Method and device for parameterizing a pseudo-2-dimensional electrochemical battery model

Abstract

The invention relates to a computer-implemented method for determining model parameters for an electrochemical battery model of a device battery (2), wherein the electrochemical battery model is formed as a computational model of a differential equation system with nonlinear differential equations with several model parameters, comprising the following steps: - determining (S1) impedance curves at different operating points by measuring the device battery (2) using impedance spectroscopy in the frequency domain in order to obtain impedance spectra; - carrying out (S4) a pre-optimisation phase in order to determine a starting value for a subsequent main optimisation phase for one or more selected model parameters by evaluating at least one of the obtained impedance spectra, - Acquisition (S2) of measurement data time series; - performing (S5) a main optimization phase based on a starting value for the one or more selected model parameters, predetermined starting values ​​for the remaining model parameters and the measured data time series using a numerical optimization method to obtain the model parameters.

Description

Technical field

[0001] The invention relates to portable batteries and a pseudo-2-dimensional (P2D) electrochemical battery model for simulating portable batteries. The method particularly relates to the parameterization of such a P2D battery model. Technical background

[0002] In off-grid technical devices, such as electric vehicles, powerful portable batteries, especially lithium-ion batteries, are used for energy storage. During the development phase of technical devices, the electrical behavior of such portable batteries is often described using battery models, thus avoiding costly and complex hardware prototypes and improving the entire development process. Electrochemical P2D battery models are particularly suitable for lithium-ion batteries, allowing them to describe battery behavior during use in a particularly efficient manner.

[0003] The P2D (pseudo-two-dimensional) battery model is a mathematical model used to describe the electrochemical processes in a lithium-ion battery. The P2D battery model is capable of predicting the performance and behavior of batteries under various operating conditions, and in particular, of modeling the terminal voltage of a portable battery. It is often used to optimize battery designs and analyze and optimize the behavior of portable batteries to evaluate their performance.

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

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

[0006] For example, the P2D battery model can be used to determine internal states of the device battery, from which the device battery's aging status can be derived or to monitor the device battery for anomalies. Furthermore, the internal states can be used to generate charging curves, allowing charging processes to be carried out in aging-friendly operating ranges. An example of an aging-critical internal state is the anode overpotential, which must be kept positive.

[0007] The parameterization of a P2D battery model is based on time series of measurement data using numerical optimization methods. These are very computationally intensive, and powerful computers are required to determine the model parameters with sufficient accuracy. Disclosure of the invention

[0008] According to the invention, a method for parameterizing an electrochemical P2D battery model according to claim 1 and a corresponding device according to the independent claim are provided.

[0009] Further embodiments are specified in the dependent claims.

[0010] According to a first aspect, a method for determining model parameters for an electrochemical battery model of a device battery is provided, wherein the electrochemical battery model is formed as a computational model of a differential equation system with nonlinear differential equations with a plurality of model parameters, comprising the following steps: - Determining the impedance characteristics / impedance curves of the device battery at different operating points by applying electrochemical impedance spectroscopy in the frequency domain to obtain impedance spectra; - Carrying out a pre-optimisation phase in order to determine a starting value for a subsequent main optimisation phase for one or more selected model parameters by evaluating at least one of the obtained impedance spectra, - Recording of measurement data time series; - Performing a main optimization phase based on an initial value for the one or more selected model parameters, predetermined initial values ​​for the remaining model parameters and the measured data time series using a numerical optimization procedure to obtain the model parameters.

[0011] To monitor vehicle, stationary or device batteries from a variety of devices, e.g. for anomalies or to determine an aging condition, an electrochemical battery model is usually used.

[0012] Such electrochemical battery models are known, for example, from publications US 2016 / 023,566, US 2016 / 023,567, and US 2020 / 150,185. The electrochemical battery model is typically based on a system of differential equations with a plurality of nonlinear differential equations parameterized with model parameters. The battery model is evaluated using temporal operating parameter data (battery voltage, battery current, state of charge, and battery temperature), which enable modeling of the current battery state using a time integration method.

[0013] To use the battery model, it must be parameterized. To parameterize the electrochemical battery model, a numerical optimization of between 10 and 30 kinetic parameters is performed using measured data in the time domain, e.g., based on load data from pulse tests, driving cycles, and rate tests. The optimization procedure determines the model parameters of the electrochemical battery model using an iterative least-squares method. Internal battery states can be calculated from the model parameters.

