In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
4, D
e
c
e
m
ber
201
9,
pp.
2065~
20
75
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp2065-2075
2065
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Smooth transi
t
ion fr
om grid to
standalone solar diesel mode
hybrid generation sys
tem with
a battery
A
ya M.
El
s
h
erb
in
y
1
,
A
d
el S. Nada
2
,
M
o
h
a
mm
ed
K
am
a
l
3
1
,
2,
3
Dep
a
rt
em
ent of E
lect
rical
p
o
w
er E
ng
in
e
e
r
i
n
g
,
A
l-
A
z
h
a
r
Un
iv
e
r
si
t
y,
E
gy
p
t
1
N
e
w Dam
i
ett
a
Hi
g
he
r
Instit
u
t
e f
o
r
Engin
eering
&
T
echno
lo
gy
, Eg
y
pt
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Mar
26,
2
0
1
9
Re
vise
d A
p
r
20,
201
9
A
c
c
e
pte
d
J
u
l
21,
201
9
Th
is
p
ap
er
d
es
c
r
i
b
ed
a
s
elf
-
su
p
p
ly
s
m
a
rt
m
i
c
rog
r
id
w
h
i
ch
m
ay
b
e
a
l
o
w
vo
lt
age
or
m
edium
vo
l
t
ag
e
d
i
s
t
ri
butio
n
netwo
r
k.
I
t
con
s
i
d
ered
a
n
eff
i
c
i
ent
energ
y
s
ys
tem
in
w
hi
ch
d
iff
e
ren
t
r
en
ewabl
e
s
ources
a
s
ph
ot
o-vo
l
t
a
ic
a
rray,
win
d
,
or
c
on
ve
n
t
io
na
l
a
s
d
ie
se
l
ge
n
e
ra
tor,
a
nd
sto
r
a
g
e
ca
lle
d
d
is
tr
i
b
u
t
e
d
gen
e
rators
w
hi
c
h
o
rg
a
n
ized
t
o
chan
ce
th
e
l
o
ad
p
ower
d
em
an
d
at
a
ny
tim
e
with
r
eli
a
bili
ty.
It
can
oper
a
t
e
e
it
her
on
-grid
o
r
o
f
f
-
g
r
i
d
c
o
n
figu
rati
on,
esp
eciall
y
limited
are
a
s
f
a
r
f
r
om
t
h
e
u
ti
lity
g
rid
n
e
e
d
ed
a
n
o
t
h
er
b
ac
k
u
p
po
wer.
B
y
u
s
in
g
M
a
tl
ab/Sim
u
l
ink,
a
s
o
l
ar
P
V
sy
stem
i
s
mo
del
e
d
,
sim
u
l
a
ted,
and
det
e
rm
in
e
d
t
he
c
h
a
r
acteris
ti
c
of
a
p
art
i
cular
p
h
o
t
ov
oltai
c
cell
pan
e
l und
er
th
e
i
n
flu
e
nce
of
d
iff
e
rent
v
alues
o
f
a
m
b
i
e
nt
c
on
di
ti
ons.
Taki
ng
i
n
t
o
con
s
i
d
erati
o
n
MP
P
T
a
lg
ori
t
hm
w
h
i
ch
i
ncreas
e
s
t
he
s
olar
e
nerg
y
e
ff
i
c
iency
by
I
ncrem
e
nt
al
c
on
duct
a
nce
te
ch
ni
que
t
o
track
M
P
P
c
orrect
ly
w
it
h
f
a
st
resp
on
se.
P
o
wer
el
ectro
nic
DC/DC
co
nvert
er
a
nd
D
C/
AC
i
nv
erter
a
re
u
sed
with
P
WM
t
echn
i
qu
e.
T
o
co
m
p
en
sate
t
h
e
p
o
w
er
f
l
u
ctu
a
ti
on
s
of
t
h
e
s
y
s
t
e
m
un
der
di
fferen
t
p
o
s
s
i
b
l
e
t
r
ans
i
ent
cases,
a
hi
gh
p
e
r
f
o
rm
a
n
ce
co
nt
rol
b
a
s
e
d
on
an
i
mp
rov
e
d
virtu
a
l
sy
nch
r
on
o
u
s
gen
e
rat
o
r
i
s
a
dd
ed
t
o
con
f
i
r
m
s
m
ooth
vari
ant
s
i
n
v
o
lt
a
g
e,
f
req
u
en
cy
a
n
d
acti
v
e
p
o
w
e
r
du
ring
t
ran
s
i
e
n
t
condit
ion
s
.
Th
e
resu
lts
s
h
o
w
th
e
P
V
/
D
iesel
gen
e
rat
o
r/
bat
t
ery/
po
wer/f
r
eq
uen
c
y
an
d
vo
lt
age p
e
rfo
rmance at
tw
o
diff
e
ren
t
co
nditi
ons.
K
eyw
ord
s
:
H
ybri
d
A
C/D
C
m
ic
rogrid
MATLAB/S
i
mulink
Incr
em
ental c
o
nd
uc
tance
MPP
T
PID
c
o
ntro
ller
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Mo
ham
m
e
d
Kam
al,
D
e
pa
rtem
ent o
f
E
lectr
i
c
a
l p
o
w
e
r
Enginee
r
in
g,
Al
-Azh
ar Un
i
versi
t
y
,
A
l
Mo
k
h
a
yam
A
l
D
ae
m, Egy
pt.
Em
ail:
mK
a
l
sh
a
ear
@yah
o
o
.c
om
1.
I
N
TR
OD
U
C
TI
O
N
The
tra
d
iti
ona
l
p
o
w
e
r
gri
d
u
t
i
l
i
ze
s
foss
il
f
u
e
l
s
a
s
i
ts
p
rim
a
ry
s
o
u
rc
es
o
f
ener
gy
wh
ic
h
ca
use
d
u
st
e
m
i
s
sio
n
s,
c
l
i
m
a
t
e
c
h
a
n
g
e
,
ca
rb
on
d
i
oxi
d
e
,
a
n
d
cont
i
nuo
us
s
h
o
r
t
age
of
f
oss
il
fue
l
s.
B
ut
r
e
c
e
n
tl
y,
r
ene
w
abl
e
ene
r
g
y
s
o
u
r
ces
(
RES
s
)
ba
sed
distri
bu
te
d
ge
ne
rat
i
o
n
(
D
G
)
u
n
its
a
re
p
r
e
ferred
cause
its
s
ev
e
r
al
a
dv
a
n
t
a
ges
suc
h
a
s
flex
i
b
le
e
x
t
ens
i
bil
ity,
e
n
vi
r
o
nm
enta
l
-
frie
n
d
l
i
n
e
ss,
h
i
g
h
e
f
fic
i
e
n
c
y
a
n
d
i
mpr
ove
d
r
e
lia
bi
lit
y.
Conse
que
n
tly,
the
hybr
id
m
ic
rogri
d
c
o
n
c
e
pt
i
s
a
l
so
s
ug
ges
t
e
d
t
o
o
v
e
rco
m
e
t
h
e
d
e
f
ect
s
c
a
u
s
ed
b
y
the
i
n
d
i
v
i
dua
l
a
ppl
ica
t
i
o
n
du
e
to
its
f
le
x
i
b
i
lit
y
a
n
d
e
f
fic
i
e
n
c
y.
I
t’s
very
i
m
porta
nt
f
or
f
ar
aw
ay
a
re
as
t
o
bu
il
d
up
a
com
p
l
e
t
e
s
y
s
tem
able
t
o
me
et
t
he
i
r
n
e
e
d
d
em
an
ds
a
n
d
overc
o
me
d
i
s
c
o
n
n
ec
ted
fr
om
t
he
u
t
i
lit
y
gri
d
w
i
t
h
hi
gh
ef
fic
i
e
n
c
y
a
n
d
s
ta
bi
lit
y.
S
o,
t
his
resea
r
ch
w
i
l
l
pre
s
e
n
t
a
p
ro
po
sed
hyb
rid
po
wer
g
e
ne
ra
t
i
o
n
s
y
s
t
e
m
wh
ich
usefu
l
to
th
is a
pp
lica
t
io
ns
and discuss in det
a
i
ls.
M
i
cr
o
g
r
i
d
(M
G
)
i
s
a
buil
d
in
g
b
l
oc
k
o
f
a
d
i
s
t
r
ibu
t
e
d
s
ys
te
m
that
c
om
b
i
n
e
s
st
or
age,
l
oa
d
s
,
t
r
adi
tio
na
l
and
r
e
new
a
b
l
e
so
urce
s.
I
t
ha
s
tw
o
st
a
t
es
:
firstly,
'off
-gr
i
d
co
nfig
urat
i
o
n
'
t
o
g
e
nera
t
e
a
nd
h
a
n
d
o
u
t
p
ow
e
r
ac
ross
iso
l
a
t
e
d
r
em
ot
e
a
r
ea
s
dur
in
g
d
i
sco
n
t
i
n
u
ity
o
r
a
n
y
i
n
terr
up
tin
g
from
t
h
e
u
t
i
l
i
t
y
g
ri
d
.
S
ec
o
ndl
y
wh
e
r
e
the
sys
t
em
i
s
able
t
o
gi
v
e
-a
nd-ta
ke
p
o
w
er
f
r
o
m
the
gri
d
i
s
na
m
e
d
'gr
i
d-c
o
nne
cted
c
o
n
fi
gur
a
t
i
o
n
'
.
The
pe
rform
anc
e
o
f
a
M
G
i
s
ver
y
i
m
por
ta
nt
duri
n
g
sw
i
t
chi
n
g
m
ode
.
