EP4010837A1 - Simulation of a battery - Google Patents

Abstract

The invention relates to general technology for monitoring the status of a battery, e.g. a lithium ion battery. A thermal simulation model is used for this purpose. Different examples relate to the parameterising of the thermal simulation model.

Description

Simulation of a battery

TECHNICAL AREA

Various examples of the invention relate to the simulation of a battery. Various examples relate in particular to the parameterization of a simulation model.

BACKGROUND

Thermal and electrical simulation models are known for simulating a battery. It is often complicated and problematic to determine the right simulation model or the right combination of simulation models to precisely describe the electrical and thermal behavior of the battery. In addition, it is often difficult to set the parameter values of such simulation models according to the actual properties of the battery (parameterization). However, accurate parameterization is helpful in order to obtain precise results from the simulation.

BRIEF DESCRIPTION OF THE INVENTION

Therefore, there is a need for improved techniques for simulating a battery. In particular, there is a need for improved techniques for parameterizing simulation models.

This object is achieved by the features of the independent claims. The features of the dependent claims define embodiments.

A computer-implemented method for the discrete-time simulation of a battery comprises the application of a thermal model to obtain a discrete-time temperature characteristic of the battery. The thermal model includes: a thermal cell model for cells of the battery, an air model for heat exchange between the cells of the battery and ambient air, and also a thermal system model for heat exchange between the cells of the battery and a respective environment. When using the thermal model for a magazine, a cell temperature of the cells of the battery is determined by means of the thermal cell model as a function of an ambient air temperature obtained from the air model in a previous magazine and also as a function of one from the thermal system model in the previous magazine - determined ambient heat flow. When applying the thermal model for the time step, the air temperature of the air model and the ambient heat flow of the thermal model are determined depending on the cell temperature of the cells.

This is followed by an alternating determination of the cell temperature on the one hand, and the air temperature and the ambient temperature on the other. This iterative process is continued for several time steps.

A combination of the thermal model with an electrical model can take place in various examples. A thermal-electrical co-simulation can take place in this way. For example, the development of the temperature or the electrical state variables of the battery could alternately be determined for a magazine.

In addition, the simulation (which can include the thermal model and the electrical model) can be combined with an aging prediction. For example, the decrease in capacity could be predicted. The aging model can be linked to the simulation. This means that the corresponding aging can be predicted for each magazine.

Using the computer-implemented method, it is therefore possible to characterize the state of the battery particularly precisely.

In some examples it would be possible to use such a characterization of the state of the battery in order to adjust the further operation of the battery appropriately. This could, for example, prevent a particularly rapid decrease in the capacity of the battery from occurring.

The simulation can be carried out for a large number of batteries. In particular, it would be possible for the simulation to be carried out for a large number of battery types. The simulation is parameterized accordingly so that different properties of different battery types or batteries can be taken into account.

According to the examples described herein, various model parameters of the simulation can be parameterized in a type-specific manner. This means that different parameter settings can be used for different battery types. In some examples it would also be possible for the parameters to be set in a battery-specific manner. In other words, this means that different parameter values are used for the models for different batteries of the same type. In this way, for example, different types of battery installation, different cooling concepts, different load profiles, etc. can be taken into account in the simulation.

The simulation can be carried out repeatedly. This means that the simulation can be triggered at several times. In this way, the status of the battery can be repeatedly monitored. In some examples it would be possible for the parameterization to be carried out once, e.g. when registering the corresponding battery type or the corresponding battery in a database. In another example it would also be possible for the parameterization to be carried out repeatedly. This means that different parameter values can be determined repeatedly for the simulation models for one and the same battery. In this way it would be possible, for example, for different, time-variable operating boundary conditions (for example activated / deactivated active cooling, different load profiles, etc.) to be taken into account dynamically by means of the simulation.

The features set out above and features that are described below can not only be used in the corresponding explicitly set out combinations, but also in further combinations or in isolation without departing from the scope of protection of the present invention.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 schematically illustrates a system comprising several batteries and a server according to various examples.

FIG. 2 schematically illustrates details in connection with the batteries according to various examples.

FIG. 3 schematically illustrates details in connection with the server according to various examples.

FIG. 4 is a flow diagram of an exemplary method according to various examples. FIG. 5 schematically illustrates the use of a simulation of cells of the battery in connection with the aging modeling of a battery in accordance with various examples.

FIG. 6 schematically illustrates an electrical-thermal simulation of the cells of the battery and the use of an aging model.

FIG. 7 is a flow diagram according to various examples, which illustrates the use of an electrical simulation model and a thermal simulation model.

FIG. 8 illustrates details in connection with the thermal simulation model from FIG. 7th

FIG. 9 is a flow diagram according to various examples, which illustrates details in connection with the parameterization of the thermal simulation model.

FIG. 10 illustrates an electrical simulation model according to various examples.

FIG. 11 is a flowchart according to various examples, which illustrates details in connection with the parameterization of the electrical simulation model.

DETAILED DESCRIPTION OF EMBODIMENTS

The above-described properties, features and advantages of this invention and the way in which they are achieved will become clearer and more clearly understandable in connection with the following description of the exemplary embodiments, which are explained in more detail in connection with the drawings.

The present invention is explained in more detail below on the basis of preferred embodiments with reference to the drawings. In the figures, the same reference symbols denote the same or similar elements. The figures are schematic representations of various embodiments of the invention. Elements shown in the figures are not necessarily shown to scale. Rather, the various elements shown in the figures are shown in such a way that their function and general purpose can be understood by a person skilled in the art. Connections and couplings between functional units and elements shown in the figures can also be used as indirect connections binding or coupling can be implemented. A connection or coupling can be implemented wired or wirelessly. Functional units can be implemented as hardware, software, or a combination of hardware and software.

Techniques related to the characterization of rechargeable batteries are described below. The techniques described herein can be used in connection with the most varied of types of batteries, for example in connection with batteries based on lithium ions, such as lithium-nickel-manganese-cobalt oxide batteries or lithium manganese oxide batteries.

The batteries described herein can be used in different fields of application, for example for batteries that are used in devices such as motor vehicles or drones or portable electronic devices such as mobile radio devices. It would also be conceivable to use the batteries described here in the form of stationary energy stores.

The techniques described herein make it possible to characterize the battery based on condition monitoring. The condition monitoring can include ongoing monitoring of the load on the battery and / or a condition forecast of the battery. This means that the state of the battery can be tracked by monitoring the load and / or can be predicted for a certain forecast interval in the future. In particular, an aging estimate of the state-of-health (SOH) of the battery can be made.

As a general rule, the SOH will decrease as the battery ages. Increasing aging can occur if the capacity of the battery decreases and / or if the impedance of the battery increases.

Various of the examples described herein can be implemented at least partially on the server side. This means that at least part of the logic associated with the status monitoring can be carried out on a central server, separate from the battery or the battery-operated device. For this purpose, a communication link can be established between the server and one or more management systems of the battery. By implementing at least part of the logic on the server, particularly precise and computationally intensive models and / or simulations can be used in connection with the condition monitoring. This makes it possible to carry out the condition monitoring particularly precisely. It may also be possible Collecting and processing data for an ensemble of batteries, for example in connection with machine-learned models.

Various examples described herein can perform condition monitoring during use of the battery based on measurement data from the battery. This means that the condition monitoring is carried out especially at a certain point in time during the life of the battery - with reduced SOH. The battery can then be used in the field. In this way, it may in particular be possible to also take into account the previous aging behavior of the battery. This also makes it possible to carry out the status monitoring particularly precisely.

The status monitoring can in particular include a simulation of the status of the battery. The simulation of the state of the battery can be carried out on the basis of the measurement data. Then parameters of the condition of the battery that are not directly observed can also be determined in connection with the simulation. Examples of parameters that are sometimes not directly observable would be an internal temperature or temperature distribution, current or voltage values, etc. On the basis of such information, particularly precise condition monitoring can be carried out.

An aging model can also be used in connection with simulating the condition of the battery. The aging model can describe the aging of the battery and in particular the internal condition of the batteries as a function of the load. In that the simulation is carried out together with the aging model, the future development of parameters of the state of the battery can be predicted for the prediction interval.

