Receding horizon regression analysis for battery impedance parameter estimation

Abstract

Vehicle, comprising: a traction battery (14); and a control unit (22) which is configured output impedance parameters associated with the battery (14) based on regressions of battery input current data (403) and corresponding battery output voltage data (405) falling within a moving window (508) having a time duration (tdur), wherein the time duration (tdur) of the moving window (508) is calibrated based on several factors, including determining whether to maintain a difference in the estimated model parameters with respect to at least one battery parameter value previously measured during the offline tests; output a performance capability for the battery (14) defining a maximum power limit and a minimum power limit based on the impedance parameters; and to operate the battery (14) to keep a power associated with the battery (14) within the limits.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to techniques for parameter estimation of elements forming a battery model and providing control of an associated battery. In particular, the disclosure relates to a vehicle comprising a traction battery and a control unit. Furthermore, the disclosure relates to a traction battery system comprising a plurality of cells and a control unit. BACKGROUND

[0002] Hybrid electric vehicles (HEVs) use a combination of an internal combustion engine and an electric motor to provide the power to propel a vehicle. This arrangement provides improved fuel economy over a vehicle with only an internal combustion engine. One method for improving fuel economy in an HEV involves shutting down the internal combustion engine during times when the internal combustion engine is operating at low efficiency and is not required to power the vehicle. In these situations, the electric motor, connected to a battery system, is used to provide all the power required to propel the vehicle.When the driver's power demand increases to the point where the electric motor can no longer provide enough power to meet the demand, or in other cases when the battery's state of charge (SOC) falls below a certain level, the internal combustion engine should be started quickly and smoothly in a manner that is barely noticeable to the driver.

[0003] DE 10 2008 053 ​​344 A1 discloses a system and method for estimating the lifespan of a secondary cell using an adaptive array filter algorithm. WO 2012 / 060 597 A2 discloses a device for announcing the replacement time of a battery. US 2004 / 0 239 332 A1 discloses a method and device for determining the starting capability of a vehicle. SUMMARY

[0004] A vehicle is proposed, comprising: a traction battery; and a controller configured to output impedance parameters associated with the battery based on regressions of battery input current data and corresponding battery output voltage data falling within a shifting window having a time duration, wherein the time duration of the shifting window is calibrated based on several factors, including determining to maintain a difference in the estimated model parameters with respect to at least one battery parameter value previously measured during offline testing; output a performance capability for the battery defining a maximum power limit and a minimum power limit based on the impedance parameters; and operate the battery to maintain a power associated with the battery within the limits.

[0005] Furthermore, a traction battery system is proposed, comprising: a plurality of cells; and a control unit configured to implement a shifting window having a time duration to filter input current data and corresponding output voltage data associated with the cells; output impedance parameters associated with the cells based on regressions of the input current data and corresponding output voltage data; change the time duration based on a difference between a value of at least one impedance parameter and a predefined value such that subsequent values ​​of the at least one impedance parameter fall within a predefined range around the predefined value; output a performance capability for the cells defining a maximum performance limit and a minimum performance limit based on the impedance parameters;and to charge and discharge the cells so that the associated power remains within these limits.;

[0006] A battery system includes a battery pack having one or more cells and a control unit configured to provide control for the battery pack. The system may include one or more equivalent circuits configured to model the battery pack using generalized linear regression analysis. The generalized linear regression analysis is performed using a dataset of independent variable vectors and a dependent variable vector formed from a series of battery pack input currents and corresponding battery pack voltage responses that fall within a shifting window. BRIEF DESCRIPTION OF THE DRAWINGS Fig. Figure 1 shows a schematic block diagram of a hybrid electric vehicle illustrating typical propulsion and energy storage components; Fig. Figure 2 shows a schematic diagram of an equivalent circuit for a Li-ion battery; Fig. 3 shows a flowchart of an algorithm for identifying one or more battery model parameters; Fig. Figure 4 shows graphical representations illustrating a shifting time window in which a current input and a voltage output of a battery are detected; Fig. Figure 5 shows graphs representing measured current and voltage data of a battery used in the generalized regression analysis; and Fig. Figure 6 shows plots representing estimated battery parameters generated from the receding horizon statistical regression approach. DETAILED DESCRIPTION

[0007] Detailed embodiments of the present invention are disclosed in this specification as required, but it is to be understood that the disclosed embodiments are merely examples of the invention that may be embodied in various and alternative forms. The figures are not necessarily drawn to scale; some features may be greatly exaggerated or reduced to show details of particular components. Therefore, the specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a typical basis for teaching one skilled in the art how to variously employ the present invention.

