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lex
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y
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rid
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m
s.
K
ey
w
o
r
d
s
:
Du
al
ac
tiv
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b
r
id
g
e
Gain
-
s
ch
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u
led
PI
c
o
n
tr
o
ller
M
ax
im
u
m
p
o
wer
p
o
i
n
t tr
ac
k
in
g
Ph
o
to
v
o
ltaic
p
a
n
el
Sin
g
le
p
h
ase
s
h
if
t m
o
d
u
latio
n
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
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r
:
Kh
alid
Sab
h
i
Dep
ar
tm
en
t o
f
Ph
y
s
ics,
L
ab
o
r
ato
r
y
o
f
I
n
f
o
r
m
atio
n
Pro
ce
s
s
in
g
,
Facu
lty
o
f
Scien
ce
s
B
en
M’
Sick
Hass
an
I
I
Un
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s
ity
o
f
C
asab
lan
ca
C
asab
lan
ca
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Mo
r
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cc
o
E
m
ail: sab
h
i.k
h
alid
.
im
t@
g
m
ai
l.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
Stan
d
alo
n
e
p
h
o
to
v
o
ltaic
(
PV
-
b
atter
y
)
s
y
s
tem
s
ar
e
ess
en
tial
f
o
r
p
o
wer
in
g
o
f
f
-
g
r
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d
lo
ca
ti
o
n
s
.
T
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eir
p
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f
o
r
m
an
ce
d
ep
en
d
s
o
n
two
m
ain
f
ac
to
r
s
:
th
e
PV
-
b
atter
y
c
o
m
b
in
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n
an
d
th
e
a
d
o
p
ted
c
o
n
tr
o
l
s
tr
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y
.
PV
p
an
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n
d
er
g
o
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p
id
v
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s
in
s
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ad
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G
[
1
]
,
[
2
]
,
wh
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ca
n
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s
e
cu
r
r
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s
cillatio
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s
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in
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ate
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MPP)
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an
d
a
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u
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v
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all
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[
3
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[6
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F
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in
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[
7
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-
[
9
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.
T
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m
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PV
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ased
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DC
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ates
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[
1
0
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[
1
2
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.
T
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s
tr
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im
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b
u
t
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th
e
d
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n
d
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o
n
th
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d
u
ty
cy
cle
d
ir
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m
o
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f
ies
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
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3
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Sep
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20
2
6
:
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3
1
3
1300
co
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s
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in
d
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p
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4
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u
d
p
ass
ag
e)
,
wh
er
ea
s
m
o
s
t
ex
is
tin
g
s
tr
ateg
ies
ar
e
o
n
ly
v
alid
ated
o
n
ab
r
u
p
t
G
s
tep
s
,
an
d
r
ea
l
-
wo
r
ld
d
y
n
am
ics
ar
e
co
n
tin
u
o
u
s
an
d
s
ig
n
if
ica
n
tly
alter
th
e
s
m
all
-
s
ig
n
al
b
eh
av
io
r
at
ea
ch
o
p
er
atin
g
p
o
i
n
t
[
1
5
]
,
[
1
6
]
.
M
o
r
eo
v
e
r
,
th
e
p
r
o
n
o
u
n
ce
d
n
o
n
lin
ea
r
ity
o
f
th
e
p
h
o
to
v
o
ltaic
(
PV)
g
en
er
a
to
r
,
co
u
p
le
d
with
th
e
b
ilin
ea
r
ch
ar
ac
ter
is
tics
o
f
p
o
wer
tr
a
n
s
f
er
in
th
e
DAB,
r
en
d
er
s
t
h
e
s
y
s
tem
p
er
f
o
r
m
a
n
ce
,
s
p
ec
if
ically
in
te
r
m
s
o
f
s
p
ee
d
a
n
d
d
am
p
in
g
,
h
ig
h
ly
co
n
tin
g
en
t
o
n
th
e
o
p
er
atin
g
p
o
in
t
wh
en
u
tili
zin
g
a
co
n
v
e
n
tio
n
al
p
r
o
p
o
r
tio
n
a
l
-
in
teg
r
al
PI
co
n
tr
o
ller
.
Ver
y
f
ew
s
tu
d
ies
h
av
e
p
r
o
p
o
s
ed
a
s
im
p
le
an
d
s
y
s
tem
atic
r
ec
alcu
latio
n
o
f
th
e
g
a
in
s
in
r
ea
l
tim
e
with
ex
p
licit
co
m
p
en
s
atio
n
f
o
r
m
ea
s
u
r
ab
le
d
is
tu
r
b
an
ce
s
(
G
a
n
d
T
s
lo
p
es)
with
o
u
t
a
co
m
p
l
ex
o
b
s
er
v
er
o
r
co
m
p
u
tatio
n
all
y
in
ten
s
iv
e
an
aly
s
is
[
1
7
]
-
[
2
0
]
.
T
h
is
s
tu
d
y
p
r
o
p
o
s
e
d
a
g
ain
-
s
ch
ed
u
led
PI
with
ex
p
licit
p
er
tu
r
b
atio
n
co
m
p
en
s
atio
n
,
r
e
ca
lcu
latin
g
g
ain
s
an
d
ev
er
y
1
u
s
b
y
f
ast
l
o
ca
l
lin
ea
r
izatio
n
o
f
th
e
n
o
n
li
n
ea
r
PV
-
DAB
-
b
atter
y
m
o
d
el
an
d
in
jectin
g
a
co
r
r
ec
tio
n
ter
m
b
ased
o
n
th
e
m
ea
s
u
r
ed
d
er
i
v
ativ
es
o
f
G
a
n
d
T
.
As
d
ep
icted
i
n
Fig
u
r
e
1
,
t
h
is
co
n
tr
o
l,
wh
ic
h
is
n
o
v
el
in
th
e
liter
atu
r
e
f
o
r
th
is
to
p
o
lo
g
y
[
2
1
]
,
[
2
2
]
,
e
n
s
u
r
es
s
tr
ictly
s
ec
o
n
d
-
o
r
d
er
d
y
n
am
ics,
ch
ar
ac
ter
ized
b
y
a
co
n
s
tan
t
r
esp
o
n
s
e
tim
e
an
d
o
v
er
s
h
o
o
t
ac
r
o
s
s
th
e
en
tire
o
p
e
r
atin
g
r
a
n
g
e.
I
t
ef
f
ec
tiv
ely
eli
m
in
ates
o
s
cillatio
n
s
an
d
tr
ac
k
i
n
g
lo
s
s
es
o
f
th
e
r
ef
er
en
ce
cu
r
r
en
t
d
u
r
in
g
r
ea
li
s
tic
p
r
o
g
r
ess
iv
e
ir
r
ad
ian
ce
v
ar
iatio
n
s
,
s
u
ch
as
co
n
tin
u
o
u
s
s
lo
p
es
th
at
s
im
u
lat
e
clo
u
d
p
ass
ag
e.
Fu
r
th
er
m
o
r
e,
it
ac
h
iev
es
th
ese
o
u
tco
m
es
with
o
u
t
th
e
n
ee
d
f
o
r
a
co
m
p
lex
o
b
s
er
v
e
r
o
r
ex
ce
s
s
iv
e
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
,
th
er
eb
y
o
f
f
er
in
g
a
s
tr
aig
h
tf
o
r
war
d
a
n
d
r
o
b
u
s
t
s
o
lu
tio
n
th
at
ca
n
b
e
d
ir
ec
tly
i
m
p
lem
en
ted
in
DAB
-
b
ased
PV
-
b
atter
y
s
y
s
tem
s
[
2
3
]
,
[
2
4
]
.
