Method for determining at least one estimated operating parameter of a battery

Abstract

The invention relates to a method for determining at least one estimated operating parameter (9) of a battery (1), having the steps of: receiving at least one measured operating parameter (5) of the battery (1); and determining the at least one estimated operating parameter (9) from the at least one measured operating parameter (5) using a mathematical battery model (10) which is based on an equivalent circuit diagram (11) of the battery (1), said equivalent circuit diagram comprising at least one RC circuit (13), wherein the battery model (10) defines, on the basis of model parameters (12), a relationship between a battery voltage (U Cell) being applied to the battery (1) and a battery current (I Cell) flowing through the battery (1), said model parameters comprising at least one time constant and / or at least one electric resistance (R 0, R 1) with respect to the equivalent circuit diagram (11), and the battery model (10) takes into consideration the nth power of a Taylor series of the at least one time constant and / or of the at least one electric resistance (R 0, R 1) at a working point of the battery (1), where n > 0.

Description

[0001] METHOD FOR DETERMINING AT LEAST ONE ESTIMATED

[0002] BATTERY OPERATING PARAMETERS

[0003] Technical area

[0004] The present invention relates to a computer-implemented method for determining at least one estimated operating parameter of a battery. Furthermore, the invention relates to a data processing device, a battery management system, a battery, a computer program, and a computer-readable medium for executing the method.

[0005] State of the art

[0006] To maximize the service life of a battery, such as a traction battery for an electric vehicle, the current maximum performance of the battery and / or its permissible operating range should be known at all times. To this end, the dynamic behavior of the battery can be represented in a multidimensional state space, which can be parameterized by various state variables such as temperature, state of charge, and / or current.

[0007] The mathematical modeling of the battery can, for example, be based on an equivalent circuit of the battery, which can include one or more RC elements. The model parameters of such a model can be defined with respect to various operating points of the battery, such as certain states of charge and / or temperatures. Typically, time constants and certain resistances in the vicinity of an operating point are assumed to be constant. This assumption enables sufficiently accurate predictions for relatively short prediction periods and / or relatively low current amplitudes. However, especially with sporty driving styles, it is important that accurate predictions regarding the battery's performance can also be made for longer periods.

[0008] Forecast periods and / or higher current amplitudes can be determined.

[0009] Description of the invention

[0010] The object of the invention is to improve the estimation of operating parameters of a battery. In particular, the object of the invention can be seen in providing a method that improves the estimation with longer prediction periods and / or higher current amplitudes in terms of accuracy and / or computational efficiency.

[0011] This object is achieved by the subject matter of the independent claims. Advantageous developments of the invention are specified in the dependent claims, the description, and the accompanying figures.

[0012] A first aspect of the invention relates to a computer-implemented method for determining at least one estimated operating parameter of a battery.The method comprises at least the following steps: receiving at least one measured operating parameter of the battery; and determining the at least one estimated operating parameter from the at least one measured operating parameter using a mathematical battery model based on an equivalent circuit of the battery comprising at least one RC element, wherein the battery model defines a relationship between a battery voltage applied to the battery and a battery current flowing through the battery as a function of model parameters that comprise at least one time constant and / or at least one electrical resistance with respect to the equivalent circuit, wherein the battery model takes into account an n-th power of a Taylor series expansion of the at least one time constant and / or the at least one electrical resistance around an operating point of the battery, where n > 0.

[0013] In other words, the relevant model parameter can be approximated in the vicinity of the operating point as the development center using an nth-degree approximation polynomial with n > 0. Thus, the model parameter can be linearized in the vicinity of the operating point (instead of being assumed to be approximately constant, as previously). This enables very accurate estimates even at high battery currents and / or long prediction periods, for example, of 10 s or longer, especially of 20 s or longer.

[0014] Nevertheless, an analytical solution of the battery model, i.e. the system of differential equations simulating the equivalent circuit, is enabled, which improves computational efficiency and / or reduces memory requirements.

[0015] The process can be carried out automatically by a processor.

[0016] The battery may comprise one or more galvanic battery cells, which may be connected in series and / or parallel to form the battery.

