Method and system for optimizing the charging process of lithium-ion batteries to instantaneously mitigate cell degradation

Abstract

A method and system are disclosed for optimizing the charging process of a lithium-ion battery by utilizing a determined parameter (e.g., the Lyapunov exponent) as an indicator of cell degradation (e.g., anodic overpotential). The system and method achieve intelligent charging and may involve an integrated controller that adjusts the charging current in real-time (or near real-time, or otherwise) based on the cell degradation indicator calculated by probing the battery. This method offers various potential benefits, which can be tuned to include extended battery life, optimized charging timing, and improved safety.

Description

[0001] Cross-references to related applications

[0002] The Patent Cooperation Treaty (PCT) application relates to and claims priority to U.S. Provisional Application No. 63 / 540,921, filed September 27, 2023, entitled “Method and System for Optimal Charging Process of Lithium-Ion Batteries to Mitigate Cell Degradation in Real Time,” which is hereby incorporated herein by reference. Technical Field

[0003] This disclosure relates to an inventive method for obtaining data from a battery and calculating parameters (e.g., Lyapunov Exponent) or information indicating said parameters and / or related to said parameters from the response of a battery cell stimulated by a probe signal, to provide real-time insights into the health and degradation of the battery cell and, based thereon, control the charging or discharging of the battery. Background Technology

[0004] Battery-powered devices have proliferated and become ubiquitous, leading device manufacturers to continuously demand improvements in battery performance, especially as batteries are incorporated into devices with relatively high current and power requirements. Simultaneously, consumers demand longer battery life, longer charging intervals, and shorter charging times. Therefore, there is a constant need for improvements in how batteries are managed, charged, and discharged to enhance performance. These observations, along with many other factors, have conceived various aspects of this disclosure. Summary of the Invention

[0005] This disclosure relates to a method for charging a battery, comprising: obtaining a Lyapunov index value based on at least one measurement from the battery; and changing charging parameters of the battery based on the Lyapunov index value relative to a threshold.

[0006] In various aspects, the at least one measurement is at least one of a voltage measurement or a current measurement. The voltage or current measurement may be performed in the presence of a probe signal, which includes a transition from an active period containing current flowing into the battery to a quiescent period. In some aspects, the measurement is performed during the active period, or the measurement is performed during the quiescent period, wherein the quiescent period is a time during which no current is applied to the battery and the voltage measurement transitions to the open-circuit voltage of the battery. The measurement may also be performed during the transition from the active period to the quiescent period. In some cases, the current is a charging current, and the quiescent period includes a period of time during which no charging current flows after the charging current.

[0007] The threshold can represent the transition to chaotic behavior of the battery, indicating that the anode overpotential is 0. Typically, the threshold is set to vary the charging parameters to maintain the anode overpotential greater than 0, or not lower than 0 (becoming negative). In some cases, charge control may result in a negative anode overpotential, which is quickly eliminated and returns to a positive value.

[0008] The altered charging parameter can be the charging current, which may involve a decrease in the charging current, or an increase in the charging current, or a change in some other property of the charging signal. Another property can affect the average charging current, for example, by modifying the pulse width or duty cycle of the pulse charging.

[0009] As will be understood from this specification, the Lyapunov index is related to the anodic overpotential, thereby allowing the anodic overpotential to be assessed without directly measuring it.

[0010] Another aspect of this disclosure relates to a battery charging method comprising: applying a probe waveform to a battery; measuring at least one of a current or a voltage at the battery in the presence of the probe waveform; calculating a value associated with a Lyapunov exponent based on the measurement; and at a PID controller, comparing the Lyapunov exponent with a decay threshold and generating a charging current adjustment value based on the comparison of the Lyapunov exponent with the decay threshold.

