**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.

**Figure 1.** 3S3P pack (**a**) LabVIEW-controlled fixture; (**b**) enlarged view of the pack; (**c**) schematic.

#### *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.

**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 Δ*Ted* and the change in capacity at the end of discharge *Qed* over two subsequent cycles, as seen in Figure 4b. These results strongly sugges<sup>t</sup> that temperature managemen<sup>t</sup> 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 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).

**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 {<sup>Z</sup>*Batt*}, is approximately equal to the ohmic resistance of the battery [36]. Z*Batt* 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 mΩ (7.6%) compared to a 0.64 mΩ 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.

**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 Δ*Qed* vs. temperature of the cell at the end of discharge Δ*T*; (**c**) more details on capacity variation of a single cell over time.

**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.

**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 8 shows 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.

**Figure 7.** Individual capacities of the baseline pack comprised of new cells.

**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 7 fade 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 sugges<sup>t</sup> 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 7 and 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 managemen<sup>t</sup> 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 1 shows the capacities of the recovered cells.


**Table 1.** Capacity of the recovered cells.

Table 2 shows 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.

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 sugges<sup>t</sup> 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].

**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 *Voc*, *Rcell*, *R*1, *C*1, *R*2, and *C*2 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* + *R*1 + *R*2 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* + *R*1 + *R*2 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.

**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 arrangemen<sup>t</sup> 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

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.

An alternative approach is to arrange the cells in a manner that equalizes their string capacities. This arrangemen<sup>t</sup> minimizes string-to-string equalization, which, in turn, minimizes the losses during rest periods. While the previous arrangemen<sup>t</sup> only requires sorting, the string equalization is slightly more demanding. The arrangemen<sup>t</sup> shown in Table 4 was 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.


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

$$
\eta = \frac{Q\_{pd}}{Q\_{pc}} \tag{1}
$$

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.

**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.

**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* = {<sup>Z</sup>*Batt*}, and the *y*-axis being the negative imaginary part of the impedance, *Y* = − {<sup>Z</sup>*Batt*}. Both *R* and *Y* are expressed in <sup>m</sup>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:


**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.

**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

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.

**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.

**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 Δ*T* exceeded 10 ◦C for each of the three packs. The *x*-axis is temperature difference Δ*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 Δ*T* of the bottom plot is considerably smaller than the maximum Δ*T* of the histogram. Thus, the tails of the histogram did not correspond to the aging, but to random variation. An alternative view of the data are provided in the supplementary file.

**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 *ϕ*1–*ϕ*3, 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 *ϕ*1–*ϕ*3.

**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.

**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.

**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.
