Method and apparatus for parameterizing pseudo 2-dimensional electrochemical battery model

Abstract

The invention relates to a computer-implemented method for determining model parameters of an electrochemical cell model of a system cell (2), the electrochemical cell model being formed as a calculation model of a differential equation set having a non-linear differential equation with a plurality of model parameters, the method comprises the following steps: determining impedance curves at different operating points in each case by measuring the device battery (2) by means of impedance spectroscopy analysis in the frequency domain in order to obtain impedance spectra; performing a pre-optimization phase in order to determine, for each of the one or more selected model parameters, a starting value for a subsequent main optimization phase by evaluating at least one of the obtained impedance spectra; detecting a measurement data time sequence; a main optimization phase is performed by means of a numerical optimization method on the basis of the starting values of one or more selected model parameters, the specified starting values of the remaining model parameters and the time series of measurement data in order to obtain the model parameters.

Description

Technical Field

[0001] The present invention relates to a device battery pack and a pseudo two-dimensional (P2D) electrochemical battery pack model for simulating the device battery pack. The method particularly relates to the parameterization of such a P2D battery pack model. Background Art

[0002] In off-grid technical devices, such as electric vehicles, high-performance device battery packs, especially lithium-ion battery packs, are used as energy accumulators. During the development phase of a technical device, the electrical behavior of such device battery packs is usually described by means of battery pack models, so that expensive and complex hardware prototypes can be avoided and the overall development process can be improved. Electrochemical P2D battery pack models are particularly suitable for lithium-ion battery packs, and through these battery pack models, the battery pack behavior can be described in a particularly efficient manner during use.

[0003] The P2D (pseudo two-dimensional) battery pack model is a mathematical model for describing the electrochemical processes in a lithium-ion battery pack. The P2D battery pack model is capable of predicting the performance and behavior of the battery pack under various operating conditions, and in particular, modeling the terminal voltage of the device battery pack. This battery pack model is usually used to optimize the battery pack design and analyze and optimize the behavior of the device battery pack in order to evaluate the performance of these device battery packs.

[0004] The P2D model takes into account various physical and chemical processes in the battery pack, such as lithium-ion transfer (transfer of lithium ions between and within the anode and cathode materials), electron transfer (transfer of electrons through the anode, electrolyte, and cathode), electrochemical reactions (reactions that occur during battery pack charging and discharging), and heat generation and dissipation during the battery pack operation time.

[0005] The P2D model uses partial differential equations to describe these processes and predict how the battery pack will behave under different operating conditions. This model can be used in computer simulations for optimizing the battery pack design.

[0006] For example, with the help of the P2D battery pack model, the internal state of the device battery pack can be determined, from which the aging state of the device battery pack can be derived or whether there are abnormalities in the device battery pack can be monitored using these internal states. In addition, these internal states can be used to generate a charging curve so that the charging process can be performed within an anti-aging operating range. An example of an aging-critical internal state is the anode overpotential, which must remain positive.

[0007] By means of numerical optimization methods, the model parameters of the P2D battery pack model are parameterized based on a time series of measurement data. The computational amount of these numerical optimization methods is very large, and a high-performance computer is required to determine the model parameters with sufficient accuracy. Summary of the Invention

[0008] According to the present invention, there is provided a method for parameterizing an electrochemical P2D battery pack model according to claim 1, and a corresponding device according to the co-pending independent claims.

[0009] Other design alternatives are described in the dependent claims.

[0010] According to a first aspect, there is provided a method for determining model parameters of an electrochemical battery pack model of a device battery pack, wherein the electrochemical battery pack model is formed as a computational model of a system of differential equations having non-linear differential equations with a plurality of model parameters, the method comprising the following steps:

[0011] - By applying electrochemical impedance spectroscopy analysis in the frequency domain, determining the impedance characteristics / impedance curves of the device battery pack at different operating points in order to obtain an impedance spectrum;

[0012] - Performing a pre-optimization phase in order to determine, for one or more selected model parameters, starting values for a subsequent main optimization phase by evaluating at least one of the obtained impedance spectra;

[0013] - Detecting a time series of measurement data;

[0014] - Based on the starting values of one or more selected model parameters, the specified starting values of the remaining model parameters, and these time series of measurement data, performing a main optimization phase by means of a numerical optimization method in order to obtain the model parameters.

