CN103970983A - Method And System For Battery Diagnosis - Google Patents

Abstract

The present invention relates to a kind of methods for battery diagnosis, the amount Δ EModell [t0 of theoretical energy balance is determined at the time point (t0, t1) for wherein limiting Diagnostic Time section at two according to the theoretical model of battery, t1], amount E ' Neg [the t0 of the energy extracted from battery is wherein determined in the Diagnostic Time section, t1] and supply battery energy amount E ' Pos [t0, t1], and it wherein determines efficiency factor ε, allows the assessment of accumulator status. ε is as equation for the efficiency factor Solution calculate, k1 and k2 is real number in formula. In addition, they are particularly arranged for carrying out the above method the present invention relates to battery diagnostic system, battery management system, vehicle and computer program.

Description

For the method and system of accumulator diagnosis

Technical field

The present invention relates to the method and system for accumulator diagnosis.

In addition, theme of the present invention is especially arranged for accumulator diagnostic system, battery management system, vehicle and the computer program of carrying out said method.

Background technology

In electric vehicle and motor vehicle driven by mixed power, use high efficiency accumulator for storage of electrical energy, these accumulators are called high pressure traction accumulator.Important feature when the operation of high pressure traction accumulator is their efficiency in the time of storage and output electric energy.It is the important qualitative character of accumulator in the high efficiency of whole life period.The life period of high pressure traction accumulator due to aging or damage efficiency can variation.The efficiency of accumulator is lower, and also just loss is larger for the energy in the time of storage and absorption and output energy.This works to the length of stroke of for example vehicle and effective toxic emission.Therefore, for the operation of electric vehicle and hybrid vehicle be in particular the efficiency of observing legal OBD standard and need to understand accumulator.

Known design for the efficiency calculation of traction accumulator only can realize limited OBD, because they are often taking zero energy equilibrium or zero SOC balance as prerequisite.And this can not ensure for example essential control rate in each driving cycle.

DE10 2,008 006 461A1 describe a kind of method of the load data for definite vehicle battery, wherein, obtain the operation variable of accumulator, state-of-charge, charging or discharge current and the temperature of for example accumulator.These operation variablees are supplied with to control module, these control module classed load data.By time integral electric current is carried out to calculated load integration, to obtain the basic load of accumulator.

DE10 2,009 027 594A1 describe a kind of deterioration for energy storage device and determine equipment, its have accumulator based on being preserved by vehicle with the historical assessment unit of assessing the degradation mode of accumulator; And there is the second assessment unit of determining degradation mode in the time charging on charging station according to the data of collecting.The degradation mode of energy storage device is determined as lower assessment or is determined from the mean value of weighting if necessary.

Summary of the invention

Specify in the method for the accumulator diagnosis for determining the efficiency factor ε that can evaluate battery condition according to the present invention, at the time point (t in two restriction Diagnostic Time intervals ₀, t ₁) locate to determine according to the theoretical model of accumulator the amount Δ E of theoretical energy equilibrium _modell[t ₀, t ₁], the interior amount E ' that determines the energy extracting from this accumulator during this external this Diagnostic Time _neg[t ₀, t ₁] and the amount E ' of energy that this accumulator is supplied with _pos[t ₀, t ₁], and efficiency factor ε is as equation

$k_1\·\mathrm{\ϵ}\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]+\frac{k_2}{\mathrm{\ϵ}}\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]={\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1]$

Solution calculate, k in formula ₁and k ₂it is real number.

Preferably k ₁and k ₂between 0.1 and 10, between 0.5 and 2, more particularly preferably k ₁and k ₂equal respectively 1.K ₁and k ₂value especially can differ from one another.K ₁and k ₂the optimal value for putting into practice object for example can determine according to cycle tests or simulation.K ₁and k ₂the important restriction of value produce as follows, efficiency factor ε should be between 0 and 1 under all actual conditions.For k ₁and k ₂equal respectively 1 situation, efficiency factor ε can be served as equation

$\mathrm{\ϵ}\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]+\frac{1}{\mathrm{\ϵ}}\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]={\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1]$

Solution calculate.