[0008] An HEV battery system may implement a battery management strategy that estimates values ​​describing the current operating conditions of the battery pack and / or one or more battery cells. The operating conditions of the battery pack and / or the one or more battery cells include a battery state of charge, power fade, capacity fade, and immediately available power. The battery management strategy may be able to estimate values ​​as the cells age during the battery pack's lifetime. Accurately estimating some parameters and improving prediction of battery dynamics using the estimated parameters can improve the battery pack's performance and resilience and can ultimately extend the battery pack's useful life.For the battery system described here, estimating some parameters of the battery pack and / or cells can be performed as discussed below.

[0009] Fig. 1 shows a typical hybrid electric vehicle. A typical hybrid electric vehicle 2 may include one or more electric motors 4 mechanically connected to a hybrid transmission 6. The hybrid transmission 6 is also mechanically connected to an internal combustion engine 8. The hybrid transmission 6 is also mechanically connected to a driveshaft 10, which in turn is mechanically connected to the wheels 12. In a further embodiment, not shown, the hybrid transmission may be a non-selectable manual transmission that includes an electric motor. The electric motors 4 may provide propulsion and braking capability when the internal combustion engine 8 is turned on or off. The electric motors 4 also serve as generators and may provide fuel economy benefits by recovering energy that would normally be lost as heat in the friction braking system.The electric motors 4 can also provide reduced pollutant emissions because the hybrid electric vehicle 2 can be operated in electric mode under certain conditions.

[0010] A battery pack 14 may include, but is not limited to, a traction battery having one or more battery cells that store energy that can be used by the electric motors 4. The vehicle battery pack 14 typically provides a high-voltage DC output and is electrically connected to a power electronics module 16. The power electronics module 16 may communicate with one or more control modules that form a vehicle computer system 22. The vehicle computer system 22 may control multiple vehicle functions, systems, and / or subsystems. The one or more modules may include, but are not limited to, a battery management system. The power electronics module 16 is also electrically connected to the electric motors 4 and provides the capability to transfer energy in both directions between the battery pack 14 and the electric motors 4.For example, a typical battery pack 14 may provide a DC voltage, while the electric motors 4 may require three-phase AC power to operate. The power electronics module 16 may convert the DC voltage into the three-phase AC power required by the electric motors 4. In a regenerative mode (generator mode), the power electronics module 16 converts the three-phase AC power from the electric motors 4, which serve as generators, into the DC voltage required by the battery pack 14.

[0011] In addition to providing power for propulsion, the battery pack 14 can also provide power to other electrical systems of the vehicle. A typical system may include a DC / DC converter module 18 that converts the high-voltage DC output of the battery pack 14 into a low-voltage DC supply compatible with other vehicle loads. Other high-voltage loads can be connected directly without the use of the DC / DC converter module 18. In a typical vehicle, the low-voltage systems are electrically connected to a 12-volt battery 20.

[0012] The battery pack 14 may be controlled by the power electronics module 16, which may receive instructions from a vehicle computer system 22 having one or more control modules. The one or more modules may include, but are not limited to, a battery control module. The one or more control modules may be configured to control the battery pack 14 using a battery model parameter estimation method that estimates an average of the effective internal battery resistance during operation to determine the battery's performance. Predicting performance allows the battery pack 14 to avoid overcharging or overdischarging, which may result in reduced battery life, vehicle powertrain performance issues, and so on.

[0013] The battery parameter prediction method and / or strategy can support the real-time (i.e., during operation) determination of the battery's current limits and performance capabilities. Many battery parameter estimation methods are compromised by the accuracy of battery models and unforeseen environmental conditions or unexpected disturbances during battery operation. For example, when a battery is in a charge-depleting mode, a simple battery model cannot capture the complex system dynamics of the associated voltage output and current input that are attempted to be measured.The method or strategy for a vehicle battery measurement may use an equivalent circuit model that uses one or more resistant-capacitor (RC) circuits in different configurations to measure the battery pack in the vehicle to provide the electrochemical impedance during operation.

