I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
s
(
I
J
P
E
DS)
Vo
l.
1
6
,
No
.
1
,
Ma
r
ch
20
2
5
,
p
p
.
2
7
8
~
2
8
6
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
6
.i
1
.
p
p
2
7
8
-
286
278
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Co
ntrol o
f
shu
nt
a
ctive po
wer
filt
e
r f
o
r powe
r qualit
y
impro
v
ements wi
th
P
V sy
stem
usin
g
MPC appro
a
ch
L
a
ro
uci H
eg
uig
1
,
Na
dh
ir
M
e
s
ba
hi
2
,
Ya
cine
G
uet
t
a
f
1
1
La
b
o
r
a
t
o
r
y
o
f
I
n
st
r
u
me
n
t
a
t
i
o
n
a
n
d
M
a
t
e
r
i
a
l
s Ap
p
l
i
e
d
(
LI
M
A
)
,
N
o
u
r
B
a
c
h
i
r
U
n
i
v
e
r
s
i
t
y
C
e
n
t
e
r
,
E
l
B
a
y
a
d
h
,
A
l
g
e
r
i
a
2
La
b
o
r
a
t
o
i
r
e
d
e
G
é
n
i
e
E
l
e
c
t
r
i
q
u
e
e
t
d
e
s E
n
e
r
g
i
e
s
R
e
n
o
u
v
e
l
a
b
l
e
s
d
’
El
O
u
e
d
(
LG
EER
E)
,
U
n
i
v
e
r
si
t
y
o
f
El
O
u
e
d
,
E
l
O
u
e
d
,
A
l
g
e
r
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
u
l 5
,
2
0
2
4
R
ev
is
ed
Sep
1
3
,
2
0
2
4
Acc
ep
ted
Oct
2
3
,
2
0
2
4
Th
e
m
a
jo
r
issu
e
fa
c
in
g
t
h
e
e
lec
tri
c
a
l
g
rid
is
th
e
e
x
c
e
ss
iv
e
u
se
o
f
n
o
n
-
li
n
e
a
r
lo
a
d
s,
wh
ic
h
p
u
ll
d
isto
rte
d
(
n
o
n
-
sin
u
s
o
id
a
l)
c
u
rre
n
t
fr
o
m
th
e
g
ri
d
.
Co
n
sid
e
ri
n
g
t
h
is
c
o
n
stra
in
t
,
t
h
e
o
b
jec
ti
v
e
is
to
re
m
o
v
e
a
n
y
h
a
rm
o
n
ic
c
u
rre
n
ts
fro
m
th
e
g
ri
d
.
T
h
e
a
c
ti
v
e
fil
teri
n
g
m
e
th
o
d
h
a
s
b
e
e
n
se
lec
ted
,
p
a
rti
c
u
larly
fo
c
u
sin
g
o
n
t
h
e
u
se
o
f
th
e
sh
u
n
t
a
c
ti
v
e
fil
ter,
wh
ich
p
r
o
v
i
d
e
s
n
u
m
e
ro
u
s
b
e
n
e
fit
s.
Th
e
re
fo
re
,
in
o
rd
e
r
to
a
c
h
iev
e
e
ffe
c
ti
v
e
h
a
rm
o
n
ic
c
o
m
p
e
n
sa
ti
o
n
,
a
su
it
a
b
le
a
n
d
re
sili
e
n
t
c
o
n
tro
l
s
y
st
e
m
is
n
e
c
e
ss
a
ry
fo
r
th
e
sh
u
n
t
a
c
t
iv
e
fil
ter.
Th
e
sy
ste
m
o
u
tl
in
e
d
i
n
th
is
st
u
d
y
c
o
m
p
rise
s
a
p
h
o
t
o
v
o
lt
a
ic
g
e
n
e
ra
to
r
c
o
n
n
e
c
ted
to
t
h
e
d
istri
b
u
ti
o
n
e
lec
tri
c
a
l
g
ri
d
v
ia
a
sh
u
n
t
a
c
ti
v
e
fil
te
r
in
o
rd
e
r
to
sim
u
lt
a
n
e
o
u
sl
y
e
n
su
re
th
e
i
n
jec
ti
o
n
o
f
re
n
e
wa
b
le
p
o
we
r
g
e
n
e
ra
ted
b
y
th
e
p
h
o
to
v
o
lt
a
ic
g
e
n
e
ra
to
r
in
to
t
h
e
g
rid
a
n
d
th
e
imp
r
o
v
e
m
e
n
t
o
f
th
e
e
lec
tri
c
a
l
e
n
e
rg
y
q
u
a
li
t
y
.
In
t
h
is
stu
d
y
,
a
m
o
d
e
l
p
re
d
icti
v
e
c
u
rre
n
t
is
i
n
tro
d
u
c
e
d
fo
r
sh
u
n
t
a
c
ti
v
e
p
o
we
r
with
f
u
z
z
y
lo
g
ic
c
o
n
tr
o
l
to
o
p
ti
m
ize
th
e
trac
k
in
g
o
f
th
e
m
a
x
imu
m
p
o
we
r
p
o
in
t
fo
r
t
h
e
p
h
o
t
o
v
o
lt
a
ic
g
e
n
e
ra
to
r.
Th
e
s
y
ste
m
wa
s
stu
d
ied
u
n
d
e
r
v
a
rio
u
s
c
o
n
d
it
i
o
n
s,
a
n
d
t
h
e
sim
u
lati
o
n
wa
s
c
a
rried
o
u
t
u
sin
g
M
ATLAB
/S
imu
li
n
k
o
n
t
h
e
e
n
ti
re
sy
ste
m
.
K
ey
w
o
r
d
s
:
Fu
zz
y
lo
g
ic
co
n
tr
o
l
Ma
x
im
u
m
p
o
wer
p
o
i
n
t tr
ac
k
in
g
Mo
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
Ph
o
to
v
o
ltaic
s
y
s
tem
Sh
u
n
t
ac
tiv
e
p
o
wer
f
ilter
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
:
Nad
h
ir
Me
s
b
ah
i
L
ab
o
r
ato
ir
e
d
e
Gén
ie
E
lectr
iq
u
e
et
d
es E
n
er
g
ies R
en
o
u
v
elab
lesd
’
E
lOu
ed
(
L
GE
E
R
E
)
Un
iv
er
s
ity
o
f
E
l O
u
e
d
E
l O
u
ed
,
Alg
er
ia
E
m
ail:
n
ad
h
ir
-
m
esb
ah
i@
u
n
iv
-
elo
u
ed
.
d
z
1.
I
NT
RO
D
UCT
I
O
N
E
n
v
ir
o
n
m
en
tal
p
o
llu
tio
n
is
o
n
e
o
f
th
e
m
ajo
r
is
s
u
es
ar
is
i
n
g
f
r
o
m
n
o
n
-
r
en
ewa
b
le
en
e
r
g
ies.
T
h
is
ch
allen
g
e
h
as
s
p
u
r
r
ed
th
e
d
ev
elo
p
m
en
t
o
f
r
en
ewa
b
le
en
er
g
ies,
with
s
o
lar
p
o
wer
s
ta
n
d
in
g
o
u
t
as
a
to
p
co
n
ten
d
er
.
W
h
at
s
ets
s
o
lar
en
er
g
y
ap
ar
t
is
its
s
im
p
le
in
s
tal
l
atio
n
p
r
o
ce
s
s
an
d
th
e
ab
s
en
ce
o
f
ac
tiv
e
m
o
v
in
g
co
m
p
o
n
en
ts
[
1
[
,
[
2
[
.
T
o
b
o
o
s
t
en
er
g
y
o
u
tp
u
t
f
r
o
m
a
s
o
lar
p
o
wer
s
y
s
tem
,
it
is
cr
u
cial
to
r
u
n
th
e
p
h
o
to
v
o
ltaic
g
en
er
ato
r
at
its
p
ea
k
ca
p
ac
ity
.
E
m
p
lo
y
in
g
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
tech
n
i
q
u
es
is
es
s
en
tial
in
th
ese
s
y
s
tem
s
to
en
s
u
r
e
o
p
tim
al
p
er
f
o
r
m
an
ce
.
R
ec
en
tly
,
ex
ten
s
iv
e
r
esear
ch
h
as
b
ee
n
co
n
ce
r
n
e
d
d
ev
is
in
g
v
ar
io
u
s
MPPT
m
eth
o
d
s
aim
e
d
at
m
ax
im
izin
g
th
e
ef
f
icien
c
y
o
f
s
o
lar
en
er
g
y
p
r
o
d
u
ctio
n
.
T
h
ese
m
eth
o
d
s
v
ar
y
f
r
o
m
s
m
ar
t te
ch
n
iq
u
es to
th
o
s
e
r
o
o
ted
i
n
co
n
t
r
o
l th
eo
r
y
[
3
]
.
On
e
o
f
th
e
m
o
s
t
p
o
p
u
lar
al
g
o
r
ith
m
s
u
s
ed
f
o
r
tr
ac
k
in
g
in
M
PP
T
is
p
er
tu
r
b
atio
n
a
n
d
o
b
s
er
v
atio
n
o
r
P&
O
alg
o
r
ith
m
.
I
t
is
f
av
o
r
ed
f
o
r
its
s
im
p
licity
an
d
lo
w
co
m
p
lex
ity
.
Ho
wev
er
,
its
d
r
awb
ac
k
s
o
v
er
s
h
ad
o
w
its
b
en
ef
its
,
with
a
s
ig
n
if
ican
t
is
s
u
e
b
ein
g
a
co
n
s
is
ten
t
d
is
tu
r
b
an
ce
s
tep
in
tr
ac
k
i
n
g
th
e
o
p
tim
al
p
o
in
t,
alo
n
g
wit
h
its
s
lo
w
co
n
v
er
g
en
ce
to
th
is
p
o
in
t
]
4
]
.
Fu
zz
y
lo
g
ic
is
th
e
m
o
s
t
ef
f
icien
t
way
to
s
wif
tly
r
ea
ch
th
e
p
er
f
ec
t
p
o
in
t
with
o
u
t
an
y
co
m
p
licatio
n
s
o
r
s
y
s
tem
m
o
d
ellin
g
.
T
h
is
tech
n
o
lo
g
y
ac
h
ie
v
es
g
o
o
d
a
n
d
s
tab
le
r
esu
lts
co
m
p
ar
ed
to
th
e
P&
O
al
g
o
r
ith
m
.
Mo
r
e
o
v
er
,
it
r
em
ain
s
ef
f
ec
tiv
e
in
all
wea
th
er
c
o
n
d
itio
n
s
,
n
o
m
atte
r
th
e
v
ar
iatio
n
s
in
tem
p
er
atu
r
e
o
r
s
h
ad
e
[
5
]
.
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
6
9
4
C
o
n
tr
o
l o
f sh
u
n
t a
ctive
p
o
w
er filter
fo
r
p
o
w
er q
u
a
lity imp
r
o
v
eme
n
ts
w
ith
P
V
s
ystem
…
(
La
r
o
u
ci
Heg
u
ig
)
279
On
th
e
o
th
er
h
an
d
,
with
r
a
p
id
ad
v
an
ce
m
en
t
in
p
o
wer
elec
tr
o
n
ics,
th
e
wid
esp
r
ea
d
u
s
e
o
f
n
o
n
-
lin
ea
r
lo
ad
s
h
as
ca
u
s
ed
s
ig
n
if
ican
t
d
is
r
u
p
tio
n
s
lik
e
h
ar
m
o
n
ics,
u
n
b
alan
ce
d
cu
r
r
en
ts
,
a
n
d
m
o
r
e
to
b
e
in
tr
o
d
u
ce
d
in
to
th
e
p
o
wer
g
r
id
.
T
h
ese
h
ar
m
o
n
ics
lo
wer
ef
f
icien
cy
,
d
ec
r
ea
s
e
th
e
p
o
we
r
f
ac
to
r
,
r
aise
lo
s
s
es,
an
d
r
esu
lt
in
elec
tr
o
m
ag
n
etic
in
ter
f
er
en
ce
with
n
ea
r
b
y
c
o
m
m
u
n
icatio
n
l
in
es,
lead
in
g
to
v
ar
io
u
s
a
d
v
e
r
s
e
ef
f
ec
t
s
]
6
]
.