Where
M
G
i
s
re
spons
i
b
le
t
o
ad
just
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
0
6
5
– 2
075
2
066
the
vo
l
t
a
g
e
a
nd
fr
eque
nc
y
w
itho
u
t
a
ny
sup
p
o
rt
f
rom
t
h
e
u
t
ili
ty
gri
d
duri
n
g
t
h
e
t
r
ans
i
en
t
ca
se
s
[1-4]
.
P
V
m
odule
c
a
n
u
se
d
as th
e
f
un
dam
e
n
t
a
l
p
o
w
e
r
t
ra
nsform
ati
o
n
u
n
i
t
of a P
V
gener
at
or sy
s
tem
w
h
ere
its ou
t
put
cha
r
ac
t
e
ris
tic
d
e
p
e
n
ds
o
n
t
h
e
sol
a
r
insu
la
tio
n
a
nd
t
h
e
c
e
ll
t
e
m
pe
rat
u
r
e
[
5-9].
Be
ca
use
P
V
m
odu
le
h
as
no
n
l
i
n
ea
ri
t
y
c
ha
rac
t
e
r
is
tics,
i
t
s
d
esi
g
n
esse
nt
ia
ll
y
m
o
d
e
le
d
a
n
d
si
m
u
la
t
e
d
t
h
r
o
u
g
h
m
a
x
i
m
um
pow
e
r
p
o
i
nt
trac
k
i
n
g
(
MPPT
)
[5]
.
U
sua
l
l
y
M
P
P
T
sym
b
o
liz
es
b
y
a
p
o
wer
elec
t
r
o
nic
circ
u
it
w
h
i
c
h
offe
rs
a
n
int
e
rfac
e
betw
ee
n
P
V
a
nd
l
oa
d
b
y
u
s
i
ng
s
om
e
me
t
h
ods
a
s
N
e
ura
l
N
etw
o
rk
[
5]
,
Incre
m
e
n
ta
l
C
o
nd
u
c
tance
(
I
C
)
[
1
0
]
,
F
u
z
z
y
L
o
gi
c
[11],
P
e
rturb
&
O
b
se
rve
[12],
and
Cuc
koo
s
e
a
r
ch
a
l
g
ori
t
hm
[
13]
.
IC
i
s
c
o
m
m
only
i
m
ple
m
ented
and
trac
ke
d
co
ntr
o
l
s
t
rate
gy
be
cau
se
o
f
i
t
s
env
i
ro
nm
en
tal
ada
p
t
a
b
ilit
y
a
n
d
h
i
gh
e
r
s
t
eady
-
st
at
e
ac
c
u
ra
cy
[
1
4
]
.
MP
P
T
i
s
a
p
p
l
i
e
d in the
b
o
o
s
t
c
on
verter
b
y a
S
i
muli
n
k
/
m
od
el w
her
e
t
h
e d
u
ty
cyc
le
(
D
)
i
s
a
u
tom
a
tic
a
l
l
y
v
a
r
ie
d
uses
I
G
B
T
w
i
t
h
f
ast
sw
i
t
c
h
i
n
g
spe
e
d
a
nd
l
o
w
o
u
t
pu
t
impe
dance
to
g
e
n
er
ate
t
h
e
neede
d
v
ol
ta
ge
t
o
e
x
tr
act
ma
ximum
po
w
e
r
[3].The
DC
/
D
C
co
n
v
ert
e
r
s
c
a
n
b
e
fi
x
e
d
t
h
e
o
u
t
put
v
o
l
t
age
by
c
h
a
n
g
i
ng
du
ty
c
ycle
o
f
trans
i
s
t
or
s.
I
t
ca
n
be
u
se
d
s
e
par
a
te
ly
f
or
eac
h
so
urc
e
o
r
used
as
a
s
i
n
g
l
e
D
C
/
D
C
c
o
n
ve
rter
f
or
w
hol
e
syste
m
[
15].
T
h
e
s
y
nc
h
r
o
n
ous
m
achi
n
e
is
o
ne
o
f
t
h
e
m
o
st
i
m
p
orta
nt
p
a
r
t
of
t
he
p
ow
er
g
r
i
d,
d
iese
l
e
n
g
i
n
e
go
vern
or
s
y
s
t
e
m,
its
r
efe
r
en
c
e
a
n
d
m
e
a
su
red
spee
d,
m
ec
han
i
ca
l
p
ow
e
r
,
volta
ge
r
eg
ula
t
or
a
n
d
e
xc
ita
t
i
o
n
syste
m
[
16-1
9
]
.
Ener
gy storag
e
sy
s
t
em
(
E
S
S
)
i
s
u
s
e
d
a
s
an
a
u
x
il
iar
y
sour
ce
[
20].
I
n
t
h
i
s
st
u
dy,
t
he
P
V
pane
l
a
n
d
diese
l
g
e
n
e
r
ator
a
re
u
se
d
a
s
t
h
e
m
a
in
p
o
w
er
g
ene
r
ator
i
n
t
h
e
sys
t
em
.
A
nd
d
u
e
to
t
h
e
c
o
n
t
i
n
u
ous
d
em
and
for
e
n
e
r
gy,
E
S
S
d
ev
i
c
e
s
a
r
e
r
e
qu
ired
t
o
c
o
mpe
n
sa
t
e
t
he
p
ow
er
i
n
c
a
se
the
l
o
ad
d
em
and
is
l
e
ss.
S
ec
t
i
o
n
2
r
e
p
rese
nt
e
d
t
he
w
ho
le
s
ys
t
e
m
c
on
fi
g
u
rat
i
o
n
.
S
ecti
on
3
s
how
e
d
the
sim
u
l
a
t
i
on
o
f
t
h
e
prop
os
ed
h
y
b
ri
d
p
o
w
e
r
sys
t
em
a
n
d
r
esults
un
d
e
r
di
ff
e
r
e
n
t
p
o
ssi
ble
t
r
an
si
ent
c
a
s
es
a
s
sw
it
c
h
i
n
g
from
gr
i
d
-
c
o
n
n
ec
t
e
d
to
i
s
l
a
nde
d
w
i
t
h
v
ari
o
us
d
ynam
i
c
lo
a
d
s.
F
i
n
al
ly
,
s
e
c
t
ion
4
&
5
out
li
n
e
s
re
su
l
t
s
di
sc
ussi
o
n
a
nd
conc
lus
i
o
n
of t
h
e pa
per.
2.
S
Y
S
T
EM
C
O
N
F
I
GU
R
A
TI
O
N
Thi
s
s
y
s
t
e
m
comp
o
s
ed
o
f
mai
n
i
t
e
ms
a
s
PV
,
Di
es
el
g
e
n
era
t
o
r
,
b
a
t
te
ry, an
d
dyna
mic
l
o
ad.
The w
h
o
l
e
com
p
o
n
e
n
t
s
are inter
c
o
n
n
ec
te
d as
s
how
n
i
n
F
igure
1
the
n
d
isc
u
ss
e
d
in
de
t
a
ils.
F
i
gur
e 1.
S
i
n
g
l
e
li
ne
d
ia
gra
m
of
pro
p
o
se
d hy
bri
d
sys
tem
2.1.
PV
syste
m
The
bas
i
c
de
vic
e
o
f
a
P
V
s
yste
m
is
t
he
P
V
c
e
ll
w
h
i
c
h
dire
c
t
l
y
c
on
ve
rts
s
u
n
l
ig
h
t
i
nt
o
D
C
e
le
c
t
rica
l
e
n
ergy
. C
el
l
s
c
a
n
b
e
c
o
l
l
ect
e
d
t
o
fo
rm
p
an
el
s
o
r
a
rra
y
s
an
d
mo
d
u
l
e
s
for
h
i
gher p
o
w
e
r ap
pl
ica
t
io
ns.
I
n
o
rde
r
to
P
V
cell
has
a
no
nli
n
ea
r
vo
l
t
a
g
e-c
u
rre
nt
(
V
-
I)
c
har
acte
r
ist
i
c
,
i
t
can
b
e
mo
de
l
e
d
us
ing
c
u
rrent
s
ourc
e
s,
d
i
o
des
and
re
s
i
s
t
ors.
S
eve
r
al
m
eth
o
d
s
ha
ve
b
ee
n
de
ve
l
ope
d
to
m
ode
l
a
P
V
p
a
ne
l
a
s
m
a
t
he
ma
ti
c
a
l
m
ode
li
ng
a
n
d
softw
a
re
/sim
ula
tio
n.
S
in
g
l
e-di
o
d
e
a
n
d
d
o
u
b
le
-d
iode
m
od
e
l
s
are
c
om
monl
y
us
ed
t
o
s
i
mu
la
te
P
V
cha
r
ac
t
e
ris
tics bu
t
one d
i
o
d
e
m
odel
e
q
u
i
va
l
e
nt
c
i
r
cu
i
t
i
s
p
o
p
u
l
ar
m
ode
l
u
s
ed to
e
v
a
l
ua
te
t
he
p
e
rform
anc
e
d
a
t
a
w
h
ic
h
are
re
prese
n
t
e
d
by
P
-
V
c
h
ara
c
terist
i
c
c
urves
[2
1].
A
n
i
de
a
l
s
in
g
l
e
-
diode
m
o
d
el
i
n
F
i
g
u
re
2
(a
)
has
thre
e
c
o
mp
on
en
ts:
ph
oto
-
c
u
rre
n
t
so
u
r
ce
,
di
od
e
para
l
l
e
l
to
s
o
u
rce
,
o
u
t
p
u
t
c
u
rre
n
t
.
