electronics
Article
Study on the Systematic Design of a Passive Balancing
Algorithm Applying Variable Voltage Deviation
Heewook Song and Seongjun Lee *
Department of Mechanical Engineering, Chosun University, Gwangju 61452, Republic of Korea;
20161889@chosun.kr
* Correspondence: lsj@chosun.ac.kr; Tel.: +82-62-230-7173
Abstract: A balancing circuit in a multi-series battery pack prevents a specific cell from being
overcharged by reducing the voltage difference between the cells. Passive cell balancing is widely
used for easy implementation and volume and size reduction. For optimal passive cell balancing,
the charging/discharging current conditions and the state of charge (voltage condition) of the
battery must be determined. In addition, the balancing algorithm must determine an allowable
voltage deviation threshold between the cells connected in series to determine whether a specific
cell performs a balancing operation. However, previous studies have not dealt with the design of
balancing operating conditions in detail. In addition, the balancing time and efficiency improvement
effect under specific conditions for arbitrary battery cells used in each previous study were mainly
presented. Therefore, this study proposes a variable voltage deviation method in which the threshold
for determining the voltage to be balanced is changed by reflecting the battery capacity, rated current
specification, open-circuit voltage, and resistance of the balancing circuit. In addition, the voltage
management performance and efficiency analysis results of the existing balancing algorithm and
the proposed balancing method for the case where there is parameter deviation in the cells of the
battery pack are also presented. The proposed method was verified through the simulation and
experimental results of a reduced battery module in which three types of battery cells, INR 18650-30Q,
INR 18650-29E, and INR 21700-50E, were arranged in 4-series.
Citation: Song, H.; Lee, S. Study on
Keywords: energy storage system (ESS); passive balancing; lithium-ion battery; variable voltage
deviation
the Systematic Design of a Passive
Balancing Algorithm Applying
Variable Voltage Deviation.
Electronics 2023, 12, 2587. https://
doi.org/10.3390/electronics12122587
Academic Editors: Dmitry Baimel
and Inna Katz
Received: 8 April 2023
Revised: 4 June 2023
Accepted: 6 June 2023
Published: 8 June 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1. Introduction
Recently, as the demand for electric vehicles, electric ships, and energy storage systems
(ESS) has increased, research on high-voltage and large-capacity lithium-battery systems
has been actively conducted. Large-capacity battery packs are manufactured by connecting
multiple battery cells in series and parallel. The battery pack has variations in the state of
charge, internal resistance, and capacity for each applied battery cell due to manufacturing
and assembly errors of the applied battery cells. In addition, as the battery supplies current
to the load, temperature deviations occur between the modules and cells in the pack, which
cause the aging rate of the battery cells to change [1–3]. Therefore, because the voltage
deviation between the cells of a battery pack gradually increases as cycling progresses,
a balancing circuit is applied to prevent a specific cell from being overcharged. The cellbalancing circuit equalizes the state of charge of the cells applied to the battery pack by
consuming the energy of a cell with a high state of charge or transferring it to another cell.
At this time, voltage or SOC can be used as a criterion for determining whether the state of
charge is high or low; A. Petri [4] mentioned that balancing operations using SOC require
high estimation accuracy. Therefore, in this paper, the switch of the balancing circuit is
controlled by the voltage difference between cells.
The passive balancing method balances each cell by connecting a resistor in parallel
with the battery and lowering the energy of the cell with a relatively high voltage to the
Electronics 2023, 12, 2587. https://doi.org/10.3390/electronics12122587
https://www.mdpi.com/journal/electronics
Electronics 2023, 12, 2587
2 of 19
resistor. It is widely used owing to its simple circuit configuration, small volume, and
low price; however, it has the disadvantages of low energy efficiency and heat problems.
Passive balancing methods are divided into fixed and switched shunting resistor methods [5–15]. The fixed shunting resistor method is a circuit in which a resistor is connected
in parallel to a battery, as shown in Figure 1a. The voltage of each battery cell is determined
by the ratio of the balancing resistor so that a specific cell can be prevented from being
overcharged. However, because the resistance is always connected, it causes large energy
loss. Accordingly, as shown in Figure 1b, the switched shunting resistor method, which can
selectively connect a resistor through a switch, has been widely applied. This can reduce the
voltage deviation between cells by discharging energy through a resistor only in cells with a
relatively high voltage through a switch on/off control. The active balancing method is generally a method of transferring energy from a cell with relatively high energy to a cell with
relatively low energy by using a power conversion circuit. Figure 1c shows a representative
balancing circuit using the buck–boost method and Figure 1d shows a flyback converter.
Active balancing has the advantages of faster balancing speed and higher efficiency than
passive balancing, but has a disadvantage in that size increases as the number of parts
increases compared to passive balancing. Therefore, in the case of an active balancing
circuit, it is necessary to study to minimize the size by determining the power capacity to
be processed in the balancing circuit of the battery pack. In addition, converters applied to
active balancing must apply a high-efficiency topology through efficiency analysis including switching loss and conduction loss of the applied power semiconductor switch and
loss in the case of applying a transformer. The balancing time that can stabilize the voltage
deviation also depends on the converter topology and serial/parallel configuration of the
input/output. Therefore, the selection of the optimal active balancing topology should be
determined through a trade-off between energy efficiency, balancing speed, volume, and
cost of circuit implementation, as suggested in [16]. On the other hand, passive balancing
is widely used in industries because it can be integrated into a battery monitoring board
due to a simple circuit and control. However, if the number of balancing operations is not
reduced, there is a disadvantage of poor efficiency, and a design method for performing
balancing is not systematically presented. Therefore, in this paper, research on an efficient
operation method of the passive balancing circuit is conducted.
Because a balancing circuit must be applied to ensure the voltage stability of a battery
pack in which multiple battery cells are connected in series, several studies on passive
balancing have been conducted. Existing studies have primarily focused on reducing the
balancing time and analyzing the efficiency according to balancing algorithms. However,
because previous studies did not suggest a design method for the charging/discharging
current condition for balancing, cell voltage deviation threshold, or voltage range to apply
the balancing function, it is challenging to apply the proposed method immediately when
the battery cell changes [17–20]. Thiruvonasundari researched reducing the balancing time
by connecting additional balancing resistors in parallel when the voltage deviation between
cells increases in a circuit, in which several passive balancing resistors and switches can be
selectively connected in parallel [17]. The balancing operation algorithm operates under a
charging stage of 0.2 C-rate or less and a cell voltage of 3.3 V or more. For voltage deviation
of 10 mV or more and 25 mV or less, one balancing resistor was connected; additional
balancing resistors were connected for deviations of 2 5 mV or more. Another study, [18],
presented an algorithm that performs balancing when the cell voltage is 3.9 V or more
and the voltage deviation is 30 mV or more. However, even in this study, a method for
setting the voltage deviation threshold of the balancing algorithm and the operating range
for balancing was not presented. Ismail researched increasing the balancing current using
the internal resistance of a MOSFET power semiconductor as the balancing resistance in a
battery pack with a 15-series of 200 Ah high-capacity cells [19]. Since the balancing current
of this study is larger than the current limit of 100 mA when using the switch built into
the battery management system (BMS) monitoring IC, it is suggested that balancing is
performed when the battery cell with a full charge voltage of 3.6 V is over 3.55 V. S. Kivrak
Electronics 2023, 12, 2587
iconductor switch and loss in the case of applying a transformer. The balancing time that
can stabilize the voltage deviation also depends on the converter topology and serial/parallel configuration of the input/output. Therefore, the selection of the optimal active balancing topology should be determined through a trade-off between energy efficiency, balancing speed, volume, and cost of circuit implementation, as suggested in [16]. On the
3 of 19
other hand, passive balancing is widely used in industries because it can be integrated
into a battery monitoring board due to a simple circuit and control. However, if the number of balancing operations is not reduced, there is a disadvantage of poor efficiency, and
a presented
design method
for performing
not systematically
presented.
