Method for model-based estimation of the impedance of a galvanic cell of a secondary battery and its use, as well as battery cell monitoring device and vehicle

Description

[0001] The invention relates to a method for model-based estimation of the impedance of a galvanic cell of a secondary battery by means of an estimation model executed on a computing unit according to the type defined in more detail in the preamble of claim 1, a battery cell monitoring device according to the type defined in more detail in the preamble of claim 6, the use of said method for determining the service life of battery cells of a traction battery of a vehicle according to the type defined in more detail in claim 7 and a vehicle according to the type defined in more detail in the preamble of claim 8.

[0002] Due to their high energy and power density, lithium-ion batteries are essential for the development and operation of electromobility concepts in electric vehicles. A battery management system (BMS) controls the battery packs used in mobile applications and ensures their optimal performance.

[0003] An accurate assessment of the state of health (SOH) is crucial for the operational safety of electric vehicles. The increase in internal resistance, also known as state-of-health resistance (SOHR), with aging is considered one of the most important degradation phenomena that limit the performance and service life of battery cells. Furthermore, internal resistance is essential for cell thermal analysis and temperature monitoring. The internal resistance of a cell depends strongly on temperature and the state of charge (SOC).

[0004] Accurate prediction of internal cell resistance prevents unnecessarily large failure reserves in battery design and use, thus enabling the exploitation of actual performance and service life limits in real-world operation. This prevents premature and unnecessary battery replacement, significantly increasing the sustainability of electric vehicles.

[0005] The impedance, i.e., the alternating current resistance of battery cells, can be measured using electrochemical impedance spectroscopy. However, this is comparatively expensive and time-consuming due to the required measurement technology and the effort involved. Measuring the impedance of battery cells in a vehicle is therefore impractical.

[0006] Instead, the impedance curve of the battery cells in a vehicle's traction battery is estimated during operation using computational models. Such a computational model is based on an electrical equivalent model of the battery, which in turn is based on an electronic equivalent circuit. The components contained in such an equivalent circuit, such as resistors, coils, capacitors, and the like, are equally subject to aging effects, which affect the impedance. In order to calculate a realistic impedance, it is therefore necessary to correctly estimate the parameters of these electronic components over their lifetime, taking aging into account.

[0007] For example, DE 10 2019 127 384 A1 discloses a method for parameter estimation in an impedance model of a lithium-ion cell. The parameters determined by measurement are implemented in a vehicle's computing unit for application by a computational model for determining the impedance. The measurements are performed in the vehicle.

[0008] A comprehensive overview of common methods for battery parameter estimation can also be found in Y: C. Fleischer, W. Waag, H.-M. Heyn, and DU Sauer. On-line adaptive battery impedance parameter and state estimation considering physical principles in reduced order equivalent circuit battery models: Part 1. requirements, critical review of methods and modeling. Journal of Power Sources, 260:276-291, 2014. The authors also present an estimation model they developed themselves, which is described in a second paper together with the calculation results and an evaluation of the prediction accuracy. See Y: C. Fleischer, W. Waag, H.-M. Heyn, and DU Sauer. On-line adaptive battery impedance parameter and state estimation considering physical principles in reduced order equivalent circuit battery models part 2. parameter and state estimation. Journal of Power Sources, 262:457-482, 2014.

[0009] To find relevant model parameters, a computationally intensive closed-form optimization problem is solved online in the vehicle during operation. A recursive estimator based on the least squares method is used for this purpose. This is only possible due to the linearity of the simplified computational model, as the computing resources in the vehicle are limited, solving an optimization problem is computationally and time-consuming, and thus a solution cannot otherwise be obtained in the vehicle within a reasonable time. The temperature dependence of the model parameters is also estimated on-board. Estimating the temperature dependence degrades the prediction quality. In addition, a computationally intensive iterative mutation algorithm is used to estimate the current dependence.

[0010] The present invention is based on the object of providing an improved method for model-based estimation of the impedance of a galvanic cell of a secondary battery, which is suitable for use in vehicles during their operation and has an increased prediction quality.