[0014] Empirical values ​​are used as starting values ​​for the optimization. Currently, the optimization of all parameters takes a very long time and is extremely dependent on the selected start and limit values ​​in the optimization process. Even with long optimization times, the root mean square error (RMSE) remains relatively high due to the large number of model parameters during validation. Furthermore, some model parameters are very sensitive to fluctuations in the measurement data quality at certain operating points compared to other model parameters. Accordingly, lower accuracies may result for these model parameters during the optimization process. Errors in measurement data can occur, for example, in time series measurements at high currents if the operating point shifts due to changes in battery temperature and state of charge, thus causing a parameterization error.

[0015] The goal of the above procedure is to improve the parameterization process of electrochemical P2D battery models. The goal of this optimization is to adapt the battery model parameters so that the electrical battery behavior can be reproduced as accurately as possible, e.g., so that a terminal voltage behavior simulated with the battery model is as close as possible to the measured battery voltage.

[0016] For optimization, starting and limit values ​​of the model parameters are often determined based on empirical or literature values ​​and only inaccurately cover a range of the battery model. This, combined with the large number of model parameters to be optimized, creates a very high risk that model parameters are determined for a local minimum and / or that the model parameters are overfitted to the given test data set. There is also a risk that the optimization process will not converge.

[0017] Using the above method, the robustness of the optimization process can be increased and the overall duration of the optimization process can be significantly reduced. This is achieved by combining a pre-optimization phase and a main optimization phase, whereby the identified parameter values ​​from the pre-optimization phase are used as starting values ​​for the subsequent main optimization phase. In order to improve the optimization in the main optimization phase for adapting the model parameters to the measured data in the time domain and to make it more robust, the starting value of at least one model parameter in the preceding pre-optimization phase can be used to determine starting and limit values ​​based on an impedance spectrum (impedance curve) (electrochemical impedance spectroscopy → EIS data) at specific operating ranges, i.e. a state of charge (SOC) and a battery temperature.Such an impedance curve can be recorded using impedance spectroscopy.

[0018] The original starting and limit values, which are based on specifications and empirical values, are used as starting values ​​for the pre-optimization phase. The limit values, based on empirical values, are used during pre-optimization to restrict the value range.

[0019] During pre-optimization, the parameters of the P2D model are determined so that the P2D model's shape is as close as possible to the recorded impedance curves. The selected sensitive parameters of the P2D model become variable parameters during optimization. The non-sensitive parameters are kept constant. The sensitive parameters behave with varying sensitivity in different frequency ranges and operating points (e.g., depending on the state of charge and temperature). This is taken into account using a frequency-dependent weighting function.

[0020] To simulate the impedance characteristics, the P2D model is excited with a sinusoidal current corresponding to the measurement points of the impedance spectroscopy. The system response in the form of the alternating voltage is then evaluated, and the complex resistance is calculated. This then yields the impedance curve. Through iterative optimization, this impedance curve is fitted to the impedance curve from the impedance spectroscopy. Gradient-based optimization may be preferable in this case. The objective function to be optimized can be derived from the complex nonlinear least squared (CNLS) approach: f(Θ,ω)=min{Θ∈ℝ+,ω∈Ψ}{∑i=1Nviwi[(Zre,i−Zre(wi,Θ))2+(Zim,i−Zim(wi,Θ)2]}

[0021] The factor w i from the formula is: wi=[(Zre,i)2+(Zim,i)2]

[0022] N corresponds to the number of measuring points at an operating point Θ over the entire measured frequency range Ψ, Z re,ithe real part of the impedance of the measuring point, Z re (w i , v j , Θ) the model value of the real part from the P2D model, Z im,i the imaginary part of the impedance of the measuring point, Z im (w i ,v i ,Θ) the model value of the imaginary value from the P2D model.

[0023] The number of parameters to be optimized varies depending on the sensitivity of the parameters at a specific operating point.

[0024] The frequency-dependent weighting function is supplemented in the above minimization function by an additional weighting factor v i taken into account.

[0025] To identify the model parameters via model fitting to impedance spectra, an alternative approach could be to use a linearized impedance model that contains the overvoltage components to be determined, e.g. from Li migration / solid-state diffusion. This could be fitted directly to the recorded impedance spectra in the frequency domain.

