Indonesian
J
our
nal
of
Electrical
Engineering
and
Computer
Science
V
ol.
22,
No.
1,
April
2021,
pp.
28
37
ISSN:
2502-4752,
DOI:
10.11591/ijeecs.v22i1.pp28-37
r
28
Methodology
to
impr
o
v
e
the
accuracy
of
the
model
in
photo
v
oltaic
systems
J
ose
Galarza
Department
of
Electrical
and
Electronic
Engineering,
National
Uni
v
ersity
of
the
Center
of
Peru,
Peru
Article
Inf
o
Article
history:
Recei
v
ed
Oct
9,
2020
Re
vised
Dec
26,
2020
Accepted
Jan
15,
2021
K
eyw
ords:
Cell
temperature
Experimental
measurements
Irradiance
P
arameter
estimation
Photo
v
oltaic
system
Statistical
indicators
ABSTRA
CT
The
present
research
proposes
a
methodology
to
impro
v
e
the
estimation
of
the
un-
kno
wn
parameters
of
the
unitary
diode
model
of
the
photo
v
oltaic
panel.
T
o
check
the
accurac
y
,
a
comparison
with
other
methodologies
kno
wn
in
the
scientific
literature
is
made.
Through
an
iterati
v
e
process,
the
best
v
alue
of
the
series
resistance
and
the
ideality
f
actor
for
dif
fere
nt
temperature
and
irradiance
conditions
are
identified.
The
objecti
v
e
is
to
determine
a
simplified
model
that
accurately
estimates
the
po
wer
sup-
plied
by
a
photo
v
oltaic
installation.
T
o
check
the
ef
fecti
v
eness
of
the
methodology
,
a
comparison
w
as
made
between
the
po
wer
estimat
ed
by
the
model
and
the
po
wer
measurements
of
an
e
xperim
ental
photo
v
oltaic
installation.
The
results
based
on
sta-
tistical
indicators
sho
w
t
hat
the
proposed
methodology
determines
a
simplified
model
of
the
unitary
diode
with
a
better
capacity
and
accurac
y
with
respect
to
the
kno
wn
methodologies.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Jose
Galarza
Department
of
Electrical
and
Electronic
Engineering
National
Uni
v
ersity
of
the
Center
of
Peru
3909
Mariscal
Castilla
A
v
enue,
Huancayo,
Peru
Email:
jg
alarza@uncp.edu.pe
1.
INTR
ODUCTION
Statistical
information
on
rene
w
able
ener
gies
sho
ws
that
these
technologies
are
gro
wing
w
orldwide,
with
the
highest
participation
rates
in
Europe
and
Asia
[1].
In
2050,
electricity
generation
with
solar
and
wind
systems
will
ha
v
e
a
79
%
share
of
the
electricity
generation
matrix
in
the
United
States,
and
electricity
gener
-
ation
for
self-consumption
through
photo
v
oltaic
(PV)
panels
will
increase
fi
v
efold
[2].
The
scientific
literature
presents
dif
ferent
models
of
the
PV
system;
the
single
diode
model
(SDM)
is
accepted
for
its
simplicity
and
accurac
y
[3–12].
In
the
SDM,
the
I-V
characteristic
of
the
PV
system
is
represented
by
a
non-linear
equation
coupled
with
fi
v
e
parameters:
photoelectric
current
(
I
L
),
in
v
erse
diode
saturation
current
(
I
o
),
ideal
diode
f
ac-
tor
(
n
i
),
series
resistance
(
R
s
),
and
paral
lel
resistance
(
R
sh
)
[6].
The
fi
v
e-parameter
SDM
can
be
simplified
to
four
parameters
by
ne
glecting
the
R
sh
v
alue
[13,
14].
The
technical
data
of
the
PV
pro
vided
by
the
manuf
ac-
turer
are
used
to
determine
the
fi
v
e
parameters
of
the
SDM
under
standard
test
conditions
(STC).
In
[15,
16]
R
s
,
R
sh
and
n
i
are
considered
constant,
calculated
with
empirical
and
thermal
formulations;
in
[17]
the
f
actor
n
i
is
chosen
according
to
the
PV
technology;
in
[13,
14,
18,
19],
e
xperimental
data
w
as
used
for
the
estima-
tion
of
n
i
through
thermal
equations
and
coef
ficients
that
allo
wed
the
adjustment
of
I-V
curv
es.
T
emperature
and
irradiance
v
ariables
directly
af
fect
the
fi
v
e
parameters
of
the
SDM.
Through
the
superposition
principle,
the
parameters
calculated
in
STC
are
corrected
for
dif
ferent
temperature
and
irradiance
conditions
[4–8].
The
calculation
of
the
parameters
of
the
SDM
has
been
widely
e
v
aluated
with
commercial
PV
modules.
Se
v
eral
J
ournal
homepage:
http://ijeecs.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
29
authors
establish
dif
ferent
criteria
f
o
r
the
calculation
of
the
parameters.