[0015] In order to monitor, for example, whether there are anomalies or to determine the aging state of vehicle battery packs, stationary battery packs or device battery packs from among a plurality of devices, electrochemical battery pack models are typically used.

[0016] Such electrochemical battery pack models are known, for example, from the published documents US2016 / 023566, US 2016 / 023567 and US2020 / 150185. Electrochemical battery pack models are typically based on a system of differential equations having a plurality of non-linear differential equations, which non-linear differential equations are parameterized using model parameters. The battery pack model is evaluated using time-dependent operating parameter data (battery pack voltage, battery pack current, state of charge and battery pack temperature), which time-dependent operating parameter data enables the current battery pack state to be modeled by means of a time integration method.

[0017] To use the battery pack model, the battery pack model must be parameterized. For the parameterization of the electrochemical battery pack model, numerical optimization of 10 to 30 kinetic parameters is performed using time-domain measurement data, such as load data from pulse tests, driving cycles, and rate tests. This optimization method determines the model parameters of the electrochemical battery pack model by means of iterative least squares. Based on these model parameters, the internal state of the battery pack can be calculated.

[0018] Empirical values are used as the starting values for the optimization. Currently, the optimization of all parameters takes a very long time and is extremely dependent on the starting values and limit values selected in this optimization method. Even though the optimization time is long, due to the large number of model parameters, the root mean square error (RMSE) is still relatively high during validation. In addition, some model parameters show very high sensitivity to fluctuations in the quality of the measurement data at specific operating points compared to other model parameters. Correspondingly, lower accuracy may be obtained for these model parameters during the optimization process. For example, when measuring a time series at a high current intensity, if the operating point shifts due to changes in the battery pack temperature and state of charge and this causes parameterization errors, errors may occur in the measurement data.

[0019] The aim of the above method is to improve the parameterization process of the electrochemical P2D battery pack model. The purpose of this optimization is to adjust the model parameters of the battery pack model, with the aim that the electrical behavior of the battery pack can be mimicked as precisely as possible. For example, the terminal voltage behavior simulated using the battery pack model is as close as possible to the measured battery pack voltage.

[0020] For optimization, the starting values and limit values of the model parameters are usually specified by means of empirical values or literature values and only imprecisely cover a region of the battery pack model. Thus and due to the large number of model parameters to be optimized, there is a very high risk that the model parameters are determined as local minima and / or these model parameters are overfitted to the specified test data set. There is also a risk that the optimization process does not converge.

[0021] Using the above method, the robustness of the optimization method can be increased and the total duration of the optimization process can be significantly reduced. This is achieved through the combination of a pre-optimization phase and a main optimization phase, where the identified parameter values from the pre-optimization phase are used as the starting values for the subsequent main optimization phase. To improve the optimization in the main optimization phase to adapt the model parameters to the time-domain measurement data and make the optimization more robust, based on the impedance spectrum (impedance curve) in a specific operating range (i.e., state of charge (SOC) and battery pack temperature), the starting values of at least one model parameter from the previous pre-optimization phase can be used to determine the starting values and limit values. Such impedance curves can be detected by means of impedance spectrum analysis.

[0022] The original starting values and limit values based on default values and empirical values are used as the starting values for the pre-optimization phase. The limit values based on empirical values are used to limit the value range in the pre-optimization phase.

