Electrode diagnostics for lithium-ion batteries

Abstract

The present disclosure provides an electrical device, comprising: a battery cell; a voltage sensor operably coupled to the battery cell to measure a voltage level of the battery cell; a current sensor operably coupled to the battery cell to measure an amount of current drawn from or supplied to the battery cell; and a battery management system (BMS). The battery management system comprises a controller in communication with the voltage sensor and the current sensor. The controller is configured to execute a program stored in the BMS to calculate a health state of each battery electrode constituting the battery cell using a first differential voltage point, a second differential voltage point, and a characteristic curve of a new battery electrode of a new battery cell, wherein the battery cell comprises a second battery electrode that does not exhibit a significant phase change during a charge-discharge cycle.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Patent Application No. 62 / 715,014, filed on August 6, 2018.

[0003] A note about federally funded research

[0004] not applicable. Background Art

[0005] 1. Field of the Invention

[0006] The present invention relates to an apparatus and method for estimating the state of health in two electrodes of a battery cell using voltage and current measurements in combination with a reference curve of a new reference electrode potential.

[0007] 2. Related technical description

[0008] Lithium-ion batteries play an important role as energy storage devices in many applications. For example, electric vehicles (EVs) require durability and robustness of batteries throughout their nearly decade-long service life. In addition, the safe use and reuse of batteries depends on a thorough understanding of the battery's state of health (SOH). Therefore, it is necessary to develop a method for monitoring the SOH of batteries. SOH is usually estimated by identifying the changes in battery model parameters over the battery life. For example, many efforts have been made to estimate the capacity or resistance of the battery, such as SOH indicators at the cell level (Refs. 2.1-2.4), which affects the prediction of the maximum driving range and peak power of EV applications. On the other hand, less attention has been paid to the state of health (eSOH) of individual electrodes in the battery, which can provide detailed information about the battery degradation state and help prevent dangerous failures.

[0009] The open circuit voltage (OCV) curves of a hypothetical new battery cell and an aged battery cell are as follows: Figure 1 (b) and Figure 6 In this example, the negative electrode capacity is reduced by 20% at full discharge, assuming loss of active material due to aging, simulating the OCV of an aged cell. Since the negative electrode is usually designed to have excess capacity in a cell, this particular degradation results in only a 5% reduction in capacity for cells operating between the same voltage limits (see Figure 1 (b) and Figure 6 (b)).

[0010] Conventional cell-level SOH estimation techniques cannot provide information about electrode SOH. In order to understand what is happening inside the battery, Figure 1 (a) and Figure 6 (a) (for nickel manganese cobalt oxide is U p(y)) and Figure 1 (c) and Figure 6 (c) (U for graphite) n (x)) to plot the half-cell potential curve of each electrode. The decrease in the negative electrode capacity causes a change in the electrode utilization range ([y0,y 100 ] represents the positive electrode, [x0,x 100 ] represents the negative electrode). The utilization range represents the portion of the half-cell potential curve utilized when the cell OCV operates between a certain voltage window.

[0011] exist Figure 1 (a) and (c) and Figure 6 In (a) and (c) of FIG. 1 , the superscript f represents a new battery cell and α represents an aged battery cell. In particular, Figure 1 (c) and Figure 6 The negative electrode utilization rate x is observed in (c) 100 has moved to the low potential region marked by red / yellow shading. At near zero potential, metallic lithium tends to deposit on the graphite surface rather than being intercalated, which accelerates the capacity decay of the battery and can cause internal short circuits due to the formation of dendrites (Ref. 2.5). This example highlights the importance of understanding the electrode SOH beyond the cell level to inform the battery management system (BMS) and potentially better protect the cell.

[0012] Several studies on electrode level SOH (eSOH) estimation are available in the literature. Early work proposed a model framework that explains the relationship between the cell OCV and individual electrodes under various degradation modes (Refs. 2.6, 2.7). Various methods have been proposed for eSOH estimation. Existing methods can be divided into two categories: voltage fitting and differential analysis.

[0013] Voltage fitting methods employ optimization algorithms to find a parameter set that provides the best fit for the cell voltage curve between the measured data and the model. The authors in Ref. 2.8 parameterized the battery cell OCV model with electrode capacity and utilization range and identified these electrode parameters by fitting the cell voltage curve using a genetic algorithm. Birkl et al. based on the model framework of Ref. 2.7, classified degradation modes (e.g., loss of active materials and loss of lithium inventory) and performed degradation diagnostics by fitting the model to the measured pseudo-OCV curve (Refs. 2.9, 2.10). In Ref. 2.11, an electrochemical model was used for state of charge (SOC) and SOH estimation, but aging only considered changes in the utilization range.

[0014] On the other hand, differential analysis has been widely used in the electrochemical community, mainly to obtain more physical information from electrode materials. The two most common differential analyses are differential voltage analysis (DVA) (Refs. 2.6, 2.12-2.14) and incremental capacity analysis (IGA) (Ref. 2.15), which have an inverse relationship. The basic idea of ​​differential analysis is that valuable electrochemical information is hidden in the raw voltage data. Therefore, the voltage data is used to differentiate the battery capacity (i.e., dV / dQ for DVA; the inverse of DVA is ICA dQ / dV) to reveal the hidden information of each electrode material. Since the electrode materials have their own electrochemical characteristics (such as the phase change of the material during lithium insertion (Refs. 2.16, 2.17)), these obvious characteristics can be used to identify the contribution of each electrode to the battery cell.

[0015] Both of the aforementioned methods have the same assumption that the half-cell potential of each electrode does not change due to aging. Instead, it is assumed that degradation only affects specific electrode parameters, such as the capacity and utilization of each electrode. These parameters scale and move the half-cell potential utilized on the cell OCV curve, so it is usually assumed in the estimation that the changes in the OCV curve due to aging can be captured by scaling and moving the half-cell potential corresponding to the quantitative changes in the electrode parameters. Therefore, the same half-cell potential function is used for eSOH estimation throughout the cell life. Experiments have shown that this assumption about the only quantitative changes in electrode parameters is valid (References 2.8, 2.10, 2.18). In fact, no significant changes in the half-cell potential curves with respect to aging were observed for lithium iron phosphate (LFP) (Reference 2.19) and graphite (References 2.19, 2.20). In particular for graphite, it was observed that the peak position associated with the phase transition is almost unchanged with cell aging in the differential voltage dV / dQ curve, and not just the potential curve itself (Ref. 2.21).

[0016] The first known approach is the least squares based voltage fitting (VF) method used in the battery management system (BMS) community, which finds the unknown electrode parameters by minimizing the voltage error between the model output and the data. This method relies on the invariance of the electrode half-cell potential over utilization range excursions and capacity scales. Its reliance on this invariance can be a disadvantage because the electrode potentials of some electrode materials can be distorted as they age.

[0017] The second known method in differential analysis techniques is differential voltage analysis (DVA) widely used in the electrochemical community, which relies on the presence of a distinct phase transition characteristic in the differential voltage (dV / dQ) curve of each electrode. Its reliance on the presence of a distinct phase transition constitutes a disadvantage of this method, as some electrode chemistries do not possess such phase transitions.

[0018] Therefore, there is a need for an improved method and apparatus for estimating the state of health (SOH) of a battery. Summary of the invention

[0019] The present invention provides a method to accurately estimate the state of health in the positive and negative electrodes of a battery cell, where the battery cell may have only one electrode with a distinct phase change. A SOH estimation method called peak alignment (PA) is disclosed herein that is useful when one of the electrodes may not have a distinct feature in the dV / dQ curve to be used.

[0020] In one aspect, the present disclosure provides an electrical device, comprising: a battery cell; a voltage sensor operably coupled to the battery cell to measure a voltage level of the battery cell; a current sensor operably coupled to the battery cell to measure an amount of current drawn from the battery cell; and a battery management system. The battery management system includes a controller in electrical communication with the voltage sensor and the current sensor. The controller is configured to: execute a program stored in the controller to receive a plurality of voltage values ​​from the voltage sensor; receive a plurality of current values ​​from the current sensor, wherein each current value is associated with one of the voltage values; calculate a plurality of total discharge values, wherein each total discharge value is associated with one of the current values; calculate a differential voltage curve using the voltage values ​​and the total discharge values; determine a first differential voltage point and a second differential voltage point on the differential voltage curve, wherein each of the first differential voltage point and the second differential voltage point is at a local peak; and calculate an electrode level health state of the battery cell using the first differential voltage point, the second differential voltage point, and a characteristic curve of a new reference battery electrode of a reference battery cell, wherein the reference battery cell includes a second reference battery cell electrode that does not exhibit significant phase change during a charge-discharge cycle. In addition, the controller is configured to execute a program stored in the battery management system to identify qualitative shape changes in the half-cell potential curve due to aging and to correct the aged half-cell potential function by refitting the coefficients of the basis function.

[0021] The differential voltage curve calculated using the voltage value and the total discharge value may have a local peak originating from the anode. The differential voltage curve may have a local peak originating from the cathode. The reference battery cell may include a cathode composed of an active material selected from the group consisting of lithium metal phosphate, lithium metal oxide, or any other combination. The reference battery cell may include a cathode composed of an active material selected from the group consisting of lithium iron phosphate, lithium nickel-manganese-cobalt oxide, or any other combination. The reference battery cell may include an anode composed of an active material selected from the group consisting of graphite, lithium titanate, hard carbon, tin / cobalt alloy, and silicon carbon. The characteristic curve may be a differential voltage curve of the reference battery electrode.

[0022] The controller may be configured to execute a program stored in the controller to calculate the health state of the battery cell based on a utilization range calculated according to a lower limit of the utilization range of the anode of the battery cell. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the health state of the battery cell based on an upper limit of the utilization range of the anode of the battery cell. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the health state of the battery cell based on the electrode capacity of the anode of the battery cell. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the health state of the battery cell based on a lower limit of the utilization range of the cathode of the battery cell. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the health state of the battery cell based on an upper limit of the utilization range of the cathode of the battery cell. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the health state of the battery cell based on the electrode capacity of the cathode of the battery cell.