The
resul
ts
estimated
by
each
method-
ology
are
dif
ferent
for
the
e
v
aluation
of
the
same
photo
v
oltaic
panel,
in
some
cases
v
ery
di
v
er
gent
[5–7,
17,
20].
In
this
research,
the
SDM
is
analyzed
using
e
xperimental
measurements
to
determine
a
simple
and
accurate
model,
considering
only
four
parameters
(
R
s
,
n
i
,
I
L
,
and
I
o
).
The
contrib
utions
of
this
w
ork
are
the
follo
wing:
•
Determination
of
I
L
and
I
o
through
an
analytical
method;
in
an
iterati
v
e
w
ay
R
s
w
as
determined
through
a
progressi
v
e
increase
of
n
i
.
•
Study
of
the
v
ariation
and
influence
of
R
s
and
n
i
in
the
accurac
y
of
SDM.
•
Determination
of
the
sim
plified
SDM
to
accurately
estimate
the
po
wer
supplied
by
the
PV
system
to
the
electric
grid.
•
The
proposed
methodology
is
analyzed
using
e
xperimental
measurements
of
a
3
kWp
installat
ion.
The
results
sho
w
that
the
v
ariation
of
n
i
during
the
day
follo
ws
the
beha
vior
of
the
ir
radiance.
The
estimation
of
this
coef
ficient
is
determined
to
obtain
the
accurac
y
in
the
SDM.
This
paper
is
or
g
anized
as
follo
ws.
Section
2
addresses
the
single
diode
model
and
the
proposed
methodol-
ogy
.
Section
3
reports
the
simulations
results
and
statistical
indicators
for
PV
po
wer
assessment.
Finally
the
conclusion
is
gi
v
en
in
section
4.
2.
MA
TERIALS
AND
METHODS
2.1.
Experimental
PV
system
The
e
xperimental
PV
system
used
in
this
research
is
part
of
the
pilot
project
e
x
ecuted
by
the
Minis
try
of
Ener
gy
of
Peru.
The
instal
lation
is
located
in
the
city
of
Huancayo,Peru,
as
part
of
the
Rene
w
able
Ener
gy
Laboratory
of
the
F
aculty
of
Electrical
Engineering
of
the
Na
tional
Uni
v
ersity
of
the
Center
of
Peru.
The
PV
system
is
sho
wn
in
Figure
1.
The
project
has
10
poly-crystalli
ne
silicone
panels
MAXPO
WER
CS6U-
325
[21]
from
the
manuf
acturer
CanadianSolar
.
The
technical
characteristics
are
sho
wn
in
T
able
1.
These
panels
ha
v
e
been
installed
on
a
rigid
base
with
a
12
inclination,
corresponding
to
the
lati
tude
of
the
city
of
Huancayo.
The
DC/A
C
con
v
ersion
is
performed
by
a
three-phase
S
MA-SUNNY
TRIPO
WER
5000TL
in
v
erter
with
the
maximum
po
wer
point
(MPP)
function
enabled.
Irradiance
is
measured
by
the
SMP3-A
class
2
p
yranometer
from
the
manuf
acturer
KIPP-ZONEN.
The
temperature
is
recorded
by
the
A
GS54+
sensor
from
the
manuf
acturer
Thermok
on.
El
ectrical
measurement
s
(v
oltage,
current,
and
po
wer)
and
en
vironmental
measurements
(temperature
and
irradiance)
are
recorded
in
a
data-logger
e
v
ery
5
minutes
during
the
day
.
Figure
1.
Experimental
PV
system
T
able
1.
Datasheet
MAXPO
WER
CS6U-325
P
arameter
Description
V
alue
P
max
Nominal
Max.
Po
wer
-
STC
a
325
W
V
mp
Optimal
Operating
V
oltage
-
STC
37
V
I
mp
Optimal
Operating
Current
-
STC
8.78
A
V
oc
Open
Circuit
V
oltage
-
STC
45.5
V
I
sc
Short
Circuit
Current
-
STC
9.34
A
k
v
T
emperature
Coef
ficient
-
V
oc
-0.31%/
C
k
i
T
emperature
Coef
ficient
-
Isc
0.05%/
C
N
s
Cell
Arrangement
72
(6x12)
T
NMO
T
Nominal
Module
Operating
T
emperature
-
NMO
T
b
43
C
T
a
Ambient
T
emperature
-
NMO
T
20
C
a
STC:
Standard
T
est
Conditions.
b
NMO
T
:
Nominal
Module
Operating
T
emperature.
Methodolo
gy
to
impr
o
ve
the
accur
acy
of
the
model
in
photo
voltaic
systems
(J
ose
Galarza)
Evaluation Warning : The document was created with Spire.PDF for Python.
30
r
ISSN:
2502-4752
2.2.