T
h
e
r
em
ain
d
er
o
f
th
is
m
an
u
s
cr
ip
t
is
s
tr
u
ctu
r
ed
as
f
o
llo
ws:
Sectio
n
2
estab
lis
h
es
th
e
co
m
p
lete
n
o
n
lin
ea
r
m
ath
e
m
atica
l
m
o
d
e
l
o
f
th
e
PV
-
DAB
-
b
atter
y
s
u
b
s
y
s
tem
an
d
its
lo
ca
l
l
in
ea
r
izatio
n
at
ea
ch
in
s
tan
t;
Sectio
n
3
d
etails
th
e
d
esig
n
o
f
th
e
PI
with
p
r
o
g
r
am
m
ed
g
ain
s
,
th
e
an
aly
tical
ca
lcu
latio
n
o
f
th
e
g
ain
s
K_
p
an
d
K_
i
as
a
f
u
n
ctio
n
o
f
th
e
in
s
t
an
tan
eo
u
s
o
p
er
atin
g
p
o
in
t,
an
d
th
e
ad
d
itio
n
o
f
th
e
c
o
m
p
e
n
s
atio
n
ter
m
f
o
r
th
e
m
ea
s
u
r
ed
d
is
tu
r
b
an
ce
s
;
Sectio
n
4
p
r
esen
ts
th
e
r
esu
lts
o
f
th
e
MA
T
L
AB
/Si
m
u
lin
k
s
im
u
latio
n
s
u
n
d
er
r
ea
lis
tic
ir
r
ad
ian
ce
p
r
o
f
iles
(
co
n
tin
u
o
u
s
s
lo
p
es),
co
m
p
ar
es
th
e
p
er
f
o
r
m
an
ce
with
th
at
o
f
a
co
n
v
en
ti
o
n
al
PI
with
f
ix
ed
g
ain
s
,
an
d
d
em
o
n
s
tr
ates
th
e
p
er
f
ec
t
co
n
s
tan
cy
o
f
th
e
s
ec
o
n
d
-
o
r
d
er
d
y
n
am
ics
as
we
ll
as
th
e
co
m
p
lete
elim
in
atio
n
o
f
o
s
cillatio
n
s
;
f
i
n
ally
,
Sectio
n
5
co
n
clu
d
es
w
ith
th
e
c
o
n
tr
ib
u
tio
n
s
o
f
th
is
s
tu
d
y
,
d
is
cu
s
s
es
th
e
r
em
ain
in
g
lim
itatio
n
s
(
ac
tu
a
l
m
ea
s
u
r
em
en
t
u
n
ce
r
tain
ties
,
r
ea
l
-
tim
e
im
p
lem
e
n
tatio
n
)
,
an
d
o
u
tlin
es
th
e
ex
p
er
im
en
tal
p
e
r
s
p
ec
tiv
es a
n
d
p
o
s
s
ib
le
ex
ten
s
io
n
s
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
th
e
s
y
s
tem
an
d
co
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
MPP
T
c
o
n
tr
o
l o
f a
P
V
-
b
a
tter
y
s
ystem
u
s
in
g
a
g
a
in
-
s
ch
e
d
u
le
d
a
d
a
p
tive
P
I
c
o
n
tr
o
ller
…
(
K
h
a
lid
S
a
b
h
i
)
1301
2.
M
E
T
H
O
D
2
.
1
.
Sim
ula
t
i
o
n pla
t
f
o
r
m
a
n
d v
a
lid
a
t
io
n pro
t
o
co
l
All
th
e
r
esu
lts
p
r
esen
ted
in
th
i
s
ar
ticle
wer
e
o
b
tain
ed
th
r
o
u
g
h
s
im
u
latio
n
s
u
s
in
g
MA
T
L
A
B
/Si
m
u
lin
k
R
2
0
2
3
b
(
with
o
u
t
Simscap
e
E
lectr
ical
)
with
a
f
ix
ed
-
s
tep
s
o
lv
er
o
f
1
×
10
−
6
(
f
ix
ed
-
s
tep
,
a
u
to
s
o
lv
er
)
.
T
h
e
DAB
co
n
v
er
ter
was
m
o
d
eled
in
th
e
s
witch
ed
s
tate
(
s
witch
in
g
m
o
d
el)
f
o
r
m
ax
im
u
m
ac
cu
r
ac
y
[
2
5
]
.
T
h
e
b
atter
y
is
r
ep
r
esen
ted
b
y
th
e
s
tan
d
ar
d
Simu
lin
k
"
b
atte
r
y
"
b
l
o
ck
(
lith
iu
m
-
io
n
,
n
o
m
in
al
v
o
ltag
e
5
0
0
V,
ca
p
ac
ity
2
0
0
Ah
)
[
2
6
]
,
[
2
7
]
.
T
h
e
v
ar
iatio
n
s
in
s
u
n
lig
h
t
wer
e
g
en
er
ated
ac
co
r
d
in
g
to
r
ea
lis
tic
p
r
o
f
iles
in
s
p
ir
ed
b
y
th
e
E
N
5
0
5
3
0
s
tan
d
ar
d
(
r
am
p
s
o
f
1
0
–
5
0
W
/m
²/s
,
s
tep
s
1
0
0
–
1
0
0
0
W
/m
²
an
d
cl
o
u
d
p
ass
ag
es
o
f
a
f
ew
s
ec
o
n
d
s
)
.
2
.
2
.
Sy
s
t
e
m
mo
delin
g
a
nd
s
i
zing
2
.
2
.
1
.
P
ho
t
o
v
o
lt
a
ic
s
o
urce
T
h
e
s
im
u
lated
p
h
o
t
o
v
o
ltaic
a
r
r
ay
d
eliv
e
r
ed
a
p
ea
k
p
o
wer
o
f
6
4
k
W
u
n
d
e
r
STC
co
n
d
itio
n
s
(
G
=
1
0
0
0
W
/m
²,
T
=
2
5
°C
)
.
I
t
co
n
s
is
ts
o
f
1
5
p
ar
allel
b
r
an
ch
es
(
Np
=
1
5
)
,
ea
ch
c
o
m
p
r
is
in
g
2
0
m
o
d
u
les
in
s
er
ies
(
Ns
=
2
0
)
,
a
n
d
ea
c
h
m
o
d
u
le
is
co
m
p
o
s
ed
o
f
6
0
ce
lls
in
s
er
ies
(
Nc
=
6
0
)
.
T
h
e
elec
tr
ical
m
o
d
el
u
s
ed
is
th
e
class
ic
s
in
g
le
-
d
io
d
e
m
o
d
el
with
s
er
ies
an
d
p
ar
allel
r
esis
to
r
s
(
s
in
g
le
-
d
io
d
e
m
o
d
el
[
2
8
]
)
,
wh
ic
h
h
as
b
ee
n
wid
ely
v
alid
ated
in
th
e
liter
atu
r
e.
T
h
e
m
o
d
e
l
p
a
r
a
m
e
t
e
r
s
,
w
h
i
ch
w
e
r
e
d
e
t
e
r
m
i
n
e
d
t
o
a
c
c
u
r
a
t
e
l
y
r
e
p
r
o
d
u
c
e
t
h
e
m
a
n
u
f
a
c
t
u
r
e
r
'
s
c
h
a
r
a
ct
e
r
is
t
i
c
p
o
i
n
t
s
a
t
d
i
f
f
e
r
e
n
t
l
e
v
el
s
o
f
s
o
l
a
r
i
r
r
a
d
i
a
n
c
e
a
n
d
t
e
m
p
e
r
a
t
u
r
e
,
a
r
e
l
i
s
t
e
d
i
n
T
a
b
l
e
1
.
