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
.
2
,
J
u
n
e
2
0
1
8
,
p
p
.
610
~
6
2
1
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/i
j
p
ed
s
.
v
9
.
i
2
.
p
p
6
1
0
-
621
610
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
PSO ba
sed Di
rect
P
o
w
er Control for a
Multif
unction
a
l G
rid
Co
nnected
P
ho
to
v
o
ltaic Sy
ste
m
M
.
R.
B
eng
o
urina
1
,
M
.
Ra
hli
2
,
S.
Sla
m
i
3
,
L
.
H
a
s
s
a
ine
4
1
,2
L
a
b
o
ra
to
ir
L
ORE,
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Un
iv
e
rsity
o
f
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
lo
g
y
Ora
n
,
A
l
g
e
ria
3
S
c
ien
c
e
s an
d
T
e
c
h
n
o
l
o
g
y
F
a
c
u
lt
y
Un
iv
e
rsit
y
o
f
Dje
l
f
a
,
A
lg
e
ria
4
Ce
n
tre d
e
Dé
v
e
lo
p
p
e
m
e
n
t
d
e
s E
n
e
rg
ies
Re
n
o
u
v
e
lab
les
(CDER),
A
l
g
e
ria
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ma
y
2
8
,
2
0
1
7
R
ev
i
s
ed
J
an
1
4
,
2
0
1
8
A
cc
ep
ted
J
an
2
8
,
2
0
1
8
T
h
is
p
a
p
e
r
p
re
se
n
ts
a
g
rid
-
c
o
n
n
e
c
ted
p
h
o
t
o
v
o
lt
a
ic
sy
ste
m
(P
V
)
u
se
d
a
s
a
sh
u
n
t
a
c
ti
v
e
p
o
w
e
r
f
il
ter
(S
A
P
F
)
to
p
ro
v
id
e
th
e
p
o
w
e
r
f
a
c
to
r
c
o
rre
c
ti
o
n
,
h
a
rm
o
n
ic
e
li
m
in
a
ti
o
n
,
re
a
c
ti
v
e
p
o
w
e
r
c
o
m
p
e
n
sa
ti
o
n
a
n
d
to
sim
u
lt
a
n
e
o
u
sly
su
p
p
ly
p
o
w
e
r
f
ro
m
a
P
V
s
y
ste
m
to
th
e
u
ti
li
ty
.
A
d
irec
t
p
o
we
r
c
o
n
tro
l
(DP
C
)
m
e
th
o
d
is
u
se
d
f
o
r
c
o
n
tr
o
ll
i
n
g
th
e
s
y
ste
m
to
f
e
e
d
th
e
p
h
o
to
v
o
lt
a
ic
e
n
e
rg
y
in
s
y
n
c
h
ro
n
iza
ti
o
n
w
it
h
g
rid
a
n
d
p
r
o
v
id
e
p
o
w
e
r
q
u
a
li
ty
i
m
p
ro
v
e
m
e
n
t.
T
h
e
P
I
p
a
ra
m
e
ters
o
f
DC
-
li
n
k
v
o
lt
a
g
e
c
o
n
tro
ll
e
r
a
re
t
u
n
e
d
u
si
n
g
th
e
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
(P
S
O)
a
lg
o
rit
h
m
with
o
u
t
th
e
n
e
e
d
f
o
r
a
n
e
x
a
c
t
m
a
t
h
e
m
a
ti
c
a
l
m
o
d
e
l
o
f
s
y
st
e
m
.
T
h
is
P
I
-
P
S
O
c
o
n
tr
o
ll
e
r
g
iv
e
s
b
e
tt
e
r
re
su
lt
s
f
o
r
r
o
b
u
st
n
e
ss
,
h
a
rm
o
n
ic
m
in
im
iz
a
ti
o
n
a
n
d
re
d
u
c
e
s
th
e
o
v
e
rsh
o
o
t
a
n
d
u
n
d
e
rsh
o
o
ts
o
f
P
I
c
o
n
tro
ll
e
r.
T
h
e
o
v
e
ra
ll
c
o
n
tr
o
l
o
f
s
y
ste
m
is
te
ste
d
in
M
a
tl
a
b
/S
im
u
li
n
k
e
n
v
iro
n
m
e
n
t.
T
h
e
n
,
t
h
e
sim
u
latio
n
s
re
su
l
ts
d
e
m
o
n
stra
te
th
e
r
o
b
u
stn
e
ss
a
n
d
f
e
a
sib
il
it
y
o
f
p
ro
p
o
se
d
m
e
th
o
d
.
K
ey
w
o
r
d
:
Dir
ec
t o
n
tr
o
l o
f
P
o
w
er
P
ar
ticle
S
w
ar
m
Op
ti
m
iza
tio
n
P
h
o
to
v
o
ltaic
s
y
s
te
m
P
I
co
n
tr
o
ller
Sh
u
n
t
A
cti
f
P
o
w
er
Fil
ter
Co
p
y
r
ig
h
t
©
2
0
1
8
In
stit
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
:
Mo
h
a
m
ed
R
id
a
B
en
g
o
u
r
i
n
a,
L
ab
o
r
ato
ir
L
OR
E
,
Fac
u
lt
y
o
f
E
lectr
ical
E
n
g
i
n
ee
r
i
n
g
,
Un
i
v
er
s
it
y
o
f
Scie
n
ce
a
n
d
T
ec
h
n
o
lo
g
y
Or
a
n
(
UST
O)
,
A
lg
er
i
a
B
P
1
5
0
5
,
Or
an
E
l
M’
n
ao
u
er
,
A
l
g
er
ia
E
m
ail:
b
en
g
o
u
r
i
n
a.
r
id
a@
y
ah
o
o
.
f
r
,
r
id
a.
b
en
g
o
u
r
in
a
@
u
n
i
v
-
u
s
to
.
d
z
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
s
o
lar
en
er
g
y
i
s
th
e
m
o
s
t
p
o
p
u
lar
s
o
u
r
ce
a
m
o
n
g
th
e
al
ter
n
ati
v
e
en
er
g
y
r
e
s
o
u
r
ce
w
it
h
o
u
t
e
m
is
s
io
n
o
f
p
o
llu
tan
t
s
en
er
g
y
co
n
v
er
s
i
o
n
is
d
o
n
e
[
1
]
.
I
n
an
ef
f
o
r
t
to
u
s
e
th
e
s
o
lar
en
er
g
y
e
f
f
ec
ti
v
ely
,
a
g
r
ea
t
d
ea
l
o
f
r
esear
ch
h
as
b
ee
n
d
o
n
e
o
n
th
e
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
g
en
er
atio
n
s
y
s
te
m
s
.
I
n
P
V
s
y
s
te
m
s
co
n
n
ec
ted
to
t
h
e
g
r
id
,
th
e
i
n
v
er
ter
t
h
at
co
n
v
er
ts
th
e
o
u
tp
u
t
d
ir
ec
t
c
u
r
r
en
t
(
DC
)
o
f
th
e
s
o
lar
m
o
d
u
les
to
t
h
e
alter
n
ate
c
u
r
r
en
t
(
AC
)
is
r
ec
eiv
i
n
g
in
cr
ea
s
ed
i
n
t
er
est in
o
r
d
er
to
g
en
er
ate
p
o
w
er
to
u
tili
t
y
[
2
]
.