[0014] Fig. 2 shows a schematic diagram of a simple equivalent circuit modeling a battery. The circuit may model a battery including a battery pack and / or one or more battery cells. The simple equivalent circuit model 200 may include a Randles circuit model and / or one or more RC circuits. The Randles circuit (e.g., an RC circuit) consists of an active electrolytic resistor R 1202 which is connected to a parallel capacitor C 204 and an active charge transfer resistor R 2 206 is connected in series. The Randles circuit allows measuring a terminal voltage v t 212, an open circuit voltage of the battery v OC 214, an internal battery voltage v 1 216 and the voltage of the RC circuit v 2 210. The Randles circuit can be implemented in an HEV battery management system to provide predictive calculations for one or more battery parameters.

[0015] The HEV battery management system may implement a Randles circuit model to predict a battery's dynamic responses, such as battery terminal voltage responses relative to the electrical current inputs to the battery pack. The Randles circuit model may enable fast calculations by the battery management system without adding additional hardware and / or increasing system complexity. The equivalent circuit model 200 may allow the calculation of predictive battery system parameters, including, but not limited to, the battery pack's impedance, internal resistance, and its correlated dynamics. The measured values ​​may be recorded, calculated, and stored in one or more control modules within the vehicle computer system, including the battery's energy control module.

[0016] The model parameters in a Randles circuit model can be estimated from measurements of the battery inputs and outputs using various algorithms. Battery performance can be predicted from the battery model using estimated model parameters that represent resistive behavior, charge transfer dynamics, and scattering dynamics during vehicle operation (e.g., real-time operation). Battery performance can be affected by the current state of the battery and its correlated dynamics. A battery's performance can be determined by measuring its internal states and can be inferred using external system outputs that are subject to system disturbances during battery operation.Battery system performance calculations can be improved by applying a receding horizon to the battery measurements to make the estimated parameter(s) less sensitive to system disturbances.

[0017] The real-time estimation algorithm for the battery model parameters can be designed to obtain estimated model parameters that are less sensitive to model inaccuracies and sensor disturbances by combining generalized linear regression analysis with a receding horizon (or moving window) approach. The model of a Randles circuit is represented by the following equation: v˙2=−1R2Cv2+1Ci where equation (1) is discretized to be applied to a moving window using the following equation: v˙2=v2,k−v2,k−1Δt

[0018] The discrete form of equation (1) is derived based on equation (2) into the following equation: v2,k=(1−ΔtR2C)v2,k−1+ΔtCik−1=av2,k−1+bik−1

[0019] Where v 2,k 210 the voltage across the RC circuit in the simplified model of a Randles circuit at the current time step t=t k is, v 2,k-1 the voltage across the RC circuit in the simplified model of a Randles circuit at the previous time step t=t k-1 is, Δt is the duration of a time step and i k-1 the input current at the previous time step t=t k-1 An alternative way to implement equation (3) is to replace the input current i k-1 at the previous time step by the input current i k at the current time step.

[0020] As formulated in equation (3), a new model parameter a is defined in the following equation: a=1−ΔtR2C and another model parameter b is defined in the following equation: b=ΔtC

[0021] The battery response, which represents the battery dynamics, is defined in the following equation: yk=vOC,k−vt,k=v2,k+R1ik

[0022] Where y k is the voltage response of the battery, which represents the battery dynamics at a given battery state of charge (SOC), v OC,k the open circuit voltage at a current time step t=t k is and v t,k is the terminal voltage applied to the battery terminals at the current time step t=t k is measured.

[0023] To derive a system response equation that includes the battery responses defined in equation (6) and the input currents, the following equation transforms equation (6) into: v2,k=yk−R1ik

[0024] Then, equation (7) is combined with equation (3), resulting in an equation of system dynamics expressed in terms of input currents and system responses as follows: yk=ayk−1+R1ik+(b−aR1)ik−1

[0025] The resulting equation is expressed in the form of a linear function consisting of the coefficients a, R 1 and (b-aR 1 ) and independent variables. The linear coefficients a, R 1 , (b-aR 1 ) and independent variables represent the measured voltage response of the system y k-1 at the previous time step t=t k-1 , the power input to the battery pack i kat the current time step t=t k and the power input to the battery pack i k-1 at the previous time step t=t k-1 .

