I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
w
er
E
lect
ro
nics
a
nd
Driv
e
Sy
s
t
e
m
(
I
J
P
E
DS
)
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
201
8
,
p
p
.
1
3
1
1
~
1
3
2
0
I
SS
N:
2088
-
8
694
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v
9
.i
3
.
pp
1
3
1
1
-
1
3
2
0
1311
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e.
co
m/jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JP
E
DS
Co
m
pa
riso
n b
etw
een P
I
and P
R Cu
rrent Co
ntrollers
o
f
a
G
ri
d
-
Co
nnected
P
ho
to
v
o
ltaic Sy
ste
m
u
n
der Lo
a
d Varia
ti
o
n
So
u
k
a
ina
E
s
s
a
g
hir
,
M
o
ha
m
e
d B
encha
g
ra
,
No
ureddin
e
E
l
ba
rbri
Na
ti
o
n
a
l
S
c
h
o
o
l
o
f
A
p
p
li
e
d
S
c
ien
c
e
s,
IS
ERT
L
a
b
o
ra
to
r
y
,
ENS
A
-
Kh
o
u
r
ib
g
a
,
Ha
ss
a
n
1
st
Un
iv
e
rsity
,
M
o
r
o
c
c
o
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
28
,
2
0
1
7
R
ev
i
s
ed
A
p
r
13
,
2
0
1
8
A
cc
ep
ted
A
u
g
6
,
2
0
1
8
T
h
is
p
a
p
e
r
p
re
se
n
ts
a
c
u
rre
n
t
c
o
n
tro
l
tec
h
n
iq
u
e
f
o
r
a
th
re
e
-
p
h
a
se
g
rid
-
c
o
n
n
e
c
ted
DC/A
C
in
v
e
rter
w
h
ich
is
u
se
d
in
p
h
o
to
v
o
l
taic
sy
ste
m
s.
A
P
r
o
p
o
rti
o
n
a
l
-
Re
so
n
a
n
t
(
P
R)
c
o
n
tr
o
ll
e
r
is
u
se
d
f
o
r
re
p
lac
in
g
th
e
c
o
n
v
e
n
ti
o
n
a
l
P
r
o
p
o
rti
o
n
a
l
-
I
n
teg
ra
l
(P
I)
c
o
n
tr
o
l
ler
in
th
is
sy
ste
m
.
B
y
c
o
m
p
a
riso
n
w
it
h
th
e
c
o
n
v
e
n
ti
o
n
a
l
P
I
c
o
n
tr
o
l
m
e
th
o
d
,
t
h
e
P
R
c
o
n
tr
o
l
c
a
n
in
tr
o
d
u
c
e
a
n
in
f
in
it
e
g
a
in
a
t
th
e
f
u
n
d
a
m
e
n
tal
f
re
q
u
e
n
c
y
a
n
d
h
e
n
c
e
c
a
n
a
c
h
iev
e
z
e
ro
ste
a
d
y
-
sta
te
e
rro
r.
T
h
e
p
ro
p
o
se
d
m
o
d
e
l
is
b
a
se
d
o
n
tw
o
c
o
n
tro
l
l
o
o
p
s:
t
h
e
f
irst
c
o
n
tr
o
l
l
o
o
p
re
g
u
late
s
DC
li
n
k
v
o
lt
a
g
e
a
n
d
t
h
e
se
c
o
n
d
o
n
e
is
u
se
d
to
k
e
e
p
t
h
e
in
jec
ted
c
u
rre
n
t
to
th
e
g
rid
in
p
h
a
se
w
it
h
th
e
v
o
lt
a
g
e
b
y
m
e
a
n
s
o
f
a
P
h
a
s
e
L
o
c
k
e
d
L
o
o
p
(
P
L
L
)
in
o
rd
e
r
t
o
a
c
h
iev
e
a
u
n
it
p
o
w
e
r
fa
c
to
r
a
n
d
t
o
a
d
ju
st
th
e
o
u
t
p
u
t
p
o
w
e
r
a
s
re
q
u
ired
.
In
o
r
d
e
r
t
o
e
x
a
m
in
e
th
e
e
ff
e
c
ti
v
e
n
e
ss
o
f
th
e
su
g
g
e
ste
d
c
o
n
t
ro
l,
a
si
m
u
latio
n
u
si
n
g
th
e
M
a
tl
a
b
/S
im
u
li
n
k
so
f
t
w
a
re
h
a
s
b
e
e
n
d
o
n
e
a
n
d
it
’s
c
o
n
c
lu
d
e
d
f
ro
m
th
e
si
m
u
latio
n
re
su
lt
s
th
a
t
th
e
p
re
se
n
ted
c
o
n
tr
o
l
b
y
u
sin
g
th
e
P
R
c
o
n
tro
ll
e
r
c
a
n
b
e
a
b
le
to
m
a
in
tain
m
a
x
i
m
u
m
a
c
ti
v
e
p
o
we
r
a
n
d
t
o
k
e
e
p
a
lwa
y
s a
u
n
it
y
p
o
w
e
r
f
a
c
to
r
d
e
s
p
i
te v
a
riatio
n
lo
a
d
K
ey
w
o
r
d
:
Gr
id
P
L
L
P
r
o
p
o
r
tio
n
al
i
n
teg
r
al
P
r
o
p
o
r
tio
n
al
r
eso
n
an
t
P
V
s
y
s
te
m
Un
it
y
p
o
w
er
f
ac
to
r
Co
p
y
rig
h
t
©
201
8
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
So
u
k
a
in
a
E
S
S
A
GHI
R
,
Natio
n
al
Sc
h
o
o
l o
f
A
p
p
lied
Scien
ce
s
,
Ha
s
s
a
n
1
st
Un
i
v
er
s
it
y
,
C
1
,
A
l W
ah
d
a
h
o
u
s
in
g
estate
,
Kh
o
u
r
ib
g
a
-
Mo
r
o
cc
o
E
m
ail: e
s
s
a
g
h
ir
s
o
u
k
ain
a
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
I
n
th
e
p
r
esen
t
s
ce
n
ar
io
o
f
w
o
r
ld
en
er
g
y
s
ec
to
r
,
r
en
e
w
ab
le
s
o
u
r
ce
s
ar
e
g
r
o
w
i
n
g
th
eir
i
m
p
o
r
tan
ce
d
a
y
b
y
d
a
y
.
No
w
ad
a
y
s
,
m
o
r
e
an
d
m
o
r
e
i
n
ter
est
o
f
p
h
o
to
v
o
ltaic
(
P
V)
en
er
g
y
h
a
s
b
ee
n
f
o
cu
s
ed
o
n
in
ter
co
n
n
ec
tio
n
b
et
w
ee
n
t
h
e
P
V
p
o
w
er
s
y
s
te
m
s
an
d
th
e
g
r
id
.
T
h
e
co
n
n
ec
tio
n
o
f
t
h
e
p
h
o
to
v
o
ltaic
s
y
s
te
m
to
th
e
g
r
id
g
en
er
ate
s
a
p
h
ase
s
h
i
f
t
b
et
w
ee
n
th
e
v
o
l
tag
e
a
n
d
th
e
cu
r
r
en
t
i
n
j
ec
ted
in
to
g
r
id
,
an
d
m
o
r
eo
v
er
,
d
u
r
in
g
a
v
ar
ia
tio
n
lo
ad
,
f
l
u
ctu
a
tio
n
s
ap
p
ea
r
in
t
h
e
v
o
lt
ag
e
an
d
i
n
th
e
o
u
tp
u
t
p
o
w
er
a
n
d
th
e
s
t
u
d
ied
s
y
s
te
m
b
ec
o
m
e
s
u
n
s
tab
le.
Fo
r
th
i
s
r
ea
s
o
n
,
w
e
n
ee
d
a
p
o
w
er
f
a
cto
r
co
n
tr
o
l
w
h
ic
h
allo
w
s
t
h
e
ac
h
iev
e
m
e
n
t
o
f
u
n
it
y
p
o
w
er
f
ac
to
r
an
d
th
e
ad
j
u
s
t
m
e
n
t o
f
t
h
e
o
u
tp
u
t p
o
w
e
r
as r
eq
u
ir
ed
[
1
,
2
]
.
Gen
er
all
y
,
t
h
e
g
r
id
-
co
n
n
ec
ted
P
V
p
o
w
er
s
y
s
te
m
s
m
a
in
l
y
co
n
s
i
s
t
o
f
a
b
o
o
s
t
DC
/DC
co
n
v
e
r
ter
an
d
a
DC
/
A
C
i
n
v
er
ter
.
