batteries
Article
Study on Factors for Accurate Open Circuit Voltage
Characterizations in Mn-Type Li-Ion Batteries
Natthawuth Somakettarin * and Tsuyoshi Funaki
Division of Electrical, Electronic and Information Engineering, Graduate School of Engineering,
Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan; [email protected]
* Correspondence: [email protected]; Tel.: +81-66-879-7709
Academic Editor: Maciej Swierczynski
Received: 1 September 2016; Accepted: 8 March 2017; Published: 12 March 2017
Abstract: Open circuit voltage (OCV) of lithium batteries has been of interest since the battery
management system (BMS) requires an accurate knowledge of the voltage characteristics of any
Li-ion batteries. This article presents an OCV characteristic for lithium manganese oxide (LMO)
batteries under several experimental operating conditions, and discusses factors for accurate OCV
determination. A test system is developed for OCV characterization based on the OCV pulse test
method. Various factors for the OCV behavior, such as resting period, step-size of the pulse test,
testing current amplitude, hysteresis phenomena, and terminal voltage relationship, are investigated
and evaluated. To this end, a general OCV model based on state of charge (SOC) tracking is developed
and validated with satisfactory results.
Keywords: lithium-ion; battery characterization; lithium manganese oxide (LMO); open circuit
voltage (OCV); battery test system; battery modeling
1. Introduction
Nowadays, Li-ion batteries (LIBs) can be considered as progressive energy storage devices.
They have been widely adopted in many applications, such as electric vehicles, renewable energy
storage systems, and telecommunication backup and standby systems. These energy systems require
enormous batteries, which consist of large amounts of cells to obtain the desired power, energy, rated
current, and voltage. The battery management system (BMS) is necessary for the batteries to estimate
the state of charge (SOC), monitor the electrical state and the state of health (SOH), protect and control
all of the batteries, and maximize the performance during the operations. The understanding of
characteristics and behaviors of the batteries is important for the engineers who develop the BMS
algorithms. An open circuit voltage (OCV) of LIBs is one of the important elements, which displays
the electrode properties in the battery and acts as an equivalent voltage source of the LIBs.
In recent years, many researchers had studied and proposed the achievements regarding the
usability of the OCV as a function of the SOC in LIB applications such as with the battery modeling,
estimations of state parameters, cell capacity, and capacity loss in batteries. A non-linear OCV model
with single-variable SOC functions based on a practical and usable capacity was introduced by
Chen and Rincon-Mora [1] to apply in the LIB model for predicting battery runtime and electrical
performance. This model was validated in good agreement with different step-sizes of the testing
current for polymer Li-ion and nickel-metal hydride batteries. Pattipati et al. [2] applied a normalized
OCV model to a battery fuel gauge in the BMS application, summarizing that the OCV-SOC curves
remain the same regardless of the age or temperature of the battery as long as the actual battery
capacity is used in the characterization process. However, Roscher and Sauer [3] proposed applying
recovery and hysteresis factors to the OCV function of olivine-type cathode batteries (LiFePO4 or
LFP) for the SOC estimation. The empirical OCV model extracted from the experiments can also
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be applied into a dual extended Kalman filter (DEKF) algorithm in order to estimate the SOC and
battery capacity for the online applications by using a concept of normalized capacity computation
with the same base cut-off voltage [4]. While the OCVs of different aged cells had shown a similar
pattern and given a corresponding hysteresis gap, the cycling capacity loss of LIBs can also be
approximated from them. Roscher et al. [5] proposed a residual factor that was extracted from the
difference between the experiment and the model of the OCV for detecting the percentage of capacity
loss of the aged LFP cells. The benefits of the OCVs are not limited only to the state and parameter
estimations, and can also be applied for investigating and studying the electrode properties and phase
transformation behaviors of the batteries. As we know, for LIBs, the electrode properties can be
identified by measuring the battery voltages under very low-current conditions. Petzl and Danzer [6]
demonstrated the advancements in the measurement of the OCV by considering the differential voltage
and incremental capacity techniques to study the electrode property and the phase transition of LFP
batteries. The abovementioned previous studies allow us to realize the limitations and substantial
benefits obtained from the OCV characterization. However, the viewpoints of these studies do not
concentrate on the comprehensive factors that affected all accurate OCV determinations. Without
the investigation of precise conditions, some of the estimation models can only work correctly in a
linear range (20%–80% SOC) [7]. By considering the suitable adjusting parameters (e.g., step-size of
pulse tests, resting period of the cell, and testing current), the characterization of OCV can help us
to collect OCV information in a precise manner with a minimum testing time, especially in testing
conditions under non-linear regions of low and high ranges of the SOC. In order to obtain an accurate
battery model, it is necessary to investigate the OCV determination with the implementation of
testing-parameter adjustments. This is a delicate task for model-based state estimations in the BMS [8].
In this research, we focus on the factors for a precise OCV characterization under different
experimental conditions. Several aspects of the adjusting factors for the OCV are discussed and
evaluated such as the different step-sizes of pulse tests, resting periods of the cell, testing current
amplitudes (C-rates) of the pulse, and continuous charge-discharge tests, hysteresis phenomena, and
terminal voltage relationships. The OCV as a function of SOC calculated with an actual capacity is
characterized by using a developed programmable test system. In this study, a commercial rechargeable
lithium manganese oxide (LMO) battery was used. The working principle and structure of the
LMO were summarized in [9]. The characteristic changes of the OCV depend on the difference
in electrochemical potentials of their specific material properties of electrodes and the effective
concentration of Lithium during operations. The LMO cell comprises of a positive electrode LiMn2 O4 ,
which has distinctive features such as high nominal voltage per cell, low internal resistance, moderate
to high energy density, high discharge current rupturing, better thermal stability for over-charge,
and higher safety than a conventional type such as lithium cobalt oxide (LCO) batteries [10–12].
The negative electrode is made from carbon-based lithiated graphite (LiC6 ), and has a prominent
property in high storage capacity due to its flat potential profile [13]. However, the negative graphite
electrode has significant influences on the reduction of the potential for full cell operations, OCV
patterns, and the usable capacity, especially after cycling due to the loss of active material and
the degradation from a dissolution of the solid electrolyte interface (SEI) layer [14,15]. Moreover,
a characteristic of the graphite electrode on the OCV pattern is more distinguished, especially when
compared with other flat potential cathodes, such as LFP batteries [16].
The aim of this study is to understand nonlinear characteristics of the OCV in the LMO, as well as
the factors that affect the accurate OCV characteristics in order to obtain precise OCV information for
modeling the battery parameters properly in the BMS application.
The remainder of this article is organized as follows: Section 2 describes the OCV determination
method for the LMO and its definition. Section 3 shows a developed test system for the precise OCV
characterization. In Section 4, we discuss and summarize the study results for the factors that affected
the accurate OCV determination. Section 5 introduces a general mathematical equation of the OCV
model in a function of the SOC for the BMS implementation and the model validation by comparing
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itcomparing
with the experimental
data. Finally,data.
conclusions
future recommended
research directions
are
it with the experimental
Finally,and
conclusions
and future recommended
research
comparing it with the experimental data. Finally, conclusions and future recommended research
given
in
Section
6.
directions are given in Section 6.
directions are given in Section 6.
2.
2. Open
Open Circuit
Circuit Voltage
VoltageDetermination
Determinationfor
forLi-Ion
Li-IonBattery
Battery
2. Open Circuit Voltage Determination for Li-Ion Battery
The
in the
theelectrical
electricalequivalent
equivalentcircuit
circuitmodel
model
shown
in Figure
is extracted
The OCV
OCV in
ofof
thethe
LIBLIB
shown
in Figure
1 is 1extracted
as a
The OCV in
the electrical
equivalent
circuit (VT)
model
of the
LIB shown
in Figure
1 is extracted
a
as
a
measured
voltage
at
the
battery
terminals
after
resting
to
recover
the
battery
close to
toasits
measured voltage at the battery terminals (VT) after resting to recover the battery close
its
measured
voltage
at
the
battery
terminals
(VT)
after
resting
to
recover
the
battery
close
to
its
equilibrium
equilibrium state
state [6].
[6]. In
In Figure
Figure 2,
2, the
the OCVs
OCVs are
are determined
determined as
as aa terminal
terminal voltage
voltage after
after relaxing
relaxing from
from
equilibrium
state pulse
[6]. Incurrents
Figure 2,both
the OCVs
are
determined
as a terminal
voltage
after
relaxingcalled
from
the
applied
short
on
the
discharge
and
charge
operations.
