T
E
L
KO
MNIK
A
, V
ol
.
15
,
No.
1,
Ma
r
c
h
20
1
7,
p
p.
7
9~
92
IS
S
N: 1
69
3
-
6
93
0
,
accr
ed
ited
A
by
DIK
T
I,
Decr
ee
No:
58
/DI
K
T
I/K
ep
/20
13
DOI:
10.12928/TE
LK
OM
N
IK
A
.v
1
5
i
1
.
3160
â—¼
79
Rec
ei
v
ed
S
ep
te
mb
er 19
,
2
01
6
;
Rev
i
s
ed
Dec
e
mb
er
9
,
20
1
6
; A
c
c
ep
t
ed
J
a
nu
ary
3
,
20
1
7
MP
PT
fo
r P
V S
ystem
Base
d o
n
Var
iable Ste
p Si
z
e P&O
Algo
ri
th
m
Aw
ang
Jusoh
*
1
,
Ro
z
ana
Alik
2
, T
an Ka
r
G
u
an
3
, To
le
S
u
t
ikno
4
1
,2
,3
Dep
a
r
tm
e
n
t
o
f
Po
wer
E
l
e
c
t
ro
n
i
c
s
,
Un
i
v
e
rs
i
t
i
T
e
k
n
o
l
o
g
i
M
a
l
a
y
s
i
a
,
J
o
h
o
r,
M
a
l
a
y
s
i
a
4
Dep
a
rt
m
e
n
t
o
f
El
e
c
tr
i
c
a
l
En
g
i
n
e
e
ri
n
g
,
Un
i
v
e
r
s
i
t
a
s
A
h
m
a
d
D
a
h
l
a
n
,
Yo
g
y
a
k
a
rta
,
In
d
o
n
e
s
i
a
*C
o
rre
s
p
o
d
i
n
g
a
u
t
h
o
r,
e
-
m
a
i
l
:
a
wan
g
@fk
e
.u
t
m
.
m
y
Ab
strac
t
Th
i
s
p
a
p
e
r p
re
s
e
n
ts
s
o
m
e
i
m
p
ro
v
e
m
e
n
t
s
o
n
t
h
e
Pe
r
tu
rb
a
n
d
Obs
e
rv
e
(P&O
) m
e
th
o
d
t
o
o
v
e
rc
o
m
e
th
e
c
o
m
m
o
n
d
ra
w
b
a
c
k
s
o
f
c
o
n
v
e
n
ti
o
n
a
l
P&O
m
e
t
h
o
d
.
Th
e
m
a
i
n
a
d
v
a
n
ta
g
e
o
f
th
i
s
m
o
d
i
fi
e
d
a
l
g
o
ri
th
m
i
s
i
t
s
s
i
m
p
l
i
c
i
t
y
wit
h
h
i
g
h
e
r
a
c
c
u
ra
c
y
re
s
u
l
ts
,
c
o
m
p
a
re
d
to
th
e
c
o
n
v
e
n
t
i
o
n
a
l
m
e
th
o
d
s
.
Th
e
o
p
e
r
a
ti
o
n
o
f
th
e
e
n
ti
r
e
s
o
l
a
r
M
a
x
i
m
u
m
Po
wer
P
o
i
n
t
Tra
c
k
i
n
g
(M
PPT)
s
y
s
te
m
wa
s
o
b
s
e
rv
e
d
th
r
o
u
g
h
two
d
i
ff
e
re
n
t
a
p
p
r
o
a
c
h
e
s
,
whi
c
h
a
re
th
r
o
u
g
h
M
ATL
AB/Si
m
u
l
i
n
k
s
i
m
u
l
a
ti
o
n
a
n
d
h
a
r
d
wa
re
i
m
p
l
e
m
e
n
ta
t
i
o
n
.
A
s
m
a
l
l
s
c
a
l
e
o
f
h
a
rd
war
e
d
e
s
i
g
n
,
whi
c
h
c
o
n
s
i
s
ts
o
f
s
o
l
a
r
PV
c
e
l
l
,
b
o
o
s
t
c
o
n
v
e
rte
r
a
n
d
Ard
u
i
n
o
M
e
g
a
2
5
6
0
m
i
c
ro
c
o
n
t
ro
l
l
e
r,
h
a
d
b
e
e
n
u
ti
l
i
z
e
d
f
o
r
f
u
rth
e
r
v
e
ri
f
i
c
a
ti
o
n
o
n
t
h
e
s
i
m
u
l
a
ti
o
n
r
e
s
u
l
ts
.
T
h
e
s
i
m
u
l
a
t
i
o
n
re
s
u
l
ts
th
a
t
wa
s
c
a
r
ri
e
d
o
u
t
b
y
t
h
i
s
m
o
d
i
fi
e
d
P&O
a
l
g
o
ri
t
h
m
s
h
o
w
e
d
i
m
p
ro
v
e
m
e
n
t
a
n
d
a
p
r
o
m
i
s
i
n
g
p
e
r
fo
rm
a
n
c
e
:
f
a
s
te
r
c
o
n
v
e
r
g
e
n
c
e
s
p
e
e
d
o
f
0
.6
7
s
,
s
m
a
l
l
o
s
c
i
l
l
a
t
i
o
n
a
t
s
t
e
a
d
y
s
t
a
te
re
g
i
o
n
a
n
d
p
r
o
m
i
s
i
n
g
e
ff
i
c
i
e
n
c
y
o
f
9
5
.
2
3
%
.
B
e
s
i
d
e
s
,
fro
m
t
h
e
h
a
rd
ware
re
s
u
l
t
s
,
th
e
c
o
n
v
e
r
g
e
n
c
e
ti
m
e
o
f
t
h
e
p
o
wer
c
u
r
v
e
was
a
b
l
e
to
m
a
i
n
ta
i
n
a
t
0
.2
s
a
n
d
g
i
v
e
a
l
m
o
s
t
z
e
ro
o
s
c
i
l
l
a
t
i
o
n
d
u
r
i
n
g
s
te
a
d
y
s
ta
te
.
It
i
s
e
n
v
i
s
a
g
e
d
th
a
t
th
e
m
e
th
o
d
i
s
u
s
e
f
u
l
i
n
fu
t
u
re
re
s
e
a
r
c
h
o
f
Ph
o
to
v
o
l
t
a
i
c
(PV)
s
y
s
t
e
m
.
Key
w
ords
:
p
e
r
tu
rb
a
n
d
o
b
s
e
r
v
e
,
M
PPT,
v
a
ri
a
b
l
e
s
t
e
p
s
i
z
e
,
p
h
o
to
v
o
l
ta
i
c
s
y
s
te
m
Copy
righ
t
©
2
0
1
7
Uni
v
e
rsi
t
a
s
Ahm
a
d
D
a
hl
a
n.
All
righ
t
s
r
e
s
e
rve
d
.
1.
Int
r
o
d
u
ctio
n
T
od
ay
’
s
s
c
i
en
t
i
s
ts
an
d
en
g
i
ne
ers
ha
v
e
i
ntro
du
c
ed
nu
me
r
ou
s
r
es
ea
r
c
he
s
an
d
de
v
el
op
m
en
t
w
i
th
r
eg
ard
t
o
r
en
ewa
bl
e
en
ergy
,
i
n
or
de
r
to
ov
erc
om
e
t
he
i
nc
r
e
as
i
ng
n
eg
a
ti
v
e
i
mp
ac
ts
c
au
s
ed
by
the
c
on
v
en
ti
o
na
l
en
ergy
s
ou
r
c
es
.
T
he
r
e
i
s
a
m
aj
or
d
em
a
nd
i
n
s
ol
ar
e
ne
r
gy
as
us
ab
l
e
al
t
ernat
i
v
e
en
erg
y
s
ou
r
c
e,
du
e
t
o
i
ts
s
us
tai
n
ab
i
l
i
ty
,
c
l
ea
nn
es
s
,
ea
s
y
m
a
i
nte
na
nc
e
a
nd
no
i
s
e
-
fr
e
e
c
ha
r
ac
teri
s
t
i
c
s
.
Mo
r
eo
v
er,
t
he
r
e
are
ma
n
y
tr
op
i
c
al
c
o
un
tr
i
es
i
n
t
hi
s
wor
l
d
wh
i
c
h
r
ec
ei
v
e d
i
r
ec
t s
ol
ar i
r
r
ad
i
at
i
on
ar
o
un
d
10
00
W
/m
2
[1
-
4]
.
Des
pi
t
e
th
e
f
ac
t
th
at
s
o
l
ar
en
ergy
i
s
a
prom
i
s
i
n
g
e
ne
r
gy
,
i
t
s
ti
l
l
ha
s
s
om
e
di
s
ad
v
an
ta
ge
s
i
n
t
erm
o
f
i
ts
pe
r
for
ma
nc
e.
Refe
r
e
nc
e
[
5]
s
tat
es
tha
t,
the
e
ffi
c
i
en
c
y
of
the
s
ol
ar
P
V
to
tr
a
ns
fer
s
un
l
i
gh
t
i
nt
o
el
ec
tr
i
c
al
en
er
gy
i
s
qu
i
t
e
l
ow,
a
pp
r
ox
i
ma
t
el
y
12
%
un
t
i
l
2
0%.
T
h
e
s
ol
ar
P
V
o
pe
r
at
es
ac
c
ordi
ng
t
o
th
e
s
un
l
i
g
ht
i
nte
ns
i
ty
,
c
el
l
t
em
pe
r
atu
r
e
an
d
arr
ay
c
on
f
i
gu
r
ati
on
[6
]
.
Numb
ers
of
me
th
od
s
ha
v
e
b
ee
n
i
ntro
d
uc
ed
by
r
es
ea
r
c
he
r
s
,
an
d
on
e
of
t
he
m
os
t
po
p
ul
ar
a
pp
r
oa
c
h
i
s
the
ma
x
i
m
um
p
ower
p
oi
nt
tr
a
c
k
i
ng
(
MP
P
T
)
.
