Method and system for efficiently monitoring a device battery in an external central unit

Abstract

The invention relates to a computer-implemented method for monitoring a device battery (1) based on a high-resolution cell voltage profile of a battery cell (2), wherein the high-resolution cell voltage profile of a second battery cell (2) is reconstructed based on a high-resolution cell voltage profile of a first battery cell (2) and a low-resolution cell voltage profile of the second battery cell (2) and a high-resolution cell current profile, comprising the following steps: - Calculating (S9) a differential voltage between the low-resolution time cell voltage profile of the second battery cell (2) and a high-resolution time cell voltage profile of the first battery cell (2) downsampled to a low time resolution using a delta voltage response model, which is formulated as a linear differential equation, depending on the high-resolution time cell current profile; - Reconstructing (S7) the high-resolution time cell voltage profile of the second battery cell (2) by applying the differential voltage to the high-resolution time cell voltage profile of the first battery cell (2).

Description

Technical area

[0001] The invention relates to systems in which one or more device batteries are monitored by a device-external central unit. The invention further relates to methods for reducing the amount of data relating to operating parameter profiles of the one or more device batteries that must be transmitted to a device-external central unit. Technical background

[0002] The power supply for off-grid electrical devices and machines, such as electrically powered vehicles, is usually provided by device batteries or vehicle batteries. These provide electrical energy to operate the devices.

[0003] Portable batteries degrade over their service life and depending on their load and use. This so-called aging leads to a continuously decreasing maximum power or storage capacity. The state of aging corresponds to a measure of the aging of batteries. According to convention, a new portable battery can have an aging state (in terms of its capacity, SOH-C) of 100%, which decreases noticeably over the course of its service life. The measure of the aging of a portable battery (change in the aging state over time) depends on the individual load on the portable battery, i.e. in the case of vehicle batteries, the driver's usage behavior, external ambient conditions, and the vehicle battery type.

[0004] In order to monitor the battery states of device batteries from a large number of devices, operating variable data is usually recorded continuously and transmitted in blocks as operating variable profiles to a central unit on the device. The operating variables can include an electrical battery current, a battery voltage, a battery temperature and a state of charge of the device battery. In the case of device batteries with a large number of battery cells, the operating variables can also be recorded at the cell level and transmitted to the central unit in compressed form. To evaluate the operating variable data, in particular to determine aging states in models based on differential equations, time series of operating variable data are sampled with a comparatively high temporal resolution (sampling rates), for example between 1 and 100 Hz, and a battery state or aging state is determined from this using a time integration method.

[0005] In addition, high-capacity portable batteries can contain up to several thousand battery cells per device battery. For each individual battery cell, a cell aging state is then determined in a digital twin implemented in the central unit. From these cell aging states, an overall aging state of such a device battery is determined based on the topology and configuration of the device battery.

[0006] In order to continuously determine the cell aging states for each battery cell, the availability of temporal profiles of the operating parameter data in high temporal resolution for all battery cells is therefore necessary, so that a large amount of data for each device battery to be monitored must be transmitted to the central unit and evaluated there.

[0007] One challenge is that with a high number of battery cells, a high data transfer takes place between the device battery and the central unit (cloud), which, if bandwidth is limited, can lead to delays in providing operating parameter data in the central unit and in determining the battery states.

[0008] Document CN 1 10 826 023 A discloses a method for improving the resolution of battery data by fitting the voltage data using a monotonically increasing function and combining it with the voltage plateau data.

[0009] Document DE 10 2022 200 008 A1 discloses a method for efficient monitoring of battery cells in a central unit. By continuously measuring the operating parameters of only a portion of the cells and modeling the remaining battery behavior, the amount of data is reduced and the load on the communication link is minimized.

[0010] The document DE 10 2021 203 729 A1 discloses a method and a device for modeling and predicting the state of health (SOH) of battery storage systems, using machine learning methods and usage pattern models to fill gaps in the recorded operating data. Disclosure of the invention

[0011] According to the invention, a method for reconstructing temporally high-resolution cell voltages of a battery cell of a device battery depending on a temporally low-resolution cell voltage curve of the battery cell according to claim 1 and a device according to the superordinate claim are provided.

