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batteries
Article
Cell Replacement Strategies for Lithium Ion
Battery Packs
Nenad G. Nenadic *,†, Thomas A. Trabold †and Michael G. Thurston †
Rochester Institute of Technology, Rochester, NY 14623, USA; tatasp@rit.edu (T.A.T.); mgtasp@rit.edu (M.G.T.)
*Correspondence: nxnasp@rit.edu; Tel.: +1-585-662-8250
† These authors contributed equally to this work.
Received: 13 May 2020; Accepted: 17 July 2020; Published: 23 July 2020
Abstract:
The economic value of high-capacity battery systems, being used in a wide variety of
automotive and energy storage applications, is strongly affected by the duration of their service
lifetime. Because many battery systems now feature a very large number of individual cells, it is
necessary to understand how cell-to-cell interactions can affect durability, and how to best replace
poorly performing cells to extend the lifetime of the entire battery pack. This paper first examines the
baseline results of aging individual cells, then aging of cells in a representative 3S3P battery pack,
and compares them to the results of repaired packs. The baseline results indicate nearly the same
rate of capacity fade for single cells and those aged in a pack; however, the capacity variation due
to a few degrees changes in room temperature (
'±
3
◦
C) is significant (
'±
1.5% of capacity of new
cell) compared to the percent change of capacity over the battery life cycle in primary applications
(
'
20–30%). The cell replacement strategies investigation considers two scenarios: early life failure,
where one cell in a pack fails prematurely, and building a pack from used cells for less demanding
applications. Early life failure replacement found that, despite mismatches in impedance and capacity,
a new cell can perform adequately within a pack of moderately aged cells. The second scenario for
reuse of lithium ion battery packs examines the problem of assembling a pack for less-demanding
applications from a set of aged cells, which exhibit more variation in capacity and impedance than
their new counterparts. The cells used in the aging comparison part of the study were deeply
discharged, recovered, assembled in a new pack, and cycled. We discuss the criteria for selecting the
aged cells for building a secondary pack and compare the performance and coulombic efficiency of
the secondary pack to the pack built from new cells and the repaired pack. The pack that employed
aged cells performed well, but its efficiency was reduced.
Keywords: capacity fade; secondary applications; end-of-life; cell balancing; temperature effects
1. Introduction
Large lithium-ion battery packs are emerging in both vehicular and stationary energy storage
applications, with rapidly increasing market penetration expected in the coming decades. The extent
of battery system commercialization in both vehicle and renewable energy applications will depend upon
the environmental and economic benefits that can be realized relative to incumbent technologies and other
advanced mobility and energy technologies, such as fuel cells [
1
]. The effective cost of battery systems can
be reduced by amortizing the cost over longer usage cycles. Two ways to extend the usage cycle of battery
systems are (1) to extend the life of cells and packs in the original application, and (2) to reuse cells for other
applications. For example, several studies have indicated that the cost of plug-in hybrid vehicle battery packs
may be offset by repurposing vehicle batteries in grid support systems [
2
], and some automotive original
equipment manufacturers (OEMs) are actively pursuing this option with energy technology companies [
3
,
4
].
For vehicle applications, Marano et al. [
5
] built a general, high-level model and, based on conservative
Batteries 2020,6, 39; doi:10.3390/batteries6030039 www.mdpi.com/journal/batteries
Batteries 2020,6, 39 2 of 19
assumptions, estimated that vehicles equipped with lithium ion batteries can last up to 10 years and provide
the equivalent of 150,000 miles of travel. For battery packs that have failures or significant capacity loss prior
to reaching the expected life-cycle, some means of recapitalization of the cell value is important to the overall
cost to benefit ratio. Although many studies have addressed fundamental degradation modes of common
battery electrode materials, these studies are often conducted at the “button cell” or single-cell 18650 scale
where effects of assembly, packaging, and integration are not fully comprehended. The importance of
acquiring a detailed understanding of cell aging, individually and in packs, has been recognized previously,
and much recent research has focused on techniques for battery health monitoring and prognostics of
battery packs in electric vehicles (e.g., review articles by [
6
–
8
]). Designing and implementing strategies for
first identifying and then isolating failures of individual cells within a pack is challenging, although some
potential methods have been proposed [
9
–
13
]. Recently, Li et al. [
14
] proposed three categories of approaches
for multicell state estimation:
• treating the battery pack as a single cell of high voltage and capacity;
•
applying single-cell state-of-charge (SOC) estimation methods to every cell in a pack, but this
approach is computationally intensive and cumbersome for practical application;
•
quantifying individual cell SOC by analyzing variations in open circuit voltage and internal
resistance.
The difficulty in assessing and comparing many of these advanced battery system-level
monitoring approaches is that direct, in-situ data from electric vehicles or storage systems are not
readily available in the open literature. Therefore, many researchers have relied on experimental and
modeling studies that start with simpler multi-cell systems and then attempt to extrapolate these
findings to more complex, commercial-scale systems. Dubarry et al. have reported on cell aging and
the degradation mechanisms of a composite positive electrode [
15
,
16
]. Understanding the origins
of cell variations can be used for building more robust packs [
17
]. Moreover, it is well known that
multi-cell (pack) aging behavior can be quite different from that associated with single cells, due to the
need for cell balancing and thermal management, among other effects [
18
,
19
]. Thus, it is important
to first fully characterize aging behavior at the individual cell level as a function of the pertinent
operating parameters and for different electrode materials [
20
]. The cell characterization can be used
for accelerated estimation of remaining capacity and state of charge [21].
In the current research program, after quantifying the aging of individual LiCo 18650 cells at
a statistically significant level, the evaluation process was systematically extended to small packs
which represent small-scale versions of larger commercial battery systems. Pack-level testing was
intended to gain insight into a variety of practical issues associated with commercial battery systems.
The selected pack was a 3
×
3 cell arrangement (three cells are connected in series to form a string and
then three strings are connected in parallel, i.e., 3S3P configuration), with its associated charging and
discharging processes, and enabled comparison of aging of cells in the pack versus individual cell
aging. The replacement strategies considered two scenarios.