[0011] The decay threshold can be a chaos threshold or an anode overpotential threshold. In some instances, the charging current adjustment value is a multi-step charging current reduction, wherein each step of the charging current reduction occurs when the value associated with the Lyapunov exponent approaches or reaches the decay threshold. The value associated with the Lyapunov exponent is related to the anode overpotential, thereby allowing the anode overpotential to be evaluated without directly measuring it, and wherein the decay threshold is set based on an anode overpotential of 0. The PID controller attempts to adjust the charging current adjustment value to maintain a positive anode overpotential. Attached Figure Description

[0012] The above and other objects, features, and advantages of this disclosure set forth herein will become apparent from the following description of specific embodiments of the inventive concepts as illustrated in the accompanying drawings. It should be noted that the drawings are not necessarily drawn to scale; however, the emphasis is on illustrating the principles of the inventive concepts. Furthermore, in the drawings, the same reference numerals may refer to the same or similar parts throughout different views. It is intended that the embodiments and figures disclosed herein be considered illustrative rather than restrictive.

[0013] Figure 1A The current measurement of the probe waveform is shown.

[0014] Figure 1B Showing Figure 1A Voltage measurement of the probe waveform.

[0015] Figure 2A Measurements were shown from batteries at charging rates of 1C, 3C, and 5C, with SOC between 0% and 100% (e.g., ...). Figure 1B The Lyapunov exponent calculation (normalized between -1 and 1) is obtained from the back-edge voltage measurement (transition from active charging current to quiescent current) shown in the figure.

[0016] Figure 2B The measurements are shown from batteries at charging rates of 1C, 3C, and 5C, where the chaos threshold (dashed line) is 0 (e.g., as...). Figure 1B The Lyapunov exponent calculation (normalized between -1 and 1 and divided by the minimum current value of the corresponding charge rate) is obtained from the back edge measurement (transition from active to stationary) shown in the figure.

[0017] Figure 3 The LE calculation of the trailing edge of the voltage waveform at different temperatures (-5, 25, 27, 30 and 34 degrees Celsius) is shown, where the voltage waveform may be a probe waveform.

[0018] Figure 4This is a graph showing the correlation between LE calculation and anode overpotential for a multi-step charging process.

[0019] Figure 5 This is a system diagram of an LE-based feedback controller used to optimize charging. The system adjusts charging based on LE calculations and the correlation between LE and anode overpotential.

[0020] Figure 6 This is a graph showing a comparison between a multi-step charging protocol generated from a feedback controller using LE and a conventional constant current constant voltage (CCCV) charging protocol.

[0021] Figure 7 This is a graph showing the voltage curve of a multi-step charging protocol triggered by calculations based on LE and anode overpotential threshold, compared to the charging process of a conventional CCCV protocol.

[0022] Figure 8 The measured battery temperatures were compared with those of the conventional CCCV protocol, demonstrating that the multi-step charging protocol generates less heat while achieving the same or better total charging time.

[0023] Figure 9 This shows the LE value relative to the threshold and Figure 10 Measurement.

[0024] Figure 10 The simulation results of the anode overpotential are shown, comparing the multi-step charging protocol with the conventional CCCV protocol.

[0025] Figure 11 Simulation results of SEI layer resistance in the multi-step charging protocol compared to the CCCV protocol.

[0026] Figure 12 Simulation results show the capacity loss due to lithium plating in the multi-step charging protocol compared to the CCCV protocol.

[0027] Figure 13 Simulation results show the capacity loss due to SEI growth in the multi-step charging protocol compared to the CCCV protocol.

[0028] Figure 14 Simulation results show the total capacity loss of the multi-step charging protocol relative to the CCCV protocol. Detailed Implementation

[0029] Lithium plating and anodic overpotential

[0030] Lithium plating is a major cause of battery degradation in lithium-ion batteries. Lithium plating, also known as lithium metal plating, occurs when lithium ions are deposited unevenly and uncontrolled onto the anode surface during charging. Lithium plating reduces the number of lithium ions available for normal battery operation, thus decreasing battery capacity over time. Lithium plating can also induce the formation of metallic lithium, which can accumulate on the anode surface and form dendritic structures. In some cases, dendrites can penetrate the separator between electrodes (e.g., the separator between the anode and cathode), leading to internal short circuits and battery failure, which can also cause thermal runaway in some situations.