T
o
d
ay
,
th
e
w
id
esp
r
ea
d
u
s
e
o
f
n
o
n
li
n
ea
r
lo
ad
s
in
p
o
w
er
s
y
s
t
e
m
s
ca
u
s
es
cir
cu
latio
n
o
f
h
ar
m
o
n
ic
s
an
d
r
ea
ctiv
e
c
u
r
r
en
ts
i
n
t
h
e
d
is
tr
i
b
u
tio
n
l
in
e
s
[
3
]
[
4
]
.
I
f
t
h
e
g
r
id
-
co
n
n
ec
ted
P
V
s
y
s
te
m
is
a
p
p
lied
to
n
o
n
li
n
ea
r
lo
ad
s
,
th
e
p
o
w
er
q
u
alit
y
i
s
r
elativ
el
y
p
o
o
r
er
.
T
o
av
o
id
th
ese
p
r
o
b
lem
s
,
th
e
g
r
id
-
co
n
n
ec
ted
P
V
s
y
s
te
m
s
h
o
u
ld
no
t
o
n
l
y
s
u
p
p
l
y
ac
t
iv
e
p
o
w
er
to
th
e
s
y
s
te
m
v
ia
MP
PT
,
b
u
t
also
i
m
p
r
o
v
e
th
e
p
o
w
er
q
u
al
it
y
(
lo
w
T
HD
an
d
u
n
i
t
y
p
o
w
er
f
ac
to
r
)
[
5
]
.
B
y
m
o
d
i
f
y
in
g
th
e
co
n
tr
o
l
o
f
th
e
in
v
er
ter
,
ac
tiv
e
f
ilter
i
n
g
f
ea
t
u
r
e
ca
n
also
b
e
in
clu
d
ed
in
th
e
P
V
in
ter
f
ac
in
g
i
n
v
er
ter
an
d
t
h
u
s
s
av
e
s
th
e
co
s
t
o
f
ad
d
itio
n
al
ac
tiv
e
f
ilter
.
Var
io
u
s
co
n
tr
o
l
t
y
p
es
o
f
s
h
u
n
t
ac
ti
v
e
f
ilter
w
er
e
p
r
esen
ted
in
th
e
lit
er
atu
r
e
[
6
]
.
I
n
th
is
ar
ticle,
w
e
p
r
o
p
o
s
e
th
e
d
ir
ec
t
p
o
w
er
co
n
tr
o
l
(
DP
C
)
.
T
h
e
DP
C
s
tr
ateg
y
is
b
ased
o
n
th
e
i
n
s
ta
n
tan
eo
u
s
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
co
m
p
ar
ato
r
s
.
T
h
e
ac
tiv
e
p
o
w
er
co
m
m
a
n
d
is
p
r
o
v
id
ed
f
r
o
m
a
d
c
-
b
u
s
v
o
lta
g
e
co
n
tr
o
ller
b
lo
ck
,
w
h
ile
t
h
e
r
ea
ctiv
e
p
o
w
er
co
m
m
a
n
d
is
d
ir
ec
tl
y
g
iv
e
n
f
r
o
m
th
e
o
u
ts
id
e
o
f
th
e
co
n
tr
o
ller
.
E
r
r
o
r
s
b
etw
ee
n
th
e
co
m
m
a
n
d
s
a
n
d
th
e
esti
m
ated
f
ee
d
b
ac
k
p
o
w
er
ar
e
in
p
u
t
to
th
e
h
y
s
ter
esi
s
co
m
p
ar
ato
r
s
[
7
]
[
8
]
.
I
n
th
e
DP
C
tech
n
iq
u
e,
th
e
a
ctiv
e
p
o
w
er
is
d
eliv
er
ed
f
r
o
m
th
e
o
u
ter
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
P
I
)
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:
2
0
8
8
-
8694
P
S
O
b
a
s
ed
Dir
ec
t P
o
w
er C
o
n
tr
o
l fo
r
a
Mu
ltif
u
n
ctio
n
a
l G
r
id
C
o
n
n
ec
ted
P
h
o
to
vo
lta
ic
.
.
.
(
M.R
.
B
en
g
o
u
r
in
a
)
611
co
n
tr
o
ller
.
T
h
is
P
I
co
n
tr
o
ller
i
s
f
o
r
m
u
lated
as
an
o
p
ti
m
izatio
n
p
r
o
b
lem
[
9
]
.
I
n
th
is
w
o
r
k
,
w
e
p
r
o
p
o
s
e
th
e
u
s
e
o
f
th
e
p
ar
ticle
s
w
ar
m
o
p
ti
m
izati
o
n
(
P
SO)
m
et
h
o
d
to
s
ea
r
ch
f
o
r
th
e
o
p
ti
m
al
p
ar
a
m
eter
s
o
f
a
P
I
co
n
tr
o
ller
.
D
P
C
b
ased
o
n
class
ical
P
I
r
eg
u
lat
o
r
an
d
P
SO
alg
o
r
ith
m
is
d
e
v
elo
p
ed
an
d
a
co
m
p
ar
is
o
n
s
t
u
d
y
is
p
r
ese
n
ted
.
T
o
s
h
o
w
t
h
e
p
er
f
o
r
m
a
n
ce
s
,
a
n
u
m
er
ical
s
i
m
u
latio
n
is
p
er
f
o
r
m
ed
.
2.
SYS
T
E
M
S CO
NF
I
G
U
RAT
I
O
NS
T
h
e
s
tr
u
ctu
r
e
o
f
t
h
e
g
r
id
-
co
n
n
ec
ted
P
V
s
y
s
te
m
is
s
h
o
w
n
i
n
Fi
g
u
r
e.
1
.
I
t
co
n
s
is
ts
o
f
a
p
h
o
to
v
o
ltaic
ar
r
ay
co
n
n
ec
ted
t
h
r
o
u
g
h
a
d
c
-
d
c
b
o
o
s
t c
o
n
v
er
ter
to
a
th
r
ee
-
p
h
ase
i
n
v
er
ter
th
at
is
co
n
n
ec
ted
to
a
g
r
id
th
r
o
u
g
h
a
s
i
m
p
le
f
ilter
a
n
d
n
o
n
li
n
e
ar
lo
ad
.
Fig
u
r
e
1
.
Gr
id
-
C
o
n
n
ec
ted
I
n
v
er
ter
I
n
ter
f
ac
ed
w
i
th
P
V
S
y
s
te
m
2
.
1
.
P
V
Arr
a
y
M
o
del
T
h
e
P
V
m
o
d
u
le
is
th
e
u
n
it
y
o
f
b
ase
f
o
r
th
e
co
n
s
tr
u
ctio
n
o
f
a
P
V
ar
r
ay
.
