I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
(
I
J
P
E
DS)
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
,
p
p
.
1147
~
1
1
5
9
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
16
.i
2
.
p
p
1
1
4
7
-
1
1
5
9
1147
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
O
ptima
l ann
ua
l s
o
la
r P
V pen
etrati
o
n f
o
r impro
v
ed
v
o
ltag
e
regu
la
tion a
nd po
wer los
s red
uctio
n under
uncertain
ty co
ndi
tions
Sa
leh Ba
-
s
wa
im
i
1
-
3
,
Renug
a
Ver
a
y
ia
h
1
,2
,
Vig
na
K
.
Ra
ma
cha
nd
a
ra
m
urt
hy
1
,2
,
Sa
ee
d A
li B
ina
j
j
a
j
3
,
Sa
nje
ev
ik
um
a
r
P
a
dm
a
na
ba
n
4
1
I
n
st
i
t
u
t
e
o
f
P
o
w
e
r
E
n
g
i
n
e
e
r
i
n
g
,
U
n
i
v
e
r
si
t
i
T
e
n
a
g
a
N
a
s
i
o
n
a
l
(
U
N
I
TEN
)
,
S
e
l
a
n
g
o
r
,
M
a
l
a
y
s
i
a
2
C
o
l
l
e
g
e
o
f
G
r
a
d
u
a
t
e
S
t
u
d
i
e
s,
U
n
i
v
e
r
s
i
t
i
Te
n
a
g
a
N
a
s
i
o
n
a
l
(
U
N
I
TEN
)
,
S
e
l
a
n
g
o
r
,
M
a
l
a
y
si
a
3
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
o
n
i
c
a
n
d
C
o
m
m
u
n
i
c
a
t
i
o
n
s
En
g
i
n
e
e
r
i
n
g
,
C
o
l
l
e
g
e
o
f
E
n
g
i
n
e
e
r
i
n
g
a
n
d
P
e
t
r
o
l
e
u
m,
H
a
d
h
r
a
m
o
u
t
U
n
i
v
e
r
s
i
t
y
,
M
u
k
a
l
l
a
,
H
a
d
h
r
a
m
o
u
t
,
Y
e
m
e
n
4
D
e
p
a
r
t
me
n
t
o
f
El
e
c
t
r
i
c
a
l
En
g
i
n
e
e
r
i
n
g
,
I
T
a
n
d
C
y
b
e
r
n
e
t
i
c
s,
U
n
i
v
e
r
s
i
t
y
o
f
S
o
u
t
h
-
Ea
s
t
e
r
n
N
o
r
w
a
y
,
P
o
r
sg
r
u
n
n
,
N
o
r
w
a
y
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ap
r
2
5
,
2
0
2
4
R
ev
is
ed
Dec
23
,
2
0
2
4
Acc
ep
ted
J
an
2
5
,
2
0
2
5
G
iv
e
n
th
e
ir
tec
h
n
o
l
o
g
ica
l,
e
c
o
n
o
m
ic,
a
n
d
e
n
v
iro
n
m
e
n
tal
a
d
v
a
n
tag
e
s,
th
e
wid
e
sp
re
a
d
a
d
o
p
ti
o
n
o
f
re
n
e
wa
b
le
d
istri
b
u
ted
g
e
n
e
ra
to
rs
(
RDG
s)
in
d
istri
b
u
ti
o
n
sy
ste
m
s
(DSs)
is
b
e
c
o
m
in
g
m
o
re
p
re
v
a
len
t
.
Ho
we
v
e
r,
s
o
lar
p
h
o
to
v
o
lt
a
ic
d
istri
b
u
ted
g
e
n
e
ra
to
rs
(P
V
-
DG
s)
fa
c
e
th
e
c
h
a
ll
e
n
g
e
o
f
in
term
it
ten
t
b
e
h
a
v
i
o
r,
w
h
ich
r
e
su
lt
s
in
p
o
we
r
o
u
t
p
u
t
flu
c
t
u
a
ti
o
n
s
a
n
d
in
c
re
a
se
d
g
rid
u
n
c
e
rtain
ty
.
Th
e
re
fo
re
,
a
d
d
re
ss
in
g
t
h
e
se
u
n
c
e
rt
a
in
ti
e
s
is
c
ru
c
ial
wh
e
n
d
e
term
in
in
g
th
e
ir
o
p
ti
m
a
l
a
ll
o
c
a
ti
o
n
.
T
h
e
p
ro
p
o
se
d
m
e
th
o
d
c
o
n
sid
e
rs
u
n
c
e
rtain
ti
e
s
re
late
d
t
o
b
o
t
h
l
o
a
d
d
e
m
a
n
d
a
n
d
s
o
lar
i
rra
d
iatio
n
.
Th
e
m
o
d
e
l
is
fo
rm
u
late
d
a
s
a
sto
c
h
a
stic
m
ix
e
d
-
in
teg
e
r
n
o
n
li
n
e
a
r
o
p
ti
m
iza
ti
o
n
p
r
o
b
lem
,
w
h
ich
i
s
so
lv
e
d
u
sin
g
t
h
e
w
h
a
le
o
p
t
imiz
a
ti
o
n
a
lg
o
rit
h
m
(W
OA
).
T
h
e
sta
n
d
a
rd
IEE
E
3
3
-
b
u
s
sy
ste
m
is
u
se
d
t
o
v
a
li
d
a
te
th
e
p
ro
p
o
se
d
a
p
p
r
o
a
c
h
,
a
n
d
d
e
m
a
n
d
v
a
riatio
n
s
a
re
m
o
d
e
led
b
a
se
d
o
n
th
e
IEE
E
re
li
a
b
il
it
y
tes
t
sy
ste
m
(IE
EE
-
R
TS
).
T
h
e
o
b
jec
ti
v
e
is
t
o
sim
u
lt
a
n
e
o
u
sl
y
m
in
imiz
e
to
tal
e
x
p
e
c
ted
v
o
lt
a
g
e
d
e
v
iatio
n
,
re
a
l
p
o
we
r
l
o
ss
,
a
n
d
re
a
c
ti
v
e
p
o
we
r
l
o
ss
w
h
il
e
i
n
c
re
a
sin
g
so
lar
P
V
p
e
n
e
t
ra
ti
o
n
.
T
h
e
tec
h
n
iq
u
e
f
o
r
o
rd
e
r
o
f
p
re
fe
re
n
c
e
b
y
sim
il
a
rit
y
t
o
th
e
i
d
e
a
l
so
l
u
ti
o
n
(TOP
S
I
S
)
is
a
p
p
li
e
d
t
o
se
lec
t
th
e
b
e
st
so
l
u
ti
o
n
.
S
imu
late
d
re
su
lt
s
in
d
ica
te
sig
n
ifi
c
a
n
t
imp
r
o
v
e
m
e
n
ts:
a
1
9
.
3
9
%
re
d
u
c
ti
o
n
in
v
o
lt
a
g
e
d
e
v
iatio
n
,
a
n
1
8
.
4
2
%
d
e
c
re
a
se
in
to
tal
re
a
l
p
o
we
r
lo
ss
,
a
n
d
a
n
1
8
.
5
3
%
re
d
u
c
ti
o
n
i
n
re
a
c
ti
v
e
p
o
we
r
lo
ss
c
o
m
p
a
re
d
to
th
e
b
a
se
c
a
se
.
Ad
d
it
i
o
n
a
ll
y
,
th
e
m
o
d
e
l
a
c
c
o
m
m
o
d
a
tes
a
to
tal
o
f
3
.
2
0
6
6
2
5
M
W
o
f
so
lar
P
V p
o
we
r
in
t
h
e
DS
.
K
ey
w
o
r
d
s
:
Po
wer
lo
s
s
PV p
en
etr
atio
n
So
lar
PV a
llo
ca
tio
n
Un
ce
r
tain
ty
Vo
ltag
e
r
eg
u
latio
n
W
h
ale
o
p
tim
izatio
n
alg
o
r
ith
m
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
R
en
u
g
a
Ver
ay
iah
I
n
s
titu
te
o
f
Po
wer
E
n
g
in
ee
r
in
g
,
Un
iv
er
s
iti T
en
ag
a
Nasio
n
al
(
UNI
T
E
N)
Stre
et
I
k
r
am
-
Un
iten
,
Kaja
n
g
4
3
0
0
0
,
Selan
g
o
r
,
Ma
lay
s
ia
E
m
ail:
r
en
u
g
a@
u
n
iten
.
e
d
u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
A
co
u
n
tr
y
'
s
ec
o
n
o
m
ic
ad
v
an
c
em
en
t
h
ea
v
ily
r
elies
o
n
th
e
p
iv
o
tal
r
o
le
o
f
elec
tr
icity
.
Go
v
er
n
m
en
ts
ar
o
u
n
d
th
e
g
lo
b
e
a
r
e
s
tr
iv
in
g
t
o
estab
lis
h
an
af
f
o
r
d
ab
le,
s
u
s
tain
ab
le,
an
d
s
ec
u
r
e
elec
tr
icity
s
u
p
p
ly
to
m
ee
t
th
e
n
ee
d
s
o
f
m
o
d
er
n
s
o
ciety
.
Fo
r
d
ev
elo
p
in
g
co
u
n
tr
ies,
h
a
v
in
g
a
s
u
f
f
icien
t
an
d
s
u
s
tain
ab
le
e
lectr
icity
s
u
p
p
ly
is
ess
en
tial
f
o
r
s
tim
u
lat
in
g
ec
o
n
o
m
ic
g
r
o
wth
b
y
f
ac
ilit
atin
g
in
d
u
s
tr
ial
o
p
er
atio
n
s
a
n
d
u
ltima
tely
en
h
an
cin
g
th
e
well
-
b
ein
g
o
f
th
e
p
o
p
u
latio
n
.
Ma
in
tain
in
g
h
i
g
h
p
o
wer
q
u
ali
ty
is
a
p
r
im
ar
y
f
o
c
u
s
f
o
r
elec
tr
ical
u
tili
ties
as
it
g
u
ar
an
tees a
s
tab
le
s
u
p
p
l
y
to
c
o
n
s
u
m
er
s
[
1
]
,
[
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
1
4
7
-
1159
1148
As
d
ev
elo
p
in
g
co
u
n
tr
ies
e
x
p
er
ien
ce
r
ap
id
ec
o
n
o
m
ic
ex
p
an
s
io
n
,
p
o
p
u
latio
n
g
r
o
wth
,
an
d
u
r
b
an
izatio
n
,
th
eir
o
v
e
r
all
elec
tr
icity
d
em
an
d
h
as
s
ig
n
if
ican
tly
r
is
en
[
3
]
,
[
4
]
.