[0026] The model parameters can include the Bruggerman constant of the negative electrode, the diffusion constant of the negative electrode, the Bruggerman constant of the positive electrode, the diffusion constant of the positive electrode and the initial lithium concentration in the electrolyte.

[0027] For optimization, all impedance curves are preferably used for fitting. There are no frequency-fixed curves, but rather typical ranges in which some parameters typically act. The sensitivities can be included in the objective function as an additional weighting factor according to a weighting function depending on the operating point (see Fig. 4). The individual residuals of the impedance curve fits are added together to take all operating points into account. The total residual is then calculated as ∑i=1nresi=resges With resi=viwi[(Zre,i−Zre(wi,Θ))2+(Zim,i−Zim(wi,Θ)2]

[0028] The individual residuals are composed of the optimization function f given above.

[0029] Depending on the sensitivity of the individual model parameters, impedance curves at specific operating points, each of which can be determined by a state of charge and a battery temperature, can be used for pre-optimization. Sensitivity indicates the extent to which the value of the model parameter to be determined reacts to variations in impedance in a specific frequency range and operating range during optimization.To determine the sensitivities of the individual model parameters at specific frequency ranges and operating points, either 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 a previous sensitivity analysis can be used.

[0030] The results of the pre-optimization phase can be used as starting values ​​for the model parameters in the main optimization phase. This can also significantly reduce the permissible parameter space in the main optimization.

[0031] The above method involves performing electrochemical impedance spectroscopy, which does not exhibit any operating point shift during measurement.

[0032] One idea of ​​the invention is the determination of impedance curves for different operating points and their evaluation in a pre-optimization phase. Starting and limit values ​​of specific model parameters for the optimization procedure of the main optimization phase can be derived from the impedance curves in order to improve the robustness of the main optimization.

[0033] Preferably, when evaluating the impedance curve, different frequency ranges can be considered, which can be achieved using a weighting function. For each model parameter to be optimized, the weighting function considers a frequency range in which the parameter is particularly sensitive. The upper frequency of the entire frequency range is typically limited by the system sampling rate (e.g., 0.1 to 1 MHz), and the lowest frequency is limited by the load phases that are just about stationary (e.g., 10-100 MHz).

[0034] Impedance curves are recorded for various states of charge and battery temperature ranges. In particular, the operating conditions considered during parameterization using measured data during the main optimization phase should be taken into account, including very high and very low states of charge (e.g., >95% and <5%), and very high and very low temperatures (e.g., 40°C and -10°C). Furthermore, the measurement can be performed at an average temperature of, for example, 25°C and a state of charge of, for example, 50%.

[0035] To determine a particular value of a model parameter in the pre-optimization phase, an impedance curve at a specific operating point and a weighting curve can be selected. The weighting curve increases consideration of the frequency range in which the model parameter in question exhibits the greatest sensitivity. This means that the impedance curve acquired at an operating point with the highest sensitivity for determining the value of the model parameter in question is selected first. This procedure can be performed for several model parameters in the pre-optimization phase.

[0036] In the pre-optimization phase, the entire impedance curve is always selected, and only the areas with increased sensitivity are given a higher weighting using the weighting curve. Operating points are determined by temperature and state of charge. Temperatures are particularly important for activation energies.

[0037] The frequency ranges of the sensitivities sometimes overlap considerably because the individual processes cannot be clearly separated from one another. Depending on the operating point, some frequency ranges are weighted much less heavily. Using the example in the table, a weighting curve could be highly weighted for low and medium frequencies, such as at an operating point with a low state of charge (e.g. SOC=10%) and low temperatures (e.g. 0 °C). Other parameters are more sensitive for operating points with high frequencies. As a result, the weighting curve for high frequencies is less heavily weighted than for low and medium frequencies. However, there may also be other operating points at which these parameters are more sensitive. In these cases, for example, high frequencies are given a higher weight.

[0038] The impedance curve can be recorded using or consist of sampling points, with each sampling point indicating the impedance of the device battery (or vehicle or stationary battery) at a specific frequency at the operating point assigned to the impedance curve. Due to measurement time constraints, the number of sampling points per decade in the low-frequency detection range is often lower than in the higher-frequency detection range.