W
e
h
av
e
u
s
ed
th
e
P
V
m
o
d
u
l
e
m
o
d
el
o
f
a
s
in
g
le
d
io
d
e.
T
h
is
m
o
d
el
i
s
th
e
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
d
u
e
to
g
o
o
d
r
esu
lts
[
1
0
]
.
T
h
e
cu
r
r
en
t
-
v
o
ltag
e
r
elatio
n
s
h
ip
is
g
iv
e
n
b
y
:
P
V
p
h
d
s
h
I
I
I
I
(
1
)
.
.
.
e
x
p
.
1
P
V
s
P
V
P
V
s
P
V
P
V
p
h
s
sh
V
R
I
V
R
I
I
I
I
q
A
k
T
R
(
2
)
W
h
er
e:
I
p
h
:
th
e
c
u
r
r
en
t
g
en
er
ated
b
y
t
h
e
in
c
id
en
t
li
g
h
t;
I
s
:
t
h
e
r
e
v
er
s
e
s
at
u
r
atio
n
o
r
leak
a
g
e
cu
r
r
e
n
t
o
f
t
h
e
d
io
d
e;
R
s
:
th
e
eq
u
iv
a
len
t
s
er
ie
s
r
esis
ta
n
c
e;
R
s
h
:
t
h
e
eq
u
iv
ale
n
t
p
ar
allel
r
esis
tan
ce
;
q
:
th
e
elec
tr
o
n
ch
ar
g
e
(
1
.
6
0
2
1
7
6
4
6
×
10
-
1
9
C
)
; k
: th
e
B
o
ltz
m
a
n
n
co
n
s
ta
n
t (
1
.
3
8
0
6
5
0
3
×
1
0
−2
3
J
/K)
;
A
: Q
u
a
lit
y
Facto
r
o
f
d
io
d
e
.
Fig
u
r
e
2
.
E
q
u
iv
ale
n
t Ci
r
c
u
it o
f
a
P
V
C
e
ll
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N:
2
0
8
8
-
8694
I
n
t
J
P
o
w
E
lec
&
Dr
i S
y
s
t,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
610
–
621
612
(
a)
(
b
)
Fig
u
r
e
3
.
(
a)
I
-
V
C
h
ar
ac
ter
is
ti
cs,
(
b
)
P
-
V
C
h
ar
ac
ter
i
s
tics
T
h
e
P
V
m
o
d
el
is
s
i
m
u
lated
u
s
in
g
t
h
e
Su
n
P
o
w
er
SP
R
-
305E
-
W
HT
-
D
P
V
p
a
n
el.
T
h
e
s
i
m
u
lated
I
-
V
an
d
P
-
V
ch
ar
ac
ter
is
tic
s
o
f
th
e
SP
R
-
305E
-
W
HT
-
D
P
V
m
o
d
u
le
at
s
tan
d
ar
d
cli
m
atic
co
n
d
i
ti
o
n
s
ar
e
s
h
o
w
n
i
n
Fig
u
r
e.
3
.
(
a)
an
d
(
b
)
,
r
esp
ec
ti
v
el
y
.
2
.
2
.
B
o
o
s
t
Co
nv
er
t
er
M
o
delin
g
Fig
u
r
e.
4
s
h
o
w
s
t
h
e
eq
u
i
v
ale
n
t
cir
c
u
it
o
f
th
e
DC
-
D
C
b
o
o
s
t
co
n
v
er
ter
.
T
h
ese
co
n
v
er
t
er
s
ca
n
b
e
d
escr
ib
ed
u
s
in
g
o
r
d
in
ar
y
d
i
f
f
e
r
en
tiatio
n
eq
u
atio
n
s
as f
o
llo
w
s
:
Fig
u
r
e
4
.
C
o
n
tr
o
l Sch
e
m
e
o
f
DC
-
DC
B
o
o
s
t Co
n
v
er
ter
1
L
b
o
o
s
t
dV
pv
I
I
C
pv
dt
(
3
)
2
1
dc
d
c
L
b
o
o
s
t
dV
I
D
I
C
dt
(
4
)
(
1
)
L
b
o
o
s
t
p
v
d
c
dI
V
D
V
L
dt
(
5
)
D:
is
th
e
d
u
t
y
c
y
cle.
T
h
e
s
w
itc
h
is
o
n
f
o
r
a
p
er
io
d
e
q
u
al
to
DT
,
an
d
th
e
s
w
itc
h
is
o
f
f
f
o
r
an
in
ter
v
al
ti
m
e
eq
u
al
to
(
1
–
D)
T
.
2
.
3
.
M
a
x
i
m
u
m
P
o
w
er
P
o
int
T
ra
cking
Sev
er
al
p
u
b
licatio
n
s
o
n
MP
P
m
eth
o
d
s
ar
e
r
eg
u
lar
l
y
p
u
b
li
s
h
ed
in
t
h
e
liter
atu
r
e.
Fo
r
o
u
r
s
tu
d
y
,
w
e
ch
o
s
e
t
h
e
MP
P
T
alg
o
r
ith
m
o
f
P
&
O.
P
&
O
m
et
h
o
d
is
o
n
e
o
f
t
h
e
p
o
p
u
lar
m
et
h
o
d
s
to
tr
ac
k
t
h
e
m
ax
i
m
u
m
-
p
o
w
er
p
o
in
t
an
d
p
r
o
b
ab
ly
th
e
m
o
s
t
f
r
eq
u
en
tl
y
u
s
ed
i
n
p
r
ac
tice,
m
ai
n
l
y
d
u
e
to
it
s
ea
s
y
i
m
p
le
m
e
n
ta
tio
n
.
[
1
1
][1
2
]
.
T
h
e
w
o
r
k
i
n
g
p
r
in
cip
le
o
f
P
&
O
i
s
d
ep
icted
b
y
th
e
f
lo
w
c
h
ar
t in
Fi
g
u
r
e.
5
.
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:
2
0
8
8
-
8694
P
S
O
b
a
s
ed
Dir
ec
t P
o
w
er C
o
n
tr
o
l fo
r
a
Mu
ltif
u
n
ctio
n
a
l G
r
id
C
o
n
n
ec
ted
P
h
o
to
vo
lta
ic
.
.
.
(
M.R
.
B
en
g
o
u
r
in
a
)
613
Fig
u
r
e
5
.
Flo
w
c
h
ar
t o
f
t
h
e
P
&
O
A
l
g
o
r
ith
m
2
.
4
.
Act
iv
e
P
o
w
er
F
ilte
r
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
ac
ti
v
e
f
il
ter
co
n
s
is
ts
es
s
e
n
tiall
y
o
f
t
w
o
p
ar
ts
,
a
p
o
w
er
an
d
a
co
n
tr
o
l
p
ar
t.
T
h
e
p
o
w
er
p
ar
t
co
n
s
is
ts
o
f
an
i
n
v
e
r
ter
,
a
co
u
p
lin
g
f
il
ter
an
d
a
s
o
u
r
ce
o
f
en
er
g
y
.
