A battery model for constant-power discharge including rate effects

Abstract

A battery discharge model is developed to predict terminal voltage and current for a constant-power discharge. The model accounts for the impact of discharge rate on the effective capacity. The model utilizes empirically-determined coefficients, easily obtainable from product data sheets. The model is intended to provide estimates for initial predictions and system sizing; total computational and engineering costs to develop the inputs and obtain results are low. Comparison of model predictions with experimental data in the development and testing of alkaline primary cell battery packs shows good agreement.

Full text

NUWC-NPT
Technical
Memo
12-052
Generic
Battery
Rate-Effect
Model
Mark
E.
Fuller
Autonomous
and
Defensive
Systems
Department
August
2012
MAX/SEA
WARFARE
CENTERS
NEWPORT
Naval
Undersea
Warfare
Center
Division
Newport,
Rhode
Island
Approved
for
public
release;
distribution
is
unlimited.
5O\2.O
c
\\
c
\035

ABSTRACT
This
document
presents
a
model
for
estimating
battery
performance
as
a
function
of
the
power
level
demanded.
General
values
or
data
specific
to
a
particular
battery
may
be
used
to
generate
the
required
parameters
for
the
model.
All
required
information
may
be
obtained
from
a
typical
vendor
data
sheet
that
includes
constant-current
discharge
profiles.
The
total
model
is
constructed
of
three
separate
components:
(1)
a
model
of
cell
open-circuit
voltage
as
a
function
of
battery
state-of-charge,
(2)
capacity
de-rating
for
constant-current
discharge
per
Peukerf
s
equation,
and
(3)
application
of
Peukerfs
equation
to
variable
current
discharge.
ADMINISTRATIVE
INFORMATION
This
document
was
prepared
under
NUWC
Division
Newport
Project
No.
03307,
"UUV
Energy
Sizing
Model,"
principal
investigator
Benjamin
Martin
(Code
8231).
The
sponsoring
activity
is
the
Office
of
Naval
Research
(ONR-333).

TABLE
OF
CONTENTS
Section
Page
1
INTRODUCTION
1
2
EFFECT
OF
DISCHARGE
CURRENT
ON
EFFECTIVE
CAPACITY
2
2.1
Peukert's
Equation
2
2.2
Application
of
Peukerfs
Equation
2
3
OPEN-CIRCUIT
POTENTIAL
AS
A
FUNCTION
OF
STATE-OF-CHARGE
3
4
A
CONSTANT-POWER,
CONSTANT-TEMPERATURE
DISCHARGE
MODEL
4
4.1
Ordinary
Differential
Equation
for
Capacity
4
4.2
Application
to
Sizing
Estimations
5
REFERENCES
6
APPENDIX
A—DERIVATION
OF
EQUATION
(5)
A
-l
APPENDIX
B—DERIVATION
OF
EQUATION
(7)
B
-l
APPENDIX
C—APPLICATION
OF
MODEL
TO
AN
ACTUAL
BATTERY
C
-
l
LIST
OF
ILLUSTRATIONS
Figure
Page
1
Identification
of
Discharge
Profile
Characteristic
Values
C-l
Saft
VL
52
E
Modeled
Performance
With
and
Without
Manufacturer
Limits
C
-3
LIST
OF
TABLES
Table
Page
1
Battery
Model
Input
Parameters
1
2
Additional
Variables
1
C-l
Saft
VL
52
E
Model
Parameters
C
-
l
C-2
Saft
VL
52
E
Discharge
Rate
and
Capacity
Calculated
forpe
=
1.035
C
-
2
i
(ii
blank)

