o
o
ste
r
c
o
n
v
e
rters
th
a
t
a
re
re
g
u
late
d
b
y
t
h
e
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
i
n
g
(
M
P
P
T
)
i
n
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
a
lg
o
r
it
h
m
to
m
a
in
t
a
in
a
c
o
n
sta
n
t
d
c
v
o
lt
a
g
e
.
Th
e
sy
ste
m
is
e
x
a
m
in
e
d
u
n
d
e
r
v
a
rio
u
s lo
a
d
c
o
n
d
it
io
n
s wit
h
M
ATLAB
S
imu
li
n
k
m
o
d
e
l.
K
ey
w
o
r
d
s
:
Ma
x
im
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
i
n
g
alg
o
r
ith
m
Ph
o
to
v
o
ltaic
a
r
r
a
y
Po
in
t o
f
c
o
m
m
o
n
c
o
u
p
lin
g
Pu
ls
e
w
id
th
m
o
d
u
latio
n
Sy
n
ch
r
o
n
o
u
s
r
ef
e
r
en
ce
f
r
am
e
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
B
o
g
im
i
Sirish
a
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
U
n
iv
er
s
ity
C
o
lleg
e
o
f
E
n
g
in
ee
r
i
n
g
(
A)
Osma
n
ia
Un
iv
er
s
ity
Osma
n
ia
Un
iv
er
s
ity
Ma
in
R
d
,
Am
b
er
p
et,
Hy
d
er
ab
a
d
,
T
elan
g
an
a
5
0
0
0
0
7
,
I
n
d
ia
E
m
ail: sirish
ab
@
o
s
m
an
ia.
ac
.
i
n
1.
I
NT
RO
D
UCT
I
O
N
I
n
cr
ea
s
ed
c
o
n
s
u
m
p
tio
n
o
f
p
o
wer
b
y
d
iv
er
s
e
l
o
ad
s
th
r
o
u
g
h
o
u
t
th
e
wo
r
ld
is
ca
u
s
in
g
d
em
an
d
f
o
r
elec
tr
ical
p
o
wer
g
en
er
atio
n
to
in
cr
ea
s
e
d
a
y
b
y
d
ay
.
T
r
ad
iti
o
n
al
m
eth
o
d
s
(
d
iesel
g
en
er
at
o
r
s
,
th
er
m
al
p
lan
ts
,
an
d
n
u
clea
r
p
lan
ts
)
o
f
lar
g
er
p
r
o
d
u
ctio
n
o
f
elec
tr
ic
p
o
wer
is
ca
u
s
in
g
th
e
d
ev
astat
in
g
ef
f
ec
ts
o
f
th
e
en
v
ir
o
n
m
en
t
.
As
a
r
esu
lt
o
f
th
ese
m
e
th
o
d
s
o
f
p
r
o
d
u
ctio
n
,
h
az
ar
d
o
u
s
waste
an
d
g
ases
ar
e
p
r
o
d
u
ce
d
.
W
h
ic
h
in
tu
r
n
t
h
ese
p
o
wer
p
lan
ts
p
lay
a
v
ital
r
o
le
f
o
r
in
cr
ea
s
e
in
g
lo
b
al
war
m
in
g
m
ak
i
n
g
ea
r
th
a
b
ad
p
lace
f
o
r
s
u
r
v
iv
al
o
f
liv
in
g
th
in
g
s
o
n
th
e
p
lan
et.
B
etter
en
er
g
y
g
en
er
atio
n
f
r
o
m
r
e
n
ewa
b
le
s
o
u
r
ce
s
is
th
e
o
n
ly
way
to
s
af
eg
u
ar
d
th
e
ea
r
th
an
d
m
ak
e
it
a
b
etter
p
lace
in
th
e
f
u
tu
r
e
[
1
]
.
H
y
d
r
o
p
o
wer
p
lan
ts
,
s
o
lar
p
o
wer
p
lan
ts
,
win
d
f
ar
m
s
,
b
io
g
as
f
ac
ilit
ies,
an
d
tid
al
wav
e
u
n
its
ar
e
ex
am
p
les
o
f
th
ese
ty
p
es
o
f
g
en
er
at
o
r
s
.
W
in
d
f
ar
m
s
,
wh
ich
g
en
er
ate
lar
g
e
am
o
u
n
ts
o
f
elec
tr
icity
y
et
m
ay
b
e
co
n
s
tr
u
cte
d
in
r
em
o
te
p
lace
s
d
is
tan
t
f
r
o
m
civ
ilizatio
n
,
ar
e
an
in
s
tan
t
alt
er
n
ativ
e
f
o
r
h
y
d
r
o
p
o
wer
p
lan
ts
.
So
lar
p
o
wer
p
lan
ts
ar
e
th
e
b
est
alter
n
ativ
e
f
o
r
g
en
er
atin
g
lar
g
e
o
r
li
ttle
am
o
u
n
ts
o
f
elec
tr
icity
.
Su
n
p
lan
ts
ar
e
m
ad
e
u
p
o
f
a
s
er
ies
o
f
p
h
o
to
v
o
ltaic
p
l
an
es
th
at
u
s
e
s
o
lar
ir
r
ad
iatio
n
to
cr
ea
te
DC
elec
tr
icity
.
Ph
o
to
v
o
ltaic
ar
r
ay
s
ar
e
d
if
f
er
en
t
p
ar
allel
an
d
s
er
ie
s
co
n
f
ig
u
r
atio
n
s
o
f
th
ese
p
an
els
(
PVA)
[2
]
-
[
6]
.
B
ec
au
s
e
th
e
lo
ad
s
r
u
n
o
n
AC
v
o
ltag
e,
th
e
DC
p
o
wer
f
r
o
m
th
e
p
h
o
to
v
o
ltaic
ar
r
a
y
m
u
s
t
b
e
co
n
v
er
ted
to
eith
er
s
in
g
le
p
h
ase
AC
o
r
th
r
ee
p
h
ases
AC
.
Mu
lti
lev
el
i
n
v
er
ter
in
v
o
lv
es
a
k
ey
r
o
le
in
th
e
p
r
o
ce
s
s
o
f
c
o
n
v
e
r
s
io
n
[
7
]
.
E
x
ten
s
iv
e
r
esear
ch
on
p
r
o
ce
s
s
o
f
co
n
v
er
s
io
n
u
s
in
g
wid
e
c
o
n
v
er
ter
s
f
o
r
h
ig
h
er
ef
f
icien
cy
an
d
l
o
wer
h
ar
m
o
n
i
c
g
en
er
atio
n
[
8
]
-
[
10
].
I
n
th
is
p
ap
er
a
n
ested
n
eu
t
r
al
p
o
in
t
clam
p
ed
f
iv
e
lev
el
v
o
ltag
e
s
o
u
r
ce
in
v
e
r
ter
[
11
]
is
in
ter
co
n
n
ec
t
ed
to
g
r
id
b
y
u
s
in
g
s
y
n
ch
r
o
n
o
u
s
r
ef
er
e
n
ce
f
r
am
e
(
SR
F
)
co
n
tr
o
ller
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
g
r
id
in
terco
n
n
ec
ted
n
ested
n
eu
tr
a
l p
o
in
t c
la
mp
e
d
in
ve
r
ter w
ith
vo
lta
g
e
s
yn
ch
r
o
n
iz
a
tio
n
… (
B
o
g
imi
S
ir
is
h
a)
365
T
h
e
r
e
n
ewa
b
le
e
n
er
g
y
in
p
u
t
is
o
b
tain
ed
b
y
m
ea
n
s
o
f
p
h
o
to
v
o
ltaic
ar
r
a
y
t
h
r
o
u
g
h
a
DC
-
D
C
b
o
o
s
ter
c
o
n
v
e
r
ter
c
o
n
tr
o
lled
b
y
in
cr
e
m
en
tal
co
n
d
u
ctan
ce
m
ax
i
m
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
tech
n
iq
u
e
,
s
o
th
at,
d
c
o
u
tp
u
t
o
b
tain
ed
is
s
tab
ilized
b
y
in
j
ec
tin
g
p
o
wer
with
l
o
w
h
ar
m
o
n
ic
d
is
to
r
tio
n
[
1
2
]
.
