DE102009050273B4 - Method for determining the capacity of a battery - Google Patents

Abstract

A method for determining the capacity of a battery, wherein the battery is subjected to load phases, in particular during starting processes of a vehicle, is characterized for the simplest possible achievement of an automatic determination of the capacity of an unknown battery, characterized in that from several of the load phases battery parameters (a, b, a, b) of the battery are determined that from the battery parameters (a, b, a, b) for characteristics (F, T) of a plurality of reference batteries in each case a deviation measure (ε, ε, ε, ε, ε) is calculated, the reference batteries have different but known capacities, and that based on an analysis of the deviation measures (ε, ε, ε, ε, ε), the capacity of the battery is estimated.

Description

The invention relates to a method for determining the capacity of a battery, wherein the battery is subjected to load phases, in particular during starting processes of a vehicle.

Previous battery monitoring systems and power management software in on-board electrical systems assume that the battery size, i. the capacity of the battery is known. Traditionally, the battery characteristics are communicated to the monitoring system by input. This manual entry means a lot of effort and high costs. In addition, there is a risk that the monitoring system will operate with incorrect parameters when changing the battery and entering changed battery characteristics.

In the CA 233 4404 A For example, there is disclosed a method and apparatus for determining an unknown capacity of a battery. For this purpose, the battery is supplied with a voltage or current signal having a specific frequency and the current or voltage response determined therefor. From this, parameters of a battery impedance model are determined, which in turn are used to calculate the capacity. The disadvantage here is that frequency considerations are necessary and that the battery must be acted upon by a signal active.

The DE 102 28 351 A1 discloses a method and apparatus in which the aging condition is determined via the bilayer capacitance. For this purpose, a coil is connected in parallel to the battery and determines the resonant frequency of the resonant circuit thus formed. The changing with increasing aging of the battery double-layer capacity affects the resonant frequency. The disadvantage here is that an additional component is needed. Furthermore, the operating conditions dependent inductance of the additional coil must be known exactly at each evaluation.

In January 1975, the article "Double-Layer Capacity Determination of Porous Electrodes" was published in the magazine "Electrochemical Science and Technology", which explains the determination of the bilayer capacity by means of non-stationary charge. However, the method presented there depends on the operating phase of the battery.

Furthermore, from the WO 2007/059725 A1 a method for estimating the capacity of a battery known. The capacity is estimated based on battery voltage, battery current and temperature by iterative approximation. A corresponding method is in the WO 2008/104721 A2 disclosed. The DE 10 2004 004 280 A1 shows a method for diagnosing batteries. A method for determining the amount of charge removable is described in US Pat DE 102 36 958 B4 demonstrated.

The present invention is therefore based on the object to provide an automatic determination of the battery size in the vehicle available, the above-mentioned disadvantages should be avoided.

According to the invention the above object is solved by the features of claim 1. Thereafter, the method in question is characterized in that from several of the loading phases battery parameters of the battery are determined that from the battery parameters for characteristics of several reference batteries each a deviation measure is calculated, the reference batteries have different but known capacities, and that based on a Analysis of deviation measures the capacity of the battery is estimated.

This is achieved in that characteristics of a load phase of the battery (battery current and battery voltage), in particular during a start of a motor vehicle, are evaluated in a special form and compared with a value scale of parameters from a reference battery. The evaluation of the loading phase assumes that the current-voltage behavior of the battery immediately at the beginning of the loading phase is determined exclusively by the battery and in particular its double-layer capacity, ie its true surface. Because of the fixed for the respective battery constructions of battery capacity (battery size) and true surface, so can determine the evaluation of the load phase, the battery size. 1 illustrates the process.

Hereinafter, instead of the general term of the loading phase - without limitation to this application - the terms start or start phase of a motor vehicle are used. However, it should be expressly understood that also loads of the battery can be used with high currents by other consumers. However, starting a motor vehicle represents a particularly preferred loading phase. Accordingly, the invention will be described below based on the application in a vehicle. It should also be pointed out that the method steps described below do not necessarily have to be performed. Rather, it will be apparent to those skilled in the art which steps may be omitted or substituted for other equivalent steps.

Description of a preferred embodiment:

• • Spannungseinbruch beim Start,
• • Maximalstromwert beim Start und
• • Startstromverlauf in den ersten 100ms.