[0023] During pre-optimization, the parameters of the P2D model are determined such that the variation process of the P2D model is as close as possible to the recorded impedance curve. In this case, the selected sensitive parameters of the P2D model become variable parameters during optimization. The non-sensitive parameters remain constant. These sensitive parameters behave differently sensitive in different frequency ranges and operating points (e.g., depending on the state of charge and temperature). This is taken into account by a frequency-dependent weighting function.

[0024] To simulate the impedance characteristics, the P2D model is excited with a sinusoidal current corresponding to the measurement points of the impedance spectrum analysis. Then, the system response in the form of an alternating voltage is evaluated, and the complex resistance is calculated. Then, this complex resistance yields the impedance curve. Through iterative optimization, this impedance curve is adapted to the impedance curve from the impedance spectrum analysis. In this case, optimization based on gradients can be preferred. The objective function to be optimized can be derived according to the complex nonlinear least squares (CNLS) method:

[0025]

[0026] The factor w in the formula i is:

[0027] w i =[(Z re,i ) 2 +(Z im,i ) 2

[0028] N corresponds to the number of measurement points at the operating point Θ within the entire measurement frequency range Ψ, Z re,i corresponds to the real part of the impedance of the measurement point, Z re ​(w i , v i , Θ) corresponds to the model value from the real part in the P2D model, Z im,i corresponds to the imaginary part of the impedance at the measurement point, Z im (w i , v i , Θ) corresponds to the model value from the imaginary value in the P2D model.

[0029] The number of parameters to be optimized varies according to the sensitivity of these parameters at a specific operating point.

[0030] In the above minimization function, a frequency-dependent weighting function is considered by adding a weighting factor v i .

[0031] Alternatively, to identify model parameters by fitting the model to the impedance spectrum, a linearized impedance model may be used, which includes overvoltage components to be determined from, for example, Li migration / solid-state diffusion, and the linearized impedance model may be directly fitted to the recorded impedance spectrum within a frequency range.

[0032] Model parameters may include the negative electrode Bruggeman constant, the negative electrode diffusion constant, the positive electrode Bruggeman constant, the positive electrode diffusion constant, and the initial lithium concentration in the electrolyte.

[0033] For optimization, it is preferable to use all impedance curves for fitting. There are no frequency-rigid curves, but rather typical regions where some parameters usually have an impact. Sensitivity can be included in the objective function as an additional weighting factor corresponding to a weighting function depending on the operating point (see Figure 4 ). The individual residuals of the impedance curve fitting are added together to consider all operating points. Then, the total residual is calculated by the following equation:

[0034]

[0035] where res i = v i w i [(Z re,i - Z re (w i , Θ)) 2 + (Z im,i - Z im (w i , Θ) 2

[0036] Each residual consists of the optimization function f indicated above.

[0037] ​Based on the sensitivity of each model parameter, impedance curves at specific operating points can be used for pre-optimization, and these specific operating points can be determined by the state of charge and the battery pack temperature respectively. This sensitivity indicates the degree to which the value of the model parameter to be determined responds to impedance changes within a specific frequency range in a specific operating range during optimization. To determine the sensitivity of each model parameter in a specific frequency range and at an operating point, the results from the literature (Buddhi Wimarshana, "Parameter sensitivity analysis of a physico-chemical lithium-ion battery model with combined discharge voltage and electrochemical impedance data", Journal of Power Sources, 2022 and Claudio Rabissi, "A Comprehensive Physical-Based Sensitivity Analysis of the Electrochemical Impedance Response of Lithium-Ion Batteries", 2021, Energy Technology) or previous sensitivity analyses can be used.

[0038] The results of the pre-optimization phase can be used as the starting values of these model parameters in the main optimization phase. Here, the allowable parameter space can also be significantly reduced during the main optimization.

[0039] The above method stipulates that electrochemical impedance spectroscopy analysis is performed, and there is no operating point shift during the measurement.

[0040] The idea of the present invention is to determine the impedance curves at different operating points and evaluate them in the pre-optimization phase. From these impedance curves, the starting values and limit values of specific model parameters for the optimization method in the main optimization phase can be derived to improve the robustness of the main optimization.