T
h
e
p
r
o
to
ty
p
e
m
o
d
el
an
d
an
aly
s
is
o
f
th
e
s
y
s
tem
is
ca
r
r
i
ed
o
u
t
u
n
d
er
v
a
r
io
u
s
co
n
d
itio
n
s
o
f
lo
a
d
.
Sectio
n
1
p
r
esen
ts
th
e
n
ested
n
eu
tr
al
p
o
in
t
clam
p
ed
co
n
v
er
ter
,
s
ec
tio
n
2
d
escr
ib
es
th
e
SR
F
co
n
t
r
o
l
s
tr
u
ctu
r
e
,
s
ec
tio
n
3
g
iv
es
PVA
m
o
d
u
le
with
MPPT
alg
o
r
ith
m
,
an
d
s
ec
tio
n
4
p
r
esen
ts
th
e
r
esu
lts
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
at
d
if
f
er
en
t
lo
ad
co
n
d
itio
n
s
.
T
h
e
f
in
al
s
ec
tio
n
5
h
as c
o
n
clu
s
io
n
s
.
2.
N
E
S
T
E
D
NE
U
T
RA
L
P
O
I
N
T
CL
A
M
P
E
D
I
NV
E
R
T
E
R
N
ested
n
eu
tr
al
p
o
in
t
clam
p
e
d
(
NNPC
)
in
v
er
ter
is
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
to
p
o
lo
g
y
h
as
eig
h
t
s
witch
es
in
ea
ch
leg
.
Ou
tp
u
t
v
o
ltag
e
lev
els
f
o
r
th
e
s
witch
in
g
ar
e
cr
ea
ted
b
y
th
e
v
o
ltag
e
d
iv
id
in
g
ca
p
ac
i
t
o
r
s
C1
,
C2
,
an
d
C
3
[
6
]
.
T
h
e
m
a
in
f
ea
tu
r
e
is
th
at,
t
h
at
th
e
n
u
m
b
er
o
f
d
io
d
es
an
d
ca
p
a
cito
r
s
f
o
r
clam
p
in
g
a
r
e
m
in
im
is
ed
.
T
h
e
co
n
v
er
te
r
also
d
o
es
n
o
t
n
ee
d
an
y
is
o
lated
DC
s
o
u
r
ce
at
th
e
in
p
u
t
f
o
r
r
eg
en
e
r
ativ
e
ap
p
licatio
n
s
.
Als
o
,
th
e
in
ter
co
n
n
ec
ted
ca
p
ac
ito
r
s
cr
ea
te
s
tab
ilized
o
u
tp
u
t
v
o
ltag
es
with
r
e
d
u
ce
d
o
v
er
s
h
o
o
ts
in
th
e
o
u
t
p
u
t
[
1
3
]
-
[
1
6
]
.
T
h
e
ca
p
ac
ito
r
s
C
n
1
an
d
C
n
2
(
n
=a
,
b
,
c)
a
r
e
c
h
ar
g
e
d
to
a
v
o
ltag
e
o
f
¼
Vd
c
an
d
th
e
ca
p
ac
ito
r
C
n
3
is
ch
ar
g
e
to
v
o
ltag
e
o
f
¾
Vd
c.
Fig
u
r
e
1
.
Fiv
e
lev
el
NNPC
in
v
er
ter
to
p
o
l
o
g
y
T
h
e
f
iv
e
lev
el
v
o
ltag
es
in
cl
u
d
in
g
ze
r
o
v
o
ltag
e
ar
e
g
en
e
r
ated
as
p
er
th
e
s
witch
in
g
o
f
th
e
eig
h
t
s
witch
es
o
f
o
n
e
leg
.
T
h
e
ze
r
o
v
o
ltag
e
lev
el
in
clu
d
es
ch
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
o
f
ca
p
a
cito
r
s
f
o
r
ac
h
iev
in
g
ca
p
ac
ito
r
v
o
ltag
e
b
alan
cin
g
m
ak
in
g
th
e
c
o
n
v
e
r
ter
r
ed
u
n
d
a
n
c
y
to
v
o
ltag
e
v
ar
iatio
n
s
.
T
h
e
r
e
latio
n
b
etwe
en
V
k
an
d
L
k
ca
n
b
e
g
iv
en
a
s
(
1
)
.
=
(
4
−
8
)
∗
/
16
(
1
)
In
-
p
h
ase
d
is
p
o
s
itio
n
(
PD)
ca
r
r
ier
m
o
d
u
latio
n
tech
n
iq
u
e
[
17
]
,
[
1
8
]
is
em
p
lo
y
ed
f
o
r
th
e
g
e
n
er
atio
n
o
f
p
u
ls
es.
I
n
th
is
m
eth
o
d
all
th
e
ca
r
r
ier
wav
ef
o
r
m
s
ar
e
in
p
h
ase
with
n
o
p
h
ase
s
h
if
t.
T
h
e
r
ef
e
r
en
ce
s
in
wav
ef
o
r
m
f
o
r
t
h
e
ab
o
v
e
PD
m
o
d
u
latio
n
tech
n
iq
u
e
is
g
e
n
er
ated
b
y
S
R
F
co
n
tr
o
ller
wh
ic
h
g
e
n
er
ate
s
r
ef
er
en
ce
s
ig
n
al
in
s
y
n
ch
r
o
n
izatio
n
to
th
e
g
r
id
.
2
.
1
.
Ca
pa
cit
o
r
v
o
lt
a
g
es
R
ed
u
n
d
an
t
s
witch
in
g
s
tates
at
lev
els
1
,
2
,
an
d
3
to
ch
ar
g
e
an
d
d
is
ch
ar
g
e
fly
in
g
ca
p
ac
ito
r
s
.
B
u
t
,
th
er
e
ar
e
n
o
t
an
y
r
ed
u
n
d
a
n
cy
s
witch
in
g
s
tates
at
0
,
4
lev
els.
Ag
ain
,
l
ev
el
1
is
n
ice
to
co
n
tr
o
l
v
o
ltag
es
o
f
ca
p
ac
ito
r
C
x3
an
d
C
x2
,
an
d
f
u
r
th
e
r
l
ev
el
3
is
g
o
o
d
t
o
co
n
t
r
o
l
th
e
v
o
ltag
e
o
f
ca
p
a
cito
r
s
C
x3
an
d
C
x1
.
Fu
r
th
er
,
th
e
r
e
ar
e
r
ed
u
n
d
an
cy
s
tates
f
o
r
lev
el
s
1
,
2
,
an
d
3
.
E
ac
h
r
ed
u
n
d
a
n
c
y
s
tate
b
ased
o
n
d
ir
ec
tio
n
o
f
o
u
tp
u
t
cu
r
r
en
t
ca
n
ch
ar
g
e
o
r
d
is
ch
ar
g
e
3
fly
i
n
g
c
ap
ac
ito
r
s
.
T
h
u
s
,
m
in
im
ize
th
e
d
if
f
er
e
n
ce
b
etwe
en
n
o
m
in
al
v
o
ltag
e
v
alu
es
an
d
m
ea
s
u
r
ed
v
o
ltag
e
v
alu
es.
T
h
e
flo
wch
ar
t
o
f
Fig
u
r
e
2
illu
s
tr
ates
th
e
p
r
o
ce
s
s
to
co
n
tr
o
l
v
o
ltag
e
o
f
fly
in
g
ca
p
ac
ito
r
s
in
ea
ch
p
h
ase.
T
h
e
s
y
n
ch
r
o
n
o
u
s
r
ef
er
en
ce
f
r
a
m
e
(
SR
F)
co
n
tr
o
ller
[
1
9
]
is
m
ajo
r
m
o
d
u
le
in
th
e
p
r
o
p
o
s
ed
t
est
s
y
s
te
m
wh
ich
co
n
tr
o
ls
th
e
o
u
t
p
u
t
v
o
lt
ag
e
o
f
th
e
m
u
ltil
ev
el
in
v
er
ter
.
