WO2008154956A1

WO2008154956A1 - Charging method based on battery model

Info

Publication number: WO2008154956A1
Application number: PCT/EP2007/056162
Authority: WO
Inventors: Jasim Ahmed; Mario Roessler; John Christensen
Original assignee: Robert Bosch Gmbh
Priority date: 2007-06-20
Filing date: 2007-06-20
Publication date: 2008-12-24

Abstract

The invention relates to a method for charging a battery by delivering electrical energy to the battery in a charging step. The method comprises: providing a model of the battery, the model linking at least one external parameter of the battery with at least one internal parameter of the battery, the model mapping the at least one internal parameter on a side reaction and relating the at least one internal parameter to at least one limit being linked with the side reaction; determining at least one reference value for the step of delivering electrical energy to the battery based on the model and the at least one external parameter. The charging step comprises monitoring external parameters and delivering electrical energy to the battery according to the at least one reference value. Further, the invention relates to a method for determining at least one internal parameter of a battery. The method comprises measuring external parameters of the battery and applying the external parameters to a model implementing at least one reaction. The battery is adapted to perform said at least one reaction, and the model provides internal parameters by mapping external parameters onto internal parameters, the mapping being based on the model.

Description

Title

Charging Method based on Battery Model

Background of the invention

The technical field of the invention is the operation of rechargeable batteries, in particular a method for charging a battery to its full capacity in the shortest possible time without damaging the battery.

Batteries are typically charged at a constant current until the voltage at the battery terminals reaches a specified cut-off voltage. After having reached the specified cut-off voltage, the battery is charged with a constant voltage, for example the voltage which has been reached in the constant current charging process. The change from constant current to constant voltage after having reached a specified cut-off voltage is a measure known in the art to avoid overcharge situations.

However, finishing the charging process with a constant voltage that eliminates the risk of overcharging leads to a tapering current and it takes an infinite amount of time (due to an asymptotic progress) for the open circuit potential to reach a state of charge of 100 %. Therefore, terminating the charging process with a constant voltage leads to a long duration of the complete charging operation.

Another approach to avoid damages due to overcharging situations is to use a pulse charg- ing mechanism. According to this approach, the average charging current is reduced according to the duty cycle of the current pulses. However, this approach is based on an asymptotic approximation to the maximum voltage in order to avoid overcharging situations, too.

In US 5,828,202, US 5,905,364 and "Charging, Monitoring and Control" by van Schalk- vijk, Advances in Lithium-ion Batteries, Eds. Kluwer Academic, New York, 2002, charging mechanisms for rechargeable batteries are disclosed which all terminate with a constant voltage charging step. In "The effects of pulse charging on cycling characteristics of commercial lithium- ion batteries", by Li, J. et al, Journal of Power Sources, 102 (2001) 302 and "Rapid Charging of Lithium-ion Batteries Using Pulsed Currents: A Theoretical Analysis" by Purushotaman, B. K. et al., Journal of the Electrochemical Society, 153, (2006) 533, pulse-charging mechanisms are described in which the duty cycle of the applied current is reduced when approaching the end of the charging process.

Further, models for Li-ion-batteries are known, which are used for research and development in order to optimize the characteristics of a Li- ion-battery before manufacturing.

All known charging algorithms use an asymptotical approach for the last charging phase, using an external parameter, i.e. the open circuit voltage, as a measure for terminating the charging process. Thus, the last charging phase is characterized by small charging currents for slowly approaching the charging limit. Consequently, the asymptotic approach is inher- ently linked with a low and time consuming charging current at the last charging phase.

It is therefore an object of the invention to reduce the overall charging time for rechargeable batteries, in particular to provide a method with an accelerated charging step at the end of the charging operation.

Summary of the invention

According to the invention, a charging current and/or a charging voltage of a battery is determined by applying a model of the battery, the model reflecting the behavior of the bat- tery. The model can be based on a set of equations providing all or the most dominant physical or chemical reactions in the battery. A first function of the model is to map external parameters onto internal parameters and vice versa such that external measurements can be interpreted in terms of internal processes, reactions and internal values (derived or estimated) such that inner parameters can be indirectly measured as external parameters. A sec- ond function of the model is to implement side reactions, i.e. unwanted effects occurring e.g. in overcharge situations. These side reactions can be determined by comparing current internal parameters with limits related to side reactions. Due to the correspondence between internal and external parameters (1^st function), measured external parameters (in particular the developing of the parameters over time) provide information related to side reactions, e.g. the degree of occurrence of side reactions. The model can be implemented by a numerical simulation or by an appropriate algorithm instead of a physical implementation.