A
c
o
nv
en
t
i
on
a
l
M
P
P
T
s
y
s
tem
c
on
s
i
s
ts
of
a
s
wi
tc
h
-
mo
de
po
w
e
r
c
on
v
erter
,
p
l
a
c
ed
i
n
b
etwe
en
of
the
s
o
l
a
r
P
V
an
d
the
l
o
ad
.
T
h
e
du
t
y
c
y
c
l
e
of
the
c
on
v
erter
i
s
me
as
ured
by
a
c
on
tr
o
l
a
l
go
r
i
th
m,
t
o
a
l
l
ow
tr
ac
k
i
ng
of
t
he
ma
x
i
mu
m
p
ower
p
oi
nt
[
7]
.
T
he
r
e
are
mo
r
e
th
an
19
d
i
s
ti
nc
t
M
P
P
T
t
ec
hn
i
qu
es
av
ai
l
ab
l
e
an
d
b
ei
ng
r
es
ea
r
c
h
ed
i
n
th
e
p
as
t
few y
ea
r
s
[8]
.
T
he
e
as
i
es
t
way
to
a
pp
l
y
t
he
M
P
P
T
c
i
r
c
ui
t
a
nd
ob
t
ai
n
the
ma
x
i
mu
m
p
ower
po
i
nt
(
MP
P
)
i
s
F
r
ac
ti
on
al
O
pe
n
Ci
r
c
ui
t
V
ol
tag
e
(
F
O
CV
)
m
eth
od
[9]
.
It
i
s
al
s
o
k
n
own
as
a
c
o
ns
tan
t
v
o
l
ta
ge
tec
hn
i
qu
e
whi
c
h
em
p
l
oy
s
t
he
l
i
ne
ar
r
el
at
i
o
ns
hi
p
be
tw
e
en
v
ol
t
ag
e
at
M
P
P
(
V
MPP
)
a
nd
op
en
c
i
r
c
ui
t
v
ol
ta
g
e
(
V
OC
)
as
V
MPP
=
K1
×
V
OC
.
L
i
k
ewi
s
e
,
F
r
ac
ti
o
na
l
S
ho
r
t
C
i
r
c
ui
t
C
urr
en
t
(
F
S
CC)
tec
hn
i
qu
e
uti
l
i
z
es
th
e
s
am
e
c
on
c
e
pt
as
F
O
CV
m
eth
o
d.
T
h
e
e
q
ua
ti
on
us
ed
f
or
F
S
CC
i
s
V
MPP
=
K2
×
V
OC
where
a
l
i
ne
ar
r
el
at
i
o
ns
hi
p
be
twe
en
th
e
P
V
s
ho
r
t
c
i
r
c
ui
t
c
urr
en
t
(
I
SC
)
an
d
c
urr
en
t
at
MP
P
(
I
MPP
)
i
s
s
ho
wn
i
n
t
hi
s
m
eth
od
.
T
h
e
v
al
ue
of
proport
i
on
al
i
ty
c
o
ns
tan
ts
(
K1
an
d
K2
)
are
af
fec
ted
by
the
ty
pe
s
of
s
ol
ar
P
V
,
s
urr
ou
n
d
i
ng
t
em
p
erature
a
nd
i
r
r
a
di
a
nc
e
[10]
.
A
c
c
ordi
n
g
to
r
efe
r
en
c
e
[11
]
,
the
r
an
ge
v
al
ue
for
K1
i
s
b
et
ween
0.
71
un
ti
l
0.7
8
w
hi
l
e
K2
i
s
r
a
ng
i
ng
b
etwe
en
0.7
8
a
nd
0.9
2.
Howev
er,
th
es
e
tec
hn
i
qu
e
s
un
ab
l
e
to
tr
ac
k
the
ac
c
u
r
ate
MP
P
be
c
a
us
e
es
ti
ma
t
i
on
i
s
us
e
d
to
i
de
nti
fy
t
h
e
l
i
ne
ar r
e
l
at
i
o
ns
h
i
p a
s
de
s
c
r
i
be
d b
y
r
efe
r
en
c
e
[12
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
â—¼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
MNIK
A
V
ol
.
15
,
No
.
1,
M
arc
h 2
0
17
:
79
–
92
80
It
i
s
wi
de
l
y
k
no
wn
t
ha
t
P
ert
urb
an
d
O
bs
erv
e
(
P
&
O
)
as
wel
l
as
Hi
l
l
Cl
i
mb
i
n
g
(
HC)
MP
P
T
are
the
mo
s
t
fav
or
ab
l
e
me
tho
ds
to
be
us
e
i
n
fi
nd
i
ng
the
r
ea
l
ma
x
i
mu
m
p
ower
p
oi
nt
(
M
P
P
)
o
n
the
P
V
c
urv
e
[13]
.
T
he
ma
i
n
ad
v
a
nta
g
e
of
t
he
s
e
tec
hn
i
qu
es
i
s
r
e
l
at
i
v
el
y
s
tr
ai
gh
tf
orw
ard
c
om
pa
r
e
d
t
o
t
he
oth
er
art
i
f
i
c
i
al
tec
hn
i
q
ue
s
[
14
]
.
B
es
i
d
es
,
th
es
e
t
ec
hn
i
qu
es
are
a
l
s
o
ea
s
y
t
o
be
i
mp
l
e
me
nt
ed
i
n
prac
ti
c
a
l
a
pp
l
i
c
ati
on
wi
t
ho
ut
pri
or
k
no
wl
ed
ge
on
P
V
c
el
l
’
s
c
h
ara
c
teri
s
t
i
c
s
an
d
i
t
c
an
be
us
ed
i
n a
ny
m
i
c
r
oc
on
tr
ol
l
er or
Di
gi
t
al
S
i
gn
al
P
r
o
c
es
s
i
ng
(
DS
P
)
s
y
s
tem
[
15
]
.
Non
eth
e
l
es
s
,
P
&
O
al
go
r
i
t
hm
i
s
a
l
s
o
r
e
fe
r
r
ed
as
H
i
l
l
C
l
i
mb
i
ng
(
HC)
MP
P
T
by
s
o
me
r
es
ea
c
he
r
s
s
i
nc
e
i
t
us
es
the
s
am
e
c
on
c
e
pt
i
n
p
ertur
bi
n
g
the
M
P
P
[
16
]
.
T
he
o
nl
y
di
ffe
r
en
c
e
i
s
the
ou
t
pu
t
c
on
tr
ol
v
ari
ab
l
e;
P
&
O
M
P
P
T
prov
i
d
es
r
efe
r
en
c
e
v
ol
t
ag
e
t
o
th
e
po
w
er
c
on
v
erter
wh
i
l
e
HC
M
P
P
T
y
i
el
ds
t
he
c
ha
ng
e
fr
om
the
du
ty
c
y
c
l
e
.
In
f
ac
t,
r
efe
r
e
nc
e
[1
7]
s
ta
t
ed
th
at
t
he
tr
a
ns
i
e
nt
r
es
po
ns
e
of
P
&
O
i
s
be
tte
r
th
an
HC.
Y
et,
th
es
e
me
th
od
s
ha
v
e
two
m
aj
or
d
r
awba
c
k
s
:
os
c
i
l
l
a
ti
o
n
prob
l
em
arou
nd
the
MP
P
a
nd
un
ab
l
e
to
tr
ac
k
t
he
r
e
al
M
P
P
d
urin
g
f
as
t
c
ha
ng
i
n
g
o
f
w
ea
t
he
r
c
o
nd
i
ti
on
w
hi
c
h
b
ee
n
ex
pl
a
i
ne
d i
n d
eta
i
l
i
n
the
S
e
c
ti
on
4.
Inc
r
em
en
tal
Con
du
c
ta
nc
e
(
INC)
me
t
ho
d
i
s
an
o
the
r
v
er
s
i
on
of
Hi
l
l
C
l
i
mb
i
ng
(
HC)
.
I
t
us
es
the
ba
s
i
c
c
on
c
e
pt
of
HC
wh
i
c
h
the
s
l
o
pe
of
P
-
V
c
urv
e
wi
l
l
be
z
ero
at
th
e
M
P
P
,
p
o
s
i
ti
v
e
at
th
e
l
ef
t
s
i
de
an
d
n
eg
a
ti
v
e
at
th
e
r
i
gh
t
s
i
d
e
of
the
c
urv
e.
T
h
e
c
ha
r
ac
t
eris
ti
c
of
INC
c
o
mp
en
s
a
te
the
weak
ne
s
s
es
of
P
&
O
m
eth
od
as
i
t
c
a
pa
b
l
e
t
o
tr
ac
k
the
M
P
P
du
r
i
ng
r
ap
i
d
v
a
r
i
ati
on
of
s
u
n
i
r
r
ad
i
an
c
e
[9,
1
2]
.
Nev
erth
el
es
s
,
i
t
i
s
di
ffi
c
u
l
t
to
ob
tai
n
a
c
on
s
t
an
t
M
P
P
i
n
prac
t
i
c
al
,
p
l
us
,
th
i
s
me
th
od
r
e
qu
i
r
ed
a
dd
i
ti
on
a
l
s
en
s
ors
s
uc
h
as
c
urr
en
t
an
d
v
o
l
ta
ge
s
e
ns
or
wh
i
c
h
i
nc
r
ea
s
es
th
e
c
os
t a
nd
c
o
mp
l
ex
i
ty
o
f th
e
s
y
s
tem
.
F
uz
z
y
Lo
gi
c
Co
ntrol
(
F
L
C
)
i
s
the
m
os
t
po
pu
l
ar
art
i
f
i
c
i
a
l
c
on
tr
o
l
m
eth
o
d
d
ue
t
o
the
i
nv
en
t
i
o
n
o
f
m
i
c
r
oc
on
tr
o
l
l
er,
wh
ereby
a
ny
c
om
pl
i
c
ate
d
c
od
i
ng
or
a
l
g
orit
h
m
c
an
be
ea
s
i
l
y
progr
am
me
d
an
d
i
m
pl
e
me
nte
d.
T
he
m
ai
n
ad
v
an
tag
e
of
F
LC
i
s
a
bl
e
to
ha
nd
l
e
n
on
-
l
i
ne
arit
y
an
d
i
mp
r
ec
i
s
e
i
np
ut.