[0023] In another aspect, the present disclosure provides an electrical device, comprising: a battery cell; a temperature sensor operably coupled to the battery cell to measure the temperature of the battery cell; and a battery management system comprising a controller in electrical communication with the temperature sensor. The controller may be configured to execute a program stored in the controller to determine a state of health of the battery based on a temperature read from the temperature sensor.

[0024] The controller may be configured to execute a program stored in the controller to calculate the negative electrode parameter from the first differential voltage point and the second differential voltage point. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the utilized positive electrode potential from the negative electrode parameter. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the positive electrode parameter from the first differential voltage point and the second differential voltage point. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the utilized negative electrode potential from the positive electrode parameter. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to select a characteristic curve from a plurality of characteristic curves stored in the controller. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to select a second characteristic curve from a plurality of characteristic curves. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the electrode level health state of the battery cell based on the first characteristic curve and the second characteristic curve of the reference battery electrode of the reference battery cell.

[0025] The characteristic curve may be a differential voltage curve of the reference battery electrodes, which may contain a distinct phase change.

[0026] The controller may be configured to execute a program stored in the controller to calculate the positive electrode parameters from the positive electrode potential. The positive electrode parameters may be calculated using optimization techniques. Alternatively or additionally, the controller may be configured to execute a program stored in the controller to calculate the negative electrode parameters from the negative electrode potential. The negative electrode parameters may be calculated using optimization techniques.

[0027] In another aspect, the present disclosure provides a method for determining a percentage of a state of health of a battery cell. The method includes: measuring a voltage in the battery cell; measuring a current drawn from the battery cell; and calculating the state of health of the battery cell in a controller based on: (i) the measured voltage, (ii) the measured current, (iii) a total discharge calculated based on the measured current, (iv) a differential voltage curve calculated based on the measured voltage and the calculated total discharge, (v) a first differential voltage point and a second differential voltage point, wherein each of the first differential voltage point and the second differential voltage point is at a local peak, and (vi) a characteristic curve of a new reference battery electrode of a reference battery cell, wherein the reference battery cell includes a second reference battery electrode that does not exhibit significant phase change during a charge-discharge cycle.

[0028] The differential voltage curve has a local peak originating from the anode. Alternatively or additionally, the differential voltage curve has a local peak originating from the cathode. The reference battery cell may include a cathode composed of an active material selected from the group consisting of lithium metal phosphates, lithium metal oxides, or any other combination. Additionally or alternatively, the reference battery cell may include a cathode composed of an active material selected from the group consisting of lithium iron phosphate, lithium nickel-manganese-cobalt oxide, or any other combination. Additionally or alternatively, the reference battery cell may include an anode composed of an active material selected from the group consisting of graphite, lithium titanate, hard carbon, tin / cobalt alloy, and silicon carbon. The characteristic curve may be a differential voltage curve of the reference battery electrode.

[0029] In another aspect, the present disclosure provides a method for determining a health status percentage of a battery cell. The method includes the following steps: measuring a temperature of the battery cell, and calculating the health status of the battery cell in a controller based on the measured temperature.

[0030] In another aspect, the present disclosure provides a method in a data processing system. The data processing system includes at least one processor and at least one memory, wherein the at least one memory includes instructions executed by the at least one processor to implement a battery health state estimation system. The method may include: (a) receiving a plurality of voltage values ​​from a voltage sensor operably coupled to a battery cell; (b) receiving a plurality of current values ​​from a current sensor operably coupled to the battery cell, each current value being associated with a voltage value included in the plurality of voltage values; (c) calculating a plurality of total discharge values, each total discharge value being associated with a current value included in the plurality of current values; (d) calculating a differential voltage curve based on the voltage values ​​and the total discharge values; (e) determining a first differential voltage point and a second differential voltage point on the differential voltage curve, wherein the first differential voltage point and the second differential voltage point are both at a local peak; (f) determining a first set of positive electrode potential values ​​from the differential voltage curve; (g) determining a goodness of fit based on the positive electrode potential values; (h) comparing the goodness of fit with a predetermined threshold; and (i) estimating a state of health of the battery cell, wherein when the goodness of fit is at or below the predetermined threshold, the state of health of the battery cell is estimated using the first set of positive electrode potential values, and wherein when the goodness of fit is above the predetermined threshold, the state of health of the battery cell is estimated using a second set of positive electrode potential values ​​calculated based on the plurality of total discharge values.

[0031] Step (e) in the method may further include finding a match of the first differential voltage point and the second differential voltage point at the battery cell level and at the single electrode level having a half-battery cell potential. The method may further include using the first differential voltage point and the second differential voltage point to estimate a set of negative electrode parameters.

[0032] A second set of positive electrode potential values ​​may be determined based on the half-cell potential values. The half-cell potential values ​​may be obtained from a characteristic curve of a reference battery electrode of a reference battery cell, wherein the half-cell potential values ​​are a result of aging. The second set of positive electrode potential values ​​may be more accurate than the first set of positive electrode potential values. The differential voltage curve may include a local peak originating from the anode. Additionally or alternatively, the differential voltage curve may include a local peak originating from the cathode.

[0033] We have developed a method to estimate the state of health of each of the two electrodes in a lithium-ion battery, rather than the traditional lumped state of health based on battery capacity. This method uses open circuit voltage to provide the necessary diagnostics to protect the battery from aging or failure mechanisms such as lithium plating that can lead to short circuits and dangerous thermal runaway.

[0034] The method for estimating the state of health is successful even for electrode materials without obvious phase transitions, such as the widely used commercial nickel-manganese-cobalt (NMC) lithium-ion batteries. It is also shown that the developed method is insensitive to the exact potential of the battery cell and is able to provide robust and accurate electrode parameter estimates even in the presence of degradation mechanisms such as dissolution of transition metal ions of the material leading to changes in the half-cell potential.

[0035] An advantage of the present invention is therefore that it provides accurate health status readings for both electrodes in a battery cell, even though one electrode may not have a significant phase change.

[0036] These and other features, aspects and advantages of the present invention will become better understood with consideration of the following detailed description, drawings and appended claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Shown are the open circuit potentials of half cells for a range of utilizations: (a) positive electrode, (c) negative electrode, and (b) the open circuit voltage of a new cell (blue) and the open circuit voltage of an aged cell (red).

[0038] Figure 2 Voltage and differential voltage curves for a cell that does not contain a peak in the positive electrode material (e.g., nickel-manganese-cobalt oxide) are shown. The peak is depicted in the differential curve in: (a) positive electrode, (b) full cell, and (c) negative electrode.

[0039] Figures 3(a) to 3(f)Results for a new battery cell for the voltage fitting (VF) and peak alignment (PA) methods are shown: Figures 3(a) and 3(b) show the voltage curves, Figures 3(c) and 3(d) show the differential voltage curves, and Figures 3(e) and 3(f) show the normalized parameter estimates, verifying that the VF and proposed PA methods work well and are matched when the battery cell is new.

[0040] Figures 4(a) to 4(f) The results of the aged battery at room temperature (RT) for the voltage fitting (VF) and peak alignment (PA) methods are shown: Figures 4(a) and 4(b) show the voltage curves, Figures 4(c) and 4(d) show the differential voltage curves, and Figures 4(e) and 4(f) show the normalized parameter estimates, showing the difference in results between the two methods.

[0041] Figures 5(a) to 5(f) The results of the aged battery at high temperature (NT) for the voltage fitting (VF) and peak alignment (PA) methods are shown: Figures 5(a) and 5(b) show the voltage curves, Figures 5(c) and 5(d) show the differential voltage curves, and Figures 5(e) and 5(f) show the normalized parameter estimates, showing the difference in results between the two methods.

[0042] Figure 6 Examples of battery degradation are shown: (a) half-cell potential with a positive electrode with a range of utilization variations, (b) open circuit voltage of a new cell and an aged cell, and (c) half-cell potential with a negative electrode with a range of utilization variations. The shaded area indicates the potential near zero where lithium plating may occur.

[0043] Figure 7 The working principle of the peak alignment (PA) method proposed in the present disclosure is shown.

[0044] Figure 8 Schematic voltage and dV / dQ curves of a MNC / graphite cell are shown. Peaks are depicted in the dV / dQ curves in: (a) positive electrode (PE), (b) full cell, and (c) negative electrode (NE).

[0045] Figures 9(a) to 9(f) The results for a new battery cell for conventional voltage fitting (VF) and peak alignment (PA) methods are shown: Figures 9(a) and 9(b) show the voltage curves, Figures 9(c) and 9(d) show the differential voltage curves, and Figures 9(e) and 9(f) show the normalized parameter estimates, verifying that the VF and proposed PA methods work well and are matched when the battery cell is new.

[0046] Figures 10(a) to 10(f)Results for the aged battery cells for the conventional voltage fitting (VF) and peak alignment (PA) methods are shown: FIGS. 10(a) and 10(b) show the voltage curves, FIGS. 10(c) and 10(d) show the differential voltage curves, and FIGS. 10(e) and 10(f) show the parameter estimates, showing substantial disagreement between the two methods.

[0047] Figures 11(a) to 11(f) shows the updated positive electrode potential function U P (y) After that, the results of the aged batteries of the conventional voltage fitting (VF) method and the proposed peak alignment (PA) method: Figures 11(a) and 11(b) show the voltage curves, Figures 11(c) and 11(d) show the differential voltage, and Figures 11(e) and 11(f) show the normalized parameter estimates, showing excellent consistency of the results and validating the proposed method.

[0048] Fig.12 It shows that from the proposed P (y) Positive electrode half-cell potential changes identified in the calibrated peak alignment (PA) method. DETAILED DESCRIPTION

[0049] Before explaining any embodiment of the present invention in detail, it should be understood that the present invention is not limited to the construction details and component configurations set forth in the following specification or shown in the accompanying drawings in this application. The present invention can be applied to other embodiments, and practice or execute in various ways. Moreover, it should be understood that the wording and terminology used herein are for the purpose of description and should not be considered as restrictive. In this article, the use of "including", "comprising" or "having" and its variants is meant to cover the items listed afterwards and their equivalents and additional items.