The first scenario, the replacement of an early life failure, addresses an important open question for
maintenance of battery packs. The traditional approach in pack maintenance is to replace all cells at once to
control the mismatches. This approach is clearly untenable for very large battery packs. Even for packs
built in a hierarchical fashion, where cells are first assembled into sub-modules, which, in turn, form larger
modules, this replacement philosophy does not work because replacement of a single cell in a module would
require replacement of all the cells in the module, and, by extension of this approach, all the sub-modules,
etc. Replacement of all cells as a result of an early-life failure in a large pack is clearly not economically
viable; therefore, an alternative strategy needs to be established. One strategy for minimizing imbalance
and premature aging in this scenario is to maintain an inventory of cells aged to different levels of capacity
fade and to select the appropriately aged cell, or cells, to effect the repair. The experimental results reported
here have been obtained on a small pack, which is a module that could be used in larger packs. Since larger
packs are built hierarchically, where modules are often treated as larger cells, the conclusions of this study
should provide important insight into the behavior of larger packs as well.
Batteries 2020,6, 39 3 of 19
The second scenario addresses the problem of secondary uses for the cells in a less demanding
application after the end of useful life in a higher-performance application. These cells, while no
longer suitable for the original applications, may be deemed adequate for less demanding applications.
For example, studies have indicated that the cost of plug-in hybrid vehicle battery packs may be
reduced by repurposing vehicle batteries in grid support systems because modules would be sold to
the secondary user and the primary user would not have to assume the processing cost associated with
safe disposal [
2
,
22
,
23
]. For example, Schneider et al. [
24
], who developed methods for assessment and
reuse of nickel metal hydride (NMH) cells, found that, on average, about 37% of discarded cells have
sufficient remaining capacity for reuse. Lih et al.
[25]
identified technological challenges and analyzed
secondary uses of lithium ion batteries from an economic point of view. The potential of lithium ion
batteries, after they serve their useful life, for grid applications has been considered by Kamath of the
Electric Power Research Institute (EPRI) [
26
], who hypothesized that cost per production volume may
be lower than lead-acid batteries. Neubauer et al. have performed a techno-economic analysis of vehicle
batteries for secondary uses [
27
–
29
]. They concluded that an uninterruptible power supply (UPS)
system based on used lithium ion batteries has the potential to be more cost effective than lead-acid
batteries, with superior longevity, specific energy, and energy density. The considerable potential for
secondary applications has been widely recognized. The present study examines empirically practical
problems of maintenance and rebuilding of packs using a small 3 ×3 pack as the platform.
2. Methodology
The objective of the empirical study was twofold: to compare aging of lithium ion cells
individually and in small packs and to test investigate cell rebuilding packs in the context of two case
studies. This objective was executed by three sets of tests: the first set compared aging of single 1860
LiCo cells to their aging in small packs, the second set examined performance of a used pack after one
of the cell was replaced by a new cell and the third set examined scenarios of rebuilding packs from two
packs that were considered “failed”. The details of individual set of tests are described in subsequent
sub-sections. The main metrics were capacity fade, impedance changes, and coulombic efficiency.
The study employed two test stands: one for single-cell testing and the other for battery pack
evaluations. The single-cell apparatus was a Maccor 4600 battery test system, used for initial cell
characterization, pre-aging of individual cells, and periodic monitoring of the cells subjected to
pack-level cycling. Additional details on the test procedure are provided in the supplementary material.
The test stand for pack testing is shown in Figure 1a. The packs consisted of nine cells in 3S3P
configuration: three strings of three serially connected cells were connected in parallel, as shown in
Figure 1b. The pack employed passive cell balancing, based on the commercial, off-the-shelf balancing
circuit. A diagram of the test stand is depicted in Figure 1c. More details on cell balancing are provided
in the supplementary material.
ST1-C1
30 Ohms
ST1-C2
30 Ohms
ST1-C3
30 Ohms
I1
V1
V2
V3
V4
V5
V6
Equalizer Control
T1
T2
T3
ST2-C1
30 Ohms
ST2-C2
30 Ohms
ST2-C3
30 Ohms
I2
V8
V7
V10
V9
V12
V11
Equalizer Control
T4
T5
T6
ST3-C1
30 Ohms
ST3-C2
30 Ohms
ST3-C3
30 Ohms
I3
V14
V13
V16
V15
V18
V17
Equalizer Control
T7
T8
T9
Labview Control
Charging Supply CC/CV
Electronic Load
10 Amp
V19
ST1-CS ST2-CS ST3-CS
5 Amp 5 Amp 5 Amp
ST1-C3-CB “-“
ST1-C3“+“
ST1-C2“+“
ST1-C1“+“
ST1-C2-CB “-“
ST1-C1-CB “-“
ST2-C3-CB “-“
ST2-C3“+“
ST2-C2“+“
ST2-C1“+“
ST2-C2-CB “-“
ST2-C1-CB “-“
GND
ST3-C3-CB “-“
ST3-C3“+“
ST3-C2“+“
ST3-C1“+“
ST3-C2-CB “-“
ST3-C1-CB “-“
ST1-VIN“+“ ST2-VIN“+“ ST3-VIN“+“
VIN
T10 Ambient temperature
Rly2 Rly1
GPIB 0-10v Control
(c)
Figure 1. 3S3P pack (a) LabVIEW-controlled fixture; (b) enlarged view of the pack; (c) schematic.
Batteries 2020,6, 39 4 of 19
2.1. Individual and Pack Aging of 18650 LiCo Cells
For this study, cell aging was limited to full charge-discharge cycles of battery cells. A typical
full charge-discharge cycle, shown in Figure 2a, consisted of discharge at 2.33 A (1
Qn
) and the best
C-rate (
Ic
= 1.63 A, or 0.7
Qn
) – constant voltage (at
Vc
= 4.2 V) charge, separated by 20-min rest
periods.
Qn
denotes nominal capacity of a new cell. The tests were conducted at ambient temperature,
but the temperature was monitored in all tests. The motivation for operating both cells and pack
at ambient temperature came from many practical pack implementation, which do not control the
ambient temperature. The cells were operated in the same environment as the packs. The cells in a
pack (see Figure 1) were aged essentially in the same way, as illustrated in Figure 2b.
3.0
3.4
3.8
4.2
Vc
[V]
Rest
Rest
−2.3
0.0
1.6
Ic
[A]
I
= const.
charge
V
= const.
charge
I
= const.
discharge
13:14:00
15:40:00
13:34:00
16:00:00
14:46:00
16:59:00
22
26
30
34
Tc
[C
o
]
09:28:19
12:18:58
10:53:23
12:39:07
09:48:28
13:32:08
−3
−1
1
3
Is
[A]
Is
fluctuations
3.0
3.4
3.8
4.2
4.6
Vc
[V]
Rest
I
-controlled
charge
V
-controlled
charge discharge
Rest
(a) (b)
Figure 2. Waveforms associated with charge-discharge cycle (a) single-cell testing; (b) pack testing.