T
o
tack
le
th
e
is
s
u
e
o
f
h
a
r
m
o
n
ic
d
is
tu
r
b
an
ce
s
,
v
a
r
io
u
s
s
o
lu
tio
n
s
h
av
e
b
ee
n
s
u
g
g
ested
.
R
ec
en
t
r
esear
ch
e
f
f
o
r
ts
in
th
is
f
ield
h
a
v
e
g
r
ea
tly
aid
e
d
i
n
d
e
v
elo
p
in
g
s
o
lu
tio
n
s
an
d
c
o
n
f
ig
u
r
atio
n
s
b
ased
o
n
s
in
g
le
-
p
h
ase
an
d
3
-
p
h
ase
d
io
d
e
r
ec
tifie
r
s
with
s
p
ec
ial
d
esig
n
s
,
p
ass
iv
e
f
ilter
s
,
ac
t
iv
e
f
ilter
s
an
d
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
PW
M
)
r
ec
tifie
r
s
.
Mo
r
eo
v
er
,
th
ese
m
eth
o
d
s
r
ely
o
n
u
s
in
g
p
ass
iv
e
f
ilter
s
,
wh
ich
a
r
e
a
co
m
m
o
n
an
d
v
iab
le
s
o
lu
tio
n
.
Sp
ec
if
ically
,
in
d
u
cto
r
d
an
ca
p
ac
ito
r
o
r
LC
p
ass
iv
e
f
ilter
s
ac
t
as
tr
ap
s
f
o
r
f
ilter
in
g
o
u
t
h
a
r
m
o
n
ic
cu
r
r
e
n
ts
b
ased
o
n
th
eir
h
ar
m
o
n
ic
o
r
d
er
s
[
7
]
.
T
h
ey
ca
n
also
h
elp
o
f
f
s
et
r
e
ac
tiv
e
p
o
wer
.
Ho
wev
er
,
th
ese
d
ev
ices
h
av
e
th
eir
d
r
awb
ac
k
s
.
Fo
r
in
s
tan
ce
,
th
e
y
m
ay
s
tr
u
g
g
le
to
ad
ap
t
to
ch
an
g
es
in
g
r
id
im
p
e
d
an
ce
o
r
lo
ad
s
,
p
o
ten
tially
lead
in
g
to
r
eso
n
an
ce
is
s
u
es with
th
e
g
r
id
im
p
ed
a
n
ce
[
8
]
.
I
n
ce
r
tain
ca
s
es,
th
is
r
eso
n
an
ce
ca
n
ca
u
s
e
a
s
u
r
g
e
in
h
ar
m
o
n
ic
cu
r
r
en
t
an
d
v
o
ltag
e
with
in
th
e
g
r
id
an
d
th
e
f
ilter
ca
p
ac
ito
r
[
9
]
.
T
h
is
lim
itatio
n
p
o
s
es
a
s
ig
n
if
ican
t
ch
allen
g
e,
esp
ec
ially
in
s
p
ec
if
ic
s
ce
n
ar
io
s
.
An
o
th
er
s
o
lu
ti
o
n
t
o
av
o
id
d
r
a
wb
ac
k
s
o
f
p
ass
iv
e
f
ilter
s
in
v
o
lv
es
im
p
lem
en
tin
g
a
s
y
s
tem
o
f
ac
tiv
e
p
o
wer
f
ilter
(
APF),
wh
ich
is
an
ef
f
ec
tiv
e
m
ea
n
s
o
f
co
m
p
en
s
atin
g
cu
r
r
e
n
t
o
r
v
o
ltag
e
h
ar
m
o
n
ics
g
en
e
r
ated
b
y
n
o
n
-
lin
ea
r
lo
ad
s
.
T
o
b
est
ad
d
r
ess
in
d
u
s
tr
ial
co
n
s
tr
ain
ts
,
ac
tiv
e
f
ilt
er
s
ar
e
u
s
ed
in
p
ar
allel,
s
er
ies,
o
r
co
m
b
in
e
d
co
n
f
ig
u
r
atio
n
s
[
1
0
]
.
I
n
th
is
s
tu
d
y
,
we
h
a
v
e
o
p
ted
f
o
r
a
s
h
u
n
t
ac
tiv
e
p
o
wer
f
ilter
(
SAPF
)
d
e
s
ig
n
ed
f
o
r
f
ilter
in
g
h
ar
m
o
n
ic
c
u
r
r
e
n
ts
.
C
u
r
r
en
tly
,
th
is
f
ilter
r
ep
r
esen
ts
th
e
m
o
s
t
s
u
itab
le
ad
v
an
ce
d
s
o
lu
ti
o
n
f
o
r
p
o
llu
tio
n
c
o
n
tr
o
l,
wh
eth
er
at
th
e
p
r
o
d
u
ctio
n
o
r
d
is
tr
ib
u
tio
n
lev
el
[
1
1
]
.
Activ
e
f
ilter
s
r
ely
o
n
v
ar
io
u
s
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
th
eir
p
er
f
o
r
m
an
ce
.
O
n
e
o
f
m
o
s
t
f
am
o
u
s
m
eth
o
d
s
p
r
o
p
o
s
ed
in
liter
atu
r
e
is
s
lid
in
g
m
o
d
e
co
n
tr
o
l,
d
ir
ec
t
p
o
wer
co
n
tr
o
l,
h
y
s
ter
esis
cu
r
r
e
n
t
co
n
tr
o
l
an
d
p
r
ed
ictiv
e
c
o
n
tr
o
l,
m
a
in
o
b
jectiv
e
o
f
all
th
ese
s
tr
ate
g
ies
is
to
elim
in
ate
h
ar
m
o
n
ic
cu
r
r
e
n
ts
an
d
im
p
r
o
v
e
p
o
wer
f
ac
to
r
,
d
esp
ite
th
ei
r
d
if
f
er
e
n
t
o
p
er
atin
g
p
r
in
cip
l
es
[1
2
]
.
Fo
r
m
an
y
y
ea
r
s
,
m
o
d
el
p
r
ed
ictiv
e
c
o
n
tr
o
l
(
MPC
)
h
as
g
ain
ed
g
r
ea
t
p
o
p
u
lar
ity
in
th
e
p
r
o
ce
s
s
an
d
ch
em
ical
in
d
u
s
tr
ies,
th
an
k
s
to
its
co
m
p
lex
m
o
d
els
an
d
s
lo
w
-
s
p
ee
d
d
y
n
am
ics [
1
3
]
.
Un
l
ik
e
c
h
em
i
ca
l
p
r
o
c
ess
es
,
p
o
wer
el
ec
t
r
o
n
ics
c
o
n
v
er
te
r
s
h
a
v
e
f
aste
r
d
y
n
a
m
ics
a
n
d
c
o
m
p
le
x
m
o
d
els,
p
r
o
m
p
ti
n
g
n
ee
d
f
o
r
e
n
h
a
n
ce
m
en
ts
i
n
ca
p
a
b
il
iti
es
o
f
m
ic
r
o
p
r
o
c
ess
o
r
a
n
d
s
e
p
a
r
a
te
m
o
d
el
to
b
e
a
b
le
t
o
u
s
e
MPC
in
s
u
ch
c
o
n
v
e
r
te
r
s
.
H
ig
h
r
eli
a
b
il
it
y
an
d
d
y
n
a
m
i
c
r
es
p
o
n
s
e
o
f
MPC
a
tt
r
ac
te
d
all
t
h
e
r
ec
e
n
t
r
es
ea
r
c
h
to
u
s
e
it
i
n
d
i
f
f
er
e
n
t
u
s
es
co
u
n
ti
n
g
p
o
we
r
c
o
n
v
e
r
t
er
s
an
d
f
il
te
r
i
n
g
as
a
r
es
u
lt
[
14
]
.
T
h
e
d
is
ti
n
c
ti
v
e
f
ea
t
u
r
e
o
f
th
e
MPC
m
et
h
o
d
c
o
m
p
a
r
ed
to
o
t
h
e
r
s
is
i
ts
ea
s
e
o
f
i
m
p
le
m
e
n
t
ati
o
n
.
T
h
e
p
r
o
c
ess
d
o
es
n
o
t
r
e
q
u
i
r
e
l
in
ea
r
o
r
n
o
n
li
n
ea
r
co
n
t
r
o
ll
er
s
i
n
t
h
e
i
n
t
er
n
a
l
lo
o
p
s
,
n
o
r
d
o
es
it
r
e
q
u
ir
e
a
c
ar
r
i
er
m
o
d
u
la
to
r
,
as
i
n
th
e
ca
s
e
o
f
PW
M
m
o
d
u
l
ati
o
n
.
Fu
r
th
e
r
m
o
r
e
,
co
n
s
t
r
a
in
ts
ar
e
c
o
n
s
id
e
r
e
d
th
an
k
s
t
o
its
f
l
ex
ib
i
lit
y
,
s
i
g
n
if
ica
n
t
ly
r
e
d
u
ci
n
g
th
e
o
v
e
r
all
c
o
s
t
o
f
t
h
e
d
r
iv
e
s
y
s
te
m
[
1
5
]
.
T
h
r
e
e
b
asi
c
p
a
r
ts
en
s
u
r
e
t
h
e
o
u
ts
ta
n
d
in
g
p
e
r
f
o
r
m
a
n
ce
o
f
t
h
e
a
cti
v
e
f
i
lt
er
i
n
c
o
m
p
e
n
s
at
in
g
h
a
r
m
o
n
i
c
cu
r
r
e
n
ts
:
f
i
r
s
tl
y
,
t
h
e
s
tr
at
eg
y
f
o
r
ex
tr
ac
ti
n
g
r
e
f
e
r
e
n
c
e
cu
r
r
e
n
ts
,
s
ec
o
n
d
ly
,
c
o
n
tr
o
lli
n
g
t
h
e
v
o
lta
g
e
o
f
th
e
DC
v
o
l
ta
g
e
,
t
h
i
r
d
l
y
,
an
d
m
et
h
o
d
o
f
c
u
r
r
e
n
t
c
o
n
t
r
o
l
u
s
e
d
t
o
c
o
n
v
e
r
t
p
u
ls
e
g
e
n
e
r
ati
o
n
f
o
r
t
h
e
i
n
v
er
te
r
.
T
h
e
m
o
r
e
a
d
v
a
n
ce
d
th
e
tec
h
n
i
q
u
es
em
p
l
o
y
e
d
,
t
h
e
m
o
r
e
p
r
ec
is
e
a
n
d
ef
f
ec
ti
v
e
t
h
e
o
u
tc
o
m
es
[
16
]
,
[
17
].
T
h
is
p
ap
er
s
h
ed
s
lig
h
t
o
n
t
h
e
to
p
ic
o
f
en
e
r
g
y
q
u
ality
u
s
in
g
cu
ttin
g
-
e
d
g
e
tec
h
n
iq
u
e
s
f
o
u
n
d
in
liter
atu
r
e
k
n
o
w
n
f
o
r
th
eir
p
r
e
cisi
o
n
an
d
q
u
ick
r
esp
o
n
s
e.
T
h
e
d
etailed
p
r
esen
tatio
n
o
f
t
h
e
s
h
u
n
t
ac
tiv
e
p
o
wer
f
ilter
-
p
h
o
to
v
o
ltaic
o
r
SAPF
-
PV
in
clu
d
ed
tr
ac
k
in
g
th
e
m
ax
im
u
m
p
o
i
n
t
u
s
in
g
f
u
zz
y
lo
g
ic
co
n
tr
o
l
(
FLC)
tech
n
iq
u
es
a
n
d
d
eter
m
in
i
n
g
r
e
f
er
en
ce
cu
r
r
e
n
ts
th
r
o
u
g
h
a
m
o
d
if
ied
s
y
n
c
h
r
o
n
o
u
s
r
ef
er
e
n
ce
f
r
am
e
s
tr
ateg
y
.
T
o
m
an
ag
e
t
h
e
tr
ac
k
in
g
o
f
r
e
f
er
e
n
ce
cu
r
r
en
ts
a
p
r
e
d
ictiv
e
c
o
n
t
r
o
l
s
tr
ateg
y
was
im
p
lem
e
n
ted
.
Stu
d
y
was
ca
r
r
ied
out
in
th
r
ee
c
ases
.
C
ase
0
1
is
ab
o
u
t
p
er
f
o
r
m
an
ce
SAPF
-
PV
u
n
d
er
th
e
b
alan
ce
d
c
o
n
d
itio
n
o
f
th
e
g
r
id
v
o
ltag
es
.