[0041] Preferably, when evaluating the impedance curves, the frequency range can be considered in different ways, which can be achieved through a weighting function. This weighting function takes into account the frequency range in which the model parameter to be optimized is particularly sensitive for each model parameter. The upper limit frequency of the entire frequency range is usually limited by the sampling rate in the system (e.g., 0.1 to 1 MHz), and the lowest frequency is limited by the load stage that is detected almost in a fixed manner (e.g., 10 - 100 mHz).

[0042] Here, impedance curves are detected for different states of charge and battery pack temperature ranges. In particular, the operating states that are also considered during the parameterization using measurement data during the main optimization phase should be considered at very high and very low states of charge, such as >95% and <5%, or at very high and very low temperatures, such as 40 °C and -10 °C. Additionally, measurements can be performed, for example, at a medium temperature of, for example, 25 °C and a state of charge of, for example, 50%.

[0043] To determine the corresponding values of the model parameters in the pre-optimization phase, an impedance curve at a specific operating point can be selected and a weighting curve can be chosen. The weighting curve increases the consideration of the frequency range in which the relevant model parameters have the greatest sensitivity. That is, first, an impedance curve detected at an operating point is selected where there is the highest sensitivity for determining the value of the relevant model parameter. This process can be performed for multiple model parameters among these model parameters during the pre-optimization phase.

[0044] In the pre-optimization phase, the entire impedance curve is always selected, and here, only the regions with increased sensitivity are given relatively higher weights by means of the weighting curve. Here, the operating point is determined by the temperature and the state of charge. Temperature is particularly important for the activation energy.

[0045] The frequency ranges of sensitivity sometimes overlap severely because the individual processes cannot be precisely separated from each other. Depending on the operating point, some frequency ranges are given much smaller weights. As an example in a table, the weighting curve may be highly weighted especially for low and medium frequencies, as in the case of an operating point at a low state of charge (e.g., SOC = 10%) and a low temperature (e.g., 0 °C). Other parameters are more sensitive to operating points at high frequencies. Thus, the weighting curve is given a smaller weight for high frequencies compared to low and medium frequencies. However, there may also be other operating points where these parameters are more sensitive. There, then, for example, high frequencies will be given a higher weight.

[0046] The impedance curve can be detected based on or consist of support points, where these support points respectively indicate the impedance of the device battery pack (or vehicle or stationary battery pack) at a specific frequency at the operating point assigned to this impedance curve. Due to measurement time reasons, the number of support points per decade in the low-frequency detection range is usually less than that in the high-frequency detection range.

[0047] It can be stipulated that for at least one selected model parameter, a pre-optimization stage is performed by optimizing based on the total residual in the case of a constant specified starting value of the remaining model parameters of at least one impedance curve, where the total residual is the sum of the residuals weighted by corresponding weights at all frequency points in the detection frequency range of the at least one impedance curve, where the residuals are indicated according to the deviation of the model parameter from the model parameter to be optimized for each frequency point of the at least one impedance curve, and where the weights are determined according to the corresponding frequency points and according to the operating points assigned to the at least one impedance curve. Description of the Drawings

[0048] Subsequently, the embodiments are explained in more detail with reference to the accompanying drawings. Among them:

[0049] Figure 1 shows a schematic diagram of a test bench for measuring a vehicle battery pack by means of impedance spectroscopy analysis;

[0050] Figure 2 shows an impedance curve as a result of measurement by means of electrochemical impedance spectroscopy analysis;

[0051] Figure 3 shows a flowchart for elucidating a method for performing parameterization of an ESB battery pack model; and

[0052] Figure 4 shows an example of a weight curve for frequency-dependent weighting of an impedance curve at a specific operating point. Detailed Description of the Embodiments

[0053] Figure 1 shows a schematic diagram of a test bench 1 for measuring a device battery pack 2, in particular a lithium-ion battery pack, for parameterizing an electrochemical battery pack model. The test bench 1 includes a measurement unit 11, which is designed to perform measurements based on a plurality of test cycles, which in particular have long and short pulse and cycle tests with different C-rates and (e.g., WLTP) load cycles.