in
a balancing
algorithmbalancing
when theisvoltage
difference between
cellsTherefore,
is more than
this
paper,
research
on anasefficient
operation
method
the passive
balancing
circuit
is
50 mV
using
a MOSFET
a balancing
resistor,
but a of
voltage
deviation
threshold
setting
conducted.
method was not presented in this study [20].
Electronics 2023, 12, x FOR PEER REVIEW
3 of 20
(a)
(b)
(c)
(d)
Figure
circuits:
(a) (a)
Fixed-shunt
resistor
passive
balancing,
(b)
Figure 1.
1. Passive
Passiveand
andactive
activecell-balancing
cell-balancing
circuits:
Fixed-shunt
resistor
passive
balancing,
switched-shunt resistor passive balancing, (c) buck–boost active balancing circuit, (d) flyback active
(b) switched-shunt resistor passive balancing, (c) buck–boost active balancing circuit, (d) flyback
balancing circuit.
active balancing circuit.
Because
a balancing
must be study,
applied
to ensure
the voltage
stability of
a battery
As mentioned
above,circuit
in a previous
a circuit
topology
for increasing
the
balancpack
in
which
multiple
battery
cells
are
connected
in
series,
several
studies
on
passive
ing current in passive balancing and the voltage management performance between
cells
balancing
have
conducted.
Existing
studies
have
primarily
focused
on reducing
the
according to
the been
balancing
operation
time and
voltage
deviation
was
conducted.
The design
balancing
time and analyzing
the efficiency
according
balancing
algorithms.
However,
values
of previously
studied balancing
algorithms
aretolisted
in Table
1. However,
it was
because
previous
studies
did
not
suggest
a
design
method
for
the
charging/discharging
challenging to directly utilize the design method when the battery cell was changed because
current
forthe
balancing,
voltage has
deviation
threshold,
orin
voltage
range studies.
to apply
a designcondition
method for
balancingcell
algorithm
not been
presented
the existing
the balancing function, it is challenging to apply the proposed method immediately when
the battery
cell changes
researched
Table
1. Balancing
algorithm[17–20].
operatingThiruvonasundari
conditions in previous
studies. reducing the balancing
time by connecting additional balancing resistors in parallel when the voltage deviation
Currentin which several passive balancing resistors and
between
cellsAlgorithm
increases in a circuit,
Balancing
Voltage Condition
Voltage Threshold
Condition
switches can be selectively connected in parallel [17]. The balancing operation algorithm
D. Thiruvonasundari
[17]
above
25 mV
operates
under a charging
stageCharge
of 0.2 C-rate or less
and3.3a Vcell voltage of 3.3
V or more.
D. Thiruvonasundari
above
V one balancing
30resistor
mV
For
voltage deviation[18]
of 10 mVCharge
or more and 25 mV
or 3.9
less,
was
K. Ismail [19]
Charge
above 3.55–3.6 V
50 mV
connected; additional balancing resistors were connected for deviations of 2 5 mV or more.
S. Kivrak [20]
Charge
whole range
50 mV
Another study, [18], presented an algorithm that performs balancing when the cell voltage
is 3.9 V or more and the voltage deviation is 30 mV or more. However, even in this study,
Therefore,
this study
proposed
a methodthreshold
to systematically
design thealgorithm
voltage deviation
a method
for setting
the voltage
deviation
of the balancing
and the
threshold range
and the
andwas
voltage
conditions,
which
are the design
variables
of the
operating
forcurrent
balancing
not presented.
Ismail
researched
increasing
the balancpassive
balancing
algorithm,
when
the
battery
cell
is
determined.
The
voltage
deviation
ing current using the internal resistance of a MOSFET power semiconductor as the balthreshold
is designed
to have pack
a variable
according
the
operating point
of
ancing
resistance
in a battery
with avalue
15-series
of 200to
Ah
high-capacity
cells(voltage)
[19]. Since
the
battery,
considering
the
battery
cell
capacity,
open-circuit
voltage
(OCV),
load
current,
the balancing current of this study is larger than the current limit of 100 mA when using
andswitch
balancing
The proposed
method
was validated
through the
and
the
builtresistance.
into the battery
management
system
(BMS) monitoring
IC,simulation
it is suggested
experimental
results
of
a
reduced
module
with
three
types
of
cylindrical
battery
cells
(INR
that balancing is performed when the battery cell with a full charge voltage of 3.6 V is over
18650-30Q, INR 18650-29E, and INR 21700-50E) in series.
3.55 V. S. Kivrak presented a balancing algorithm when the voltage difference between
The remainder of this paper is organized as follows. Section 2 presents the variable
cells is more than 50 mV using a MOSFET as a balancing resistor, but a voltage deviation
voltage deviation threshold and algorithm operation range design method proposed in this
threshold setting method was not presented in this study [20].
As mentioned above, in a previous study, a circuit topology for increasing the balancing current in passive balancing and the voltage management performance between
cells according to the balancing operation time and voltage deviation was conducted. The
design values of previously studied balancing algorithms are listed in Table 1. However,
Electronics 2023, 12, 2587
4 of 19
paper. Section 3 presents a case where there is parameter deviation of the battery cell and
the battery algorithm performance results in terms of voltage management performance
and efficiency when the cells are changed. Section 4 demonstrates the feasibility of the
proposed method through a balancing experiment on a scaled-down module using three
types of battery cells. Finally, Section 5 summarizes the study.
2. Balancing Algorithm Design Methodology
2.1. Balancing Voltage Deviation Determination
The proposed balancing method is a variable voltage deviation method in which the
allowable voltage deviation between cells varies according to the voltage operating point
of the battery. When a battery with a capacity of Ah and a state of charge of SOC is charged
with Irated , which is the rated charging current, Tch , representing the time required to be
fully charged, can be summarized as in Equation (1).
Tch =
Ah × (1 − SOC )
× 3600
Irated
(1)
However, when charging proceeds while balancing a specific cell inside the battery
pack, the cell is charged with a current reduced by the balancing current shown in Equation
(2); thus, it is fully charged at the time shown in Equation (3), where Ibal represents the
balancing current, Vnom is the nominal voltage of the battery, and Rbal is the balancing
resistance.
