Method and device for determining the cell impedance of a battery cell using a fractional model and method for providing a fractional battery model

Abstract

The invention relates to a computer-implemented method for providing a cell impedance model (11) for a battery cell, which is based on an equivalent circuit model (11) with components having at least temperature-dependent component values ​​and is designed to calculate a terminal voltage and / or a cell impedance (Z zelle ) using the following steps: - Providing (S1) at least one measurement time series of measured values ​​in time steps, wherein the measured values ​​each represent a measured terminal voltage (U mess ), a measured cell current (I mess ), a measured cell external temperature (T mess ) or a measured ambient temperature, - Performing an optimization procedure for the model parameters of the cell impedance model, where in each iteration ◯ on a provisionally parameterized cell impedance model (11) a profile of the cell internal temperature (T mod) for the time steps (t) of the measurement time series based on a given temperature model (12) depending on the respectively measured cell external temperature (T mess ) or the measured ambient temperature and a power loss (P) is determined (S4) , and ◯ furthermore, the model parameters of the cell impedance model (11) by minimizing the total of the voltage differences between the measured terminal voltage (U mess ) and a terminal voltage modelled with the cell impedance model (U mod ) are optimized for the time steps of the measurement time series (S7), whereby the modeled terminal voltages (U mod ) depending on the cell internal temperature (T mod ) of the respective time step (t) using the cell impedance model (11).

Description

Technical area

[0001] The invention relates to battery cells and the modeling of cell impedances using a fractional battery model. The invention further relates to the consideration of cell temperature for determining cell impedance. Technical background

[0002] The behavior of a battery can be simulated using a suitable battery model. In practice, equivalent circuit models, particularly in the form of a fractional model, have proven effective. These models simulate the electrical behavior, particularly the impedance of the battery cell, using a combination of resistances and capacitances. Due to their nonlinearity, the component values, i.e., the resistance and capacitance values, are not constant, but are represented in the fractional model as variables depending on the battery cell's aging state, the state of charge, the current, and the cell temperature.

[0003] In particular, such battery models are used to simulate batteries to determine whether specified current or load profiles can be met. Furthermore, the battery model can be used to predict how long a current or power requested by the higher-level controller can be provided without violating one of the operating limits specified by the battery cell manufacturer.

[0004] For the application of the cell impedance model, the aging state SOH-R of the battery cell related to an impedance change is determined using a separate aging state model.

[0005] The state of charge can be determined by integrating all charge inputs and outputs over time. The cell temperature can be determined by a temperature sensor that is thermally well connected to the battery cell. Disclosure of the invention

[0006] According to the invention, a method for using a cell impedance model for a battery cell according to claim 1 and a method for providing a cell resistance model according to the independent claim are provided.

[0007] Further embodiments are specified in the dependent claims.

[0008] According to a first aspect, a method for providing a cell impedance model for a battery cell, which is based on an equivalent circuit model with components having at least temperature-dependent component values ​​and is designed to model a terminal voltage and / or a cell impedance, comprising the following steps: - Providing at least one measurement time series of measured values ​​in time steps, wherein the measured values ​​each comprise a measured terminal voltage, a measured cell current, a measured cell external temperature or a measured ambient temperature, - Performing an optimization procedure for the model parameters of the cell impedance model, where in each iteration ◯ on a provisionally parameterised cell impedance model, a profile of the cell internal temperature is determined for the time steps of the measurement time series based on a predefined temperature model depending on the respectively measured cell external temperature or the measured ambient temperature and a power loss, and ◯ furthermore, the model parameters of the cell impedance model are optimised by minimising the total voltage differences between the measured terminal voltage and a terminal voltage modelled with the cell impedance model for all time steps, whereby the modelled terminal voltages are each determined using the cell impedance model depending on the cell internal temperature determined for the respective time step.

[0009] The temperature model can be created using a tool such as Ansys, for example, using mechanical parameters and electrochemical properties of the materials used in the battery cell.

[0010] One problem with modeling a battery cell based on a cell temperature measured using a temperature sensor is that the measured temperature cannot be measured directly inside the battery cell. A typical temperature sensor, although thermally well connected, is located at a distance from the battery cell core. Therefore, the cell temperature reading is often inaccurate, exhibits a low-pass filter with respect to the actual temperature, and depends, in particular, on the ambient temperature and the current installation situation of the battery cell.

