Inter
national
J
our
nal
of
P
o
wer
Electr
onics
and
Dri
v
e
System
(IJPEDS)
V
ol.
16,
No.
3,
September
2025,
pp.
2072
∼
2081
ISSN:
2088-8694,
DOI:
10.11591/ijpeds.v16.i3.pp2072-2081
❒
2072
Digital
twin-based
perf
ormance
e
v
aluation
of
a
photo
v
oltaic
system:
A
r
eal-time
monitoring
and
optimization
framew
ork
Mustafa
F
adel
1,2
,
F
ajer
M.
Alelaj
2,3
1
Electrical
Engineering
Department,
Mustansiriyah
Uni
v
ersity
,
Baghdad,
Iraq
2
School
of
Engineering,
Ne
wcastle
Uni
v
ersity
,
Ne
wcastle
upon
T
yne,
United
Kingdom
3
K
uw
ait
Institute
for
Scientic
Research,
K
uw
ait
City
,
K
uw
ait
Article
Inf
o
Article
history:
Recei
v
ed
May
23,
2025
Re
vised
Jun
17,
2025
Accepted
Jul
23,
2025
K
eyw
ords:
Digital
twin
Optimization
Photo
v
oltaic
system
Real-time
monitoring
Rene
w
able
ener
gy
system
ABSTRA
CT
The
digital
t
win
(DT)
technology
implementation
in
photo
v
oltaic
(PV)
systems
pro
vides
an
inno
v
ati
v
e
approach
to
real-time
performance
monitoring
and
predicti
v
e
maintenance.
In
this
paper
,
an
end-to-end
DT
frame
w
ork
for
real-time
performance
analysis,
f
ault
detection,
and
optimization
of
a
250
W
PV
system
is
propos
ed.
A
ph
ysics-based
equation
and
AI-based
prediction
h
ybrid
DT
model
is
de
v
eloped
t
hrough
MA
TLAB/Simulink,
trained
from
real
data
acquired
by
means
of
a
testbed.
The
DT
simulates
the
dynamic
ph
ysical
PV
system
beha
vior
and
adjusts
itself
using
self-correcting
algorithms
to
enhance
precision
in
prediction
and
forecast
po
wer
out
put
at
high
delity
.
Results
indicate
that
the
DT
gi
v
es
the
true
response
of
the
PV
system
with
v
ery
small
dif
ferences
attrib
utable
to
model
approximations
and
sensor
f
aults,
95%
error
minimization
after
compensation,
and
a
root
mean
square
error
(RMSE)
of
2.8
W
,
indicating
its
applicability
for
real-time
monitoring
and
predicti
v
e
main-maintenance.
The
w
ork
here
focuses
on
the
feasibility
of
applying
DTs
t
o
w
ards
the
autonomous
optimization
of
distrib
uted
rene
w
able
ener
gy
systems.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Mustaf
a
F
adel
Electrical
Engineering
Department,
Mustansiriyah
Uni
v
ersity
Baghdad,
Iraq
Email:
mustaf
a
1988abbas@uomustansiriyah.edu.iq
1.
INTR
ODUCTION
Rene
w
able
ener
gy
systems
based
on
photo
v
oltaic
(PV)
ener
gy
ha
v
e
become
a
crucial
part
of
sustainable
ener
gy
portfolios
w
orldwide,
with
increasing
adoption
dri
v
en
by
their
sustainability
and
declining
cost.
Ho
we
v
er
,
lar
ge
PV
systems
are
subjected
to
man
y
challenges
that
af
fect
their
performance
and
ef
cienc
y
,
due
to
their
outdoor
installations
[1],
[2].
Challenges
such
as
technical
system
issues
and
en
vironmental
conditions
act
as
obstacles
af
fecting
the
system’
s
reliability
and
life
span.
The
technical
challenges
include
v
oltage
and
current
uctuations,
high
DC
v
oltage
ripple,
con
v
ersion
ef
cienc
y
,
po
wer
quality
issues,
thermal
management,
and
de
grada
tion
o
v
er
time
[3],
[4].
En
vironmental
challenges,
including
dust,
sno
w
co
v
erage,
and
weather
v
ariability
,
also
play
important
roles
by
impacting
the
PV
system
performance
[5],
[6].
T
o
maintain
high
operational
ef
cienc
y
under
dif
ferent
en
vironmental
and
technical
conditions,
sophisticated
monitoring
and
optimization
techniques
are
required.
Digital
twin
(DT)
technology
emer
ges
as
g
ame-changing,
by
pro
viding
a
virtual
match
to
the
real-w
orld
system
in
real-time.
This
mirror
model
of
the
ph
ysical
system
can
J
ournal
homepage:
http://ijpeds.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
2073
of
fer
unprecedented
potential
in
autonomous
optimisation
and
predicti
v
e
analytics
[7].
DT
f
acilitates
ongoing
e
v
aluation
of
PV
system
performance
by
fus
ing
sensor
-dri
v
en
data
collection
and
computational
modelling,
enabling
proacti
v
e
f
ault
diagnosis
and
impro
v
ed
predicti
v
e
maintenance
techniques.