1.
INTRODUCTION
As
an
alternative
to
the
now-common
method
of
battery
system
modeling
by
estimating
overall
values
of
specific
energy
and
specific
power
on
gravimetric
and
volumetric
bases,
independent
of
the
rate
of
discharge,
the
model
presented
here
is
recommended
for
estimating
battery
performance
as
a
function
of
the
power
level
demanded.
General
values
or
data
specific
to
a
particular
battery
may
be
used
to
generate
the
required
parameters
for
the
model,
shown
in
table
1.
All
required
information
may
be
obtained
from
a
typical
vendor
data
sheet
that
includes
constant-current
discharge
profiles.
Additionally,
development
of
the
model
requires
the
variables
in
table
2.
The
total
model
is
constructed
of
three
separate
components:
•
a
model
of
cell
open-circuit
voltage
as
a
function
of
battery
state-of-charge,'
•
capacity
de-rating
for
constant-current
discharge
per
Peukert's
equation^
and
•
application
of
Peukert's
equation
to
variable
current
discharge.
3
Table
L
Battery
Model
Input
Parameters
Symbol
Battery
Parameter
Eh
in.
Fully-charged
potential
EEXP
Potential
at
end
of
exponential
zone
ESOM
Potential
at
end
of
nominal
zone
ECUT
Cutoff
potential
/#
Specified/measured
discharge
current
m
Mass
\pe
Peukert
effect
exponent
QEXP
Capacity
discharged
at
end
of
exponential
zone
QsOM
Capacity
discharged
at
end
of
nominal
zone
Qcur
Capacity
discharged
at
cutoff
\Rc
Internal
resistance
V
Volume
Table
2.
Additional
Variables
Symbol
Variable
C
Capacity
discharged
Eoc
Open-circuit
potential
ED
Energy
density
(volumetric
basis)
ES
Specific
energy
(gravimetric
basis)
I
Actual
discharge
current
P
Discharge
power
t
Time
r
Total
discharge
time

2.
EFFECT
OF
DISCHARGE
CURRENT
ON
EFFECTIVE
CAPACITY
2.1
PEUKERT'S
EQUATION
In
his
study
of
lead-acid
batteries,
Peukert
2
observed
a
decrease
in
the
available
capacity
of
the
battery
with
increasing
discharge
current,
which
could
be
modeled
as
I
p
e
-t
=
constant,
where
/
is
the
discharge
current,
/
is
the
time
of
discharge,
and
pe
is
a
coefficient
("Peukert
effect
exponent")
greater
than
one.
Rearranging
Peukert's
law
in
terms
of
capacity
C,
Peukert's
equation
may
be
written
to
express
the
capacity
(C|)
for
a
particular
discharge
current
(I\)
as
a
function
of
a
known
current
and
capacity
pairing
(such
as
the
nominal
values
frequently
reported
for
commercial
batteries,
designated
here
as
/o
and
Co):
C
1=
C
0
.
g
p.
(1)
The
value
of
pe
is
empirically
determined
from
experimental
discharge
data.
2.2
APPLICATION
OF
PEUKERT'S
EQUATION
To
model
systems
where
the
requirement
is
a
constant
delivered
power,
not
a
constant
current
discharge,
equation
(1)
must
be
written
in
such
a
way
as
to
allow
computation
of
C\
from
a
variable
7|.
If
time
t
is
allowed
to
be
an
independent
variable
against
which
the
various
battery
parameters
may
be
tracked
(i.e.,
the
battery
capacity
C\
is
discharged
at
a
rate
of
I\
in
time
t\
)
,
then
£i
=
(!o\
/o\
p
e
~
1
_l
l
h
_
I,
'o'to
'Effective
11
v
p
e-l
^Effective
=
'l
'
\J~)
>
(2)
^•Effective
=
Y\}Effective
*
At)
.
(3)
The
total
capacity
that
may
be
discharged,
per
equation
(3),
may
be
set
equal
to
the
nominal
capacity
of
the
battery
for
determination
of
the
available
capacity
during
a
variable-current
discharge.
3