Acc
u
r
ate
p
an
el
m
o
d
elin
g
is
es
s
en
tial
f
o
r
m
o
n
ito
r
in
g
MPPs
a
n
d
m
an
ag
i
n
g
en
v
ir
o
n
m
e
n
tal
v
ar
iatio
n
s
.
An
e
q
u
iv
ale
n
t
d
ia
g
r
am
(
Fig
u
r
e
2
)
b
ased
o
n
t
h
e
s
in
g
le
d
io
d
e
m
o
d
el
ca
p
tu
r
es
t
h
e
n
o
n
lin
ea
r
b
eh
av
i
o
r
s
,
cu
r
r
en
t
g
en
er
ato
r
(
ℎ
)
f
o
r
p
h
o
t
o
cu
r
r
e
n
t,
p
ar
allel
d
io
d
e
(
)
f
o
r
p
-
n
ju
n
ctio
n
a
n
d
p
ar
asit
ic
r
esis
tan
ce
s
f
o
r
im
p
er
f
ec
tio
n
s
.
R
esp
ec
tiv
ely
ℎ
r
ep
r
esen
ts
d
ef
ec
t
lo
s
s
es
(
s
h
o
r
t
cir
cu
its
,
im
p
u
r
ities
)
,
an
d
r
esis
tiv
e
lo
s
s
es
(
m
etal
co
n
tacts,
s
em
ico
n
d
u
cto
r
lay
er
s
)
.
T
h
e
co
m
p
lete
s
tr
u
ctu
r
e,
s
h
o
w
n
in
Fig
u
r
e
3
,
ad
ap
ts
th
e
v
o
lta
g
e
an
d
cu
r
r
en
t
to
th
e
r
e
q
u
ir
em
en
ts
o
f
th
e
DAB
-
b
atter
y
s
y
s
tem
.
T
h
e
to
t
al
p
an
el
c
u
r
r
en
t
,
p
h
o
to
c
u
r
r
e
n
t
t
ℎ
,
an
d
d
i
o
d
e
c
u
r
r
en
t
ar
e
e
x
p
r
ess
ed
as
f
o
llo
ws
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=
ℎ
−
−
ℎ
(
1
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ℎ
=
ℎ
_
0
1000
(
1
+
(
−
25
)
)
(
2
)
=
0
(
(
)
−
1
)
(
3
)
wh
er
e
=
1
.
602
∗
10
−
19
(
elem
en
tar
y
ch
a
r
g
e
)
,
=
0
.
98119
(
d
io
d
e
id
ea
lity
f
ac
to
r
,
id
ea
l
ju
n
ctio
n
d
ev
iatio
n
s
)
,
a
n
d
=
1
.
381
∗
10
−
23
/
(
B
o
ltzm
an
n
co
n
s
tan
t,
th
er
m
al
en
er
g
y
)
.
T
h
e
d
io
d
e
v
o
ltag
e
,
s
h
u
n
t
cu
r
r
en
t
ℎ
,
r
ep
r
esen
tin
g
th
e
lo
s
s
es in
ℎ
,
ar
e:
=
+
(
4
)
ℎ
=
ℎ
+
ℎ
(
5
)
w
h
er
e
is
th
e
p
an
el
v
o
ltag
e,
is
th
e
s
er
ies
r
esis
tan
ce
,
an
d
ar
e
th
e
n
u
m
b
er
o
f
ce
lls
in
s
er
ies
a
n
d
to
tal.
Fig
u
r
e
2
.
E
q
u
iv
alen
t sin
g
le
-
d
i
o
d
e
cir
cu
it o
f
a
PV c
ell,
s
h
o
win
g
th
e
p
h
o
to
c
u
r
r
en
t so
u
r
ce
ip
h
,
d
i
o
d
e,
s
er
ies
r
esis
tan
ce
R
s
,
an
d
s
h
u
n
t r
esis
t
an
ce
R
s
h
Fig
u
r
e
3
.
E
q
u
iv
alen
t
d
iag
r
am
o
f
th
e
PV p
an
el
u
s
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
2
9
9
-
1
3
1
3
1302
T
ab
le
1
.
Ph
o
t
o
v
o
ltaic
m
o
d
el
p
ar
am
eter
s
at
STC (
1
0
0
0
W
/m
²
,
2
5
°C
)
P
a
r
a
me
t
e
r
V
a
l
u
e
Li
g
h
t
-
g
e
n
e
r
a
t
e
d
c
u
r
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e
n
t
I
L
7
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8
6
5
4
A
D
i
o
d
e
s
a
t
u
r
a
t
i
o
n
c
u
r
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e
n
t
I
₀
2
.
9
2
7
3
×
1
0
⁻
¹⁰ A
D
i
o
d
e
i
d
e
a
l
i
t
y
f
a
c
t
o
r
a
0
.
9
8
1
1
9
S
e
r
i
e
s r
e
si
s
t
a
n
c
e
R
s
(
p
e
r
m
o
d
u
l
e
)
0
.
3
9
3
8
1
Ω
S
h
u
n
t
r
e
si
st
a
n
c
e
R
sh
(
p
e
r
m
o
d
u
l
e
)
3
1
3
.
0
5
5
3
Ω
T
o
v
alid
ate
t
h
e
ac
cu
r
ac
y
o
f
th
e
ad
o
p
ted
o
n
e
-
d
io
d
e
m
o
d
el
,
th
e
s
im
u
lated
I
–
V
ch
a
r
ac
te
r
is
tics
ar
e
co
m
p
ar
ed
with
th
e
m
an
u
f
ac
tu
r
er
’
s
d
atash
ee
t
o
f
th
e
p
h
o
to
v
o
ltaic
m
o
d
u
le
A1
0
Gr
ee
n
T
ec
h
n
o
lo
g
y
A
1
0
J
-
M6
0
-
2
2
0
.
T
h
e
m
o
d
el
p
ar
am
eter
s
ar
e
ad
ju
s
ted
to
m
atch
th
e
k
ey
el
ec
tr
ical
s
p
ec
if
icatio
n
s
at
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
STC),
in
clu
d
in
g
o
p
en
-
ci
r
cu
it
v
o
ltag
e,
s
h
o
r
t
-
cir
cu
i
t
cu
r
r
en
t,
a
n
d
m
ax
im
u
m
p
o
wer
p
o
in
t.
As
s
h
o
wn
in
F
ig
u
r
e
4
,
th
e
o
b
tain
ed
I
–
V
cu
r
v
es
u
n
d
er
d
if
f
er
en
t
ir
r
ad
ian
ce
lev
els
an
d
ce
ll
tem
p
er
atu
r
es
d
em
o
n
s
tr
ate
a
g
o
o
d
ag
r
ee
m
e
n
t
with
th
e
ex
p
ec
ted
b
eh
a
v
io
r
o
f
th
e
m
o
d
u
le,
co
n
f
ir
m
in
g
th
e
v
alid
ity
o
f
th
e
ad
o
p
ted
m
o
d
el.
(
a)
(
b
)
Fig
u
r
e
4
.
