CN109143092B

CN109143092B - Method and device for generating cell model and acquiring cell voltage and battery management system

Info

Publication number: CN109143092B
Application number: CN201710464261.2A
Authority: CN
Inventors: 张炳雁; 蒋治亿
Original assignee: Contemporary Amperex Technology Co Ltd
Current assignee: Contemporary Amperex Technology Co Ltd
Priority date: 2017-06-19
Filing date: 2017-06-19
Publication date: 2021-01-12
Anticipated expiration: 2037-06-19
Also published as: CN109143092A

Abstract

The embodiment of the invention provides a method and a device for generating a cell model and acquiring cell voltage and a battery management system. In the embodiment of the present invention, by obtaining an equivalent working circuit of a battery cell, the equivalent working circuit includes: concentration polarization circuit, then, according to equivalent working circuit, obtain the initial model of electric core operating voltage, include the constant coefficient of unknown numerical value in the initial model to, through the working data of gathering electric core, the working data includes: the method comprises the steps of working state, working time, working current and working voltage, therefore, based on an initial model, performing approximate fitting processing on working data to obtain the numerical value of each constant coefficient in the initial model, and further obtaining an acquisition model of the working voltage of the battery cell according to the numerical value of each constant coefficient and the initial model. Therefore, the technical scheme provided by the embodiment of the invention can improve the accuracy of obtaining the model of the working voltage of the battery cell to a certain extent and reduce the potential safety hazard.

Description

Method and device for generating cell model and acquiring cell voltage and battery management system

[ technical field ] A method for producing a semiconductor device

The invention relates to the technical field of batteries, in particular to a method and a device for generating a battery cell model and acquiring a battery cell voltage and a battery management system.

[ background of the invention ]

In a Battery Management System (BMS), a calculation and prediction model of a real-time operating voltage of a Battery cell is one of core blocks in the BMS, which is also called a core algorithm. In recent years, with the gradual popularization of the application range of the lithium ion battery cell, the application condition is more and more severe, the requirement on a core algorithm for acquiring the battery cell voltage by the BMS is higher and higher, and the safety early warning problem of the battery cell and the performance of the battery cell are important.

Currently, in the BMS, a core algorithm for obtaining the cell model is generally implemented based on an electrochemical model of a second-order RC circuit (Resistance-Capacitance Circuits). Specifically, the second-order RC circuit is a physical equivalent working circuit of the battery cell, and the voltage division caused by the concentration polarization phenomenon of the battery cell is calculated as a simple physical device such as a resistor or a capacitor, so as to obtain an acquisition model of the working voltage of the battery cell.

In the process of implementing the invention, the inventor finds that at least the following problems exist in the prior art:

the existing acquisition model of the working voltage of the battery cell is obtained according to a second-order RC circuit, and the battery cell is equivalent to the second-order RC circuit, and the second-order RC circuit only considers the partial voltage generated by concentration polarization as the partial voltage generated by a common physical device, so that the accuracy of the existing acquisition model of the working voltage of the battery cell is low, and certain potential safety hazards exist.

[ summary of the invention ]

In view of this, embodiments of the present invention provide a method, an apparatus, and a battery management system for generating a cell model and acquiring a cell voltage, so as to improve accuracy of an acquisition model of a cell working voltage and reduce potential safety hazards to a certain extent.

In a first aspect, an embodiment of the present invention provides a method for generating a cell model, including:

obtaining an equivalent working circuit of the battery cell, wherein the equivalent working circuit comprises: a concentration polarization circuit;

obtaining an initial model of the cell working voltage according to the equivalent working circuit, wherein the initial model comprises a constant coefficient of an unknown value;

acquiring working data of the battery core, wherein the working data comprises: working time, working current and working voltage;

performing approximate fitting processing on the working data based on the initial model to obtain numerical values of constant coefficients in the initial model;

and obtaining an obtaining model of the working voltage of the battery cell according to the numerical value of each constant coefficient and the initial model.