3.
OPEN-CIRCUIT
POTENTIAL
AS
A
FUNCTION
OF
STATE-OF-CHARGE
A
simple
model
tor
determining
battery
open-circuit
potential
from
the
state
of
charge
was
developed
in
Tremblay
et
al.
1
This
model
is
meant
to
simulate
a
battery
as
it
is
charged
and
discharged;
i.e.,
it
is
applicable
to
secondary
battery
systems.
The
model
specifically
omits
voltage
recovery
(an
increase
in
voltage
independent
of
the
state-of-chargc)
and
assumes
the
following:
•
constant
internal
resistance,
•
discharge
characteristics
of
the
battery
represent
the
reverse
of
charge
(reversible
process),
•
no
effect
of
current
on
capacity
(no
Peukert
effect).
•
no
temperature
effects,
•
no
self-discharge,
•
no
memory
effects.
The
model,
as
presented
by
Tremblay
et
al.,
is
Eoc
=
E
0
-
(£^)
+
(A
■
exp(-ß
•
C))
,
(4)
where
A
=
Eptu
i
—
E
B
=
FULL
C
E
XP
>
3
QEXP
'
u
_
(EFULL
-
ENOM
+
A(exp(-B
■
QNQM)
-
i))
•
(QCUT
-
QNOM)
ft
—
"
QNOM
£o
=
EFULL
+
K
+
(Re
'
W
"
A
.
The
model
parameters
are
found
from
published
manufacturer
data
and
by
inspection
of
constant-current
discharge
curves.
Determination
of
the
several
values
of
£
and
Q
from
a
discharge
curve
may
be
made
according
to
figure
1.
EFVLL
(and
QFULU
which
is
by
definition
zero)
would
be
read
from
the
point
labeled
"Fully
charged
voltage."
Similarly.
EEXP
Böd
QEXP
would
be
read
from
"End
of
exponential
zone,"
EHOM
an<
J
QNOM
would
be
read
from
"End
of
nominal
zone,"
and
Ecui
and
Qcui
would
be
read
from
the
end
of
the
curve.
In
the
case
of
an
abscissa
marked
in
time
and
not
capacity,
as
in
figure
I,
determination
of
the
values
of
Q
is
the
product
of
the
value
of
the
discharge
current
and
the
time
indicated
at
each
point.
Additional
details
may
be
found
in
Tremblay
et
al.
1

Nominal
Current
Discharge
Characteristic
0
12
3
4
Time
(hours)
Figure
1.
Identification
of
Discharge
Profile
Characteristic
Values'
The
model
was
validated
against
discharge
curves
for
an
individual
Panasonic
cell
of
each
of
the
following
chemistries
(all
secondary
cells):
•
lead-acid,
•
nickel-cadmium,
•
lithium,
and
•
nickel-metal
hydride.
The
authors
of
the
above
model
presented
a
revised
version
of
equation
(4)
in
Tremblay
and
Dessaint,
including
equations
tailored
specifically
to
each
of
the
four
secondary
cell
chemistries.
The
fine
degree
of
increased
accuracy
provided
by
this
improved
model
is
insufficient
to
outweigh
the
costs
of
sacrificing
a
general
equation
of
cell
voltage
for
chemistry-specific
formats;
consequently,
this
revised
model
has
been
disregarded
here.
4.
A
CONSTANT-POWER,
CONSTANT-TEMPERATURE
DISCHARGE
MODEL
4.1
ORDINARY
DIFFERENTIAL
EQUATION
FOR
CAPACITY
While
many
battery
cells
may
demonstrate
nearly
full
capacity
discharge
at
currents
near
the
published
or
nominal
rates,
it
is
desirable
to
make
theoretical
predictions
of
battery
behavior
when
systems
are
stressed.
Integration
of
a
capacity
de-rating
model"
into
a
model
for
potential
makes
possible
a
more
conservative
evaluation
of
cell
discharge
at
increased
currents.
Further,
the
model
may
be
rearranged
to
define
a
constant-power
state:
<t(C
E
ff
ective
)
_
[b-Vb2~
dt
[
fr-vV-4
a-p
\
p
e
-[
2a
\
'
(5)