[0039] It can be provided that the pre-optimization phase for at least one selected model parameter is carried out by an optimization based on a total residual with constant predetermined starting values ​​of the other model parameters for the at least one impedance curve, wherein the total residual results as the sum of residuals weighted with a respective weighting over all frequency points of a detection frequency range of the at least one impedance curve, wherein the residuals are specified for each of the frequency points of the at least one impedance curve as a function of a deviation of the model parameter from the model parameter to be optimized, wherein the weighting is determined as a function of the respective frequency point and as a function of the operating point assigned to the at least one impedance curve. Brief description of the drawings

[0040] Embodiments are explained in more detail below with reference to the attached drawings. They show: Fig. 1 a schematic representation of a test bench for measuring a vehicle battery using impedance spectroscopy; Fig. 2 an impedance curve as a result of a measurement using electrochemical impedance spectroscopy; Fig. 3 a flowchart illustrating a method for performing a parameterization of an ESB battery model; and Fig. 4 an example of a weighting curve for frequency-dependent weighting of an impedance curve at a specific operating point. Description of embodiments

[0041] Fig.Figure 1 shows a schematic representation of a test bench 1 for measuring a portable battery 2, in particular a lithium-ion battery, with the aim of parameterizing an electrochemical battery model. The test bench 1 comprises a measuring unit 11 configured to perform a measurement based on a plurality of test cycles, which in particular comprise long and short pulse and cycling tests with different C-rates and (e.g., WLTP) load cycles.

[0042] The electrochemical battery model represents a computational model and can comprise a differential equation system of several nonlinear differential equations and model parameters that specify physical or chemical states and parameters of the device battery, such as contact resistance, an initial lithium concentration in the electrolyte, film thicknesses at anodes and cathodes, activation energies for the film thickness reactions, for the diffusion constants and reaction rates, anode and cathode reaction rates, diffusion constants of the anode and cathode, porosities, ionic and electronic conductivities, etc.

[0043] Furthermore, the test bench 1 comprises an impedance spectroscopy unit 12 in order to Impedance spectroscopy for different states of charge and for different battery temperatures and to obtain corresponding impedance curves. Such an impedance curve is shown in Fig. 2 shown.

[0044] The imaginary part of the characteristic impedance curve (here especially as a locus curve) is plotted on the ordinate, which is typically plotted mirrored on the x-axis. The abscissa corresponds to the real part of the impedance. When considering the high-frequency portion of the measured data, inductive behavior becomes apparent. This range is marked in the figure with kHz and MHz.

[0045] The one with R 0The resistance corresponds approximately (strictly speaking, it must first be corrected for inductive processes) to the intersection point of the impedance curve with the abscissa and corresponds to the purely ohmic conduction behavior of the device battery. This is made up of the sum of the resistances of the arresters, the active materials, the conductive additives, and the electrolyte paths. If measured at the battery level (cell clusters), connection and contact resistances are added. The following area, labeled PrCo and PrCT / SEI, shows two intersecting circular arcs, which are caused by the SEI and the effects of charge transfer as well as the double-layer capacitance, respectively for the anode and cathode. This section of the impedance curve can intersect depending on the electrode design and, for example, at high SOC, so that only a possibly flattened semicircle is visible. Towards the lower frequencies, with Pr DiffThe imaginary part often increases relatively linearly with respect to the real part, initially at an angle of approximately 45°. This part of the impedance curve characterizes diffusion processes in the active materials at the electrodes. It should be noted that, depending on the physical and chemical design of the battery, electrode and cell impedances may differ in frequency response.

[0046] Some of the electrochemical model parameters are very sensitive to a portion of the frequency spectrum at specific operating points. The entire impedance spectrum can be divided into three frequency ranges. A high frequency range, for example, can be between 10 kHz and 1 MHz, a medium frequency range can be between 10 Hz and 10 kHz, and a low frequency range between 0.001 Hz and 10 Hz. The sensitivity is further enhanced by specific operating points (low (5%), medium (50%), and high (95%) state of charge and low (-10°C), medium (20°C), and high (40°C) temperatures), depending on the processes involved. Some examples can be found in the following table: Name of the parameter Most sensitive frequency range of the impedance curve Most sensitive operating points Bruggerman constant of the negative electrode Mid frequency range - Low SOC - Low temperature Diffusion constant of the negative electrode Low frequency range - Low SOC - Low temperature Bruggerman constant of the positive electrode Mid frequency range - High SOC - Low temperature Diffusion constant of the positive electrode Low frequency range - High SOC - Low temperature Initial electrolyte concentration Low frequency range - - Low SOC - Low temperature

[0047] These a priori known sensitivities can be used to optimize some of the electrochemical model parameters of the P2D battery model in a pre-optimization phase using acquired impedance curves. Empirical values ​​or values ​​from the literature are used as starting values ​​for this process.