It can be seen from this that the status monitoring can be helpful for the ACTUAL status as well as for a predicted status.

The techniques described here enable parameterization of simulation parameters of the simulation. In particular, by means of the techniques described herein, it can be possible to determine the values for parameters of the simulation particularly precisely, so that the status monitoring of the battery can be carried out particularly precisely.

Various examples relate in particular to the modeling of thermal behavior. This concerns, for example, a thermal cell model. Next, details of the thermal cell model will be described. The temperature profile of a battery cell over time, e.g. a lithium-ion cell or another rechargeable cell, is determined on the one hand by the heat generation within the cell and on the other hand by the heat flows in the cell and between the cell and the environment. Correspondingly, when modeling the thermal behavior, a distinction is made between heat generation and heat dissipation models.

In contrast to electrochemical energy, heat is a form of energy that is not material-bound and therefore not a state variable, but a process variable. Heat generation effects in battery cells occur in electrochemically active as well as all current-carrying materials. In principle, a distinction can be made between the following heat generation mechanisms:

The irreversible heat generation or Joule heat is created by the Transport of lithium ions through the electrolyte and the intercalation electrodes (including the passage of charge at phase boundaries and the diffusion resistance of passivation layers) and through the electron flow through the active materials and arresters. These effects each lead to overvoltages, which is why the irreversible heat generation Q _irr in electrical-thermal cell models can be described. This relationship is only a worst-case estimate because it is assumed that all processes that contribute to the voltage increase U (t) - Uocv (t) run with the same current I (t). The resulting heat is always exothermic. If an equivalent circuit model is used for the electrical modeling, the irreversible power loss from Eq. (1) can also be calculated using the sum of the power losses of all resistive elements:

The reversible heat generation is achieved by intercalation or deinter- calation of lithium ions in the host lattice of anode and cathode and the associated chemical reactions and can be endothermic or exothermic depending on the direction of the current and the entropy coefficient. With Gibb's equation the reversible Power loss according to Eq. (2.3) can be derived, where corresponds to the so-called entropy coefficient

The entropy coefficient can be determined experimentally using calorimetry or potentiometric measurements. An analytical calculation is only possible with precise knowledge of the cell structure and all partial reactions.

In the following, techniques are described by means of which it is possible to use the thermal simulation model with a cell model that takes heat generation and heat dissipation into account. Parameterization techniques are described.

FIG. 1 illustrates aspects related to a system 80. The system 80 includes a server 81 connected to a database 82. System 80 also includes communication links 49 between server 81 and each of a plurality of batteries 91-96. The communication links 49 could for example be implemented via a cellular network.

In general, different battery types can be used in the various examples described herein. This means that the batteries 91-96 can be of several types. Different types of batteries can differ, for example, with regard to one or more of the following properties: shape of the cell (ie round cell, prismatic cell, etc.), cooling system (air cooling with an active or passive concept, coolant in coolant hose, passive cooling elements, etc.) .), cell chemistry (for example electrode materials used, electrolytes, etc.), etc. There may also be a certain variance in connection with such properties between batteries 91-96 of the same type. For example, it can happen that batteries 91-96 of the same type are mounted differently and thus different cooling systems are used. In addition, the same battery cells can sometimes be arranged differently, so that an electrical and thermal system view of the ensemble of cells varies. As a general rule, such battery-specific and / or type-specific effects in connection with the simulation can be taken into account in the various examples described herein. In particular, it may be possible for models of the simulation to be parameterized type-specifically and / or battery-specifically.

In FIG. 1 illustrates by way of example that the batteries 91-96 can send status data 41 to the server 81 via the communication links 49. For example, it would be possible that the status data 41 are indicative of one or more operating values of the respective battery 91-96, i.e. can indicate measurement data. The status data 41 could be sent event-driven or according to a predetermined time scheme.

These status data 41 can be used, for example, in connection with a thermal simulation and / or an electrical simulation of the respective battery 91-96. For this purpose, a simulation model for each of the batteries 91-96 can be stored in the server 81. It is possible to use different simulation models for different batteries 91-96. It would also be possible to use different parameterizations for the respective simulation model for different batteries 91-96. In this way, a “digital twin” can be made possible for each of the batteries 91-96. In the following, techniques are described which enable the configuration and parameterization of the simulation models for the various batteries 91-96 precisely and quickly. In this way, a well-fitting simulation model or well-fitting parameterization can be used on a large number of batteries 91-96.

In FIG. 1 is also illustrated by way of example that the server 81 can send control data 42 to the batteries 91-96 via the communication links 49. For example, it would be possible for the control data 42 to indicate one or more operating limits for the future operation of the respective battery 91-96. For example, the control data could indicate one or more control parameters for thermal management of the respective battery 91-96 and / or charge management of the respective battery 91-96. By using the control data 42, the server 81 can therefore influence or control the operation of the batteries 91-96.

In FIG. 1 the respective SOH 99 is also illustrated schematically for each of the batteries 91-96. As a general rule, the SOH 99 of a battery 91-96 can include one or more different parameters depending on the implementation. Typical parameters of the SOH 99 can be, for example: electrical capacity, ie the maximum possible stored charge; and / or electrical impedance, i.e. the frequency response of the resistance or Alternating current resistance as the ratio between electrical voltage and electrical current strength.

Techniques for condition monitoring are described below which make it possible to determine the SOH 99 and / or other characteristic parameters for the condition of the batteries 91-96 for each of the batteries 91-96 during the use of the batteries 91-96. This means that, for example, the electrical impedance and / or the electrical capacitance can be determined. This can be done using the simulation model on the server. The server 81 could then provide corresponding information about the SOH 99 in turn to the batteries 91-96, for example via the control data 42. A management system for the batteries 91-96 could then adapt an operating profile for the batteries, for example to further reduce the SOH 99 to avoid.

FIG. 2 illustrates aspects related to batteries 91-96. The batteries 91-96 are coupled to a respective device 69. This device is powered by electrical energy from the respective battery 91-96.

The batteries 91-96 comprise or are associated with one or more management systems 61, e.g. a BMS or other control logic such as an on-board unit in the case of a vehicle. The management system 61 can be implemented by software on a CPU, for example. Alternatively or additionally, for example, an application-specific circuit (ASIC) or a field-programmable gated array (FPGA) could be used. The batteries 91-96 could communicate with the management system 61 via a bus system, for example. The batteries 91-96 also include a communication interface 62. The management system 61 can set up a communication link 49 with the server 81 via the communication interface 62.

While in FIG. 2 the management system 61 is drawn separately from the batteries 91-96, in other examples it would also be possible that the management system 61 is part of the batteries 91-96.

In addition, the batteries 91-96 comprise one or more battery blocks 63. Each battery block 63 typically comprises a number of battery cells connected in parallel and / or in series. Electrical energy can be stored there.

The management system 61 can typically access one or more sensors in the one or more battery blocks 63. The sensors can, for example, the Measure the current flow and / or the voltage in at least some of the battery cells. As an alternative or in addition, the sensors can also measure other variables in connection with at least some of the battery cells, for example to determine the temperature, volume, pressure, etc. of the battery and send them to the server 81 in the form of status data 41. The management system 61 can also be set up to implement thermal management and / or charge management of the respective battery 91-96. In connection with the thermal management, the management system 61 could, for example, control cooling and / or heating. In connection with the charging management, the management system 61 could control a charging rate or a depth of discharges, for example. The management system 61 can therefore set one or more operating boundary conditions for the operation of the respective battery 91-96, for example based on the control data 42.

FIG. 3 illustrates aspects in connection with the server 81. The server 81 comprises a processor 51 and a memory 52. The memory 52 can comprise a volatile memory element and / or a non-volatile memory element. In addition, the server 81 also comprises a communication interface 53. The processor 51 can set up a communication connection 49 with each of the batteries 91-96 and the database 82 via the communication interface 53.