The above-mentioned aspect and any possible implementation further provide an implementation, where the equivalent operating circuit further includes: the circuit comprises an open-circuit voltage source, a first resistor, a capacitor and a second resistor;

the concentration polarization circuit includes: a concentration polarization element;

the open-circuit voltage source, the first resistor and the second resistor are connected in series with the concentration polarization element;

the capacitor is connected with the second resistor in parallel.

As to the aspect described above and any possible implementation manner, there is further provided an implementation manner that obtains an initial model of the cell operating voltage according to the equivalent operating circuit, including:

according to the equivalent working circuit, respectively obtaining the divided voltage of the first resistor, the divided voltage of the second resistor, the divided voltage of the concentration polarization element and the open-circuit voltage, wherein the open-circuit voltage is the voltage of the open-circuit voltage source, and the divided voltage of the first resistor, the divided voltage of the second resistor and the divided voltage of the concentration polarization element contain constant coefficients of unknown values;

and generating an initial model of the cell working voltage according to the open-circuit voltage, the divided voltage of the first resistor, the divided voltage of the second resistor and the divided voltage of the concentration polarization element.

As to the above-mentioned aspect and any possible implementation manner, there is further provided an implementation manner, when the operating state of the battery cell is a charging state, the initial model of the battery cell operating voltage is:

U_t＝U_oc+U₁+U₂-U₃

when the working state of the battery cell is a discharging state, the initial model of the battery cell working voltage is as follows:

U_t＝U_oc-U₁-U₂+U₃

wherein, U_tRepresents the cell operating voltage, U_ocRepresents the open circuit voltage, U, of the cell₁Representing the divided voltage of said first resistance, U₂Representing the voltage division, U, of said second resistance₃Representing the partial pressure of the concentration polarization member.

The above-described aspect and any possible implementation manner further provide an implementation manner, where obtaining the divided voltage of the concentration polarization element according to the equivalent operating circuit includes:

obtaining a partial pressure of the concentration polarization element by the following formula:

wherein, U₃Represents a partial pressure of the concentration polarization element, and oc represents a polarization coefficient, wherein oc is d1 × SOC^d2And τ represents a transition time, wherein,

b is the first coefficient, g1 × I^g2×e^g3×T，E_aIs a second coefficient representing diffusion activation energy, E_a＝f1×SOC^f2The SOC represents the residual capacity of the battery cell, T represents the working time of the battery cell, I represents the working current of the battery cell, T represents the working temperature, R is an ideal gas constant, F is a Faraday constant, n is the amount of a substance, and d1, d2, g1, g2, g3, F1 and F2 are constant coefficients.

The above aspect and any possible implementation manner further provide an implementation manner, where obtaining the divided voltage of the second resistor according to the equivalent operating circuit includes:

obtaining the voltage division of the second resistor by the following formula:

wherein, U₂Representing the partial voltage of the second resistor, I representing the working current of the battery cell, t representing the working time of the battery cell, R₂Is the resistance value of the second resistor, wherein R₂＝b1×SOC^b2×e^b3×TC is the capacitance of the capacitor, h1 × SOC^h2×e^h3×TB1, b2, b3, h1, h2 and h3 are constant coefficients, T represents the operating temperature, and SOC represents the residual capacity of the battery cell.

The above aspect and any possible implementation manner further provide an implementation manner, where obtaining the divided voltage of the first resistor according to the equivalent operating circuit includes:

obtaining the voltage division of the first resistor by the following formula:

U₁＝I×R₁

wherein, U₁Representing the partial voltage of the first resistor, I representing the working current of the battery cell, R₁Is the resistance value of the first resistor, wherein R₁＝a1×SOC^a2×e^a3×TA1, a2 and a3 are all constant coefficients, T represents the operating temperature, and SOC represents the remaining capacity of the battery cell.

