Inter
national
J
our
nal
of
P
o
wer
Electr
onics
and
Dri
v
e
Systems
(IJPEDS)
V
ol.
9,
No.
1,
March
2018,
pp.
357
–
364
ISSN:
2088-8694
357
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Corr
elation
between
Battery
V
oltage
under
Loaded
Condition
and
Estimated
State
of
Char
ge
at
V
alv
e-Regulated
Lead
Acid
Battery
on
Dischar
ge
Condition
using
Open
Cir
cuit
V
oltage
Method
Ahmad
Qurthobi
,
Anggita
Bayu
Krisna
P
amb
udi
,
Dudi
Darmawan
,
and
Reza
F
auzi
Iskandar
Department
of
Engineering
Ph
ysics,
School
of
Electrical
Engineering,
T
elk
om
Uni
v
ersity
,
Indonesia
Article
Inf
o
Article
history:
Recei
v
ed
No
v
ember
24,
2017
Re
vised
January
23,
2018
Accepted
February
18,
2018
K
eyw
ord:
Battery
State
of
Char
ge
Open
Circuit
V
oltage
ABSTRA
CT
One
of
the
common
methods
that
de
v
eloped
to
predict
sta
te
of
char
ge
is
open
circuit
v
oltage
(OCV)
method.
The
probl
em
which
commonly
occurs
is
to
find
the
correc-
tion
parameter
between
open
circuit
v
oltage
and
loaded
v
oltage
of
the
battery
.
In
this
research,
correlation
between
state
of
char
ge
measurement
at
loaded
condition
of
a
P
anasonic
LC-V
A1212N
A1,
which
is
a
v
alv
e-re
gulated
lead
acid
(VRLA)
battery
,
and
open
circuit
v
oltage
had
been
analyzed.
Based
on
the
results
of
research,
cor
-
relation
between
battery’
s
measured
v
oltage
under
loaded
condition
and
open
circuit
v
oltage
could
be
approached
by
tw
o
linearization
area.
It
caus
ed
by
K
v
’
s
v
alues
tend
to
increase
when
measured
v
oltage
under
loaded
condition
V
M
<
11
:
64
v
olt.
Ho
w-
e
v
er
,
K
v
v
alues
w
ould
be
relati
v
ely
sta
ble
for
e
v
ery
V
M
11
:
64
v
olts.
Therefore,
estimated
state
of
char
ge
v
alue,
in
respect
to
loaded
battery
v
oltage,
w
ould
increase
slo
wer
on
V
M
<
11
:
64
v
olts
and
f
aster
on
other
range.
Copyright
c
2018
Insitute
of
Advanced
Engineeering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Ahmad
Qurthobi
Department
of
Engineering
Ph
ysics,
School
of
Electrical
Engineering,
T
elk
om
Uni
v
ersity
Jalan
T
elek
omunikasi
No
1
T
erusan
Buah
Batu
+62-813-20262968
qurthobi@telk
omuni
v
ersity
.ac.id
1.
INTR
ODUCTION
Lead
acid
battery
is
a
type
of
dry
elements.
Its
commonly
used
as
ener
gy
backup
storage
for
r
emote
communities,
telecommunication
systems,
or
electric
v
ehicles[1]-[4].
The
problems
which
commonly
occur
on
lead
acid
type
batteries
are
o
v
erchar
ge
and
o
v
erdischar
ge.
Both
condition
create
temperature
changes
and
ph
ysical
deformation
on
the
battery
which
af
fect
on
its
performances.
Therefore,
it
needs
to
analyzed
battery’
s
state
of
char
ge
(SoC)[5]-[10].
State
of
char
ge
(SoC)
is
a
ratio
between
a
v
ailable
and
maximum
electrical
char
ge
that
stored
in
t
he
battery[2],[11].
SoC
is
a
non-dimentional
unit
and
it
could
be
e
xpressed
in
percent
or
v
alue
between
0
and
1.
SoC
is
an
important
parameter
which
not
only
to
a
v
oid
harmful
condit
ion,
such
as
o
v
erchar
ge
and
o
v
erdis-
char
ge,
b
ut
also
to
e
xpand
the
battery
lifetime.
One
of
the
methods
used
to
estimate
state-of-char
ge
is
open
circuit
v
oltage
(OCV).