The method determines the battery size on the basis of empirical parameters, which are calculated by means of obtained measurement data in the vehicle. The determination of the battery size refers to an average nominal capacity (Q _nominal ). From laboratory measurements it is known how much the actual capacity (with fully charged battery) deviates from the average rated capacity. The battery size is determined by evaluating the following characteristics of the start:

• • Voltage drop at start,
• • Maximum current value at start and
• • Starting current in the first 100ms.

• Temperatur, Fahrzeug, Ladezustand, Betriebsphasen der Batterie im Fahrzeug (Ruhe, Laden, Entladen) und Batterietechnologie.

The determination process is independent of the parameters:

• Temperature, vehicle, state of charge, operating phases of the battery in the vehicle (rest, charge, discharge) and battery technology.

From the parameters observed from each start a time constant τ is calculated. From this one calculates for each start the starting parameters of the battery. From a start sequence of several (for example 10) starts, the cumulative integration between the start parameters determines the battery parameters, which depend only on the battery size.

The connection between the battery parameters takes place by means of the cumulative integration, which establishes a relationship between the battery parameters by means of polynomial order 2 and 3 generated. The polynomials form the parameter equations dependent on battery sizes.

The identification of the battery size is performed by deriving these parameter equations. The derivative results in a deviation for each of the battery size dependent parameter equations. If the deviation is smallest, it indicates a battery size. By means of a deviation analysis of all battery size-dependent parameter equations, the battery size determination takes place.

• 1 ein Blockdiagramm mit einem Ablauf eines erfindungsgemäßen Verfahrens zur Bestimmung von Batteriegrößen,
• 2 ein Diagramm, das einen Zusammenhang zwischen F_Bat und T_Bat für verschiedene Batteriegrößen wiedergibt,
• 3 ein Diagramm mit einem typischen Spannungsverlauf bei einem Startvorgang eines Fahrzeugs,
• 4 ein Diagramm mit einem entsprechenden Stromverlauf bei dem Startvorgang nach 3,
• 5 ein Diagramm mit der Kondensatorkapazität C_st der Batterie in Abhängigkeit des Spannungseinbruchs U_E bei einem Startvorgang,
• 6 ein Diagramm zur Verdeutlichung der kumulativen Integration,
• 7 ein Diagramm zur Verdeutlichung des Zusammenhangs zwischen der Kondensatorkapazität C_st und des Spannungseinbruchs U_E,
• 8 ein Diagramm zur Darstellung der Integrationsbeziehung zwischen a_c und b_c für verschiedene Batteriegrößen,
• 9 ein Blockdiagramm mit einem Ablauf zur Ermittlung von Batterieparametern und
• 10 ein weiteres Blockdiagramm mit einem Ablauf zur Ermittlung der Batteriegröße.

These and other preferred embodiments of the invention are described in more detail in the dependent claims and in the following explanation of a preferred embodiment of the invention with reference to the drawing. In conjunction with the explanation of the preferred embodiment of the invention with reference to the drawing, generally preferred embodiments and developments of the teaching are explained. In the drawing show

• 1 a block diagram with a sequence of a method according to the invention for determining battery sizes,
• 2 a diagram showing a relationship between F _Bat and T _Bat for different battery sizes,
• 3 a diagram with a typical voltage curve during a starting process of a vehicle,
• 4 a diagram with a corresponding current course after the startup 3 .
• 5 a diagram with the capacitor capacitance C _{st of} the battery as a function of the voltage drop U _E during a starting process,
• 6 a diagram to illustrate the cumulative integration,
• 7 a diagram illustrating the relationship between the capacitor capacitance C _st and the voltage drop U _E ,
• 8th 3 is a diagram showing the integration relationship between a _c and b _c for different battery sizes,
• 9 a block diagram with a procedure for the determination of battery parameters and
• 10 another block diagram with a procedure for determining the size of the battery.

• • U_E: Spannungseinbruch bei I_max als U_st - U_filter
• • C_st: Kondensatorkapazität der Batterie bei einem Start.
• • P_st Leistungsabgabe der Batterie am Anfang des Starts.
• • Q_l: abgegebene Ladungsmenge über die ersten 100ms [Q(l(0-100ms))].