Using the relations mentioned above, the charging current can be exactly matched with the internal processes in the battery and the internal processes can be monitored and controlled directly. In contrast to the prior art in which external parameters are used as control variables, the present invention allows to exactly define internal process parameters and to control the occurrence (or the inhibition) of side reactions in detail.

The model can be implemented as a online simulation tracking internal parameters, external parameters and side reaction implemented by a set of variables defining a set of reactions in the battery. Further, the model can be implemented as numerical or arithmetical approximation reflecting the behavior of the battery, i.e. the internal processes of the battery. Still further, the model can be implemented by a table the entries which reflect the behavior of the battery and provide relationships between external parameters and the charging current and/or the charging voltage, the relationships reflecting the side reactions and the processes in the battery. The implementation of the model can be based on empirical data and/or on physical laws. Additionally, interpolation and extrapolation algorithms can be used. In particular, extrapolation can be combined with a table of entries. In an embodiment, in which only a predefined table (and extrapolation algorithms) is used, the behavior is not simulated or tracked online, i.e. during charging. Rather, the behavior has been evaluated beforehand and is stored as entries in the table or as approximation equations. In this case, the control is carried out by up-to-date internal and/or external parameters and by relationships and rules which have been completely predefined by a previous simulation and/or by empirical data related to the battery's behavior.

A preferred embodiment of the method does not only monitor external operational parameters, e.g. the charging current flowing into the battery, the voltage at the terminals of the battery and the temperature measured at a surface of the battery and adequately sets the charging voltage / charging current. Rather, the selection of the operating point (defined by external parameters like charging current, terminal voltage, battery temperature...) is focus- sed on internal parameters. A relationship is used to map the external parameters onto internal parameters, the relationship being based on a model, on empirical data or on numerical extrapolation. The same model, empirical data or numerical approximation / extrapolation can be used to determine, if the internal parameters are within allowable intervals or if the internal parameters are close to or in areas, which correspond to undesired side effects, e.g. lithium deposition, solvent, salt or impurity reduction or solvent, salt or impurity oxidation. These side effects define the internal physical constraints for the internal parameters.

Examples of the internal parameters are the electrode-electrolyte potential drop in the negative electrode, which has to be maintained above certain limits to prevent or minimize side reactions that can occur at the negative / positive electrode. In order to avoid lithium deposition, the potential drop must be above 0 V vs. the Lithium metal potential. To avoid solvent, salt, or impurity reduction at the anode, the potential drop must be maintained above a certain limit defined by the open-circuit potential (OCP) of the side reaction. In this example, the OCP is one of the internal parameters essential for deriving an internal status of a battery model. This limit is preferably necessarily below the OCP of the respective side reaction, but it should be chosen to minimize the extent of reaction such that the resulting unde- sired reactions can be neglected or tolerated. The extent of reaction can be determined by an appropriate kinetic relationship, e.g., the Butler-Volmer or Tafel equations known to a person skilled in the art. Further, these relationships can be part of a model and/or can be implemented as empirical data reflected by numerical approximations, tables, or extrapolations. Further, heuristic algorithms, neural networks and fuzzy logic can be used for ex- trapolation, approximation or model mapping. Additionally, the state of charge can be regarded as an internal parameter according to the applied model. Alternatively, the state of charge can be regarded as an external parameter, according to another model. [I didn't understand this last point. SOC is not an external parameter.]

A further example of the internal parameters is the electrode-electrolyte potential drop in the positive electrode. Preferably, this is maintained below certain limits to prevent or minimize oxidation side reaction at the positive electrode. To avoid solvent, salt, or impurity oxidation, the potential drop must be maintained below a certain limit, similar to the strategy regarding the electrode-electrolyte potential drop in the negative electrode.