[0017] The battery model can be time-variant, meaning the model parameters can be continuously updated during battery operation, for example, to account for aging effects. The dynamic behavior of the battery typically changes with increasing battery age. To account for this, a suitable parameter estimator can be provided to adjust the model parameters, for example, an extended Kalman filter. A time-invariant battery model is also conceivable.

[0018] The electrical resistance can, for example, be an ohmic resistance, also called (equivalent) series resistance, or a resistance of the RC element. The time constant can be equal to the product of the resistance and the capacitance of the RC element.

[0019] The measured operating parameter(s) may have been determined by a sensor system, which may, for example, be part of the battery and / or a battery management system for monitoring and / or controlling the battery. The sensor system may, for example, comprise one or more current, voltage, and / or temperature sensors.

[0020] Examples of possible measured and / or estimated operating parameters include the electrical battery voltage applied to the battery terminals (with or without load), the electrical battery current flowing through the battery, or the battery temperature. Other examples of possible estimated operating parameters include the state of charge (SOC), the state of health (SOH), the state of power (SOP), an upper or lower voltage limit, an upper or lower temperature limit, an upper or lower current limit, a charging power, a discharging power, an available energy, or a removable energy from the battery.

[0021] The SOC can be interpreted as the battery's filling level in percent, with 100% corresponding to a fully charged battery. The SOC can be determined, for example, by integrating the (measured) battery current.

[0022] The state of aging (SOH) can be a parameter that quantifies the battery's ability to provide a requested power compared to the battery in its new state.

[0023] The power state (SOP) can be a parameter that quantifies the battery's ability to deliver a currently requested power in its current state—i.e., its performance capability. The power state (SOP) can depend on the battery's state of charge (SOC), its state of aging (SOH), and its temperature.

[0024] The operating point can be defined, for example, by the state of charge and / or the temperature of the battery and / or by a temporal progression of at least one of these two variables.

[0025] The model parameters can, for example, have been determined for each operating point from a set of predefined operating points or can be determined continuously, for example for charge states from 0% to 100%, which can follow one another with a certain step size (e.g. 1%, 5% or 10%).

[0026] Other examples of possible model parameters are an open circuit voltage of the battery, the capacity of the RC element and / or the battery or a voltage drop across the capacity of the RC element.

[0027] The battery model can also be based on two or more RC elements, which can be connected in series, for example. While this can improve accuracy, it can also significantly increase resource consumption. If battery aging is not taken into account, the approach presented here can also be advantageously applied to such an equivalent circuit model with multiple RC elements. Thus, an improvement in the validity range and / or prediction accuracy can be achieved compared to a comparable conventional equivalent circuit model.

[0028] Depending on the number of RC elements, the model parameters can also include several time constants and / or several electrical resistances, whose n-th powers of the Taylor series expansion around the operating point as the center of expansion (with n > 0) can be taken into account by the battery model in the same or similar way as with only one RC element.

[0029] A battery management system and its software are typically required to estimate the battery's balance and current state and to perform power prediction for different time periods, e.g., "short," "medium," and "long." Power prediction is necessary to enable a driver request, for example, when the driver presses the accelerator pedal. At very low states of charge, it should be ensured that the battery voltage does not fall below a certain voltage limit when the predicted power is released. For this purpose, a battery model based on an equivalent circuit can be implemented in the battery management system's software, which may include one or more RC elements.

[0030] The accuracy of the battery model should be just as good for medium and long prediction times as for short prediction times, especially at high discharge currents. This can be the case, for example, during sporty driving. The approach described here enables very accurate power prediction even for medium and long prediction times. In addition to power prediction, other applications are possible. For example, the approach presented here can be transferred to higher-level battery or equivalent circuit models and / or used to improve a Kalman filter or other parameter estimator.

[0031] An equivalent circuit with a single RC element can be described by a system of two first-order differential equations. A special analytical solution for the differential equations exists, which can be used to find a fitting function. By comparing the values ​​of the fitting function with measured values, an appropriately optimized parameter set can be generated.