T
h
e
DC
/
A
C
in
v
er
ter
i
s
co
n
s
id
er
ed
as
t
h
e
c
o
r
e
o
f
th
e
w
h
o
le
s
y
s
te
m
b
ec
au
s
e
o
f
an
i
m
p
o
r
ta
n
t
r
o
le
in
g
r
id
-
co
n
n
ec
ted
o
p
er
atio
n
,
f
o
r
t
h
is
r
ea
s
o
n
t
h
e
c
u
r
r
en
t
co
n
tr
o
ller
ca
n
h
a
v
e
a
s
ig
n
i
f
ican
t
e
f
f
ec
t
o
n
th
e
q
u
alit
y
o
f
th
e
cu
r
r
e
n
t
s
u
p
p
lie
d
to
th
e
g
r
id
b
y
th
e
P
V
in
v
e
r
ter
,
t
h
er
ef
o
r
e,
it
is
i
m
p
o
r
tan
t
th
at
th
e
co
n
tr
o
ller
p
r
o
v
id
es
a
h
i
g
h
q
u
ali
t
y
s
i
n
u
s
o
id
al
o
u
tp
u
t
by
li
m
it
i
n
g
t
h
e
h
ar
m
o
n
ics
g
e
n
er
ated
b
y
th
e
s
e
i
n
v
er
ter
s
in
o
r
d
er
to
o
v
o
id
th
e
ad
v
er
s
e
ef
f
ec
ts
o
n
t
h
e
g
r
id
p
o
w
er
q
u
alit
y
.
T
w
o
co
n
tr
o
ller
s
w
h
ic
h
ar
e
u
s
ed
in
cu
r
r
en
t
co
n
tr
o
lled
P
V
in
v
er
ter
s
ar
e
th
e
co
v
en
tio
n
n
a
l
P
I
co
n
tr
o
ller
an
d
th
e
P
R
co
n
tr
o
ller
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
w
o
r
k
is
f
o
cu
s
ed
o
n
a
c
o
m
p
a
r
is
o
n
b
et
w
ee
n
P
I
an
d
P
R
cu
r
r
en
t
c
o
n
tr
o
ller
s
o
f
a
G
r
id
-
C
o
n
n
ec
ted
P
h
o
to
v
o
ltaic
S
y
s
te
m
U
n
d
er
L
o
ad
Var
iatio
n
[
3
]
.
T
h
e
r
est
o
f
th
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
.
Sectio
n
2
in
tr
o
d
u
ce
s
s
o
m
e
i
n
f
o
r
m
atio
n
s
o
n
th
e
s
tu
d
ied
s
y
s
te
m
.
Sectio
n
3
,
d
ev
elo
p
th
e
o
v
er
all
co
n
tr
o
l
s
ch
e
m
e
s
f
o
r
b
o
th
t
y
p
es
o
f
co
n
tr
o
ller
s
(
P
I
an
d
P
R
co
n
tr
o
ller
s
)
.
T
h
en
,
th
e
o
b
tain
e
d
r
esu
lts
u
s
i
n
g
Ma
tlab
/Si
m
u
li
n
k
ar
e
p
r
esen
ted
in
s
ec
t
io
n
4
.
Fin
all
y
,
co
n
cl
u
s
io
n
is
g
i
v
i
n
g
i
n
s
ec
t
io
n
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
3
1
1
–
1
3
2
0
1312
2.
DE
SCR
I
P
T
I
O
N
O
F
T
H
E
S
T
UDI
E
D
S
YST
E
M
I
n
t
h
is
p
ap
er
,
th
e
d
esi
g
n
o
f
a
t
h
r
ee
-
p
h
a
s
e
g
r
id
co
n
n
ec
ted
P
V
in
v
er
ter
is
p
r
esen
ted
.
T
h
e
P
V
ar
r
ay
u
s
ed
co
n
s
is
ts
o
f
6
6
s
tr
i
n
g
s
o
f
5
s
er
ies
-
co
n
n
ec
ted
m
o
d
u
les
co
n
n
e
cted
in
p
ar
alle
l.
A
DC
-
D
C
B
o
o
s
t
co
n
v
er
ter
an
d
a
th
r
ee
-
le
v
el
v
o
lta
g
e
i
n
v
er
ter
ar
e
u
s
ed
to
p
r
o
v
id
e
t
h
e
f
le
x
ib
ili
t
y
o
f
th
e
s
y
s
te
m
a
n
d
t
h
e
q
u
al
i
t
y
o
f
th
e
g
e
n
er
ated
w
a
v
es.
T
h
e
co
n
n
ec
tio
n
b
et
w
e
en
th
e
g
e
n
er
ato
r
an
d
th
e
DC
b
u
s
o
f
th
e
i
n
v
er
ter
r
eq
u
ir
e
an
in
ter
f
ac
e
to
ad
ap
t
th
e
lev
els
o
f
v
ar
iatio
n
o
f
th
e
v
o
lta
g
e
an
d
th
e
c
u
r
r
en
t
b
et
w
ee
n
th
ese
t
w
o
d
ev
ice
s
.
C
o
n
tr
o
llin
g
t
h
e
g
e
n
er
ated
p
o
w
er
r
eq
u
ir
es
v
ar
y
in
g
t
h
e
a
m
p
lit
u
d
e
o
f
th
e
v
o
lta
g
e
at
t
h
e
en
d
s
o
f
th
e
g
en
er
ato
r
,
w
it
h
o
u
t
c
h
an
g
i
n
g
t
h
e
v
o
lta
g
e
at
t
h
e
DC
b
u
s
.
T
h
e
th
r
ee
-
le
v
el
Vo
lt
ag
e
So
u
r
ce
I
n
v
er
ter
(
VSI
)
r
eg
u
la
tes
D
C
b
u
s
v
o
ltag
e
a
n
d
k
ee
p
s
u
n
it
y
p
o
w
er
f
ac
to
r
u
n
d
er
v
ar
iatio
n
lo
ad
.
I
n
f
ac
t,
t
h
e
co
n
tr
o
l
s
y
s
te
m
u
s
e
s
t
w
o
co
n
tr
o
l
lo
o
p
s
,
an
e
x
ter
n
a
l
co
n
tr
o
l
lo
o
p
w
h
ic
h
r
eg
u
late
s
DC
li
n
k
v
o
lta
g
e
an
d
an
in
ter
n
al
lo
o
p
w
h
ic
h
r
eg
u
l
ates
ac
tiv
e
an
d
r
ea
ctiv
e
cu
r
r
e
n
ts
co
m
p
o
n
e
n
t
s
(
I
d
an
d
I
q
).
T
h
e
o
u
tp
u
t v
o
lt
ag
e
o
f
th
e
co
n
v
er
ter
a
n
d
th
e
i
n
v
er
ter
is
co
n
tr
o
lled
b
y
t
h
e
P
W
M
m
o
d
u
lato
r
[4
-
10
].
T
h
e
p
r
in
cip
a
l sp
ec
if
icatio
n
s
f
o
r
th
is
s
y
s
te
m
ar
e
g
iv
e
n
i
n
T
ab
l
e
1
.
3.
ACT
I
VE
AN
D
RE
A
CT
I
VE
P
O
WE
R
CO
NT
RO
L
3
.
1
.
P
V
P
o
w
er
Ca
lcula
t
io
n
T
h
e
co
n
ce
p
t
o
f
th
is
t
y
p
e
o
f
c
o
n
tr
o
l
is
to
i
m
p
o
s
e
t
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
v
a
lu
e
s
in
j
ec
ted
in
to
g
r
id
i
n
o
r
d
er
to
k
ee
p
u
n
it
y
p
o
w
er
f
ac
to
r
.
B
y
ac
ti
n
g
o
n
t
h
e
P
W
M
co
n
tr
o
l,
th
e
co
n
tr
o
l
lo
o
p
s
,
m
u
s
t
i
m
p
o
s
e
t
h
e
in
s
ta
n
ta
n
eo
u
s
v
al
u
es
o
f
th
e
c
u
r
r
en
ts
d
eli
v
er
ed
b
y
t
h
e
in
v
e
r
ter
(
i
o1
,
i
o
2
,
i
o
3
)
i
n
s
u
c
h
a
w
a
y
th
at
t
h
e
c
u
r
r
en
t
s
s
u
p
p
lied
b
y
th
e
g
r
id
(
i
a
,
i
b
,
i
c
)
b
ec
o
m
e
s
i
n
u
s
o
id
al
an
d
i
n
p
h
ase
w
it
h
th
e
co
r
r
esp
o
n
d
i
n
g
s
i
n
g
le
v
o
lta
g
es
(V
a
,
V
b
,
V
c
)
[
1
1
]
.
W
e
d
escr
ib
e
th
e
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
o
f
t
h
e
t
h
r
ee
-
p
h
a
s
e
g
r
id
-
co
n
n
ec
t
ed
V
SI
in
t
h
e
P
ar
k
r
ef
er
en
ce
(
d
,
q
)
,
w
e
o
b
tain
t
h
e
f
o
llo
w
in
g
eq
u
at
io
n
s
:
3
(
.