C
u
r
r
e
n
t
–
v
o
ltag
e
ch
a
r
ac
ter
is
tics
o
f
th
e
p
h
o
to
v
o
ltaic
m
o
d
u
le
A1
0
Gr
ee
n
T
ec
h
n
o
lo
g
y
A1
0
J
-
M6
0
-
2
2
0
:
(
a)
u
n
d
er
v
a
r
io
u
s
ir
r
a
d
ian
ce
le
v
els
an
d
(
b
)
u
n
d
er
d
i
f
f
er
en
t c
e
ll tem
p
er
atu
r
es
2
.
2
.
2
.
Av
er
a
g
e
inp
ut
curr
ent
a
na
ly
s
is
f
o
r
DAB co
nv
er
t
er
T
h
e
p
h
o
to
v
o
ltaic
ar
r
ay
is
in
ter
f
ac
ed
with
th
e
b
atter
y
v
ia
a
DAB
co
n
v
er
ter
(
Fig
u
r
e
1
)
with
th
e
f
o
llo
win
g
s
im
u
latio
n
p
ar
am
ete
r
s
:
-
L
ea
k
ag
e
in
d
u
ctan
ce
(
r
ef
er
r
e
d
t
o
th
e
PV sid
e)
: L
=
5
0
µH
-
Switch
in
g
f
r
eq
u
e
n
cy
: f
s
=
1
0
k
Hz
-
T
r
an
s
f
o
r
m
atio
n
r
atio
: n
=
1
:1
-
Fil
ter
in
g
ca
p
ac
itan
ce
o
n
th
e
P
V
s
id
e:
C
p
v
=
3
m
F
-
C
o
n
tr
o
l:
s
in
g
le
p
h
ase
s
h
if
t
(
SP
S)
with
a
n
o
r
m
alize
d
p
h
ase
r
at
io
d
∈
[
0
,
0
.
5
]
SP
S
co
n
tr
o
l
was
ch
o
s
en
f
o
r
its
s
im
p
licity
,
r
o
b
u
s
tn
ess
,
an
d
ex
ten
s
iv
e
v
alid
atio
n
[
2
9
]
in
h
ig
h
-
p
o
wer
PV
-
b
atter
y
ap
p
licatio
n
s
;
ad
v
an
ce
d
m
o
d
u
latio
n
s
(
E
PS
,
DPS,
an
d
T
PS
)
wer
e
b
ey
o
n
d
th
e
s
co
p
e
o
f
th
is
s
tu
d
y
.
T
h
is
ex
p
r
ess
io
n
f
o
r
th
e
a
v
er
ag
e
DAB
in
p
u
t
cu
r
r
en
t
1
[
3
0
]
,
w
h
ich
is
cr
u
cial
f
o
r
s
izin
g
co
m
p
o
n
e
n
ts
an
d
o
p
tim
izin
g
co
n
v
er
ter
c
o
n
tr
o
l,
PV
in
p
u
t
cu
r
r
en
t,
,
s
p
lit
b
etwe
en
f
ilter
ca
p
ac
ito
r
cu
r
r
en
t
an
d
DAB
in
p
u
t
cu
r
r
en
t,
1
,
in
(
6
)
.
=
+
1
(
6
)
T
h
e
DAB
co
n
n
ec
ts
two
ac
tiv
e
b
r
id
g
es
v
ia
a
leak
a
g
e
in
d
u
ct
an
ce
tr
an
s
f
o
r
m
er
L
with
a
r
at
io
of
n
=1
.
B
r
id
g
e
1
(
PV
s
o
u
r
ce
)
:
in
p
u
t
v
o
ltag
e
,
o
u
tp
u
t
1
.
B
r
id
g
e
2
(
b
atter
y
)
:
in
p
u
t
v
o
ltag
e
,
o
u
tp
u
t
2
.
Vo
ltag
es
1
an
d
2
g
en
er
ated
b
y
s
q
u
ar
e
s
ig
n
als
1
an
d
2
,
f
r
eq
u
en
c
y
=
1
,
p
h
ase
s
h
i
f
t
=
2
,
d
in
[
0
,
1
]
n
o
r
m
alize
d
,
d
escr
ib
ed
in
Fig
u
r
e
1
.
T
h
e
in
d
u
ctan
ce
cu
r
r
en
t
is
g
o
v
er
n
e
d
b
y
(
7
)
.
=
1
−
2
(
7
)
T
h
e
SP
S
co
m
m
an
d
g
e
n
er
ates
f
o
u
r
d
is
tin
ct
p
h
ases
with
in
a
p
er
io
d
,
wh
ich
is
d
eter
m
in
ed
b
y
th
e
s
tates
o
f
1
an
d
2
,
as
s
h
o
wn
in
Fig
u
r
e
5
.
T
h
ese
p
h
ases
ar
e
d
escr
ib
ed
b
y
(
8
)
-
(
1
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
MPP
T
c
o
n
tr
o
l o
f a
P
V
-
b
a
tter
y
s
ystem
u
s
in
g
a
g
a
in
-
s
ch
e
d
u
le
d
a
d
a
p
tive
P
I
c
o
n
tr
o
ller
…
(
K
h
a
lid
S
a
b
h
i
)
1303
=
1
∫
(
+
)
(
8
)
=
1
∫
(
−
)
(
9
)
=
1
∫
(
−
−
)
(
1
0
)
=
1
∫
(
−
+
)
(
1
1
)
T
h
e
in
p
u
t c
u
r
r
e
n
t o
f
b
r
id
g
e
1
i
s
d
ef
in
ed
as f
o
llo
ws
(
12
)
:
1
=
1
(
1
2
)
T
h
e
av
er
ag
e
v
alu
e
<
1
>
is
ca
lcu
la
ted
b
y
ex
p
lo
itin
g
th
e
s
y
m
m
et
r
y
o
f
th
e
wav
ef
o
r
m
an
d
th
e
i
n
teg
r
als
[
3
1
]
;
we
o
b
tain
th
e
e
x
p
r
ess
io
n
(
1
3
)
,
wh
ich
will b
e
s
im
p
lifie
d
in
(
1
4
)
.
<
1
>
=
2
(
1
−
|
|
)
(
1
3
)
<
1
>
=
(
1
4
)
W
h
er
e
=
(
1
−
|
|
)
ca
p
tu
r
es th
e
ef
f
ec
t o
f
t
h
e
p
h
ase
s
h
if
t,
an
d
=
2
g
r
o
u
p
s
th
e
s
y
s
tem
p
ar
am
eter
s
.
Fig
u
r
e
5
.
F
o
u
r
o
p
er
atin
g
m
o
d
e
s
o
f
th
e
d
u
al
ac
tiv
e
b
r
id
g
e
co
n
v
er
ter
with
in
o
n
e
s
witch
in
g
p
e
r
io
d
T
s
,
d
eter
m
in
ed
b
y
th
e
s
tates o
f
b
r
i
d
g
es s1
an
d
s
2
2
.
2
.
3
.
PV
-
DAB
-
b
a
t
t
er
y
m
o
d
el
Fro
m
th
e
p
r
ev
i
o
u
s
ly
estab
li
s
h
ed
av
er
a
g
e
DAB
m
o
d
el
(
14
)
an
d
th
e
p
h
y
s
ical
m
o
d
el
o
f
t
h
e
p
h
o
to
v
o
ltaic
d
io
d
e
,
a
u
n
iq
u
e
n
o
n
lin
ea
r
d
y
n
a
m
ic
eq
u
atio
n
f
o
r
th
e
av
e
r
ag
e
c
u
r
r
en
t
⟨
iPV
⟩
was
d
er
iv
ed
.