Mo
r
eo
v
er,
fas
t
c
on
v
erg
en
c
e
s
p
ee
d
a
n
d
r
ob
us
t
pe
r
f
orma
nc
e
o
f
fu
z
z
y
l
og
i
c
ha
v
e
be
en
de
m
on
s
tr
at
ed
du
r
i
ng
s
ud
de
n
c
h
an
g
e
of
s
urr
ou
n
di
n
g
c
on
d
i
ti
on
as
s
tat
ed
i
n
r
efe
r
en
c
e
[1
8]
.
B
es
i
d
es
,
A
r
ti
fi
c
i
al
Ne
ural
Network
(
A
NN)
i
s
an
o
t
he
r
tec
hn
i
qu
e
tha
t
f
i
ts
th
e
op
erat
i
o
n
of
mi
c
r
oc
on
tr
o
l
l
er
an
d
d
i
g
i
ta
l
s
i
gn
a
l
proc
es
s
or.
Refe
r
en
c
e
[19]
pro
po
s
e
d
a
s
ol
ar
s
y
s
tem
wi
th
m
ul
t
i
-
l
ev
el
ne
ur
o
-
fuz
z
y
mo
de
l
fo
r
MP
P
T
.
T
he
s
y
s
tem
h
as
be
en
prov
en
c
a
pa
b
l
e
i
n
pr
od
uc
i
ng
b
ett
er
eff
i
c
i
en
c
y
a
nd
r
e
pres
en
t
i
n
g
no
n
l
i
ne
ar
c
ha
r
ac
ter
i
s
ti
c
o
f
P
V
arr
ay
un
d
er
w
i
de
r
an
g
e
of
op
erati
on
c
i
r
c
um
s
tan
c
e c
o
mp
are
d t
o
c
on
v
en
ti
on
a
l
ne
ura
l
ne
tw
ork
al
g
orit
h
m.
H
owev
er,
i
t
i
s
un
de
ni
ab
l
e t
ha
t
the
s
y
s
tem
w
i
th
A
NN
ne
ed
s
to
be
pe
r
i
od
i
c
al
l
y
trai
ne
d
t
o g
u
arant
ee
t
he
h
i
g
he
s
t a
c
c
urac
y
.
B
as
i
c
a
l
l
y
,
th
e
c
on
v
en
t
i
o
na
l
al
go
r
i
t
hm
s
are
r
at
he
r
s
i
mp
l
e
me
t
ho
ds
.
Y
et,
t
he
y
us
ua
l
l
y
c
au
s
e
po
or
eff
i
c
i
e
nc
y
.
O
n
the
oth
er
ha
nd
,
s
o
ft
c
om
pu
ti
ng
al
go
r
i
t
hm
s
are
m
ore
c
om
p
l
ex
,
bu
t
de
l
i
v
er
hi
gh
er
ef
fi
c
i
en
c
y
[2
0]
.
In
r
e
l
at
i
on
t
o
the
as
s
um
pti
o
n,
th
i
s
pa
p
er
i
s
foc
us
i
n
g
on
m
od
i
fy
i
n
g
an
d
i
m
prov
i
n
g
t
he
P
&
O
MP
P
T
to
ov
erc
om
e
t
he
drawbac
k
s
es
pe
c
i
al
l
y
t
he
s
tea
dy
s
ta
te
os
c
i
l
l
ati
on
probl
em
.
T
he
c
o
nv
en
ti
on
a
l
P
&
O
al
go
r
i
t
hm
i
s
mo
d
i
fi
ed
t
o
h
av
e
v
aria
bl
e
s
tep
s
i
z
e
wi
t
h
s
om
e
c
om
bi
na
t
i
on
of
HC
me
th
od
w
i
l
l
be
d
es
c
r
i
be
d
i
n
de
t
ai
l
i
n
S
ec
ti
on
4
as
w
e
l
l
as
v
erif
i
c
a
ti
on
throug
h s
i
m
ul
ati
on
MA
T
L
A
B
/S
i
m
ul
i
nk
a
nd
h
ardwar
e
i
mp
l
em
e
nta
t
i
o
n i
n S
ec
ti
o
n 5
.
2.
P
h
o
t
o
volt
ai
c (P
V
)
Mod
e
lling
A
s
i
ng
l
e
d
i
od
e
mo
d
el
(
F
i
g
ure
1(
a))
i
s
the
m
os
t
s
u
i
t
ab
l
e
mo
d
el
for
M
P
P
T
r
es
ea
r
c
h,
r
eg
ardl
es
s
of
a
l
l
we
l
l
-
es
ta
bl
i
s
h
ed
P
V
c
el
l
m
od
e
l
l
i
n
g
c
i
r
c
ui
ts
fr
om
oth
er
r
efe
r
e
nc
es
[21
,
22
]
.
F
urthermor
e
,
s
om
e
r
es
ea
c
he
r
s
ha
d
c
om
e
ou
t
wi
th
s
ev
eral
P
V
mo
de
l
l
i
ng
c
i
r
c
u
i
t
s
s
uc
h
as
two
di
o
de
m
od
el
(
F
i
gu
r
e
1(b)
)
a
nd
s
i
m
pl
i
f
i
ed
mo
d
el
(
F
i
gu
r
e
1(c
)
)
.
It
i
s
no
ti
c
e
ab
l
e
th
at
tw
o
-
di
od
e
c
o
nfi
gu
r
at
i
on
of
P
V
p
r
ov
i
de
s
h
i
gh
ac
c
urac
y
of
ou
tp
ut
r
es
po
ns
e
be
c
au
s
e
i
t
i
nv
o
l
v
es
the
v
aria
nc
e
i
n
l
o
w
l
ev
el
c
urr
e
nt
fl
o
w
i
n
the
s
em
i
c
o
nd
uc
t
or‟
s
de
p
l
et
i
on
r
eg
i
on
[
23
]
.
Y
et,
i
t
i
s
di
f
fi
c
u
l
t
t
o
i
m
pl
e
me
nt
t
h
e
e
qu
at
i
o
n
i
n
r
ea
l
l
i
f
e
s
i
t
ua
t
i
on
.
L
i
k
ewi
s
e
,
the
s
i
mp
l
i
f
i
ed
mo
d
el
of
P
V
ab
l
e
t
o
n
eg
l
ec
t
th
e
pr
es
en
c
e
of
s
h
un
t
r
es
i
s
tan
c
e,
he
nc
e
the
ma
th
em
a
ti
c
a
l
eq
u
ati
on
m
o
r
e
fea
s
i
b
l
e
[
24
]
.
N
ev
erthe
l
es
s
,
the
s
i
ng
l
e
d
i
od
e
mo
d
el
s
ti
l
l
of
fers
a
be
tte
r
ba
l
an
c
e
be
tw
ee
n
s
i
m
pl
i
c
i
ty
an
d a
c
c
urac
y
.
A
de
ta
i
l
ed
a
na
l
y
s
i
s
an
d
eq
ua
ti
on
s
are
prov
i
d
ed
by
r
ef
erenc
e
[21]
t
o
i
d
en
t
i
fy
the
v
al
u
e
of
ea
c
h
c
om
po
n
en
t
of
t
he
s
i
ng
l
e
d
i
od
e
P
V
mo
de
l
.
T
he
c
ha
r
ac
teri
s
ti
c
eq
u
ati
on
s
o
f
s
i
ng
l
e
di
od
e
mo
de
l
d
i
s
pl
ay
ed
i
n
th
e
eq
u
ati
o
n
s
be
l
ow
ar
e
di
v
i
de
d
i
n
to
fou
r
ty
p
es
;
the
ou
tp
ut
c
urr
en
t
of
s
o
l
ar
P
V
(
I
PV
)
,
c
urr
en
t
ge
ne
r
at
e
d
by
l
i
gh
t
ph
ot
on
(
I
PH
)
,
c
e
l
l
r
ev
ers
e
s
atu
r
at
i
on
c
urr
e
n
t
(
I
S
)
an
d
c
el
l
s
atu
r
ati
on
c
urr
en
t a
t re
fere
nc
e t
em
pe
r
at
ure (
I
RS
).
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
MNIK
A
IS
S
N: 1
69
3
-
6
93
0
â—¼
MP
P
T
fo
r
P
V
S
y
s
tem
B
as
e
d o
n
V
ar
i
ab
l
e
S
te
p S
i
z
e
P
&
O
A
l
g
orit
hm
(
A
wan
g J
us
oh
)
81
F
i
gu
r
e
1.
S
ol
ar P
V
m
od
el
l
i
n
g:
(
a) S
i
ng
l
e
di
od
e
mo
de
l
(
b) T
wo d
i
od
e m
od
e
l
(
c
)
S
i
m
pl
i
fi
e
d m
od
e
l
O
utp
ut
c
urr
e
nt
of
s
ol
ar
P
V
(
I
PV
):
I
PV
=
I
P
–
I
S
[ e
q (V
PV
+
I x R
S
)/k
T
C
A
–
1]
–
[
q (V
PV
+
I
x
R
S
)
/R
SH
]
(
1)
I
PV
c
an
a
l
s
o b
e repr
es
en
te
d
as
i
n
E
q
ua
t
i
on
(
2):
I
PV
=
I
–
(
A
1/
A
2)
(
2)
A
1 =
I
PH
–
I
–
I
S
[e
q (V
PV
+
I x R
S
)/kT
C
A
–
1]
(
3)
A
2 =
–
I
–
I
S
[e
q (
V
PV
+
I x R
S
)/kT
C
A
–
1]
[q
(
R
S
)
/k
T
C
A]
(
4)
Cur
r
en
t g
en
er
ate
d
by
l
i
gh
t
ph
ot
on
(
I
PH
):
I
PH
=
[I
SC
+
K
i
(T
C
–
T
ref
)
] G
(
5)
Cel
l
r
ev
ers
e s
atu
r
a
ti
o
n c
urr
en
t (I
S
):
I
S
=I
RS
(T
C
/T
ref
)
3/
A
[e
qE
G
(1/T
r
ef
–
1/T
C
)/kA
]
(
6)
Cel
l
s
atu
r
a
ti
o
n c
urr
en
t
at
r
e
ferenc
e t
em
p
erature
(
I
RS
):
I
RS
=
I
SC/
[e
qV
OC
/kAN
s
T
C
-
1]
(
7)
G
R
s
h
R
s
I
P
H
I
D
1
I
s
h
I
P
V
V
P
V
G
G
R
s
h
R
s
I
P
H
I
s
h
I
P
V
D
1
D
1
I
D
1
I
D
1
V
P
V
D
2
I
D
2
I
D
2
R
s
I
P
H
I
D
1
I
P
V
V
P
V
D
1
a
)
b
)
c
)
G
R
s
h
R
s
I
P
H
I
D
1
I
s
h
I
P
V
V
P
V
G
G
R
s
h
R
s
I
P
H
I
s
h
I
P
V
D
1
D
1
I
D
1
V
P
V
D
2
I
D
2
R
s
I
P
H
I
D
1
I
P
V
V
P
V
D
1
a
)
b
)
c
)
Evaluation Warning : The document was created with Spire.PDF for Python.