[0032] For this specific analytical solution, certain assumptions were previously made regarding the dependencies of the parameters. In order to be able to compare the values ​​of the analytical solution with the measured values, certain restrictions also applied regarding the magnitude and duration of the current loads. The validity range of the resulting fully parameterized battery model at a given accuracy is therefore limited. Exceeding the validity range would therefore result in lower accuracy. This problem can now be solved by at least partially disregarding the previous assumptions that were usually made when deriving the analytical solution.

[0033] Put simply, the approach presented here is based on a mathematical battery model that, in terms of validity and accuracy, lies between an equivalent circuit model with only one RC element (also called a 1-RC model) and an equivalent circuit model with two RC elements (also called a 2-RC model). A parameter estimator for (continuously) estimating the model parameters, for example to account for battery aging, can therefore be significantly less complex than standard 2-RC models. The hardware requirements of such a simplified parameter estimator are roughly comparable to those of a conventional 1-RC model. The time horizon for power prediction is also longer, meaning that the available power of the battery can be predicted for a longer period with the same accuracy.

[0034] This allows the available memory (RAM) and CPU performance of a battery management system to be used more efficiently, meaning that additional (and more complex) algorithms can be implemented without significant hardware changes. Under certain circumstances, efficiency can be improved to such an extent that even less powerful and correspondingly cheaper hardware components could be used without any performance loss. Such a method enables, for example, improved battery health detection in electric vehicles, thus ensuring gentle and safe battery operation throughout its lifetime.

[0035] A second aspect of the invention relates to a data processing device having a processor configured to execute the method described above and below. The data processing device may comprise hardware and / or software modules. In addition to the processor, the data processing device may comprise a memory and data communication interfaces for data communication with peripheral devices. The data processing device may, for example, be a controller of a battery management system, a control unit of a vehicle, a PC, server, laptop, or mobile device in the form of a smartphone or tablet. The term "vehicle" may be understood to mean a vehicle equipped with an electric drive, for example a car, truck, bus, motorcycle, or autonomously moving robot.

[0036] Features of the method can also be understood as features of the data processing device and vice versa.

[0037] A third aspect of the invention relates to a battery management system comprising a sensor system for determining at least one measured operating parameter of a battery and a data processing device as described above and below. The sensor system can be arranged, for example, in and / or on a housing of the battery.

[0038] A fourth aspect of the invention relates to a battery, in particular a lithium-ion battery, for example a battery for supplying an electric drive of an electric vehicle with electrical energy. The battery comprises the data processing device described above and below or the battery management system described above and below.

[0039] Further aspects of the invention relate to a computer program and a computer-readable medium on which the computer program is stored. The computer program comprises instructions that, when the computer program is executed by the processor, cause the method described above and below.

[0040] The computer-readable medium may be a volatile or non-volatile data storage device. For example, the computer-readable medium may be a hard disk, a USB storage device, RAM, ROM, EPROM, or flash memory. The computer-readable medium may also be a data communications network that enables downloading of program code, such as the Internet or a data cloud.

[0041] Features of the method described above and below may also be understood as features of the computer program and / or the computer-readable medium and vice versa.

[0042] Possible features and advantages of embodiments of the invention may be considered, among other things, and without limiting the invention, as being based on the ideas and findings described below.

[0043] It is possible for the at least one measured operating parameter to be received in several consecutive journals. This can be understood to mean that at least one measured value for the same measured operating parameter or at least one measured value for different measured operating parameters is received in each journal. The at least one estimated operating parameter can be determined in a current journal from the measured values ​​of different time steps, for example from the measured value or values ​​of the current time step and the time step immediately preceding the current journal. For example, the at least one estimated operating parameter can be determined in the current journal for at least one future journal following the current journal.

[0044] The at least one estimated operating parameter can be determined, for example, using a Kalman filter, in particular an extended Kalman filter, and / or a particle filter. What was stated above with regard to the determination of the estimated operating parameter(s) can also apply correspondingly to a (continuous) estimation of the model parameters.