[0011] A cell impedance model, often referred to as an equivalent circuit model (ECM), is used to model the cell impedance of a battery cell based on an equivalent circuit that can be used to simulate the current-voltage characteristics of the battery cell. It typically consists of a combination of resistors, capacitors, and a voltage source that specifies an open-circuit voltage according to a known OCV (open-circuit voltage) characteristic. Series resistors represent the instantaneous voltage drop in the battery under load and are caused by the internal resistance of the battery cell.Furthermore, one or more polarization resistors and one or more capacitors may be included as RC elements with one or more time constants that model slower electrochemical processes in the battery, whereby the polarization resistor models the delay in the voltage change due to chemical reactions in the battery cell and the capacitance of the capacitor models the ability of the battery to store and release charge and indicates the time delay in the voltage response.

[0012] It may be provided that the model parameters of the cell impedance model further indicate a dependence of the component values ​​on a state of charge and / or an aging state and / or a cell current.

[0013] The resistance and capacitance values ​​of the components of the cell impedance model represent model parameters of the battery model and can usually depend not only on the cell temperature but also on the aging state and / or state of charge and / or cell current.

[0014] The parameters of the cell impedance model are determined from measurement time series using a well-known parameterization method, so that the behavior modeled with the equivalent circuit model corresponds to the actual behavior of the battery cell. The parameterization method includes an iterative optimization procedure in which the parameter values ​​are determined incrementally. The measurement time series include time series of current-voltage measurements and / or frequency series of impedances and phase shifts, e.g., determined using electrochemical impedance spectroscopy (EIS).

[0015] It is therefore planned to expand the cell impedance model by specifying the temperature dependence of the model parameters, i.e., the resistance and capacitance values, using an internal cell temperature determined using a temperature model. The resulting internal cell temperature will be used instead of the external cell temperature measured using the temperature sensor.

[0016] The temperature model provides for the use of the power loss in the battery cell resulting from the current operating point of voltage and / or current and cell resistance, the measured temperature outside the battery cell, possibly an ambient temperature and the like in a temperature model in order to model a temperature indication for an internal cell temperature as it exists inside the battery cell.

[0017] The temperature model considers a heat flow balance and can be modeled as a first-order differential equation model or by more complex models or data-based models.

[0018] This temperature model is taken into account in each iteration to parameterize the cell impedance model, so that the model parameters of the resistance values ​​and capacitance values ​​are always optimized in relation to a cell internal temperature of the temperature model.

[0019] Furthermore, the parameterization can be carried out by minimizing the voltage differences between the measured terminal voltage and the terminal voltage modeled with the cell impedance model of the considered measurement time series.

[0020] Thus, when parameterizing the cell impedance model and the temperature model, an iterative optimization process based on time series of measured variables can be performed. Instead of a measured temperature value, a modeled internal cell temperature profile is used for each iteration. The respective internal cell temperature (for each time step) to be considered via the cell impedance model is determined from the power loss in the equivalent circuit for a time step t. P(t)=i(t)2R0+u1(t)2R1+u2(t)2R2+...

[0021] With the cell current i(t), the series resistance R0, the voltages (terminal voltages) u1(t), u2(t), ...across each of the RC elements R1, C1, R2, C2, ...

[0022] The temperature model is predefined. Alternatively, the temperature model can be parameterized when configuring the cell impedance model.

[0023] According to a further aspect, a method for determining a cell impedance of a battery cell using a cell impedance model at a time step is provided, comprising the following steps: - Determining an internal cell temperature of the battery cell depending on a measured external cell temperature or a measured ambient temperature as well as depending on an electrical power loss converted in the battery cell in a previous time step using a given temperature model; - Determination of component parameters depending on the internal cell temperature; - Determine the cell impedance depending on the cell impedance of the previous time step using the cell impedance model designed with the determined component parameters.

[0024] When evaluating the cell impedance model, a cell temperature reading is first determined using the parameterized temperature model. For this purpose, the electrical power dissipated in the battery cell is determined at each time step, a temperature outside the battery cell is recorded, for example, using the temperature sensor, and, if necessary, an ambient temperature is recorded. The temperature model, based on time series integration, can then be used to determine a temperature reading for the current time step.

[0025] Furthermore, the cell impedance model is evaluated, whereby the model parameters are determined and used depending on the modeled temperature specification so that the cell impedance can be determined. Brief description of the drawings

[0026] Embodiments are explained in more detail below with reference to the attached drawings. They show: Fig. 1 is a schematic representation of an equivalent circuit of a cell impedance model; and Fig. 2 a functional block diagram illustrating the function of the extended cell impedance model; Fig. 3 shows a flowchart illustrating a method for parameterizing the cell impedance model. Description of embodiments

[0027] Fig. Figure 1 schematically shows a cell impedance model that corresponds to an equivalent circuit model to represent the electrical behavior of a battery cell.

[0028] The equivalent circuit is constructed with electrical components, each of which has one or more parameterizable electrical quantities. The parameterizable electrical quantities can further depend on parameters such as cell temperature, state of charge, and cell current. The equivalent circuit comprises a series resistor R0 connected in series with several (n) series-connected RC elements (R in parallel with C) with a first resistor R1 and a first capacitance C1 or an nth resistor R n and an n-th capacity C n is electrically connected.