For example, program code can be stored in memory 52 and loaded by processor 51. The processor 51 can then execute the program code. Execution of the program code causes processor 51 to perform one or more of the following processes, as described in detail in connection with the various examples herein: characterization of batteries 91-96; Carrying out one or more status predictions for one or more of the batteries 91-96, for example based on operating values that are received as status data 40 from the corresponding batteries 91-96 via the communication link; Perform electrical simulation of batteries 91-96; Performing a thermal simulation of batteries 91-96; Performing condition monitoring of batteries 91-96; Performing an aging estimation of batteries based on one or more operating profiles; Sending control data 42 to batteries 91-96, for example to set operating boundary conditions; Storing a result of the status monitoring of a corresponding battery 91-96 in a database 82; Etc..

FIG. 4 is a flow diagram of an exemplary method. The procedure is carried out by a server. The method is used to characterize a battery on the server side. This means that the method of FIG. 4 is used to monitor the condition of the battery. For example, it would be possible that the method according to FIG. 4 is executed by the processor 51 of the server 81 based on program code from the memory 52 (cf. FIG. 3). Optional blocks are shown in FIG. 4 shown with dashed lines.

First, in block 1001, one or more operating values are obtained from the battery to be characterized. For this purpose, status data can be received in block 1001, for example, via a communication link between the battery and the server. This means that measurement data can be received from the batteries to be characterized.

The one or more operating values can relate to an SOH of the battery, for example. The one or more operating values can relate to a capacity of the battery and / or an impedance of the battery, for example. In general, it would also be possible for one or more further or other characteristic variables of the operation of the battery to be indicated by the one or more operating values. For example, in some examples it would be possible for current data (for example a time series) and / or voltage data (for example a time series) to be indexed by the operating values. This means that the operating values could, for example, describe a time profile of the current in one or more cells of a battery block of the battery or could describe a time profile of the electrical voltages in one or more cells of a battery block of the battery. The operating values could, for example, also describe a temperature in one or more areas of a battery. The operating values could, for example, describe a corresponding time series of temperature data. The operating values could also include an operating profile, i.e., for example, a load characterization, such as depth of discharge (DOD), discharge rate, charge rate, SOC cycles, etc.

Subsequently, in block 1002, status monitoring is carried out for the battery in order to characterize it. The condition monitoring can include the determination of the actual condition of the battery, as well as a condition prediction using an aging model.

A plurality of state predictions can be carried out in block 1002. If several state predictions are carried out in block 1002, these can be associated with different boundary conditions for the operation of the battery. For example, the operating constraints considered in block 1002 could be one or more The following elements relate to: a control parameter of a thermal management of the battery and / or a control parameter of a charge management of the battery. In general, the operating boundary conditions can determine certain conditions for the operation of the battery that are detached from the specific operating profile, which is determined, for example, by the use of the respective device 69 that is associated with the corresponding battery (ie, for example, load , removed load, discharge rate, charge rate, depth of discharge, etc.).

The one or more state predictions in block 1002 can be based on an operating profile which is derived from an operating profile which, for example, is indexed for the respective battery in a monitoring interval by the operating values from block 1001. For example, it would be possible for the operating profile used for the one or more state predictions in block 1002 to be determined based on measurements on the battery in the monitoring interval. This means that, for example, the measured DOD and / or measured SOC cycles and / or measured charge rates etc. can be used in connection with the one or more state predictions in block 1002. By using an operating profile for the one or more condition predictions in block 1002, which is based on the specific operation of the corresponding battery in the monitoring interval, a particularly reliable or precise condition prediction can be made possible.

As a result, the state prediction can output a time course of the aging for a prediction interval. This is shown in FIG. 5 shown.

FIG. 5 illustrates aspects relating to the aging of a battery, for example one of the batteries 91-96 from FIG. 1. In FIG. 5 shows the SOH 99 as a function of time. The SOH 99 decreases as a function of time. This acceptance of the SOH 99 can be monitored by the status monitoring according to FIG. 4: Block 1002 can be determined.

In detail, the SOH 99 decreases during a monitoring interval 151. The SOH 99 can be determined particularly precisely by means of a simulation - which includes, for example, a thermal model and / or an electrical model; for this purpose, one or more parameters of the battery can be precisely determined, which otherwise cannot be measured or can only be measured imprecisely. This can be based on the operating values from FIG. 4: Block 1001 take place. Then, at point in time 155 (ACTUAL point in time), the battery is characterized by performing several state predictions 181-183 for the battery. As a result, state predictions 181-183 provide a prediction for the aging of the battery, ie the SOH 99 during a prediction interval 152. From FIG. 5 it can be seen that the SOH 99 varies between the various state predictions 181-183, which is due to the different operating profiles on which the simulation is based. The operating profiles can differ in terms of temperature, idle state of charge, charge and discharge rate, end point of charge and discharge, cycle depth and / or mean state of charge during charge and discharge and combinations thereof. For example, it would be possible that the state prediction 181 - which results in a comparatively small decrease in the SOH 99 as a function of time during the prediction interval 152 - compared to the state prediction 183 - which results in a comparatively strong decrease in the SOH 99 as a function of the Time during the prediction interval 152 results - a different configuration of the thermal management and a lower DOD assumes. For example, the thermal management of the battery could enable lower operating temperatures through active cooling as an operating boundary condition for the state prediction 181.

Now referring again to FIG. 4: As a general rule, the status monitoring results from block 1002 can be used in different ways.

In one example it would be possible that a management system, which is associated with the respective battery, based on the results of the condition monitoring from block

1002 is controlled, see block 1003. For example, it would be possible for control data (compare FIG. 1: control data 42) to be determined based on the comparison of the results and for this control data to be sent to the management system. As a general rule, one or more different parameters of the operation of the respective battery can be set. For example, it would be possible for the control data to specify one or more operating limits for the future operation of the battery. Alternatively or additionally, it would also be possible for the control data to specify one or more control parameters for thermal management and / or charging management of the battery. Such a feedback of the results of one or more state predictions or in general the characterization of the battery can make it possible to enable particularly sustainable operation of the respective battery.

However, it is not necessary in all examples for the results of the one or more state predictions to be fed back into the operation of the battery. So far is Block

1003 an optional block. In some examples it would alternatively or additionally be possible for results of the state predictions to be stored in a database (compare FIG. 1: database 82), see block 1004.

Next, an exemplary implementation of performing the (optional) one or more state predictions in block 1002 in connection with the flow diagram in FIG. 6 described.

FIG. 6 is a flow diagram of an exemplary method. The method according to FIG. 6 can be run from a server. For example, it would be possible that the method according to FIG. 6 is executed by the processor 51 of the server 81 based on program code from the memory 52 (cf. FIG. 3).

The method according to FIG. 6 is used to predict the state of a battery. If several state predictions are to be carried out, the method according to FIG. 6 carried out several times.

In block 1011, the operating values for the capacity and the impedance of the respective battery are first obtained. Block 1011 thus corresponds to block 1001. This means that a current value for the SOH 99 of the battery is obtained. This is typically done based on status data that is received by the respective management system that is associated with the corresponding battery. This could also include the use of a simulation - e.g. with an electrical and / or a thermal model - in order to determine e.g. certain hidden state parameters of the battery that cannot be measured directly. These operating values are used to initialize the condition prediction.

Several iterations 1099 of blocks 1012-1014 are then performed. The different iterations 1099 correspond to time steps for the state prediction; H. advancing time during the prediction interval 152.

In this context, an electrical state of the battery and a thermal state of the battery are initially simulated in block 1012 by means of corresponding simulation modules for the respective journal of the corresponding iteration 1099. In block 1012, the simulation takes place taking into account a corresponding operating boundary condition of the battery. This depends on the respective state prediction 181-183. In addition, a corresponding operating profile can be assumed for operating the battery.

To simulate the electrical and thermal state, an electrical simulation module can be coupled with a thermal simulation module. This is shown in FIG. 7 illustrated.

FIG. 7 is a flow diagram of an exemplary method. FIG. 7 illustrates aspects in connection with the simulation of a battery, e.g. in the context of condition monitoring.

The first step is initialization in block 1021. As part of the initialization, e.g. measured ACTUAL operating values can be obtained from the battery.

A simulation of electrical parameters of the cells is then carried out with the electrical model in block 1022. This can be based on the measured ACTUAL operating values of the battery.