Single
diode
model
-
photo
v
oltaic
panel
The
PV
system
can
be
modeled
through
the
single-diode
model
[22].
Figure
2
sho
ws
the
electrical
circuit
that
defines
this
model.
The
characteristic
equation
I-V
of
the
PV
system
from
the
electrical
circuit
is
represented
in
(1):
I
=
I
L
I
o
exp
V
+
I
R
s
n
i
N
s
V
t
1
V
+
I
R
s
R
sh
(1)
where
I
and
V
represent
the
current
and
v
oltage
of
the
PV
module
respecti
v
ely
,
I
L
represents
the
photoelectric
current,
I
o
the
in
v
erse
saturation
current
of
the
diode,
the
ideal
f
actor
of
the
diode
represented
by
n
i
,
whereas
N
s
represents
the
cells
connected
in
series,
and
V
t
the
thermal
v
oltage.
The
resistors
R
s
and
R
sh
represent
the
series
and
shunt
losses
respecti
v
ely
[19].
The
transcendental
equation
e
xpressed
in
(1)
is
solv
ed
through
numerical
methods.
The
methodology
of
Gauss-Seidel
is
used
in
[18];
ho
we
v
er
the
method
of
Ne
wton-Rapshon
is
most
commonly
used
in
the
scientific
literature
[5,
7,
17].
There
are
more
sophisticated
PV
models
than
the
SDM
[4];
ho
we
v
er
,
the
SDM
is
the
most
studied
model
and
presents
accurate
results
when
e
v
aluated
under
v
ariable
temperature
and
irradiance
conditions
[5–8,
13,
14,
17–20,
23,
24].
Figure
2.
Single
diode
model
-
PV
system
2.3.
PV
system
parameter
estimation:
Kno
wn
methods
This
section
refers
to
the
kno
wn
methods
to
estimate
the
fi
v
e
parameters
of
the
SDM;
the
est
imation
procedure
is
done
in
STC
and
not
STC.
2.3.1.
P
arameter
estimation
under
STC
The
methodologies
propose
an
iterati
v
e
and
analytical
process
to
calculate
the
unkno
wn
parame
ters.
Basically
,
the
methods
are
used
to
estimate
the
I-V
and
P-V
curv
es
of
the
PV
system.
The
method
proposed
in
[5]
simplifies
the
SDM
considering
I
L
=
I
sc
.
The
I
o
is
obtained
through
(2)
and
the
R
s
,
R
sh
,
and
n
i
parameters
are
obtained
by
simultaneously
solving
(3),
(4),
and
(5).
I
o
=
I
L
V
oc
=R
sh
exp
[
V
oc
=
(
n
i
N
s
V
t
)
1]
(2)
I
mp
=
1
(
I
sc
V
oc
I
sc
R
s
R
sh
)
2
(3)
1
R
sh
=
1
R
sh
3
4
1
+
R
s
3
4
+
R
s
R
sh
(4)
I
mp
+
V
mp
2
3
1
R
sh
1
+
R
s
2
3
+
R
s
R
sh
=
0
(5)
where
the
f
actors
1
=
I
sc
(
V
mp
+
I
mp
R
s
I
sc
R
s
)
=R
sh
,
2
=
exp
[(
V
mp
+
I
mp
R
s
V
oc
)
=
(
n
i
N
s
V
t
)]
,
3
=
(
I
sc
R
sh
V
oc
+
I
sc
R
s
)
=
(
n
i
N
s
V
t
R
sh
)
,
and
4
=
exp
[(
I
sc
R
s
V
oc
)
=
(
n
i
N
s
V
t
)]
.
The
approach
proposed
in
[7]
considers
the
four
-parameter
SDM,
ne
glecting
the
v
alue
of
R
sh
,
con-
sidering
I
L
=
I
sc
.
The
I
o
is
obtained
through
(6).
The
n
i
f
actor
depends
on
the
PV
module
technology
and
is
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
22,
No.
1,
April
2021
:
28
–
37
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
31
constant.
The
estimation
of
R
sh
and
R
s
is
done
in
the
MPP
of
the
I-V
curv
e.
The
estimation
of
R
sh
is
done
according
to
(7)
through
a
gradual
increase
of
R
s
.
I
o
=
I
L
exp
[
V
oc
=
(
n
i
N
s
V
t
)
1]
(6)
R
sh
=
V
mp
(
V
mp
+
I
mp
R
s
)
5
(7)
where
5
=
V
mp
I
L
V
mp
I
o
exp
[(
V
mp
+
I
mp
R
s
)
=
(
n
i
N
s
V
t
)]
+
V
mp
I
o
P
max;e
.
The
method
proposed
in
[8]
pro
vides
an
iterati
v
e
solution
to
find
the
v
alues
of
R
s
,
R
sh
e
I
L
con-
sidering
const
ant
the
v
al
ue
of
n
i
that
depends
on
the
type
of
technology
of
the
PV
module.