[0011] According to the invention, this object is achieved by a method for the model-based estimation of the impedance of a galvanic cell of a secondary battery having the features of claim 1. Advantageous embodiments and further developments as well as the use of such a method for determining the service life of battery cells of a traction battery of a vehicle, a battery cell monitoring device for carrying out the method, and a vehicle with such a battery cell monitoring device emerge from the dependent claims.

[0012] A generic method for model-based estimation of the impedance of a galvanic cell of a secondary battery by means of an estimation model executed on a computing unit, wherein at least some of the model parameters of an equivalent circuit of the cell are adapted over the lifetime of the cell in a cell model contained in the estimation model, wherein the equivalent circuit comprises at least one resistance element and one capacitance element, is further developed according to the invention in that the following method steps are carried out before the actual use of the cell: Initial parameterization of the cell model based on series of electrochemical impedance spectroscopy measurements of an identical cell; Generation of a reference database, comprising an assignment of model parameter reference values ​​and corresponding impedance reference values ​​over a lifetime characteristic map of the identical cell, by: Imposing a plurality of temperature-specific charging and discharging profiles, each comprising a voltage curve of the cell over time, on the estimation model; In doing so, tracking the model parameters of the equivalent circuit to be adjusted using a nonlinear optimizer, whereby a difference between the measured cell voltage and that calculated by the cell model is formed and minimized, whereby model parameters found in respective minima are used to generate the model parameter reference values; and Calculating the impedance reference values ​​corresponding to the model parameter reference values;Fitting a respective model parameter reference value from the reference database using a polynomial fit and storing the fitting coefficients determined in a data storage; ; and the following procedural steps are carried out during the actual use of the cell: Determining the difference between a measured cell voltage and a cell voltage calculated using the cell model; setting a gain factor and multiplying the voltage difference determined in the previous process step by the gain factor; and incrementally determining the impedance of the cell, whereby the next increment of the impedance is calculated by adding the current increment of the impedance to the product of the gain factor and the voltage difference calculated in the previous process step, whereby the variable model parameters are then adjusted to the next increment of the impedance calculated in this way, taking into account the fitting coefficients.

[0013] The method according to the invention allows a particularly precise and therefore reliable estimation of the impedance of battery cells and has a comparatively low computational requirement. The method is therefore particularly suitable for use during ongoing vehicle operation. No optimization is required in the vehicle itself to determine the model parameters appropriate for the respective operating state of the battery. Instead, these model parameters are initially estimated in a laboratory or a test vehicle, i.e. off-board a production vehicle, and determined for all possible states using fitting. These reference values ​​are then used for the respective actual application in the (production) vehicle. The voltage difference between the measured and estimated terminal voltage used to calculate the impedance is evaluated for each sampling period, which allows for a particularly high-resolution analysis.

[0014] The method according to the invention provides for gathering information about changes in electrical cell behavior over their service life offline or off-board, i.e. not during operation of the vehicle itself, but for example in a laboratory or test vehicle. This cell behavior is typical for cells of a certain type and can therefore be transferred to cells of the same design. The process steps carried out before the cell is actually used can therefore be carried out on any cell of the same design in a laboratory, and the process steps carried out during the cell's actual use can be carried out on a different secondary battery with corresponding identical cells. The secondary battery can be used as a voltage source in any machine, such as a vehicle, to operate it.

[0015] Creating an equivalent circuit diagram of a cell and implementing it in a computing unit is common practice. However, the question arises as to how aging-dependent model parameters can be adapted to their physically correct values ​​over the lifetime of the secondary battery. For the cell type under consideration, a complete parameterization of the estimation model or equivalent circuit diagram, and thus of the electrical part of the cell model, is performed based on electrochemical impedance spectroscopy measurements (EIS measurements) of a brand-new cell. This allows the physical behavior of this "beginning-of-life" (BOL) cell to be reproduced comparatively physically accurately. The physical behavior of the cell depends on temperature and state of charge.The EIS measurements involve performing various measurement series at different states of charge between 0 and 100% and temperatures, for example, between -20°C and +45°C. Temperature dependencies are fitted based on Arrhenius functions. Arrhenius functions describe the relationship between reaction kinetics in the battery cell and respective temperatures. The Arrhenius functions thus determined are saved and permanently integrated into the estimation model for later use. The dependencies on different states of charge are stored in the estimation model in the form of factors from look-up tables. In addition to the temperature dependency, the dependency on different states of charge (SOC) also remains constant over the lifetime of the galvanic cell.