[0012] Further embodiments are specified in the dependent claims.

[0013] According to a first aspect, a computer-implemented method for monitoring a device battery based on a temporally high-resolution cell voltage curve of a battery cell is provided, wherein the temporally high-resolution cell voltage curve of a second battery cell is reconstructed based on a temporally high-resolution cell voltage curve of a first battery cell and a temporally low-resolution cell voltage curve of the second battery cell and a temporally high-resolution cell current curve, comprising the following steps: - Calculating a differential voltage between the temporally low-resolution cell voltage curve of the second battery cell and a temporally high-resolution cell voltage curve of the first battery cell downsampled to a low temporal resolution using a delta voltage response model in the form of a linear differential equation, depending on the temporally high-resolution cell current curve; - Reconstructing the temporally high-resolution cell voltage curve of the second battery cell by applying the differential voltage to the temporally high-resolution cell voltage curve of the first battery cell.

[0014] Furthermore, the differential voltage for a time step within the temporally low-resolution cell voltage curve can be determined as a function of a first voltage difference, which is determined as a result of a first optimization of a cell voltage based on an evaluation of an OCV characteristic curve as a function of a charge change at the time step, which depends on the cell current at the time step, at a temporally low resolution.

[0015] In particular, before the first optimization, the temporally low-resolution cell voltage curve of the second battery cell can be low-pass filtered with a first cutoff frequency.

[0016] It can be provided that the differential voltage for a time step within the temporally high-resolution cell voltage curve is determined as a function of a second voltage difference, which is determined as a result of a second optimization of the cell voltage based on an evaluation of a behavior of the RC element and as a function of a cell voltage of the second battery cell corrected by the first voltage difference.

[0017] In particular, before the second optimization, the temporally low-resolution cell voltage curve of the second battery cell can be low-pass filtered with a second cutoff frequency that is higher than the first cutoff frequency.

[0018] Furthermore, the differential voltage for a time step within the temporally high-resolution cell voltage curve can be determined as a function of a third voltage difference, which is determined as a result of determining a resistance difference between the series resistance of the second and the first battery cell as a function of a cell voltage of the second battery cell corrected by the first and the second voltage difference.

[0019] The state of health (SOH) of portable batteries is the key parameter used to indicate the remaining battery capacity or remaining battery charge, which is the battery health of the device battery. The state of health of a device battery is not typically measured directly. This would require a series of sensors inside the device battery, making the production of such a device battery costly and complex and increasing the space required. Furthermore, practical measurement methods for directly determining the state of health in portable batteries are not yet available on the market.

[0020] The state of age represents a measure of the ageing of the device battery. In the case of a device battery, a battery module, or a battery cell, the state of age can be specified as the capacity retention rate (SOH-C). The capacity retention rate SOH-C, i.e. the capacity-related state of age, is specified as the ratio of the measured instantaneous capacity to the initial capacity of the fully charged battery and decreases with increasing age. Alternatively, the state of age can be specified as the increase in internal resistance (SOH-R) relative to the internal resistance at the beginning of the device battery's service life. The relative change in internal resistance SOH-R increases with increasing battery age.

[0021] The aging state of a portable battery is therefore informative regarding the battery condition, which indicates its future usability. Knowledge of other battery conditions that indicate the internal electrochemical state of the portable battery is also useful, for example, if an anomaly or fault in the portable battery is to be detected early. Such internal electrochemical conditions can include, for example, a layer thickness (e.g., SEI thickness), an indication of a change in cyclable lithium due to anode / cathode side reactions, an indication of rapid electrolyte consumption, an indication of slow electrolyte consumption, an indication of a loss of active material in the anode, an indication of a loss of active material in the cathode, etc.The aging state as well as the internal electrochemical states of the device battery as battery states can be determined using an electrochemical battery model with the aid of an evaluation of nonlinear differential equations depending on the operating variables.