In
F
igure
2
(
b)
b
e
cause
t
h
e
s
hu
nt
resistance
R
sh
i
s
l
a
r
g
e
,
s
o
i
t
u
s
u
a
l
l
y
c
a
n
b
e
n
e
g
l
e
c
t
e
d
t
h
e
n
p
r
a
c
t
i
c
a
l
m
o
d
e
l
sim
p
ly
a
dded
s
er
ies
r
e
sistance
R
s
[
1
4
].
I
n
Figure
2(c)
p
ra
ctica
l
m
o
d
e
l
w
i
t
h
series
r
es
is
ta
nce
R
s
a
nd
s
hu
n
t
r
e
s
i
s
ta
nc
e
R
sh
i
s
selected
t
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Sm
oot
h t
r
a
n
si
ti
on
f
r
om
grid
t
o
sta
n
d
a
l
o
n
e
so
l
a
r
d
i
esel m
o
de
… (
A
ya M.
Elsher
biny
)
2
067
sim
u
la
t
e
t
he
b
ehav
i
o
r
of
a
P
V
pane
l,
t
hr
o
u
gh
ma
the
m
a
tic
al
m
ode
l
in
g
[
7
]
.
S
un
P
o
w
e
r
S
P
R-
305E-
W
H
T
-
D
so
lar
pa
ne
l
pr
o
v
ide
s
h
ig
her
e
f
fic
i
e
n
cy
a
n
d
p
er
f
o
r
m
ance
t
ha
n
c
o
n
ven
t
i
o
na
l
de
si
g
n
s
a
nd
t
h
in
f
i
l
m
so
lar
p
a
nel
s
.
S
o
,
i
t
s
a
v
es
b
o
t
h
tim
e
a
nd
m
o
ney
an
d
c
o
mm
on
l
y
u
se
d
[
4
]
.
2.
1.
1.
M
at
h
e
mat
i
c
a
l
mod
e
l
o
f
P
V
Case
(
a
)
:
n
egl
e
c
tin
g
t
h
e
in
ter
n
a
l
l
o
s
se
s
of
t
he
C
ur
r
e
nt
,
by
ap
p
ly
i
n
g
Ki
r
c
hh
of
f
'
s
l
a
w
:
I
=
I
ph
–
I
d
(1
)
I
d
= I
O
[e
xp
(
.
.
)
–
1
]
(2
)
V
t
=
K
.
T
C
/q
(
3)
(a
)
(b
)
(c)
F
i
gur
e
2.
T
he
e
qu
i
v
ale
n
t
c
i
r
c
u
i
t
o
f
P
V
device
,
(
a
)
I
d
ea
l
si
ngl
e
d
io
de
m
ode
l
(
b
) P
r
ac
t
i
c
a
l m
ode
l wit
h
R
s
(c)
P
racti
c
al mo
d
el w
i
t
h
R
s
a
nd
R
sh
Where
I
i
s
t
h
e
out
pu
t
c
u
r
r
ent,
I
ph
i
s
t
h
e
ph
ot
o
c
u
rrent
,
I
d
i
s
the
d
i
o
d
e
c
u
r
r
e
nt
w
hi
c
h
p
r
o
por
t
i
o
n
a
l
t
o
t
he
sa
tura
tio
n curr
ent,
I
O
i
s the
r
e
ver
s
e
sat
u
r
a
tio
n or
l
e
a
k
ag
e
cu
r
r
ent of the
d
io
de (
A
)
,
V
is the
volt
a
ge
im
pos
e
d
o
n
the
d
i
ode,
V
t
is
c
a
l
l
ed
t
he t
herm
al v
olta
ge
be
cause
of i
t
s e
x
clu
s
i
v
e de
pen
d
e
nc
e
of tem
per
a
tur
e
,
T
C
i
s
t
h
e
ac
tu
a
l
c
e
l
l
t
e
m
p
e
r
a
t
u
r
e
(
K
)
,
K
i
s
B
o
l
t
z
ma
nn
con
s
t
a
n
t
(
1
.
38
1×10
-
23
J
/
K
)
,
q
i
s
cha
r
g
e
o
f
el
ect
ron
(1
.602
×
1
0
-1
9
C
)
,
an
d
Ns
i
s
th
e
num
ber
of
P
V
ce
l
l
s
co
n
n
e
c
t
e
d
i
n
s
e
r
ie
s.
A
i
s
t
h
e
i
d
ea
lit
y
fa
c
t
o
r
w
h
i
ch
d
ep
end
s
o
n
PV
c
el
l
tec
h
n
o
lo
gy.
C
a
s
e
(b)
:
n
e
g
lec
t
serie
s
re
si
s
t
anc
e
R
s
a
nd
s
hu
nt
r
esi
s
t
a
n
c
e
R
sh
d
u
e
t
o
th
e
i
r
ef
fect
o
n
th
e
effi
c
i
ency
of
t
he
P
V
cell a
nd
m
o
d
u
l
e
.
W
hen
R
s
o
n
l
y i
s
t
ake
n
i
n
t
o co
ns
i
d
era
tio
n
the
eq
ua
ti
on
will
be
a
s
the n
e
x
t
fo
rm [6
]
.
I
d
= I
O
[e
xp
(
.
.
)
–
1
]
(4
)
C
a
s
e(c
)
:
wh
ere
R
s
i
s
t
h
e
s
u
m
of
s
e
v
er
al
s
t
r
u
c
tura
l
re
si
s
t
an
c
e
s
in
t
he
s
ola
r
c
e
l
l
a
nd
R
sh
r
ep
re
se
nt
s
t
h
e
l
e
a
k
ag
e
e
ffe
c
t
of t
h
e so
lar
ce
ll
s
em
i
c
o
n
d
u
c
t
or m
ate
r
i
a
l [5
]
.
B
y
ap
pl
yin
g
K
i
r
c
hh
of
f
'
s
law
:
I
=
I
ph
–
I
d
–
I
sh
(5
)
I
=
I
ph
–
I
O
[ex
p
(
.
.
)
–
1]
–
(
)
(6
)
S
o
l
a
r
c
e
lls
a
r
e
a
r
r
anged
i
n
s
e
r
ies
an
d
/
or
p
a
r
alle
l
i
n
P
V
module
s
to
o
b
t
a
i
n
hi
g
h
er
v
a
l
u
e
s
of
v
o
l
t
a
ge
s
a
nd
c
u
r
r
e
nt
s
a
s
s
how
n
i
n
F
igur
e
3.
I
t
c
a
n
be
r
e
a
lize
d
t
ha
t
the
nu
mb
er
o
f
se
ri
e
s
m
odu
l
e
s
(
N
se
r
)
is
d
irec
tl
y
pr
opor
ti
ona
l
t
o
t
he
e
qu
iva
l
e
n
t
ser
i
es
a
nd
p
ar
a
lle
l
r
e
sis
t
a
n
ce
a
nd
t
h
e
n
u
m
b
e
r
of
p
a
r
al
l
e
l
mo
dul
e
s
(
N
par
)
is
in
ver
s
e
l
y
pr
op
or
t
i
o
n
a
l
t
o
t
h
e
m
.
S
o
,
the
o
u
t
p
u
t
v
olta
ge
i
s
inc
r
e
a
s
e
d
r
egu
l
a
r
ly
w
ith
n
um
ber
of
m
o
d
u
l
es
c
o
n
n
ec
ted
in
s
e
r
ies
wher
e
the
curre
nt
r
e
m
ain
u
n
a
f
fec
t
ed.
Simila
r
l
y
the
vo
ltage
s
t
a
y
u
n
cha
n
g
e
d
w
h
er
e
t
h
e
out
put
c
u
rren
t
i
s
i
m
p
r
ov
ed
p
r
o
po
rti
o
n
a
lly
t
o
nu
mb
er
o
f
mo
d
u
l
e
s
c
o
nn
ected
i
n
par
a
ll
e
l
[
1
1
]
.
T
he
e
q
u
a
t
i
o
n
fo
r array
u
s
in
g
N
ser
& N
par
i
s
give
n
b
y
:
I
=
I
ph
N
par
–
I
O
N
par
[e
x
p
(
.
.
) –
1
]
–
(
)
(7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
2
065
–
2
075
2
068
F
i
gur
e
3.
S
e
r
i
e
s
&
pa
r
a
lle
l
c
o
n
n
e
c
t
io
n
o
n
I
-V
c
har
a
cter
i
s
t
i
c
s
[
8]
2
.
1
.
2
.
E
ffect
o
f
a
m
b
i
en
t
co
ndi
t
i
o
n
s o
n
I
-V
& P-
V
cha
ra
cteristic
s of
P
V
P
o
w
e
r
out
p
u
t
of
P
V
m
odu
le
i
s
dir
e
c
tly
p
r
o
por
ti
o
n
al
t
o
so
lar
r
a
d
ia
t
i
o
n
.
S
e
lec
t
i
n
g
t
h
e
be
st
l
oc
a
t
io
n
is
ess
e
nt
i
a
l
t
o
i
nst
a
ll
P
V
mo
dul
e
a
n
d
t
h
e
st
re
ng
th
o
f
so
l
a
r
r
a
d
i
at
io
n
nee
d
t
o
be
c
o
n
s
i
de
r
e
d
.
Besi
d
es
t
ha
t,
l
oca
l
cl
i
m
at
e
and
env
i
ro
n
m
ent
a
l
f
act
o
r
s
su
c
h
a
s
te
mp
e
r
at
u
r
e
,
w
i
n
d
,
a
n
d
hu
mi
d
i
t
y
n
e
e
d
to
b
e
ob
se
r
v
ed
a
s
it
h
a
s
a
n
e
ffe
c
t
o
n
t
h
e
o
u
t
p
ut
pow
er
o
f
P
V
m
odule.