[0050] The following discussion is provided to enable those skilled in the art to make and use embodiments of the present invention. Various modifications to the illustrated embodiments will be readily apparent to those skilled in the art, and the general principles herein may be applied to other embodiments and applications without departing from embodiments of the present invention. Therefore, embodiments of the present invention are not intended to be limited to the illustrated embodiments, but should conform to the widest scope consistent with the principles and features disclosed herein. Those skilled in the art will recognize that the embodiments provided herein have many useful alternatives and fall within the scope of embodiments of the present invention.

[0051] The embodiments described herein provide a method for estimating the state of health of each of the two electrodes in a lithium-ion battery. In one embodiment, the method uses the open circuit voltage to provide the necessary diagnostics to protect the battery from aging or failure mechanisms, such as lithium plating that leads to short circuits and dangerous thermal runaway. The method enables quantification of electrode-specific health states based on estimating the capacity and utilization range of each electrode, which is a scaling and sliding factor of the electrode half-cell potential relative to the battery cell capacity axis.

[0052] The method is further compatible with electrode materials that do not have obvious phase transitions, such as the widely used commercial nickel-manganese-cobalt (NMC) lithium-ion batteries. Even in the presence of degradation mechanisms (such as dissolution of transition metal ions of the material leading to changes in the half-cell potential), the method is insensitive to the exact potential of the battery cell and is able to provide robust and accurate electrode parameter estimates.

[0053] Further embodiments herein provide an algorithm for electrode state of health (eSOH) diagnostics of lithium-ion batteries. eSOH is critical to understanding the detailed degradation state of the battery and preventing dangerous failures within an advanced battery management system (BMS). Electrode diagnostics can be performed by estimating specific parameters of the electrode, such as the capacity and utilization range of the electrode.

[0054] In another embodiment, a method for electrode health state estimation is further described herein. The method is developed by relaxing the assumption of invariance of the half-cell potential of the positive electrode during aging of a battery cell composed of a transition metal oxide in the positive electrode. The method not only estimates the electrode parameters, but also identifies qualitative shape changes in the half-cell potential curve of the electrode due to aging, and corrects the aged half-cell potential function by refitting the coefficients of the basis function.

[0055] Example

[0056] The following examples are provided to demonstrate and further illustrate certain embodiments and aspects of the invention and should not be construed as limiting the scope of the invention.

[0057] Example 1

[0058] Overview

[0059] Example 1 provides a method to accurately estimate the state of health in the positive and negative electrodes of a battery cell, where the battery cell may have only one electrode with a distinct phase change. A SOH estimation method called peak alignment (PA) is disclosed that is useful when one of the electrodes may not have a distinct feature in the dV / dQ curve to be used.

[0060] The voltage fitting (VF) method is commonly used in battery management systems (BMS) because it works well with limited data and can be performed recursively in real time. The VF method relies on the invariance of the electrode open circuit potential (OCP), which makes the accuracy of the electrode SOH estimation of the VF method vulnerable when the OCP is distorted due to aging.

[0061] Differential voltage analysis (DVA), which is used offline in the electrochemical community, relies on distinct phase transitions at individual electrodes to link them to electrode SOH parameters. However, this becomes inapplicable when the electrode materials do not have distinct phase transitions.

[0062] The proposed PA method performs well in electrode SOH estimation when the OCR has changed and even when one of the electrodes does not show a phase change. This was experimentally verified by applying the proposed PA method to an aged battery with NMC as the positive electrode, which does not show a strong phase change, thus posing a challenge to DVA, and its OOP changes due to the dissolution of metal ions at high temperatures, posing a challenge to the VF method. Therefore, a discernible peak misalignment is observed from the VF method, indicating that the electrode SOH parameter estimation is incorrect, even though it estimates the battery cell capacity very accurately. Therefore, it is shown that accurate voltage reconstruction and accurate battery cell capacity estimation do not necessarily produce accurate electrode parameter estimation results. On the contrary, by exploiting the electrochemical characteristics of phase changes when there are phase changes, the proposed PA method successfully provides a robust and accurate electrode SOH estimation and combines the information with the VF method. A non-limiting example method has been demonstrated to estimate the state of health (SOH) of NMC cathodes and graphite anodes in lithium-ion batteries. Specifically, the electrode SOH estimation is to estimate the capacity and utilization range of both the positive electrode and the negative electrode. The proposed method, called peak alignment (PA), overcomes the limitations of existing methods.

[0063] In a lithium-ion battery, as the cell is charged (backward reaction), the lithium mole fraction or stoichiometry x in the negative electrode increases. This increase is balanced by a decrease in the lithium mole fraction or stoichiometry y in the positive electrode. Likewise, as the cell is discharged, the forward reaction decreases the stoichiometry x in the negative electrode while increasing the stoichiometry y in the positive electrode. The stoichiometric states x and y∈[0,1] represent the lithium mole fractions of each electrode material. A fully charged negative electrode would have x=1. At certain stoichiometric states, an equilibrium potential is defined relative to lithium metal, called the half-cell open circuit potential (OCP), which is expressed by U p (y) represents the positive electrode and U n(x) represents the negative electrode. When no current is drawn from the cell and the lithium concentration in each electrode is in equilibrium, the terminal voltage of the cell is equal to OCV, which is the positive U p (y) electrode and negative U n (x) the potential difference between the OCPs of the electrodes,

[0064] V oc (z) = U p (y)-U n (x) (1.1)

[0065] where z is the depth of discharge (DOD) of the battery cell. Since each electrode is within the specified battery cell voltage limit V max With V min The term “utilization range” is used for each electrode to represent the stoichiometric range actually used. Therefore, the utilization range of each electrode can be expressed as [x0, x 100 ] and the positive electrode's [y0, y 100 ] range. At the upper and lower voltage limits, the following conditions hold:

[0066] V max =U p (y 100 )-U n (x 100 ) (1.2)

[0067] V min =U p (y0)-U n (x0) (1.3)

[0068] The parameter (x0, y0) corresponds to the lower limit voltage, and the parameter (x 100 ,y 100 ) is associated with the upper voltage limit. The parameters (x0, y0) are also called the lower limits of the utilization range of the negative electrode and the positive electrode, respectively. 100 ,y 100 ) are also referred to as the upper limits of the utilization range of the negative electrode and the positive electrode, respectively. It should be noted that in practice it is not expected that the battery is fully discharged, and during a typical charging scheme, it can be expected to reach a higher stoichiometric state (x) at full charge. 100 ,y 100 ). For battery cell discharge, the stoichiometric state of each electrode (x, y) satisfies the following relationship,

[0069]

[0070] Where Q is the ampere-hour from a fully charged state, and C represents the total capacity of the battery cell defined by the upper and lower voltage limits. Then, the battery cell capacity relative to the capacity of a single electrode has the following equation,

[0071] C=C p (y0-y 100 )=C n (x 100 -x0) (15)

[0072] Among them C p , C n is the capacity of the positive electrode and the negative electrode. Combining equations (1.4) and (1.5), the stoichiometric state can be written as a function of ampere-hour Q as follows:

[0073]

[0074] Finally, equation (1.1) can be expressed as a function of ampere-hour Q, where each electrode parameter = [C p , C n ,y 100 , x 100 ],

[0075]

[0076] Electrode state of health (eSOH) estimation is performed by estimating the electrode parameters that change with battery life. The parameters to be estimated are the capacity and utilization range of a single electrode, θ = [C p , C n ,y 100 , x 100], they scale and slide the utilized half-cell potential of each electrode on the capacity axis. All methods assume that changes in the OCV curve due to aging can be captured by scaling and / or shifting the stoichiometric range, which is equivalent to a quantitative change in the capacity and utilization range of the electrode material, rather than a qualitative shape change in the half-cell OCR curve. Therefore, the same half-cell OCR model, characterized by a half-coin cell made of the electrode materials of a new cell, is used for electrode parameter estimation over the entire life cycle. In most cases, this assumption holds. In fact, no significant changes in the half-cell OCR curves were observed for lithium iron phosphate (LFP) (Ref. 1.11) and graphite (Refs. 1.11, 1.12). In addition, it has been shown that this assumption is valid by adopting the VF method and DVA for these chemical cells (Refs. 1.4, 1.13). It is worth pointing out that the total cell capacity C can also be estimated and the verification of the electrode parameter estimation method will be provided by incorporating the lower voltage limit formula (1.3) for the discharge ampere-hour Q after estimating the electrode parameters and substituting them into formula (1.6).

[0077]

[0078] Least squares voltage fitting

[0079] The least squares-based voltage fitting (VF) method has been widely used for battery parameter estimation and degradation analysis (References 1.4-17, 1.14). Since field use and limited SOC windows cannot guarantee data richness, its effectiveness in onboard battery management systems cannot be analyzed even when data is sparse (References 1.6, 1.7). In this method, all electrode parameters θ = [C p , C n ,y 100 , x 100 ] to jointly minimize the sum of all squared voltage errors between the model output and the measured data. The OCV model is a function of ampere-hours and electrode parameters consisting of the positive electrode half-cell OCR and the negative electrode half-cell OCR, as shown in equation (1.7). The total battery capacity C can also be estimated based on the equality constraints of the voltage limit described in equation (1.8) and used to independently verify the proposed estimation method by comparing with the measured discharge capacity. Due to the nonlinearity in equation (1.7), the optimization problem P1.1 is a non-convex problem with respect to parameters. There may be local minima, and the optimization solution is affected by the initial guess. Therefore, a global solution can be obtained by exploring multiple initial guesses using methods known in the art.