T
h
e
co
n
tr
o
l
p
ar
t
is
u
s
ed
to
co
n
tr
o
l
th
e
s
w
i
tch
in
g
o
f
s
e
m
ico
n
d
u
c
t
o
r
elem
e
n
t
s
f
o
r
m
in
g
t
h
e
i
n
v
er
ter
f
r
o
m
t
h
e
p
o
w
er
p
ar
t.
Au
t
h
r
o
u
g
h
ap
p
r
o
p
r
iate
co
n
tr
o
l
s
tr
ateg
ies,
it
is
p
o
s
s
i
b
le
to
g
en
er
ate
h
ar
m
o
n
ic
s
i
g
n
als
at
th
e
o
u
tp
u
t
o
f
th
e
i
n
v
er
ter
to
o
f
f
s
et
th
o
s
e
p
r
esen
t o
n
th
e
p
o
w
er
g
r
id
,
s
u
c
h
as.
[
1
3
]
s
lf
i
i
i
(
6
)
i
s
: c
u
r
r
en
t o
f
s
o
u
r
ce
.
;
i
l
: c
u
r
r
e
n
t o
f
t
h
e
lo
ad
;
i
f
: c
u
r
r
en
t c
o
m
p
en
s
atio
n
.
3.
DIRE
CT
P
O
W
E
R
CO
NT
R
O
L
T
h
e
m
ain
id
ea
o
f
t
h
e
d
ir
ec
t
p
o
w
er
co
n
tr
o
l
(
DP
C
)
o
r
ig
i
n
all
y
p
r
o
p
o
s
ed
b
y
Oh
n
is
h
i
(
1
9
9
1
)
an
d
f
u
r
th
er
d
ev
elo
p
ed
b
y
No
g
u
c
h
i
an
d
T
ak
ah
ac
h
i
i
n
1
9
9
8
,
is
s
i
m
ilar
to
th
e
d
ir
ec
t
to
r
q
u
e
co
n
tr
o
l
(
DT
C
)
o
f
in
d
u
ctio
n
m
ac
h
in
e
s
.
I
n
s
tead
o
f
f
lu
x
a
n
d
to
r
q
u
e,
th
e
ac
tiv
e
p
o
w
er
(
P
)
an
d
r
ea
ctiv
e
p
o
w
er
(
q
)
ar
e
s
elec
ted
as
t
w
o
in
s
ta
n
ta
n
eo
u
s
m
ag
n
it
u
d
es
to
co
n
tr
o
l
[
1
4
]
[
7
]
.
T
h
e
f
ig
u
r
e
.
2
s
h
o
w
s
th
e
co
n
f
ig
u
r
atio
n
o
f
t
h
e
d
ir
ec
t
p
o
w
e
r
co
n
tr
o
l
w
it
h
o
u
t v
o
lta
g
e
s
e
n
s
o
r
f
o
r
a
th
r
ee
p
h
ase
in
v
er
ter
.
Fig
u
r
e
6
.
Gen
er
al
Stru
ct
u
r
e
o
f
Sh
u
n
t
A
cti
v
e
Fil
ter
C
o
n
tr
o
lled
b
y
DP
C
T
h
e
esti
m
ated
v
al
u
es
o
f
(
p
s
)
an
d
(
q
s
)
in
ter
m
s
o
f
t
h
e
th
r
ee
p
h
ase
lin
e
cu
r
r
en
ts
an
d
v
o
lta
g
es
ca
n
b
e
d
er
iv
ed
as: [
1
4
]
s
S
S
S
P
j
Q
(
7
)
.
.
.
S
s
a
s
a
s
b
s
b
s
c
s
c
P
v
i
v
i
v
i
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N:
2
0
8
8
-
8694
I
n
t
J
P
o
w
E
lec
&
Dr
i S
y
s
t,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
610
–
621
614
1
.
.
.
3
S
s
b
s
c
s
a
s
c
s
a
s
b
s
a
s
b
s
c
Q
v
v
i
v
v
i
v
v
i
(
9
)
T
h
e
p
h
ase
o
f
th
e
p
o
w
er
-
s
o
u
r
ce
v
o
lta
g
e
v
ec
to
r
is
co
n
v
er
ted
to
th
e
d
ig
itized
s
i
g
n
a
l
N
E
rr
o
r
!
Ref
er
ence
s
o
urce
no
t
f
o
un
d.
.
Fo
r
th
is
p
u
r
p
o
s
e,
th
e
w
o
r
k
in
g
p
lan
e
(
α
,
β)
is
d
iv
id
ed
in
to
1
2
s
ec
to
r
s
in
Fi
g
u
r
e.
7
.
T
h
e
s
ec
to
r
s
ca
n
b
e
n
u
m
er
ic
all
y
d
eter
m
i
n
ed
b
y
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
.
[
7
]
.
Or
:
N=
1
,
2
,
3
….
1
2
is
th
e
n
u
m
b
er
o
f
th
e
s
ec
to
r
V
A
r
c
tg
V
(1
0
)
Fig
u
r
e
7
.
P
lan
t (
α
,
β
)
Div
id
ed
in
1
2
Secto
r
3
.
1
.
H
y
s
t
er
esis
co
ntr
o
l a
nd
s
w
it
ching
t
a
ble
T
h
e
r
ef
er
en
ce
s
o
f
r
ea
ctiv
e
p
o
w
er
(
q
r
ef
)
an
d
ac
tiv
e
p
o
w
er
(
p
r
ef
)
ar
e
co
m
p
ar
ed
w
it
h
th
e
esti
m
ated
r
ea
ctiv
e
(
qs
)
a
n
d
ac
ti
v
e
(
ps
)
v
alu
e
s
.
E
r
r
o
r
s
b
et
w
ee
n
th
e
c
o
m
m
a
n
d
s
a
n
d
t
h
e
e
s
ti
m
ated
f
ee
d
b
ac
k
p
o
w
er
ar
e
in
p
u
t
to
t
h
e
h
y
s
ter
esi
s
co
m
p
a
r
ato
r
s
an
d
d
ig
i
tized
to
t
h
e
s
ig
n
als
Sp
a
n
d
Sq
.
T
h
e
o
u
tp
u
t
s
ig
n
a
l
o
f
t
h
e
ac
ti
v
e
p
o
w
er
co
n
tr
o
ller
is
d
ef
i
n
ed
:
0
1
r
e
f
s
p
r
e
f
p
s
p
p
p
p
S
pp
h
hS
(1
1
)
An
d
s
i
m
ilar
l
y
f
o
r
th
e
r
ea
cti
v
e
p
o
w
er
co
n
tr
o
ller
as:
0
1
r
e
f
s
q
r
e
f
q
s
q
q
q
q
S
qq
h
hS
(1
2
)
Fo
r
all
s
ec
to
r
s
th
e
s
w
i
tch
i
n
g
ta
b
le
p
r
o
p
o
s
ed
is
r
ep
r
esen
ted
in
th
e
T
ab
le
1
.
T
ab
le
1
.
