METHOD FOR MODEL-BASED ESTIMATION OF IMPEDANCE OF GALVANIC CELLS OF A SECONDARY BATTERY AND USE THEREOF, AS WELL AS BATTERY CELL MONITORING DEVICE AND VEHICLE - Patent application

Abstract

The invention relates to a 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) implemented in a calculation unit (3). The invention relates to a method for model-based estimation of the impedance of a galvanic cell (1) of a secondary battery (2), the method comprising the following method steps, which are carried out before the actual use of the cell (1): - an initial parameterization of the cell model (6); - forming a reference database (7); - fitting each model parameter reference value from the reference database (7) using a polynomial fit and storing the fitting coefficients obtained in the process in a data memory; Including, and the following subsequent method steps carried out during the actual use of the cell (1): -Measured cell voltage (U mes ) and the calculated cell voltage (U rec ) step to find the difference; - setting an amplification factor and multiplying the voltage difference determined in the previous method step by the amplification factor; and - a step of incrementally determining the impedance of cell (1), calculating the next increment of impedance by adding the current increment of impedance to the product of the amplification factor and the voltage difference calculated in the previous method step, followed by a step of updating the variable model parameters to the next increment of impedance thus calculated, taking into account the fitting coefficients.

Description

[Technical field]

[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 implemented in a computing unit as defined in more detail in the preamble of claim 1, a battery cell monitoring device as defined in more detail in the preamble of claim 6, a use of the method for determining the service life of a battery cell of a traction battery of a vehicle as defined in more detail in claim 7 as well as a vehicle as defined in more detail in the preamble of claim 8. [Background technology]

[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. Battery Management Systems (BMS) control battery packs used in mobile applications and ensure their optimal performance.

[0003] An accurate estimation of the state of health, also called SOH (State-of-Health), is crucial for the safety of operation of electric vehicles. The increase in internal resistance, also called SOHR (State-of-Health-Resistance), during aging is considered one of the most important degradation phenomena that limit the performance and service life of battery cells. Furthermore, the internal resistance is of great importance for the thermal analysis and temperature monitoring of cells. The internal resistance of a cell depends strongly on the temperature and the state of charge, also called SOC (State-of-Charge).

[0004] Accurate prediction of cell internal resistance allows battery design and utilization to avoid oversizing of failure reserves and thus fully utilize the actual performance and life limits in real operation, thus preventing premature and unnecessary battery replacement and significantly improving the sustainability of electric vehicles.

[0005] The impedance, i.e. the AC resistance of a battery cell, can be measured using electrochemical impedance spectroscopy. However, this measurement is relatively expensive and time consuming due to the measurement techniques required and the effort that needs to be performed. Therefore, it is not practical to measure the impedance of a battery cell in a vehicle.

[0006] Instead, the impedance curve of the battery cells of the vehicle's traction battery is estimated during operation using a calculation model. The basis of such a calculation model is an electrical equivalent model of the battery, which is also based on an electronic equivalent circuit. Components contained in such an equivalent circuit, such as resistors, coils, capacitors, etc., are also subject to aging and therefore affect the impedance. In order to be able to calculate an impedance that is close to reality, it is therefore important to accurately estimate the parameters of these electronic components over their lifetime, taking their aging into account.

[0007] For example, US Pat. No. 6,399,633 discloses a method for estimating parameters of an impedance model of a lithium-ion battery. The parameters found by measurements are implemented in a computational unit of the vehicle for use by a computational model to determine the impedance. Here, measurements are performed in the vehicle. A comprehensive overview for estimating battery parameters is also known from [1]. Furthermore, the authors present an estimation model that they developed themselves, which is described in a second paper together with the calculation results and an evaluation of the prediction accuracy, see [2]. To find the relevant model parameters, a computationally complex closed-form optimization problem is solved online on the vehicle while the vehicle is in operation. For this purpose, a recursive estimator based on the least squares method is used. This is only possible due to the linearity of the simplified computational model, since the computational resources in the vehicle are limited and the solution of the optimization problem is computationally intensive and time-consuming, and otherwise cannot be obtained on the vehicle within a reasonable time. The temperature dependence of the model parameters is also estimated on-board. The estimation of the temperature dependence deteriorates the prediction quality. Furthermore, a computationally complex iterative genetic algorithm is used for the estimation of the current dependence. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] DE102019127384A1 [Non-patent literature]