This
method
the applied short pulse currents both on the discharge and charge operations. This method is
is called
the applied
short pulse
currents both
on the dischargeintermittent
and charge operations.
This method is called
the
the OCV
OCV pulse
pulse test
test method
method based
based on
on the
the galvanostatic
galvanostatic intermittent titration
titration technique
technique [17].
[17].
the OCV pulse test method based on the galvanostatic intermittent titration technique [17].
Figure 1.
1. Electrical equivalent
equivalent circuit model
model of the
the Li-ion battery
battery (LIB).
Figure
Figure 1. Electrical
Electrical equivalent circuit
circuit model of
of the Li-ion
Li-ion battery (LIB).
(LIB).
Figure 2. Current and voltage response for pulse tests to extract the open circuit voltage (OCV).
Figure 2.
2. Current
Current and
and voltage
voltage response
response for
for pulse
pulse tests
tests to
to extract
extract the
theopen
opencircuit
circuitvoltage
voltage(OCV).
(OCV).
Figure
After a long resting of at least 60 min for our tested LMO to make sure that the cell voltage is
After a long resting of at least 60 min for our tested LMO to make sure that the cell voltage is
constant
closeresting
to its equilibrium
shownsure
in Section
battery
Afterand
a long
of at least 60(The
minexperimental
for our testeddetails
LMO are
to make
that the4.2),
cellthe
voltage
is
constant and close to its equilibrium (The experimental details are shown in Section 4.2), the battery
current (Iand
B) and
voltages
across the (The
effective
series resistance
(VESR
) and in
transient
elements
(Vtrans)
constant
close
to its equilibrium
experimental
details are
shown
Section 4.2),
the battery
current (IB) and voltages across the effective series resistance (VESR) and transient elements (Vtrans)
become(Izero.
Then,
the VT
in Equation
(1) canseries
be assumed
for (V
the OCV:
current
voltages
across
the effective
resistance
) and transient elements (V trans )
B ) and
become zero.
Then, the VT in Equation (1) can be assumed for theESR
OCV:
become zero. Then, the VT in Equation (1)
assumed
VT can
= be
OCV
−V
−for
Vtransthe OCV:
(1)
VT = OCV − VESR
(1)
ESR − Vtrans
ESR −=VVESR
(2)
ESR −I BVtrans
(1)
VT = OCV
ESR = VESR I B
(2)
From Figure 1, the other parameters will
be=ignored
such
as:
(1)
effective
series
resistance
(ESR),
ESR
V
/I
(2)
B
ESR such
From Figure 1, the other parameters will be ignored
as: (1) effective series resistance (ESR),
which reflects the resistances of the connecting wires, electrodes, separator and electrolyte; and
which
reflects
the
resistances
of
the
connecting
wires,
electrodes,
andseries
electrolyte;
and
From Figure 1, the other parameters will be ignored such as:separator
(1) effective
resistance
(2) transient elements, which reflect the charge-transfer resistance (R1), double-layer capacitance
1
),
double-layer
capacitance
(2)
transient
elements,
which
reflect
the
charge-transfer
resistance
(R
(ESR), which reflects the resistances of the connecting wires, electrodes, separator and electrolyte;
(C1), diffusion process resistance (R2), and its capacitance (C2) because they have no effect on the
(C1),(2)
diffusion
resistance reflect
(R2), and charge-transfer
its capacitance (C2) because
have no effect
on the
and
transientprocess
elements,
(R1they
), double-layer
capacitance
OCV.
Usually,
the
OCV iswhich
illustrated asthe
a function of theresistance
SOC in order
to compare between
the
OCV.
Usually,
the
OCV
is
illustrated
as
a
function
of
the
SOC
in
order
to
compare
between
the
(C
process
resistance
(R2 ), the
andstudies.
its capacitance
(C2 )calculation
because they
haveon
no the
effect
on the
1 ), diffusion
different
testing
conditions
during
The SOC
based
coulomb
different
testing
during as
thea studies.
The
SOC
calculation
on the
coulomb
OCV.
Usually,
theconditions
OCV
is illustrated
of the
SOC
inthe
order
tobased
compare
the
counting
method,
is
shown
in Equation
(3),function
and is calculated
from
actual
capacity
ofbetween
the battery.
countingtesting
method,
is shownduring
in Equation
(3), andThe
is calculated
from the
actual
capacity
of thecounting
battery.
different
conditions
the
studies.
SOC
calculation
based
on
the
coulomb
In addition, the SOCs between 0% and 100% are set within the operating voltage ranges of the cell
In addition,
the SOCs
between
0%
and
100% are set
within
the operating
voltage
rangesInofaddition,
the cell
method,
shown
Equation
(3),
and
is calculated
from
the actual
capacity of
the battery.
betweenis3.0
V andin4.2
V, respectively:
between 3.0 V and 4.2 V, respectively:
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the SOCs between 0% and 100% are set within the operating voltage ranges of the cell between 3.0 V
and 4.2 V, respectively:
tcut − off
tcut
Z −off
SOC (t ) = SOC 0 −

SOC (t) = SOC0 −
t0
t0
IB
IB
dt
3600 × Q B dt
(3)
(3)
3600 × Q B
where IB is the battery current, which is positive for discharging and negative for charging; QB is an
where IB is the battery current, which is positive for discharging and negative for charging; QB is an
accumulated capacity of the battery in Ah; and SOC0 is an initial value of the SOC.
accumulated capacity of the battery in Ah; and SOC0 is an initial value of the SOC.
3.
Characterization System
System
3. Open
Open Circuit
Circuit Voltage
Voltage Characterization
The
The OCV
OCV characteristics
characteristics are
are different
different and
and unique
unique depending
depending on
on their
their active
active electrode
electrode materials
materials
for
the
different
types
of
the
LIB
[18].
It
takes
a
significant
amount
of
time
to
characterize
for the different types of the LIB [18]. It takes a significant amount of time to characterize the
the OCV.
OCV.
In
to identify
identify the
the precise
precise OCV
OCV characteristics
In order
order to
characteristics based
based on
on the
the sequential
sequential pulse
pulse tests,
tests, aa reliable
reliable LIB
LIB
test
system
is
needed.
A
manganese-type
single
cell
from
NEC-Tokin
(Chiyoda,
Tokyo,
Japan)
was
test system is needed. A manganese-type single cell from NEC-Tokin (Chiyoda, Tokyo, Japan) was
used
1. In
In this
this section,
section, the
the developed
developed test
used in
in this
this study.
study. A
A cell
cell specification
specification is
is shown
shown in
in Table
Table 1.
test system
system
with
computer-based
controlling
is
introduced
for
the
OCV
characterization,
as
illustrated
in
Figure
with computer-based controlling is introduced for the OCV characterization, as illustrated in Figure 3.
3.
The
system is
developed in
the Labview
Labview environment
The test
test system
is developed
in the
environment (Japan
(Japan National
National Instrument
Instrument Inc.,
Inc., Minato,
Minato,
Tokyo,
Japan) for
for controlling
controlling the
the instruments
instruments to
to charge
charge and
and discharge
discharge the
the LIB
LIB via
via aa general-purpose
general-purpose
Tokyo, Japan)
interface
interface bus
bus (GPIB)
(GPIB) controller.
controller.
Table 1. Cell specification.
Description
Specification
Description
Specification
Electrode/type
Spinel single cell
Electrode/type
Spinel single cell
Positive
Manganese
(LiMn2O4)
Positive
Manganese (LiMn2 O4 )
Negative
Lithiated
graphite
Negative
Lithiated graphite(LiC
(LiC66))
Rated
capacity
(Typical)
Rated
capacity
3.5 3.5
AhAh
(Typical)
Voltage
V (Nominal)
Voltage
3.83.8
V (Nominal)
Description
Description
Operating voltage
Operating voltage
Maximum current (C-rate)
Maximum current (C-rate)
Operating
temp.
Operating
temp.
Cell
Celldimension
dimension
Weight
Weight
Charging
Discharging
Discharging
3.0 V
4.2 V
3.0 V
4.2 V
3.5
A
(1C)
20.0
A (5.7C)
3.5 A (1C)
20.0 A (5.7C)
◦
0–40
°C
−10–50
0–40 C
−10–50 ◦ C °C
82 82
mm
× 171
mmmm
× 4.7
mm
× 171
× mm
4.7 mm
100
g (Maximum)
100
g (Maximum)
Charging
Figure
for OCV
OCV characterization.