.
)
2
d
d
q
q
P
V
i
V
i
(
1
)
3
(
.
.
)
2
d
q
q
d
Q
V
i
V
i
(2
)
W
e
s
u
p
p
o
s
e
th
at
th
e
th
r
ee
-
p
h
a
s
e
g
r
id
v
o
ltag
e
i
s
id
ea
ll
y
s
i
n
u
s
o
id
al
th
en
,
th
e
g
r
id
v
o
lta
g
e
v
e
cto
r
in
th
e
d
,
q
f
r
am
e
i
s
g
i
v
e
n
b
y
th
e
f
o
ll
o
w
i
n
g
eq
u
atio
n
s
:
d
VV
(3
)
0
q
V
(
4
)
C
o
n
s
eq
u
en
tl
y
,
eq
u
at
io
n
s
(
1
)
an
d
(
2
)
ca
n
b
e
r
ew
r
itte
n
as (
5
)
an
d
(
6
)
:
3
(
.
)
2
dd
P
V
i
(5
)
3
(
.
)
2
dq
Q
V
i
(
6
)
W
e
n
o
te
f
r
o
m
t
h
e
last
eq
u
atio
n
t
h
at
th
e
ac
ti
v
e
p
o
w
er
d
ep
en
d
s
o
n
t
h
e
d
-
a
x
is
cu
r
r
en
t,
an
d
t
h
e
r
ea
cti
v
e
p
o
w
er
d
ep
en
d
s
o
n
t
h
e
q
-
ax
i
s
cu
r
r
en
t.
F
u
r
t
h
er
m
o
r
e,
to
ac
h
i
ev
e
u
n
it
y
p
o
w
er
f
ac
to
r
,
th
e
q
co
m
p
o
n
en
t
o
f
t
h
e
co
m
m
a
n
d
cu
r
r
en
t
v
ec
to
r
is
s
h
o
u
ld
b
e
s
et
to
ze
r
o
.
T
h
e
r
elatio
n
s
h
ip
b
et
w
ee
n
t
h
e
in
s
ta
n
ta
n
eo
u
s
ac
ti
v
e
p
o
w
er
ex
ch
a
n
g
ed
b
et
w
ee
n
t
h
e
P
V
ar
r
ay
a
n
d
t
h
e
g
r
id
i
n
th
e
e
v
e
n
t
o
f
a
lo
s
s
le
s
s
p
o
w
er
tr
an
s
m
i
s
s
i
o
n
b
et
w
ee
n
t
h
e
t
w
o
is
g
i
v
e
n
b
y
(
7
)
:
3
(
.
)
2
p
v
d
d
P
P
V
i
(7
)
3
.
2
.
DC
bu
s
v
o
lt
a
g
e
re
g
ula
t
i
o
n
T
h
e
r
eg
u
latio
n
o
f
D
C
b
u
s
v
o
ltag
e
is
e
f
f
ec
ted
b
y
ab
s
o
r
b
in
g
o
r
s
u
p
p
l
y
in
g
t
h
e
ac
tiv
e
p
o
w
er
to
th
e
elec
tr
ical
g
r
id
.
I
n
th
e
D
C
v
o
lt
ag
e
lo
o
p
,
w
e
r
e
g
u
late
th
e
Vd
c
v
o
ltag
e
to
a
co
n
s
ta
n
t
v
alu
e
wh
ich
i
s
Vd
c_
r
ef
,
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
C
o
mp
a
r
is
o
n
b
etw
ee
n
P
I
a
n
d
P
R
C
u
r
r
en
t Co
n
tr
o
ller
s
o
f a
Gri
d
-
C
o
n
n
ec
ted
…
(
S
o
u
k
a
in
a
E
s
s
a
g
h
ir
)
1313
er
r
o
r
is
d
ef
in
ed
a
s
th
e
d
if
f
er
e
n
ce
b
etw
ee
n
th
e
m
ea
s
u
r
ed
v
o
ltag
e
Vd
c
an
d
th
e
r
ef
er
en
ce
v
o
ltag
e
Vd
c_
r
ef
,
(
=
−
Vdc
_
r
e
f
)
[1
2
,
1
3
]
.
I
n
th
e
ca
s
e
w
h
er
e
a
P
I
co
r
r
ec
to
r
is
u
s
ed
,
th
e
o
u
tp
u
t
o
f
t
h
is
co
r
r
ec
to
r
is
th
e
r
ef
er
e
n
ce
o
f
th
e
d
ir
ec
t c
o
m
p
o
n
e
n
t o
f
t
h
e
cu
r
r
en
t i
n
j
ec
ted
in
to
g
r
id
I
d
_
r
ef
as s
h
o
w
in
f
ig
u
r
e
1
.
Fig
u
r
e
1
.
DC
b
u
s
v
o
ltag
e
co
n
t
r
o
l lo
o
p
T
h
e
clo
s
ed
-
lo
o
p
tr
an
s
f
er
f
u
n
ctio
n
o
f
d
c
v
o
l
ta
g
e
r
eg
u
lat
io
n
,
o
b
tain
ed
f
r
o
m
f
ig
u
r
e
1
,
h
as
th
e
f
o
llo
w
in
g
f
o
r
m
:
2
_
1
1
p
d
c
i
p
d
c
re
f
ii
K
p
VK
K
c
V
pp
KK
(8
)
T
h
e
d
am
p
in
g
r
atio
2
p
ni
K
K
an
d
2
1
ni
c
K
.
T
h
u
s
,
th
e
p
ar
a
m
eter
s
o
f
t
h
e
v
o
lta
g
e
r
eg
u
lato
r
ca
n
b
e
d
esig
n
ed
as
f
o
llo
w
s
:
2
.
2
.
.
n
n
K
i
c
K
p
c
3
.
3
.
Sy
nchro
nis
a
t
i
o
n o
f
t
he
P
V
pa
nn
el
w
it
h g
rid
T
h
e
s
y
n
c
h
r
o
n
izatio
n
co
n
tr
o
l
o
v
er
th
e
ev
o
l
u
tio
n
o
f
t
h
e
n
et
wo
r
k
v
o
ltag
es
i
s
b
ased
o
n
th
e
th
r
ee
-
P
h
a
s
e
L
o
ck
ed
L
o
o
p
.
I
t c
o
n
s
is
ts
to
ap
p
ly
a
n
i
n
v
er
s
e
P
ar
k
tr
an
s
f
o
r
m
a
tio
n
o
n
t
h
e
p
h
ase
v
o
ltag
e
s
o
f
t
h
e
g
r
id
.
T
h
e
q
-
ax
i
s
co
m
p
o
n
e
n
t
g
e
n
er
ated
b
y
t
h
i
s
t
r
an
s
f
o
r
m
atio
n
is
lo
ck
ed
to
ze
r
o
b
y
ac
tin
g
o
n
t
h
e
a
n
g
le
o
f
t
h
e
P
ar
k
r
ef
er
en
ce
i
n
o
r
d
er
t
o
g
en
er
ate
th
e
s
y
n
ch
r
o
n
izatio
n
an
g
le
θ.
W
h
en
t
h
e
d
if
f
er
en
ce
b
et
w
ee
n
g
r
id
p
h
ase
an
g
le
θr
an
d
th
e
i
n
v
er
ter
p
h
ase
an
g
le
θ
is
r
ed
u
ce
d
to
ze
r
o
(
∆θ
=
(
θr
-
θ
)
=
0
)
,
th
e
P
L
L
b
ec
am
e
ac
ti
v
e
[
1
4
,
1
5
]
.
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
a
m
o
f
P
L
L
3
.
4
.
Curre
nt
co
ntr
o
l
3
.
4
.
1
.
P
I
Co
ntr
o
ller
Desig
n
T
o
c
o
n
n
ec
t
t
h
e
v
o
lta
g
e
i
n
v
er
t
er
in
p
ar
allel
w
it
h
th
e
g
r
id
an
d
m
a
k
e
it
w
o
r
k
s
a
s
a
p
o
w
er
s
o
u
r
ce
,
w
e
co
n
s
id
er
an
in
v
er
ter
co
n
n
ec
te
d
to
g
r
id
,
v
ia
r
e
s
is
to
r
R
an
d
in
d
u
c
tan
ce
L
[1
6
]
.
T
h
e
eq
u
i
v
alen
t
t
h
r
ee
-
p
h
ase
s
y
s
te
m
i
n
ter
m
s
o
f
f
u
n
d
a
m
en
t
al
co
m
p
o
n
e
n
t i
s
s
h
o
w
n
i
n
Fi
g
u
r
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
3
1
1
–
1
3
2
0
1314
Fig
u
r
e
3
.