[0031] Anode overpotential is a measure of the difference between the actual potential of the anode and its equilibrium potential. Ideally, during charging, lithium ions should deposit and embed into the anode at a voltage consistent with the anode equilibrium potential. In reality, due to various factors, including the resistance in the electrolyte and at the anode-electrolyte interface, the actual voltage required to drive lithium deposition is typically higher than the equilibrium potential. This voltage difference is the anode overpotential.

[0032] Lithium plating is closely related to anode overpotential. When the anode overpotential drops to zero or becomes negative, there is insufficient voltage to drive lithium ions into the anode material as intended. This situation can lead to lithium plating. However, outside of a controlled laboratory environment, measuring anode overpotential in real time to indicate cell degradation in commercial lithium-ion batteries may be impractical, at least due to cost, and other requirements and obstacles such as the need for additional connections to and into the cell structure of the battery (in addition to the conventional two connections for charging and discharging the anode and cathode).

[0033] This disclosure relates to a novel method for obtaining information from a battery and calculating parameters or indication parameters from the response of a battery cell stimulated by a probe signal to provide real-time insights into the health and degradation of the battery cell. In one example, the parameters are strongly correlated with the anode overpotential, and based on the parameter values, the charging or discharging of the battery can be controlled to alter the anode overpotential, and thus place the battery in a charging or discharging state, wherein various degradations associated with the anode overpotential are reduced or eliminated.

[0034] Battery cell detection and LE calculation

[0035] This disclosure relates to a method for optimally charging a battery to reduce or avoid battery degradation. First, the battery is probed to generate data from which parameters (e.g., the Lyapunov exponent) can be calculated. In one example, the battery is probed using a unipolar pulse waveform, an example of which is shown in [example missing]. Figure 1AThe detection waveform can be a momentary pulse of the charging signal or a portion thereof, can be a different detection signal (e.g., during a short period when charging stops), or can be combined with charging or discharging or otherwise initiated. Figure 1A In this example, the probe waveform involves a charging phase 100 and a resting phase 102, with a transition 104 (or edge) between them. In this example, the total duration (period) of the current probe waveform is 20 seconds, comprising a 10-second charging phase and a 10-second resting phase. It should be noted that a “charging phase” can be any length of time during which charging is active, and the resting phase is a brief pause (e.g., 10 seconds) before charging resumes. In the example shown, the charging current is 3 A. It should be understood that the duration and shape of the probe waveform can vary, the charging phase and / or resting phase can vary, and the current level can vary depending on various factors including the battery type.

[0036] Using data, such as voltage and / or current measurements from the battery, parameters are calculated based on the probe signal. In one instance, measurements can be taken during the charging phase of the probe signal. In another instance, measurements can be taken shortly after the probe signal transitions to a quiescent phase, at which point the current immediately drops to zero (e.g., ...). Figure 1A (as shown in the image), and as Figure 1B As shown, the voltage transitions to the battery voltage within seconds. During charging, the voltage measured at the battery is higher than the voltage when no charge is applied. However, the voltage does not immediately drop to the battery's open-circuit voltage. During the transition 104 from an active signal (which could be charging current 100) to a resting state 102, the anode overpotential decreases and other battery states are less active, so information related to the anode overpotential may be more prevalent during this transition period. In one specific instance, the system calculates the Lyapunov exponent (LE) or obtains one or more values ​​indicating the Lyapunov exponent. While the Lyapunov exponent can be calculated directly, a proxy can also be used to calculate it. In one specific instance, the voltage waveform of a time-voltage value pair, which could be time-series data, is captured during the relaxation period after the current is turned off, and the time series is used to calculate the Lyapunov exponent. The use of the Lyapunov exponent calculation is related to battery cell degradation and can therefore be used, as discussed herein, to manage battery charging to avoid or minimize degradation.

[0037] The Lyapunov exponent is a mathematical concept used to measure the sensitivity of a dynamic system to small perturbations. The Lyapunov exponent is a measure of the average rate at which nearby trajectories diverge or converge in phase space, where phase space is the space of all possible states of the system.