Another example of the internal parameters is the internal temperature and rate of heat generation, which must be maintained below certain safety thresholds. The thresholds are dependent on the chemistry of the battery and could be defined based on empirical and/or model-based evidence for safety hazards and/or premature degradation of the cell. An en- ergy balance on the cell relates measurable quantities, i.e. external parameters (e.g. external temperature, voltage, and current) to the internal temperature and rate of heat generation. The energy balance can be a part of the model, which can be implemented as one equation of a system of equations, which reflects the behaviour of the battery, or can be implemented as a table, approximation functions or recursive approximation algorithms, which can be at least partly based on empirical data.

In order to determine whether the constraints are satisfied, i.e. if the internal parameters match to allowable values or limits, preferably an electrochemical model of the battery is used reflecting, emulating or simulating the most important or all known behaviours of the battery. The electrochemical model that includes material balances, charge balances, energy balances, and/or constitutive equations for mass transport, charge transport, and kinetics is used to calculate internal battery states such as the temperature, state of charge (SOC), and electrode and electrolyte potentials based on the temperature of the environment and the current that is passed through the cell. These examples of internal states cannot be meas- ured directly for a cell, but are essential in order to determine the status and the resulting maximum allowable charging current / charging voltage of the battery.

As an additional or alternative measure for determining whether the constraints are satisfied, external parameters or states can be used. Preferably, these states can be directly measured or can be determined indirectly. E.g. the overall amount of charge transferred to the battery can be determined indirectly, by integrating the charging current. Further examples of these external parameters or status are the current passed through the battery, the voltage of the battery, and the temperature external to the battery, e.g. the temperature of an outer surface of the battery. These states are related to the internal states via model equations, approximations, or empirical data / extrapolation.

In order to estimate the values of the internal parameters from the external parameters, appropriate relationships or mechanisms are used. Such mechanisms comprise a control strat- egy, which is implemented to use the measured external values of the voltage, current, and temperature to correct both the measurable and immeasurable states of the model. Several approaches may be employed, including any approximate linear or recursive mechanism for error reduction, e.g. an algorithm for minimizing the mean square error, preferably a KaI- man filter, or an extended Kalman filter (for nonlinear systems) or a moving horizon estima- tor. Ideally, the electrochemical model perfectly replicates the physical processes of the battery, in which case no such filter is required. In an implementation, a suboptimal model could be used and error reduction algorithms could be used. There is a trade-off between the quality of the model and the requirements of the control strategy, such that both can be adapted to the requirements of the application.

In order to determine the difference between reference and instantaneous value regarding internal parameters (= instantaneous value) and the physical constraints, i.e. limits (= reference), estimates of the appropriate internal states (e.g., electrode-electrolyte potential drop at a particular location in the cell) are compared to the constraints, e.g. physical constraints defined above. The current passed to the battery is corrected or set in order to prevent the states of interest from moving beyond the constraints or limits. A single or multiple constraints may be employed for any given application. The particular errors between limit and instantaneous value of the particular internal parameters can be weighted according to relevance and averaged. The control mechanisms can be open loop control mechanisms or closed loop mechanisms.

Based on the model, the internal/external parameters and the resulting error with regard to the limits, the voltage source or the current source providing the charging current / charging voltage of the battery are preferably controlled according to the control mechanisms such - - that the appropriate internal states, e.g. the desired current as estimated as mentioned above is passed to the cell at every step in the charging process. The updating of the model, the limits, the internal parameters and the external parameters can be performed by continuous, repeated or periodic calculation or measurement. In general, the reference value resulting from the application of the model on external and/or internal parameters with regard to the limits can be used as controlling parameter for the delivery of electrical energy. The delivery of electrical energy according to the control can be continuous, e.g. a current source delivering a current to the battery, which is constantly or periodically updated by the reference value. Alternatively, the delivery of the electrical energy according to the control can be in discrete steps, e.g. constant current and constant voltage steps, which are applied alternat- ingly and which are defined by discrete, single values.

In one embodiment of the invention, the state of charge, SOC, is determined or measured and provides the criterion for terminating the charging step. According to a preferred con- trol structure or model, the SOC of the battery is linearly related to a subset of the internal states (i.e., the concentration of lithium in the solid phase of the electrodes) and can be calculated easily using the approach described above with regard to the determination whether the constraints are satisfied. Once the SOC exceeds the desired threshold (e.g. defined as 100% or 95 % of the battery's capacity), the charging step is terminated.