Diag
r
a
m
o
f
an
i
n
v
er
t
er
co
n
n
ec
ted
to
g
r
id
Usi
n
g
P
ar
k
tr
an
s
f
o
r
m
atio
n
,
t
h
e
co
m
p
o
n
e
n
t
s
o
f
th
e
ac
t
iv
e
a
n
d
r
ea
ctiv
e
cu
r
r
en
t a
r
e
g
i
v
e
n
b
y
(
9
)
:
1
d
d
d
d
q
q
q
q
R
i
i
V
e
d
L
i
i
V
e
R
d
t
L
L
(
9
)
Fu
r
t
h
er
m
o
r
e,
b
y
u
s
i
n
g
P
I
-
t
y
p
e
r
eg
u
lato
r
s
,
a
f
ast
-
d
y
n
a
m
ic
r
esp
o
n
s
e
an
d
ze
r
o
s
tead
y
-
s
ta
te
er
r
o
r
s
ca
n
b
e
ac
h
iev
ed
.
T
h
e
tw
o
n
e
w
v
ar
iab
les
p
r
esen
ted
in
(
10
)
p
r
ese
n
t
ar
e
th
e
o
u
tp
u
ts
o
f
t
h
e
co
n
tr
o
l
s
y
s
te
m
co
n
s
i
s
ti
n
g
o
f
t
w
o
P
I
co
n
tr
o
ller
s
:
12
11
(
)
&
(
)
d
d
q
q
X
V
e
X
V
e
LL
(
10
)
T
h
e
v
alu
es o
f
i
dref
an
d
i
qref
ar
e
th
e
r
ef
er
e
n
ce
s
o
f
t
h
e
ac
ti
v
e
an
d
r
ea
ctiv
e
cu
r
r
en
ts
:
1
(
)
(
)
i
dre
f
d
p
q
K
X
i
i
K
i
p
(
11
)
2
(
)
(
)
i
qre
f
q
p
d
K
X
i
i
K
i
p
(1
2
)
W
e
ap
p
ly
t
h
e
L
ap
lace
tr
an
s
f
o
r
m
at
io
n
to
(
9
)
,
(
10
)
,
(
11
)
,
(
12
)
.
W
e
o
b
tain
th
e
clo
s
ed
-
lo
o
p
tr
an
s
f
er
f
u
n
ctio
n
o
f
cu
r
r
e
n
t lo
o
p
s
as sh
o
w
n
in
(
1
3
)
:
2
1
()
1
p
q
di
d
r
e
f
q
r
e
f
p
ii
K
p
i
iK
Fp
R
ii
K
p
L
p
KK
(1
3
)
T
h
e
d
am
p
i
n
g
r
atio
2
p
ni
R
K
L
K
an
d
2
11
ni
K
T
h
u
s
,
th
e
p
ar
a
m
eter
s
o
f
th
e
c
u
r
r
en
t
r
eg
u
lato
r
ca
n
b
e
d
esig
n
ed
as f
o
llo
w
s
[
1
7
]:
2
2
Ki
n
R
Kp
n
L
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
C
o
mp
a
r
is
o
n
b
etw
ee
n
P
I
a
n
d
P
R
C
u
r
r
en
t Co
n
tr
o
ller
s
o
f a
Gri
d
-
C
o
n
n
ec
ted
…
(
S
o
u
k
a
in
a
E
s
s
a
g
h
ir
)
1315
3
.
4
.
2
.
P
R
Co
ntr
o
ller
Desig
n
T
h
e
P
R
cu
r
r
en
t c
o
n
tr
o
ller
G
PR
(
s
)
is
r
ep
r
esen
ted
b
y
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
22
0
P
R
P
I
s
G
K
K
s
(1
4
)
W
h
er
e,
K
I
i
s
t
h
e
i
n
te
g
r
al
g
ai
n
ter
m
,
ω
0
is
th
e
r
eso
n
an
t f
r
eq
u
e
n
c
y
[
1
8
,
1
9
]
an
d
K
P
is
th
e
p
r
o
p
o
r
tio
n
al
g
ai
n
ter
m
,
it
d
eter
m
in
e
s
th
e
d
y
n
a
m
ic
s
o
f
th
e
s
y
s
te
m
; b
an
d
w
id
t
h
,
p
h
ase
an
d
g
ai
n
m
ar
g
i
n
s
.
T
h
e
id
ea
l r
eso
n
an
t te
r
m
o
n
it
s
o
w
n
in
t
h
e
P
R
co
n
tr
o
ller
p
r
o
v
id
es a
n
in
f
i
n
ite
g
ain
at
t
h
e
ac
f
r
eq
u
en
c
y
ω
0
a
n
d
n
o
p
h
ase
s
h
i
f
t
an
d
g
ain
at
t
h
e
o
th
er
f
r
eq
u
e
n
cies
as p
r
ese
n
ted
in
[
2
0
].
Un
f
o
r
tu
n
atel
y
,
t
h
e
id
ea
l
P
R
co
n
tr
o
ller
ac
ts
lik
e
a
n
et
w
o
r
k
w
it
h
a
n
in
f
i
n
ite
q
u
ali
t
y
f
ac
to
r
,
w
h
ich
i
s
h
ar
d
to
i
m
p
le
m
e
n
t
t
h
e
P
R
co
n
tr
o
ller
in
r
ea
l
it
y
.
Fir
s
tl
y
,
t
h
e
i
n
f
in
i
te
g
ai
n
i
n
tr
o
d
u
ce
d
b
y
P
R
co
n
tr
o
ller
lead
s
to
an
in
f
i
n
ite
q
u
a
lit
y
f
ac
to
r
w
h
ic
h
ca
n
n
o
t b
e
ac
h
iev
ed
i
n
eit
h
er
an
alo
g
o
r
d
ig
ital s
y
s
te
m
.
Seco
n
d
l
y
,
th
e
g
ai
n
o
f
P
R
co
n
tr
o
ller
is
m
u
c
h
r
ed
u
ce
d
at
o
th
er
f
r
eq
u
en
cies
a
n
d
it
is
n
o
ad
eq
u
ate
to
e
li
m
i
n
ate
h
ar
m
o
n
ic
in
f
l
u
en
c
e
ca
u
s
ed
b
y
g
r
id
v
o
lta
g
e.
Fo
r
th
e
s
e
r
ea
s
o
n
,
i
n
o
u
r
s
t
u
d
y
w
e
ch
o
s
e
a
n
ap
p
r
o
x
im
a
tin
g
id
ea
l (
n
o
n
-
id
ea
l)
P
R
co
n
tr
o
ller
w
h
ich
is
g
i
v
e
n
b
y
(
8
)
,
u
s
i
n
g
a
h
i
g
h
-
g
ai
n
lo
w
-
p
ass
f
i
lter
to
s
o
lv
e
th
e
p
r
o
b
lem
s
m
e
n
tio
n
ed
ab
o
v
e.
E
q
u
atio
n
(
1
2
)
r
e
p
r
e
s
en
ts
an
id
ea
l
P
R
c
o
n
tr
o
ller
w
h
ic
h
ca
n
g
iv
e
s
tab
ilit
y
p
r
o
b
lem
s
b
ec
au
s
e
o
f
th
e
in
f
in
ite
g
ai
n
.
T
o
av
o
id
th
ese
p
r
o
b
lem
s
,
t
h
e
P
R
co
n
tr
o
ller
ca
n
b
e
m
ad
e
n
o
n
-
id
ea
l
b
y
in
tr
o
d
u
cin
g
d
a
m
p
in
g
a
s
s
h
o
w
n
in
(
1
3
)
b
elo
w
:
22
0
2.
2.
P
R
P
I
c
s
G
K
K
ss
(1
5
)
W
h
er
e,
ω
c
is
th
e
b
an
d
w
id
th
ar
o
u
n
d
th
e
ac
f
r
eq
u
e
n
c
y
o
f
ω
0
.
W
ith
(
1
3
)
th
e
g
ain
o
f
th
e
P
R
co
n
tr
o
ller
at
th
e
ac
f
r
eq
u
en
c
y
ω
0
i
s
n
o
w
f
i
n
ite
b
u
t
it
i
s
s
t
ill
lar
g
e
en
o
u
g
h
to
p
r
o
v
id
e
o
n
l
y
a
v
er
y
s
m
al
l
s
tead
y
s
tate
er
r
o
r
.
T
h
is
eq
u
atio
n
also
m
a
k
es
t
h
e
co
n
tr
o
ller
m
o
r
e
ea
s
il
y
r
ea
liza
b
le
in
d
i
g
ital
s
y
s
te
m
s
d
u
e
to
t
h
eir
f
in
ite
p
r
ec
is
io
n
[
21
-
2
3
].