The electrical simulation module can use an equivalent circuit model (ECM) for the battery. The ECM can include electrical components (resistance, inductance, capacitance). The parameters of the components of the ECM can, for example, be determined using a Nyquist plot with the characteristic frequency ranges of the transmission behavior of the cell block of the battery. As a result of the implementation on the server 81, the number of RC elements can be selected to be particularly high, e.g. greater than three or four. A particularly high accuracy of the electrical simulation can thereby be achieved. One ECM can be used for each cell of a cell block.

The simulation of thermal parameters of the cells then takes place with a thermal model in block 1023.

The thermal simulation model makes it possible to determine the temperature profile over time and, optionally, the local temperature. Heat sources (heat generation) and heat sinks (heat dissipation) can be taken into account. The heat dissipation to the environment can be taken into account. Details on the heat generation model are described, for example, in: D. Bernandi, E. Pawlikowski, and J. Newman, “A General Energy Balance for Battery Systems, Journal of the Electrochemical Society, 1985. Analytical or numerical models for local temperature distribution can be used. The influence of thermal management can be taken into account. Sh. e.g. M.-S. Wu, KH Liu, Y.-Y. Wang, and C.-C. Wan, “Heat dissipation design for lithium-ion batteries,” Journal of Power Sources, Vol. 109, Rn. 1, pp. 160-166, 2002.

Then - if a more extensive prediction is to be made - a new journal can be initialized, block 1024, and the electrical and thermal models applied again. Otherwise the simulation is finished.

Based on such an electrical-thermal modeling - again with reference to FIG. 6 - an aging estimate is performed in block 1013, i. H. the capacity and the impedance of the battery are determined for each magazine based on a result of the simulation of the electrical condition and the thermal condition of the battery.

Different techniques can be used in connection with the aging estimation. The aging estimate can include, for example, an empirical aging model and / or a machine-learned aging model. For example, an empirical aging model and a machine-learned aging model could be used in parallel and the results of these two aging models could then be combined by averaging, for example weighted averaging.

As a general rule, the empirical aging model could include one or more empirically determined parameters which relate an operating profile of the battery, which is obtained from the simulation from block 1012, to a deterioration in the SOH 99, for example a reduction in capacity and / or increasing the impedance. The parameters can be determined in laboratory measurements, for example. An exemplary empirical aging model is described in: J. Schmalstieg, S. Käbitz, M. Ecker, and DU Sauer, “A holistic aging model for Li (NiMnCo) 02 based 18650 lithium-ion batteries,” Journal of Power Sources, Vol. 257, pp. 325-334, 2014.

In contrast to this, a machine-learned aging model can be continuously adapted by machine learning on the basis of status data obtained from different batteries of the same type. For example, artificial neural networks such as convolutional neural networks could be used. Another technique involves the so-called support vector method machine). For example, data from an ensemble of batteries (compare FIG. 1: batteries 91-96) can be used to train a corresponding algorithm by means of machine learning.

A check is then made in block 1014 to determine whether a termination criterion has been met. If this is not the case, block 1012 is carried out again for a next time step in the prediction interval 152, ie for the next iteration 1099. The capacitances and impedances determined in the previous iteration 1099 are used, ie the simulations in block 1012 build on each other. The iterative adaptation of capacitance and impedance enables a particularly precise state prediction.

If the termination criterion in block 1014 is met, the state prediction is complete. Examples of termination criteria include: number of iterations 1099; End of prediction interval 152 reached; Exceeding or falling below threshold values for the capacity and / or the impedance; Etc.

Next, details of the thermal model (see FIG. 7: block 1023) and the electrical model (see FIG. 7: block 1022) are described.

FIG. 8 illustrates aspects related to the thermal model.

In FIG. 8 it is shown that the thermal model comprises several sub-models 6001-6003. In particular, the thermal model 6000 comprises a cell model 6001, i. H. a thermal model for the individual cells of the battery. The thermal model 6000 also includes an air model 6003. The air model 6003 describes a heat exchange between the cells of the battery and ambient air. The thermal model 6000 also includes a thermal system model 6002. This describes the heat exchange between the cells of the battery with a respective environment.

The following explains how the Thermal Model 6000 works. The model is initialized at 1101. During the initialization 1101, a number of parameters 1102 are transferred. Exemplary parameters 1102 include, in particular, the temperature of the various cells. This temperature can be measured and, as operating values, can be obtained in the form of status data 41. In addition, the current strength I is obtained in the various cells and a state of charge SOC. The various overvoltages can also be obtained. These values can in turn be measured or, for example, obtained from the electrical simulation model. These parameters are then fed to the calculation of the irreversible heat generation at 1103 and the calculation of the reversible heat generation at 1104.

The irreversible portion of the heat generation in block 1103 depends on the electrical cell voltage and the cell current flow in the cells. The reversible portion of the heat generation model in block 1104 is dependent on an entropy coefficient, the temperature and the cell current.

The heat generation models represent the interface between the electrical state or the output of the electrical model and the thermal model. In addition to the irreversible, Joule heat generation (block 1103) which results directly from the electrical model based on the sum of the overvoltages U _ov multiplied by the current / is determined by means of the entropy coefficient and the temperature T in the heat generation model also takes the reversible heat into account (block 1104):

The entropy coefficient can typically be assumed to be constant over temperature.

The entropy coefficient is determined, for example, using potentiometric measurements. Other examples include capturing an open circuit voltage curve at multiple temperatures or taking a calorimetric measurement.

A reference implementation for potentiometric measurements is described e.g. in: A. Eddahech, O. Briat, and J.-M. Vinassa, “Thermal characterization of a high-power lithium-ion battery: Potentiometry and calorimetric measurement of entropy changes,” Energy, Vol. 61, pp. 432-439, 2013.

With the potentiometric measurement, a temperature jump can be applied at several temperatures and the change in the open-circuit voltage can be measured. In a specific example, in the potentiometric measurements the cells are each discharged from the fully charged state in 10% SOC steps with 1C at 25 ° C and then relaxed (min. 5 h, depending on the cell up to 48 h) until the rest voltage with a gradient of adjusts. Defined temperature jumps to 5, 25 and 45 ° C with a waiting time of 5 hours are then made for acclimatization. The rest voltage values at the end of the acclimatization phases are saved and used to form the linear entropy coefficient used for the respective SOC step.

It is then possible for the potentiometric measurement to be carried out with several charge states of the cells, i.e. H. if there are several SOC values. In this way the entropy coefficient can be determined for the several charge states. In particular, the entropy coefficient can be dependent on the state of charge. For example, it has been observed that there is a significant deviation in the entropy coefficient for charge states of less than 20%. As an alternative or in addition, it would also be possible for the entropy coefficient for charging and discharging the battery to be determined separately. This means that the multiple charge states can be determined depending on a direction of charge or a direction of discharge.

It is then possible to use different values for the entropy coefficient in connection with the reversible heat generation in block 1104, depending on the SOC and / or the charging or discharging direction.

The cell temperature can be determined in block 1105 as a function of the heat generation from blocks 1103-1104. Block 1105 implements a heat dissipation model. As a general rule, different types of heat dissipation models are conceivable. In particular, differently complex heat dissipation models can be used, depending on the cell type or the required accuracy.

When choosing the heat dissipation model, one can choose between differently complex modeling approaches. The temperature differences and heat gradients that occur for a given battery system under anticipated load scenarios and should be modeled accordingly are crucial here.

The cell format, cooling system and battery pack design used have a major influence on this. For an aging prediction of lithium-ion cells, the Temperature development in the electrode coil of interest. For example, a connection between the volumetrically averaged winding temperature and the cell degradation of thermally homogeneous cells at the same temperature was established. On the other hand, it was found that the thermal inhomogeneity itself does not show any significant additional degradation. For a battery pack configuration with an expected inhomogeneous cell winding temperature, however, it must therefore be possible to calculate the volumetric mean value in order to enable valid status monitoring. In addition, if there are high temperature differences within the cell, knowledge of their distribution is necessary in order to detect any safety-critical hot spots. To determine the thermal gradients and thus the necessary spatial dimensionality of the thermal model for a given battery system, there are basically two options:

First: Experimental measurement: Temperature sensors installed on and above all in the cell measure the temperature development as a result of exposure directly. The introduction of temperature sensors into the cell interior can represent a considerable preparation effort. The temperature distribution in the active material can only be estimated by sensors on the cell housing because it is influenced by the comparatively good conductive housing material (aluminum or steel).