[0022] The electrochemical battery model comprises a system of differential equations that, based on differential equations parameterized via model parameters, models internal battery states, in particular equilibrium states and, if applicable, kinetic states, using a time integration method. It provides a relationship between operating variables of the battery cells of the portable battery, namely a battery current, a battery voltage, a battery temperature, and a state of charge of the portable battery. Such electrochemical battery models are known, for example, from the publications US 2016 / 023,566, US 2016 / 023,567, and US 2020 / 150,185. The aging state of the respective portable battery can be approximately determined, for example, as a linear combination of the internal electrochemical states.The electrochemical battery model can be evaluated in the central unit or in a control unit for an individual device battery to determine the internal battery conditions.

[0023] Model parameters of the electrochemical battery model can be fitted or parameterized (adjustment of the model parameters by minimizing the squared errors) in the central unit based on operating parameter profiles of a large number of portable batteries of the same type recorded during rest phases within short periods (a few minutes to a few hours). Electrochemical equilibrium parameters and kinetic model parameters can be derived, which can include, for example, electrolyte concentrations, reaction rates, layer thicknesses, porosity, etc. Parameterization can be based on a highly accurate measurement of the aging state of the portable batteries. Based on the fitted electrochemical model parameters, internal battery states and / or the aging state can be determined as described above. The electrochemical battery state can also be evaluated in anomaly detection processes.

[0024] Based on the fitted electrochemical model parameters, the aging state can be determined. An aging-dependent open-circuit voltage characteristic curve can be calculated analytically using a batch algorithm. By comparing the open-circuit voltage, detailed electrochemical model parameters of the electrochemical battery model can be directly derived, thus allowing the aging state of the battery cells to be determined.

[0025] Due to the limited computing capacity available within the device, the monitoring of device batteries in a large number of devices is often performed in an external central unit. For this purpose, the devices transmit temporal operating parameters of the device batteries' operating parameters to the central unit, where the central unit determines the current electrochemical state and / or aging state.

[0026] Depending on the model used, time series of operating variables are continuously recorded as operating variable profiles, such as time series of at least one of the following variables: battery current, battery temperature, state of charge, and / or battery voltage. These time series are transmitted in blocks and, if necessary, in compressed form to the central unit. There, the operating variable profiles are evaluated. For example, based on one or more battery models, a device-specific battery state and, if necessary, other variables can be calculated / determined. In addition, the operating variable profiles from the multitude of device batteries can be evaluated using statistical methods to improve the applied electrochemical battery models, so that the determination and prediction of the internal battery states of the device batteries can be noticeably improved.

[0027] Device batteries typically have a large number of battery cells that can be monitored separately, in groups, or as a complete device battery. This can be achieved by simulating the states of the battery cells in a computing unit in the form of a "digital twin," particularly using a known battery model or battery performance model.

[0028] In particular, such monitoring can be used to identify low-performing or vulnerable battery cells and prevent them from being overloaded during charging. Furthermore, to determine the aging state of the entire device battery, the cell aging states can be determined and offset against each other according to the topology or configuration of the device battery with regard to the arrangement and interconnection of the battery cells to determine the aging state for the entire device battery. For example, the capacity-related aging state can be determined from the battery cells connected in parallel and series based on Kirchhoff's node and mesh rule.

[0029] For this reason, the current individual electrochemical state and / or aging state of the battery cells of one or more device batteries (as cell aging states) is continuously updated and monitored in the central unit. This represents a remotely implemented "digital twin" of the respective device battery, since the cell aging states for the individual battery cells of each of the monitored device batteries are always available in the central unit.

[0030] To monitor the individual battery cells of the device battery, the internal states of the device battery can be further developed in the central unit based on the cell operating parameter curves, e.g., starting from a commissioning point (start of service life) / reference point using the time integration method. From this, a battery state can be determined based on a model. This requires that high-resolution operating parameter curves for the battery cells and / or the device battery are continuously available.

[0031] Furthermore, an aging state model can be provided that includes an electrochemical physical aging model, which is also evaluated based on a time integration method. A possible aging state model can be provided in the form of a hybrid aging state model, which corresponds to a combination of a physical electrochemical aging model with a data-based correction model. In a hybrid aging state model, a physical aging state can be determined using a physical or electrochemical aging model (in the form of a battery model), and this can be applied with a correction value resulting from the data-based correction model, in particular by addition or multiplication.