C
ase
0
2
is
ab
o
u
t
p
er
f
o
r
m
an
ce
SAPF
-
P
V
u
n
d
er
t
h
e
u
n
b
alan
c
ed
co
n
d
itio
n
o
f
th
e
g
r
i
d
v
o
ltag
es
wh
ile
c
ase
0
3
is
ab
o
u
t
p
e
r
f
o
r
m
an
ce
SAPF
-
PV
u
n
d
er
t
h
e
d
is
to
r
ted
c
o
n
d
itio
n
o
f
th
e
g
r
i
d
v
o
ltag
es.
2.
G
E
NE
R
AL
S
YST
E
M
T
h
e
s
y
s
tem
an
al
y
ze
d
in
t
h
is
s
tu
d
y
,
as
s
h
o
wn
in
Fig
u
r
e
1
(
s
ee
Ap
p
en
d
ix
)
,
is
p
r
im
ar
ily
c
o
m
p
o
s
ed
o
f
f
o
u
r
ess
en
tial
elem
en
ts
.
F
ir
s
tl
y
,
a
3
-
p
h
ase
elec
tr
ical
g
r
id
;
s
ec
o
n
d
ly
,
a
co
m
b
in
atio
n
o
f
lin
ea
r
an
d
n
o
n
-
lin
ea
r
lo
ad
s
;
an
d
th
ir
d
ly
,
a
p
h
o
t
o
v
o
lt
aic
s
y
s
tem
co
n
n
ec
ted
to
a
b
o
o
s
t
co
n
v
er
ter
,
wh
o
s
e
m
ax
im
u
m
p
o
in
t
is
tr
ac
k
ed
b
y
a
f
u
zz
y
lo
g
ic
co
n
tr
o
l.
T
h
is
p
r
o
ce
s
s
is
in
ten
d
ed
to
en
s
u
r
e
a
s
u
p
p
ly
o
f
s
u
itab
le
v
o
ltag
e
to
p
o
wer
th
e
f
o
u
r
t
h
elem
en
t,
wh
ich
is
a
SAPF
co
n
tr
o
lled
b
y
an
MPC
s
tr
ateg
y
.
3.
P
V
SYST
E
M
T
h
e
p
h
o
t
o
v
o
l
t
a
i
c
p
o
w
e
r
g
e
n
e
r
a
t
i
o
n
s
y
s
t
e
m
r
el
i
es
o
n
t
w
o
m
a
i
n
c
o
m
p
o
n
e
n
t
s
.
Fi
r
s
t
,
t
h
e
s
o
la
r
p
a
n
e
l
s
,
m
a
d
e
f
r
o
m
s
i
l
i
c
o
n
j
u
n
c
t
i
o
n
s
,
a
r
e
c
o
n
f
i
g
u
r
e
d
i
n
e
i
t
h
e
r
s
e
r
i
e
s
,
p
a
r
a
l
l
e
l
,
o
r
a
c
o
m
b
i
n
a
t
i
o
n
o
f
b
o
t
h
.
T
h
e
y
p
l
a
y
a
c
r
u
c
i
a
l
r
o
l
e
i
n
t
h
e
s
y
s
t
e
m
b
y
g
e
n
e
r
a
t
i
n
g
v
o
l
t
a
g
e
.
T
h
e
s
e
c
o
n
d
c
o
m
p
o
n
e
n
t
i
s
t
h
e
b
o
o
s
t
c
o
n
v
e
r
t
e
r
,
w
h
i
c
h
n
o
t
o
n
l
y
e
n
h
a
n
c
e
s
t
h
e
i
n
p
u
t
v
o
l
t
a
g
e
b
u
t
a
l
s
o
r
e
g
u
l
a
te
s
f
l
u
ct
u
a
t
i
o
n
s
i
n
p
h
o
t
o
v
o
l
t
a
i
c
v
o
l
t
a
g
e
.
T
h
e
d
i
r
e
ct
c
u
r
r
e
n
t
c
o
n
v
e
r
t
e
r
i
s
c
o
n
t
r
o
l
l
e
d
b
y
a
n
M
P
PT
c
o
n
t
r
o
ll
e
r
,
w
h
i
c
h
t
r
a
c
k
s
t
h
e
p
e
a
k
p
o
we
r
u
n
d
e
r
s
u
d
d
e
n
c
h
a
n
g
e
s
i
n
r
a
d
i
a
t
i
o
n
[
1
8
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
278
-
286
280
3
.
1
.
P
V
p
a
nel
A
s
o
lar
p
an
el
is
m
a
d
e
u
p
o
f
a
co
llectio
n
o
f
s
o
lar
ce
lls
th
at
f
u
n
ctio
n
as
r
e
ce
iv
er
s
f
o
r
s
u
n
li
g
h
t.
T
h
ese
ce
lls
ar
e
in
ter
co
n
n
ec
ted
with
in
a
s
p
ec
if
ic
f
r
a
m
e
an
d
a
r
e
co
n
n
ec
ted
eith
er
in
s
er
ies
o
r
in
p
a
r
allel.
So
lar
p
a
n
els
f
o
r
m
t
h
e
ess
en
tial
elem
en
t
in
a
s
o
lar
e
n
er
g
y
s
y
s
tem
[
1
9
]
.
T
h
e
s
in
g
le
-
d
i
o
d
e
m
o
d
el
is
wi
d
ely
u
s
ed
in
s
o
lar
p
an
el
m
o
d
ellin
g
b
ec
a
u
s
e
o
f
its
ex
ce
llen
t p
er
f
o
r
m
an
ce
.
An
eq
u
iv
alen
t c
ir
cu
it d
ia
g
r
am
is
p
r
e
s
en
ted
in
Fig
u
r
e
2
.
T
o
f
in
d
th
e
lo
ad
c
u
r
r
en
t
th
e
s
in
g
le
-
d
io
d
e
m
o
d
el
ca
n
b
e
ch
a
r
ac
ter
ized
u
s
in
g
Kir
ch
h
o
f
f
'
s
l
aw
cu
r
r
en
t
as in
(
1
)
.
=
ℎ
−
−
+
×
(
1
)
W
h
er
e
I
ph
is
th
e
p
h
o
t
o
c
u
r
r
en
t;
I
D
is
th
e
cu
r
r
en
t
th
r
o
u
g
h
d
io
d
e;
V
pv
r
e
p
r
esen
ts
PV
ce
ll
v
o
ltag
e;
R
s
is
s
er
ies;
an
d
R
p
is
th
e
p
ar
allel
r
esis
tan
ce
o
f
th
e
PV c
ell.
T
h
e
p
h
o
to
cu
r
r
en
t,
I
ph
ca
n
b
e
wr
itten
as in
(
2
)
.
ℎ
=
[
ℎ
+
(
−
)
]
(
2
)
W
h
er
e
T
cell
an
d
T
ref
r
ep
r
esen
t
PV
c
ell
an
d
s
tan
d
ar
d
tem
p
er
atu
r
es
in
k
elv
i
n
;
G
d
en
o
tes
is
o
latio
n
;
an
d
µ
sc
r
ep
r
esen
ts
tem
p
er
atu
r
e
co
ef
f
ic
ien
t
.
Fig
u
r
e
2
.
E
q
u
iv
alen
t c
ir
c
u
it o
f
a
s
o
lar
ce
ll
3
.
2
.
M
P
P
T
co
ntr
o
ller
des
ig
n
FLC
is
o
n
e
o
f
t
h
e
m
o
s
t
f
am
o
u
s
a
r
t
if
ici
al
i
n
t
ell
ig
e
n
ce
-
b
as
ed
s
ch
em
es
i
n
c
o
n
tr
o
l
u
n
i
ts
d
u
e
to
its
h
i
g
h
an
d
e
x
ce
l
le
n
t
p
e
r
f
o
r
m
a
n
c
e
a
n
d
l
o
w
co
m
p
le
x
i
ty
in
p
r
o
g
r
am
i
m
p
le
m
e
n
t
ati
o
n
.
I
t
is
b
ase
d
o
n
t
h
r
ee
i
m
p
o
r
t
a
n
t
s
tep
s
:
f
u
zz
i
f
i
ca
t
io
n
,
r
u
l
e
e
v
a
lu
ati
o
n
,
an
d
d
e
f
u
zz
if
ic
ati
o
n
.
I
n
t
h
e
f
u
zz
if
ic
ati
o
n
s
ta
g
e
,
t
h
e
m
ea
s
u
r
e
d
c
h
a
n
g
es
i
n
th
e
p
h
o
to
v
o
lt
aic
o
u
t
p
u
t
c
u
r
r
e
n
t
a
n
d
v
o
lta
g
e
a
r
e
u
s
e
d
t
o
d
e
te
r
m
i
n
e
th
e
m
e
m
b
e
r
s
h
ip
f
u
n
ct
io
n
s
(
MFs
)
o
f
t
h
e
F
L
C
-
b
as
ed
MP
PT
c
o
n
t
r
o
l u
n
it
.
D
u
r
i
n
g
t
h
e
r
u
le
ev
al
u
a
ti
o
n
s
t
ag
e,
t
h
e
co
n
t
r
o
l
p
r
o
c
e
d
u
r
e
is
d
et
e
r
m
i
n
e
d
d
e
p
e
n
d
s
o
n
th
e
lin
g
u
is
t
ic
r
u
l
es
o
f
FLC
,
as
ill
u
s
tr
a
te
d
in
t
h
e
T
a
b
l
e
1
[
2
0
]
,
[
2
1
]
.
I
n
t
h
e
d
e
f
u
zz
if
ica
ti
o
n
s
t
a
g
e
o
f
t
h
e
F
L
c
o
n
tr
o
l
u
n
it
,
t
h
e
e
x
p
ec
te
d
v
a
lu
e
o
f
t
h
e
MF
o
u
t
p
u
t
is
o
b
t
ai
n
e
d
an
d
f
e
d
i
n
t
o
th
e
r
es
t
o
f
t
h
e
s
y
s
t
em
.
A
f
u
z
z
y
c
o
n
t
r
o
lle
r
is
d
esi
g
n
e
d
wi
th
tw
o
in
p
u
ts
a
n
d
o
n
e
o
u
t
p
u
t.
F
ig
u
r
e
3
il
lu
s
t
r
at
es
t
h
e
m
ec
h
an
is
m
o
f
f
u
z
z
y
l
o
g
ic
.
T
h
e
i
n
p
u
t
v
a
r
i
ab
les
a
r
e
t
h
e
e
r
r
o
r
(
E
)
a
n
d
th
e
e
r
r
o
r
c
h
a
n
g
e
(
CE
)
,
as
d
e
f
i
n
ed
i
n
(
3
)
a
n
d
(
4
)
f
o
r
t
h
e
s
a
m
p
li
n
g
t
im
es
(
k
)
.
(
)
=
(
)
−
(
−
1
)
(
)
−
(
−
1
)
(
3
)
(
)
=
(
)
−
(
−
1
)
(
4
)
Fig
u
r
e
3
.
Fu
zz
y
lo
g
ic
s
tr
u
ctu
r
e
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
6
9
4
C
o
n
tr
o
l o
f sh
u
n
t a
ctive
p
o
w
er filter
fo
r
p
o
w
er q
u
a
lity imp
r
o
v
eme
n
ts
w
ith
P
V
s
ystem
…
(
La
r
o
u
ci
Heg
u
ig
)
281
T
ab
le
1
.
T
h
e
r
u
les o
f
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
C
E/
E
NB
NM
NS
ZE
PS
PM
PB
NB
NB
NB
NB
NB
NM
NS
ZE
NM
NB
NB
NB
NM
NS
ZE
PS
NS
NB
NM
NM
NS
ZE
PS
PM
ZE
NB
NM
NS
ZE
PS
PM
PB
PS
NM
NS
ZE
PS
PB
PB
NS
PM
NS
ZE
PS
PM
PB
PB
ZE
PB
PB
ZE
PS
PM
PB
PB
PB
N
o
t
e
:
C
h
a
n
g
e
o
f
Er
r
o
r
/
Er
r
o
r
(
C
E/
E)
N
é
g
a
t
i
f
-
B
i
g
(
N
B
)
,
N
é
g
a
t
i
f
-
M
e
d
i
u
m
(
N
M
)
,
N
é
g
a
t
i
f
-
S
ma
l
l
(
N
S
)
,
Ze
r
o
(
ZE)
,
P
o
si
t
i
f
-
B
i
g
(
P
B
)
,
P
o
si
t
i
f
-
M
e
d
i
u
m (P
M
)
,
P
o
si
t
i
f
-
S
m
a
l
l
(
P
S
)
4.