W
he
r
e
t
he
p
er
f
o
r
m
a
n
ce
of
P
V
module
d
e
p
e
nd
on
the
q
u
a
n
ti
ty
o
f
so
lar
r
a
di
a
t
ion
and
t
h
e
tem
p
er
atur
e o
f
sur
r
o
u
n
d
i
ng
.
F
i
g
u
r
e
4
i
s
s
how
e
d
I
–V
a
nd P
–
V
cha
r
ac
ter
i
st
i
c
s in
c
ase o
f
va
r
y
in
g
ir
r
a
d
i
a
tio
n
w
i
t
h
c
o
n
st
ant
te
mpe
r
at
ur
e
.
W
hen ir
r
a
dia
t
i
o
n
i
n
c
re
ase
s
,
t
h
e
c
u
rrent
i
nc
rea
s
e
s
o
bv
i
ously
but
vo
l
t
age
o
u
t
p
u
t
i
nc
r
e
a
s
e
s
s
l
i
gh
t
l
y.
T
his
r
e
su
lts
i
ncr
e
asi
ng
i
n
o
ut
put
p
ow
er
i
n
t
h
is
o
p
e
r
a
ti
n
g
c
o
n
d
i
t
i
o
n
.
I
n
F
igur
e
5
I
–
V
a
nd
P
–
V
cha
r
ac
t
e
r
i
s
tic
s
un
de
r
var
y
i
ng
tem
p
er
a
t
u
r
e
a
nd
c
o
n
s
ta
nt
i
r
r
a
di
a
tio
n.
W
he
n
the
opera
t
i
n
g
t
em
per
a
t
u
re
i
n
c
rea
s
es,
t
h
e
cur
r
ent
o
u
t
p
u
t
r
ises
m
ar
gina
ll
y
b
u
t
the
v
o
l
t
a
ge
o
utp
u
t
de
cr
e
a
ses
dr
astic
al
ly.
Thi
s
i
n
d
ica
t
e
s
a
n
e
t
d
r
o
p
in
p
ow
er
out
p
u
t
w
i
t
h
i
nc
re
ase
i
n
t
em
pe
ratur
e
[9].
F
i
gur
e
4.
I
–V
a
nd
P
–
V
c
h
ar
a
c
ter
i
s
tic
s
un
de
r
va
r
y
in
g
ir
r
a
di
a
tio
n
[
8
,
1
0
]
F
i
gur
e
5.
I
–V
a
nd
P
–
V
char
acter
i
s
tic
s
un
de
r
va
r
y
in
g
tem
p
er
a
t
ur
e
[
8
,
1
0
]
2.
1.
3.
M
aximu
m
p
o
wer
p
o
in
t
t
r
ac
kin
g
(
MPPT)
F
o
r
ma
xi
m
i
z
i
n
g
t
he
P
V
c
onv
er
sio
n
e
ff
ic
ie
n
c
y,
M
P
P
T
is
i
m
p
lem
e
n
t
e
d
.
M
P
P
T
i
s
n
o
t
a
m
e
c
h
a
n
i
c
a
l
tra
c
k
i
n
g
b
ut
a
t
the
sam
e
t
im
e
it
c
a
n
b
e
use
d
w
ith
a
m
e
c
hani
c
a
l
tr
a
c
ki
n
g
s
ys
tem
.
M
P
P
doe
s
n
o
t
l
i
e
a
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Sm
oot
h t
r
a
n
si
ti
on
f
r
om
grid
t
o
sta
n
d
a
l
o
n
e
so
l
a
r
d
i
esel m
o
de
… (
A
ya M.
Elsher
biny
)
2
069
a
par
t
ic
ular
p
o
i
nt
b
ut
i
t
m
ove
s
ar
ou
n
d
P
-
V
c
ur
ve
d
e
p
en
ds
o
n
li
g
h
t
i
ntensity
a
nd
t
emp
e
ratu
re
a
s
Figu
re
6
(a)
.
I
C
i
s
t
h
e
m
o
st
c
om
mon
l
y
m
e
th
o
d
due
t
o
i
t
s
be
tter
per
f
o
r
m
a
n
ce,
f
a
s
t
e
r
tr
a
c
k
i
ng
t
i
m
e
a
nd
h
as
n
o
osc
i
l
l
a
t
i
on
[
12]
.
The
pr
inc
i
p
l
e
of
I
C
is
a
c
h
ie
ve
d
w
h
e
n
t
he
s
lo
p
e
o
f
t
he
P
-
V
c
ur
ve
i
s
z
e
r
o
a
t
t
h
e
MP
P
,
pos
it
iv
e
a
t
t
he
l
e
f
t
o
f
t
he
M
P
P
,
and
nega
t
i
ve
a
t
the
r
i
ght
o
f
the
MP
P
.
B
y
c
o
mpa
r
i
ng
the
inst
anta
ne
ou
s
co
n
duc
ta
nc
e
(
I
/V
)
to
t
he
i
nc
r
e
m
e
ntal
c
ond
uc
t
a
nce
(
Δ
I
/
Δ
V
),
M
P
P
c
a
n
b
e
fo
u
n
d
[
2
2]
.
Th
i
s
a
l
g
or
i
t
h
m
sh
ow
n
i
n
F
i
g
u
r
e
6(
b)
i
s
b
ased
o
n
t
h
e
p
r
i
n
ci
pl
e
t
h
at
th
e
M
PP i
s re
ac
h
e
d
wh
en
(
/
=
0)
[
14]
.
.
I
V
I
V
0
(
8
)
Th
e
n
Vp
=
Vmpp
When
0
,
Th
e
n
Vp
>
Vmpp
righ
t
to
MP
P,
When
0
,
T
he
n
V
p
<V
m
p
p
lef
t
t
o
MP
P
(
a
)
(b)
F
i
gure
6. (
a)
B
a
s
i
c
i
dea
of
I
C m
e
tho
d
o
n
a I-V
& P-
V Curv
e
(b)
F
l
ow
cha
r
t
of
t
he
b
as
i
c
I
C
al
gor
i
t
hm
2.
1.
4.
B
oost
con
v
er
t
e
r
I
n
g
ener
a
l
l
y
,
P
V
s
yst
e
ms
u
se
d
D
C
/D
C
c
onve
r
t
er
s
ste
p
up
or
s
te
p
d
o
w
n
t
he
P
V
vol
tage
a
n
d
a
u
tom
a
t
i
ca
l
l
y
var
y
i
n
g
t
h
e
du
ty
c
y
c
le
(
D
)
i
n
or
der
t
o
g
e
n
e
r
ate
t
he
r
e
q
u
i
r
e
d
v
o
l
ta
ge
t
o
acc
esses
m
a
x
i
m
u
m
pow
e
r
[
3]
.
A
bo
os
t
c
o
nver
t
e
r
i
s
a
l
so
n
a
m
e
d
a
s
te
p
u
p
c
o
nver
t
er
be
ca
use
t
h
e
o
u
t
p
ut
v
ol
ta
ge
i
s
h
i
ghe
r
th
a
n
t
h
e in
p
u
t
vo
lt
ag
e. As
a
res
u
l
t
t
o
ac
hi
ev
e p
o
w
e
r
b
al
a
n
c
e
,
t
h
e
o
u
tp
ut cu
rren
t
i
s lo
wer
th
an
th
e
i
npu
t cu
rr
ent
[23
]
.
The
dc
v
o
l
ta
g
e
i
s
e
sse
nt
i
a
ll
y
r
e
gu
la
te
d
th
r
ough
th
e
D
C
/D
C
c
o
n
v
e
r
t
er
t
o
fi
x
the
o
u
tp
ut
c
a
p
a
c
i
t
y
a
nd
de
t
e
r
m
ine
d
t
he
m
icr
ogr
i
d
t
ot
al
pow
er
o
u
t
p
u
t
[
2
]
.
T
he
d
u
t
y
r
a
t
i
o
o
f
t
h
e
cho
p
p
e
r
is
i
nc
re
a
s
ed
l
in
e
a
rly
wi
th
i
n
c
r
e
a
s
e
i
n
cel
l
t
e
mp
erat
u
r
e
a
n
d
th
erefo
r
e
th
e
int
e
n
s
it
y
[11
]
.
Th
e
i
n
p
u
t–
out
put
v
ol
t
a
g
e
r
el
a
t
ion
s
hi
p
fo
r
c
o
n
tin
u
o
u
s
c
on
duc
tio
n
m
ode
i
s
gi
ven
b
y
:
,
1
,
f
o
r
D
∈
0,1
(9
)
2.
1.
5.
I
n
v
e
r
t
e
r
I
n
g
r
i
d-
c
o
nnec
t
e
d
P
V
system
s;
c
o
n
v
er
t
i
n
g
t
he
D
C
ou
tpu
t
o
f
th
e
s
o
l
ar
m
o
d
u
l
e
s
to
A
C
p
o
we
r
t
h
rough
the
i
nver
t
e
r
i
s
i
m
por
ta
nt
t
o
c
o
nnec
t
w
i
t
h
u
t
ili
ty
a
n
d
s
up
p
l
y
i
ng
l
ocal
l
oad
s
.
Cur
r
ent-
c
o
nt
r
o
l
l
e
d
H
-
b
r
i
dge
P
WM
in
ver
t
e
r
w
it
h low
-
pass
ou
t
p
u
t
f
il
ter
s
i
s the
mos
t
c
omm
o
n
co
ntr
o
l
str
u
ct
ur
e
f
o
r
the
D
C
/A
C
gr
i
d
c
on
ver
t
er
[
2
4
]
.