Ibal = Vnom/Rbal
(2)
Tch,bal =
Irated
× Tch
( I rated − Ibal )
(3)
Assuming that the relationship between the battery SOC and voltage is linear, Vs,rate
representing the voltage change rate per second can be expressed by Equation (4). In
addition, when the battery is charged with the rated current, the time required to reach the
full-charge voltage Vmax from Vset , which is the minimum voltage at which the balancing
function operates, Tch,set , can be summarized using Equation (5). Therefore, the allowable
voltage deviation threshold between cells at a specific operating point of the battery can be
represented by Equation (6).
(Vmax − Vset )
Tch,set
(4)
Ah × (1 − SOC set )
× 3600
Irated
(5)
Vdi f f = ( Tch,bal − Tch,set ) × Vs,rate
(6)
Vs,rate =
Tch,set =
Therefore, if the voltage deviation between the cells at the full charge voltage of
the battery is defined as Vdiff,target , the voltage deviation threshold (Vth ) for the balancing
operation can be designed as shown in Equation (7).
Vth = Vdi f f ,target + Vdi f f
(7)
Figure 2 shows the OCV-SOC and Vs,rate graphs of three types of batteries with different
capacities and characteristics to show the voltage deviation design method described above.
Vset , representing the lower limit voltage for performing the balancing operation, was
selected at approximately 20% SOC to avoid a balancing operation at low SOC, where the
deviation between battery cells is essentially significant.
𝑉 =𝑉
,
𝑉
(7)
Figure 2 shows the OCV-SOC and Vs,rate graphs of three types of batteries with different capacities and characteristics to show the voltage deviation design method described
above. Vset, representing the lower limit voltage for performing the balancing operation,
5 of 19
was selected at approximately 20% SOC to avoid a balancing operation at low SOC, where
the deviation between battery cells is essentially significant.
Electronics 2023, 12, 2587
(a)
(b)
(c)
Figure 2. Algorithm design variables for a total of three types of batteries with different capacities;
Figure
2. Algorithm design variables for a total of three types of batteries with different capacities;
(a) INR 18650-30Q, (b) INR 18650-29E, and (c) INR 21700-50E.
(a) INR 18650-30Q, (b) INR 18650-29E, and (c) INR 21700-50E.
The proposed variable voltage deviation method has the advantage of being able to
The proposed
deviation
method
hasfor
the
advantage
being able
design
the voltagevariable
deviationvoltage
between
cells to be
managed
each
operatingofvoltage
of to
design
the
voltage
deviation
between
cells
to
be
managed
for
each
operating
voltage
the battery when the capacity, OCV characteristics, and balancing resistance of the cellof the
battery
when
the
capacity,
characteristics,
thedifferent,
cell applied
applied
to the
battery
packOCV
are known.
Therefore,and
evenbalancing
when the resistance
battery cellsofare
to athe
battery
pack
are
known.
Therefore,
even
when
the
battery
cells
are
different,
a
voltage-deviation threshold for balancing can be systematically established. Figure
3
voltage-deviation
threshold
for balancing
canthree
be systematically
established.
Figure
3 shows
shows the variable
voltage deviations
for the
types of batteries
with different
capactheities
variable
voltage deviations
fortothe
typesmethod.
of batteries
with
different
capacities
and characteristics
according
thethree
proposed
At this
time,
the allowable
and
characteristics
to thecells
proposed
method.
At this
time,
allowable
voltage
voltage
deviation according
target between
at full charge
voltage
and
the the
balancing
resistor
were set target
to 10 mV
and 33 cells
Ω, respectively,
considering
of the
dedicated
deviation
between
at full charge
voltage the
andspecifications
the balancing
resistor
were set
for cell
monitoring
and balancing
In all three cases,
the operating
to IC
10 used
mV and
33 voltage
Ω, respectively,
considering
the[21].
specifications
of theasdedicated
IC used
of themonitoring
battery decreased,
there was
time
until the
battery
was fully
forvoltage
cell voltage
and balancing
[21].
Intoallbalance
three cases,
as the
operating
voltage
increasing
the allowable
voltage
between
In addition,
because
of charged,
the battery
decreased,
there was
timedeviation
to balance
untilthe
thecells.
battery
was fully
charged,
the voltage
threshold
high at abetween
low SOC,
thecells.
balancing
circuit operation
increasing
thedeviation
allowable
voltagewas
deviation
the
In addition,
because
Electronics 2023, 12, x FOR PEER REVIEW
6 of 20 the
was
minimized
at
a
low
SOC.
voltage deviation threshold was high at a low SOC, the balancing circuit operation was
minimized at a low SOC.
Figure
voltage
deviation
according
to battery
type.type.
Figure3.3.Allowable
Allowable
voltage
deviation
according
to battery
2.2.Load
LoadCondition
Condition
Determination
Balancing
2.2.
Determination
forfor
Balancing
Thebalancing
balancingalgorithm
algorithm
consumes
energy
of the
corresponding
cell through
a
The
consumes
thethe
energy
of the
corresponding
cell through
a
resistor
voltage
deviation
between
the the
cellscells
exceeds
the threshold
voltage.
How-Howresistorwhen
whenthe
the
voltage
deviation
between
exceeds
the threshold
voltage.
ever,
efficiency
depending
ever,because
becausethe
thebalancing
balancingoperation
operationaffects
affectsthe
thecharge/discharge
charge/discharge
efficiency
depending on
on
whether
it
is
a
charge
or
discharge
condition,
it
is
necessary
to
determine
the
load
con-condiwhether it is a charge or discharge condition, it is necessary to determine the load
ditions
for
balancing.
Therefore,
the
effect
of
the
balancing
algorithm
operation
according
tions for balancing. Therefore, the effect of the balancing algorithm operation according
to the charge/discharge/rest load conditions was analyzed using a simulation model of a
reduced module with four INR 18650-30Q battery cells in series.
Research on various electrical equivalent circuit models (ECMs) to simulate the characteristics of lithium batteries has been conducted [22–25]. A lithium battery can be modeled by including an RC ladder in which a resistor and a capacitor are connected in paral-
Electronics 2023, 12, 2587
6 of 19
to the charge/discharge/rest load conditions was analyzed using a simulation model of a
reduced module with four INR 18650-30Q battery cells in series.
Research on various electrical equivalent circuit models (ECMs) to simulate the characteristics of lithium batteries has been conducted [22–25]. A lithium battery can be modeled
by including an RC ladder in which a resistor and a capacitor are connected in parallel in
addition to modeling represented by an open voltage source and a resistor [22]. At this
time, the number of RC ladders affects the improvement of modeling accuracy, so it is
determined by considering the accuracy and calculation amount. Additionally, J. Meng
proposed a modeling method in which a resistance was added in parallel to the battery
terminals mentioned above to detect the defect of the battery’s internal short circuit [26].