G
E
NE
R
AT
I
NG
RE
F
E
RE
N
CE
H
ARMON
I
C
CUR
RE
N
T
S (
M
SRF
-
M
E
T
H
O
D)
T
h
is
m
eth
o
d
is
b
ased
o
n
th
e
SR
F
tech
n
iq
u
e
an
d
in
v
o
lv
es
t
h
e
s
im
p
lifie
d
g
en
er
atio
n
o
f
u
n
it
v
ec
to
r
s
r
ath
er
th
an
a
p
h
ase
-
lo
ck
ed
lo
o
p
(
PLL
)
cir
c
u
it
f
o
r
s
y
n
ch
r
o
n
iz
atio
n
p
u
r
p
o
s
es
[
2
2
]
,
[
2
3
]
.
T
h
i
s
m
eth
o
d
h
as
b
ee
n
s
h
o
wn
to
ac
h
iev
e
b
etter
p
er
f
o
r
m
an
ce
ev
en
wh
en
th
e
g
r
id
is
d
is
tu
r
b
ed
o
r
u
n
b
alan
ce
d
.
I
t
in
v
o
lv
es
th
e
tr
an
s
itio
n
f
r
o
m
a
b
alan
ce
d
3
-
p
h
ase
s
y
s
te
m
(
abc
)
to
a
2
-
p
h
ase
s
y
s
tem
(
dq
)
.
T
h
e
tr
a
n
s
itio
n
f
r
o
m
th
e
r
ea
l
(
abc
)
s
y
s
tem
to
th
e
(
)
s
y
s
tem
is
ac
h
iev
ed
th
r
o
u
g
h
th
e
C
lar
k
tr
an
s
f
o
r
m
a
tio
n
in
th
e
f
ix
ed
a
n
d
o
r
th
o
g
o
n
al
(
)
r
ef
er
e
n
ce
f
r
am
e,
f
o
llo
we
d
b
y
a
x
is
r
o
tatio
n
.
B
ased
o
n
th
e
Par
k
tr
a
n
s
f
o
r
m
atio
n
,
th
is
m
eth
o
d
tr
an
s
itio
n
s
th
e
cu
r
r
en
ts
(
,
)
f
r
o
m
th
e
lo
a
d
to
cu
r
r
en
ts
(
,
)
in
a
2
-
p
h
ase
(
dq
)
r
ef
er
en
ce
f
r
am
e.
T
h
is
tr
an
s
f
o
r
m
atio
n
is
ac
h
iev
ed
b
y
th
e
elec
tr
ical
an
g
le
.
Her
e,
we
u
s
e
lo
w
-
p
ass
f
ilter
s
(
L
PF
)
to
m
i
n
im
ize
th
e
v
o
ltag
e
h
ar
m
o
n
ics
o
f
th
e
in
p
u
t sig
n
als,
as
th
ey
a
r
e
ce
n
t
r
al
to
th
e
co
n
t
r
o
l
[
2
4
]
.
T
h
e
b
asic
c
o
n
f
ig
u
r
at
io
n
o
f
th
e
m
u
lti
-
s
p
atial
r
ec
ep
t
iv
e
f
ield
o
r
MSR
F
m
eth
o
d
is
s
h
o
wn
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
B
lo
ck
d
iag
r
am
o
f
M
SR
F d
iag
r
am
5.
M
P
C
S
T
RAT
E
G
Y
F
O
R
CU
RREN
T
CO
NT
RO
L
T
h
e
MPC
d
e
p
e
n
d
s
o
n
o
n
l
y
a
f
i
n
i
te
n
u
m
b
e
r
o
f
p
o
s
s
i
b
le
s
witc
h
i
n
g
s
t
at
es
ca
n
b
e
g
e
n
e
r
ate
d
b
y
a
n
in
v
e
r
t
er
an
d
th
at
s
y
s
t
em
m
o
d
e
ls
ca
n
b
e
u
t
ili
ze
d
i
n
p
r
ed
ict
in
g
t
h
e
b
eh
av
io
r
o
f
t
h
e
v
a
r
i
a
b
le
s
at
e
ac
h
s
wi
tc
h
i
n
g
s
tate
.
T
o
a
p
p
l
y
t
h
e
p
r
o
p
e
r
s
w
itc
h
i
n
g
s
ta
te
,
a
s
el
ec
t
io
n
c
r
ite
r
i
o
n
m
u
s
t
b
e
d
e
f
i
n
e
d
.
T
h
is
s
e
lect
io
n
cr
ite
r
i
o
n
is
ex
p
r
ess
e
d
in
t
h
e
f
o
r
m
o
f
a
c
o
s
t
f
u
n
ct
io
n
,
w
h
i
ch
wil
l
b
e
d
e
t
er
m
i
n
e
d
f
o
r
th
e
ex
p
e
ct
ed
v
al
u
es
o
f
th
e
v
a
r
i
ab
les
u
n
d
er
c
o
n
t
r
o
l
[
2
5
]
,
[
2
6
[
.
T
h
e
s
witc
h
i
n
g
s
t
ate
w
h
i
ch
m
in
im
i
ze
s
th
e
co
s
t
f
u
n
cti
o
n
is
c
h
o
s
e
n
.
A
f
u
n
c
ti
o
n
al
s
c
h
e
m
e
o
f
th
e
MPC
u
s
e
d
o
n
cu
r
r
e
n
t
c
o
n
tr
o
l
f
o
r
a
3
-
p
h
as
e
in
v
er
te
r
is
il
lu
s
tr
at
ed
i
n
Fi
g
u
r
e
5
.
T
h
e
f
u
n
d
a
m
e
n
ta
l
s
te
p
s
o
f
th
is
co
n
t
r
o
l
a
p
p
r
o
ac
h
ca
n
b
e
l
im
it
e
d
to
th
r
e
e
s
te
p
s
:
i
)
C
r
ea
ti
n
g
a
m
o
d
el
f
o
r
p
r
e
d
ic
ti
n
g
th
e
f
u
tu
r
e
b
e
h
av
io
r
o
f
v
a
r
i
ab
les
th
r
o
u
g
h
o
u
t
t
im
e
;
ii
)
C
r
ea
ti
n
g
a
c
o
s
t
f
u
n
cti
o
n
to
c
o
m
p
u
t
e
t
h
e
d
i
f
f
er
e
n
ce
b
etw
ee
n
th
e
m
o
d
el
a
n
d
its
r
e
f
e
r
e
n
c
e
v
al
u
e
;
a
n
d
iii
)
Fi
n
all
y
,
t
h
e
b
est
p
e
r
f
o
r
m
a
n
ce
is
a
ch
i
ev
ed
b
y
r
e
d
u
ci
n
g
th
e
c
o
s
t
f
u
n
c
tio
n
.
5
.
1
.
I
nv
er
t
er
m
o
del
T
h
e
2
-
l
e
v
e
l
i
n
s
u
l
a
t
e
d
-
g
at
e
b
i
p
o
l
a
r
t
r
a
n
s
i
s
t
o
r
(
I
G
B
T
)
-
b
as
e
d
3
-
p
h
a
s
e
v
o
l
t
a
g
e
i
n
v
e
r
t
e
r
a
r
e
c
o
m
p
o
s
e
d
o
f
s
i
x
b
i
d
i
r
e
c
ti
o
n
a
l
c
u
r
r
e
n
t
s
wi
t
ch
e
s
(
c
o
n
t
r
o
l
l
e
d
f
o
r
t
u
r
n
-
o
n
a
n
d
t
u
r
n
-
o
f
f
)
c
o
n
d
u
c
t
i
n
g
c
u
r
r
e
n
t
i
n
b
o
t
h
d
i
r
e
c
t
i
o
n
s
t
h
r
o
u
g
h
a
n
t
i
-
p
a
r
a
l
l
e
l
d
i
o
d
es
.
Us
u
a
l
l
y
,
it
is
c
o
n
n
e
c
t
e
d
t
o
t
w
o
p
a
s
s
i
v
e
s
t
a
g
e
s
—
o
n
e
o
n
t
h
e
AC
s
i
d
e
a
n
d
o
n
e
o
n
t
h
e
D
C
s
i
d
e
.
T
h
e
p
a
s
s
i
v
e
s
t
a
g
e
o
n
t
h
e
A
C
s
i
d
e
p
r
i
m
a
r
i
l
y
s
e
r
v
es
f
o
r
f
i
l
t
e
r
i
n
g
a
n
d
i
s
c
o
m
p
o
s
e
d
o
f
o
u
t
p
u
t
i
n
d
u
c
t
a
n
c
e
[
2
7
[
.
T
h
e
o
u
t
p
u
t
v
o
l
t
a
g
e
c
a
n
b
e
d
e
s
c
r
i
b
e
d
as
a
s
p
a
ce
v
e
c
t
o
r
i
n
a
s
t
at
i
o
n
a
r
y
f
r
a
m
e
(
αβ
)
a
c
c
o
r
d
in
g
t
o
t
h
e
(
5
)
.
=
+
+
(
5
)
W
h
er
e
R
f
an
d
L
f
r
ef
e
r
to
th
e
v
alu
es
o
f
th
e
f
ilter
'
s
r
esis
tan
ce
an
d
in
d
u
ctan
ce
,
i
αβ
r
ef
er
s
to
t
h
e
cu
r
r
e
n
t
p
ass
in
g
th
r
o
u
g
h
th
e
f
ilter
,
v
αβ
is
th
e
v
o
ltag
e
ca
r
r
ier
o
u
tp
u
t b
y
th
e
SA
PF
,
an
d
e
αβ
is
th
e
esti
m
ated
b
ac
k
-
em
f
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
278
-
286
282
Fig
u
r
e
5
.
Pre
d
ictiv
e
cu
r
r
e
n
t c
o
n
tr
o
l f
u
n
ctio
n
al
d
ia
g
r
am
5
.
2
.
Dis
cr
et
e
-
t
im
e
mo
del f
o
r
pre
dict
io
n
T
h
e
k
e
y
o
f
MPC
tech
n
iq
u
e
lies
in
u
n
d
er
s
tan
d
in
g
th
e
p
r
o
p
er
m
ec
h
an
is
m
to
tr
ac
k
th
e
m
ea
s
u
r
ed
cu
r
r
en
t
o
f
th
e
f
ilter
an
d
its
r
ef
er
en
ce
th
r
o
u
g
h
o
u
t
th
e
s
am
p
lin
g
p
er
io
d
.
T
o
ac
h
ie
v
e
g
o
o
d
r
esu
lts
an
d
h
ig
h
p
r
ec
is
io
n
p
er
f
o
r
m
an
ce
,
a
d
is
c
r
ete
-
tim
e
m
o
d
el
is
r
eq
u
ir
ed
[
2
8
[
,
b
y
ap
p
l
y
in
g
a
d
is
cr
ete
tim
e
m
o
d
el
d
u
r
in
g
th
e
s
am
p
lin
g
tim
e
T
s
an
d
d
e
p
en
d
s
o
n
t
h
e
E
u
ler
ap
p
r
o
x
im
atio
n
o
f
(
5
)
,
th
e
f
u
tu
r
e
v
alu
e
o
f
th
e
f
i
lter
cu
r
r
en
t
at
tim
e
(
k+1
)
ca
n
b
e
p
r
e
d
icted
as
in
(
6
)
.
(
+
1
)
=
(
1
−
)
(
)
+
(
(
)
−
̂
(
)
)
(
6
)
Fro
m
(
6
)
,
we
ex
tr
ac
t th
e
esti
m
ated
b
ac
k
-
em
f
as
in
(
7
)
:
̂
(
−
1
)
=
(
−
1
)
−
(
)
−
(
−
)
(
−
1
)
(
7
)
wh
er
e
̂
(
−
1
)
is
th
e
esti
m
ated
v
alu
e
o
f
̂
(
)
.
5
.
3
.