The
D
C
/A
C
c
o
nver
t
er
s
i
n
ser
t
s
inus
o
i
da
l
c
u
r
r
ent
i
n
to
t
he
g
r
i
d
c
o
n
t
r
o
l
l
i
ng
t
h
e
pow
er
f
ac
t
o
r
.
I
nver
t
e
r
c
on
t
r
ol
l
e
r
c
o
n
f
ir
m
the
c
o
nt
r
o
l
of
a
c
tive
and
r
e
a
c
t
i
v
e
p
o
w
e
r
ge
ner
a
t
e
d
to
t
he
g
r
i
d,
t
hus
t
he
c
o
n
t
r
o
l
of
D
C
-
l
i
n
k
v
o
lta
ge
i
s
a
c
hie
v
e
d
w
i
t
h
hi
gh
qua
l
ity
o
f
the
i
n
jec
t
ed
p
ow
er
a
nd
g
r
i
d
syn
c
h
roni
z
a
ti
on
[
3
]
.
P
W
M
i
s
a
t
e
c
h
n
i
qu
e
wh
ich
the
sw
itc
he
d
vo
l
t
age
p
u
l
se
s
ar
e
pr
od
uc
e
d
f
or
d
i
ffe
r
e
n
t
o
u
t
pu
t
f
r
e
q
u
e
nc
i
e
s
an
d
vo
l
t
a
g
e
s
.
A
d
i
sti
n
ct
i
v
e
m
odu
la
tor
pr
o
duce
s
a
n
a
v
er
a
g
e
v
o
lta
ge
v
a
l
ue
e
q
u
al
t
o
the
r
e
fe
r
e
n
c
e
v
o
l
t
a
g
e
w
i
t
h
i
n
e
a
c
h
P
W
M
p
e
r
i
o
d
.
P
W
M
pr
ovi
des
a
w
a
y
t
o
d
ecr
ease
t
h
e
To
ta
l
H
a
r
m
onic
D
i
s
t
or
t
i
o
n
(
T
H
D
)
of
l
oa
d
cur
r
en
t.
T
H
D
r
e
qui
r
e
m
e
nt
c
a
n
b
e
m
e
t
when the
o
ut
put
o
f a
P
W
M i
nver
t
e
r
is f
ilter
e
d [2
3].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
0
6
5
– 2
075
2
070
2.2.
D
i
esel
g
en
e
r
at
or
(D
G
)
In
nuc
lear
p
o
w
e
r
p
l
a
n
t
s
esp
e
c
i
al
ly,
DG
i
s
one
o
f
t
h
e
fu
n
d
am
enta
l
ins
t
r
u
m
e
nt
s
ne
e
d
ed
t
o
m
ode
le
d
and
a
n
a
l
yze
d
d
yna
mica
l
l
y.
D
ue
t
o
i
t
s
cri
t
i
ca
l
func
tio
n
a
s
a
b
ac
k
u
p
s
our
ce
t
o
e
nab
l
e
the
MG
p
erfor
m
a
n
ce
i
n
safe
u
n
d
e
r
t
r
a
ns
ien
t
c
on
dit
i
o
n
s
a
nd
i
t
s
ro
le
i
n
freq
ue
ncy
and
v
olta
ge
r
e
g
u
l
ari
t
y
.
Ini
t
i
a
lly
D
G
i
s
i
n
st
and
b
y
mode
a
n
d
d
e
l
i
v
er
ing
no
ac
ti
ve
p
ow
e
r
.
The
pla
n
t
is
f
e
d
b
y
t
h
e
d
i
s
t
rib
u
tio
n
ne
t
w
or
k
and
the
s
y
n
c
hr
ono
us
ma
chine
(S
M)
oper
a
tes a
s
a
c
on
de
nse
r
to ke
ep
t
he
b
us v
o
l
t
a
ge
a
t
1.
0
p.u.
2.2.
1. Gover
n
or
Ini
t
i
a
lly
t
h
e
g
o
v
ern
o
r
and
it
s
de
sig
n
p
a
r
am
ete
r
s
ar
e
obse
r
v
e
d
t
o
se
t
a
t
s
te
a
dy
s
t
a
t
e
va
lue
'ze
r
o
'
a
n
d
the
r
e
fe
re
nc
e
m
e
c
h
ani
cal
p
o
w
e
r
a
lso
o
b
se
rved
f
rom
n
o
s
pee
d
d
e
v
i
a
t
i
o
n
sce
n
ar
io.
Th
i
s
a
ss
umpt
i
on
w
h
e
n
ma
chine
at
t
he
i
ni
tial
i
za
t
i
o
n
s
tate
a
n
d
c
ha
ng
ed
d
ire
c
t
l
y
onc
e
c
omi
ng
i
n
to
t
he
p
ra
ct
ica
l
s
t
a
te
[
1
6
].
I
t
has
tw
o
in
put
t
erm
i
nal
s
;
o
n
e
is
t
he
r
e
f
er
ence
s
pe
e
d
a
nd
a
no
the
r
i
s
t
h
e
ac
tua
l
s
pee
d
a
nd
o
n
e
ou
t
p
u
t
t
er
m
i
nal
is
t
h
e
me
c
h
ani
cal
p
o
w
e
r
(
Pm
).
T
h
i
s
prod
uce
d
Pm
i
s
f
e
d
i
nt
o
the
sy
nc
hro
n
o
u
s
gene
ra
tor
bl
ock.
T
he
s
ha
ft
s
pee
d
t
h
at
s
e
n
sed
from
t
h
e
g
e
n
erat
or
b
l
o
c
k
i
s
f
e
d
ba
ck
t
o
t
h
e
di
e
s
el
en
gi
ne
b
l
o
c
k
a
n
d
t
he
d
if
f
e
rence
(error)
b
et
ween
t
h
e
ref
e
ren
c
e
an
d
a
c
t
u
al
s
pe
ed
i
s
me
a
s
u
r
ed
a
nd
c
on
t
r
ol
l
e
d
wit
h
he
lp
o
f
su
it
ab
le
P
I
D
c
ontro
ller
w
h
i
c
h
minim
i
z
e
t
he
s
pe
e
d
e
r
r
or.
The
a
c
t
u
at
or
g
e
t
s
si
g
n
al
f
r
o
m
go
ve
rno
r
t
o
a
dj
us
t
the
fue
l
i
n
j
ec
tio
n
ra
te
w
hic
h
ma
int
a
ins
t
h
e
c
ons
t
a
n
t
f
r
e
q
u
e
n
cy ou
t
put
f
ro
m
t
h
e
sys
t
em
[
17].
T
he
t
rans
fe
r
func
ti
on
an
d
the
fee
dba
ck loo
p
o
f
the m
ode
le
d
g
over
nor
i
s
sh
o
w
n in F
i
g
ur
e 7.
F
i
gure
7. S
imuli
n
k m
odel
of
d
iese
l e
n
g
i
ne
go
v
er
nor
2.2.
2. Exc
ite
r
The
pre
s
ence
o
f
e
x
c
i
t
e
r
is
v
e
r
y
im
p
o
rta
n
t
in
a
ny
ge
ner
a
t
o
r
bec
a
u
s
e
o
f
i
ts
a
bi
l
ity
t
o
co
n
t
rol
the
fie
l
d
and
term
ina
l
v
ol
ta
ges
d
u
ri
ng
norm
a
l
an
d
ab
norm
a
l
sit
u
at
i
o
ns.
A
l
so
a
r
ole
in
v
o
l
tage
i
n
s
ta
bi
lit
y
b
y
c
o
n
t
rol
lin
g
ac
t
i
ve
a
nd
re
acti
v
e
pow
er
i
n
ge
nera
tor
[1
6
]
.
A
u
toma
tic
V
ol
tage
R
e
gu
la
tor
(
A
V
R
)
system
i
s
c
ont
ro
ll
ed
t
he
exc
ita
t
i
o
n
c
urr
e
nt
b
y
usi
n
g
t
h
e
term
ina
l
v
o
l
t
a
ge
e
r
r
or
a
s
a
con
tro
l
i
n
p
u
t
i
n
t
he
e
xci
t
a
t
io
n
co
n
t
ro
l
lo
op
a
n
d
s
o
t
h
e
g
e
n
e
ra
t
o
r
o
u
tp
ut
vol
t
a
g
e
i
s
con
t
in
uousl
y
d
et
e
c
t
e
d
un
ti
l
t
h
i
s
e
rror
bec
o
me
s
ze
ro
[
1
8
]
.
G
ener
ator’s
exc
ita
t
i
o
n
c
on
t
r
ol
i
s
a
t
y
pica
l
no
n-l
i
near
tim
e-va
rian
t
co
n
t
r
o
l
s
ys
tem
tha
t
i
m
p
l
e
me
nts
a
SM
v
o
lta
ge
r
egu
l
a
t
o
r
and
ex
ci
ter
ba
se
d
on
t
he
I
EE
E
t
ype
A
C1A
exc
ita
t
i
o
n
s
ys
t
e
m
model
.
It
s
o
u
tp
ut
i
s
th
e
fie
l
d
vo
lt
a
g
e
(Vf
)
w
h
i
ch
con
s
i
d
ere
d
a
n
in
p
u
t
to
S
M
b
l
oc
k.
T
he
v
o
lta
ge
w
ave
f
orm
of
t
he
i
s
ola
t
e
d
g
rid
is
g
ener
ate
d
b
y
t
h
e
S
M
a
nd
its
A
V
R
con
trol
s t
h
e
vo
lta
ge d
ur
ing
the
tw
o m
o
des
of o
pe
rat
i
o
n [1
9]
.
2.3.