I
t
is
p
r
o
jecte
d
th
at
th
is
s
u
r
g
e
i
n
d
em
an
d
will
co
n
tr
ib
u
te
to
ap
p
r
o
x
im
ately
9
0
%
o
f
th
e
to
tal
g
lo
b
al
d
em
a
n
d
g
r
o
wth
b
y
th
e
y
ea
r
2
0
4
0
.
T
o
m
ee
t
th
is
in
cr
ea
s
e
in
elec
tr
ici
ty
co
n
s
u
m
p
tio
n
f
r
o
m
s
af
e,
s
tab
le,
s
u
s
tain
ab
le,
an
d
en
v
ir
o
n
m
en
tall
y
f
r
ien
d
ly
s
o
u
r
ce
s
,
co
u
n
tr
ies
an
d
c
o
m
p
a
n
ies
ar
o
u
n
d
th
e
w
o
r
ld
h
av
e
b
ee
n
d
e
v
elo
p
in
g
tech
n
o
lo
g
y
f
o
r
p
r
o
d
u
cin
g
e
n
er
g
y
f
r
o
m
v
ar
io
u
s
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
[
5
]
.
Ad
d
itio
n
ally
,
o
t
h
er
tech
n
ical
is
s
u
es,
ec
o
n
o
m
ic
in
ce
n
tiv
es,
an
d
tech
n
o
lo
g
ical
a
d
v
an
ce
m
e
n
t h
a
v
e
also
co
n
tr
ib
u
ted
to
t
h
e
p
u
s
h
to
war
d
r
en
ewa
b
le
en
er
g
y
[
6
]
,
[
7
]
.
Ph
o
to
v
o
ltaic
(
PV)
s
o
lar
en
er
g
y
h
as
em
er
g
ed
as
a
h
ig
h
l
y
p
r
o
m
is
in
g
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
,
lead
in
g
to
a
s
ig
n
if
ica
n
t
in
cr
ea
s
e
in
s
o
lar
p
lan
ts
wo
r
l
d
wid
e
in
r
e
ce
n
t
y
ea
r
s
.
T
h
is
f
o
r
m
o
f
en
er
g
y
h
as
g
a
r
n
er
ed
co
n
s
id
er
ab
le
atten
tio
n
in
ter
m
s
o
f
r
esear
ch
an
d
f
u
n
d
in
g
d
u
e
to
its
co
s
t
-
ef
f
ec
tiv
en
ess
an
d
en
v
ir
o
n
m
en
tal
f
r
ien
d
lin
ess
.
T
h
e
in
ter
n
atio
n
al
r
en
ewa
b
le
en
er
g
y
ag
en
c
y
(
I
R
E
NA)
r
ep
o
r
ted
th
at
th
e
g
lo
b
al
ca
p
ac
ity
o
f
s
o
la
r
en
er
g
y
r
ea
c
h
ed
1
9
2
GW
in
2
0
2
2
,
m
ar
k
i
n
g
a
2
2
%
y
ea
r
-
on
-
y
ea
r
in
cr
ea
s
e.
So
lar
en
er
g
y
h
a
n
d
led
ap
p
r
o
x
im
ately
6
5
%
o
f
th
e
o
v
er
all
g
r
o
wth
in
g
lo
b
al
r
e
n
ewa
b
le
e
n
er
g
y
ca
p
a
city
d
u
r
i
n
g
t
h
at
y
ea
r
,
wh
ich
s
aw
a
to
tal
r
e
n
ewa
b
le
g
en
er
atio
n
ca
p
ac
ity
r
is
e
o
f
2
9
5
GW
(
+9
.
6
%)
[
8
]
.
At
th
e
en
d
o
f
2
0
2
0
,
th
e
to
tal
g
lo
b
al
in
s
talled
s
o
lar
PV
ca
p
ac
ity
h
a
d
r
ea
ch
ed
7
1
0
GW
,
with
a
n
a
d
d
itio
n
al
ap
p
r
o
x
im
ately
1
2
5
GW
o
f
n
ew
s
o
lar
P
V
ca
p
ac
ity
ad
d
e
d
in
th
e
s
am
e
y
ea
r
[
9
]
.
Du
r
in
g
th
e
y
ea
r
2
0
2
1
,
r
en
ewa
b
le
g
en
e
r
atio
n
ca
p
ac
it
y
witn
ess
ed
a
g
r
o
wth
o
f
2
5
7
GW
(
r
ep
r
esen
tin
g
a
9
.
1
%
in
cr
ea
s
e)
.
T
h
e
m
aj
o
r
c
o
n
tr
ib
u
t
o
r
to
th
is
ca
p
ac
ity
g
r
o
wth
was
s
o
lar
e
n
er
g
y
,
w
h
ich
ad
d
ed
1
3
3
GW
(
a
1
9
%
in
c
r
ea
s
e)
,
f
o
llo
wed
b
y
win
d
en
e
r
g
y
with
9
3
GW
(
a
1
3
%
in
cr
ea
s
e)
[
1
0
]
.
B
y
th
e
en
d
o
f
th
e
p
r
ec
ed
in
g
y
ea
r
,
th
e
wo
r
ld
wi
d
e
r
en
ewa
b
le
g
e
n
er
atio
n
ca
p
ac
ity
h
ad
r
ea
ch
e
d
3
.
3
7
T
W
,
with
s
o
lar
e
n
er
g
y
m
ak
in
g
u
p
1
.
0
5
T
W
(
eq
u
iv
al
en
t
to
3
1
.
2
%
o
f
t
h
e
to
tal
ca
p
a
city
)
[
8
]
.
Mo
r
eo
v
e
r
,
th
e
co
s
t
o
f
s
o
lar
PV
en
er
g
y
witn
ess
ed
a
r
em
ar
k
ab
le
d
ec
lin
e
o
f
8
2
% f
r
o
m
2
0
1
0
to
2
0
1
9
[
1
1
]
.
W
h
ile
r
en
ewa
b
le
en
er
g
y
b
r
i
n
g
s
m
an
y
ad
v
an
tag
es
in
ter
m
s
o
f
ec
o
n
o
m
ics,
s
o
ciety
,
en
v
ir
o
n
m
en
t,
an
d
tech
n
o
lo
g
y
,
th
e
in
ter
m
itten
t
n
atu
r
e
o
f
ce
r
tain
r
e
n
ewa
b
le
s
o
u
r
ce
s
lik
e
win
d
tu
r
b
in
es
(
W
T
)
an
d
s
o
lar
PV
s
y
s
tem
s
in
tr
o
d
u
ce
s
s
ev
er
al
o
b
s
tacle
s
to
th
e
elec
tr
icity
s
u
p
p
l
y
.
T
h
ese
ch
allen
g
es
in
clu
d
e
is
s
u
es
s
u
ch
as
p
o
wer
s
y
s
tem
in
s
tab
ilit
y
,
p
o
wer
f
lu
ctu
atio
n
s
,
v
o
ltag
e
r
eg
u
latio
n
p
r
o
b
lem
s
,
an
d
r
ed
u
ce
d
r
eliab
ilit
y
[
1
2
]
.
T
h
e
s
ev
er
ity
o
f
th
ese
ch
allen
g
es
d
ep
en
d
s
o
n
f
ac
to
r
s
s
u
ch
as
th
e
s
ca
le,
p
lan
n
in
g
,
an
d
p
e
n
etr
atio
n
le
v
el
[
1
3
]
,
[
1
4
]
.
T
h
e
in
ter
m
itten
t
n
atu
r
e
o
f
s
o
lar
P
V
co
u
ld
lim
it
a
n
etwo
r
k
'
s
ab
ilit
y
to
co
n
n
ec
t
h
ig
h
PV
p
e
n
etr
atio
n
b
u
ilt
u
p
o
n
s
p
ec
if
ic
s
itu
atio
n
s
o
cc
u
r
r
in
g
f
o
r
a
f
ew
h
o
u
r
s
an
n
u
ally
[
1
5
]
.
Ho
wev
er
,
v
o
ltag
e
r
eg
u
latio
n
i
s
th
e
m
ain
ch
allen
g
e
in
d
is
tr
ib
u
t
io
n
s
y
s
tem
s
(
DSS),
wh
ich
lim
its
th
e
in
cr
ea
s
e
o
f
P
V
p
en
etr
atio
n
[1
6
]
,
[
1
7
]
.
T
h
e
p
r
o
p
er
allo
ca
tio
n
o
f
d
is
tr
ib
u
ted
g
e
n
er
atio
n
s
(
DGs)
i
n
m
o
d
e
r
n
DSs
p
lay
s
a
cr
itic
al
r
o
le
in
en
h
an
cin
g
o
v
e
r
all
s
y
s
tem
ef
f
icien
cy
.
C
o
n
s
eq
u
en
tly
,
d
eter
m
in
in
g
th
e
o
p
tim
al
allo
ca
tio
n
o
f
DG
u
n
its
is
a
cr
u
cial
asp
ec
t o
f
DG
in
teg
r
atio
n
p
lan
n
i
n
g
[1
8
]
.
B
y
ap
p
r
o
p
r
i
ately
id
en
tify
in
g
th
e
s
ize
an
d
p
lace
m
en
t o
f
DGs in
th
e
DS,
v
ar
io
u
s
p
er
f
o
r
m
a
n
ce
f
ac
to
r
s
lik
e
v
o
ltag
e
p
r
o
f
ile,
p
o
wer
lo
s
s
r
ed
u
ctio
n
,
an
d
v
o
lt
ag
e
s
tab
ilit
y
ca
n
b
e
im
p
r
o
v
e
d
[1
9
]
.
I
n
th
e
liter
atu
r
e
r
ev
iew,
n
u
m
er
o
u
s
an
aly
tical
tech
n
iq
u
es
h
a
v
e
b
ee
n
s
u
g
g
es
ted
f
o
r
i
d
en
tify
in
g
th
e
m
o
s
t o
p
tim
al
s
ize
an
d
p
lace
m
en
t o
f
DG,
b
ased
o
n
alg
e
b
r
aic
ex
p
r
ess
io
n
s
.