[0048] When recording the impedance curves, inductive effects in the impedance curve can often be neglected. An initial impedance measurement can be used to determine the impedance spectrum over an entire recording frequency range. If the impedance curves are recorded according to the minimum criteria mentioned above, nine impedance curves are produced (typical example). During pre-optimization, each impedance curve is weighted across the frequency using a predefined weighting function depending on the sensitivity of the parameters at the respective operating point. This means that deviations at different frequency points have different weightings in the residual calculation. The sum of the residuals for the measured operating points could be calculated and these could be explicitly included in the quality function.

[0049] In Fig.Figure 4 shows an example of a frequency-dependent weighting of an impedance curve at a specific operating point. The abscissa represents the frequency, and the ordinate represents the weighting. Such a weighting curve can be provided separately for each of the impedance curves recorded at different operating ranges.

[0050] The weighting curve allows for continuous frequency-dependent weighting and has overlapping regions. These can be divided into typical frequency ranges where certain processes dominate (see above). These ranges can vary from cell type to cell type and cell chemistry to cell chemistry.

[0051] The exemplary weighting could be explained here, for example, by the higher sensitivity of the kinetic parameters present in low and medium frequency ranges, whereby these ranges are weighted more heavily than the high frequency ranges. Large or medium time constants are therefore weighted more heavily at this operating point. Accordingly, these frequency ranges can be used for the optimization of, for example, diffusion and Bruggeman constants. The peak at high frequency ranges can be explained by the intersection point of the impedance curve with the real axis. The frequencies at which the peak in Fig. which typically lies between medium and high frequencies, is caused by the purely ohmic part of the battery, which can be used, for example, to optimize the contact resistance, the reaction rate at the electrodes and the film resistance.

[0052] Through the Fig.The weighting function recorded in Figure 4 would therefore heavily weight low and medium frequencies at the specific operating points. Higher frequency ranges are barely considered, with the exception of the range where the ohmic component of the battery becomes apparent.

[0053] Further weighting can be achieved by adjusting the threshold values ​​depending on the operating point and model parameters, depending on the respective sensitivities. The threshold values ​​can correspond to upper and lower limits for parameter variation as boundary conditions for optimization. The physical parameters involved in the cell design often have natural quantities and limitations (e.g., electrolyte or solid-state conductivities and diffusion coefficients as f(concentration)), which are known from the literature and prior knowledge.

[0054] If a model parameter is highly sensitive at one of the specified operating points, the parameter space is expanded, and vice versa. This allows the corresponding model parameters that exhibit high sensitivities at a specific operating point to be determined more precisely, since only these can be significantly modified during optimization. Insensitive parameters are varied accordingly less significantly. This means that the weighting of the frequency ranges via the weighting function is dependent only on the operating point.

[0055] Using the two weightings described, the residuals at different frequencies for an operating range can be combined in such a way that an improved determination of the initial values ​​of the model parameters is achieved.

[0056] The results of the pre-optimization can then be used as starting values ​​for the main optimization. The value range of the pre-optimized model parameters can also be significantly restricted. The described parameterization procedure can be used for both initial calibration and recalibration.

[0057] The pre-optimization phase yields values ​​for at least some of the model parameters, which are then used as starting values ​​for a subsequent main optimization phase. The main optimization phase performs an optimization using the least-squares method based on measured data collected in the time domain.

[0058] In addition, the value range for the pre-optimized model parameters can be significantly reduced. This makes the main optimization more robust and significantly reduces the parameterization time.

[0059] Pre-optimization in the frequency domain allows primarily linear processes in a lithium-ion cell to be modeled. Main optimization also models and considers nonlinear, load-dependent processes.

[0060] The regular measurement by the measuring unit 11 leads to current / voltage time series and is used to parameterize the electrochemical battery model in the main optimization phase using a numerical optimization method.

[0061] In Fig. Figure 3 shows a flowchart illustrating a method for determining the model parameters of an electrochemical battery model.

[0062] For this purpose, in step S1, the impedance curves for different states of charge and different battery temperatures are first recorded using electrochemical impedance spectroscopy.

[0063] Furthermore, in step S2, measurement data in the form of current and voltage time series are recorded during a pulse test, driving cycles and the like at different operating points.