En
er
g
y
stora
g
e
system
In practice, any
t
ype
o
f
ba
tte
ries can
b
e u
s
e
d
in RESs suc
h a
s
lead-
a
c
i
d,
n
i
c
kel-c
a
d
m
i
um
,
and
ni
c
k
e
l
-
iro
n
b
a
t
te
r
i
es
a
nd
pra
c
t
i
ca
ll
y
f
oun
d
t
h
a
t
t
h
e
m
ost
usua
l
l
y
use
d
i
n
RE
S
s
i
s
the
deep
-
d
i
s
c
h
arge
l
ea
d-ac
id
bat
t
ery
[1
5].
Thi
s
t
ype
i
s
pr
e
f
e
rred
bec
a
u
s
e
of
its
a
dva
n
t
a
g
e
s
in
cl
udi
ng
t
h
e
p
e
rfo
rman
c
e
,
p
ri
ce
a
n
d
ba
t
t
e
ry
l
i
f
et
i
m
e.
T
hi
s
d
e
si
gn
i
s
p
r
e
p
are
d
t
o
p
r
ov
i
d
e
smal
l
amo
unt
s
o
f
p
o
w
e
r
over
l
ong
p
e
r
i
ods
c
o
n
tinu
o
u
s
l
y
a
nd
i
t
s
di
sc
harge
u
p
t
o
80%
o
f
the
t
o
ta
l
b
a
tter
y
c
a
p
ac
it
y
w
i
th
o
u
t
dam
a
g
i
n
g
t
h
e
bat
t
ery
[2
0].
Lea
d
-ac
i
d
ba
t
t
eries
i
s
presum
ed
a
n
e
l
ec
t
r
oc
hem
i
cal
s
tor
a
ge
f
or
t
h
i
s
sta
nda
l
one
D
C
m
i
cr
o
g
ri
d
ta
ki
n
g
i
n
t
o
c
ons
i
d
er
at
i
o
n
its
r
e
l
a
t
i
v
e
l
y
low
c
o
s
t
a
nd
m
ature
d
t
ech
n
o
l
o
g
y
. In or
der to
p
rotec
t
t
he
b
atter
i
e
s fr
om o
ver-
rec
h
argin
g
a
nd o
v
er-
d
i
s
c
h
a
r
gi
ng,
the
ba
tter
i
e
s
S
O
C
B
i
s
li
m
i
te
d
betw
e
e
n
S
O
C
B_
M
A
X
a
n
d
S
O
C
B_
M
I
N
a
s
u
p
p
e
r
and
l
o
w
e
r
li
m
i
ta
ti
o
n
r
e
s
pe
cti
v
e
l
y,
as show
n
in
(
1
0
)
[1].
SOC
B_ MI
N
S
O
C
B
(t)
S
O
C
B_ M
AX
(
1
0
)
The
tem
p
era
t
ure
is
a
m
a
i
n
fac
t
or
f
or
b
at
t
e
ry
p
erfor
m
ance
.
Anoth
er
i
m
portan
t
f
ac
tor
tha
t
cha
r
ac
t
e
rize
s
t
h
e
ba
t
t
e
r
y
be
h
a
vior
i
s
the
sta
t
e
of
c
har
g
e
(S
O
C
)
o
f
a
ba
t
t
e
r
y
[25].
O
f
te
n
S
O
C
i
s
e
qu
iva
l
e
n
t
t
o
a
f
u
e
l
g
a
u
g
e
f
o
r
a
b
a
t
t
e
r
y
f
r
e
i
g
h
t
a
n
d
i
t
s
u
n
i
t
s
a
r
e
s
y
m
b
o
l
i
z
e
d
b
y
a
per
centa
ge
p
o
i
nts
(
i.e
.
,
0
%
i
s
e
mp
t
y
,
and
1
0
0
%
is
f
ul
l
)
.
Ther
e
is
a
s
u
b
s
t
i
t
u
te
f
orm
of
t
he
s
a
m
e
me
asu
re
t
ha
t
c
a
lle
d
t
h
e
dep
t
h
of
d
isc
h
arge
(
D
O
D
)
,
and
e
qua
l
to
o
ne
m
in
us
t
he
S
O
C
(
i.
e
.
,
100%
i
s
e
m
pty,
0
%
i
s
f
u
l
l
)
.
The
S
O
C
is
c
omm
onl
y
use
d
t
o
si
g
n
ify
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Sm
oot
h t
r
a
n
si
ti
on
f
r
om
grid
t
o
sta
n
d
a
l
o
n
e
so
l
a
r
d
i
esel m
o
de
… (
A
ya M.
Elsher
biny
)
2
071
the
c
u
rr
ent
sta
t
e
of
a
b
a
tte
ry
i
n
use
a
nd
when
d
i
s
c
u
ss
i
n
g
the
l
i
f
eti
m
e
o
f
t
h
e
b
a
t
t
e
ry
a
ft
er
r
e
p
ea
t
e
d
u
s
e,
th
e
DOD
i
s
m
o
s
t o
f
t
e
n
u
s
ed
[
20
].
2.
4.
L
oad
The
loa
d
u
se
d
i
n
t
h
i
s
pa
per
is
5
00
kw
a
s
a
c
o
ns
tan
t
l
oad
a
t
g
r
i
d
-c
o
n
n
ect
ed
m
o
d
e
a
nd
a
v
ari
a
bl
e
l
o
ad
tha
t
i
ni
t
i
a
l
l
y
1
00
kw
r
esis
tive
lo
ad
a
nd
the
n
v
ar
i
a
nt
i
n
t
o
3
0
0
k
w
.
Th
is
l
o
a
d
inser
t
e
d
i
n
si
m
u
lat
i
o
n
a
t
i
sla
nde
d
m
ode
w
i
t
h
s
te
p
ti
m
e
1
0s
a
p
p
r
ox
ima
t
e
.
T
he
i
n
v
er
ter
c
o
nver
t
s
t
h
e
D
C
i
nput
f
ro
m
t
h
e
P
V
m
o
d
u
l
e
o
r
t
h
e
b
a
tt
ery
de
pe
n
d
i
ng
on
t
h
e
mode
o
f
o
p
e
r
a
tion
in
to
A
C
v
o
lta
ge
w
it
h
R
M
S
v
a
l
ue
o
f
35
0
0
V
.
3
.
S
I
MULAT
I
ON OF
PRO
P
OS
E
D
H
YB
RID
PO
WER
S
Y
S
T
EM
Al
l
t
h
e
e
l
e
m
en
ts
o
f
t
h
e
si
mu
l
a
t
e
d
s
y
st
e
m
w
h
i
ch
s
ho
wn
i
n
Fi
gu
re
8
a
r
e
con
n
e
c
te
d
t
o
one
m
o
d
u
l
e
thr
o
u
g
h
t
he
p
o
i
n
t
o
f
c
o
mm
on
c
ou
p
lin
g
(P
C
C
).
M
a
tla
b
/
S
i
m
u
li
nk
i
s
u
s
e
d
t
o
g
a
i
n
r
e
s
ul
t
s
i
n
di
ffe
rent
c
on
diti
ons
e
i
t
h
e
r
g
r
i
d-
c
o
nnec
t
e
d
m
ode
o
r
isla
n
d
e
d
m
ode
.
S
y
stem
’
s
f
r
e
que
nc
y
i
s
s
e
t
a
t
5
0
H
z
a
n
d
o
p
e
r
a
t
e
s
i
n
g
r
i
d
-
c
o
n
n
ec
ted
m
o
de
b
e
f
or
e
4s
t
hen
t
h
e
M
G
i
s
disco
n
n
e
c
te
d
fr
om
t
h
e
u
t
i
l
i
t
y
a
t
4s.
The
fr
e
que
nc
y
an
d
v
o
l
t
a
g
e
dur
in
g
tr
ans
i
t
i
on
m
o
de
a
r
e
r
e
g
u
l
a
t
ed
t
o
be
c
o
n
sta
n
t
jus
t
m
ini
m
u
m
dr
o
op
a
t
t
his
mo
m
e
nt.
Th
is
d
r
o
o
p
i
s
im
pr
o
v
ed
by
u
s
i
n
g
P
I
D
c
ont
r
o
ller
o
n
t
he
p
o
w
er
o
f
the
ba
tte
r
y
d
e
pe
n
d
o
n
the
di
ffere
n
ce
b
etwe
e
n
r
efe
r
enc
e
a
nd
a
c
t
ual
spe
e
d
o
f
t
he
g
ove
r
nor
.
This
m
et
ho
d
i
s
p
r
o
p
o
se
d
an
d
r
e
s
u
l
t
s
a
r
e
t
a
k
e
n
w
i
t
h
P
I
D
a
n
d
w
i
t
h
o
u
t
t
o
c
o
mpa
r
e
the
pe
r
f
or
m
a
nc
e
of
t
he
s
ystem
i
n
d
if
fer
e
n
t
p
ar
am
eter
s.
A
l
so
w
he
n
t
h
e
loa
d
c
ha
n
g
es
dur
in
g
the
i
s
la
ndi
n
g
m
ode,
a
l
l
the
DGs rea
ct pr
o
mptl
y t
o
sta
bi
l
i
z
e
t
he
s
ys
tem
and
ma
tch
t
h
e
l
o
ad
a
u
t
om
at
ica
l
l
y
.
F
i
gur
e
8.
S
i
m
uli
n
k
m
odel
of
p
r
o
p
o
sed
h
y
b
r
i
d
pow
er
s
yste
m
3
.
1
.