[0080]

[0081] Differential Voltage Analysis

[0082] The electrode materials undergo several phase changes during lithium insertion, and their potentials show step curves in which the plateaus correspond to the coexistence of two phases, and the steps between the plateaus represent the single-phase stage when the phase change is completed (Ref. 1.15). The rapid voltage changes in the steps appear as peaks in the differential voltage curve (dV / dQ vs. Q). Therefore, the dV / dQ curve can more clearly see the features in the OCV curve. The estimation accuracy of DVA depends largely on the data quality of the dV / dQ curve, which can be corrupted by noisy voltage measurements. Test data recommends the use of low C-rate constant current (e.g., C / 20) pseudo-OCV data and signal processing (Ref. 1.16-1.18). Since OCV is just the potential difference between the positive and negative electrodes, the contribution of the two electrodes increases linearly with the differential voltage (Ref. 1.16). Therefore, by comparing the dV / dQ curve of the battery cell with the differential voltage of the individual single electrode half-cells (i.e., dU p / dy,dU n / dx) can be compared to estimate the parameters of each electrode independently. The positive and negative material C is extracted from the accumulated ampere-hours between the two peaks p and C n capacity and obtain the utilization range [x0, x1] by matching the peak position with respect to the ampere-hour from the single-electrode half-cell to the full-cell. 100 ] and [y0,y 100 ]. Good experimental studies can be found in Ref. 1.17. One disadvantage of DVA is that it cannot be applied to battery cells containing electrode materials that do not have the distinct peaks to be used, e.g. Figure 2 The case of the NMC positive electrode shown in .

[0083]

[0084] Differential Peak Alignment

[0085] The PA algorithm proposed here is based on the differential voltage dU of the graphite negative electrode. n =dx, the differential voltage of the graphite negative electrode has several peaks in the differential voltage curve. The main effect of this method is that the positive electrode parameter estimation can be successfully performed even without using peaks, which is common for many positive electrode materials (e.g., nickel manganese cobalt (NMC) oxide or lithium iron phosphate (LFP)). Figure 2 As shown in (a) and in reference 1.16, the NMC material does not show a clear peak. In this case, the peak in the dV / dQ curve ( Figure 2(b)) comes only from the negative electrode ( Figure 2 (c) in the figure, so the negative electrode parameters can be directly estimated using equation (1.3). Using equation (1.14) for the restored positive half-cell, the potential A least squares-based voltage fit was performed to estimate the positive electrode parameters after accounting for the reconstructed aged negative electrode in the cell OCV.

[0086] Alternatively, in a battery cell having a positive electrode that exhibits a distinct phase transition and a negative electrode that does not exhibit a distinct phase transition, the peak Q j The corresponding peak [y 1 ,y 2 ] match. In addition, equations (1.13) and (1.14) will be replaced by equations (1.15) and (1.16) respectively. P1.2 will replace the positive electrode potential with the negative electrode potential recovered in equation (1.16), and use the negative electrode OOP model instead of the positive electrode OCP model to find the negative electrode parameters.

[0087]

[0088]

[0089]

[0090] Parameter estimation results for new and aged cells are presented. Results from two methods are compared: (i) voltage fitting (VF), and (ii) peak alignment (PA) according to the present disclosure, since the selected positive electrode material does not have peaks. The validity of the parameter estimation is checked by the alignment of the peaks in the dV / dQ curves, since the alignment of the peak positions implies a correct estimation of the utilization of the individual electrodes in the cell.

[0091] Testing battery cells and aging conditions

[0092] Table 1.1

[0093] New battery cells Aging battery cell RT Aging battery cell HT Battery Cell SOH 100％ 80％ 71％ Aging temperature - 25℃ 55℃ Aging current - 0.5C / 1C 0.5C / 1.5C SOC Swing - 100％-10％ 95％-15％

[0094] Samsung SDI's prismatic battery cell is used for electrode SOH estimation. The battery chemistry is nickel manganese cobalt (NMC) oxide for the positive electrode and graphite for the negative electrode. The single-electrode OOP model features a half-coin cell made of the same materials used in the full battery cell. The OCP model featuring graphite is able to capture the dU n The two most obvious peaks in the / dx curve are Figure 2 In this study, C / 20 discharge data operated in the voltage range of 4.2 V and 3.0 V at 25°C were used as pseudo OCV data for analysis.

[0095] In order to see the trend of the parameter estimation results, two different aged cells were selected. The aging test conditions are summarized in Table 1.2. The SOH of the cell is determined by the ratio of the C / 20 discharge capacity of the aged cell to the new cell; for example, the aged cell RT shows an SOH of 80% (C aged，RT =0.80C fresh , where C fresh is the measured C / 20 discharge capacity). Aged cells RT means the aging temperature is room temperature. Similarly, aged cells HT are cycled at elevated temperatures. The aging current represents the C rate of the charge / discharge cycle and the specified state of charge (SOC) swing.

[0096] result

[0097] Figures 3(a) to 3(f) , Figures 4(a) to 4(f) and Figures 5(a) to 5(f) Estimation results for one new cell and two aged cells are given in Figure 1 for discharge operation. In each figure, the results obtained from the VF method are shown on the left, while the results obtained from the PA method of the present disclosure are shown on the right. In each row, the voltage curve of the measured data and the reconstructed model output are plotted at the top, the dV / dQ curve is plotted in the middle, and finally, the utilization potential of each electrode and the estimated parameters are shown at the bottom. The estimated battery capacity C is compared with the measured C / 20 discharge capacity and their errors are explained. Note that the estimated parameters are obtained by measuring the new cell C fresh The C / 20 discharge capacity is normalized.

[0098] (1) New battery cell: The results of the new battery cell are shown in Figure 3(a) to Figure 3(f) First, the voltage curves of the measured data and the model output, as well as the root mean square error (RMSE) of the voltage, are shown in Figures 3(a) and 3(b). For the case of a new battery cell, the measured data shows good consistency with the model output since the RMSE values ​​of both methods are less than 5 mV. The validity of the parameter estimation can be checked by checking the alignment of the peaks in the dV / dQ curves shown in Figures 3(c) and 3(d) because the alignment of the peaks indicates an accurate estimate of the utilization of a single electrode in a full battery cell. As shown in Figure 3(c), the VF method cannot guarantee perfect alignment of the peaks. Therefore, the parameter estimates obtained from the two methods are slightly different but within an acceptable range, as shown in Figures 3(e) and 3(f). Here, the utilized half-cell potentials of the positive and negative electrodes are decoupled. The dotted line for each electrode potential represents the full utilization, while the solid line represents the full utilization represented by [y 100 ,y0],[x 100, x0] represents the actual utilization range. More specifically, the capacities associated with the full utilization range are represented by positive C p Electrode and negative C n The capacity of the electrodes is shown. The estimated total cell capacity C is also shown along with the estimated error.

[0099] (2) Aged battery cell RT: The results of applying the VF and the proposed PA method of the present disclosure on the aged battery cell RT are summarized in Figure 4(a) to Figure 4(f) . Again, since there is no obvious phase change in the NMC at the positive electrode, the DVA technique cannot be used. The aged battery cell RT was cycled at room temperature at a moderate C rate until the capacity reached 80% of the capacity of the new battery cell. In the voltage curves, the RMSE values ​​of both methods increased compared to the new battery cell shown in Figures 4(a) and 4(b). One thing to note is that the increase in RMSE of the PA method of the present disclosure is much higher than the increase in RMSE of the VF method. Another thing is that, also in the case of the new battery cell, a discernible peak misalignment is observed in the VF method of Figure 4(c), which brings about the difference in the parameter estimates of Figures 4(e) and 4(f): the model shows that the ampere-hour between the two peaks is smaller, so the C estimated by the VF method is n Less than the C of the PA method of the present disclosure n The degree of misalignment increases and, therefore, differences in parameter estimates become apparent. However, both capacity estimates are very accurate, showing an estimation error of less than 0.25%.

[0100] (3) Aging Cell HT: The results of aging cell HT are summarized in Figure 5(a) to Figure 5(f). The battery cell was aged at a high temperature of 55°C, while the battery capacity was 71% of the nominal capacity. The RMSE values ​​increased in both the VF method and the PA method of the present disclosure. Similar to the aged battery cell RT case, the RMSE of the PA method is much higher than that of the new battery cell, but the VF method still shows good consistency between the model output and the data, with the RMSE value of the voltage being less than 7 mV. However, the VF method shows a substantial deviation of the peak in the dV / dQ curve of Figure 5(c) from the maximum value of the normalized battery cell capacity of 6.61%, even though the battery cell capacity estimation is very accurate, resulting in an error of less than 0.25%. Recalling the fact that the alignment of the peaks means the accuracy of the estimation of the utilization of a single electrode in the full battery cell, the misalignment of the VF method indicates that the electrode parameter estimation is incorrect. Therefore, the lower RMSE and accurate battery cell capacity estimation results in the conventional VF method cannot always provide accurate electrode SOH parameter estimates for NMC / graphite battery cells aged at high temperatures. In contrast, in the PA method of the present disclosure, since the peaks in the full cell match the phase change of the graphite negative electrode, the negative electrode parameter estimates can be used to reliably estimate the positive electrode parameters compared to the negative electrode parameter estimates obtained according to the VF method. Finally, in the bottom row, the normalized parameter estimates and the resulting utilized electrode potentials are shown in Figures 5(e) and 5(f).