To compare pack aging of cells with individual cell aging, we aged sixteen cells on the Maccor
single-cell tester and nine cells in a pack. Figure 3a shows the capacity fade of individually aged cells
vs. number of cycles, measured at discharge. Each of the sixteen cells was aged until its capacity
faded to 90% of new (i.e., 10% capacity fade). The bottom plot of Figure 3a displays a histogram of
number of cycles that led to 10% capacity fade. The average rate of capacity fade for the group of
sixteen cells was computed from all the measurement points using the least mean squares, and the
result (
−
0.11%/cycle) is indicated in the plot. As shown in Figure 3b, capacity fade of cells aged in a
pack had a very similar degradation rate (−0.1%/cycle).
Note that the capacity fade profiles are not strictly monotonic but generally display multiple
local maxima and minima. These variations are largely due to sensitivity of capacity to relatively
small variations in the ambient temperature, as can be seen in Figure 4. The cell temperature at the
end of discharge (the red dashed trace of the bottom of Figure 4a) follows the ambient temperature
(the orange trace of the bottom of Figure 4a). Moreover, very strong linear correlation coefficient of
0.99 was observed between the change in temperature at the end of discharge over two subsequent
cycles
∆Ted
and the change in capacity at the end of discharge
Qed
over two subsequent cycles, as seen
in Figure 4b. These results strongly suggest that temperature management is very important in
practical applications for which it is not reasonable to maintain the ambient temperature at a fixed
value. However, controlling the range of this variability is very important. The temperature variation
between cycles can be perceived as noise. From Figure 4b, the change in capacity was 0.46%/
◦
C.
Recall that the degradation rate described above was 0.11%/cycle. Thus, it is seen that the “error” in
capacity due to change in ambient temperature of only 1
◦
C was more than four times larger than
Batteries 2020,6, 39 5 of 19
normal cycle-to-cycle degradation. Temperature variation may affect internal resistance, which, in turn,
affects the terminal voltage and effective SOC. Figure 4c zooms into temporal variation of the capacity
for an individual cell. The inset shows a histogram of the coulombic efficiency, defined as the ratio
of charge at the end of discharge and the end of charge,
η=Qcd/Qcc
. It is important to note that
coulombic efficiency was used in this study and not the energy efficiency (the ratio of total energy
during discharge and charge). In many places in the text below, we state this explicitly, by referring to
it as coulombic efficiency. Sometimes, we refer to it simply as efficiency, but this paper considers only
coulombic efficiency. The histogram shows that, within a single cycle, the efficiency can be even higher
than 100%. This means that capacity measured during charge (EOC) is sometimes lower than capacity
measured during discharge (EOD). Of course, this efficiency could not be sustained over many cycles;
however, the average efficiency was very high over a range of 40 cycles (99.85% average efficiency over
cycles 20 to 60).
0 20 40 60 80 100 120
Cycles
N
2.05
2.10
2.15
2.20
2.25
2.30
2.35
Cell Capacity at Disch.
Qcd
[Ah]
∆
Qcd
N
≈
-0.11 %/cycle 90
92
94
96
98
100
102
Percent of Nominal
0 20 40 60 80 100 120
4
2
0
←
Count
Total number of cycles
Nmax
µNmax
= 99.38
σNmax
= 9.45
0
12
25
Rel. freq. [%]
20 60 100
Cycles
N
2.05
2.10
2.15
2.20
2.25
2.30
2.35
Cell Capacity
Qc
[Ah]
∆
Qc
∆
N
≈
-0.1 %/cycle
Qavg
(
N
=0)
= 101.0 %
Qavg
(
N
=100)
= 91.3 %
C1S1
C1S2
C1S3
C2S1
C2S2
C2S3
C3S1
C3S2
C3S3
average
Avg. slope
90
92
94
96
98
100
102
Percent of Nominal
Qc/Qn
(a) (b)
Figure 3.
(
a
) capacity fade (100–90%) as function of number of cycles; (
b
) capacity fade of nine cells
within a pack over 100 cycles.
A common health indicator of battery aging is impedance [
13
,
30
–
35
]. Figure 5a shows the average
impedance spectrogram of new cells, and of the same cells after they have been aged to 90% of their
nominal capacity. Several key frequencies are indicated by arrows. The standard frequency used for
health indication is
f
= 1 kHz. For this lithium ion chemistry, the resistance at
f
= 1 kHz corresponds to
the high-frequency intercept with the real axis. This resistance, denoted by
<{ZBatt}
, is approximately
equal to the ohmic resistance of the battery [
36
].
ZBatt
has a convenient equivalent circuit representation
and is relatively easy to extract [
37
], but it is not the most sensitive parameter for indirect monitoring
of cell aging. Figure 5b shows the change of the real part of the impedance at 1 kHz for sixteen
cells as they are aged to 90% of their new capacity, with the colored markers indicating individual
measurements, and dashed lines indicating the shape of the fitted normal distributions. The real part
of the impedance at
f
= 1 kHz is the standard metric for the impedance; the impedance spectra of
Figure 5a indicates that, for these cells, larger impedance change occurred at lower frequencies, in the
[0.1, 1] Hz range. This indication is further confirmed in Figure 5c, which illustrates the change in the
real part of the impedance for the same group of sixteen cells at
f
= 1.0 Hz. The absolute change of the
mean resistance, averaged over sixteen cells, at
f
= 1.0 Hz was 4.12 m
Ω
(7.6%) compared to a 0.64 m
Ω
change in resistance (1.6%) at
f
= 1.0 kHz. The disadvantage of measuring impedance at
f
= 1 Hz,
at the corner of Warburg region, is that measurements take longer.
Batteries 2020,6, 39 6 of 19
3.0
3.4
3.8
4.2
Vc
[V]
−3
−1
1
Icell
[A]
03:00:00
06:00:00
09:00:00
12:00:00
15:00:00
18:00:00
21:00:00
00:00:00
03:00:00
06:00:00
09:00:00
20
24
28
32
T
[C
o
]
Tc
Ta
Ted
−3 −2 −1 012 3 4
∆
Ted
[
o
C]
−0.04
−0.03
−0.02
−0.01
0.00
0.01
0.02
0.03
0.04
∆
Qcd
[Ah]
∆
Qc
[
Ahr
]
= -0.003264
+0.010540
×
∆
T
[
oC
]
∆
Qc
[%] = -0.14+0.46
×
∆
T
[
oC
]
Correlation coefficient
ρ
= 0.99
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
∆
Qcd/Qn
[%]
(b)
20 25 30 35 40 45 50 55 60
Number of Cycles
N
2.14
2.16
2.18
2.20
2.22
2.24
2.26
2.28
2.30
Capacity
Qc
[Ah]
Discharge
Charge
94
95
96
97
98
99
100
Percent of nominal
Qc/Qn
100.0 101.5
Efficiency
η
[%]
0
4
8
12
16
Count
N
µ
= 99.85
(a) (c)
Figure 4.