Second: Simulative investigation: Using a three-dimensionally resolved cell model that takes into account the connection of the cooling system via temperature or heat flow boundary conditions, the temperature differences that occur during operation can be analyzed using the heat generation from, for example, an electrical model. This can be done with a finite element simulation for different cooling configurations.

Both the experimental measurement and the simulative investigation can be based on an operating profile that is obtained, for example, from the status data 41 for the specific battery in the context of field operation. This means that, for example, load, removed charge, discharge rate, charge rate, depth of discharge, etc. can be taken into account depending on the specific operation.

It is then possible to take into account the result of such a simulative and / or experimental investigation of the spatial temperature gradients in the cells in order to determine the spatial dimensionality of the heat dissipation model. If, for example, significant temperature gradients in the spatial area are determined experimentally or by means of simulation, then a higher dimensional heat dissipation model can be used, which is defined in 2-D or 1-D, for example. Otherwise a 0-D heat dissipation model could be used. As a general rule, 3-D heat dissipation models would also be possible. For example, it was found that a 3-D heat dissipation model can be particularly helpful for cells that are not arranged in a Cartesian coordinate system, but rather offset from one another, for example.

It was found that, depending on the cell type and / or depending on the cooling system of the battery, it can already be determined without experimental or simulative investigation whether sufficiently good results can already be achieved in the spatial area using a heat dissipation model of low dimensionality. For example, it was determined that a 0-D heat dissipation model can be sufficient for a round cell, regardless of the specific cooling variant (jacket cooling, conduction cooling or no cooling). This is different with a prismatic cell. A 2-D model for heat dissipation may typically be required there.

The cell model can be analytically defined for a spatial dimensionality of 0-D and numerically defined with finite elements for a spatial dimensionality of 1-D or 2-D (with a mesh density for the simulation in the context of the state over- monitoring can be significantly lower than a mesh density for the calibration simulation to determine the required spatial dimensionality, as described above). The same can apply to a 3-D spatial dimension.

To validate the choice of spatial dimension of the dissipation models, the stationary and unsteady heat conduction can be considered in a calorimeter measurement with a defined power loss specification. This prevents any error propagation from the electrical model. The following load cycles are selected, for example:

• Constant power loss: Several phases with alternating charging / discharging pulses (duration 1s) at varying charging rates (C rate). Defined pauses between the various C rates. The duration of the load and the pause are selected so that a steady temperature level is reached.

• Sinus profile: constant power profile modeled with a sinusoidal signal, which results in a sinusoidal power loss profile from 0 to P _max . The amplitude and frequency are selected in such a way that a sinusoidal temperature response with constant amplitude and frequency results. Both load cycles are SOC-neutral (apart from the 1 s pulses), which means that no reversible heat generation that cannot be directly measured occurs. The irreversible heat generation is based on terminal voltage calculated and specified according to the dissipation model:

To analyze the temperature distribution of the cells, these can each be provided with several temperature sensors on the cell housing.

Measurements can be carried out in a thermal cabinet at constant temperature. The ambient temperature is measured. Initially, only free convection and radiation are assumed as types of heat transport. For example, the cells are placed upright on a rubber mat.

Then the temperature distribution of the cells can be viewed in both validation cycles, e.g. with a maximum constant power loss of approx. 0.3 W. Depending on the size of the temperature distribution, it can then be checked whether, for example, the choice of a heat dissipation model with 0-D spatial dimensionality is justified.

The heat dissipation model can thus be configured as above and receives the heat generation from blocks 1103 and 1104 as input. From FIG. 7 it can be seen that the determination of the cell temperature with the heat dissipation model in block 1105 also takes place as a function of a heat flow from the system (block 1113) and as a function of the air temperature (block 1118). The system model 6002 and the air model 6003 are used for this.

The cell model calculates the cell temperatures for each magazine based on the reversible and irreversible power loss P _v and the heat dissipation currents (block 1107). The dissipation _currents are composed of convective heat flow P _conv and heat radiation P _wheel (from the air model, block 1106) as well as the various heat flows of the system model P _pack . In the OD heat dissipation model, the cell temperature is calculated according to: Where m is the cell mass and c _{p is} the heat capacity. In the 2-D heat dissipation model, the power loss P _{v is} evenly distributed over the active material and the temperature distribution within the cell is calculated using Fourier's differential equation using the finite element method. The dissipation flows through the air and system components are taken into account according to the defined side surfaces.

Next, details of the air model 6003 will be described. In the case of the air model 6003, a distinction is made between free or forced convection (block 1114) depending on the air speed (block 1115). With free convection, a thermal air mass of the surrounding air is initialized for each cell. This is linked to the neighboring air masses or the environment (temperature boundary condition) via resistors (block 1117). Forced convection is mapped using a flow network model (block 1116). In the cell model, the heat flows between the cells and the associated air control volumes are first calculated using correlation relationships (block 1106). In relation to the defined flow direction, the heat flows from cells with parallel flow are then added to P _{conv in the air model} and _calculated according to Eq. (6) the temperature increase AT of the air mass flow certainly.

Next, details of the system model 6002 will be described. The system model 6002 bundles three cross-cell effects: heat exchange between the cells (block 1110), heat exchange between cells and peripheral elements (block 1109) and heat exchange between cells and a fluid cooling element, e.g. a hose through which coolant flows (block 1111). These effects are added in block 1112.

The heat exchange between cells can be defined in 2-D and parameterized with the associated contact resistances. Conduction with peripheral elements, such as current conductors, heat conducting plates or assembly elements or other solid-state cooling elements, can also be set individually for each cell. The parameterization of the peripheral elements is e.g. B. initially carried out analytically and corrected in the experiment if necessary. In addition to the influence of solids, the peripheral model can also be used to map temperature control using refrigerants, as long as this is present in two phases with constant temperature. The Mapping of coolant flowing through the battery pack with changing temperature is accomplished in block 1111 of system model 6002. The order in which the coolant passes through the cells is set using a matrix in 2-D.

There are various strategies for parameterizing the system model 6002, i.e. for obtaining the values for the various parameters, such as contact resistance, heat capacities, etc.

In one example, the parameterization of contact resistances and / or heat capacities of the heat exchange between the cells of the battery with one another, the heat exchange of the cells with the solid-state cooling element and the heat exchange of the cells with the fluid cooling element could be based on predetermined reference values. These can be obtained e.g. for the various materials from the literature. Material and substance-specific parameters of peripherals and cooling systems can be found in the literature.

It would then be possible to subsequently adapt this parameterization in order to obtain a higher level of accuracy. In particular, such a validation can take place at cell level or system level (i.e. taking into account the system model 6002 and the air model 6003).

The heat capacities of individual cells can be determined with a calorimeter. With the cell inserted, temperature jumps of ± 1 ° C, for example, are carried out and the necessary thermal output P _{z is} recorded. The jumps can be repeated with an empty calorimeter (thermal output PB). The heat capacity of the cell results from Eq. (7) to:

Typical specific heat capacities are in the range from 700 to 1000 J / (kg K).

A calorimetric measurement of the heating can also be used to determine the coupling of several cells to one another and to the periphery or air. Several cells can be placed in a reference matrix arrangement. This means that neighboring cells can be arranged at a distance from one another. In this way, the forced convection can be measured for a flow network model with correlation relationships will. The reference matrix arrangement can be introduced into a flow channel. The flow speed can be adjusted by means of an axial fan. The temperature distribution can be measured by temperature meters distributed along the reference matrix arrangement. The parameterization of the contact resistances and / or the thermal capacities can then be adapted from this.

The anisotropic thermal conductivity values of the cells as well as their heat transfer coefficient for certain reference configurations can be determined by means of thermal impedance spectroscopy (TIS). A sinusoidal power loss of different frequency is impressed on the cell and the temperature response is measured on the cell surface. Characteristic thermal parameters can thus be determined via the transfer function of the thermal dissipation model and the calculated thermal impedance.