where
(
2(pe-iK
l
0
"
e
)
■
^Effective\t=0
=
0.
The
derivation
of
equation
(5)
is
given
in
appendix
A.
4.2
APPLICATION
TO
SIZING
ESTIMATIONS
Integration
from
zero
time
until
C/,//
(
,
m
<
is
equal
to
Qci
i
allows
determination
of
the
run
time
of
the
battery
at
the
chosen
power
level:
^Effective\t=T
=
QcUT-
For
sizing
purposes,
the
battery's
specific
energy
and
energy
density
may
be
determined
from
integration
of
equation
(5):
ES
=
Z-L,
ED=^.
(6)
m
v
Through
inclusion
in
a
computer
program,
sizing
simulations
may
be
carried
out
to
determine
available
energy
for
the
particular
power
level
demanded,
rather
than
relying
on
a
more
approximate
value.
An
additional
benefit
of
modeling
battery
behavior
in
this
way
is
the
handicapping
of
maximum
power.
The
use
of
constant
values
for
energy
content
requires
a
similarly
crude
estimation
of
maximum
power
output
for
a
battery
system,
i.e.,
values
for
the
battery's
specific
energy,
specific
power,
and
energy
density.
For
the
model
presented
here,
the
maximum
power
is
automatically
limited
to
r
M
aximum
~
4
.
R
*
''
The
derivation
of
equation
(7)
is
given
in
appendix
B.
Appendix
C
presents
an
example
to
demonstrate
the
process
by
which
this
model
might
be
used
to
predict
battery
performance.

REFERENCES
1.
Oliver
Tremblay,
Louis-A.
Dessaint,
and
Abdel
Illah
Dekkiche,
"A
Generic
Battery
Model
for
the
Dynamic
Simulation
of
Hybrid
Electric
Vehicles,"
IEEE
0-7803-9761-4/07,
2007.
2.
W.
Peukert,
"Über
die
Abhängigkeit
der
Kapacität
von
der
Entladestromstärke
bei
Bleiakkumulatoren,"
Elektrotechnische
Zeitschrift,
vol.
20,
pp.
20-21,
1897.
3.
D.
Doerfel
and
S.
Sharkh,
"A
Critical
Review
of
the
Peukert
Equation
for
Determining
the
Remaining
Capacity
of
Lead-Acid
and
Lithium-Ion
Batteries."
Journal
of
Power
Sources,
vol.
155,
pp.
395-400,2006.
4.
O.
Tremblay
and
L-A.
Dessaint,
"Experimental
Validation
of
a
Battery
Dynamic
Model
for
EV
Applications,
World
Electric
Journal,
vol.
3,
2009.

APPENDIX
A
DERIVATION
OF
EQUATION
(5)
The
voltage
across
the
terminals
of
a
battery
is
equivalent
to
the
open-circuit
voltage
of
the
cell,
less
the
voltage
drop
as
calculated
by
Ohm's
law:
E
=
E
0C
-
(
R
c
'
/)•
(A-l)
Drawing
on
the
model
developed
in
Tremblay
et
al.,
1
we
may
compute
the
open-circuit
potential
as
a
function
of
the
state-of-charge
as
in
equation
(4).
Substituting
(4)
into
(A-l)
and
applying
equation
(2)
yields
j_
I
=
yEffectiveVot
))
>
E
=
E
0
-
(p£HL)
+
(A
•
exp(-ß
•
O)
-
\R
C
■
(lErrecuAW
1
)
)
\pe
(A-2)
Also,
as
the
original
model
presented
in
Tremblay
et
al.
1
is
for
a
constant-capacity
system
with
no
Peukert
effect,
the
tracked
capacity
in
equation
(A-2)
should
be
the
effective
capacity.
The
effective
capacity
discharged
at
a
particular
current
(equation
(3)),
evaluated
for
a
current
that
is
a
function
of
time,
may
be
written
alternatively
as
an
integral:
^Effective
=
Yj^Effective
'
At)
=
J
hffectiveWdt
.
If
the
current
function
is
assumed
to
be
smooth,
then
it
may
be
rewritten
as
the
derivative
of
capacity
discharged
with
respect
to
time:
^=Wc
ti
«(t).
(A-3)
Removing
references
to
current
and
replacing
them
with
capacity,
we
obtain
a
final
expression
for
potential:
E
=
K
"
c
Effeciive
£
°
-
(<iÄ=)
♦
o
«»<-»
•
wJ)
-
k
•
pr^cr*))
\pe
(A-4)
For
a
constant-power
system,
Eoc
=
E
0
-
(f-
2
^)
+
(A
■
exp(-B
•
C))
,
A-l