T
h
ese
m
eth
o
d
s
ca
n
h
an
d
le
s
in
g
le
o
b
jectiv
e
f
u
n
ctio
n
s
,
s
u
ch
as
v
o
ltag
e
im
p
r
o
v
em
e
n
t
o
r
p
o
wer
lo
s
s
r
ed
u
ctio
n
[
2
0
]
,
[
2
1
]
,
o
r
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
s
,
f
o
r
in
s
tan
ce
,
p
o
wer
lo
s
s
an
d
v
o
ltag
e
p
r
o
f
ile
[
2
2
]
,
[
2
3
]
.
W
h
ile
an
aly
tical
m
eth
o
d
s
o
f
f
e
r
a
co
m
p
r
eh
e
n
s
iv
e
u
n
d
er
s
tan
d
in
g
o
f
t
h
e
s
y
s
tem
'
s
b
eh
av
io
r
,
th
e
y
m
ay
n
o
t
alwa
y
s
p
r
o
v
id
e
t
h
e
o
p
tim
al
s
o
lu
tio
n
.
Hen
ce
,
m
an
y
s
tu
d
ies
h
a
v
e
f
o
c
u
s
ed
o
n
o
p
tim
izin
g
DG
p
lan
n
i
n
g
co
n
s
id
er
in
g
r
ea
l
p
o
wer
lo
s
s
[
2
4
]
,
[
2
5
]
th
e
r
ea
l
p
o
wer
with
v
o
ltag
e
p
r
o
f
ile
im
p
r
o
v
em
e
n
t
[2
6
]
,
[2
7
]
,
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
l
o
s
s
es
[2
8
]
,
v
o
ltag
e
p
r
o
f
ile,
r
ea
l
p
o
wer
lo
s
s
,
an
d
r
ea
ctiv
e
p
o
we
r
lo
s
s
[2
9
]
.
Ho
we
v
er
,
th
ese
s
tu
d
ies
wer
e
lim
ited
to
th
e
in
te
g
r
atio
n
o
f
DGs
at
a
co
n
s
tan
t
p
ea
k
lo
ad
,
lim
itin
g
th
eir
ap
p
licab
ilit
y
.
T
o
r
ef
le
ct
r
ea
l
-
wo
r
ld
s
ce
n
ar
io
s
in
r
en
ewa
b
le
d
is
tr
ib
u
ted
g
en
er
ato
r
s
(
R
DGs)
s
y
s
tem
s
,
it
is
ess
en
tial
to
co
n
s
id
er
th
e
u
s
e
o
f
p
r
o
b
ab
ilis
tic
in
ter
m
itten
t so
lar
PV
with
tim
e
-
v
ar
y
in
g
lo
ad
d
em
an
d
.
So
m
e
s
tu
d
ies
h
av
e
e
x
am
in
ed
th
e
im
p
l
em
en
tatio
n
o
f
p
r
o
b
ab
ilis
tic
in
t
er
m
itten
t
s
o
lar
PV
s
y
s
tem
s
with
v
ar
y
in
g
lo
ad
d
e
m
an
d
s
u
s
in
g
an
al
y
tical
m
eth
o
d
s
.
T
h
e
o
b
jectiv
e
o
f
th
ese
s
tu
d
ies
was
to
o
p
tim
ize
s
p
ec
if
ic
o
b
jec
tiv
e
f
u
n
ctio
n
s
,
f
o
r
in
s
tan
ce
,
m
in
im
izin
g
p
o
wer
lo
s
s
th
r
o
u
g
h
th
e
i
n
teg
r
atio
n
o
f
win
d
en
er
g
y
[
3
0
]
,
[
3
1
]
,
o
r
in
c
o
r
p
o
r
atin
g
a
c
o
m
b
in
at
io
n
o
f
win
d
p
o
wer
,
s
o
lar
PV,
an
d
b
io
m
ass
in
d
iv
id
u
ally
o
r
in
co
m
b
in
atio
n
[
1
8
]
.
Ho
wev
er
,
d
ed
icatin
g
a
PV u
n
it so
lely
to
m
in
im
ize
ac
tiv
e
o
r
r
ea
ctiv
e
p
o
wer
lo
s
s
m
ig
h
t
r
estrict
th
e
ex
ten
t
o
f
PV
p
en
etr
atio
n
.
T
h
e
DG
o
p
tim
al
p
lan
n
in
g
was
p
er
f
o
r
m
ed
u
s
in
g
e
v
o
lu
tio
n
a
r
y
p
r
o
g
r
am
m
in
g
(
E
P)
to
m
itig
ate
v
o
ltag
e
v
io
latio
n
s
,
b
u
t
it
c
o
u
ld
lead
to
h
ig
h
s
y
s
tem
lo
s
s
e
s
if
a
DG
was
d
e
s
ig
n
ated
s
o
lely
f
o
r
m
i
n
im
izin
g
v
o
ltag
e
d
e
v
iatio
n
[
3
2
]
.
As
a
r
esu
lt,
r
esear
ch
er
s
h
av
e
in
tr
o
d
u
ce
d
m
u
lti
-
o
b
jectiv
e
an
aly
tical
tech
n
i
q
u
es
aim
e
d
at
m
itig
atin
g
p
o
wer
lo
s
s
es
an
d
v
o
ltag
e
p
r
o
f
ile
d
ev
iat
io
n
s
u
s
in
g
v
ar
i
o
u
s
tim
e
-
v
ar
y
in
g
v
o
ltag
e
-
d
e
p
en
d
e
n
t
lo
ad
m
o
d
els
[
2
3
]
,
[
3
3
]
.
T
o
o
b
tain
a
n
o
p
tim
al
s
o
lu
tio
n
,
o
p
tim
izatio
n
alg
o
r
ith
m
s
m
u
s
t
b
e
u
s
ed
to
id
en
tify
th
e
o
p
tim
al
p
lace
m
en
t
an
d
s
ize
o
f
DG
u
n
its
th
at
m
ax
im
ize
v
o
ltag
e
r
eg
u
latio
n
an
d
m
in
im
ize
p
o
wer
lo
s
s
es
th
r
o
u
g
h
o
u
t
th
e
y
ea
r
.
I
n
th
i
s
s
tu
d
y
,
th
e
wh
a
le
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
(W
OA
)
is
ap
p
lied
to
ac
h
iev
e
t
h
e
h
ig
h
e
s
t
s
o
lar
PV
in
teg
r
atio
n
f
o
r
v
o
l
tag
e
r
eg
u
latio
n
an
d
m
in
im
izin
g
p
o
wer
lo
s
s
es in
th
e
I
E
E
E
3
3
-
b
u
s
s
y
s
tem
.
T
h
is
p
ap
er
p
r
esen
ts
th
e
f
o
llo
win
g
co
n
tr
ib
u
tio
n
s
an
d
in
n
o
v
atio
n
s
:
i)
T
h
e
s
tu
d
y
ad
d
r
ess
e
s
a
cr
u
cial
asp
ec
t
o
f
th
e
s
o
lar
p
h
o
to
v
o
ltaic
d
is
tr
ib
u
ted
g
en
er
ato
r
(
PV
-
DG
)
allo
ca
tio
n
p
r
o
b
lem
b
y
in
co
r
p
o
r
atin
g
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Op
tima
l a
n
n
u
a
l so
la
r
P
V
p
en
e
tr
a
tio
n
fo
r
imp
r
o
ve
d
vo
lta
g
e
r
eg
u
la
tio
n
a
n
d
p
o
w
er
…
(
R
en
u
g
a
V
era
yia
h
)
1149
u
n
ce
r
tain
ties
th
at
ar
is
e
f
r
o
m
b
o
th
lo
a
d
d
em
a
n
d
an
d
s
o
la
r
ir
r
ad
iatio
n
;
a
n
d
ii)
T
h
e
allo
ca
tio
n
p
r
o
b
lem
is
ef
f
ec
tiv
ely
s
o
lv
ed
b
y
co
n
s
id
er
in
g
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
s
in
clu
d
in
g
r
ea
l
p
o
wer
lo
s
s
,
r
ea
ctiv
e
p
o
wer
lo
s
s
,
an
d
v
o
ltag
e
d
e
v
iatio
n
.
T
h
e
ar
ticle's
s
tr
u
ctu
r
e
is
a
s
f
o
llo
ws:
i)
Sect
io
n
2
d
escr
ib
es
th
e
m
eth
o
d
o
lo
g
ical
ap
p
r
o
ac
h
u
s
ed
f
o
r
m
o
d
elin
g
d
y
n
am
i
c
lo
a
d
p
r
o
f
iles
a
n
d
s
o
lar
PV
p
r
o
f
iles
an
d
d
ef
in
es
th
e
p
r
o
b
lem
;
ii)
Sectio
n
4
is
d
ed
icate
d
to
p
r
esen
tin
g
a
n
d
d
is
cu
s
s
in
g
th
e
s
tu
d
y
'
s
f
in
d
in
g
s
;
an
d
iii)
I
n
th
e
e
n
d
,
t
h
e
co
n
clu
s
io
n
s
d
r
awn
f
r
o
m
th
e
r
esear
ch
an
d
r
ec
o
m
m
en
d
atio
n
s
f
o
r
f
u
t
u
r
e
s
tu
d
ies ar
e
s
u
m
m
ar
ized
in
s
ec
tio
n
5
.
2.
M
E
T
H
O
D
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
ad
d
r
ess
es
a
s
to
ch
asti
c
p
r
o
b
lem
co
n
ce
r
n
in
g
th
e
o
p
tim
al
allo
ca
tio
n
o
f
PV
-
DGs
in
b
alan
ce
d
r
ad
ial
DSs
.
T
h
e
o
p
tim
izatio
n
alg
o
r
ith
m
s
co
n
s
id
er
th
e
u
n
ce
r
tain
ties
ass
o
ciate
d
with
PV
-
DGs
an
d
lo
ad
d
em
an
d
to
r
ep
r
esen
t
a
r
ea
lis
tic
PV
-
DG
a
llo
ca
tio
n
.
T
h
e
o
p
tim
izatio
n
o
b
jectiv
es
en
co
m
p
ass
v
o
ltag
e
d
ev
iatio
n
,
r
ea
l
p
o
we
r
lo
s
s
,
an
d
r
ea
ctiv
e
p
o
wer
l
o
s
s
to
ac
h
ie
v
e
an
o
p
tim
al
PV
-
DG
allo
ca
tio
n
.
T
h
e
s
im
u
lated
DG
is
a
s
o
lar
-
b
ased
r
en
ewa
b
l
e
en
er
g
y
s
o
u
r
ce
th
at
s
u
p
p
lies
o
n
ly
r
ea
l
p
o
wer
;
th
er
e
f
o
r
e,
it
i
s
p
r
esu
m
ed
th
at
th
e
DG
o
p
er
ates a
t a
p
o
wer
f
ac
to
r
o
f
u
n
ity
.