Statistically
,
correlation
between
state
of
char
ge
and
open
circuit
v
oltage
could
be
repre-
sented
as
an
linear
equation.
Ho
we
v
er
,
as
loads
attached
to
the
battery
,
the
loading
ef
fect
w
ould
be
occured.
It
w
ould
create
g
ap
between
measured
v
oltage
and
open
c
ircuit
v
oltage[12].
Therefore,
correlation
between
open
circuit
v
oltage
and
loaded
battery
v
oltage
which
culminated
on
their
correlation
with
state
of
char
ge
should
be
determined.
J
ournal
Homepage:
http://iaescor
e
.com/journals/inde
x.php/IJPEDS
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
,
DOI:
10.11591/ijpeds.v9n1.pp357-364
Evaluation Warning : The document was created with Spire.PDF for Python.
358
ISSN:
2088-8694
Figure
1.
An
e
xample
of
typical
correlation
between
state
of
char
ge
and
open
circuit
v
oltage[13]
In
pre
vious
research,
correlation
between
both
v
ariables
in
a
Y
uasa
SWL2500
could
be
written
as
a
constant
v
alue
for
se
v
eral
e
xamination
point[1].
Therefore,
in
this
research,
correlation
between
loaded
battery
v
oltage
on
dischar
ge
condition
and
open
circuit
v
oltage
had
been
analyzed
on
a
P
anasonic
LC-V
A1212N
A1,
which
is
a
v
alv
e-re
gulated
lead
acid
(VRLA)
battery
.
This
research
observ
es
the
changes
of
rest
period
param-
eter
on
the
battery
based
on
its
loaded
v
oltage
at
se
v
eral
points
which
leads
to
produce
a
preci
se
estimation
of
state
of
char
ge.
2.
RESEARCH
METHOD
2.1.
State
of
Char
ge
and
Open
Cir
cuit
V
oltage
As
mentioned
in
section
1.,
state
of
char
ge
or
SoC
is
a
non-dimentional
unit
which
represents
ratio
between
a
v
ailable
and
maximum
char
ge
stored
in
a
battery
.
Hence,
SoC
is
proportional
to
char
ge
residues
inside
a
battery
and
it
could
be
represented
as
equation
(1),
where
q
t
and
q
max
represent,
current
and
maximum
char
ges
v
alues
inside
battery
,
respecti
v
ely
.
SOC
%
=
q
t
q
max
100
(1)
On
the
real
condition,
neither
zero
point
of
a
battery
equal
to
zero
char
ge
(
q
0
6
=
0
)
nor
its
maximum
v
alue
equal
to
peak
char
ge
(
q
max
=
q
peak
).
The
minimum
and
maximum
char
ges
v
alues
inside
the
battery
are
frequently
mentioned
by
the
manuf
acturers
o
n
battery’
s
datasheet
to
k
eep
its
performances.
Hence,
equation
(1)
should
be
re
written
as
equation
(2),
where
q
min
represents
minimum
char
ges
v
alue.
SOC
%
=
q
t
q
min
q
max
q
min
100
(2)
There
are
some
methods
de
v
eloped
for
SoC
estimation.
One
of
those
esti
mation
methods
is
open
circuit
v
oltage
(OCV)[1].
OCV
method
has
been
de
v
eloped
based
on
an
assumption
that
a
battery
is
equal
to
a
capacitor
and
the
amount
of
char
ges
(
q
)
inside
a
capacitor
is
linearly
proportional
to
its
output
v
oltage
(
V
t
)(see
equation
(3)).
V
t
=
q
t
C
(3)
Statistically
,
if
it
is
assumed
that
typical
correlation
between
SoC
and
OCV
is
sho
wn
by
figure
1,
it
could
be
approached
by
a
linear
formula
such
as
equation
(4)[13],
where
V
min
,
1
,
and
2
are,
respecti
v
ely
,
battery’
s
minimum
v
oltage
(recommended
by
manuf
acturer),
a
multiplier
constant,
and
a
correction
f
actor
.
SOC
%
=
1
(
V
t
V
min
)
+
2
(4)
IJPEDS
V
ol.
9,
No.
1,
March
2018:
357
–
364
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
359
Figure
2.