The
recent
state
of
the
art
highlights
the
importance
of
emer
ging
DT
in
rene
w
able
ener
gy
systems,
where
researchers
in
[8]
found
that
the
DT
system
could
detect
dif
ferent
f
aults,
such
as
20%
drift
in
sensor
reading
in
the
PV
con
v
ersion
unit,
within
a
short
duration.
Delussu
et
al.
[9]
compare
tw
o
dif
ferent
DT
approaches
to
predict
solar
ener
gy
production
and
create
a
h
ybrid
DT
system
by
combining
the
tw
o
studied
systems
to
impro
v
e
predictions.
Lee
et
al.
[10]
propose
a
no
v
el
generati
v
e
data-dri
v
en
model
based
on
numerical
weather
prediction
that
ef
fecti
v
ely
produces
en
vironmental
data
to
simulate
the
future
beha
viour
of
PV
DT
systems.
Moreo
v
er
,
the
study
in
[11]
introduces
an
inno
v
ati
v
e
DT
system
that
inte
grates
a
no
v
el
circuit-long
short-term
memory
(LSTM)
model
with
a
proposed
triangle-shading
pattern
estimation
method,
eliminating
dependencies
on
direct
irradiance
sensing
and
historical
data.
2.
DIGIT
AL
TWIN
TECHNOLOGY
T
o
understand
ho
w
a
DT
functions,
tw
o
k
e
y
aspects
must
be
addressed.
This
section
will
outline
the
DT
design
requirements,
including
the
necessary
tools
for
b
uildi
ng
an
ef
cient
virtual
system.
Furthermore,
it
e
xplores
the
de
v
elopment
stages
of
the
DT
,
focusing
on
its
intended
function
and
operational
capabilities.
2.1.
Digital
twin
design
r
equir
ements
T
o
de
v
elop
an
ef
fecti
v
e
DT
,
there
are
se
v
eral
technical,
data,
softw
are,
and
engineering
requirement
s
that
must
be
met
to
ensure
simulation
accurac
y
and
optimize
performance.
Figure
1
illustrates
the
DT
design
system,
where
each
PV
DT
needs
hardw
are
infrastructures
represented
as
dif
f
erent
types
of
sensors
such
as
en
vironmental
sensors
represented
by
Pyranometers
that
are
used
to
measure
the
amount
of
f
alling
irradiance
on
PV
modules,
temperature
sensors
for
PV
panels
and
ambient,
humidity
,
wind
speed,
and
dust
sensors
to
assess
the
impact
of
the
en
vironment
on
performance,
or
electrical
measurements
sensors
such
as
v
oltage,
current,
and
po
wer
measurements
from
PV
modules
and
in
v
erters
[12],
[13].
In
addition,
each
DT
requires
an
edge
computing
unit
that
is
used
to
process
the
initial
data
before
sending
it
to
the
cloud
to
reduce
latenc
y
and
impro
v
e
DT
responsi
v
eness.
T
o
ensure
data
inte
grity
,
a
reliable
communication
netw
ork
is
required,
for
e
xample,
dif
ferent
IoT
protocols
such
as
Mess
age
Queuing
T
elemetry
T
ransport
(MQTT),
Open
Platform
Communications
Unied
Architecture
(OPC
U
A),
or
Modb
us
is
required,
especially
for
applications
needing
f
ast
response
and
in
remote
locations
[4],
[5].
Moreo
v
er
,
the
quality
of
recei
v
ed
data
and
its
accurac
y
play
a
crucial
role
in
DT
per
formance,
where
data
must
be
up-to-date,
accurate,
and
uninterrupted
to
ensure
the
reliability
of
the
numerical
simulation.
Additionally
,
using
cloud
databases
can
be
ef
cient
for
big
data
processing
g
athered
from
real-time
analysis
and
using
machine
learning
(ML)
techniques
to
analyze
big
data,
predict
f
ailures,
and
impro
v
e
performance.
The
presence
of
softw
are
support
is
essential
in
b
uilding
a
rugged
DT
system
[14],
[15].
Data
management
and
articial
intelligence
(AI)
platforms
can
predict
ener
gy
consumption,
detect
f
aults,
and
create
interacti
v
e
dashboards
to
display
data
and
analyze
performance.
Furthermore,
softw
are
programs
lik
e
MA
TLAB/Simulink
©
and
NSYS
©
that
use
modelling
and
simulation
engines
can
play
an
important
role
in
de
v
eloping
accurate
ph
ysical
numerical
models
based
on
PV
performance
equations
and
the
ef
fect
of
heat
on
solar
panels.
Engineering
and
ph
ysical
requirements
are
important
to
design
inte
grated
models
for
PV
systems,
where
the
DT
must
be
able
to
simulate
all
PV
system
components.
Components
such
as
solar
panels
and
the
ef
fect
of
gradual
corrosion,
in
v
erters’
ef
fect
on
performance,
batteries
(storage
systems)
and
their
life
c
ycle
based
on
char
ging
and
dischar
ging
patterns,
and
inte
gration
with
the
elect
rical
grid
and
ener
gy
o
w
management
[16].