[0009] [Non-Patent Document 1] Y: C. Fleischer, W. Waag, H.-M. Heyn and DUSauer, 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 [Non-Patent Document 2] Y:C.Fleischer, W.Waag, H.-M.Heyn and DUSauer, 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 Summary of the Invention [Problem to be solved by the invention]

[0010] The problem on which the invention is based is to provide an improved method for model-based estimation of the impedance of a galvanic cell of a secondary battery, which is suitable for use in a vehicle, even during operation of the vehicle, and which has an improved prediction quality. [Means for solving the problem]

[0011] According to the invention, this problem is solved by a method for model-based estimation of the impedance of a galvanic cell of a secondary battery with the features of claim 1. Advantageous configurations and 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 implementing the method as well as a vehicle equipped with such a battery cell monitoring device are evident from the claims dependent on claim 1.

[0012] A method as mentioned in the introduction for model-based estimation of the impedance of a galvanic cell of a secondary battery by means of an estimation model executed in a calculation unit, in which at least a part of the model parameters of an equivalent circuit of the cell are adapted over the life of the cell in a cell model contained in the estimation model, the equivalent circuit including at least resistive and capacitive elements, comprises according to the invention the following method steps prior to the actual use of the cell: - an initial parameterization of a cell model based on a series of measurements by electrochemical impedance spectroscopy of cells of the same structure; a reference database including a correspondence between model parameter reference values ​​and corresponding impedance reference values ​​over the lifetime characteristic map of cells of the same structure, providing a plurality of temperature specific charge and discharge profiles, each including a voltage history of the cell over time, to an estimation model; In this case, the model parameters of the equivalent circuit to be adapted are updated using a nonlinear optimizer, the difference between the measured cell voltage and the calculated cell voltage according to the cell model is formed and minimized, and the model parameters found at the respective minimum values ​​are used to form the model parameter reference values, and calculating an impedance reference value corresponding to the model parameter reference value; forming said substrate by forming said substrate; - fitting each model parameter reference value from the reference database using a polynomial fit and storing the fitting coefficients obtained in the polynomial fit in a data memory. was carried out; and the subsequent steps during the actual use of the cell: - determining the difference between the measured cell voltage and the calculated cell voltage according to the cell model; - setting an amplification factor and multiplying the voltage difference determined in the previous step by the amplification factor; and - incrementally determining the impedance of the cell, calculating the next increment of impedance by adding the current increment of impedance to the product of the amplification factor and the voltage difference calculated in the previous method step, and then updating the variable model parameters to the next increment of impedance thus calculated, taking into account the fitting coefficients; This will be further developed by implementing the following:

[0013] The method according to the invention allows a particularly accurate and therefore reliable estimation of the impedance of the battery cell and requires a relatively small amount of calculations. The method is therefore particularly suitable for application during the operation of the vehicle. This means that there is no need to carry out an optimization in the vehicle itself to determine model parameters adapted to the respective operating state of the battery. Instead, the model parameters are first estimated in a laboratory or in a test vehicle, i.e. outside the vehicle of a commercially available vehicle, and are determined for all possible states by means of fitting. These reference values ​​are used for each real application case in a (mass-produced) vehicle. The voltage difference between the measured terminal voltage and the estimated terminal voltage, which is considered to calculate the impedance, is evaluated for each sampling period, which allows a very high time resolution.

[0014] In the method according to the invention, results on the change in electrical cell characteristics over the service life are collected offline or off-board, i.e. not during operation of the vehicle itself, but for example in a laboratory or a test vehicle. The cell characteristics are typical for a cell of a certain construction type and can therefore be transferred to cells of the same construction. Thus, the method steps carried out before the cell is put into practical use can be carried out in the laboratory on any cell of the same construction, and the method steps carried out during the cell's practical use can be carried out on another secondary battery with a corresponding cell of the same construction. Here, the secondary battery can be used in any machine, such as a vehicle, as a voltage source for operating the machine.