[0026] The coefficients of the linear equation in equation (8) are represented in a 1×3 vector form as follows: β=[a R1 (b−aR1)]T=[β1 β2 β3]T

[0027] The independent variables of the linear equation in equation (8) are expressed in the form of the following vector: Xk=[yk−1 ik ik−1]

[0028] The coefficient vector β is estimated from the one or more data sets containing measurement data within the moving window using the following equation: β^=(XTX)−1XTy

[0029] Where β̂ is the identified coefficient vector and X is the data matrix of the independent variables. If the number of data in the time window is N, the data matrix X of the independent variables in equation (11) is an N×3 matrix formed from the following vector: X=[yk−N ik−N+1 ik−N⋮⋮⋮yk−1 ik ik−1]

[0030] A data vector of the dependent variable in equation (11) is an N×1 vector formed by: y=[yk−N+1⋮yk]

[0031] Once the coefficient vector β̂ is identified, the model parameters of the battery R 1 , R 2 and C can be calculated from the vector using the following equations, which are derived from equations (4), (5) and (9): R1=β^2 R2=β^3+β^1β^21−β^1 C=Δtβ^3+β^1β^2

[0032] Fig. Figure 3 shows a flowchart of an algorithm for identifying one or more battery model parameters used in the management and control of a battery pack. The method may be implemented using software code contained in the vehicle's control module. In further embodiments, the method 300 may be implemented in other vehicle control units or distributed across multiple vehicle control units.

[0033] In relation to Fig. 3 will be in Fig. 1 and Fig. 2 and its components are referred to with the same reference numerals throughout the discussion of the method to facilitate understanding of various aspects of the present disclosure. The method for controlling the prediction of battery parameters in a hybrid electric vehicle may be implemented by a computer algorithm, machine code, or software instructions programmed in one or more suitable programmable logic units of the vehicle, such as the vehicle's control module, the hybrid control module, another control unit in communication with the vehicle computer system, or a combination thereof.Although various steps shown in flowchart illustration 300 appear to occur in a chronological order, at least some of the steps may occur in a different order, or some steps may be performed concurrently or not at all.

[0034] At step 302, the vehicle computing system may begin powering up the one or more modules during a key-on event that allows the vehicle to be powered on. Powering up the one or more modules may cause variables related to the battery management system to be initialized before allowing one or more algorithms to execute in the vehicle computing system at step 304.

[0035] For example, it may be necessary to initialize battery parameters during a key-on event because the dynamics of a battery cell at rest include a self-discharge / charge depletion condition. The battery management method may initialize the system before measuring input current and output voltage to predict battery terminal voltage, current limits, and / or other battery-related parameters that characterize battery dynamics. Battery dynamics may vary during a key-on event due to several factors, including, but not limited to, the length of time the vehicle has been idle without a charge, battery life, battery operating modes, and / or environmental conditions.

[0036] At 306, the system may receive measured battery voltage outputs and current inputs from sensors in the battery system or from algorithms designed to estimate system responses. The system may monitor the number of data points consisting of current measurements and voltage measurements at step 308. If the number of data points is less than the desired amount of data points measurable in a predetermined, moving window, the system may request the collection of additional data points before performing a generalized linear regression analysis at 312. The number of data points in the predetermined, moving window may be calculated, for example, by determining the window length t durdivided by the time step Δt. In another example, the system can collect data points in the moving window until their number is equal to or greater than a calibratable number of data points required to calculate the battery parameter predictions using receding horizon analysis. If the system has not received the required number of data points, it can continue measuring and collecting additional input current and output voltage data.

[0037] According to the invention, the duration (or size) of the shifting window is calibrated based on several factors, including the determination of maintaining the discrepancy between the estimated model parameters and the battery parameter value(s) previously measured during offline testing. The discrepancy may be based on a predefined range between the estimated model parameters and the previously measured battery parameter values. The true value(s) may be identified and / or measured offline using a calibration process. The ranges may be expressed as functions of the battery state of charge, temperature, and / or other characteristic variables of the battery.

[0038] If the number of data points is equal to or greater than the required number of data points in the moving window, in step 310 a new data point is added to the data set while the oldest data point is removed from the data set. The time frame window is Fig. 4 is presented and explained in more detail.

[0039] Once the system has the data, which includes the battery voltage and current measurements prepared by steps 306, 308, and 310, the system may perform a generalized linear regression analysis of the data sets in step 312 to estimate the battery model parameters that characterize the battery dynamics in the equivalent circuit model. The generalized linear regression analysis uses a data set that has explanatory variables (or independent variables) and response variables (or dependent variables) to estimate the coefficients in the linear regression equation for the best data fit. The data sets are prepared by recording the current and voltage measurements acquired in the moving window. The battery parameters may include, but are not limited to, the internal battery resistance and the RC circuit parameters in the equivalent circuit 200.The battery parameters may vary due to the structure of the equivalent circuit model used in the battery management method.