P
=
El
=
K,
?>
(,pe-\\
\
~~l'o
))
(
d
(
C
Effective)
,
/"'
i
f
d
{
C
E
ff
ective
)
f,pe-l\\P
e
{
dt
v'o
))
•
P
=
£
oc
'I
(d(C
E
ff
ective
)
dt
or'if-
Re
•
(^^(/r
1
)
)
&
1
fl
#
/£(££££££iU£)\pi
_
^
#
/
d
(
C
E//eflt
,
e
)
\
p
7
_^_
p
_
^
(A-5)
where
2(pe-i)\
«
=
«c-
'o"
e
*>s
[*„-(
■
f
QCUT
QCUT
-
^Effective/
)
+
(A
■
exp(-B
•
C
t
Effective
The
derived
function
for
a
constant-power
system
(equation
(A-5))
has
the
form
of
a
quadratic
equation,
which
may
be
solved
for
the
value
of
the
time-derivative
of
the
effective
capacity
raised
to
the
power
of
the
reciprocal
of
the
Peukert
effect
exponent.
As
a
quadratic
equation,
there
are
two
solutions:
the
positive
and
the
negative
radical
in
the
numerator.
By
inspection,
the
physically
correct
solution
to
the
differential
equation
is
the
negative
of
the
radical
so
as
to
have
zero
current
in
the
zero-power
case.
In
this
form,
the
equation
is
an
ordinary
differential
equation
(ODE)
and
may
be
integrated
to
solve
for
the
effective
discharge
against
time,
assuming
an
initial
condition
for
battery
discharge,
e.g.,
that
at
the
start
(t
=
0)
the
battery
has
not
been
discharged
(CEffect
™
=
0).
The
result
is
equation
(5):
^Effective)
_
dt
^Effective\t=0
=
0
•
b-^b
2
-
4
a
P
2a
pe
A-2

APPENDIX
B
DERIVATION
OF
EQUATION
(7)
The
power
delivered
by
a
cell
is
equivalent
to
the
product
of
the
potential
and
current:
P
=
E
■
I
.
The
cell
potential
may
be
written
as
the
open-circuit
potential
less
the
ohmic
loss
due
to
internal
resistance:
E
=
Eoc
—
f
'
Re
•
The
open-circuit
voltage
is
maximized
for
a
fully-charged
cell
at
Vn
IL%
making
the
equation
for
power
a
function
of
two
constants
(open-circuit
potential
and
cell
resistance)
and
one
variable
(current):
P
=
I
•
(E
oc
-I
•
R
c
)
,
P
=
E
0C
l-Rc
'
I
2
-
(B-l)
Taking
the
derivative
and
setting
to
zero,
we
find
the
location
of
the
maximum:
dP
"57
=
E
oc
-2
•
R
c
•
I,
0
m
Eoc
-
2
•
R
c
•
/,
/
-
E
°
c
'Maximum
Power
~
2
.
R
•
Substituting
into
equation
(B-l),
we
determine
the
maximum
power
and
we
recover
equation
(7):
o
—
c
E
°
c
Q
(loc_\
2
_
(EFULL)
2
Maximum-
*OC
'
2
.
R
c
K
C'\
2
.
R
c
)
~
4Rc
■
B-l
(B-2
blank)