The
I
o
v
alue
is
approximated
by
(6),
the
iterati
v
e
process
ends
when
the
lo
west
v
alue
is
obtained
for
the
(8),
(9)
y
(10)
e
xpressions.
E
r
r
1
=
V
mp
I
mp
R
s
n
i
N
s
V
t
R
sh
I
o
R
sh
2
+
n
i
N
s
V
t
(8)
E
r
r
2
=
V
mp
+
I
mp
R
s
I
L
I
mp
I
o
(
2
1)
R
sh
(9)
E
r
r
3
=
R
s
+
R
p
R
p
I
sc
I
L
(10)
2.3.2.
P
arameter
estimation
in
non-STC
The
parameters
of
the
SDM
depend
on
the
en
vironmental
conditions
of
temperature
and
ir
radiance.
The
con
v
ersion
of
STC
to
other
conditions
dif
ferent
from
temperature
and
irradiance
is
necessary
for
each
parameter
[19].
The
dependence
of
temperature
and
irradiance
on
the
parameters
of
the
SDM
is
based
on
the
principle
of
o
v
erlapping
[25].
In
[4,
5,
7]
the
PV
cell
temperature
is
assumed
to
be
the
ambient
temperature.
In
[8]
the
PV
cell
temperature
is
approximated
from
the
ambient
temperature,
which
allo
ws
for
a
better
charac-
terization
for
the
PV
panel
model.
T
able
2
sho
ws
the
comparison
of
dif
ferent
c
riteria
for
the
dependence
of
the
SDM
parameters
on
temperature
and
irradiance.
T
able
2.
Dependence
of
the
SDM
parameters:
T
emperature
(T)
and
Irradiance
(I)
Reference
P
arameter
R
s
R
sh
n
i
I
o
I
L
[4]
T
-
T
T
-I
T
-I
[5]
-
-
-
T
-I
T
-I
[6]
T
-I
-
-
T
-I
T
-I
[7]
-
-
-
T
T
-I
[8]
-
-
-
T
T
-I
[13]
-
-
-
T
-I
T
-I
[14]
-
-
T
T
T
-I
[19]
T
-I
I
T
T
T
-I
2.4.
PV
system
parameter
estimation:
pr
oposed
methodology
The
scientific
literature
in
[26]
sho
ws
the
classificati
on
of
irradiance
(W/m
2
)
in
tw
o
le
v
els:
the
v
alues
belo
w
250
are
re
g
arded
as
lo
ws
le
v
els
whereas
highs
le
v
els
include
v
alues
abo
v
e
500.
In
this
in
v
estig
ation,
the
classification
of
irradiance
according
to
[26]
is
made
by
adding
the
a
v
erage
le
v
el
of
irradiance
for
v
alues
between
200
and
500.
The
SDM
with
lo
w
irradiance
le
v
els
has
little
accurac
y
in
modeling
poly-crystalline
silicone
panels
[27].
In
this
research,
a
methodology
is
implemented
to
e
v
aluate
the
four
-parameter
SDM
at
the
medium
(200-500)
and
high
(500)
irradiance
le
v
els,
considering
the
approximation
of
the
module
tem-
perature
from
the
ambient
temperature.
The
proposed
methodology
considers
the
e
xperimental
measurements
(irradiance,
DC
current,
ambient
temperature,
and
DC
v
oltage)
to
solv
e
equation
(1)
and
estimate
the
R
s
and
n
i
v
alues.
The
four
-parameter
SDM
mak
es
an
e
xact
approximation
of
both
parameters
[26].
The
four
-step
methodology
is
presented
belo
w:
Methodolo
gy
to
impr
o
ve
the
accur
acy
of
the
model
in
photo
voltaic
systems
(J
ose
Galarza)
Evaluation Warning : The document was created with Spire.PDF for Python.
32
r
ISSN:
2502-4752
•
Step
I
-
Calculation
of
the
temperature
f
actor
K
T
:
T
o
obtain
an
accurate
model
and
approximate
the
real
beha
vior
of
the
PV
system,
the
ambient
temperature
(
T
m
)
is
used
to
estimate
the
cell
temperature
(
T
cel
l
)
according
to
[8].
The
K
T
is
calculated
through
(11)
using
the
module
operation
temperature
(
T
N
M
O
T
),
the
ambient
temperature
(
T
a
),
and
the
irradiance
le
v
el
(
I
r
r
a
);
these
three
parameters
under
NMO
T
conditions.
Finally
the
irradiance
measurement
(
G
)
is
corrected
with
K
T
and
T
m
according
to
(12).
•
Step
II
-
Calculation
of
the
current
I
o
:
The
accurac
y
of
the
SDM
is
impro
v
ed
through
(13)
to
cancel
the
error
of
the
model
in
the
vicinity
of
V
oc
and
simplify
the
model
[7].