[0040] In step 314, predicting battery responses, including battery performance, allows the system to determine how to manage battery power and energy at each time step or any time step. Battery performance may include setting a maximum and minimum power limit for battery operation based on the calculated impedance. Accurately predicting battery response may avoid or mitigate battery overuse by adjusting battery operation within safe limits, thereby improving battery life. Accurately predicting battery response may also improve the performance of the powertrain system or other associated systems / subsystems by extending the use of the battery pack in the battery electric vehicle or hybrid electric vehicle.

[0041] If the system detects a key-off event, the system may terminate the one or more algorithms used to manage the battery pack and / or the one or more battery cells in step 316. If the system does not receive a key-off request, the system may continue to measure the battery current and the battery pack output voltage, which are used to estimate the battery parameters. In step 318, the vehicle computing system may include a key-off mode that allows the system to store one or more parameters in non-volatile memory such that those parameters can be used by the system for the next key-on event.

[0042] Fig. Figure 4 shows plots illustrating a receding horizon statistical regression approach that receives voltage and current data from one or more moving windows. The plots show a battery input current profile 403, a battery output voltage profile 405, and moving windows with a duration of t durat different time locations 408, 410, 412. The graphical representation 400 of the profile of a battery input current consists of an x-axis representing time 402, a y-axis representing current 404, and a profile of the battery input current 403. The graphical representation 401 of a profile of a battery output voltage consists of an x-axis representing time 408, a y-axis representing voltage 406, and a profile of the battery output voltage 405. The current profile 403 and the voltage profile 405 can be measured by sensors or estimated by various algorithms.

[0043] The receding horizon (or moving window) allows a real-time estimation of one or more battery parameters, although only the amount of energy in the moving window during the time period t durstored battery response data. The generalized linearized regression analysis of the acquired data 403, 405 in the moving windows 408, 410, 412 filters the measurement noise and processes the noise in the data by minimizing the discrepancies between the data and a regression equation. The window time period t dur is determined by comparing the performance of noise suppression and the performance of detecting the true parameter values.

[0044] Fig. 5 shows graphs representing battery current and voltage measurements used to form independent variable data and dependent variable data in the generalized linear regression analysis. The graphs show a moving window 508 to capture the battery current and voltage measurements. The battery voltage output profile graph 500 shows the battery voltage output 510, which is calculated from the battery terminal voltage minus the battery open circuit voltage (OCV). The battery voltage output profile 500 consists of an x-axis representing time 502 and a y-axis representing voltage 504. The battery current input profile graph 501 shows the battery current input 512 by having an x-axis representing time 502 and a y-axis representing current 506.The window, which has a predefined duration of the time step 510 and moves towards new data, acquires a new data point of battery current and voltage at the current time and discards the oldest data point in the window.

[0045] Fig.6 shows graphs representing battery parameters estimated using a receding horizon statistical regression approach. The internal resistance (or active electrolyte resistance) profile graph 600 shows the internal resistance estimation results over time using a receding horizon method 610 and a conventional method 608. The conventional method 608 may include, but is not limited to, an extended Kalman filter estimation approach. The graph 600 consists of an x-axis representing time 602, a y-axis representing resistances in ohms 604, and the estimated internal resistance profiles 608, 610.The active charge transfer resistance profile graph 601 shows the estimated charge transfer resistance profiles using a regression analysis 612 and a conventional method 614, which may be performed using, but is not limited to, an extended Kalman filter. The charge transfer resistance profile consists of an x-axis representing time 602 and a y-axis representing resistances in ohms 606.

[0046] The estimated battery model parameters may include, but are not limited to, the internal resistance R 1 , the charge transfer resistance R 2and the charge transfer capacity C, and they may allow the battery control unit to calculate (or estimate) the battery's performance capabilities or other battery responses in real time. The calculated battery model responses help to effectively utilize the battery pack while avoiding excessive operation of the battery beyond the battery's usage limits, thereby improving the lifespan and performance of the battery pack and / or the one or more battery cells.

[0047] Although exemplary embodiments have been described above, these embodiments should not be construed as describing all possible forms of the invention. Rather, the terms used in this specification are to be understood as terms of description, not limitations, and it is understood that numerous changes may be made without departing from the spirit and scope of the invention. Furthermore, the features of the various implemented embodiments may be combined to form further embodiments of the invention.

