DE102013000572A1 - Method for determining model parameters of electrochemical energy storage of e.g. electric vehicle, involves defining parameter record variant as new reference dataset to describe battery model and to determine maximum power of storage - Google Patents

Abstract

The dynamic behavior is described in operation by an electric reference model (M) comprised of a capacitor (C) and the associated resistor (R1). Deviation of the sum of over-voltages and the initial voltage with respect to the currently measured voltage is determined and integrated. The parameter data set version with the smallest square error is assigned. The parameter record variant is defined as a new reference dataset for the description of battery model and for the predictive determination of the maximum power of the energy storage. The dynamic behavior is described in operation by an electric reference model. The reference model is comprised of a capacitor and the associated resistors. The parameter values are added to form a parameter data set and are adapted to the current state during the operation of energy storage. Starting from a reference parameter data set, several parameter data record variants are formed for each of the iteration based on the measured current and over-voltage (Umodell-t) of the energy storage. Deviation of the sum of over-voltages and the initial voltage with respect to the currently measured voltage is determined and integrated. The parameter data set version with the smallest square error is assigned. The parameter record variant is defined as a new reference dataset for the description of battery model and for the predictive determination of the maximum power of energy storage. An independent claim is included for a battery management system.

Description

The invention relates to a method and a system for determining the model parameters of an electrochemical energy storage such as a battery, in particular for electric or hybrid vehicles, the dynamic behavior is described in operation by an electrical reference model, at least comprising a capacitance and a first resistor associated therewith Parameters of the reference model are linked and in the reference model descriptive mathematical equations, wherein the parameter values of the parameters together form a parameter data set and adapted during operation of the energy storage device to its current state.

The preferred technical field of application of the method according to the invention is a self-adapting, predicative determination of the maximum power of the energy store available for a predefined time. This plays a decisive role especially in batteries, whose performance is monitored and predicted by so-called battery management systems (BMS).

Each battery system of an electric or hybrid vehicle has such a battery management system, which has the task of the state of the battery, in particular to determine their performance or to forecast for a defined period. In addition, their state of charge, aging state and application-specific states such as the available maximum power are determined and this information is made available to a higher-level energy management system. This task is particularly complicated by the fact that the characteristic properties of the battery change significantly during operation and over time due to aging. It is therefore advantageous to design the battery management system self-adaptively in order to be able to track these changes and to be able to take these into account in the power calculation.

Since the battery conditions are not directly measurable, directly accessible battery sizes such as current, voltage and temperature are measured during operation and appropriate algorithms are used to determine the desired battery conditions. In electric and hybrid vehicles this includes in particular the determination of the performance of the battery. This is typically defined as a prediction of the maximum power that the battery can supply for a predefined time.

• – Maximal zulässiger Strom. Für eine Batterie werden vom Hersteller die maximal zulässigen Ströme definiert. Diese können temperatur- und/oder zeitabhängig, d. h. abhängig von der Dauer der Strombelastung definiert sein.
• – Bei einer Strombelastung wird die Batterie geladen oder entladen. Dabei sinkt oder erhöht sich der Ladezustand. Der Ladezustand muss in bestimmten Grenzen gehalten werden, um ein Überladen bzw. Tiefentladen der Batterie zu vermeiden.
• – Maximal zulässige untere und obere Spannungsgrenzen an jeder Batteriezelle im Batteriepack. Beim Entladen einer Batterie sinkt deren Spannung, entsprechend erhöht sich diese bei einem Ladevorgang. Diese Spannungen müssen aus Sicherheitsgründen in bestimmten Grenzen gehalten werden.
• – Maximal zulässige Temperatur. Bei einer Strombelastung erwärmt sich die Batterie, darf sich jedoch nicht über die maximal zulässige Vorgabe des Herstellers bewegen.

The maximum performance depends on the following factors:

• - Maximum permissible current. For a battery, the manufacturer defines the maximum permissible currents. These can be temperature- and / or time-dependent, ie defined depending on the duration of the current load.
• - At a current load, the battery is charged or discharged. The state of charge drops or increases. The state of charge must be kept within certain limits in order to avoid overcharging or over-discharging the battery.
• - Maximum permissible lower and upper voltage limits at each battery cell in the battery pack. When a battery is discharged, its voltage drops, and it increases accordingly during a charging process. For safety reasons, these voltages must be kept within certain limits.
• - Maximum permissible temperature. At a current load, the battery heats up, but must not exceed the maximum permissible specification of the manufacturer.

The challenge is always the consideration of the voltage limits, for which an exact battery voltage must be predicted. As a reference case for the determination of the maximum available power, a current pulse with a freely selectable duration Δt is typically defined. Based on this, the current intensity I (t) is sought, so that the battery voltage does not exceed the predetermined limits when the battery is charged with this current.

Today, various methods are used to predict the maximum available power of the battery during operation. A first possibility is the use of static maps. Here is a measurement of the battery in the laboratory for example by means of so-called HPPC tests, which determine the performance of the battery under different conditions such as state of charge (SoC) and temperature. The results are displayed in a map, e.g. In the form of a look-up table or approximated by one or more functions as in the US Patent 7,518,375 B1 described, stored. During operation of the battery, a value from this map is read out according to the operating condition (SoC, temperature) and output as available power. The disadvantage here is the neglect of the over the life significantly changing properties of the battery. Because compared to the new condition, the performance of the battery at the end of the life decreases to only about 50% of the initial value. In order to For example, these non-adaptive methods can be reliably used only for determining the performance of the battery when new.

A known extension of said first option is to make the map dynamic. This means that this map is continuously adapted during operation. Each time the battery delivers power while reaching the voltage limit, that power is defined as the maximum available power. This is compared with the value stored in the map. If a deviation is detected, the value in the map is adjusted to the actually measured power. A disadvantage of adaptive maps is that reliable results are only delivered if the maximum power is regularly called up, since only then is the possibility of map adaptation possible. But this is a very rare event in most applications. For example, electric vehicles only reach the power limit after a longer acceleration phase, which almost never occurs in city traffic. Another disadvantage is that the adaptation of the map can take place only in the respective current operating point (temperature, state of charge, current), since the method has no information about the basic characteristics of the battery in the form of a model, etc. Another disadvantageous aspect of the implementation is that the stored characteristic map consists of several dimensions (SoC, temperature, load duration, current intensity) and must also be resolved higher, which leads to a large number of interpolation points and thus to a large storage requirement on the microcontroller.

An alternative power prediction capability is the use of simplified battery models that model the voltage of the battery for a given current, see for example WO2005050810 , In this method, a current pulse having a freely selectable duration Δt is typically defined as a reference case for determining the maximum available power. Based on this, the current intensity I (t) is sought, so that the battery voltage does not exceed the predetermined limits when the battery is charged with this current. A simplified battery model is used. When this current has been determined, it is compared with the maximum allowable current given conditions (temperature and / or current pulse duration). From both values the minimum is chosen. With the resulting value, the available power is again calculated with the battery model by multiplying the voltage at the end of the pulse by the current of the pulse from the battery model. Above all, this method requires an exact battery model in order to calculate the battery voltage from a current. The parameters of the battery model can be determined in the laboratory.

Various techniques are known to extend these methods, in particular by adapting the parameters of the battery model to the current state of the battery during battery operation. This approach provides the most promising results and therefore offers the best potential, which is why it is currently being used as the most promising method in safety-critical and demanding applications. The accuracy of the method depends primarily on how well the adaptation method adapts the model parameters to the state of the battery. On the other hand, the complexity of the battery model used determines the accuracy.

One of the biggest drawbacks of the models used so far, however, is the unaccounted for current dependence of the battery resistance. The performance limits of the battery are achieved especially at high currents and lower temperatures, so the current dependence should be considered. In 1 exemplifies the current dependence of the battery resistance for a new and aged 40 Ah battery. Not considering the current dependence is due to the adopted adaptation method:
Especially widespread is the use of Kalman filter based techniques, see for example the publication " Gregory L. Plett, "Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 3. State and parameter estimation", Journal of Power Sources, Vol. 134, No. 2, pp. 277-292, 2004 , and " M. Urbain, S. Rael, B. Davat, and P. Desprez, "State Estimation of a Lithium Ion Battery Through Kalman Filter," June 2007, pp. 2804-2810 ". Also similar adaptive digital filters, like in US Pat. No. 7,486,079 B1 described, are used.

The Kalman filter was initially developed only for linear models. However, extensions such as Extended Kalman Filter or Unscented Kalman Filter have been adapted to nonlinear models. However, such methods only approximate the non-linearity and converge reliably and stably only when the operating point in which the linearization takes place changes slowly over time. However, since the current changes dynamically very rapidly, the nonlinearity of the battery associated with the current can not be taken into account. Only the non-linearity between the voltage at rest of the battery and its state of charge is meaningfully taken into account. She is however for the Performance forecast hardly relevant. In addition, it is assumed that the disturbances including the model inaccuracy assume a Gaussian distribution, which however is an idealized approximation and in reality does not have to occur in this way. Another disadvantage of the Kalman filter is that the calculation of the corresponding Kalman equations involves a high computation effort. Among other things, matrices must be calculated here. This is also associated with a low numerical stability, if the calculation must take place on a microcontroller with low accuracy of the number representation.

Another technique besides the Kalman filters are recursive load-square algorithms (RLS), see for example DE 10 2009 049 320 A1 , The application of such an algorithm for the determination of a battery impedance requires a high-pass filtering and a transformation of the parameters between the frequency and time domain. Both operations are applicable only to linear systems. In DE 10 2009 049 320 A1 It is shown that one can apply multiple instances of the algorithm for different current ranges to account for current dependency. However, it is unclear how the falsification of the current dependency by the high-pass filtering (basically applicable only to linear systems) is taken into account. However, only a very rough consideration of the current dependence in a few current ranges is even possible. The algorithm also has no prediction capability because no basic information about the current dependence of the model parameters is used in the procedure. This means that the model parameters are seldom adapted for large currents that occur very seldom during operation.

Also, a direct determination of the battery resistance from current and voltage changes is to call alternative to Kalman filtering, as for example in US 6,832,171 . DE 10 2009 054 547 A1 . US 6,469,512 B and US 2011/0172939 is described. These methods offer a relatively simple implementation, by the determination of only one parameter, namely the battery resistance. The dynamics of the battery is therefore not considered. This leads to large inaccuracies, especially at lower temperatures and aged batteries. The consideration of the current dependence is possible in principle if the resistance is determined separately for several current ranges.