(
a
) characteristic waveforms for a single cell: voltage
Vc
, current
Ic
, temperature
Tc
,
and ambient temperature
Ta
; (
b
) scatter plot of change in capacity at discharge in subsequent cycles
∆Qed
vs. temperature of the cell at the end of discharge
∆T
; (
c
) more details on capacity variation of a
single cell over time.
40 45 50 55 60 65 70
ℜ
Z
Batt
[m
Ω
]
−15
−10
−5
0
5
10
15
20
ℑ
Z
Batt
[m
Ω
]
f
= 0.01 Hz
f
= 0.10 Hz
f
= 1.00 Hz
f
= 10 Hz
f
= 100 Hz
f
= 1000 Hz
(a)
SOC
= 100 %
New
90 % of New
New 90 % of New
38
40
42
44
46
48
50
ℜ
ZBatt
at
f
= 1.0 kHz
(b)
∆
Ravg
= 0.6 m
Ω
(1.6 %)
95
100
105
110
115
120
Percent of initial mean
New 90 % of New
50
52
54
56
58
60
62
64
66
ℜ
ZBatt
at
f
= 1.0 Hz
(c)
∆
Ravg
= 4.1 m
Ω
(7.6 %)
95
100
105
110
115
120
Percent of initial mean
Figure 5.
Impedance changes during single-cell aging. (
a
) average impedance spectra; (
b
) real part
change for individual cells at f= 1 kHz; (c) real part change for individual cells at f= 1 Hz.
The impedance spectra of pack aging data are given in Figure 6: Figure 6a shows the evolution of
averaged spectra, Figure 6b shows the evolution of distributions of impedance real parts of individual
cells at f= 1 kHz, and Figure 6c shows the evolution of real part of impedance at f= 1 Hz.
Batteries 2020,6, 39 7 of 19
40 45 50 55 60 65
ℜ
Z
Batt
[m
Ω
]
−10
−5
0
5
10
ℑ
Z
Batt
[m
Ω
]
(a)
SOC
= 100 %
Initial
40 cyc
60 cyc
80 cyc
100 cyc
0 40 60 80 100
Cycles
N
39
40
41
42
43
44
45
46
47
ℜ
Z
Batt
at
f
= 1.0 kHz
(b)
∆
Ravg
= 0.5 m
Ω
(1.3 %)
95
100
105
110
Percent of initial mean
0 40 60 80 100
Cycles
N
53
54
55
56
57
58
59
60
61
62
ℜ
Z
Batt
at
f
= 1.0 Hz
(c)
∆
Ravg
= 2.8 m
Ω
(5.1 %)
98
100
102
104
106
108
110
112
Percent of initial mean
Figure 6.
Impedance changes during pack cell aging. (
a
) average impedance spectra; (
b
) real part
change for individual cells at f= 1 kHz; (c) real part change for individual cells at f= 1 Hz.
2.2. Scenario 1: Early Life Failure
The first scenario represents the case when one cell in a pack fails early with respect to the expected
life of the pack. To simulate this situation, we pre-aged cells in the individual pack tester to 90% of their
initial capacity. In demanding applications, such as electric vehicles, the cells are considered usable
only when the capacity is higher than 80% of the nominal capacity. Therefore, for these applications,
cells aged down to 90% of their nominal capacity are less than 50% of their useful life because cell
degradation is nonlinear and typically slows down (see Figure 7).
Nine individually-aged cells were formed into a pack (3S3P), where the cells were matched based
on their capacity and impedance. Then, after a few cycles, one of the aged cells was replaced by a new
cell. Figure 8shows capacity of individual cells first aged separately until their capacity faded to 90%
of nominal, and then assembled into a pack. Individual cell capacities are considered here as the key
metric because they exclude effects of other pack components, such as equalization circuit. The traces
are labeled by the location of the cell in the pack CiSj where i denotes the cell within a string and j
denotes the string. For example, C1S2 is the first cell in the second string. The cells were always placed
in the same location throughout the testing, except in the case of the C1S1 site, where the replacement
took place. The original cell is denoted by C1S1o and the replacement cell by C1S1r.
20 60 100 140 180 220
Cycles
N
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
Capacity
Qc
[Ah]
Deep discharge event
→
←
Rapid
degradation
→ ←
Degradation
slows down
→
C1S1
C1S2
C1S3
C2S1
C2S2
C2S3
C3S1
C3S2
C3S3 75
80
85
90
95
100
Percent of Nominal
Figure 7. Individual capacities of the baseline pack comprised of new cells.
Batteries 2020,6, 39 8 of 19
New
Single-cell aged
20 cyc.
40 cyc.
60 cyc.
80 cyc.
100 cyc.
100 cyc. after rest
After deep disch.
Cycles
N
1.8
1.9
2.0
2.1
2.2
2.3
2.4
Cell Capacity
Qc
[Ah]
Deep
discharge
event
Pack cycling
New cell
90 % cells
C1S1o
C1S1r
C1S2
C1S3
C2S1
C2S2
C2S3
C3S1
C3S2
C3S3
80
85
90
95
100
Percent of Nominal
Qc/Qn
Figure 8.
Capacities of individual cells in an early life failure scenario where one cell C1S1 is replaced
with a new cell after 10% capacity fade. Traces are labeled by the site of the cell in the pack.
Comparing capacity fades of the cells of the pack, comprised of eight aged and one new cell to the
capacity fades of the reference pack, plotted in Figure 7, shows that a new cell nicely coexists with the
aged cells and did not introduce any obvious increase in the overall rate of capacity fade. The slope of
the capacity fade of the new cell is higher than that of the aged cells, but this behavior is consistent
with cell aging in general. Capacities of the new cells in Figure 7fade faster over the course of the first
100 cycles and the relative rate of capacity degradation slows down.
2.3. Scenario 2: Rebuilding a Pack from Two Failed Packs
The pack with eight pre-aged cells and one new was behaving well for one hundred cycles before
it was subjected to deep discharge to generate cells for the second scenario. A deep discharge event is
a very severe case of cell degradation and it was induced here to simulate a harsh case of field failure
because future integrators of packs for secondary applications may not have access to the usage history
of cells in their primary applications.