[0054] The electrochemical battery pack model is a computational model and can include a system of differential equations consisting of a plurality of non-linear differential equations and include model parameters, which indicate the physical or chemical state and parameters of the device battery pack, such as contact resistance, initial lithium concentration in the electrolyte, film thickness on the anode and cathode, activation energy of the film thickness reaction, diffusion constant and reaction rate, anode and cathode reaction rates, diffusion constants of the anode and cathode, porosity, ionic and electronic conductivities, etc.

[0055] The test bench 1 further includes an impedance spectrum analysis unit 12, which is configured to perform impedance spectrum analysis for different states of charge and different battery pack temperatures and obtain corresponding impedance curves. Such impedance curves are exemplarily shown in Figure 2 as follows.

[0056] The imaginary part is plotted on the ordinate of the characteristic impedance curve (here especially as a locus curve), where the imaginary part is usually plotted mirror-symmetrically on the x-axis. The abscissa corresponds to the real part of the impedance. If the high-frequency components of the measurement data are considered, the inductive behavior becomes apparent. This range is marked in the figure with kHz and MHz.

[0057] The resistance named R 0 approximately corresponds to the intersection point of the impedance curve with the abscissa (precisely, the inductive process must be pre-corrected first), and corresponds to the pure ohmic conduction behavior of the device battery pack. This resistance consists of the sum of the resistances of the conductor, the active material, the conductive additive, and the electrolyte path. If the measurement is performed at the battery pack level (battery complex), the connection and contact resistances are also added. The next region, marked as PrCo and PrCT / SEI, shows two intersecting arcs, which are caused by the influence of the SEI and the charge channels for the anode and cathode respectively, as well as the double-layer capacitance. This part of the impedance curve can intersect each other according to the electrode design and, for example, at high SOC, so that only a possibly flattened semi-circle can still be seen. Towards the low frequency marked with Pr Diff the imaginary part usually linearly increases at an angle of approximately 45° with respect to the real part first. This part of the impedance curve represents the diffusion process in the active material on the electrode. It should be noted here that: according to the physicochemical design of the battery pack, the electrode and battery impedance may vary in terms of frequency response.

[0058] Some of the electrochemical model parameters are very sensitive to a part of the spectrum at a specific operating point. The entire impedance spectrum can be divided into three frequency ranges. For example, the high-frequency range can be between 10 kHz and 1 MHz, the medium-frequency range can be between 10 Hz and 10 kHz, and the low-frequency range can be between 0.001 Hz and 10 Hz. Depending on the process involved, the sensitivity is increased again by specific operating points (low state of charge (5%), medium state of charge (50%), and high state of charge (95%), as well as low temperature (-10 °C), medium temperature (20 °C), and high temperature (40 °C)). Some examples can be seen from the following table:

[0059]

[0060] These a priori known sensitivities can be used to optimize some of the electrochemical model parameters of the P2D battery pack model with the detected impedance curve during the pre-optimization phase. Empirical values or values from the literature are used as the starting values for this process.

[0061] Here, when recording the impedance curve, the inductive effect in the impedance curve can usually be neglected. Through the initial impedance measurement, the impedance spectrum over the entire detection frequency range can be determined. If, for example, the impedance curve is recorded according to the above-mentioned minimum criteria, nine impedance curves (typical example) are obtained. During pre-optimization, each impedance curve is weighted by means of a specified weighting function with respect to frequency according to the sensitivity of the parameters at the corresponding operating point, whereby the deviations at different frequency points have different weights in the residual calculation. The sum of the residuals of the measured operating points may be calculated and explicitly included in the quality function.