[0032] The electrochemical physical aging model is based on electrochemical model equations, which characterize electrochemical battery states of a nonlinear differential equation system with regard to aging reactions, continuously calculates them according to a time integration method based on temporal operating variable profiles with high temporal resolution and maps these to the physical aging state for output, as SOH-C and / or as SOH-R.

[0033] Furthermore, the correction model of the hybrid data-based aging state model can be designed with a probabilistic or artificial intelligence-based probabilistic regression model, in particular a Gaussian process model, and can be trained to correct the aging state obtained by the physical aging model. For this purpose, a data-based correction model of the aging state exists for correcting the SOH-C and / or at least one further one for correcting the SOH-R. Possible alternatives to the Gaussian process are other supervised learning methods, such as those based on a random forest model, an AdaBoost model, a support vector machine, or a Bayesian neural network.

[0034] The central unit is now designed to monitor the cell aging states of each individual battery cell for each device battery by maintaining an associated electrochemical battery model and / or aging state model. These models are updated or evaluated as soon as operating parameter profiles are available for the respective battery cell / device battery in such a way that the internal battery state and / or aging state assigned to the respective battery cell can be updated. This creates a representation of the device battery as a "digital twin" in the central unit, whereby an internal battery state and an aging state can be specified for each battery cell of the monitored device batteries.

[0035] However, evaluating the battery condition using the temporal operating variables, e.g. using the electrochemical battery model and / or the electrochemical aging model, requires the operating variables to be provided in a high temporal resolution, i.e. with a high sampling frequency, e.g. between 1 Hz and 100 Hz. The transmission of operating variables for the battery cells and / or the device battery in a high temporal resolution leads to large amounts of data that must be transmitted from the large number of devices to the central unit.

[0036] Since the model evaluation is usually performed remotely from the device, firstly to consider data from a large number of portable batteries of the same type, e.g., to adapt and refine the corresponding battery performance model and / or the electrochemical aging model, and secondly to be able to provide the high computational load required for model adaptation or model evaluation, the above method provides for the time series of the operating parameter curves to be transferred with a low temporal resolution and transformed into a corresponding high-resolution time series using a suitable data-based time series model. The low temporal resolution can, for example, be in the range between 0.1 Hz and 1 Hz.

[0037] Portable batteries are typically constructed from a large number of nearly identical battery cells, initially connected in parallel, with the parallel modules connected in series. Therefore, the current through all battery cells can be considered identical. Since the current signal serves as the excitation variable for the dynamic system of battery cells, any differences in the resulting cell voltage that cannot be attributed to sensor noise can be attributed to minor differences in the model parameters or initial conditions.

[0038] The battery cells of such a portable battery can be described based on a first-order equivalent circuit that adequately represents the dynamic behavior of the battery cell. The equivalent circuit model provides a series resistance R0 and a parallel circuit consisting of a first resistor R1 and a first capacitor C1 (RC element) connected in series with it.

[0039] The electrical behavior of such a battery cell can be described based on the first-order equivalent circuit with a voltage response model x˙=[100−1R1⋅C1]⋅x+[1C01C1]⋅it, x(0)=x0 vt=vOC(x1)+x2+R0⋅it. where the state x = [C SoC v RC ] T Where C0 corresponds to the battery capacity (in Ah or As, depending on the time unit of the equation) and C SoC the state of charge of the battery cell, and v OC The open-circuit voltage derived from the battery cell's OCV curve (open-circuit voltage curve), which is dependent on the state of charge. The OCV curve is assumed to be known for the battery cells and is usually specified by the battery manufacturer. The OCV curve may be specified depending on the battery cell's aging condition.

[0040] The stress response model corresponds to a linear differential equation, which can be written in discrete form as: xk=[100exp(−TsR1⋅C1)]⋅xk−1+[TsC0R1⋅(1−exp(−TsR1⋅C1))]⋅it,k−1, x(k=0)=x0 vt,k=vOC(x1,k)+x2,k+R0⋅it,k