[0029] The resistance and capacitance values ​​of the individual components of the equivalent circuit model depend on the cell temperature T and can also be modeled depending on an aging state SOH of the battery cell and a state of charge SOC of the battery cell and a cell current I. R0=f(SOH, SOC, T, I) R1...n=g(SOH, SOC, T, I) C1...n=h(SOH, SOC, T, I)

[0030] To parameterize the cell impedance model and its parameters, one or more measurement time series are recorded at consecutive sampling points in time steps t=1...k, taking into account the respective terminal voltage, the current state of charge, the associated battery current, and the current cell temperature. The state of charge can be determined, for example, by temporally integrating the charge inflows and outflows.

[0031] The aging state can be determined using a known aging state model to determine an aging state SOH-R relating to the cell impedance change and can be assumed to be constant for the duration of the time series measurement.

[0032] Fig. 2 shows a block diagram of a model setup 10 for providing the cell impedance model 11 in conjunction with a temperature model 12.

[0033] When a battery current I is applied mess (t), at a certain state of charge SOC and a certain cell temperature T, a cell voltage U mess measured and compared with the terminal voltages U modelled using the cell impedance model 11 mod (t) can be compared.

[0034] The parameterization of the cell impedance model 11 is generally based on time series of measurement data sets, in order to accurately represent the temporal behavior resulting from the capacitances of the capacitors and the temperature inertia of the cell's internal temperature. The measurement is performed by recording time series of the battery current I mess (t), the cell external temperature T mess (t) or the ambient temperature and the cell voltage U mess (t). umod(t)=i(t)∗Z cell with the cell impedance Z zelle .

[0035] By minimizing the voltage differences between the measured and modeled terminal voltage U mess (t), U mod (t) in the totality of all time steps of the time series, a parameterization of the model parameters of the cell impedance model 11 can be carried out. However, this approach conventionally leads to high voltage differences between the measured and modeled terminal voltage U due to the inaccurate information on the cell's internal temperature. mess (t), U mod (t), so that it is proposed herein to extend the cell impedance model 11 by a temperature model 12, which provides a more precise indication of the cell internal temperature.

[0036] The temperature model 12 can provide, depending on time series of a measured cell external temperature T mess(t), which is usually measured outside the battery cell using a temperature sensor, and depending on a time series of the power losses P(t) converted in the battery cell, an internal cell temperature T mod (t) as the current temperature.

[0037] In order to take historical power losses into account in particular, the temperature model 12 is designed in the form of a differential equation or a data-based recurrent model, which makes it possible to calculate the cell internal temperature T from the time series of power losses and the time series of cell external temperatures. mod (t) as a temperature value. Additionally or alternatively, an ambient temperature T u (t) of the battery cell must be taken into account. When using the ambient temperature T u (t) the recording of the cell external temperature can also be omitted.

[0038] The temperature model can, for example, have the following form of a differential equation. dx(t) / dt=A*x(t)+B*u(t) Tmod(t)=C*x(t) with u(t)=(Tu(t); P(t))T P(t)=i(t)2R0+u1(t)2R1+u2(t)2R2+⋯ with the parameters A, B, C of the temperature model.

[0039] In contrast to the conventional method of applying an optimization method to minimize the voltage differences between the time series of the measured terminal voltage and the time series of the modeled terminal voltage, in an iteration step of the optimization method, the temperature values ​​for each time step of the measurement time series are first determined depending on the current parameter values ​​of the model parameters and, based on the voltage difference, the parameters of the model parameters of the cell impedance model 11 are then determined assuming a previously determined current cell temperature value T mod(t). The adjusted model parameters can be evaluated with the cell impedance model, resulting in a cell impedance Z zelle The resulting cell impedance Z zelle is used recursively to calculate a power loss P in a power loss block 13 based on the battery current I mess (t) and the modeled cell impedance Z zelle and to calculate the power loss P(t) and the cell external temperature T mess (t) in the temperature model 12.

[0040] In the next iteration step, this power loss P(t) is used to determine the course of the cell internal temperature T mod (t) as the temperature value for the time steps. The resulting curve of the cell's internal temperature T mod (t) is now reapplied in the cell impedance model 11 to obtain an updated cell impedance Z zelle to obtain.

[0041] In Fig.Figure 3 shows a flow chart to illustrate the process of the parameterization procedure.

[0042] In step S1, a measurement time series is provided, whereby the battery cell is relaxed at the beginning of the measurement time series, ie the terminal voltage corresponds to the OCV voltage and the cell internal temperature T mod (t) as a temperature specification corresponds to the ambient temperature. Furthermore, an initially parameterized temperature model is provided.