The
I
o
current
is
estimated
according
to
(13),
using
the
temperature
coef
ficients
K
i
and
K
v
.
•
Step
III
-
Calculation
of
the
photo-current
I
L
:
The
superposition
principle
is
used
to
establish
the
dependence
of
irradiance
and
temperature
for
the
I
L
[25].
This
current
is
estimated
with
(14),
considering
the
nominal
irradiance
(
G
S
T
C
),
I
s
c
,
T
S
T
C
based
on
the
datasheet,
the
v
alues
pre
viously
calculated,
T
cel
l
,
K
T
,
and
the
measurement
of
irradiance
G
.
•
Step
IV
-
Calculation
of
series
resistance
R
s
and
n
i
:
The
R
s
v
alue
obtained
from
(1)
is
sho
wn
in
(15),
ne
glecting
t
he
v
alue
of
R
sh
.
In
the
e
v
ent
that
I
L
I
is
ne
g
ati
v
e,
the
R
s
presents
imaginary
v
alues
due
to
the
log
arithmic
f
actor
.
This
situation
occurs
at
lo
w
irradiance
and
temperature
le
v
els.
The
formulation
in
(15)
presents
tw
o
unkno
wns:
R
s
and
n
i
,
to
estimate
both
v
ariabl
es.
This
equation
is
solv
ed
in
an
iterati
v
e
w
ay
to
ca
lculate
the
best
v
alue
of
R
s
with
an
increase
of
n
i
from
0
to
5.
The
justification
for
the
e
xtreme
v
alue
of
5
corresponds
to
t
he
a-Si-H
T
riple
type
panel
technology
[17].
The
best
v
alue
of
R
s
corresponds
to
the
lo
west
v
alue
a
v
ailable
for
n
i
.
This
iterati
v
e
procedure
is
repeated
for
each
of
the
measurements
recorded
during
the
day
.
K
T
=
(
T
N
M
O
T
T
a
)
=I
r
r
a
(11)
T
cel
l
=
GK
T
+
T
m
(12)
I
o
=
I
sc
+
K
i
(
T
cel
l
T
S
T
C
)
exp
h
V
oc
+
K
v
(
T
cell
T
S
T
C
)
n
i
N
s
V
t
i
1
(13)
I
L
=
(
G=G
S
T
C
)
[
I
S
C
+
K
T
(
T
cel
l
T
S
T
C
)]
(14)
R
s
=
f
(
l
og
[(
I
L
I
)
=I
o
+
1]
(
n
i
N
s
V
t
)
V
g
=I
(15)
3.
RESUL
TS
AND
DISCUSSION
In
this
research,
through
Mat
lab/Simulink
programming,
the
methodologies
e
xposed
in
[5,
7,
8]
ha
v
e
been
used
to
calculate
the
parameters
of
the
SDM
and
to
determine
the
parameters
for
dif
ferent
v
alues
of
temperature
and
irradiance
during
the
day
(8:00
-
16:00
hours).
The
PV
po
wer
estimation
capacity
of
the
SDM
using
the
kno
wn
methodologies
and
the
proposed
methodology
is
v
alidated
through
the
e
xperimental
po
wer
measurements
of
the
3
kWp
e
xperimental
installation.
The
accurac
y
of
the
dif
ferent
methodologies
including
the
proposed
methodology
is
analyzed
through
tw
o
statistical
indicators:
The
root-mean-square
error
(RMSE)
and
the
relati
v
e
root-mean-square
error
(RRMSE).
These
indicators
e
xpress
the
model’
s
accurac
y
[28,
29].
3.1.
Estimation
of
the
parameters
of
the
MAXPO
WER
CS6U-325
module
in
STC
The
technical
characteristics
sho
wn
in
T
able
1
are
used
to
estimate
the
fi
v
e
unkno
wn
parameters
of
the
SDM
according
to
section
2.3,
where
the
methodologies
e
xposed
in
[5,
7,
8]
are
used.
The
estimated
parameters
of
the
SDM
are
sho
wn
in
T
able
3.
About
R
s
and
R
sh
,
the
v
alues
obtained
are
not
con
v
er
gent,
because
each
methodology
has
a
combination
of
analytical
and
iterati
v
e
aspects
to
determine
the
parameters
of
the
SDM.
F
or
the
results
of
R
s
with
the
[5]
and
[7]
methods,
a
dif
ference
of
59
m
w
as
determined
and
between
the
[5]
and
[7]
methods
a
dif
ference
of
42
m
.
Re
g
arding
the
v
alue
of
R
sh
,
the
results
sho
w
a
sizeable
dif
ference
between
the
three
methods
used.
The
v
alue
of
n
i
sho
ws
a
similarity
when
using
the
methods
e
xposed
in
[7]
and
[8].
Ho
we
v
er
,
when
using
the
met
hod
e
xposed
in
[5],
it
results
in
a
dif
ference
of
9%
in
comparison
to
the
other
methodologies.