â—¼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
MNIK
A
V
ol
.
15
,
No
.
1,
M
arc
h 2
0
17
:
79
–
92
82
where,
I
SC
: S
h
ort c
i
r
c
ui
t c
urr
e
nt
of
s
ol
ar c
el
l
V
OC
: O
pe
n c
i
r
c
ui
t v
o
l
ta
ge
o
f s
ol
ar c
el
l
R
S
: E
q
ui
v
a
l
en
t
s
erie
s
R
SH
: S
h
un
t res
i
s
tan
c
e
G
: S
u
n i
r
r
ad
i
at
i
o
n
A
: Id
e
al
i
ty
fa
c
tor
N
S
: Num
be
r
of
c
el
l
s
i
n s
er
i
es
q
: E
l
ec
tr
on
C
ha
r
g
e,
1.
6 ×
10
-
19
C
k
:
B
o
l
tz
ma
nn
‟
s
c
on
s
ta
nt,
1.
3
8 ×
10
-
23
J
/
K
T
C
: Cel
l
Te
mp
er
atu
r
e
T
ref
: Ref
ere
nc
e Te
mp
era
ture
K
i
: Temp
erature
Coe
ffi
c
i
en
t‟
s
Curr
en
t
Regu
l
arly
,
s
o
me
of
t
he
P
V
pa
r
am
ete
r
s
s
uc
h
as
o
pe
n
c
i
r
c
ui
t
v
o
l
ta
ge
,
s
h
ort
c
i
r
c
ui
t
c
urr
en
t
an
d
te
mp
erature
c
oe
ffi
c
i
en
t
ha
v
e
be
e
n
prov
i
de
d
i
n
t
he
da
t
a
s
he
et
of
s
ol
ar
P
V
ba
s
ed
on
t
he
S
tan
da
r
d
T
es
t
C
on
d
i
t
i
on
(
S
T
D)
:
10
0
0W
/m
2
of
s
ol
ar
i
r
r
ad
i
ati
on
an
d
2
5°
C
of
t
em
p
erature.
A
l
l
th
e
eq
ua
ti
o
ns
me
nti
on
e
d a
bo
v
e we
r
e
us
ed
i
n t
he
MA
T
L
A
B
/S
i
m
ul
i
nk
s
i
m
ul
ati
on
l
at
er i
n S
ec
t
i
on
5.
3.
S
w
it
ch
ed Mod
e
DC
-
DC
Bo
o
st Co
n
ve
r
t
e
r
DC
-
DC
c
on
v
erter
i
s
l
oc
at
ed
b
etwe
en
the
r
efe
r
r
ed
ph
ot
ov
ol
t
ai
c
mo
d
ul
e
an
d
l
oa
d
i
n
MP
P
T
s
y
s
tem
th
at
al
t
ers
a
DC
v
ol
tag
e
to
an
oth
er
l
ev
el
o
f
DC
v
ol
t
ag
e.
It
i
s
i
mp
o
r
tan
t
t
o
d
es
i
gn
the
DC
-
DC
c
o
nv
erter
c
orr
ec
tl
y
i
n
or
de
r
t
o
e
ns
ure
t
he
P
V
s
y
s
tem
i
s
op
erati
n
g
at
th
e
be
s
t
eff
i
c
i
en
c
y
as
r
eq
u
i
r
ed
.
T
h
ere
are
thre
e
ma
i
n
ty
p
es
tha
t
fr
eq
ue
ntl
y
us
e
d
ac
c
ordi
ng
to
the
s
y
s
tem
ap
p
l
i
c
at
i
on
:
s
te
p
up
the
i
n
pu
t
v
o
l
ta
ge
(
bo
os
t
c
on
v
ert
er)
,
s
tep
do
w
n
t
he
i
np
ut
v
ol
tag
e
(
b
uc
k
c
on
v
erter
)
or c
om
b
i
n
ati
on
o
f b
ot
h o
p
erati
on
s
(
bu
c
k
-
bo
o
s
t c
on
v
erter
)
[25]
.
B
uc
k
c
on
v
erter
an
d
B
o
os
t
c
on
v
erter
are
the
mo
s
t
p
op
ul
ar
c
i
r
c
ui
t
an
d
c
o
mm
on
l
y
us
ed
i
n
the
s
o
l
ar
MP
P
T
s
y
s
tem
d
ue
t
o
t
he
s
i
mp
l
i
c
i
ty
an
d
l
o
w
c
os
t
i
mp
l
em
en
t
ati
on
[16]
.
Non
eth
el
es
s
,
bo
os
t
c
o
nv
erter
i
s
mo
r
e
pr
efe
r
ab
l
e
c
om
pa
r
e
to
the
b
u
c
k
c
on
v
erter
s
i
nc
e
t
he
ou
t
p
ut
P
V
v
ol
tag
e
are
us
u
al
l
y
l
ower
th
an
the
de
s
i
r
ed
v
ol
tag
e
at
t
he
ex
ter
na
l
l
oa
d
.
A
dd
i
t
i
on
al
l
y
,
t
he
c
on
fi
gu
r
at
i
o
n
o
f
bu
c
k
c
on
v
erter
(
s
wi
tc
h
i
ng
c
om
po
n
en
t
i
s
p
l
ac
e
at
i
np
ut
s
i
d
e
a
nd
s
eri
es
wi
t
h
i
np
ut
v
ol
t
ag
e)
ha
d
c
au
s
ed
d
i
s
c
on
ti
nu
ou
s
c
urr
en
t
f
l
ow
i
ns
i
de
t
he
s
y
s
tem
an
d
r
es
u
l
t
i
n
e
ne
r
gy
l
os
s
es
du
r
i
n
g
p
ower
ge
ne
r
ati
on
proc
es
s
.
Co
ns
eq
ue
ntl
y
,
bo
os
t
c
on
v
ert
er
pres
en
ts
a
gre
at
ad
v
an
tag
es
i
n
ter
ms
of
c
os
t s
av
i
ng
a
nd
hi
g
h e
f
fi
c
i
e
nc
y
[26]
.
T
he
r
efo
r
e,
i
n
th
i
s
pa
pe
r
,
b
oo
s
t
c
on
v
ert
er
i
s
c
ho
s
e
n
t
o
l
ev
el
u
p
t
he
i
np
ut
v
ol
tag
e
a
nd
c
on
tr
ol
th
e
l
ev
e
l
of
o
utp
u
t
po
wer
to
t
he
l
o
ad
.
F
u
nd
a
m
en
ta
l
l
y
,
th
e
bo
os
t
c
on
v
ert
er
i
s
c
on
s
i
s
ts
of
an
i
n
du
c
tor,
a
di
od
e
,
a
h
i
g
h
fr
eq
u
en
c
y
po
wer
MO
S
F
E
T
s
wi
tc
h
an
d
c
a
pa
c
i
t
or.
T
h
e
i
np
ut
v
ol
tag
e
of
bo
os
t
c
on
v
erter
i
s
c
on
tr
ol
l
ed
by
the
P
V
m
od
e
l
l
i
n
g
c
i
r
c
ui
t
a
nd
t
he
d
uty
c
y
c
l
e
f
or
the
c
o
nv
erter
i
s
v
arie
d
ac
c
ordi
ng
to
t
he
o
utp
ut
of
MP
P
T
. F
i
gu
r
e 2
i
l
l
u
s
tr
ate
s
th
e
ba
s
i
c
c
i
r
c
ui
t
of
b
oo
s
t c
on
v
erter
us
ed
fo
r
t
hi
s
p
ap
er.
T
he
o
pe
r
at
i
o
n
of
a
bo
os
t
c
on
v
erter
i
s
ma
i
n
l
y
r
e
l
y
o
n
th
e
op
e
ni
ng
an
d
c
l
os
i
ng
of
the
s
wi
tc
h
.
T
h
e
c
h
argi
ng
s
ta
te
i
s
oc
c
urr
ed
wh
en
the
s
wi
tc
h
i
s
c
l
os
ed
an
d
s
ec
on
d
m
od
e
of
op
erat
i
on
(
di
s
c
ha
r
gi
ng
s
tat
e)
wi
l
l
b
e
i
ni
t
i
ate
d
by
op
en
i
ng
t
he
s
wi
tc
h.
T
he
eq
ua
t
i
on
us
ed
to
ob
ta
i
n
th
e
du
ty
c
y
c
l
e f
or thi
s
c
o
nv
erter
i
s
s
ho
wn
i
n
the
E
q
ua
t
i
on
(
8).
In
ord
er
to
en
s
ure
t
he
bo
os
t
c
on
v
erter
o
pe
r
at
es
at
c
o
n
ti
nu
ou
s
c
urr
en
t
mo
de
(
CC
M),
the
s
i
z
e
of
i
n
du
c
tor
us
ed
pl
a
y
s
an
i
mp
ort
an
t
r
ol
e.He
n
c
e,
the
v
al
ue
of
the
i
nd
uc
tor
mu
s
t
be
c
al
c
ul
a
ted
prec
i
s
el
y
.