T
h
e
ass
u
m
p
tio
n
s
m
ad
e
s
tr
o
n
g
f
o
r
w
ar
d
b
ias o
f
th
e
p
a
n
el
(
Vp
v
≫
VT
)
an
d
s
lo
w
clim
atic
v
ar
iatio
n
s
co
m
p
ar
e
d
to
th
e
elec
tr
ical
d
y
n
am
ics
o
f
th
e
co
n
v
er
ter
(
≥
1
0
0
m
s
v
s
.
≤
5
0
µs)
,
wh
ich
ar
e
wid
ely
v
alid
ated
in
th
e
liter
atu
r
e
f
o
r
th
is
ty
p
e
o
f
ap
p
licatio
n
[
23
]
.
T
h
e
h
y
b
r
i
d
ap
p
r
o
ac
h
p
r
esen
ted
in
th
is
s
ec
tio
n
c
o
m
b
in
es
th
e
two
m
o
d
els
to
o
b
tain
an
ac
c
u
r
ate
an
d
an
aly
ti
ca
l r
ep
r
esen
tatio
n
o
f
th
e
c
o
m
p
lete
s
y
s
tem
.
T
h
is
s
ec
tio
n
an
aly
ze
s
th
e
av
er
ag
e
eq
u
atio
n
o
f
,
wh
ich
is
d
er
i
v
ed
f
r
o
m
th
e
PV
d
i
o
d
e
a
n
d
th
e
DAB
cir
cu
it
.
T
o
m
o
d
el
th
e
s
y
s
tem
,
th
e
im
p
ac
t
o
f
en
v
ir
o
n
m
en
tal
v
ar
iatio
n
s
s
h
o
u
ld
b
e
ass
ess
ed
.
T
h
e
h
y
b
r
i
d
m
eth
o
d
co
m
b
in
es
th
e
two
m
o
d
els.
F
ir
s
t
,
d
er
iv
ed
f
r
o
m
d
io
d
e
p
h
y
s
ics,
s
im
p
lifie
s
(
1
)
b
y
ass
u
m
in
g
>
>
>
0
in
f
o
r
war
d
b
ias,
wh
ich
r
esu
lts
in
(
1
5
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
2
9
9
-
1
3
1
3
1304
≈
ln
(
0
)
(
1
5
)
Neg
lectin
g
ℎ
as
ac
co
r
d
in
g
to
(
1
)
,
we
o
b
tain
(
16
)
,
wh
er
e
ℎ
d
ep
en
d
s
o
n
th
e
ir
r
ad
ia
n
ce
G
an
d
tem
p
er
atu
r
e
T
.
I
ts
tim
e
d
er
iv
ativ
e
is
ex
p
r
ess
ed
as
(
17
)
.
≈
ℎ
−
(
1
6
)
ℎ
=
ℎ
0
1000
[
(
1
+
(
−
25
)
)
+
]
(
1
7
)
T
ak
in
g
th
e
tim
e
d
er
iv
ativ
e
o
f
(
1
5
)
g
i
v
es
(
1
8
)
.
=
1
(
1
8
)
Su
b
s
titu
tin
g
th
e
d
io
d
e
cu
r
r
e
n
t
ex
p
r
ess
io
n
(
1
6
)
in
to
(
1
8
)
g
iv
es
(
1
9
)
.
=
(
ℎ
−
)
(
ℎ
−
)
(
1
9
)
Su
b
s
titu
tin
g
(
1
7
)
in
to
(
1
9
)
a
n
d
ex
p
an
d
in
g
:
=
(
ℎ
−
)
(
N
p
ℎ
0
1000
[
(
1
+
(
−
25
)
)
+
]
−
di
pv
dt
)
(
2
0
)
Dif
f
er
en
tiatin
g
t
h
e
r
esis
tiv
e
d
io
d
e
v
o
ltag
e
ex
p
r
ess
io
n
(
4
)
wit
h
r
esp
ec
t
to
tim
e
y
ield
s
th
e
s
e
co
n
d
ex
p
r
ess
io
n
f
o
r
:
=
1
+
(
2
1
)
T
h
e
(
2
0
)
,
(
2
1
)
,
an
d
s
o
lv
i
n
g
f
o
r
,
y
ield
s
(
2
2
)
with
co
e
f
f
icien
ts
A
3
,
A
4
,
a
n
d
A
5
d
ef
in
ed
i
n
(
2
3
)
-
(
2
5
)
.
=
3
+
4
+
5
(
2
2
)
W
ith
:
3
=
−
(
ℎ
−
)
−
(
2
3
)
4
=
ℎ
0
(
1
+
(
−
25
)
)
1000
(
ℎ
−
)
(
2
4
)
5
=
ℎ
0
1000
(
ℎ
−
)
(
2
5
)
T
h
is
ex
p
r
ess
io
n
(
2
6
)
is
th
en
s
u
b
s
titu
ted
in
to
th
e
cu
r
r
en
t
co
n
s
er
v
atio
n
(
6
)
in
th
e
av
er
a
g
e
m
o
d
el.
Hen
ce
,
th
e
ter
m
is
ex
p
r
ess
ed
a
s
(
2
7
)
.
=
+
<
1
>
(
2
6
)
=
+
(
2
7
)
Su
b
s
titu
tin
g
(
2
2
)
in
to
(
2
7
)
,
an
d
id
en
tif
y
in
g
t
h
e
co
e
f
f
icien
ts
,
y
ield
s
(
2
8
)
,
wh
er
e
1
=
3
,
2
=
4
an
d
3
=
5
,
d
ef
in
ed
in
(
2
9
)
-
(
3
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
MPP
T
c
o
n
tr
o
l o
f a
P
V
-
b
a
tter
y
s
ystem
u
s
in
g
a
g
a
in
-
s
ch
e
d
u
le
d
a
d
a
p
tive
P
I
c
o
n
tr
o
ller
…
(
K
h
a
lid
S
a
b
h
i
)
1305
=
+
1
(
,
,
)
+
2
(
,
,
)
+
3
(
,
,
)
(
2
8
)
W
h
er
e:
1
=
−
(
(
ℎ
−
)
+
)
(
2
9
)
2
=
(
ℎ
0
(
1
+
(
−
25
)
)
1000
(
ℎ
−
)
)
(
3
0
)
3
=
ℎ
0
1000
(
ℎ
−
)
(
3
1
)
T
h
e
an
aly
s
is
s
h
o
w
ed
th
at
1
act
ed
as
a
d
y
n
am
ic
ally
s
tab
il
izin
g
r
esis
to
r
.
T
h
e
ter
m
s
2
an
d
3
,
s
en
s
itiv
e
to
an
d
T
,
in
teg
r
a
te
th
er
m
al
an
d
g
eo
m
etr
ic
ef
f
ec
ts
es
s
en
tial
to
ad
ap
tiv
e
MP
PTs.
T
h
e
co
m
m
o
n
d
ep
en
d
e
n
ce
o
n
th
is
eq
u
atio
n
h
ig
h
lig
h
ts
th
e
im
p
o
r
tan
ce
o
f
f
o
r
war
d
b
ias.
T
h
is
eq
u
ati
o
n
allo
ws
f
o
r
t
h
e
s
im
u
latio
n
o
f
tr
an
s
ien
ts
(
e.
g
.
,
clo
u
d
p
ass
ag
e)
a
n
d
th
e
d
esig
n
o
f
o
f
an
ef
f
icien
t f
iltra
tio
n
.
2.