Co
s
t
f
un
ct
io
n
T
h
e
er
r
o
r
b
etwe
en
th
e
r
ef
er
en
ce
cu
r
r
en
ts
an
d
p
r
ed
icted
cu
r
r
en
ts
at
s
am
p
lin
g
tim
e
is
ev
alu
ated
th
r
o
u
g
h
th
e
co
s
t
f
u
n
ctio
n
.
T
h
i
s
f
u
n
ctio
n
ca
n
b
e
ex
p
r
ess
ed
b
y
s
ev
er
al
an
aly
tical
ex
p
r
ess
io
n
s
[
2
9
[
.
I
n
o
u
r
s
tu
d
y
,
we
in
tr
o
d
u
ce
a
n
ex
p
r
ess
io
n
f
o
r
th
is
f
u
n
ctio
n
,
wh
ich
is
d
ef
i
n
e
d
b
y
u
s
in
g
th
e
f
o
r
m
i
n
(
8
)
:
=
|
∗
(
+
1
)
−
(
+
1
)
|
+
|
∗
(
+
1
)
−
(
+
1
)
|
(
8
)
wh
er
e
∗
(
+
1
)
an
d
∗
(
+
1
)
r
ep
r
esen
t
th
e
r
ea
l
an
d
im
ag
in
ar
y
co
m
p
o
n
en
ts
o
f
th
e
r
ef
er
e
n
ce
cu
r
r
e
n
t,
an
d
(
+
1
)
an
d
(
+
1
)
also
r
ep
r
esen
t
th
e
r
ea
l
an
d
im
ag
in
a
r
y
c
o
m
p
o
n
en
ts
o
f
th
e
p
r
e
d
ictiv
e
cu
r
r
en
t.
T
h
e
f
lo
wch
ar
t o
f
th
e
alg
o
r
ith
m
o
f
MPC
f
o
r
th
e
SAPF
is
s
h
o
wn
i
n
Fig
u
r
e
6
.
Fig
u
r
e
6
.
Step
s
o
f
th
e
p
r
e
d
ictiv
e
cu
r
r
e
n
t c
o
n
tr
o
l
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
6
9
4
C
o
n
tr
o
l o
f sh
u
n
t a
ctive
p
o
w
er filter
fo
r
p
o
w
er q
u
a
lity imp
r
o
v
eme
n
ts
w
ith
P
V
s
ystem
…
(
La
r
o
u
ci
Heg
u
ig
)
283
6.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
T
o
ev
alu
ate
th
e
ef
f
icien
cies
o
f
th
e
SAPF
p
o
wer
ed
b
y
a
PV
g
en
er
ato
r
u
s
in
g
th
e
MPC
ap
p
r
o
ac
h
,
we
u
tili
ze
d
MA
T
L
AB
/Si
m
u
li
n
k
s
o
f
twar
e
to
p
r
esen
t
in
d
etail
th
e
r
esu
lts
o
f
o
u
r
wo
r
k
with
p
ar
am
eter
s
lis
ted
i
n
T
ab
le
2
.
W
e
will
b
eg
in
b
y
co
m
p
ar
in
g
th
e
p
er
f
o
r
m
an
c
e
o
f
f
u
zz
y
co
n
tr
o
l
with
th
e
tr
ad
itio
n
al
P&
O
m
eth
o
d
u
n
d
e
r
th
e
in
f
lu
e
n
ce
o
f
s
u
d
d
en
c
h
an
g
es
i
n
s
h
ad
e
an
d
tem
p
er
atu
r
e
as
in
Fig
u
r
e
s
7
(
a)
an
d
7
(b
)
.
Als
o
,
th
e
s
y
s
tem
's
o
v
er
all
p
er
f
o
r
m
an
ce
will
b
e
d
em
o
n
s
tr
ated
u
n
d
er
s
ev
er
al
o
p
er
atin
g
c
o
n
d
i
tio
n
s
,
as
s
h
o
wn
in
Fig
u
r
e
s
8
(
a)
-
8
(
c)
.
T
ab
le
2
.
Par
am
eter
s
o
f
th
e
s
im
u
latio
n
SAPF
P
a
r
a
me
t
e
r
V
a
l
u
e
P
a
r
a
me
t
e
r
V
a
l
u
e
V
s
,
f
s
2
2
0
V
,
5
0
H
z
R
f
,
L
f
5
m
Ω
,
5
mH
R
s
,
L
s
2
5
m
Ω
,
1
9
.
6
µH
R
,
L
2
6
Ω
,
5
mH
R
c
,
L
c
1
.
2
m
Ω
,
0
.
3
mH
K
i
,
K
p
0
.
5
6
,
0
.
5
2
V
dc
,
C
dc
8
0
0
V
,
2
3
5
0
µF
(
a)
(
b
)
Fig
u
r
e
7
.
Po
wer
o
f
th
e
p
h
o
to
v
o
ltaic
g
en
er
ato
r
with
P&
O
an
d
FLC co
n
tr
o
ls
f
o
r
:
(
a)
T
=2
5
°C
; E
=5
0
0
-
1
0
0
0
W
/m
2
an
d
(
b
)
T
=2
5
-
50
°C
; E
=1
0
0
0
W
/m
2
(
a)
(
b
)
(
c)
F
i
g
u
r
e
8
.
S
A
P
F
s
i
m
u
l
a
t
i
o
n
r
e
s
u
l
t
s
:
(
a
)
b
a
l
a
n
c
e
d
s
i
n
u
s
o
i
d
a
l
g
r
i
d
v
o
l
t
a
g
e
,
(
b
)
u
n
b
a
l
a
n
c
e
d
g
r
i
d
,
a
n
d
(
c
)
d
i
s
t
o
r
t
e
d
g
r
i
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
278
-
286
284
T
h
e
s
im
u
latio
n
r
esu
lts
wer
e
o
b
tain
ed
f
o
r
a
PV
m
o
d
u
le
u
n
it
with
th
e
ch
ar
ac
ter
is
tics
(
P
max
=
150
W
,
V
max
=
3
5
.
5
V
,
I
max
=
4
.
3
4
A
,
I
sc
=
5
.
5
A
,
an
d
V
oc
=
45
V)
an
d
d
e
m
o
n
s
tr
ated
th
at
t
h
e
P&
O
alg
o
r
ith
m
is
r
elativ
ely
ea
s
y
to
ap
p
ly
,
b
u
t
i
t
ten
d
s
to
o
s
cillate
ar
o
u
n
d
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
d
u
e
to
its
p
er
tu
r
b
ativ
e
n
atu
r
e.
T
h
is
b
eh
av
io
r
ca
n
ca
u
s
e
s
y
s
tem
in
s
tab
ilit
y
an
d
r
ed
u
ce
th
e
ef
f
icien
cy
o
f
MPPT.
On
th
e
o
th
er
h
an
d
,
f
u
zz
y
co
n
tr
o
l
h
as
s
h
o
wn
r
em
ar
k
ab
ly
im
p
r
ess
iv
e
r
esu
lts
co
m
p
ar
ed
to
P&
O,
o
f
f
er
in
g
a
b
etter
r
esp
o
n
s
e
tim
e
th
an
P&
O
co
n
tr
o
l.
Fu
r
th
er
m
o
r
e,
if
th
e
m
ax
im
u
m
p
o
i
n
t
is
ac
h
iev
ed
,
f
u
zz
y
co
n
tr
o
l
r
e
m
ain
s
clo
s
er
to
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
th
an
P&
O
co
n
tr
o
l
i
n
b
o
th
ca
s
es
(
a
an
d
b
)
.
T
h
is
s
tab
ilit
y
en
s
u
r
e
s
a
co
n
s
tan
t
v
o
ltag
e
s
u
p
p
ly
f
o
r
p
o
wer
in
g
th
e
in
v
er
t
er
u
s
ed
in
f
iltra
tio
n
.
T
h
e
r
esu
lts
s
h
o
w
a
n
o
ticea
b
l
e
d
is
to
r
tio
n
i
n
th
e
lo
ad
c
u
r
r
e
n
t
d
u
e
to
th
e
n
o
n
-
lin
ea
r
lo
ad
.
Ho
wev
er
,
wh
en
th
e
SAPF
cu
r
r
en
t
is
in
je
cted
in
to
th
e
g
r
id
,
th
e
g
r
id
cu
r
r
en
t
r
eg
ain
s
its
o
r
ig
in
al
s
h
ap
e
ac
r
o
s
s
all
o
u
r
ca
s
es
(
a,
b
,
an
d
c
)
as
s
h
o
wn
in
Fig
u
r
es
8
an
d
9
.
Fu
r
t
h
er
m
o
r
e,
in
Fig
u
r
e
1
0
,
th
e
v
o
ltag
e
o
f
th
e
D
C
-
DC
co
n
v
er
ter
V
dc
p
r
ec
is
ely
f
o
llo
ws
its
r
ef
er
en
ce
,
with
v
er
y
litt
le
d
ev
iatio
n
f
r
o
m
th
e
r
ef
er
e
n
ce
v
alu
e.
Ad
d
iti
o
n
ally
,
t
h
e
a
n
aly
s
is
o
f
th
e
s
p
ec
tr
u
m
in
Fig
u
r
e
1
1
in
d
icate
s
a
s
ig
n
if
ican
t
d
ec
r
ea
s
e
in
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
o
f
th
e
g
r
id
c
u
r
r
en
t.
Gr
id
cu
r
r
e
n
t
T
H
D
h
as
b
ee
n
m
in
im
ized
f
r
o
m
2
8
.
5
6
%
to
1
.
6
1
%,
it
ca
n
b
e
n
o
t
ed
f
r
o
m
th
is
v
alu
e
th
at
T
HD
o
f
g
r
i
d
cu
r
r
en
t
is
r
estricte
d
as
p
er
I
E
E
E
-
5
1
9
s
ta
n
d
ar
d
.
I
t
ca
n
t
h
er
ef
o
r
e
b
e
c
o
n
clu
d
ed
t
h
at,
u
n
d
er
th
ese
co
n
d
itio
n
s
,
th
is
m
eth
o
d
is
s
u
itab
le
an
d
allo
ws
f
o
r
th
e
c
o
r
r
ec
t
id
e
n
tific
atio
n
o
f
th
e
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
o
f
th
e
lo
a
d
cu
r
r
en
ts
.
Fig
u
r
e
9
.
Fil
ter
cu
r
r
en
t
Fig
u
r
e
1
0
.
DC
-
lin
k
v
o
ltag
e
Fig
u
r
e
1
1
.
Har
m
o
n
ic
s
p
ec
t
r
u
m
o
f
g
r
i
d
cu
r
r
en
t p
h
ase
-
a
6.
CO
NCLU
SI
O
N
T
h
is
p
a
p
e
r
p
r
o
p
o
s
e
d
a
p
h
o
t
o
v
o
lt
aic
(
P
V)
in
te
r
f
ac
e
tw
o
-
l
ev
e
l
v
o
lt
a
g
e
s
o
u
r
ce
i
n
v
er
te
r
-
b
ase
d
3
-
p
h
as
e
s
h
u
n
t
a
cti
v
e
p
o
we
r
f
i
lte
r
to
e
n
h
a
n
c
e
p
o
we
r
q
u
alit
y
u
n
d
e
r
id
e
al
as w
ell
as
n
o
n
-
i
d
e
al
g
r
i
d
v
o
l
tag
e
c
o
n
d
i
ti
o
n
s
.
T
h
e
in
t
er
est
o
f
t
h
is
s
y
s
t
em
lies
in
th
e
m
in
im
i
za
ti
o
n
o
f
en
v
i
r
o
n
m
e
n
ta
l
p
o
ll
u
ti
o
n
b
y
a
d
d
in
g
a
r
e
n
e
wa
b
l
e
e
n
e
r
g
y
s
o
u
r
ce
P
V
t
o
an
SAPF
t
o
ass
u
r
e
g
o
o
d
p
o
w
er
q
u
alit
y
in
t
h
i
s
in
s
tal
lati
o
n
.
T
o
e
n
h
a
n
ce
t
h
e
p
e
r
f
o
r
m
a
n
c
e
o
f
t
h
e
SAPF
,
M
SR
F
t
h
e
o
r
y
an
d
P
I
r
eg
u
l
at
o
r
a
r
e
i
n
c
o
r
p
o
r
a
te
d
.