Figure 3.
3. A
A developed
developed LIB
LIB test
test system
system with
with computer
computer based
based control
control for
characterization.
The test system should operate automatically following the sequential programs with a safety
The test system should operate automatically following the sequential programs with a safety
for the test parameters such as C-rates, pulse durations, rest times, pulse cycles and protective
for the test parameters such as C-rates, pulse durations, rest times, pulse cycles and protective setting
setting values for operations without malfunctions for any LIB types. The system also records the
values for operations without malfunctions for any LIB types. The system also records the related
related parameters and status of the LIB during the testing such as battery voltage, current,
parameters and status of the LIB during the testing such as battery voltage, current, left-cycle, piecewise
left-cycle, piecewise pulse duration, rest duration, date, time, status of testing, and the alarm
pulse duration, rest duration, date, time, status of testing, and the alarm message in case of reaching
message in case of reaching the protection limits via the display monitor. The sampling interval
the protection limits via the display monitor. The sampling interval is set to 10 ms/sampling, which is
is set to 10 ms/sampling, which is sufficient to observe the pulse transient response for the precise
sufficient to observe the pulse transient response for the precise OCV characterization.
OCV characterization.
4. Discussion on the Factors for Accurate Open Circuit Voltage Determination
4. Discussion on the Factors for Accurate Open Circuit Voltage Determination
In this section, the effects of the step-sizes and resting periods of the cell during the pulse tests
In
this section,
the effects
thepulse
step-sizes
and restingcharge-discharge
periods of the cell
during
the pulse tests
and current
amplitudes
duringofthe
and continuous
tests
are experimentally
and current amplitudes during the pulse and continuous charge-discharge tests are experimentally
investigated and discussed for the suitability of testing conditions to provide an accurate OCV
characterization by using the developed test system in Section 3.
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investigated and discussed for the suitability of testing conditions to provide an accurate OCV
characterization
Batteries 2017, 3, 8 by using the developed test system in Section 3.
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4.1.
4.1. Effects
Effects of
of Step-Sizes
Step-Sizes during
during Pulse
Pulse Tests
Testson
onthe
theOpen
OpenCircuit
CircuitVoltage
VoltageCharacteristic
Characteristic
For
OCVs
were
extracted
fromfrom
the pulse
tests at
different
step-sizes.
Step-sizes
(∆SOC)
For this
thisstudy,
study,
OCVs
were
extracted
the pulse
tests
at different
step-sizes.
Step-sizes
◦ C with 10 min resting)
are
set
at
0.5%,
1%,
5%,
and
10%
using
the
same
condition
(at
1C-rate
20
(ΔSOC) are set at 0.5%, 1%, 5%, and 10% using the same condition (at 1C-rate 20°C with 10 min
separately
for each pulse
charge
and
discharge.
∆SOC 0.5%,
1%, 5%,
and
10%,
means
the setting
resting) separately
for each
pulse
charge
and discharge.
ΔSOC
0.5%,
1%,
5%,which
and 10%,
which
means
of
the
step-size
of
the
pulse
tests
was
equally
at
0.5%,
1%,
5%,
and
10%,
respectively,
between
0%
and
the setting of the step-size of the pulse tests was equally at 0.5%, 1%, 5%, and 10%, respectively,
100%
of the
on theΔSOC
other1%–5%
hand means
theother
variable
pulse
between
0%SOC
andrange.
100% ∆SOC
of the 1%–5%
SOC range.
on the
handstep-size
means of
thethe
variable
tests
has aof1%
fortests
the 0%–10%
SOC
which are
in non-linear
operating
step-size
thestep
pulse
has a 1%and
stepthe
for90%–100%
the 0%–10%
andranges,
the 90%–100%
SOC
ranges, which
are in
regions
of
the
battery,
and
a
5%
step
for
the
10%–90%
SOC
range,
which
is
in
the
linear
region.
The
non-linear operating regions of the battery, and a 5% step for the 10%–90% SOC range, which tests
is in
were
performed
within
the limits
the rated voltage
between
V and
4.2 V. voltage
The effect
of step-sizes
of
the linear
region.
The tests
wereof
performed
within the
limits3 of
the rated
between
3 V and
pulse
tests
to
the
OCV
characteristic
are
shown
in
Figure
4.
∆SOC
1%
and
0.5%
give
the
same
OCV
4.2 V. The effect of step-sizes of pulse tests to the OCV characteristic are shown in Figure 4. ΔSOC 1%
characteristic
allsame
SOC ranges.
∆SOC 5% also
the same
OCV
result
thegives
SOC range
between
and 0.5% giveforthe
OCV characteristic
forgives
all SOC
ranges.
ΔSOC
5%for
also
the same
OCV
10%
However,
it gives 10%
an inconsistent
OCV foritthe
SOC
belowOCV
10%for
and
above
resultand
for 90%.
the SOC
range between
and 90%. However,
gives
anranges
inconsistent
the
SOC
90%
(non-linear
regions).
During
these
non-linear
regions
(windows
A
and
C
in
Figure
4),
the
larger
ranges below 10% and above 90% (non-linear regions). During these non-linear regions (windows A
step-size
the OCVprominently
pattern. Moreover,
wide
causeMoreover,
the incomplete
OCV
and C in prominently
Figure 4), theaffects
largertostep-size
affects to
thesteps
OCV also
pattern.
wide steps
measurement
a low SOC OCV
rangemeasurement
(0%–10%), as illustrated
by the
blue(0%–10%),
and green dots
in Window
of
also cause theinincomplete
in a low SOC
range
as illustrated
byBthe
Figure
4b.
These
incomplete
and
incorrect
OCVs
resulted
from
a
long
pulse
release
time
that
caused
blue and green dots in Window B of Figure 4b. These incomplete and incorrect OCVs resulted from a
the
resolution
forcaused
OCV extraction.
longinadequate
pulse release
time that
the inadequate resolution for OCV extraction.
In
summary,
the
1%
step-size
In summary, the 1% step-size is
is sufficient
sufficient for
for precise
precise OCV
OCV characterization
characterization for
for SOC
SOC ranges
ranges
below
10%
and
above
90%,
and
the
5%
step-size
for
the
10%–90%
SOC
range.
Figure
4
shows
below
above 90%, and the 5% step-size for the 10%–90% SOC range. Figure 4 alsoalso
shows
the
the
extracted
OCVs
a step-size
∆SOC1%–5%.
1%–5%.ΔSOC
∆SOC1%–5%
1%–5%also
also gives
gives aa satisfactory OCV
extracted
OCVs
for for
a step-size
at atΔSOC
OCV
characteristic.
characteristic. Therefore,
Therefore, the
the ∆SOC
ΔSOC 1%–5%
1%–5% should
should be
be chosen
chosen to
to apply
apply for
for all
all of
of our
our tests.
tests.
(a)
(b)
Figure 4.4.Effects
Effectsofofstep-sizes
step-sizes
during
pulse
on OCV
the OCV
characteristic
20 °C10with
10 min
Figure
during
pulse
teststests
on the
characteristic
at 20 ◦at
C with
min resting:
resting:
(a)
under
the
charge
test;
and
(b)
under
the
discharge
test.
(a) under the charge test; and (b) under the discharge test.
4.2. Effects
Effects of
of Resting
Resting Periods
Periods during
during Pulse
Pulse Tests
Testson
onthe
theOpen
OpenCircuit
CircuitVoltage
VoltageCharacteristic
Characteristic
4.2.
In order
orderto
tostudy
studythe
theeffects
effectsofofresting
resting
periods
during
pulse
tests,
voltage
of
In
periods
of of
thethe
cellcell
during
thethe
pulse
tests,
the the
voltage
of the
the was
cell measured
was measured
forSOC
eachstep
SOC
of the
slope percentage
of the
relaxed
voltage
cell
for each
in step
termsinofterms
the slope
percentage
of the relaxed
voltage
(%Slope
rv ).