In this paper, since the analysis of the voltage management characteristics between cells
according to the design of the balancing algorithm is being studied, a reduced module
simulation model was designed using the electrical equivalent circuit cell model as shown
in Figure 4. The battery cell can be represented by Equation (8). The open-circuit voltage is
simulated by VOCV , and the Ri , Rdiff , and Cdiff parameters are used to simulate the dynamics
of the voltage versus current. The ECM parameters according to the SOC of the battery cell
are shown in Figure 5 and the detailed values are summarized in Table A1 in Appendix A.
Additionally, the voltage accuracies of the MATLAB/Simulink battery simulation model
to which the parameters were applied are shown in Figure 6. Figure 6 shows that the
simulation model shows a voltage error of up to 0.18 V in low SOC with large nonlinearity,
but it can simulate a real battery well within the root mean squared error (RMSE) error of
0.0121 V in the entire operating range of the battery.
Electronics
2023,
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FOR
PEER
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Electronics 2023, 12, x FOR PEER REVIEW
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Vtermial = VOCV − IRi − IRdi f f 1 − e − t/τ
(8)
where, τ = Rdi f f × Cdi f f
Figure
4. Equivalent electrical
circuit model
of lithium
battery.
Figure
Figure4.4.Equivalent
Equivalentelectrical
electricalcircuit
circuitmodel
modelof
oflithium
lithiumbattery.
battery.
Ri Parameter
OCV Parameter
0.023
4
0.022
3.5
0.021
3
0
50
100
SOC(%)
Rdiff Parameter
0.02
0
3000
0.06
50
100
SOC(%)
Cdiff Parameter
2500
0.05
2000
0.04
1500
0.03
0.02
1000
0
50
SOC(%)
100
0
50
100
SOC(%)
Figure
5. Extracted
battery
parameters
of INR
18650-30Q.
Figure
5. Extracted
battery
parameters
of of
INR
18650-30Q.
Figure
5. Extracted
battery
parameters
INR
18650-30Q.
2000
0.04
1500
0.03
0.02
Electronics 2023, 12, 2587
1000
0
50
100
0
50
SOC(%)
100
SOC(%)
7 of 19
Figure 5. Extracted battery parameters of INR 18650-30Q.
Figure 6.
6. Simulation
Simulation modeling
and
simulation
voltage
Figure
modeling verification
verificationof
ofINR
INR18650
1865030Q;
30Q;(a)
(a)experimental
experimental
and
simulation
voltresults,
(b) battery
current,
andand
(c) modeling
errorerror
rate.rate.
age
results,
(b) battery
current,
(c) modeling
To determine whether the balancing operation should be performed under a load
condition among a charging process, discharging process, or rest condition, a simulation
analysis using a reduction module including a balancing circuit and the algorithm shown
in Figure 7 was performed. The parameters of each block in Figure 7 are shown in Table A4
of Appendix A. As shown in Table 2, an SOC deviation of 3%, capacity deviation of 1%,
OCV deviation of 0.05%, and resistance deviation of 10% were set for one cell (cell #3) of the
reduced battery module. The reduced battery module was fully discharged and charged.
Table 2. Simulation initial conditions.
Initial Condition
Parameter
SOC
Cn
OCV
Ri /Rdiff
Cell #1, #2, #4
Cell #3
100%
100% (3.0 Ah)
OCV parameter of Figure 5
Ri , Rdiff /Cdiff parameters of Figure 5
97%
99%
+0.05% compared to other cells
+10% compared to other cells
Figure 8a shows the simulation results of balancing under the discharge conditions. A
balancing loss energy of 0.24 Wh was generated to satisfy the target voltage deviation of
10 mV at the full charge point during the balancing operation under discharge conditions.
Figure 8b shows the result of the balancing operation in the rest condition; a balancing
loss of 0.53 Wh occurred to satisfy the target voltage deviation. Figure 8c is the result of
the balancing operation under the charging condition; a balancing loss of 0.22 Wh was
generated to satisfy the voltage deviation target of 10 mV. Table 3 summarizes the energy
loss during one charge/discharge cycle according to the balance by the load condition.
Electronics 2023, 12, 2587
condition among a charging process, discharging process, or rest condition, a simulation
analysis using a reduction module including a balancing circuit and the algorithm shown
in Figure 7 was performed. The parameters of each block in Figure 7 are shown in Table
A4 of Appendix A. As shown in Table 2, an SOC deviation of 3%, capacity deviation of
1%, OCV deviation of 0.05%, and resistance deviation of 10% were set for one cell (cell #3)
8 of 19
of the reduced battery module. The reduced battery module was fully discharged and
charged.
Figure 7. 4s1p battery module simulation model.
Figure 7. 4s1p battery module simulation model.
Table 3. Balancing loss according to current conditions.
Balancing Condition
Balancing Loss Energy during 1-CC/CV Cycle
Discharging
Rest
Charging
0.24 Wh
0.53 Wh
0.22 Wh
The following conclusions were drawn from the simulation analysis of the three
conditions to establish a balancing algorithm. First, balancing should not be performed
during rest at low SOC. Even if the state of charge is the same at a low SOC, the voltage
deviation between cells is significant, so the balancing operation can change the state of
charge. This is confirmed by the simulation results in Figure 8b. Second, Figure 8a,c show
that balancing at a specific voltage (set to 3.4 V in this case) or higher in the discharge
or charge phase can manage the voltage deviation between the cells while consuming a
Electronics 2023, 12, 2587
Cn
100% (3.0 Ah)
99%
OCV
OCV parameter of Figure 5
+0.05% compared to other cells
Ri/Rdiff
Ri, Rdiff/Cdiff parameters of Figure 5
+10% compared to other cells
Figure 8a shows the simulation results of balancing under the discharge conditions.
9 of 19
A balancing loss energy of 0.24 Wh was generated to satisfy the target voltage deviation
of 10 mV at the full charge point during the balancing operation under discharge conditions.
8benergy.
shows the
result ofbalancing
the balancing
operation
in the rest
condition;
balancsimilarFigure
level of
However,
during
the discharging
phase
furtherareduces
ing
loss of 0.53
Whofoccurred
to satisfy
the balancing
target voltage
Figure
is the
result
the usable
energy
the battery,
allowing
to bedeviation.
performed
while8cthe
battery
is
of
the
balancing
operation
under
the
charging
condition;
a
balancing
loss
of
0.22
Wh
was
charged, which can increase the usable energy. Therefore, based on this analysis result,
generated
to satisfy
the voltage
target
of 10deviation
mV. Tablethreshold
3 summarizes
energy
an algorithm
to balance
above deviation
the variable
voltage
underthe
charging
loss
during
one
charge/discharge
cycle
according
to
the
balance
by
the
load
condition.
conditions was designed, as shown in Figure 9.
Electronics 2023, 12, x FOR PEER REVIEW
(a)
10 of 20
(b)
(c)
Figure
8.
operation
results
according
to
conditions
(a)
(b)
Figure
8. Balancing
Balancing
operation
results
accordingvoltage
to load
load deviation
conditions during
during
(a) discharge,
discharge,
(b) rest,
rest, and
and
algorithm
to balance
above
the variable
threshold
under charging
con(c)
charge
phases.