Moreo
v
er
,
the
DT
must
be
designed
to
be
e
xpandable
to
include
lar
ge
solar
po
wer
plants
or
inte
grated
smart
electrical
grids,
and
the
design
must
be
compatible
with
the
e
xisting
solar
infrastructure
to
f
acilitate
inte
gration
without
the
need
to
redesign
the
system
from
scratch
[17].
2.2.
Digital
twin
de
v
elopment
stages
Digital
twin
creation
is
a
highly
adv
anced
process
that
mo
v
es
in
dif
ferent
steps
to
de
v
elop
an
accurat
e
digital
model
of
the
ph
ysical
system’
s
real
life.
As
indicated
in
Figure
2,
the
process
of
DT
de
v
elopment
can
be
di
vided
into
a
series
of
stages.
Data
collection
and
system
inte
gration
phase,
where
the
DT
is
based
primarily
on
real
data
coming
from
the
s
olar
system
pro
vided
by
dif
ferent
types
of
sensors
deplo
yed,
and
ensuring
that
data
coming
from
dif
ferent
de
vices
and
sources
is
synchronized.
Furthermore,
pro
viding
communication
Digital
twin-based
performance
e
valuation
of
a
photo
voltaic
system:
A
r
eal-time
...
(Mustafa
F
adel)
Evaluation Warning : The document was created with Spire.PDF for Python.
2074
❒
ISSN:
2088-8694
infrastructure
to
ensure
that
the
netw
ork
can
transmit
data
in
real
time
wi
thout
signicant
delay
and
store
the
g
athered
data
in
an
appropriate
storage
mechanism
[5].
Model
de
v
elopment
and
simulation
is
the
ne
xt
phase
of
DT
de
v
elopment,
where
in
this
stage
the
DT
will
be
b
uilt
depending
on
type
select
ion
whether
it
is
a
ph
ysics-based
twin
that
relies
on
ph
ysical
equations
to
model
the
beha
vior
of
the
system,
data-dri
v
en
twin
that
relies
on
AI
and
data
analysis,
or
h
ybrid
twin
that
combines
ph
ysical
modeling
and
AI
to
inc
rease
accurac
y
[16].
At
this
stage,
model
v
alidation
and
calibration
are
e
xamined
by
comparing
DT
results
with
real
data
to
detect
discrepancies
and
correct
errors,
and
tune
the
model
based
on
actual
operating
data
to
impro
v
e
accurac
y
and
reliability
.
The
ne
xt
stage
is
system
inte
gration
and
control,
where
the
digital
twin
is
link
ed
to
the
actual
s
y
s
tems,
and
intelligent
control
mechanisms
are
acti
v
ated.
Inte
gration
with
systems
t
o
monitor
the
performance
of
the
PV
system
and
to
sho
w
information
and
analysis.
Additionally
,
with
the
use
of
predicti
v
e
analytics
for
f
ault
detection
in
adv
ance
by
de
v
eloping
deep
learning
systems
and
analyzing
patterns
for
impro
v
ed
ener
gy
ef
cienc
y
,
and
enabling
automatic
control
and
performance
optimization
t
hrough
dynamic
adjustment
of
solar
in
v
erter
parameters
based
on
actual
operating
condit
ions
[14].
The
stage
of
softw
are
de
v
elopment
is
the
nal
and
continuous
observ
ation,
wherein
DT
must
be
e
x
ecuted
and
observ
ed
so
that
the
goals
to
be
realized
are
achie
v
ed
by
e
x
ecuting
and
testing
the
system
in
real
l
ife
to
see
ho
w
the
digital
twin
beha
v
es
for
dif
ferent
operating
conditions
to
conrm
its
stability
,
and
comparing
the
predicted
results
with
real
data
from
the
real
system.
Furthermore,
continuously
updating
digital
models
as
ne
w
operating
data
becomes
a
v
ailable
and
tuning
softw
are
and
algorithms
to
impro
v
e
performance
based
on
changes
in
operating
conditions
by
relying
on
the
DT
to
predict
potential
f
ailures
and
tak
e
proacti
v
e
measures,
and
run
real-time
analytics
to
detect
an
y
decline
in
system
ef
cienc
y
[18].
D
i
g
i
t
al
d
at
a
ex
ch
an
g
e
Rea
l
-
t
i
me
d
at
a
A
ct
i
o
n
A
g
g
reg
at
e
Fee
d
b
ack
A
n
a
l
y
s
e
Co
n
t
ro
l
Sen
s
o
rs
D
at
a
A
n
a
l
y
t
i
cs
A
ct
u
at
o
r
Ph
y
s
i
cal
s
y
s
t
em
V
i
rt
u
al
s
y
s
t
em
Figure
1.