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ut
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s
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on f
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a
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n
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2
073
(a)
(
b
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(
e
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f
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F
i
gure
1
2
. S
imula
t
io
n r
e
su
l
t
s
a
t
tw
o
c
o
ndi
t
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o
n
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w
h
en
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m
2
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c
rogr
id F
req
u
ency,
(b)
Mi
c
r
ogr
id
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hase
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olt
a
ge,
(c) P
V
pow
e
r
, (d)
D
i
esel
pow
er, (e
)
B
a
t
t
er
y power,
(f
) Battery
s
tat
e
of
char
ge
4
.
R
E
S
U
L
T
S
D
I
SC
U
S
SI
O
N
M
P
P
T
i
s
a
c
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ie
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e
d
st
ep
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ep
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r
ea
ch
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00k
w
by
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si
ng
I
C
m
et
ho
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un
der
di
ff
ere
n
t
ambi
en
t
con
d
i
t
i
on
s
w
hoever
inc
r
ea
si
ng
tem
p
era
t
ure
from
2
5
:
40
℃
o
r
irradia
n
ce
fr
om
400
:
100
0
w
/
m
2
a
s
sho
w
e
d
i
n
F
i
gure
9(b)
&
10(
b).
The
pro
pos
ed Ma
t
l
a
b
/
S
i
muli
n
k
i
s
pr
ove
d
tha
t
whe
n
i
r
r
adia
nc
e
is
i
ncre
ased,
P
V
powe
r
i
s
incre
a
se
d
fr
eq
uen
t
ly
a
s
sh
o
w
ed
i
n
F
i
gure
1
1
(c
).
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lso
w
h
en
t
e
m
pe
ra
ture
i
s
i
n
cre
a
se
d,
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V
pow
e
r
i
s
de
cre
a
se
d
as
s
h
o
w
e
d
i
n
F
igure
12(c)
.
I
-
V
a
nd
P
-
V
c
h
ara
c
h
t
eris
ti
c
s
o
f
P
V
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re
s
how
e
d
a
t
c
ons
t
a
n
t
t
e
m
pe
rat
u
re
a
n
d
varia
n
t
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e
a
n
d
v
ic
e
v
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rsa.
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ode
l
i
n
g
i
s
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p
ar
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t
hat
w
h
en
a
d
d
i
n
g
PI
D
c
o
n
t
r
o
ller
to
E
S
S
,
th
us
t
he
re
su
lt
s
i
ndi
cat
ed
t
h
a
t
th
e
p
e
rfo
rman
c
e
of
w
h
o
l
e
sy
st
em
i
s
b
e
t
t
e
r
tha
n
w
i
t
h
o
u
t
P
I
D
c
o
n
n
e
c
t
i
on.
T
his
i
s
v
ery
clea
r
in
f
r
e
q
u
e
n
c
y
,
vo
lta
ge
,
S
O
C,
d
iese
l
po
w
e
r
and
ba
tter
y
p
ow
e
r
w
a
vefor
m
s.
M
icrogr
id
f
re
q
u
e
n
cy
i
s
ke
epe
d
con
s
ta
n
t
a
t
50
H
Z
w
ith
a
s
m
a
ll
d
ro
op
a
t
d
isc
o
nti
n
u
i
t
y
f
ro
m
the
u
til
i
t
y
g
r
id
a
t
s
t
e
p
t
ime
4s
a
p
p
r
o
xi
m
a
te
a
n
d
w
h
en
l
oa
d
i
s
i
ncre
ased
2
0
0kw
a
t
step
t
im
e
10s
a
ppro
x
i
m
a
te
.
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l
so
m
i
c
rogr
id
phase
v
o
l
ta
ge
i
s
regu
la
t
e
d
at
3
500R
M
S
v
alue
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t
h
hi
g
her
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p
wh
e
n
l
o
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s i
n
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r
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a
s
e
d
,
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t
add
i
ng P
I
D
c
o
n
t
r
o
l
l
er
is re
duce
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t
his
dro
p
. This
ac
hi
e
v
e
d
s
m
o
o
t
h tran
si
t
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o
n
s thr
oug
h the
pr
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p
o
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e
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ys
tem
a
nd new
a
dd
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t
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f
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ID
to
s
t
a
b
i
liz
e the
sys
t
e
m
and
ma
tch
t
h
e
loa
d
a
ut
oma
tica
l
ly
s
pec
i
a
l
l
y
w
hen
the
loa
d
c
ha
n
g
es
d
u
ring
t
h
e
is
l
a
n
d
i
n
g
m
od
e.
S
o
all
the
D
G
s
a
r
e
reacted
prom
ptly.
Initia
l
l
y
D
G
i
s
in
s
tandby
m
ode
a
n
d
deliverin
g
no
a
c
tive
pow
e
r
t
h
e
n
it
i
s
i
nc
rea
s
ed
i
t
s
pow
er
w
hen
d
i
con
t
in
u
i
t
y
fro
m
t
h
e
gr
id
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n
d
w
hen
loa
d
i
s
incr
ease
d
t
o
c
om
pan
s
ate
w
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ol
e
re
quire
d
p
o
w
e
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of
dem
a
nd.
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ut a
dd
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n
g
P
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D
i
s
reduc
e
d
i
ts ge
n
era
t
e
d
p
ow
e
r
t
ha
t
'
s
c
l
e
a
rl
y in in F
i
g
u
re
1
0(d)
&
1
2(d)
. A
l
so bat
ter
y
pow
er
w
he
n
u
s
i
ng
P
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D
is
p
r
o
d
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ce
d
2
0
0kw
t
o
m
e
e
t
t
he
n
eed
d
em
an
d
as
d
ie
sel
pow
er
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s
re
d
u
ced.
It
s
S
O
C
Fr
e
q
(H
Z
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Sing
le
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se
V
ol
tag
e
R
MS
V
al
ue
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v
(
K
W
)
P
di
es
el
(
K
W
)
P
B
(K
W
)
SOC
(%
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
0
6
5
– 2
075
2
074
s
l
o
p
e
p
e
r
f
o
r
m
a
n
c
e
i
s
r
e
d
u
c
e
d
w
i
t
h
i
n
t
i
m
e
w
h
e
n
a
d
d
i
n
g
P
I
D
c
o
n
t
r
o
ller
a
s
s
how
e
d
i
n
F
i
gure
1
0
(
f
)
&
12(
f)
w
h
ic
h ke
ep
it l
o
n
g
l
ife
tim
e.
5
.
CONCL
U
S
ION
Thi
s
p
ap
e
r
i
s
i
n
t
r
odu
ce
d
a
st
udy
o
f
hyb
ri
d
p
o
w
e
r
g
en
e
r
a
t
ion
sys
t
e
m
inc
l
ud
ed
r
e
n
ewab
l
e
e
n
e
rgy
source
s
a
n
d
c
o
nve
n
tio
na
l
w
h
i
c
h
ha
s
tw
o
o
p
e
r
a
t
i
on
m
ode
s
;
g
ri
d-c
o
nn
e
c
t
e
d
a
n
d
i
s
ol
at
ed
s
y
s
t
e
m.
T
h
e
s
ola
r
P
V
syste
m
i
s
m
o
dele
d
a
n
d
si
m
u
l
a
te
d
us
i
n
g
Ma
t
l
ab
/S
i
m
u
l
i
n
k
t
o
s
tu
d
y
the
in
flue
nce
of
d
iffer
e
n
t
a
mbie
nt
con
d
i
t
i
on
s.
A
l
s
o,
D
iesel
ge
ne
rator
a
nd
st
ora
g
e
is
o
rga
n
iz
e
d
t
o
cha
n
c
e
t
h
e
l
oa
d
p
o
w
e
r
dem
a
nd.
T
he
o
b
t
ai
n
e
d
re
su
lt
s
are
c
onf
i
r
med
st
a
b
il
i
t
y
of
t
h
e
s
y
s
t
e
m
t
h
oug
h
vol
t
a
g
e
a
n
d
fre
q
uen
c
y
o
f
M
G
i
n
d
iffer
e
n
t
t
ra
nsie
n
t
c
a
s
es
.
Thi
s
p
rop
o
s
e
d
m
et
h
o
d
i
s
v
ali
d
at
ed
a
s
eff
ect
i
v
e,
f
ea
si
bl
e
an
d
ea
s
y
t
o
im
plem
en
t
a
nd
c
a
n
b
e
de
ve
lo
p
e
d
in
the f
u
tur
e
to se
rve
re
mote
p
la
ce
s
.
Thi
s
rese
a
r
c
h
h
a
s
a fu
t
ur
e visi
o
n
to a
d
v
a
nc
e the
pro
p
o
s
ed s
yst
e
m
with
o
ther
sub
g
ri
d
s
t
o
de
v
e
lo
p
a fixe
d m
u
lt
i m
i
crogr
id
s
ystem
able t
o
w
o
rk
under transient
cases
with high ef
f
i
ciency.
ACKNOW
LEDG
E
MEN
T
S
The
au
th
ors a
r
e
gratefu
l
t
o t
h
e
r
e
fe
ree
s
for
their
v
a
l
ua
b
l
e sug
ge
st
io
ns.
REFE
RENCES
[1]
C.
Y
in
,
H.
W
u,
F
.
Lo
c
m
ent,
a
n
d
M
.
S
echilari
u,
"
E
n
erg
y
M
an
agem
en
t
of
D
C
M
i
cro
g
ri
d
Based
on
P
h
o
t
ovo
lt
a
i
c
Com
b
i
n
ed
w
it
h
D
i
esel
G
enerat
o
r
a
nd
S
upercap
acit
o
r,"
Ener
gy Con
vers
i
o
n
an
d
M
a
n
a
g
emen
t
,
v
o
l
.
1
5
,
no.
1
32,
pp
.
1
4-27
,
2
0
1
7
.
[2]
J
.
L
iu
,
M
J
.
Ho
ss
a
i
n,
J
.