Fo
r
t
h
e
o
u
tp
u
t
v
o
lta
g
e
m
atch
to
t
h
e
g
r
id
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
6
4
–
372
366
am
p
litu
d
e,
p
h
ase
a
n
d
f
r
eq
u
en
cy
th
e
SR
F
co
n
tr
o
ller
ta
k
es
f
ee
d
b
ac
k
[
2
0
]
f
r
o
m
th
e
g
r
id
th
r
ee
p
h
ase
v
o
ltag
es,
cu
r
r
en
ts
an
d
DC
lin
k
v
o
ltag
e
a
t th
e
in
p
u
t.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
SR
F c
o
n
tr
o
ller
is
g
iv
en
in
Fi
g
u
r
e
3
.
Fig
u
r
e
2
.
Flo
wch
ar
t t
o
co
n
t
r
o
l
th
e
v
o
ltag
e
o
f
f
ly
i
n
g
ca
p
ac
ito
r
Fig
u
r
e
3
.
B
lo
ck
d
iag
r
am
o
f
S
R
F c
o
n
tr
o
l stru
ctu
r
e
f
o
r
PVA
g
r
id
in
ter
c
o
n
n
ec
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
g
r
id
in
terco
n
n
ec
ted
n
ested
n
eu
tr
a
l p
o
in
t c
la
mp
e
d
in
ve
r
ter w
ith
vo
lta
g
e
s
yn
ch
r
o
n
iz
a
tio
n
… (
B
o
g
imi
S
ir
is
h
a)
367
T
h
e
SR
F
co
n
tr
o
ller
u
s
es
Par
k
s
tr
an
s
f
o
r
m
atio
n
f
o
r
co
n
tr
o
ll
in
g
th
e
cu
r
r
en
t
o
f
th
e
i
n
v
er
te
r
.
T
h
e
d
q
co
m
p
o
n
en
ts
o
f
th
e
cu
r
r
e
n
ts
ar
e
ca
lcu
lated
with
r
esp
ec
t
to
P
L
L
m
o
d
u
le
[
19
]
-
[
2
5
]
wo
r
k
in
g
in
s
y
n
ch
r
o
n
izatio
n
to
th
e
g
r
id
v
o
ltag
e.
T
h
e
d
q
ax
i
s
ca
lcu
latio
n
f
o
r
th
e
g
iv
en
co
n
tr
o
ller
is
g
iv
en
as p
er
th
e
eq
u
a
tio
n
s
g
iv
en
b
el
o
w
.
L
et
r
v
ec
to
r
i
n
ab
c
c
o
o
r
d
in
ate
s
y
s
tem
, a
n
g
le
b
etwe
en
ab
,
ab
,
an
d
ca
ar
e
1
2
0
d
eg
r
ee
s
.
⃗
=r
a
.
̂
+ r
b
.
̂
+ r
c
.
̂
(
2
)
W
h
er
e,
r
a
,
r
b
,
a
n
d
r
c
b
e
p
r
o
jecti
o
n
s
o
f
r
v
ec
to
r
i
n
d
ir
ec
tio
n
o
f
a
,
b,
an
d
c
.
⃗
=r
α
.
̂
+ r
β
.
̂
(
3
)
W
h
er
e,
r
α
p
r
o
jectio
n
o
f
r
v
ec
t
o
r
in
d
ir
ec
tio
n
o
f
α
,
r
β
p
r
o
jectio
n
o
f
r
v
ec
to
r
in
d
ir
ec
tio
n
o
f
β
.
T
o
g
et
r
elatio
n
b
etwe
en
α
β an
d
a
b
c
:
=
⃗
.
̂
(
4
)
=
{
.
̂
+
.
̂
+
.
̂
}
.
̂
=
̂
.
̂
+
̂
.
̂
+
̂
.
̂
=
+
(
120
0
)
+
(
240
0
)
=
−
1
2
−
1
2
(
5
)
r
β
p
r
o
jectio
n
o
f
r
v
ec
to
r
in
th
e
d
ir
ec
tio
n
o
f
β is
=
⃗
.
̂
(
6
)
=
{
.
̂
+
.
̂
+
.
̂
}
.
̂
=
̂
.
̂
+
̂
.
̂
+
̂
.
̂
=
+
(
30
0
)
+
(
150
0
)
=
0
+
√
3
2
−
√
3
2
[
r
α
r
β
r0
]
=
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
1
√
2
1
√
2
1
√
2
]
[
r
a
r
b
rc
]
(
7
)
[
⃗
d
⃗
q
0
]
=
[
c
os
θ
s
in
θ
0
−
s
in
θ
c
os
θ
0
0
0
1
]
[
⃗
α
⃗
β
0
]
(
8
)
B
y
u
s
in
g
C
lar
k
s
t
r
an
s
f
o
r
m
atio
n
an
d
f
r
o
m
α
β
-
co
o
r
d
in
ates to
d
q
-
co
o
r
d
in
ates (
Par
k
s
t
r
a
n
s
f
o
r
m
atio
n
)
we
g
et
[
r
⃗
d
r
⃗
q
0
]
=
√
2
3
[
c
os
θ
−
1
2
c
os
θ
+
√
3
2
Sin
θ
−
1
2
c
os
θ
−
√
3
2
s
in
θ
−
s
in
θ
1
2
s
in
θ
+
√
3
2
c
os
θ
1
2
s
in
θ
−
√
3
2
c
os
θ
1
√
2
1
√
2
1
√
2
]
(
9
)
T
h
e
v
o
ltag
e
c
o
n
tr
o
ller
is
a
PI
co
n
tr
o
ller
with
in
p
u
t
tak
en
b
y
co
m
p
ar
is
o
n
o
f
DC
v
o
ltag
e
at
th
e
DC
lin
k
ca
p
ac
ito
r
an
d
r
ef
er
e
n
ce
v
alu
e
g
iv
e
n
b
y
th
e
u
s
er
.
T
h
e
o
u
tp
u
t
o
f
th
e
v
o
ltag
e
co
n
tr
o
ller
is
d
ir
ec
t
ax
is
co
m
p
o
n
en
t
r
ef
er
e
n
ce
an
d
q
u
a
d
r
atu
r
e
ax
is
r
ef
er
e
n
ce
co
m
p
o
n
en
t
is
co
n
s
id
er
ed
to
b
e
0
.
T
h
e
cu
r
r
en
t
co
n
tr
o
ller
g
en
er
ates
th
e
r
eq
u
ir
ed
r
ef
er
en
ce
d
q
v
o
ltag
e
r
ef
e
r
en
ce
co
m
p
o
n
en
t
with
PI
co
n
tr
o
ller
in
it.
T
h
e
r
ef
er
e
n
ce
d
q
v
o
ltag
e
co
m
p
o
n
e
n
ts
(
Vd
*
an
d
Vq
*
)
[
1
9
]
a
r
e
co
n
v
er
ted
to
s
in
u
s
o
id
al
b
y
in
v
e
r
s
e
p
ar
k
s
t
r
an
s
f
o
r
m
atio
n
.
T
h
e
f
in
al
th
r
ee
p
h
ase
s
in
u
s
o
id
al
r
ef
er
en
ce
wav
ef
o
r
m
s
ar
e
co
m
p
a
r
ed
to
p
h
ase
d
is
p
o
s
itio
n
m
u
lti
ca
r
r
ier
m
o
d
u
latio
n
tech
n
iq
u
e
f
o
r
g
en
er
atio
n
o
f
p
u
ls
es
f
o
r
th
e
n
o
v
el
f
iv
e
lev
el
in
v
er
ter
.
As
th
e
SR
F
co
n
tr
o
ller
u
s
es
PLL
to
g
en
er
ate
th
e
r
ef
er
e
n
ce
s
ig
n
als
an
d
th
e
PLL
is
o
p
e
r
ated
with
g
r
id
v
o
ltag
e
as
f
ee
d
b
ac
k
,
th
e
in
v
er
ter
o
p
er
ates
i
n
s
y
n
ch
r
o
n
izatio
n
with
th
e
g
r
id
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
6
4
–
372
368
3.