[0038] More precisely, the Lyapunov exponent is defined as the logarithmic limit of the ratio of the interval between two nearby trajectories to their initial interval when the interval becomes zero. Mathematically, it can be expressed as follows:

[0039]

[0040] Where λ is the Lyapunov exponent, t is time, δx(t) is the interval vector between two nearby trajectories at time t, and δx(0) is the initial interval vector between the two trajectories.

[0041] In simpler terms, the Lyapunov exponent measures the average rate at which a nearby trajectory in phase space diverges or converges over time. If λ is positive, the trajectory diverges exponentially, and the system is said to be chaotic, indicating that small differences in initial conditions can lead to drastically different outcomes over time. If λ is negative, the trajectory converges exponentially, and the system is stable, indicating that small differences in initial conditions will converge over time.

[0042] The Lyapunov exponent is a fundamental concept in chaos theory and provides insights into the long-term behavior of complex systems, and can help predict the stability or instability of a system over time.

[0043] This disclosure relates to a unique understanding of the strong correlation between the Lyapunov index and anodic overpotential. Therefore, the Lyapunov component can be used as an indicator of lithium plating and charging (or discharging) control can be modified based on said indicator. Thus, the calculation of LE provides information related to anodic overpotential without modifying the battery, which would otherwise require direct measurement of anodic overpotential, and offers other advantages.

[0044] Figure 2A The calculation of the Lyapunov exponent based on measurements taken during the transition period between the rest and charging phases of the probe waveform is demonstrated. In the example probe waveform, voltage and current measurements are taken within approximately 10 seconds at the transition point 104 of the probe waveform. In other words, LE is calculated from measurements taken at the trailing edge of the probe waveform. Figure 2A In this example, LE calculations were performed under different charging states during the charging process. LE values ​​are used for brand new 30T lithium-ion battery cells with fewer than 10 previous charge-discharge cycles, exhibiting different charge rates of 1C (200), 3C (202), and 5C (204). For comparison purposes, LE values ​​were normalized to [-1, 1]. It can be seen that the LE curves with different charge rates begin to diverge at approximately 20% SOC (206).

[0045] Figure 2BInformation is presented in different forms. Here, the LE calculation is normalized to [-1,1] and then divided by the minimum current value for each charging rate (1C (208), 3C (210) and 5C (212) respectively).

[0046] Figure 2A The plot in Figure 2(B) shows that the higher the charging rate, the faster the LE value decreases. This indicates that the higher the charging rate, the more severe the battery cell degradation. In Figure 2(B), when charging at 5C, the LE value exceeds the chaos threshold 212 at approximately 24% SOC; when charging at 3C, the LE value exceeds the chaos threshold 214 at approximately 38%; and when charging at 1C, the LE value does not exceed the chaos threshold 218 until approximately 90%. Therefore, this information reveals that adjusting the charging rate based on a chaos threshold close to the LE can be used to prevent or reduce battery degradation. Thus, for example, if charging at 5C, the system can reduce the charging rate at or before reaching the chaos threshold (e.g., at 24% SOC).

[0047] exist Figure 3 In the study, 30T battery cells were charged at a 0.5C charging rate at different temperatures. It can be seen that at higher temperatures (25°C, 27°C, 30°C, and 34°C), the Lyapunov index value is close to zero, indicating insignificant battery cell degradation. At lower temperatures (-5°C), the Lyapunov index value decreases at approximately 30% SOC, indicating significant battery cell degradation due to the low temperature.

[0048] Therefore, this information also indicates that battery cell temperature can be used in conjunction with the calculation of the LE component to inform and control the charging rate. For example, charging may pause for a period of time until the battery temperature rises, or it may begin slow charging at low temperatures, and other possibilities exist.