Further, the temperature of the battery as well as the progress, e.g. the change rate, of the temperature is monitored to detect unwanted mechanisms in the battery. In general, for this detection, internal parameters are estimated from external parameters using models, approximations or other interrelationships, preferably based on reactions taking place in the battery. Additionally or alternatively, the internal resistance of the battery is monitored by determining and/or tracking the current as well as the voltage at the battery and by monitoring the ratio of the voltage to the current. Of course, if the constant voltage or the constant current is used, this constant value does not have to be measured or determined but is already known. Preferably, the charge transferred to the battery is tracked by constantly inte- grating or summing up a current over time which is known or which is constantly or periodically measured. In this way, overcharge situations can be determined by the amount of charge transferred to the battery in relation to the capacity of the battery. Thus, the state of charge (SOC), i.e. the relationship between available amount of charge to overall capacity, is monitored. According to one embodiment, the constant current step [need not be con- stant current] is terminated after the state of charge (SOC) of the battery has reached a certain limit, i.e. 90 %, 92 %, 95 % or 98 %. The overall capacity of the battery can be estimated or determined by monitoring respective operational parameters of the battery during a discharge or charge process. For estimating the overall capacity of the battery, the same parameters can be used which are also used for the detection of unwanted side effects or overcharge situation as described above. In the same way, the SOC can be monitored by tracking the charge transfer to the battery as well as by monitoring the operational parameters which are also used for determining the occurrence of undesired side effects or overload situations.

According to the best mode for carrying out the invention, the charging parameters, e.g. the duration of one or more constant voltage steps, of one or more constant current steps, the magnitude of the constant current and/or the magnitude of the constant voltage, are optimized in view of physical constraints of the battery. The physical constraints give the maxi- mum allowable charging parameter that leads to an operating point close to an operating point related to undesired side reactions. The maximum allowable charging parameter can be related to an acceptable degree of undesired side reactions, to a neglectable degree of undesired side reactions or to an operating point spaced apart from parameters related to undesired side reactions and located within a safety margin.

In one embodiment of the invention, the open circuit potential (OCP) of the battery terminal is measured for determining the current status of the battery, in particular in order to determine the SOC or the internal resistance of the battery. The OCP can be measured directly by measuring the terminal voltage at a current I = OA. Alternatively, the OCP can be estimated from measuring at least two voltages at two different current values. The measured open circuit potential can be used in order to determine any of the above-mentioned limits, the charging current and/or the charging voltage. Further, the SOC can be derived from the OCP, for example using a table with predefined entries or a respective predefined numerical approximation, which have been established by a model simulation and/or by em- pirical studies. The derived SOC can be used to determine whether the charging process should be stopped if a maximum allowable SOC is reached.

In order to monitor or determine the absolute amount of charge transferred to the rechargeable battery or the corresponding relative measured SOC, a so-called Coulomb counter is preferably used that periodically or constantly tracks the current flowing to the battery or the current flowing from the battery. The current values are summed up or are integrated in order to determine the amount of charge and, therewith, determining the SOC. Alternatively, the SOC can be estimated from the battery voltage, the battery current and an estimated value of the battery's internal resistance. Further, the battery's internal resistance can be measured by using the battery voltage and the battery current.

In order to obtain external parameters, the method according to the invention preferably comprises: continuously, repeatedly and/or periodically measuring the voltage occurring at terminals of the battery, the current flowing to the terminals of the battery. Further, the -o- method preferably comprises measuring the time having passed since the beginning of the charging step and/or the beginning of the ongoing constant current step or ongoing constant voltage step and/or determining a relative and/or absolute state of charge by continuously, repeatedly and/or periodically measuring the voltage and the current at the terminals of the battery and continuously, repeatedly and/or periodically calculating the internal resistance of the battery based on the measured current and the measured voltage.

According to one embodiment, the method further comprises continuously, repeatedly and/or periodically measuring the current flowing to the terminals of the battery and deter- mining the amount of charge being transferred to the battery by integrating or summing up the measured current or by multiplying a constant current value and a time value, the time value corresponding to a duration during which the constant current has been transferred to the battery. In this way, the total charge transferred to the accumulator and the charge stored in the accumulator can be determined.