P
VA
-
M
O
DUL
E
T
h
e
PVA
is
a
DC
s
o
u
r
ce
wh
ich
g
en
er
ates
p
o
wer
b
y
c
o
n
v
er
tin
g
s
o
lar
ir
r
ad
iatio
n
.
T
h
e
DC
v
o
ltag
e
f
r
o
m
th
e
PVA
is
n
o
t a
lway
s
c
o
n
s
tan
t a
s
th
e
s
o
lar
ir
r
ad
iatio
n
is
v
ar
iab
le
with
ch
an
g
e
in
cli
m
aticc
o
n
d
itio
n
s
.
Fo
r
co
n
s
tan
t
DC
v
o
ltag
e
g
en
er
atio
n
,
th
e
PVA
is
co
n
n
ec
ted
to
a
s
tab
ilizin
g
D
C
-
DC
b
o
o
s
ter
co
n
v
er
ter
co
n
tr
o
lled
b
y
MPPT
tech
n
iq
u
e
[
22
]
f
o
r
m
ain
tain
in
g
th
e
o
u
tp
u
t
v
o
ltag
e
at
a
s
p
ec
if
ied
v
al
u
e.
A
DC
-
DC
b
o
o
s
ter
co
n
v
e
r
ter
is
u
tili
ze
d
f
o
r
th
is
p
u
r
p
o
s
e
s
o
as
to
in
cr
ea
s
e
th
e
i
n
p
u
t
v
o
ltag
e
to
t
h
e
in
v
er
ter
as
th
e
AC
lo
ad
s
o
p
er
ate
at
h
ig
h
v
o
ltag
es.
T
h
e
d
u
ty
r
atio
f
o
r
th
e
I
GB
T
s
w
itch
is
g
en
er
ate
d
b
y
i
n
cr
em
en
tal
co
n
d
u
ctan
c
e
MPPT
alg
o
r
ith
m
[
20
]
-
[
2
5
]
.
T
h
is
alg
o
r
ith
m
is
co
n
s
id
er
ed
to
b
e
r
o
b
u
s
t
an
d
o
p
er
ates
with
f
aster
r
esp
o
n
s
e
r
ate
as
co
m
p
ar
ed
to
tr
ad
itio
n
al
P&
O
MPPT
alg
o
r
ith
m
wh
ich
is
u
s
ed
in
m
o
s
t o
f
t
h
e
MPPT
tech
n
iq
u
es.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
p
r
o
to
ty
p
e
o
f
PVA
r
en
e
wab
le
s
o
u
r
ce
co
n
n
ec
ted
to
n
ested
n
eu
tr
al
p
o
in
t
clam
p
e
d
f
iv
e
lev
el
in
v
er
ter
co
n
tr
o
lled
b
y
SR
F
co
n
tr
o
ller
in
ter
co
n
n
ec
ted
to
th
r
e
e
p
h
ase
g
r
id
is
m
o
d
elled
is
s
i
m
u
lated
MA
T
L
AB
Simu
lin
k
.
T
h
e
p
ar
am
eter
s
o
f
s
im
u
latio
n
ar
e
g
i
v
en
in
T
ab
le
1
.
T
ab
le
1
.
P
ar
am
eter
s
o
f
Simu
lin
k
b
lo
c
k
d
iag
r
am
P
a
r
a
me
t
e
r
V
a
l
u
e
I
n
p
u
t
d
c
l
i
n
k
v
o
l
t
a
g
e
V
i
n
=
6
0
0
V
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
F
sh
=
2
0
0
0
H
z
D
i
o
d
e
R
i
n
=
0
.
0
0
1
o
h
ms,
F
o
r
w
a
r
d
v
o
l
t
a
g
e
=
0
.
8
V
F
l
y
i
n
g
c
a
p
a
c
i
t
o
r
C
=
1
0
0
0
µ
F
I
G
B
T
sw
i
t
c
h
R
i
n
=
0
.
0
0
1
o
h
ms
M
o
d
u
l
a
t
i
o
n
i
n
d
e
x
M
I
=
0
.
9
5
F
u
n
d
a
m
e
n
t
a
l
f
r
e
q
u
e
n
c
y
F
=
5
0
Hz
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
F
s=2
0
0
0
Hz
R
-
l
o
a
d
R
=
1
0
0
o
h
ms
RL
-
l
o
a
d
w
i
t
h
0
.
7
p
o
w
e
r
f
a
c
t
o
r
l
a
g
g
i
n
g
P
=
7
0
0
W
,
Q
L
=
7
1
4
.
1
4
V
A
R
LC
-
f
i
l
t
e
r
L=
1
0
mH
,
C
=
8
1
0
µ
f
3
-
p
h
a
s
e
b
r
e
a
k
e
r
B
r
e
a
k
i
n
g
r
e
s
i
st
a
n
c
e
(
R
ON
)
=
0
.
0
1
o
h
ms
S
w
i
t
c
h
i
n
g
t
i
me
=
0
.
1
sec
f
o
r
a
l
l
3
p
h
a
se
s
F
r
e
q
u
e
n
c
y
=
5
0
Hz
P
o
l
e
s
=4
(
R
s)
=
0
.
5
5
o
h
ms
(
Ls)
=
0
.
0
0
2
8
8
H
(
R
r
)
=
0
.
7
8
o
h
ms
(
Lr
)
=
0
.
0
0
2
8
6
H
(
Lm)
=
0
.
0
9
0
5
H
I
n
e
r
t
i
a
(
J)
=
0
.
0
1
9
k
g
-
m
2
F
r
i
c
t
i
o
n
f
a
c
t
o
r
(
B
)
=
0
.
0
0
2
9
8
5
N
m
-
sec
R
a
t
i
n
g
o
f
g
r
i
d
c
o
n
n
e
c
t
e
d
Ph
-
P
h
v
o
l
t
a
g
e
R
M
S
=
1
3
2
K
V
3
-
p
h
a
s
e
s
h
o
r
t
c
i
r
c
u
i
t
l
e
v
e
l
a
t
b
a
s
e
v
o
l
t
a
g
e
(
V
A
)
=
2
5
0
0
M
V
A
F
r
e
q
u
e
n
c
y
=
5
0
Hz
X
/
R
r
a
t
i
o
=7
R
a
t
i
n
g
o
f
t
r
a
n
sf
o
r
m
e
r
s
S
t
e
p
d
o
w
n
t
r
a
n
sf
o
r
mer
1
1
0
0
K
V
A
,
11
K
V
/
2
6
0
V
S
t
e
p
d
o
w
n
t
r
a
n
sf
o
r
mer
2
47
M
V
A
,
1
3
2
K
V
/
1
1
KV
S
t
e
p
d
o
w
n
t
r
a
n
sf
o
r
mer
3
1
0
0
K
V
A
,
1
1
K
V
/
4
0
0
V
R
a
t
i
n
g
s
o
f
LC
-
f
i
t
t
e
r
R
e
si
st
a
n
c
e
(
R
L
),
I
n
d
u
c
t
a
n
c
e
(
L)
=
3
.
1
4
mO
h
ms,
0
.
5
mH
A
c
t
i
v
e
p
o
w
e
r
(
P
)
,
R
e
a
c
t
i
v
e
p
o
w
e
r
(
Q
C
)
=
1
0
0
W
,
1
0
K
V
A
R
Fig
u
r
e
4
s
h
o
ws
th
e
Simu
lin
k
d
iag
r
am
o
f
p
r
o
to
ty
p
e
m
o
d
el
with
SR
F
co
n
tr
o
ller
with
in
d
u
ctio
n
m
o
to
r
lo
ad
.
Fig
u
r
e
5
s
h
o
ws
th
e
o
u
t
p
u
t
v
o
ltag
es
o
f
Nested
n
eu
tr
al
p
o
in
t
clam
p
ed
i
n
v
er
ter
with
0
.
9
5
m
o
d
u
latio
n
in
d
ex
.