(%Slope
rv ). The %Sloperv can be calculated with Equation (4). The tests were performed at
The %Sloperv can be calculated with Equation (4). The tests were performed at different resting periods
different
periodsafrom
1 s relaxation
to 3 h to identify
a suitable
relaxation
period for the accurate
from
1 s toresting
3 h to identify
suitable
period for
the accurate
OCV determination:
OCV determination:
VSOCi − VSOCi−1
(VSOCi −tVSOCi−1 )
%Sloperv = 100 ×
(4)
% Sloperv = 100 ×tSOCi −
SOCi−1
(4)
(t − t )
SOCi
SOCi −1
where VSOCi and tSOCi are the voltage and time at the end of the relaxation state for each SOC step,
V
and
are the
and time
theatstarting
where
and
arevoltage
the voltage
and at
time
the endofofthe
therelaxation
relaxationstate
statefor
foreach
eachSOC
SOCstep.
step,
SOCi−1 V
SOCi t SOC
i −1 t SOCi
VSOCi−1 and t SOCi −1 are the voltage and time at the starting of the relaxation state for each SOC step.
The slopes of the relaxed voltage versus the resting periods illustrated in Figure 5 show that the
variation of voltage decayed down near zero after 1 min of resting. The slopes for all SOCs decayed
Batteries 2017, 3, 8
6 of 13
The slopes
Batteries
2017, 3, 8of the relaxed voltage versus the resting periods illustrated in Figure 5 show that
6 of 13the
Batteries 2017,
3, 8
6 of 13
variation
of voltage
decayed down near zero after 1 min of resting. The slopes for all SOCs decayed
down
zero
min
resting.Therefore,
Therefore, the
the resting
resting period
period should
1 min
down
to to
zero
at at
6060
min
ofofresting.
shouldbe
beevaluated
evaluatedbetween
between
1 min
down
to
zero
at
60
min
of
resting.
Therefore,
the
resting
period
should
be
evaluated
between
1
min
and
60
min
to
observe
the
influence
on
the
extracted
OCV.
and 60 min to observe the influence on the extracted OCV.
and 60 min to observe the influence on the extracted OCV.
Figure5.5.Slopes
Slopesof
ofthe
therelaxed
relaxed voltage
voltage versus
Figure
versus the
theresting
restingperiods.
periods.
Figure 5. Slopes of the relaxed voltage versus the resting periods.
Figure 6 shows the effect of different resting periods to the extracted OCV under the same
Figure
6 shows
the1C-rate
effect
of
resting
periods
to the
OCVOCV
under
same
testing
Figure
6 shows
the
effect
of with
different
resting
periods
to extracted
the
extracted
under
the same
testing
condition
(at
20different
°C
ΔSOC
1%–5%).
The
low
resting
period
gives
athe
bloated
OCV
◦ C with ∆SOC 1%–5%). The low resting period gives a bloated OCV between
condition
(at
1C-rate
20
testing
condition
1C-rate
°Ccannot
with ΔSOC
The
lowcharacteristic
resting period
gives
bloated
between
60% and(at
80%
SOCs,20
and
reflect1%–5%).
the actual
OCV
both
on athe
chargeOCV
and
60%
and 80%
SOCs,
and From
cannot
reflect
the reflect
actuala the
OCV
characteristic
both
on the
charge
discharge
between
60%
and 80%
SOCs,
and
cannot
actual
OCV characteristic
both
on
theand
charge
and
discharge
operations.
the
experiments,
recommended
resting
period
for
accurate
OCV
for
operations.
From
a recommended
resting
period
accurate
for this itOCV
cell
type
discharge
operations.
experiments,
recommended
resting
period OCV
for
accurate
for
this cell type
isthe
at experiments,
60 From
min tothe
ensure
that the acell
has reached
itsfor
equilibrium.
However,
can
be is
at 60
min
to
ensure
that
the
cell
has
reached
its
equilibrium.
However,
it
can
be
reduced
to
30
min
or
this
cell
type
is
at
60
min
to
ensure
that
the
cell
has
reached
its
equilibrium.
However,
it
can
be
reduced to 30 min or 10 min for a fast OCV approximation.
10 reduced
min for atofast
OCVorapproximation.
30 min
10 min for a fast OCV approximation.
Figure 6. Effects of resting periods on the OCV characteristic.
Figure6.6.Effects
Effectsof
ofresting
resting periods
periods on
Figure
on the
the OCV
OCVcharacteristic.
characteristic.
4.3. Effects of Current Amplitudes during Pulse Tests on the Open Circuit Voltage Characteristic
4.3. Effects of Current Amplitudes during Pulse Tests on the Open Circuit Voltage Characteristic
4.3. Effects
of Current
Amplitudes
Tests on
the Open (C-rates)
Circuit Voltage
In order
to investigate
theduring
effectsPulse
of current
amplitudes
on theCharacteristic
OCV, the pulse charge
In
order
to
investigate
the
effects
of
current
amplitudes
(C-rates)
on
the
OCV,
theΔSOC
pulse 1%–5%
charge
and discharge tests were performed under the same testing condition (at 20 °C with
In order to investigate the effects of current amplitudes (C-rates) on the OCV, the pulse charge
and discharge
tests for
were
performed
under
thewere
sameextracted
testing condition
(at 20
°C with
ΔSOCC/4
1%–5%
60 min resting
each
pulse). The
OCVs
for different
C-rates
between
and
and discharge tests were performed under the same testing condition (at 20 ◦ C with ∆SOC 1%–5% and
and
60 min
resting
forpulse
eachC-rates
pulse). on
The
OCVs
extracted
for different
C-rates between C/4 and
1C. The
effects
of the
the
OCVwere
are shown
in Figure
7.
60 1C.
minThe
resting forofeach
pulse).
The OCVs
were extracted
forFigure
different
C-rates between C/4 and 1C.
pulse
C-rates
on an
theadequate
OCV are relaxing
shown inperiod
7. that the voltage patterns for
Theeffects
extractedthe
OCV
results
under
show
Thethe
effects
of
the
pulse
C-rates
on
the
OCV
are
shown
in
Figure
7.
The extracted
OCV
results under
an adequate
relaxing
period
show
the voltage
patterns
for
different
C-rates
correspond
to both
charge and
discharge
tests.
In that
addition,
the ESRs
are also
the
different
C-rates
correspond
to
both
charge
and
discharge
tests.
In
addition,
the
ESRs
are
also
extracted from an instantaneous response of the pulse charge and discharge tests. The ESRs are
extracted
from an
response
of the pulse
charge 8.and
discharge
tests. The
are
almost constant
forinstantaneous
the SOC and C-rates
as illustrated
in Figure
It can
be concluded
that ESRs
the pulse
almost
for the
SOC
and C-rates
illustrated
Figure 8. It can
be concluded
the pulse
currentconstant
amplitudes
have
no effect
on the as
OCV
and ESRincharacteristics
under
a constantthat
temperature
current
haveperiod.
no effect
on the9 OCV
andthe
ESR
characteristics
under
a constant
temperature
and theamplitudes
same resting
Figure
shows
OCV
comparison
between
charge
(chg) and
and
the same
period.
Figure
9 shows
the OCV
comparison
between acharge
and
discharge
(dis) resting
under the
different
C-rates.
During
the charge
and discharge,
small (chg)
hysteresis
discharge
(dis)
under
the
different
C-rates.
During
the
charge
and
discharge,
a
small
hysteresis
occurs in the range of 5%–40% SOC, which is magnified in Figure 10.
occurs in the range of 5%–40% SOC, which is magnified in Figure 10.
Batteries 2017, 3, 8
7 of 13
Batteries 2017, 3, 8
7 of 13
Batteries 2017, 3, 8
7 of 13
Batteries 2017, 3, 8
7 of 13
(a)
(b)
Figure 7. Effects of pulse current amplitudes on the OCV characteristic at 20 °C with 60 min resting:
Figure 7. Effects of pulse current amplitudes on the OCV characteristic at 20 ◦ C with 60 min resting:
(a) under the charge test; and (b) under the discharge test.
(a) under the charge test; and (b) under the discharge test.
The extracted OCV results under an adequate relaxing period show that the voltage patterns for
the different C-rates correspond to both charge and discharge tests. In addition, the ESRs are also
extracted from an instantaneous response of the pulse charge and discharge tests. The ESRs are almost
constant for the SOC and C-rates as illustrated in Figure 8. It can be concluded that the pulse current
amplitudes have no effect on the OCV and ESR characteristics under a constant temperature and the
(a)
(b)
(a) 9 shows the OCV comparison between charge
(b) (chg) and discharge (dis)
same resting period. Figure
7. Effects
of pulse
current
amplitudes
OCV
athysteresis
20 °C
°Cwith
with60
60min
minresting:
resting:
under Figure
theFigure
different
C-rates.