[0041] The objective of the above method is to reconstruct a voltage difference between the reference cell voltage of a reference battery cell, i.e., the first battery cell, for which a high-resolution cell voltage curve is available, and a high-resolution cell voltage curve of the second battery cell, for which only a low-resolution cell voltage curve is available. This is to be achieved using a delta voltage response model, which can be used to determine a difference between the cell voltage of the first battery cell and the reconstructed cell voltage of the second battery cell. The following applies: vΔ=vref−vcell vΔ=vOC(X1,ref)−vOC(X1,cell)︸vOC,Δ+X2,ref−X2,cell︸X2,Δ+(R0,ref−R0,cell)︸R0,Δ⋅it

[0042] Assuming a small difference in the charge states of the first and second battery cells, the first difference term v OC,Δ be received as: vΔ=[v¯OC 1]⋅xΔ+R0,Δ⋅it where the linearized OCV characteristic curve v OC and the corresponding part of the stress response model results in: x˙Δ=[100−1R1,Δ⋅C1,Δ]⋅xΔ+[1C0,Δ1C1,Δ]⋅it, xΔ(0)=x0,Δ where C 0,Δ the capacity difference between the first and second battery cell, R 1,Δ the resistance difference of the first resistor of the first and second battery cell and C 1,Δ corresponds to the capacity difference between the first and second battery cells. According to the discrete-time form of the differential equation of the voltage response model given above, the following formula results: xk=[100exp(−TSR1,ΔC1,Δ)]xk−1+[TsC0,ΔR1,Δ(1−exp(−TSR1,ΔC1,Δ))]it,k−1 x(k=0)=x0

[0043] Finally, this model describes an impedance difference between the first and second battery cell depending on a difference in the state of charge trajectory.

[0044] To solve the system of equations, the parameters to be identified correspond to the initial state x 0,Δ , the capacity difference C 0,Δ , the differences of the elements of the RC element R 1,Δ , C 1,Δ and R 0,Δ the difference in the series resistance of the first and second battery cells. Since the dynamics of the state of charge, the RC element, and the series resistance are based on different time scales, the parameters of the delta voltage response model are identified sequentially.

[0045] In a first step, only the slowest dynamics of the state of charge or the change in the state of charge are considered, and the parameters are identified. The voltage difference after parameterizing the state of charge dynamics is then passed on in a subsequent step using the second-slowest dynamics of the RC element.

[0046] In the first step of parameter determination, the above delta voltage response model is based on the cell voltage v t,ref the first battery cell, the cell voltage to be reconstructed v t,cell the second battery cell and the current signal I t fitted.

[0047] The signals or temporal profiles with the high temporal resolution are subsequently marked with a roof ̂ and the signals or temporal profiles with the low temporal resolution with an inverted roof ̌. First, the charge flow rate q is calculated and converted to the low temporal charge flow rate curve. q^k=q^k−1+Ts⋅l^k, q^0=0 q⌣1=q^fak⋅l+1, 1=0,1,…

[0048] Where I corresponds to the time steps of the low time resolution and fak the factor between the temporal resolutions and can be, for example, between 5 and 50, preferably 10.

[0049] Furthermore, in the same way, the cell voltage curve of the first battery cell is reduced to the cell voltage curve with a low temporal resolution. vt,cellk^=vt,cellk−1^+TS⋅l^k, q^0=0

[0050] To consider only low-frequency dynamics in the first step, the low-resolution voltage signals are low-pass filtered, for example, with a cutoff frequency of 1 mHz to 0.1 Hz, preferably 6 mHz. Filtering can be performed forward and backward in time to avoid possible phase shifts. Filtered signals are marked with an apostrophe *.

[0051] The linearized OCV characteristic is shown as an example for a state of charge of just over 10% as v¯OC=0.812v%SOC assumed, with the state of charge being given in %.

[0052] This results in an optimization problem that can be described as follows: minθ1,i J1, i∈{1,2} θ1={C0,Δ,CSoC0,Δ} st θ_1,i≥θ1,i≤θ¯1,i where θ_1,i and θ¯1,i specify the lower and upper parameter limits and C SoC0,Δindicates the initial state of charge difference between the first and second battery cells. A good starting value for the initial state of charge difference can be calculated using the first n voltage values CSoC0,Δ,0=1n⋅v¯OC∑i=1n(v⌣ref,i−v⌣cell,i) where the initial value of the capacity difference can be set to zero. The cost function corresponds to: J1=12‖v⌣ref'−(v⌣cell'+v⌣Δ,1)‖2 v⌣Δ,1=v¯OC⋅(q⌣⋅θ1,1+θ1,2)

[0053] Finally, the reconstruction of the temporally high-resolution cell voltage curve is obtained in the first step as follows: v^cell=v^ref−v^Δ1, v^Δ1=v¯OC⋅(q^⋅θ1.1*+θ1.2*) where θ1* corresponds to the optimized parameters.