The conventional knowledge in battery integration systems has been that new cells should never
be mixed with old cells. Before conducting this experiment, it was suggested by some domain experts
that the pre-aging cells for replacement may be required for reliable operation of the repaired pack.
Our results suggest that the potentially expensive proposition of maintaining an inventory of pre-aged
cells may not be necessary.
To create the second scenario for cell replacement strategy, two 3S3P packs were first subjected
to deep discharges, as shown in Figures 7and 8. The deep discharge events caused what can be
considered to be major pack failures, and the cells recovered from these deeply discharged packs
are good candidates for simulating cell repurposing processes. To simulate a failure in the battery
management system, the cells were left overnight to discharge through a set of resistors used for cell
balancing, allowing the terminal voltages to drop considerably below the minimum value required
by the cell manufacturer. This scenario intended to mimic one of the worst-case practical situations
because the operational history of cells in primary application, including failures, is not available to
the integrator of the packs based on used cells. After the deep discharges, the individual cells were
recovered by charging them at low current (100 mA). This process was able to recover twelve out
of the original eighteen cells. The remaining six cells had their current interrupt devices triggered
which rendered them unusable for the Scenario 2 experiments. After the recovery, the cell capacity
was measured on the single-cell tester. Table 1shows the capacities of the recovered cells.
Batteries 2020,6, 39 9 of 19
Table 1. Capacity of the recovered cells.
Cell ID Cell Capacity Qc(Ah)
6 1.83
8 1.85
14 2.11
16 2.11
17 2.06
19 2.13
20 max→2.14
21 2.12
23 1.73
24 1.69
25 min →1.58
27 2.02
µ1.95
σ0.20
Table 2shows the real part of the impedance of the surviving cells at frequencies of 0.1, 1 and
1000 Hz. In the first part of the study, we found that resistance at 1 Hz showed more sensitivity to
aging than the typically used value at 1 kHz.
Table 2. Resistances of the recovered cells.
Cell ID Rf=0.1 Hz(mΩ)Rf=1 Hz(mΩ)Rf=1 kHz(mΩ)
6 88.18 77.98 49.01
8 90.24 80.41 max→52.23
14 64.85 62.12 44.00
16 72.07 70.09 51.55
17 72.42 69.55 50.27
19 64.47 61.74 43.56
20 min→62.61 min→60.64 44.74
21 64.15 61.54 43.56
23 max →113.70 max→86.66 min→43.41
24 99.37 79.64 49.14
25 105.02 83.75 49.15
27 69.98 65.81 45.65
µ80.59 71.66 47.19
σ17.96 9.56 3.36
The relationship between the capacity and real part of the impedance at 1 Hz has a high correlation
coefficient of
ρ
=
−
0.92 (Figure 9). The high correlation between resistance and capacity was expected
(see e.g., [
38
]). While we recognize that there are several degradation mechanisms in lithium ion cells
(including degradation of active material, impedance rise by formation of solid-electrolyte interphase
layer, lithium inventory loss by side reactions, and loss of carbon as conductive additive from the
cathode [
39
]), the impedance change was the dominant feature that was readily detectable in our
phenomenological approach. It is reasonable to suggest that some of the scatter is due to measurement
of the impedance spectra. The ability to reasonably assess cell condition from impedance is very
important for rebuilding a pack because the capacity measurement is a considerably longer process.
The real part of the resistance at
f
= 1 Hz can be measured within seconds, whereas determining
the capacity at 1
Qn
may take several hours, depending on cell capacity and the rest period. More
accuracy in capacity estimation can be achieved by taking more data and applying considerably more
computation [2].
Batteries 2020,6, 39 10 of 19
1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
Cell Capacity
Qc
[Ah]
60
65
70
75
80
85
90
Resistance
RBatt
at
f
= 1.0 Hz
Correlation coefficient
ρ
= -0.92
Figure 9. Capacities of individual cells in early life failure scenario.
As stated above, negative correlation between remaining capacity and impedance increase has
been observed (e.g., [
38
]). An equivalent circuit model, such as double-exponential model [
37
],
depicted in Figure 10, provides an intuitive, phenomenological way to provide simple, first-order
interpretation. The model consists of two electrical ports: hidden and terminal. The state of the hidden
port, model by capacitance, and
˙
Q
denotes the rate of charge. It contains a current-dependent current
source, which is simply unity multiplied by the cell current, cell capacity
Ccell
, and self-discharge
resistance
Rsd
. The terminal port has two directly measurable quantities, viz. battery terminal cell
voltage
Vc
and cell current
Ic
. The circuit components of the terminal port, open-circuit voltage
Vo c
,
Rcell
,
R1
,
C1
,
R2
, and
C2
are not directly observable and have to be inferred [
21
]. In addition, they are
functions of charge level
Q
. At low frequencies, the impedance approaches its real (purely resistive
component) component
ZBatt → <{ZBatt}=Rcell +R1+R2
as
f→
0. During the discharge at a
constant current, the impedance is approximately purely resistive. As this resistive part increases,
so does the effective voltage drop across it, which effectively reduces the terminal cell voltage
Vc
,
whose level is used to limit the charge and discharge, based upon manufacturer’s specifications. Thus,
increase in
Rcell +R1+R2
effectively reduces discharge capacity. The impedance at 1 Hz strongly
depends on state of charge [
40
], which was accounted for by measuring impedance at the same level of
SOC. However, temperature also significantly affects the low-frequency impedance. This aspect was
only accounted for in a statistical manner, by comparing the two sets of distributions, which seemed to
be separated significantly.
−
+Voc(Q)
IcRcell(Q)
R1(Q)R2(Q)
C1(Q)
−+
vC1
C2(Q)
−+
vC2
Vc
+
−
Terminal port
Rsd Ccell
˙
Q
Ic
Hidden port
Figure 10. Equivalent circuit model (adapted from [37]).
There are many ways to arrange the 12 recovered cells into a 9-cell pack. One approach is to
maximize the capacity of the pack. This arrangement is achieved simply by first grouping the cells
in descending order with respect to their capacity and then populating the pack across the strings
starting from left to right in the first pass (where “left-to-right” signifies arbitrary signed direction
perpendicular to the direction along the strings), and then continuing from right to left in the second
Batteries 2020,6, 39 11 of 19
pass, etc. For the case at hand, only three such passes are required. The resulting pack configuration is
shown in Table 3.