T
h
e
r
e
f
e
r
e
n
ce
cu
r
r
e
n
t
f
o
r
c
o
m
p
e
n
s
ati
o
n
is
g
e
n
e
r
a
te
d
u
s
i
n
g
MSR
F
t
h
e
o
r
y
,
a
n
d
th
e
co
n
t
r
o
l
f
o
r
t
h
e
m
ai
n
t
e
n
a
n
c
e
o
f
s
m
o
o
th
DC
li
n
k
v
o
lt
ag
e
is
p
r
o
v
i
d
e
d
b
y
t
h
e
P
I
r
e
g
u
la
to
r
.
I
n
a
d
d
iti
o
n
,
f
o
r
t
h
e
p
u
r
p
o
s
e
o
f
s
u
p
p
r
ess
i
n
g
th
e
h
a
r
m
o
n
i
cs
in
t
h
e
s
y
s
t
em
,
th
e
MPC
a
p
p
r
o
a
c
h
is
em
p
l
o
y
e
d
t
o
c
o
n
tr
o
l
s
h
u
n
t
a
cti
v
e
p
o
we
r
f
ilt
er
d
u
e
t
o
i
ts
s
im
p
l
icit
y
.
T
h
e
s
i
m
u
la
ti
o
n
r
es
u
l
ts
o
b
ta
in
e
d
c
o
n
f
i
r
m
t
h
e
ef
f
e
cti
v
e
n
ess
a
n
d
p
er
f
o
r
m
a
n
ce
im
p
r
o
v
em
e
n
t
o
f
th
e
p
r
o
p
o
s
e
d
s
ch
em
e
u
n
d
e
r
v
a
r
i
o
u
s
g
r
i
d
v
o
lt
ag
e
co
n
d
it
io
n
s
.
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
6
9
4
C
o
n
tr
o
l o
f sh
u
n
t a
ctive
p
o
w
er filter
fo
r
p
o
w
er q
u
a
lity imp
r
o
v
eme
n
ts
w
ith
P
V
s
ystem
…
(
La
r
o
u
ci
Heg
u
ig
)
285
AP
P
E
NDI
X
Fig
u
r
e
1
.
C
o
m
p
r
eh
en
s
iv
e
s
y
s
t
em
p
lan
RE
F
E
R
E
NC
E
S
[
1
]
Y
.
D
u
a
n
,
Y
.
Z
h
a
o
,
a
n
d
J.
H
u
,
“
A
n
i
n
i
t
i
a
l
i
z
a
t
i
o
n
-
f
r
e
e
d
i
s
t
r
i
b
u
t
e
d
a
l
g
o
r
i
t
h
m
f
o
r
d
y
n
a
m
i
c
e
c
o
n
o
mi
c
d
i
s
p
a
t
c
h
p
r
o
b
l
e
ms
i
n
m
i
c
r
o
g
r
i
d
:
M
o
d
e
l
i
n
g
,
o
p
t
i
mi
z
a
t
i
o
n
a
n
d
a
n
a
l
y
s
i
s,
”
S
u
st
a
i
n
a
b
l
e
En
e
r
g
y
,
G
ri
d
s
a
n
d
N
e
t
w
o
rks
,
v
o
l
.
3
4
,
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
se
g
a
n
.
2
0
2
3
.
1
0
1
0
0
4
.
[
2
]
C
.
Y
a
n
,
Y
.
Z
o
u
,
Z
.
W
u
,
a
n
d
A
.
M
a
l
e
k
i
,
“
Ef
f
e
c
t
o
f
v
a
r
i
o
u
s
d
e
s
i
g
n
c
o
n
f
i
g
u
r
a
t
i
o
n
s
a
n
d
o
p
e
r
a
t
i
n
g
c
o
n
d
i
t
i
o
n
s
f
o
r
o
p
t
i
mi
z
a
t
i
o
n
o
f
a
w
i
n
d
/
s
o
l
a
r
/
h
y
d
r
o
g
e
n
/
f
u
e
l
c
e
l
l
h
y
b
r
i
d
mi
c
r
o
g
r
i
d
sy
s
t
e
m
b
y
a
b
i
o
-
i
n
s
p
i
r
e
d
a
l
g
o
r
i
t
h
m,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
H
y
d
r
o
g
e
n
E
n
e
r
g
y
,
v
o
l
.
6
0
,
p
p
.
3
7
8
–
3
9
1
,
M
a
r
.
2
0
2
4
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
i
j
h
y
d
e
n
e
.
2
0
2
4
.
0
2
.
0
0
4
.
[
3
]
S
.
O
u
c
h
e
n
,
S
.
A
b
d
e
d
d
a
i
m,
A
.
B
e
t
k
a
,
a
n
d
A
.
M
e
n
a
d
i
,
“
Ex
p
e
r
i
me
n
t
a
l
v
a
l
i
d
a
t
i
o
n
o
f
sl
i
d
i
n
g
mo
d
e
-
p
r
e
d
i
c
t
i
v
e
d
i
r
e
c
t
p
o
w
e
r
c
o
n
t
r
o
l
o
f
a
g
r
i
d
c
o
n
n
e
c
t
e
d
p
h
o
t
o
v
o
l
t
a
i
c
s
y
s
t
e
m,
f
e
e
d
i
n
g
a
n
o
n
l
i
n
e
a
r
l
o
a
d
,
”
S
o
l
a
r
En
e
rg
y
,
v
o
l
.
1
3
7
,
p
p
.
3
2
8
–
3
3
6
,
2
0
1
6
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
so
l
e
n
e
r
.
2
0
1
6
.
0
8
.
0
3
1
.
[
4
]
S
.
O
u
c
h
e
n
,
A
.
B
e
t
k
a
,
S
.
A
b
d
e
d
d
a
i
m
,
a
n
d
R
.
M
e
c
h
o
u
m
a
,
“
D
e
s
i
g
n
a
n
d
e
x
p
e
r
i
m
e
n
t
a
l
v
a
l
i
d
a
t
i
o
n
s
t
u
d
y
o
n
d
i
r
e
c
t
p
o
w
e
r
c
o
n
t
r
o
l
a
p
p
l
i
e
d
o
n
a
c
t
i
v
e
p
o
w
e
r
f
i
l
t
e
r
,
”
2
0
1
6
,
d
o
i
:
1
0
.
1
1
0
9
/
I
EPS
.
2
0
1
6
.
7
5
2
1
8
7
2
.
[
5
]
M
.
M
a
o
,
L.
C
u
i
,
Q
.
Zh
a
n
g
,
K
.
G
u
o
,
L.
Z
h
o
u
,
a
n
d
H
.
H
u
a
n
g
,
“
C
l
a
ssi
f
i
c
a
t
i
o
n
a
n
d
s
u
mm
a
r
i
z
a
t
i
o
n
o
f
s
o
l
a
r
p
h
o
t
o
v
o
l
t
a
i
c
M
P
P
T
t
e
c
h
n
i
q
u
e
s:
A
r
e
v
i
e
w
b
a
s
e
d
o
n
t
r
a
d
i
t
i
o
n
a
l
a
n
d
i
n
t
e
l
l
i
g
e
n
t
c
o
n
t
r
o
l
s
t
r
a
t
e
g
i
e
s,”
En
e
rg
y
R
e
p
o
r
t
s
,
v
o
l
.
6
,
p
p
.
1
3
1
2
–
1
3
2
7
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
e
g
y
r
.
2
0
2
0
.
0
5
.
0
1
3
.
[
6
]
A
.
M
a
h
a
mm
e
d
i
,
A
.
K
o
u
z
o
u
,
A
.
H
a
f
a
i
f
a
,
a
n
d
B
.
Ta
l
b
i
,
“
A
n
e
w
t
e
c
h
n
i
q
u
e
f
o
r
p
h
o
t
o
v
o
l
t
a
i
c
sy
s
t
e
m
e
f
f
i
c
i
e
n
c
y
u
n
d
e
r
f
a
s
t
c
h
a
n
g
i
n
g
so
l
a
r
i
r
r
a
d
i
a
t
i
o
n
,
”
E
EA
-
El
e
c
t
r
o
t
e
h
n
i
c
a
,
El
e
c
t
ro
n
i
c
a
,
Au
t
o
m
a
t
i
c
a
,
v
o
l
.
6
7
,
n
o
.
4
,
p
p
.
1
2
–
1
9
,
2
0
1
9
.
[
7
]
S
.
R
.
K
i
r
a
n
,
M
.
M
u
r
a
l
i
,
C
.
H
u
s
sai
a
n
B
a
s
h
a
,
a
n
d
F
.
F
a
t
h
i
m
a
,
“
D
e
si
g
n
o
f
A
r
t
i
f
i
c
i
a
l
I
n
t
e
l
l
i
g
e
n
c
e
-
B
a
se
d
H
y
b
r
i
d
M
P
P
T
C
o
n
t
r
o
l
l
e
r
s
f
o
r
P
a
r
t
i
a
l
l
y
S
h
a
d
e
d
S
o
l
a
r
P
V
S
y
st
e
m
w
i
t
h
N
o
n
-
i
so
l
a
t
e
d
B
o
o
st
C
o
n
v
e
r
t
e
r
,
”
i
n
C
o
m
p
u
t
e
r
Vi
si
o
n
a
n
d
R
o
b
o
t
i
c
s
:
Al
g
o
r
i
t
h
m
s
f
o
r
I
n
t
e
l
l
i
g
e
n
t
S
y
s
t
e
m
s
,
2
0
2
2
,
p
p
.
3
5
3
–
3
6
3
,
d
o
i
:
1
0
.
1
0
0
7
/
9
7
8
-
981
-
16
-
8
2
2
5
-
4
_
2
8
.
[
8
]
J.
C
.
D
a
s
,
“
P
a
ss
i
v
e
f
i
l
t
e
r
s
-
P
o
t
e
n
t
i
a
l
i
t
i
e
s
a
n
d
l
i
m
i
t
a
t
i
o
n
s,
”
i
n
I
E
EE
C
o
n
f
e
re
n
c
e
Re
c
o
r
d
o
f
An
n
u
a
l
P
u
l
p
a
n
d
Pa
p
e
r
I
n
d
u
s
t
r
y
T
e
c
h
n
i
c
a
l
C
o
n
f
e
r
e
n
c
e
,
2
0
0
3
,
p
p
.
1
8
7
–
1
9
7
,
d
o
i
:
1
0
.
1
1
0
9
/
p
a
p
c
o
n
.
2
0
0
3
.
1
2
1
6
9
1
6
.
[
9
]
M
.
Es
mae
i
l
i
,
H
.
S
h
a
y
e
g
h
i
,
K
.
V
a
l
i
p
o
u
r
,
A
.
S
a
f
a
r
i
,
a
n
d
F
.
S
e
d
a
g
h
a
t
i
,
“
P
o
w
e
r
q
u
a
l
i
t
y
i
m
p
r
o
v
e
m
e
n
t
o
f
mu
l
t
i
mi
c
r
o
g
r
i
d
u
s
i
n
g
i
mp
r
o
v
e
d
c
u
st
o
m p
o
w
e
r
d
e
v
i
c
e
c
a
l
l
e
d
a
s
d
i
st
r
i
b
u
t
e
d
p
o
w
e
r
c
o
n
d
i
t
i
o
n
c
o
n
t
r
o
l
l
e
r
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
T
r
a
n
sa
c
t
i
o
n
s o
n
E
l
e
c
t
ri
c
a
l
E
n
e
r
g
y
S
y
s
t
e
m
s
,
v
o
l
.
3
0
,
n
o
.
3
,
M
a
r
.
2
0
2
0
,
d
o
i
:
1
0
.
1
0
0
2
/
2
0
5
0
-
7
0
3
8
.
1
2
2
5
9
.
[
1
0
]
M
.
S
h
a
f
i
u
l
l
a
h
,
M
.
A
.
M
.
K
h
a
n
,
a
n
d
S
.
D
.
A
h
me
d
,
“
P
Q
d
i
s
t
u
r
b
a
n
c
e
d
e
t
e
c
t
i
o
n
a
n
d
c
l
a
ss
i
f
i
c
a
t
i
o
n
c
o
mb
i
n
i
n
g
a
d
v
a
n
c
e
d
si
g
n
a
l
p
r
o
c
e
ss
i
n
g
a
n
d
m
a
c
h
i
n
e
l
e
a
r
n
i
n
g
t
o
o
l
s
,
”
i
n
Po
w
e
r
Q
u
a
l
i
t
y
i
n
M
o
d
e
r
n
P
o
w
e
r
S
y
s
t
e
m
s
,
E
l
se
v
i
e
r
,
2
0
2
1
,
p
p
.