APPENDIX
C
APPLICATION
OF
MODEL
TO
AN
ACTUAL
BATTERY
To
demonstrate
the
process
by
which
this
model
might
be
used
to
predict
battery
performance,
the
following
example
is
presented.
To
begin,
a
battery
cell
of
interest
is
selected
and
its
data
sheet
is
analyzed
to
determine
the
parameters
defined
in
table
1
in
the
main
text.
It
is
important
to
state
that
determination
of
the
battery's
parameters
is
a
subjective
and
inexact
process.
The
same
data
sheet
may
produce
two
slightly
different
sets
of
values
when
analyzed
by
two
different
engineers
as
this
battery
model
is
an
idealization
of
the
real
discharge
behavior
of
battery
cells.
For
this
example,
the
chosen
cell
is
the
Saft
Li-Ion
VL
52
E
cell
(see
data
sheet
at
the
end
of
this
appendix).
The
values
of
the
parameters
for
this
cell
are
listed
in
table
C-l.
Table
C-L
Saft
VL
52
E
Model
Parameters
Symbol
Battery
Parameter
EFVLL
4.1
volts
EEXP
3.9
volts
ENOM
3.2
volts
Ear
2.5
volts
\lo
48.9
amperes
m
1.0
kg
\pe
1.035
QEXP
2.5
A-hr
QsOM
45
A-hr
QCUT
48.9
A-hr
Re
2e-3
ohms
V
0.48
liter
The
mass
and
volume
of
the
cell
are
explicitly
defined
in
the
data
sheet
as
1.0
kg
and
0.48
liter,
respectively.
By
inspection
of
the
C-rate
discharge
curve*
at
25°C
on
the
back
side
of
the
data
sheet,
the
value
of
£>/
/./
is
4.1
volts,
EEXP
is
4.0
volts,
E
d
\oM
is
3.2
volts,
and
E
(
i
/
is
2.5
volts.
The
corresponding
capacities
are
approximately
QEXP
=
2.5
A-hr.
QHOU
~
45
A-hr,
and
QCLT
=
48.9
A-hr.
As
the
discharge
is
listed
as
the
C-rate,
the
value
of
/o
is
equivalent
to
Qcur
•"Orate"
is
an
industry
term
for
the
current
that
will
completely
discharge
the
cell
in
1
hour.
Other
discharge
currents
arc
expressed
relative
to
this
\aluc:
e.g.,
"C/10"
is
one-tenth
of
the
C-rate.
or
the
rate
at
which
the
cell
should
fully
discharge
in
10
hours,
barring
any
effect
of
discharge
rate
on
capacity.
These
values
are,
obviously,
approximations.
C-l

Table
C-2.
Safi
VL
52
E
Discharge
Rate
and
Capacity
Calculated
for
pe
=
1.035
Discharge
Rate
(C-Rate)
Data
Sheet
Capacity
<A-hr)
Calculated
Capacity
(A-hr)
C
48.9
48.8
e/2
50.0
50.0
C/3
50.9
50.7
C/5
51.7
51.6
C/7
52.0
52.2
C/10
52.9
52.9
divided
by
1
hour,
48.9
A.
The
value
of
the
Peukert
effect
exponent
is
estimated
by
measuring
the
cell
capacity
against
the
discharge
rate
from
the
discharge
curves
on
the
data
sheet.
The
\
alucs
measured
from
the
data
sheet
and
the
calculated
values
for
the
estimated
Peukert
effect
exponent
of
1.035
are
shown
in
table
C-2.
Lastly,
the
value
of
the
internal
resistance
of
the
cell
Re
is
estimated
from
the
observed
initial
drop
in
the
C-rate
discharge
curve.
(In
many
cases
a
value
of
internal
resistance
is
provided
by
the
manufacturer
and
estimation
is
not
required.)
At
zero
discharged
capacity,
the
cell
voltage
decreases
from
4.1
to
4.0
volts.
By
Ohm's
law,
the
difference
in
voltage
is
equal
to
the
product
of
the
current
and
the
resistance,
so
Re
~
0.1
volt/
A)
s
0.002
ohm.
To
solve
equation
(5),
a
short
program
was
written
for
MATLAB
that
employed
the
solver
ODE45.
To
avoid
integrating
over
an
uncertain
time
interval,
the
ODE
is
inverted
and
integrated
over
the
capacity
interval
of
0
to
QCVT-
Derivation
of
this
format
is
as
follows:
d(C
E
ffective)
_
dt
b-ylb
2
-4
a
■
P
2
a
pe
dt
d
(
c
Effective)
=
f
,
2
a
r=
2a
b
+
y/b
2
-
4
a
P
b
-
Vb
2
-
4
a
P
ft
+
Vft
2
-4-a-P
'
pe
dt
_
f
(
2
-
a)(b
+
Vb
z
-4aP)
1
P
[
b
+Vfo
2
-4
a
P
i
d(C
Effective
)
~
[
b
2
-
b
2
+
4a-P
J
"[
2-P
J
pe
dt
^Effective)
2-
P
pe
((-i)
C-2