[0015] It is common to create an equivalent circuit of a cell and implement it in a calculation unit. However, the question arises how to adapt the model parameters, which depend on aging, to their physically correct values ​​over the life of the secondary battery. In this regard, for the type of cell considered, a complete parameterization of the estimation model or equivalent circuit, and thus the electrical part of the cell model, is carried out on the basis of electrochemical impedance spectroscopy (EIS measurements) of a brand new cell, which results in a relatively physically correct reproduction of the physical properties of this "beginning-of-life" (BOL) cell. The physical properties of the cell depend on the temperature and the state of charge. When carrying out EIS measurements, a series of different measurements are carried out for different states of charge between 0 and 100% and at temperatures between, for example, -20°C and +45°C. The temperature dependence is fitted on the basis of an Arrhenius function. The Arrhenius function describes the relationship between the reaction kinetics in the battery cell for each temperature. The Arrhenius function so found is stored and fixedly incorporated into the estimation model for further use. The dependencies for the different states of charge are stored in the estimation model in the form of elements of a look-up table. Besides the temperature dependency, the dependencies for the different states of charge (SOC) also remain constant over the life of the galvanic cell.

[0016] Here, the EIS measurements may be performed on one or more individual cells or on various cells integrated into one battery module.

[0017] In a next step, the "start" parameterization found for those (one or more) brand new cells (BOL cells) is adapted over the life of the cell. An estimation model is introduced into the battery cell monitor in order to find the evolution of all relevant model parameters that take on values ​​that change over the aging of the cell. Such a battery cell monitor comprises detection means for detecting the current that can be delivered 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 monitor comprises a data memory and a calculation unit in which the estimation model is implemented. Here, an already aged secondary battery is used, which comprises several cells of the same structure, and the discharge and charge profiles emulated or simulated or actually found for said secondary battery are recorded.

[0018] Such a discharge profile and a charging profile are generated, for example, by a test drive of the vehicle. For example, the discharging is performed during a relatively long drive of the vehicle, for example of two hours. In this case, the vehicle can also drive a corresponding electric motor in generator mode and thus supply the secondary battery with electrical energy for charging the battery cells on the basis of regeneration. The corresponding charging process lasts for a relatively short period of time, for example of the order of a few seconds. The charging profile is, for example, a charging process that is actually performed at a charging station. For example, the secondary battery is charged from a 20% state of charge to an 85% state of charge within a few minutes, for example within 40 minutes. The recording of the discharge profile and the charging profile can be performed in the vehicle itself or in a traction battery that is removed and installed on a test bench. The discharge profile and the charging profile that are actually found or that are simulated or emulated are then recorded on this test bench.

[0019] Each cell of the secondary battery exhibits different aging states over the course of its service life. Correspondingly, the individual battery cells of the traction battery considered exhibit different impedances. Using the estimation model and the measured characteristic quantities, a reference database is formed. The model parameters, which change over the service life and with the corresponding aging, are determined by means of a nonlinear optimizer. For this purpose, the estimation model compares the measured voltage values ​​with the estimated voltage values ​​and minimizes the deviation until it is minimal, ideally until it is zero. The model parameters found at the respective minimums are then used to form the model parameter reference values. These are concrete values ​​(corresponding to the series of measurements carried out). However, in the subsequent operation of the vehicle, the cells typically take on arbitrary impedance values, which are not necessarily included in the series of measurements. Nevertheless, for these impedance values, a fitting function is determined for each model parameter, which corresponds to the course of the variable model parameter with respect to the impedance, in order to include the model parameters in the reference database.

[0020] For this purpose, general polynomial fitting methods are used. Polynomials of degree n can be used. However, the use of polynomials of degree 2, i.e. quadratic functions, has proven to be particularly advantageous due to their good ratio of accuracy to computational cost.

[0021] This provides a knowledge base of what values ​​each ageing-specific model parameter takes via each impedance value, which is the core idea of ​​the present invention, since it shifts the computationally intensive optimization from the vehicle to the laboratory or test vehicle and it only has to be performed once for each different type of cell.

[0022] The calculated fitting coefficients are stored in a data memory, which is part of a computing device or a test bench. The fitting coefficients can be distributed from the data memory to any further computing unit and implemented therein, for example a battery management system for the traction battery of the vehicle.

[0023] The estimation model can then be used to estimate the impedance of the battery cells of the vehicle's traction battery during operation of the vehicle, which realizes an estimation of the impedance of the cells of the vehicle's traction battery during operation of the vehicle. For this purpose, the estimation model is implemented in a computing unit of the vehicle, such as a separate computing unit, a BMS, or a battery cell monitor.