Particularly advantageously, can use function to determine the amount Δ E of theoretical energy equilibrium _modell[t ₀, t ₁], this function is provided by battery management system in practice.An example is for this reason so-called " energy predicting " function, and it comes into operation in applicant's battery management system.Call average current during state-of-charge and interval between diagnosis in the beginning of interval between diagnosis and while finishing " energy predicting " function as input quantity.Transmit also current capacity and the interior resistance of reference of very new accumulator as other input quantity to this function.Obtain the energy value as output variable, this energy value the beginning of interval between diagnosis is described in the case of also very new high efficiency accumulator and finish between the energy difference of above-mentioned model.

Preferably, for determining the amount Δ E of theoretical energy equilibrium _modell[t ₀, t ₁] first determine the first and second state-of-charge SOC (t of accumulator ₀), SOC (t ₁), and determine poor SOC (t by this first and second state-of-charge ₀)-SOC (t ₁).As the amount Δ E that can be used in theoretical energy equilibrium _modell[t ₀, t ₁] input quantity, respectively according to the battery model using, use the current capacity of for example current value, accumulator and can be generally also the complicated interior resistance of reference.The result of energy equilibrium is two energy differences between state-of-charge, and wherein, the transition between state-of-charge is for example because input current value occurs.So efficiency factor ε is as equation

$k_1\·\mathrm{\ϵ}\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]+\frac{k_2}{\mathrm{\ϵ}}\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]={\mathrm{\ΔE}}_{\mathrm{Modell}}[\mathrm{SOC}\left(t_0\right)-\mathrm{SOC}\left(t_1\right)]$

Solution calculate, Δ E here _modell[t ₀, t ₁] depend on the poor SOC (t of the first and second state-of-charges ₀)-SOC (t ₁).

E ' _pos[t ₀, t ₁] be the amount of the energy of effective supply, it also can be called the rechargeable energy of accumulator within the scope of the invention.This rechargeable energy can for example be supplied with at charging station, but at the energy obtaining by regeneration that also comprises in service that travels.E ' _neg[t ₀, t ₁] be the amount of the energy of actual output, it also can be called the discharge energy of accumulator within the scope of the invention.

For determining amount E ' actual output and energy effective supply _pos[t ₀, t ₁], E ' _neg[t ₀, t ₁], preferably take advantage of the temporal mean value of electric current and the product of integral voltage and electric current with the magnitude of voltage of accumulator.Produce actual output and energy effective supply as the result of the integration of the product of temporal electric current and voltage.

A special advantage of the present invention is, taking its simple and understandable efficiency Model as basis, this efficiency Model will illustrate below.With the accumulator of the efficiency work of shortcoming no longer can be in the energy of its storage the energy of the output number percent that also very new accumulator can reach.What for example also very new lithium-ion high tension battery can to system output, it comprises effectively is greater than 90% energy.On the contrary, the lithium-ion high tension battery of tape jam work only can provide be less than it energy 90% for system.In addition, in the accumulator of the efficiency work with shortcoming, in the time of batteries to store energy, also lose.The accumulator of this tape jam only can be stored certain the percentile energy that is less than than the energy of the accumulator supply to also very new.For example also very new lithium ion high tension battery can be stored and is greater than 90% of the energy supplied with to it.The lithium ion high tension battery of reverse band fail operation only can be stored 90% the energy of being less than of the energy supplied with to it.This failure condition is for example raise and is produced by the interior resistance of accumulator.