Table 3. Cell and string capacities (in (Ah) for Option 1) that maximizes total pack capacity.
Configuration String 1 String 2 String 3
C12.14 2.13 2.12
C22.06 2.11 2.11
C32.02 1.85 1.83
Total 6.22 6.09 6.06
An alternative approach is to arrange the cells in a manner that equalizes their string capacities.
This arrangement minimizes string-to-string equalization, which, in turn, minimizes the losses during
rest periods. While the previous arrangement only requires sorting, the string equalization is slightly
more demanding. The arrangement shown in Table 4was arrived at by employing an optimization
procedure, which was in this case implemented in Python.
Table 4.
Cell and string capacities (in (Ah) for Option 2) that best match capacity among the
three strings.
Configuration String 1 String 2 String 3
C11.83 2.11 2.06
C21.85 2.12 1.73
C31.85 1.58 2.02
Total 5.81 5.81 5.81
The second option, attractive from the efficiency viewpoint, proved less reliable for the pack.
It turned out that the safety features embedded in our pack design were less tolerant to mismatches
within a string then string-to-string mismatches. The cells with considerably lower capacity and higher
resistance were difficult to balance. Thus, maximizing the capacity of the pack was found simpler,
and more robust within our pack implementation.
3. Results and Analysis
While there are several important metrics for battery packs, this study focused on coulombic
efficiency because it is strongly affected by mismatches among cells in packs built for secondary
applications. We also consider temperature effects and the effect of cell balancing scheme, viz. passive
vs. active cell balancing.
3.1. Efficiency Comparison
The pack performance is assessed with respect to its overall efficiency. Figure 11 shows a composite
plot for pack efficiency. The top subplot shows the capacity at the end of discharge
Qpd
and capacity at
the end of charge Qpc. Their ratio, pack coulombic efficiency ηp, defined as
η=Qpd
Qpc (1)
and expressed in percent, is plotted on the bottom subplot. It is important to note that, while the pack
was charged using constant current and constant voltage conditions, the discharge was conducted
only in constant current condition. This approach is consistent with the single-cell charge-discharge
profile and is reasonable from the pragmatic viewpoint of the user. The histogram of the efficiency is
plotted in the right subplot in the horizontal direction, where the
y
-axis of the histogram is scaled to
match the y-axis of the efficiency plot.
Batteries 2020,6, 39 12 of 19
0 50 100 150 200
Cycles
N
82
86
90
94
Pack
Efficency
ηp
[%]
5.8
6.2
6.6
7.0
7.4
Pack
Capacity
Qp
[Ah]
Charge
Qpc
Discharge
Qpd
0 10 20 30 40 50
82
86
90
94
Count
(total
N
= 184)
Figure 11. Coulombic efficiency of a pack during cycling (new cells).
The main mode of the distribution of the coulombic efficiency of a pack comprised of all new
cells is approximately 93%. As mentioned above, the pack cycling was interrupted periodically to take
capacity measurements of individual cells and to record impedance spectra. Sometimes, after the test
was resumed, the pack may have operated at somewhat different global capacity. This explains the
occasional large step-shaped drops in efficiency. In addition to these abrupt drops, one can see that the
overall efficiency degraded slowly, at approximately the same rate as the cell capacity. The efficiency
of individual cells was about 99% on average (see Section 2.1, Figure 4c). The additional energy loss
was attributed to cell balancing.
Figure 12 shows the efficiency of the pack built for Scenario 1 (early life failure study). Comparing
this figure to Figure 11, it appears that the efficiency corresponding to the dominant mode of the
distribution was very comparable to that of the pack comprised of new cells.
0 10 20 30 40 50 60 70 80
Cycles
N
70
80
90
100
110
Pack
Efficency
ηp
[%]
5
6
7
8
Pack
Capacity
Qp
[Ah]
Charge
Qpc
Discharge
Qpd
0 5 10 15 20 25 30 35
70
80
90
100
110
Count
(total
N
= 78)
Figure 12. Coulombic efficiency of a pack during cycling (Scenario 1).
However, for the Scenario 1 pack, we observed more frequent abrupt drops in efficiency. One of
the main indicators of cell aging is impedance increase [
33
]. Spectra of average impedance associated
with the aged early life failure pack are displayed in Figure 13 in the usual way, with the
x
-axis being
the real part of the impedance,
R=<{ZBatt}
, and the
y
-axis being the negative imaginary part of the
impedance,
Y=−={ZBatt }
. Both
R
and
Y
are expressed in m
Ω
, with the frequency ranging from
10 mHz to 10 kHz. The plotted impedance traces are averages of nine individual-cell impedance
measurements. There is a total of ten sets of measurements:
•Initial signifies the measurements on new cells.
•
Few cycles signifies the impedance of nine cells after they were initially run in the pack for three
cycles.
•
10% fade signifies the measurements on the cell after they were individually aged on the single-cell
tester to 90% of their nominal capacity.
Batteries 2020,6, 39 13 of 19
•
Replacement signifies resistance measurements after one cell was replaced with a new cell; +20
cycles,+40 cycles,+60 cycles,+80 cycles, and +100 cycles signify measurements as the “repaired”
pack was operated for 100 cycles.
•Recovered cells signify the impedance of a few cells that survived the deep discharge event.
40 50 60 70 80
ℜ
Z
Batt
[m
Ω
]
−15
−10
−5
0
5
10
15
20
ℑ
Z
Batt
[m
Ω
]
After the deep
discharge
event
Charged
Initial
Few cycles
10% fade
Replacement
+20 cycles
+40 cycles
+60 cycles
+80 cycles
+100 cycles
Recovered cells
Figure 13.
Average impedance spectra of a pack comprised of eight aged cells and one new (Scenario 1).
At a high level, the shifts in the impedance spectra were larger initially. During the aging phase
(+20 cycles through +100 cycles), the shifts were relatively small. Larger shifts occur at the points that
correspond to lower frequencies. While
R[f=
1
kHz]
changed significantly after the deep discharge
event on average, two of the six surviving cells were only moderately affected. This observation
suggests that even after relatively violent failures, a subset of cells from a pack may retain nearly the
same characteristics as before the failure.
Figure 14 shows distribution of the real part of the impedance measurements at
f
= 1 Hz. Here,
the history of the testing is shown in the form of the
x
-axis tick marks. The measurements of individual
cells are labeled with unique markers. Nine individual cell measurements correspond to each
x
-axis
tick mark. The solid line connects the means of the nine cells, while the dashed curves represent the
fitted normal distributions. While average resistance increased significantly after the deep discharge
event, two cells were barely affected, as noted above.