The above aspect and any possible implementation manner further provide an implementation manner, where when the operating state of the battery cell is a charging state, the remaining capacity of the battery cell is obtained through the following formula:

when the working state of the battery cell is a charging state, acquiring the residual electric quantity of the battery cell by the following formula:

therein, SOC₀Represents the initial electric quantity of the battery cell, C₀For the rated capacity of the battery cell, I represents the working current of the battery cell, and t represents the working time of the battery cell.

As to the above-mentioned aspect and any possible implementation manner, there is further provided an implementation manner, where performing approximate fitting processing on the working data based on the initial model to obtain a numerical value of each constant coefficient in the initial model, including:

performing curve fitting on the working data based on the initial model to obtain a plurality of fitting voltage curves;

acquiring a real voltage curve of the battery cell according to the working time and the working voltage;

acquiring one fitting voltage curve with the highest approximation degree with the real voltage curve from the plurality of fitting voltage curves as a target curve;

and acquiring the numerical value of each constant coefficient in the target curve to serve as the numerical value of each constant coefficient in the initial model.

As to the above-mentioned aspect and any possible implementation manner, there is further provided an implementation manner that obtains an obtaining model of the cell operating voltage according to the value of each constant coefficient and the initial model, where the obtaining model includes:

and substituting the obtained numerical value of each constant coefficient into the initial model to obtain an obtaining model of the working voltage of the battery core.

One of the above technical solutions has the following beneficial effects:

in the embodiment of the invention, the cell working voltage is equivalent to the partial voltage of the first-order RC circuit and the partial voltage of the concentration polarization circuit by acquiring the equivalent working circuit of the cell, and based on the equivalent working circuit, the partial voltage of the concentration polarization in the cell working voltage can be determined according to the relation between the current density and the concentration polarization according to the acquisition model acquired by the equivalent working circuit, so that the more accurate partial voltage of the concentration polarization is obtained, the accuracy of acquiring the cell working voltage according to the acquisition model is also improved, and the potential safety hazard problem caused by larger error of the working voltage is reduced. Therefore, the technical scheme provided by the embodiment of the invention can improve the accuracy of the model for obtaining the working voltage of the battery cell to a certain extent and reduce the potential safety hazard.

In a second aspect, an embodiment of the present invention provides a cell voltage obtaining method, including:

collecting working data of the battery core, wherein the working data comprises: operating current and operating time;

acquiring the cell working voltage by using an acquisition model of the cell working voltage based on the working data; the battery cell working voltage obtaining model is obtained by using any one of the above realization modes and the battery cell model generating method.

One of the above technical solutions has the following beneficial effects:

in the embodiment of the invention, the working voltage of the battery cell can be acquired according to the acquisition model of the working voltage of the battery cell only by acquiring the working time and the working current of the battery cell in the working process, the implementation mode is simple, and the acquisition efficiency is high.

In a third aspect, an embodiment of the present invention provides an electrical core model generating apparatus, including:

the first acquisition unit is used for acquiring an equivalent working circuit of the battery cell, and the equivalent working circuit comprises: a concentration polarization circuit;

the second obtaining unit is used for obtaining an initial model of the cell working voltage according to the equivalent working circuit, wherein the initial model comprises a constant coefficient of an unknown value;

the collection unit is used for collecting the working data of the battery core, and the working data comprises: working time, working current and working voltage;

the processing unit is used for carrying out approximation fitting processing on the working data based on the initial model to obtain the numerical value of each constant coefficient in the initial model;

and the third obtaining unit is used for obtaining an obtaining model of the cell working voltage according to the numerical value of each constant coefficient and the initial model.

the capacitor is connected with the second resistor in parallel.