2
.
1
.
P
r
o
ba
bil
is
t
ic
m
o
delin
g
o
f
s
o
la
r
po
wer
T
h
e
B
eta
PDF
in
(
1
)
was
u
tili
ze
d
to
m
o
d
el
s
o
lar
ir
r
ad
ian
ce
,
co
n
s
id
er
in
g
h
is
to
r
ical
d
ata
s
p
an
n
in
g
th
r
ee
y
ea
r
s
.
T
o
ac
co
m
m
o
d
ate
d
aily
v
ar
iatio
n
s
,
ea
ch
d
ay
was
d
iv
id
ed
in
to
2
4
h
o
u
r
s
,
with
ea
ch
h
o
u
r
h
a
v
in
g
its
s
p
ec
if
ic
s
o
lar
ir
r
ad
ian
ce
PDF.
T
h
e
s
h
ap
e
(
)
an
d
s
ca
le
(
)
p
ar
am
eter
s
o
f
th
e
B
eta
PDF
wer
e
co
m
p
u
ted
f
o
r
ea
ch
h
o
u
r
,
u
tili
zin
g
th
e
m
ea
n
(
)
an
d
s
tan
d
ar
d
d
e
v
iatio
n
(
)
o
b
tain
ed
f
r
o
m
h
is
to
r
ical
d
ata,
a
s
o
u
tlin
ed
in
(
2
)
an
d
(
3
)
[
3
4
]
.
T
o
r
ep
r
esen
t
th
e
v
ar
iatio
n
s
in
th
e
s
o
lar
ir
r
ad
ian
ce
,
ea
ch
h
o
u
r
was
s
u
b
d
iv
id
ed
in
to
2
0
s
ce
n
ar
io
s
,
with
a
s
tep
s
ize
o
f
0
.
0
5
k
W
/m
²,
r
ep
r
esen
tin
g
v
ar
y
in
g
s
o
la
r
r
ad
iatio
n
lev
els.
B
y
u
s
in
g
t
h
e
d
eter
m
in
ed
m
ea
n
an
d
s
tan
d
ar
d
d
e
v
iatio
n
,
a
PDF
f
o
r
s
o
lar
ir
r
ad
ian
ce
was
g
en
er
ated
f
o
r
ea
ch
o
f
th
e
2
0
s
c
en
ar
io
s
with
in
ev
er
y
h
o
u
r
,
alo
n
g
with
th
e
ass
o
ciate
d
p
r
o
b
a
b
ilit
ies
f
o
r
ea
ch
s
ce
n
ar
io
o
f
s
o
lar
r
ad
iatio
n
.
B
ased
o
n
th
ese
PDFs
,
th
e
PV o
u
tp
u
t p
o
we
r
was d
eter
m
i
n
e
d
f
o
r
ea
ch
h
o
u
r
[
3
5
]
.
(
)
=
{
(
+
)
(
)
(
)
(
−
1
)
(
1
−
)
(
−
1
)
,
0
≤
≤
1
,
≥
0
0
,
ℎ
(
1
)
=
(
1
−
)
×
(
(
1
+
)
2
−
1
)
(
2
)
=
(
×
)
1
−
(
3
)
T
h
e
p
r
o
b
a
b
ilit
y
f
o
r
a
s
p
ec
if
ic
s
o
lar
ir
r
ad
ian
ce
s
ce
n
ar
io
(
s
)
d
u
r
in
g
an
y
h
o
u
r
ca
n
b
e
ca
lcu
l
ated
u
s
in
g
(
4
)
.
T
h
e
o
u
tp
u
t
p
o
wer
g
en
er
at
ed
b
y
a
s
o
lar
PV
m
o
d
u
le
f
r
o
m
(
4
)
is
s
u
b
ject
to
s
ev
er
al
f
ac
to
r
s
,
s
u
ch
as
am
b
ien
t
tem
p
er
atu
r
e,
s
o
lar
ir
r
a
d
ian
ce
,
an
d
PV
m
o
d
u
le
s
p
ec
if
icatio
n
s
.
T
o
r
e
p
r
e
s
e
n
t
t
h
e
m
a
x
i
m
u
m
p
o
w
e
r
o
u
t
p
u
t
f
r
o
m
t
h
e
P
V
m
o
d
u
l
e
u
n
d
e
r
a
s
p
e
ci
f
i
c
s
o
la
r
i
r
r
a
d
i
a
n
c
e
l
e
v
e
l
(
S
)
(
6
)
-
(
9
)
c
a
n
b
e
e
m
p
l
o
y
e
d
.
A
d
d
i
t
io
n
a
l
l
y
,
t
h
e
a
v
e
r
a
g
e
o
u
t
p
u
t
p
o
w
e
r
,
r
e
p
r
e
s
e
n
t
i
n
g
t
h
e
t
o
t
a
l
e
x
p
e
c
te
d
o
u
t
p
u
t
p
o
w
e
r
o
f
a
s
o
l
a
r
PV
m
o
d
u
l
e
o
v
e
r
a
s
p
e
c
i
f
i
e
d
p
e
r
i
o
d
(
t
)
,
d
e
n
o
t
e
d
a
s
(
)
(
w
h
e
r
e
t
=
1
h
)
,
c
a
n
b
e
d
e
r
i
v
e
d
u
t
i
l
i
zi
n
g
(
1
)
,
(
4
)
,
a
n
d
(
5
)
a
s
i
n
(
1
0
)
a
n
d
(
1
1
)
.
{
}
=
∫
(
)
2
1
(
4)
°
(
)
=
×
×
×
(
5
)
=
×
×
(
6
)
=
[
+
×
(
−
25
)
]
(
7
)
=
−
×
(
8
)
=
+
(
−
20
0
.
8
)
(
9
)
(
)
=
°
(
)
×
(
)
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
1
4
7
-
1159
1150
(
)
(
)
1
0
S
P
V
t
P
V
S
P
G
d
s
=
(
1
1
)
T
h
e
n
u
m
b
e
r
o
f
PV
m
o
d
u
les
is
d
en
o
ted
as
N.
C
ell
tem
p
er
at
u
r
e
an
d
am
b
ien
t
tem
p
er
at
u
r
e
ar
e
d
en
o
ted
b
y
T
c
y
an
d
T
A
r
esp
ec
tiv
ely
.
T
h
e
v
o
l
tag
e
an
d
c
u
r
r
en
t
c
o
ef
f
icien
ts
ar
e
d
en
o
te
d
b
y
Ki
an
d
Kv
r
esp
ec
tiv
ely
.
No
m
in
al
o
p
er
atin
g
tem
p
er
a
tu
r
e
is
d
en
o
t
ed
b
y
NOT
.
2
.
2
.
L
o
a
d dema
nd
m
o
delin
g
D
u
e
t
o
t
h
e
i
n
h
e
r
e
n
t
u
n
c
e
r
t
ai
n
t
y
i
n
l
o
a
d
d
e
m
a
n
d
f
l
u
c
t
u
a
t
i
o
n
s
o
v
e
r
t
i
m
e
,
t
h
e
u
n
c
e
r
t
ai
n
t
y
o
f
l
o
ad
d
e
m
a
n
d
a
t
e
a
c
h
b
u
s
(
M
V
A
)
i
s
r
e
p
r
e
s
en
t
e
d
u
s
i
n
g
a
n
o
r
m
a
l
P
DF
(
(
)
,
a
s
s
h
o
w
n
i
n
(
1
2
)
.
T
h
e
m
e
a
n
(
M
V
A
)
a
n
d
s
t
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
(
M
V
A
)
f
o
l
l
o
w
t
h
e
I
E
E
E
r
e
l
i
a
b
i
l
it
y
t
e
s
t
s
y
s
t
e
m
(IEEE
-
R
T
S
)
s
t
a
n
d
a
r
d
s
,
a
s
o
u
t
l
i
n
e
d
i
n
F
i
g
u
r
e
1
[
3
6
]
.
T
h
i
s
a
p
p
r
o
a
c
h
i
s
u
s
e
d
i
n
t
h
e
a
b
s
e
n
c
e
o
f
a
s
t
a
n
d
a
r
d
i
z
e
d
d
y
n
a
m
i
c
l
o
a
d
p
r
o
f
i
le
f
o
r
t
h
e
t
y
p
i
c
a
l
I
E
E
E
d
i
s
t
r
i
b
u
ti
o
n
s
y
s
t
e
m
a
n
d
h
a
s
b
ee
n
e
x
t
e
n
s
i
v
el
y
a
p
p
l
i
e
d
i
n
p
r
e
v
io
u
s
s
t
u
d
i
es
,
s
u
c
h
a
s
[
35]
.
As
i
llu
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
1
,
t
h
e
l
o
a
d
c
u
r
v
e
r
e
p
r
e
s
e
n
ts
f
o
u
r
d
i
s
t
i
n
ct
2
4
-
h
o
u
r
p
e
r
i
o
d
s
(
9
6
h
o
u
r
s
)
c
o
r
r
e
s
p
o
n
d
i
n
g
t
o
t
h
e
f
o
u
r
s
e
a
s
o
n
s
.
(
)
=
1
×
√
2
[
−
(
−
)
2
2
(
)
2
]
(
1
2
)
Fig
u
r
e
1
.
I
E
E
E
3
3
-
b
u
s
s
y
s
tem
d
y
n
am
ic
lo
a
d
p
r
o
f
ile
f
o
llo
win
g
th
e
I
E
E
E
-
R
T
S lo
ad
p
atter
n
2
.
3
.
P
r
o
blem
f
o
rm
ula
t
io
n
I
f
a
DG
u
n
it
is
s
p
ec
if
ically
all
o
ca
ted
to
m
in
im
ize
eith
er
ac
tiv
e
o
r
r
ea
ctiv
e
p
o
wer
lo
s
s
,
it
m
ay
ca
u
s
e
lim
itatio
n
s
o
n
PV
p
en
etr
atio
n
d
u
e
t
o
h
ig
h
v
o
ltag
e
d
ev
iat
io
n
s
.
On
th
e
o
th
er
h
an
d
,
if
a
PV
u
n
it
is
s
o
lely
d
esig
n
ated
to
m
in
im
ize
th
e
v
o
ltag
e
d
ev
iatio
n
s
,
it
m
ay
allo
w
f
o
r
h
ig
h
p
e
n
etr
atio
n
lev
els
b
u
t
co
u
ld
lead
to
in
cr
ea
s
ed
s
y
s
tem
lo
s
s
es
[
2
3
]
.