Fig
u
r
e
6
s
h
o
ws
th
e
th
r
ee
p
h
ase
lin
e
v
o
ltag
es
Vab
c
o
f
NNPC
in
v
er
ter
wh
ic
h
is
s
in
u
s
o
id
al,
b
u
t
I
ab
c
is
“M
-
W
ty
p
e”
s
in
u
s
o
id
al
cu
r
r
e
n
t
b
ec
au
s
e
s
y
s
tem
is
co
n
n
ec
t
ed
to
n
o
n
-
lin
ea
r
lo
ad
ac
r
o
s
s
th
e
3
-
p
h
ase
p
o
we
r
s
u
p
p
ly
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
g
r
id
in
terco
n
n
ec
ted
n
ested
n
eu
tr
a
l p
o
in
t c
la
mp
e
d
in
ve
r
ter w
ith
vo
lta
g
e
s
yn
ch
r
o
n
iz
a
tio
n
… (
B
o
g
imi
S
ir
is
h
a)
369
Fig
u
r
e
4
.
Simu
lin
k
d
iag
r
am
w
ith
SR
F
c
o
n
tr
o
ller
with
i
n
d
u
cti
o
n
m
o
t
o
r
l
o
ad
Fig
u
r
e
5
.
Fiv
e
lev
el
o
u
tp
u
t v
o
l
tag
e
f
o
r
m
o
d
u
latio
n
in
d
e
x
=0
.
9
5
with
R
-
L
o
ad
(
R
=1
0
0
Ω)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
6
4
–
372
370
Fig
u
r
e
6
.
Gr
id
v
o
ltag
e
an
d
g
r
i
d
cu
r
r
e
n
t
I
n
d
u
ctio
n
m
o
to
r
–
l
o
a
d
:
T
a
=
G
r
o
s
s
m
ec
h
an
ical
to
r
q
u
e
(
o
r
)
m
o
to
r
t
o
r
q
u
e
T
sh
(
o
r
)
T
L
=
L
o
ad
to
r
q
u
e
T
loss
=L
o
s
s
d
u
e
to
f
r
ictio
n
,
win
d
ag
e
,
an
d
ir
o
n
lo
s
s
es.
=
+
ℎ
(
)
=
ℎ
∗
ℎ
=
=
10
∗
746
2
∗
1
4
4
0
60
=
49
.
47
−
.
C
o
n
s
id
er
4
9
.
4
7
N
-
m
as f
u
ll l
o
ad
.
So
,
co
n
s
id
er
2
4
.
7
3
N
-
m
as
h
al
f
-
l
o
ad
,
1
2
.
3
6
N
-
m
as
h
al
f
–
l
o
a
d
,
an
d
0
N
-
m
as
n
o
-
l
o
a
d
.
Fig
u
r
e
7
s
h
o
ws
th
e
v
a
r
iatio
n
o
f
l
o
ad
to
r
q
u
e
ap
p
lied
.
Fig
u
r
e
8
a
n
d
Fig
u
r
e
9
s
h
o
ws
as
t
h
e
lo
ad
is
d
ec
r
ea
s
ed
f
r
o
m
f
u
ll
-
lo
a
d
to
h
a
lf
-
lo
ad
to
q
u
ar
ter
-
lo
ad
to
n
o
-
lo
ad
,
th
e
r
o
tatin
g
m
ag
n
etic
f
ield
p
r
o
d
u
ce
d
will a
ls
o
d
ec
r
ea
s
e.
So
,
th
e
cu
r
r
en
t
r
e
q
u
ir
ed
to
p
r
o
d
u
ce
R
MF
is
als
o
d
ec
r
ea
s
e
as
s
h
o
wn
I
s
_
ab
c
&
I
r
_
ab
c
.
(
f
u
ll
-
lo
ad
s
tar
ted
at
0
.
6
s
ec
)
.
Fig
u
r
e
7
.
L
o
ad
t
o
r
q
u
e
a
p
p
lied
to
i
n
d
u
ctio
n
m
o
to
r
Fig
u
r
e
8
.
S
tato
r
a
n
d
r
o
to
r
c
u
r
r
en
ts
I
abc
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
g
r
id
in
terco
n
n
ec
ted
n
ested
n
eu
tr
a
l p
o
in
t c
la
mp
e
d
in
ve
r
ter w
ith
vo
lta
g
e
s
yn
ch
r
o
n
iz
a
tio
n
… (
B
o
g
imi
S
ir
is
h
a)
371
Fig
u
r
e
9
.
Sp
ee
d
,
T
e
v
s
tim
e
T
ab
le
2
s
h
o
ws
%THD
o
f
p
h
ase
v
o
ltag
es
at
o
u
t
p
u
t
f
o
r
v
a
r
io
u
s
ty
p
es
o
f
lo
ad
s
with
o
u
t
SR
F
co
n
tr
o
ller
T
HD
o
b
tain
ed
is
h
ig
h
er
,
f
u
r
th
er
T
HD
is
m
in
im
ized
b
y
SR
F c
o
n
tr
o
ller
th
e
r
e
b
y
elim
in
atin
g
th
e
h
ar
m
o
n
ics.
T
ab
le
2.
O
u
tp
u
t p
h
ase
v
o
ltag
e
T
HD
o
f
in
v
er
ter
s
id
e
f
o
r
R,
RL
,
an
d
in
d
u
ctio
n
m
o
to
r
–
lo
ad
C
a
se
s
t
u
d
i
e
s
%T
H
D
o
f
P
h
-
P
h
o
u
t
p
u
t
v
o
l
t
a
g
e
W
i
t
h
o
u
t
S
R
F
c
o
n
t
r
o
l
l
e
r
W
i
t
h
S
R
F
c
o
n
t
r
o
l
l
e
r
R
-
Lo
a
d
2
5
.
3
5
%
0
.
0
6
%
RL
-
L
o
a
d
4
8
.
7
5
%
0
.
0
7
%
I
n
d
u
c
t
i
o
n
m
o
t
o
r
-
l
o
a
d
3
0
8
.
1
9
%
0
.
0
5
%
5.
CO
NCLU
SI
O
N
Nested
n
eu
tr
al
p
o
in
t
clam
p
ed
f
iv
e
lev
el
in
v
er
ter
in
ter
c
o
n
n
ec
ted
to
g
r
id
co
n
tr
o
lled
b
y
SR
F
s
tr
u
ctu
r
e
with
PD
m
u
lti
ca
r
r
ie
r
m
o
d
u
l
atio
n
tech
n
i
q
u
e
is
a
n
aly
s
ed
.
T
h
e
co
n
n
ec
tio
n
to
g
r
id
b
y
m
ea
n
s
o
f
in
v
er
ter
is
s
y
n
ch
r
o
n
ize
d
an
d
th
e
p
o
wer
f
r
o
m
th
e
PVA
is
in
jecte
d
to
th
e
s
y
s
tem
co
m
p
en
s
atin
g
th
e
lo
ad
s
co
n
n
ec
ted
at
PC
C
.
T
h
e
s
y
s
tem
is
well
te
s
te
d
f
o
r
b
o
th
s
tatic
an
d
d
y
n
am
ic
l
o
ad
co
n
d
itio
n
s
.
T
h
e
r
esu
lts
s
h
o
w
th
e
r
ed
u
ctio
n
o
f
o
u
tp
u
t
p
h
ase
v
o
ltag
e
T
HDs
with
i
n
th
e
p
e
r
m
is
s
ib
le
lim
it
(
<1
%)
.
T
h
e
s
y
s
tem
ca
n
b
e
f
u
r
th
er
ex
ten
d
ed
with
m
u
ltip
le
r
en
ewa
b
le
s
o
u
r
ce
s
th
at
ca
n
b
e
c
o
n
n
ec
te
d
at
th
e
i
n
p
u
t
to
th
e
in
v
er
te
r
a
n
d
o
p
tim
al
co
n
tr
o
ller
ca
n
b
e
in
co
r
p
o
r
ated
f
o
r
b
etter
v
o
ltag
e
.
RE
F
E
R
E
NC
E
S
[1
]
D.
Lee
a
n
d
L.