The above-described aspect and any possible implementation manner further provide an implementation manner, where the second obtaining unit is configured to:

U_t＝U_oc+U₁+U₂-U₃

U_t＝U_oc-U₁-U₂+U₃

As for the above-mentioned aspect and any possible implementation manner, an implementation manner is further provided, where the second obtaining unit is specifically configured to:

obtaining the voltage division of the second resistor by the following formula:

obtaining the voltage division of the first resistor by the following formula:

U₁＝I×R₁

As for the above-mentioned aspect and any possible implementation manner, an implementation manner is further provided, where the second obtaining unit is further specifically configured to:

The above-described aspect and any possible implementation further provide an implementation, where the processing unit is specifically configured to:

As for the above-mentioned aspect and any possible implementation manner, an implementation manner is further provided, where the third obtaining unit is specifically configured to:

One of the above technical solutions has the following beneficial effects:

In a fourth aspect, an embodiment of the present invention provides a cell voltage obtaining apparatus, including:

the acquisition unit is used for acquiring the working data of the battery core, and the working data comprises: operating current and operating time;

the acquisition unit is used for acquiring the cell working voltage by utilizing an acquisition model of the cell working voltage based on the working data; the battery cell working voltage obtaining model is obtained by using any one of the above realization modes and the battery cell model generating method.

One of the above technical solutions has the following beneficial effects:

In a fifth aspect, an embodiment of the present invention provides a battery management system, including:

the cell model generation apparatus according to any of the above implementation manners; and

the cell voltage acquisition device is described above.

One of the above technical solutions has the following beneficial effects:

in the embodiment of the invention, the cell working voltage is equivalent to the partial voltage of the first-order RC circuit and the partial voltage of the concentration polarization circuit by acquiring the equivalent working circuit of the cell, and based on the equivalent working circuit, the partial voltage of the concentration polarization in the cell working voltage can be determined according to the relation between the current density and the concentration polarization according to the acquisition model acquired by the equivalent working circuit, so that the more accurate partial voltage of the concentration polarization is obtained, the accuracy of acquiring the cell working voltage according to the acquisition model is also improved, and the potential safety hazard problem caused by larger error of the working voltage is reduced. In addition, in the embodiment of the invention, the working voltage of the battery cell can be acquired according to the acquisition model of the working voltage of the battery cell only by acquiring the working time and the working current of the battery cell in the working process, the implementation mode is simple, and the acquisition efficiency is higher. Therefore, the technical scheme provided by the embodiment of the invention can improve the accuracy of the model for obtaining the working voltage of the battery cell to a certain extent and reduce the potential safety hazard.

[ description of the drawings ]

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

Fig. 1 is a schematic flow chart of a cell model generation method according to an embodiment of the present invention;

fig. 2 is a schematic structural diagram of an equivalent operating circuit of a battery cell in an embodiment of the present invention;

FIG. 3 is a graph illustrating a relationship between a remaining capacity and an open circuit voltage according to an embodiment of the present invention;

fig. 4 is a schematic diagram of a target curve and a real voltage curve of a 20Ah hard shell cell in a charging state at a 20A operating current (1C rate) in an embodiment of the present invention;

fig. 5 is a schematic diagram of a target curve and a real voltage curve of a 20Ah hard shell battery cell in a charging state at a 100A operating current (5C rate) in an embodiment of the present invention;

fig. 6 is a schematic diagram of a target curve and a real voltage curve of a 20Ah hard shell cell in a discharge state at a 20A operating current (1C rate) in an embodiment of the present invention;

fig. 7 is a schematic diagram of a target curve and a real voltage curve of a 20Ah hard shell battery cell in a discharge state at a working current (5C rate) of 100A in an embodiment of the present invention;

fig. 8 is a schematic diagram of the working data of the 12Ah PHEV cell collected in the embodiment of the present invention;

fig. 9 is a schematic diagram of a relationship curve between the remaining capacity and the open-circuit voltage of a 12Ah PHEV cell in the embodiment of the present invention;

fig. 10 is a schematic diagram of a target curve and a real voltage curve of a 12Ah PHEV cell in an embodiment of the present invention;

fig. 11 is a schematic flow chart of a cell voltage obtaining method according to an embodiment of the present invention;

fig. 12 is a functional block diagram of a cell model generation apparatus according to an embodiment of the present invention;

fig. 13 is a functional block diagram of a cell voltage acquisition apparatus according to an embodiment of the present invention;

fig. 14 is a functional block diagram of a battery management system according to an embodiment of the present invention.