During
the
chargeon
and
discharge,
a smallat
occurs
in
the range of
7. Effects
of pulse
current
amplitudes
onthe
the
OCV characteristic
characteristic
20
(a) SOC,
under
the
charge
test;
and
(b)
under
the
discharge
test.
5%–40%
which
is
magnified
in
Figure
10.
(a) under the charge test; and (b) under the discharge test.
Figure 8. Effects of pulse current amplitudes on the effective series resistance (ESR) characteristic
tested at 20 °C with 60 min resting.
Figure 8. Effects of pulse current amplitudes on the effective series resistance (ESR) characteristic
Figure
8. 8.
Effects
of of
pulse
current
amplitudes
on on
thethe
effective
series
resistance
(ESR)
characteristic
tested
Figure
Effects
pulse
current
amplitudes
effective
series
resistance
(ESR)
characteristic
tested
at 20 °C with 60 min resting.
◦
attested
20 C at
with
60 with
min 60
resting.
20 °C
min resting.
Figure 9. Hysteresis occurrence on the OCV characteristics tested at 20 °C with 60 min resting.
Figure 10 shows that the C-rates of the pulse tests also have no effect on the hysteresis character.
The hysteresis, which results from mechanical stress, thermo-dynamical entropic effects and
microscopic distortions within the active electrode material during Li-intercalation, is unique for
each cell material [19]. This cell type illustrates a narrow hysteresis property between the charge
and discharge.
The difference in OCV (ΔOCV) for the charge and discharge to the averaged values is shown in
Figure 11. The maximum and minimum voltage gaps of the averaged OCV that occurred at 25% SOC
are only ±14.368 mV, or ±0.379% of its average value.
Figure 9. Hysteresis occurrence on the OCV characteristics tested at 20 °C with 60 min resting.
Figure9.9.Hysteresis
Hysteresisoccurrence
occurrence on
on the
the OCV
characteristics
tested
atat2020
°C◦ C
with
60 60
min
resting.
Figure
OCV
characteristics
tested
with
min
resting.
Figure 10 shows that
the C-rates of
the
pulse
tests also have
no effect
on the
hysteresis
character.
The hysteresis, which results from mechanical stress, thermo-dynamical entropic effects and
Figure 10 shows that the C-rates of the pulse tests also have no effect on the hysteresis character.
microscopic distortions within the active electrode material during Li-intercalation, is unique for
The hysteresis, which results from mechanical stress, thermo-dynamical entropic effects and
each cell material [19]. This cell type illustrates a narrow hysteresis property between the charge
microscopic
distortions within the active electrode material during Li-intercalation, is unique for
and discharge.
each cellThe
material
[19].inThis
typefor
illustrates
a narrow
hysteresis
charge
difference
OCVcell
(ΔOCV)
the charge
and discharge
to theproperty
averagedbetween
values is the
shown
in
andFigure
discharge.
11. The maximum and minimum voltage gaps of the averaged OCV that occurred at 25% SOC
Batteries 2017, 3, 8
Batteries 2017, 3, 8
Batteries 2017, 3, 8
8 of 13
8 of 13
8 of 13
Figure 10. Zoom of the hysteresis occurrence tested at 20 °C
Figure
10. Zoom of the hysteresis occurrence tested at 20 ◦ Cwith
with6060min
minresting.
resting.
Figure 10 shows that the C-rates of the pulse tests also have no effect on the hysteresis
character. The hysteresis, which results from mechanical stress, thermo-dynamical entropic effects
and microscopic distortions within the active electrode material during Li-intercalation, is unique
for each cell material [19]. This cell type illustrates a narrow hysteresis property between the charge
and discharge.
The difference in OCV (∆OCV) for the charge and discharge to the averaged values is shown in
Figure 11. The maximum and minimum voltage gaps of the averaged OCV that occurred at 25% SOC
are only ±14.368
mV,10.
orZoom
±0.379%
its average
value. tested at 20 °C with 60 min resting.
Figure
of theofhysteresis
occurrence
Figure 11. ΔOCV for the averaged charge and discharge values tested at 20 °C with 60 min resting.
4.4. Effects of Current Amplitudes during Continuous Charge and Discharge Tests on the Open Circuit
Voltage Approximation
In this study, continuous charge and discharge tests were performed with different current
amplitudes (C-rates) between C/40 and 1C within the operating voltage ranges of the cell in order to
study the influence of C-rates on the terminal voltage characteristics (VTs), and then to investigate
the relationship of VTs on the OCV approximation. The effects of different C-rates on the terminal
voltage characteristic are shown in Figure 12. The C-rates lower than C/20 do not obviously show the
characteristic difference. However, the lower C-rates clearly illustrate the appearance of curly trends
on both charge and discharge voltage profiles, especially between 60% and 80% SOCs as shown in
Figure 11.
11. ∆OCV
ΔOCV for
the averaged
averaged charge
charge and
and discharge
discharge values
values tested
tested at
at 20
20 ◦°C
with 60
60 min
min resting.
resting.
Figure
for the
C with
Figure
12a,b, respectively.
Figure 13 shows the relationship between the average OCV and charge/discharge terminal
4.4. Effects of Current Amplitudes during Continuous Charge and Discharge Tests on the Open Circuit
4.4.voltages
Effects ofunder
Current
Amplitudes
during
Continuous
Charge
andVTs
Discharge
on the
Open Circuit
different
C-rates.
Figure
13a shows
that the
for lowTests
C-rates
precisely
illustrate
Voltage Approximation
Approximation
Voltage
the OCV. The polarization voltage gaps between charge and discharge VTs at the same C-rate can be
reduced
the low
C-rate. The
polarization
mechanism
the VTs
is directly
influenced
the
In this
thisfor
study,
continuous
charge
and discharge
discharge
testsofwere
were
performed
with
differentby
current
In
study,
continuous
charge
and
tests
performed
with
different
current
C-rate. The(C-rates)
cell operating
at the
higher
current
presents
more polarization
effects. of
Asthe
aforementioned
amplitudes
between
C/40
and
1C
within
the
operating
voltage
ranges
cell
in
order
to
amplitudes (C-rates) between C/40 and 1C within the operating voltage ranges of the cell in order
in
Section
4.3,
the
ESRs
and
OCVs
for
each
charging
and
discharging
do
not
change
for
the
C-rates.
study
thethe
influence
ofofC-rates
to investigate
investigate
to
study
influence
C-ratesononthe
theterminal
terminalvoltage
voltagecharacteristics
characteristics(VTs),
(VTs), and
and then
then to
Therefore,
the voltage
drops
across
the
ESR depend on
theeffects
current,
resulting
in
the increment
of the
the
relationship
of
VTs
on
the
OCV
approximation.
The
of
different
C-rates
on
the
terminal
the relationship of VTs on the OCV approximation. The effects of different C-rates on the terminal
terminal
voltage. It are
canshown
be recommended
that
the OCVlower
characteristic
be approximated
bythe
voltage
characteristic
inFigure
Figure12.
12.The
TheC-rates
C-rates
thanC/20
C/20can
do not
not
obviously show
show
voltage
characteristic
are shown
in
lower than
do
obviously
the
measuring a terminal voltage at the low testing current.
characteristic
difference.
However,
the
lower
C-rates
clearly
illustrate
the
appearance
of
curly
trends
characteristic
However,
C-rates
clearly
appearance
of curly trends
Figure difference.
13b shows the
mean ofthe
thelower
squared
residuals
of illustrate
the errorsthe
(MSE
C-rate) between the OCV
on both
both charge
charge and
and discharge
discharge voltage
voltage profiles,
profiles, especially
especially between
between 60%
60% and
and 80%
80% SOCs
SOCs as
as shown
shown in
in
on
and terminal voltage for each C-rate of Figure 13a, and shows a testing time reduction for the
OCV
Figure 12a,b,
12a,b, respectively.
respectively.
Figure
approximation
under different rates of continuous testing current.
Figure 13 shows the relationship between the average OCV and charge/discharge terminal
voltages under different C-rates. Figure 13a shows that the VTs for low C-rates precisely illustrate
the OCV. The polarization voltage gaps between charge and discharge VTs at the same C-rate can be
reduced for the low C-rate. The polarization mechanism of the VTs is directly influenced by the
C-rate. The cell operating at the higher current presents more polarization effects. As aforementioned
in Section 4.3, the ESRs and OCVs for each charging and discharging do not change for the C-rates.