Preferably, the battery voltage (i.e. the voltage present at the battery terminals) used within the constant current step is monitored or tracked, and the current supplied to the battery in the constant voltage step is determined, known or measured. In this way, the SOC (state of charge) is continuously monitored and is preferably used as a criterion for terminating the last charging step, e.g. the constant current step [or some other step — could even be CV in this case]. In combination with the duration of the constant current step, i.e. the time between the beginning of the last constant current step and the end of the last constant current step before terminating the charging step, any overcharging situations can be avoided. Further, the voltage and the current parameters are chosen as to avoid detrimental and/or unde- sired side reactions which are pertaining to the over-current situation and/or are pertaining to battery operations with impaired efficiency. Examples for an impaired efficiency are the reduction of battery capacity or other side effects like deposition of Lithium at the negative electrode of a Lithium-ion battery. Together with the duration of the time period of the constant current step, the constant current can be selected according to known relationships realized in a table or in approximation equations. In the constant current step [or some other step], the voltage at the battery terminal, in particular the behavior of the voltage over time, is tracked and examined in order to detect the begin of undesired side reactions or other situations which would impair the capacity characteristics of the battery.

According to another embodiment which can be used with the embodiments described above, the method comprises a charging step with a plurality of constant current steps and constant voltage steps which are carried out alternatingly and repeatedly within the same charging step. A constant current step is terminated and a constant voltage step is started if one of the monitored operational parameters shows a specific behavior which can be ex- ceeding or undershooting a certain limit, e.g., if the temperature or the voltage in the constant current step reaches a certain limit or if the rate of change of these or of other operational parameters exceeds a certain threshold, e.g. if the voltage at the battery terminals suddenly shows a steep edge. According to the model, the occurrence of such an event is explicitly or implicitly linked with a side reaction implemented in the model. Preferably, the constant voltage step comprises to charge the battery with a constant voltage value which corresponds to the voltage at the battery terminals at the end of the constant current step or corresponds to this value minus a certain margin. In the same way, the constant voltage step is terminated and a constant current step is started if, in the constant voltage step, a certain operational parameter, for example the charging current, the rate of change of the charging current, the temperature and/or the amount of charge transferred into the battery during this step has reached a certain limit which corresponds to a certain behavior relating to an unde- sired side effect or an overcharge situation. In particular, also behaviors can be detected and used as trigger for changing the constant current step to the constant voltage step and vice versa which occur before the undesired effect takes place or the overcharge situation begins. In this way, critical situations can be detected beforehand and measures can be taken (i.e. changing constant current to constant voltage and vice versa) in order to avoid the occurrence of the undesired side reactions or the overcharge situation. Alternatively or in combination thereto, the charging steps can be exchanged (i.e., a constant current step is terminated and a constant voltage step is started or vice versa) in order to avoid the occurrence of undesired side reactions or the overcharge situation. Further, the charging steps can be exchanged (i.e. a constant current is terminated and a constant voltage step is started or vice versa) if a certain amount of time has lapsed since the start of the respective constant voltage or constant current step.

Apart from the protection against undesired side reactions or overcharge situations, the present invention allows the maximum allowable voltage or the maximum allowable current for a minimum charge duration. In other words, the present invention allows to follow the maximum allowable voltage or current and therefore to follow the border to operational parameters corresponding to undesired effects or overcharge situations as close as possible. The current and voltage values can be determined a priori, either experimentally or via simulation, or adaptively using an on-board battery management system. In general, the current used during the constant current step and the voltage used during the constant voltage step are predetermined and can be given in a table as entries corresponding to one or more respective operational parameters at which the respective current or voltage should be applied. The relationship between the operational parameters (voltage, current, SOC, charge, temperature or the respective changing rates) is pre-stored in a memory in the form of the model and gives the optimum current or the optimum voltage to each operating point defined by the operational parameter or operational parameters, i.e. the maximum allowable current or maximum allowable voltage. Instead of storing this realization of the model in the memory in form of a table, predefined numerical approximations can be used. Further, crite- rions of internal and/or external parameters can be used, as well as limits and constraints as described above. The relationships between the internal, external parameters, limits and/or constraints can be based on the above mentioned models, which can be implemented as tables, approximations, set of equations, together or without the control mechanisms described above.