Wan
g
,
“
S
m
a
ll
-
sig
n
a
l
sta
b
il
it
y
a
n
a
ly
sis
o
f
a
n
a
u
to
n
o
m
o
u
s
h
y
b
rid
re
n
e
wa
b
le
e
n
e
rg
y
p
o
we
r
g
e
n
e
ra
ti
o
n
/en
e
rg
y
sto
ra
g
e
sy
ste
m
p
a
rt
i:
ti
m
e
-
d
o
m
a
in
sim
u
lati
o
n
s
,
”
in
IE
EE
T
r
a
n
s
a
c
ti
o
n
s
o
n
E
n
e
rg
y
Co
n
v
e
rs
io
n
,
v
o
l.
2
3
,
n
o
.
1
,
p
p
.
3
1
1
-
3
2
0
,
M
a
r
.
2
0
0
8
,
d
o
i:
1
0
.
1
1
0
9
/
TE
C.
2
0
0
7
.
9
1
4
3
0
9
.
[2
]
M
.
El
m
a
lah
,
A
.
Ba
-
ra
z
z
o
u
k
,
M
.
G
u
isse
r,
E
.
Ab
d
e
lmo
u
n
im,
a
n
d
M
.
M
a
d
a
rk
,
“
Ba
c
k
ste
p
p
in
g
b
a
se
d
p
o
we
r
c
o
n
tro
l
o
f
a
th
re
e
-
p
h
a
se
s
in
g
le
-
sta
g
e
g
rid
-
c
o
n
n
e
c
ted
P
V
sy
ste
m
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
9
,
n
o
.
6
,
p
p
.
4
7
3
8
-
4
7
4
8
,
De
c
.
2
0
1
9
,
d
o
i
:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
9
i6
.
p
p
4
7
3
8
-
4
7
4
8
.
[3
]
A.
Ra
h
n
a
m
a
e
i
a
n
d
M
.
S
a
li
m
i,
“
A
n
o
v
e
l
g
r
id
c
o
n
n
e
c
ted
p
h
o
to
v
o
l
taic
s
y
ste
m
,
”
Bu
ll
e
ti
n
o
f
El
e
c
tric
a
l
E
n
g
i
n
e
e
rin
g
a
n
d
In
f
o
rm
a
ti
c
s
,
v
o
l.
5
,
n
o
.
2
,
p
p
.
1
3
3
-
1
4
3
,
Ju
n
.
2
0
1
6
,
d
o
i
:
1
0
.
1
1
5
9
1
/ee
i.
v
5
i2
.
5
2
3
.
[4
]
F.
Blaa
b
jer
g
,
R
.
Teo
d
o
re
sc
u
,
M
.
Li
se
rre
,
a
n
d
A.
V.
Ti
m
b
u
s,
“
O
v
e
rv
iew
o
f
c
o
n
tro
l
a
n
d
g
ri
d
sy
n
c
h
ro
n
iza
ti
o
n
fo
r
d
istri
b
u
ted
p
o
we
r
g
e
n
e
ra
ti
o
n
sy
st
e
m
s
,
”
in
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stri
a
l
El
e
c
tro
n
ics
,
v
o
l.
5
3
,
n
o
.
5
,
p
p
.
1
3
9
8
-
1
4
0
9
,
Oc
t.
2
0
0
6
,
d
o
i:
1
0
.
1
1
0
9
/T
I
E.
2
0
0
6
.
8
8
1
9
9
7
.
[5
]
M
.
L
ise
rre
,
R.
Teo
d
o
re
sc
u
,
a
n
d
F
.
Blaa
b
jer
g
,
“
S
tab
il
i
ty
o
f
p
h
o
t
o
v
o
lt
a
ic
a
n
d
win
d
tu
r
b
in
e
g
ri
d
-
c
o
n
n
e
c
ted
in
v
e
rters
fo
r
a
larg
e
se
t
o
f
g
rid
imp
e
d
a
n
c
e
v
a
lu
e
s,
”
in
IEE
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
1
,
n
o
.
1
,
p
p
.
2
6
3
-
2
7
2
,
Ja
n
.
2
0
0
6
,
d
o
i:
1
0
.
1
1
0
9
/T
P
EL
.
2
0
0
5
.
8
6
1
1
8
5
.
[6
]
L
.
A.
d
e
S
.
Ri
b
e
iro
,
O
.
R.
S
a
a
v
e
d
ra
,
J
.
G
.
d
e
M
a
to
s,
S
.
L.
Li
m
a
,
G
.
Bo
n
a
n
,
a
n
d
A
.
S
.
M
a
rt
in
s,
“
De
sig
n
,
c
o
n
tro
l
,
a
n
d
o
p
e
ra
ti
o
n
o
f
a
h
y
b
ri
d
e
lec
tri
c
a
l
g
e
n
e
ra
ti
o
n
s
y
ste
m
b
a
se
d
o
n
re
n
e
wa
b
le
e
n
e
rg
y
so
u
rc
e
s,”
Rev
ista
El
e
trô
n
ica
d
e
Po
tên
c
ia
-
S
o
b
ra
e
p
,
v
o
l.
1
5
,
n
o
.
4
,
p
p
.
3
1
3
-
3
2
2
,
2
0
1
0
.
[7
]
V.
Ka
u
ra
a
n
d
V.
Blas
k
o
,
“
Op
e
ra
ti
o
n
o
f
a
p
h
a
se
lo
c
k
e
d
l
o
o
p
sy
st
e
m
u
n
d
e
r
d
isto
r
ted
u
t
il
it
y
c
o
n
d
it
io
n
s,
”
in
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stry
A
p
p
li
c
a
ti
o
ns
,
v
o
l.
3
3
,
n
o
.
1
,
p
p
.
5
8
-
6
3
,
Ja
n
.
-
F
e
b
.
1
9
9
7
,
d
o
i
:
1
0
.
1
1
0
9
/
2
8
.
5
6
7
0
7
7
.
[8
]
Y.
Zh
a
n
g
,
G
.
P
.
Ad
a
m
,
T.
C.
Li
m
,
S
.
J.
F
in
n
e
y
,
a
n
d
B
.
W.
Wi
ll
iam
s,
“
Hy
b
rid
m
u
lt
i
lev
e
l
c
o
n
v
e
rter:
c
a
p
a
c
it
o
r
v
o
lt
a
g
e
b
a
lan
c
in
g
li
m
it
s
a
n
d
it
s
e
x
ten
sio
n
,
”
in
IE
EE
T
ra
n
sa
c
ti
o
n
s o
n
In
d
u
stri
a
l
In
fo
rm
a
ti
c
s
,
v
o
l.
9
,
n
o
.
4
,
p
p
.
2
0
6
3
-
2
0
7
3
,
N
o
v
.
2
0
1
3
,
d
o
i
:
1
0
.
1
1
0
9
/T
I
I.
2
0
1
2
.
2
2
3
5
8
4
6
.
[9
]
S
.
R.
P
u
l
ik
a
n
t
i
a
n
d
V.
G
.
A
g
e
li
d
is,
“
Hy
b
ri
d
fl
y
i
n
g
-
c
a
p
a
c
it
o
r
-
b
a
se
d
a
c
ti
v
e
-
n
e
u
tral
-
p
o
in
t
-
c
la
m
p
e
d
fiv
e
-
lev
e
l
c
o
n
v
e
rter
o
p
e
ra
ted
wit
h
S
HE
-
P
WM
,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stria
l
El
e
c
tro
n
ics
,
v
o
l
.
5
8
,
n
o
.
1
0
,
p
p
.
4
6
4
3
-
4
6
5
3
,
Oc
t.
2
0
1
1
,
d
o
i:
1
0
.
1
1
0
9
/T
I
E.
2
0
1
1
.
2
1
0
6
0
9
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
7
9
2
I
n
t J
Ap
p
l Po
wer
E
n
g
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
3
6
4
–
372
372
[1
0
]
R.
B.
B
o
ll
i
p
o
,
S
.
M
i
k
k
il
i
,
a
n
d
P
.
K.