[0024] In an advantageous development of the method according to the invention, the equivalent circuit of the cell comprises at least one of the following further additional elements: -ZARC element; - coil element; - finite length Warburg elements; and / or - Finite space Warburg elements.

[0025] The equivalent circuit of the cell is supplemented with the above mentioned elements to form a particularly realistic equivalent circuit and thus an electrical cell model, which allows the physical processes of the individual cells to be described as mathematically as possible, where the individual resistances represent the electrical resistance of conductive materials such as the conductors in the electrodes, the cables in the battery and the limited conductivity of the electrolyte.

[0026] A coil can be included in the equivalent circuit to represent the inductive properties, which arise due to the metallic contacts within the cell.

[0027] The ZARC element consists of an ohmic resistance connected in parallel with a capacitance. The ZARC element reproduces the effects of the double layer and charge transport. This allows the nonlinear voltage dependence to be taken into account. With the ZARC element the high frequency part of the cell impedance can be described.

[0028] The low frequency portion of the cell impedance can be described using Warburg elements, which capture the process describing the relatively slow ion diffusion in the electrodes. Finite space Warburg elements represent non-conductive boundary layers at the maximum diffusion length, whereas finite length Warburg elements represent perfectly conductive boundary layers at the maximum diffusion length.

[0029] According to another advantageous embodiment of the method, the voltage difference between the measured cell voltage and the calculated cell voltage is low-pass filtered before multiplication with the amplification factor, so that the parametric simulation of the model parameters is stable and short-term model errors can be differentiated as far as possible from parameter learning errors.

[0030] In another advantageous configuration of the method, the cell model considers one term each for the overvoltage, the hysteresis voltage and the no-load voltage to calculate the cell voltage, where the no-load voltage is approximated by a weighted average value of the low-pass filtered difference of the terminal voltage and the overvoltage and the no-load voltage calculated by current integration. For example, the hysteresis stress is provided by a parallel software module according to the modified Plett model published by D. Wycisk, M. Oldenburger, M. G. 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 no-load voltage is approximated by a weighted average value of two different voltage estimates: a first voltage estimate is obtained from the low-pass filtered difference of the terminal voltage and the overvoltage, and a second voltage estimate is obtained from the no-load voltage calculated by current integration.

[0031] According to a further advantageous configuration of the method according to the invention, the amplification factor is determined in dependence on the following four terms: -Basic amplification term; - battery current sign term; - the power term of the absolute value of the cell current; and -Exponential decay term.

[0032] The amplification factor may be greater than, less than, or equal to 1, and may be positive or negative.

[0033] The sign of the battery current can be used to take into account whether the cell is currently being charged or discharged.

[0034] The power term of the absolute value of the cell current controls the order of cell overvoltage for which the residual error is smallest. Higher values ​​improve agreement for high overvoltages and fault tolerance for low overvoltages, and vice versa.

[0035] The exponential decay term allows for faster learning of the model parameters after a parameter reset, using a decay constant that accelerates learning of the reset parameters, and can further include a coefficient that allows for slower learning immediately after controller startup before the voltages of the model RC elements are learned through dynamic charging and discharging.

[0036] In a battery cell monitoring device comprising detection means for detecting the current available from at least one cell of a secondary battery, the terminal voltage and the battery temperature of the cell, as well as a data memory and a calculation unit, the detection means, the data memory and the calculation unit are designed according to the invention to carry out the method steps carried out during the actual use of the cell. The battery cell monitoring device may be part of a battery management system or may form such a battery management system. As detection means, the battery cell monitoring device may include or be connected to current, voltage and temperature sensors. The data memory is a non-volatile memory, complemented by a volatile memory if necessary. The calculation unit is a computer, a system on chip (SoC) or the like. The data memory may be integrated in the calculation unit.

[0037] The 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 powertrain, the method steps being carried out during the actual use of the cells being carried out in the vehicle. As described above, the method according to the invention can be used to estimate the ageing state of the battery cells of the traction battery of the vehicle particularly accurately and therefore particularly reliably. This is synonymous with the impedance of each cell. The cells are, for example, lithium-ion batteries. However, the method according to the invention is also suitable for different types of battery cells, such as, for example, sodium-ion batteries.