It is the object of the present invention to provide a simple and effective method for determining the current parameters of a model describing the dynamic behavior of the energy store or adapting the parameters of this model during operation of the energy store, which is responsible for the very good predicative determination of the maximum available power of the energy store for a predefined duration (.DELTA.t) can be used starting from the current operating point.

This object is achieved by a method according to claim 1. Advantageous developments of the method are specified in the subclaims.

• a. Verwendung eines initialen Parameterdatensatzes (P_start) als Referenzparameterdatensatz (P_ref) für das Referenzmodell,
• b. Messen des durch den Energiespeicher fließenden Stroms (I_mess(t)) und der an diesem anliegenden Spannung (U_mess(t)),
• c. Bildung einer Mehrzahl (N) an Parameterdatensatzvarianten (P_i, mit i = 1 bis N),
• d. Berechnung der sich aus dem Referenzmodell infolge eines fließenden Stroms (I(t)) ergebenden Überspannung (U_modell(I_mess(t), P_i)) am Energiespeicher für jeden der Parameterdatensatzvarianten (P_i) unter Verwendung der aktuellen Strommesswerte (I_mess(t)) und
• e. Berechnung einer Anfangsspannung (U_0,Pi) aus der Differenz (U_0,Pi = U_mess(t) – U_modell(I_mess(t), P_i)) dieser Überspannung (U_modell(I_mess(t), P_i)) und der gemessenen Spannung (U_mess(t)), wobei die Spannung (U_c,Pi(t)) über der Kapazität (C) für jede Parameterdatensatzvariante (P_i) gleich der Spannung (U_c,Pref(t)) über der Kapazität (C) gesetzt wird, die sich aus dem Referenzmodell bei der Verwendung des Referenzparameterdatensatzes (P_ref) ergibt,
• f. erneutes Messen des durch den Energiespeicher fließenden Stroms (I_mess(t)) und der an diesem anliegenden Spannung (U_mess(t)) sowie
• g. erneute Berechnung der sich aus dem Referenzmodell (1) für jede Parameterdatensatzvariante (P_i) ergebende Spannung (U_c,Pi(t)) über der Kapazität (C) und der Überspannung (U_modell(I_mess(t), P_i)) am Energiespeicher,
• h. Berechnung einer Abweichung (ΔQ_Pi) zwischen der gemessenen Spannung (U_mess(t)) und der Summe aus Überspannung (U_modell(I_mess(t), P_i)) und Anfangsspannung (U_0,Pi) für jeden der Parameterdatensatzvarianten (P_i) mittels einer Funktion, die umso größere Werte liefert, je höher die Differenz zwischen der gemessenen Spannung (U_mess(t)) und der Summe aus Überspannung (U_modell(I_mess(t), P_i)) und Anfangsspannung (U_0,Pi) ist, und
• i. Wiederholung der Schritte f. bis h. so oft, bis zumindest eine zweite Bedingung erfüllt ist, wobei die jeweils neu berechnete Abweichung (ΔQ_Pi) bei jeder Wiederholung der Schritte zu der zuvor berechneten Abweichung (Q_{Pi_alt}) addiert wird (Q_{Pi_neu} = Q_{Pi_alt} + ΔQ_Pi), und
• j. Bestimmung derjenigen Parameterdatensatzvariante (P_n, n ∊ [1...N]), die die kleinste Abweichung (Q_{Pi_neu} neu = QP_{i_alt} + ΔQ_Pi) besitzt, wobei diese bestimmte Parameterdatensatzvariante (P_n) unmittelbar oder mittelbar als neuer Referenzparameterdatensatz (P_ref) definiert wird.

According to the invention, a method for determining the model parameters of an electrochemical energy store, in particular for electric or hybrid vehicles whose dynamic behavior is described in operation by an electrical reference model, at least comprising a capacitance (C) and a first resistor (R ₁ , R ₂ ), which are parameters (C, R ₁ , R ₂ ) of the reference model and mathematical equations describing the reference model, wherein the parameter values of the parameters (C, R ₁ , R ₂ ) together form a parameter data set and during operation of the Energy storage adapted to its current state, and wherein the method comprises the following steps:

• a. Use of an initial parameter data record (P _start ) as a reference parameter data record (P _ref ) for the reference model,
• b. Measuring the current flowing through the energy store (I _mess (t)) and the voltage applied thereto (U _mess (t)),
• c. Formation of a plurality (N) of parameter data set variants (P _i , with i = 1 to N),
• d. Calculation of the overvoltage (U _model (I _mess (t), P _i )) resulting from the reference model as a result of a flowing current (I (t)) at the energy store for each of the parameter _{data set variants} (P _i ) using the current current _measured values (I _mess (t)) and
• e. Calculation of an initial voltage (U _{0, Pi} ) from the difference (U _{0, Pi} = U _mess (t) - U _model (I _mess (t), P _i )) of this overvoltage (U _model (I _mess (t), P _i )) and the measured voltage (U _mess (t)), wherein the voltage (U _{c, Pi} (t)) across the capacitance (C) for each parameter _{data set variant} (P _i ) equal to the voltage (U _{c, Pref} (t )) is set above the capacity (C) resulting from the reference model when using the reference parameter data set (P _ref ),
• f. again measuring the current flowing through the energy store (I _mess (t)) and the voltage applied thereto (U _mess (t)) and
• G. recalculation resulting from the reference model ( 1 ) for each parameter data set variant (P _i ) resulting voltage (U _{c, Pi} (t)) over the capacitance (C) and the overvoltage (U _model (I _mess (t), P _i )) at the energy storage,
• H. Calculating a deviation (.DELTA.Q _Pi) between the measured voltage (U _mess (t)) and the sum of surge (U _model (I _mess (t), P _i)) and initial voltage (U _{0, Pi)} (for each of the parameter data set variants P _i ) by means of a function which delivers the greater values, the higher the difference between the measured voltage (U _mess (t)) and the sum of overvoltage (U _model (I _mess (t), P _i )) and initial voltage ( U _{0, Pi} ), and
• i. Repetition of steps f. until h. so often until at least a second condition is satisfied, wherein the respectively newly calculated deviation (ΔQ _Pi ) is added to the previously calculated deviation (Q _{Pi_old} ) at each repetition of the steps (Q _{Pi_new} = Q _{Pi_old} + ΔQ _Pi ), and
• j. Determining the parameter _{data set variant} (P _n , n ε [1 ... N]) which has the smallest deviation (Q _{Pi_new} new = QP _{i_old} + ΔQ _Pi ), this specific parameter _{data set variant} (P _n ) being used directly or indirectly as a new reference parameter data set ( P _ref ) is defined.

With the parameter data set variant found in the last step for implementing the reference model, this has been adapted to the actual dynamic behavior of the energy store, so that calculations based on this reference model provide the best possible results, in particular for the predicative determination of the maximum power of the energy store available for a certain period of time.

In this case, a particular advantage is that the adaptation of the parameters takes place during operation of the energy store, so that age-related, temperature-related and / or weather-related property changes of the energy store can be taken into account directly by the parameter adaptation in the reference model.

In contrast to the method using a Kalman filter, no complex calculations, which mainly consist of matrix operations, need to be carried out here. As a result, the implementation of the method according to the invention is given on a microcontroller.

By a direct calculation of the reference model or of the model-forming equations with a plurality of parameter data sets, ie with the parameter data set variants (P _i ), and the subsequent, direct selection of one of the parameter data set variants (P _n ), ie a suitable combination of varied parameter values, the inventive adaptation method converges greatly stable.

The energy store may be a battery with one or more cells. However, the energy store can also be a single cell of such a battery. Further, the method may be performed separately for each cell of a battery. In this case, the capacitance (C) of the reference model reproduces the double-layer capacitance of the battery or a cell, the resistance (R ₁ , R ₂ ) of the reference model represents the internal resistance of the battery. Alternatively, the energy store can be a double-layer capacitor.

Preferably, the adaptation of the parameters (R ₁ , R ₂ , C) takes place only during an evaluation interval, which is initiated when at least one of the measured quantities (I _mess (t), U _mess (t)) and / or at least one variable variable (I _C (t)) of the reference model (M) calculated from this satisfies a first condition. To initiate the evaluation interval, either one of the two or both measured quantities of current and voltage or at least one variable of the reference model calculated therefrom can be used. The first condition that can be used is, for example, that the measured current (I _mess (t)) changes only slowly by the energy store. If the variable (I _C (t)) is used for the first condition, its calculation before step c. using the reference parameter data set (P _ref ) and the measured quantities current (I _mess (t)) and voltage (U _mess (t)).

As a variable, the current flowing in the capacitance (C) (I _C (t)) can be used, and then preferably the first condition is such that this current (I _C (t)) within a predetermined period in relation to the maximum Current (i _max ) through the energy storage is small. This means physically that the gradient of the energy stored in the capacitance, ie the current change in the stored energy over time, is small. If the total battery current is constant or changes very slowly, it flows primarily through the resistance, which is parallel to the capacitance in the reference model. The voltage and thus the energy in the capacity does not change then, but probably the total energy of the battery, ie its rest voltage. If the said first condition is met, power is thus withdrawn from the energy store.

The examination of this first condition can be carried out, for example, by checking whether the current I _C (t) lies below a limit in the capacitance for a few measured values or over a predetermined period of time, for example one or more seconds. This limit is a fixed design constant and can be specified relative to the maximum current (i _max ), for example, 2% of the maximum current. Alternatively, an absolute limit value can also be specified, for example 3A to 5A, preferably 4A.

In principle, any model can be used as reference model of the energy storage, which describes the impedance of the energy storage. The reference model may be graphically illustrated as an equivalent electrical circuit diagram including a parallel connection of the capacitance (C) and the first resistor (R ₂ ). If the quiescent voltage of the energy store is taken into account, a voltage source is connected in series with said parallel circuit in the equivalent circuit diagram. A more accurate model of impedance is obtained by additionally considering a second resistor (R ₁ ) in series with the parallel circuit. Since this second resistor (R ₁ ) at moderate and low temperatures is significantly smaller than the first resistor (R ₂ ), can be dispensed with the second resistor (R ₁ ).