A
ll Sec
to
r
s
S
w
itch
in
g
T
ab
le
S
p
S
q
θ
1
θ
2
θ
3
θ
4
θ
5
θ
6
θ
7
θ
8
θ
9
θ
10
θ
11
θ
12
1
1
V
6
V
7
V
1
V
0
V
2
V
7
V
3
V
0
V
4
V
7
V
5
V
0
1
0
V
7
V
7
V
0
V
0
V
7
V
7
V
0
V
0
V
5
V
7
V
0
V
0
0
1
V
6
V
1
V
1
V
2
V
2
V
3
V
3
V
4
V
4
V
5
V
5
V
6
0
0
V
1
V
2
V
2
V
3
V
3
V
4
V
4
V
3
V
3
V
6
V
6
V
1
3
.
2
.
P
I
co
ntr
o
ller
T
h
e
r
eg
u
latio
n
o
f
t
h
e
co
n
ti
n
u
o
u
s
v
o
lt
a
g
e
o
f
i
n
v
er
ter
is
e
n
s
u
r
ed
b
y
a
r
eg
u
lato
r
o
f
P
I
ty
p
e
.
T
h
e
er
r
o
r
b
et
w
ee
n
th
e
v
o
lta
g
e
o
f
t
h
e
ca
p
ac
ito
r
V
dc
an
d
th
e
r
ef
er
en
ce
v
o
ltag
e
V
dcref
i
s
u
s
ed
as
a
n
i
n
p
u
t
to
P
I
C
o
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:
2
0
8
8
-
8694
P
S
O
b
a
s
ed
Dir
ec
t P
o
w
er C
o
n
tr
o
l fo
r
a
Mu
ltif
u
n
ctio
n
a
l G
r
id
C
o
n
n
ec
ted
P
h
o
to
vo
lta
ic
.
.
.
(
M.R
.
B
en
g
o
u
r
in
a
)
615
an
d
th
e
o
u
tp
u
t is t
h
e
r
ef
er
e
n
ce
ac
tiv
e
p
o
w
er
p
ref
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
P
I
C
o
n
tr
o
ller
i
s
:
ki
G
s
k
p
s
(1
3
)
W
h
er
e,
k
P
i
s
t
h
e
p
r
o
p
o
r
tio
n
al
co
n
s
ta
n
t
g
ain
a
n
d
k
i
i
s
t
h
e
i
n
te
g
r
al
co
n
s
tan
t
g
ai
n
.
T
h
ese
g
ai
n
s
ar
e
tu
n
ed
b
y
u
s
i
n
g
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
P
SO)
.
4.
P
ARTI
C
L
E
SWA
RM
O
P
T
I
M
I
Z
AT
I
O
N
T
h
e
p
ar
ticle
s
w
ar
m
o
p
ti
m
iza
tio
n
(
P
SO)
alg
o
r
ith
m
w
as
f
ir
s
t
d
escr
ib
ed
in
1
9
9
5
b
y
Ke
n
n
ed
y
a
n
d
E
b
er
h
ar
t
[
1
5
]
[
1
6
]
.
T
h
e
tech
n
iq
u
e
h
as
e
v
o
l
v
ed
g
r
ea
tl
y
s
i
n
ce
t
h
en
.
P
SO
i
s
a
s
to
ch
ast
i
c,
p
o
p
u
latio
n
b
ased
ev
o
lu
tio
n
ar
y
co
m
p
u
ter
alg
o
r
ith
m
f
o
r
p
r
o
b
lem
s
o
l
v
in
g
.
I
n
a
P
SO
s
y
s
te
m
,
a
s
w
ar
m
o
f
in
d
iv
id
u
al
s
(
ca
lled
p
ar
ticles)
f
l
y
t
h
r
o
u
g
h
t
h
e
s
ea
r
ch
s
p
ac
e.
E
ac
h
p
ar
ticle
r
ep
r
esen
t
s
a
ca
n
d
id
ate
s
o
lu
tio
n
t
o
th
e
o
p
tim
izat
io
n
p
r
o
b
lem
.
T
h
e
p
o
s
itio
n
o
f
a
p
ar
ticle
is
in
f
l
u
e
n
ce
d
b
y
t
h
e
b
est
p
o
s
itio
n
v
is
ited
b
y
its
e
lf
(
i.e
.
,
its
o
w
n
ex
p
er
ien
ce
)
an
d
th
e
p
o
s
it
io
n
o
f
th
e
b
est
p
a
r
ticle
in
i
ts
n
ei
g
h
b
o
u
r
h
o
o
d
(
i.e
.
,
th
e
ex
p
er
ie
n
ce
o
f
n
ei
g
h
b
o
r
in
g
p
ar
ticles).
W
h
en
th
e
n
ei
g
h
b
o
u
r
h
o
o
d
o
f
a
p
ar
tic
le
is
th
e
en
tire
s
w
ar
m
,
th
e
b
es
t
p
o
s
itio
n
in
th
e
n
eig
h
b
o
u
r
h
o
o
d
is
r
ef
er
r
ed
t
o
as
th
e
g
lo
b
al
b
est
p
ar
ticle,
an
d
th
e
r
esu
lti
n
g
alg
o
r
ith
m
is
r
ef
er
r
ed
to
a
g
lo
b
al
b
est
PS
O.
W
h
en
s
m
al
ler
n
eig
h
b
o
u
r
h
o
o
d
s
ar
e
u
s
ed
,
th
e
alg
o
r
ith
m
is
g
e
n
er
all
y
r
e
f
er
r
ed
to
a
lo
ca
l b
est P
SO.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
ea
c
h
p
ar
ticle
(
i.e
.
,
h
o
w
clo
s
e
th
e
p
a
r
ticle
is
f
r
o
m
t
h
e
g
lo
b
al
o
p
ti
m
u
m
)
i
s
m
ea
s
u
r
ed
u
s
i
n
g
a
f
it
n
e
s
s
f
u
n
ctio
n
th
at
v
ar
ies
d
ep
en
d
in
g
o
n
th
e
o
p
ti
m
izatio
n
p
r
o
b
le
m
.
E
ac
h
p
ar
ticle
in
th
e
s
w
ar
m
i
s
r
ep
r
esen
ted
b
y
th
e
f
o
llo
w
i
n
g
ch
ar
ac
ter
is
tics
[
1
5
]
[
1
7
]
:
x
i
is
th
e
cu
r
r
en
t
p
o
s
itio
n
o
f
t
h
e
p
ar
ticle;
v
i
is
th
e
cu
r
r
en
t
v
elo
cit
y
o
f
t
h
e
p
ar
ticle;
y
i
is
t
h
e
p
er
s
o
n
al
b
est
p
o
s
itio
n
o
f
th
e
p
ar
ticle
i
s
t
h
e
n
eig
h
b
o
u
r
h
o
o
d
b
est
p
o
s
itio
n
o
f
t
h
e
p
ar
ticle.
T
h
e
p
er
s
o
n
al
b
est
p
o
s
itio
n
o
f
p
ar
ticle
i
is
t
h
e
b
est
p
o
s
itio
n
v
is
ited
b
y
p
ar
ti
cle
i
s
o
f
ar
.