[0038] In a vehicle with an at least partially electrified powertrain, including a traction battery and a battery cell aging identification device, according to the invention, the battery cell aging identification device comprises a battery cell monitoring device as described above. The battery cell aging identification device may be a higher-level computing unit of the battery cell monitoring device. The battery cell monitoring device may be an integrated component of the battery cell aging identification device. For example, the battery cell aging identification device may be a battery management system in which the battery cell monitoring device is integrated.

[0039] Further advantageous configurations of the method according to the invention for model-based estimation of the impedance of a galvanic cell of a secondary battery will become apparent from the exemplary embodiments which are explained in more detail below with reference to the drawings. [Brief description of the drawings]

[0040] [Figure 1] 1 shows a schematic diagram of a battery cell monitoring device according to the present invention; [Diagram 2] 2 shows a schematic diagram of an equivalent circuit of a cell implemented in a cell model of an estimation model executed in the battery cell monitoring device shown in FIG. 1 and an impedance spectrum belonging thereto. [Diagram 3] 13 shows a graph illustrating the progression of model parameters of components included in an equivalent circuit over the impedance of a cell. [Figure 4] The equation set of equations stored in the estimated model is shown. [Diagram 5] 2 shows a flow chart of a method according to the invention for estimating the impedance of a galvanic cell of a secondary battery. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0041] The battery cell monitor 8 depicted in Fig. 1 comprises a calculation unit 3 that is used to execute an estimation model 4. Using the battery cell monitor 8, the cells 1 of the secondary battery 2 are monitored, thereby estimating an impedance that depends on the ageing of the cells 1 over the lifetime of the secondary battery 2. The estimated impedance can be used to provide information regarding the ageing of the secondary battery 2.

[0042] A unique battery cell monitoring device 8 may be provided for each cell 1 of the secondary battery 2, however, multiple cells 1 may also be monitored by one and the same battery cell monitoring device 8. As input quantities, the estimation model 4 includes the current I flowing through each cell 1, the measured voltage U mes The terminal voltage U of the secondary battery 2, also referred to as the charge voltage V, the temperature T of the cells 1 to be preferably monitored, and the calculated estimated state of charge SOC of each cell 1 are used. The state of charge SOC is provided in a conventional manner and is determined, for example, by a battery management system BMS, which may be part of the calculation unit 3 or, as shown, may be provided separately from the calculation unit 3.

[0043] Estimation model 4 is the measured voltage U mes The cell model 6 includes an electrical cell model 6.1 and a thermal cell model 6.2. The electrical cell model 6.1 determines the resistance of the cell 1 under consideration as an output quantity, or the loss current P loss The thermal cell model 6.2 outputs the temperature T abg The estimation model 4 further comprises a reference database 7 which contains the evolution of the model parameters contained in the electrical cell model 6.1 of the equivalent circuit over the service life.

[0044] Using cell model 6, calculate voltage U ber is calculated. Measurement voltage U mes and the calculated voltage U berare combined and subtracted from each other in a subtractor 10 to determine a difference between the characteristic quantities. It is important to minimize this difference, which is referred to here as the error ε. This means that the error ε is zero if the model parameters of the equivalent circuit 5 or the electrical cell model 6.1 shown in FIG. 2, which depend on the service life of the cell 1, correspond to the actual physical values. The error ε can optionally be passed through a filter module 11 for smoothing, for example with a low-pass filter. The error ε is then fed to a control system 12, for example a PID controller. As a result, the control system 12 feeds the determined aging state of the cell 1 in the form of an estimated internal resistance, i.e. an impedance. The impedance is also referred to as SOHR (State-of-Health-Resistance). The impedance is fed back in the estimation model 4 and is used as an input quantity for the cell model 6. Similarly, the impedance can be derived from the estimation model 4, or even from the calculation unit 3, to serve as an input quantity for another calculation model, for example an input quantity for a driver assistance system.

[0045] In the illustrated structure of the estimation model 4, the impedance is calculated iteratively, i.e. incrementally, so that the most recent increment of impedance fed back is used to calculate the next increment.

[0046] 2 shows the structure of an electrical equivalent circuit 5 of each cell 1. This equivalent circuit 5 includes a resistive element R, two consecutive ZARC elements ZARC, followed by two consecutive Warburg elements, where the two Warburg elements are a finite space Warburg element FSW and a finite length Warburg element FLW. The ZARC element itself includes a capacitive element C connected in parallel to the resistive element R.