3
.
Desig
n a
nd
im
plem
ent
a
t
io
n o
f
g
a
in
-
s
chedule
d P
I
co
ntr
o
ller
f
o
r
P
V
-
DAB
-
ba
t
t
er
y
s
y
s
t
em
Un
lik
e
co
n
v
e
n
tio
n
al
f
i
x
ed
-
g
ain
PI
co
n
tr
o
ller
s
wh
ich
a
s
s
u
m
e
co
n
s
tan
t
d
y
n
a
m
ics,
1
v
ar
ies
s
ig
n
if
ican
tly
with
th
e
o
p
er
atin
g
p
o
i
n
t.
Fig
u
r
e
6
illu
s
tr
ates
th
e
v
ar
iatio
n
o
f
th
e
tim
e
co
n
s
tan
t
1
(
,
,
)
as
a
f
u
n
ctio
n
o
f
ir
r
ad
ian
ce
G
an
d
PV
cu
r
r
en
t
ip
v
at
T
=
2
5
°C
.
Ho
wev
er
,
r
eg
ar
d
less
o
f
o
p
er
atin
g
co
n
d
itio
n
s
,
1
is
an
aly
tically
b
o
u
n
d
ed
b
y
(
1
<
−
=
−
1
.
575
in
o
u
r
s
y
s
tem
)
.
Sin
ce
f
o
r
all
p
h
y
s
ical
o
p
er
ati
n
g
co
n
d
itio
n
s
(
G>
0
,
T
>0
K,
ℎ
>
)
,
th
e
ter
m
(
ℎ
−
)
>
0
alwa
y
s
.
T
h
is
v
ar
iatio
n
o
f
1
is
p
r
ec
is
ely
th
e
m
o
tiv
atio
n
f
o
r
th
e
p
r
o
p
o
s
ed
g
ain
-
s
ch
ed
u
lin
g
ap
p
r
o
ac
h
:
th
e
g
ai
n
s
an
d
ar
e
r
ec
alcu
lated
at
ea
ch
1
µs
s
am
p
le
v
ia
(
4
1
)
a
n
d
(
4
2
)
to
co
m
p
en
s
ate
f
o
r
th
is
n
o
n
lin
ea
r
ity
an
d
m
ain
tain
co
n
s
tan
t c
lo
s
ed
-
l
o
o
p
d
y
n
am
ics.
(
a)
(
b
)
Fig
u
r
e
6
.
T
im
e
co
n
s
tan
t
1
v
ar
ia
tio
n
u
n
d
er
T
=2
5
°C
: (
a)
1
vs
.
pv
f
o
r
d
if
f
e
r
en
t G
v
al
u
es a
n
d
(
b
)
1
vs
.
G
f
o
r
d
if
f
er
en
t
pv
v
alu
es
T
h
e
n
o
n
lin
ea
r
d
y
n
am
ics
o
f
th
e
s
y
s
tem
in
(
2
8
)
-
(
3
1
)
ar
e
lo
c
ally
lin
ea
r
ized
ar
o
u
n
d
th
e
in
s
tan
tan
eo
u
s
o
p
er
atin
g
p
o
in
t.
All
c
o
n
tr
o
l
ca
lcu
latio
n
s
(
Kp
,
Ki
g
ai
n
ad
j
u
s
tm
en
t,
an
ticip
atio
n
d
is
tu
r
b
a
n
ce
co
m
p
en
s
atio
n
,
s
atu
r
atio
n
p
r
o
tectio
n
,
an
d
p
h
a
s
e
-
s
h
if
t
s
atu
r
atio
n
)
wer
e
p
er
f
o
r
m
ed
e
v
er
y
1
u
s
(
1
MH
z
co
n
tr
o
l
f
r
eq
u
en
cy
)
.
T
h
is
ex
tr
em
ely
h
ig
h
s
am
p
lin
g
f
r
eq
u
en
cy
is
n
ec
ess
ar
y
b
ec
a
u
s
e
t
h
e
ass
u
m
p
tio
n
o
f
lo
ca
l
lin
ea
r
ity
an
d
th
e
d
is
cr
ete
tim
e
s
im
p
lific
atio
n
s
r
em
ain
v
alid
o
n
ly
if
th
e
PV
v
o
ltag
e
an
d
cu
r
r
e
n
t
ar
e
co
n
s
id
er
e
d
q
u
asi
-
co
n
s
tan
t
o
v
er
a
DAB
s
witch
in
g
cy
cle
(
1
0
µs)
.
Su
ch
a
p
r
ec
is
e
co
n
tr
o
l
s
tep
en
s
u
r
es
s
ec
o
n
d
-
o
r
d
e
r
clo
s
ed
-
lo
o
p
b
eh
a
v
io
r
an
d
ex
ce
llen
t
d
is
tu
r
b
an
ce
r
ejec
tio
n
,
ev
en
with
r
ap
id
ir
r
ad
ian
ce
ch
an
g
es,
with
o
u
t
co
m
p
r
o
m
i
s
in
g
th
e
n
u
m
e
r
ical
ac
cu
r
ac
y
[
3
2
].
Dy
n
am
ic
m
o
d
elin
g
o
f
th
e
PV
-
DAB
s
y
s
tem
(
2
8
)
lead
s
to
th
e
d
esig
n
o
f
a
g
ain
-
s
ch
ed
u
led
PI
co
n
tr
o
ller
an
d
d
is
tu
r
b
a
n
ce
co
m
p
en
s
atio
n
,
en
s
u
r
in
g
p
r
ec
is
e
tr
ac
k
in
g
o
f
to
war
d
s
,
d
esp
ite
v
ar
iatio
n
s
in
G
an
d
T
.
T
h
e
b
asic sy
s
tem
,
with
o
u
t d
is
tu
r
b
an
ce
s
,
is
m
o
d
elled
as
(
3
2
)
.
=
+
1
(
,
,
)
(
3
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
2
9
9
-
1
3
1
3
1306
T
h
e
p
er
tu
r
b
in
g
ter
m
s
2
an
d
3
ar
e
co
m
p
e
n
s
ated
s
ep
ar
ately
.
T
h
e
k
ey
ass
u
m
p
tio
n
is
th
at
=
1
is
s
u
f
f
icien
tly
s
m
all
co
m
p
ar
ed
to
th
e
s
y
s
tem
d
y
n
am
ics
(
ty
p
icall
y
m
illi
s
ec
o
n
d
s
)
;
th
is
s
m
all
s
ca
le
allo
ws
u
s
to
u
s
e
th
e
T
ay
lo
r
ap
p
r
o
x
im
atio
n
to
esti
m
ate
th
e
v
ar
iatio
n
s
o
f
q
u
an
titi
es
o
n
.
T
h
e
T
ay
lo
r
s
er
ies
o
f
(
+
)
ar
o
u
n
d
is
ex
p
r
ess
ed
as:
(
+
)
≈
(
)
+
(
)
×
,
(
3
3
)
with
=
1
μ
,
an
d
ass
u
m
in
g
s
lo
w
d
y
n
am
ics (
e.
g
.
(
)
×
)
o
f
th
e
o
r
d
e
r
o
f
10
−
4
,
t
h
en
:
(
+
)
≈
(
)
(
3
4
)
T
h
is
ap
p
r
o
x
im
atio
n
f
ac
ilit
ates
q
u
asi
-
co
n
tin
u
o
u
s
an
aly
s
is
,
alth
o
u
g
h
n
u
m
er
ical
v
alid
atio
n
is
r
eq
u
ir
ed
to
co
n
f
i
r
m
its
r
o
b
u
s
tn
ess
ag
ain
s
t
f
ast
p
er
tu
r
b
atio
n
s
.