B
es
i
d
es
,
th
e
c
a
pa
c
i
t
or
i
s
ne
c
es
s
ary
to
di
mi
ni
s
h
th
e
r
i
pp
l
e
a
nd
no
i
s
e
a
t
t
he
ou
tp
ut
s
i
de
of
the
bo
os
t
c
on
v
erter
a
nd
f
urther
s
mo
oth
e
n
o
ut
t
he
l
o
ad
v
ol
t
ag
e
an
d
c
urr
en
t
s
i
gn
a
l
s
.
E
qu
ati
on
(
9)
an
d
(
10
)
are
th
e
us
ef
ul
eq
ua
t
i
o
ns
to
c
o
mp
u
te
t
he
v
al
u
e
o
f
i
n
du
c
tor
an
d
c
ap
ac
i
tor r
es
p
ec
ti
v
e
l
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
MNIK
A
IS
S
N: 1
69
3
-
6
93
0
â—¼
MP
P
T
fo
r
P
V
S
y
s
tem
B
as
e
d o
n
V
ar
i
ab
l
e
S
te
p S
i
z
e
P
&
O
A
l
g
orit
hm
(
A
wan
g J
us
oh
)
83
F
i
gu
r
e
2.
A
DC
-
DC
B
o
os
t C
on
v
erter
Duty
c
y
c
l
e,
D =
1
–
(V
S/
V
o
)
(
8)
Ind
uc
tor,
L =
(
V
S
D/∆
i
o
f)
(
9)
Capa
c
i
tor,
C =
(
V
o
D/∆
V
o
Rf)
(
10
)
where,
V
S
: In
p
ut
v
ol
tag
e f
r
om
s
ol
ar
P
V
V
o
: O
utp
ut
v
ol
t
ag
e
at
l
oa
d s
i
d
e
∆i
o
: Ri
p
pl
e o
u
tpu
t
c
urr
en
t
∆V
o
: Ri
p
pl
e o
u
tpu
t
v
ol
t
ag
e
4.
De
sign
V
ar
i
able
S
t
ep S
iz
e P
&O
Algo
r
it
h
m
T
he
o
pe
r
at
i
o
n
for
P
&
O
a
l
go
r
i
th
m
i
s
th
eo
r
et
i
c
al
l
y
a
b
ou
t
pe
r
turb
i
n
g
or
s
h
i
ft
i
ng
t
he
P
V
op
erat
i
o
n
p
oi
nt
ba
s
e
d
o
n
th
e
s
i
g
n
of
the
l
as
t
i
nc
r
em
en
t
of
P
V
po
w
er
[
27
]
,
as
pres
e
nte
d
i
n
F
i
gu
r
e
3(a)
.
In
oth
er
wor
ds
,
the
o
p
erati
o
n
po
i
nt
k
ee
ps
i
nc
r
ea
s
i
ng
as
the
P
V
po
wer
i
nc
r
ea
s
es
.
O
nc
e
the
P
V
po
wer
s
t
arts
to
d
ec
r
ea
s
e,
t
he
op
erati
on
po
i
nt
g
oe
s
i
n
r
ev
ers
ed
di
r
ec
t
i
on
.
E
v
en
t
ua
l
l
y
,
i
t
k
e
ep
s
os
c
i
l
l
ati
ng
aro
un
d
the
M
P
P
wi
th
a
fi
x
e
d
s
tep
s
i
z
e.
F
i
g
ure
3(b)
i
l
l
us
tr
ate
s
th
e
o
pe
r
ati
on
for
P
&
O
al
g
orit
h
m t
o
war
ds
th
e s
ol
ar
P
V
un
de
r
c
on
s
ta
nt
i
r
r
ad
i
ati
on
[2
8]
.
T
ec
hn
i
c
a
l
l
y
,
l
arg
er
s
tep
s
i
z
e
c
on
tr
i
bu
t
es
to
hi
gh
er
po
w
er
l
os
s
es
,
s
i
nc
e
th
e
tr
ac
k
e
d
po
i
n
t
i
s
away
fr
om
the
r
ea
l
M
P
P
.
T
he
r
efo
r
e,
t
o
tr
i
m
do
wn
t
he
os
c
i
l
l
at
i
on
a
t
the
po
wer
pe
ak
,
s
ma
l
l
er
s
tep
s
i
z
e
i
s
c
ho
s
en
f
or
the
P
&
O
a
l
go
r
i
th
m.
Nev
ert
he
l
e
s
s
,
the
tr
an
s
i
e
nt
r
es
po
ns
e
of
the
s
y
s
tem
i
s
s
l
ow
an
d
i
nfl
ue
nc
es
the
ov
eral
l
p
erfor
ma
nc
e
of
s
o
l
ar
P
V
.
B
es
i
d
e
s
,
th
e
c
o
nv
en
t
i
o
na
l
a
l
go
r
i
thm
i
s
un
ab
l
e
to
w
ork
wel
l
u
nd
er
v
ario
us
we
ath
er
c
on
d
i
ti
on
s
,
as
wr
on
g
pe
r
t
urbat
i
on
c
ou
l
d
ha
pp
e
n
a
nd
c
au
s
e
the
op
erati
ng
p
oi
nt
to
m
ov
e
furth
er
aw
ay
fr
om
th
e
p
ea
k
po
i
nt
.
In
s
h
ort,
the
s
e
two
c
on
di
t
i
o
ns
ha
v
e
be
c
om
e t
h
e c
r
i
ti
c
a
l
draw
ba
c
k
s
of
th
e
c
on
v
en
ti
on
a
l
P
&
O
me
t
ho
d.
Refe
r
en
c
e
[29]
propos
e
d
a
v
ol
tag
e
ho
l
d
o
pti
mi
z
a
ti
on
of
P
&
O
me
t
ho
d
w
h
ere
an
ad
d
i
ti
on
a
l
s
tag
e
of
de
c
i
s
i
on
i
s
ne
e
de
d
to
v
er
i
fy
the
c
h
a
ng
es
of
i
r
r
ad
i
an
c
e
l
ev
e
l
.
T
h
e
ou
t
pu
t
of
P
V
v
ol
tag
e
(
V
PV
)
i
s
be
i
n
g
h
ol
d
un
ti
l
t
he
i
r
r
ad
i
an
c
e
v
aria
ti
on
i
s
s
t
op
i
n
order
to
av
oi
d
an
y
wr
on
g
tr
ac
k
i
ng
d
i
r
ec
ti
o
n.
T
he
s
t
ep
s
i
z
e
i
s
r
eg
u
l
arly
d
ec
r
ea
s
ed
as
the
tr
ac
k
i
n
g
i
s
ap
proac
h
i
ng
MP
P
.
T
he
r
es
ul
ts
de
p
i
c
ted
t
he
ap
pl
i
ed
s
y
s
tem
ha
d
l
ow
os
c
i
l
l
ati
o
ns
an
d
r
ea
l
M
P
P
wa
s
s
uc
c
es
s
ful
l
y
ob
ta
i
ne
d i
n rea
l
-
ti
me
un
d
er
v
ario
us
i
r
r
a
di
a
nc
e l
ev
el
.
F
urthermor
e
,
th
e
three
p
oi
nts
w
ei
g
ht
P
&
O
m
eth
o
d
an
d
two
s
ta
ge
a
l
g
orit
h
m
are
s
ug
ge
s
te
d
by
r
ef
erenc
e
[
1
5]
to
prev
en
t
fa
i
l
i
ng
du
r
i
ng
r
ap
i
d
v
aria
t
i
o
n
of
i
r
r
ad
i
at
i
on
.
I
n
fac
t,
an
i
ns
tan
tan
eo
us
s
am
pl
i
ng
an
d
pe
ak
c
urr
en
t
c
on
tr
ol
a
pp
r
oa
c
he
s
tha
t
de
p
en
d
o
n
th
e
c
ha
ng
es
of
r
efe
r
en
c
e
c
urr
en
t
ha
s
al
s
o
be
en
r
ec
o
mm
e
nd
e
d
by
r
ef
erenc
e
[30
,
3
1]
to
fi
n
d
a
tr
a
d
eo
ff
b
etwe
e
n
the
w
ea
k
ne
s
s
es
of
P
&
O
s
y
s
tem
.
I
n
d
u
c
t
o
r
D
i
o
d
e
S
w
i
t
c
h
C
a
p
a
c
i
t
o
r
R
e
s
i
s
t
o
r
I
n
d
u
c
t
o
r
D
i
o
d
e
S
w
i
t
c
h
C
a
p
a
c
i
t
o
r
R
e
s
i
s
t
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
â—¼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
MNIK
A
V
ol
.
15
,
No
.
1,
M
arc
h 2
0
17
:
79
–
92
84
F
i
gu
r
e
3.
O
p
erati
on
f
or P
ertur
b a
n
d Obs
erv
e M
P
P
T
Te
c
hn
i
q
ue
(
a) F
l
owc
ha
r
t
for P
&
O
A
l
go
r
i
th
m
(
b) P&
O
Tr
ac
k
i
n
g o
n t
h
e P
-
V
Curv
e
un
d
er Cons
t
an
t Irr
ad
i
ati
on
B
y
r
efe
r
r
i
n
g
al
l
ex
i
s
t
ed
m
et
ho
ds
,
th
i
s
pa
pe
r
prop
os
ed
a
mo
d
i
f
i
ed
al
go
r
i
t
hm
c
om
e
s
wi
th
three
c
on
di
t
i
o
ns
,
whi
c
h
ar
e
A
,
B
an
d
C,
as
s
ee
n
i
n
the
f
l
owc
ha
r
t
(
F
i
gu
r
e
4).
T
hs
me
th
od
i
s
ba
s
i
c
al
l
y
c
om
b
i
n
i
ng
t
he
i
de
a
of
ha
v
i
ng
v
ari
ab
l
e
s
tep
s
i
z
e
of
P
&
O
a
l
g
orit
h
m
an
d
p
r
i
nc
i
p
al
of
H
C
me
th
od
.
T
he
S
ec
ti
on
A
s
i
gn
i
fi
es
th
e
os
c
i
l
l
at
i
o
n
s
up
pres
s
i
on
s
ta
ge
.