In a first step and for determining the empirical electrical parameters, the relevant battery parameters are determined for a plurality of reference batteries of known capacity. For this purpose, the reference batteries are successively subjected to load phases, in particular during starting processes of a vehicle, and battery current and battery voltage are measured during the charging phase. The measured data obtained leads to the following starting parameters after each start (s. 3 and calculation B2):

• • U _E : Voltage dip at I _max as U _st - U _filter
• • C _st : Capacitor capacity of the battery at startup.
• • P _st power output of the battery at the beginning of the start.
• • Q _l : amount of charge delivered over the first 100ms [Q (l (0-100ms))].

U _st is the voltage immediately after the start of the boot process, U _filter is the low-pass filtered voltage on the battery before starting.

berechnet man die Zeitkonstante (τ) wie folgend: $$\tau ={\left|\frac{I\text{/}dl}{1000}\right|}_{avg}$$

Mittels τ und der Startparameter U_E, C_st, P_st und Q_l werden anhand der kumulativen Integration über mehrere Startvorgänge die Batterieparameter wie folgend berechnet (s. 6 und 7): $${\displaystyle \int C_{st}}\cdot \Delta U_E=a_c\cdot U_E+b_c$$

$${\displaystyle \int Q_l\cdot \Delta P_{st}=a_q\cdot P_{st}}+b_q$$

Depending on the starting current curve and on the basis that the instantaneous mean value of the starting current in the first 100 ms corresponds to a course 4 assumes (see calculation B1): $$I\left(t\right)=a\cdot e^{-t\text{/}\tau }$$

calculate the time constant (τ) as follows: $$\tau ={\left|\frac{I\text{/}\mathrm{<figure-callout\; id="1000"\; label="d\; l"\; filenames="DE102009050273B4\_0026.png"\; state="\{\{state\}\}">d\; </figure-callout>}l}{1000}\right|}_{avG}$$

By means of τ and the start parameters U _E , C _st , P _st and Q _l , the battery parameters are calculated as follows, based on the cumulative integration over several starting processes (see FIG. 6 and 7 ): $${\displaystyle \int C_{st}}\cdot \Delta U_e=a_c\cdot U_e+b_c$$

$${\displaystyle \int Q_l\cdot \Delta P_{st}=a_q\cdot P_{st}}+b_q$$

$${\displaystyle \int a_q\cdot a_c=P_{1cq}\cdot a_c^2+P_{2cq}\cdot a_c+P_{3cq}}$$

$${\displaystyle \int a_q\cdot b_c=P_{1qq}\cdot b_c^2+P_{2qq}\cdot b_c+P_{3qq}}$$

$${\displaystyle \int b_q\cdot a_q=P_{1q}\cdot a_q^3+P_{2q}\cdot a_q^2+P_{3q}\cdot a_q+P_{4q}}$$

$${\displaystyle \int b_q\cdot b_c=P_{1qp}\cdot b_c^3+P_{2qp}\cdot b_c^2+P_{3qp}\cdot b_c+P_{4qp}}$$

Where the parameters a _c , b _c , a _q , b _{q are} the battery parameters that characterize the battery size. These battery parameters are linked together as follows (s. 8th ): $${\displaystyle \int b_c\cdot a_c=P_{1c}\cdot a_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="DE102009050273B4\_0026.png,DE102009050273B4\_0029.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+P_{2c}\cdot a_c+P_{3c}}$$

$${\displaystyle \int a_q\cdot a_c=P_{1cq}\cdot a_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="DE102009050273B4\_0026.png,DE102009050273B4\_0029.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+P_{2cq}\cdot a_c+P_{3cq}}$$

$${\displaystyle \int a_q\cdot b_c=P_{1qq}\cdot {\mathrm{<figure-callout\; id="2"\; label="b\; c"\; filenames="DE102009050273B4\_0026.png,DE102009050273B4\_0029.png"\; state="\{\{state\}\}">b\; </figure-callout>}}_c^{}+P_{2qq}\cdot b_c+P_{3qq}}$$

$${\displaystyle \int b_q\cdot a_q=P_{1q}\cdot a_{\mathrm{<figure-callout\; id="3"\; label="q"\; filenames="DE102009050273B4\_0029.png,DE102009050273B4\_0032.png"\; state="\{\{state\}\}">q</figure-callout>}}^3+P_{2q}\cdot a_{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="DE102009050273B4\_0026.png,DE102009050273B4\_0029.png"\; state="\{\{state\}\}">q</figure-callout>}}^2+P_{3q}\cdot a_q+P_{4q}}$$