T
o
ad
d
r
ess
th
ese
ch
allen
g
es,
a
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
(
MO
F)
ca
n
b
e
u
tili
ze
d
,
co
m
b
in
in
g
v
o
ltag
e
d
ev
iatio
n
,
ac
tiv
e
p
o
wer
lo
s
s
,
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
.
2.
3
.
1
.
O
bje
ct
iv
e
f
un
ct
io
ns
T
h
e
m
o
d
el
is
s
tr
u
ctu
r
ed
as
a
s
to
ch
asti
c
m
ix
ed
-
in
teg
e
r
n
o
n
lin
ea
r
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
p
r
o
b
lem
,
as
d
ep
icted
in
(
1
3
)
.
T
h
e
f
itn
ess
f
u
n
ctio
n
in
cl
u
d
e
s
th
r
ee
co
m
p
o
n
en
ts
:
to
tal
v
o
l
tag
e
d
ev
iatio
n
(
1
)
,
to
tal
r
ea
l
p
o
wer
lo
s
s
(
2
)
,
an
d
t
o
tal
r
ea
ctiv
e
p
o
wer
lo
s
s
(
3
)
.
T
h
ese
o
b
jectiv
es
ar
e
im
p
o
r
tan
t
in
DS
o
p
er
atio
n
an
d
p
lan
n
in
g
,
as th
ey
r
elate
to
th
e
q
u
ality
o
f
p
o
we
r
s
u
p
p
ly
,
s
y
s
tem
ef
f
icien
cy
,
a
n
d
s
tab
ilit
y
.
T
o
tal
v
o
ltag
e
d
ev
iatio
n
,
as
in
(
1
3
)
,
is
a
m
ea
s
u
r
e
o
f
th
e
d
ev
i
atio
n
o
f
t
h
e
v
o
ltag
e
m
ag
n
itu
d
e
f
r
o
m
its
n
o
m
in
al
v
alu
e,
w
h
ich
ca
n
af
f
e
ct
th
e
p
er
f
o
r
m
an
ce
o
f
elec
tr
ica
l
eq
u
ip
m
en
t
an
d
th
e
q
u
ality
o
f
th
e
p
o
wer
s
u
p
p
ly
.
T
h
e
to
tal
ex
p
ec
ted
r
ea
l
p
o
wer
lo
s
s
is
a
m
ea
s
u
r
e
o
f
t
h
e
en
er
g
y
wasted
d
u
e
to
th
e
f
lo
w
o
f
cu
r
r
en
t
th
r
o
u
g
h
th
e
tr
an
s
m
is
s
io
n
lin
es,
as in
(
1
4
)
,
wh
ich
ca
n
lead
to
in
ef
f
icien
cies a
n
d
in
cr
ea
s
ed
co
s
ts
.
T
h
e
to
tal
ex
p
ec
ted
r
ea
ctiv
e
p
o
wer
lo
s
s
is
a
m
ea
s
u
r
e
o
f
th
e
p
o
wer
r
e
q
u
ir
ed
t
o
m
ain
tain
t
h
e
v
o
ltag
e
lev
els
in
t
h
e
p
o
wer
s
y
s
tem
,
as
in
(
1
5
)
,
wh
ich
ca
n
also
af
f
ec
t t
h
e
ef
f
ic
ien
cy
an
d
s
tab
ilit
y
o
f
th
e
s
y
s
te
m
.
=
(
1
,
2
,
3
)
(
1
3
)
1
=
∑
∑
∑
|
−
,
,
|
=
1
=
1
=
1
(
1
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Op
tima
l a
n
n
u
a
l so
la
r
P
V
p
en
e
tr
a
tio
n
fo
r
imp
r
o
ve
d
vo
lta
g
e
r
eg
u
la
tio
n
a
n
d
p
o
w
er
…
(
R
en
u
g
a
V
era
yia
h
)
1151
2
=
∑
∑
∑
(
,
)
,
,
2
+
(
,
)
,
,
2
(
,
)
,
,
2
×
(
(
,
)
,
,
)
=
1
≠
=
1
=
1
(
1
5
)
3
=
∑
∑
∑
(
,
)
,
,
2
+
(
,
)
,
,
2
(
,
)
,
,
2
×
(
(
,
)
,
,
)
=
1
≠
=
1
=
1
(
1
6
)
an
d
,
,
ar
e
th
e
r
ef
er
en
ce
(
o
r
n
o
m
in
al)
v
o
ltag
e
a
n
d
ac
tu
al
v
o
ltag
e,
r
esp
ec
tiv
ely
.
+
an
d
+
d
en
o
te
th
e
r
ec
eiv
in
g
r
ea
l a
n
d
r
ea
ctiv
e
p
o
wer
f
lo
w,
r
esp
ec
tiv
ely
.
2
.
3
.
2
.
Co
ns
t
ra
ints
Du
r
in
g
th
e
o
p
tim
izatio
n
p
r
o
ce
s
s
f
o
r
th
is
s
tu
d
y
,
b
o
th
eq
u
ality
an
d
in
eq
u
al
ity
co
n
s
tr
a
in
ts
wer
e
co
n
s
id
er
ed
.
T
h
ese
co
n
s
tr
ain
ts
in
clu
d
e
t
h
e
p
o
wer
f
lo
w
eq
u
a
tio
n
s
,
(
1
6
)
an
d
(
1
7
)
,
m
ax
im
u
m
p
o
wer
tr
an
s
f
er
i
n
ea
ch
b
r
an
c
h
(
1
8
)
,
a
n
d
m
a
x
im
u
m
DG
allo
ca
tio
n
in
th
e
DS (
1
9
)
.
,
,
−
,
,
=
∑
(
,
,
2
×
(
,
)
−
,
,
×
,
,
(
(
,
)
(
,
)
,
,
+
(
,
)
(
,
)
,
,
)
)
∈
≠
(
1
7
)
,
,
−
,
,
=
∑
(
−
,
,
2
×
(
,
)
−
,
,
×
,
,
(
(
,
)
(
,
)
,
,
−
(
,
)
(
,
)
,
,
)
)
∈
≠
(
1
8
)
√
(
,
)
,
,
+
(
,
)
,
,
≤
(
,
)
,
,
(
1
9
)
{
∈
{
0
,
1
}
=
∑
=
1
≤
(
2
0
)
W
h
er
e
(
)
is
a
b
in
ar
y
n
u
m
b
er
t
o
id
en
tify
th
e
av
ailab
ilit
y
o
f
PV
-
DGs
at
ea
ch
b
u
s
.
an
d
r
ep
r
esen
t
th
e
n
u
m
b
er
an
d
m
ax
im
u
m
n
u
m
b
er
o
f
PV
-
DG
lo
ca
tio
n
s
in
t
h
e
DS.
2
.
3
.
3
.
So
lv
ing
m
e
t
ho
d
T
h
e
o
p
tim
izatio
n
is
s
u
e
is
f
o
r
m
u
lated
as
a
m
ix
ed
in
teg
er
n
o
n
lin
ea
r
p
r
o
g
r
am
m
in
g
:
m
u
lti
-
o
b
jectiv
e
f
u
n
ctio
n
to
s
im
u
ltan
eo
u
s
ly
v
o
ltag
e
d
ev
iatio
n
,
ac
tiv
e
p
o
wer
lo
s
s
,
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
.
T
h
e
tech
n
iq
u
e
f
o
r
r
an
k
in
g
p
r
e
f
er
en
ce
b
y
s
im
ilar
ity
to
th
e
id
ea
l
s
o
lu
tio
n
(
T
OP
SIS)
is
em
p
lo
y
ed
to
s
elec
t
th
e
o
p
tim
al
s
o
lu
tio
n
f
r
o
m
a
s
et
o
f
n
o
n
-
d
o
m
in
ated
s
o
lu
tio
n
s
.
T
OPSIS
is
a
m
u
lt
i
-
cr
iter
ia
d
ec
is
io
n
-
m
a
k
in
g
m
e
th
o
d
th
at
ca
n
r
an
k
s
o
lu
tio
n
s
in
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
p
r
o
b
lem
s
.
T
h
is
tech
n
iq
u
e
is
ap
p
lied
at
th
e
en
d
o
f
ea
ch
iter
atio
n
to
th
e
o
p
tim
al
s
et
o
f
o
b
jectiv
e
f
u
n
ctio
n
s
.
T
h
e
s
tep
s
f
o
r
a
p
p
ly
in
g
T
OPSIS
to
ch
o
o
s
e
th
e
o
p
ti
m
al
s
o
lu
tio
n
f
r
o
m
a
s
et
o
f
n
o
n
-
d
o
m
in
ate
d
s
o
lu
tio
n
s
ar
e
illu
s
tr
ated
in
[
3
7
]
.
T
h
e
o
p
tim
izatio
n
p
r
o
b
lem
was
s
o
lv
ed
b
y
u
tili
zin
g
th
e
W
OA.
T
h
e
W
OA
co
n
s
is
t
s
o
f
a
p
air
o
f
m
ain
p
h
ases
:
ex
p
l
o
r
atio
n
an
d
ex
p
lo
itatio
n
.
Du
r
in
g
th
e
ex
p
lo
itatio
n
p
h
ase,
th
e
alg
o
r
ith
m
u
s
es
two
m
eth
o
d
s
to
u
p
d
ate
th
e
s
ea
r
c
h
ag
e
n
t'
s
p
o
s
itio
n
:
th
e
p
r
ey
-
e
n
cir
clin
g
tec
h
n
iq
u
e
,
wh
ich
is
r
ep
r
esen
ted
b
y
(
2
1
)
-
(
2
5
)
,
a
n
d
th
e
s
p
ir
al
b
u
b
b
le
-
n
e
t
attac
k
in
g
tech
n
iq
u
e
,
r
ep
r
ese
n
ted
b
y
(
2
6
)
.
B
o
th
tech
n
iq
u
es
u
tili
ze
th
e
lo
ca
tio
n
o
f
th
e
b
est
s
ea
r
ch
ag
en
t
t
o
u
p
d
ate
th
e
c
u
r
r
e
n
t
ag
e
n
t'
s
p
o
s
it
io
n
.