[0054] In the second step, the low-resolution cell voltage curve of the first battery cell is again low-pass filtered at a higher cutoff frequency, for example, between 10 mHz and 100 mHz. Additionally, the cell voltage curve of the second battery cell can be compensated by the cell voltage difference obtained in the first step and also low-pass filtered. Here, too, filtering can be performed forward and backward in time to avoid the effects of any phase shift. The cell current curve provided with the high temporal resolution can also be converted into a low-resolution cell current curve.

[0055] Next, the sign of the voltage response of the RC element is calculated.

[0056] The voltage response model only provides a positive correlation when the battery current and the cell voltage are correlated, so that the sign τ=1R⋅C is always positive and therefore the differential equation system is stable. However, since a delta voltage response model is described, the correlation between the current and the voltage difference curve may be negative, which can lead to unstable behavior of the differential equation. Thus, the sign of the correlation is calculated and taken into account in the voltage response model to determine the parameters. It results from the correlation of the current curve Ǐ t and the cell voltage curves v⌣res'=v⌣cell,comp,1'−v⌣ref' the second battery cell and the first battery cell a sign: s=sign(cov(v⌣res',i⌣t)σvres'⌣⋅σi⌣t) where σ x̌ corresponds to the respective standard deviation.

[0057] Using an optimization problem, the parameters of the parameter vector θ2 can now be determined. minθ2,i J2, i∈{1,2,3} θ2={vδ,0,R1,Δ,C1,Δ} st θ_2,i≥θ2,i≤θ2,i¯; τ_≤R1,Δ⋅C1,Δ≤τ¯

[0058] Where v corresponds to δ,0 the initial state of the initial polarization of the RC element and τ_ and τ¯ the lower and upper limits of the time constant. The limits can be specified, for example, with 10 s and 200 s. The initial value for v δ,0,ini can be obtained by averaging the first n samples of the voltage difference curve: Vδ,0,ini=1n∑i=1n(v⌣'cell,comp,1,i−v⌣'ref,i)

[0059] The initial values ​​of the other two parameters must be chosen so that they satisfy the selected conditions.

[0060] The cost function corresponds to J2=12‖v⌣'ref−(v⌣'cell,comp,1−s⋅v⌣'Δ,2)‖2 where s⋅v⌣'Δ,2 the sign-compensated solution of the discrete delta voltage response model, which takes into account the behavior of the RC element.

[0061] In addition, the temporally highly resolved cell voltage curve is obtained in the second adjustment step: v^cell=v^ref−v^Δ,1−s⋅v^Δ,2, where v̂ Δ,2 corresponds to the solution of the delta stress response model with optimized parameter vector θ*2.

[0062] In the third step, no further low-pass filtering is required. The cell voltage curve of the second battery cell is given by v̌ Δ,1 and s · v̌ Δ,2 to v̌ cell,komp,2 compensated. The ohmic resistance can be calculated by simple regression: R0,Δ=i⌣t−1⋅v⌣cell,comp,2 so that the reconstruction of the temporally high-resolution cell voltage curve results in the third step: v^cell=v^ref−v^Δ,1−s⋅v^Δ,2−v^Δ,3 v^Δ,3=R0,Δ⋅it^ Brief description of the drawings

[0063] Embodiments are explained in more detail below with reference to the attached drawings. They show: Fig. 1 shows a representation of a device battery with a plurality of battery cells; Fig. 2 an equivalent circuit diagram of a battery cell; and Fig. 3 a flowchart illustrating a method for determining a cell voltage with a high temporal resolution for a battery cell for which only a cell voltage curve with a low temporal resolution is created. Description of embodiments

[0064] Fig. Figure 1 schematically shows a device battery 1 with a plurality of battery cells 2. Battery cells are connected in parallel, with the battery cells 2 connected in parallel to modules 3 and the modules 3 connected in series to increase the voltage. A battery current i bat, which flows through the device battery 1, leads to essentially identical cell currents i t =i bat / m (m: number of battery cells connected in parallel per module 3) , since the through impedance of the individual battery cells 2 differs very little from each other.