A
s
t
he
p
ower
p
ea
k
i
s
att
a
i
ne
d,
t
he
s
t
ep
s
i
z
e
of
th
e
du
ty
r
ati
o
i
s
d
i
v
i
d
ed
by
a
c
on
s
tan
t
nu
mb
er,
ß
,
i
n
ord
er
to
r
e
du
c
e
i
t
to
ne
arly
z
ero
an
d
c
l
os
er
t
o
the
r
e
al
MP
P
.
T
h
e
c
on
s
t
an
t
ß
i
s
r
a
nd
o
ml
y
p
i
c
k
ed
a
s
l
on
g
as
i
t
i
s
l
arger
t
ha
n
1.
S
i
nc
e
th
e
r
ea
l
pe
ak
po
i
nt
i
s
i
nc
o
nc
ei
v
ab
l
e
to
b
e
ac
h
i
ev
e
d,
a
m
argi
n
of
p
ower
v
aria
ti
on
ha
d
be
en
de
fi
n
ed
,
whi
c
h
wer
e
fr
o
m
-
0.0
0
1W
to
0.0
0
1W
.
T
he
n,
s
ta
ge
A
wi
l
l
be
i
ni
t
i
at
ed
as
th
e c
o
nd
i
ti
o
n i
s
me
t.
Se
c
ti
on
B
,
as
de
p
i
c
ted
i
n
F
i
gu
r
e
4
i
s
uti
l
i
z
ed
t
o
s
en
s
e
the
r
ap
i
d
v
aria
t
i
o
n
of
s
urr
o
un
d
i
ng
c
on
di
t
i
o
ns
.
T
he
i
de
a
c
o
me
s
fr
om
the
I
-
V
c
urv
e
o
f
the
P
V
p
an
el
,
as
s
ho
wn
i
n
F
i
g
ure
5.
T
he
DC
l
oa
d
l
i
ne
s
ho
wn
i
n
the
f
i
gu
r
e
r
ep
r
es
en
ts
th
e
eq
u
i
v
a
l
en
t
r
es
i
s
tan
c
e
fr
om
th
e
i
np
ut
at
the
s
pe
c
i
fi
c
v
al
ue
of
du
ty
l
on
g
as
r
at
i
o.
F
r
om
th
e
fi
gu
r
e,
whe
n
the
s
un
i
r
r
ad
i
ati
on
w
as
50
0
W
/m
2
,
the
op
erat
i
n
g
p
oi
nt
was
l
oc
at
e
d
at
A
.
W
h
en
th
e
s
u
n
i
r
r
a
di
at
i
o
n
r
a
pi
dl
y
c
h
an
g
ed
to
75
0
W
/
m
2
,
th
e
op
erat
i
n
g
p
oi
nt
c
ha
ng
ed
a
nd
w
as
l
oc
ate
d
at
p
oi
n
t
B
.
T
he
r
ef
ore,
i
t
c
a
n
be
c
o
nc
l
ud
ed
th
at,
the
ma
gn
i
tu
de
of
P
V
c
urr
en
t
an
d
P
V
v
ol
t
ag
e
w
ou
l
d
ei
t
he
r
i
nc
r
ea
s
e
or
de
c
r
ea
s
e
s
i
mu
l
tan
eo
us
l
y
when
s
urr
ou
nd
i
ng
c
o
nd
i
ti
o
n
s
c
ha
ng
e
r
ap
i
d
l
y
.
Henc
e
,
fr
om
s
ec
ti
o
n
B
i
n
F
i
gu
r
e
4
,
a
c
on
di
t
i
o
n
ha
d
be
en
s
et,
i
n
ord
er
to
s
e
ns
e
the
r
ap
i
d
c
ha
ng
es
,
by
w
hi
c
h
i
f
th
e
s
urr
ou
n
di
ng
w
a
s
s
ub
j
ec
ted
to
r
ap
i
d c
h
an
ge
, t
he
w
ho
l
e a
l
g
orit
h
m wo
ul
d
be
i
n
i
t
i
al
i
z
ed
i
n o
r
de
r
t
o o
bta
i
n f
as
t trans
i
en
t res
po
ns
e.
In
ad
di
t
i
on
,
S
ec
ti
o
n
C
i
n
F
i
gu
r
e
4
prov
i
d
es
the
v
ari
ab
l
e
s
tep
s
i
z
e
p
ertur
b
ati
on
,
w
he
r
eb
y
the
v
a
l
u
e
of
s
tep
s
i
z
e,
α
i
s
v
arie
d
by
d
i
v
i
d
i
ng
or
mu
l
ti
pl
y
i
ng
α
w
i
th
1.1
[3
2]
de
p
en
d
on
the
v
al
ue
of
th
e
s
l
op
e
P
V
c
urv
e,
∆
P
/
∆V.
A
s
th
e
s
l
o
pe
of
t
he
c
urv
e
de
c
r
ea
s
e,
th
i
s
m
ea
ns
t
h
at
th
e
o
pe
r
at
i
n
g
po
i
nt
i
s
ap
pr
oa
c
h
i
n
g
th
e
MP
P
;
as
a
r
es
ul
t,
th
e
s
te
p
s
i
z
e
w
i
l
l
au
to
ma
t
i
c
al
l
y
r
ed
uc
e
s
o
t
ha
t
an
ac
c
urate M
P
P
c
an
b
e t
r
ac
k
ed
.
a
)
b
)
S
t
a
r
t
M
e
a
s
u
r
e
V
[
n
]
,
I
[
n
]
,
V
[
n
-
1
]
,
I
[
n
-
1
]
P
[
n
]
=
V
[
n
]
–
I
[
n
]
P
[
n
-
1
]
=
V
[
n
-
1
]
–
I
[
n
-
1
]
∆
P
=
P
[
n
]
–
P
[
n
-
1
]
∆
V
=
V
[
n
]
–
V
[
n
-
1
]
∆
P
=
0
∆
P
>
0
∆
V
>
0
∆
V
<
0
V
o
l
t
a
g
e
I
n
c
r
e
a
s
e
V
o
l
t
a
g
e
d
e
c
r
e
a
s
e
R
e
t
u
r
n
Y
e
s
Y
e
s
Y
e
s
N
o
N
o
N
o
S
t
a
r
t
M
e
a
s
u
r
e
V
[
n
]
,
I
[
n
]
,
V
[
n
-
1
]
,
I
[
n
-
1
]
P
[
n
]
=
V
[
n
]
–
I
[
n
]
P
[
n
-
1
]
=
V
[
n
-
1
]
–
I
[
n
-
1
]
∆
P
=
P
[
n
]
–
P
[
n
-
1
]
∆
V
=
V
[
n
]
–
V
[
n
-
1
]
∆
P
=
0
∆
P
>
0
∆
V
>
0
∆
V
<
0
V
o
l
t
a
g
e
I
n
c
r
e
a
s
e
V
o
l
t
a
g
e
d
e
c
r
e
a
s
e
R
e
t
u
r
n
Y
e
s
Y
e
s
Y
e
s
N
o
N
o
N
o
a
)
b
)
S
t
a
r
t
M
e
a
s
u
r
e
V
[
n
]
,
I
[
n
]
,
V
[
n
-
1
]
,
I
[
n
-
1
]
P
[
n
]
=
V
[
n
]
–
I
[
n
]
P
[
n
-
1
]
=
V
[
n
-
1
]
–
I
[
n
-
1
]
∆
P
=
P
[
n
]
–
P
[
n
-
1
]
∆
V
=
V
[
n
]
–
V
[
n
-
1
]
∆
P
=
0
∆
P
>
0
∆
V
>
0
∆
V
<
0
V
o
l
t
a
g
e
I
n
c
r
e
a
s
e
V
o
l
t
a
g
e
d
e
c
r
e
a
s
e
R
e
t
u
r
n
Y
e
s
Y
e
s
Y
e
s
N
o
N
o
N
o
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
MNIK
A
IS
S
N: 1
69
3
-
6
93
0
â—¼
MP
P
T
fo
r
P
V
S
y
s
tem
B
as
e
d o
n
V
ar
i
ab
l
e
S
te
p S
i
z
e
P
&
O
A
l
g
orit
hm
(
A
wan
g J
us
oh
)
85
F
i
gu
r
e
4.
P
r
op
os
e
d M
od
i
fi
e
d P
&
O
M
P
P
T
F
i
gu
r
e
5.
I
-
V
Curv
e w
i
th
DC
Lo
a
d
L
i
ne
[28]
Y
e
s
S
T
A
R
T
S
T
A
R
T
D
=
0
.
5
,
∆
D
=
0
.
0
2
D
=
0
.
5
,
∆
D
=
0
.
0
2
V
[
n
]
,
I
[
n
]
V
[
n
]
,
I
[
n
]
P
[
n
]
=
I
[
n
]
*
V
[
n
]
P
[
n
]
=
I
[
n
]
*
V
[
n
]
∆
P
=
P
[
n
]
-
P
[
n
-
1
]
∆
P
=
P
[
n
]
-
P
[
n
-
1
]
∆
P
<
1
&
&
∆
P
>
-
1
∆
P
<
1
&
&
∆
P
>
-
1
∆
P
>
0
∆
V
[
n
-
1
]
<
0
&
&
∆
I
[
n
-
1
]
>
0
∆
P
/
∆
D
>
0
D
[
n
]
=
D
[
n
-
1
]
+
(
α
×
1
.
1
)
D
[
n
]
=
D
[
n
-
1
]
–
(
α
/
1
.
1
)
∆
D
=
∆
D
[
n
-
1
]
/
ß
N
o
N
o
Y
e
s
Y
e
s
N
o
A
B
C
Y
e
s
S
T
A
R
T
S
T
A
R
T
D
=
0
.
5
,
∆
D
=
0
.
0
2
D
=
0
.
5
,
∆
D
=
0
.
0
2
V
[
n
]
,
I
[
n
]
V
[
n
]
,
I
[
n
]
P
[
n
]
=
I
[
n
]
*
V
[
n
]
P
[
n
]
=
I
[
n
]
*
V
[
n
]
∆
P
=
P
[
n
]
-
P
[
n
-
1
]
∆
P
=
P
[
n
]
-
P
[
n
-
1
]
∆
P
<
1
&
&
∆
P
>
-
1
∆
P
<
1
&
&
∆
P
>
-
1
∆
P
>
0
∆
V
[
n
-
1
]
<
0
&
&
∆
I
[
n
-
1
]
>
0
∆
P
/
∆
D
>
0
D
[
n
]
=
D
[
n
-
1
]
+
(
α
×
1
.