[0047] In figure 2, below the equivalent circuit 5, the impedance spectrum of each element as well as the impedance spectrum of the complete model are also shown: on the horizontal axis the real part of the impedance is plotted and on the vertical axis the imaginary part of the impedance is plotted in ohms.

[0048] In order to execute the estimation model 4 in the vehicle at high speed and with high computational efficiency, correlations are required that describe what values ​​each model parameter of the equivalent circuit 5, i.e., impedance or SOHR (State-Of-Health-Resistance), takes depending on the aging state of the cell 1. These correlations are stored in a reference database 7 shown in FIG.

[0049] FIG. 3 is a graphical illustration of the process for obtaining the information stored in the reference database 7. The provided calculation model is used for the analysis of a real battery in a test environment. The real battery contains a number of cells 1 with different degrees of aging. The calculation model is parameterized beforehand on the basis of EIS measurements of new cells. Here, the course of the model parameters of the impedance is determined. Exemplarily, in FIG. 3 a course for the individual resistance R is shown. In this regard, simulated or emulated real discharge and charge profiles of an aged secondary battery 2 are recorded, for example in a laboratory, a test bench or a test vehicle. In order to determine the course of the individual model parameters of the impedance or the SOHR (State-Of-Health-Resistance), an optimization algorithm is used. The optimization algorithm has the task of minimizing the error ε in the estimation model 4. In so doing, the respective values ​​of the model parameters are changed. Thereby, for each cell 1 to be examined, for each measurement point in the characteristic map of the discharge and charge profiles, respectively, for the individual cells 1 of the battery, corresponding model parameters are obtained (black circles in the graph).

[0050] However, since in real operation values ​​for all impedance values ​​are required, i.e. not only where the black dots are located in the graph but also the continuous course, a fitting is performed, whereby a best-fit curve 13 is obtained. The fitting coefficients determined for determining the best-fit curve 13 are stored in the reference database 7. Thus, it is realized that adapted model parameter values ​​are determined for all values ​​of impedance, i.e. SOHR (State-Of-Health-Resistance). In this case, it is not necessary to perform the optimization again in the calculation unit 3, i.e. in each vehicle, during subsequent operation, which significantly reduces the calculation costs and therefore realizes a very fast implementation in terms of time of the method according to the invention and thus the calculation of the impedance.

[0051] FIG. 4 shows a set of equations that can be stored in a computational model.

[0052] Equation 1G-1 describes the formula for defining the various model parameters. Term 1-0 represents each model parameter. Term 1-1 describes each order of the model parameters and is used to scale all model parameters to the same order. Term 1-2 describes the coefficients. Term 1-3 represents the original impedance. The impedance exhibits the exponent j. Ideally, j=2. This is a compromise between a sufficiently fast calculation and sufficiently accurate results. The formula is a second order polynomial.

[0053] Equation 2G-2 is used to describe the voltage difference at the subtractor 10. The term 2-0 represents the measured voltage U mes and calculated voltage U ber The index "n" refers to the current increment or iteration, i.e., multiple iterations are performed during the sampling or calculation step. Term 2-1 describes a filter constant that can take values ​​between 0 and 1, where α is much smaller than 1. Term 2-2 describes the measured voltage U for the current increment. mes Corresponding to this, item 3-0 is the calculated voltage U for the current increment.ber Terms 2-4 correspond to the voltage difference for the previous increment "n-1".

[0054] Equation 3 G-3 is the calculated voltage U ber is used to describe the overvoltage. Term 3-1 corresponds to the overvoltage. Term 3-2 corresponds to the no-load voltage. Term 3-4 corresponds to the hysteresis voltage. Term 4-0 corresponds to the low-pass filtered difference of the clamp voltage and the overvoltage, and term 3-3 corresponds to the no-load voltage calculated by current integration. The characteristic quantity β is a weighting and filter constant and can take values ​​between 0 and 1.

[0055] Equation 4G-4 describes the calculation of item 4-0. Item 4-1 is the measurement voltage U mes Term 4-2 describes the increment of the preceding term 4-0.

[0056] Equation 5G-5 is used to describe the impedance at the next increment "n+1", i.e., the State-Of-Health-Resistance (SOHR). Term 5-0 corresponds to the impedance of cell 1. It consists of term 5-1, i.e., the impedance for current increment "n", plus the product of both terms, term 6-0 and term 2-0, where term 6-0 corresponds to the amplification factor and term 2-0 corresponds to the voltage difference mentioned above.