Because
all
three
methods
use
I
L
=
I
sc
,
the
result
of
I
o
is
ne
gligible.
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
22,
No.
1,
April
2021
:
28
–
37
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
33
T
able
3.
PV
System
P
arameters
Estimation
-
STC
P
arameter
Method
[5]
[7]
[8]
R
s
(m
)
256.360
197
214
R
sh
(k
)
4.752
36.933
0.980
n
i
1.180
1.300
1.300
I
o
(nA)
8.247
56.650
56.136
I
L
(A)
9.340
9.340
9.340
3.2.
Classification
of
irradiance
and
temperatur
e
measur
ements
The
foll
o
wing
research
used
eight-day
irradiance
and
temperature
measurements
for
2019
and
2020.
The
measurements
were
t
ak
en
from
8:00
-
16:00
hours
(the
time
of
highest
irradiance)
with
a
record
tak
en
do
wn
e
v
ery
5
minutes.
In
total,
97
measurements
were
used
for
each
day
.
T
able
4
sho
ws
the
calculation
of
standard
de
viation
(
),
mean
(
x
),
and
coef
ficient
of
v
ariation
(
=
x
).
F
or
the
ei
ght
cases
analyzed,
the
x
is
representati
v
e
because
all
v
alues
for
the
coef
ficient
of
v
ariation
are
lo
wer
than
80%.
W
ith
the
x
inde
x,
the
classification
of
medium
and
high
irradiance
according
to
Section
2.4
is
made.
T
able
4.
Clasification
of
Experimental
Measurements:
Irradiance
and
T
emperature
Case
Irradiance
(W/m
2
)
T
emperature
(K)
x
=
x
x
=
x
Medium
Irr
adiance
2020/03/30
140.6689
297.9555
0.4721
2.5124
285.3475
0.0088
2020/04/29
202.7555
444.7498
0.4559
3.0318
293.2009
0.0103
2020/01/20
169.8526
444.7233
0.3819
2.8156
292.5276
0.0096
2019/11/30
216.2121
481.5473
0.4490
2.4849
294.1576
0.0084
High
Irr
adiance
2020/01/06
156.3721
569.0823
0.2748
3.6622
294.1918
0.0124
2020/02/21
202.5199
562.3305
0.3601
4.0584
294.5444
0.0138
2019/08/10
181.3876
766.6862
0.2366
2.9421
294.2186
0.0100
2020/05/13
230.0101
735.7995
0.3126
4.1659
294.1500
0.0142
3.3.
Estimation
of
the
parameters
of
the
MAXPO
WER
CS6U-325
module
in
non-STC
Each
of
the
methodologies
in
[5,
7,
8]
has
a
dif
ferent
criterion
for
correcting
and
estimating
the
pa-
rameters
of
the
SDM
under
conditions
other
than
STC.
As
described
in
Section
2.3
and
T
able
2,
the
correction
of
the
results
of
T
able
3
w
as
made.
The
SDM
parameters
allo
wed
for
solving
the
transcendental
equation
of
the
PV
through
Ne
wton
Raphson’
s
Method
and
obtaining
the
v
alue
of
I
in
the
8:00
to
16:00
hours.
Consequently
,
with
the
DC
v
oltage
measured
the
PV
po
wer
w
as
also
obtained
for
the
SDM.
3.4.
MAXPO
WER
CS6U-325
module
parameter
estimation:
Pr
oposed
methodology
The
methodology
proposed
in
Section
2.4
is
used
to
calcul
ate
the
four
unkno
wn
parameters
of
the
SDM
using
the
analytical
and
iterati
v
e
approach.
The
v
alue
of
R
sh
is
ne
glected.
3.4.1.
Series
r
esistance
calculation
-
v
ariable
condition
Using
the
e
xperimental
measurements
of
irradiance
and
temperature,
the
final
calculation
of
R
s
is
made,
considering
only
the
positi
v
e
v
alues.
The
results
of
Figure
3
sho
w
that,
for
medium
irradiance,
the
R
s
is
v
ariable
from
1
m
to
v
alues
close
to
6
m
.
Figure
4
corresponds
to
high
v
alues
of
irradiance,
the
beha
vior
of
R
s
is
practically
constant
with
v
alues
lo
wer
than
3
m
.
The
results
with
null
v
alues
in
Figures
3
and
4
correspond
to
re
gions
where
the
v
alue
of
R
s
is
imaginary
.
This
phenomenon
occurs
when
I
L
I
is
ne
g
ati
v
e.
In
these
short
periods
of
tim
e,
there
are
lo
w
le
v
els
of
irradiance
and
temperature
due
to
a
partially
cloudy
sk
y
.
The
R
s
is
not
constant
because
it
is
a
function
of
the
beha
vior
of
n
i
,
which,
in
turn,
is
a
function
of
temperature
and
irradiance
according
to
equations
(11),
(12),
(13),
(14),
and
(15).