[0101] discuss

[0102] A limitation of the conventional least squares-based voltage fitting (VF) method is that it does not necessarily guarantee peak alignment in the dV / dQ curve. This is because peaks that are only discernible in the differential voltage are not explicitly considered in the least squares formula. Instead, the solution to the optimization problem (P1.1) is obtained by minimizing the sum of the voltage squared errors between the model and the data, which can only account for quantitative changes in the capacity and utilization range of each electrode. Therefore, even if the OCP curve changes, the VF method always finds the best combination of electrode parameters that returns the minimum RMSE result. At the same time, since the PA method of the present disclosure explicitly uses peak information to estimate electrode parameters, it is more robust and reliable in electrode SOH estimation. Regarding the changes in the OCP curve of the electrode material, metal ion dissolution is a well-studied degradation mechanism for battery cells containing transition metal oxides (e.g., Ni, Mn, Co) as positive electrodes. The capacity decay of battery cells containing LiMn2O4 has been attributed to several mechanisms, but manganese dissolution is generally considered to be the most important factor causing capacity decay (reference 1.19). Similarly, long-term cycling degradation of battery cells composed of NMC is accelerated due to increased dissolution of active materials in the electrolyte at high states of charge (Ref. 1.20). More importantly, it was found that dissolution can be accelerated at elevated temperatures (Refs. 1.19, 1.21-1.23). Here, aged battery cells HT were cycled at an elevated temperature of 55°C until they reached 71% of their original C / 20 capacity. Under such aging conditions, the dissolution of transition metals in the NMC positive electrode is promising. This suggestion has been experimentally verified using parameter estimation results from the peak alignment method. In Table 1.2 below, the maximum deviation in electrode parameters between new and aged battery cells is the positive electrode capacity C that causes the battery cell capacity decay. p This is most likely due to the loss of active material in the positive electrode caused by the dissolution of transition metals. If the composition ratio of transition metals contained in the positive electrode changes, the crystal structure of the electrode material may change (reference 1.24), resulting in a corresponding OCP U p (y) The shape of the positive electrode changes. One indication of a change in the positive electrode OCP is that the RMSE of the PA method of the present disclosure increases significantly even though the peaks are aligned. Recall that the PA algorithm, after identifying the graphite negative electrode being used, Recovery potential and half-cell OCP model The positive electrode parameters are estimated by minimizing the error between . Therefore, the increase in RMSE is attributed to the mismatch in the positive electrode potential, which may be caused by the change in the OCP curve due to aging.

[0103] Table 1.2

[0104] Summary of parameter estimates and biases for new and aged cells using both methods

[0105]

[0106] Regarding the negative electrode capacity C n Another interesting finding can be found in Table 1.2. Even though the decrease in cell capacity and positive electrode capacity is smaller compared to the aged cell HT, the aged cell RT has a significant decrease in negative electrode capacity C n The degradation on the negative electrode is much larger. For graphite, it is known that it has expansion and contraction behavior during lithium insertion. This means that a wider range of graphite utilization has greater expansion and contraction, which can cause the growth of the solid electrolyte interface (SEI) and accelerate the passivation of the graphite active material at the negative electrode. This proposition is consistent with the parameter estimation results in Table 1.2. Negative electrode capacity C n The decrease in indicates that a relatively high percentage of aged cells in RT have a wider range of utilization of the negative electrode [x0, x 100 ].

[0107] Summarize

[0108] For the case of new battery cells, overall, the conventional voltage fitting (VF) method and peak alignment (PA) method of the present disclosure show good consistency. However, in the case of aged battery cells RT and aged battery cells HT, the parameter estimation results are inconsistent, showing peak misalignment in the dV / dQ curves of the VF method. More specifically, at the aged battery cell HT cycled at a high temperature of 55°C, the application of the PA method of the present disclosure shows a significant decrease in the capacity of the positive electrode Cp. This is most likely due to the dissolution of transition metals and resulting loss of positive electrode active materials. The VF method attributes the battery cell capacity decay to the reduction in the capacity of the positive and negative electrodes. Therefore, the VF method and PA method of the present disclosure show more than 20% inconsistency in the negative electrode parameters, although both methods estimate the total battery cell capacity very accurately with an error of less than 0.25%. This inconsistency occurs due to the assumption of invariance of the half-battery cell OCP, which may reduce the accuracy of the electrode parameter estimation when the half-battery cell OCP changes. In the VF method, despite having lower RMSE values ​​and accurate cell capacity estimation, misalignment of peaks was observed in the dV / dQ curves, indicating that the single electrode parameter estimation was incorrect. On the other hand, since the PA method of the present disclosure uses peaks as physical information of the phase transition of the graphite negative electrode, the proposed PA method is less sensitive to the exact shape of the OCR curve and is able to provide robust and accurate electrode SOH estimation. This claim is verified by the alignment of peaks in the differential voltage curves.

[0109] Although in this Example 1, the cell chemistry used is nickel-manganese-cobalt (NMC) oxide for the positive electrode and graphite for the negative electrode, it is foreseeable that the method of the present invention can be used with other cell chemistries for such cells, whose cathodes contain an active material selected from the group consisting of lithium metal phosphates (e.g., lithium iron phosphate), lithium metal oxides, or any combination thereof, and whose anodes contain an active material selected from the group consisting of lithium titanate, hard carbon, tin / cobalt alloys, and silicon carbon. The anode active materials and cathode active materials are not limited to these examples. The method is particularly advantageous in cases where one electrode does not exhibit significant phase changes during charge-discharge cycles.

[0110] Example 2

[0111] Overview

[0112] Example 2 provides a method for estimating the health state of an electrode by estimating specific parameters such as the capacity and utilization range of the electrode. The method utilizes the phase change of the electrode material to separate the contribution of a single electrode to the battery cell voltage. This separation provides an estimate of the utilization potential of each electrode and makes the parameter estimation more accurate by reducing the number of unknown parameters.

[0113] An electrode state of health (eSOH) estimation method is proposed based on the assumption that the half-cell potential may decrease due to electrode level degradation mechanisms. The rationale behind this assumption is explained through experimental results from the literature and a comparison of the eSOH estimation results obtained by the proposed method and the conventional voltage fitting method for nickel-manganese-cobalt (NMC) / graphite battery cells aged at high temperature. The proposed method is an improvement on the existing methods by combining their advantages to perform robust and accurate estimation. In addition, the proposed method identifies qualitative shape changes in the half-cell potential curve of the electrode due to aging and corrects the aged half-cell potential function by refitting the coefficients of the basis function.

[0114] Electrode state of health (eSOH) is crucial to understand the detailed degradation state of the battery and prevent dangerous failures. Several methods for eSOH estimation have been proposed based on the assumption of invariance of the half-cell potential of each electrode in the battery cell under aging. Literature research shows that this assumption is valid for various chemical reactions of the battery cell. In this study of Example 2, a novel eSOH estimation method is proposed based on the following assumption: under certain aging conditions, the assumption of invariance of the half-cell potential may not be applicable to battery cells of certain chemical properties. The rationale behind this assumption is explained by comparing the eSOH estimation results obtained by the traditional voltage fitting method and the proposed method for nickel-manganese-cobalt (NMC) / graphite battery cells aged at elevated temperatures. The proposed method is an improvement over the two existing methods in that it exploits the electrochemical properties (phase change of the electrode material) to separate the contribution of a single electrode to the battery cell voltage. In addition, the proposed method identifies qualitative shape changes in the half-cell potential curve of each electrode due to aging, and corrects the aged half-cell potential function by refitting the coefficients of the basis function. Example 2 is an extension of Example 1, with the addition of a detailed algorithm and half-cell potential function calibration.

[0115] OCV Model

[0116] This section describes the relationship of the OCV model and electrode parameters related to the health state of individual electrodes. For a lithium-ion battery with lithium metal oxide LiMO2 for the positive electrode (PE) and graphite C6 for the negative electrode (NE), as the cell is charged (backward reaction), the stoichiometric state x in the graphite increases. This increase is balanced by a decrease in the stoichiometric state y in the metal oxide. Similarly, as the cell is discharged, the forward reaction occurring at each electrode is as follows:

[0117]

[0118]

[0119] The stoichiometric states x and y represent the lithium mole fraction of each electrode material. x C6, fully lithiated graphite has x=1, i.e., one lithium atom for every six carbon atoms. When the cell is in equilibrium and no current flows, the terminal voltage of the cell is equal to OCV, which is U p (y) Positive electrode and U n (x) the potential difference between the half-cell potentials of the negative electrode,

[0120] V oc (z) = U p (y)-U n (x), (2.1)

[0121] Where z is the depth of discharge (DOD) of the battery cell (i.e., DOD = 1-SOC), and satisfies the following relationship with the stoichiometric state of each electrode x and y, where the range of electrodes x and y is and

[0122]

[0123] where Q is the discharge ampere-hours from a fully charged state found by coulomb counting and C represents the upper voltage V determined by satisfying the following conditions: max and the lower limit voltage V min Defined battery cell capacity

[0124] V max =U p (y 100 )-U n (x 100 ), (2.3)

[0125] V min =U p (y0)-U n (x0), (2.4)

[0126] The subscripts 100 and 0 denote the stoichiometric states at the upper and lower voltage limits, respectively, at the ends of the utilization range. Battery manufacturers specify voltage limits to prevent overcharging or overdischarging, so that the individual electrodes are not fully utilized. Note that when the battery is fully depleted, in practice using a typical constant current constant voltage (CCCV) charging protocol, the lower limit V min More often the battery voltage V max And therefore, Equation (2.3). Then, for the capacity PE of a single electrode, C p and NE C n , relative to the battery cell capacity C, the following equation holds

[0127] C=C p (y0-y 100 )=C n (x 100 -x0), (2.5)

[0128] Combining equations (2.2) and (2.5), the stoichiometric state of each electrode can be written as a function of the discharge ampere-hour Q

[0129]

[0130] Finally, equation (2.1) can be expressed as a function of discharge ampere-hours Q, where the electrode parameters (i.e., electrode capacity and utilization range) θ = [C p , C n ,y 100 , x 100 ],

[0131]

[0132] Degradation Modes and Diagnosis

[0133] For aging diagnostics, we refer to the commonly defined degradation modes: loss of lithium inventory (LLI) for the entire cell and loss of active material (LAM) for each electrode (Refs. 2.7, 2.9). LLI is the most common degradation mode of cell capacity decay, where it represents irreversible lithium consumption due to parasitic reactions (such as surface film formation and lithium plating), as well as lithium loss associated with the loss of lithiated active materials. LAM means that the active material is no longer available for lithium insertion, which can occur at each electrode, and therefore it is further divided into LAM of the positive electrode. PE and LAM of negative electrode NE . LAM PE It may be caused by structural disorder, dissolution or loss of electrical contact, while LAM NE It is caused by particle cracking or blocking of active sites in the resistive surface layer. These mechanisms can lead to cell capacity and power degradation.