[0062] In Figure 4 an example of the frequency-dependent weighting of the impedance curve at a specific operating point is shown. The frequency is shown on the abscissa and the weight is shown on the ordinate. Such a weight curve can be provided individually for each impedance curve recorded in different operating ranges.

[0063] The weight curve enables continuous frequency-dependent weighting and has ranges that intersect each other. The weight curve can be divided into typical frequency ranges in which a specific process dominates (see above). These ranges may vary depending on the battery type and battery chemistry.

[0064] Here, the exemplary weighting may be explained, for example, by the higher sensitivity of the current kinetic parameters in the low-frequency range and the mid-frequency range, whereby these ranges have a higher weight than the high-frequency range. Thus, at this operating point, large or medium time constants are given a higher weight. Correspondingly, these frequency ranges can be used to optimize, for example, the diffusion constant and the Bruggeman constant. The high point in the high-frequency range can be explained by the intersection of the impedance curve with the real axis. In Figure 3 the frequency at which a high point usually appears between the mid-frequency and the high-frequency is caused by the pure ohmic component of the battery pack, which can be used, for example, to optimize the contact resistance, the reaction rate on the electrode, and the film resistance.

[0065] Thus, through the weighting function recorded exemplarily in Figure 4 the low frequency and the mid frequency are given high weights at a specific exemplary operating point. Except for the range in which the ohmic component of the battery pack becomes obvious, the higher frequency ranges are hardly considered.

[0066] Further weighting can be achieved by adjusting the limit values according to the corresponding sensitivities depending on the operating point and model parameters. These limit values can correspond to the upper and lower limits during parameter variation and serve as the boundary conditions for optimization. Generally, the physical parameters involved in battery design have natural magnitudes and limitations (such as electrolyte or solid conductivity and diffusion coefficient as f(concentration)), which are known from the literature and through prior knowledge.

[0067] If a model parameter is very sensitive at one of the mentioned operating points, the parameter space will expand, and vice versa. Thus, the corresponding model parameters with high sensitivity at a specific operating point can be determined more precisely because only these model parameters can be changed significantly during optimization. The degree to which insensitive parameters are changed is relatively small. That is, the frequency range is weighted by a weighting function only according to the operating point.

[0068] By the two weights described, the residuals at different frequencies for the operating range can be combined, enabling the improvement of the determination of the initial values of the model parameters.

[0069] Then, the result of the pre-optimization can be used as the initial value for the main optimization. In this way, the value range of the pre-optimized model parameters can also be strictly restricted. The described parameterization process can be used for the first calibration and re-calibration.

[0070] The pre-optimization stage yields the values of at least some of these model parameters, which are then used as the initial values for the subsequent main optimization stage. The main optimization stage performs optimization using the least squares method based on the measurement data detected in the time domain.

[0071] In addition, the value range of the pre-optimized model parameters can be significantly reduced. Thus, the main optimization becomes more robust, and the parameterization duration is significantly shortened.

[0072] Through pre-optimization in the frequency domain, in particular, the linear processes in a lithium-ion battery can be described. Through the main optimization, the nonlinear, load-related processes are also depicted and considered.

[0073] Regular measurements performed by the measuring unit 11 generate a current / voltage time series and are used to parameterize the electrochemical battery pack model in the main optimization stage with the aid of numerical optimization methods.

[0074] In Figure 3 a flowchart is shown to illustrate the method for determining the model parameters of an electrochemical battery pack model.

[0075] For this purpose, in step S1, first, impedance curves at different states of charge and different battery pack temperatures are recorded by means of electrochemical impedance spectroscopy analysis.

[0076] In addition, in step S2, measurement data in the form of current and voltage time series at different operating points are recorded during pulse tests, driving cycles, and the like.

[0077] In step S3, data preprocessing is performed. If multiple frequency portions with different numbers of measurement points per decade are recorded, the two portions can be interpolated to the same number of measurement points per decade. Thereby, overweighing of model parameters in favor of the first measurement range during optimization is prevented. In addition, outliers in the impedance curve can be eliminated.