Similar
ly
,
i
n
t
h
e
s
am
e
way
we
ca
n
n
e
g
lect
th
e
v
a
r
iatio
n
s
o
f
G
an
d
T
in
a
s
am
p
le.
T
h
e
last
ap
p
r
o
x
im
atio
n
is
n
ec
ess
ar
y
f
o
r
ca
lcu
latin
g
t
h
e
co
m
p
e
n
s
atio
n
co
m
m
an
d
.
Mo
r
eo
v
er
,
th
is
h
y
p
o
th
esis
is
b
ased
o
n
th
e
lo
ca
l lin
e
ar
ity
.
T
h
e
co
n
tr
o
l
s
tr
ateg
y
co
m
b
in
e
s
a
class
ical
PI
co
n
tr
o
ller
(
3
5
)
,
wh
er
e
e
is
th
e
er
r
o
r
(
3
6
)
,
c
o
n
s
id
er
in
g
th
e
co
m
p
e
n
s
atio
n
ter
m
(
3
7
)
t
h
at
p
r
o
v
id
es to
tal
c
o
n
tr
o
l
(
3
8
)
.
=
+
∫
(
)
(
3
5
)
=
−
,
(
3
6
)
=
−
1
(
2
(
,
,
)
+
3
(
,
,
)
)
(
3
7
)
=
+
(
3
8
)
T
h
is
s
ep
ar
atio
n
h
a
n
d
les
th
e
m
ain
r
eg
u
latio
n
v
ia
PI
a
n
d
ca
n
c
els
th
e
ex
ter
n
al
ef
f
ec
ts
v
ia
.
T
h
e
g
ain
s
an
d
ar
e
d
er
iv
e
d
to
alig
n
th
e
r
esp
o
n
s
e
to
a
s
ec
o
n
d
-
o
r
d
er
s
y
s
tem
with
a
n
atu
r
al
f
r
eq
u
en
cy
an
d
d
a
m
p
in
g
f
ac
to
r
.
T
h
e
clo
s
ed
-
lo
o
p
tr
a
n
s
f
er
f
u
n
ctio
n
is
g
iv
en
b
y
(
3
9
)
.
(
)
=
+
−
1
2
+
(
1
+
)
+
(
3
9
)
T
h
e
s
tab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
is
in
h
er
en
t
to
its
s
tr
u
ctu
r
e:
r
ath
er
th
an
s
tab
ilizin
g
an
u
n
s
tab
le
s
y
s
tem
,
th
e
g
ain
-
s
ch
ed
u
lin
g
l
aw
en
f
o
r
ce
s
a
d
esire
d
s
ec
o
n
d
-
o
r
d
er
b
e
h
av
io
r
wh
o
s
e
s
tab
ilit
y
is
g
u
ar
an
teed
b
y
co
n
s
tr
u
ctio
n
.
T
h
e
clo
s
ed
-
lo
o
p
p
o
les ar
e
an
aly
tically
im
p
o
s
ed
at
ea
ch
s
am
p
lin
g
in
s
tan
t a
s
(
4
0
)
.
1
,
2
=
−
±
√
2
−
1
(
4
0
)
Fo
r
an
y
ξ>0
an
d
>0
,
th
e
r
ea
l
p
ar
t
o
f
t
h
e
p
o
les
is
s
tr
ictly
n
eg
ativ
e,
g
u
ar
an
teei
n
g
clo
s
e
d
-
lo
o
p
s
tab
ilit
y
r
eg
ar
d
less
o
f
t
h
e
o
p
er
atin
g
p
o
in
t.
B
y
id
en
tific
atio
n
with
th
e
s
tan
d
ar
d
s
ec
o
n
d
-
o
r
d
er
s
y
s
tem
,
th
e
g
ain
s
an
d
ar
e
d
er
iv
e
d
as
(
4
1
)
an
d
(
4
2
)
.
=
−
1
2
(
4
1
)
=
−
1
+
2
1
(
4
2
)
T
o
m
ain
tain
s
ec
o
n
d
-
o
r
d
er
d
y
n
am
ics
d
esp
ite
v
ar
iatio
n
s
in
1
(
r
elate
d
to
,
G,
T
)
,
an
d
ar
e
f
ix
e
d
,
an
d
t
h
e
g
ain
s
ar
e
r
ec
alcu
lated
,
p
r
eser
v
in
g
th
e
tr
an
s
ien
t
r
esp
o
n
s
e.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
(
3
9
)
also
co
n
tain
s
a
ze
r
o
at
−
=
−
1
2
1
+
2
1
.
Sin
ce
−
1
2
>
0
alwa
y
s
,
th
e
s
ig
n
o
f
z
d
ep
en
d
s
o
n
th
e
d
en
o
m
in
ato
r
1
+
2
1
.
A
le
f
t
-
h
alf
-
p
lan
e
ze
r
o
(
z<
0
)
is
ess
en
tial
to
en
s
u
r
e
m
in
im
u
m
-
p
h
a
s
e
b
eh
av
io
r
:
a
r
ig
h
t
-
h
alf
-
p
lan
e
ze
r
o
(
z>
0
)
wo
u
ld
ca
u
s
e
an
u
n
d
er
s
h
o
o
t
in
th
e
s
tep
r
esp
o
n
s
e.
Fro
m
th
e
an
a
ly
tical
b
o
u
n
d
1
<
−
th
e
d
en
o
m
i
n
a
to
r
s
atis
f
ies
1
+
2
1
<0
,
an
d
th
e
r
ef
o
r
e
z<
0
,
p
r
o
v
id
ed
th
at:
>
2
(
4
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
MPP
T
c
o
n
tr
o
l o
f a
P
V
-
b
a
tter
y
s
ystem
u
s
in
g
a
g
a
in
-
s
ch
e
d
u
le
d
a
d
a
p
tive
P
I
c
o
n
tr
o
ller
…
(
K
h
a
lid
S
a
b
h
i
)
1307
Fig
u
r
e
7
illu
s
tr
ates
th
is
g
u
a
r
an
teed
m
in
im
u
m
-
p
h
ase
r
eg
io
n
in
th
e
(
)
d
esig
n
s
p
ac
e.
All
th
r
ee
s
im
u
latio
n
ca
s
es
ar
e
well
with
in
th
is
r
eg
i
o
n
,
co
n
f
i
r
m
in
g
th
at
th
e
clo
s
ed
-
lo
o
p
ze
r
o
r
em
ai
n
s
s
tr
ictly
in
th
e
le
f
t
-
h
alf
-
p
lan
e
ac
r
o
s
s
th
e
en
tire
o
p
er
atin
g
r
a
n
g
e,
r
e
g
ar
d
less
o
f
G,
T
,
an
d
ip
v
.
T
h
is
f
lo
wch
ar
t
p
r
esen
ts
th
e
Gain
-
Sch
ed
u
led
PI
co
n
t
r
o
l
alg
o
r
ith
m
(
Fig
u
r
e
8
)
f
o
r
our
s
y
s
tem
s
.
I
t
ca
lcu
lates
th
e
p
h
ase
r
atio
(
d
)
f
r
o
m
th
e
in
p
u
ts
(
cu
r
r
en
t,
ir
r
ad
ian
ce
,
tem
p
er
a
tu
r
e)
,
in
teg
r
atin
g
th
e
er
r
o
r
,
PI
o
u
tp
u
t,
co
m
p
en
s
atio
n
,
an
d
co
n
tr
o
l
s
ig
n
al
lim
itatio
n
s
.