[0134] By identifying the electrode parameters θ = [C p , C n ,y 100 , x 100 ] Quantify these degradation modes to perform electrode diagnostics. Estimated electrode capacity C p and C n The change in LLI directly indicates the LAM of the positive and negative electrodes. LLI can usually be expressed as a ratio of the total lithium inventory. At any time, the total lithium inventory can be defined by the sum of the lithium contents in the individual electrodes. Since the stoichiometric states x and y are the degrees of lithiation of the corresponding active materials, the lithium content in one electrode (e.g., Li PE =y*C p ). Therefore, once the electrode parameters are identified, the degradation pattern can be quantified as follows:

[0135]

[0136]

[0137]

[0138] where the superscript f represents the estimate from a new battery cell, and α represents the estimate from an aged battery cell.

[0139] As the battery ages, electrode parameters are regularly estimated to understand the main degradation modes and protect the battery cell from dangerous failures. Under the assumption of invariance of the half-cell potential of the electrodes in the battery cell, the unknown electrode parameters are the capacity and utilization range of the positive and negative electrodes, θ = [C p , C n ,y 100 , x 100 ]. Therefore, the parameters are determined by perturbing the electrode parameters to find the best representation of the battery data (e.g., voltage or dV / dQ curve). Therefore, the OCV model equation (2.7) In traditional eSOH estimation methods, the same half-cell potential function is maintained for new and aged cells. The half-cell potential function is typically characterized by coin cell measurements, which are typically performed with the electrode material of a new cell and lithium metal as a reference electrode.

[0140] Based on experimental studies in the literature on the aging of PE materials, especially those composed of transition metals (e.g., Ni, Mn, Co), a hypothesis is proposed that some PE materials do not always remain intact under certain aging conditions. Note that as the cell ages, the cell capacity C also becomes an unknown parameter. Since this cell capacity is defined as the total number of ampere-hours between specified voltage windows, it can also be estimated by the proposed method when the electrode parameters are identified and the voltage limits are specified.

[0141] Voltage Fit (VF)

[0142] The voltage fitting (VF) method based on least squares has been widely used in battery parameter estimation and aging diagnosis (references 2.8, 2.9). Even for partial data windows, the effectiveness of this method in onboard battery management systems has been analyzed to ensure the robustness of its estimation (reference 2.23), because the application in practice cannot guarantee the richness of data measurement. The detailed process is given in Algorithm 2.1. In this method, the electrode parameters are estimated by minimizing the sum of squares of the voltage errors between the model and the measured data. As given in equation (2.7), the model here is an OCV model composed of two half-battery unit potential functions, where the unknown parameters are the electrode capacity and utilization rate θ = [C p , C n ,y 100 , x 100 ] and the battery cell capacity C. Half-battery cell potential function U p (y) and U n(x) is given from experimental measurements of half-coin cell batteries (Ref. 2.16) or from some popular chemistry literature (Refs. 2.24-2.27). The voltage data can be measured from a low C-rate constant current (e.g., C / 20 rate) as a pseudo-OCV, and the voltage data can be further processed by filtering and downsampling using interpolation to achieve computational advantages. Note that the optimization problem P2.1 has an equality constraint on the maximum voltage limit, which results in providing additional information for the parameters and improving the estimation accuracy. Since the optimization problem P2.1 is a non-convex problem with respect to the parameters, there may be local minima and the optimization solution is affected by the initial guess. Therefore, a global optimum is usually recommended.

[0143]

[0144] Peak Alignment (PA)

[0145] The electrode materials undergo several phase changes during lithium insertion, and their potentials show a step curve in which the plateaus correspond to the coexistence of two phases, and the steps between the plateaus represent the single-phase stage when the phase change is completed (Refs. 2.16, 2.24). This sharp change at the step appears as a peak in the differential voltage curve (dV / dQ vs. Q). Therefore, the derivative of the voltage makes the electrochemical characteristics clearly appear as peaks in the dV / dQ curve. Differential voltage analysis (DVA) uses the dV / dQ curve to identify electrode parameters (Ref. 2.6). Since OCV is the potential difference between the two electrodes, each electrode potential can be simply separated by subtracting one of the electrode potentials from the cell OCV. By comparing the dV / dQ curve of the cell with the half-cell dV / dQ curve of the electrode (i.e., dU p / dy、dU n / dx) to identify the utilization of a single electrode. Electrode capacity C p and C n is the scaling factor that extends the half-cell potential curve to the cell capacity axis. By matching the peak positions from the single-electrode half-cell to the full-cell, the utilization range y at the fully charged state can be identified. 100 and x 100 .

[0146] By utilizing conventional DVA to separate the electrode potential from the cell OCV, a novel method named peak alignment (PA) is proposed. The algorithm 2.2 proposed in this paper is formulated using graphite anode and its electrochemical properties (i.e., phase transition). One of the main contributions of this method is that it can successfully complete PE parameter estimation using voltage fitting even if the PE material does not have obvious peaks for conventional DVA. Figure 8 As shown in (a), since NMC has no peak, Figure 8The peaks in the dV / dQ curve of the battery cell in (b) are all attributed to Figure 8 The graphite anode in (c) of FIG. 1 is shown in FIG. 1 . The estimation of the NE parameters uses this unique peak information (refer to Eq. (2.11)); the scaling from the half-cell potential (in this case, Un of the NE) to the cell OCV is obtained by the ratio of the ampere-hour distance between two distinct peaks in the cell dV / dQ curve to the stoichiometric distance between two corresponding peaks in the NE dV / dQ curve. Furthermore, the corresponding peaks (e.g., Q) are aligned by shifting the scaled half-cell potential. 1 and x 1 ), providing a utilization range x 100 Identification of the NE parameters allows the separation of the PE potential from the cell OCV via equation (2.12), and then, by extracting the PE potential A least squares-based voltage fit is performed to estimate the PE parameters, as described in P2.2. Regarding the problem of the absence of peaks in the electrode material, Honkura et al. (reference 2.12) and Dahn et al. (reference 2.13) proposed using a least squares fit on the differential voltage curve, which increases the sensitivity of the cost function associated with the electrode parameters. However, both assume that the half-cell potential is constant.

[0147]

[0148] Peak alignment by half-cell potential calibration

[0149] In terms of battery parameter changes, battery degradation can be caused in two different ways. One is that the electrode parameters (e.g., electrode capacity and utilization range θ = [C p , C n ,y 100 , x 100]). These quantitative changes are related to the degradation mode of the battery cell: LLI and LAM as described in Section II-B. Another approach is the qualitative change of the structure of the electrode material, which may affect its electrochemical performance (including potential changes). In the electrochemical community, the aging effects of various electrode materials have been extensively studied experimentally (References 2.19, 2.20, 2.28, 2.29). First, transition metal (TM) dissolution is a recognized degradation mechanism for cathode materials (Reference 2.30). In addition, when a battery cell composed of an NMC cathode degrades from long-term cycling to its end of life (EOL), degradation is accelerated due to increased dissolution of active materials into the electrolyte at high charge states (Reference 2.31). More importantly, it was found that TM dissolution can be accelerated at elevated temperatures (References 2.32-2.34). Another important degradation mechanism of the cathode is structural disorder and surface film modification. The authors in (Reference 2.32) show that the heat-aged NMC cathode has a significant lattice expansion, and the growth of the SEI film thickness indicates that the impedance of the battery cell is increased. Therefore, the assumption of invariance of half-cell potential for eSOH estimation may not be valid in some cases.

[0150] If there are changes in the potential distribution of a single electrode, it will affect the accuracy of conventional eSOH estimation, and becomes more likely when an aged battery cell approaches its end of life (EOL). Therefore, the proposed method calibrates the half-cell potential function when necessary and identifies the electrode parameters. In this study of Example 2, based on studies in the literature on graphite anode aging (References 2.19, 2.20), the invariance assumption was relaxed only for NMC PE, but not for graphite NE. In particular, in Reference 2.21, it was observed that in the differential voltage curve of the graphite anode, not only the half-cell potential distribution, but also the peak position associated with the phase change is almost unchanged.

[0151] The calibration of the PE half-cell potential function is formulated in step 10 of Algorithm 2.2, where the fitting parameters are now both the PE parameters θ p is the coefficient of the half-cell potential basis function θ Up Two additional constraints take into account U p (y) For the cases y = 0 and y = 1, the upper and lower voltage limits of the electrode materials are assumed to be constant in the fully lithiated and delithiated states. These constraints help to avoid overfitting problems in the optimization problem P2.3 due to the increased number of fitting parameters. Basic functions for various electrode materials can be found in the literature (Refs. 2.24-2.27). A possible half-cell potential function for NMC PE is

[0152] U p (y) = a0 + a1y + a2y2 +a3y 3 +a4exp(a5y+a6),

[0153] where θ Up =[α0,...,α6].

[0154] Estimation of battery cell capacity

[0155] It is worth pointing out that when identifying the electrode parameters, by incorporating the lower voltage limit V min Constraints can estimate the battery cell capacity C. Once the electrode parameters (i.e., ), it is possible to find a specific ampere-hour C that satisfies the lower voltage constraint, as shown in equation (2.13), by solving the unconstrained optimization problem P2.4 as follows,

[0156]

[0157]

[0158] Testing battery cells and aging conditions

[0159] In this study, Samsung SDI's prismatic nickel-manganese-cobalt (NMC) oxide / graphite battery cells were used. C / 20 discharge data operating between voltage limits of 4.2V and 3.0V at 25°C were measured as pseudo OCV data. The half-cell potential function of each electrode was characterized by the voltage data of the coin cell at C / 20 rate. The graphite half-cell potential function was able to capture the dU n The two most obvious peaks in the / dx curve are Figure 8 (c) is shown. The aging test conditions are summarized in Table 2.1. The aged battery cell selected here has an SOH of 66%, which is beyond the typical definition of EOL (i.e., EOL is defined as when the battery cell capacity decreases by 20% from the new state). Constant current has been applied to the aged battery cell at an aging cycle of 0.5C / 1.5CC rate to continuously charge / discharge between 15% and 95% SOC at an elevated temperature of 45°C. Note that there are more similar aged battery cells that produce similar results, so only one aged battery cell result is given.