[0045] According to one embodiment, n = 1. In other words, the battery model can consider a linearization of the at least one time constant and / or the at least one electrical resistance when determining the at least one estimated operating parameter. Experiments have shown that, contrary to conventional assumptions that only constant approximations of the time constant or the electrical resistance allow for an analytical solution, the prediction accuracy can be significantly improved in this way without requiring additional computational resources.

[0046] According to one embodiment, the battery model may be defined by the following equation: where U Cell the battery voltage, I Cell is the battery current, τ is the time constant, SOC is the state of charge of the battery, T is the temperature of the battery, and λ, ψ, η are coefficients (independent variable is time t). For example, ICell be constant. The linear term tψ was also clearly evident in measurements for long pulse durations and high current amplitudes.

[0047] According to one embodiment, at least one of the coefficients λ, ψ, η can be defined as a function of the n-th power of the Taylor series expansion of the at least one electrical resistance around the state of charge SOC(t0) as the operating point. For example, each coefficient λ, ψ, η can be defined by a different coefficient equation. The state of charge SOC(t0) can be a reference state of charge, for example an initial state of charge of the battery, at a reference time t0, for example an initial time. The coefficients can have been determined experimentally and / or optimized by comparison with suitable measurements. It is possible for the coefficients to be continuously updated during operation of the battery, i.e. online.

[0048] The coefficients can be stored, for example, in the form of lookup tables for different operating points. Alternatively, the coefficients can be calculated using mathematical functions (the coefficient equations).

[0049] According to one embodiment, the coefficient λ can be defined as a function of the n-th power of the Taylor series expansion of a resistance of the RC element as the electrical resistance.

[0050] According to one embodiment, the coefficient η can be defined as a function of the n-th power of the Taylor series expansion of an ohmic resistance as the electrical resistance.

[0051] According to one embodiment, the coefficient ψ can be defined as a function of the n-th powers of the Taylor series expansions of different electrical resistances, for example as a function of a first n-th power for the ohmic resistance and a second n-th power for the resistance of the RC element.

[0052] According to one embodiment, at least one of the coefficients λ, ψ, η can additionally be defined as a function of the battery current, i.e., its magnitude and / or direction. For example, each of the coefficients λ, ψ, η can be defined as a function of the battery current. Contrary to conventional assumptions, according to which the model parameters are assumed, at least initially, to be independent of the battery current, the accuracy of the method can be significantly improved in this way, especially at higher battery currents.

[0053] According to one embodiment, at least one of the coefficients λ, ψ, η can additionally be defined as a function of the time constant. For example, the coefficient A can additionally be defined as a function of the time constant. According to one embodiment, at least one of the coefficients λ, ψ, η can additionally be defined as a function of an n-th power of a Taylor series expansion of an open circuit voltage of the battery around the state of charge SOC(t0), where n > 0, in particular where n = 1. The open circuit voltage can, for example, have been determined as an open circuit voltage curve as a function of the state of charge SOC. For example, the coefficients ψ and η can additionally be defined as a function of the n-th power of the Taylor series expansion of the open circuit voltage.

[0054] Short character description

[0055] Advantageous embodiments of the invention are further explained below with reference to the accompanying drawings, wherein neither the drawings nor the explanations are to be interpreted as limiting the invention in any way.

[0056] Fig. 1 shows a battery according to an embodiment of the present invention.

[0057] Fig. 2 shows an equivalent circuit diagram for use in a method according to an embodiment of the present invention.

[0058] Fig. 3 shows an estimated voltage curve determined in a method according to an embodiment of the present invention, compared to a measured voltage curve at a first operating point.

[0059] Fig. 4 shows an estimated voltage curve determined in a method according to an embodiment of the present invention, compared to a measured voltage curve at a second operating point.

[0060] The figures are merely schematic and not to scale. The same reference numerals designate the same or equivalent features in the various drawings.

[0061] Detailed description

[0062] Fig. 1 shows a battery 1, for example, a lithium-ion battery for supplying an electric drive of an electric vehicle with electrical energy. The battery 1 comprises a plurality of galvanic battery cells 2, which can be connected in series and / or parallel.