T
h
e
f
r
eq
u
en
c
y
r
esp
o
n
s
e
o
f
(
1
2
)
is
s
h
o
w
n
in
Fi
g
.
4
(
a
)
,
u
n
f
o
r
tu
n
a
tel
y
,
t
h
e
id
ea
l
P
R
co
n
tr
o
ll
er
ac
ts
lik
e
a
n
et
w
o
r
k
w
ith
a
n
in
f
i
n
ite
q
u
a
lit
y
f
ac
to
r
,
w
h
ic
h
is
h
ar
d
to
i
m
p
le
m
e
n
t
t
h
e
P
R
co
n
tr
o
l
ler
i
n
r
ea
lit
y
.
First
l
y
,
th
e
in
f
in
ite
g
a
in
in
tr
o
d
u
ce
d
b
y
P
R
co
n
tr
o
ller
lead
s
to
an
i
n
f
i
n
ite
q
u
alit
y
f
ac
to
r
w
h
ic
h
ca
n
n
o
t
b
e
ac
h
ie
v
ed
in
ei
th
er
an
alo
g
o
r
d
ig
ital
s
y
s
te
m
.
Seco
n
d
l
y
,
th
e
g
a
in
o
f
P
R
co
n
tr
o
ller
is
m
u
c
h
r
ed
u
ce
d
a
t
o
th
er
f
r
eq
u
en
cie
s
a
n
d
it
i
s
n
o
ad
eq
u
ate
to
eli
m
in
ate
h
ar
m
o
n
i
c
in
f
l
u
en
ce
ca
u
s
ed
b
y
g
r
id
v
o
l
tag
e.
T
h
e
f
r
eq
u
e
n
c
y
r
esp
o
n
s
e
o
f
(
1
3
)
is
s
h
o
w
n
i
n
Fig
u
r
e
4
(
b
)
,
w
h
er
e
t
h
e
r
eso
n
an
t
p
ea
k
n
o
w
h
as
a
f
i
n
ite
g
ain
o
f
4
0
d
B
w
h
ich
is
s
ati
s
f
ac
to
r
il
y
h
i
g
h
f
o
r
eli
m
i
n
a
ti
n
g
th
e
v
o
ltag
e
tr
ac
k
i
n
g
er
r
o
r
[
2
4
]
.
Fig
u
r
e
4
.
a.
Fre
q
u
en
c
y
r
esp
o
n
s
es o
f
an
id
ea
l P
R
co
n
tr
o
ller
w
i
th
Kp
=1
,
Ki
=1
0
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
3
1
1
–
1
3
2
0
1316
Fig
u
r
e
4
.
b
.
Fre
q
u
en
c
y
r
esp
o
n
s
es o
f
a
n
o
n
-
id
ea
l P
R
co
n
tr
o
ller
w
it
h
Kp
=1
,
Ki=1
0
0
,
ω
c
=1
0
(
r
ad
/s
)
.
4.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
h
e
o
b
tain
ed
r
esu
lt
s
u
s
i
n
g
M
atlab
/Si
m
u
li
n
k
ar
e
d
is
c
u
s
s
ed
in
t
h
i
s
s
ec
t
io
n
,
F
ig
u
r
e
5
s
h
o
w
s
t
h
e
f
u
ll
d
etailed
m
o
d
el
w
h
ich
co
n
tai
n
s
a
P
V
ar
r
ay
d
eliv
er
i
n
g
to
th
e
g
r
id
a
m
ax
i
m
u
m
p
o
w
er
o
f
1
0
0
k
W
at
1
0
0
0
W
/m
2
s
u
n
ir
r
ad
ian
ce
.
T
h
e
d
etailed
m
o
d
el
co
n
tain
:
a.
P
V
ar
r
ay
d
eliv
er
i
n
g
a
m
ax
i
m
u
m
p
o
w
er
o
f
1
0
0
k
W
at
1
0
0
0
W
/
m
2
s
u
n
ir
r
ad
ian
ce
.
b.
B
o
o
s
t c
o
n
v
er
ter
in
cr
ea
s
es
v
o
lt
ag
e
f
r
o
m
P
V
v
o
lta
g
e
(
2
7
3
.
5
V
DC
at
m
a
x
i
m
u
m
p
o
w
er
)
to
5
0
0
VDC
c.
S
w
itc
h
in
g
d
u
t
y
c
y
cle
o
f
t
h
e
b
o
o
s
t
co
n
v
er
ter
is
o
p
ti
m
ized
b
y
th
e
MP
PT
co
n
tr
o
ller
th
at
u
s
e
s
t
h
e
P
&
O
tech
n
iq
u
e.
d.
1
9
8
0
Hz
th
r
ee
-
lev
e
l
t
h
r
ee
-
p
h
ase
VSI
.
T
h
e
VSI
co
n
v
er
ts
t
h
e
5
0
0
VDC
l
in
k
v
o
ltag
e
to
2
6
0
VA
C
a
n
d
k
ee
p
s
u
n
it
y
p
o
w
er
f
ac
to
r
.
e.
C
u
r
r
en
t r
eg
u
lato
r
w
h
ic
h
p
r
o
v
id
e
a
u
n
it
y
p
o
w
er
f
ac
to
r
u
s
i
n
g
t
h
e
P
I
an
d
P
R
r
eg
u
lato
r
s
.
f.
1
0
0
k
VA
,
2
6
0
V/2
5
k
V
th
r
ee
-
p
h
ase
co
u
p
lin
g
tr
an
s
f
o
r
m
er
.
g.
Gr
id
s
p
ec
if
icatio
n
s
(
2
5
k
V
d
is
tr
ib
u
tio
n
f
ee
d
er
an
d
1
2
0
k
V
eq
u
iv
ale
n
t tr
a
n
s
m
is
s
io
n
s
y
s
te
m
)
.
Fig
u
r
e
5
.
Fu
ll d
etailled
m
o
d
el
an
d
co
n
tr
o
l u
s
i
n
g
Ma
tlab
/Si
m
u
li
n
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
C
o
mp
a
r
is
o
n
b
etw
ee
n
P
I
a
n
d
P
R
C
u
r
r
en
t Co
n
tr
o
ller
s
o
f a
Gri
d
-
C
o
n
n
ec
ted
…
(
S
o
u
k
a
in
a
E
s
s
a
g
h
ir
)
1317
Fig
u
r
e
6
s
h
o
w
s
t
h
at
t
h
e
v
o
lta
g
e
an
d
c
u
r
r
en
t
i
n
j
ec
ted
to
g
r
i
d
ar
e
in
p
h
ase
,
w
h
ic
h
e
x
p
lain
s
th
e
s
i
n
g
le
in
j
ec
tio
n
o
f
th
e
ac
ti
v
e
p
o
w
e
r
,
an
d
ac
co
r
d
in
g
to
F
ig
u
r
e
7
w
e
n
o
tice
th
at
t
h
e
r
ea
ctiv
e
p
o
w
er
is
ze
r
o
an
d
th
at
th
e
ac
tiv
e
p
o
w
er
r
ea
ch
es
i
ts
m
a
x
i
m
u
m
v
al
u
e
(
9
6
.
1
4
k
W
)
w
h
ich
m
ea
n
s
th
at
th
e
s
i
m
u
lati
o
n
h
as
g
i
v
e
n
u
s
t
h
e
ex
p
ec
ted
r
esu
lt
s
an
d
th
e
co
n
tr
o
l th
at
w
e
h
a
v
e
estab
li
s
h
ed
m
a
k
es it p
o
s
s
ib
le
to
h
a
v
e
a
u
n
it
y
p
o
w
er
f
ac
to
r
.
Fig
u
r
e
6
.
L
in
e
to
li
n
e
v
o
lta
g
e
an
d
cu
r
r
en
t i
n
j
ec
ted
in
to
g
r
id
Fig
u
r
e
7
.
C
h
ar
ac
ter
is
t
ic
o
f
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
in
j
ec
ted
in
to
g
r
id
Fig
u
r
e
8
.
a
an
d
F
ig
u
r
e
8
.b
s
h
o
w
t
h
e
f
r
eq
u
e
n
c
y
a
n
al
y
s
is
o
f
th
e
g
r
id
cu
r
r
e
n
t
a
n
d
its
T
H
D
v
al
u
e
b
y
u
s
i
n
g
th
e
P
I
an
d
P
R
co
n
tr
o
ller
,
r
esp
ec
tiv
el
y
.