[0078] In step S4, in the pre-optimization phase, starting values of the selected model parameters are derived from the recorded impedance curves. The selected model parameters respectively correspond to the model parameters that have the maximum sensitivity for a specific operating point and a specific frequency range of the impedance curve. Maximum sensitivity means that the value of the model parameter to be determined during optimization responds particularly strongly to impedance changes within a specific frequency range in a specific operating range. This can be indicated by the operating point-dependent weight curves of the relevant model parameters for each operating point (i.e., each of these impedance curves). In the optimization method in the pre-optimization phase, the optimization is performed based on the minimization of the total residual, especially when all other model parameters are kept constant.

[0079] The total residual is the sum of the weighted residuals within the frequency range. For this purpose, the residuals are respectively assigned weights, which are obtained by evaluating the weight curves assigned to the operating points at the considered frequencies.

[0080] Step S4 is performed for all the selected model parameters in order to obtain the optimized values of the selected model parameters. These optimized values are used as the starting values for the subsequent main optimization phase.

[0081] After determining the starting values of the model parameters, in step S5, an iterative numerical optimization method (main optimization phase) is performed based on the time series measurement data. Here, the starting values are assumed as initial values so that the optimization converges faster and thus requires less computational effort. For example, the optimization method can be carried out in a gradient-based manner.

[0082] Now, the model parameters thus obtained can be used in step S6 to simulate the measured device battery pack by means of differential equation methods.

Claims

1. A computer-implemented method for determining model parameters of an electrochemical battery model of a device battery (2), wherein: The electrochemical battery model is formed as a computational model having a system of differential equations with a nonlinear differential equation with a plurality of model parameters, and the method comprises the following steps: - determining (S1) the impedance curve at different working points by measuring the device battery pack (2) by means of impedance spectrum analysis in the frequency domain, so as to obtain an impedance spectrum; - performing (S4) a pre-optimization phase in order to determine, for one or more selected model parameters, starting values ​​for a subsequent main optimization phase, respectively, by evaluating at least one of the impedance spectra obtained; - detecting (S2) measuring data time series; - Based on the starting values ​​of one or more selected model parameters, the specified starting values ​​of the remaining model parameters and the measurement data time series, performing (S5) a main optimization phase by means of a numerical optimization method in order to obtain the model parameters.

2. The method according to claim 1, wherein: Depending on the operating point, in particular at different states of charge and / or different battery pack temperatures, a plurality of impedance curves are detected.

3. The method according to claim 1 or 2, wherein: The impedance curve is detected as a function of support points or is composed of the support points, wherein the support points respectively indicate the impedance of the device battery (2) at a specific frequency at an operating point assigned to the impedance curve.

4. The method according to claim 3, wherein: The number of support points per decade in the low-frequency detection range is less than that in the high-frequency detection range.

5. The method according to any one of claims 1 to 4, in, performing, for at least one selected model parameter, the pre-optimization phase by optimizing based on the total residual at constant specified starting values ​​of the remaining model parameters of at least one impedance curve, The total residual is the sum of the residuals weighted by corresponding weights at all frequency points in the detection frequency range of the at least one impedance curve, wherein the residual is indicated according to a deviation of the model parameter from the model parameter to be optimized for each of the frequency points of the at least one impedance curve, Therein, the weight is determined according to the corresponding frequency point and according to the working point assigned to the at least one impedance curve.

6. The method according to any one of claims 1 to 5, wherein: The obtained model parameters are used to simulate the measured device battery pack.

7. A device, in particular a data processing device, for carrying out the method according to any one of claims 1 to 6.

8. A computer program product comprising instructions which, when the program is executed by at least one data processing device, cause the data processing device to carry out the steps of the method according to any one of claims 1 to 6.

9. A machine-readable storage medium comprising instructions which, when executed by at least one data processing device, cause the data processing device to implement the steps of the method according to any one of claims 1 to 6.

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