The balance equation of the principle of the assessment of efficiency factor based on observing below:

E _Pos[t ₀，t ₁]+E _Neg[t ₀，t ₁]＝ΔE _Modell[t ₀，t ₁]。

Supply with energy and and extract energy with form energy equilibrium.This balance equation is all time t ₀and t ₁be suitable for, but be only that the accumulator of inefficent loss is applicable.Determine if the amount Δ E of theoretical energy equilibrium _modell[t ₀, t ₁] and the poor SOC (t of consideration the first and second state-of-charges ₀)-SOC (t ₁), this balance equation is corresponding becomes

E _Pos[t ₀，t ₁]+E _Neg[t ₀，t ₁]＝ΔE _Modell[SOC(t ₀)-SOC(t ₁)]。

In the case of existing loss due to the efficiency of imperfectization, this efficiency represents with ε below and gets certain value between 0 to 1, in the immovable situation of SOC curve, draws

E′ _Neg[t ₀，t ₁]＝k ₁·ε·E _Neg[t ₀，t ₁]，

That is to say, the discharge energy of output in the time of identical SOC lifting height, diminish and corresponding to

${E^{\′}}_{\mathrm{Pos}}[t_0,t_1]=k_2\·\frac{1}{\mathrm{\ϵ}}{E}_{\mathrm{Pos}}[t_0,t_1],$

That is to say when to charge in batteries and must in accumulator, flow into more energy.Here E ' _neg[t ₀, t ₁] and E ' _pos[t ₀, t ₁] represent actual measurable energy.

Particularly advantageously, for calculating expeditiously the diagnosis of " independent of direction ground " definition of efficiency factor ε, that is to say as supply with to accumulator and by the ratio of the energy of accumulators store, its be with output and from the same ratio of the energy of accumulator extraction, k in this case ₁and k ₂equal respectively 1.The variation of efficiency is not considered self discharge in this case, but similarly treats discharge energy with rechargeable energy.

For meeting balance equation above, must set up

$\mathrm{\ϵ}\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]+\frac{1}{\mathrm{\ϵ}}\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]={\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1].$

The advantage of definition of efficiency factor ε is, it exists in quadratic equation, and it can calculate without approximation method by the method for algebraically.This quadratic equation has solution

${\mathrm{\ϵ}}_{\mathrm{1,2}}=\frac{{\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1]\±\sqrt{{{\mathrm{\ΔE}}_{\mathrm{Modell}}}^2[t_0,t_1]-4\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]}}{2\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]},$

Wherein, establish for simplicity k here and below ₁and k ₂all equal 1.Also can consider to be not equal to 1 factor k ₁and k ₂.Draw the only given border that is positioned at efficiency in two solutions by simulation.That is to say efficiency factor ε conduct here

$\mathrm{\ϵ}=\frac{{\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1]+\sqrt{{{\mathrm{\ΔE}}_{\mathrm{Modell}}}^2[t_0,t_1]-4\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]}}{2\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]}$

Draw.That is to say that efficiency factor ε is an amount between 0 and 1, it is corresponding to the efficiency between (and an also very new accumulator comparison) 0% and 100%.

In addition, the present invention, to be not unessential knowledge as basis, measures E ' under the actual conditions of all tests _pos[t ₀, t ₁] non-vanishing.There is not singular point in the equation for the counting yield factor in the end representing therefore in practice.Therefore battery management system can with time interval of rule check accumulator efficiency and completely can OBD (on board diagnosis).Therefore, the present invention has realized at the life period of high pressure traction accumulator in view of by aging or damage the monitoring of the efficiency of the high pressure traction accumulator of the change that causes efficiency.

At E ' _neg[t ₀, t ₁] be that zero situation produces another kind of border condition.Can be for example this situation at charging station place.Be insignificant formula for the simplified formula of the counting yield factor in this case

$\mathrm{\ϵ}=\frac{{\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1]}{{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]}.$

Generally do not carry out OBD at charging station, make this situation with actual uncorrelated.In the interval between diagnosis relevant to OBD at each, both accepted in practice the positive contribution of energy equilibrium also to accept the contribution of bearing, these are contributed in the time interval relevant to OBD at each and cause significant efficiency factor ε.

Can advantageously expand and improve by the measure illustrating in the dependent claims the method illustrating in independent claims.