[0057] Equation 6 G-6 represents the calculation rule for determining the amplification factor. Term 6-1 indicates the basic amplification for feeding back the voltage difference. Term 6-2 describes the sign of the battery current. Term 6-3 describes the power term of the absolute value of the cell current, which controls the order of cell overvoltage with the smallest residual error. The characteristic quantity v can take values ​​between 0 and 1. A higher v value improves the agreement in the case of high overvoltage and increases the fault tolerance in the case of low overvoltage. The reverse relationship also holds. Term 6-4 describes the exponential decay term. Term 6-4.1 describes the decay time t after the parameter reset. absallows for a K0'' times faster learning of the parameters in . The decay constant λ determines the time decay rate of this additional amplification to accelerate the learning of the reset parameters. Item 6-4.2 allows for a K0'' times slower learning from the moment the computation unit 3 is started up until the voltages at the RC elements of the model are learned by dynamic charging and discharging.

[0058] Figure 5 shows an implementation of an estimation model 4 in an embedded system in the form of a flow chart to explain the method steps of the method according to the invention executed in a vehicle. The embedded system is formed by a calculation unit 3 representing a discrete-time controller. Preferably, this is a fixed-point implementation, which improves performance while reducing memory consumption compared to a floating-point implementation in the embedded system. In Figure 5, the calculation unit 3 may preferably be the battery management system of the vehicle. For example, the tick rate of the battery management system is set to a frequency of 50 Hertz.

[0059] The real-time operating system RTOS of the computation unit 3 is triggered by an initialization event to execute an initialization call 550, on the basis of which the cell model 6 is initialized. For this purpose, the values ​​stored for the model parameters during the last execution time, i.e. before the shutdown of the computation unit 3, are read from the non-volatile memory EEPROM and subsequently written to the volatile memory RAM. In method step 501, the ageing-dependent model parameter curves are read from the reference database 7. In method step 502, the last processed voltage values ​​are read. In method step 503, the voltage distributions for the RC elements of the cell model 6 are read. In method step 504, the RC voltages are newly calculated before the computation unit 4 goes into sleep mode.

[0060] The computing unit 3 or the real-time operating system RTOS then executes a cyclic call of the executable main function of the estimation model 4 in method step 560. In method step 505, the measured cell voltages, currents and estimated cell temperatures are detected, whereby, if necessary, a phase adaptation of the measured voltage values ​​is performed in order to synchronize the current and voltage signals. The subsequent method steps 506 to 515 can be performed successively for a number of cells 1, preferably all cells 1, of the secondary battery 2. For this purpose, the method steps 506 to 515 can be realized, for example, as a FOR loop which is repeated over the individual cells 1. Here, in method step 506, the cell iterations are counted.

[0061] In method step 507, ageing-dependent model parameters for the current impedance are calculated, processing values ​​written from the reference database 7 into the volatile memory RAM.

[0062] The already mentioned Arrhenius equation and the correlation with temperature are also taken into account. This is carried out in method step 508 together with a calculation step taking into account the state of charge SOC. In method step 509, the sleep duration of the calculation unit 3 is read out and handed over to the model. This is necessary after a restart in order to determine the voltage values ​​of the RC elements in method step 511. For this purpose, the corresponding voltage values ​​are required to be read out from the volatile RAM memory before the calculation unit 3 goes to sleep. Now, in process step 510, it is checked whether the calculation unit 3 is being initialized after start-up.

[0063] In method step 512, a forward calculation is carried out in order to calculate the terminal voltage, the cell voltage and the heat loss as output signals. The considered aging factor, i.e. the impedance, is tracked via feedback of the voltage values. The updated aging factor, i.e. the calculated impedance for the following increment, is fed back in order to adapt the calculation of the model parameters. In method step 513, it is checked whether the current exceeds the current minimum value and, in so doing, whether the change in current exceeds the corresponding limit value. If so, in method step 514, the impedance is updated and written to the volatile memory RAM. In method step 515, it is checked whether the cell is the last cell 1 to be monitored.