L
e
t
F
d
en
o
te
th
e
o
b
j
ec
tiv
e
f
u
n
c
tio
n
.
T
h
en
t
h
e
p
er
s
o
n
al
b
est
o
f
a
p
ar
ticle
at
ti
m
e
s
tep
t
is
u
p
d
ated
as:
(
)
(
(
1
)
(
(
)
)
(
1
)
(
1
)
(
(
1
)
(
(
)
)
i
i
i
i
i
i
i
y
t
F
x
t
F
y
t
if
yt
x
t
F
x
t
F
y
t
if
(1
4
)
Fo
r
th
e
g
b
est
m
o
d
el,
th
e
b
est
p
ar
ticle
is
d
eter
m
in
ed
f
r
o
m
th
e
en
tire
s
w
ar
m
b
y
s
elec
ti
n
g
th
e
b
est
p
er
s
o
n
al
p
o
s
itio
n
.
I
f
t
h
e
p
o
s
iti
o
n
o
f
th
e
g
lo
b
al
b
est p
ar
ticle
is
d
en
o
ted
b
y
t
h
e
v
ec
to
r
th
en
:
W
h
er
e:
0
m
i
n
(
(
t
)
)
,
.
.
.
.
.
.
.
.
.
.
.
,
F
(
(
)
)
s
y
F
y
y
t
)
(1
5
)
An
d
:
s
d
en
o
tes t
h
e
s
ize
o
f
th
e
s
w
ar
m
.
T
h
e
v
elo
cit
y
u
p
d
ate
s
tep
is
s
p
ec
if
ied
f
o
r
ea
ch
d
i
m
en
s
io
n
:
j
,
1
,
.
.
.
.
.
.
.
.
.
.
.
,
N
d
j
Hen
ce
,
,
ij
v
r
ep
r
esen
ts
t
h
e
jth
elem
en
t
o
f
th
e
v
elo
cit
y
v
ec
to
r
o
f
th
e
ith
p
ar
ticle.
T
h
u
s
th
e
v
el
o
cit
y
o
f
p
ar
ticle
i
is
u
p
d
ated
u
s
i
n
g
t
h
e
f
o
llo
w
in
g
eq
u
at
io
n
:
,
,
1
1
2
2
.
(
)
.
.
i
j
i
j
vv
t
c
c
(1
6
)
W
h
er
e:
1
1
,
,
,
.
(
(
)
(
)
)
j
i
j
i
j
r
y
t
x
t
(1
7
)
2
2
,
,
.
(
(
)
(
)
)
n
j
j
i
j
r
y
t
x
t
(
18
)
ω
is
th
e
i
n
er
tia
w
eig
h
t,
1
c
an
d
2
c
ar
e
th
e
ac
ce
ler
atio
n
co
n
s
tan
ts
,
a
n
d
r
an
d
o
m
co
ef
f
icie
n
ts
d
is
tr
ib
u
ted
as:
1,
j
r
an
d
2,
0
.
1
j
r
T
h
e
p
o
s
itio
n
o
f
p
ar
ticle
i
,
i
x
is
th
en
u
p
d
ated
u
s
i
n
g
t
h
e
f
o
llo
w
i
n
g
eq
u
atio
n
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N:
2
0
8
8
-
8694
I
n
t
J
P
o
w
E
lec
&
Dr
i S
y
s
t,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
610
–
621
616
(
1
)
(
)
(
1
)
i
i
i
x
t
x
t
v
t
(
19
)
T
h
is
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
til
a
s
p
ec
if
ied
n
u
m
b
er
o
f
iter
atio
n
s
is
ex
ce
ed
ed
,
o
r
v
elo
city
u
p
d
ates
ar
e
clo
s
e
to
ze
r
o
.
T
h
e
q
u
alit
y
o
f
p
ar
ticles
is
m
ea
s
u
r
e
d
u
s
in
g
a
f
it
n
es
s
f
u
n
c
tio
n
w
h
ich
r
e
f
lects
th
e
o
p
ti
m
alit
y
o
f
a
p
ar
ticu
lar
s
o
lu
tio
n
.
T
h
e
f
o
llo
win
g
s
tep
s
s
u
m
m
ar
ize
th
e
b
asic
P
SO a
lg
o
r
ith
m
:
4
.
1
.
P
SO
Alg
o
rit
h
m
F
o
r
ea
ch
p
a
r
ticle
i=1
,
……
s
d
o
R
a
n
d
o
mly
in
itia
liz
e
x
i
R
a
n
d
o
mly
in
itia
liz
e
v
i
(
o
r
ju
s
t set v
i
to
z
ero
)
S
et
y
i
=x
i
en
d
fo
r
R
ep
ea
t
F
o
r
ea
ch
p
a
r
ticle
i=1
,
…,
s
d
o
E
va
lu
a
te
th
e
fitn
ess
o
f p
a
r
ticle
i,
f(
x
i
)
Up
d
a
te
y
i
u
s
in
g
eq
u
a
tio
n
(
1
6
)
Up
d
a
te
y
)
u
s
in
g
eq
u
a
tio
n
(
1
8
)
F
o
r
ea
ch
d
imen
s
io
n
j= 1
,
…,
N
d
do
A
p
p
ly
ve
lo
city
u
p
d
a
te
u
s
in
g
eq
u
a
tio
n
(
1
9
)
En
d
lo
o
p
A
p
p
ly
p
o
s
itio
n
u
p
d
a
te
u
s
in
g
e
q
u
a
tio
n
(
2
1
)
E
n
d
lo
o
p
Un
itl s
o
me
co
n
ve
r
g
en
ce
crit
eria
is
s
a
tis
fied
4
.
2
.
O
bje
ct
iv
e
f
un
ct
io
n f
o
rm
ula
t
io
n
I
n
th
is
s
tu
d
y
,
th
e
P
SO
alg
o
r
i
th
m
i
s
p
r
o
p
o
s
ed
to
tu
n
e
th
e
P
I
p
ar
am
eter
s
o
f
v
o
lta
g
e
co
n
tr
o
ller
b
y
m
i
n
i
m
izi
n
g
t
h
e
co
s
t
f
u
n
ct
io
n
.
So
th
at,
th
e
p
r
o
p
o
r
tio
n
al
(
kp
)
an
d
in
te
g
r
al
(
ki
)
g
ain
s
o
f
P
I
co
n
tr
o
ller
is
d
ef
in
ed
as th
e
p
r
o
b
le
m
p
ar
a
m
eter
s
t
h
at
s
h
o
u
ld
b
e
o
p
ti
m
ized
.
T
h
u
s
,
ea
ch
i
n
d
i
v
id
u
al
o
f
p
o
p
u
latio
n
is
co
m
p
o
s
ed
o
f
th
e
co
n
tr
o
ller
p
ar
a
m
eter
s
kp
an
d
ki.
T
h
en
,
t
h
e
o
p
tim
izatio
n
p
r
o
b
le
m
o
f
P
I
c
o
n
tr
o
ller
is
f
o
r
m
u
lated
as
th
e
m
in
i
m
iza
tio
n
o
f
t
h
e
in
te
g
r
al
ti
m
e
ab
s
o
lu
te
er
r
o
r
I
T
A
E
an
d
o
f
th
e
m
ax
i
m
u
m
o
v
er
s
h
o
o
t.