[ detailed description ] embodiments

For better understanding of the technical solutions of the present invention, the following detailed descriptions of the embodiments of the present invention are provided with reference to the accompanying drawings.

It should be understood that the described embodiments are only some embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The terminology used in the embodiments of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the examples of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

It should be understood that the term "and/or" as used herein is merely one type of association that describes an associated object, meaning that three relationships may exist, e.g., a and/or B may mean: a exists alone, A and B exist simultaneously, and B exists alone. In addition, the character "/" herein generally indicates that the former and latter related objects are in an "or" relationship.

It should be understood that although the terms first, second, third, etc. may be used to describe the resistors in the embodiments of the present invention, the resistors should not be limited to these terms. These terms are only used to distinguish one resistor from another. For example, a first resistance may also be referred to as a second resistance, and similarly, a second resistance may also be referred to as a first resistance, without departing from the scope of embodiments of the present invention.

The word "if" as used herein may be interpreted as "at … …" or "when … …" or "in response to a determination" or "in response to a detection", depending on the context. Similarly, the phrases "if determined" or "if detected (a stated condition or event)" may be interpreted as "when determined" or "in response to a determination" or "when detected (a stated condition or event)" or "in response to a detection (a stated condition or event)", depending on the context.

Aiming at the problems that the accuracy of the existing acquisition model of the cell working voltage is lower and potential safety hazards exist, the embodiment of the invention provides the following solution ideas: the cell is equivalent to an equivalent working circuit comprising a concentration polarization circuit, the cell working voltage is obtained by obtaining the partial voltage of each part assembly in the equivalent working circuit, and the accuracy of the obtaining model of the cell working voltage can be improved and the potential safety hazard caused by the reduction of the accuracy can be reduced by accurately calculating the partial voltage occupied by the concentration polarization circuit.

Under the guidance of this idea, the present embodiment provides the following feasible embodiments.

Example one

The embodiment of the invention provides a cell model generation method. In a specific implementation, the method may be applied in a BMS.

Specifically, please refer to fig. 1, which is a schematic flow chart of a method for generating a cell model according to an embodiment of the present invention, and as shown in fig. 1, the method includes the following steps:

and S101, obtaining an equivalent working circuit of the battery cell.

It should be noted that, in the embodiment of the present invention, the equivalent operating circuit includes: concentration polarization circuit.

Referring to fig. 2, a schematic structural diagram of an equivalent operating circuit of a battery cell in an embodiment of the present invention is shown in fig. 2, where the equivalent operating circuit may include, but is not limited to: concentration polarization circuit 22. Specifically, as shown in fig. 2, the equivalent operating circuit further includes: an open circuit voltage source 201, a first resistor 202, a capacitor 203 and a second resistor 204; concentration polarization circuit 22 includes: concentration polarization element 205. As shown in fig. 2, the connection relationship between the devices in the equivalent operating circuit is: an open-circuit voltage source 201, a first resistor 202, and a second resistor 204 are connected in series with a concentration polarization element 205, and a capacitor 203 is connected in parallel with the second resistor 204.

It is understood that, as shown in fig. 2, the capacitor 203 is connected in parallel with the second resistor 204, and based on this, the divided voltage of the capacitor 203 is equal to the divided voltage of the second resistor 204, so that the divided voltage of the capacitor 203 can be obtained by obtaining the divided voltage of the second resistor 204.

In a specific implementation, as shown in FIG. 2, U_tRepresenting the working voltage of the cell, the voltage of the open-circuit voltage source 201 is the open-circuit voltage U of the cell_ocThe first resistor 202 may represent an ohmic polarization internal resistance of the battery cell, the second resistor 204 may represent an electrochemical polarization internal resistance, and the capacitor 203 may be an electrochemical reaction double-layer capacitor.

And S102, obtaining an initial model of the cell working voltage according to the equivalent working circuit, wherein the initial model comprises a constant coefficient of an unknown value.

And S103, acquiring the working data of the battery cell.