[0063] In addition, the battery 1 comprises a battery management system 3 with a sensor system 4 for determining at least one measured operating parameter 5 of the battery 1 and a data processing device 6. The sensor system 4 can, for example, comprise one or more voltage, current and / or temperature sensors, which can be placed on and / or in a housing of the battery 1.

[0064] The data processing device 6, for example a microcontroller, comprises a processor 7 which is configured to determine at least one estimated operating parameter 9 from the measured operating parameter(s) 5 by executing a computer program stored in a memory 8, using a method described in more detail below.

[0065] The estimated operating parameter(s) 9 are determined using a mathematical battery model 10 based on an equivalent circuit 11 of the battery 1 (see Fig. 2) and comprising several model parameters 12. In particular, the battery model 10 can be an equivalent circuit model with only one RC element 13 consisting of a resistor R1 and a capacitor C1, which makes the method particularly computationally efficient.

[0066] For example, the model parameters 12 may include one or more of the following quantities of the equivalent circuit 11: an ohmic resistance R0, the resistance R1, the capacitance C1, a voltage drop U1 across the capacitance C1, and a time constant τ = R1C1.

[0067] In addition, Fig. 2 shows a battery current I flowing through the battery 1 Cell , a battery voltage U applied to battery 1 Cell , an open circuit voltage U OCV . a current I C1 by the capacitance C1 and a current IR1 through the resistor R1.

[0068] For example, the battery current I Cell and a temperature T of the battery 1 are received as measured operating parameters 5 in the data processing device 6, wherein the battery voltage U Cell can be determined by the data processing device 6 as the estimated operating parameter 9. Further examples of the estimated operating parameter 9 are a state of charge SOC, an aging state SOH, a power state SOP, an upper or lower voltage limit, an upper or lower temperature limit, an upper or lower current limit, a charging power, a discharging power, an available energy, or a removable energy of the battery 1.

[0069] To determine the estimated operating parameter(s) 9, the battery model 10 can consider (for example, in addition to a zeroth) a first power of a Taylor series expansion of the time constant τ and / or at least one of the resistances R0, R1 around an operating point of the battery 1 as the center of expansion. The operating point can be defined by the state of charge SOC and / or the temperature T. The values ​​of R and C depend on the temperature T and the state of charge SOC.

[0070] Battery Model 10 is described in more detail below.

[0071] The simulated voltage response is according to the equivalent circuit diagram 11 : U Cell (SOC(t), T(t)) (1)

[0072] = U OCV (SOC(t), T(t)) + R0(SOC(t), T(t))I Cell (t) + U1(SOC(t),T(t)) where U1(t) is the solution of the differential equation. where C Cellis the capacity of a battery cell 2 (battery 1 here comprises 36 battery cells, for example).

[0073] The values ​​of R and C can be determined via parameter identification. The parameterization can be performed using a fitting function determined by a special analytical solution of the differential equations, for example, for pulse discharges and a rest period after a constant charge and / or discharge.

[0074] In addition to parameterization, the fit function can also be used for other tasks, for example

[0075] • to determine a limit current at a given state of charge, temperature and voltage limit for performance prediction in electric vehicles,

[0076] • to develop a state observer or parameter estimator,

[0077] • to develop an (extended) Kalman filter.

[0078] The following assumptions are made in the literature for the analytical solution of the differential equations.

[0079] 1. The open circuit voltage U OCV is a function U OCV (SOC, T) is already well determined regardless of the current direction.

[0080] 2. All parameters are initially current-independent, both with regard to current direction and current amplitude.

[0081] 3. Near each operating point (SOC. T) the values ​​R0, R1, C1 and τ are constant.

[0082] The values ​​of U OCV , R, and C depend, among other things, on the state of charge (SOC) and thus, according to equation (1), explicitly on the current and time. Therefore, points 2 and 3 should not be considered independent of each other. The larger the current amplitude, the shorter the time should be chosen for which the values ​​of R0, R1, and C1 are assumed to be constant.