Digital
twin
system
architecture
D
i
g
i
t
al
T
w
i
n
T
ech
n
o
l
o
g
y
Dat
a
Sen
s
i
n
g
D
at
a
Visu
al
i
s
at
i
o
n
D
i
g
i
t
al
T
u
n
i
n
g
Cl
o
u
d
Co
mp
u
t
i
n
g
D
at
a
In
t
e
g
ra
t
i
o
n
D
at
a
Ana
l
y
s
i
s
A
ct
u
al
s
y
s
t
e
m
A
rt
i
fi
ci
al
In
t
e
l
l
i
g
en
ce
Figure
2.
Digital
twin
de
v
elopment
stages
3.
DIGIT
AL
TWIN
APPLICA
TIONS
IN
PV
SYSTEM
The
modern
PV
systems
utilise
the
DT
to
predict
and
optimise
their
performance.
Pro
viding
rea
l-time
monitoring
to
the
full
PV
system
can
maximise
its
performance
under
dif
ferent
en
vironmental
conditions.
Real-time
data
are
g
athered
from
the
PV
system
to
be
analysed
by
the
virtual
twin,
resulting
in
early
prediction
of
future
system
issues
[6].
Moreo
v
er
,
by
using
AI
tools,
the
DT
can
predict
possible
f
aults
in
the
PV
system,
whether
at
the
PV
side
le
v
el,
such
as
PV
modules
ef
cie
n
c
y
dropping
due
to
en
vironmental
condition
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
16,
No.
3,
September
2025:
2072–2081
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
2075
uctuations,
or
con
v
erter
le
v
el,
where
components
f
ail
(inductor
,
capacitor
,
or
switches).
Spotting
these
issues
can
increase
the
system’
s
reliability
by
reducing
system
f
ault
periods
and
enabling
predicti
v
e
maintenance
[19],
[20].
Furthermore,
increasing
the
PV
system
ef
cienc
y
can
be
achie
v
ed
by
inte
grating
such
technology
and
e
xperimenting
with
dif
ferent
scenarios,
such
as
PV
module
implementation
angles
to
optimise
irradiance
e
xposure,
the
shado
wing
ef
fect,
and
dif
ferent
en
vironmental
conditions,
pro
viding
the
best
settings
to
increase
system
ef
cienc
y
[21].
Also,
the
DT
can
be
used
in
smart
grids
to
distrib
ute
the
po
wer
ef
ciently
by
storing
it
or
redirecting
it
to
the
main
grid
when
needed.
Moreo
v
er
,
incorporating
DT
can
help
to
modify
the
system
design,
such
as
adding
ne
w
units
or
changing
storage
technologies
before
implementing
the
ph
ysical
system,
impacting
the
cost
and
time
[22].
4.
CHALLENGES
OF
DT
IN
PV
SYSTEM
In
spite
of
man
y
benets
being
link
ed
with
combining
DT
technology
with
PV
systems,
there
are
se
v
eral
issues
related
to
the
use
of
such
technologies.
Use
of
DT
entails
se
v
eral
technical
issues,
including
the
creation
of
a
precise
virtual
model
for
the
PV
system
that
requires
proper
understanding
of
dif
ferent
beha
viour
of
the
components
of
the
PV
system,
such
as
PV
modules,
in
v
erters,
batteries,
and
en
vironmental
conditions.
Modelling
such
a
system
requires
adv
anced
calculations,
including
the
dynamic
changes
in
irradiance,
ambient
temperature,
and
normal
ageing
in
PV
modules
[14].
In
a
dd
i
tion,
dif
ferent
designs
and
PV
system
performance
can
v
ary
from
one
location
to
another
making
it
challenging
to
de
v
elop
a
general
model
that
suits
all
applications.
Furthermore,
DT
relies
on
data
acquired
from
sensor
equipment,
ener
gy
transducers,
weather
databases,
and
IoT
analytics,
with
non-unied
standardisation
for
v
arious
system
equipment
mak
es
it
dif
cult
to
inte
grate
information
from
dif
ferent
m
ak
ers
[23].
Response
time
and
real-time
analysi
s
are
others
tough
ones,
in
which
the
DT
must
assess
data
and
handle
errors
in
real
time,
that
can
be
back
ed
by
po
werful
cloud
computing
serv
ers
and
rapid
connecti
vity
netw
orks
[16].
Latenc
y
in
data
transmission
may
af
fect
the
speed
of
decision-making
in
critical
situations,
such
as
sudden
f
ailures
or
lo
w
ener
gy
ef
cienc
y
.
In
addition,
DT
accurac
y
can
be
af
fected
by
uctuations
in
weather
f
actors,
where
DT
depends
on
the
a
v
ailability
of
accurate
climate
data,
and
some
areas
lack
of
accurate
data
or
are
af
fected
by
une
xpected
climate
changes,
such
as
dust
storms
or
sudden
irradiance
changes
that
may
af
fect
the
accurac
y
of
DT
forecasts
[5].
Furthermore,
operating
in
harsh
en
vironments
requires
re
gular
maintenance
and
continuous
replacement,
leading
to
increase
operating
and
maintenance
costs.
5.