In the embodiment of the present invention, the working data of the battery cell may include, but is not limited to: operating time, operating current and operating voltage.

It should be noted that, in the process of actually implementing the scheme, when the step is executed, some working data related to the attributes of the battery core itself may also be collected at the same time. For example, the open circuit voltage of the battery cell, the operating temperature of the battery cell, the initial charge of the battery cell, and the rated capacity of the battery cell are the operating data. This part of the operating data is fixed for a certain cell.

And S104, performing approximate fitting processing on the working data based on the initial model to obtain the numerical value of each constant coefficient in the initial model.

And S105, obtaining an obtaining model of the cell working voltage according to the numerical value of each constant coefficient and the initial model.

The following describes an implementation of the method illustrated in fig. 1 in detail with reference to fig. 1 and 2.

In this embodiment of the present invention, when S102 is executed, the divided voltage of the first resistor, the divided voltage of the second resistor, the divided voltage of the concentration polarization element, and the open-circuit voltage may be respectively obtained according to the equivalent working circuit, where the open-circuit voltage is a voltage of an open-circuit voltage source, and the divided voltage of the first resistor, the divided voltage of the second resistor, and the divided voltage of the concentration polarization element include constant coefficients with unknown values, and further, an initial model of the cell working voltage is generated according to the open-circuit voltage, the divided voltage of the first resistor, the divided voltage of the second resistor, and the divided voltage of the concentration polarization element.

It should be noted that, because the cell has different influences on the cell operating voltage due to the divided voltage of the concentration polarization in different operating states, when this step is executed, initial models of different cell operating voltages may be generated based on different operating states.

The working state related to the embodiment of the invention can comprise: a charged state or a discharged state. Therefore, when the operating state of the battery cell is the charging state, the generated initial model of the battery cell operating voltage can be expressed as:

U_t＝U_oc+U₁+U₂-U₃

when the operating state of the battery cell is a discharging state, the generated initial model of the battery cell operating voltage may be represented as:

U_t＝U_oc-U₁-U₂+U₃

wherein, U_tRepresents the cell operating voltage, U_ocIndicating the open circuit voltage, U, of the cell₁Representing the voltage division of the first resistance, U₂Representing the voltage division of the second resistance, U₃Representing the partial pressure of the concentration polarization element.

In a specific implementation process, the voltage division of the first resistor in the initial model may be obtained through the following formula:

U₁＝I×R₁

wherein, U₁The partial voltage of the first resistor is represented, I represents the working current of the battery cell, and R represents₁Is the resistance of the first resistor.

In the embodiment of the invention, the voltage division of the first resistor is the voltage division caused by ohmic polarization, and the resistance value R of the first resistor₁Only the remaining capacity SOC and the operating temperature T of the battery cell. Specifically, the resistance value R of the first resistor₁Can be expressed as:

R₁＝a1×SOC^a2×e^a3×T

wherein a1, a2 and a3 are all constant coefficients, T represents the operating temperature, and SOC represents the remaining capacity of the battery cell.

In a specific implementation process, the voltage division of the second resistor in the initial model may be obtained through the following formula:

wherein, U₂The voltage division of the second resistor is represented, I represents the working current of the battery cell, t represents the working time of the battery cell, and R₂Is the resistance of the second resistor, and C is the capacitance of the capacitor.

In the embodiment of the invention, the resistance value R of the second resistor₂The capacitance value C of the capacitor is only equal to the residual electric quantity of the battery cellSOC and operating temperature T. Wherein, the resistance R of the second resistor₂Can be expressed as:

R₂＝b1×SOC^b2×e^b3×T

the capacitance value C of the capacitor can be expressed as:

C＝h1×SOC^h2×e^h3×T

wherein b1, b2, b3, h1, h2 and h3 are constant coefficients, T represents the operating temperature, and SOC represents the residual capacity of the battery cell.