Initial
Few cycles
10% fade
Replacement
+20 cycles
+40 cycles
+60 cycles
+80 cycles
+100 cycles
Recovered cells
50
55
60
65
70
75
ℜ
Z
Batt
[m
Ω
]
128.0 %
Charged, at
f
= 1.0 Hz
C3S2
C3S1
C1S1
C1S3
C1S2
C2S2
C2S1
Avg.
100
110
120
130
140
Percent of initial mean
Deep discharge event
→
Figure 14.
Real part of the impedance at
f
= 1 Hz at different stages of aging of early life failure pack
(Scenario 1).
The coulombic efficiency of the rebuilt pack (Scenario 2) is shown in Figure 15. This pack clearly
operates at lower efficiency than the new pack (Figure 11) and the early life failure pack (Figure 12). Its
dominant mode was at 85% efficiency. The reduced efficiency was due to larger mismatches among
the comprising cells which required more balancing because passive cell balancing circuits dissipate
imbalanced charge on a resistor. This result suggests that an active cell-balancing scheme may have
Batteries 2020,6, 39 14 of 19
potential for the pack based on repurposed cells because the return on the investment for these packs
is faster. We return to this point at the end of the section.
0510 15 20 25 30 35 40 45
Cycles
N
60
80
100
120
Pack
Efficency
ηp
[%]
3.5
4.5
5.5
6.5
7.5
Pack
Capacity
Qp
[Ah]
Charge
Qpc
Discharge
Qpd
0 5 10 15 20 25 30
60
80
100
120
Count
(total
N
= 42)
Figure 15. Coulombic efficiency of a pack during cycling (Scenario 2).
Figure 16 compares the histograms of coulombicic efficiency of the three packs: the pack composed
of new cells, the pack with an early failure, and the pack rebuilt from used cells. The dominant modes
of the pack composed of new cells and the pack with an early failure largely overlap, and the dominant
mode associated with the “rebuilt pack” is noticeably lower.
70 80 90 100 110 120
Pack Efficiency
ηp
[%]
0.0
0.1
0.2
0.3
0.4
0.5
Relative Frequency
New
Early-life fail.
Rebuilt
Figure 16. Overlaid coulombic efficiencies for the three packs.
3.2. Temperature Effects
Local cell temperature variations and overall pack heating are important concerns in pack design.
Within the confines of this study, we examined how temperature of individual cells increased during
pack operation.
Figure 17 shows the distribution of temperature differences between individual cells and ambient
temperature for the three packs. All test temperature measurements are included. There were no
significant pack-to-pack differences in heating of individual cells, but the distribution of temperature
differences of the rebuilt pack was slightly wider than the other two temperature distributions.
The objective of the time domain plot on the bottom is to show that the “tail” of the distribution
was not associated with the last cycles. The plot aligns the last event where
∆T
exceeded 10
◦
C for each
of the three packs. The
x
-axis is temperature difference
∆T
and was scaled to be the same as that of the
histogram above; the
y
-axis is time. The peak corresponds to the end of discharge. The maximum
∆T
of the bottom plot is considerably smaller than the maximum
∆T
of the histogram. Thus, the tails of
Batteries 2020,6, 39 15 of 19
the histogram did not correspond to the aging, but to random variation. An alternative view of the
data are provided in the supplementary file.
−5 0510 15 20
∆
T
=
T
−
Tamb
[
o
C]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Relative frequency
Rebuilt pack has a
wider distribution
to higher
∆
T
New (3.7 million pts.)
Early-life fail. (2.7 million pts.)
Rebuilt (1.2 million pts.)
−5 0510 15 20
Time
t
→
Last events where
∆
T >
10
o
C.
∆
T
of rebuilt pack
did not grow in time
New
Early-life fail.
Rebuilt
Figure 17. Comparison of heating of aging batteries.
3.3. Effects of Balancing Scheme
As stated above, the mismatched cells required more balancing, and increased balancing directly
translated into reduced efficiency. Some of the lost efficiency could be recovered by employing active
cell balancing for the repurposed packs. To demonstrate this empirically, we created a pack consisting
of a single string of three new serially connected cells and cycled this simple pack employing either
passive or active balancing. The passive balancing scheme was the same as that employed for the test
described Section 2.1, with the details provided in the supplementary material.
The active balancing circuits employed a capacitor and solid state switches, as illustrated in
Figure 18. The logic of the switches, denoted by symbols
ϕ1
–
ϕ3
, connected only one of the cells in
parallel with the capacitor. The cells took turns with respect to their connection to the capacitor in a
circularly cyclical manner, as shown by the sketched waveforms of ϕ1–ϕ3.
φ1
Cell 1
Cell 2
Cell 3
Balancing
Capacitor
φ1
φ2
φ2
φ3
φ3
φ3
φ2
φ1
1 F
f = 1 Hz
Figure 18. Circuit for active balancing of a 3S1P pack.
The data are shown in Figure 19a where total pack current waveforms are given in the top subplot
and total charge associated with charge (bottom subplots) for a few charge/discharge cycles of the 3S1P
pack while passive balancing scheme was used. The red and green colors were used to indicate charge
and discharge cycles, while the blue color signifies the rest period. The efficiencies of individual cycles
were denoted near the discharge points. The pack with passive cell balancing had 92.5% efficiency.
Figure 19b shows the same information as Figure 19a when the pack employed active cell balancing.
Batteries 2020,6, 39 16 of 19
−2.0
−1.5
−1.0
−0.5
0.0
0.5
Current
I
(A)
13:00:00
19:00:00
01:00:00
07:00:00
13:00:00
19:00:00
01:00:00
07:00:00
1.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
Charge
Q
(Ah)
η
= 92.32%
η
= 92.51%
η
= 92.60%
η
= 92.53%
charge
discharge
−2.0
−1.5
−1.0
−0.5
0.0
0.5
Current
I
(A)
11:00:00
14:00:00
17:00:00
20:00:00
23:00:00
02:00:00
05:00:00
08:00:00
11:00:00
14:00:00
17:00:00
1.0
1.5
2.0
Charge
Q
(Ah)
η
= 96.30%
η
= 96.60%
η
= 96.64%
η
= 96.88%
charge
discharge
(a) (b)
Figure 19. Comparison of cell balancing for a 3S1P (a) passive; (b) active.