[0016] The EIS measurements can be carried out on one or more individual cells or on different cells combined to form a battery module.

[0017] The next step involves adapting the "start" parameterization found for this brand-new cell or cells (BOL cells) over its lifetime. To determine the course of all relevant model parameters, which assume changed values ​​over cell aging, the estimation model is incorporated into a battery cell monitoring device. Such a battery cell monitoring device comprises detection means for detecting the current deliverable by at least one cell of the secondary battery, the terminal voltage, and the battery temperature at any point, in particular the cell temperature of the monitored cell. Furthermore, the battery cell monitoring device comprises a data memory and a computing unit on which the estimation model is implemented.Now an already aged secondary battery, comprising a large number of identical cells, is used and emulated, simulated or actually experienced discharge and charge profiles are applied to this secondary battery.

[0018] Such discharging and charging profiles can be generated, for example, during test drives with a vehicle. Discharging takes place, for example, while the vehicle is driving for a longer period of time, such as two hours. The vehicle can also operate a corresponding electric motor in generator mode and thus, through recuperation, feed electrical energy into the secondary battery to charge the battery cells. Corresponding charging processes take a comparatively short time, on the order of several seconds. A charging profile is, for example, a real charging process carried out at a charging station. For example, the secondary battery is charged from a state of charge of 20% to a state of charge of 85% within several minutes, for example 40 minutes.The discharge and charge profiles can be applied in the vehicle itself or with a removed traction battery installed on a test bench. The actual, simulated, or emulated discharge and charge profiles are then applied on this test bench.

[0019] Each cell of the secondary battery exhibits a different aging state over its service life. Accordingly, the individual battery cells of the traction battery under consideration exhibit different impedances. The reference database is then constructed using the estimation model and the measured variables. The model parameters, which vary over the service life and corresponding aging, are determined using a nonlinear optimizer. To do this, the estimation model compares the measured and estimated voltage values ​​and minimizes them until the deviation is minimal, ideally zero. The model parameters found in the respective minima are then used to generate the model parameter reference values. These are concrete values ​​(corresponding to the series of measurements performed).During later operation of a vehicle, however, the cells will typically assume arbitrary impedance values, which are not necessarily included in these measurement series. To nevertheless include model parameters for these impedance values ​​in the reference database, fitting functions are determined for each model parameter. These fitting functions correspond to a curve of the variable model parameter over the impedance. Common polynomial fitting methods are used for this purpose. Nth-order polynomials can be used. However, the use of second-order polynomials, i.e., quadratic functions, has proven particularly advantageous, as this represents a good balance between accuracy and computational effort.

[0020] This provides a knowledge base regarding the characteristics of each aging-specific model parameter for each impedance value. This is a core idea of ​​the invention, as it allows the computationally intensive optimization to be outsourced from the vehicles to the laboratory or a test vehicle and only needs to be performed once for each different cell type.

[0021] The fitting coefficients calculated in this way are stored in a data storage unit. The data storage unit is part of the computing device or a test bench. From the data storage unit, the fitting coefficients can be distributed to any other computing units and implemented there. For example, this could be the battery management system of a vehicle's traction battery.

[0022] The estimation model can then be used during operation of a vehicle to estimate the impedance of the battery cells of the vehicle's traction battery. This enables the estimation of the impedance of the cells of the vehicle's traction battery during operation. For this purpose, the estimation model is implemented in the vehicle's computing unit, for example, in a separate computing unit, the BMS, or a battery cell monitoring device, or the like.

[0023] An advantageous development of the method according to the invention provides that the equivalent circuit diagram of the cell contains at least one additional of the following further elements: a ZARC element; a coil element; a finite-length Warburg element; and / or a finite-space Warburg element.

[0024] By adding these elements to the cell's equivalent circuit, a particularly realistic equivalent circuit and thus an electrical cell model can be created. This provides the best possible mathematical description of the physical processes of the individual cells. A single resistor represents the electrical resistance of conductive materials, such as the conductors on the electrodes, cables within the battery, and the limited conductivity of the electrolyte.