Lead
acid
equi
v
alent
netw
ork
for
both
dischar
ge
and
char
ge[12]
Figure
3.
T
ypical
v
oltage
and
current
profile
for
a
constant
current
dischar
ge[12]
2.2.
Battery
Modelling
and
Rest
P
eriod
Equation
(3)
is
only
v
alid
in
specific
conditions,
such
as
when
all
of
its
loads
are
disconnected
from
the
battery
.
Ho
we
v
er
,
remo
ving
loads
from
the
battery
for
v
oltages
e
xamination
creates
a
non-real
time
mea-
surement.
Barsali
and
Ceraolo(2002)
define
a
lead
acid
battery’
s
dynamic
model
to
in
v
estig
ate
its
dischar
ging
dynamic
beha
vior[12].
Lead
acid
equi
v
alent
netw
ork
for
char
ge
and
dischar
ge
are
sho
wn
by
figure
(2).
Further
-
more,
the
y
also
represent
typical
v
oltage
and
current
profile
for
constant
current
dischar
ge
as
sho
wn
on
figure
3.
Figure
3
sho
ws
that
there
is
e
xist
a
transition
time
required
by
the
battery
to
sho
w
it
open
cir
cuit
v
oltage
v
alue
after
loads
are
remo
v
ed.
This
transition
time
kno
wn
as
rest
period
[1],[2],[12].
Hence,
OCV
(
V
t
oc
)
of
a
battery
could
be
written
as
equation
(5)[1],
where
V
M
is
measured
v
oltage
when
loads
a
re
attached
to
the
battery
and
K
v
is
a
parameter
deri
v
ed
from
V
t
oc
V
M
after
the
battery
is
rested.
V
t
oc
=
V
M
K
v
(5)
2.3.
Obser
ving
K
v
As
mentioned
in
subsection
2.2.,
K
v
is
a
parameter
deri
v
ed
from
dif
ferences
between
open
circuit
v
oltage
and
loaded
v
oltage.
It
v
alues
could
be
v
aries
on
e
v
ery
point.
Therefore,
it
needs
to
observ
e
K
v
v
alues
at
se
v
eral
point
to
determine
it
correlation
with
battery’
s
v
oltage.
T
o
determine
the
v
alue
of
K
v
at
some
specified
point,
a
testing
had
beed
done
with
this
follo
wing
steps:
1.
As
pre-conditioning
process,
a
VRLA
battery
(P
anasonic
LC-V
A1212N
A1)
has
being
char
ged
until
it
reach
its
maximum
v
oltage
v
alue
recommended
by
its
manuf
acturer
,
in
this
case
is
13
v
olt[14](Figure
4(a)).
2.
Connect
the
battery
with
a
10
w
att
load
and
measure
its
terminal
v
oltage
v(Figure
4(b)).
Corr
elation
between
Loaded
Battery
V
olta
g
e
and
Estimated
SoC
at
VRLA
Battery
...
(Qurthobi)
Evaluation Warning : The document was created with Spire.PDF for Python.
360
ISSN:
2088-8694
Figure
4.
Battery
char
ging
and
dischar
ging
process
Figure
5.
The
changes
of
battery
v
oltage
measurement
for
150
minutes
3.
As
soon
when
terminal
v
oltage
reach
first
point,
remo
v
e
load
from
battery
and
l
ea
v
e
it
rest
for
150
minutes.
4.
Monitor
the
change
in
battery
v
oltage
v
alues,
starting
from
the
load
released
until
the
rest
period
ends.
5.
Repeat
step
(2)
to
(4)
for
another
monitoring
point.
3.
RESUL
T
AND
AN
AL
YSIS
Figure
5
sho
ws
the
change
of
e
xperimental
bat
tery’
s
v
oltage
v
alue
when
it
rested
for
150
minutes.
This
figure
sho
ws
that
loading
ef
fects
which
occurs
on
the
battery
results
the
measured
v
oltage
at
loaded
con-
dition
is
lo
wer
than
its
open
circuit
v
oltage.
The
v
alues
are
v
aries
in
range
0.22
-
0.74
v
olt.
Correlation
between
measured
v
oltage
under
loaded
condition
V
M
and
open
circuit
v
oltage
V
oc
after
rest
period
on
the
battery
are
sho
wn
in
figure
6.