In a specific implementation, the partial pressure of the concentration polarization element in the initial model can be obtained by the following formula:

wherein, U₃Indicating the partial pressure of the concentration polarization element,. alpha.indicating the polarization coefficient,. tau.indicating the transition time,. T indicating the operation time of the cell,. T indicating the operation temperature,. R being the ideal gas constant,. F being the Faraday constant, and n being the amount of the substance; the polarization coefficient ∈ is only related to the remaining charge SOC of the battery cell, and can be expressed as: oc is d1 × SOC^d2；

In the embodiment of the present invention, the transition time τ may be represented as:

where B is a first coefficient, B is related to the operating temperature T and the operating current I, and can be expressed as: g1 × I^g2×e^g3×T；E_aIs a second coefficient representing diffusion activation energy, E_aOnly the remaining capacity SOC of the battery cell is related to, and may be represented as: e_a＝f1×SOC^f2(ii) a The SOC represents the residual capacity of the battery cell, the I represents the working current of the battery cell, and d1, d2, g1, g2, g3, f1 and f2 are constant coefficients.

In the embodiment of the invention, the open-circuit voltage U related in the formula_ocThe obtaining method can be as follows:through the residual capacity SOC and the open-circuit voltage U_ocThe relationship between them is determined.

Specifically, considering that the operating temperature T has a small influence on the balance voltage of the lithium ion battery cell, the remaining capacity SOC and the open-circuit voltage U can be measured at normal temperature (25 ℃)_ocDetecting to obtain the residual capacity SOC and the open-circuit voltage U_ocThe corresponding relation between them. At this time, reference may be made to fig. 3, which is a schematic diagram illustrating a relationship between the remaining capacity and the open-circuit voltage in the embodiment of the present invention. In fig. 3, the remaining capacity is expressed in percentage, and the open circuit voltage is in V. Based on the relationship curve in fig. 3, the corresponding open-circuit voltage U may be determined according to the remaining battery SOC of the battery cell in the actual working state_oc。

Based on this, the above formulas may have various manners of acquiring the remaining battery SOC of the battery cell. For example, the remaining capacity of the battery cell may be obtained from a measured operation curve of the remaining capacity of the battery cell and the operation time, or the remaining capacity of the battery cell may be obtained by integrating the operation current with the operation time.

In a specific implementation process, the remaining capacity of the battery cell can be obtained by an ampere-hour integration method. At this time, according to the different operating states of the battery cells, the following two situations may also be included:

firstly, when the working state of the battery cell is the charging state, the remaining capacity of the battery cell is obtained through the following formula:

secondly, when the working state of the battery cell is the charging state, the remaining capacity of the battery cell is obtained through the following formula:

therein, SOC₀Indicates the initial electric quantity of the cell, C₀For rated capacity of cell, I tableAnd (4) indicating the working current of the cell, and t indicating the working time of the cell.

Based on the above, the initial models of the telecommunication working voltage can be obtained by substituting the expressions of the partial voltage of each part into the acquisition model of the cell working voltage, and the initial models comprise constant coefficients in the expressions of the partial voltage of each part.

It should be noted that at least two types of coefficients are involved in the embodiment of the present invention. The constant coefficient refers to a constant as a coefficient, and for an acquisition model of the working voltage of one battery cell under a fixed condition, the constant coefficient does not change once being determined, for example, b1, d2, g1, b2, h1 and the like in the above expression; another type of coefficient is a coefficient that varies with a variable, for example, the polarization coefficient ℃; the first coefficient B and the second coefficient E in the above expression_aAnd the like.

Based on the above, after substituting the expressions of each part in the initial model of the cell operating voltage into the expression of the initial model, the following two initial models of the cell operating voltage can be obtained:

when the working state of the battery cell is the charging state, the initial model of the working voltage of the battery cell is as follows:

when the working state of the battery cell is a discharging state, the initial model of the working voltage of the battery cell is as follows:

based on the initial model, the embodiment of the present invention executes the step of acquiring the working data of the battery cell in S103. The working voltage acquired in the step is the real working voltage of the battery cell, the working current is the real working current of the battery cell, and both the working voltage and the working current can be acquired through detection equipment. The working time can be divided into charging time and discharging time according to the working state of the battery cell.