[0065] The battery cells 2 are equipped with voltage sensors 4 to continuously sample the cell voltage and thus record the respective cell voltage curve. The cell voltages and battery current are recorded and sampled using a battery management system 5. A communication unit 6 transmits the voltage and current curves to a central unit 7 (cloud) remote from the device.

[0066] To evaluate the battery status, for example in the form of a digital twin in the central unit 7 remote from the device, the cell voltages of the battery cell 2 and the cell current must be available with a high temporal resolution, e.g., 10 Hz. Since the transmission of the cell voltage with a high temporal resolution, e.g., 10 Hz, occupies a considerable amount of transmission capacity, it can be provided to transmit at least some of the cell voltages with a low temporal resolution (e.g., 10 times slower (by a factor of fak), e.g., 1 Hz) to the central unit 7 and to reconstruct the cell voltage curves there in such a way that they are provided with a high temporal resolution.

[0067] The method described herein enables the reconstruction of the cell voltages of the battery cell 2 based on a temporally high-resolution cell voltage curve of a first of the battery cells, which serves as a reference cell, and low-resolution cell voltage curves of the remaining battery cells.

[0068] The reconstruction is based on a delta voltage response model, which is designed as a differential equation model. The differential equation model is based on an equivalent circuit of a battery cell, which is used as an example in Fig. 2. The equivalent circuit diagram includes a series resistor R0 and an RC element with a first resistor R1 and a first capacitor C1.

[0069] In Fig.3 is a flowchart illustrating a method for reconstructing a cell voltage curve of an exemplary second battery cell 2 with a high temporal resolution based on a cell voltage curve of a first battery cell with a high temporal resolution and the cell voltage curve of the second battery cell with a low temporal resolution.

[0070] In step S1, voltage values ​​of a cell voltage curve of the first battery cell with a high temporal resolution, a cell voltage curve of one or more second battery cells with a low temporal resolution and a cell current curve with a high temporal resolution are continuously provided.

[0071] In step S2, the charge flow rate and cell voltage curve of the reference cell are downsampled to a low temporal resolution in a first adjustment step. The resulting signals are then low-pass filtered at a cutoff frequency between 1 and 10 mH.

[0072] In a next step S3, a first optimization problem is solved to optimize the parameters of a first parameter vector θ1. θ1 corresponds to min J1θ1,i, i ∈{1,2} θ1={C0,Δ,CSoC0,Δ} st θ_1,i≥θ1,i≤θ1,i¯

[0073] An initial value for the initial state of charge difference can be calculated, for example, by CSoC0,Δ0=1n⋅v¯OC∑i=1n(v⌣ref,i−v⌣cell,i) and the initial value of the capacity difference C 0,Δ can be assumed to be zero.

[0074] The cost function corresponds to J1=12‖v⌣'ref−(v⌣cell+v⌣Δ,1)‖2 v⌣Δ,1=v¯OC⋅(q⌣⋅θ1,1+θ1,2) so that a preliminary temporally highly resolved cell voltage curve is obtained with v^cell=v^ref−v^Δ,1 v^Δ,1=v¯OC⋅(q^⋅θ1,1*+θ1,2*)

[0075] In a subsequent step S4, the preliminary cell voltage curve v̂ ref the first battery cell with the low temporal resolution is again low-pass filtered with a higher second cutoff frequency of, for example, 50 mH.

[0076] The cell voltage curve v⌣'cell,comp,1 the second battery cell is compensated by the previously determined voltage difference and also low-pass filtered to v⌣res' to obtain.