T
h
er
ef
o
r
e,
th
e
o
b
j
ec
ti
v
e
f
u
n
ctio
n
i
s
d
ef
i
n
ed
as:
0
1
.
n
ts
t
t
j
t
e
r
r
d
t
(
20
)
m
i
n
m
a
x
p
p
p
k
k
k
,
i
m
i
n
i
m
a
x
i
k
k
k
W
h
er
e:
n
: is th
e
to
tal
n
u
m
b
er
o
f
p
o
in
ts
f
o
r
w
h
ic
h
th
e
o
p
ti
m
izatio
n
i
s
ca
r
r
ied
o
u
t.
ts
: is t
h
e
ti
m
e
r
an
g
o
f
s
i
m
u
lati
o
n
o
r
s
i
m
u
latio
n
p
er
io
d
.
Fig
u
r
e
8
.
I
n
s
er
tio
n
o
f
P
SO
A
p
p
r
o
ac
h
w
it
h
th
e
P
I
C
o
n
tr
o
ller
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
AND
ANA
L
YS
I
S
T
h
e
s
y
s
te
m
d
ep
icted
in
Fi
g
u
r
e.
1
an
d
6
h
as
b
ee
n
s
i
m
u
lat
ed
u
s
in
g
th
e
Si
m
P
o
w
er
S
y
s
te
m
w
it
h
S
-
f
u
n
ctio
n
o
f
Ma
tlab
/S
i
m
u
li
n
k
i
n
s
tal
led
o
n
a
co
m
p
u
ter
s
y
s
te
m
w
it
h
I
n
tel
C
o
r
e
i5
-
4
2
1
0
C
PU,
1
.
7
0
GHz
s
p
ee
d
an
d
4
GO
o
f
m
e
m
o
r
y
.
P
ar
am
et
er
s
u
s
ed
in
s
i
m
u
latio
n
ar
e
as
f
o
llo
w
s:
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:
2
0
8
8
-
8694
P
S
O
b
a
s
ed
Dir
ec
t P
o
w
er C
o
n
tr
o
l fo
r
a
Mu
ltif
u
n
ctio
n
a
l G
r
id
C
o
n
n
ec
ted
P
h
o
to
vo
lta
ic
.
.
.
(
M.R
.
B
en
g
o
u
r
in
a
)
617
T
ab
le
2
.
P
ar
am
eter
s
o
f
P
SO
A
l
g
o
r
ith
m
P
a
r
a
me
t
e
r
V
a
l
u
e
s
S
w
a
r
m si
z
e
10
N
u
mb
e
r
o
f
i
t
e
r
a
t
i
o
n
s
1
0
0
r1
0
.
3
r2
0
.
9
5
c1
1
.
4
5
c2
1
.
4
5
T
ab
le
3
.
P
ar
am
eter
s
o
f
DC
-
D
C
B
o
o
s
t Co
n
v
er
ter
P
a
r
a
me
t
e
r
V
a
l
u
e
s
f
sw
i
t
c
h
i
n
g
5
k
H
z
O
u
t
p
u
t
v
o
l
t
a
g
e
4
0
0
V
I
n
d
u
c
t
o
r
L
1
0
m
H
C
a
p
a
c
i
t
o
r
C
1
0
0
µ
F
T
ab
le
4
.
SA
P
F P
ar
am
eter
s
.
P
a
r
a
me
t
e
r
V
a
l
u
e
s
S
o
u
r
c
e
v
o
l
t
a
g
e
1
2
5
V
S
u
p
p
l
y
f
r
e
q
u
e
n
c
y
5
0
H
z
S
o
u
r
c
e
i
mp
e
d
a
n
c
e
R
S
,
L
S
0
.
1
Ω
,
0
.
1
mH
F
i
l
t
e
r
i
mp
e
d
a
n
c
e
R
f
, L
f
0
.
1
Ω
,
2
.
6
mH
L
i
n
e
i
mp
e
d
a
n
c
e
R
l
, L
l
0
.
1
Ω
,
0
.
5
mH
DC
-
l
i
n
k
c
a
p
a
t
i
t
o
r
C
2
.
2
µ
H
D
i
o
d
e
r
e
c
t
i
f
i
e
r
l
o
a
d
R
L
, L
L
2
0
Ω
,
2
mH
T
h
e
s
o
u
r
ce
cu
r
r
en
t
an
d
i
ts
s
p
ec
tr
u
m
b
ef
o
r
e
co
n
n
ec
ti
n
g
S
AP
F
f
ee
d
b
y
P
V
s
y
s
te
m
ar
e
ill
u
s
tr
ated
i
n
Fig
u
r
e
9
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
s
y
s
te
m
is
a
f
f
ec
ted
b
y
th
e
n
o
n
lin
ea
r
lo
ad
d
u
r
in
g
th
e
o
p
er
atio
n
.
W
h
er
e,
th
e
T
o
tal
Har
m
o
n
ic
Di
s
to
r
tio
n
(
T
HD)
o
f
th
e
s
u
p
p
l
y
c
u
r
r
en
t is
h
i
g
h
a
n
d
eq
u
als 2
7
.
5
7
%.
(
a)
(
b
)
Fig
u
r
e
9
.
(
a)
Su
p
p
ly
C
u
r
r
e
n
t b
ef
o
r
e
Har
m
o
n
ic
s
C
o
m
p
e
n
s
at
io
n
,
(
b
)
Har
m
o
n
ic
Sp
ec
tr
u
m
.
To
v
er
if
y
th
e
p
er
f
o
r
m
an
ce
s
a
n
d
r
o
b
u
s
tn
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
an
d
th
e
r
esear
ch
al
g
o
r
ith
m
o
f
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
tr
ac
k
i
n
g
(
MP
PT
)
,
a
v
ar
iab
le
p
r
o
f
ile
ir
r
ad
ian
ce
to
s
w
ee
p
all
m
o
d
es
o
f
o
p
er
atio
n
o
f
o
u
r
s
y
s
te
m
i
s
d
o
n
e.
Fig
u
r
e
1
0
s
h
o
w
s
t
h
e
s
o
lar
ir
r
ad
ian
ce
lev
el
s
tar
ts
f
r
o
m
0
W
/
m
2
,
t
h
en
i
n
cr
ea
s
es
to
6
0
0
W
/m
2
,
af
ter
th
at
d
ec
r
ea
s
e
s
to
2
0
0
W
/
m
2
an
d
f
in
al
l
y
i
n
cr
ea
s
es to
1
0
0
0
W
/
m
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N:
2
0
8
8
-
8694
I
n
t
J
P
o
w
E
lec
&
Dr
i S
y
s
t,
Vo
l.
9
,
No
.
2
,
J
u
n
e
2
0
1
8
:
610
–
621
618
(
a)
(
b
)
Fig
u
r
e
1
0
.
(
a)
So
lar
R
ad
iatio
n
.