FIG. 9 is a flow diagram of an exemplary method. The various techniques described above for parameterizing the thermal model 6000 are shown in FIG. 9 summarized. Using the technique of FIG. 9 a parameterization of the thermal model 6000 (see FIG. 8) is possible.

There can be various trigger criteria that trigger a parameterization according to the method in FIG. 9. In one example, a type-specific parameterization could take place. This means that the server 81 can manage, for example, a catalog of different types of batteries 91-96 in the database 82 (see FIG. 1). Whenever a simulation is initialized (compare FIG. 7: block 1021) the server 81 could access the database and read out the corresponding values of the parameters, in each case for the current battery type. In other examples it would also be possible for a battery-specific parameterization to take place. In such a case, a catalog of different batteries 91-96 from the server 81 could be managed in the database 82. The server 81 could then identify the current battery and load the corresponding operating parameter values. Finally, it would also be possible for a parameterization to be at least partially adapted for each simulation. Then a new parameterization could be initiated when executing block 1021. An exemplary application scenario concerns, for example, the selection of the complexity of the simulation model. Sometimes, based on the specific operating profile of a corresponding battery 91-96, for example, it may be sufficient to select a less complex simulation model. One example concerns, for example, the spatial dimension of a heat dissipation model of the thermal simulation. If the operating profile indicates, for example, a low load on the battery (slow charging or discharging, etc.) then temperature gradients can be used inside the battery. Then a lower spatial dimension can be used for the heat dissipation model.

First, in block 1031, the model for the heat generation is quantified. In particular, a reversible component can be parameterized for this purpose. For example, a potentiometric measurement can be carried out for this purpose and an entropy coefficient can be determined in this way. Compare Eq. 3.

Subsequently, in block 1032, the spatial dimension of the heat dissipation model is determined. There are various possibilities. For example, a finite element simulation of the cell geometry could be carried out, whereby a particularly high level of accuracy can be used in connection with this simulation (narrow simulation grid, mesh). In particular, a 3-D simulation can be carried out. Then a temperature gradient can be considered. If the temperature gradient does not fall below a certain threshold value for typical load parameters, then, for example, a 0-D model could be used for heat dissipation. Such a 0-D model can in particular be determined analytically. Otherwise a 1-D or 2-D model could be used. The size of the thermal gradient often also depends on the operating profile. Therefore, in block 1032, the operating profile could be considered. For example, a current operating profile could be obtained from the respective battery by means of status data 41. With less load on the battery, less heat can be generated and thus the thermal gradient can be smaller and a 0-D or 1-D model is sufficient (instead of a 2-D model).

The cell model, the air model and / or the system model 6001-6003 are then parameterized in block 1033. For this purpose, literature values can be assumed for the thermal capacity and / or the thermal conductivity of certain contact resistances, for example. It would also be possible to carry out one or more calorimetric measurements, for example in order to initially adapt initialized values, see block 1034. A heat capacity of the cells can be determined by means of the calorimetric measurement. A TIS could also be carried out in block 1034, for example in order to determine the anisotropic heat transfer coefficient of the thermal cell model 6001.

FIG. 10 illustrates aspects related to the electric model 900, see FIG. FIG. 7: Block 1022. The electrical model 900 is based on an equivalent circuit model. The electrical model can provide the cell current flow and the cell voltage. These variables can then serve as an input for the heat generation model (see FIG. 8, block 1102). The underlying principle of equivalent circuit diagram models (ECM) is the mapping of the electrochemical cell behavior with the help of a link between electrotechnical components 901-906. Depending on the level of detail, individual effects of the cell components can be combined or viewed separately. The general structure of an ECM is to be motivated in the following on the basis of the impedance spectrum of an exemplary cell (Panasonic NCR18650PF).

FIG. 10 illustrates the impedance spectrum 950 of the cell in a Nyquist plot. In the negative area of the Nyquist plot at high frequencies, the inductive behavior is shown due to the arresters to the poles and the metal housing itself. This is usually modeled by a constant inductance L 901 in series with the remaining ECM components 902-906.

The point of intersection of the impedance curve with the real part axis typically occurs in the region of 1 kHz and corresponds to the purely ohmic internal resistance of the cell as the sum of the limited conductivity of the current arrester, the electrode material, the electrolyte and the separator. A purely ohmic resistor R _0hm 902 can be used for modeling, depending on the SOC, temperature and state of aging.

After the zero crossing, a first circular arc follows, which reflects the polarization effects on the passivation layers of the anode (solid electrolyte interface, SEI) and cathode (solid permeable interface, SPI). The effect of the SPI layer is usually less pronounced than that of the SEI. The SEI layer growth is seen as the main aging mechanism in lithium-ion cells with graphite anode, which is why this dynamic effect is more pronounced as the state of aging progresses and often cannot be observed separately in new cells.

This is followed by a second semicircular arc due to the charge transfer reaction at the electrode-electrolyte boundary layers in combination with the double-layer capacitance. The double-layer capacitance C _dl (dl for "double layer") is the charge zone that is created at the contact surfaces of the anode and cathode with the electrolyte. The amount of charge stored in it depends on the electrode potential. Since the double-layer capacitance arises at the electrode-electrolyte boundary layers, it occurs parallel to the charge transfer redox reaction at the anode and cathode. This causes a polarization overvoltage due to the transition from ionic to electrical conduction, which in ECM is usually represented by the charge transfer resistance R _ct (ct for "charge transfer"). Since anode and Cathode basically have different parameters, two separate semicircular arcs can also appear in the impedance curve. From the individual arc of the cell examined, it can be concluded that either the charge resistance of one electrode (e.g. the graphite anode) is comparatively small to the other electrode or that both charge transfer reactions show a similar dynamic behavior. The double-layer capacitance C _dl and the charge resistance R _ct basically depend on the SOC, temperature, current rate and state of aging.

In the case of the semicircular arcs of charge passage / double-layer capacitance and SEI layer, it is noticeable that these have a compressed shape in the direction of the imaginary part axis. This phenomenon occurs when the time constant of the electrochemical effect does not have a fixed value but has a distribution around an average value. The distribution arises from the superimposition of parallel processes (such as the simultaneous passage of charge carriers at the anode and cathode) and the spatial expansion of the electrode / electrolyte boundary layer in the case of porous electrodes. However, since a regular RC element only depicts an ideal semicircle in the complex plane, so-called Zarc elements 903 are used to model compressed circular arcs.

In the low-frequency range, the impedance spectrum ends almost at a 45 ° angle, which is created by the diffusion behavior as a result of ion concentration differences in the electrolyte and the electrodes. A precise modeling of the mass transport phenomena through diffusion with R-L-C elements is difficult. A suitable approach for mapping the porous electrode structure are so-called transmission lines. However, since these have a complex transfer function and a large number of necessary parameters, so-called Warburg elements are used in the literature. A distinction can be made between three variants, which differ in the boundary conditions at the end of the diffusion path.

With a combination of the elements presented above, the impedance curve of a lithium-ion cell can be simulated well and the characteristics of the individual electrochemical effects can be analyzed. When transforming the transmission behavior into the time domain, however, some elements of the frequency domain (constant phase, Zarc and Warburg elements) must be approximated due to the lack of a Laplace transformation. In addition to conductor networks, serially connected RC elements are the most common approximation variant. For Zarc elements 903, an odd number of RC elements (3, 5, ...) is recommended in order to reproduce the compressed semicircular shape as best as possible. The number of RC elements used to approximate the dynamic cell behavior over the frequency range relevant to the application always represents a compromise between accuracy, computing time and parameterization effort.

In addition to the dynamic cell behavior, the static behavior without load can also be modeled in an electrical ECM. The so-called open circuit voltage (OCV) depends on the electrode materials used and their balance, which can change in the course of aging. It is usually modeled by an SOC-dependent ideal voltage source. Furthermore, a temperature dependency due to entropy changes can be taken into account, but this is typically less pronounced. With certain electrode materials, such as LFP cathodes, there is also a clear hysteresis effect with regard to the previous current load.