$${\displaystyle \int b_q\cdot b_c=P_{1qp}\cdot {\mathrm{<figure-callout\; id="3"\; label="b\; c"\; filenames="DE102009050273B4\_0029.png,DE102009050273B4\_0032.png"\; state="\{\{state\}\}">b\; </figure-callout>}}_c^{}+P_{2qp}\cdot {\mathrm{<figure-callout\; id="2"\; label="b\; c"\; filenames="DE102009050273B4\_0026.png,DE102009050273B4\_0029.png"\; state="\{\{state\}\}">b\; </figure-callout>}}_c^{}+P_{3qp}\cdot b_c+P_{4qp}}$$

The P-factors in equations (5 to 9) depend only on the battery size and are generally factors of the above second and third degree equations. Integration is again a cumulative integration. These equations form the link between the battery parameters and are referred to as battery parameter dependent parameter equations.

The block diagram after 9 shows by way of example the steps for determining the battery parameters.

In a next step, factors are determined which representatively represent the battery capacity. First of all, the battery parameters a _c and b _c with the parameter equation are considered 5 , By deriving the parameter equation 5, one obtains: $$F_{Bat}=P_{Ba\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="DE102009050273B4\_0026.png,DE102009050273B4\_0029.png"\; state="\{\{state\}\}">t</figure-callout>}2}\cdot a_c+P_{Ba\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="DE102009050273B4\_0029.png,DE102009050273B4\_0032.png"\; state="\{\{state\}\}">t</figure-callout>}3}$$

By examining the relationship between a _c , b _c and F _Bat , the determined factor T _{Bat is} as follows: $$T_{Bat}=P_{Ba\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102009050273B4\_0026.png"\; state="\{\{state\}\}">t</figure-callout>}1}\cdot a_c+b_c$$

Where: P _Bat2 = 2P _1c , P _Bat3 = P _2c and P _Bat1 determined.

It follows: $$T_{Bat}=P_{Ba\mathrm{<figure-callout\; id="4"\; label="t"\; filenames="DE102009050273B4\_0030.png,DE102009050273B4\_0032.png"\; state="\{\{state\}\}">t</figure-callout>}4}\cdot F_{Bat}+P_{Ba\mathrm{<figure-callout\; id="5"\; label="t"\; filenames="DE102009050273B4\_0032.png"\; state="\{\{state\}\}">t</figure-callout>}5}$$

The connections are in 2 for some reference batteries with different capacities. From these equations, the factors P _Bat1 , P _Bat2 , P _Bat3 , P _Bat4, and P _Bat5 , which are representative of a battery _size , result. These factors are calculated for each of the reference batteries studied and stored together with the respective capacity of the reference battery in a database, for example in the form of a table, in a non-volatile memory. This results in a database with empirical electrical parameters of batteries.

To determine the capacity of an unknown battery, the steps are performed in a similar manner. First, a series of starts, for example, 10 starts, are performed, and from these, using the equations (1) to (4), the battery parameters a _c , b _c , a _q, and b _{q are determined} for the unknown battery. Thereafter, it is assumed that the unknown battery has the capacity of one of the reference batteries from the database. Using the factors P _Bat1 , P _Bat2 , P _Bat3 , P _Bat4 and P _Bat5 stored in the database, the factors F _Bat and T _{Bat are} calculated by means of equations (10) and (12). From this, a factor b _{c (comparison) is} calculated by means of equation (11), which in turn is used to calculate a deviation measure ε _c . These steps are repeated for several of the reference batteries stored in the database. All useful reference batteries or even all the reference batteries in the database can be used for the calculations. One of the thus calculated deviation measures ε _c will assume a minimum amount. This smallest ε _c leads to a battery size A _{c of} the reference battery whose P _Bat factors for the Calculation of this smallest ε _{c has been} assumed.