It is particularly advantageous if in the reference model a current dependence of the first resistor (R ₂ ) is taken into account, ie the parameter value of the first resistor (R ₂ ) is not considered to be constant, which is very important for the accuracy of the power prediction based thereon. Thus, the parameter value of the first resistor (R ₂ ) can be converted into a current-dependent resistance value (R ₂ (I)) depending on the current flowing through it, and this current-dependent resistance value (R ₂ (I)) in the reference model (1) for the method according to the invention Calculations are used. However, when using the current through the first resistor (R ₂ ), the power prediction calculations become much more complex and complicated because they would only have to be calculated iteratively and not by a closed formula. The first resistor (R ₂ ) can therefore be simplified as a function of the total current (I (t)) modeled by the energy storage, ie the measured current. This maps the energy storage in the model a little less well, but still good enough, allowing easier calculations.

oder gemäß der Gleichung

mit

R₂:

stromunabhängiger Widerstandswert

R₂(I):

stromabhängiger Widerstandswert

a:

wählbare Konstante

kI:

Stromfaktor

I:

gemessener Strom I_mess(t) durch den Energiespeicher

I_B:

Bezugsstromwert

erfolgen.The conversion or consideration of the current dependence can according to the equation

or according to the equation

With

R ₂ :

current-independent resistance value

R ₂ (I):

current-dependent resistance value

a:

selectable constant

kI:

power factor

I:

measured current I _mess (t) through the energy storage

I _B :

Reference current value

respectively.

The current-independent resistance value R ₂ is the parameter value that is varied during the formation of the plurality of parameter data record variants (P _i ). In contrast to a RLS algorithm with high-pass filtering and multiple current ranges to account for the current dependence, the current dependence of the parameter R ₂ is taken into account in the inventive method by an empirical formula (first equation) or a physically justified formula (second equation). As a result, the algorithm has a very good prediction and interpolation capability for currents that have not or rarely occurred in the course of the parameter adaptation.

The current factor kI is a mathematical scaling variable for the current dependence. In both equations, the current factor is defined differently. It is dimensionless in the first equation 1 and has the dimension [1 / A] in the second equation. Accordingly, the values are quite different. The current factor can basically be defined as a constant. However, since the current dependency changes with the operating temperature and over the life of the battery, it is advantageous to treat the current factor kI as a variable parameter which represents an additional parameter of the reference parameter data set (P _ref ) and which in the formation of the plurality ( N) is also varied according to parameter data set variants (P _i ). In this way, the current dependence of the second resistor can be better adapted to the actual electrical properties of the energy storage.

It may further be provided that also the parameter value of the second resistor (R ₁ ) is converted into a current-dependent resistance value (R ₁ (I)) in accordance with one of the equations as a function of the current flowing through the second resistor (R ₁ ), and this current-dependent resistance value (R ₁ (I)) is used in the reference model. In this way, an adaptation of the current dependence to the actual properties of the energy store can also take place in the case of the second resistor (R ₁ ).

For independent consideration of the current dependencies, a separate equation R (I) and / or a separate current factor kI _R1 , kI _R2 can be used for the first and the second resistor (R ₁ , R ₂ ), each of which can be varied. This results in a further parameter kI _R2 , which is also to be varied.

Alternatively, however, it is also possible to use an identical parameter value R for the first and the second resistor (R ₁ , R ₂ ). If the current dependence of the first resistor is taken into account, identical or different current dependency equations, ie identical equations for calculating the current dependency and an identical current factor kI, can additionally or alternatively be used for the first and the second resistor. In this way, the reference model is simplified and only a single resistance value (R) is to be varied and taken into account with regard to the current dependence or with regard to the current factor kI.

The current factor (kI) can be defined differently in each of the described embodiments for positive and negative currents (I (t)). As a result, an uneven current dependence for charging and discharging currents (unbalanced function in 1 ), which is observed on some batteries.

The initial parameter data set (P _start ) contains start values for the parameters (R ₁ , R ₂ , C, kI), which were previously determined and stored by measurement, for example. High accuracy of these starting values is not important since the parameter values are adjusted anyway during the operation of the energy store. Thus, the starting values may also be rough estimates. This has particular advantages, since it is no longer necessary to test each energy storage or energy storage type for determining the starting values. Manufacturing-related differences of the parameter values in energy stores of the same type in particular do not affect the quality of a performance prediction later.

The use of metrologically determined or estimated starting values for the initial parameter data set (P _start ) is important when the energy store is first put into operation, ie when the method according to the invention is carried out for the first time. If the method has already been carried out, it makes sense to use the parameter data record variant (P _n ) selected after the last execution as the initial parameter data record (P _start ) for the next execution of the method. This means that the initial parameter data set (P _start ) corresponds to the last parameter data set _variant (P _n ) selected as reference data record (P _ref ) after the evaluation interval.

The formation of the parameter data record variants (P _i ) can take place in various ways. For example, in each case at least one of the parameters (R ₁ , R ₂ , C, kI) of the reference parameter data record (P _ref ) can be varied one or more times and from this a parameter data set variant (P _i ) can be formed, consisting of the variant of the varied parameter (R _{1, i} , R _2,1 , C _i , k _i ) and the other parameters (R ₁ , R ₂ , C, kI) of the reference parameter data set P _ref .

In a simple parameter adaptation, for example, only one of the parameters needs to be varied. This will be sufficient especially if one of the parameters is known to change significantly depending on the operating case (state of charge, temperature) and age, whereas the remaining parameters remain approximately the same. Also, a single variation could be sufficient, if it is known that the corresponding one Anyway changes parameters in one direction only. Thus, for example, in the case of the capacitance C, a variation downwards, for example between 1 and 10%, preferably 5%, could take place: C _i = 0.95 * C, with i = 1. From this a parameter data set variant (P _i ) can then be formed consisting of this variant of the varied parameter C _i and the other, unchanged parameters of the reference parameter data set P _ref , P ₁ = (R1, R2, 0.95 · C, kI).

This procedure can be repeated for the other parameters (R1, R2, kI). So can be increased by 2%, for example, the first resistor R _2, the second resistor R ₁ are reduced by 6%. From this also parameter data set variants P _i can be formed in each case, consisting of the varied parameters and the unmodified parameters of the reference parameter data set: P ₂ = (1.02 × R 1, R ₂ , C, k I), P ₃ = (R 1, 0.94 × R2, C, kI), etc.

In order to obtain more parameter data set variants P _i , and thus to obtain a faster convergence of the method, a parameter can also be varied two or more times. So z. B. the first resistor by + 2%, + 4% and + 6% are increased, so that correspondingly further parameter data set variants P _{i can be created} from these variants and the other parameters of the reference data set P _ref : P ₂ = (1.02 · R1, R2, C, kI), P ₄ = (1.04 · R1, R2, C, kI), P5 = (1.06 · R1, R2, C, kI).

In order to ensure the convergence of the method in each case, it makes sense to increase the parameter value (R ₁ , R ₂ , C, kI) of the parameter to be varied by one value upwards and one value downwards, starting from its value in the reference parameter data set P _ref to change. However, this can not be done in particular by the same values, for example ± 1%, ± 2% or ± 5%. In a corresponding manner as before, parameter data set variants P _{i can be created} from these variants and the other parameters of the reference data set P _ref : P ₁ = (1.05 × R1, R2, C, kI), P ₂ = (0.95 × R1 , R2, C, kI), P ₃ = (R1, R2 1.05 ·, C, kI), P ₃ = (R1, R2 0.95 *, C, kI), etc. the amount of change is here empirically and can hiss for example 1% and 10%.

Overall, K parameters of the reference model and V variants of each parameter result in N = K * V parameter data sets. An advantage is the small number of parameter sets. The disadvantage, however, is that in each optimization step, the correlation between variations of several parameters is not taken into account, which can lead to slow convergence and instability.

For the formation of the parameter data record variants (P _i ), therefore, preferably each of the parameters (R ₁ , R ₂ , C, kI) of the reference parameter data set (P _ref ) may be one or more times, in particular as previously explained, by an amount upwards and an amount downwards can be varied, in which case a parameter data record variant (P _i ) is formed for each variant of a parameter (R _{1, i} , R _{2, i} , C _i , k _i ), consisting of this variant of the varied parameter (R _{1, i} , R _{2, i} , C _i , k _{i i} ) and other varied parameters (R _{1, i} , R _{2, i} , C _i , k _i ). In this way, a complete permutation is formed between all variants of all parameter variants, ie each parameter variant is linked in a parameter data record variant with a parameter variant of another parameter. Overall, K parameters of the reference model and V variants N = V ^K result in parameter data records. The disadvantage here is indeed the large number of resulting parameter data sets. However, this can be reduced by reducing the number of parameters, for example, by using identical resistance values for the first and the second resistor, and possibly an identical current dependency. However, it is advantageous in this permutation-based parameter data record formation that every possible permutation is taken into account, thereby achieving faster and stable convergence.

The number of variations of one of the parameters (R _{1, i} , R _{2, i} , C _i , k _i ) and / or the degree of variation need not necessarily be fixed during the process. Rather, it is advantageous if the number and / or the degree is determined dynamically depending on the results of previous calculations. Thus, for example, the variation of a parameter value of a parameter (R _{1, i} , R _{2, i} , C _i , kI _i ), which has been adapted several times successively in the direction of larger or smaller values, can be stronger in the next evaluation interval in the corresponding direction, to allow accelerated convergence to the actual value.

The second condition is to determine if the evaluation interval is to be ended. As a second condition, in the method according to the invention, it is preferable to use the check as to whether the duration of the evaluation interval has reached a predetermined maximum duration. Only then can enough information be available to evaluate the deviations. The maximum duration may be a time indication, for example between 5 and 20 seconds, preferably about 10 seconds. alternative can determine the maximum duration by specifying the number of repetitions of steps h., i. and J. be expressed. In this case, a counter is used. If the measured values are recorded, for example, in 0.1 second steps, one hundred repetitions of the steps result in a maximum duration of approx. 10 seconds.

Additionally or alternatively, as a second condition, the check can be used as to whether the duration of the evaluation interval has reached a predetermined minimum duration, for example between 2 and 5 seconds, preferably 3 seconds, and at the same time the first condition for initiating a new evaluation interval is fulfilled. Even if the duration of the evaluation interval has not exceeded the maximum duration, but has reached a minimum duration and the condition for starting the next interval is fulfilled, d. H. In particular, the current in the capacitance C of the reference model is small in a predefined period of time, the evaluation interval can be terminated and evaluated, because then immediately after the new evaluation interval can be started.