[0025] A coil can be included in the equivalent circuit to represent inductive behavior. Inductive behavior occurs due to metallic contacts within the cell.

[0026] A ZARC element consists of an ohmic resistor connected in parallel with a capacitor. A ZARC element simulates the effect of double layers and charge transfer. This allows nonlinear voltage dependencies to be taken into account. ZARC elements can be used to describe the high-frequency part of cell impedances.

[0027] The low-frequency part of the cell impedances can be described using Warburg elements. Warburg elements capture processes that describe the comparatively slow ion diffusion within the electrodes. A finite-space Warburg element represents a non-conductive boundary layer at a maximum diffusion length, whereas a finite-length Warburg element describes a perfectly conductive boundary layer at a maximum diffusion length.

[0028] According to a further advantageous embodiment of the method, the voltage difference between the measured cell voltage and the calculated cell voltage is low-pass filtered before multiplication by the gain factor. This stabilizes the parameter tracking of the model parameters and makes it possible to distinguish, as far as possible, short-term model errors from parameter learning errors.

[0029] A further advantageous embodiment of the method further provides that the cell model for calculating the cell voltage takes into account a term each for the overvoltage, the hysteresis voltage, and the open-circuit voltage. The open-circuit voltage is approximated by the weighted average of the low-pass filtered difference between the clamping and overvoltage and the open-circuit voltage calculated by current integration. The hysteresis voltage is provided, for example, by a parallel software module according to the modified Plett model presented by D. Wycisk, M. Oldenburger, MG Stoye, T. Mrkonjic, and A. Latz. Modified plett-model for modeling voltage hysteresis in lithium-ion cells. Journal of Energy Storage, 52:105016, 2022. The open-circuit voltage is approximated by weighted averages of two different voltage estimates.The first voltage estimate results from the low-pass filtered difference between the clamping voltage and the overvoltage and the second estimate from the open-circuit voltage calculated by current integration.

[0030] According to a further advantageous embodiment of the method according to the invention, the gain factor is determined as a function of the following four terms: a fundamental gain term; a battery current sign term; a power term of the absolute value of the cell current; and an exponential decay term.

[0031] The gain factor can be greater than, less than or equal to 1 and can take positive or negative values.

[0032] The battery current sign term can be used to take into account whether the cell is currently being charged or discharged.

[0033] The power term of the absolute value of the cell current controls the magnitude of the cell overvoltage with the smallest residual error. Higher values ​​induce better agreement at high overvoltages and more error tolerance at low overvoltages, and vice versa.

[0034] The exponential decay term allows for faster learning of the model parameters after a parameter reset. A decay constant can be used to accelerate the learning of reset parameters. The term can also include a factor that allows for slower learning immediately after a control unit wakes up, until the voltage at the model's RC elements is learned through dynamic charging and discharging.

[0035] In a battery cell monitoring device, comprising detection means for detecting the current deliverable by at least one cell of a secondary battery, the terminal voltage, and a battery temperature of cells, as well as a data memory and a computing unit, the detection means, the data memory, and the computing unit are configured according to the invention to carry out the method steps of a method described above that are carried out during the actual use of the cell. The battery cell monitoring device can be part of a battery management system or form such a system. The battery cell monitoring device can comprise current sensors, voltage sensors, and temperature sensors as detection means, or can be connectable to them. The data memory is a non-volatile memory, optionally supplemented by volatile memory.The computing unit is a computer, a system-on-a-chip (SoC), or similar device. The data storage can be integrated into the computing unit.

[0036] A method described above is used according to the invention to determine the service life of battery cells of a traction battery of a vehicle with an at least partially electrified drive train, wherein the method steps carried out during the actual use of the cell are carried out in the vehicle. As already mentioned, the aging state of battery cells of a traction battery of the vehicle can be estimated particularly accurately and thus particularly reliably with the aid of the method according to the invention. This is synonymous with the impedance of the respective cells. The cell can be a lithium-ion cell, for example. However, the method according to the invention is also suitable for battery cells of different types, such as sodium-ion cells.