In various examples, it would be possible, as an alternative or in addition to an SOC-dependent ideal voltage source for modeling the open circuit voltage, to also take into account a hysteresis in connection with the modeling of the open circuit voltage. This can therefore mean that the no-load voltage is dependent on the direction of the current flow. In order to be able to model the no-load voltage when changing from one current direction to the other, corresponding transition coefficients can be taken into account. These can model the transition from the characteristic curve of the open circuit voltage, which is associated with one current direction, to the characteristic curve of the open circuit voltage, which is associated with the other current direction.

The previous section explained the modeling of lithium-ion batteries at the cell level. The step for the electrical simulation of a battery system - i.e. the electrical system model - can take place at different levels of detail:

(i) Scaling cell system: In this simplest case, the entire battery pack is represented by a single cell model. The system voltage is the product of the cell voltage and the number of serial cells and the system current is divided by the number of parallel cells and applied to the cell model. In this way, the parameters of the cell model do not have to be adjusted.

(ii) Modeling series connection, scaling cell-parallel connection: Here, each serial cell line is represented by its own cell model. This can already result in parameter spreads and resulting effects such as SOC drifts and uneven aging behavior of the serial strings. Existing parallel connections in the battery system are simulated as in 1.).

(iii) Modeling series and parallel connection: At this level of detail, each cell in the battery system is simulated using its own cell model. In addition to (ii), effects of the parallel connection, such as different current loads and the resulting SOC window in the case of parameter scatter, can thus also be mapped.

The accuracy of electrical equivalent circuit models depends largely on the quality of the model parameters.

When parameterizing the dynamic equivalent circuit parameters, a fundamental distinction can be made between methods in the time and frequency domain. One method in the time domain is the dynamic stress test measurement (DST), see. USABC Electric Vehicle Battery Test Procedures Manual, Rev. 2 (1996). Another method in the time domain is the evaluation of the voltage response of a cell to an impressed current jump (current pulse characterization measurement). Using the transfer function of the model and an error-minimizing optimization algorithm, a parameter set can be determined numerically (fitting), which simulates the measured voltage response with a maximum defined error. The problem with this method is that mathematically meaningful values for simulating the voltage response can be found in the optimization due to local minima, but these do not have the intended electrochemical correspondence and thus inevitably lead to simulation errors with other load profiles. Another possibility for parameterization in the time domain is the calculation of direct current resistances on impressed, constant current pulses after defined periods of time. The times should be defined in such a way that the resistance values have an electrochemical meaning (e.g. for the charge carrier resistance). In electrochemical impedance spectroscopy measurement (EIS) in the frequency range, the cell is subjected to a sinusoidal excitation signal (usually current, galvanostatic EIS) with constant frequency points in a defined frequency band and the amplitude and phase shift of the system response (voltage in the galvanostatic EIS) are measured. The advantage here is that dynamic effects with different time constants can be observed separately. A common form of representation of the impedance curve is the Nyquist diagram according to FIG. 10. With the complex transfer function of the equivalent circuit, the dynamic model parameters can again be determined by means of the fitting process within the framework of parameterization. Since the actual excitation signal with the EIS is sinusoidal alternating current around the zero position, a Current rate dependency an additional DC offset impressed. However, this changes the state of charge, which is why a suitable compromise has to be found between DC offset and EIS measurement duration.

There are two different methods for parameterizing the ideal voltage source in the ECM for modeling the no-load voltage: In the relaxation current measurement, the lithium-ion cell is gradually discharged or charged from the fully or discharged state to a defined state of charge and then for a defined period of time without Load waited in which all kinetic effects such as overvoltages and concentration gradients are to be reduced. The waiting time is typically in the range of several hours, whereby the subsidence of all overvoltages can take several days depending on the SOC and cell temperature. The relaxed voltage values at the end of the waiting time then result in a charging and discharging rest voltage curve. If you compare the two curves for the same SOC, you will notice a discrepancy between the values, which is known as the hysteresis effect. This dependence of the rest voltage on the previous history depends on the cell chemistry, the SOC and, to a lesser extent, on the temperature. It is particularly pronounced in electrode materials with two-phase transitions such as lithium iron phosphate. When measuring the constant current to parameterize the ideal voltage source in the ECM, the lithium-ion cell is charged and discharged over the entire SOC range with a low, constant current. Due to the low current rate (usually between C / 50 and C / 10), a quasi-stationary state with only low overvoltages can be assumed. These are eliminated by averaging the charging and discharging curves and a quasi no-load voltage characteristic is obtained. In comparison to the relaxation measurement, the test time is usually significantly shorter and the number of measuring points is significantly higher due to the continuous measurement. However, hysteresis effects cannot be quantified using this method. Constant current curves are also often used in the literature to determine the intercalation potentials of half or full cells by means of differential voltage analysis (DVA).

FIG. 11 is a flow diagram of an exemplary method. The method according to FIG. 11 can be used to parameterize the electrical model 900.

First, in block 1041, one or more relevant stress areas in the frequency space can be identified. The load areas correspond to those areas that are represented in the load profile of the battery - that is, present with a significant amplitude are. For this purpose, the operating profile of the battery can be taken into account, for example indicated by the status data 41.

Such techniques are based on the following knowledge: In order to be able to map the current and voltage behavior and thus heat generation and aging factors as precisely as possible for a specific application, the respective electrical load and environmental profile should be taken into account when defining the model. For use in vehicle batteries in the vehicle development process, this can be derived either from relevant driving cycles in connection with a longitudinal dynamics simulation or from measurements on the real vehicle. From this, on the one hand, the operating ranges of current, temperature and SOC of the battery pack and thus the required ranges of the model parameterization can be determined by means of amplitude analysis.

On the other hand, by means of discrete Fourier transformation of the current signal, the dynamics of the system excitation can be quantified in frequency spectra and thus the relevant frequency ranges can be determined with regard to the electrical model. For a typical measurement on a passenger vehicle, this results in a relevant range of up to approx. 1 Hz, for example. This can depend on the driver's driving style. With this information and the dynamic transfer behavior of the lithium-ion cells of the battery pack through EIS, the relevant electrochemical processes for modeling and thus the system order of the dynamic electrical model can be determined in the next step.

This means that the dynamic model order is then defined in block 1042. Due to the sequential measurement of different frequency ranges, electrochemical impedance spectroscopy is particularly suitable for identifying the impedance effects relevant for an application and their specific time constants. To define the dynamic model order, the respective cells are therefore measured in the operating ranges of temperature and SOC identified in block 1041 with a hybrid EIS in the frequency range from 5 kHz to 10 mHz. The number of support points represents a compromise between resolution and measurement time.

With the help of the impedance curves obtained, the relevant electrochemical effects to be mapped in the electrical model can then be identified on the basis of their time constants, for example the inductive components of the impedance or the impedance sections with a negative imaginary component. To assess the modeling quality of the impedance behavior and to parameterize various ECMs (i.e. to determine the number of RC elements, for example), a parameter fitting for EIS measurements can be used, based on the method of least squares:

In the cost function S place or each represents the real and imaginary part of the measurement and model fit with the parameter vector P. Via w _i , frequency-dependent weighting factors can be added. result from the transfer function of the selected ECM, for 2RC for example:

The above equations result in a non-linear cost function which is composed of two independent functions. A solution can be found with gradient-based or derivative-free optimization algorithms.

It would be possible to fit several transfer functions to differently complex models. The accuracy can then be checked and the complexity of the ECM, for example the number of RC elements, determined using the EIS. It was observed that models with Warburg elements depict the diffusion branch better than pure ones RC models. However, if there are 2 or more RC elements for diffusion, this can be approximated sufficiently well. A 3 or 4 RC element model represents a good compromise between computation and parameterization effort and accuracy. Here 1 or 2 RC elements are assigned to the high-frequency dynamic effects and the diffusion behavior is modeled with 2 RC elements.

After the definition of the dynamic model order in block 1042, the identification and parameterization of the static cell behavior takes place in block 1043.