It is further advantageous if step j. is carried out only if the change in the current (I (t)) by the energy store in the evaluation interval was greater than a predefined minimum value (ΔI _min ). This means that the evaluation interval after step i. if necessary, but not evaluated, or evaluated if necessary, but the parameter data set _variant P _n with the smallest deviation is not adopted as a new reference parameter data set P _ref , if in the measured values I _mess (t), U _mess (t) of the current interval not enough information about the Battery impedance is present. This is especially the case when the current change in the evaluation interval was smaller than the predefined minimum value (ΔI _min ). Therefore, this predefined minimum value (ΔI _min ) should be exceeded when the current reference data set P _{ref is} changed.

Alternatively or cumulatively to the aforementioned condition of exceeding a predefined minimum value (ΔI _min ) for the current (I (t)) by the energy store, a minimum predefined voltage change (ΔU _min ) for the voltage at the capacitance (C) or for the measured Total voltage (U _mess (t)) are required. However, using the measured total voltage (U _mess (t)) is easier. The two minimum values ΔI _min , ΔU _min must be adapted to the properties of the measuring system (quantization accuracy (resolution) for the measured values). For example, the minimum changes should be greater than about 10 to 20 times the resolution.

In the calculation of the deviation, according to the invention, a function is used which delivers the greater the higher the difference between the measured voltage (U _mess (t)) and the sum of overvoltage (U _model (I _mess (t), P _i ) ) and initial voltage (U _{0, Pi} ). For example, a quadratic deviation can be used here, ie a function in which the difference is squared. This has the advantage that higher deviations are weighted more heavily. Alternatively, however, the amount of the difference or the power 4 could also be used.

According to another aspect of the method according to the invention, the change in the quiescent voltage (ΔOCV) of the energy store can be taken into account in the calculation of the deviation. For this purpose the measured current (I _mess (t)) of the energy store can be integrated during the evaluation interval and the change of the rest voltage (ΔOCV) calculated on the basis of this integral, in the determination of the quadratic deviation (ΔQ _Pi ) to the measured voltage U _mess (t ) are added: Q _{Pi_new} = Q _{Pi_old} + ΔQ _Pi ΔQ _Pi = (U _{model, Pi} + U _{0, Pi} - U _mess + ΔOCV (∫I (t))) ²

The integral (∫I (t)) represents an ampere-hour conversion. ΔOCV (∫I (t)) describes a functional dependence of the rest voltage on this ampere-hour conversion.

For the rest voltage, the following is explained: The total voltage of a battery is composed of the rest voltage (voltage when no current flows, open circuit voltage (OCV)), a slowly changing diffusion voltage and the voltage across the battery impedance, here as overvoltage ( U _model (t))), together. For the purposes of the present description, the term initial voltage is understood to be the sum of the quiescent voltage and the diffusion voltage. A complete battery model would therefore be obtained if the in 2 shown battery impedance is extended by a voltage source lying in series, which represents the temporally slowly changing rest voltage. A diffusion overvoltage can be simplified neglect or assume that they are also included in this voltage source. Now, when the battery is charged / discharged, the quiescent voltage changes slowly.

For a lithium-ion battery, the quiescent voltage is about 3.5 V in the discharged state and 4.2 V in the charged state. The dependence of the rest voltage on the state of charge OCV (SoC) is called the Entladekurve. This is due to the battery technology and can be measured in the laboratory.

Previously, it was assumed that the rest voltage in the initial voltage (U _{0, Pi} = U _mess (t) - U _model (I _mess (t), P _i )) is implicit and remains constant over the duration of an evaluation interval. In fact, this changes slightly. In order to take this into account, the change in the rest voltage ΔOCV as a result of the change in the state of charge, which is the ampere hourly charge / battery capacity, can be determined from a rest voltage curve, which has been measured, for example, in the laboratory and stored in the battery management system: ΔOCV = f (∫I ( t)). The equation component ΔOCV (∫I (t)) describes a functional dependence. This consideration makes the determination more accurate.

In addition or as an alternative to the above-mentioned further developments, a weighting of the respectively newly calculated deviation (ΔQ _Pi ) with a weighting factor (G) can take place during the calculation of the voltage deviation, the deviation (ΔQ _Pi ) only then becoming the previously calculated deviation (Q _{Pi_old} ). is added, (Q _Pi = Q _Pi + G · ΔQ _Pi ). This weighting factor (G) controls the degree of adaptation. In particular, this weighting factor can be implemented depending on the current, in particular such that it is suitable for larger ones. Currents is higher and smaller for smaller currents. In this case, the adaptation is controlled so that the model emulates better the properties of the battery, especially at high currents. As a current, preferably the total current can be used by the energy storage.

As in step j. called the method, the found parameter data set variant (P _n ) can be defined directly or indirectly as a new reference parameter data set (P _ref ). Immediately in this context means that the particular parameter _{data set variant} (P _n ) is defined directly as a new reference parameter data set (P _ref ) (P _{ref_new} = P _n ).

Alternatively, the specific parameter data set variant (P _n ) can be indirectly defined by a low-pass filtering as a new reference parameter data record (P _ref ). This has the advantage that the history of the impedance of the energy storage is taken into account and any errors in the parameter determination are smoothed over time. In this case, the old reference parameter data set (P _{ref, old} ) is preferably multiplied by a weighting factor (k) and the specific parameter data _{record variant} (P _n ) multiplied by the complement (1-k) to one of this weighting factor (k). The sum of the thus weighted parameter data _sets (P _{ref, old} , P _n ) is then defined as a new reference parameter data set (P _{ref_new} = k * P _{ref_old} + (1-k) * P _n ). The weighting factor (k) has a value between zero and one. For the value zero (k = 0) results in the embodiment variant in which the found parameter data set _variant (P _n ) is defined directly as a new reference parameter data _record ( _Pref ).

The low-pass filtering can be the same for all parameters of the reference parameter data set (P _ref ), ie the same weighting factor (k) applies to all parameters (R _{1, n} , R _{2, n} , C _n , k _n ) of the particular parameter data set variant (P _n ) , This simplifies the calculation and reduces the computing power accordingly. In order to obtain a more precise adaptation of the parameters (R ₁ , R ₂ , C, kI) and to ensure respective convergence of the parameter search, it is advantageous to carry out the low-pass filtering on a parameter-specific basis. For this purpose, each parameter (R ₁ , R ₂ , C, kI) can be assigned its own weighting factor (k _X ). Preferably, then, each parameter (R _1, R _2, C, kI) of the old reference parameter data set (P _{ref, old)} multiplied by its weighting factor (k _X) and the parameters (R _{1, n,} R _{2, n,} C _n, kI _n ) of the determined parameter data set variant (P _n ) is multiplied by the complement (1 - k _X ) to one of the respective weighting factor (k _X ). Subsequently, the respective sums of the parameters so weighted ([R ₁ , R _{1, n} ], [R ₂ , R _{2, n} ], [C, C _n ], [kI, kI _n ]) become parameter values of the new reference parameter data set P _{ref_neu} defined.

As already mentioned, the method according to the invention is particularly suitable for use in the context of a predicative determination of the maximum power of the energy store available for a predefined time, as implemented in particular in battery management systems, since this is done at the actual time State of the energy storage adapted reference model is particularly important to provide reliable, accurate prediction values. It is therefore proposed to use the method according to the invention for the predicative determination of the maximum power of the energy store available for a predefined time.

Furthermore, a battery management system is proposed for the self-adapting, predicative determination of the maximum power of an electrochemical energy store available for a predefined time, in particular for electric or hybrid vehicles, comprising means for the measurement the current flowing through the energy store (I _mess (t)) and the voltage applied thereto (U _mess (t)) and a microcontroller to which a program is loaded with instructions for carrying out the method according to the invention.

Further advantages and features of the method according to the invention are explained below with reference to an embodiment using the figures. Show it:

1 : Current dependence of the battery resistance using the example of a 40 Ah lithium-ion battery; left: for a new cell; right: for an aged cell.

2 : Equivalent circuit diagram to simulate the dynamic characteristics of a battery

3 : Flow chart for the performance prediction of a battery

4 : Algorithm for adapting the model parameters

5 : Battery impedance model used for one embodiment

6 : Curves for the verification of the process

7 : Enlargement of the curves 6

8th : Enlargement of the curves 6

1 illustrates the age-related change in the current dependence of the internal resistance xR (I ₁ ) of a 40 Ah battery for a vehicle at the temperatures 15 ° C, 10 ° C and 0 ° C, which was determined by measurement. The left picture shows the current dependence of a new battery, called cell there, the right picture shows the current dependency of an aged battery. It should be noted that the battery consists of several cells connected in series. When connected in series, however, the battery capacity remains (in Ah) as in a cell (here 40 Ah). Apart from the knowledge that the dependence of the internal resistance xR (I ₁ ) of the current I is greater, the lower the temperature, illustrated 1 in that the current dependency in an aged battery is more pronounced at the same temperature. This is recognizable by the steepness of the curves. This means that the use of a constant resistance value in an underlying battery model is not suitable for the prediction of the performance of the battery or leads to poor prediction values, which become increasingly worse with increasing age of the battery. For this reason, in the following embodiment, the current dependence of the internal resistance of the energy storage, here a battery, taken into account, ie modeled in the battery model.

oder abgeleitet von der sogenannten Buttler-Volmer Gleichung

wobei R₂ der stromunabhängige Widerstandswert, R₂(I) der stromabhängige Widerstandswert, a ein an die gegebene Batterie anzupassender, statischer Parameter, kI ein Stromfaktor, I der berechnete Strom durch den Widerstand R₂ und I_B ein Bezugsstromwert ist. Der Stromfaktor kI definiert die Abhängigkeit des ersten Widerstandes R₂ vom Strom I. I_B ist der einstündige Entladestrom, d. h. derjenige Strom, der erforderlich ist, um die Batterie in einer Stunde von 100% auf 0% zu entladen. Als Bezugsgröße kann grundsätzlich auch eine andere Stromstärke gewählt werden. 2 shows a simplified equivalent circuit of the impedance of a lithium-ion battery used as a model. It includes a real internal resistance R _1, which describes the ohmic resistance of the battery, and a capacitor C connected in series therewith, which maps the double layer capacitance of the battery. Another resistor R ₂ (I) is modeled parallel to capacitance C and maps the resistance of the charge transfer reaction. This is in contrast to R ₁ current-dependent and therefore modeled here as dependent on the current flowing through the energy storage current. Generally speaking, when referring to the battery impedance, it is meant the sum of R ₁ + R ₂ from the two resistors R ₁ , R ₂ . So is also in terms of 1 Generally speaking of the current dependence of the internal resistance, although it is known that only the resistor R _{2, which is} parallel to the capacitance, has a current dependency. A calculation of the current-dependent resistance value takes place with the empirical equation

or derived from the so-called Buttler-Volmer equation

where R _{2 is} the current-independent resistance value, R ₂ (I) is the current-dependent resistance value, a is a static parameter to be fitted to the given battery, kI is a current factor, I is the calculated current through the resistor R _2, and I _{B is} a reference current value. The current factor kI defines the dependence of the first resistor R ₂ on the current I. I _B is the one-hour discharge current, ie the current required to discharge the battery from 100% to 0% in one hour. As a reference, in principle, another current can be selected.