The
v
alues
obtained
for
medium
irradiances
are
dif
ferent
from
the
results
of
the
methods
proposed
i
n
[5,
7,
8];
ho
we
v
er
,
for
high
irradiances,
this
parameter
can
be
considered
constant.
Methodolo
gy
to
impr
o
ve
the
accur
acy
of
the
model
in
photo
voltaic
systems
(J
ose
Galarza)
Evaluation Warning : The document was created with Spire.PDF for Python.
34
r
ISSN:
2502-4752
(a)
(b)
(c)
(d)
Figure
3.
Results
of
series
resistance
calculation
-
medium
Irradiance,
(a)
2020-03-30,
(b)
2020-04-29,
(c)
2020-01-20
and
(d)
2019-11-30
(a)
(b)
(c)
(d)
Figure
4.
Results
of
series
resistance
calculation
-
high
irradiance,
(a)
2020-01-06,
(b)
2020-02-21,
c)
2019-08-10
and
(d)
2020-05-13
T
able
5.
Statistical
indicators:
V
ariable
and
fix
ed
series
resistance
for
PV
po
wer
assessment
Case
V
ariable
R
s
Fix
ed
R
s
RMSE
(
W
)
RRMSE
(%)
R
RMSE
(
W
)
RRMSE
(%)
R
Medium
Irr
adiance
2020/01/20
2.6e-14
2.0e-14
1
0.2317
0.1749
0.9999
High
Irr
adiance
2019/08/10
3.8e-14
1.7e-14
1
0.3919
0.1712
0.9999
T
able
6.
Statistical
indicators:
PV
po
wer
assessment
Data
RMSE
(
W
)
RRMSE
(%)
[5]
[7]
[8]
[PM]
a
[5]
[7]
[8]
[PM]
Medium
Irr
adiance
2020/03/30
12.3075
13.8956
11.9573
2.7368
7.1675
8.0924
6.9635
2.6758
2020/04/29
11.0267
13.3221
12.6768
4.2320
6.5282
7.8872
7.5051
3.0277
2020/01/20
9.83510
4.4872
12.1362
0.2317
9.6160
4.3873
11.8659
0.1749
2019/11/30
12.2952
13.0749
11.0958
1.7152
8.7962
9.3540
7.9381
1.2034
High
Irr
adiance
2020/01/06
12.4220
15.0071
7.5600
3.8402
9.3764
11.3277
5.7064
2.2364
2020/02/21
20.1444
21.4444
16.0448
0.7861
14.1336
15.0457
11.2572
0.4654
2019/08/10
9.9995
12.6058
14.1610
0.3919
4.3698
5.5088
6.1884
0.1713
2020/05/13
17.3125
16.8730
20.6361
14.8959
7.5927
7.3999
9.0503
6.5328
a
[PM]:
Proposed
Methodology
.
3.4.2.
Series
r
esistance
calculation
-
fixed
condition
This
case
considers
a
constant
R
s
in
order
to
r
educe
the
comple
xity
of
the
SDM.
The
authors
in
[5,
7,
8]
represent
di
v
erse
criteria
to
correct
series
resistance
in
dif
ferent
conditions
of
temperature
and
irradiance,
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
22,
No.
1,
April
2021
:
28
–
37
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
35
in
the
present
methodology
a
constant
v
alue
of
this
parameter
is
considered
for
conditions
dif
fer
ent
from
STC.
The
v
alue
of
R
s
has
been
considered
constant.
The
chosen
v
alue
corresponds
to
the
maximum
v
alue
of
the
eight
cases
e
v
al
uated
(
6
m
)
as
sho
wn
in
Figures
3
and
4.
T
able
5
sho
ws
the
error
incurred
in
making
this
approach,
is
ne
gligible
with
the
v
alues
sho
wn
for
RMSE
and
RRMSE.
The
results
obtained
allo
w
us
to
conclude
that
considering
R
s
constant
has
tw
o
main
adv
antages:
The
first
adv
antage
corresponds
to
the
small
error
committed
in
the
SDM
as
sho
wn
in
T
able
5.
The
second
adv
antage
corresponds
to
the
elimination
of
null
v
alues
in
the
calculation
of
R
s
.
When
considering
const
ant
this
v
ariable,
all
the
calculations
of
n
i
are
also
v
alid.
T
able
6
sho
ws
a
comparison
between
the
methodologies
described
in
[5,
7,
8]
and
the
proposed
methodology
.
The
statistical
results
sho
w
that
the
proposed
methodology
has
less
error
than
the
other
con
v
entional
methodologies.
The
RRMSE
indicator
sho
ws
v
alues
less
than
6.5%
in
all
cases,
which
corresponds
to
an
e
xcellent
classification
[30,
31].
Figures
5a,
5b,
5c,
5d,
6a,
6b,
6c,
and
6d
sho
w
the
po
wer
estimation
during
8:00
to
16:00
hours
for
each
case.