[0037] In a vehicle with an at least partially electrified drive train, comprising a traction battery and a battery cell aging determination device, according to the invention, the battery cell aging determination device has a battery cell monitoring device as described above. The battery cell aging determination device can be a computing unit superordinate to the battery cell monitoring device. The battery cell monitoring device can also be an integral part of the battery cell aging determination device. For example, the battery cell aging determination device can be a battery management system into which the battery cell monitoring device is integrated.

[0038] Further advantageous embodiments of the method according to the invention for the model-based estimation of the impedance of a galvanic cell of a secondary battery also result from the exemplary embodiments which are described in more detail below with reference to the figures.

[0039] Showing: Fig. 1 is a schematic representation of a battery cell monitoring device according to the invention; Fig. 2 is a schematic representation of a cell model of a battery cell monitoring device according to the invention. Fig. 1Fig. 3 shows a diagram of an equivalent circuit diagram of a cell implemented in the estimation model implemented by the battery cell monitoring device shown, and the associated impedance spectra; Fig. 3 shows a diagram showing the course of a model parameter of a component contained in the equivalent circuit diagram over the impedance of the cell; Fig. 4 shows a set of equations stored in the estimation model; and Fig. 5 shows a flowchart of an inventive method for estimating the impedance of a galvanic cell of a secondary battery.

[0040] One in Figure 1The battery cell monitoring device 8 shown comprises a computing unit 3, which serves to execute an estimation model 4. With the aid of the battery cell monitoring device 8, the cells 1 of a secondary battery 2 are monitored in order to estimate their age-dependent impedance over the service life of the secondary battery 2. With the aid of the estimated impedance, a statement can be made about the ageing of the secondary battery 2.

[0041] A separate battery cell monitoring device 8 can be provided for each cell 1 of the secondary battery 2, or several cells 1 can be monitored with one and the same battery cell monitoring device 8. The input variables used by the estimation model 4 are the current I flowing through a respective cell 1, the terminal voltage U, also referred to as the measured voltage U mes, a temperature T of the secondary battery 2, preferably of the cell 1 to be monitored, and the computationally estimated state of charge SOC of the respective cell 1. The state of charge SOC can be provided by conventional methods, for example determined by a battery management system BMS. The battery management system BMS can be part of the computing unit 3 or, as shown, implemented separately therefrom.

[0042] The estimation model 4 can have a phase adjustment module 9 for adjusting the phase of the measured voltage U mes . The cell model 6 has an electrical cell model 6.1 and a thermal cell model 6.2. The electrical cell model 6.1 outputs a resistance of the cell 1 under consideration, or a power loss P loss , as an output variable, and the thermal cell model 6.2 outputs the temperature T abg of the respective cell 1. Furthermore, the estimation model 4 has a reference database 7 containing the development of model parameters included in the electrical cell model 6.1 of an equivalent circuit over the lifetime.

[0043] Using cell model 6, a calculated voltage U ber is calculated. The measured voltage U mes and the calculated voltage U ber are combined in a subtractor 10 and subtracted from each other to determine the difference between these values. The difference, referred to here as error ε, must be minimized. Thus, the error ε is 0 if the model parameters of the cell 1 dependent on the lifetime of the cell Figure 2shown equivalent circuit diagram 5 or the electrical cell model 6.1 correspond to the real physical values. The error ε can optionally be passed through a filter module 11 for smoothing, for example using a low-pass filter. It is then fed into a control system 12, for example a PID controller. As a result, the control system 12 provides the desired aging state of the cell 1 in the form of the estimated internal resistance, i.e. the impedance. The impedance is also referred to as the state-of-health resistance SOHR. The impedance is fed back into the estimation model 4 and serves as an input variable for the cell model 6. The impedance can also be derived from the estimation model 4 and even from the computing unit 3 in order to be available as an input variable for further computing models, for example as an input variable for a driver assistance system.

[0044] The structure of estimation model 4 shown here provides for an iterative, i.e., incremental, calculation of the impedance. The current, fed-back impedance increment is thus used to calculate the next increment.

[0045] Figure 2 shows the structure of the electrical equivalent circuit 5 of a respective cell 1. This comprises a resistance element R and two consecutive ZARC elements ZARC followed by two consecutive Warburg elements. These are a finite space Warburg element FSW and a finite length Warburg element FLW. A ZARC element, in turn, comprises a capacitance element C connected in parallel with a resistance element R.