[0049] Correlation between anodic overpotential and Lyapunov index calculation

[0050] Based on LE as an indicator of lithium plating, further support is given to using LE as a trigger for charge control (e.g., calculating LE based on data collected during the probe waveform). This is because of the strong correlation between LE and anode overpotential. Figure 4 As shown in the diagram, negative anode potential triggers lithium plating in lithium-ion batteries. Figure 4The charging current (400), anode overpotential (402), and Lyapunov exponent (404) of a multi-step CCCV charging process on a 30T battery cell are shown. The current curves show the battery cell being charged at a constant current of 12.2 A from approximately 5% SOC to approximately 60% SOC, and then charged at a constant current of 8.4 A to approximately 81% SOC, at which point the charging scheme changes to constant voltage charging, where the battery terminal voltage is kept constant by steadily decreasing the charging current. LE is calculated in 5% SOC intervals during charging. In one instance, charging can be interrupted for a very short period, and a probe signal can be injected into the battery. In another instance, the charging current can be changed, for example, by turning it off for a period of time, such as 10 seconds, and battery measurements can be taken during the transition from the charging current to 0 or some relatively low charging current. Curve 402 is a simulated anode overpotential based on the charging current distribution using a PyBaMM model of the 30T battery cell. It can be seen that the anode overpotential continuously decreases during the first stage of charging (12.2 A charging). The anodic overpotential drops to zero at approximately 20% SOC, indicating the onset of significant lithium plating. After 60% SOC, when the charging current decreases to 8.4 A, the anodic overpotential immediately increases by 406 to slightly above zero, and then begins to decrease almost immediately. Since the charging current is still relatively high at this point, for example compared to a 1C charging rate, the anodic overpotential rapidly decreases by 408 to a negative value for continued plating. Nevertheless, due to the increase in anodic overpotential (even if brief), the current change to a smaller current appears to have slowed or stopped lithium plating. After the charging process enters the constant voltage phase, the overpotential begins to increase again by 410, while the charging current steadily decreases, and at the end of charging, the charging current transitions back to a positive value at approximately 6 A and a smaller charging current (approximately 97% SOC). Here, it can be observed that the LE curve is strongly correlated with the anodic overpotential throughout the charging process, making it possible to use LE as an indicator of lithium plating, which can be considered real-time.

[0051] Optimal charging controller based on real-time battery cell degradation feedback

[0052] Based on the information presented above, Figure 5 An example of a system for controlling battery charging is shown. The controller is configured to control charging based on real-time battery cell degradation feedback. Generally, the controller implements a method for real-time monitoring of battery cell degradation using probe waveforms via LE calculations to dynamically adjust the charging current, thereby optimizing battery performance and extending its lifespan. The method and its variations can be implemented in other controllers, wherein... Figure 5 One possible instance is presented.

[0053] Figure 5A block diagram of the feedback controller 500 is shown. A probe waveform 502 is applied to the battery cell 504, and current and voltage probe waveforms are used to calculate one or more LE values ​​506, which are then sent as input to a proportional-integral-derivative (PID) controller 508. A battery cell degradation threshold 510 is set as a target value for the PID controller (e.g., -0.1). The target value can be set to 0 or a negative value (less than 0). It should be understood that if normalization, averaging, or other calculations are performed to convert the value into a quantity (without positive or negative meaning), a negative LE value in the sense of LE calculation is expected. Based on the difference between the calculated LE value and the target value, the PID controller outputs an adjustment to the charging current and applies an optimal charging current to the battery cell. Thus, for example, the charging current can be dynamically adjusted as the LE reader changes to 0. In one example, the charging current can be reduced.

[0054] Verification Test

[0055] Figure 6 This demonstrates charging using LE-based feedback control compared to conventional CCCV charging at a 1.5C rate. The feedback controller is applied to a 30T battery cell to generate an optimal charging protocol. Figure 6 In the diagram, the multi-step charging protocol generated in real time from the feedback controller is shown as curve 600. The charging current is adjusted every 5% SOC based on the real-time battery cell degradation state. Curve 602 illustrates a standard CCCV charging protocol with a 1.5C charging rate. Figure 6 In the example, it can be seen that the initial charge rate of 9 amps 604 is maintained until 20% SOC, at which point the charging current gradually decreases 606 in response to the LE calculation meeting the threshold indicating 0 or negative anode overpotential and the start of plating. The charging current then gradually decreases in subsequent steps based on the same LE calculation. During the 1.5 CC charging time up to 95% SOC, at some point during constant current charging, the anode overpotential will become negative, leading to plating, and conventional charging protocols do not detect this condition or change the charging, resulting in lithium plating and battery degradation even under moderately fast charging at 1.5C. Both charging protocols have approximately the same charging time, but the LE feedback reduces or eliminates plating.