Thes
e
v
alues
correspond
to
the
po
wer
of
a
single
PV
panel.
The
results
sho
w
that,
for
daytime
conditions
when
the
irradiance
v
aries
slo
wly
and
quickly
,
the
proposed
method
con
v
eniently
estimates
the
v
alue
of
the
photo
v
oltaic
po
wer
,
in
the
time
interv
als
when
there
is
a
lo
w
irradiance
(Figure
5a,
5b,
5d,
6a,
6b,
and
6d).
A
slight
dif
ference
is
sho
wn
concerning
the
measurements.
This
is
due
to
the
o
wn
accurac
y
of
the
unitary
diode
[27].
Additionally
,
it
is
determined
that
the
SDM
as
presented
in
this
research,
depends
basically
on
the
v
alue
of
n
i
.
This
parameter
is
not
constant
and
depends
on
the
beha
vior
of
irradiance.
Figure
7a
sho
ws
the
cases
for
lo
w
irradiance
in
the
case
of
partially
cloudy
and
sunn
y
days
that
are
quite
heterogeneous.
In
the
time
interv
als
when
the
irradiance
is
v
ariable,
the
n
i
f
actor
has
a
greater
de
gree
of
dependenc
y
.
Figure
7b
sho
ws
the
case
of
high
irradiance
where
the
n
i
f
actor
also
v
aries
according
to
the
le
v
el
of
irradiance.
(a)
(b)
(c)
(d)
Figure
5.
T
est
result
sho
wing
the
measured
and
model
data
of
photo
v
oltaic
po
wer
-
medium
irradiance,
(a)
2020-03-30,
(b)
2020-04-29,
(c)
2020-01-20
and
(d)
2019-11-30
(a)
(b)
(c)
(d)
Figure
6.
T
est
result
sho
wing
the
measured
and
model
data
of
photo
v
oltaic
po
wer
-
high
irradiance,
(a)
2020-01-06,
(b)
2020-02-21,
(c)
2019-08-10
and
(d)
2020-05-13
Methodolo
gy
to
impr
o
ve
the
accur
acy
of
the
model
in
photo
voltaic
systems
(J
ose
Galarza)
Evaluation Warning : The document was created with Spire.PDF for Python.
36
r
ISSN:
2502-4752
(a)
(b)
Figure
7.
T
est
result
sho
wing
the
measured
and
model
data
of
ideal
diode
f
actor
,
(a)
2020-01-20
(medium
irradiance)
and
(b)
2019-08-10
(high
irradiance)
4.
CONCLUSION
In
the
present
w
ork,
an
analytical
and
iterati
v
e
methodology
has
been
proposed
to
determine
the
parameters
of
the
unitary
model
of
the
PV
panel.
It
has
been
used
as
a
model
with
four
parameters,
where
I
L
and
I
o
are
calculated
analytically
.
It
w
as
determ
ined
that
the
parameter
R
s
depends
on
the
irradiance
and
temperature;
ho
we
v
er
,
if
considered
constant,
the
results
sho
w
that
the
model
has
a
ne
gligible
error
.
The
f
actor
n
i
sho
ws
beha
viors
closely
related
to
irradiance.
Accordingly
,
this
parameter
must
be
v
ariable
to
obtain
a
more
accurate
model.
Through
the
statis
tical
indicators
RMSE
and
RRMSE,
it
has
been
demonstrated
that
the
proposed
methodology
is
more
precise
than
the
con
v
entional
ones.
This
methodology
can
be
used
to
accurately
estimate
the
four
unkno
wn
parameters
of
the
single
diode
model
and
to
estimate
the
po
wer
produced
by
a
PV
system.
A
CKNO
WLEDGMENT
The
author
thanks
the
National
Uni
v
ersity
of
the
Center
of
Peru
(UNCP)
and
the
Department
of
Electrical
and
Electronic
Engineering
for
the
technical
f
acilities
used
for
the
de
v
elopment
of
this
research.
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BIOGRAPHY
OF
A
UTHOR
J
ose
Galarza
recei
v
ed
the
MSc.
de
gree
in
Electrical
E
ngineering
from
the
Polytechnic
Uni
v
ersity
of
Madrid.
He
is
af
filiated
to
the
Department
of
Electrical
Engineering
-
National
Uni
v
ersity
of
the
Center
of
Peru.
His
research
interests
include
rene
w
able
ener
gy
technologies,
HVDC
electric
po
wer
transmission
system
and
po
wer
electronic
con
v
erters
for
motion
control.
Further
info
on
his
homepage:
https://orcid.or
g/0000-0001-5569-6541
Methodolo
gy
to
impr
o
ve
the
accur
acy
of
the
model
in
photo
voltaic
systems
(J
ose
Galarza)
Evaluation Warning : The document was created with Spire.PDF for Python.