(c)
chargewas
phases.
ditions
designed, as shown in Figure 9.
Table 3. Balancing loss according to current conditions.
Balancing Condition
Discharging
Rest
Charging
Balancing Loss Energy during 1-CC/CV Cycle
0.24 Wh
0.53 Wh
0.22 Wh
The following conclusions were drawn from the simulation analysis of the three conditions to establish a balancing algorithm. First, balancing should not be performed during rest at low SOC. Even if the state of charge is the same at a low SOC, the voltage deviation between cells is significant, so the balancing operation can change the state of charge.
This is confirmed by the simulation results in Figure 8b. Second, Figure 8a,c show that
balancing at a specific voltage (set to 3.4 V in this case) or higher in the discharge or charge
phase can manage the voltage deviation between the cells while consuming a similar level
of energy. However, balancing during the discharging phase further reduces the usable
energy of the battery, allowing balancing to be performed while the battery is charged,
which can increase the usable energy. Therefore, based on this analysis result, an
Figure9.9.Proposed
Proposedpassive
passivebalancing
balancingalgorithm.
algorithm.
Figure
3. Performance Analysis of the Proposed Method
This section analyzes the voltage management performance of the proposed balancing method for battery cell parameters and type variations through a simulation. In addition, by analyzing the efficiency of the proposed method and the balancing algorithms
with a fixed voltage deviation presented in previous studies, it is suggested that the proposed method is equivalent to or better than the existing method.
Electronics 2023, 12, 2587
10 of 19
3. Performance Analysis of the Proposed Method
This section analyzes the voltage management performance of the proposed balancing
method for battery cell parameters and type variations through a simulation. In addition,
by analyzing the efficiency of the proposed method and the balancing algorithms with a
fixed voltage deviation presented in previous studies, it is suggested that the proposed
method is equivalent to or better than the existing method.
3.1. Performance Analysis According to Parameter Deviation
Simulations reflecting the parameter deviations were performed in the INR 18650-30Q
cell four-series reduced modules. As shown in Figure 10, the battery cell parameters were
set by considering the parameter deviation of the cell measured in the experiment. At this
time, the average value of the measured parameters was applied to the parameters of the
three battery cells, and cell #4 was set to −1% capacity, +10% resistance, and +0.5% OCV
to the average value, which was slightly higher than the deviation between the
Electronics 2023, 12, xcompared
FOR PEER REVIEW
cells. In addition, the SOC of cell #4 was set to 1.5% higher than that of the other cells to
generate an initial voltage deviation.
(a)
(b)
(c)
(d)
11
Figure deviation
10. Parameter
deviation
of INR
Capacity,
Ri, and (d) Rdiff
Figure 10. Parameter
of INR
18650-30Q:
(a) 18650-30Q:
Capacity, (b)(a)OCV,
(c) Ri ,(b)
andOCV,
(d) R(c)
diff .
Figure 11 shows
the 11
simulation
results
of CC-CV
charging
(constant
current–constant
Figure
shows the
simulation
results
of CC-CV
charging
(constant current–con
voltage) with avoltage)
charging
current
of
0.5C-rate
while
the
battery
is
fully
discharged.
Figure
11a
with a charging current of 0.5C-rate while the battery is fully
discharged.
Fi
shows the battery
cell voltage,
andcell
Figure
11b and
shows
the 11b
voltage
deviation
of the
cell
11a shows
the battery
voltage,
Figure
shows
the voltage
deviation
of th
with the minimum
and
maximum
and voltages
the variable
deviation
target
with the
minimum
andvoltages
maximum
and voltage
the variable
voltage
deviation ta
value. Figurevalue.
11c shows
of the
battery
module,
Figure
11d
shows
the
Figurethe
11ccurrent
shows the
current
of the
batteryand
module,
and
Figure
11d
shows the
balancing operation
flag
of
each
cell.
The
fully
discharged
battery
is
charged
with
the
rated
ancing operation flag of each cell. The fully discharged battery is charged with the r
current, and balancing
begins
when begins
the cellwhen
voltage
3.4 Vreaches
or higher,
SOC
20% the SOC
current, and
balancing
thereaches
cell voltage
3.4the
V or
higher,
point. Although
there
is
a
voltage
deviation
owing
to
a
difference
in
the
initial
state
point. Although there is a voltage deviation owing to a difference in theofinitial sta
charge, the voltage
managed
the target by
variable
voltage
deviation
as balancing
is balanci
charge,isthe
voltageby
is managed
the target
variable
voltage
deviation as
performed inperformed
the charging
As described
above,
the proposed
balancing
algorithm
in stage.
the charging
stage. As
described
above, the
proposed
balancing algor
using variable
voltage
deviation
can
perform
cell-to-cell
voltage
management
well
even
using variable voltage deviation can perform cell-to-cell voltage management
well
under manufacturing deviation and differences in the state of charge of each cell us
the battery module.
Electronics 2023, 12, 2587
11 of 19
Electronics 2023, 12, x FOR PEER REVIEW
12 of 20
under manufacturing deviation and differences in the state of charge of each cell used in
the battery module.
Figure11.
11.Balancing
Balancing
algorithm
operation
results
according
to parameter
error:
(a) Cell
voltages,
Figure
algorithm
operation
results
according
to parameter
error:
(a) Cell
voltages,
(b)
variable
deviation
boundary,
(c) (c)
Load
Current,
(d) (d)
Cells
(b)Cell
Cellvoltage
voltagedeviation
deviationand
andproposed
proposed
variable
deviation
boundary,
Load
Current,
Cells
balancing
balancingon/off
on/offcommand
command.
3.2.Performance
PerformanceAnalysis
Analysisaccording
AccordingtotoBattery
BatteryCell
CellType
Type
3.2.
Thissection
section presents
presents the
the voltage
voltage management
This
managementperformance
performanceofofthe
theproposed
proposedbalancing
balancmethod
when
a
reduced
module
using
three
cylindrical
lithium
batteries
(INR
18650-30Q,
ing method when a reduced module using three cylindrical lithium batteries
(INR
18650INR INR
18650-29E,
and INR
is fullyischarged
at a current
of 0.5C-rate.
To facilitate
the
30Q,
18650-29E,
and21700-50E)
INR 21700-50E)
fully charged
at a current
of 0.5C-rate.
To faanalysis
parameter
deviation influence,
three cells
the reduced
module
set the
same
cilitate
theofanalysis
of parameter
deviationthe
influence,
theof
three
cells of the
reduced
module
parameters
and
applied
the
parameter
deviation
to
only
one
cell.
The
battery
parameters
set the same parameters and applied the parameter deviation to only one cell. The battery
used in the used
simulation
shown in
Figure
5 for
INR 18650-30Q,
in Figures
12in
and
13
parameters
in the are
simulation
are
shown
in Figure
5 for INRand
18650-30Q,
and
Figfor
INR
18650-29E
and
INR
21700-50E,
respectively.