[0056] Although Figure 6The diagram illustrates a continuous decrease in charging current, initially charging at a rate higher than the CCCV and then at a lower rate, but the PID controller can also command the charging current to increase (or remain unchanged). Furthermore, other properties of the charging signal can be controlled. For example, the controller can increase the current over a period of time to reduce charging time, or raise the charging current to its maximum safe level over a period of time. In another example, if some form of pulse charging is used, the average current value during the active phase of the pulse can be changed, the duty cycle can be changed, the duration of any rest periods between pulses can be changed, and other aspects of the pulse can be controlled. Thus, some aspects of the charging signal (or discharging) can be controlled in response to the LE value (or information representing LE).

[0057] Figure 7 The charging and discharging voltage curves for the two protocols are shown (charging from 0 to 100% SOC and then discharging from 100% SOC to 0). It can be seen that, compared to the conventional CCCV protocol 706, the voltage curve of the multi-step charging protocol 700 has a larger ratio of constant current to constant voltage during the charging process, indicating a healthier charging process. In other words, using LE feedback control for charging results in a shorter duration 702 at 4.2 V, and therefore, a significantly shorter time at voltages where adverse processes might occur within the battery cell (compared to the constant voltage portion 704 of the CCCV protocol at 1.5C).

[0058] Figure 8 The measured temperatures during a similar full charge and discharge process in the LE multi-step process 800 are shown compared to the conventional CCCV process 802. During the charging process, the multi-step charge 802A exhibits a peak temperature at approximately 40% to 50% SOC and a decreasing temperature at the end of charging. Therefore, as shown, during discharging, the LE charge ends at a lower temperature due to the lower starting point, while discharging after CCCV ends at a higher temperature before the discharge phase. Even during charging, the temperature actually decreases; it should be noted that the ambient temperature was low during the tests. For a conventional charging process, in the same ambient environment, the temperature remains elevated until the end of charging 800A. Figure 8 As can be seen, compared to CCCV, the multi-step charging protocol has a smaller overall temperature rise throughout the cycle, and compared to CCCV, the multi-step charging protocol can maintain the battery cell within a healthy temperature range throughout the charging cycle, which may cause the battery cell to heat up to a suboptimal temperature range.

[0059] Figure 9This demonstrates the LE calculated using the PID controller discussed above at different SOCs, with the probe waveform applied to the battery cell at the measurement point. The target threshold is set to -0.1. Setting -0.1 instead of 0 as the target threshold is intended to leave some margin for the controller to avoid battery cell degradation associated with positive LE values. Figure 6 In the charging scenario described, when the LE value approaches 0.1, the PID controller changes the charging current, and after SOC > 50% (after LE approaches -0.1), it appropriately maintains the Lyapunov exponent near the target threshold. By maintaining the LE value in this way, the anode overpotential remains within a healthy range, due to its correlation with the anode overpotential.

[0060] To further investigate the performance of the multi-step charging protocol generated by the controller as discussed above based on real-time LE calculations, a PyBaMM model of a 30T battery cell was used to simulate the anode overpotential, SEI growth, and capacity loss of the multi-step charging protocol and the CCCV protocol. Figure 10 The anode overpotentials of the two charging protocols during the charging process are shown. It can be seen that the anode overpotential of the CCCV protocol 1000 drops to zero near the end of charging, a value associated with the start of lithium plating, while the anode overpotential of the multi-step charging protocol 1002 remains consistently above zero with a relatively large margin above zero. Even though the anode overpotential drops rapidly at the start of charging due to the large initial charge amount, it remains relatively stable above zero throughout the remaining charging process.