Further, if the constant current and the constant voltage step are applied alternatingly, the sequence, in particular the duration of each step can be adapted to the battery degradation due to aging. Thus, the limits triggering the change from a constant current to a constant voltage step or vice versa can be lowered or increased in order to reflect the change of characteristics due to aging. Additionally, the model can be updated with regard to aging processes. Further, temperature changes in the battery can be reflected by updating the model or by lowering or increasing the limits.

In another embodiment of the invention, a step of charging the battery with a constant voltage is exchanged by a step of charging the battery with a constant current upon occurrence of certain events, e.g. reaching a level or exceeding a threshold. Thus, one embodiment of the method further comprises terminating the constant voltage step and starting the constant current step upon reaching at least one of the following limits: a predefined charging current limit, a predefined battery temperature change rate limit, a predefined battery's internal resistance limit, a predefined battery's internal resistance change rate limit, a predefined amount of charge limit, the charge being transferred to the battery during the constant volt- age step and/or estimating a rate of internal heat generation, an electrode/electrolyte potential drop at the anode or an electrode/electrolyte potential drop at the cathode linked with degradation mechanisms according to an extrapolation based on a battery model or a diagnostic technique.

In a similar way, a step of charging the battery with a constant current is exchanged by a step of charging the battery with a constant voltage upon occurrence of certain events. Thus, in a similar embodiment, a constant current step is followed by a constant voltage step, the constant current step being terminated and the constant voltage step being started upon reaching at least one of the following limits: a time limit referring to the duration of the constant current step, a predefined voltage limit, a predefined battery temperature limit, a predefined battery temperature change rate limit, a predefined battery's internal resistance limit, a predefined battery's internal resistance change rate limit and/or a predefined amount of charge limit, the charge being transferred to the battery during the constant current step or since the start of the charging step. In the above, the term battery is used for any kind of accumulator, galvanic cell or capacitor which is based on the chemical storage of energy an is based on electrodes / electrolyte. Of course, the models used for mapping the external on the internal parameters and for provid- ing the control mechanisms as well as the limits have to be adapted to the reactions occurring in the particular battery type. Examples for batteries comprise rechargeable Li-Ion-, Lithium-Polymer-, NiMH-, NiCd-, wet or gel Pb-accumulators as single cells or as cell packages.

Further, the invention can be implemented by a method for determining internal parameters by monitoring and measuring external parameters, applying the external parameters on the model, the model providing information about the current internal status of the battery, e.g. by providing the current internal states applied to the model and/or by comparing the internal parameters to the physical (or chemical) constraints set by the undesired side effects or by overload situations. This method can provide information regarding probabilities and/or percentages regarding the occurrence of reactions, which form the basis of the model. As mentioned above, the model implements at least one reaction taking place in the battery upon occurrence of internal/external event.

Brief description of the drawings

Exemplary embodiments of the invention are depicted in the figure and are described in detail in the following description.

Figure 1 shows the developing of the terminal voltage of a battery for three different embodiments of the invention.

The embodiments are optimized with regard to a limit which corresponds to Lithium deposition in a Lithium-ion battery. Of course, other side reactions could be used as limiting fac- tor.

The curve L in Fig.1 shows the limit above which Lithium deposition occurs or is to expect. Hence, the hatched region corresponds to operating points (defined by charging current and corresponding charging voltage) at which Lithium deposition occur. Therefore, the first and the second embodiment of the method according to the invention applies respective an alternating constant current (CC) and constant voltage (CV) steps which are used to keep to the limit as close as possible. In general, if the electrical energy is delivered in discrete steps of constant current and constant voltage, the CC and CV steps are carried out alternatingly. In this embodiment, a CV step is carried out for a predefined time period and directly followed by a CC step. In contrast to the CV step, a CC step is terminated upon reaching a critical cell voltage as defined by the L. Thus, CC step is carried out as long as the side effect, i.e. Lithium deposition, does not occur. A next CV step is carried out directly after termination of the preceding CC step. The voltage of a CV step is defined by the terminal voltage at the end, i.e. directly before termination of the preceding CC step. The current of a CC step is defined by the maximum allowable current with regard to the side reaction(s), i.e. is defined by the respec- tive limit. The alternating CC and CV steps form a staircase pattern.