Therefore, the voltage drops across the ESR depend on the current, resulting in the increment of the
Batteries 2017, 3, 8
9 of 13
Batteries 2017, 3, 8
9 of 13
(a)
(b)
Figure 12. Effects of current amplitudes on the terminal voltage characteristic at 20 °C: (a) under
Figure 12. Effects of current amplitudes on the terminal voltage characteristic at 20 ◦ C: (a) under
continuous
Batteries
2017, 3, 8 charging; and (b) under continuous discharging.
9 of 13
continuous charging; and (b) under continuous discharging.
Figure 13 shows the relationship between the average OCV and charge/discharge terminal
voltages under different C-rates. Figure 13a shows that the VTs for low C-rates precisely illustrate
the OCV. The polarization voltage gaps between charge and discharge VTs at the same C-rate can
be reduced for the low C-rate. The polarization mechanism of the VTs is directly influenced by the
C-rate. The cell operating at the higher current presents more polarization effects. As aforementioned
in Section 4.3, the ESRs and OCVs for each charging and discharging do not change for the C-rates.
Therefore, the voltage drops across the ESR depend on the current, resulting in the increment of
the terminal voltage. It can be recommended that the OCV characteristic can be approximated by
measuring a terminal voltage at the low testing current.
(a)
(b)
(b)
Figure 13b shows the
mean of the squared residuals of the errors (MSE
C-rate ) between the OCV
Figure 12.
13. Effects
Terminal
voltage
relationship
to the
OCV
approximation:
(a) polarization
differences
of OCV
and terminal
voltage
for
C-rate
of Figure
13a,
and
shows
testing
timeatreduction
for the
Figure
of each
current
amplitudes
on
the
terminal
voltageacharacteristic
20 °C:
(a) under
terminal
voltages
under
different
rates
of
continuous
testing
current
on
the
average
OCV;
(b)
mean
of
continuous
charging;
and (b)rates
under
discharging.
approximation
under
different
ofcontinuous
continuous
testing current.
the squared residuals of the errors (MSE) and testing time reduction for OCV approximation under
different rates of continuous testing current.
The MSEC-rate can be determined separately for charge and discharge by using Equation (5):
SOC
MSEC−rate =
(
2
)
n
1
VTSOCi − OCV (SOCi )
n SOC
(5)
i =1
where VTSOCi is a measured terminal voltage at SOCi for a continuous test, OCV(SOC)i is an open
circuit voltage obtained by OCV averaging at the different C-rates as a function of SOCi for a
sampling number n separately for charge and discharge.
A recommended (a)
continuous testing current rate for the OCV approximation
is C/20 because it
(b)
can save time for charge and discharge tests from 82.86 h to 40.71 h (or 50.87%) with low MSEs of
Figure 13. Terminal voltage relationship to the OCV approximation: (a) polarization differences of
Figure
13. ×Terminal
voltage
relationship
approximation:
(a) respectively.
polarization differences
only
0.1284
10−3 V2 and
0.0771
× 10−3 V2 to
forthe
theOCV
charge
and discharge,
Moreover,ofit is
terminal voltages under different rates of continuous testing current on the average OCV; (b) mean of
terminal
voltages
under
different
rates
of
continuous
testing
current
on
the
average
OCV;
mean
−3 V2 of
also the
faster
than the C/40 rate by 52.39% with the difference of MSEs of only 0.0197 (b)
× 10
and
squared residuals of the errors (MSE) and testing time reduction for OCV approximation under
the
squared
residuals
of
the
errors
(MSE)
and
testing
time
reduction
for
OCV
approximation
under
−3
2
0.0263
×
10
V
for
the
charge
and
discharge,
respectively.
different rates of continuous testing current.
different rates of continuous testing current.
5. Open
Modeling separately for charge and discharge by using Equation (5):
The Circuit
MSEC-rateVoltage
can be determined
The
MSE
can
be
determined
separatelyisfor
charge and discharge
by using Equation (5):
C-rate
A model
of the OCV characteristic in LIBsSOC
essential for the BMS
2 in order to estimate the state
n
1 of the batteries have been proposed [2,20]. They are
variables during operations. Many
OCV
models
MSE
VTSOCi − OCV (SOCi )
(5)
2
C−rate =SOC
n
n SOC
1
related to the internal chemical
variation
of
the
batteries
to
fit
with
the
tested
results,
depending
on(5)
i =1
MSEC−rate =
VTSOCi − OCV (SOCi )
∑ The
n SOC
the purpose of the study and their applications.
factors
that
affected
the
OCV
pattern
are
studied
1 SOCi for a continuous test, OCV(SOC)i is an open
where VTSOCi is a measured terminal voltagei=at
in Section 4, and the step-size of the pulse test and resting period are adjusted to obtain the accurate
i an
foropen
a
circuit
voltage
byalso
OCV
averaging
the
different
C-rates
as test,
a function
of no
SOC
where
aobtained
measured
terminal
voltage
at
SOC
for testing
a continuous
OCV(SOC)
OCV.VT
At
thei is
same
time, we
found
that theat
rates
of
current
(C-rates)
have
effect
on
SOC
i the
i is
sampling
number
n
separately
for
charge
and
discharge.
circuit
voltage
obtained
by
OCV
averaging
at
the
different
C-rates
as
a
function
of
SOC
for
a
sampling
the OCV. The representative of a precise OCV from the experiments under these conditions
can be
i
current rate for the OCV approximation is C/20 because it
numberAnrecommended
separately forcontinuous
charge andtesting
discharge.
can save time for charge and discharge tests from 82.86 h to 40.71 h (or 50.87%) with low MSEs of
only 0.1284 × 10−3 V2 and 0.0771 × 10−3 V2 for the charge and discharge, respectively. Moreover, it is
also faster than the C/40 rate by 52.39% with the difference of MSEs of only 0.0197 × 10−3 V2 and
0.0263 × 10−3 V2 for the charge and discharge, respectively.
(
5. Open Circuit Voltage Modeling
)
Batteries 2017, 3, 8
10 of 13
A recommended continuous testing current rate for the OCV approximation is C/20 because it
can save time for charge and discharge tests from 82.86 h to 40.71 h (or 50.87%) with low MSEs of
only 0.1284 × 10−3 V2 and 0.0771 × 10−3 V2 for the charge and discharge, respectively. Moreover,
it is also faster than the C/40 rate by 52.39% with the difference of MSEs of only 0.0197 × 10−3 V2 and
0.0263 × 10−3 V2 for the charge and discharge, respectively.
5. Open Circuit Voltage Modeling
A model of the OCV characteristic in LIBs is essential for the BMS in order to estimate the state
variables during operations. Many OCV models of the batteries have been proposed [2,20]. They are
related to the internal chemical variation of the batteries to fit with the tested results, depending on the
purpose of the study and their applications. The factors that affected the OCV pattern are studied in
Section 4, and the step-size of the pulse test and resting period are adjusted to obtain the accurate OCV.
At the same time, we also found that the rates of the testing current (C-rates) have no effect on the OCV.
The representative of a precise OCV from the experiments under these conditions can be obtained
by averaging
the
simplified
Batteries 2017,
3, 8OCV under C-rates separately for the charge and discharge. Therefore, a 10
of 13
OCV model for the LMO can only be developed as a function of SOC, and then it is validated with the
obtained by
averaging
the OCV
under high-order
C-rates separately
for the is
charge
Therefore,
a
experimental
OCV
data. The
empirical
polynomial
usedand
fordischarge.
implementing
the model
simplified
OCV
model
for
the
LMO
can
only
be
developed
as
a
function
of
SOC,
and
then
it
is
with a real-time calculation in the BMS application, as shown in Equation (6):
validated with the experimental OCV data. The empirical high-order polynomial is used for
BMS application, as shown in
n in the
implementing the model with a real-time calculation
OCV (SOC ) = ∑ k j SOC j
Equation (6):
(6)
j=0
n
SOC )
(6)
 (kwith
The coefficients (kj ) in Equation (6) are determined
MATLAB (MathWorks Japan, Nagoya,
OCV ( SOC ) =
j
j
j=0
Aichi, Japan) for the experimental SOC and OCV data from the previous section by using a non-linear
The coefficients (kj) in Equation (6) are determined with MATLAB (MathWorks Japan, Nagoya,
least Aichi,
squareJapan)
estimation
technique. The objective function is given, as in Equation (7):
for the experimental SOC and OCV data from the previous section by using a
non-linear least square estimation technique. The objective
m function is given, as in Equation (7):
2
min k f (k, SOC ) − OCV k2 = min ∑
m [ f ( k, SOCi ) − OCVi ]
min f (k , SOC ) − OCV
k
2
k
(7)

k i = 1[ f (k , SOC ) − OCV ] 2
= min
i
i
k
(7)
i =1
where k is the SOC coefficient to be optimized; j is the degree of polynomial; n is the highest-order of
where k is the SOC coefficient to be optimized; j is the degree of polynomial; n is the highest-order of
polynomial; and m is the length of SOC and OCV data.
polynomial; and m is the length of SOC and OCV data.