The first resistor R ₂ , the second resistor R ₁ , the capacitance C and the current factor kI form parameters of the equivalent circuit diagram or of the model whose exact values are decisive for the correct description of the battery. It is known that these parameters are not all constant, but depend on the temperature of the battery, its state of charge and its age. Therefore, in a more complex model, all parameters can also be current-dependent and additionally or alternatively also temperature-dependent modeled. However, this is neglected here for the sake of simplicity.

The following is a battery management system used in an electric or hybrid vehicle to monitor the battery to estimate the maximum power the battery can deliver for a future period of time. 3 shows a flowchart of this prediction method. The battery management system uses a battery impedance model according to FIG 2 with corresponding parameters R ₁ , R ₂ , C and kI and parameter values for this. According to the parameters of the equivalent circuit diagram are adapted during operation to the aging state of the battery.

In a first step 1 the measurement of total current I _mess (t), total voltage U _mess (t) of the battery and. In a second step 2 the automatic adaptation of the parameters according to the invention to the actual state of the battery takes place.

There are steps closing 3 . 4 and 5 for calculating the maximum charging current I _LAD and the maximum discharging current I _ELA, each taking into account the voltage limits, the state of charge limits (SoC) and the current limits.

step 3 :
First, the starting voltage of the battery is calculated, which can be interpreted as an estimate of the rest voltage): U _start = U _mess (t) - U _model (I _mess (t)) With U _model (I _mess (t)) = R ₁ * I _mess (t) + (I _mess (t) _{-I c} (t)) * R ₂ (I _mess (t)), where I _c (t) is the estimated current in the capacitance C.

Then, for the discharge case, the difference to a lower voltage limit U _min and for the load case to an upper voltage limit U _{max is} calculated: ΔU _ELA = U _start - U _min , ΔU _LAD = U _max - U _start .

Thereafter, each time using an iterative method (eg Newton-Raphson search method [ P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Berlin: Springer, 2004 ]) I _{LAD, V} and I _{ELA, V} searched so that the following conditions are met: U _model (I _{LAD, V} , Δt) = ΔU _LAD U _model (I _{ELA, V} , Δt) = ΔU _ELA .

Here, U _max , U _{min are} the predefined voltage limits, U _model (I _{LAD, V} , Δt) and Umodell (I _{ELA, V} , Δt) calculated from the model of battery impedance voltages, if appropriate, the currents I _{LAD, V} and I. _{ELA, V are applied} over a predefined duration Δt _pulse (in sec.): U _model (I _{LAD, V} , Δt _pulse ) = R ₁ * I _{LAD, V} + R ₂ (I _{LAD, V} ) * I _{LAD, V} * (1-exp (-Δt _pulse / (R ₂ (I _{LAD, V} ) * C))) + R ₂ (I _{LAD, V} ) * I _c (t) * exp (-Δt _pulse / (R ₂ (I _{LAD, V} ) * C)); U _model (I _{ELA, V} , Δt _pulse ) = R ₁ * I _{ELA, V} + R ₂ (I _{ELA, V} ) * I _{ELA, V} * (1-exp (-Δt _pulse / (R ₂ (I _{ELA, V} ) * C))) - R ₂ (I _{ELA, V} ) * l _c (t) * exp (-Δt _pulse / (R ₂ (I _{ELA, V} ) * C));

step 4 : I _{LOAD, SOC} = (SOC _max -SOC (t)) / 100 * C _bat * 3600 / Δt _pulse I _{ELA, SOC} = (SOC (t) - SOC _min ) / 100 * C _bat * 3600 / Δt _pulse

Here, SOC _max and SOC _{min are} the predefined SOC limits in%, C _bat is the battery capacity in Ah, which is not to be confused with the double-layer capacitance C in the model.

step 5 :
I _{LAD, I} and I _{LAD, I} are determined from a pre-parameterized map as a function of the battery temperature.

These steps 3 . 4 . 5 are not subject to any particular order and are therefore interchangeable. Thus, in each case three maximum charging currents I _{LAD, V} , I _{LAD, SoC} , I _{LAD, I} and three maximum discharge currents I _{ELA, V} , I _{ELA, SoC} , I _{ELA, I are} calculated. Subsequently, minima are formed, respectively for the charging currents I _LAD = min (I _{LAD, V} , I _{LAD, SoC} , I _{LAD, I} ) and for the discharge currents I _ELA = min (I _{ELA, V} , I _{ELA, SoC} , I _{ELA , I} ), step 6 ,

In step 7 the battery voltage is calculated for the determined minimum currents, U _LAD = f (I _LAD ), U _ELA = f (I _ELA ):

First, for the step in 6 calculated current I _LAD the model _voltage calculated at the end of the current pulse duration Δt _pulse : ΔU _LAD = U _model (I _LAD , P _ref ) ΔU _LAD = R ₁ × I _LAD + R ₂ (I _LAD ) × I _LAD × (1-exp (-Δt _pulse / (R ₂ (I _LAD ) × C))) + R ₂ (I _LAD ) × I _c (t) · exp (-Δt _pulse / (R ₂ (I _LAD ) · C));

For the one in step 6 calculated current I _ELA , the model voltage at the end of the current pulse duration .DELTA.t _{pulse is} calculated: .DELTA.U _ELA = U _model (I _ELA , P _ref ). ΔU _ELA = R ₁ × I _ELA + R ₂ (I _ELA ) × I _ELA × (1-exp (-Δt _pulse / (R ₂ (I _ELA ) × C)) - R ₂ (I _ELA ) × I _c (t) · exp (-Δtpulse / (R ₂ (I _ELA ) · C));

Thereafter, the desired charging voltage U _LAD and the discharge voltage U _ELA with the consideration of in step 3 calculated starting voltage U _start calculated: U _LAD = ΔU _LAD + U _start , U _ELA = -ΔU _ELA + U _start .

From the product of the respective minimum current I _LAD , I _ELA and the voltages correspondingly calculated therefrom, U _LAD , U _ELA is finally calculated the available battery power during a charging process P _LAD = U _LAD * I _LAD and during a discharge process P _ELA = U _ELA · I _ELA , step 8th ,

Both performance forecasts are relevant when driving with an electric or hybrid vehicle. Although the battery is always discharged when driving on average, but it can also be charged by recuperative braking for a short time to recover the kinetic energy and not to destroy in conventional braking. For both processes - acceleration and braking - it must therefore be predicted, which maximum battery power is available. Both can occur sporadically in the next moment, which is why both are predicted in parallel. There are therefore no separate battery parameters, only one parameter set describes the current state of the battery.

The invention described herein represents a method such as the steps 2 . 3 and 7 can be performed efficiently and taking into account the current dependence of the battery resistance. The basic building block is a method which makes it possible to efficiently calculate the battery parameters necessary for the power prediction. The dynamic behavior of the battery is replaced by the equivalent circuit diagram 2 modeling representing a model of battery impedance. The parameters to be adapted to the battery state are the resistors R ₁ , R ₂ , the capacitance C and the current factor kI.

4 illustrates the inventive method for adapting the parameters to the current state of the battery based on a flowchart. The procedure is such that during operation of the battery on short evaluation intervals in each case several parameter data set variants P _i calculated and then from these according to predefined criteria, the most appropriate parameter data set variant P _{n is} selected. This is then marked as best current estimate and stored as a reference parameter data set P _ref .

At the beginning of the process, ie at the start of the battery management system, the battery model M in step 11 initialized using an initial parameter record P _start . This means that the parameters capacitance C, first resistor R ₂ , second resistor R ₁ and current factor kI are assigned first parameter values of the parameter data set P _start = (R ₁ , R ₂ , C, kI), previously determined or estimated by measurement in the laboratory and have been stored. These values are first defined as reference parameter data set P _ref , P _ref = P _start . The reference parameter data set P _ref represents at all times the best estimate of the model parameters are continuously updated and will. The battery model M thus represents a reference model from which the parameter adaptation takes place.

In step 12 , waits for new measured values, ie the current I (t) = I _mess (t) flowing through the battery and the voltage U _mess (t) applied to the poles of the battery. The measurement is repeated in discrete time steps. As a measurement already in step 1 from 3 took place, they lie for step 12 in 4 just before. Subsequently, the reference model M is calculated using these measured values and the reference parameter data set P _ref , step 13 , Among other things, the current through the capacitance I _C (t) and the voltage applied thereto U _C (t) is determined here. The method according to the invention can only be carried out when the battery is charged, otherwise I (t) = 0, and identification of the parameters is impossible.

The model equations describing the reference model are:

The current factor kI can have a value between 0 and 0.5 and the constant a can have a value between 0.03 and 0.06. I _B corresponds to the battery capacity, which is typically between 10 and 100 Ah for hybrid or electric vehicles.

The adaptation of the parameters takes place in an evaluation interval. Since different calculation steps are carried out at the beginning of an evaluation interval than during the interval and are always to be used for the calculations with current measured values I _mess (t), U _mess (t), the first step is Block 14 a query as to whether an evaluation interval is already running. This is not the case at the beginning of the procedure, so at step 15 is continued.