Lu
,
FH
.
R
a
fi
,
a
n
d
H.
L
i,
"
A
h
y
b
r
id
A
C
/
D
C
Microg
rid
Cont
rol
S
y
stem
B
ased
o
n
a
Vi
rtu
a
l
Synchronous
G
e
nerator
for
Sm
o
o
th
T
ransient
P
erf
o
rm
ances
,"
Elect
ri
c
Power
Sys
t
ems
Res
e
a
r
ch
,
v
o
l.
3
0
,
n
o.
162,
p
p
.1
69
-18
2
, 2
01
8.
[3]
S
.
G
a
u
rav,
C
.
Birl
a,
A
.
Lam
b
a,
S
.
U
m
a
s
han
k
ar,
and
S
.
G
an
e
s
an,
"
Energ
y
M
an
a
g
em
ent
of
P
V
-
batt
ery
Bas
e
d
M
i
crog
rid
S
y
ste
m
,
"
P
r
o
c
ed
ia
T
echn
o
l
ogy
,
vo
l.
1
,
no.
21,
p
p
.
1
03
-11
1
,
2
01
5.
[4]
J
.
H
u
,
Y
.
S
h
a
n
,
Y
.
X
u
,
a
n
d
J
M
.
G
u
e
r
r
e
r
o
,
"
A
c
o
o
r
d
i
n
a
t
e
d
C
o
n
t
r
o
l
o
f
H
y
b
r
i
d
A
C
/
D
C
M
i
c
r
o
g
r
i
d
s
w
i
t
h
P
V
-
w
i
n
d
-
bat
t
ery
under
Variabl
e
G
enerat
i
o
n
and
Load
C
onditions,"
In
ter
n
at
io
nal Jou
r
n
a
l of
El
ectr
i
cal
Po
wer
&
Ener
g
y
Sys
t
ems
,
v
o
l
.
1
, n
o.
1
04
,
p
p
.
5
83-59
2,
2
01
9.
[5]
S.
A
s
s
ahout,
H
.
E
l
aissaoui,
A
.
El
Oug
li,
B
.
Ti
dhaf
,
and
H.
Z
r
o
u
ri
,
"
A
N
eu
ral
Net
w
ork
an
d
Fu
zzy
L
o
g
ic
b
as
e
d
MPP
T
A
lg
o
r
ith
m
f
or
P
ho
to
vo
lta
ic
P
u
m
ping
S
y
s
te
m
,
"
In
tern
a
t
io
na
l Jou
r
na
l of Po
wer
Electroni
cs an
d Dr
ive
Sys
t
ems
(I
J
P
ED
S)
,
vol.
9
,
n
o
.
4
,
pp
.
1
82
3-18
33
, 2
018
.
[6]
H.
B
ellia,
R.
Y
oucef
,
and
M.
F
a
t
im
a,
"
A
d
e
tailed
M
odel
i
n
g
o
f
P
h
ot
ov
o
l
t
a
ic
M
od
ule
Using
M
A
T
LA
B,
"
NR
I
A
G
J
o
urna
l
o
f
Astro
n
omy
an
d Ge
op
hy
sic
s
,
vo
l. 3
, n
o
. 1,
pp
.
53
-61
,
2
01
4
.
[7]
O.
N
zim
a
ko
,
and
R.
W
i
e
rck
x
,
"
M
od
eli
ng
an
d
Simu
la
t
i
o
n
o
f
A
grid
-
integ
r
at
ed
P
h
o
to
vo
lt
aic
S
y
s
t
em
U
s
i
n
g
a
R
eal-
time
Dig
i
tal
Simulat
o
r,"
I
E
EE
T
r
an
s
a
c
t
i
o
ns
o
n
In
d
u
s
t
r
y
Ap
p
l
i
c
at
i
o
ns
,
vol
.
5
3
,
no.
2
,
pp
.
1
326
-13
3
6
, 2
016
.
[8]
S
B
.
As
gh
ar,
and
RK
.
Sin
g
h
,
"
S
i
m
u
lin
k
Based
Anal
ys
is
a
nd
Real
iza
ti
o
n
o
f
So
l
a
r
PV
S
y
s
te
m
,
"
Energ
y
an
d Po
wer
En
gi
neeri
n
g
, vo
l
. 7
, n
o.
11
,
pp
. 5
46
-5
56
,
2
0
1
5
.
[9]
XH
.
N
guy
en,
and
M
P
.
N
guy
en,
"Mat
hem
a
ti
c
a
l
Mo
del
i
n
g
o
f
P
h
oto
v
o
l
t
aic
cel
l/
mo
dule/
array
s
w
ith
T
ags
i
n
Matl
a
b
/S
i
m
u
link
,
"
En
vir
onment
a
l
System
s
R
e
sea
r
ch
,
v
o
l
.
4
, no
.
1
, p
p. 2
4,
20
1
5
.
[10]
K.
V
is
wesw
ara,
"
An
i
nv
est
i
gatio
n
of
I
n
c
remental
C
ond
uc
t
a
nce
Bas
ed
M
a
x
im
u
m
P
o
w
er
P
oint
T
racki
n
g
f
o
r
P
h
o
t
o
v
ol
t
a
i
c
S
ys
t
e
m
,
"
E
n
erg
y
Proced
ia
,
v
o
l
.
1
,
n
o
.
5
4
,
p
p.
11-2
0
,
20
14.
[11]
G.
B
al
asub
ram
a
ni
a
n
,
and
S
.
S
ing
a
ravel
u
,
"F
uz
zy
L
og
ic
B
ased
C
o
n
t
roll
er
f
or
a
S
tand
-alo
ne
H
y
b
ri
d
Gen
e
ra
t
i
o
n
S
y
s
t
e
m
U
s
i
n
g
W
ind
and
P
h
o
t
ovol
ta
i
c
E
n
e
rg
y,
"
In
tern
atio
nal J
o
u
r
n
a
l
o
f
Ad
v
a
nces
in
Engin
eering
&
T
ech
no
logy
,
v
o
l.
3
,
no
. 2
,
p
p
.
6
68
-67
9
, 2
01
2.
[12]
RI.
Putr
i
,
S
.
Wi
bowo,
and
M
.
R
if
a’I,
"
M
a
xi
mum
Po
wer
Point
T
r
ack
i
ng
f
o
r
P
h
o
t
ov
oltai
c
U
s
i
n
g
I
ncrem
e
nt
al
Co
nd
uc
ta
n
c
e
Meth
o
d
,"
En
erg
y
Pr
oced
ia
,
vol.
1,
no.
6
8
,
p
p.
2
2-30,
201
5.
[13]
S
.
O
bu
kh
ov,
A
.
Ib
rahim,
a
nd
R
.
Ab
oelsaud
,
"
M
a
xi
m
u
m
P
o
we
r
P
o
int
Track
in
g
o
f
P
arti
all
y
S
hadi
ng
P
V
S
y
stem
Us
ing
Cu
cko
o
S
earch
A
lgo
r
it
h
m
,"
Interna
t
ion
a
l Journal o
f
P
o
wer
Elect
ro
n
i
c
s
a
n
d
D
r
i
v
e
Sy
s
t
ems
(I
J
P
E
D
S
)
,
vo
l.
10,
n
o
.
2
,
pp.
1
08
1-10
89
,
2
01
9
.
[14]
S
.
M
ot
ahhi
r,
A
.
El
G
hzi
zal,
S.
S
eb
ti,
and
A.
D
ero
u
i
c
h,
"
Mod
e
lin
g
of
P
ho
tov
o
l
t
a
i
c
S
y
st
em
w
it
h
M
o
d
i
fi
ed
Increm
ent
a
l Con
d
uct
a
nce Al
gori
th
m
f
o
r
Fas
t
Cha
nges
o
f Irradi
anc
e,"
In
tern
atio
na
l Jo
ur
nal o
f
P
hotoen
e
rg
y
, 2
01
8.
[15]
Z.
R
a
s
in,
a
n
d
A.
J
id
in
,
"
De
sign
a
nd
D
e
v
e
l
op
me
n
t
o
f
Grid
-c
on
n
e
c
ted
Quasi-Z-S
o
urce
PV
I
nverter,
"
International
Jou
r
n
a
l
o
f
Po
we
r Electr
onics
and D
r
i
ve Sys
t
ems
(I
J
P
ED
S
)
,
vol.
9
,
no
.
4,
p
p
.
1
989-20
05
,
2
0
1
8
.
[16]
S
.
T
a
l
pu
r,
"
Testi
ng
and
M
odel
Val
i
d
a
ti
on
o
f
R
o
u
n
d
R
o
t
or
S
y
n
ch
ro
n
o
u
s
G
ener
ato
r
(
GE
NROU
),"
Re
ne
w
a
b
l
e
a
nd
Su
st
a
i
n
a
b
l
e E
n
e
r
gy
R
eviews,
vol.
1,
no.
8
0
,
p
p.
880
-88
7
,
2
01
7.
[17]
G.
K
on
ar,
AK
.
S
i
ngh,
a
n
d
N
.
Chak
rabort
y
,
"M
od
eli
n
g
and
S
i
m
u
l
a
ti
on
o
f
S
t
a
n
dalon
e
M
icro
H
yd
ro-d
iesel
Hy
bri
d
Pow
e
r
Pl
ant
f
o
r
Indi
an
h
i
l
l
y
r
egi
on,
"
Chen
na
i Fo
urth
In
ter
natio
nal Confer
en
ce on
S
u
s
t
ainabl
e
E
n
er
gy an
d
I
n
t
e
ll
i
g
en
t S
y
st
ems
,
20
13
,
p
p
.
15
9
-
16
6.
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