The
time
calculated
as
corresponding
to
the
value
of
QCUT
allows
for
the
determination
of
the
cell
energy
as
a
function
of
power.
While
this
is
a
useful
tool
for
estimating
battery
performance,
a
conservative
approach
requires
imposing
additional
limits
on
the
battery
operation.
The
cell
used
in
this
example—the
Saft
VL
52
E—has
a
stated
maximum
discharge
current
of
52
amperes,
corresponding
approximately
to
the
1-C
rate.
The
published
specific
energy
is
also
given
as
185
W-h/kg.
Figure
C-l
plots
the
results
of
this
model
for
the
VL
52
E
both
with
and
without
the
power
and
energy
limits
on
the
cell
specified
by
the
manufacturer.
Programatically,
these
bounds
may
be
applied
using
a
pair
of
k
i
F
"
statements;
i.e.
if
the
required
power
exceeds
the
limit,
the
energy
is
zero,
and
if
the
calculated
energy
exceeds
the
limit,
it
is
reduced
to
the
limiting
value.
—
D
erived
Model
—Limits
Applied
100
150
Specific
Energy
(Wh/kg)
250
Figure
C-l.
VL
52
E
Modeled
Performance
With
and
Without
Manufacturer
Limits
C-3
(C-4
blank)

I
Rechargeable
lithium-ion
battery
VL
52
E
-
high
energy
cell
Benäht»
•
Excellent
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end
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•
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Typical
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•
Nickel
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•
Sold
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battenee
•
Incorporation
of
electronics
for
performance
efficiency
-
Cherge/floating/otacnorge
managernent
Cell
bolerong
hill
■■■■■■
■
!
fc
■
II
■
wnrai
voaage
38V
Lower
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fcmc
for
discharge
25V
Meatmum
oieononps
current
at
Ml
oonunuouo
tttaH.
Nommel
capaccy
at
4
1
V/2
5
V
and
26*
C
52P/7)Ah
Space«
energy*
185Wh/Kg
Energy
donaiO/"
385Wh/l
Mechanical
charectenetica
Nominal
onrnetar
KU#n.i\>l
ii
an
Jii
20B
mm
rvjomnei
wetgnc
1
0
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Nominal
volume
046!
Co«
aa»i
eUne,
cowaTtiaw
Charge
method
Constant
ourrent/conatont
vokege
(CCCV)
Chergng
vokape
4U004V
Ftecommended
iWHUinuoua
charge
current
at
25
C
C/7
Operating
temperature
Charge
Oocherge
♦
5
#
C
to
♦
35"
C
3
to
♦
55*
C
Scorege
and
tranapuitauon
tampareture
-
40»
C
to
♦
85»
C
cna
of
cnerge
aececuon
150
mA
lotal
Ml
ohergng
tame
hears
WKtUO&S
tamwiato
'Charge
Bo
4.1
VanaC/Wrmta
r
level
eafety
•
Incorporation
of
several
levels
of
redundant
safety
features
to
prevent
abuse
conditions
euch
as
Overcharge,
over
discharge
and
short
circuit
August
2008
C-5

I
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Rat«
capability
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from
4.1
V
<
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Capeccy(Ah)
Rats
capability
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from
4.1
V
to
2.5
V
CapoL-t,
!Ah
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&
Defense
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107
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Court
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MO
21030
USA
TeJ
+1
410
771
3200
Fox+1
410
771
1144
www.
saftbatteries.