[0046] Under the equivalent circuit diagram 5, Figure 2The impedance spectra of the respective elements and the impedance spectrum of the complete model are also shown. The real part of the impedance is plotted on the abscissa and the imaginary part on the ordinate in ohms.

[0047] For a fast and computationally efficient execution of the estimation model 4 in the vehicle, a relationship is required that describes the characteristics of a respective model parameter of the equivalent circuit 5 depending on the aging state of the cell 1, i.e. the impedance or the state-of-health resistance SOHR. These relationships are shown in the Figure 1 shown reference database 7.

[0048] Figure 3illustrates the process for obtaining the information stored in the reference database 7 using a diagram. The provided calculation model is used in a test environment to analyze a real battery. The real battery contains differently aged cells 1. The calculation model is pre-parameterized based on an EIS measurement of a brand-new cell. The next step is to determine the course of the model parameters over the impedance. An example is shown in Figure 3the curve for the individual resistance R is shown. For this purpose, real, simulated, or emulated discharge and charge profiles are imposed on an aged secondary battery 2, for example, in a laboratory, on a test bench, or in a test vehicle. An optimization algorithm is used to determine the curve of the individual model parameters over the impedance or over the state-of-health resistance SOHR. The optimization algorithm has the task of minimizing the error ε in the estimation model 4. In the process, the respective values ​​of the model parameters are changed. Thus, for each cell 1 examined, corresponding model parameters are obtained for each measuring point in the characteristic map of the respective discharge and charge profiles for the individual cells 1 of the battery (black circles in the diagram).

[0049] However, since values ​​for all impedance values ​​are required in real operation, i.e., a continuous curve and not just at the points where black circles are located in the diagram, a fitting is carried out, whereby the compensation curve 13 is obtained. The fitting coefficients determined to determine the compensation curve 13 are then stored in the reference database 7. This makes it possible to determine suitable model parameter values ​​for all impedance manifestations, i.e., State-Of-Health-Resistance SOHR. It is then not necessary to carry out another optimization on the computing unit 3, i.e., in the respective vehicle during subsequent operation, which saves a considerable amount of computing effort and thus enables a particularly rapid execution of the method according to the invention and thus calculation of the impedance.

[0050] Figure 4 shows a set of equations as it can be stored in the calculation model.

[0051] Equation one, G-1, describes the formula for defining different model parameters. Term 1-0 represents a respective model parameter. Term 1-1 describes the respective order of magnitude of the model parameter and serves to scale all model parameters to the same order of magnitude. Term 1-2 describes a coefficient. Term 1-3 represents the actual impedance. The impedance is raised to the power j. Ideally, j=2. This represents a compromise between a sufficiently fast calculation and a sufficiently accurate result. It is then a quadratic polynomial.

[0052] Equation two G-2 describes the voltage difference in subtractor 10. Term 2-0 describes the voltage difference between the measured and calculated voltages U mes and U ber . The index "n" references the current increment or iteration. Thus, multiple iterations occur during a sampling or calculation step. Term 2-1 describes a filter constant that can assume a value between 0 and 1, whereby alpha is much smaller than 1. Term 2-2 corresponds to the measured voltage U mes at the current increment, and term 3-0 corresponds to the calculated voltage U ber at the current increment. Term 2-4 corresponds to the voltage difference from the previous increment "n-1."

[0053] Equation three G-3 describes the calculated voltage U over . Term 3-1 corresponds to the overvoltage. Term 3-2 corresponds to the open-circuit voltage. Term 3-4 corresponds to the hysteresis voltage. Term 4-0 corresponds to the low-pass filtered difference between the clamping and overvoltage, and term 3-3 corresponds to the open-circuit voltage calculated by current integration. Beta is a weighting and filtering constant that can take a value between 0 and 1.

[0054] Equation 4 G-4 describes the calculation of term 4-0. Term 4-1 describes the difference between the measured voltage U mes and the overvoltage. Term 4-2 describes the difference between term 4-0 and the previous increment.

[0055] Equation 5 G-5 describes the impedance, i.e., the state-of-health resistance (SOHR) in the next increment "n+1." The term 5-0 corresponds to the impedance of cell 1. This is composed of the term 5-1, i.e., the impedance at the current increment "n," plus the product of the two terms 6-0 and 2-0, where the term 6-0 corresponds to a gain factor and the term 2-0 to the aforementioned voltage difference.