Preferably in the case of determining that efficiency factor ε is lower than trigger action the numerical value of regulation.Relative efficiency factor ε and threshold value in this case, the size of this threshold value can require to arrange and can or determine by experiment in the mode of simulation according to legal OBD.The in the situation that of state deteriorating, can take measures the situation that situation occurs or EARLY RECOGNITION battery efficiency reduces of avoiding dangerous.This measure can for example be present in, with the mode of error code in the non-volatile region memory storage of data-carrier store wrong or for example in the mode of little control lamp to the warning of driver's output safety and/or activate the emergency function of vehicle, to avoid corresponding loss.Emergency function can for example comprise so-called limp-home mode, wherein implements the restriction to engine capacity or engine speed, or carries out the switching to pure internal combustion engine operation in the situation that of motor vehicle driven by mixed power.

Therefore, this method is preferably used in the traction accumulator system for vehicle, especially in lithium battery system, uses.This method can or be used in storage battery of electric motor, in motor vehicle driven by mixed power accumulator at large in battery system.

This method, preferably with the repetition interval of regulation, that is to say with the repetitive cycling of rule and carries out.The repetition interval of regulation can have for example length between one minute and one hour.

Preferably, diagnose so frequently, make to meet the legal OBD requirement for accumulator diagnosis.The legislation of the U.S. particularly CCR1968.2 and European legislation particularly exemplarily specifies for the detailed rules for the implementation 692 2008 of EU5/6, under which type of condition, in each driving cycle, increase denominator (" denominator ") and increase molecule under which type of condition, how its explanation, diagnose frequently.Here regulation, the interruption of generation does not allow lower than boundary value.Finally it can be translated as according to the requirement of diagnosis, and it is every operation in 10 minutes, to reach all the time 100% here.Therefore preferably specify, official hour interval has the length of approximately 10 minutes.

According to a kind of embodiment, Diagnostic Time interval was divided with the time interval of prescribed level, and determined the temporal mean value of electric current in each time interval of prescribed level.For determining the temporal mean value of electric current, electric current this time interval upper integral and with final integral result the length divided by the time interval.The time interval of prescribed level for example has the size between 1ms and 100ms, especially has the size of about 10ms.In the case of the interval of the 10ms in the cycle for 10 minutes, according to actual conditions test, draw in all cases E ' _pos[t ₀, t ₁] positive value.This point is, in fact can not occur in load long acceleration in lower 10 minutes or travel of accumulator, stores in battery system and do not have a small amount of energy to return.

Within each time interval, determine according to the symbol of the temporal mean value of electric current, accumulator is extracted energy or is supplied to energy within this time interval.Within the related time interval, determine amount E ' actual extracting and energy supply _neg[t ₀, t ₁], E ' _pos[t ₀, t ₁] time, be multiplied by the temporal mean value of electric current and the product of integral voltage and electric current with the magnitude of voltage of accumulator.Therefore can be apart from each other to the energy summation of extracting with supply with.

In addition according to the present invention proposes a kind of computer program, in the time that this computer program is carried out on programmable computer installation, carry out the method for explanation here according to this program.Described computer program for example can relate to accumulator diagnostic system for realizing vehicle or the module of battery management system or its subsystem.

This computer program can be stored on machine-readable storage medium, for example, on the permanent or rewritable storage medium that belongs to computer installation, or on dismountable CD-ROM, DVD or USB rod, stores.Additionally or alternatively, this computer program can for example be provided for downloading on computer installation on server or cloud system, for example, by the data network of for example the Internet or the communication connection of for example telephone wire or wireless connections.

According to another aspect, a kind of accumulator diagnostic system is provided, it has the amount Δ E for determine theoretical energy equilibrium according to the theoretical model of accumulator _modell[t ₀, t ₁] device, for determining the amount E ' of the energy that is extracted _neg[t ₀, t1] and the amount E ' of energy that supplies with _pos[t ₀, t ₁] device and for determining the device of efficiency factor ε that allows assessment battery condition, wherein efficiency factor ε is as equation

$k_1\·\mathrm{\ϵ}\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]+\frac{k_2}{\mathrm{\ϵ}}\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]={\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1]$

Solution calculate, k in formula ₁and k ₂it is real number.