An adaptation of the parameters should take place only if the energy stored in all model elements that can store energy changes only slightly over time, ie the change is small. On the equivalent circuit / reference model M after 2 When applied, this means that the energy stored in the capacitor C may change only slightly over time, ie the current I _C (t) should be small due to the capacitance C.

To start the calculation of the model for different sets of parameters, an initial estimate of the voltage or current on / in the energy-storing elements of the model is necessary. Here one can speak of an "initialization" of the model. This estimation is again necessary for the calculation of an initial voltage U _{0, Pi} . It is essential that this initial voltage U _{0, Pi} is calculated as accurately as possible, as it then applies to the entire evaluation interval.

This estimate is the more accurate the less voltage / current in the energy storage elements will vary at the beginning of the calculation. In general, this means that there is only a small variation in the energy stored in these elements. The estimate is taken from the reference model M with the reference data set P _ref . The higher accuracy with slow current / voltage changes follows because the model is still a significant simplification of the real dynamic battery behavior, and this is simulated better at relatively slow load dynamics than at very fast dynamics. As soon as the model is initialized and the initial voltage U _{0, Pi is} calculated, the dynamics of the load may also be fast, the errors then being compensated over the entire evaluation interval.

At this point, it should be noted that depending on the driving profile and / or battery, the time proportion with the condition "I _C (t) = small" in relation to the total driving time is very large. That is, this condition is almost always met. Instead of using this condition as a criterion for the initiation of an evaluation interval, it is also theoretically possible to start an evaluation interval at any time, if necessary, without considering a condition. Although this sometimes leads to more errors in the parameter determination. However, it can still provide useful results on average.

It is therefore expedient to initiate an evaluation interval only when at least one variable of the reference model (M) fulfills a first condition. As a variable, the current I _C (t) is used by the capacitance C. This must fulfill the condition to be small over a certain period of time. The period can be between 0.5 s and 0.8 s. For the condition, a comparison with a limit I _{C, grenz} , for example, an absolute value, z. B. 4A, or with a standing in relation to the maximum current of the battery value, for example, 2% of the maximum current. The verification of this condition is part of the block 15 , For this I _C (t) is continuously calculated in the reference model. If it falls below the limit I _{C, grenz} , a time _counter is started. This time counter is reset when the current I _C (t) is again greater than the limit I _{C, limit} . If the time counter has reached the predefined value, for example 0.5 s, the condition for the small current I _C (t) is fulfilled.

As part of the block 15 Accordingly, the current I _C (t) is determined by the capacitance C and compared with the limit I _{C, border} , or this stream has already been in step 13 determined, so in block 15 only the first condition needs to be checked. The current I _C (t) through the capacitance C results from I _C (t) = I (t) - U _C (t) / R ₂ (I) (Eq. 5)

For I (t) the measured value I _mess (t) is to be used. U _C (t) is determined by the iterative solution of Equation Eq. 4 is calculated in the time-discrete region with the time-discrete step k at time t _k with the reference parameter data set P _ref = (R ₁ , R ₂ , kI, C) as follows:

If the current I _C (t) is below the limit I _{C, grenz} by the capacitance C for the predetermined period of time, a new evaluation _interval is initiated. If not, the procedure at step 12 continued. This also takes place as long as the predetermined period has not yet ended.

If the first condition is met, first in block 16 N durchsparchnende parameter data sets P _i , with i = 1 to N defined. In this case, starting from the reference parameter data set P _ref for each parameter R ₁ , R ₂ , C, kI of this reference parameter data set P _ref, at least two variations R _{1, i} , R _{2, i} , C _i , k 1, namely a parameter value increase and a parameter value reduction are created , The amount of parameter value change is empirical and may be between 1% and 10% of the reference parameter value. In particular, several variations can be created. Preferably, the increase and decrease of the parameter value are the same. For example, the second resistor R ₁ to ± 5% is varied, so that parameter values 0.95 x R _1; 1 × R ₁ and 1.05 × R ₁ .

For each variant of the parameter R _{1, i} , systematically parameter data set variants P _{i are} formed, consisting of the respective variant of the varied parameter R _1,1 = 0.95 * R ₁ , R _1,2 = 1 * R ₁ and R _{1 , 3} = 1.05 * R ₁ and the other (here initially) unchanged parameters R ₂ , C, kI of the reference parameter data set P _ref . If the other parameters R ₂ , C, kI are not changed, there are already three parameter data record variants P _i , i = 1 to 3: P ₁ = (0.95.R ₁ , R ₂ , C, kI), P ₂ = (1 × R ₁ , R ₂ , C, kI), P ₃ = (1.05 × R ₁ , R ₂ , C, kI)

If this is also carried out for the first resistor R ₂ , three further variants are obtained for each of the three parameter data set variants P _i , i = 1 to 3, namely for 0.95 * R ₂ ; 1 · R ₂ and 1.05 · R ₂ , so that a total of nine parameter data set variants P _i , i = 1 to 9 arise: P ₁ = (0.95 * R ₁ , 0.95 * R ₂ , C, kI) P ₄ = (0.95 * R ₁ , 1 * R ₂ , C, kI) P ₇ = (0.95 × R ₁ , 1.05 × R ₂ , C, kI) P ₂ = (1 × R ₁ , 0.95 × R ₂ , C, kI) P ₅ = (1 × R ₁ , 1 × R ₂ , C, kI) P ₈ = (1 × R ₁ , 1.05 × R ₂ , C, kI) P ₃ = (1.05 × R ₁ , 0.95 × R ₂ , C, k I) P ₆ = (1.05 × R ₁ , 1 × R ₂ , C, kI) P ₉ = (1.05 × R ₁ , 1.05 × R ₂ , C, kI)

A variation can now also be made for the capacitance C and for the current factor kI. In sum, for this example case, with two variations (± 5%) per parameter, which corresponds to three variants per parameter (± 5% and unchanged parameters), then 81 parameter data set variants P _i , i = 1 to 81 are generated. Thus, if all K = 4 parameters are varied twice, resulting in a total of V = 3 variants per parameter, a complete permutation is formed between all variants of all parameters, resulting in a total of N = 3 ⁴ = 81 parameter data set variants P _o .

Subsequently, the reference model M is initialized for all parameter data set variants P _i , step 17 , This means that an initial voltage U _{0, Pi is} calculated from the reference model M for each parameter data set _variants P _i and the current measured values U _mess (t), I _mess (t).

Since equation Eq. 4 is a differential equation, it must be calculated recursively in combination with equation Eq. 3. The recursive calculation always requires the result of the last calculation. At the beginning this therefore requires an initialization, ie an initial estimate. For this purpose, the voltage U _C (t) over the capacitance C for each parameter data set variant P _{i is set} equal to the voltage across the capacitance C in the reference model M, ie the voltage which results from the model when using the reference parameter data set P _ref : U _{C, Pi} = U _{C, pref} . This voltage U _{C, Pref} was in step 13 calculated.

Then, for each parameter set P _i = (R ₁ , R ₂ , C _i , k _i ), an initial voltage is calculated: U ₀ , P _i = U _meas - U _model (Imess, P _i ), with I _meas and U _mess as actual measured battery current and battery voltage. The initial voltage essentially corresponds to the quiescent voltage of the battery, but also includes diffusion overvoltages that change very slowly compared to the length of the evaluation interval. U _model (I _mess , P _i ) is the one from the reference model ( 2 ) calculated overvoltage, ie the voltage across the battery impedance for the measured current I _mess and the given parameter set P _i . U _model (I _mess , P _i ) is calculated according to Equation Eq. 3, in which equation for the voltage U _C (t) over the capacitance the value previously calculated from the reference model is used (step 13 ).

If the initialization of the reference model M has been carried out for all parameter data record variants P _i , the method according to the invention is performed in step S 12 continued. The next measured values for the total current and the total voltage are awaited.

Accordingly, a renewed measurement of the current flowing through the energy store (I _mess (t)) and the voltage applied to this (U _mess (t)). The measurement takes place in discrete time steps of typically 0.1 s. This means that new readings are available every 0.1 seconds. The steps 13 to 17 are carried out between two measured values. There is thus a time window of 0.1 seconds available to perform all calculations.

If the new measured values are available, the reference model M is recalculated with the reference data record P _ref and the current measured values, step 13 , Thus, the reference model with the reference parameter data set is always calculated continuously, which ensures a continuous calculation of the current Ic (differential equations must be calculated iteratively). If an interruption took place here, the current state would be lost, and it would take considerable time to settle after another (inaccurate) initialization.

As an evaluation interval previously in step 15 was initiated and is still running, the query is in block 14 confirmed with "yes". It is then first the reference model M in 2 updated for all N parameter sets P _i , step 18 , The situation resulting from the reference model M for each parameter data record variant P _i voltage U _{C, Pi} (t) across the capacitor C, and the voltage U _model (I _mess (t), P _i) are calculated at the energy storage. The overvoltage U _model (I _mess (t), P _i ) is given by Equation Eq. 3 or time-discrete according to the following equation U _model (I _mess (t _k ), P _i ) = U _C , P _i (t _k ) + I _mess (t _k ) · R ₁ .

The calculation of U _{C, Pi} (t _k ) takes place in time-discrete step k at time t _{k as} follows:

After that, in step 19 For each parameter data set variant, a quadratic deviation ΔQ _Pi between the measured battery voltage U _mess (t) and the sum of calculated overvoltage U _model (I _mess (t), P _i ) and initial voltage U _{0, Pi is} determined: ΔQ _Pi = (U _model ( I _mess (t), P _i ) + U _{0, Pi '} - U _mess (t)) ² .

The steps 18 and 19 are repeatedly executed as long as one in block 20 the criterion to be checked does not terminate the evaluation interval. In these repetitions, the respectively newly calculated quadratic deviation ΔQ _{Pi is added} to the previously calculated quadratic deviation Q _{Pi_old} , so that as a new quadratic deviation Q _{Pi_new} results: Q _{Pi_new} = Q _{Pi_old} + (U _{model, Pi} + U _{0, Pi} - Umess) ² . (Equation 6)

This corresponds to a numerical integration of the quadratic deviation ΔQ _Pi during the duration T _{evaluation of} the evaluation _interval .