[0083] These assumptions, which only apply in the limiting case of "pulse time approaching zero," provide a parameter set, e.g., for the operating point (SOC = 50%, T = 25 °C). Once the parameters have been defined for all operating points, which can, for example, correspond to SOC increments of 10%, the simulation results of the parameterized model can be compared with another measurement, e.g., from a driving cycle with longer pulse times. Depending on the comparison result, the parameters can then be optimized manually and / or automatically using another optimization algorithm. This process typically finds a parameter set that mathematically exhibits the smallest squared error as a local minimum.

[0084] Point 3 means mathematically that, for example, the Taylor series of R1 with the expansion point (SOC, T), here at a constant temperature T, is terminated after the first term:

[0085] T0R1(SOC(t),SOC(t0)) = R1SOC(t0)) (3)

[0086] In order to increase the accuracy of the parameterization, the fit function can be used not only for U OCV at the development point, but also the slope of the function U OCV SOC(t) must be taken into account. This does not affect the specific analytical solution of the differential equation (2) for U1(t).

[0087] Investigations have shown that for a closed, analytical solution of the differential equation, the assumptions in points 2 and 3 are not necessary. Instead, another term in the Taylor series, e.g., of R1, is considered:

[0088] This can also be referred to as the linearization of R1 at the point SOC(t0). If all Taylor series for R0, R1 or τ - e.g. T1R1SOC(t), T) for R1SOC(t), T) - are inserted into the differential equation (2), a new fitting function can be found that contains five parameters instead of three. The solution is quite complicated, however, which is why it will not be discussed further here. However, the second term of the Taylor series of τ(SOC(t), T(t)) is interesting. With the new fitting function, it could be explicitly confirmed that this function has a very small, negligible dependence on the state of charge for common battery cells.

[0089] The complete stress response without the assumptions according to point 1 and point 2 and taking into account the simplification τ(SOC(t), T(t)) = τ(SOC(t0),T(t)) is then: where: and / Cellis a constant battery current. The coefficients λ, ψ, η can be model parameters 12, which can be optimized, for example, by comparing them with measurements using the least squares method. The new linear term tψ, which is considered in the fitting function, is also clearly visible in pulse measurements for long pulse durations and high current amplitudes.

[0090] The additional determination of the parameter ψ does not, in principle, represent an additional hurdle for the least squares method.

[0091] The term is well known because of point 1 (see above).

[0092] This results in a linear system of equations with the three equations (6), (7), (8) and two unknowns, namely the derivatives

[0093] These derivatives can be solved according to the rules of linear algebra.

[0094] The additional term tψ can also be used in an extended Kalman filter. The resulting fit function thus enables an accurate description of the linear behavior even for longer pulse durations with higher current amplitudes.

[0095] Fig. 3 shows a comparison between a voltage curve 14 estimated using battery model 10 and a measured voltage curve 15 for the same period at a state of charge (SOC) of 90% and a temperature T of 25 °C. For comparison purposes, another voltage curve 16 is also shown, which was estimated using a conventional 1-RC equivalent circuit model. It can be seen that battery model 10 and the conventional 1-RC equivalent circuit model produce very similar results for short prediction times (t ≈ 3 s), but battery model 10 is closer to the measured voltage curve 15 for longer prediction times (t » 3 s).

[0096] Fig. 4 shows the three voltage curves 14, 15, 16 at a state of charge SOC of 80% and a temperature T of 25 °C.

[0097] From Fig. 3 and Fig. 4 it can be seen that the results obtained with the battery model 10 are clearly distinguishable from the results obtained with the conventional 1-RC equivalent circuit model.

[0098] Since the devices and methods described in detail above are exemplary embodiments, the devices and methods can be modified widely by those skilled in the art without departing from the scope of the invention. In particular, the mechanical arrangements and the relative dimensions of the individual elements are to be considered exemplary.

[0099] Finally, it should be noted that terms such as "having," "comprising," etc., do not exclude other elements or steps, and indefinite articles such as "a" or "an" do not exclude a plurality. Furthermore, it should be noted that features or steps described with reference to one of the above embodiments may also be used in combination with features or steps described with reference to other of the above embodiments. Reference signs in the claims are not to be considered as limitations.