1
)
D
[
n
]
=
D
[
n
-
1
]
–
(
α
/
1
.
1
)
∆
D
=
∆
D
[
n
-
1
]
/
ß
N
o
N
o
Y
e
s
Y
e
s
N
o
A
B
C
Evaluation Warning : The document was created with Spire.PDF for Python.
â—¼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
MNIK
A
V
ol
.
15
,
No
.
1,
M
arc
h 2
0
17
:
79
–
92
86
5.
S
i
mu
latio
n
(
Ma
t
l
ab/S
im
u
link)
T
he
MP
P
T
al
go
r
i
thm
i
s
i
mp
l
em
en
te
d
us
i
n
g
M
A
T
LA
B
fu
nc
ti
on
b
l
oc
k
,
wh
i
l
e
t
he
S
i
m
po
wer
s
y
s
tem
l
i
brar
y
i
s
us
e
d t
o c
r
ea
te
th
e s
u
bs
y
s
tem
bl
oc
k
s
for P
V
c
el
l
an
d
b
oo
s
t c
o
nv
e
r
ter. S
i
m
pl
i
fi
ed
mo
de
l
l
i
n
g
c
i
r
c
ui
t
of
P
V
c
el
l
s
i
s
ap
p
l
i
ed
to
an
a
l
y
s
e
th
e
c
ha
r
ac
teri
s
t
i
c
s
of
t
he
p
a
ne
l
.
T
he
b
as
i
c
l
ay
ou
t
of
t
he
MA
T
L
A
B
/S
i
m
ul
i
nk
i
s
d
i
s
pl
ay
ed
i
n F
i
gu
r
e
6.
F
i
gu
r
e
6.
M
A
T
L
A
B
/S
i
m
ul
i
n
k
La
y
ou
t
T
he
propos
e
d
al
go
r
i
t
hm
i
s
pl
ac
e
d
at
the
M
P
P
T
b
l
oc
k
be
twe
en
th
e
s
o
l
ar
P
V
an
d
bo
os
t
c
on
v
erter
wh
i
c
h
P
V
c
urr
en
t
an
d
v
o
l
tag
e
(
I
a
an
d
V
a
)
a
r
e
the
i
np
u
ts
wh
i
l
e
t
he
du
t
y
c
y
c
l
e
i
s
t
he
r
eq
ui
r
e
d
ou
t
pu
t
f
or
the
M
P
P
T
s
y
s
tem
.
T
he
pa
r
a
me
t
ers
us
ed
for
bo
os
t
c
on
v
erter
are:
22
0µF
of
c
ap
ac
i
tor,
30
mH
of
i
n
du
c
tor
an
d
3
1k
Hz
of
s
wi
tc
h
i
ng
fr
e
qu
e
nc
y
.
F
urth
ermor
e,
a
c
on
s
ta
nt
i
r
r
ad
i
ati
on
o
f
10
00
W
/
m
2
a
n
d
r
ap
i
d
c
ha
ng
e
of
i
r
r
ad
i
ati
o
n
fr
om
80
0
W
/
m
2
t
o
10
00
W
/m
2
ha
d
be
en
ap
p
l
i
e
d
to
the
s
y
s
tem
.
T
h
e
r
es
ul
t
of
t
he
o
utp
ut
p
ow
er
wav
efo
r
m
was
o
bs
erv
e
d
throu
gh
t
he
s
c
op
e f
or c
om
pa
r
i
s
o
n.
T
he
s
i
m
ul
a
ti
o
n
h
ad
b
ee
n
c
arr
i
ed
o
ut
w
i
th
v
ari
ou
s
s
tep
s
i
z
es
;
l
arge
s
t
ep
s
i
z
e,
s
m
a
l
l
s
te
p
s
i
z
e
an
d
v
ari
ab
l
e
s
tep
s
i
z
e
s
.
T
he
r
es
ul
ts
of
th
e
s
ol
ar
c
el
l
p
ower
are
pres
e
nte
d
i
n
F
i
gu
r
e
7(a)
,
7(b)
,
7(c
)
an
d
7(d)
,
r
es
pe
c
ti
v
el
y
.Fr
om
t
he
ob
tai
ne
d
r
es
ul
ts
,
the
r
e
wer
e
s
om
e
i
mp
r
ov
e
me
nts
s
ho
wn
by
the
v
ar
i
ab
l
e
s
tep
s
i
z
e
ov
er
t
he
c
on
v
e
nt
i
on
al
me
t
ho
d
(
s
m
al
l
or
l
arg
e
s
te
p
s
i
z
e).
W
he
n
s
ma
l
l
s
te
p
s
i
z
e
was
us
ed
,
al
th
ou
g
h
t
he
r
e
was
j
us
t
a
s
ma
l
l
os
c
i
l
l
ati
on
du
r
i
ng
m
a
x
i
mu
m
p
ower,
the
s
y
s
tem
’
s
c
o
nv
ergenc
e
s
pe
ed
was
r
el
a
ti
v
e
l
y
s
l
o
w,
whi
c
h
to
ok
aro
un
d
0.
5s
to
b
e a
t
t
he
s
t
ea
dy
s
tat
e.
O
n
th
e
ot
he
r
ha
nd
,
when
t
he
s
y
s
tem
w
as
ap
p
l
i
ed
w
i
th
l
arg
e
s
tep
s
i
z
e
,
th
e
c
on
v
erge
nc
e
s
pe
ed
ha
d
i
mp
r
ov
ed
to
0.
05
s
.
How
ev
er,
t
he
s
t
ea
dy
s
tat
e
os
c
i
l
l
at
i
o
n
be
c
am
e
wor
s
e
w
i
th
the
r
i
pp
l
e
p
ower
of
13
m
W
.
B
o
th
c
a
s
es
de
m
on
s
tr
ate
d
th
e
ge
ne
r
a
l
dra
wbac
k
s
of
c
on
v
en
ti
o
na
l
P
&
O
al
g
orit
h
m.
In
ord
er
to
s
ol
v
e
th
i
s
i
s
s
ue
,
v
aria
b
l
e
s
tep
s
i
z
e
a
l
g
orit
h
m
was
ap
p
l
i
ed
,
wi
t
h
pr
ov
en
r
es
ul
t
as
s
ho
wn
i
n
F
i
g
ure
7(c
)
r
eg
ardi
ng
i
ts
eff
i
c
i
en
c
y
an
d
e
ffe
c
ti
v
en
es
s
.
B
y
us
i
n
g
v
ari
ab
l
e
s
tep
s
i
z
e
al
g
orit
h
m,
c
on
v
erg
en
c
e
s
p
ee
d
c
ou
l
d
be
s
uc
c
es
s
ful
l
y
ma
i
nta
i
ne
d
i
n
0.0
5s
,
wh
i
l
e
the
os
c
i
l
l
a
ti
o
n
was
s
up
pres
s
ed
du
r
i
ng
s
te
ad
y
s
tat
e.
T
he
s
y
s
tem
was
al
s
o
s
i
m
ul
ate
d
u
nd
er
r
ap
i
d
c
ha
ng
e
d
of
i
r
r
ad
i
at
i
on
l
ev
el
fr
o
m
80
0
W
/m
2
to
1
00
0
W
/m
2
a
t
s
i
mu
l
at
i
o
n
t
i
me
of
1
.0
s
,
by
us
i
ng
v
aria
b
l
e
s
tep
s
i
z
e
a
l
go
r
i
thm
.
T
he
r
es
u
l
t
of
po
wer
c
urv
e
i
s
de
m
on
s
tr
ate
d
i
n
F
i
gu
r
e
7(d)
.
R
e
s
ul
t
i
n
F
i
gu
r
e
7(
d)
s
ho
ws
the
s
at
i
s
fy
i
ng
pe
r
forma
nc
e
fr
o
m
v
aria
bl
e
s
tep
s
i
z
e
P
&
O
al
g
orit
h
m
i
n
de
a
l
i
ng
w
i
th
r
a
pi
d
c
ha
ng
e
of
s
un
i
r
r
ad
i
ati
on
l
ev
e
l
.
I
p
v
V
p
v
I
a
V
a
I
a
1
P
p
v
D
u
t
y
D
u
t
y
+
V
i
n
-
V
i
n
+
V
o
u
t
-
V
o
u
t
P
m
o
d
S
o
l
a
r
P
V
B
o
o
s
t
c
o
n
v
e
r
t
e
r
1
2
:
3
4
D
i
g
i
t
a
l
C
l
o
c
k
M
P
P
T
1
0
0
0
Ω
I
p
v
V
p
v
I
a
V
a
I
a
1
P
p
v
D
u
t
y
D
u
t
y
+
V
i
n
-
V
i
n
+
V
o
u
t
-
V
o
u
t
P
m
o
d
S
o
l
a
r
P
V
B
o
o
s
t
c
o
n
v
e
r
t
e
r
1
2
:
3
4
D
i
g
i
t
a
l
C
l
o
c
k
M
P
P
T
1
0
0
0
Ω
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
MNIK
A
IS
S
N: 1
69
3
-
6
93
0
â—¼
MP
P
T
fo
r
P
V
S
y
s
tem
B
as
e
d o
n
V
ar
i
ab
l
e
S
te
p S
i
z
e
P
&
O
A
l
g
orit
hm
(
A
wan
g J
us
oh
)
87
F
i
g
ure
7.
S
ol
ar Ce
l
l
P
o
wer
Cur
v
e wi
t
h D
i
ffe
r
e
nt
S
tep
S
i
z
e (a)
La
r
ge
S
tep
S
i
z
e (0. 1
V
)
(
b) S
ma
l
l
S
tep
S
i
z
e (0.0
1V
)
(
c
)
V
aria
bl
e
S
te
p
S
i
z
e (d)
V
ari
ab
l
e
S
tep
S
i
z
e w
i
th
R
ap
i
d I
r
r
ad
i
an
c
e V
aria
ti
o
n
F
i
gu
r
e
8(a)
,
8(b)
an
d
8(c
)
de
pi
c
t
th
e
v
aria
ti
o
n
of
d
uty
c
y
c
l
e
s
tep
s
i
z
e
wi
th
r
es
pe
c
t
t
o
ti
m
e
for
al
l
thre
e
c
as
es
.