It
informs
the
gradient
of
correlation
curv
e
of
V
M
and
V
oc
for
V
M
11
:
64
v
olt
is
relati
v
ely
constant
with
@
V
oc
@
V
M
1
with
small
zero
of
fset
addition.
Ho
we
v
er
,
for
IJPEDS
V
ol.
9,
No.
1,
March
2018:
357
–
364
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
361
Figure
6.
Correlation
between
measured
v
oltage
V
M
under
loaded
condition
and
open
circuit
v
oltage
V
oc
after
150
minutes
of
rest
period
Figure
7.
Correlation
between
measured
v
oltage
V
M
under
loaded
condition
and
correction
parameter
K
v
Figure
8.
Measured
v
oltage
under
loaded
condition
and
estimated
open
circuit
v
oltage
in
respect
to
time
Corr
elation
between
Loaded
Battery
V
olta
g
e
and
Estimated
SoC
at
VRLA
Battery
...
(Qurthobi)
Evaluation Warning : The document was created with Spire.PDF for Python.
362
ISSN:
2088-8694
Figure
9.
Correlation
between
V
M
and
SOC
p
(%)
V
M
<
11
:
64
,
correlation
between
both
v
ariabl
e
relati
v
ely
fluctuati
v
e
and
could
be
approached
by
equation
(6).
V
oc
=
0
:
50
V
M
+
6
:
02
(6)
This
condition
yeilds
correlation
between
K
v
and
V
M
had
ne
g
ati
v
e
gradient
for
e
v
ery
V
M
<
11
:
64
v
olts.
In
the
other
hand,
it
is
relati
v
ely
stable
with
a
v
erage
K
v
=
0
:
23
v
olt
for
V
M
11
:
64
v
olts
(see
figure
7).
Hence,
e
v
olution
o
v
K
v
could
be
de
vided
into
tw
o
linearization
condition
and
could
be
written
as
equation(7).
K
v
=
0
:
49
V
M
+
5
:
90;
for
V
M
<
11
:
64
0
:
23;
for
others
(7)
Ho
we
v
er
,
the
result
sho
ws
dif
ferent
outcome
with
another
research
with
another
VRLA
battery
,
where
K
v
v
alues
are
almost
constant
for
e
v
ery
inspection
points(80%,
60%,
40%,
and
20%
of
SoC)
on
Y
uasa
SWL2500
battery
with
240
minutes
of
rest
period[1].
Based
on
equation
(5)
and
(7),
correlation
between
measured
loaded
v
oltage
and
estimated
open
ci
rcuit
v
oltage
v
alue
in
respect
to
time
could
be
dra
wn
as
figure
8.
As
results
of
implementation
of
K
v
v
alues,
the
g
ap
between
both
curv
es
w
ould
increase
as
soon
as
measured
v
oltage
under
loaded
condition
is
less
than
11.64
v
olts.
Therefore,
correlation
between
state
of
char
ge
and
V
M
could
be
sho
wn
as
figure
9
and
could
be
written
as
equation
(8).
SoC
%
=
20
:
44
V
M
184
:
64;
for
V
M
<
11
:
64
40
V
M
+
410
:
8;
for
others
(8)
As
v
alidation
process,
testing
on
subsection
2.3.
had
been
repeated
with
addition
of
ne
w
e
xamination
point
at
V
M
=
12
:
24
v
olts.
Figure
10
sho
ws
correlation
between
estimated
open
circuit
v
oltage
V
toc
p
and
actual
v
oltage
V
real
.
This
figure
sho
ws
correlation
between
both
v
ariables
could
be
approached
with
a
linear
formula
and
could
be
written
as
equation
(9).
It
also
informs
the
a
v
erage
absolute
error
between
V
toc
p
and
V
real
is
0.02
v
olt.
V
real
=
1
:
02
V
toc
p
+
0
:
28
(9)
4.
CONCLUSION
Based
on
the
results
of
research,
correlation
between
battery’
s
measured
v
oltage
under
loaded
con-
dition
and
open
circuit
v
oltage
could
be
approached
by
tw
o
linearization
area.
It
caused
by
K
v
’
s
v
alues
tend
to
increase
when
measured
v
oltage
V
M
<
11
:
64
v
olt
and
correlation
between
both
v
ariables
could
be
written
as
0
:
49
V
M
+
5
:
90
v
olt.