Bo
n
th
a
g
o
rla,
‘
H
y
b
ri
d
,
o
p
ti
m
a
l,
in
telli
g
e
n
t
a
n
d
c
las
sic
a
l
P
V
M
P
P
T
tec
h
n
iq
u
e
s:
A
re
v
iew
,
”
in
CS
EE
J
o
u
rn
a
l
o
f
Po
we
r
a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
7
,
n
o
.
1
,
p
p
.
9
-
3
3
,
Ja
n
.
2
0
2
1
,
d
o
i:
1
0
.
1
7
7
7
5
/CS
E
EJP
ES
.
2
0
1
9
.
0
2
7
2
0
.
[1
1
]
K.
Wan
g
,
Z
.
Zh
e
n
g
,
Y.
L
i,
K.
Li
u
,
a
n
d
J.
S
h
a
n
g
,
“
Ne
u
tral
-
p
o
i
n
t
p
o
ten
ti
a
l
b
a
lan
c
in
g
o
f
a
fiv
e
-
lev
e
l
a
c
ti
v
e
n
e
u
tral
-
p
o
i
n
t
-
c
lam
p
e
d
in
v
e
rter
,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
s
tri
a
l
El
e
c
t
ro
n
ics
,
v
o
l.
6
0
,
n
o
.
5
,
p
p
.
1
9
0
7
-
1
9
1
8
,
M
a
y
2
0
1
3
,
d
o
i:
1
0
.
1
1
0
9
/T
IE
.
2
0
1
2
.
2
2
2
7
8
9
8
.
[1
2
]
T
.
Laa
g
o
u
b
i,
M
.
Bo
u
z
i
,
M
.
Be
n
c
h
a
g
ra
,
“
M
P
P
T
&
p
o
we
r
fa
c
to
r
c
o
n
tro
l
fo
r
g
r
id
c
o
n
n
e
c
t
e
d
P
V
sy
ste
m
s
with
F
u
z
z
y
lo
g
ic
c
o
n
tr
o
ll
e
rs
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(IJ
PE
DS
)
,
v
o
l.
9
,
n
o
.
1
,
p
p
.
1
0
5
-
1
1
3
,
M
a
r
.
2
0
1
8
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
p
e
d
s.v
9
n
1
.
p
p
1
0
5
-
1
1
3
.
[1
3
]
Z.
Xu
,
X.
Z
h
e
n
g
,
T.
Li
n
,
J.
Ya
o
,
a
n
d
A.
I
o
in
o
v
ici
,
“
S
witc
h
e
d
-
c
a
p
a
c
it
o
r
m
u
lt
i
-
lev
e
l
in
v
e
rter
wit
h
e
q
u
a
l
d
istri
b
u
ti
o
n
o
f
t
h
e
c
a
p
a
c
it
o
rs
d
isc
h
a
r
g
in
g
p
h
a
se
s,
”
in
C
h
in
e
se
J
o
u
rn
a
l
o
f
El
e
c
t
ric
a
l
E
n
g
i
n
e
e
rin
g
,
v
o
l.
6
,
n
o
.
4
,
p
p
.
4
2
-
5
2
,
De
c
.
2
0
2
0
,
d
o
i:
1
0
.
2
3
9
1
9
/CJEE
.
2
0
2
0
.
0
0
0
0
2
9
.
[1
4
]
R.
Ab
d
u
ll
a
h
,
N.
A.
Ra
h
im,
S
.
R.
S
.
Ra
ih
a
n
,
a
n
d
A.
Z
.
Ah
m
a
d
,
“
F
i
v
e
-
lev
e
l
d
i
o
d
e
-
c
lam
p
e
d
in
v
e
rter
with
th
re
e
-
lev
e
l
b
o
o
st
c
o
n
v
e
rter,
”
i
n
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
v
o
l
.
6
1
,
n
o
.
1
0
,
p
p
.
5
1
5
5
-
5
1
6
3
,
Oc
t.
2
0
1
4
,
d
o
i:
1
0
.
1
1
0
9
/
TIE
.
2
0
1
3
.
2
2
9
7
3
1
5
.
[1
5
]
S
.
T
h
iele
m
a
n
s,
A.
Ru
d
e
rm
a
n
,
B
.
Re
z
n
ik
o
v
,
a
n
d
J.
M
e
l
k
e
b
e
e
k
,
“
I
m
p
ro
v
e
d
n
a
tu
ra
l
b
a
lan
c
in
g
with
m
o
d
ifi
e
d
p
h
a
se
-
sh
ift
e
d
P
WM
fo
r
sin
g
le
-
leg
fiv
e
-
lev
e
l
fl
y
in
g
-
c
a
p
a
c
it
o
r
c
o
n
v
e
rters
,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
w
e
r
El
e
c
tro
n
ics
,
v
o
l.
2
7
,
n
o
.
4
,
p
p
.
1
6
5
8
-
1
6
6
7
,
Ap
r
.
2
0
1
2
,
d
o
i:
1
0
.
1
1
0
9
/T
P
EL
.
2
0
1
1
.
2
1
6
9
9
9
3
.
[1
6
]
M
.
Na
rima
n
i,
B
.
W
u
,
a
n
d
N.
R.
Zarg
a
ri,
“
A
n
o
v
e
l
fiv
e
-
le
v
e
l
v
o
lt
a
g
e
so
u
rc
e
i
n
v
e
rter
wit
h
si
n
u
s
o
id
a
l
p
u
lse
wi
d
t
h
m
o
d
u
lat
o
r
f
o
r
m
e
d
i
u
m
-
v
o
l
tag
e
a
p
p
li
c
a
ti
o
n
s,
”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
E
lec
tro
n
ics
,
v
o
l
.
3
1
,
n
o
.
3
,
p
p
.
1
9
5
9
-
1
9
6
7
,
M
a
r
.
2
0
1
6
,
d
o
i:
1
0
.
1
1
0
9
/
T
P
EL
.
2
0
1
5
.
2
4
4
0
6
5
6
.
[1
7
]
W.
Jia
n
g
,
X.
Hu
a
n
g
,
J.
Wan
g
,
J.
Wan
g
,
a
n
d
J.
Li
,
“
A
c
a
rrier
-
b
a
se
d
P
WM
stra
teg
y
p
ro
v
id
i
n
g
n
e
u
tr
a
l
-
p
o
i
n
t
v
o
lt
a
g
e
o
sc
il
latio
n
e
li
m
in
a
ti
o
n
fo
r
m
u
lt
i
-
p
h
a
se
n
e
u
tral
p
o
in
t
c
lam
p
e
d
3
-
lev
e
l
in
v
e
rter,
”
in
IE
EE
Acc
e
ss
,
v
o
l
.
7
,
p
p
.
1
2
4
0
6
6
-
1
2
4
0
7
6
,
2
0
1
9
,
d
o
i:
1
0
.
1
1
0
9
/ACC
ES
S
.
2
0
1
9
.
2
9
3
8
6
2
3
.
[1
8
]
X.
Qu
a
n
a
n
d
A.
Q.
H
u
a
n
g
,
“
PI
-
b
a
se
d
sy
n
c
h
ro
n
o
u
s
re
fe
re
n
c
e
fra
m
e
fre
q
u
e
n
c
y
-
l
o
c
k
e
d
l
o
o
p
,
”
in
IE
E
E
T
ra
n
s
a
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
v
o
l.
6
8
,
n
o
.
5
,
p
p
.
4
5
4
7
-
4
5
5
3
,
M
a
y
2
0
2
1
,
d
o
i
:
1
0
.
1
1
0
9
/T
I
E.
2
0
2
0
.
2
9
8
5
0
0
2
.
[1
9
]
A.
M
.
Dia
b
e
t
a
l.
,
“
F
a
st
a
n
d
si
m
p
le
tu
n
i
n
g
r
u
les
o
f
sy
n
c
h
r
o
n
o
u
s
re
fe
re
n
c
e
fra
m
e
p
r
o
p
o
rti
o
n
a
l
-
in
teg
ra
l
c
u
rre
n
t
c
o
n
tro
ll
e
r,
”
in
IEE
E
Acc
e
ss
,
v
o
l.