The pack using the same cells and active balancing scheme had 96.6% efficiency, a 4.1%
improvement over the passive balancing. In both cases, we ignored the first estimate because it
would be based on a partial cycle. Because the average efficiency of new cells is almost 99.8% (see
Section 2.1, Figure 4c), the improvement due to active balancing recovered more than half of the
reduced efficiency, as illustrated in Figure 20.
92.5 96.6 99.8
Efficiency
η
[%]
Passive
balancing Active
balancing Individual
cells
Eff. Improvement
100 43.8 0
Eff. percent change wrt individual cells [%]
Figure 20. Efficiency of passive balancing, active balancing, and individual cells.
The remaining losses were due to the equalization process which required additional current
flows between the cells and the capacitor and the resistive imperfections of real solid-state switches
(their on-state resistance), real equalizing capacitor (its equivalent series resistance), and the cells’
internal resistance. For example, during a charge cycle of an individual cell test, the current only flows
into the cell, whereas during a charge cycle of the cell in a string, the current mostly flowed into the
cell, but small amounts of current often flowed out of the cell during its connection to the capacitor.
The balancing currents were completely dissipated if passive balancing circuit was used, and only
partially dissipated in parasitic resistance of real circuit components in the active balancing circuit.
4. Conclusions
This study examined fundamental properties of aging lithium ion battery cells. We described
the testing methodology and established that the cells in a carefully designed pack aged at the same
rate as when they are individually aged. The careful design consisted of matching overall capacities
of serial connections to minimize charge exchanges between strings and the associated dissipation,
and also to match impedances within a serial connection to minimize equalization with its associated
losses. We then considered two common scenarios in cell replacements: replacing a prematurely
failed cell and building a new pack from cells of the damaged packs for less demanding applications.
Less demanding applications considered here are those that can tolerate capacity of less than 70%.
Stationary applications, e.g., microgrid storage, where the overall pack weight is not a limiting factor,
Batteries 2020,6, 39 17 of 19
are considered good examples of less demanding applications that can be source their cells and
modules from high-demanding applications (e.g., transportation).
The first scenario is important for maintenance of existing packs and modules, especially large
packs. We found that, at least for demanding applications where the pack operates until its cell drop to
about 80% of the original capacity, a new cell coexisted well within a pack of aged cells. Therefore,
within these applications, there may not be a need for a potentially expensive process of pre-aging cells.
The second scenario addressed the problem of repurposing of used cells in less demanding
applications. To examine a severe case of a pack failure, we deeply discharged two packs and
assembled a pack from the surviving cells. The deep discharge event was so severe that 6 of the
original 18 cells were permanently damaged. Two approaches to rebuilding the packs were considered,
but only matching the cells within a string worked robustly in our pack. After the pack was rebuilt
in this fashion, more than forty cycles were successfully completed. Comparing the modes of the
distribution, it was found that the overall pack efficiency of the rebuilt pack was about 8% lower
than that of pack comprised of new cells. However, the heating of individual cells within the three
packs was compared and no significant differences were found. We finally showed that increased
losses due to larger mismatches can be partially compensated by employing active instead of passive
cell balancing. The balancing scheme may be particularly critical for secondary applications where
cells cannot be matched as well as in the primary applications, and where the initial mismatches are
expected to grow further over time.
Lessons learned from this study will be employed in our future work of assessing opportunities
for repurposing larger packs, where secondary applications may have specific use profiles distinctly
different from the primary applications. For example, this information could be used in considering
reuse of vehicle batteries in grid applications, such as peak shaving and smoothing of solar-generated
power vs. their reuse in much smaller systems such as power tools, or toys. The future work may also
consider other criteria, including economic and environmental performance.
Supplementary Materials:
The following are available online at http://www.mdpi.com/2313- 0105/6/3/39/s1,
Figure S1: High-level view of the research program; Figure S2: Initial characterization and single-cell testing;
Figure S3: Histogram of cell weights; Figure S4: Characteristic waveforms of a typical cycle; Figure S5:Impedance
spectroscopy. (a) Average spectra. (b) Repeatability and potentiostat comparison; Figure S6: Schematic diagram
of the 3S3P battery pack; Figure S7: (a) LabVIEW-controlled battery pack test stand. (b) Enlarged view of the
pack; Figure S8:Voltage and current waveforms for a cell during pack cycling; Figure S9: Current distribution
of three strings over four cycles; Figure S10:Voltage distribution of three cells within string 1 over four cycles;
Figure S11: Cell balancing for one of the strings. Pack design employed 106 Astro "Blinky" from AstroFlight Inc.
as the commercial cell balancer; Figure S12: Voltage distribution of three cells within string 1 over four cycles for
active cell balancing; Figure S13:(a) Representative capacity of individual cells diverging in time (18650, lithium
cobaltoxide chemistry). (b) Scatter plot of capacity fade vs. percent recovery; Figure S14: Capacity fade of eight
lithium cobalt cells; Figure S15: Thermal image of the pack; Figure S16: Comparison of heating of lithium ion
batteries; Table S1.Effect of Taon Ted; Algorithm S1: Charge cycle.
Author Contributions:
Conceptualization, N.G.N., T.A.T., and M.G.T.; methodology, N.G.N. and T.A.T.; software,
N.G.N.; validation, N.G.N., T.A.T., and M.G.T.; formal analysis, N.G.N. and T.A.T.; investigation, N.G.N., T.A.T.,
and M.G.T.; data curation, N.G.N.; writing—original draft preparation, N.G.N.; writing—review and editing,
N.G.N., T.A.T., and M.G.T.; visualization, N.G.N.; supervision, M.G.T.; project administration, M.G.T.; funding
acquisition, M.G.T. All authors have read and agreed to the published version of the manuscript.
Funding: This work was made possible by the Office of Naval Research under Award No. N0004-07-1-0823.
Disclaimer
: Any opinions, findings, and conclusions or recommendations expressed in this material are those of
the author(s) and do not necessarily reflect the views of the Office of Naval Research.
Acknowledgments:
We gratefully acknowledge the help of our colleagues from Rochester Institute of Technology:
Scott Dewey for his assistance in pack assembly and instrument setup, Robert Kosty for his assistance in collecting
data and debugging the fixtures, and Joseph Wodenscheck and Art Dee for skillful LabVIEW implementation of
the charge cycle and discharge cycle on the battery pack test stand.
Conflicts of Interest:
The authors declare no conflict of interest.The funders had no role in the design of the study;
in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish
the results.
Batteries 2020,6, 39 18 of 19
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