PR
OPOSED
DT
SYSTEM
T
o
understand
the
DT
w
ork
and
test
it
in
a
real
e
n
vi
ronment,
it
is
essential
to
e
xamine
it
in
real
-w
orld
circumstances
with
actual
data.
The
full
PV
system
is
illustrated
in
Figure
3(a),
which
consists
of
multiple
PV
units,
each
connected
to
the
main
DC-b
us
through
DC
boost
con
v
erter
and
connected
to
a
central
in
v
erter
for
microgrid
applicat
ion.
The
e
xamination
will
tak
e
place
through
b
uilding
a
virtual
twin
that
simulates
the
performance
of
the
ph
ysical
system
via
sensing
and
analysing
real-w
orld
data,
where
a
data
acquisition
unit
logging
me
asurements
at
1-minute
interv
als
through
sensor
netw
ork
for
capturing
irradiance,
temperature,
v
oltage,
and
current.
The
model
uses
a
trained
feedforw
ard
neural
netw
ork
(FNN)
de
v
eloped
using
MA
TLAB’
s
Neural
Netw
ork
T
oolbox
with
10,080
training
samples
(1-week,
1-minute
resolution).
It
is
a
tw
o-hidden-layer
,
10
then
15
neuron
model,
and
uses
Le
v
enber
g-Marquardt
(trainl
m)
training
algorithm.
There
is
a
module
for
detecting
errors,
which
measures
the
dif
ference
between
the
prediction
and
actual
po
wer
.
When
the
dif
ference
e
xceeds
5W
,
a
rolling
a
v
erage
for
5
interv
als
is
computed
and
is
used
to
bia
s
the
prediction
result
adapti
v
ely
.
Resulting
in
a
mirrored
system
uses
a
feedback
loop
for
error
detection
and
correction,
used
to
o
pt
imise
the
o
v
erall
system
performance
and
minimise
future
maintenance.
Figure
3(b)
sho
ws
the
circuit
diagram
of
the
DC/DC
boost
con
v
erter
po
wered
by
a
PV
module
with
its
specications
illustrated
in
T
able
1.
Building
the
DT
will
be
based
on
modelling
the
basic
ph
ysical
beha
viour
of
the
PV
system
using
mathematical
equations
for
the
PV
cell
[
?
].
F
or
a
single-diode
PV
module,
the
current-v
oltage
relationship
for
a
PV
module
is
gi
v
en
by
(1).
I
pv
=
I
ph
−
I
d
exp
V
+
I
pv
R
s
nV
t
−
1
−
V
+
I
pv
R
s
R
sh
(1)
Where
I
pv
is
the
PV
output
current,
V
pv
is
output
v
oltage,
I
ph
is
the
photocurrent,
I
0
is
the
diode
re
v
erse
saturation
current,
R
s
is
the
series
resistance,
R
sh
is
the
shunt
resistance,
n
diode
ideality
f
actor
,
and
V
t
is
the
Digital
twin-based
performance
e
valuation
of
a
photo
voltaic
system:
A
r
eal-time
...
(Mustafa
F
adel)
Evaluation Warning : The document was created with Spire.PDF for Python.
2076
❒
ISSN:
2088-8694
thermal
v
oltage
gi
v
en
by
V
t
=
k
T
q
.
Where
k
is
Boltzmann
constant
(
1
.
380649
×
10
−
23
J/K),
T
is
the
PV
cell
temperature,
and
q
is
the
electron
char
ge
(
1
.
602176634
×
10
−
19
C).
G
ri
d
G
1
,T
1
+
_
+
_
D
C co
n
v
ert
er
PV
mo
d
u
l
e
G
2
,T
2
P
V
1
+
_
+
_
P
V
2
+
_
+
_
P
V
n
G
n
,T
n
D
C/
A
C
Co
n
v
er
t
er
D
C bus
D
i
g
i
t
al
T
w
i
n
Co
n
t
ro
l
A
n
a
l
y
s
e
&
Feed
b
ack
G
,T
I
pv
,V
pv
I,V
(
boost
)
Ph
y
s
i
cal
s
y
s
t
em
V
i
rt
u
al
t
w
i
n
(a)
C
in
D
b
o
o
s
t
I
D
I
c
in
I
pv
+
_
G, T
PV
PV
PV
+
_
I
L
I
b
o
o
s
t
L
b
o
o
s
t
C
b
o
o
s
t
I
c
o
S
b
o
o
s
t
(b)
Figure
3.
The
o
v
erall
DT
proposed
system:
(a)
PV
po
wer
system
and
(b)
po
wer
con
v
ersion
unit
T
able
1.
PV
panel
parameters
P
arameter
Symbol
V
alue
Unit
Rated
po
wer
P
pv
r
ated
250
W
V
oltage
at
max
po
wer
V
mp
30
V
Current
at
max
po
wer
I
mp
8.33
A
Open-circuit
v
oltage
V
oc
37
V
Short-circuit
current
I
sc
8.75
A
Number
of
cells
N
cells
60
-
T
emperature
coef
cient
of
po
wer
β
-0.45
%
/
◦
C
T
emperature
coef
cient
of
v
oltage
K
V
-0.34
V
/
◦
C
T
emperature
coef
cient
of
current
K
I
0.05
A
/
◦
C
The
photocurrent
(
I
ph
)
released
by
the
PV
cell
is
a
function
of
the
solar
irradiance
(
G
)
and
temperature
(
T
)
gi
v
en
as
(2)
[8].
