Voltage Reference Realignment Cell Balance to Solve Overvoltage Caused by Gradual Damage of Series-Connected Batteries

: This paper analyzes the cause of electric vehicle battery ﬁres. The fundamental cause is attributed to a low cell balance current, and it is proven that the variation in the battery’s internal voltage due to temperature change is the decisive reason for battery ﬁres. In this paper, the authors studied a method of solving the problem by changing only the software of the existing Battery Management System (BMS) without changing the hardware. Batteries cannot be made with 100% capacity, resulting in voltage division. Cell balancing is performed to prevent such phenomena, but a low cell balance current prevents the proper operation of cell balancing. As a result, relatively small batteries, due to progressive degradation, have continuous voltage rise toward overvoltage. Subsequently, an additional voltage rise occurs as the chemical activity of the battery increases due to temperature rise. In this paper, a new cell balancing method is proposed to limit the aging process of cells with a relatively small capacity and peak voltage. In addition, it was validated through simulation using MATLAB R2019a.


Introduction
The emergence of lithium-ion batteries, which have high energy density, has enabled the popularization of batteries. This has allowed for their application in various fields, and they have been widely adopted in society. However, there is a lack of research on the fundamental causes of battery fires.

Series Connection of Batteries
When series-connected batteries are charged from a source, a voltage distribution occurs across each battery . When 100% capacity is equal, the voltage is evenly distributed. However, it is impossible to produce batteries with 100% identical capacity in mass production. In fact, with series-connected batteries, the voltage is not evenly distributed across each battery. That is, different batteries have different charging voltages. Additionally, each change in the capacity of series-connected batteries with a single current loop also represents a different charging rate. Batteries with relatively small capacities quickly rise in the state of charge (SOC). Conversely, batteries with relatively large capacities have a slow rise in the SOC. The case of discharge is similar [15][16][17][18][19][20][21][22]. Different SOCs have different Direct Current Internal Resistances (DCIRs) [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. This causes a large potential difference between each battery. In this way, each battery repeats charging and discharging under different conditions. capacity, which differ according to the settings. The batteries in Figure 1 use the lithium-ion battery library provided by MATLAB R2019a, and the CC-CV battery charger library also provided by MATLAB R2019a was used.
2.1.1. In the Case of Having Cell Balancing and in the Case of Not Having It The authors conducted simulations for four series-connected batteries with and without cell balancing. Bat #1, Bat #2, Bat #3, and Bat #4 were set to 60 Ah, 59.4 Ah, 60.6 Ah, and 60 Ah, respectively, assuming a battery tolerance of ±1%. Figure 1a shows the simulation model with and without cell balancing. Figure 1b shows the battery aging settings, where all aging cycle variables for the batteries are the same, except for the values related to capacity, which differ according to the settings. The batteries in Figure 1 use the lithiumion battery library provided by MATLAB R2019a, and the CC-CV battery charger library also provided by MATLAB R2019a was used.   Figure 1. Figure 2a shows the Stateflow applied to Charts #1, #2, #3, and #4, which demonstrates a simple voltage comparison cell balancing method commonly used in the industry. Cell balancing is activated when a voltage difference of 30 mV or more is detected among the batteries and stops when the voltage difference decreases to 10 mV or less. Figure 2b shows the Stateflow for Chart #5, which illustrates the conditions for charging and discharging. Charging was performed at 2 C and ended at 0.5 C in the constant voltage (CV) region, while discharging was performed at 2 C.   Figure 1. Figure 2a shows the Stateflow applied to Charts #1, #2, #3, and #4, which demonstrates a simple voltage comparison cell balancing method commonly used in the industry. Cell balancing is activated when a voltage difference of 30 mV or more is detected among the batteries and stops when the voltage difference decreases to 10 mV or less. Figure 2b shows the Stateflow for Chart #5, which illustrates the conditions for charging and discharging. Charging was performed at 2 C and ended at 0.5 C in the constant voltage (CV) region, while discharging was performed at 2 C. Figure 3 shows the simulation results of Figure 1, where (a) shows the voltage results and (b) shows the SOC results. The difference between the cases with and without cell balancing cannot be easily observed due to a low cell balance. In Figure 3a, it was confirmed that the voltage of Bat #3 was the highest during charging and the lowest during discharging. This phenomenon was explained in the paper "Effect of capacity variation in series-connected batteries on aging" as occurring because the discharge and charge of relatively smaller batteries occur relatively quickly. Appl. Sci. 2023, 13, Figure 3 shows the simulation results of Figure 1, where (a) shows the voltage results and (b) shows the SOC results. The difference between the cases with and without cell balancing cannot be easily observed due to a low cell balance. In Figure 3a, it was confirmed that the voltage of Bat #3 was the highest during charging and the lowest during discharging. This phenomenon was explained in the paper "Effect of capacity variation in series-connected batteries on aging" as occurring because the discharge and charge of relatively smaller batteries occur relatively quickly. During the constant current (CC) charging phase, if the ideal capacity of the batteries is the same, the voltage of each battery should be equally distributed, as shown in Equation (1).