FromFrom
Equation
(6), the highest-order (n) for smooth fitting of the OCV analytic function for this
Equation (6), the highest-order (n) for smooth fitting of the OCV analytic function for this
LMOLMO
is 17th
for
both
charging
and
thisorder,
order,the
theMSEs
MSEs
the maximum
is 17th for both
charging
anddischarging.
discharging. For
For this
areare
lessless
thanthan
the maximum
−
5
2
criteria
(≤1 (≤1
× 10
isprecise
preciseenough
enough
fitting
model.
The extracted
OCV are
models
that is
forfor
fitting
the the
OCVOCV
model.
The extracted
OCV models
criteria
× 10−5VV2)) that
are shown
lineininFigure
Figure
shownby
by the
the solid
solid line
14.14.
(a)
(b)
Figure 14. OCV fitting results for the lithium manganese oxide (LMO) at 20 °C:◦(a) fitting result for
Figure
14. OCV fitting results for the lithium manganese oxide (LMO) at 20 C: (a) fitting result for
charging; and (b) fitting result for discharging.
charging; and (b) fitting result for discharging.
The fitting results from Figure 14 show that the proposed OCV model can illustrate the voltage
The
fitting results
from
Figure
14 show
the proposed
model
can illustrate
the voltage
characteristics
correctly
along
the SOC
rangethat
on both
charge andOCV
discharge
operations
separately
by
the hysteresis
phenomena.
A SOC
comparison
of both
the MSEs
of estimation
at separately
different by
characteristics
correctly
along the
range on
chargeand
anderrors
discharge
operations
polynomial orders for OCV model fitting is shown in Figure 15. The optimum SOC coefficients of the
OCV model for charge and discharge are shown in Table 2.
Table 2. Optimum state of charge (SOC) coefficients of the OCV model for charge and discharge.
SOC Coefficient
Charge
Discharge
SOC Coefficient
Charge
Discharge
Batteries 2017, 3, 8
11 of 13
the hysteresis phenomena. A comparison of the MSEs and errors of estimation at different polynomial
orders for OCV model fitting is shown in Figure 15. The optimum SOC coefficients of the OCV model
forBatteries
charge2017,
and3, discharge
are shown in Table 2.
8
11 of 13
Batteries 2017, 3, 8
11 of 13
(a)
(b)
Figure 15. Comparison results of MSEs and errors of estimation at different polynomial orders:
Figure 15. Comparison results of MSEs and errors of estimation at different polynomial orders: (a)
(a) results for charge; and (b) results for discharge.
results for charge; and (b) results for discharge.
The errors of OCV model are evaluated in Figure 16 by MSE). The MSEs for charging and
Table 2. Optimum state of charge (SOC) coefficients of the OCV model for charge and discharge.
discharging are only 0.7414 × 10−5 V2 and 0.3848 × 10−5 V2, respectively.
The minimum, maximum,
and average
values of SOC
the estimation
error forCharge
charge are −4.7265
× 10−3 V,
SOC Coefficient
Charge
Discharge
Coefficient
Discharge
−3
−8
6.9326 × 10 V, and 7.8056 × 10 V (or −0.1437%, 0.1961%, and 0.00008%), respectively,
while the
k0
3.0037
3.0016
k9
1.0595 × 10−9
8.4261 × 10−10
−3 −11
(a)
(b)
minimum,
maximum,
and
average
values
of
the
estimation
error
for
discharge
are
−3.0394
× 10
−
1
−
1
−
11
k1
k10
2.3163 × 10
2.0082 × 10
−2.2638 × 10
−1.8003
× 10V,
−
2 −7 V −
6.3308
1.1389
×results
10
(or
−0.0931%,
0.1802%,
0.00004%),
respectively.
k2 × 10−3 V, and
kand
−6.5271
× 10
5.0440
×and
10−2errors
3.6337
× polynomial
10−13
2.8847
× 10−13
11
Figure
15. Comparison
of
MSEs
of estimation
at different
orders:
k3
1.4950 × 10−2
1.1287 × 10−2
(a)
and
for discharge.
3 results
k results for−charge;
2.3529 ×
10−(b)
−1.7962
× 10−3
k12
−4.3564 × 10−15
k
3.8402 × 10−17
4
13
k5
k14
2.5025 × 10−4
1.9382 × 10−4
−2.4147 × 10−19
k6
−1.8436
10−5 are
−1.4444
× 10−5in Figure k16
10−21 for
The
errors of
OCV×model
evaluated
The ×MSEs
15 by MSE).1.0246
−
7
−
7
k7
k16
9.6864
× 10 × 10−5 V7.6498
10
−2.6280 × 10−24
2 and ×
discharging
are only
0.7414
0.3848
× 10−5 V2, respectively.
k8
k17
−3.7174 × 10−8
−2.9500 × 10−8
3.0772 × 10−27
−3.4474 × 10−15
3.0257 × 10−17
−1.8926 × 10−19
−22
7.9827 × 10and
charging
−2.0344 × 10−24
2.3659 × 10−27
−3
The minimum, maximum, and average values of the estimation error for charge are −4.7265 × 10 V,
6.9326 × 10−3 V, and 7.8056 × 10−8 V (or −0.1437%, 0.1961%, and 0.00008%), respectively, while the
The errors
of OCV and
model
are evaluated
in estimation
Figure 16 error
by MSE).
The MSEs
for charging
and
minimum,
maximum,
average
values of the
for discharge
are −3.0394
× 10−3 V,
5 V2 and 0.3848 × 10−5 V2 , respectively.
−3 V,
discharging
only
10−7−V
6.3308 × 10are
and0.7414
1.1389 ×
× 10
(or −0.0931%, 0.1802%, and 0.00004%), respectively.
(a)
(b)
Figure 16. Error evaluation for the OCV model validation for the LMO at 20 °C: (a) error of estimation
for charge; and (b) error of estimation for discharge.
6. Conclusions
This article studied the factors for the accurate OCV characterization of manganese-type Li-ion
batteries for the BMS application. The charge and discharge test system is developed for use with the
OCV pulse test method. An automatic battery test system is proposed for OCV characterization.
(a)
(b)
From this study, we found that the accurate OCV for LMO can be obtained with a small step-size
evaluation for
the OCV
model10%
validation
for the
LMO
at 20 °C:
(a) error the
of estimation
pulseFigure
of 1%16.
forError
the non-linear
regions
below
and above
90%
SOCs.
However,
step-size can
Figure 16. Error evaluation for the OCV model validation for the LMO at 20 ◦ C: (a) error of estimation
for
charge;
and
(b)
error
of
estimation
for
discharge.
be increased up to 5% in the range of 10%–90% SOC for faster extraction with a small error. The
for charge; and (b) error of estimation for discharge.
short resting period of the pulse test directly affects the error of the OCV pattern. A recommended
6. Conclusions
resting
period for accurate OCV on this battery type is 60 min. The testing current rates (C-rate) of
The
minimum,
maximum,
and OCV
average
values
of the
estimationcell
error
for charge
are
the pulse
tests have
no the
effect
to the
and ESROCV
patterns.
This studied
illustrates a Li-ion
small
This article
studied
factors
for the accurate
characterization
of manganese-type
−
3
−
3
−
8
−4.7265
× 10effect
V, between
6.9326 ×charge
10 V, and
7.8056 × 10 V with
(or −the
0.1437%,
0.1961%,
and
hysteresis
maximum
voltage
gap0.00008%),
of only
batteries for
the BMS
application. and
The discharge
charge andoperations
discharge test system
is developed
for use
with
the
respectively,
while
the
minimum,
maximum,
and
average
values
of
the
estimation
28.736
mV. For
relationship
of VTs tobattery
OCV, the
measuring
of
terminalfor
voltage
of
the cellerror
underfor
OCV pulse
test the
method.
An
automatic
test
system
is
proposed
OCV
characterization.