[0061] Figure 11 The increased SEI layer resistance of the multi-step charging protocol (denoted as PF) and the conventional CCCV protocol 1100 are shown separately. It can be seen that the CCCV charging protocol is associated with a slightly larger SEI layer resistance at the end of charging 1102, indicating a larger SEI layer thickness growth. Here, the LE-based charging protocol produces less SEI growth, thus resulting in less capacity decay and better overall charging performance compared to the equivalent CCCV charging protocol.

[0062] Figures 12 to 14 Capacity loss due to lithium plating was demonstrated for two charging protocols (in only one charging cycle). Figure 12 ), capacity loss due to SEI growth ( Figure 13 ) and total capacity loss ( Figure 14 For all possible sources of capacity loss, the CCCV protocol results in greater capacity loss at the end of charging compared to multi-step charging protocols. In other words, multi-step charging protocols based on the LE value can be used to charge batteries with relatively less capacity loss and other adverse effects compared to the CCCV protocol. Figures 12 to 14 The simulation results shown further demonstrate that, compared to the conventional CCCV protocol, the multi-step charging protocol exhibits less battery cell degradation during the charging process.

Claims

1. A method for charging a battery, comprising: The Lyapunov index value is obtained based on at least one measurement from the battery; as well as The charging parameters of the battery are changed based on the Lyapunov index value relative to a threshold.

2. The method according to claim 1, wherein the at least one measurement is at least one of a voltage measurement or a current measurement.

3. The method of claim 2, wherein at least one of the voltage measurement or the current measurement is performed in the presence of a probe signal, the probe signal including a transition from an active period containing current flowing into the battery to a quiescent period.

4. The method of claim 3, wherein the at least one measurement is performed during the activity period.

5. The method of claim 3, wherein the at least one measurement is performed during the quiescent period, wherein the quiescent period is a period in which no current is applied to the battery and the voltage measurement transitions to the open-circuit voltage of the battery.

6. The method of claim 3, wherein the at least one measurement is performed during the transition from the active period to the quiescent period.

7. The method of claim 3, wherein the current is a charging current, and the quiescent period includes a time period after the charging current during which no charging current flows. The method of claim 1, wherein the threshold represents the transition of the battery to chaotic behavior.

8. The method of claim 1, wherein the threshold represents an anode overpotential of 0.

9. The method of claim 7, wherein the threshold is set to change the charging parameters to maintain the anode overpotential greater than 0.

10. The method according to claim 1, wherein the charging parameter is a charging current value.

11. The method of claim 11, wherein changing the charging parameters includes changing the charging current value.

12. The method of claim 12, wherein alternating the charging parameters comprises changing the charging current value by decreasing the charging current value.

13. The method of claim 1, wherein the Lyapunov index is related to the anodic overpotential, thereby allowing the anodic overpotential to be evaluated without directly measuring it.

14. A battery charging method, comprising: Apply the probe waveform to the battery; In the presence of the probe waveform, measure at least one of the current or voltage at the battery; The value associated with the Lyapunov index is calculated based on the measurement. At the PID controller, the Lyapunov exponent is compared with a decay threshold, and a charging current adjustment value is generated based on the comparison between the Lyapunov exponent and the decay threshold.

15. The battery charging method according to claim 14, wherein the attenuation threshold is a chaos threshold or an anode overpotential threshold.

16. The battery charging method of claim 14, wherein the probe waveform includes a charging current portion, a transition to a quiescent period without charging, and a portion of the measurement used to calculate the value associated with the Lyapunov exponent is performed after the transition to the quiescent period.

17. The battery charging method of claim 14, wherein the charging current adjustment value is a multi-step charging current reduction, wherein each step of the charging current reduction occurs when the value associated with the Lyapunov exponent approaches or reaches the decay threshold.

18. The battery charging method of claim 15, wherein the value associated with the Lyapunov index is related to the anode overpotential, thereby allowing the anode overpotential to be evaluated without directly measuring it, and wherein the decay threshold is set based on the anode overpotential being 0.

19. The battery charging method according to claim 19, wherein the PID controller attempts to adjust the charging current adjustment value to maintain the positive anode overpotential.

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