However, if there is a deviation in the battery capacity, as shown in Figure 3, Equation (2) applies. In Equation (2), the initial voltage of each battery is different, there is no   Figure 3 shows the simulation results of Figure 1, where (a) shows the voltage results and (b) shows the SOC results. The difference between the cases with and without cell balancing cannot be easily observed due to a low cell balance. In Figure 3a, it was confirmed that the voltage of Bat #3 was the highest during charging and the lowest during discharging. This phenomenon was explained in the paper "Effect of capacity variation in series-connected batteries on aging" as occurring because the discharge and charge of relatively smaller batteries occur relatively quickly. During the constant current (CC) charging phase, if the ideal capacity of the batteries is the same, the voltage of each battery should be equally distributed, as shown in Equation (1).
However, if there is a deviation in the battery capacity, as shown in Figure 3, Equation (2) applies. In Equation (2), the initial voltage of each battery is different, there is no During the constant current (CC) charging phase, if the ideal capacity of the batteries is the same, the voltage of each battery should be equally distributed, as shown in Equation (1).
However, if there is a deviation in the battery capacity, as shown in Figure 3, Equation (2) applies. In Equation (2), the initial voltage of each battery is different, there is no voltage limit during the CC phase, and the rise in voltage is determined by the internal resistance of each battery because the charging current is the same for all batteries.
V bat1 = V bat1 + I CC × R bat1 , V bat2 = V bat2 + I CC × R bat2 , V bat3 = V bat3 + I CC × R bat3 , V bat4 = V bat4 + I CC × R bat4 V bat#n : each battery's charging voltage; V bat#n : each battery's initial charging voltage; I CC : steady-state current of the constant current region; R bat#n : the DCIR for each battery's SOC. During the CV phase that follows, voltage redistribution occurs due to the voltage limit of the charging voltage and the different SOCs, as shown in Equation (3).
2 )/R total V CV : charger's target charging voltage; I CV : changing current in the constant voltage region; R total : the total DCIR of series-connected batteries.