[0160] Table 2.1

[0161] Testing battery cells and aging conditions

[0162] New battery cells Aging battery cells Battery Cell SOH 100％ 66％ Aging temperature - 45℃ Aging current - 0.5C / 1.5C SOC Swing - 95％-15％

[0163] eSOH estimation results

[0164] Figures 9(a) to 9(f) , Figures 10(a) to 10(f) and Figures 11(a) to 11(f) The estimated results for new and aged cells are given in . In each figure, the results obtained from the conventional VF method are plotted on the left, while the results obtained from the proposed PA method are plotted on the right. In each row, the voltage curves of the measured data and the model output are plotted at the top, the dV / dQ curves are plotted in the middle, and finally, the utilization potentials of the individual electrodes together with the estimated parameters are plotted at the bottom. The estimated battery capacity C is compared with the measured C / 20 discharge capacity, and their errors are stated in brackets. For clarity, all capacity values ​​here are obtained by averaging the capacity of the new battery C. fresh The C / 20 discharge capacity was normalized.

[0165] (1) New battery cell: The results of the new battery cell are shown in Figures 9(a) to 9(f) First, the voltage curves of the measured data and the model output, as well as the RMSE of the voltage, are plotted in Figures 9(a) and 9(b). For the new battery, the data and the model show good agreement (i.e., the RMSE values ​​for both methods are less than 5mV). As shown in Figures 9(c) and 9(d), the validity of the estimation is checked by checking the alignment of the peaks in the dV / dQ curves. As shown in Figure 9(c), the VF method cannot guarantee perfect alignment of the peaks. This is because the VF method does not take into account the peak information when estimating the parameters, but for the new battery cell, it still shows a reasonable fit of the dV / dQ curve.

[0166] Identifying the electrode parameters allows the electrodes to be decoupled, as shown in Figure 9(e) and Figure 9(f). The dashed line for each electrode potential represents the entire range, while the solid line represents the range from [y 100 ,y0],[x 100 , x0] represents the actual utilization range in the battery cell. The capacities associated with the entire range are PE C p and NE C n As in typical cell designs, the capacities of both electrodes exceed the cell capacity, with NE having a larger capacity than PE. Finally, the estimated cell capacity C is expressed as its error. When the entire OCV curve data is available, the capacity estimate is very accurate with an error of less than 0.1%. The slight misalignment in Figure 9(c) illustrates the deviation in the parameter estimates of the two methods, but the deviation is small.

[0167] (2) Aged cells: The estimation results for aged cells are summarized in Figure 10(a) to Figure 10(f)In the estimation, the same OCV model was used (i.e., the change in the half-cell potential was not taken into account). The RMSE values ​​in Figure 10(a) and Figure 10(b) have increased for both methods, but the PA method has a more significant increase (23.9 mV), while the VF method still shows relatively good agreement between the data and the model. However, the VF method shows a severe misalignment of the peaks in the dV / dQ curve in Figure 10(c). Even though the estimation of the cell capacity is very accurate, the peak at higher SOC drifts by 5.14% of the normalized cell capacity. Recalling the fact that the alignment of the peaks implies a correct estimation of the NE contribution in the full cell, the misalignment observed from the VF method indicates that the estimation results are incorrect. Specifically, the NE capacity C n shows a 17% difference between the two methods, and thus the range of NE utilization becomes very different. Note that the NE utilization at the fully discharged state x0 is crucial to identifying the utilized graphite anode potential, as shown in Figure 10(e). The VF method's estimate of x0 = 0.01 corresponds to a sudden increase in the potential of the graphite half-cell and attributes the inflection point of the OCV curve of the NMC / graphite cell to the NE alone. For the VF method, this identified NE utilization results in a smaller range of PE utilization and a smaller capacity reduction, showing that the PE capacity C of the two methods is significantly different. p The difference is 16%. Throughout the comparison, it was found that the good agreement of the voltage curves and the accurate battery cell capacity estimation of the conventional VF method do not always provide accurate electrode parameter estimates for NMC / graphite battery cells aged at elevated temperatures. In contrast, in the proposed PA method, since the peaks are forced to align between the data and the model, at least the NE parameters can be accurately estimated using Eq. (2.11). The NE estimate shows that the inflection point of the battery cell OCV curve comes from the two electrode potentials and leads to an estimated value of 36% reduction in the PE capacity of the new battery cell, indicating that the LAM pe is one of the main degradation modes. However, as shown in Figure 10(d), a discernible mismatch is also observed in the dV / dQ curves around the high SOC region, which also leads to voltage errors. According to the PA method, as described in P2.2, once the NE parameters are identified, the PE half-cell potential function Up(y) can be fitted to the extracted PE potential To estimate the PE parameter θ p =[C p ,y 100 ]. When the same PE half-cell potential function is used (assuming that the half-cell potential curve does not change), only by adjusting the PE parameter θ p =[C p ,y 100]The inability to obtain a good fit of the voltage curves indicates another possible aging effect, namely, a change in the half-cell potential curve. To mitigate this mismatch, calibration of the half-cell potential function was further considered.

[0168] (3) Aged batteries with half-cell potential calibration: Under the assumption that the electrode potential is constant, both conventional methods show limitations; the misalignment of the peaks found in the VF method indicates estimation errors, while a significant increase in RMSE and mismatch in the dV / dQ curves are observed from the PA method with the same half-cell potential function. To correct these shortcomings, the idea of ​​calibrating the half-cell potential function is proposed. By calibration, it is believed that the refitted The function reflects the changes in the half-cell potential curve due to aging, and therefore the estimated PE parameters are more accurate than without calibration. The function is fed into the VF and PA methods to be updated in the OCV model. Figures 11(a) to 11(f) The electrode parameter estimation in shows good agreement in the voltage curves between the data and the model, and no more discernible mismatch is observed in the dV / dQ curves. Likewise, the electrode parameters estimated by the two methods also show excellent agreement.

[0169] The calibrated PE half-cell potential curve is plotted on Fig.12 In Figure 2, the evolution of the potential curve of an aged half-cell is shown. Compared to the new half-cell potential, the aged half-cell potential is overall shifted upwards and also slightly to the left. Specifically, the voltage curve above 3.8V shows a drift to higher voltages. The overall rise in the average potential due to aging is consistent with studies in the literature (Ref. 2.35) on the cycling behavior of NCM / graphite cells.

[0170] (4) Electrode aging diagnosis: In Table 2.2, one of the most significant changes in electrode parameters in aged battery cells is the PE capacity C p This decrease indicates the loss of PE active material, i.e., LAM pe According to the definition of degradation mode in Section II-B, assuming that at 9% LAM NE Dissolution of transition metals in the NMC PE and associated growth of the SEI layer (consuming cyclable lithium in both electrodes) occurred in the tested cells at 28% and 28% LLI.

[0171] Table 2.2

[0172] Parameter estimation and its variation of new and aged battery cells using two methods

[0173]

[0174] Conclusion

[0175] A novel combination of two conventional electrode parameter estimation methods (i.e., voltage fitting and differential voltage analysis) for aging diagnosis in lithium-ion batteries is disclosed. One limitation of the conventional voltage fitting (VF) method is that it does not necessarily guarantee peak alignment in the dV / dQ curve. This is because the peak information discernible in the differential voltage is not explicitly considered in the least squares fitting formula. In addition, since this method relies only on voltage, graphite NEs with relatively low and flat voltage curves have poor observability in electrode parameter estimation. On the other hand, since the proposed peak alignment (PA) method explicitly uses peak information for estimation, individual electrode potentials can be separated from the cell voltage. Therefore, graphite NE parameters can be directly estimated by scaling and sliding the peak position in the dV / dQ curve. Once the NE utilization is identified, the utilized potential of the PE can be simply extracted by adding the cell OCV and the utilized NE potential. Therefore, even if the PE does not have a distinct peak to be used, the PA method can still estimate the PE parameters with a reduced number of unknown parameters by applying a least squares fit only to the PE potential. This electrode separation makes the developed PA method more robust in electrode SOH estimation.

[0176] The electrode parameters are estimated over the full range using pseudo OCV data from both methods without taking into account the variation in half-cell potential in new and aged cells. For new cells, both methods show good agreement. However, in the case of aged cells, which are cycled at an elevated temperature of 45°C until a typical EOL criterion is reached (i.e., SOH of 66% for aged cells), the VF method shows a significant misalignment of the peaks in the dV / dQ curves, although it still provides accurate cell capacity estimates and good voltage fits. This discrepancy arises from the assumption of invariance of half-cell potential, which can reduce the accuracy of electrode parameter estimation when this assumption is no longer held. To address this issue, a novel approach is proposed to re-fit U p (y) The idea of ​​calibrating the half-cell potential function by using the coefficients of the basis function. The improved PA method shows that the positive electrode C p The capacity of LAM decreased significantly, indicating that PE and LLI are the dominant degradation modes. This is most likely due to dissolution of transition metals and resulting growth of the SEI layer which consumes the cyclable lithium, which is likely accelerated at the elevated temperatures of our aging conditions. The aged half-cell potential of the identified NMC positive electrode shows an overall up-shifted pattern consistent with the cycling behavior of NMC / graphite cells in the literature.

[0177] Thus, the present invention provides a method for accurately measuring the state of health in a battery cell containing electrodes that do not exhibit significant phase changes during charge and discharge.