I
ph
=
(
I
ph,S
T
C
+
K
I
(
T
−
T
S
T
C
))
G
G
S
T
C
(2)
Where
the
standard
test
conditions
(STC)
are
at
T
=
25
◦
C
and
G
=
1000
W/m
2
.
The
diode
re
v
erse
saturation
current
is
represented
as
(3)
[12].
I
0
=
I
0
,S
T
C
T
T
S
T
C
3
exp
E
g
nk
1
T
S
T
C
−
1
T
(3)
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
16,
No.
3,
September
2025:
2072–2081
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
2077
Both
open-circuit
v
oltage
(
V
oc
)
and
short-circuit
current
(
I
sc
)
are
sho
wn
as
(4)
[25].
V
oc
(
T
)
=
V
oc,S
T
C
+
K
V
(
T
−
T
S
T
C
)
(4)
I
sc
(
T
)
=
I
sc,S
T
C
+
K
I
(
T
−
T
S
T
C
)
(5)
Where
K
I
and
K
V
are
the
temperature
coef
cients
of
current
(
A/
◦
C)
and
v
oltage
(
V
/
◦
C)
respecti
v
ely
.
The
maximum
PV
po
wer
is
illustrated
as
(6).
P
max
(
T
)
=
P
max,S
T
C
(1
+
β
(
T
−
T
S
T
C
))
(6)
Where
β
is
the
temperature
coef
cient
of
po
wer
.
6.
SIMULA
TION
RESUL
TS
AND
DISCUSSION
The
proposed
system
will
ha
v
e
a
250
W
PV
module,
where
a
parallel
MA
TLAB/Simuli
nk
©
model
will
simul
ate
the
e
xpected
PV
output
using
single-di
od
e
mathematical
equat
ions
and
utilise
ML
for
po
wer
forecasting.
Using
irradiance
(p
yranometer)
and
temperature
(PT100)
sensors
to
tak
e
real-time
measurements
will
help
to
compute
PV
panel
performance
under
dif
ferent
en
vironmental
conditions.
The
operation
of
the
DT
w
as
v
alidated
using
real
and
synthetic
data
under
incremental
irradiance
(200
to
1000
W/m
2
)
and
temperature
(15
◦
C
to
35
◦
C)
v
ariations.
The
proposed
system
uses
adv
anced
visualisation
by
pro
viding
comprehensi
v
e
performance
plots
for
system
beha
viour
to
v
arying
en
vironmental
f
actors.
Figure
4(a)
illustrates
both
real
and
digital
output
po
wer
response
to
step-wise
irradiance
increase,
while
Figure
4(b),
represents
the
performance
under
ambient
temperature
increase,
where
the
output
po
wer
is
af
fected
ne
g
ati
v
ely
at
higher
temperature.
Furthermore,
Figure
4(c),
re
v
eal
s
the
ef
fects
on
PV
performance
under
v
arying
sunlight
and
temperature
conditions.
From
the
illustrated
results,
it
is
noticeable
that
the
DT
correlate
d
well
with
the
measurements,
presenting
a
small
error
f
actor
.
The
AI-enriched
DT
e
xhibited
high
accurac
y
and
lo
w
lag
in
transitions.
(a)
(b)
(c)
Figure
4.
PV
output
po
wer
beha
viour
under:
(a)
increasing
irradiance,
(b)
temperature
increase,
and
(c)
v
arying
irradiance
and
temperature.
Digital
twin-based
performance
e
valuation
of
a
photo
voltaic
system:
A
r
eal-time
...
(Mustafa
F
adel)
Evaluation Warning : The document was created with Spire.PDF for Python.
2078
❒
ISSN:
2088-8694
T
o
test
the
reliability
of
DT
and
ho
w
it
can
adapt
to
sensor
errors
and
en
vironmental
changes
without
manual
interv
ention,
a
self-de
gradation
and
correction
analysis
tak
es
place
by
continuously
comparing
the
predicted
po
wer
output
with
the
actual
measured
output.
The
DT
detects
periods
when
predictions
de
viate
signicantly
from
the
real
system
be
yond
a
set
threshold
v
alue
of
5
W
(
∼
2%)
of
the
maximum
PV
po
wer
(250
W),
and
this
de
viation
persists
for
three
consecuti
v
e
samples,
it
ags
an
anomal
y
.
T
o
correct
t
his,
the
system
emplo
ys
a
v
e-frame
rolling
a
v
erage
of
past
prediction
errors
and
adjusts
subsequent
predictions
by
an
adapti
v
e
bias.
This
light-weight
correction
scheme
greatly
impro
v
es
real-time
alignment
without
computational
o
v
erhead.