Ho
wev
e
r
,
th
e
s
p
ir
al
b
u
b
b
le
-
n
et
attac
k
in
g
te
ch
n
iq
u
e
i
n
tr
o
d
u
ce
s
an
elem
e
n
t
o
f
r
a
n
d
o
m
n
ess
,
wh
ich
a
llo
ws
f
o
r
ex
p
lo
r
atio
n
.
T
h
is
r
an
d
o
m
n
ess
is
r
ef
lecte
d
i
n
(
2
6
)
.
I
n
th
e
ex
p
lo
r
atio
n
p
h
as
e,
a
r
an
d
o
m
s
ea
r
ch
is
co
n
d
u
ct
ed
,
an
d
th
e
p
o
s
itio
n
o
f
th
e
cu
r
r
en
t
s
ea
r
c
h
ag
en
t
is
u
p
d
ated
b
ased
o
n
a
r
an
d
o
m
ly
g
en
er
ated
s
ea
r
ch
ag
en
t
.
T
h
is
b
e
h
av
io
r
is
m
ath
em
atica
lly
r
ep
r
ese
n
ted
b
y
(
2
7
)
an
d
(
2
8
)
.
B
y
c
o
m
b
in
i
n
g
b
o
th
e
x
p
lo
itatio
n
a
n
d
e
x
p
lo
r
a
tio
n
tech
n
iq
u
es,
th
e
W
OA
alg
o
r
ith
m
ca
n
o
p
tim
ize
s
ea
r
ch
al
g
o
r
ith
m
s
ef
f
ec
tiv
ely
.
T
h
e
f
lo
wch
a
r
t
in
Fig
u
r
e
2
illu
s
tr
ates
th
e
o
v
er
all
m
eth
o
d
o
l
o
g
y
f
o
r
a
p
p
ly
in
g
th
e
W
OA
to
s
o
lv
e
th
e
f
o
r
m
u
lated
o
p
tim
izatio
n
p
r
o
b
lem
.
=
×
−
(
)
(
2
1
)
(
+
1
)
=
−
×
(
2
2
)
=
2
×
×
−
(
2
3
)
=
2
×
(
2
4
)
=
2
−
×
2
(
2
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
1
4
7
-
1159
1152
(
+
1
)
=
′
×
×
(
)
+
(
)
(
2
6
)
=
×
−
(
2
7
)
(
+
1
)
=
−
(
×
)
(
2
8
)
Fig
u
r
e
2
.
Flo
w
ch
a
r
t f
o
r
th
e
o
p
tim
izatio
n
p
r
o
c
ess
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
I
np
ut
da
t
a
T
h
e
s
atellite
wea
th
er
d
ata
f
o
r
th
r
ee
y
ea
r
s
(
2
0
1
7
-
2
0
1
9
)
f
o
r
a
s
p
ec
if
ic
lo
ca
tio
n
in
Seiy
u
n
,
Had
r
am
o
u
t,
Yem
en
(
co
o
r
d
in
ates
1
5
.
9
4
9
5
°
N,
4
8
.
8
0
9
6
°
E
)
was
o
b
tain
ed
f
r
o
m
th
e
n
atio
n
al
s
o
lar
r
ad
iatio
n
d
atab
ase
(
NSR
D)
[
3
8
]
.
T
h
e
d
ata
was
d
iv
id
ed
in
t
o
f
o
u
r
s
ea
s
o
n
s
,
ea
c
h
r
ep
r
esen
tin
g
th
e
ag
g
r
eg
ated
d
ata
f
o
r
th
r
ee
m
o
n
th
s
.
U
s
i
n
g
p
r
o
b
a
b
i
l
i
s
t
ic
m
o
d
e
l
i
n
g
,
t
h
e
s
e
as
o
n
a
l
d
a
t
a
w
a
s
t
h
e
n
c
o
n
v
e
r
t
e
d
i
n
t
o
a
d
ai
l
y
r
e
p
r
e
s
e
n
t
at
i
o
n
b
y
c
o
n
v
e
r
t
i
n
g
t
h
e
t
h
r
e
e
-
m
o
n
t
h
s
ea
s
o
n
a
l
d
at
a
i
n
t
o
e
q
u
i
v
a
le
n
t
2
4
s
a
m
p
l
es
.
T
h
e
f
i
n
al
d
a
t
as
e
t
c
o
n
s
i
s
t
s
o
f
4
×
2
4
=
9
6
s
a
m
p
l
es
.
I
n
t
h
e
w
i
n
t
e
r
a
n
d
s
p
r
i
n
g
s
e
a
s
o
n
s
,
s
o
l
a
r
i
r
r
a
d
i
a
ti
o
n
b
e
g
i
n
s
b
e
t
w
e
e
n
t
h
e
6
t
h
a
n
d
1
8
t
h
h
o
u
r
o
f
t
h
e
d
a
y
,
w
h
i
l
e
i
n
t
h
e
s
u
m
m
e
r
a
n
d
f
a
ll
s
e
a
s
o
n
s
,
i
t
b
e
g
i
n
s
b
e
tw
e
e
n
t
h
e
7
t
h
a
n
d
1
8
t
h
h
o
u
r
.
T
h
e
m
a
x
i
m
u
m
s
o
l
a
r
i
r
r
a
d
i
a
n
c
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Op
tima
l a
n
n
u
a
l so
la
r
P
V
p
en
e
tr
a
tio
n
fo
r
imp
r
o
ve
d
vo
lta
g
e
r
eg
u
la
tio
n
a
n
d
p
o
w
er
…
(
R
en
u
g
a
V
era
yia
h
)
1153
r
e
c
o
r
d
e
d
d
u
r
i
n
g
w
i
n
t
e
r
r
e
ac
h
es
1
1
2
8
W
/
m
2
,
w
h
e
r
e
a
s
i
n
f
al
l
,
t
h
e
m
a
x
i
m
u
m
v
al
u
e
is
l
o
w
e
r
a
t
7
6
5
W
/
m
2
.
T
h
e
p
r
o
j
e
c
t
s
i
te
r
e
c
e
i
v
es
a
n
a
v
e
r
a
g
e
o
f
4
.
5
t
o
8
.
4
p
e
a
k
s
u
n
n
y
h
o
u
r
s
t
h
r
o
u
g
h
o
u
t
t
h
e
y
e
a
r
.
B
eta
PDF
v
alu
es
f
o
r
2
0
s
tates
o
f
s
o
lar
ir
r
ad
ian
ce
at
th
r
ee
s
p
ec
if
ic
h
o
u
r
s
(
8
,
1
2
,
a
n
d
1
6
)
f
o
r
ea
ch
s
ea
s
o
n
ar
e
p
l
o
tted
in
Fig
u
r
e
3
(
a)
f
o
r
win
ter
,
Fig
u
r
e
3
(
b
)
f
o
r
s
p
r
i
n
g
,
Fig
u
r
e
3
(
c)
f
o
r
s
u
m
m
er
,
a
n
d
F
ig
u
r
e
3
(
d
)
f
o
r
f
all
.
Utilizin
g
th
e
s
ea
s
o
n
al
d
aily
ir
r
ad
ian
ce
a
n
d
s
ea
s
o
n
al
av
er
a
g
e
tem
p
er
at
u
r
e,
t
h
e
ex
p
ec
ted
h
o
u
r
ly
PV
m
o
d
u
le
o
u
tp
u
t
f
o
r
ea
ch
s
ea
s
o
n
is
co
m
p
u
ted
an
d
r
ep
r
esen
te
d
in
Fig
u
r
e
4
(
a)
.
Ad
d
itio
n
ally
,
a
n
o
r
m
alize
d
cu
r
v
e
f
o
r
th
e
ex
p
ec
ted
d
aily
PV
o
u
t
p
u
t
f
o
r
ea
ch
s
ea
s
o
n
is
illu
s
tr
ated
in
Fig
u
r
e
4
(
b
)
.
Fo
r
th
is
s
tu
d
y
,
th
e
T
r
in
a
2
5
0
W
PV
m
o
d
u
le
was
s
p
ec
if
ically
ch
o
s
en
.
T
h
e
tech
n
ical
s
p
ec
if
i
ca
tio
n
s
f
o
r
th
is
m
o
d
u
le
ca
n
b
e
f
o
u
n
d
in
T
a
b
le
1
[
3
9
]
.
T
h
e
PV
m
o
d
u
le'
s
o
u
tp
u
t
p
o
ten
tial
in
d
icate
s
th
at
it
c
an
g
en
er
ate
ap
p
r
o
x
im
ately
2
0
2
.
1
3
W
in
win
ter
,
1
9
3
.
2
2
W
in
s
p
r
in
g
,
1
9
6
.
1
3
W
in
s
u
m
m
er
,
an
d
1
8
7
.
4
8
W
in
f
all.
R
em
ar
k
ab
ly
,
r
eg
ar
d
le
s
s
o
f
th
e
s
ea
s
o
n
,
th
e
PV m
o
d
u
le
attain
s
its
m
ax
im
u
m
o
u
tp
u
t a
t th
e
1
2
th
h
o
u
r
,
wh
i
ch
s
ig
n
if
ies th
e
p
ea
k
p
er
f
o
r
m
a
n
ce
p
er
io
d
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
3
.
So
lar
i
r
r
ad
ian
ce
p
r
o
b
ab
ilit
y
f
o
r
(
a)
win
ter
,
(
b
)
s
p
r
i
n
g
,
(
c)
s
u
m
m
er
,
an
d
(
d
)
f
all
(
a)
(
b
)
Fig
u
r
e
4
.
Ou
t
p
u
t o
f
th
e
ch
o
s
en
PV m
o
d
u
le
(
a)
ex
p
ec
te
d
o
u
t
p
u
t
an
d
(
b
)
n
o
r
m
alize
d
o
u
tp
u
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
1
4
7
-
1159
1154
T
ab
le
1
.
So
lar
PV m
o
d
u
le
s
p
e
cif
icatio
n
s
C
h
a
r
a
c
t
e
r
i
s
t
i
c
s
V
a
l
u
e
C
h
a
r
a
c
t
e
r
i
s
t
i
c
s
V
a
l
u
e
V
mp
p
(
V
)
3
0
.
0
N
O
C
T
(
℃
)
44
I
mp
p
(
A
)
8
.
3
4
K
i
(
A
/
℃
)
0
.
0
0
4
4
8
V
o
c
(
V
)
3
7
.
5
K
v
(
V
/
℃
)
0
.
1
2
I
sc
(
A
)
8
.
9
7
3
.
2
.