(
b
)
C
u
r
r
en
t P
V
A
r
r
a
y
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(
f
)
Fig
u
r
e
1
1
.
Si
m
u
latio
n
R
es
u
lts
o
f
th
e
P
r
o
p
o
s
ed
D
P
C
w
it
h
P
I
C
o
n
tr
o
ller
: (
a)
So
u
r
ce
C
u
r
r
e
n
t
,
(
b
)
So
u
r
ce
Vo
ltag
e
an
d
So
u
r
ce
C
u
r
r
en
t,
(
c)
Fil
ter
C
u
r
r
en
t,
(
d
)
R
ea
ctiv
e
P
o
w
er
,
(
e)
DC
-
L
in
k
Vo
lta
g
e
v
d
c,
(
f
)
A
cti
v
e
P
o
w
er
an
d
P
V
P
o
w
er
.
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:
2
0
8
8
-
8694
P
S
O
b
a
s
ed
Dir
ec
t P
o
w
er C
o
n
tr
o
l fo
r
a
Mu
ltif
u
n
ctio
n
a
l G
r
id
C
o
n
n
ec
ted
P
h
o
to
vo
lta
ic
.
.
.
(
M.R
.
B
en
g
o
u
r
in
a
)
619
(
a)
(
b
)
(
c)
(
d
)
(
e)
(
f
)
Fig
u
r
e
1
2
.
Si
m
u
latio
n
R
es
u
lts
o
f
th
e
P
r
o
p
o
s
ed
D
P
C
w
it
h
P
I
-
P
SO Co
n
tr
o
ller
: (
a)
So
u
r
ce
C
u
r
r
en
t,
(
b
)
So
u
r
ce
Vo
ltag
e
an
d
So
u
r
ce
C
u
r
r
en
t,
(
c)
Fil
ter
C
u
r
r
en
t,
(
d
)
R
ea
ctiv
e
P
o
w
er
,
(
e)
DC
-
L
in
k
Vo
lta
g
e
Vd
c,
(
f
)
A
cti
v
e
P
o
w
er
an
d
P
V
P
o
w
e
r.
Fig
u
r
e
1
1
an
d
1
2
s
h
o
w
s
th
e
s
y
s
te
m
w
it
h
P
I
an
d
P
I
-
P
SO
co
n
tr
o
ller
s
.
T
h
e
s
o
u
r
ce
c
u
r
r
en
t
(
I
s
)
,
s
o
u
r
ce
v
o
ltag
e
(
V
s
)
,
f
ilter
cu
r
r
e
n
t
(
I
f
)
,
DC
b
u
s
v
o
lta
g
e
(
Vd
c)
,
r
ea
ctiv
e
p
o
w
er
(
q
s
)
,
ac
tiv
e
p
o
w
er
(
P
s
)
an
d
P
V
p
o
w
er
(
P
p
v
)
ar
e
d
ep
icted
.
T
h
e
r
esu
lts
s
h
o
w
t
h
at
th
e
t
h
e
n
et
w
o
r
k
cu
r
r
en
t
b
ec
o
m
e
p
er
f
ec
tl
y
s
in
u
s
o
id
al
af
ter
th
e
co
n
tr
o
l
ap
p
licatio
n
an
d
r
e
m
ai
n
in
p
h
ase
w
i
th
t
h
e
co
r
r
esp
o
n
d
in
g
v
o
ltag
e
s
.
T
h
e
ch
an
g
e
i
n
r
ad
iatio
n
d
o
n
’
t
a
f
f
ec
t
DC
li
n
k
v
o
lta
g
e
b
u
t
ch
a
n
g
e
t
h
e
li
n
e
s
id
e
ac
t
iv
e
p
o
w
er
an
d
th
e
a
m
p
lit
u
d
e
o
f
t
h
e
li
n
e
c
u
r
r
en
t.
T
h
e
r
ea
ctiv
e
p
o
w
er
is
al
w
a
y
s
ze
r
o
.
W
e
ca
n
o
b
s
er
v
ed
f
r
o
m
[
0
.
3
s
-
0
.
5
s
]
an
d
[
0
.
8
s
-
1
s
]
,
th
e
o
p
p
o
s
ite
p
h
ase
b
et
w
ee
n
v
o
lta
g
e
a
n
d
cu
r
r
en
t
s
o
u
r
ce
an
d
th
e
n
e
g
ati
v
e
s
i
g
n
o
f
th
e
u
tili
t
y
ac
ti
v
e
p
o
w
er
(
P
s
)
,
m
ea
n
in
g
t
h
e
f
il
ter
cu
r
r
en
t
h
as
i
n
f
o
r
m
atio
n
o
f
h
ar
m
o
n
i
c
a
n
d
P
V
ar
r
a
y
c
u
r
r
en
ts
to
en
s
u
r
e
eli
m
in
a
tio
n
o
f
h
ar
m
o
n
ic
a
n
d
i
n
j
ec
tio
n
o
f
c
u
r
r
en
t
to
th
e
lo
ad
.
T
h
e
d
c
lin
k
v
o
lta
g
e
r
et
u
r
n
s
to
it
s
r
ef
e
r
en
ce
v
al
u
e
i
n
f
e
w
m
il
lis
ec
o
n
d
s
,
w
i
th
o
u
t
o
v
er
s
h
o
o
t
an
d
u
n
d
er
s
h
o
o
ts
,
as
s
h
o
wn
in
Fi
g
u
r
e
1
2
e,
d
em
o
n
s
tr
ate
s
th
e
s
u
p
er
io
r
it
y
o
f
t
h
e
P
I
-
P
SO c
o
n
tr
o
ller
co
m
p
ar
ed
to
its
co
u
n
te
r
p
ar
t PI
co
n
tr
o
ller
.
Fig
u
r
e
1
3
s
h
o
w
h
ar
m
o
n
ic
s
p
ec
tr
u
m
o
f
s
o
u
r
ce
cu
r
r
en
t
at
0
W
/
m
².
T
h
e
ac
tiv
e
f
il
ter
d
ec
r
ea
s
es
th
e
to
ta
l
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
f
r
o
m
2
7
.
5
7
%
to
1
.
8
3
%
w
it
h
P
I
co
n
tr
o
ller
.
Ho
w
ev
er
,
w
ith
P
I
-
P
SO
co
n
tr
o
ller
th
e
T
HD
is
in
cr
ea
s
ed
to
1
.
2
8
%
w
h
ich
p
r
o
v
es
t
h
e
e
f
f
ec
ti
v
e
n
ess
o
f
t
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
.
P
er
f
o
r
m
an
ce
o
f
p
r
o
p
o
s
ed
co
n
tr
o
l
is
ev
alu
ated
in
ter
m
o
f
T
HDi
lev
el
b
eh
av
io
r
u
n
d
er
f
ast
ch
a
n
g
in
g
ir
r
ad
iatio
n
as
w
ell
as
ch
an
g
i
n
g
o
p
er
atio
n
m
o
d
es a
s
s
h
o
w
n
i
n
T
ab
le
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.