(3) Table 1 summarizes the simulation results of Figure 3. Although our goal was to charge the four batteries to the same voltage, voltage distribution occurred due to the capacity variation among the batteries. At the end of charging the series-connected batteries, the highest voltage was observed in the relatively smaller Bat #3, and the lowest voltage was observed in the relatively larger Bat #2, with a voltage difference of 50 mV between the batteries. In the next section, the authors investigate the impact of different charging conditions on aging.  the authors could not find significant differences due to the low current of the cell balancing. The voltage results without cell balancing are shown in Figure 4a, while Figure 4b shows the voltage results with cell balancing. There is no significant difference in the progression of aging between the two simulation results. Figure 4c,d compare the voltage results in an enlarged voltage range of 4.0 V-4.3 V. It can be observed that, due to the low cell balancing current, cell balancing actually results in a greater increase in the maximum voltage during the aging process.  Figure 5 shows simulation results that investigate the impact of aging on the state of charge (SOC). It can be observed that Bat #2, which has a relatively large capacity, experiences a reduction in its usable range as aging progresses. In contrast, Bat #3, which has a relatively small capacity, experiences an increase in its usable range. It can be inferred that batteries with larger capacities experience a slower progression of aging as their usable range decreases over time.  Figure 5 shows simulation results that investigate the impact of aging on the state of charge (SOC). It can be observed that Bat #2, which has a relatively large capacity, experiences a reduction in its usable range as aging progresses. In contrast, Bat #3, which has a relatively small capacity, experiences an increase in its usable range. It can be inferred that batteries with larger capacities experience a slower progression of aging as their usable range decreases over time. Figure 6 shows the simulation results that observe the change in the state of health (SOH) during the aging process. No significant difference was observed in the two simulation results for the SOH. Appl Figure 6 shows the simulation results that observe the change in the state of health (SOH) during the aging process. No significant difference was observed in the two simulation results for the SOH.  Table 2 summarizes the results of the aging simulation. The maximum voltage without cell balance was 4.198 V, compared to 4.213 V with cell balance. This shows that a low cell balance current has a negative effect on the overvoltage caused by the voltage distribution. In addition, the SOH of the battery was relatively quickly degraded in both cases.  Figure 6 shows the simulation results that observe the change in the state of health (SOH) during the aging process. No significant difference was observed in the two simulation results for the SOH.  Table 2 summarizes the results of the aging simulation. The maximum voltage without cell balance was 4.198 V, compared to 4.213 V with cell balance. This shows that a low cell balance current has a negative effect on the overvoltage caused by the voltage distribution. In addition, the SOH of the battery was relatively quickly degraded in both cases.  Table 2 summarizes the results of the aging simulation. The maximum voltage without cell balance was 4.198 V, compared to 4.213 V with cell balance. This shows that a low cell balance current has a negative effect on the overvoltage caused by the voltage distribution. In addition, the SOH of the battery was relatively quickly degraded in both cases. Table 3 presents the simulation results with a ±2% variation in the battery capacity under the same conditions. The effect of cell balancing was found to be negligible during aging. However, it was observed that there was an impact on the maximum voltage at full charge as aging progressed. In Table 2, the maximum voltage of Bat #3 increased by 48 mV from 4.165 V to 4.213 V after aging. In Table 3, after the same duration of aging, the maximum voltage of Bat #3 increased by 72 mV from 4.203 V to 4.275 V. Additionally, by examining the range of SOC usage, it was found that 93.16% was used in Table 2, while 94.14% was used in Table 3. Consequently, the maximum SOC difference increased from 2.84% to 5.06%. The SOC difference in series-connected batteries leads to voltage redistribution in the CV region due to their different DCIRs [7].   Table 4 shows the simulation results for a serially connected battery with an allowable capacity deviation of ±3%. During the experiment, it was found that the maximum voltage of Bat #3 exceeded the overvoltage protection (OVP) reference voltage of 4.3 V during the charge and discharge cycles. As the allowable capacity deviation increased, the energy required for cell balancing also increased. The effect of balancing was reduced due to the low cell balance current, making it difficult to distinguish the difference in the aging rate between cases with and without cell balancing. In this session, the simulation results were compared (see Table 5). It was observed that the maximum voltage of Bat #3 increased more with a lower cell balance current than when there was no cell balance. This phenomenon can be attributed to the increased range of SOC usage, as indicated by the experimental results. Additionally, it was confirmed that as the allowable capacity deviation increased, the maximum voltage of Bat #3 even more significantly increased. This was because the difference in SOC usage range increased due to the increase in the allowable capacity deviation, resulting in an increase in the DCIR difference and voltage redistribution, which in turn increased the voltage difference between each battery [51].