The
detailed
parameter
values
of
ures 12 and 13 for INR 18650-29E and INR 21700-50E, respectively. The detailed parameter
Figures
12
and
13
are
summarized
in
Tables
A2
and
A3.
As
shown
in
Table
4,
the
parameter
values of Figures 12 and 13 are summarized in Tables A2 and A3. As shown in Table 4, the
settings of the reduced module to which the three cell types were applied were set to a
parameter settings of the reduced module to which the three cell types were applied were
slightly smaller capacity and a higher SOC for cell #4.
set to a slightly smaller capacity and a higher SOC for cell #4.
Table 4. Battery simulation initial conditions.
OCV Parameter
Battery Type
Initial Condition
4
Parameter
0.028 #1, #2, #3
Cell
3.8
Module #1
with
INR 18650-30Q
Module #2
with
INR 18650-29E
Module #3
with
INR 21700-50E
Ri Parameter
0.029
Cell #4
SOC
0%
0.027 (3.0 Ah)
Cn
100%
3.4
OCV
OCV parameter of Figure 5
Ri /Rdiff
Ri , Rdiff /Cdiff
parameters of Figure 5
0.026
0
50
100
0
50
100
SOC
0%
SOC(%)
SOC(%)
Cn
100% (2.66 Ah)
Rdiff Parameter
Cdiff Parameter
6000
0.08
OCV
OCV parameter
of Figure 12
Ri /Rdiff
Ri , Rdiff /Cdiff parameters of Figure 12
SOC
0.06
4000 0%
Cn
100% (4.83 Ah)
OCV
OCV parameter of Figure 13
0.04
2000
Ri /Rdiff
Ri , Rdiff /Cdiff parameters of Figure 13
3.6
0.02
0
50
SOC(%)
100
0
0
50
SOC(%)
Figure 12. Extracted battery parameters of INR 18650-29E.
100
1.4%
99%
+0.05% compared to other cells
+10% compared to other cells
1.4%
99%
+0.05% compared to other cells
+8% compared to other cells
1%
99%
+0.02% compared to other cells
+8% compared to other cells
set the same parameters and applied the parameter deviation to only one cell. The batt
parameters used in the simulation are shown in Figure 5 for INR 18650-30Q, and in F
ures 12 and 13 for INR 18650-29E and INR 21700-50E, respectively. The detailed parame
values of Figures 12 and 13 are summarized in Tables A2 and A3. As shown in Table 4,
parameter settings of the reduced module to which the three cell types were
w
12 ofapplied
19
set to a slightly smaller capacity and a higher SOC for cell #4.
Electronics 2023, 12, 2587
Electronics 2023, 12, x FOR PEER REVIEW
13 of 20
Figure 12. Extracted battery parameters of INR 18650-29E.
Figure
12. Extracted battery parameters of INR 18650-29E.
Battery Type
Module #1
with
INR 18650-30Q
Module #2
with
INR 18650-29E
Figure 13.
13. Extracted
Extracted battery
of INR
21700-50E.
Figure
batteryparameters
parameters
of INR
21700-50E.
Figure 14a shows the charging simulation results of the reduced module using INR
18650-30Q.
Voltage
deviation
of conditions.
50 mV exceeded at 3.4 V or less, which is not balanced
Table
4. Battery
simulation
initial
due to SOC’s initial error. However, balancing is performed when the voltage deviation
Initial
Condition
between cells exceeds the threshold voltage
during
charging; when the full charge voltage
Parameter
is reached, it can be confirmed
that#3
the voltage is controlled to the 10 mVCell
target
Cell #1, #2,
#4 voltage.
SOC
Cn
OCV
Ri/Rdiff
SOC
Cn
OCV
Ri/Rdiff
SOC
0%
100% (3.0 Ah)
OCV parameter of Figure 5
Ri, Rdiff/Cdiff parameters of Figure 5
0%
100% (2.66 Ah)
OCV parameter of Figure 12
Ri, Rdiff/Cdiff parameters of Figure 12
0%
1.4%
99%
+0.05% compared to other cells
+10% compared to other cells
1.4%
99%
+0.05% compared to other cells
+8% compared to other cells
1%
Electronics 2023, 12, 2587
x FOR PEER REVIEW
(a)
1413of
of 20
19
(b)
(c)
Figure
Figure 14.
14. Simulation
Simulation results
results of
of the
the proposed
proposed balancing
balancing method
method for
for each
each battery
battery type
type (1st
(1stwaveform:
waveform:
cell voltage, 2nd: voltage deviation, 3rd: load current, 4th: balancing operation flag); (a) INR 18650cell voltage, 2nd: voltage deviation, 3rd: load current, 4th: balancing operation flag); (a) INR
30Q, (b) INR 18650-29E, (c) INR 21700-50E.
18650-30Q, (b) INR 18650-29E, (c) INR 21700-50E.
Figure
Figure 14b
14b shows
shows the
the results
results of
of the
the charging
charging simulation
simulation of
of the
the reduced
reduced module
module using
using
INR
INR 18650-29E.
18650-29E. In
In the
the charging
charging phase,
phase, balancing
balancing is
is performed
performed because
because the
the target
target variable
variable
voltage
indicated by
red dotted
dotted line,
voltage
voltage deviation
deviation of
of 35
35 mV,
mV, indicated
by the
the red
line, exceeds
exceeds the
the 3.5
3.5 V
V voltage
point. Compared with the other two batteries, the OCV characteristic of the 29E cell is that
the voltage variation
variation rate
rate of
of the OCV increases rapidly
rapidly depending
depending on
on the
the state
state of charge
(SOC); therefore, the voltage deviation is maintained for
a
long
time,
even
after
for a long time, even afterbalancing.
balancing.
However, if balancing is performed
performed up to the constant voltage (CV) control phase of the
full-charge voltage, a target voltage deviation of 10 mV can be satisfied.
Figure 14c shows the
the simulation
simulation results
results of
of the
the reduced
reduced module
module using
usingINR
INR21700-50E.
21700-50E.
As described above, if the 3.4 V voltage point is exceeded during charging, the balancing
maintained around
around the designed
designed threshold
threshold
function operates, and the voltage deviation is maintained
range as the charging progresses.
When the
theproposed
proposedmethod
methodis is
applied,
even
if the
battery
are changed,
the
When
applied,
even
if the
battery
cellscells
are changed,
the voltvoltage
deviation
between
cells
managedstably
stablyby
bysystematically
systematicallydesigning
designing the
age
deviation
between
thethe
cells
cancan
bebe
managed
design variables of the balancing algorithm.
3.3. Efficiency
Efficiency Analysis
Analysis of
of the
the Proposed
Proposed Algorithm
Algorithm
3.3.
This
section
analyzed
the
efficiencies
balancing
method
and
thethe
balancThis section analyzed the efficienciesofofthe
theproposed
proposed
balancing
method
and
baling
method
with
a
fixed
voltage
deviation.