According to another aspect, a kind of battery management system is provided, it comprises such accumulator diagnostic system and/or is set up the described method for accumulator diagnosis of carrying out.

According to another aspect of the present invention, provide a kind of automobile, it comprises such battery management system or described accumulator diagnostic system and/or is set up the described method for accumulator diagnosis of carrying out.

Brief description of the drawings

Fig. 1 shows a kind of system diagram of high pressure traction accumulator; And

Fig. 2 shows the schematic diagram of the functional part of accumulator diagnostic system.

Embodiment

Fig. 1 shows a kind of possible system outline of high tension battery.This accumulator comprises eight modules 1, and these eight modules have respectively 13 secondary battery units 2 for energy is provided.Module 1 is divided into two subelements 3, and these two subelements form battery pack 13 together.In addition; this accumulator generally includes main fuse 4, multiple current sensor 5, precharge unit 6, high-tension current bus 7, the optional alternating current charging device 9 of vehicle-mounted charging equipment 8, multiple protective device 10, multiple fuse 16 and multiple voltage sensor 15, for monitoring and protecting device 10 and fuse 16.Current sensor 5 is being implemented redundantly for the embodiment shown in object of the present invention and is being comprised point flow sensor and Hall element.

In addition, this high tension battery comprises accumulator control module 11, and multiple parts of accumulator diagnostic system and/or battery management system can be set in this battery control unit, and the plurality of parts are carried out method of the present invention.For example CAN bus of data bus is connected with this accumulator control module 11, by this bus for example can to battery management system or accumulator diagnostic system provide state-of-charge, battery current determine or the value of storage, current capacity, interior resistance or also to the fixed diagnostic value of other opertaing device transferring high voltage accumulator, for example, according to the amount E ' of the energy of supplying with to this accumulator of some embodiments _pos[t ₀, t ₁] and the amount E ' of the energy that extracts from this accumulator _neg[t ₀, t ₁].Reference numeral 12 is provided to this overall design drawing.

In addition, this high tension battery comprises voltage sensor 14, utilizes this voltage sensor to determine battery tension.Voltage sensor 14 provides the magnitude of voltage of measurement to accumulator control module 11.In addition, at least one current sensor 5 provides the current value of measurement to accumulator control module 11.By the measured value of electric current and voltage sensor 5,14, accumulator control module 11 or the unshowned control module arranging are in the back determined the amount E ' of the energy of supplying with to this accumulator especially _pos[t ₀, t ₁] and the amount E ' of the energy that extracts from this accumulator _neg[t ₀, t ₁].

Respectively according to shown in availability and the setting of voltage and current sensor 5,14, subelement 3, battery pack or secondary battery unit 2 of individual module 1 of accumulator, the subsystem arbitrarily that can be traction accumulator by above-mentioned method is determined efficiency factor.

Fig. 2 shows the schematic diagram of the functional part of accumulator diagnostic system.This accumulator diagnostic system comprises the amount Δ E for determine energy equilibrium according to the model of accumulator _modell[t ₀, t ₁] device 20, for determining the amount E ' of energy supplying with _pos[t ₀, t ₁] device 21, for determining the amount E ' of the energy that is extracted _neg[t ₀, t ₁] device 22 and for determining the device 23 of efficiency factor ε, this efficiency factor allows the assessment of battery condition.

For determining the amount Δ E of energy equilibrium _modell[t ₀, t ₁] device 20 from the device 24 for determining average current, from the device 25 for determining reference resistance, from the device 26 of the capacity for determining accumulator and from obtaining measured value and/or measurement data for the device 27 of state-of-charge of determining energy.For determining the amount Δ E of energy equilibrium _modell[t ₀, t ₁] device 20 can be for example known " energy predicting " model of applicant.