Chemical Reaction of a Battery
Batteries are components that charge and discharge electrical energy through chemical reactions. The activity of the reaction changes with the temperature. To determine whether changes in the activity of the chemical reaction affect the voltage of the battery, experiments and simulations were conducted. The configuration of the equipment was as follows [51]. The following information is based on the specifications listed in the detailed product specification sheet for the battery and was used as the basis for the charging and discharging conditions [51]. In the Case of Having Cell Balancing and in the Case of Not Having It Table 6 summarizes the experimental results for the temperature-dependent voltage changes observed after performing a full charge and then varying the temperature. The range of temperature changes was based on the operating temperature range allowed by the BMS for automotive use, and voltage changes were accordingly observed. The largest voltage change occurred when the battery was charged at room temperature (25 • C) and then subjected to temperatures of −20 • C and 55 • C, resulting in a voltage change of 18 mV. It was noticed that the largest increase in the chemical reaction activity occurred when the battery was charged at room temperature and then, after complete charging, the temperature was increased to 55 • C, resulting in the influx of thermal energy. In Table 7, experiments were conducted to observe the voltage changes with temperature variations for each SOC. The charging temperature was based on room temperature, and the charging termination condition was divided into each percentage based on the fully charged Ah. In the experimental results, the voltage change was the smallest, 1 mV, with temperature variations from −20 to 55 • C at SOC 40%. In addition, the voltage change was the largest, 32 mV, with temperature variations at SOC 0%. Such voltage changes also occurred even in the case of SOC 100%, showing a voltage change of 18 mV.  Figure 7 is a diagram that estimates the cause of the voltage change based on the experimental results of Table 7. Using the SOC-OCV graph as a reference, the solid line represents the activity change in chemical reactions due to the heat energy input into the battery caused by temperature changes. The resulting voltage change is represented by the dotted line. It can be confirmed that open-circuit voltage (OCV) changes are more pronounced near SOC 0% or 100% than the nominal voltage.
In Table 7, experiments were conducted to observe the voltage changes with temperature variations for each SOC. The charging temperature was based on room temperature, and the charging termination condition was divided into each percentage based on the fully charged Ah. In the experimental results, the voltage change was the smallest, 1 mV, with temperature variations from −20 to 55 °C at SOC 40%. In addition, the voltage change was the largest, 32 mV, with temperature variations at SOC 0%. Such voltage changes also occurred even in the case of SOC 100%, showing a voltage change of 18 mV.  Figure 7 is a diagram that estimates the cause of the voltage change based on the experimental results of Table 7. Using the SOC-OCV graph as a reference, the solid line represents the activity change in chemical reactions due to the heat energy input into the battery caused by temperature changes. The resulting voltage change is represented by the dotted line. It can be confirmed that open-circuit voltage (OCV) changes are more pronounced near SOC 0% or 100% than the nominal voltage. Based on the previous experiment, a simulation was conducted by observing the voltage change after changing the temperature from room temperature to 60 °C. Figure 8a shows the simulation model, Figure 8b shows Chart 1's flowchart, and Figure 8c shows Chart 2's flowchart. Figure 8d presents the simulation results for the battery's voltage and current, while Figure 8e displays the simulation results for the battery's state of charge (SOC). The temperature was changed from 25 °C to 60 °C at 9 × 10 4 s, and an increase in voltage can be observed in Figure 8c. However, Figure 8d indicates no change in the SOC, suggesting that no external charging occurred. Based on the previous experiment, a simulation was conducted by observing the voltage change after changing the temperature from room temperature to 60 • C. Figure 8a shows the simulation model, Figure 8b shows Chart 1's flowchart, and Figure 8c shows Chart 2's flowchart. Figure 8d presents the simulation results for the battery's voltage and current, while Figure 8e displays the simulation results for the battery's state of charge (SOC). The temperature was changed from 25 • C to 60 • C at 9 × 10 4 s, and an increase in voltage can be observed in Figure 8c. However, Figure 8d indicates no change in the SOC, suggesting that no external charging occurred. Table 8 summarizes the simulation results before and after the temperature changes in Figure 8 after a full charge. The voltage increased by 113 mV due to the temperature change from room temperature to 60 • C. This is thought to be due to the difference in the SOC-OCV curve of the simulation model, resulting in a larger voltage change.   Table 8 summarizes the simulation results before and after the temperature changes in Figure 8 after a full charge. The voltage increased by 113 mV due to the temperature change from room temperature to 60 °C. This is thought to be due to the difference in the SOC-OCV curve of the simulation model, resulting in a larger voltage change.