In Fig. 1, the curve Pl shows a first charging path corresponding to a first embodiment of the invention. The first charging path Pl starts with a first constant current CCi at a first terminal voltage (4.05 V) until a limit defined by curve L is reached, in this case a voltage of approx. 4.1 V. Then, the constant current step is switched to a first constant voltage step, CVi, which is carried out for a time period with a predefined duration. In order to keep close to the limit L and to minimize the charging time, CVi is switched to a second constant current step, CC2 , after the time period has expired. CC2 is applied until the limit L is reached and a second constant voltage step, CV2, is applied for another predefined time period. The second current voltage step is terminated and a third constant current step, CC₃, is used to bring the operating point, i.e. the charging current, closer to the limit L, until a voltage defined by L is reached. After the limit area has been reached (or a corresponding limit has been exceeded), the third constant current step is terminated and the third constant voltage step CV3 is started. CV3 is executed for another predefined time period. The change of charging steps is repeated such that a fourth constant current step CC₄ follows on the third constant voltage step CV3, again, until the limit L is reached. Similar to the steps above, after having reached the limit, the charging step moves on with a fourth constant voltage step CV₄, again until a certain time period has been exceeded. Thus, a fifth constant current step, CCs, is carried out, until a maximum voltage (4.4 V) has been reached, which is used as basis for the fifth constant voltage step CV5. CV5 is carried out for a certain time period. The voltage of CV5 is used as criterion for terminating the charging process. Alternatively, an inner parameter, e.g. the SOC can be used as criterion for termination the charging process.

Alternatively, after having reached the charging step termination criterion, the step CV₅ could be carried out until a minimum current is reached instead of being terminated by exceeding a time limit. In an alternative embodiment, the constant voltage steps are not terminated after a certain time period but are terminated, if the current (or the current density) has reached a certain distance from the limit L. Like the time periods, the distance can be constant or can be increased or decreased depending on the number of preceding CC steps or depending on the time lapsed since start of the charging process. Thus, in this alternative embodiment, CCi is switched to a first constant voltage step CVi, which is carried out until the charging current's density differs from the limit by more than a certain margin. Further, CV2 is carried out until the operating point, in particular until the charging current's density, has shifted too far from the limit L. Consequently, CV₃ is carried out until the working point, in this case the charging current density for the given voltage defined by CV₃, is too far away from the limit L. In the same way, CV₃ is terminated upon reaching a charging current being spaced apart from L by a certain distance.

P2 shows a second charging path corresponding to a second embodiment of the invention. P2 has a lower resolution than Pl. As a first step, a constant current step is carried out, which is identical with Pl . After having reached L as the limit for undesired side reactions at point Ll, CVi' is carried out for a predefined time period, which is longer than the time period of CVi. Alternatively, the allowable distance of the current from L in P2 is larger than the allowable distance in Pl. However, after having reached the termination criterion (duration of time period or distance of operation point from L), CVi' is switched to CC₂', which is carried out until L is reached (L2). CC2' is switched to the last constant voltage step, CV₂', which is carried out until the charging current density and the respective charging current falls below a certain level or is approx. 0 A.

L is formed of several interpolation points, which are connected by corresponding approximation lines. L can be constructed of empirical date (some or all interpolation points) and a corresponding approximation curve.

The first and the second embodiment comprises numerous CC and CV steps and give a dis- crete approximation of the operating point (defined by charging current/charging voltage) to the limit L. In a third embodiment, continuous approximations of the charging current to L are carried out instead of the discrete approximation with CC and CV step. Thus, in the third embodiment, the charging current is constantly updated, e.g. by periodically comparing the current charging current to the limit applying for the current internal parameters. The comparison can be carried out with a high frequency, e.g. every 10 sec, every 5 sec, every 1 sec or even more frequent. In this case, the charging current has a progression identical with L. Alternatively, the charging current can be selected to be spaced apart from L by a safety margin x, e.g. a predefined current margin. In the third embodiment, the model as well as the inner parameters has to be updated periodically in order to provide the appropriate charging current.

In the first and the second embodiment, the charging step is terminated by a constant volt- age step. Instead, the charging step can be terminated by a constant current step. The termination criterion for the last step, i.e. the constant current step can be the lapse of a time period, reaching a certain battery voltage. Alternatively, the last current step can be terminated depending on internal parameters, e.g. can be terminated, if a certain SOC has been reached. The SOC can be estimated using the model or can be calculated by approximation equa- tions. Further, the SOC can be estimated using external parameters and a correspondence table and/or approximation or estimation equations.