[0178] Although the present invention has been described in considerable detail with reference to certain embodiments, it will be appreciated by those skilled in the art that the present invention may be implemented by embodiments other than those described, which are presented for purposes of illustration and not limitation. Accordingly, the scope of the appended claims should not be limited to the description of the embodiments contained herein.

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[0238] The citation of any document shall not be construed as an admission that it is prior art to the present invention.

Claims

1. An electrical device comprising: Battery cells; a voltage sensor operatively coupled to the battery cell to measure a voltage level of the battery cell; a current sensor operatively coupled to the battery cell to measure an amount of current drawn from the battery cell; as well as A battery management system comprising a controller in electrical communication with the voltage sensor and the current sensor, the controller being configured to execute a program stored in the controller to: (i) receiving a plurality of voltage values ​​from the voltage sensor, (ii) receiving a plurality of current values ​​from the current sensor, wherein each current value is associated with one of the voltage values, (iii) calculating a plurality of total discharge values, wherein each total discharge value is associated with one of the current values, (iv) using the voltage value and the total discharge value to calculate the differential voltage curve, (v) determining a first differential voltage point and a second differential voltage point on the differential voltage curve, wherein each of the first differential voltage point and the second differential voltage point is at a local peak, and (vi) calculating a state of health of the battery cell using the first differential voltage point, the second differential voltage point, and a characteristic curve of a reference battery electrode of a reference battery cell, wherein the reference battery cell includes a second reference battery electrode that does not exhibit significant phase change during a charge-discharge cycle.

2. The device according to claim 1, characterized in that The differential voltage curve has a local peak originating from the anode.

3. The device according to claim 1, characterized in that The differential voltage curve has a local peak originating from the cathode.

4. The device according to claim 1, characterized in that The reference battery cell includes a cathode composed of an active material selected from the group consisting of lithium metal phosphates, lithium metal oxides, or any combination of lithium metal phosphates and lithium metal oxides.

5. The device according to claim 1, characterized in that The reference battery cell includes a cathode comprised of an active material selected from the group consisting of lithium iron phosphate, lithium nickel-manganese-cobalt oxide, or any combination of lithium iron phosphate and lithium nickel-manganese-cobalt oxide.

6. The device according to claim 1, characterized in that The reference battery cell includes an anode composed of an active material selected from the group consisting of graphite, lithium titanate, hard carbon, tin / cobalt alloy, silicon carbon.

7. The device according to claim 1, characterized in that The characteristic curve is a differential voltage curve of the reference battery electrodes.

8. The device according to claim 1, characterized in that The controller is configured to execute a program stored in the controller to calculate a state of health of the battery cell based on a utilization range calculated according to a lower limit of a utilization range of an anode of the battery cell.

9. The device according to claim 1, characterized in that The controller is configured to execute a program stored in the controller to calculate a state of health of the battery cell based on an upper limit of a utilization range of an anode of the battery cell.

10. The device according to claim 1, characterized in that The controller is configured to execute a program stored in the controller to calculate a state of health of the battery cell based on an electrode capacity of an anode of the battery cell.

11. The device according to claim 1, characterized in that The controller is configured to execute a program stored in the controller to calculate a state of health of the battery cell based on a lower limit of a utilization range of a cathode of the battery cell.

12. The device according to claim 1, characterized in that The controller is configured to execute a program stored in the controller to calculate a state of health of the battery cell based on an upper limit of a utilization range of a cathode of the battery cell.

13. The device according to claim 1, characterized in that The controller is configured to execute a program stored in the controller to calculate a state of health of the battery cell based on an electrode capacity of a cathode of the battery cell.

14. The apparatus of claim 1, further comprising: a temperature sensor operatively coupled to the battery cell to measure a temperature of the battery cell; wherein the controller is in electrical communication with the temperature sensor, and The controller is configured to execute a program stored in the controller to calculate the health state of the battery cell based on the temperature of the battery cell.

15. The device according to claim 1, characterized in that: The controller is configured to execute a program stored in the controller to calculate a negative electrode parameter from the first differential voltage point and the second differential voltage point.

16. The device according to claim 15, characterized in that: The controller is configured to execute a program stored in the controller to calculate the positive electrode potential from the negative electrode parameters.

17. The device according to claim 1, characterized in that: The controller is configured to execute a program stored in the controller to calculate a positive electrode parameter from the first differential voltage point and the second differential voltage point.

18. The device according to claim 17, characterized in that: The controller is configured to execute a program stored in the controller to calculate the negative electrode potential from the positive electrode parameters.

19. The device according to claim 1, characterized in that: The controller is configured to execute a program stored in the controller to select the characteristic curve from a plurality of characteristic curves stored in the controller.

20. The device according to claim 1, characterized in that: The controller is configured to execute a program stored in the controller to calculate a state of health of the battery cell based on a second characteristic curve of a second reference battery electrode of the reference battery cell.

21. The device according to claim 20, characterized in that: The controller is configured to execute a program stored in the controller to select the second characteristic curve from a plurality of characteristic curves.

22. The device according to claim 20, characterized in that The second characteristic curve contains a clear phase change.

23. The apparatus of claim 20, wherein the second characteristic curve is a differential voltage curve of the reference battery electrodes.

24. The device according to claim 16, characterized in that: The controller is configured to execute a program stored in the controller to calculate a positive electrode parameter from the positive electrode potential.

25. The device according to claim 24, characterized in that The positive electrode parameters are calculated by any mathematical algorithm that minimizes the error between the measured end cell voltage and the modeled end cell voltage by adjusting the parameters of the modeled positive electrode.

26. The device of claim 18, wherein: The controller is configured to execute a program stored in the controller to calculate a negative electrode parameter from the negative electrode potential.

27. The device according to claim 26, characterized in that The negative electrode parameters are calculated by the following steps: Scaling from half-cell potential to cell open circuit voltage is obtained by the ratio of the ampere-hour distance between two distinct peaks in the cell differential voltage curve to the stoichiometric distance between two corresponding peaks in the negative electrode differential voltage curve; as well as Mobile scaled half-cell potential.

28. A method for determining a battery cell state of health percentage, the method comprising: Measuring the voltage in the battery cells; measuring the current drawn from the battery cell; as well as The health state of the battery cell is calculated in a controller based on: (i) a measured voltage, (ii) a measured current, (iii) a total discharge calculated based on the measured current, (iv) a differential voltage curve calculated based on the measured voltage and the calculated total discharge, (v) a first differential voltage point and a second differential voltage point, wherein each of the first differential voltage point and the second differential voltage point is at a local peak, and (vi) a characteristic curve of a reference battery electrode of a reference battery cell, wherein the reference battery cell includes a second reference battery electrode, and the second reference battery electrode does not exhibit a significant phase change during a charge-discharge cycle.

29. The method of claim 28, wherein the differential voltage curve has a local peak originating from the anode.

30. The method of claim 28, wherein the differential voltage curve has a local peak originating from the cathode.

31. The method of claim 28, wherein the reference battery cell comprises a cathode comprised of an active material selected from the group consisting of lithium metal phosphates, lithium metal oxides, or any combination of lithium metal phosphates and lithium metal oxides.

32. The method of claim 28, wherein the reference battery cell comprises a cathode comprised of an active material selected from the group consisting of lithium iron phosphate, lithium nickel-manganese-cobalt oxide, or any combination of lithium iron phosphate and lithium nickel-manganese-cobalt oxide.

33. The method of claim 28, wherein the reference battery cell comprises an anode comprised of an active material selected from the group consisting of graphite, lithium titanate, hard carbon, tin / cobalt alloy, silicon carbon.

34. The method of claim 28, wherein the characteristic curve is a differential voltage curve of the reference battery electrodes.

35. The method of claim 28, further comprising: measuring the temperature of the battery cell; as well as The state of health of the battery cell is calculated in the controller based on the measured temperature.

36. A method in a data processing system, the data processing system comprising at least one processor and at least one memory, the at least one memory comprising instructions executed by the at least one processor to implement a battery health state estimation system, the method comprising: (a) receiving a plurality of voltage values ​​from a voltage sensor operatively coupled to a battery cell; (b) receiving a plurality of current values ​​from a current sensor operatively coupled to the battery cell, each current value being associated with one of the voltage values ​​included in the plurality of voltage values; (c) calculating a plurality of total discharge values, each total discharge value being associated with one of the current values ​​included in the plurality of current values; (d) calculating a differential voltage curve based on the voltage value and the total discharge value; (e) determining a first differential voltage point and a second differential voltage point on the differential voltage curve, wherein each of the first differential voltage point and the second differential voltage point is at a local peak; (f) determining a first set of positive electrode potential values ​​from the differential voltage curve; (g) determining a goodness of fit based on the positive electrode potential value; (h) comparing the fitness with a predetermined threshold; as well as (i) estimating the state of health of the battery cell, wherein when the degree of fit is at or below the predetermined threshold, the first set of positive electrode potential values ​​are used to estimate the state of health of the battery cell, and wherein, when the degree of fit is above the predetermined threshold, the second set of positive electrode potential values ​​calculated based on the multiple total discharge values ​​are used to estimate the state of health of the battery cell.

37. The method of claim 36, wherein: The second set of positive electrode potential values ​​is determined based on half-cell potential values.

38. The method of claim 37, wherein: The half-cell potential value is obtained from a characteristic curve of a reference battery electrode of a reference cell.

39. The method of claim 38, wherein: The half-cell potential values ​​are a result of aging.

40. The method of claim 36, wherein: The second set of positive electrode potential values ​​is more accurate than the first set of positive electrode potential values.

41. The method of claim 36, wherein: The differential voltage curve has a local peak originating from the anode.

42. The method of claim 36, wherein: The differential voltage curve has a local peak originating from the cathode.

43. The method of claim 36, wherein: Step (e) further includes finding a match of the first differential voltage point and the second differential voltage point at a cell level and at a single electrode level having a half cell potential.

44. The method of claim 43, wherein: Step (e) further includes estimating a set of negative electrode parameters using the first differential voltage point and the second differential voltage point.

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