Ca
s
e
s
t
ud
ies
T
o
v
alid
ate
th
e
r
esu
lts
o
b
tain
e
d
f
o
r
th
e
p
r
o
p
o
s
ed
m
o
d
el,
a
c
o
m
p
ar
is
o
n
o
f
r
esu
lts
h
as
b
ee
n
co
n
d
u
cte
d
f
o
r
th
e
f
o
llo
win
g
ca
s
e
s
tu
d
ies
:
i)
C
ase
I
:
p
r
o
b
ab
ilis
tic
p
o
wer
f
lo
w
(
PLF)
o
f
th
e
b
ase
ca
s
e
with
o
u
t
PV
-
DGs
in
s
tallatio
n
;
an
d
ii)
C
ase
I
I
:
PLF
in
co
r
p
o
r
ates
o
p
tim
al
p
lace
m
en
t
o
f
PV
-
DGS
wh
ile
ac
co
u
n
tin
g
f
o
r
two
k
ey
u
n
ce
r
tain
ties
: v
ar
iatio
n
s
in
lo
a
d
d
em
an
d
an
d
f
lu
ctu
atio
n
s
in
s
o
lar
r
ad
iatio
n
lev
els.
3
.
3
.
Num
er
ica
l r
esu
lt
s
3
.
3
.
1
.
O
bje
ct
iv
e
f
un
ct
io
ns
T
h
e
o
p
tim
al
PV
-
DGs
ar
e
s
tr
ateg
ically
in
s
talled
to
m
i
n
im
ize
th
r
ee
k
ey
o
b
jectiv
e
f
u
n
ctio
n
s
s
im
u
ltan
eo
u
s
ly
,
en
co
m
p
ass
in
g
to
tal
v
o
ltag
e
d
ev
iatio
n
,
r
ea
l
p
o
wer
lo
s
s
,
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
.
I
n
th
e
b
ase
ca
s
e,
th
e
p
r
e
-
in
s
tallatio
n
p
o
we
r
f
lo
w
an
aly
s
is
r
ev
ea
ls
a
to
tal
v
o
ltag
e
d
ev
iatio
n
o
f
9
6
.
1
6
p
u
,
r
ea
l
p
o
wer
lo
s
s
o
f
7
.
3
8
MW,
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
o
f
7
.
9
1
MV
AR
.
Up
o
n
th
e
in
s
tallatio
n
o
f
th
e
o
p
tim
al
PV
-
DGs,
a
n
o
tab
le
d
ec
r
ea
s
e
is
o
b
s
er
v
ed
ac
r
o
s
s
all
o
b
jectiv
e
f
u
n
ctio
n
s
.
Sp
ec
if
ic
ally
,
th
e
o
p
tim
al
PV
-
DGs
r
esu
lt
in
a
to
tal
v
o
ltag
e
d
ev
iatio
n
r
e
d
u
ctio
n
o
f
7
7
.
5
0
p
u
,
r
ea
l
p
o
wer
lo
s
s
o
f
6
.
0
2
MW,
an
d
r
ea
ctiv
e
p
o
wer
l
o
s
s
o
f
4
.
0
MV
AR
,
as
p
r
esen
ted
in
T
a
b
le
2
.
T
h
is
r
ed
u
ctio
n
in
o
b
jectiv
e
f
u
n
ctio
n
s
s
ig
n
if
ies
a
s
u
b
s
tan
tial
im
p
r
o
v
e
m
en
t,
with
v
o
ltag
e
d
ev
iatio
n
r
e
d
u
ce
d
b
y
1
9
.
3
9
%,
r
ea
l
p
o
wer
lo
s
s
b
y
1
8
.
4
2
%,
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
b
y
1
8
.
5
3
%.
T
ab
le
2
.
Op
tim
al
o
b
jectiv
e
f
u
n
ctio
n
O
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
C
a
se
I
C
a
se
I
I
1
(
p
u
)
9
6
.
1
6
7
7
.
5
0
9
1
2
(
M
W
)
7
.
3
8
6
.
0
2
0
3
(
M
V
A
R
)
4
.
9
1
4
.
0
0
3.
3
.
2
.
O
ptim
a
l
P
V
-
DG
a
llo
ca
t
io
n
T
h
is
s
tu
d
y
s
ee
k
s
to
ad
v
an
ce
th
e
p
en
etr
atio
n
le
v
el
o
f
PV
i
n
th
e
DS
wh
ile
r
ed
u
cin
g
th
e
o
b
jectiv
e
f
u
n
ctio
n
s
.
T
h
e
o
p
tim
al
s
ites
,
ag
g
r
eg
ate
ca
p
ac
ity
,
an
d
r
ec
o
m
m
en
d
ed
n
u
m
b
er
o
f
PV
m
o
d
u
les
ar
e
o
u
tlin
ed
in
T
ab
le
3
.
T
h
e
o
p
tim
al
s
ites
f
o
r
P
V
-
DGs
ar
e
lim
ited
to
1
0
lo
ca
tio
n
s
as
s
tated
in
(
1
8
)
.
T
h
e
ag
g
r
eg
ate
o
p
tim
al
ca
p
ac
ity
o
f
PV
-
DGs
is
3
.
2
0
6
6
2
5
MW
in
s
talled
at
d
if
f
er
en
t
p
o
in
ts
with
in
th
e
DS.
T
h
e
lar
g
est
in
s
talla
tio
n
is
at
b
u
s
3
0
with
ca
p
ac
ity
o
f
1
.
6
5
1
7
5
MW.
I
t's
wo
r
th
m
en
tio
n
in
g
th
at
th
e
m
ax
i
m
u
m
p
o
wer
o
f
th
e
PV
p
an
els
u
s
ed
in
th
is
r
esear
ch
is
2
5
0
W
.
T
ab
le
3
.
Op
tim
al
lo
ca
tio
n
an
d
s
izin
g
o
f
PV
-
DGs in
I
E
E
E
3
3
-
b
u
s
DS
Lo
c
a
t
i
o
n
(
B
u
s)
S
i
z
e
(
M
W
)
N
u
mb
e
r
o
f
P
V
m
o
d
u
l
e
s
Lo
c
a
t
i
o
n
(
B
u
s)
S
i
z
e
(
M
W
)
N
u
mb
e
r
o
f
P
V
m
o
d
u
l
e
s
27
0
.
2
0
8
8
3
2
25
0
.
0
2
7
9
7
5
1
1
2
10
0
.
4
2
5
7
5
1
7
0
3
3
0
.
5
0
5
7
5
2
0
2
3
24
0
.
2
0
5
5
8
2
2
21
0
.
0
0
7
1
2
5
29
30
1
.
6
5
1
7
5
6
6
0
7
20
0
.
0
5
1
2
0
4
28
0
.
0
6
2
2
2
5
2
4
9
16
0
.
0
6
1
5
5
2
4
6
3
.
3
.
3
.
Vo
lt
a
g
e
pro
f
ile
T
h
e
v
o
ltag
e
p
r
o
f
iles
o
f
th
e
te
s
t
s
y
s
tem
in
ea
ch
s
ea
s
o
n
with
o
u
t
PV
-
DGs
ar
e
d
ep
icted
in
Fig
u
r
e
5
(
a)
f
o
r
win
ter
,
Fig
u
r
e
5
(
b
)
f
o
r
s
p
r
i
n
g
,
Fig
u
r
e
5
(
c)
f
o
r
s
u
m
m
er
,
a
n
d
Fig
u
r
e
5
(
d
)
f
o
r
f
all
.
Acr
o
s
s
all
s
ea
s
o
n
s
,
ce
r
tain
b
u
s
es,
s
u
ch
as
B
u
s
1
0
-
1
8
an
d
B
u
s
2
9
-
3
3
,
ex
p
e
r
ien
ce
v
o
ltag
e
is
s
u
es.
T
h
e
m
o
s
t
s
ev
er
e
u
n
d
er
v
o
ltag
e
p
r
o
b
lem
s
ar
e
o
b
s
er
v
ed
d
u
r
in
g
th
e
s
u
m
m
er
s
ea
s
o
n
d
u
e
to
th
e
h
eig
h
te
n
ed
d
em
an
d
.
I
t
is
n
o
tewo
r
th
y
th
at
I
E
E
E
s
tan
d
a
r
d
lim
its
f
o
r
b
u
s
v
o
ltag
es,
with
a
m
ax
im
u
m
o
f
1
.
0
5
p
u
a
n
d
a
m
in
im
u
m
o
f
0
.
9
5
p
u
,
a
r
e
co
n
s
id
er
ed
to
id
en
tif
y
u
n
d
er
v
o
ltag
e
an
d
o
v
er
v
o
ltag
e
is
s
u
es
in
th
e
s
y
s
tem
.
W
ith
t
h
e
in
s
tallatio
n
o
f
o
p
tim
al
PV
-
DGs,
th
e
v
o
ltag
e
p
r
o
f
iles
d
u
r
in
g
all
s
ea
s
o
n
s
ar
e
s
ig
n
if
ican
tly
im
p
r
o
v
ed
,
as
d
e
p
icted
in
Fig
u
r
e
6
(
a)
f
o
r
win
t
er
,
Fig
u
r
e
6
(
b
)
f
o
r
s
p
r
in
g
,
Fig
u
r
e
6
(
c)
f
o
r
s
u
m
m
er
,
an
d
Fig
u
r
e
6
(
d
)
f
o
r
f
all
.
Ho
wev
er
,
d
u
r
i
n
g
h
ig
h
-
d
em
an
d
h
o
u
r
s
in
th
e
s
u
m
m
e
r
an
d
f
all
s
ea
s
o
n
s
,
ce
r
tain
b
u
s
es st
ill ex
p
er
ien
ce
u
n
d
e
r
-
v
o
ltag
e
is
s
u
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Op
tima
l a
n
n
u
a
l so
la
r
P
V
p
en
e
tr
a
tio
n
fo
r
imp
r
o
ve
d
vo
lta
g
e
r
eg
u
la
tio
n
a
n
d
p
o
w
er
…
(
R
en
u
g
a
V
era
yia
h
)
1155
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
5
.
B
u
s
v
o
ltag
e
p
r
o
f
ile
with
o
u
t PV
-
DGs f
o
r
(
a)
s
u
m
m
er
,
(
b
)
f
all,
(
c)
s
p
r
in
g
,
an
d
(
d
)
win
ter
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
6
.
B
u
s
v
o
ltag
e
p
r
o
f
ile
with
o
p
tim
al
PV
-
DGs f
o
r
(
a)
s
u
m
m
er
,
(
b
)
f
all,
(
c)
s
p
r
i
n
g
,
a
n
d
(
d
)
win
te
r
3
.