[0100] LIST OF REFERENCE SYMBOLS

[0101] 1 battery

[0102] 2 battery cells

[0103] 3 Battery management system

[0104] 4 Sensor technology

[0105] 5 measured operating parameters

[0106] 6 Data processing device

[0107] 7 processor

[0108] 8 storage

[0109] 9 estimated operating parameters

[0110] 10 Battery model

[0111] 11 Equivalent circuit diagram

[0112] 12 model parameters

[0113] 13 RC element

[0114] 14 estimated voltage curve

[0115] 15 measured voltage curve

[0116] 16 further voltage curve

[0117] C1Capacitance of the RC element

[0118] I Cell Battery power

[0119] I C1 Current through capacitance C1

[0120] I R1 Current through resistor R1

[0121] R0ohmic resistance R1Resistance of the RC element U Cell Battery voltage

[0122] U OCV Open circuit voltage

[0123] U1Voltage drop across capacitance C1

Claims

CLAIMS 1. Computer-implemented method for determining at least one estimated operating parameter (9) of a battery (1), wherein the method comprises: Receiving at least one measured operating parameter (5) of the battery (1); and Determining the at least one estimated operating parameter (9) from the at least one measured operating parameter (5) using a mathematical battery model (10) based on an equivalent circuit (11) of the battery (1) comprising at least one RC element (13), wherein the battery model (10) establishes a relationship between a battery voltage (U) applied to the battery (1) Cell ) and a battery current flowing through the battery (1) (I Cell) as a function of model parameters (12) comprising at least one time constant and / or at least one electrical resistance (R0, R1) with respect to the equivalent circuit (11), wherein the battery model (10) considers an nth power of a Taylor series expansion of the at least one time constant and / or the at least one electrical resistance (R0 < R1) around an operating point of the battery (1), where n > 0.

2. Method according to claim 1, wherein n = 1.

3. Method according to any one of the preceding claims, wherein the battery model (10) is defined by the following equation: where U Cell the battery voltage (U Cell ) is, I Cell the battery current (I Cell ) is, τ is the time constant, SOC is a state of charge of the battery (1), T is the temperature of the battery (1) and λ, ψ, η are coefficients.

4. Method according to claim 3, wherein at least one of the coefficients λ, ψ, η is defined as a function of the nth power of the Taylor series expansion of the at least one electrical resistance (R0,R1) around the state of charge SOC(t0) as the operating point.

5. Method according to claim 4, wherein the coefficient A is defined as a function of the nth power of the Taylor series expansion of a resistor (R1) of the RC element (13) as the electrical resistance (R0,R1).

6. Method according to claim 4 or 5, wherein the coefficient is defined as a function of the nth power of the Taylor series expansion of an ohmic resistance (R0) as of the electrical resistance (R0,R1).

7. Method according to one of claims 4 to 6, wherein the coefficient xp is defined as a function of the nth powers of the Taylor series expansions of different electrical resistances (R0, R1).

8. Method according to any one of claims 4 to 7, wherein at least one of the coefficients λ, ψ, η is additionally dependent on the battery current (I Cell ) is defined.

9. Method according to any one of claims 4 to 8, wherein at least one of the coefficients λ, ψ, η is additionally defined as a function of the time constant.

10. Method according to any one of claims 4 to 9, wherein at least one of the coefficients λ, ψ, η is additionally dependent on an nth power of a Taylor series expansion of an open-circuit voltage (U). OCV ) of the battery (1) is defined around the state of charge SOC(t0), where n > 0.

11. Data processing device (6) comprising a processor (7) configured to perform the method according to any of the preceding claims.

12. Battery management system (3), comprising: a sensor system (4) for determining at least one measured operating parameter (5) of a battery (1); and the data processing device (6) according to claim 11.

13. Battery (1), in particular a lithium-ion battery (1), comprising: the data processing device (6) according to claim 11; or the battery management system (3) according to claim 12.

14. Computer program comprising instructions that, when the computer program is executed by the processor (7), cause the method according to any one of claims 1 to 10 to be carried out.

15. Computer-readable medium on which the computer program according to claim 14 is stored.

Images