[0048] It further describes: A. Vehicle comprising: a traction battery; and a control unit that configures to output impedance parameters associated with the battery based on regressions of battery input current data and corresponding battery output voltage data falling within a moving window having a time duration; output a performance capability for the battery that defines a maximum power limit and a minimum power limit based on the impedance parameters; and to operate the battery to keep the battery's power within limits. B. Vehicle to A, wherein the time duration is based on a difference between a predefined value and a value of at least one of the impedance parameters. C. Vehicle to B, with the duration increasing as the difference increases. D. Vehicle to B, the duration decreasing as the difference decreases. E. The vehicle of claim 1, wherein the impedance parameters comprise an internal resistance, a charge transfer resistance, or a charge transfer capacitance. F. Traction battery system comprising: a multitude of cells; and a control unit configured implement a moving window having a time duration to filter input current data and corresponding output voltage data associated with the cells; output impedance parameters associated with the cells based on regressions of the input current data and corresponding output voltage data; to change the time period due to a difference between a value of at least one impedance parameter and a predefined value such that the subsequent values ​​of the at least one impedance parameter fall within a predefined range around the predefined value; output a performance capability for the cells that defines a maximum power limit and a minimum power limit based on the impedance parameters; and to charge and discharge the cells so that the corresponding power remains within these limits. G. System according to F, where the time duration increases as the difference increases. H. System according to F, where the time duration decreases as the difference decreases. I. System according to F, wherein the impedance parameters comprise an internal resistance, a charge transfer resistance or a charge transfer capacitance. J. Tax proceedings, including: Outputting impedance parameters of a traction battery based on regressions of battery input current data and corresponding battery output voltage data falling within a moving window having a time duration; Outputting a performance capability for the battery that defines a maximum power limit and a minimum power limit based on the impedance parameters; and Operating the battery to keep the battery's power within limits. K. The method of J, wherein the time period is based on a difference between a predefined value and a value of at least one of the impedance parameters. L. Method according to K, wherein the time duration increases as the difference increases. M. Method according to K, where the time duration decreases as the difference decreases. N. The method of J, wherein the impedance parameters comprise an internal resistance, a charge transfer resistance, or a charge transfer capacitance. O. Procedure according to J , where the regressions are linear regressions.

Claims

[1] Vehicle comprising: a traction battery (14); and a control unit (22) which is configured output impedance parameters associated with the battery (14) based on regressions of battery input current data (403) and corresponding battery output voltage data (405) falling within a moving window (508) having a time duration (tdur), wherein the time duration (tdur) of the moving window (508) is calibrated based on several factors, including determining whether to maintain a difference in the estimated model parameters with respect to at least one battery parameter value previously measured during the offline tests; output a performance capability for the battery (14) defining a maximum power limit and a minimum power limit based on the impedance parameters; and to operate the battery (14) to keep a power associated with the battery (14) within the limits. [2] A vehicle according to claim 1, wherein the time duration (tdur) is based on a difference between a predefined value and a value of at least one of the impedance parameters. [3] A vehicle according to claim 2, wherein the time duration (tdur) increases as the difference increases. [4] A vehicle according to claim 2, wherein the time duration (tdur) decreases as the difference decreases. [5] The vehicle of claim 1, wherein the impedance parameters comprise an internal resistance (R1 202), a charge transfer resistance (R2 206) or a charge transfer capacitance (C 204). [6] Traction battery system comprising: a multitude of cells; and a control unit (22) configured implement a sliding window (508) having a time duration (tdur) to filter input current data (403) and corresponding output voltage data (405) associated with the cells; output impedance parameters associated with the cells based on regressions of the input current data (403) and corresponding output voltage data (405); to change the time duration (tdur) due to a difference between a value of at least one impedance parameter and a predefined value, that the subsequent values ​​of the at least one impedance parameter fall within a predefined range around the predefined value; output a performance capability for the cells that defines a maximum power limit and a minimum power limit based on the impedance parameters; and to charge and discharge the cells so that the corresponding power remains within these limits. [7] Traction battery system according to claim 6, wherein the time duration (tdur) increases as the difference increases. [8] Traction battery system according to claim 6, wherein the time duration (tdur) decreases as the difference decreases. [9] The traction battery system of claim 6, wherein the impedance parameters comprise an internal resistance (R1 202), a charge transfer resistance (R2 206), or a charge transfer capacitance (C 204).

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