3
1
1
–
3
3
5
.
[
1
1
]
J.
H
e
,
Y
.
W
.
Li
,
F
.
B
l
a
a
b
j
e
r
g
,
a
n
d
X
.
W
a
n
g
,
“
A
c
t
i
v
e
h
a
r
mo
n
i
c
f
i
l
t
e
r
i
n
g
u
si
n
g
c
u
r
r
e
n
t
-
c
o
n
t
r
o
l
l
e
d
,
g
r
i
d
-
c
o
n
n
e
c
t
e
d
D
G
u
n
i
t
s
w
i
t
h
c
l
o
se
d
-
l
o
o
p
p
o
w
e
r
c
o
n
t
r
o
l
,
”
I
EEE
T
ra
n
s
a
c
t
i
o
n
s
o
n
P
o
w
e
r
El
e
c
t
r
o
n
i
c
s
,
v
o
l
.
2
9
,
n
o
.
2
,
p
p
.
6
4
2
–
6
5
3
,
2
0
1
4
,
d
o
i
:
1
0
.
1
1
0
9
/
TPE
L.
2
0
1
3
.
2
2
5
5
8
9
5
.
[
1
2
]
G
.
S
.
M
a
h
e
sh
,
H
.
M
.
R
a
v
i
K
u
mar,
a
n
d
R
.
P
.
M
a
n
d
i
,
“
C
h
a
r
a
c
t
e
r
i
z
a
t
i
o
n
o
f
p
o
w
e
r
s
y
st
e
m
a
t
t
r
i
b
u
t
e
s
f
o
r
n
o
n
l
i
n
e
a
r
l
o
a
d
s t
h
r
o
u
g
h
s
u
b
-
sp
a
c
e
s
i
g
n
a
l
me
t
h
o
d
s,
”
i
n
I
EE
E
I
n
t
e
r
n
a
t
i
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
P
o
w
e
r
E
l
e
c
t
r
o
n
i
c
s
,
D
ri
v
e
s a
n
d
E
n
e
r
g
y
S
y
st
e
m
s,
P
ED
ES
2
0
1
6
,
2
0
1
7
,
v
o
l
.
2
0
1
6
-
Ja
n
u
a
,
p
p
.
1
–
5
,
d
o
i
:
1
0
.
1
1
0
9
/
P
ED
ES
.
2
0
1
6
.
7
9
1
4
5
6
0
.
[
1
3
]
H
.
K
o
m
u
r
c
u
g
i
l
,
“
D
o
u
b
l
e
-
b
a
n
d
h
y
st
e
r
e
si
s
c
u
r
r
e
n
t
-
c
o
n
t
r
o
l
l
e
d
si
n
g
l
e
-
p
h
a
s
e
s
h
u
n
t
a
c
t
i
v
e
f
i
l
t
e
r
f
o
r
sw
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
mi
t
i
g
a
t
i
o
n
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
E
l
e
c
t
ri
c
a
l
Po
w
e
r
a
n
d
E
n
e
r
g
y
S
y
st
e
m
s
,
v
o
l
.
6
9
,
p
p
.
1
3
1
–
1
4
0
,
2
0
1
5
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
i
j
e
p
e
s
.
2
0
1
5
.
0
1
.
0
1
0
.
[
1
4
]
T.
-
L.
Le
e
a
n
d
S
.
-
H
.
H
u
,
“
A
n
A
c
t
i
v
e
F
i
l
t
e
r
W
i
t
h
R
e
s
o
n
a
n
t
C
u
r
r
e
n
t
C
o
n
t
r
o
l
t
o
S
u
p
p
r
e
ss
H
a
r
mo
n
i
c
R
e
s
o
n
a
n
c
e
i
n
a
D
i
s
t
r
i
b
u
t
i
o
n
P
o
w
e
r
S
y
s
t
e
m
,
”
I
E
EE
J
o
u
rn
a
l
o
f
Em
e
rg
i
n
g
a
n
d
S
e
l
e
c
t
e
d
T
o
p
i
c
s i
n
Po
w
e
r E
l
e
c
t
r
o
n
i
c
s
,
v
o
l
.
4
,
n
o
.
1
,
p
p
.
1
9
8
–
2
0
9
,
M
a
r
.
2
0
1
6
,
d
o
i
:
1
0
.
1
1
0
9
/
JES
TP
E.
2
0
1
5
.
2
4
7
8
1
4
9
.
[
1
5
]
R
.
B
e
l
a
i
d
i
,
M
.
H
a
t
t
i
,
A
.
H
a
d
d
o
u
c
h
e
,
a
n
d
M
.
M
.
L
a
r
a
f
i
,
“
S
h
u
n
t
a
c
t
i
v
e
p
o
w
e
r
f
i
l
t
e
r
c
o
n
n
e
c
t
e
d
t
o
a
p
h
o
t
o
v
o
l
t
a
i
c
a
r
r
a
y
f
o
r
c
o
m
p
e
n
sa
t
i
n
g
h
a
r
mo
n
i
c
s
a
n
d
r
e
a
c
t
i
v
e
p
o
w
e
r
si
m
u
l
t
a
n
e
o
u
sl
y
,
”
I
n
t
e
rn
a
t
i
o
n
a
l
C
o
n
f
e
r
e
n
c
e
o
n
Po
w
e
r
E
n
g
i
n
e
e
ri
n
g
,
En
e
r
g
y
a
n
d
El
e
c
t
r
i
c
a
l
D
r
i
v
e
s
,
p
p
.
1
4
8
2
–
1
4
8
6
,
2
0
1
3
,
d
o
i
:
1
0
.
1
1
0
9
/
P
o
w
e
r
E
n
g
.
2
0
1
3
.
6
6
3
5
8
3
4
.
[
1
6
]
P
.
K
a
n
j
i
y
a
,
V
.
K
h
a
d
k
i
k
a
r
,
a
n
d
H
.
H
.
Z
e
i
n
e
l
d
i
n
,
“
O
p
t
i
m
a
l
c
o
n
t
r
o
l
o
f
s
h
u
n
t
a
c
t
i
v
e
p
o
w
e
r
f
i
l
t
e
r
t
o
me
e
t
I
EEE
S
t
d
.
5
1
9
c
u
r
r
e
n
t
h
a
r
m
o
n
i
c
c
o
n
st
r
a
i
n
t
s
u
n
d
e
r
n
o
n
i
d
e
a
l
s
u
p
p
l
y
c
o
n
d
i
t
i
o
n
,
”
I
EEE
T
r
a
n
s
a
c
t
i
o
n
s
o
n
I
n
d
u
st
r
i
a
l
E
l
e
c
t
r
o
n
i
c
s
,
v
o
l
.
6
2
,
n
o
.
2
,
p
p
.
7
2
4
–
7
3
4
,
2
0
1
5
,
d
o
i
:
1
0
.
1
1
0
9
/
TI
E.
2
0
1
4
.
2
3
4
1
5
5
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
278
-
286
286
[
1
7
]
A
.
S
h
a
h
a
n
d
N
.
P
.
V
a
g
h
e
l
a
,
“
S
h
u
n
t
A
c
t
i
v
e
P
o
w
e
r
F
i
l
t
e
r
f
o
r
P
o
w
e
r
Q
u
a
l
i
t
y
I
m
p
r
o
v
e
m
e
n
t
i
n
D
i
s
t
r
i
b
u
t
i
o
n
S
y
s
t
e
m
s
,
”
I
n
t
e
r
n
a
t
i
o
n
a
l
J
o
u
r
n
a
l
o
f
E
n
g
i
n
e
e
r
i
n
g
D
e
v
e
l
o
p
m
e
n
t
a
n
d
R
e
s
e
a
r
c
h
,
2
0
1
3
,
[
O
n
l
i
n
e
]
.
A
v
a
i
l
a
b
l
e
:
h
t
t
p
s
:
/
/
a
p
i
.
s
e
m
a
n
t
i
c
s
c
h
o
l
a
r
.
o
r
g
/
C
o
r
p
u
s
I
D
:
2
1
2
5
5
2
5
3
3
.
[
1
8
]
A
.
K
.
P
o
d
d
e
r
,
N
.
K
.
R
o
y
,
a
n
d
H
.
R
.
P
o
t
a
,
“
M
P
P
T
me
t
h
o
d
s
f
o
r
so
l
a
r
P
V
sy
s
t
e
ms
:
A
c
r
i
t
i
c
a
l
r
e
v
i
e
w
b
a
s
e
d
o
n
t
r
a
c
k
i
n
g
n
a
t
u
r
e
,
”
I
E
T
Re
n
e
w
a
b
l
e
P
o
w
e
r Ge
n
e
r
a
t
i
o
n
,
v
o
l
.
1
3
,
n
o
.
1
0
,
p
p
.
1
6
1
5
–
1
6
3
2
,
2
0
1
9
,
d
o
i
:
1
0
.
1
0
4
9
/
i
e
t
-
r
p
g
.
2
0
1
8
.
5
9
4
6
.
[
1
9
]
S
.
S
e
y
a
m,
I
.
D
i
n
c
e
r
,
a
n
d
M
.
A
g
e
l
i
n
-
C
h
a
a
b
,
“
D
e
v
e
l
o
p
m
e
n
t
o
f
a
c
l
e
a
n
p
o
w
e
r
p
l
a
n
t
i
n
t
e
g
r
a
t
e
d
w
i
t
h
a
s
o
l
a
r
f
a
r
m
f
o
r
a
s
u
st
a
i
n
a
b
l
e
c
o
mm
u
n
i
t
y
,
”
En
e
rg
y
C
o
n
v
e
rsi
o
n
a
n
d
Ma
n
a
g
e
m
e
n
t
,
v
o
l
.
2
2
5
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
e
n
c
o
n
ma
n
.
2
0
2
0
.
1
1
3
4
3
4
.
[
2
0
]
T.
H
a
i
,
J.
Z
h
o
u
,
a
n
d
K
.
M
u
r
a
n
a
k
a
,
“
A
n
e
f
f
i
c
i
e
n
t
f
u
z
z
y
-
l
o
g
i
c
b
a
s
e
d
M
P
P
T
c
o
n
t
r
o
l
l
e
r
f
o
r
g
r
i
d
-
c
o
n
n
e
c
t
e
d
P
V
sy
s
t
e
ms
b
y
f
a
r
m
l
a
n
d
f
e
r
t
i
l
i
t
y
o
p
t
i
mi
z
a
t
i
o
n
a
l
g
o
r
i
t
h
m
,
”
O
p
t
i
k
,
v
o
l
.
2
6
7
,
2
0
2
2
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
i
j
l
e
o
.
2
0
2
2
.
1
6
9
6
3
6
.
[
2
1
]
M
.
A
l
l
o
u
c
h
e
,
K
.
D
a
h
e
c
h
,
M
.
C
h
a
a
b
a
n
e
,
a
n
d
D
.
M
e
h
d
i
,
“
T
-
S
f
u
z
z
y
c
o
n
t
r
o
l
f
o
r
M
P
P
T
o
f
p
h
o
t
o
v
o
l
t
a
i
c
p
u
mp
i
n
g
s
y
st
e
m,
”
J
o
u
rn
a
l
o
f
I
n
t
e
l
l
i
g
e
n
t
a
n
d
F
u
zzy
S
y
st
e
m
s
,
v
o
l
.
3
4
,
n
o
.
4
,
p
p
.
2
5
2
1
–
2
5
3
3
,
2
0
1
8
,
d
o
i
:
1
0
.
3
2
3
3
/
JI
F
S
-
1
7
4
0
0
.
[
2
2
]
L.
M
o
r
á
n
,
J
.
D
i
x
o
n
,
a
n
d
M
.
T
o
r
r
e
s,
“
A
c
t
i
v
e
F
i
l
t
e
r
s,
”
P
o
w
e
r
El
e
c
t
ro
n
i
c
s
H
a
n
d
b
o
o
k
,
p
p
.
1
3
0
1
–
1
3
4
1
,
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
B
9
7
8
-
0
-
3
2
3
-
9
9
2
1
6
-
9
.
0
0
0
3
5
-
4.
[
2
3
]
P
.
P
a
t
e
l
,
S
.
S
a
m
a
l
,
C
.
J
e
n
a
,
a
n
d
P
.