[0056] Equation 6, G-6, gives the calculation rule for determining the gain factor. Term 6-1 denotes a base gain for the feedback of the voltage difference. Term 6-2 describes the sign of the battery current. Term 6-3 describes a power term of the absolute value of the cell current and controls the magnitude of the cell overvoltage with the smallest residual error. The quantity v can take on a value between 0 and 1. Higher v values ​​induce better agreement at high overvoltages and more error tolerance at low overvoltages, and vice versa. Term 6-4 describes an exponential decay term. Term 6-4.1 allows for a K 0 -fold faster learning of the parameters at time t abs after a parameter reset. The decay constant λ determines the temporal decay rate of this additional gain to accelerate the learning of reset parameters. Term 6-4.2 allows a learning process slowed down by K 0 "' times immediately after the arithmetic unit 3 wakes up, until the voltage at the RC elements of the model is learned by dynamic charging and discharging.

[0057] Figure 5 shows an implementation of the estimation model 4 on an embedded system in the form of a flowchart for executing the method steps of the method according to the invention running in a vehicle. The embedded system is formed by the computing unit 3, which thus represents a time-discrete control unit. It is preferably a fixed-point implementation, which has increased performance with reduced memory consumption compared to floating-point implementations on embedded systems. Figure 5Preferably, the computing unit 3 can be the vehicle's battery management system. The tick rate of the battery management system is set, for example, to a frequency of 50 Hertz.

[0058] A real-time operating system (RTOS) of the computing unit 3 executes an initialization call 550, triggered by an initialization event, whereupon the cell model 6 is initialized. For this purpose, values ​​for the model parameters and corresponding voltages stored during the last runtime, i.e., before the computing unit 3 shuts down, are read from a non-volatile memory (EEPROM), which are then written to a volatile memory (RAM). In method step 501, the aging-dependent model parameter curves are read from the reference database 7. In method step 502, the most recently processed voltage values ​​are read. In method step 503, voltage distributions for the RC elements of the cell model 6 are read. In method step 504, the RC voltages are recalculated before the computing unit 4 goes into sleep mode.

[0059] Subsequently, in method step 560, the computing unit 3 or the real-time operating system RTOS executes a cycle call of the executable main function of the estimation model 4. In method step 505, the measured cell voltage, the current, and the estimated cell temperature are recorded. If necessary, a phase adaptation of the measured voltage values ​​is performed in order to synchronize the current and voltage signals. The following method steps 506 to 515 can be performed serially for several, preferably all, cells 1 of the secondary battery 2. For this purpose, method steps 506 to 515 can be implemented, for example, as a FOR loop, iterating over the individual cells 1. In method step 506, a cell iterator is counted.

[0060] In method step 507, the age-dependent model parameters for the current impedance are calculated, whereby the values ​​written into the volatile memory RAM from the reference database 7 are processed.

[0061] The relationship to the aforementioned Arrhenius equations and temperature is taken into account. This occurs in method step 508 together with a calculation step for considering the state of charge (SOC). In method step 509, the sleep duration of computing unit 3 is read and transferred to the model. This is required after a restart to determine the voltage values ​​of the RC elements in method step 511. For this purpose, the corresponding voltage values ​​before computing unit 3 is put to sleep are required, which are read from the volatile memory RAM. Whether this is the initialization after computing unit 3 has woken up is checked in method step 510.

[0062] In process step 512, a forward-looking calculation is performed to calculate the terminal voltage, cell voltage, and thermal losses as output signals. The considered aging factor, i.e., the impedance, is tracked via the feedback of the voltage values. The tracked aging factor, i.e., the calculated impedance to the next increment, is fed back to adjust the model parameter calculation. In process step 513, a check is made to determine whether the current is above a minimum current value and whether the change in current is above a corresponding limit value for the current change. If this is the case, the impedance is tracked in process step 514 and written to the volatile memory RAM. In process step 515, a check is made to determine whether this is the last cell 1 to be monitored.