As
sho
wn
in
Figure
5,
39
errors
were
correctly
detected,
with
no
f
alse
positi
v
es.
Observing
the
system’
s
adaptability
to
these
errors.
The
quantitati
v
e
numerical
performance
of
the
DT
model
w
as
e
v
aluated
quantitati
v
ely
ag
ainst
three
common
measures
of
error:
root
m
ean
square
error
(RMSE),
mean
absolute
error
(MAE),
and
the
coef
cient
of
determination
(R
2
).
The
DT
achie
v
ed
an
RMSE
of
2.8
W
,
which
indicates
that,
on
a
v
erage,
the
simulated
po
wer
output
de
viated
from
the
measurement
by
2.8
w
atts,
with
greater
sensiti
vity
to
lar
ger
errors.
The
MAE
w
as
2.1
W
,
representing
a
lo
w
and
relati
v
ely
stable
mean
absolute
prediction
error
o
v
er
the
dataset.
The
model
also
had
an
R
2
of
0.984,
which
conrms
that
98.4
%
of
the
v
ariance
i
n
actual
PV
po
wer
output
w
as
well
represented
by
the
predictions
from
the
DT
.
These
results
conrm
the
high
accurac
y
and
reliability
of
the
DT
model
in
the
simulation
of
the
real-time
operating
beha
viours
of
the
photo
v
oltaic
system
under
v
arious
en
vironmental
conditions.
Figure
6
displays
ho
w
self-correction
mechanisms
adjust
these
de
viations
as
the
DT
corrections
align
closely
with
real
system
performance,
with
error
reduction
after
correction
reaching
95%.
T
o
ensure
rugged
performance
under
v
arying
conditions,
po
wer
loss
trends
o
v
er
time
are
highlighted
in
Figure
7,
where
it
represents
ho
w
much
po
wer
the
DT
model
underesti
mates
compared
to
the
ph
ysical
system
o
v
er
time,
and
the
maximum
po
wer
error
found
is
11.2
W
.
This
is
crucial
as
identifying
where
and
when
the
losses
occur
can
be
ef
cient
for
rening
the
DT’
s
prediction
model,
resulting
in
optimizing
the
o
v
erall
performance.
Figure
8
compares
the
dynamic
ef
cienc
y
of
the
ph
ysical
PV
system
and
digital
twin
in
a
period
of
50
seconds.
The
tw
o
curv
es
are
virtually
identical
with
a
dif
ference
of
less
than
0.1%,
conrming
the
reliability
of
the
DT
to
reproduce
the
dynamic
performance
of
the
system.
The
agreement
pro
v
es
the
reliability
of
the
DT
to
track
ef
cienc
y
and
its
applicability
for
diagnosti
cs
and
optimization.
Figure
9
illustrates
a
histogram
of
po
wer
prediction
errors
between
the
actual
PV
system
and
digital
twin,
from
4
W
to
11
W
.
Most
errors
are
concentrated
in
the
ranges
5–6
W
and
10–11
W
,
indicating
t
hat
while
DT
is
generally
accurate,
lar
ger
de
viations
could
occur
during
dynamic
transitions
or
sensor
f
aults.
These
v
ariations
are
within
the
real-time
prediction
tolerance,
and
the
spread
w
arrants
the
use
of
DT’
s
self-correction
f
acility
to
adapti
v
ely
reduce
such
discrepancies.
Figure
5.
V
irtual
twin
f
ault
detection
and
de
viation
Figure
6.
Po
wer
output
with
digital
twin
correction
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
16,
No.
3,
September
2025:
2072–2081
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
2079
Figure
7.
Mirrored
system
po
wer
loss
o
v
er
Figure
8.
Histogram
of
digital
twin
po
wer
prediction
Figure
9.
Histogram
of
digital
twin
po
wer
prediction
errors
7.
CONCLUSION
The
imple
mentation
of
DT
technology
on
rene
w
able
ener
gy
systems
is
a
tremendous
adv
ancem
ent
in
real-time
monitoring,
f
ault
diagnosis,
performance
impro
v
ement,
and
predicti
v
e
maintenance.
A
h
ybrid
DT
model
of
a
250
W
PV
system
w
as
proposed
in
this
study
by
the
fusion
of
ph
ysics-based
equations
and
AI-based
prediction.
The
system
w
as
v
ery
accurate
in
replicating
real-w
orld
PV
beha
viour
,
with
an
RMSE
of
2.8
W
and
a
coef
cient
of
determination
(R
2
)
of
0.984.
Reliability
w
as
also
enhanced
by
an
inherent
self-correcting
mechanism,
with
reductions
in
error
de
viations
of
up
to
95%
across
39
anomalies
that
were
detected.
Po
wer
loss
analysis
sho
wed
the
11.2
W
peak
prediction
error
in
the
dynamic
en
vironment
conditions,
re
v
ealing
the
DT’
s
v
ariability
diagnosis
and
compensation
capability
in
pract
ical
operation.
System
e
xperimental
v
erication
w
as
conducted
using
r
eal-time
data,
illustrati
ng
pragmatic
usefulness.