K
.
B
a
r
i
k
,
“
S
h
u
n
t
a
c
t
i
v
e
p
o
w
e
r
f
i
l
t
e
r
w
i
t
h
M
S
R
F
-
PI
-
A
H
C
C
t
e
c
h
n
i
q
u
e
f
o
r
h
a
r
m
o
n
i
c
s
mi
t
i
g
a
t
i
o
n
i
n
a
h
y
b
r
i
d
e
n
e
r
g
y
s
y
st
e
m
u
n
d
e
r
l
o
a
d
c
h
a
n
g
i
n
g
c
o
n
d
i
t
i
o
n
,
”
Au
st
r
a
l
i
a
n
J
o
u
r
n
a
l
o
f
E
l
e
c
t
r
i
c
a
l
a
n
d
E
l
e
c
t
r
o
n
i
c
s
E
n
g
i
n
e
e
ri
n
g
,
v
o
l
.
2
0
,
n
o
.
1
,
p
p
.
6
3
–
7
7
,
2
0
2
3
,
d
o
i
:
1
0
.
1
0
8
0
/
1
4
4
8
8
3
7
X
.
2
0
2
2
.
2
1
1
4
1
5
4
.
[
2
4
]
Z.
L
y
u
,
L.
W
u
,
a
n
d
P
.
S
o
n
g
,
“
A
N
o
v
e
l
H
a
r
m
o
n
i
c
C
u
r
r
e
n
t
C
o
n
t
r
o
l
M
e
t
h
o
d
f
o
r
T
o
r
q
u
e
R
i
p
p
l
e
R
e
d
u
c
t
i
o
n
o
f
S
P
M
S
M
C
o
n
si
d
e
r
i
n
g
DC
-
Li
n
k
V
o
l
t
a
g
e
L
i
mi
t
,
”
I
E
EE
T
ra
n
s
a
c
t
i
o
n
s
o
n
P
o
w
e
r
El
e
c
t
ro
n
i
c
s
,
v
o
l
.
3
9
,
n
o
.
2
,
p
p
.
2
5
5
8
–
2
5
6
8
,
2
0
2
4
,
d
o
i
:
1
0
.
1
1
0
9
/
TPE
L.
2
0
2
3
.
3
3
2
9
9
3
4
.
[
2
5
]
Y
.
L
u
o
,
S
.
W
a
n
g
,
D
.
Y
a
n
g
,
B
.
Z
h
o
u
,
a
n
d
T
.
L
i
u
,
“
D
i
r
e
c
t
p
r
e
d
i
c
t
i
o
n
c
o
m
p
e
n
s
a
t
i
o
n
s
t
r
a
t
e
g
y
o
f
u
n
i
f
i
e
d
p
o
w
e
r
q
u
a
l
i
t
y
c
o
n
d
i
t
i
o
n
e
r
b
a
s
e
d
o
n
F
C
S
-
M
P
C
,
”
I
E
T
G
e
n
e
r
a
t
i
o
n
,
T
r
a
n
s
m
i
s
s
i
o
n
a
n
d
D
i
s
t
r
i
b
u
t
i
o
n
,
v
o
l
.
1
4
,
n
o
.
2
2
,
p
p
.
5
0
2
0
–
5
0
2
8
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
4
9
/
i
e
t
-
g
t
d
.
2
0
2
0
.
0
0
5
6
.
[
2
6
]
P
.
K
a
r
a
ma
n
a
k
o
s,
E
.
L
i
e
g
ma
n
n
,
T.
G
e
y
e
r
,
a
n
d
R
.
K
e
n
n
e
l
,
“
M
o
d
e
l
P
r
e
d
i
c
t
i
v
e
C
o
n
t
r
o
l
o
f
P
o
w
e
r
El
e
c
t
r
o
n
i
c
S
y
st
e
ms
:
M
e
t
h
o
d
s
,
R
e
s
u
l
t
s,
a
n
d
C
h
a
l
l
e
n
g
e
s
,
”
I
E
EE
O
p
e
n
J
o
u
r
n
a
l
o
f
I
n
d
u
st
r
y
Ap
p
l
i
c
a
t
i
o
n
s
,
v
o
l
.
1
,
p
p
.
9
5
–
1
1
4
,
2
0
2
0
,
d
o
i
:
1
0
.
1
1
0
9
/
O
JI
A
.
2
0
2
0
.
3
0
2
0
1
8
4
.
[
2
7
]
M
.
S
.
K
a
r
b
a
sf
o
r
o
o
sh
a
n
a
n
d
M
.
M
o
n
f
a
r
e
d
,
“
A
n
I
mp
r
o
v
e
d
R
e
f
e
r
e
n
c
e
C
u
r
r
e
n
t
G
e
n
e
r
a
t
i
o
n
a
n
d
D
i
g
i
t
a
l
D
e
a
d
b
e
a
t
C
o
n
t
r
o
l
l
e
r
f
o
r
S
i
n
g
l
e
-
P
h
a
s
e
S
h
u
n
t
A
c
t
i
v
e
P
o
w
e
r
F
i
l
t
e
r
s
,
”
I
EEE
T
r
a
n
s
a
c
t
i
o
n
s
o
n
Po
w
e
r
D
e
l
i
v
e
ry
,
v
o
l
.
3
5
,
n
o
.
6
,
p
p
.
2
6
6
3
–
2
6
7
1
,
2
0
2
0
,
d
o
i
:
1
0
.
1
1
0
9
/
TPW
R
D
.
2
0
2
0
.
2
9
7
4
1
5
5
.
[
2
8
]
P
.
K
a
r
a
ma
n
a
k
o
s
a
n
d
T.
G
e
y
e
r
,
“
G
u
i
d
e
l
i
n
e
s
f
o
r
t
h
e
D
e
s
i
g
n
o
f
F
i
n
i
t
e
C
o
n
t
r
o
l
S
e
t
M
o
d
e
l
P
r
e
d
i
c
t
i
v
e
C
o
n
t
r
o
l
l
e
r
s,”
I
EE
E
T
ra
n
s
a
c
t
i
o
n
s
o
n
P
o
w
e
r E
l
e
c
t
r
o
n
i
c
s
,
v
o
l
.
3
5
,
n
o
.
7
,
p
p
.
7
4
3
4
–
7
4
5
0
,
2
0
2
0
,
d
o
i
:
1
0
.
1
1
0
9
/
TP
EL.
2
0
1
9
.
2
9
5
4
3
5
7
.
[
2
9
]
R
.
P
.
A
g
u
i
l
e
r
a
a
n
d
D
.
E.
Q
u
e
v
e
d
o
,
“
P
r
e
d
i
c
t
i
v
e
c
o
n
t
r
o
l
o
f
p
o
w
e
r
c
o
n
v
e
r
t
e
r
s:
D
e
s
i
g
n
s
w
i
t
h
g
u
a
r
a
n
t
e
e
d
p
e
r
f
o
r
man
c
e
,
”
I
EE
E
T
ra
n
s
a
c
t
i
o
n
s
o
n
I
n
d
u
st
r
i
a
l
I
n
f
o
rm
a
t
i
c
s
,
v
o
l
.
1
1
,
n
o
.
1
,
p
p
.
5
3
–
6
3
,
2
0
1
5
,
d
o
i
:
1
0
.
1
1
0
9
/
TI
I
.
2
0
1
4
.
2
3
6
3
9
3
3
.
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
La
r
o
u
c
i
H
e
g
u
ig
wa
s
b
o
rn
o
n
5
Au
g
u
st
1
9
9
5
i
n
El
Ou
e
d
,
Alg
e
r
ia.
He
re
c
e
iv
e
d
a
m
a
ste
r’s
d
e
g
re
e
in
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
fr
o
m
th
e
U
n
iv
e
rsit
y
o
f
El
Ou
e
d
i
n
2
0
1
9
.
He
i
s
c
u
rre
n
tl
y
w
o
rk
i
n
g
t
o
wa
rd
h
is
P
h
.
D
.
th
e
sis
in
El
e
c
tri
c
a
l
En
e
rg
y
a
t
No
u
r
Ba
c
h
ir
Un
i
v
e
rsity
Ce
n
ter,
El
Ba
y
a
d
h
.
His
f
ield
s
o
f
in
tere
st
a
re
c
o
n
tro
l
tec
h
n
o
l
o
g
y
o
f
p
h
o
to
v
o
lt
a
ic
sy
ste
m
s
,
im
p
ro
v
i
n
g
p
o
we
r
q
u
a
li
t
y
,
a
n
d
m
o
d
e
l
p
re
d
icti
v
e
c
o
n
tro
l
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
l.
h
e
g
u
ig
@c
u
-
e
l
b
a
y
a
d
h
.
d
z
.
Na
d
h
ir
Mes
b
a
h
i
re
c
e
iv
e
d
th
e
En
g
.
,
M
.
S
c
.
,
a
n
d
P
h
.
D
.
d
e
g
re
e
s
in
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
fr
o
m
th
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
,
Ba
d
ji
M
o
k
h
tar
–
An
n
a
b
a
Un
iv
e
rsity
,
An
n
a
b
a
,
Alg
e
ria,
in
2
0
0
0
,
2
0
0
7
,
a
n
d
2
0
1
4
,
re
sp
e
c
ti
v
e
ly
.
He
is
c
u
rre
n
t
ly
a
f
u
ll
p
ro
fe
ss
o
r
with
th
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
U
n
iv
e
rs
it
y
o
f
El
Ou
e
d
,
Alg
e
ria.
S
in
c
e
2
0
2
1
,
h
e
h
a
s
b
e
e
n
a
re
se
a
rc
h
m
e
m
b
e
r
o
f
th
e
El
O
u
e
d
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
a
n
d
Re
n
e
wa
b
le
En
e
rg
y
Lab
o
ra
to
ry
(L
G
EE
RE).
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
c
o
n
tr
o
l
o
f
p
o
we
r
c
o
n
v
e
rters
,
a
c
ti
v
e
p
o
we
r
fil
ters
,
a
n
d
m
o
d
e
l
p
re
d
ictiv
e
c
o
n
tr
o
l.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
n
a
d
h
ir
-
m
e
sb
a
h
i@
u
n
iv
-
e
lo
u
e
d
.
d
z
.
Ya
c
in
e
G
u
e
tta
f
wa
s
b
o
rn
in
T
iare
t,
Alg
e
ria,
i
n
1
9
8
6
.
He
re
c
e
iv
e
d
th
e
m
a
g
ister
a
n
d
t
h
e
P
h
.
D
.
d
e
g
re
e
s
re
sp
e
c
ti
v
e
ly
,
in
2
0
1
2
a
n
d
i
n
2
0
1
6
fr
o
m
th
e
Un
iv
e
rsit
y
o
f
S
c
ien
c
e
s
a
n
d
Tec
h
n
o
l
o
g
y
o
f
Ora
n
(U
S
TO
M
B),
Al
g
e
ria.
His
m
a
in
r
e
se
a
rc
h
in
tere
sts
in
c
lu
d
e
m
o
d
e
ll
in
g
a
n
d
sim
u
latio
n
o
f
t
h
e
p
o
we
r
e
lec
tro
n
ics
’
d
e
v
ice
s:
m
o
re
sp
e
c
ifi
c
a
ll
y
t
h
e
a
n
a
ly
sis
a
n
d
d
e
sig
n
o
f
sw
it
c
h
e
d
m
o
d
e
p
o
we
r
su
p
p
ly
a
t
t
h
e
I
n
stru
m
e
n
tati
o
n
a
n
d
A
p
p
l
ied
M
a
teria
ls
Lab
o
ra
to
r
y
(LI
M
A),
wh
o
is
a
lso
th
e
h
e
a
d
o
f
h
is
re
se
a
rc
h
tea
m
fro
m
a
m
o
n
g
h
is
fo
u
r
tea
m
s.
He
is
a
fu
ll
p
ro
fe
ss
o
r
o
f
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
i
n
No
u
r
Ba
c
h
ir
Un
iv
e
rsity
Ce
n
ter,
El
Ba
y
a
d
h
,
Al
g
e
ria.
He
c
a
n
b
e
c
o
n
ta
c
ted
a
t
e
m
a
il
:
y
.
g
u
e
tt
a
f@c
u
-
e
lb
a
y
a
d
h
.
d
z
.
Evaluation Warning : The document was created with Spire.PDF for Python.