T
h
e
s
i
m
u
latio
n
r
esu
lt
s
s
h
o
w
t
h
at
th
e
T
HD
o
f
th
e
P
R
co
n
tr
o
ller
is
m
u
c
h
le
s
s
t
h
a
n
th
a
t
o
f
t
h
e
P
I
co
n
tr
o
ller
,
co
n
s
eq
u
e
n
tl
y
th
e
P
R
co
n
tr
o
ller
ca
n
tr
ac
k
t
h
e
s
i
n
u
s
o
id
al
r
ef
er
en
ce
an
d
m
iti
g
ate
t
h
e
h
ar
m
o
n
ic
s
b
etter
th
an
P
I
co
n
tr
o
ller
w
h
ic
h
ex
p
lai
n
th
e
h
i
g
h
p
er
f
o
r
m
an
ce
o
f
t
h
i
s
t
y
p
e
o
f
co
n
tr
o
ller
.
Fig
u
r
e
8
.
a.
FF
T
an
al
y
s
i
s
an
d
T
HD
v
alu
e
o
f
g
r
id
cu
r
r
e
n
t b
y
u
s
i
n
g
P
I
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
3
1
1
–
1
3
2
0
1318
Fig
u
r
e
8
.
b
.
FF
T
an
aly
s
is
a
n
d
T
HD
v
alu
e
o
f
g
r
id
cu
r
r
e
n
t b
y
u
s
i
n
g
P
R
co
n
tr
o
ller
U
s
in
g
a
P
I
r
eg
u
lato
r
,
F
ig
u
r
e
9
.a
s
h
o
w
s
t
h
at,
af
ter
t
h
e
ad
d
itio
n
o
f
th
e
i
n
d
u
c
tiv
e
lo
ad
at
ti
m
e
t
=
0
.
3
s
,
th
e
c
u
r
r
en
t
in
j
ec
ted
i
n
to
g
r
id
b
ec
o
m
e
s
i
n
p
h
ase
d
ela
y
co
m
p
ar
ed
to
th
e
v
o
lta
g
e
b
u
t
a
f
ter
a
f
e
w
m
illi
s
ec
o
n
d
s
,
th
e
t
w
o
q
u
a
n
tit
ies
V
a
n
d
I
b
ec
o
m
e
in
p
h
ase,
u
n
li
k
e
w
h
e
n
u
s
in
g
a
P
R
r
e
g
u
la
to
r
,
as
s
h
o
w
n
in
F
ig
u
r
e
9
.
b
,
th
e
cu
r
r
en
t
a
n
d
t
h
e
v
o
lta
g
e
i
s
al
w
a
y
s
i
n
p
h
a
s
e
d
esp
ite
th
e
ad
d
itio
n
o
f
t
h
e
i
n
d
u
cti
v
e
lo
ad
.
Fo
r
th
i
s
r
ea
s
o
n
,
t
h
i
s
f
i
g
u
r
e
s
h
o
w
s
t
h
e
i
m
p
o
r
tan
ce
o
f
th
e
c
h
o
ice
o
f
th
is
t
y
p
e
o
f
co
r
r
ec
to
r
in
o
r
d
er
to
en
s
u
r
e
a
s
y
n
ch
r
o
n
iza
tio
n
b
et
w
ee
n
th
e
v
o
ltag
e
a
n
d
th
e
c
u
r
r
en
t i
n
j
ec
ted
in
to
g
r
id
d
esp
ite
th
e
ad
d
itio
n
o
f
t
h
e
in
d
u
ctiv
e
lo
ad
.
(
a)
(
b
)
Fig
u
r
e
9
.
Vo
ltag
e
an
d
cu
r
r
en
t in
j
ec
ted
to
g
r
id
w
it
h
v
ar
iatio
n
lo
ad
b
y
u
s
in
g
a:
P
I
co
n
tr
o
ller
,
b
: P
R
co
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
C
o
mp
a
r
is
o
n
b
etw
ee
n
P
I
a
n
d
P
R
C
u
r
r
en
t Co
n
tr
o
ller
s
o
f a
Gri
d
-
C
o
n
n
ec
ted
…
(
S
o
u
k
a
in
a
E
s
s
a
g
h
ir
)
1319
S
i
m
i
lar
l
y
,
th
e
F
i
g
u
r
e
1
0
s
h
o
w
s
t
h
at
w
h
e
n
u
s
in
g
a
P
I
co
r
r
ec
to
r
,
an
d
at
t
h
e
m
o
m
e
n
t
w
h
e
n
t
h
e
in
d
u
cti
v
e
c
h
ar
g
e
is
ad
d
ed
(
t
=
0
.
3
s
)
,
th
e
r
ea
ctiv
e
p
o
w
er
Q
b
ec
o
m
es
p
o
s
iti
v
e
an
d
a
f
ter
a
f
e
w
m
i
llis
ec
o
n
d
s
it
r
etain
s
its
i
n
itial
v
a
lu
e
,
b
u
t
u
s
in
g
t
h
e
co
r
r
ec
to
r
P
R
,
th
e
r
ea
ct
iv
e
p
o
w
er
al
w
a
y
s
k
ee
p
s
its
v
a
l
u
e
w
h
ic
h
is
eq
u
al
to
ze
r
o
w
h
ic
h
ex
p
lai
n
s
th
e
h
i
g
h
p
er
f
o
r
m
an
ce
o
f
t
h
is
t
y
p
e
o
f
co
r
r
e
c
to
r
an
d
its
ab
ilit
y
to
m
ai
n
tai
n
a
s
i
n
g
le
in
j
ec
tio
n
o
f
t
h
e
ac
tiv
e
p
o
w
er
an
d
to
k
ee
p
al
w
a
y
s
a
u
n
it
y
p
o
wer
f
ac
to
r
d
esp
ite
v
ar
iatio
n
lo
ad
.
Fig
u
r
e
1
0
.
A
cti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
w
it
h
v
ar
iatio
n
lo
ad
b
y
u
s
i
n
g
P
I
ad
P
R
co
n
tr
o
ller
Fo
r
th
i
s
p
u
r
p
o
s
e,
t
h
e
s
i
m
u
la
tio
n
s
h
o
w
s
t
h
e
i
m
p
o
r
tan
ce
o
f
t
h
e
p
r
o
p
o
s
ed
w
o
r
k
an
d
g
a
v
e
u
s
th
e
ex
p
ec
ted
r
esu
lt
s
.
T
h
er
ef
o
r
e,
an
d
co
m
p
ar
ed
to
o
th
er
r
esear
ch
es [
1
1
,
2
4
]
,
th
e
P
R
co
r
r
ec
to
r
p
r
o
p
o
s
ed
allo
w
s
u
s
to
h
av
e
a
u
n
it
p
o
w
er
f
ac
to
r
d
esp
ite
th
e
ad
d
itio
n
o
f
th
e
r
ea
cti
v
e
lo
ad
an
d
esp
ec
iall
y
w
ith
o
u
t
i
n
f
l
u
en
ci
n
g
th
e
p
ac
e
o
f
th
e
r
ea
ctiv
e
p
o
w
er
an
d
w
i
t
h
o
u
t
in
tr
o
d
u
cin
g
an
y
i
n
s
tan
ta
n
eo
u
s
p
h
a
s
e
d
if
f
er
en
ce
b
et
w
e
en
t
h
e
v
o
lta
g
e
a
n
d
th
e
cu
r
r
en
t in
j
ec
ted
in
to
g
r
id
.
5.
CO
N
CL
U
SI
O
N
T
h
is
p
ap
er
h
as
p
r
esen
ted
a
co
m
p
ar
is
o
n
b
et
w
ee
n
s
tan
d
ar
d
P
I
an
d
P
R
cu
r
r
en
t
co
n
tr
o
ller
s
in
g
r
id
-
c
o
n
n
ec
ted
P
V
s
y
s
te
m
s
.
A
f
ter
th
e
m
o
d
elin
g
o
f
th
e
th
r
ee
-
p
h
ase
g
r
id
co
n
n
ec
ted
P
V
s
y
s
t
e
m
s
a
n
d
t
h
e
p
o
w
er
f
ac
to
r
co
n
tr
o
l
s
ch
e
m
es,
t
h
e
o
b
tain
ed
r
esu
lts
ar
e
v
er
y
i
m
p
o
r
ta
n
t
an
d
s
a
tis
f
ac
to
r
y
.
T
h
e
y
s
h
o
w
t
h
at
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
w
it
h
th
e
P
R
co
n
tr
o
ller
co
r
r
ec
tly
d
escr
ib
es
t
h
e
d
y
n
a
m
ic
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
P
V
s
y
s
t
e
m
s
t
u
d
ied
.