−3 V, 6.3308 × 10−3 V, and 1.1389 × 10−7 V (or −0.0931%, 0.1802%,
discharge
arestudy,
−3.0394
×
10illustrate
the
low
C-rate
of C/20
can
approximate
characteristic
with acceptable
MSE
value
From
this
we found
that the the
accurate
OCV forOCV
LMO
can be obtained
with a small
step-size
and
0.00004%),
respectively.
by
using
only
half
the
time
for
testing.
This
article
also
developed
an
OCV
model
for
the
LMO
a
pulse of 1% for the non-linear regions below 10% and above 90% SOCs. However, the step-sizeas
can
polynomial
SOC to
simplify SOC
the numerical
calculations
in error.
the BMS
be increased function
up to 5%ofin the
the range
of 10%–90%
for faster extraction
withusing
a small
The
application.
model
is validated
the affects
OCV experimental
hasAthe
MSE values
short restingThe
period
of the
pulse testwith
directly
the error of results,
the OCVwhich
pattern.
recommended
resting period for accurate OCV on this battery type is 60 min. The testing current rates (C-rate) of
the pulse tests have no effect to the OCV and ESR patterns. This studied cell illustrates a small
hysteresis effect between charge and discharge operations with the maximum voltage gap of only
Batteries 2017, 3, 8
12 of 13
6. Conclusions
This article studied the factors for the accurate OCV characterization of manganese-type Li-ion
batteries for the BMS application. The charge and discharge test system is developed for use with the
OCV pulse test method. An automatic battery test system is proposed for OCV characterization. From
this study, we found that the accurate OCV for LMO can be obtained with a small step-size pulse of 1%
for the non-linear regions below 10% and above 90% SOCs. However, the step-size can be increased up
to 5% in the range of 10%–90% SOC for faster extraction with a small error. The short resting period of
the pulse test directly affects the error of the OCV pattern. A recommended resting period for accurate
OCV on this battery type is 60 min. The testing current rates (C-rate) of the pulse tests have no effect to
the OCV and ESR patterns. This studied cell illustrates a small hysteresis effect between charge and
discharge operations with the maximum voltage gap of only 28.736 mV. For the relationship of VTs
to OCV, the measuring of terminal voltage of the cell under the low C-rate of C/20 can illustrate the
approximate OCV characteristic with acceptable MSE value by using only half the time for testing.
This article also developed an OCV model for the LMO as a polynomial function of the SOC to
simplify the numerical calculations using in the BMS application. The model is validated with the
OCV experimental results, which has the MSE values of only 0.7414 × 10−5 V2 and 0.3848 × 10−5 V2 ,
and the maximum errors are only 0.1961% and 0.1802% for charging and discharging, respectively.
However, the OCV characterization and modeling, depending on the temperatures and operating
cycles, are still challenging in practical applications. Studies on the changes of the OCV characteristics
and their behaviors with the consideration of life cycles and temperatures should be investigated next,
and are our next steps in the near future.
Acknowledgments: The authors thank the anonymous reviewers for providing useful suggestions and valuable
comments that resulted in the improved quality of the paper.
Author Contributions: Natthawuth Somakettarin and Tsuyoshi Funaki conceived and designed the experiments;
Natthawuth Somakettarin performed the experiments and analyzed the data; Natthawuth Somakettarin and
Tsuyoshi Funaki wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
Chen, M.; Rincon-Mora, G.A. Accurate electrical battery model capable of predicting runtime and I-V
performance. IEEE Trans. Energy Convers. 2006, 21, 504–511. [CrossRef]
Pattipati, B.; Balasingam, B.; Avvari, G.V.; Pattipati, K.R.; Bar-Shalom, Y. Open circuit voltage characterization
of lithium-ion batteries. J. Power Sources 2014, 269, 317–333. [CrossRef]
Roscher, M.A.; Sauer, D.U. Dynamic electric behavior and open-circuit-voltage modeling of LiFePO4 -based
lithium ion secondary batteries. J. Power Sources 2011, 196, 331–336. [CrossRef]
Lee, S.; Kim, J.; Lee, J.; Cho, B.H. State-of-charge and capacity estimation of lithium-ion battery using a new
open-circuit voltage versus state-of-charge. J. Power Sources 2008, 185, 1367–1373. [CrossRef]
Roscher, M.A.; Assfalg, J.; Bohlen, O.S. Detection of utilizable capacity deterioration in battery systems.
IEEE Trans. Veh. Technol. 2011, 60, 98–103. [CrossRef]
Petzl, M.; Danzer, M.A. Advancements in OCV measurement and analysis for lithium-ion batteries.
IEEE Trans. Energy Convers. 2013, 28, 675–681. [CrossRef]
Codeca, F.; Savaresi, S.M.; Rizzoni, G. On Battery State of Charge Estimation: A New Mixed Algorithm.
In Proceedings of the 17th IEEE International Conference on Control Applications, Part of 2008 IEEE
Multi-conference on Systems and Control, San Antonio, TX, USA, 3–5 September 2008; pp. 102–107.
Pattipati, B.; Sankavaram, C.; Pattipati, K.R. System identification and estimation framework for pivotal
automotive BMS characteristics. IEEE Trans. Syst. Man Cybern.-Part C Appl. Rev. 2011, 41, 869–884. [CrossRef]
Somakettarin, N.; Funaki, T. An Experimental Study on Modeling of Transient Response and Parameters
Identification for Mn-Type Li-Ion Battery with Temperature Dependency. In Proceedings of the International
Conference on Renewable Energy Research and Application (ICRERA), Milwaukee, WI, USA, 19–22 October
2014; pp. 804–809.
Batteries 2017, 3, 8
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
13 of 13
Julien, C.M.; Mauger, A.; Zaghib, K.; Groult, H. Comparative issues of cathode materials for Li-ion batteries.
Inorganics 2014, 2, 132–154. [CrossRef]
Kim, D.K.; Muralidharan, P.; Lee, H.W.; Ruffo, R.; Yang, Y.; Chan, C.K.; Peng, H.; Huggins, R.A.; Cui, Y.
Spinel LiMn2 O4 nanorods as Lithium ion battery cathodes. Nano Lett. Am. Chem. Soc. 2008, 8, 3948–3952.
[CrossRef] [PubMed]
Patil, A.; Patil, V.; Shin, D.W.; Choi, J.W.; Paik, D.S.; Yoon, S.J. Review issue and challenges facing rechargeable
thin film lithium batteries. Mater. Res. Bull. 2008, 43, 1913–1942. [CrossRef]
Piao, T.; Parka, S.M.; Dohb, C.H.; Moon, S.I. Intercalation of Li-ion into graphite electrodes studied by AC
impedance measurements. J. Electrochem. Soc. 1999, 146, 2794–2798. [CrossRef]
Wang, J.; Purewal, J.; Liu, P.; Garner, J.H.; Soukazian, S.; Sherman, E.; Sorenson, A.; Vu, L.;
Tataria, H.; Verbrugge, M.W. Degradation of lithium ion batteries employing graphite negatives and
nickel-cobalt-manganese oxide + spinel manganese oxide positives: Part 1, aging mechanisms and life
estimation. J. Power Sources 2014, 269, 937–948. [CrossRef]
Smith, A.J.; Burns, J.C.; Dahn, J.R. High-precision differential capacity analysis of LiMn2 O4 /graphite cells.
Electrochem. Solid-State Lett. 2011, 14, A39–A41. [CrossRef]
Safari, M.; Delacourt, C. Aging of a commercial graphite/LiFePO4 cell. J. Electrochem. 2011, 158, A1123–A1135.
[CrossRef]
Weppner, W.; Huggins, R.A. Determination of the kinetic parameters of mixed-conducting electrodes and
application to the system Li3 Sb. J. Electrochem. Soc. 1977, 124, 1569–1578. [CrossRef]
Bisquert, J. Nanostructured Energy Devices: Equilibrium Concepts and Kinetics, 1st ed.; CRC Press, Taylor &
Francis Group: Boca Raton, FL, USA, 2015; pp. 115–155.
Roscher, M.A.; Bohlen, O.; Vetter, J. OCV hysteresis in Li-ion batteries including two-phase transition
materials. Int. J. Electrochem. 2011, 2011. [CrossRef]
Hu, X.; Li, S.; Peng, H.; Sun, F. Robustness analysis of state-of-charge estimation methods for two types of
Li-ion batteries. J. Power Sources 2012, 217, 209–219. [CrossRef]
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