[0064] In step S3, data preprocessing is performed. If multiple frequency bins with different numbers of measurement points per decade were recorded, both bins can be interpolated to the same number of measurement points per frequency decade. This prevents the optimization from overweighting a model parameter in favor of the first measurement range. Furthermore, outliers can be eliminated from the impedance curves.

[0065] In step S4, in the pre-optimization phase, starting values ​​for selected model parameters are derived from the recorded impedance curves. The selected model parameters each correspond to a model parameter that exhibits 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 reacts particularly strongly to variations in impedance in a specific frequency range during optimization in the specific operating range. This can be specified by operating point-dependent weighting curves for the relevant model parameter for each operating point, i.e., each of the impedance curves. In the optimization method of the pre-optimization phase, optimization is carried out based on minimizing an overall residual, in particular while keeping all other model parameters constant.

[0066] The total residual is the sum of residuals weighted across the frequency range. Each residual is assigned a weighting determined by evaluating the weighting curve assigned to the operating point at the frequency under consideration.

[0067] Step S4 is performed for all selected model parameters to obtain optimized values ​​of the selected model parameters. These are used as starting values ​​for a subsequent main optimization phase.

[0068] After the initial values ​​for the model parameters have been determined, an iterative numerical optimization procedure (main optimization phase) is performed in step S5 based on the time series measurement data. The initial values ​​are assumed to be the initial values, allowing the optimization to converge more quickly and thus requiring less computational effort. The optimization procedure can be gradient-based, for example.

[0069] The model parameters thus obtained can now be used in step S6 to simulate the measured device battery using differential equation methods. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] US 2016 / 023,566

[0012] US 2016 / 023,567

[0012] US 2020 / 150,185

[0012] Cited non-patent literature

[0000] 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 und Claudio Rabissi, „A Comprehensive Physical-Based Sensitivity Analysis of the Electrochemical Impedance Response of Lithium-Ion Batteries“, 2021, Energy Technology

[0029]

Claims

[1] Computer-implemented method for determining model parameters for an electrochemical battery model of a device battery (2), wherein the electrochemical battery model is formed as a computational model of a differential equation system with nonlinear differential equations with several model parameters, comprising the following steps: - determining (S1) impedance curves at different operating points by measuring the device battery (2) using impedance spectroscopy in the frequency domain in order to obtain impedance spectra; - carrying out (S4) a pre-optimisation phase in order to determine a starting value for a subsequent main optimisation phase for one or more selected model parameters by evaluating at least one of the obtained impedance spectra, - Acquisition (S2) of measurement data time series; - performing (S5) a main optimization phase based on a starting value for the one or more selected model parameters, predetermined starting values ​​for the remaining model parameters and the measured data time series using a numerical optimization method to obtain the model parameters. [2] Method according to claim 1, wherein the plurality of impedance curves are detected depending on the operating point, in particular at different states of charge and / or different battery temperatures. [3] Method according to claim 1 or 2, wherein the impedance curve is recorded on the basis of or consists of support points, wherein the support points each indicate an impedance of the device battery (2) at a specific frequency at the operating point assigned to the impedance curve. [4] Method according to claim 3, wherein the number of support points per decade is lower in the low-frequency detection range than in the higher-frequency detection range. [5] Method according to one of claims 1 to 4, wherein the pre-optimization phase for at least one selected model parameter is carried out by an optimization based on a total residual with constant predetermined starting values ​​of the remaining model parameters for the at least one impedance curve, wherein the total residual results as the sum of residuals weighted with a respective weighting over all frequency points of a detection frequency range of the at least one impedance curve, wherein the residuals are specified for each of the frequency points of the at least one impedance curve as a function of a deviation of the model parameter from the model parameter to be optimized, wherein the weighting is determined as a function of the respective frequency point and as a function of the operating point assigned to the at least one impedance curve. [6] Method according to one of claims 1 to 5, wherein the obtained model parameters are used to simulate the measured device battery. [7] Device, in particular a data processing device, for carrying out one of the methods according to one of claims 1 to 6. [8] Computer program product comprising instructions which, when the program is executed by at least one data processing device, cause the latter to carry out the steps of the method according to one of claims 1 to 6. [9] Machine-readable storage medium comprising instructions which, when executed by at least one data processing device, cause the device to carry out the steps of the method according to one of claims 1 to 6.

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