T
h
e
P
R
co
r
r
ec
to
r
can
tr
ac
k
th
e
s
i
n
u
s
o
id
al
r
ef
er
en
ce
a
n
d
m
iti
g
ate
t
h
e
h
ar
m
o
n
ics
b
etter
th
a
n
P
I
co
n
tr
o
l
ler
,
m
o
r
eo
v
er
,
th
e
P
R
co
r
r
ec
to
r
allo
w
s
u
s
to
h
av
e
a
u
n
it
p
o
w
er
f
ac
to
r
d
esp
ite
th
e
ad
d
itio
n
o
f
th
e
r
ea
cti
v
e
lo
ad
an
d
esp
ec
iall
y
w
it
h
o
u
t
in
f
l
u
en
c
in
g
th
e
p
ac
e
o
f
th
e
r
ea
ctiv
e
p
o
w
er
an
d
w
it
h
o
u
t
i
n
tr
o
d
u
cin
g
an
y
i
n
s
ta
n
ta
n
eo
u
s
p
h
ase
d
if
f
er
e
n
ce
b
et
w
ee
n
t
h
e
v
o
lta
g
e
an
d
th
e
c
u
r
r
en
t in
j
ec
ted
in
to
g
r
id
.
A
P
P
E
NDI
X
T
ab
le
1
.
P
h
o
to
v
o
ltaic
P
ar
am
et
er
s
T
e
mp
e
r
a
t
u
r
e
T
25
°
C
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
V
oc
6
4
.
2
V
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
I
sc
5
.
9
6
A
V
o
l
t
a
g
e
,
max
i
mu
m
p
o
w
e
r
V
max
5
4
.
7
V
C
u
r
r
e
n
t
,
m
a
x
i
mu
m
p
o
w
e
r
I
max
5
.
5
8
A
M
a
x
i
m
u
m
p
o
w
e
r
P
max
305
W
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
3
1
1
–
1
3
2
0
1320
R
E
F
E
R
E
NC
E
S
[1
]
H.
L
iu
,
S
.
Jia
n
g
,
W
.
W
a
n
g
a
n
d
D
.
Xu
,
“
T
h
e
m
a
x
i
m
u
m
P
o
w
e
r
P
o
i
n
t
T
ra
c
k
in
g
Ba
se
d
o
n
t
h
e
Do
u
b
le
I
n
d
e
x
M
o
d
e
l
o
f
P
V
Ce
ll
s ”
,
IEE
E,
I
PE
M
C,
2
0
0
9
.
[2
]
G
.
V
.
M
a
rc
e
lo
,
G
.
Jo
n
a
s
a
n
d
RF
.
Ern
e
sto
,
“
Co
m
p
re
h
e
n
siv
e
A
p
p
ro
a
c
h
to
M
o
d
e
li
n
g
a
n
d
S
im
u
latio
n
o
f
P
h
o
to
v
o
lt
a
i
c
A
rra
y
s,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
we
r E
lec
tro
n
ics
,
2
4
,
2
0
0
9
,
p
.
4
.
[3
]
M
.
Cio
b
o
taru
,
R
.
T
e
o
d
o
re
sc
u
,
F
.
Blaa
b
jerg
,
“
Co
n
tro
l
o
f
a
S
in
g
le
-
P
h
a
se
P
V
I
n
v
e
rter”
,
EP
E2
0
0
5
,
Dre
sd
e
n
,
2
0
0
5
.
[4
]
V
.
Kh
a
n
n
a
,
B.
K.
Da
s,
D.
Bish
t,
“
M
ATLA
B/S
i
m
e
le
c
tro
n
ics
m
o
d
e
ls
b
a
se
d
stu
d
y
o
f
so
lar
c
e
ll
s,
”
I
n
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ren
e
wa
b
le E
n
e
rg
y
Res
e
a
rc
h
,
V
o
l
.
3
,
No
.
1
,
2
0
1
3
.
[5
]
W
.
Re
z
g
u
i,
L
.
H.
M
o
u
ss
,
M
.
D.
M
o
u
ss
,
“
M
o
d
e
li
n
g
o
f
a
p
h
o
to
v
o
lt
a
i
c
f
ield
in
m
a
lf
u
n
c
ti
o
n
in
g
,
”
In
Co
n
tro
l,
De
c
isio
n
a
n
d
In
f
o
rm
a
ti
o
n
T
e
c
h
n
o
lo
g
ies
(
Co
DIT),
2
0
1
3
I
n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
.
[6
]
H.
Ou
a
tma
n
,
M
.
Ou
a
ss
a
id
,
M
.
Ch
e
rk
a
o
u
i,
“
M
o
d
e
li
n
g
a
n
d
C
o
n
t
ro
l
o
f
a
G
rid
-
Co
n
n
e
c
ted
P
V
E
n
e
rg
y
Co
n
v
e
rsio
n
S
y
st
e
m
,
”
IEE
E,
W
S
EA
S
T
ra
n
sa
c
ti
o
n
s
o
n
S
y
ste
ms
a
n
d
C
o
n
tr
o
l
,
I
S
S
N:
2
2
2
4
-
2
8
5
6
,
V
o
l
1
0
,
2
0
1
5
.
[7
]
A
.
H.
M
o
ll
a
h
,
G
.
K.
P
a
n
d
a
,
P
.
K.
S
a
h
a
,
“
T
h
re
e
P
h
a
se
G
rid
Co
n
n
e
c
ted
P
h
o
to
v
o
l
taic
S
y
ste
m
w
it
h
M
a
x
i
m
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
in
g
,
”
In
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ad
v
a
n
c
e
d
Res
e
a
rc
h
in
El
e
c
trica
l,
El
e
c
tro
n
ics
a
n
d
I
n
stru
me
n
ta
ti
o
n
En
g
i
n
e
e
rin
g
,
IS
S
N:
2
2
7
8
–
8
8
7
5
,
V
o
l
.
4
,
Iss
u
e
5
,
M
a
y
2
0
1
5
.
[8
]
S.
Ju
i
n
g
-
h
u
e
i,
C.
C
h
a
o
-
L
ian
g
,
C.
Jia
n
n
-
Jo
n
g
a
n
d
W
.
Ch
ien
-
M
in
g
,
“
S
im
u
li
n
k
Be
h
a
v
io
r
M
o
d
e
l
s
F
o
r
DC
-
DC
S
w
it
c
h
in
g
Co
n
v
e
rter Ci
rc
u
it
s Us
i
n
g
P
W
M
Co
n
tr
o
l
ICs”
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
En
g
in
e
e
rin
g
Ed
u
c
a
ti
o
n
,
2
0
0
6
,
p
p
.
315
–
3
2
2
,
v
sp
a
c
e
-
7pt
.
[9
]
W
.
T
sa
i
-
F
u
,
N.
Hu
n
g
-
S
h
o
u
,
S
.
C
h
ich
-
L
u
n
g
a
n
d
C.
T
su
n
g
-
M
in
g
,
“
A
S
in
g
le
-
P
h
a
se
In
v
e
rter
S
y
ste
m
f
o
r
P
V
P
o
w
e
r
In
jec
ti
o
n
a
n
d
A
c
ti
v
e
P
o
w
e
r
F
il
tri
n
g
W
it
h
No
n
li
n
e
a
r
In
d
u
c
t
o
r
Co
n
sid
e
ra
ti
o
n
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
On
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
2
0
0
5
,
p
p
.
1
0
7
5
–
1
0
8
3
.
[1
0
]
Z.
Bin
Ib
ra
h
i
m
,
M
.
L
.
Ho
ss
a
in
,
I.
Bin
Bu
g
is,
J.
M
.
L
a
z
i,
N.
M
.
Ya
a
k
o
p
,
“
Co
m
p
a
ra
ti
v
e
A
n
a
ly
sis
o
f
P
W
M
T
e
c
h
n
iq
u
e
s
f
o
r
T
h
re
e
L
e
v
e
l
Dio
d
e
Cla
m
p
e
d
V
o
lt
a
g
e
S
o
u
rc
e
In
v
e
rt
e
r
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
w
e
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
,
Vo
l.
5
,
N
o
.
1
,
p
p
.
1
5
-
2
3
IS
S
N:
2
0
8
8
-
8
6
9
4
,
Ju
ly
2
0
1
4
.
[1
1
]
S
.
Essa
g
h
ir,
M
.
Be
n
c
h
a
g
ra
,
N.
El
Ba
rb
ri,
“
P
o
w
e
r
F
a
c
to
r
Co
n
tro
l
o
f
a
P
h
o
to
v
o
lt
a
ic S
y
ste
m
Co
n
n
e
c
ted
to
G
rid
Un
d
e
r
L
o
a
d
V
a
riatio
n
,
”
I
n
ter
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
El
e
c
trica
l
a
n
d
I
n
f
o
rm
a
ti
o
n
T
e
c
h
n
o
lo
g
ies
,
No
v
e
mb
e
r
1
5
-
1
8
,
2
0
1
7
,
M
o
ro
c
c
o
.
[1
2
]
R.
Ka
d
ri,
J.
P
.
G
a
u
b
e
rt,
M
e
m
b
e
r
IEE
E,
G
.