• • Von einer Startfolge einer unbekannten Batterie: a_c und b_c berechnen.
• • Mittels Gleichung 10: F_Bat berechnen.
• • Mittels Gleichung 12: T_Bat, berechnen.
• • Mittels Gleichung 11: b_c(vergleich) = T_Bat - P_Bat1 · a_c
• • Die Abweichung berechnet sich nach $${\epsilon }_c=\frac{\left|b_{c\left(vergleich\right)}-b_c\right|}{b_c}$$
  
• • Ist ε_c am kleinsten, führt sie zu einer Batteriegröße A_c.

In summary, the calculation steps for a _c and b _c result:

• • From a starting sequence of an unknown battery: Calculate a _c and b _c .
• • Using Equation 10: F _Bat calculated.
• • Using equation 12: T _Bat , calculate.
• • By equation 11: b _{c (comparison)} = T _Bat - P _Bat1 · a _c
• • The deviation is calculated according to $${\epsilon }_c=\frac{\left|b_{c\left(verGleicH\right)}-b_c\right|}{b_c}$$
  
• • If ε _{c is} the smallest, it leads to a battery size A _c .

• • ε_q, mittels a_q und b_q, führt zu A_q
• • s_cq, mittels a_c und a_q, führt zu A_cq
• • ε_qp, mittels b_c und b_q, führt zu A_qp
• • ε_qq, mittels b_c und a_q führt zu A_qq
• • ε_m bildet den Mittelwert von allen ε, führt zu A_m
• • ε_SD, Standerdabweichung von allen ε, führt zu A_SD

These steps are repeated for the other possible combinations of the battery parameters a _c , b _c , a _q and b _q . For this purpose, equations 6 to 9 are derived analogously in succession to a first-order equation and a smallest deviation measure ε and the associated battery size A are determined for each equation in accordance with the abovementioned steps. This results in the deviation measures and possible battery sizes:

• • ε _q , by means of a _q and b _q , leads to A _q
• • s _cq , by means of a _c and a _q , leads to A _cq
• • ε _qp , using b _c and b _q , leads to A _qp
• • ε _qq , using b _c and a _q leads to A _qq
• • ε _m is the mean of all ε, leading to A _m
• • ε _SD, Standerdabweichung all ε, leads to A _SD

These values are evaluated by a deviation analysis according to stochastic methods and from this the battery size of the unknown battery is estimated. For this purpose, for example, the mean value over all battery _quantities A _c , A _q , A _cq , A _qp and A _{qq calculated in this way} can be used.

By evaluating the results of the various deviations, a flow chart is obtained which determines the battery size by means of deviation analysis.

2 shows the relationship between F _Bat and T _Bat calculated from the battery parameters a _c and b _c for different battery sizes.

The individual steps for battery size determination are in 10 shown.

Finally, it should be expressly pointed out that the above-described embodiment of the method according to the invention are only for the purpose of discussing the claimed teaching, but do not limit it to the exemplary embodiment.

B1: CALCULATION OF TIME CONSTANT τ

Assumption: The mean value of the starting current in the first 100ms can be described by the following formula: $$l\left(t\right)=a\cdot e^{-t\text{/}\tau }$$

$$\frac{d\left(\text{In}\left(l\right)\right)}{dl}=-\frac{1}{\tau }\cdot \frac{dt}{dl}=\frac{1}{l}$$

$$dt=1ms$$

$$\Rightarrow \tau ={\left|\frac{l\text{/}dl}{1000}\right|}_{avg}\text{sec}$$

To get the value of τ, you have to edit the current formula shown above like this: $$\text{In}\left(l\right)=\text{In}\left(a\right)-\frac{t}{\tau }$$

$$\frac{d\left(\text{In}\left(l\right)\right)}{dl}=-\frac{1}{\tau }\cdot \frac{dt}{dl}=\frac{1}{l}$$

$$dt=1ms$$

$$\Rightarrow \tau ={\left|\frac{l\text{/}\mathrm{<figure-callout\; id="1000"\; label="d\; l"\; filenames="DE102009050273B4\_0026.png"\; state="\{\{state\}\}">d\; </figure-callout>}l}{1000}\right|}_{avG}\text{sec}$$