The
simulation
was
performed
under
charging
ancing method with a fixed voltage deviation. The simulation was performed under
conditions,
in which the
INR 18650-30Q
cell was fully
in the
fully discharged
charging
conditions,
in which
the INR 18650-30Q
cellcharged
was fully
charged
in the fullystate
disof
the
4-series
reduced
module.
The
passive
balancing
algorithm
was
set
to perform
charged state of the 4-series reduced module. The passive balancing algorithm
was set toa
balancinga operation
the voltage
deviation
over 10was
mV over
at 3.710
V or
perform
balancing when
operation
when the
voltagewas
deviation
mVhigher
at 3.7inVthe
or
charging phase, considering the previous research results presented in Table 1. The battery
higher in the charging phase, considering the previous research results presented in Table
cells of the reduced module used the parameters applied to Module 1, as listed in Table 4.
1. The battery cells of the reduced module used the parameters applied to Module 1, as
Figure 15a shows the voltage and current waveforms of the cells with parameter
listed in Table 4.
deviations as the battery module is charged in the cases of no balancing, balancing with
Figure 15a shows the voltage and current waveforms of the cells with parameter dea fixed voltage deviation, and balancing with the proposed variable voltage deviation.
viations as the battery module is charged in the cases of no balancing, balancing with a
Electronics 2023, 12, x FOR PEER REVIEW
15 of 20
Electronics 2023, 12, 2587
14 of 19
fixed voltage deviation, and balancing with the proposed variable voltage deviation. Figure 15b shows the maximum voltage deviation between the cells for each algorithm and
Figure 15b shows the maximum voltage deviation between the cells for each algorithm and
the energy loss in the balancing resistance. As shown in the figure, the proposed balancing
the energy loss in the balancing resistance. As shown in the figure, the proposed balancing
algorithm can maintain the voltage deviation of the cells within the target value at the
algorithm can maintain the voltage deviation of the cells within the target value at the fully
fully charged voltage point, similar to the existing methods. In addition, it can be concharged voltage point, similar to the existing methods. In addition, it can be confirmed
firmed
the energy
efficiency
can be improved
by approximately
2% (12
mWh) comthat thethat
energy
efficiency
can be improved
by approximately
2% (12 mWh)
compared
with
pared
with
the
existing
balancing
method.
This
is
because
the
proposed
balancing
algothe existing balancing method. This is because the proposed balancing algorithm avoids
rithm
avoids unnecessary
the voltagebetween
difference
the cells
unnecessary
balancing bybalancing
allowing by
theallowing
voltage difference
thebetween
cells to reach
the
to
reach thevoltage
maximum
voltagecorresponding
deviation corresponding
to operating
the voltagepoint.
operating point.
maximum
deviation
to the voltage
(a)
(b)
Figure 15. Comparison of the efficiency of the proposed and existing algorithms: (a) cell voltage and
Figure 15. Comparison of the efficiency of the proposed and existing algorithms: (a) cell voltage and
current waveforms; (b) voltage deviation and balancing loss.
current waveforms; (b) voltage deviation and balancing loss.
4.4.Experiment
ExperimentResults
Results
The
proposed
The proposedpassive
passivebalancing
balancingalgorithm
algorithmwas
wasverified
verifiedusing
usingaareduction
reductionmodule
module
with
withfour
fourbattery
batterycells
cellsof
ofthree
threetypes
typesconnected
connectedin
inseries,
series, aa charge/discharge
charge/dischargecycler,
cycler,and
andaa
BMS
BMScontroller,
controller,as
asshown
shownin
in Figure
Figure 16.
16. The
The experimental
experimental setup
setup consisted
consisted of
of aa 30
30 V/10
V/10AA
class
classbattery
batterycharge/discharge
charge/dischargecycler,
cycler,DC1651A
DC1651Amonitoring/balancing
monitoring/balancingboard
boardwith
withan
anLTC
LTC
6083IC,
IC,Arduino
Arduinocontroller
controllerin
incharge
chargeof
ofexternal
externalcommunication
communicationand
andbalancing
balancingcontrol
control
6083
logic,reduced
reducedbattery
batterymodule,
module,and
andcontrol/monitoring
control/monitoringcomputer.
computer.
logic,
To analyze the feasibility of the proposed method, three of the four batteries were
set to have the same state of charge, and one cell was additionally charged such that the
maximum voltage deviation occurred at the corresponding battery operating voltage. The
voltage deviation of each cell of the reduced module was managed using a balancing board,
and the module was fully charged under CC-CV conditions.
Figure 17a shows the experimental results for the voltage, current, maximum voltage
deviation between the cells, and balancing operation of the reduced module applied with
INR 18650-30Q. Although there is a voltage of 50 mV between cells at the 3.4 V point,
the proposed balancing algorithm operates during charging to maintain a target voltage
deviation of 10 mV at the full charge voltage. Figure 17b shows the experimental results
Electronics 2023, 12, 2587
15 of 19
for the INR 18650-29E battery module. Although there is a maximum voltage deviation
between the cells of 40 mV level at the 3.5 V point, the voltage deviation is reduced to 10 mV
level at the full charge voltage by the proposed balancing algorithm. Figure 17c shows the
experimental results obtained using the INR 21700-50E cell. Although there is a maximum
voltage deviation between the cells of 30 mV at the initial point, the proposed balancing
algorithm operates, and as charging progresses, the voltage deviation reaches the target
voltage level of 10 mV. As described above, the balancing algorithm with variable voltage
Electronics 2023, 12, x FOR PEER REVIEW
16 of 20
deviation proposed in this paper presents a design method capable of stably managing
the
voltage between cells, even when the battery cells are changed.
Electronics 2023, 12, x FOR PEER REVIEW
17 of 20
Figure16.
16.Battery
Batterymodule
moduleexperimental
experimentalconfiguration.
configuration.
Figure
(a)
To analyze the feasibility of the proposed method, three of the four batteries were set
to have the same state of charge, and one cell was additionally charged such that the maximum voltage deviation occurred at the corresponding battery operating voltage. The
voltage deviation of each cell of the reduced module was managed using a balancing
board, and the module was fully charged under CC-CV conditions.
Figure 17a shows the experimental results for the voltage, current, maximum voltage
deviation between the cells, and balancing operation of the reduced module applied with
INR 18650-30Q. Although there is a voltage of 50 mV between cells at the 3.4 V point, the
proposed balancing algorithm operates during charging to maintain a target voltage deviation of 10 mV at the full charge voltage. Figure 17b shows the experimental results for
the INR 18650-29E battery module. Although there is a maximum voltage deviation between the cells of 40 mV level at the 3.5 V point, the voltage deviation is reduced to 10 mV
level at the full charge voltage by the proposed balancing algorithm. Figure 17c shows the
experimental results obtained using the INR 21700-50E cell. Although there is a maximum
voltage deviation between the cells of 30 mV at the initial point, the proposed balancing
algorithm operates, and as charging progresses, the voltage deviation reaches the target
(b)
(c)
voltage level of 10 mV. As described above, the balancing algorithm with variable voltage
Figure 17. Experimental
of the proposed
method
for each
battery
(1st wavedeviation
proposed inresults
this paper
presentsbalancing
a design
method
capable
oftype
stably
Figure
17. Experimental
results
of the proposed
balancing
method
for
each battery
type managing
(1st waveform:
cell voltage,
2nd: charging
current,
3rd:
voltage
deviation,
4th:
balancing operation flag); (a)
the
voltage
between
cells,
even
when
the
battery
cells
are
changed.
form: cell voltage, 2nd: charging current, 3rd: voltage deviation, 4th: balancing operation flag);
INR 18650-30Q, (b) INR 18650-29E, (c) INR 21700-50E.