Now it is checked whether a second condition is met, can be ended at the evaluation interval, step 20 , This condition is fulfilled when the duration T _{evaluation of} the evaluation _{interval has} reached or exceeded a predefined maximum duration T _max . Only then can enough information be available to evaluate the quadratic deviations. The maximum duration is 10 seconds, for example.

If the second condition is not met, as is always the case at the beginning of the method, the method at step 12 continued. New measured values U _mess (t), I _mess (t) are then recorded, with which again the voltage U _C (t) over the capacitance C and the total voltage U _model (I _mess (t), P _i ) for each parameter data set _variant P _{i is} calculated. From this, the quadratic deviation Q _{Pi_new} is again determined for each parameter _{data set variant} P _i and the second condition is checked for _compliance .

If the second condition is fulfilled, however, the evaluation interval is ended. The parameter _{data set variant} P _n , n ε [1... N] with the smallest value for the quadratic deviation Q _{Pi_new is then} selected and used as the reference parameter data set P _ref for the next calculations, step 21 , The new reference parameter data record P _ref now contains parameter values for the parameters R ₁ , R ₂ , C, kI of the reference model M, which better describe the actual dynamic operating behavior of the battery.

After selecting one of the new reference parameter data set P _ref , the method at step 15 continued.

In a test step, not shown, between the steps 20 and 21 of the 4 is to be arranged, it is checked whether the change of the current I (t) by the energy storage in the evaluation interval was greater than a predefined minimum value .DELTA.I _min . The determination of the smallest quadratic deviations and the corresponding selection of a new reference parameter dataset in step 21 then takes place accordingly only if this minimum value .DELTA.I _{min is} exceeded. Otherwise, the procedure will be immediately after step 21 continued.

The checking of the exceeding of the minimum value ΔI _min can be carried out in such a way that first the maximum value I _max and the minimum value I _{min are} determined from the current measurements I _mess (t). For this purpose, the first measured current values can be set as I _max and I _min , whereupon in each subsequent measured value it is checked whether the new measured value I _mess (t) is greater than the current maximum value I _max , in which case the new measured value is new Max value I _{max is} set, or whether the new measured value I _mess (t) is smaller than the current minimum value I _min , in which case the new measured value as new Minimum value I _{min is} set. At the end of the evaluation, the difference between maximum and minimum values is then formed and tested whether this difference is greater than the predefined minimum value .DELTA.I _min (eg 20 A.), I _max - I _min> .DELTA.I _min. If this is the case, the current I (t) has changed sufficiently, so that sufficient information about the battery impedance is present in the measured values. Only in this case will then step in 21 determines the parameter data set variant P _n with the smallest quadratic deviation and defines this variant P _n as the new reference data record P _ref .

In a corresponding manner, in a step, not shown, between the steps 20 and 21 of the 4 is to be ordered, in addition to be checked whether the change in the voltage U (t) at the energy storage in the evaluation interval was greater than a predefined minimum value .DELTA.U _min . The determination of the smallest quadratic deviations and the corresponding selection of a new reference parameter data set P _ref in step 21 then takes place accordingly only if this minimum value ΔU _{min is} exceeded. Otherwise, the procedure will be immediately after step 21 continued.

Instead of the model in 2 For example, a simplified reference model M * with only three parameters R, C, kI can be used 5 is shown. For this, resistors R ₁ and R ₂ are set equal, and it is assumed that the same current dependence: R ₁ (I) = R ₂ (I) = R (I). This leads to a reduction of the multiplicity of parameter data set variants P _i .

According to another embodiment, in the last step 21 the found parameter data set _variant P _{n is} not directly defined as a new reference parameter data set P _ref , but rather indirectly. In this case, a weighted mixture of the old reference parameter data record P _ref and the new parameter data record _variant P _{n is} formed, and this mixture is used as a new reference parameter data set P _ref . In this way, the history of the battery impedance is taken into account.

The mixing takes place in such a way by a low-pass filtering that the old reference parameter data set P _{ref_alt} is multiplied k with a lying between 0 and 1 weight factor, and the parameter data set variant found P _n with the complement of k 1 corresponding weighting factor, with 1 - is multiplied by k. The weighted parameter records are then added together to give: P _{ref, new} = k · P _{ref, old} + (1-k) · P _n , where 0 <k <1,

If, for example, k = 0.5 is chosen, averaging is obtained. In the described manner, the entire reference parameter data set P _ref may be filtered, or k may be selectively or parameters specific be applied, in which case, for each parameter, a corresponding weighting factor k _X with X = R _1, R _2, C or kI and 0 ≤ k _X ≤ 1 exists. For k _X = 0 the filtering can be deactivated. For k _X = 1, the corresponding parameter can even be excluded from the adaptation according to the method. However, the latter is not required if a variant with unchanged parameter is always present in the parameter data record variants.

If the parameters R ₁ , R ₂ , C, kI of the reference model M in 2 has been adapted to the characteristics of the battery by the method according to the invention, the determination of the maximum current in step 3 from 3 as previously explained in detail. In the following, the most important steps are addressed again:
From the current measured values (U _mess , I _mess ), the starting voltage is calculated using the reference model M and the reference data set P _ref as follows: U _start = U _meas U _model (I _mess , P _ref ). Then, for the discharge case, the difference to a lower voltage limit U _min and for the load case to an upper voltage limit U _{max is} calculated: ΔU _ELA = U _start - U _min , ΔU _LAD = U _max - U _start . Thereafter charging current I _LAD and discharge current I _{ELA are} searched for, so that the resulting model voltage U _model (t) after predetermined time Δt for these currents corresponds to the calculated voltage differences: U _model (I _LAD , P _ref ) = ΔU _LAD , U _model (I _ELA , P _ref ) = ΔU _ELA .

The search for these currents can z. B. Iteratively, for example, with the Newton-Raphson search method P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Berlin: Springer, 2004 ]).

The calculation of the stress in the step 7 from 3 is performed as follows:
First, for the step in 6 calculated current I _LAD the model _voltage calculated at the end of the current pulse duration Δt _pulse : ΔU _LAD = U _model (I _LAD , P _ref ) ΔU _LAD = R ₁ * I _LAD + R ₂ (I _LAD ) * I _LAD * (1-exp (-Δt _pulse / (R ₂ (I _LAD ) * C))) + R ₂ (I _LAD ) * I _C (t) · exp (-Δt _pulse / (R ₂ (I _LAD ) · C));

For the one in step 6 calculated current I _ELA , the model voltage at the end of the current _pulse duration .DELTA.t _{pulse is} calculated: ΔU _ELA = Umodell (I _ELA , P _ref ). ΔU _ELA = R ₁ × I _ELA + R ₂ (I _ELA ) × IELA × (1-exp (-Δt _pulse / (R ₂ (I _ELA ) × C))) -R ₂ (I _ELA ) × I _C ( t) · exp (-Δt _pulse / (R ₂ (I _ELA ) · C));

Thereafter, the desired charging voltage U _LAD and the discharge voltage U _ELA with the consideration of in step 3 calculated starting voltage U _start calculated: U _LAD = ΔU _LAD + U _start , U _ELA = -ΔU _ELA + U _start .

The proposed method according to the invention for adapting the model parameters in a battery management system offers a novel method in which the battery model with several parameter variants is calculated over specific time intervals, in order subsequently to use the best variant for further calculations. So far, only Kalman filter based techniques have been introduced.

It should be emphasized in particular that the calculation is carried out on the basis of the current battery voltage for a given load (U _mess , I _mess ). Therefore, a complete battery model is not necessary. It is only required a model of the battery impedance, which (typically .DELTA.t _pulse = 1 ... 30 sec.) Describes the behavior of the battery in case of power changes to be predicted period. Previously known algorithms require a complete battery model including quiescent voltage model with hysteresis determination, etc. Abandoning other parts of the battery model (quiescent voltage, hysteresis, diffusion) makes the process simpler and more accurate because the corresponding overvoltages are directly included in measurement data and thus implicitly taken into account.

The prediction of the maximum available power of the battery in an electric vehicle is imperative for safe driving. In the following example, the algorithm described above with an impedance model of the battery according to 5 used to predict the voltage of the battery at a current. That is appropriate 3 the basic building block of performance forecasting.

A typical load profile of the battery of an electric vehicle is extended by reference current pulses to provide a deterministic basis for quantitative examination of the accuracy of the algorithm. 6 shows corresponding current and voltage curves measured on a 40 Ah lithium-ion battery cell. With the aid of the algorithm described above, the model parameters (R, C, kI) are determined and with their help the voltage of the battery is predicted five seconds after the start of the current pulse for each current pulse. The initial values for model parameters are chosen arbitrarily in order to verify adaptability. The adaptation of the resistance and the capacitance (R, C) leads to correct values in the first 200 seconds. The adaptation of the current dependence takes a little longer, since at the time of the first pulse the parameter kI responsible for the current dependence has not yet been adapted. As a result, a larger error is shown in the voltage prediction at the beginning during high currents. However, after kI is also adapted, the voltage prediction for medium and large currents gives very accurate results, see 6 . 7 and 8th ,

The adaptation method was implemented on a 16-bit microcontroller (Infineon XC2287, 80 MHz). The software only needs about 500 bytes of RAM (about 1% of the RAM memory) and about 11 kbytes of ROM (about 1.2% of the ROM memory). The utilization of the processor is about 1.7%. This result confirms the computational efficiency of the algorithm and demonstrates its applicability to cost-effective hardware, including in the automotive industry.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• US 7518375 B1 [0007]
• WO 2005050810 [0009]
• US 7486079 B1 [0011]
• DE 102009049320 A1 [0013, 0013]
• US 6832171 [0014]
• DE 102009054547 A1 [0014]
• US 6469512 B [0014]
• US 2011/0172939 [0014]

Cited non-patent literature

• Gregory L. Plett, "Extended Kalman filtering for battery management system of LIPB-based HEV battery packs: Part 3. State and parameter estimation", Journal of Power Sources, Volume 134, No. 2, pp 277-292, 2004 [. 0011]
• M. Urbain, S. Rael, B. Davat, and P. Desprez, "State Estimation of a Lithium Ion Battery Through Kalman Filter," June 2007, pp. 2804-2810 [0011]
• P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Berlin: Springer, 2004 [0078]
• P. Deuflhard, Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms. Berlin: Springer, 2004 [0132]

Claims (28)