[0064] In method step 570, the real-time operating system RTOS triggers a shutdown sequence. For this purpose, in method step 516, the voltages of the Warburg elements and the current model parameters (i.e. the model parameters adapted as a function of aging) are written into the volatile memory EEPROM for each cell 1. In method step 517, the voltage distribution of the individual Warburg elements with respect to the RC voltage is likewise written into the non-volatile memory EEPROM, but however only for a single cell 1. In method step 518, the impedances of the individual cells 1, i.e. the aging coefficients, are stored. With this, the method ends.

Claims

1. A method for model-based estimation of the impedance of a galvanic cell (1) of a secondary battery (2) using an estimation model (4) implemented in a calculation unit (3), comprising: In the method, at least a part of model parameters of an equivalent circuit (5) of the cell (1) is adapted over the useful life of the cell (1) in a cell model (6) included in the estimation model (4), the equivalent circuit (5) including at least a resistive element (R) and a capacitive element (C), Prior to the actual use of said cell (1), the following method steps are carried out: - an initial parameterization of said cell model (6) based on a series of measurements by electrochemical impedance spectroscopy of cells (1) of identical structure; a reference database (7) containing a correspondence between model parameter reference values ​​and corresponding impedance reference values ​​over the lifetime characteristic maps of said identically structured cells (1), - feeding the estimation model (4) with a plurality of temperature specific charge and discharge profiles, each including a voltage history of the cell (1) over time; In this case, a nonlinear optimizer is used to update the model parameters to be fitted to the equivalent circuit (5) and to measure the measured cell voltage (U ｍｅｓ ) and the calculated cell voltage (U ｒｅｃ ) and minimizing the difference between them, and using the model parameters found at each minimum to form the model parameter reference values; and - calculating impedance reference values ​​corresponding to said model parameter reference values; forming said substrate by - fitting each model parameter reference value from said reference database (7) using a polynomial fit and storing the fitting coefficients obtained in the process in a data memory; and the following subsequent method steps carried out during the actual use of said cell (1): - measured cell voltage (U ｍｅｓ ) and the calculated cell voltage (U ｒｅｃ ) a step of calculating the difference between the - setting an amplification factor and multiplying said difference of voltages determined in the previous method steps by said amplification factor; and - incrementally determining the impedance of the cell (1), calculating the next increment of impedance by adding the current increment of impedance to the product of the amplification factor and the difference in voltage, calculated in the previous method step, and then updating the variable model parameters to the next increment of impedance thus calculated, taking into account the fitting coefficients; The method, characterized by:

2. The equivalent circuit (5) of the cell (1) includes the following additional elements: - ZARC element (ZARC); - coil elements; - Finite length Warburg elements (FLW); and / or - finite space Warburg elements (FSW), 2. The method of claim 1, further comprising at least one of:

3. The measured cell voltage (U ｍｅｓ ) and the calculated cell voltage (U ｒｅｃ 3. The method according to claim 1, wherein the difference of the voltage with respect to the amplification factor is low-pass filtered before being multiplied by the amplification factor.

4. The cell model (6) is ｒｅｃ 4. The method according to claim 1, further comprising taking into account one term each (3-1, 3-3, 3-2) for the overvoltage, the hysteresis voltage and the no-load voltage in order to calculate the overvoltage.

5. The amplification coefficients are the following four terms (6-1, 6-2, 6-3, 6-4): - base amplification term; - the sign term of the battery current; - the power term of the absolute value of the cell current; and - exponential decay term, 5. The method according to claim 1, wherein the determination is made in dependence on

6. A battery cell monitoring device (8) comprising detection means for detecting a current that can be output from at least one cell (1) of a secondary battery (2), a terminal voltage and a battery temperature, as well as a data memory and a calculation unit (3), The battery cell monitoring device (8), characterized in that the detection means, the data memory and the calculation unit (3) are designed to perform the method steps of the method according to any one of claims 1 to 5, carried out during actual use of the cell (1).

7. Use of the method according to any one of claims 1 to 5 for determining the service life of battery cells of a traction battery of a vehicle with an at least partially electrified powertrain, comprising: The use, wherein the method steps performed during actual utilization of the cell (1) are performed in the vehicle.

8. A vehicle having an at least partially electrified powertrain including a traction battery and a battery cell aging identification device, 7. The vehicle, wherein the battery cell aging specification device comprises a battery cell monitoring device (8) according to claim 6.

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