[0043] In step S2, the cell impedance at time step t of the measurement time series with temperature information from time step t-1 is calculated using the cell impedance model initially parameterized or parameterized during this optimization procedure. Since the time series starts at time step t=1, at which the internal cell temperature corresponds to the ambient temperature or is otherwise known.

[0044] In step S3, the resulting modeled terminal voltage Umod (t) and the resulting loss P(t) is calculated in time step t.

[0045] In step S4, the cell temperature is calculated as a temperature value in time step t, depending on the power loss, using the temperature model.

[0046] In step S5, a check is made to determine whether a temperature reading has been determined for all sampling points in the measurement time series. If this is the case (alternative: yes), the process continues with step S6. Otherwise (alternative: no), the process returns to step S2 until temperature readings have been calculated for all time steps t of the measurement time series. This provides a temperature reading for the cell's internal temperature for each time step t / sample point in the measurement time series.

[0047] In step S6 it is checked whether the sum or the mean value of the squared voltage differences of the terminal voltages U modelled in step S3 mod (t) and the measured terminal voltages Umess (t) fall below a specified threshold for all time steps. If this is the case (alternative: Yes), the optimization procedure has converged and the procedure is terminated. Otherwise (alternative: No), the procedure continues with step S7.

[0048] In step S7, the model parameters of the cell impedance model are recalculated using the sum or the mean of the squared voltage differences calculated in step S6, and if applicable all results of the previous iterations, e.g. using the least squares method.

[0049] The process then continues with step S2 with a next iteration.

[0050] The optimization can be based on a gradient descent method, where over the time series of the considered measurement data set the totality (such as in the form of a sum, a sum of squares) of the voltage differences between the measured terminal voltage U mess (t) and the modeled terminal voltage U mod (t) can be used at each time step / sampling point by adjusting the model parameters of the cell impedance model 11.

Claims

[1] Computer-implemented method for providing a cell impedance model (11) for a battery cell, which is based on an equivalent circuit model (11) with components with at least temperature-dependent component values ​​and is designed to determine a terminal voltage and / or a cell impedance (Z zelle ) using the following steps: - Providing (S1) at least one measurement time series of measured values ​​in time steps, wherein the measured values ​​each represent a measured terminal voltage (U mess (t)), a measured cell current (I mess (t)), a measured cell external temperature (T mess (t)) or a measured ambient temperature, - Performing an optimization procedure for the model parameters of the cell impedance model, where in each iteration ◯ on a provisionally parameterized cell impedance model (11) a profile of the cell internal temperature (T mod(t)) for the time steps (t) of the measurement time series based on a given temperature model (12) depending on the respectively measured cell external temperature (T mess (t)) or the measured ambient temperature and a power loss (P) is determined (S2 - S4), and ◯ furthermore, the model parameters of the cell impedance model (11) by minimizing the total of the voltage differences between the measured terminal voltage (U mess (t)) and a terminal voltage modelled with the cell impedance model (U mod (t)) are optimized for the time steps of the measurement time series (S7), whereby the modeled terminal voltages (U mod (t)) depending on the cell internal temperature (T mod (t)) of the respective time step (t) using the cell impedance model (11). [2] The method according to claim 1, wherein the model parameters of the cell impedance model (11) further indicate a dependence of the component values ​​on a state of charge (SOC) and / or an aging state (SOH) and / or a cell current. [3] Method according to claim 1 or 2, wherein the parameterization is carried out by minimizing a deviation value from the voltage differences between the measured terminal voltage (U mess (t)) and the terminal voltage (U mod (t)) of the at least one measurement time series considered is carried out for all time steps (t). [4] Method for determining a cell impedance (Z zelle ) of a battery cell using a cell impedance model (11) at a time step, with the following steps: - Determination of an internal cell temperature of the battery cell depending on a measured external cell temperature (T mess(t)) or a measured ambient temperature using a temperature model (12) and depending on an electrical power loss (P(t)) converted in the battery cell in a time step (t-1) preceding the time step (t); - Determination of the component parameters depending on the cell internal temperature (T mod (t)); - Determine the cell impedance depending on the cell impedance (Z zelle ) of the previous time step (t-1) using the cell impedance model (11) designed with the determined component parameters. [5] Apparatus for carrying out one of the above methods according to one of claims 1 to 4. [6] A computer program product comprising instructions which, when executed by at least one data processing device, cause it to carry out the steps of the method according to any one of claims 1 to 4. [7] Machine-readable storage medium comprising instructions which, when executed by at least one data processing device, cause it to carry out the steps of the method according to one of claims 1 to 4.

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