Method for determining the model parameters of an electrochemical energy store, in particular for electric or hybrid vehicles, whose dynamic behavior during operation is described by an electrical reference model (M), at least comprising a capacitance (C) and a first resistor (R ₁ , R ₂ ), the parameters (R ₁ , R ₂ , C) of the reference model (M) are linked and in the reference model (M) describing mathematical equations, wherein the parameter values of the parameters (R ₁ , R ₂ , C) together a parameter data set (P _I ) and adapted during operation of the energy storage device to its current state, characterized by the following steps: a. Use of an initial parameter data set (P _start ) as a reference parameter data record (P _ref ) for the reference model (M), b. Measuring the current flowing through the energy store (I _mess (t)) and the voltage applied thereto (U _mess (t)), c. Forming a plurality (N) of parameter data set variants (P _i , with i = 1 to N), d. Calculation of the overvoltage (U _model (I _mess (t), P _i )) resulting from the reference model (M) as a result of a flowing current (I (t)) at the energy store for each of the parameter data set variants (P _i ) using the current current reading (I _mess (t)) and e. Calculation of an initial voltage (U _{0, Pi} ) from the difference (U _{0, Pi} = U _mess (t) - U _model (I _mess (t), P _i )) of this overvoltage (U _model (I _mess (t), P _i )) and the measured voltage (U _mess (t)), wherein the voltage (U _{C, Pi} (t)) across the capacitance (C) for each parameter _{data set variant} (P _i ) equal to the voltage (U _{c, Pref} (t )) is set above the capacitance (C) resulting from the reference model (M) when using the reference parameter data set (P _ref ), f. again measuring the current flowing through the energy store (I _mess (t)) and the voltage applied thereto (U _mess (t)) and g. recalculation of the voltage (U _{c, Pi} (t)) resulting from the reference model (M) for each parameter data set variant (P _i ) over the capacitance (C) and the overvoltage (U _model (I _mess (t), P _i ) ) on the energy storage, h. Calculation of a deviation (ΔQ _Pi ) between the measured voltage (U _mess (t)) and the sum of overvoltage (U _model (I _mess (t), P _i )) and initial voltage (U _{0, Pi} ) for each of the parameter data set variants ( P _i ) by means of a function which delivers the greater values, the higher the difference between the measured voltage (U _mess (t)) and the sum of overvoltage (U _model (I _mess (t), P _i )) and initial voltage ( U _{0, Pi} ), and i. Repetition of steps f. until h. so often until at least one second condition is met, the newly calculated deviation (ΔQ _Pi ) being added to the previously calculated deviation (Q _{Pi_old} ) at each repetition of the steps, and j. Determining that parameter _{data set variant} (P _n , n ε [1 ... N]), which has the smallest deviation (Q _{Pi_new} = Q _{Pi_alt} + ΔQ _Pi ), this specific parameter _{data set variant} (P _n ) directly or indirectly as a new reference parameter data set (P _ref ) is defined. Method according to Claim 1, characterized in that the adaptation of the parameters (R ₁ , R ₂ , C) is carried out only during an evaluation interval which is initiated when at least one of the measured quantities (I _mess (t), U _mess ( t)) and / or at least one variable (i _C (t)) of the reference model (M) calculated therefrom satisfies a first condition. A method according to claim 2, characterized in that the calculation of the at least one variable variable (i _C (t)) before step c. using the reference parameter data set (P _ref ) and the measured quantities current (I _mess (t)) and voltage (U _mess (t)) takes place. Method according to claim 2 or 3, characterized in that the variable magnitude of the current flowing in the capacitance (C) is (i _C (t)) and the first condition is that this current (i _C (t)) is within a predetermined value Period in relation to the maximum current (i _max ) through the energy storage is small. Method according to one of the preceding claims, characterized in that in the reference model (M), the first resistor (R ₂ ) and the capacitor (C) are parallel to each other and a second resistor (R ₁ ) in series with the capacitance (C). Method according to one of the preceding claims, characterized in that the parameter value of the first resistor (R ₂ ) is converted into a current-dependent resistance value (R ₂ (I)), in particular into one of the current flowing through the energy store (I (t)) and that this current-dependent resistance value (R ₂ (I)) is used in the reference model (M). A method according to claim 6, characterized in that the conversion according to the equation

or according to the equation

with R ₂ : current-independent resistance R ₂ (I): current-dependent resistance a: selectable constant kI: current factor I: measured current I _mess (t) through the energy store I ₁ : reference current value. A method according to claim 7, characterized in that the current factor kI represents an additional parameter of the reference parameter data set (P _ref ), which is also varied in the formation of the plurality (N) of parameter data set variants (P _i ). A method according to claim 7 or 8, characterized in that the current factor (kI) for positive and negative currents (I (t)) is defined differently. A method according to claim 7 and 5, characterized in that also the parameter value of the second resistor (R ₁ ) is converted into a current-dependent resistance value (R ₁ (I)), in particular according to one of the equations in claim 7, and this current-dependent resistance value (R ₁ (I)) in the reference model (M). Method according to one of claims 5 to 10, characterized in that identical parameter values and / or identical Stromabhängigkeitsgleichungen for the first and the second resistor (R ₁ , R ₂ ) are used. Method according to one of the preceding claims, characterized in that the initial parameter data set (P _start ) contains metrologically determined or estimated and stored starting values for the parameters (R ₁ , R ₂ , C, kI) or the last, after the evaluation interval as a reference data set ( P _ref ) corresponds to the selected parameter _{data set variant} (P _n ). Method according to one of the preceding claims, characterized in that in order to form the parameter data set variants (P _i ) at least one of the parameters (R ₁ , R ₂ , C, kI) of the reference parameter data set (P _ref ) is varied one or more times and a corresponding one Parameter data set variant (P _i ) is formed, consisting of the variant of the varied parameter (R _{1, i} , R _2,1 , C _i , kI _i ) and the other parameters (R ₁ , R ₂ , C, kI) of the reference parameter data set P. _ref . Method according to one of the preceding claims, characterized in that to form the parameter data set variants (P _i ), each of the parameters (R ₁ , R, C, kI) of the reference parameter data set (P _ref ) is varied one or more times and for each variant one Parameters (R _{1, i} , R _2.1 , C _i , kI _i ) is formed in each case a parameter data set variant (P _i ), consisting of this variant of the varied parameter (R _{1, i} , R _{2, i} , C _i , kI _i ) as well as other varied parameters (R _{1, i} , R _{2, i} , C _i , k _i ). A method according to claim 13 or 14, characterized in that the parameter to be varied (R _{1, i} , R _{2, i} , C _i , k _i ) is varied two or more times. A method according to claim 15, characterized in that the parameter to be varied (R _{1, i} , R _{2, i} , C _i , kI ₁ ), starting from its parameter value (R ₁ , R ₂ , C, kI) in the reference parameter data set P _ref a value up and a value down, in particular by the same amount is varied down. Method according to one of Claims 13 to 16, characterized in that the number of variations of one of the parameters (R _{1, i} , R _{2, i} , C _i , k _i ) and / or the degree of variation is dependent on the results of previous calculations is set dynamically. Method according to one of the preceding claims 2 to 17, characterized in that the second condition is the check whether the duration (T _evaluation ) of the evaluation _interval has reached a predetermined maximum duration (T _max ). Method according to one of Claims 2 to 17, characterized in that the second condition is the check as to whether the duration (T _evaluation ) of the evaluation _interval has reached a predetermined minimum duration (T _min ) and simultaneously fulfills the first condition for initiating a new evaluation interval is. Method according to one of the preceding claims, characterized in that step j. is carried out only if the change in the current (I _mess (t)) by the energy store in the evaluation interval was greater than a predefined minimum value (ΔI _min ). Method according to one of the preceding claims, characterized in that step j. is performed only if the change in the voltage (U _mess (t)) of the energy storage in the evaluation interval was greater than a predefined minimum value (ΔU _min ). Method according to one of the preceding claims, characterized in that the measured current (I _mess (t)) of the energy storage is integrated during the Auswerteintervall and dependent on the change of the rest voltage (.DELTA.CVV) of the energy storage is determined and then in the determination of the deviation (ΔQ _Pi ) is added to the measured voltage U _mess (t). Method according to one of the preceding claims, characterized in that the specific parameter data set variant (P _n ) is indirectly defined by a low-pass filtering as a new reference parameter data set (P _ref ), wherein the old reference parameter data set (P _{ref, old} ) is multiplied by a weighting factor (k) and the particular parameter data set _variant (P _n ) is multiplied by the complement (1-k) to one of that weighting factor (k), and the sum of the thus weighted parameter data _sets (P _{ref, old} , P _n ) is defined as the new reference parameter data set P _{ref_neu} , Method according to one of the preceding claims, characterized in that the specific parameter data record variant (P _n ) is indirectly defined by a low-pass filtering as a new reference parameter data record (P _ref ), each parameter (R ₁ , R ₂ , C, kI) having its own weighting factor (P _n ). k _X ) and each parameter (R ₁ , R ₂ , C, kI) of the old reference parameter data set (P _{ref, old} ) is multiplied by its weighting factor (k _X ) and the parameters (R _{1, n} , R _{2, n} , C _n , k I _n ) of the determined parameter data set variant (P _n ) are multiplied by the complement (1-k _X ) to one of the respective weighting factor (k _X ), and the respective sums of the thus weighted parameters ([R ₁ , R _{1, n]} , [R ₂ , R _{2, n]} , [C, C _n ], [kI, kI _n ]) are defined as parameter values of the new reference parameter data set P _{ref_new} . Method according to one of the preceding claims, characterized in that the respectively newly calculated deviation (ΔQ _Pi ) multiplied by a weighting factor (G) and only then to the previously calculated deviation (Q _{Pi_alt} ) is added. A method according to claim 25, characterized in that the weighting factor (G) is implemented depending on the current, wherein it is higher in particular for larger currents (I (t)) and smaller for smaller currents (I (t)). Use of the method according to one of Claims 1 to 26 for the predicative determination of the maximum power of the energy store available for a predefined time. Battery management system for self-adapting, predicative determination of the available for a predefined time, maximum power of an electrochemical energy storage, in particular for electric or hybrid vehicles, comprising means for measuring the flowing through the energy storage Current (I _mess (t)) and the voltage applied thereto (U _mess (t)) and a microcontroller to which a program with instructions for carrying out the method according to one of claims 1 to 26 is loaded.

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