Ho
we
v
er
,
K
v
v
alues
w
ould
be
relati
v
ely
stable
on
0.23
v
olt
for
e
v
ery
V
M
11
:
64
v
olts.
Therefore,
in
respect
to
loaded
battery
v
oltage,
estimated
state
of
char
ge
v
alue
w
ould
increase
slo
wer
on
V
M
<
11
:
64
v
olts
and
f
aster
on
other
range.
It
sho
ws
dif
ferent
outcome
with
another
research
with
another
VRLA
battery
,
where
K
v
v
alues
are
almost
constant
for
four
inspection
points(80%,
60%,
40%,
and
20%
of
SoC)
on
Y
uasa
SWL2500
battery
with
240
minutes
of
rest
period.
IJPEDS
V
ol.
9,
No.
1,
March
2018:
357
–
364
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
363
Figure
10.
Correlation
between
V
toc
p
and
V
real
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...
(Qurthobi)
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364
ISSN:
2088-8694
BIOGRAPHIES
OF
A
UTHORS
Ahmad
Qurthobi
is
a
lecturer
and
researcher
at
Department
of
Engineeering
Ph
ysics,
School
of
Electrical
Engineeering,
T
elk
om
Uni
v
ersity
(2013-present).
He
obtained
Bachelor
De
gree
in
T
elecommunication
Engineering
from
STT
T
elk
om
(Indonesia)
in
2007
and
Master
De
gree
in
in-
strumentation
and
Control
from
Institut
T
eknologi
Bandung
(Indonesia)
at
2011.
His
researches
are
in
fields
of
electric
po
wer
,
instrumentation,
control
system,
rene
w
able
ener
gy
,
and
po
wer
electronics.
He
is
af
filiated
with
PII
as
member
.
F
or
further
info
on
his
homepage:
http://qurthobi.staf
f.telk
omuni
v
ersity
.ac.id/
Anggita
Bayu
Kr
esna
P
amb
udi
is
an
engineer
of
N
ational
Electric
Compan
y
of
Indonesia.
He
obtained
Bachelor
De
gree
in
Engineering
Ph
ysics
from
T
elk
om
Uni
v
ersity
(Indonesia)
at
2016.
His
researches
are
in
fields
of
instrumentation,
and
measurement.
Beside
his
acti
vity
as
engineer
,
he
also
runs
a
start
up
design
compan
y
called
Dodlezig.
F
or
further
info
on
his
homepage:
http://www
.anggitabay
.com/
Dudi
Darmawan
is
a
lecturer
and
researcher
at
Department
of
Engineeering
Ph
ysi
cs,
School
of
Electrical
Engineeering,
T
elk
om
Uni
v
ersity
(1999-present).
He
obtained
Bachelor
De
gree
in
Ph
ysics
in
1998,
Master
De
gree
in
instrumentation
and
Control
at
2004,
and
Doc
toral
De
gree
in
Engineeering
Ph
ysics
at
2015
from
Institut
T
eknologi
Bandung(Indonesia).
His
researches
are
in
fields
of
non-destructi
v
e
testing,
instrumentation,
tomograph
y
,
and
electro-
magnetics.
F
or
further
info
on
his
homepage:
http://dudiddw
.staf
f.telk
omuni
v
ersity
.ac.id/
Reza
F
auzi
Iskandar
is
a
lecturer
and
researcher
at
Department
of
Engineeering
Ph
ysics,
School
of
Electrical
Engineeering,
T
elk
om
Uni
v
ersity
(2012-present).
He
obtained
Bachelor
De
gree
in
Ph
ysics
Education
from
Uni
v
ersitas
Pendidikan
Indonesia
at
2003,
and
Master
De
gree
in
instru-
mentation
and
Control
from
Institut
T
eknologi
Bandung
(Indonesia)
at
2011.
His
researches
are
in
fields
of
instrumentation,
control
system,
po
wer
electronics,
and
rene
w
able
ener
gy
.
F
or
further
info
on
his
homepage:
http://rezaf
auzii.staf
f.telk
omuni
v
ersity
.ac.id/
IJPEDS
V
ol.
9,
No.
1,
March
2018:
357
–
364
Evaluation Warning : The document was created with Spire.PDF for Python.