Summary of Battery Overvoltage Generation
Sections 2.1 and 2.2 describe two factors that contribute to battery fires in electric vehicles. After charging is completed, electric vehicles forcibly terminate cell balancing, which creates conditions similar to the simulations of continuous charging and discharging shown in Figures 4-6. Of course, because there is a period of time during which a vehicle is left unused after charging is complete, the battery's lifespan more rapidly decreases if a relatively low-capacity battery maintains an overvoltage state. As a result, the voltage of low-capacity Bat #3 approaches the overvoltage protection limit of 4.3 V, and subsequent voltage changes due to temperature variations cause the battery to exceed the overvoltage limit, ultimately leading to a battery fire in the electric vehicle. Therefore, to address this problem, a new cell balancing method must be used in the BMS to suppress the voltage increase in low-capacity Bat #3.

Proposed Voltage-Based Realignment Cell Balance
Cell balance can be accomplished at any time by the user. In particular, cell balance during charging requires a lot of attention. When cell balance is performed during charging in a series-connected battery, resistance is connected in parallel to the battery, reducing the total resistance value. This changes the overall voltage distribution value of the seriesconnected batteries. In the simulation results in Section 2, it is confirmed that a low cell balance current is meaningless. Rather, it causes the problem of increasing the highest voltage of a battery with a relatively small capacity. In this section, the authors investigate a new cell balance method to solve the problem without changing any hardware.

Proposed New Cell Balance Method to Prevent Overvoltage Due to Aging
In previous studies, a cell balancing method was proposed to make the SOC of all cells 100% when charging was complete [7]. However, this method can put a heavy burden on the BMS, as it requires the individual calculation of the SOC of all series-connected batteries. Therefore, in this study, a method using only the voltage is proposed to solve the problem of the maximum voltage rising due to aging. Table 5 shows that Bat #3 with the minimum capacity determines the charge-discharge current, and it can be seen that it quickly approaches overvoltage as the aging relatively quickly progresses. In addition, it is confirmed that the voltage rise of the average capacity battery suppresses the maximum voltage rise of a relatively small-capacity battery. Figure 9 shows the cell balance flow chart of the new method. Initially, the full charge and full discharge are slow-charging and without cell balancing. Measuring the highest voltage of each battery and setting the measured voltage as the reference for the cell balance voltage allows for the highest voltage of a battery to have a relatively small capacity, which is applied as the cell balance reference voltage of the remaining batteries. It is applied as the cell balance reference voltage of a relatively small-capacity battery. The reference voltage for the cell balancing of the remaining batteries is set to the highest voltage. The proposed new cell balancing method suggests low-voltage charging for batteries with a relatively low capacity. This slows down the aging process of low-capacity batteries, resulting in a slower increase in the maximum voltage. Additionally, starting from a lower maximum voltage point also slows down the time it takes to reach overvoltage. Cell balancing is performed only at voltages higher than the reference voltage, so the remaining batteries, excluding those with a relatively low capacity, have a relatively high SOC value at the end of charging, which balances the aging rate.

Simulation Verification of the Proposed Cell Balance
In this section, the potential difference realignment passive balancing method proposed above is simulated. The simulation configuration is configured as shown in Figure 10. The basic conditions are the same as in the previous simulations. However, since the conditions for Charts #1, #2, #3, and #4 are modified, the modified conditions for each simulation are set by taking the initial voltage from the series-connected batteries in Tables 1-4

Simulation Verification of the Proposed Cell Balance
In this section, the potential difference realignment passive balancing method proposed above is simulated. The simulation configuration is configured as shown in Figure  10. The basic conditions are the same as in the previous simulations. However, since the conditions for Charts #1, #2, #3, and #4 are modified, the modified conditions for each simulation are set by taking the initial voltage from the series-connected batteries in Tables 1, 2, 3, and 4, respectively. Simulation Results with Proposed Cell Balancing Implementation Simulations were performed by applying the proposed cell balance method when the allowable capacity deviation of series-connected batteries was ±1%. Figure 10 shows each chart. Taking the voltage result of the battery from Table 1, applying it to the cell balance reference