Claims

1. A method for charging a battery by delivering electrical energy to the battery in a charging step, the method comprising: providing a model of the battery, the model linking at least one external parameter of the battery with at least one internal parameter of the battery, the model mapping the at least one internal parameter on a side reaction and relating the at least one internal parameter to at least one limit being linked with the side reaction; determining at least one reference value for the step of delivering electrical energy to the battery based on the model and the at least one external parameter; the charging step comprising: monitoring external parameters and delivering electrical energy to the battery according to the at least one reference value.

2. The method of claim 1, the charging step further comprising: a constant voltage step (CV), in which a constant charging voltage is applied to the battery according to the at least one reference value, and a constant current step (CC), in which a constant charging current is applied to the battery according to the at least one reference value, the same charging step comprising at least one of the constant voltage steps and at least one of the constant current steps.

3. The method of claim 1, the charging step further comprising the step of determining at least one reference value for the step of delivering electrical energy to the battery based on the model and based on the at least one external parameter.

4. The method of claim 1, wherein the step of determining at least one reference value for the step of delivering electrical energy to the battery based on the model and based on the at least one external parameter is carried out before the start of the charging step, the step of determining further comprising the determination of a plurality of reference values corresponding to respective values of external parameters.

5. The method of claim 1, comprising a plurality of constant voltage steps (CV) and a plurality of constant current steps (CC) being carried out repeatedly and alternatingly in the same charging step; each constant voltage step (CV) comprising applying a constant charging voltage to the battery and each constant current step (CC) comprising applying a constant charging current to the battery, each of the constant voltage steps and constant current steps comprising: measuring at least one external parameter and determining at least one reference value as well as at least one internal parameter based on the model and the at least one external parameter. - -

6. The method of claim 1, wherein the charging step comprises at least one constant voltage step (CV) and at least one constant current step (CC), the at least one constant voltage step and at least one constant current step being carried out alternatingly, wherein, upon exceeding at least one limit or upon expiration of a predefined time pe- riod, one of constant voltage steps is terminated and a subsequent constant current step

(CC) is started or wherein one of constant current steps (CC) is terminated and a subsequent constant voltage step (CV) is started. [Add steps that are neither CV nor CC — could be an arbitrary current profile.]

7. The method of claim 1, wherein the model comprises a set of equations, at least one table with respective entries reflecting the behavior of the battery and/or at least one arithmetical or numerical approximation equation reflecting the behavior of the battery.

8. Method of claim 1, wherein the internal parameters include an absolute amount or rela- tive percentage of charge present in the battery, an open circuit voltage at the terminals of the battery, and/or an electrode/electrolyte voltage drop at an anode or a cathode of the battery, the external parameters comprise a terminal voltage, a terminal current, an external temperature of the battery and/or an amount of charge being transferred to the battery; the side reactions comprise lithium deposition, oxidation or reduction of sol- vent, salt or impurity or premature degradation by excessive battery temperature; the reference value comprises a maximum charging voltage, a maximum duration of the constant current step, a maximum duration of the charging step and/or a maximum charging current according to the internal parameters, the respective side reactions, a safety margin, and/or the reference value being determined based on the model and/or on an arithmetic relationship between the reference value and at least one of the internal parameters.

9. Method of claim 1, wherein the charging step is completed upon the occurrence of an event, the event comprising: reaching the at least one limit, expiration of a predefined time period starting with the charging step, with the ongoing constant voltage step or with the ongoing constant current step; reaching a predefined maximum voltage or a predefined maximum voltage change rate occurring at the battery's terminals; reaching a battery temperature limit or a limit of a battery temperature change rate; reaching a predefined relative state of charge or a predefined absolute amount of stored charge; detecting an internal resistance of the battery lying outside a predefined internal resistance interval; and/or estimating a rate of internal heat generation, an electrode/electrolyte potential drop at the anode or an electrode/electrolyte potential drop at the cathode linked with degradation mechanisms according to an extrapolation based on a battery model or a diagnostic technique.

0. Method for determining at least one internal parameter of a battery, comprising: continuously or periodically measuring external parameters of the battery, applying the external parameters to a model implementing at least one reaction, the battery being adapted to perform said at least one reaction, and the model providing internal parameters by mapping external parameters onto internal parameters, the mapping being based on the model.