(a) INR 18650-30Q, (b) INR 18650-29E, (c) INR 21700-50E.
5. Conclusions
This study proposed a variable voltage deviation threshold design method for passive balancing when the specifications of the battery cell capacity, OCV characteristics,
balancing resistance, and rated charging current are given. The proposed method can easily design and apply the algorithm even if the battery cell is changed because it presents
a voltage deviation design method that reflects the primary characteristics of the cell ap-
Electronics 2023, 12, 2587
16 of 19
5. Conclusions
This study proposed a variable voltage deviation threshold design method for passive
balancing when the specifications of the battery cell capacity, OCV characteristics, balancing
resistance, and rated charging current are given. The proposed method can easily design
and apply the algorithm even if the battery cell is changed because it presents a voltage
deviation design method that reflects the primary characteristics of the cell applied to the
battery pack.
In addition, the effect of the deviation of the parameters applied to the battery pack on
the balancing performance was analyzed and presented. In this study, an experiment was
conducted to measure the parameter deviation of the battery cell applied to the module. It
was confirmed that the cells of three different types of cylindrical lithium batteries (INR
18650-30Q, INR 18650-29E, INR 21700-50E) had an initial deviation of 0.3% in capacity, 0.3%
in OCV, and 5% in resistance. Through the balancing simulation of the reduction module
reflecting the parameter deviation of the battery cell, it was confirmed that the proposed
balancing method designed using the average value of the battery cell parameter does not
affect the voltage deviation management performance. In addition, it was found through
simulation that the balancing algorithm applying the proposed variable voltage deviation
in the charging phase brought about an efficiency improvement equal to or more than
2% compared to the balancing algorithm with a fixed voltage. The proposed method was
validated through simulations and experiments using a reduced battery module with three
cylindrical lithium batteries in series.
However, the proposed method has a limitation in that it has been verified only
for short-term charging and discharging conditions at room temperature. As the battery
module continues to be charged and discharged, a difference in temperature and aging state
between cells occurs. Therefore, after analyzing the aging and temperature distribution
characteristics of each cell through long-term cycling experiments of the battery module,
the performance of the proposed algorithm will be further analyzed.
Author Contributions: Conceptualization, S.L.; Methodology, H.S. and S.L.; Software, H.S.; Validation, H.S.; Formal analysis, H.S. and S.L.; Investigation, H.S.; Resources, S.L.; Data curation, H.S.;
Writing—Original draft preparation, H.S.; Writing—Review and editing, S.L.; Visualization, H.S.;
Supervision, S.L.; Project administration, S.L.; Funding acquisition, S.L. All authors have read and
agreed to the published version of the manuscript.
Funding: This study was supported by a research fund from Chosun University (2019).
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
The battery cell parameters at 25 ◦ C and 0.5 C-rate used in the simulation and experiment of this study are shown in Tables 2, 3 and A1. Table A1 shows INR 18650-30Q
parameters, Table A2 shows INR 18650-29E parameters and Table A3 shows INR 21700-50E
parameters.
Table A1. INR 18650-30Q battery parameters.
SOC
OCV (V)
Ri (Ω)
Rdiff (Ω)
Cdiff (F)
100%
90%
80%
70%
60%
50%
4.1682
4.0765
4.0157
3.9168
3.8204
3.7336
0.0219
0.0219
0.0213
0.0212
0.0206
0.0213
0.0331
0.0331
0.0247
0.0430
0.0305
0.0291
1058
1058
2476
1507
898
2451
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Table A1. Cont.
SOC
OCV (V)
Ri (Ω)
Rdiff (Ω)
Cdiff (F)
40%
30%
20%
10%
0%
3.6322
3.5200
3.3513
3.2019
2.8277
0.0214
0.0208
0.0215
0.0219
0.0233
0.0337
0.0339
0.0392
0.0613
0.0613
2007
1680
2525
610
610
Table A2. INR 18650-29E battery parameters.
SOC
OCV (V)
Ri (Ω)
Rdiff (Ω)
Cdiff (F)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
4.1146
4.0737
3.9748
3.8945
3.8161
3.7010
3.6322
3.5764
3.5051
3.4022
3.2543
0.0270
0.0266
0.0273
0.0268
0.0266
0.0263
0.0270
0.0270
0.0268
0.0280
0.0288
0.0174
0.0174
0.0236
0.0311
0.0328
0.0201
0.0201
0.0255
0.0242
0.0206
0.0696
2318
4330
2366
1878
1780
1232
2849
3425
2603
3039
5361
Table A3. INR 21700-50E battery parameters.
SOC
OCV (V)
Ri (Ω)
Rdiff (Ω)
Cdiff (F)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
4.1794
4.0842
4.0253
3.9215
3.8275
3.7342
3.6542
3.5677
3.4608
3.3036
2.9362
0.0281
0.0276
0.0274
0.0274
0.0276
0.0272
0.0275
0.0276
0.0283
0.0289
0.0323
0.0187
0.0164
0.0201
0.0243
0.0194
0.0181
0.0240
0.0220
0.0189
0.0377
0.0582
1616
3237
2924
2113
1506
3108
3359
3219
3556
1648
1215
The ECM parameters of the battery cell applied to the simulation model in Figure 7 are
designed as a lookup table that outputs the values of Tables 2, 3 and A1 for each SOC point.
The battery is charged and discharged with CC discharge and CC-CV charge currents
determined from blocks marked with a CC-CV Cycler. The parameters of the model block
applied to Figure 7 are shown in Table A4.
Table A4. Parameters of simulation model.
Parameters
Battery
Cell
Model
Values
OCV
Ri
Rdiff
Cdiff
Table A1 for INR 18650-30Q
Table A2 for INR 18650-29E
Table A3 for INR 21700-50E
Cn
3.0 Ah for INR 18650-30Q
2.66 Ah for INR 18650-29E
4.83 Ah for INR 21700-50E
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Table A4. Cont.
Parameters
CC-CV Cycler
Passive Balancing Model
Values
CC 1.5 A, CV 4.2 V (cutoff current 150 mA) for INR 18650-30Q
CC 1.25 A, CV 4.125 V (cutoff current 62.5 mA) for INR 18650-29E
CC 2.5 A, CV 4.2 V (cutoff current 98 mA) for INR 21700-50E
Ideal Switch and balancing resistor (30 Ω)
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