Ch
a
m
p
e
n
o
is,
M
e
m
b
e
r
IEE
E,
“
A
n
Im
p
ro
v
e
d
M
a
x
im
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
in
g
f
o
r
P
h
o
to
v
o
lt
a
ic
G
rid
-
Co
n
n
e
c
ted
I
n
v
e
rter
Ba
se
d
o
n
V
o
lt
a
g
e
-
Orie
n
ted
Co
n
tro
l
,
”
IEE
E
T
ra
n
s.
In
d
u
st
ri
a
l
El
e
c
tro
n
ics
,
V
o
l
.
5
8
,
N
o
.
1
,
Ja
n
u
r
a
y
2
0
1
1
.
[1
3
]
R.
Ba
las
u
b
ra
m
a
n
ian
,
S
.
p
a
lan
i,
“
S
im
u
latio
n
a
n
d
P
e
rf
o
rm
a
n
c
e
E
v
a
lu
a
ti
o
n
o
f
S
h
u
n
t
Hy
b
rid
P
o
w
e
r
F
il
ter
f
o
r
P
o
w
e
r
Qu
a
li
ty
I
m
p
ro
v
e
m
e
n
t
Us
in
g
P
Q
T
h
e
o
r
y
,
”
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
E
n
g
i
n
e
e
rin
g
,
Vo
l.
6
,
No
.
6
,
p
p
.
2
6
0
3
-
2
6
0
9
,
IS
S
N:
2
0
8
8
-
8
7
0
8
,
De
c
e
m
b
e
r
2
0
1
6
.
[1
4
]
L
.
Ro
li
m
,
D.
Co
sta
,
M
.
A
re
d
e
s,
“
A
n
a
l
y
sis
a
n
d
so
f
twa
re
i
m
p
le
m
e
n
tatio
n
o
f
a
ro
b
u
st
sy
n
c
h
ro
n
izin
g
P
L
L
c
ircu
it
b
a
se
d
o
n
th
e
p
q
th
e
o
ry
,
”
,
IEE
E
T
r
a
n
s.
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
Vo
l.
5
3
,
No
.
6
,
p
p
.
1
9
1
9
-
1
9
2
6
,
2
0
0
6
.
[1
5
]
O.
M.
B
en
aiss
a,
S.
Had
j
er
i,
S.
A
.
Z
id
i,
“
Mo
d
elin
g
an
d
Si
m
u
latio
n
o
f
Gr
id
C
o
n
n
ec
ted
P
V
Gen
er
atio
n
S
y
s
te
m
Usi
n
g
Ma
tlab
/Si
m
u
li
n
k
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m,
V
o
l.
8
,
No
.
1
,
p
p
.
3
9
2
-
401
,
IS
S
N:
2
0
8
8
-
8
6
9
4
,
M
a
rc
h
2
0
1
7
.
[1
6
]
E.
G
.
S
h
a
h
ra
k
i,
“
A
p
p
o
rt
d
e
l'
U
P
F
C
à
l'
a
m
é
li
o
ra
ti
o
n
d
e
la
sta
b
il
it
é
tran
sito
ire
d
e
s
ré
se
a
u
x
é
lec
tri
q
u
e
s,”
Do
c
to
ra
l
th
e
sis,
He
n
ri P
o
in
c
a
ré
N
a
n
c
y
-
I
U
n
ive
rs
it
,
2
0
0
3
.
[1
7
]
M
.
M
e
ss
a
o
u
d
,
“
M
o
d
é
li
sa
ti
o
n
e
t
o
p
ti
m
isa
ti
o
n
d
e
sy
stè
m
e
s
d
e
p
ro
d
u
c
ti
o
n
d
’é
n
e
rg
ies
re
n
o
u
v
e
lab
les
c
o
u
p
lés
a
u
ré
se
a
u
,
”
Do
c
to
ra
l
t
h
e
sis,
M
e
n
to
u
ri d
e
Co
n
sta
n
ti
n
e
Un
ive
rs
it
y
,
2
0
1
2
.
[1
8
]
D.
Zam
m
it
,
C.
S
.
S
tain
e
s,
M
.
A
p
a
p
,
‘’Co
m
p
a
riso
n
b
e
tw
e
e
n
P
I
a
n
d
P
R
C
u
rre
n
t
C
o
n
tro
ll
e
rs
i
n
G
rid
Co
n
n
e
c
ted
P
V
In
v
e
rters
,
‘’
W
o
rld
Aca
d
e
my
o
f
S
c
ien
c
e
,
E
n
g
i
n
e
e
rin
g
a
n
d
T
e
c
h
n
o
l
o
g
y
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l,
Co
mp
u
ter
,
En
e
rg
e
ti
c
,
El
e
c
tro
n
ic
a
n
d
Co
mm
u
n
ica
t
io
n
En
g
i
n
e
e
rin
g
V
o
l
:8
,
No
:
2
,
2
0
1
4
.
[1
9
]
S.M.
d
e
v
i1
,
Dr.K.
P
u
n
it
h
a
,
“
Re
so
n
a
n
t
C
u
rre
n
t
C
o
n
tr
o
ll
e
r
Ba
se
d
T
HD
Re
d
u
c
ti
o
n
In
A
C
M
icro
G
ri
d
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Eme
rg
i
n
g
T
e
c
h
n
o
l
o
g
y
in
Co
mp
u
ter
S
c
ien
c
e
&
El
e
c
tr
o
n
ics
(
IJ
ET
CS
E)
IS
S
N:
0
9
7
6
-
1
3
5
3
V
o
l
u
m
e
2
2
Iss
u
e
2
–
M
A
Y 2
0
1
6
.
[2
0
]
R.
T
e
o
d
o
re
sc
u
,
M
.
L
ise
rre
,
P
.
R
o
d
rig
u
e
z
,
“
G
rid
Co
n
v
e
rters
f
o
r
P
h
o
t
o
v
o
lt
a
ic
a
n
d
W
in
d
P
o
w
e
r
S
y
ste
m
s
”
,
W
il
e
y
,
2
0
1
1
.
[2
1
]
G
u
o
X
iao
q
ian
g
,
Zh
a
o
Qin
g
li
n
a
n
d
W
u
W
e
i
y
a
n
g
“
A
S
in
g
le
-
P
h
a
se
G
rid
-
Co
n
n
e
c
ted
In
v
e
rter
S
y
st
e
m
W
it
h
Zero
S
tea
d
y
-
S
tate
Err
o
r’’
,
in
CES
/IE
E
E
5
th
In
ter
n
a
ti
o
n
a
l
Po
we
r
El
e
c
tro
n
ics
a
n
d
M
o
ti
o
n
Co
n
tro
l
Co
n
fer
e
n
c
e
,
2
0
0
6
,
v
o
l.
1
,
p
p
.
1
-
5
,
A
u
g
.
2
0
0
6
.
[2
2
]
R.
T
e
o
d
o
re
sc
u
;
F
.
Blaa
b
jerg
;
M
.
L
ise
rr
e
a
n
d
P
.
C.
L
o
h
“
P
r
o
p
o
rt
io
n
a
l
re
so
n
a
n
t
c
o
n
tro
ll
e
rs
a
n
d
f
i
lt
e
rs
f
o
r
g
rid
-
c
o
n
n
e
c
ted
v
o
lt
a
g
e
-
so
u
rc
e
c
o
n
v
e
rters
”
,
in
IEE
Pro
c
e
e
d
in
g
s
-
El
e
c
tric
Po
we
r
Ap
p
li
c
a
ti
o
n
s
,
v
o
l.
1
5
3
,
i
ss
.
5
,
p
p
.
7
5
0
-
7
6
2
,
2
0
0
6
.
[2
3
]
D.
N.
Zm
o
o
d
,
D.
G
.
Ho
lme
s,
“
S
tatio
n
a
ry
F
ra
m
e
Cu
rre
n
t
Re
g
u
l
a
ti
o
n
o
f
P
W
M
I
n
v
e
rters
w
it
h
Zero
S
tea
d
y
-
S
tate
Err
o
r”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
ics
,
Vo
l.
1
8
,
No
.
3
,
M
a
y
2
0
0
3
.
[2
4
]
H.Ch
a
,
J.E
.
Kim
,
T
.
K.
V
u
“
De
s
ig
n
a
n
d
c
o
n
tr
o
l
o
f
P
r
o
p
o
rti
o
n
a
l
-
Re
so
n
a
n
t
c
o
n
tro
ll
e
r
b
a
se
d
P
h
o
t
o
v
o
lt
a
ic
p
o
w
e
r
c
o
n
d
i
ti
o
n
in
g
sy
ste
m
,
”
IEE
E
En
e
rg
y
Co
n
v
e
rs
io
n
Co
n
g
re
ss
a
n
d
Exp
o
siti
o
n
,
2
0
0
9
.
ECCE
2
0
0
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.