3
.
4
.
P
o
wer
lo
s
s
T
ab
le
4
p
r
esen
ts
th
e
p
o
wer
lo
s
s
o
b
s
er
v
ed
in
ea
ch
s
ea
s
o
n
b
o
th
with
an
d
with
o
u
t
th
e
in
s
tallatio
n
o
f
PV
-
DGs.
T
h
e
o
p
tim
al
in
s
tallatio
n
o
f
PV
-
DGs
s
ig
n
if
ican
tly
i
m
p
r
o
v
es
b
o
th
r
ea
l
an
d
r
ea
cti
v
e
p
o
wer
lo
s
s
ac
r
o
s
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
1
4
7
-
1159
1156
all
s
ea
s
o
n
s
.
Par
ticu
lar
ly
n
o
te
wo
r
th
y
is
t
h
e
p
r
o
n
o
u
n
ce
d
r
e
d
u
ctio
n
in
l
o
s
s
es
d
u
r
in
g
win
t
er
,
attr
ib
u
te
d
to
th
e
h
eig
h
ten
ed
s
o
lar
ir
r
ad
iatio
n
ch
ar
ac
ter
is
tic
o
f
th
at
s
ea
s
o
n
.
T
h
e
p
er
ce
n
ta
g
e
o
f
p
o
wer
lo
s
s
r
ed
u
ctio
n
is
co
n
tin
g
en
t
u
p
o
n
th
e
s
o
lar
ir
r
ad
iatio
n
lev
el
th
r
o
u
g
h
o
u
t
ea
c
h
h
o
u
r
,
as
well
as
th
e
alig
n
m
en
t
b
etwe
e
n
lo
ad
d
em
an
d
an
d
s
o
lar
PV
g
en
er
a
tio
n
.
Su
p
e
r
io
r
alig
n
m
en
t
y
iel
d
s
s
ig
n
if
ican
t
r
e
d
u
ctio
n
s
in
p
o
wer
lo
s
s
,
wh
er
ea
s
m
is
m
atch
ed
alig
n
m
en
t
r
esu
lts
in
in
cr
ea
s
ed
lo
s
s
es.
T
ab
le
4
.
Seaso
n
al
o
p
tim
al
p
o
wer
lo
s
s
S
e
a
so
n
R
e
a
l
p
o
w
e
r
l
o
ss (
M
W
)
R
e
a
c
t
i
v
e
p
o
w
e
r
l
o
ss (
M
V
A
R
)
W
i
t
h
o
u
t
P
V
-
DGs
W
i
t
h
P
V
-
DGs
W
i
t
h
o
u
t
P
V
-
DGs
W
i
t
h
P
V
-
DGs
S
u
mm
e
r
2
.
1
4
5
6
7
7
1
.
5
8
0
9
6
4
1
.
4
2
8
4
1
4
1
.
0
6
0
1
3
2
F
a
l
l
2
.
0
2
0
4
2
1
.
7
2
3
6
8
1
.
3
4
4
8
9
6
1
.
1
5
2
2
3
8
S
p
r
i
n
g
1
.
8
1
5
2
5
7
1
.
7
4
7
5
1
4
1
.
2
0
8
3
4
5
1
.
1
4
4
8
7
4
W
i
n
t
e
r
1
.
4
0
6
0
0
3
0
.
9
6
8
0
8
9
0
.
9
3
5
8
4
7
0
.
6
5
0
6
5
4
4.
CO
NCLU
SI
O
N
T
h
e
r
esear
ch
p
r
o
p
o
s
es
a
p
lan
n
in
g
m
o
d
el
f
o
r
d
eter
m
in
i
n
g
t
h
e
b
est
s
izes
an
d
d
is
tr
ib
u
tio
n
o
f
PV
-
DGs
in
DS.
T
h
e
ap
p
r
o
ac
h
is
s
tr
u
ctu
r
ed
as
a
p
r
o
b
ab
ilis
tic
m
ix
ed
-
in
teg
er
n
o
n
lin
ea
r
m
u
lti
-
cr
iter
ia
o
p
tim
izatio
n
p
r
o
b
lem
.
T
h
e
g
o
al
is
to
en
h
a
n
ce
th
e
in
teg
r
atio
n
lev
el
o
f
P
V
s
y
s
tem
s
in
th
e
DS
wh
ile
c
o
n
cu
r
r
en
tly
r
ed
u
cin
g
th
r
ee
tar
g
et
m
etr
ics:
v
o
ltag
e
d
ev
iatio
n
s
,
ac
tiv
e
p
o
wer
lo
s
s
,
an
d
r
ea
ctiv
e
p
o
wer
l
o
s
s
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
in
co
r
p
o
r
ates
v
ar
iab
ilit
ies
lin
k
e
d
with
s
o
lar
r
a
d
iatio
n
a
n
d
lo
a
d
d
em
a
n
d
.
T
h
e
W
OA
is
im
p
lem
en
ted
to
ad
d
r
e
s
s
th
e
co
n
s
tr
u
cted
m
o
d
el.
T
h
e
f
o
r
m
u
lated
m
o
d
el
o
p
tim
ally
i
n
teg
r
ates
a
s
o
lar
PV
o
u
tp
u
t
o
f
3
.
2
0
6
6
2
5
MW.
Mo
r
eo
v
er
,
it
r
ed
u
ce
s
v
o
ltag
e
d
ev
iatio
n
b
y
1
9
.
3
9
%,
r
ea
l
p
o
wer
lo
s
s
b
y
1
8
.
4
2
%,
an
d
r
ea
c
tiv
e
p
o
wer
lo
s
s
b
y
1
8
.
5
3
%.
T
h
e
m
o
d
el
d
em
o
n
s
tr
ates
v
ar
y
in
g
lev
els
o
f
p
o
wer
lo
s
s
r
ed
u
ctio
n
ac
r
o
s
s
s
ea
s
o
n
s
,
with
th
e
h
ig
h
est
r
ec
o
r
d
e
d
in
win
ter
d
u
e
to
in
cr
ea
s
ed
s
o
lar
ir
r
ad
iatio
n
.
Ad
d
iti
o
n
ally
,
th
e
v
o
ltag
e
p
r
o
f
ile
im
p
r
o
v
es
s
ig
n
if
ican
tly
ac
r
o
s
s
all
s
ea
s
o
n
s
.
H
o
w
e
v
e
r
,
u
n
d
e
r
-
v
o
l
t
a
g
e
i
s
s
u
es
p
e
r
s
i
s
t
i
n
s
o
m
e
b
u
s
e
s
d
u
e
t
o
m
is
m
a
t
c
h
es
b
e
t
w
e
e
n
l
o
a
d
a
n
d
s
o
l
a
r
P
V
g
e
n
e
r
at
i
o
n
,
h
i
n
d
e
r
i
n
g
m
a
x
i
m
u
m
p
o
w
e
r
l
o
s
s
r
e
d
u
c
t
i
o
n
.
F
u
t
u
r
e
r
e
s
e
a
r
c
h
c
o
u
l
d
f
o
c
u
s
o
n
o
p
t
i
m
a
l
d
e
m
a
n
d
r
e
s
p
o
n
s
e
p
r
o
g
r
a
m
(
D
R
P
)
s
c
h
e
d
u
l
i
n
g
i
n
DS
t
h
a
t
i
n
c
o
r
p
o
r
a
t
e
s
PV
-
D
G
p
l
a
c
e
m
e
n
t
t
o
o
f
f
e
r
f
u
r
t
h
e
r
i
m
p
r
o
v
e
m
e
n
t
s
i
n
p
o
w
e
r
l
o
s
s
a
n
d
v
o
l
t
a
g
e
d
e
v
i
a
tio
n
s
b
y
b
e
t
t
e
r
a
l
i
g
n
i
n
g
t
h
e
l
o
a
d
p
r
o
f
i
l
e
w
i
t
h
P
V
g
e
n
e
r
a
ti
o
n
p
a
t
te
r
n
s
.
ACK
NO
WL
E
DG
M
E
N
T
S
T
h
e
au
th
o
r
s
wo
u
ld
lik
e
to
ac
k
n
o
wled
g
e
B
o
ld
Gr
an
t
2
0
2
2
v
ia
Pro
ject
C
o
d
e
J
5
1
0
0
5
0
0
0
2
/2
0
2
2
0
0
3
,
2
0
2
2
0
5
0
0
1
E
T
G,
an
d
R
E
MA
C
O
f
o
r
th
e
r
esear
ch
f
ac
ilit
ies
s
u
p
p
o
r
t
an
d
APC
,
wh
ich
is
f
u
n
d
ed
b
y
UNI
T
E
N
B
o
ld
Pu
b
licatio
n
Fu
n
d
2
0
2
3
,
f
o
r
m
ak
in
g
th
is
r
esear
ch
p
r
o
jec
t a
s
u
cc
ess
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
r
esear
ch
was
f
u
n
d
ed
th
r
o
u
g
h
th
e
B
o
ld
Gr
an
t
2
0
2
2
u
n
d
er
Pro
ject
C
o
d
e
J
5
1
0
0
5
0
0
0
2
/2
0
2
2
0
0
3
,
2
0
2
2
0
5
0
0
1
E
T
G.
T
h
e
g
r
an
t
p
r
o
v
id
ed
f
in
a
n
cial
s
u
p
p
o
r
t
in
th
e
f
o
r
m
o
f
a
Gr
ad
u
ate
R
esear
ch
Ass
is
tan
ts
h
ip
(
GR
A)
to
ca
r
r
y
o
u
t th
is
s
tu
d
y
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
t
r
ib
u
to
r
R
o
les
T
a
x
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
i
d
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
Saleh
B
a
-
s
waim
i
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
R
en
u
g
a
Ver
ay
iah
✓
✓
✓
✓
✓
✓
✓
Vig
n
a
K.
R
am
ac
h
an
d
ar
am
u
r
th
y
✓
✓
✓
✓
✓
Saee
d
Ali Bi
n
ajjaj
✓
✓
✓
✓
San
jeev
ik
u
m
ar
Pad
m
an
ab
an
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
f
t
E
:
W
r
i
t
i
n
g
-
R
e
v
i
e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
su
a
l
i
z
a
t
i
o
n
Su
:
Su
p
e
r
v
i
s
i
o
n
P
:
P
r
o
j
e
c
t
a
d
mi
n
i
st
r
a
t
i
o
n
Fu
:
Fu
n
d
i
n
g
a
c
q
u
i
si
t
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.