B
as
e
d
on
th
e
fi
gu
r
es
,
i
t
c
a
n
be
c
on
c
l
u
de
d
t
ha
t,
the
op
t
i
mu
m
v
al
u
e
of
d
uty
c
y
c
l
e
was
0.
65
,
i
n
ord
er
to
en
s
ure
th
e
m
ax
i
m
um
ou
t
pu
t
po
w
er
to
be
ex
tr
ac
te
d
fr
om
t
he
s
o
l
ar
c
el
l
.
A
s
i
n
F
i
g
ure
8(c
)
,
t
he
s
te
p
s
i
z
e
was
au
t
om
ati
c
a
l
l
y
v
ari
ed
whe
n
t
he
op
erat
i
n
g
p
oi
nt
ap
pro
ac
he
d
the
ma
x
i
mu
m
pe
ak
p
ower p
oi
nt.
F
r
om
al
l
thre
e
c
as
es
,
the
p
erfor
ma
nc
e
of
th
e
M
P
P
T
w
as
c
areful
l
y
ob
s
erv
ed
thro
u
gh
the
po
wer
c
urv
e
fr
o
m
th
e
ou
tp
ut
term
i
na
l
o
f
s
ol
ar
c
el
l
,
a
s
s
ho
wn
i
n
9(a)
,
9(
b)
an
d
9(c
)
.
In
the
s
e
fi
gu
r
es
,
y
el
l
ow
c
o
l
ou
r
l
i
ne
r
ep
r
es
en
ts
the
o
utp
ut
po
w
er
fr
om
th
e
s
o
l
ar
c
el
l
t
ermi
na
l
,
wh
i
l
e
pu
r
p
l
e
c
ol
ou
r
l
i
ne
r
ep
r
es
en
ts
th
e o
utp
ut
po
w
er r
ec
ei
v
e
d b
y
th
e l
o
ad
.
Dur
i
n
g
t
he
ap
p
l
i
c
a
ti
o
n
of
t
he
s
m
al
l
s
te
p
s
i
z
e
,
t
he
c
o
nv
ergenc
e
s
pe
e
d
w
as
s
i
gn
i
fi
c
a
ntl
y
s
l
ow,
ar
ou
n
d
0.
75
s
,
w
i
th
s
ma
l
l
os
c
i
l
l
a
ti
o
n
at
th
e
ma
x
i
m
um
po
w
er
po
i
nt.
In
c
on
tr
as
t,
th
e
c
on
v
ergenc
e
s
pe
e
d
was
i
mp
r
ov
ed
fr
om
0.7
5s
to
0.3
s
when
l
ar
ge
s
te
p
s
i
z
e
wa
s
gi
v
en
to
the
s
y
s
tem
.
Howev
er,
i
t
c
on
ta
i
ne
d
a
l
o
t
of
r
i
pp
l
e
a
nd
os
c
i
l
l
a
ti
o
ns
,
es
pe
c
i
a
l
l
y
du
r
i
ng
s
te
ad
y
s
tat
e.
La
s
tl
y
,
9(c
)
de
mo
ns
tr
at
es
the
p
ower
c
urv
e
du
r
i
ng
th
e
ap
p
l
i
c
ati
on
of
v
ar
i
ab
l
e
s
tep
s
i
z
e
P
&
O
al
g
orit
h
m.
T
he
fi
gu
r
e
c
l
e
arl
y
s
ho
ws
t
he
i
mp
r
ov
em
en
t
an
d
pro
mi
s
i
ng
pe
r
for
ma
nc
e
d
el
i
v
ered
by
thi
s
m
od
i
fi
ed
P
&
O
a
l
go
r
i
t
hm
,
s
h
owi
ng
r
e
l
a
ti
v
e
l
y
fa
s
ter
c
on
v
ergenc
e
s
pe
ed
of
0.
65
s
,
s
m
al
l
os
c
i
l
l
ati
on
a
t s
tea
dy
s
tat
e r
eg
i
on
a
nd
prom
i
s
i
n
g e
ff
i
c
i
e
nc
y
of
95
.
23
%.
Evaluation Warning : The document was created with Spire.PDF for Python.
â—¼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
MNIK
A
V
ol
.
15
,
No
.
1,
M
arc
h 2
0
17
:
79
–
92
88
0
.
7
0
.
6
0
.
5
0
.
4
0
.
3
0
.
2
0
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
1
.
2
1
.
4
1
.
6
1
.
8
2
.
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
D
u
t
y
C
y
c
l
e
a
)
0
.
7
0
.
6
0
.
5
0
.
4
0
.
3
0
.
2
0
0
.
5
1
.
0
2
.
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
0
.
8
0
.
9
1
.
0
b
)
0
.
6
0
.
5
0
.
4
0
.
3
0
.
2
0
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
1
.
2
1
.
4
1
.
6
1
.
8
2
.
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
D
u
t
y
C
y
c
l
e
c
)
O
p
t
i
m
u
m
d
u
t
y
c
y
c
l
e
=
0
.
6
5
O
p
t
i
m
u
m
d
u
t
y
c
y
c
l
e
=
0
.
6
5
O
p
t
i
m
u
m
d
u
t
y
c
y
c
l
e
=
0
.
6
5
0
.
7
0
.
6
0
.
5
0
.
4
0
.
3
0
.
2
0
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
1
.
2
1
.
4
1
.
6
1
.
8
2
.
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
D
u
t
y
C
y
c
l
e
a
)
0
.
7
0
.
6
0
.
5
0
.
4
0
.
3
0
.
2
0
0
.
5
1
.
0
2
.
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
0
.
8
0
.
9
1
.
0
b
)
0
.
6
0
.
5
0
.
4
0
.
3
0
.
2
0
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
1
.
2
1
.
4
1
.
6
1
.
8
2
.
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
D
u
t
y
C
y
c
l
e
c
)
O
p
t
i
m
u
m
d
u
t
y
c
y
c
l
e
=
0
.
6
5
O
p
t
i
m
u
m
d
u
t
y
c
y
c
l
e
=
0
.
6
5
O
p
t
i
m
u
m
d
u
t
y
c
y
c
l
e
=
0
.
6
5
F
i
gu
r
e
8.
D
uty
Cy
c
l
e w
i
th
D
i
ffe
r
e
nt
S
tep
S
i
z
e (a)
S
ma
l
l
S
tep
S
i
z
e (0.0
1V
)
(
b) Large
S
te
p S
i
z
e (0.
05
V
)
(
c
)
V
aria
b
l
e
S
te
p
S
i
z
e
F
i
gu
r
e
9.
P
ow
er Cur
v
e a
t
o
utp
ut
c
el
l
te
r
m
i
n
al
an
d
l
o
ad
wi
th
Di
ff
erent
S
t
ep
S
i
z
e
(
a) Sm
a
l
l
S
t
ep
S
i
z
e (
0.0
1
V
)
(
b) Large
S
t
ep
S
i
z
e (0
.05
V
)
(
c
)
V
aria
b
l
e
S
te
p S
i
z
e
0
.
0
7
0
.
0
6
0
.
0
5
0
.
0
4
0
.
0
3
0
.
0
2
0
.
0
1
-
0
.
0
1
0
0
.
2
5
0
.
5
0
.
7
5
1
.
0
1
.
2
5
1
.
5
1
.
7
5
2
.
0
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
P
o
w
e
r
(
W
)
a
)
0
.
0
7
0
.
0
6
0
.
0
5
0
.
0
4
0
.
0
3
0
.
0
2
0
.
0
1
-
0
.
0
1
0
0
.
3
0
.
6
0
.
9
1
.
2
1
.
5
2
.
0
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
b
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
1
.
2
1
.
4
1
.
6
1
.
8
2
.
0
0
.
0
7
0
.
0
6
0
.
0
5
0
.
0
4
0
.
0
3
0
.
0
2
0
.
0
1
-
0
.
0
1
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
P
o
w
e
r
(
W
)
c
)
O
u
t
p
u
t
p
o
w
e
r
f
o
r
s
o
l
a
r
P
V
P
o
w
e
r
r
e
c
e
i
v
e
d
b
y
l
o
a
d
0
.
7
5
s
0
.
3
s
E
f
f
i
c
i
e
n
c
y
=
9
5
.
2
3
%
0
.
6
5
s
0
.
0
7
0
.
0
6
0
.
0
5
0
.
0
4
0
.
0
3
0
.
0
2
0
.
0
1
-
0
.
0
1
0
0
.
2
5
0
.
5
0
.
7
5
1
.
0
1
.
2
5
1
.
5
1
.
7
5
2
.
0
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
P
o
w
e
r
(
W
)
a
)
0
.
0
7
0
.
0
6
0
.
0
5
0
.
0
4
0
.
0
3
0
.
0
2
0
.
0
1
-
0
.
0
1
0
0
.
3
0
.
6
0
.
9
1
.
2
1
.
5
2
.
0
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
b
)
0
0
.
2
0
.
4
0
.
6
0
.
8
1
.
0
1
.
2
1
.
4
1
.
6
1
.
8
2
.
0
0
.
0
7
0
.
0
6
0
.
0
5
0
.
0
4
0
.
0
3
0
.
0
2
0
.
0
1
-
0
.
0
1
0
S
i
m
u
l
a
t
i
o
n
T
i
m
e
(
s
)
P
o
w
e
r
(
W
)
c
)
O
u
t
p
u
t
p
o
w
e
r
f
o
r
s
o
l
a
r
P
V
P
o
w
e
r
r
e
c
e
i
v
e
d
b
y
l
o
a
d
0
.
7
5
s
0
.
3
s
E
f
f
i
c
i
e
n
c
y
=
9
5
.
2
3
%
0
.
6
5
s
Evaluation Warning : The document was created with Spire.PDF for Python.