voltage, and, in the case of battery 3 having a relatively small capacity, the lowest voltage was applied as a standard for cell balance. Batteries 1, 2, and 4 applied the highest voltage as a standard for cell balance. Different charge rates resulted in differences in the DCIR. The difference in the DCIR affected the voltage distribution during charging. Therefore, it suppressed the peak voltage of a relatively small-capacity battery and suppressed the aging rate at the same time. Figure 11 shows the simulation results. Figure 11a is the simulated voltage result. Figure 11b is the result of extending the voltage of the simulated voltage result from 4.0 V to 4.35 V. Figure 11c is the simulated SOC result. Figure 11d is the simulated SOH result. In Figure 11b, it can be seen that the highest voltage of Bat #3 rises while charging and discharging is repeated. However, after 10 × 10 6 s, the highest voltage of Bat #3 is lower than in Table 2 because the cell balance reference voltage was lowered. Appl. Sci. 2023, 13,   Simulation Results with Proposed Cell Balancing Implementation Simulations were performed by applying the proposed cell balance method when the allowable capacity deviation of series-connected batteries was ±1%. Figure 10 shows each chart. Taking the voltage result of the battery from Table 1, applying it to the cell balance reference voltage, and, in the case of battery 3 having a relatively small capacity, the lowest voltage was applied as a standard for cell balance. Batteries 1, 2, and 4 applied the highest voltage as a standard for cell balance. Different charge rates resulted in differences in the DCIR. The difference in the DCIR affected the voltage distribution during charging. pressed the aging rate at the same time. Figure 11 shows the simulation results. Figure 11a is the simulated voltage result. Figure 11b is the result of extending the voltage of the simulated voltage result from 4.0 V to 4.35 V. Figure 11c is the simulated SOC result. Figure 11d is the simulated SOH result. In Figure 11b, it can be seen that the highest voltage of Bat #3 rises while charging and discharging is repeated. However, after 10 × 10 6 s, the highest voltage of Bat #3 is lower than in Table 2 because the cell balance reference voltage was lowered.  Table 9 summarizes the simulation results for Figure 11, considering the allowable capacity deviation of ±2% and ±3% in the serially connected battery. In the case of a ±1% allowable capacity deviation, the highest voltage of Bat #3 is 4.167 V; in the case of a ±2% deviation, it is 4.093 V; and, in the case of a ±3% deviation, it is 4.049 V. This proves that the prevention of the highest voltage of a relatively smaller battery from approaching the OVP voltage is achieved.  Table 9 summarizes the simulation results for Figure 11, considering the allowable capacity deviation of ±2% and ±3% in the serially connected battery. In the case of a ±1% allowable capacity deviation, the highest voltage of Bat #3 is 4.167 V; in the case of a ±2% deviation, it is 4.093 V; and, in the case of a ±3% deviation, it is 4.049 V. This proves that the prevention of the highest voltage of a relatively smaller battery from approaching the OVP voltage is achieved.

Results of the Existing Cell Balance and the Proposed Cell Balance
In Table 10, the authors compare the simulation results of the voltage-based cell balance method and the proposed voltage-based realigned cell balance method. For all the results, the proposed cell balance method showed a higher voltage rise than the voltage-based cell balance method, except for batteries with relatively small capacities. On the contrary, it was possible to be safe from a fire due to overvoltage by suppressing the voltage rise of a battery with a relatively small capacity as much as possible, such that it did not reach overvoltage. In the case of the SOC, it can be confirmed that the proposed cell balance method reduced the overall usage range, which suppressed the SOC range expansion of Bat #3. Therefore, it was confirmed that the deterioration of the battery as a whole was slowed down. The simulation results of the cell balance method proposed in Table 11 and the cell balance method of the existing simple voltage comparison method are summarized here. For the existing simple voltage comparison cell balancing method, the maximum voltage of the battery greatly increased from 4.213 V to 4.331 V as the allowable capacity deviation of the series-connected batteries increased. However, in the case of the proposed cell balance method, the highest voltage rose from 4.167 V to 4.211 V, which was relatively very small. In addition, for the existing simple voltage comparison cell balance method, it was confirmed that as the allowable capacity deviation of series-connected batteries increased, the aging of batteries with relatively small capacities more quickly proceeded. However, in the case of the proposed cell balance method, the aging and the aspect of the battery were different. This was because the use area of a battery with a relatively small capacity is limited according to the allowable capacity deviation of the battery.