To parameterize the static cell behavior for the various cell chemistries, both the relaxation (also current interruption, CI) and the constant current method (constant current, CC) can be used. With the relaxation measurement, after an initial capacity determination, each cell is discharged from the fully charged state by defined SOC steps and then charged again. The SOC increment is adjusted depending on the slope of the OCV in the upper, middle and lower SOC range. The capacity is determined with CC-CV charging and discharging according to the specified voltage window of the cells and a CV termination criterion of C / 50. This capacity value also forms the basis for the SOC-dependent parameterization of the remaining model parameters. After each discharged or charged SOC step, the cell is relaxed for at least 3 hours (in the deep SOC range up to 10 hours) and the voltage value at the end is used as a reference point for the discharge or charge curve. The voltage difference between the charging and discharging curves can be interpreted as the maximum value of the hysteresis behavior of the cells.

To integrate the hysteresis behavior in an ECM, there are a number of approaches in the literature that can be used here. One example is the hysteresis model by Verbrugge et al. in discrete time form.

The impedance behavior is then parameterized in block 1044.

Methods in the time and frequency domains can be used for this. The EIS has already been discussed in connection with block 1042. With the alternating current excitation in different frequency ranges, the different electrochemical reactions can be separately excited and identified. However, the current rate dependency of the charge carrier passage reaction can sometimes not be recorded satisfactorily because the SOC is within it due to an additionally impressed direct current component the alternating current excitation of a frequency point shifts and thus there is no longer any linear transmission behavior. Therefore, the impedance parameters can be determined on the basis of current pulses (HPPC). A distinction can be made between two variants: a) HPPC with pure parameter fitting: Here, all impedance parameters are fitted together or divided into one or more voltage curves as a result of current pulses. Due to the division, different electrochemical effects can be taken into account separately. b) HPPC fitting with predefined parameters: In contrast to a), individual impedance parameters are specified here for the fitting by means of upstream measurements, like Rohm from EIS measurements.

In addition to various C-rates, the impedance behavior is parameterized for defined SOC and temperature intervals. For the actual parameter fitting according to variants a) and b), an optimization algorithm as described above can again be used.

Finally, in block 1045, the electrical cell model is synthesized by modeling at the system level.

In accordance with the previous blocks 1041-1044, a global impedance model with no-load voltage, hysteresis behavior, ohmic resistance and up to four RC elements can be used as the electrical cell model. The transfer behavior in the state space representation (for clarity of the 2RC variant) results accordingly to: All calculations in the cell model are matrix-based, which enables efficient simulation of series and parallel connections.

Of course, the features of the embodiments and aspects of the invention described above can be combined with one another. In particular, the features can be used not only in the combinations described, but also in other combinations or on their own, without departing from the field of the invention.

Claims

PATENT CLAIMS

1. Computer-implemented method for discrete-time simulation of a battery, the method comprising:

- Applying a thermal model (6000) to obtain a time-discrete temperature characteristic of the battery, the thermal model comprising: a thermal cell model (6001) for cells of the battery, an air model (6003) for heat exchange between the cells of the battery and ambient air, and a thermal system model (6002) for a heat exchange between the cells of the battery and a respective environment, wherein when applying the thermal model for a magazine, a cell temperature of the cells of the battery by means of the thermal cell model as a function of one obtained from the air model in a previous magazine Air temperature of the ambient air and further depending on an ambient heat flow obtained from the thermal system model in the preceding journal is determined, and when applying the thermal model for the journal, the air temperature of the air model and the ambient heat flow of the thermi system model can be determined depending on the cell temperature of the cells.

2. The method according to claim 1, wherein the thermal cell model has a heat generation model with an irreversible component (1103) depending on the electrical cell voltage and cell current flow of the cells and a reversible component (1104) depending on an entropy coefficient, the temperature and the cell voltage, wherein the method further comprises:

- Carrying out a potentiometric measurement to determine an entropy coefficient of the reversible component.

3. The method of claim 2, wherein performing the potentiometric measurement comprises:

- at several temperatures: each application of a temperature jump and measurement of a change in an open circuit voltage of the respective cell.

4. The method according to claim 2 or 3, wherein the potentiometric measurement at several charge states of the cells and / or depending on a charge or Discharge direction is performed to determine the entropy coefficient for the plurality of charge states.

5. The method according to any one of the preceding claims, wherein the thermal cell model comprises a heat dissipation model for the cells of the battery, wherein the method further comprises:

- Determination of a spatial dimension of the heat dissipation model of the thermal cell model by simulative or experimental investigation of spatial temperature gradients in the cells, and / or depending on a cell type, and / or depending on a cooling system of the battery and / or depending on a measured operating profile of the cell and / or as a function of a calorimeter measurement.

6. The method according to claim 5, wherein the heat dissipation model of the thermal cell model is analytically defined for a location-space dimensionality of 0-D and is defined numerically with finite elements for a location-space dimensionality of 1-D or 2-D or 3-D.

7. The method according to any one of the preceding claims, wherein the thermal system model models one or more of the following variables: (1110) heat exchange between the cells of the battery depending on a predetermined geometric arrangement of the cells to one another, (1109) heat exchange between the cells of the battery with a solid cooling element depending on a predetermined geometric arrangement of the cells to the solid cooling element, and / or (1111) heat exchange of the cells with a fluid cooling element depending on a predetermined arrangement of the cells to the fluid cooling element.

8. The method of claim 7, further comprising:

- Initialization of a parameterization of contact resistances and / or heat capacities of the heat exchange between the cells of the battery with each other, the heat exchange of the cells of the battery with the solid-state cooling element and the heat exchange of the cells with the fluid cooling element based on predetermined reference values, and

- Carrying out a heating measurement of a reference matrix arrangement of the cells of the battery through which air flows to adapt the parameterization after initialization.

9. The method according to any one of the preceding claims, further comprising:

- Carrying out a calorimetric measurement to determine a heat capacity of the thermal cell model of the cells.

10. The method according to any one of the preceding claims, further comprising:

Performing a thermal impedance spectroscopy to determine an anisotropic heat transfer coefficient of the thermal cell model of the cells.

11. The method according to any one of the preceding claims, wherein the method further comprises:

- Applying an electrical model (900) to obtain a time-discrete dependence of cell voltage and cell current flow for the cells of the battery, the electrical model comprising: an electrical cell model for cells of the battery, an electrical system model for a current flow between and a voltage across cell strings and / or cells of the battery, the electrical cell model having an equivalent electrical circuit with a series connection of an inductance, a resistor, and two or more RC elements, the electrical cell model also having an ideal voltage source for a state-of-charge-dependent open circuit voltage, the cell voltage and the Cell current flow serve as an input for a heat generation model of the thermal cell model.

12. The method of claim 11 further comprising:

- Carrying out an electrochemical impedance spectroscopy measurement to determine the number of the two or more RC elements of the electrical cell model.

13. The method according to claim 11 or 12,

- Carrying out an electrochemical impedance spectroscopy measurement and / or a current pulse characterization measurement and / or a measurement of a dynamic stress test to determine a parameterization of the equivalent circuit of the electrical cell model.

14. The method according to claim 12 or 13, wherein the electrochemical impedance spectroscopy measurement are carried out in those frequency ranges that are represented in an operating profile of the battery.

15. The method according to any one of claims 11 to 14, further comprising:

- Carrying out a relaxation current measurement and / or a constant current measurement to determine a parameterization of the ideal voltage source.

16. The method according to any one of claims 11 to 15, wherein the ideal voltage source determines the open circuit voltage with a hysteresis in connection with a direction of the current flow.

17. Apparatus with a processor which is set up to carry out a time-discrete simulation of a battery by means of the following steps:

- Applying a thermal model (6000) to obtain a time-discrete temperature characteristic of the battery, the thermal model comprising: a thermal cell model (6001) for cells of the battery, an air model (6003) for heat exchange between the cells of the battery and ambient air, and a thermal system model (6002) for a heat exchange between the cells of the battery and a respective environment, wherein when applying the thermal model for a magazine, a cell temperature of the cells of the battery by means of the thermal cell model as a function of one obtained from the air model in a previous magazine Air temperature of the ambient air and further depending on an ambient heat flow obtained from the thermal system model in the preceding journal is determined, and when applying the thermal model for the journal, the air temperature of the air model and the ambient heat flow of the thermi system model can be determined depending on the cell temperature of the cells.

18. The device according to claim 17, wherein the processor is set up to carry out the method according to one of claims 1 to 16.