9
,
p
p
.
2
2
1
5
6
-
2
2
1
7
0
,
2
0
2
1
,
d
o
i:
1
0
.
1
1
0
9
/ACCE
S
S
.
2
0
2
1
.
3
0
5
4
8
4
5
.
[2
0
]
F
.
M
.
G
o
n
z
á
lez
-
Lo
n
g
a
tt
,
“
M
o
d
e
l
o
f
p
h
o
t
o
v
o
lt
a
ic
m
o
d
u
le
in
M
ATLAB
,
”
in
2
d
o
c
o
n
g
re
so
i
b
e
ro
a
me
ric
a
n
o
d
e
e
stu
d
ia
n
tes
d
e
i
n
g
e
n
ier
ıa
c
u
te elé
c
t
ric
a
,
e
lec
tró
n
ica
y
c
o
mp
u
ta
c
i
ó
n
(
ii
c
ib
e
lec
2
0
0
5
)
,
2
0
0
5
,
p
p
.
1
-
5.
[2
1
]
S
.
Bh
a
tt
a
c
h
a
ry
y
a
,
D.
S
.
K
u
m
a
r
P
,
S
.
S
a
m
a
n
ta
,
a
n
d
S
.
M
ish
ra
,
“
S
tea
d
y
o
u
t
p
u
t
a
n
d
fa
st
trac
k
i
n
g
M
P
P
T
(S
O
F
T
-
M
P
P
T)
fo
r
P
&
O
a
n
d
In
C
a
lg
o
r
it
h
m
s,
”
in
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
S
u
sta
in
a
b
le
En
e
rg
y
,
v
o
l.
1
2
,
n
o
.
1
,
p
p
.
2
9
3
-
3
0
2
,
Ja
n
.
2
0
2
1
,
d
o
i:
1
0
.
1
1
0
9
/T
S
TE
.
2
0
2
0
.
2
9
9
1
7
6
8
.
[2
2
]
S
.
S
e
lv
a
k
u
m
a
r,
M
.
M
a
d
h
u
sm
it
a
,
C.
Ko
o
d
a
lsa
m
y
,
S
.
P
.
S
imo
n
,
a
n
d
Y.
R.
S
o
o
d
,
“
Hig
h
-
s
p
e
e
d
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
trac
k
in
g
m
o
d
u
le
fo
r
P
V
s
y
ste
m
s,
”
in
IEE
E
T
r
a
n
s
a
c
ti
o
n
s
o
n
In
d
u
s
tria
l
El
e
c
tro
n
ics
,
v
o
l.
6
6
,
n
o
.
2
,
p
p
.
1
1
1
9
-
1
1
2
9
,
F
e
b
.
2
0
1
9
,
d
o
i:
1
0
.
1
1
0
9
/
TIE
.
2
0
1
8
.
2
8
3
3
0
3
6
.
[2
3
]
B.
S
iri
sh
a
,
P
.
S
a
ti
sh
k
u
m
a
r
,
“
A
sim
p
li
fied
sp
a
c
e
v
e
c
to
r
P
WM
fo
r
c
a
sc
a
d
e
d
H
-
b
rid
g
e
in
v
e
rter
in
c
lu
d
in
g
o
v
e
r
m
o
d
u
lati
o
n
o
p
e
ra
ti
o
n
,
”
1
3
t
h
In
ter
n
a
ti
o
n
a
l
IEE
E
I
n
d
ia
Co
n
fer
e
n
c
e
I
NDICO
N
2
0
1
6
,
a
t
IIS
C,
Be
n
g
a
l
u
ru
,
I
n
d
ia
,
De
c
.
16
-
1
8
,
2
0
1
6
,
d
o
i:
1
0
.
1
1
0
9
/INDIC
ON
.
2
0
1
6
.
7
8
3
9
0
3
8
.
[2
4
]
B.
S
iri
sh
a
,
P
.
S
a
ti
s
h
k
u
m
a
r
,
“
S
i
m
p
li
fied
sp
a
c
e
v
e
c
to
r
p
u
lse
wi
d
t
h
m
o
d
u
latio
n
b
a
se
d
o
n
sw
it
c
h
in
g
sc
h
e
m
e
s
with
re
d
u
c
e
d
sw
it
c
h
in
g
fre
q
u
e
n
c
y
a
n
d
h
a
rm
o
n
ics
fo
r
fi
v
e
le
v
e
l
c
a
sc
a
d
e
d
H
-
b
ri
d
g
e
in
v
e
rter
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l
.
8
,
no
.
5
,
p
p
.
3
4
1
7
-
3
4
2
6
,
2
0
1
7
,
d
o
i:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
8
i
5
.
p
p
3
4
1
7
-
3
4
2
6
.
[2
5
]
B.
S
iri
sh
a
a
n
d
P
.
S
.
Ku
m
a
r,
“
S
VP
WM
b
a
se
d
g
e
n
e
ra
li
z
e
d
sw
it
c
h
i
n
g
sc
h
e
m
e
s
fo
r
se
v
e
n
lev
e
l
DCM
LI
in
c
lu
d
in
g
o
v
e
r
m
o
d
u
lati
o
n
o
p
e
ra
ti
o
n
-
F
P
G
A
i
m
p
lem
e
n
tatio
n
,
”
T
ENCON
2
0
1
9
-
2
0
1
9
IEE
E
Reg
i
o
n
1
0
Co
n
fer
e
n
c
e
(T
ENCON)
,
2
0
1
9
,
p
p
.
2
1
35
-
2
1
4
2
,
d
o
i:
1
0
.
1
1
0
9
/T
ENCON
.
2
0
1
9
.
8
9
2
9
3
8
0
.
B
I
O
G
RAP
H
Y
O
F
AUTHO
R
Bo
g
i
m
i
S
irisha
S
h
e
h
o
l
d
s
a
B
.
E.
in
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
fr
o
m
Os
m
a
n
ia
Un
iv
e
rsity
,
M
.
Tec
h
P
o
we
r
Eele
c
tro
n
ics
fro
m
JN
TUH
in
2
0
0
3
,
a
n
d
a
P
h
.
D.
d
e
g
re
e
fro
m
Os
m
a
n
ia
Un
iv
e
rsity
2
0
1
8
.
S
h
e
h
a
s
o
v
e
r
1
6
y
e
a
rs
o
f
e
x
p
e
rie
n
c
e
in
re
se
a
rc
h
a
n
d
tea
c
h
in
g
a
n
d
is
c
u
rre
n
tl
y
e
m
p
lo
y
e
d
a
s
a
n
As
so
c
iate
P
ro
fe
ss
o
r
in
El
e
c
tri
c
a
l
De
p
a
rtme
n
t,
En
g
in
e
e
rin
g
C
o
ll
e
g
e
,
Os
m
a
n
ia
Un
i
v
e
rsity
,
Hy
d
e
ra
b
a
d
,
I
n
d
ia
.
S
h
e
h
a
s
p
u
b
li
sh
e
d
v
a
rio
u
s
a
rti
c
les
in
in
tern
a
ti
o
n
a
l
a
n
d
n
a
ti
o
n
a
l
j
o
u
r
n
a
l
p
u
b
li
c
a
ti
o
n
s
a
n
d
c
o
n
fe
re
n
c
e
s.
M
u
lt
il
e
v
e
l
I
n
v
e
rters
,
p
o
we
r
e
lec
tro
n
ics
a
n
d
d
ri
v
e
s,
re
n
e
wa
b
le
e
n
e
rg
y
a
p
p
l
ica
ti
o
n
s
a
n
d
sp
e
c
ial
e
lec
tri
c
a
l
m
a
c
h
in
e
s
a
re
a
m
o
n
g
h
e
r
re
se
a
rc
h
in
te
re
sts.
Os
m
a
n
ia
Un
iv
e
rsity
a
wa
rd
e
d
h
e
r
a
P
h
.
D.
in
th
e
field
o
f
m
u
lt
il
e
v
e
l
in
v
e
rters
.
Evaluation Warning : The document was created with Spire.PDF for Python.