For determining the amount E ' of the energy of supplying with _pos[t ₀, t ₁] device 21 from obtaining measured value and/or measurement data for the device 28 of determining positive battery current and from obtaining measured value and/or measurement data for the device 29 of determining battery tension.For determining the amount E ' of the energy extracting _neg[t ₀, t ₁] device 22 from obtaining measured value and/or measurement data for the device 30 of determining negative battery current and similarly from obtaining magnitude of voltage for the device 29 of determining battery tension.

For the device 23 of determining efficiency factor ε from installing the 20 amount Δ E that obtain energy equilibrium _modell[t ₀, t ₁], from installing the 21 amount E ' that obtain the energy of supply _pos[t ₀, t ₁] and from installing the 22 amount E ' that obtain the energy of extraction _neg[t ₀, t ₁].Efficiency factor is as above-mentioned calculating.Device 23 output valve is current accumulator and efficiency factor ε compared with accumulator.

The embodiment that the invention is not restricted to illustrate here and the aspect of wherein emphasizing.On the contrary, a large amount of application in the scope of specifying by claim is possible, and they belong in professional's the scope of business.

Claims (10)

1. the method for diagnosing for accumulator, wherein, at the time point (t in two restriction Diagnostic Time intervals ₀, t ₁) locate to determine according to the theoretical model of described accumulator the amount Δ E of theoretical energy equilibrium _modell[t ₀, t ₁], wherein, in described Diagnostic Time interval, also determine the amount E ' of the energy extracting from described accumulator _neg[t ₀, t ₁] and supply with the amount E ' of energy of described accumulator _pos[t ₀, t ₁], and wherein, determine efficiency factor ε, described efficiency factor allows the assessment of battery condition,

It is characterized in that, described efficiency factor ε is as equation

$k_1\·\mathrm{\ϵ}\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]+\frac{k_2}{\mathrm{\ϵ}}\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]={\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1]$

Solution calculate, wherein k ₁and k ₂it is real number.

2. method according to claim 1, is characterized in that, described efficiency factor ε is by formula

$\mathrm{\ϵ}=\frac{{\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1]+\sqrt{{{\mathrm{\ΔE}}_{\mathrm{Modell}}}^2[t_0,t_1]-4\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]}}{2\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]}$

Calculate.

3. according to the method described in any one in the claims, it is characterized in that, at definite described efficiency factor ε trigger action in the case of within limited value.

4. according to the method described in any one in the claims, it is characterized in that, carry out described method with the repetition interval being limited.

5. according to the method described in any one in the claims, it is characterized in that, described Diagnostic Time interval is split into the time interval of prescribed level and within the described time interval of each prescribed level, determines the temporal mean value of battery current.

6. method according to claim 5, is characterized in that, the time interval of prescribed level has the size between 1ms and 100ms, has especially the size of about 10ms.

7. according to the method described in claim 5 or 6, it is characterized in that, determine within each described time interval according to the symbol of the described temporal mean value of electric current, be to extract energy or it is supplied with to energy from described accumulator within the described time interval.

8. a computer program, it for carrying out according to the method described in claim 1 to 7 any one in the time that described computer program is carried out on programmable computer installation.

9. an accumulator diagnostic system, it has the amount Δ E for determine theoretical energy equilibrium according to the theoretical model of accumulator _modell[t ₀, t ₁] device (20), for determining the amount E ' of the energy that is extracted _neg[t ₀, t ₁] and the amount E ' of energy that supplies with _pos[t ₀, t ₁] device (21,22) and for determining the device (23) of efficiency factor ε, described efficiency factor allows the assessment of battery condition, wherein, described efficiency factor ε is as equation

$k_1\·\mathrm{\ϵ}\·{E^{\′}}_{\mathrm{Pos}}[t_0,t_1]+\frac{k_2}{\mathrm{\ϵ}}\·{E^{\′}}_{\mathrm{Neg}}[t_0,t_1]={\mathrm{\ΔE}}_{\mathrm{Modell}}[t_0,t_1]$

Solution calculate, k in formula ₁and k ₂it is real number.

10. a vehicle, has accumulator diagnostic system according to claim 9 or has the battery management system that comprises accumulator diagnostic system according to claim 9.