[0077] Subsequently, in step S5, the sign of the correlation between the cell voltage curve and the battery current curve is determined: sign(cov(v⌣res',i⌣t)σv⌣res'⋅σi⌣t)

[0078] Subsequently, in step S6, a second optimization problem is solved minθ2,i J2, i∈{1,2,3} θ2={vδ,0,R1,Δ,C1,Δ} st θ¯2,i≥θ2,i≤θ2,l¯; τ_≤R1,Δ⋅C1,Δ≤τ¯ with a cost function J2=12‖v⌣ref'−(v⌣cell,comp,1'−s⋅v⌣Δ,2')‖2

[0079] In the next step S7, the reconstruction of the temporally high-resolution cell voltage curve of the second battery cell is obtained as follows: v^cell=v^ref−v^Δ,1−s⋅v^Δ,2, where v̂ Δ,2 corresponds to the solution of the delta stress response model with optimized parameter vector θ*2.

[0080] Now, in step S8, the ohmic resistance of the series resistor R0 is determined. Based on the low-resolution cell voltage curve of the second battery cell, this is expressed as v̌ Δ,1 and s · v̌ Δ,2 to v̌ cell,komp,2 compensated.

[0081] The ohmic resistance of the series resistor R0 is determined by simple regression R0,Δ=i⌣t−1⋅v⌣cell,comp,2

[0082] In a subsequent step S9, the high-resolution cell voltage v̂ cell can be determined as follows: v^cell=v^ref−v^Δ,1−s⋅v^Δ,2−v^Δ,3 v^Δ,3=R0,Δ⋅it^

Claims

[1] Computer-implemented method for monitoring a device battery (1) based on a temporally high-resolution cell voltage curve of a battery cell (2), wherein the temporally high-resolution cell voltage curve of a second battery cell (2) is reconstructed based on a temporally high-resolution cell voltage curve of a first battery cell (2) and a temporally low-resolution cell voltage curve of the second battery cell (2) and a temporally high-resolution cell current curve, comprising the following steps: - calculating (S9) a differential voltage between the temporally low-resolution cell voltage curve of the second battery cell (2) and a temporally high-resolution cell voltage curve of the first battery cell (2) downsampled to a low temporal resolution using a delta voltage response model in the form of a linear differential equation, depending on the temporally high-resolution cell current curve; - Reconstructing (S7) the temporally high-resolution cell voltage curve of the second battery cell (2) by applying the differential voltage to the temporally high-resolution cell voltage curve of the first battery cell (2). [2] Method according to claim 1, the temporally high-resolution cell voltage curve has a temporal resolution between 1 Hz and 100 Hz and the temporally low-resolution cell voltage curve has a temporal resolution between 0.1 Hz and 1 Hz. [3] Method according to claim 1 or 2, wherein the difference voltage for a time step within the temporally low-resolution cell voltage curve is determined as a function of a first voltage difference which is determined as a result of a first optimization (S3) of a cell voltage based on an evaluation of an OCV characteristic curve as a function of a charge change at the time step, which depends on the cell current at the time step, at a temporally low resolution. [4] Method according to claim 3, wherein before the first optimization (S3) the temporally low-resolution cell voltage curve of the second battery cell (2) is low-pass filtered with a first cutoff frequency. [5] Method according to claim 3 or 4, wherein the difference voltage for a time step within the temporally high-resolution cell voltage curve is determined as a function of a second voltage difference which is determined as a result of a second optimization (S6) of the cell voltage based on an evaluation of a behavior of the RC element and as a function of a cell voltage of the second battery cell (2) corrected by the first voltage difference. [6] Method according to claim 5, wherein before the second optimization (S6) the temporally low-resolution cell voltage curve of the second battery cell (2) is low-pass filtered with a second cutoff frequency which is higher than the first cutoff frequency. [7] Method according to claim 5 or 6, wherein the differential voltage for a time step within the temporally high-resolution cell voltage curve is determined as a function of a third voltage difference which is the result of determining a resistance difference between the series resistance (R0) of the second and the first battery cell (2), as a function of a cell voltage of the second battery cell (2) corrected by the first and the second voltage difference. [8] Apparatus for carrying out one of the methods according to one of claims 1 to 7. [9] Computer program product comprising instructions which, when the program is executed by at least one data processing device, cause the device to carry out the steps of the method according to one of claims 1 to 7. [10] Machine-readable storage medium comprising instructions which, when executed by at least one data processing device, cause the device to carry out the steps of the method according to one of claims 1 to 7.

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