Fig
u
r
e
7
.
Gu
a
r
an
teed
m
in
im
u
m
-
p
h
ase
r
eg
i
o
n
(
z<
0
)
in
t
h
e
(
ξ
,
ω
n
)
d
esig
n
s
p
ac
e;
all
th
r
ee
s
i
m
u
latio
n
ca
s
es lie
with
in
th
e
v
alid
r
e
g
io
n
,
c
o
n
f
ir
m
in
g
lef
t
-
h
alf
-
p
lan
e
ze
r
o
p
lace
m
en
t a
cr
o
s
s
th
e
f
u
ll
o
p
er
atin
g
r
an
g
e
Fig
u
r
e
8
.
Flo
wch
ar
t
o
f
th
e
g
ai
n
-
s
ch
ed
u
led
PI
co
n
tr
o
l a
lg
o
r
it
h
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
2
9
9
-
1
3
1
3
1308
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Reg
ula
t
io
n wit
h
f
ix
ed
s
et
po
int
a
nd
v
a
ria
t
io
ns
o
f
G
Fig
u
r
e
9
s
h
o
ws
th
e
ir
r
ad
ian
ce
p
r
o
f
ile
s
p
ec
if
ically
d
esig
n
ed
to
r
ep
r
o
d
u
ce
r
ea
l
co
n
d
itio
n
s
:
a
co
n
s
tan
t
p
latea
u
o
f
1
0
0
0
W
/m
²
f
r
o
m
0
to
1
s
,
f
o
llo
wed
b
y
a
s
m
o
o
th
lin
ea
r
r
am
p
o
f
ex
ac
tly
o
n
e
s
e
co
n
d
d
escen
d
in
g
to
7
0
0
W
/m
²
,
s
im
u
latin
g
th
e
ty
p
ical
p
ass
ag
e
o
f
a
p
ar
tial
clo
u
d
,
an
d
th
en
a
co
n
s
tan
t
m
ain
ten
a
n
ce
at
7
0
0
W
/m
²
u
p
to
3
s
.
T
h
e
ce
ll
tem
p
er
atu
r
e
w
as
m
ain
tain
ed
at
2
5
°C
ac
co
r
d
in
g
to
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
STC)
th
r
o
u
g
h
o
u
t
th
is
test
s
ce
n
ar
io
in
o
r
d
er
to
is
o
late
th
e
ef
f
ec
t
o
f
ir
r
ad
ian
ce
v
ar
iatio
n
s
an
d
allo
w
d
ir
ec
t
co
m
p
ar
is
o
n
with
m
an
u
f
ac
tu
r
er
d
atash
ee
t v
al
u
es.
A
cu
r
r
en
t
s
etp
o
in
t
s
tep
f
r
o
m
0
to
7
0
A
was
ap
p
lied
at
t
=
5
m
s
(
T
e
=
1
µs)
.
Fig
u
r
es
9
to
1
1
co
m
p
ar
e:
i)
A
co
n
v
en
tio
n
al
f
ix
e
d
-
g
ai
n
PI
co
n
tr
o
ller
u
s
in
g
t
h
e
co
n
v
er
g
ed
g
ain
s
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
i
n
th
e
s
tab
ilized
s
tate
u
n
d
er
1
0
0
0
W
/m
²
(
Kp
=
3
.
7
7
5
×
1
0
⁻³;
Ki
=7
.
2
2
)
,
an
d
ii)
th
e
p
r
o
p
o
s
ed
an
aly
tical
g
ain
-
s
ch
ed
u
led
c
o
n
tr
o
ller
(
ξ
=
1
,
ω
ₙ
=
2
5
0
0
r
ad
/s
)
.
T
a
b
le
2
s
u
m
m
ar
izes
th
e
m
ea
s
u
r
e
d
p
e
r
f
o
r
m
an
ce
as
p
r
esen
ted
in
F
ig
u
r
e
10
.
Du
r
in
g
th
e
ir
r
ad
ia
n
ce
r
am
p
(
1
0
0
0
→
7
0
0
W
/m
²
in
1
s
)
,
th
e
two
co
r
r
ec
to
r
s
e
x
h
ib
ited
a
tr
an
s
ien
t
er
r
o
r
o
f
th
e
s
am
e
m
ax
im
u
m
a
m
p
litu
d
e
(
≈
1
A)
,
wh
ich
was
e
x
p
ec
ted
b
ec
a
u
s
e
b
o
th
tem
p
o
r
a
r
ily
s
atu
r
ated
th
e
D
co
n
tr
o
l a
t 0
.
2
5
.
Fig
u
r
e
11
s
h
o
ws
th
at
th
e
Kp
an
d
Ki
g
ain
s
o
f
th
e
p
r
o
p
o
s
ed
co
r
r
ec
to
r
ad
a
p
t
au
to
m
atica
lly
d
u
r
in
g
th
e
r
am
p
-
d
o
wn
(
Kp
ch
a
n
g
es f
r
o
m
≈
3
.
8
×
1
0
⁻³
to
≈
1
2
.
6
5
×
1
0
⁻³
an
d
Ki
f
r
o
m
≈
7
.
2
to
≈
1
8
.
3
w
h
en
s
witch
in
g
f
r
o
m
1
0
0
0
to
7
0
0
W
/m
²)
,
an
d
th
en
s
tab
ilize
at
th
eir
n
ew
o
p
tim
al
v
alu
es
as
s
o
o
n
as
th
e
ir
r
ad
ia
n
c
e
b
ec
o
m
es
co
n
s
tan
t
at
7
00
W
/m
².
T
h
is
r
ea
l
-
tim
e
a
d
ap
tatio
n
is
p
r
ec
is
ely
th
e
f
u
n
c
tio
n
o
f
an
al
y
tical
g
ain
s
ch
ed
u
lin
g
.
T
h
ese
r
esu
lts
d
em
o
n
s
tr
ate
th
at,
ev
en
th
o
u
g
h
a
class
ic
PI
s
et
with
o
p
tim
a
l
g
ain
s
at
1
0
0
0
W
/m
²
p
r
esen
t
s
a
m
o
r
e
ag
g
r
ess
iv
e
r
esp
o
n
s
e
th
an
th
e
p
r
o
p
o
s
ed
m
eth
o
d
.
C
o
n
v
er
s
ely
,
o
n
l
y
th
e
p
r
o
p
o
s
ed
an
aly
tical
g
ain
-
s
ch
ed
u
led
co
n
tr
o
ller
g
u
ar
an
tees
th
e
f
o
llo
win
g
:
i
)
n
eg
lig
ib
le
o
v
er
s
h
o
o
t
an
d
ab
s
en
ce
o
f
o
s
cillatio
n
s
d
ep
en
d
e
n
t
o
n
t
h
e
d
esire
d
b
eh
av
io
r
(
n
o
o
s
cillatio
n
in
o
u
r
ca
s
e)
,
a
n
d
ii)
an
o
v
er
all
r
e
s
p
o
n
s
e
tim
e
th
r
ee
tim
es
s
h
o
r
t
er
(
0
.
9
4
m
s
v
er
s
u
s
2
.
9
4
m
s
at
±
5
%).
Fig
u
r
e
9
.
I
r
r
ad
ia
n
ce
v
ar
iatio
n
s
G
ap
p
lied
to
t
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