These
ndings
depict
the
potential
of
DTs
in
f
acilitating
smart,
autonomous
ener
gy
systems
that
react
dynamically
and
pa
v
e
the
w
ay
for
inte
gration
with
storage,
smart
grids,
and
edge
computing
platforms.
A
CKNO
WLEDGMENTS
The
rst
author
w
ould
lik
e
to
thank
the
Iraqi
go
v
ernment,
represented
by
the
Ministry
of
Higher
Education
and
Scientic
Research,
Mustansiriyah
Uni
v
ersity
(www
.uomustansiriyah.edu.iq),
for
their
support
in
this
w
ork.
Digital
twin-based
performance
e
valuation
of
a
photo
voltaic
system:
A
r
eal-time
...
(Mustafa
F
adel)
Evaluation Warning : The document was created with Spire.PDF for Python.
2080
❒
ISSN:
2088-8694
FUNDING
INFORMA
TION
Authors
state
no
funding
in
v
olv
ed.
A
UTHOR
CONTRIB
UTIONS
ST
A
TEMENT
(MAND
A
T
OR
Y)
This
journal
uses
the
Contrib
utor
Roles
T
axonomy
(CRediT)
to
recognize
indi
vidual
author
contrib
utions,
reduce
authorship
disputes,
and
f
acilitate
collaboration.
Name
of
A
uthor
C
M
So
V
a
F
o
I
R
D
O
E
V
i
Su
P
Fu
Mustaf
a
F
adel
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
F
ajer
M.
Alelaj
✓
✓
✓
✓
✓
✓
✓
C
:
C
onceptualization
I
:
I
n
v
estig
ation
V
i
:
V
i
sualization
M
:
M
ethodology
R
:
R
esources
Su
:
Su
pervision
So
:
So
ftw
are
D
:
D
ata
Curation
P
:
P
roject
Administration
V
a
:
V
a
lidation
O
:
Writing
-
O
riginal
Draft
Fu
:
Fu
nding
Acquisition
F
o
:
F
o
rmal
Analysis
E
:
Writing
-
Re
vie
w
&
E
diting
CONFLICT
OF
INTEREST
ST
A
TEMENT
Authors
state
no
conict
of
interest.
D
A
T
A
A
V
AILABILITY
Deri
v
ed
data
support
ing
the
ndings
of
this
study
are
a
v
ailable
from
the
corresponding
author
,
[MF],
on
request.
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Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
2081
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BIOGRAPHIES
OF
A
UTHORS
Mustafa
F
adel
recei
v
ed
his
B.Sc.
de
gree
in
Electri
cal
Engineering
from
Mustansiriyah
Uni
v
ersity
,
Baghdad,
Iraq,
in
2010,
and
his
M.Sc.
de
gree
in
Electrical
Engineering
from
the
same
uni
v
ersity
in
2016.
He
is
currently
pursuing
a
Ph.D.
at
Ne
wca
stle
Uni
v
ersity
,
United
Kingdom.
From
No
v
ember
2016
to
May
2019,
he
serv
ed
as
an
Assistant
Lecturer
in
the
Electrical
Engineering
Department
at
Mustansiriyah
Uni
v
ersity
,
where
he
w
as
later
promoted
to
Lecturer
in
October
2019.
His
r
esearch
interests
focus
on
the
design
and
control
of
po
wer
elect
ronic
con
v
erters
f
or
rene
w
able
ener
gy
syste
ms,
el
ectric
v
ehicles,
battery
c
har
ging
systems,
and
wirele
ss
po
wer
transfer
applications.
Mustaf
a
w
as
the
recipient
of
the
First
Prize
P
aper
A
w
ard
at
the
IEEE
International
Symposium
on
Electrical,
Ele
ctronics,
and
Information
Engineering,
Leicester
,
United
Kingdom,
in
2024.
He
can
be
contacted
at
email:
mustaf
a
1988abbas@uomustansiriyah.edu.iq.
F
ajer
M.
Alelaj
w
as
a
w
arded
a
Bachelor’
s
de
gree
in
Electrical
Engineering
from
K
uw
ait
Uni
v
ersity
in
2014,
earning
a
place
on
the
honor
list
twice.
She
obtained
her
MSc
in
Electrical
Po
wer
from
Ne
wcastle
Uni
v
ersity
,
United
Kingdom,
in
2020,
graduating
with
First
Class
Honours.
She
has
recentl
y
completed
her
Ph.D.
in
Hybrid
Distrib
ution
T
ransformers
at
Ne
wcastle
Uni
v
ersity
.
She
w
as
also
the
recipient
of
the
M.Sc.
Prize
for
the
top-rank
ed
postgraduate
taught
student
in
Electrical
&
Electronic
Engineering
for
the
academic
year
2019/2020.
She
can
be
contacted
at
email:
felaj@kisr
.edu.kw
.
Digital
twin-based
performance
e
valuation
of
a
photo
voltaic
system:
A
r
eal-time
...
(Mustafa
F
adel)
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