B2: CALCULATION OF THE STARTER PARAMETERS:

$$\Rightarrow U_e=U_{st}-U_{filter}$$

$$R_{st}=\frac{U_e}{I_{\text{Max}}}$$

$$\Rightarrow C_{st}=\frac{\tau }{R_{st}}$$

$$\Rightarrow P_{st}=I_{\text{Max}}\cdot U_e=\frac{U_e^2}{R_{st}}$$

$$Q_u=C_{st}\cdot U_e$$

$$\Rightarrow Q_I={\displaystyle \underset{0}{\overset{100ma}{\int }}I\left(t\right)\cdot dt}$$

Claims (13)

Method for determining the capacity of a battery, wherein the battery is subjected to load phases, characterized in that battery parameters a _c , b _c , a _q , b _{q of} the battery are determined from a plurality of the load _phases , the battery parameters a _c , b _c , a _q , b _q abstractly characterize the capacity of the battery that the battery is compared with several reference batteries of different but known capacities such that for characteristics F _Bat , T _{Bat of} the plurality of reference batteries from the battery parameters a _c , b _c , a _q , b _q in each case a deviation _measure (ε _c , ε _q , ε _cq , ε _qp , ε _qq ) is calculated, the deviation _measure (ε _c , ε _q , ε _cq , ε _qp , ε _qq ) the deviation of the capacity of the battery from the reference battery and that based on a stochastic analysis of the deviation _measures (ε _c , ε _q , ε _cq , ε _qp , ε _qq ) the capacity of the battery is determined or estimated. Method according to Claim 1 , characterized in that are used as load phases starting operations of a vehicle. Method according to Claim 1 or 2 characterized in that the battery parameters a _c , b _c , a _q , b _q are calculated using parameter equations from a plurality of stress phases. Method according to one of Claims 1 to 3 , characterized in that for each load phase of the time course of current and voltage is evaluated and from this start parameters (U _E , C _st , P _st , Q _l ) are determined, which characterize the beginning of the loading phase. Method according to one of Claims 1 to 4 , characterized in that the time constant τ is determined from the current profile after the start of the start and this is used to calculate the capacitor capacitance C _{st of} the battery. Method according to Claim 4 or 5 , characterized in that for the calculation of the battery parameters a _c , b _c , a _q , b _q a cumulative integration between the start parameters is performed. Method according to one of Claims 3 to 6 , characterized in that the parameter equations are derived and one of the deviation measures is calculated therefrom. Method according to one of Claims 1 to 7 , characterized in that for the calculation of a deviation _measure (ε _c ε _q , ε _q , ε _qp , ε _qq ) the presence of one of the plurality of reference _{batteries is} assumed and that based on the assumed reference _battery, a deviation measure is calculated, wherein the calculation of a deviation measure for different said plurality of reference battery is repeated, and wherein the minimum of the calculated deviation extent as the minimum deviation (ε _{c, min,} ε _{q, min,} ε _{cq, min,} ε _{qp, min,} ε _{qq, min)} is selected and used for the analysis of differential measurements , Method according to Claim 8 , characterized in that for different combinations of two of the battery parameters a _c , b _c , a _q , b _q a minimum deviation _measure (ε _{c, min} , ε _{q, min} , ε _{cq, min} , ε _{qp, min} , ε _{qq, min} ) and that for each of the minimum deviation _measures the capacitance of the reference _battery (A _c , A _q , A _cq , A _qp , _Aqq ) is determined, which is used to calculate the respective minimum deviation _measure (ε _{c, min} , ε _{q, min} , ε _{cq, min} , ε _{qp, min} , ε _{qq, min} ). Method according to Claim 8 or 9 , characterized in that the minimum deviation _measures (ε _{c, min} , ε _{q, min} , ε _{cq, min} , ε _{qp, min} , ε _{qq, min} ) are subjected to a stochastic investigation and from this the capacity of the battery is estimated. Method according to Claim 10 , characterized in that the stochastic examination comprises forming the average of the minimum deviation _measures (ε _{c, min} , ε _{q, min} , ε _{cq, min} , ε _{qp, min} , ε _{qq, min} ) and that the capacity of the battery as Mean value (A _c , A _q , A _cq , A _qp , A _qq ) of the selected capacities of the reference _{batteries is} formed. Method according to one of Claims 1 to 11 , characterized in that in order to build up empirical data in a database, a plurality of reference batteries of known capacity are measured over a plurality of loading phases and evaluated using the parameter equations. Method according to Claim 12 , characterized in that for the measurement of the reference batteries at least ten load phases are evaluated.

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