[0063] In process step 570, the real-time operating system (RTOS) initiates a shutdown sequence. For this purpose, in process step 516, the voltages of the Warburg elements and the current model parameters (i.e., the model parameters adjusted according to aging) are written to the volatile memory (EEPROM) for each cell 1. In process step 517, the voltage distributions of individual Warburg elements to RC voltages are written to the non-volatile memory (EEPROM) in a similar manner, but only for a single cell 1. In process step 518, the impedances of the individual cells 1, i.e., the aging factors, are saved. This concludes the process.

Claims

1. Method for model-based estimation of the impedance of a galvanic cell (1) of a secondary battery (2) by means of an estimation model (4) executed on a computing unit (3), wherein at least some of the model parameters of an equivalent circuit diagram (5) of the cell (1) are adjusted in a cell model (6) contained in the estimation model (4) over the service life of the cell (1), wherein the equivalent circuit diagram (5) comprises at least one resistance element (R) and one capacitance element (C), characterized by the following method steps carried out before the cell (1) is actually used: - initially parameterizing the cell model (6) on the basis of series of measurements of electrochemical impedance spectroscopy of an identical cell (1); - generating a reference database (7) comprising an assignment of model parameter reference values and corresponding impedance reference values over a lifetime map of the identical cell (1), by: ∘ imposing a plurality of temperature-specific charging and discharging profiles, each comprising a voltage curve of the cell (1) over time, on the estimation model (4); ∘ thereby updating the model parameters of the equivalent circuit diagram (5) to be adjusted by means of a non-linear optimizer, wherein a difference between the measured cell voltage (Umes, Urec) calculated by the cell model (6) is formed and minimized, wherein model parameters found in relevant minima are used to form the model parameter reference values; and ∘ calculating the impedance reference values corresponding to the model parameter reference values; - fitting a relevant model parameter reference value from the reference database (7) by means of a polynomial fit and storing the fitting coefficients determined thereby in a data storage means; and the following method steps carried out while the cell (1) is actually used: - determining the difference between a measured cell voltage (Umes) and a cell voltage (Urec) calculated using the cell model (6); - specifying a gain factor and multiplying the voltage difference determined in the previous step by the gain factor; and - incrementally ascertaining the impedance of the cell (1), wherein the next increment of the impedance is calculated by adding the current increment of the impedance to the product of the gain factor and the voltage difference calculated in the previous method step, wherein the variable model parameters are then updated to the next increment of the impedance calculated in this way, taking into account the fitting coefficients.

2. Method according to claim 1, characterized in that the equivalent circuit diagram (5) of the cell (1) contains at least one additional element of the following further elements: - a ZARC element (ZARC); - a coil element; - a finite length Warburg element (FLW); and / or - a finite space Warburg element (FSW).

3. Method according to claim 1 or claim 2, characterized in that the voltage difference of the measured cell voltage (Umes) and the calculated cell voltage (Urec) is low-pass filtered before multiplication by the gain factor.

4. Method according to any of claims 1 to 3, characterized in that the cell model (6) takes into account one term (3-1, 3-3, 3-2) each for the overvoltage, the hysteresis voltage and the open-circuit voltage in order to calculate the cell voltage (Urec).

5. Method according to any of claims 1 to 4, characterized in that the gain factor is ascertained depending on the following four terms (6-1, 6-2, 6-3, 6-4): - a basic gain term; - a battery current sign term; - a power term of the absolute value of the cell current; and - an exponential decay term.

6. Battery cell monitoring device (8), comprising detection means for detecting the current that can be output by at least one cell (1) of a secondary battery (2), the terminal voltage and a battery temperature, as well as a data storage means and a computing unit (3), characterized in that the detection means, the data storage means and the computing unit (3) are designed to perform the method steps of a method according to any of claims 1 to 5 carried out while the cell (1) is actually used.

7. Use of a method according to any of claims 1 to 5, for determining the service life of battery cells of a traction battery of a vehicle having an at least partially electrified drive train, wherein the method steps carried out while the cell (1) is actually used are carried out in the vehicle.

8. Vehicle having an at least partially electrified drive train, the vehicle comprising a traction battery and a device for ascertaining battery cell aging, characterized in that the device for ascertaining battery cell aging comprises a battery cell monitoring device (8) according to claim 6.