Specifically, according to the working current and the working voltage, the current working state of the battery cell may be determined, and then which initial model is used for the subsequent steps is determined, which is not described herein again.

In the embodiment of the present invention, when step S104 is executed, curve fitting may be performed on the working data based on the obtained initial model to obtain a plurality of fitting voltage curves, and according to the working time and the working voltage, a true voltage curve of the battery cell is obtained, and then, in the plurality of fitting voltage curves, one fitting voltage curve having the highest approximation degree with the true voltage curve is obtained as a target curve, so as to obtain a numerical value of each constant coefficient in the target curve, so as to serve as a numerical value of each constant coefficient in the initial model.

It should be noted that the approximation degree of the target curve obtained by the fitting approximation scheme and the real voltage curve is the highest, that is, the target curve is one of the fitting voltage curves which is wirelessly approximated to the real voltage curve, the similarity between the target curve and the real voltage curve is the highest, and the difference between the target curve and the real voltage curve is the smallest. The degree of approximation can be measured in terms of the magnitude of the similarity. The steps of obtaining the fitted voltage curves and the actual voltage curves of the battery core may be performed simultaneously, or may be performed sequentially in a preset order, which is not particularly limited in the embodiment of the present invention.

Based on the values of the constant coefficients acquired in S104, when S105 is executed, the acquired values of the constant coefficients are substituted into the initial model, so that an acquisition model of the cell operating voltage can be obtained.

The technical scheme of the embodiment of the invention has the following beneficial effects:

Example two

Based on the cell model generation method provided in the first embodiment, two feasible implementation processes of the generation method are provided in the first embodiment of the present invention.

First, an acquisition model of the operating voltage of the 20Ah hard shell cell was generated.

Specifically, the 20Ah hard shell cell can be a cell with a cell rated capacity of 20Ah in a pure Electric vehicle (BEV).

First, an equivalent operation circuit of the 20Ah hard shell cell is obtained, and the circuit configuration thereof is the same as that of the equivalent operation circuit shown in fig. 2.

Then, according to the equivalent working circuit, an initial model of the working voltage of the 20Ah hard shell battery cell is obtained. Specifically, when the operating state of the battery cell is the charging state, the initial model of the battery cell operating voltage is as follows:

in the embodiment of the present invention, the physical meanings and expressions of the various terms in the initial model are the same as those in the first embodiment, and are not described herein again. Based on the above, the 20Ah hard shell cell working voltage U_tEach part of the initial model in (1) contains constant coefficients of unknown values.

And then, collecting working data such as working voltage, working current, working time and the like of the 20Ah hard shell battery core.

Wherein, the residual charge SOC and the open-circuit voltage U of the 20Ah hard shell battery cell are detected at 25 DEG C_ocObtaining the remaining capacity SOC and the open-circuit voltage U_ocThe corresponding relationship between the remaining battery SOC and the remaining battery SOC may refer to fig. 3, and the remaining battery SOC is obtained by an ampere-hour integration method based on the corresponding relationship shown in fig. 3, which is not described herein again.

And acquiring a relation curve of the working voltage changing along with the working time based on the acquired working voltage and the working time, namely acquiring a real voltage curve of the 20Ah hard shell battery cell.

And then, substituting the acquired working current, working time and working voltage into the initial model to obtain a plurality of fitting voltage curves, screening the fitting voltage curves based on the real voltage curves, and obtaining a fitting voltage curve which is wireless and approximate to the real voltage curve as a target curve, so that the numerical value of each constant coefficient in the item of standard curve is obtained as the numerical value of each constant coefficient in the initial model.

Specifically, at 25 ℃, the working data of the 20Ah hard shell battery cell in the charging state and the discharging state respectively at the working current of 20A (1C rate), and the working data of the 20Ah hard shell battery cell in the charging state and the discharging state respectively at the working current of 100A (5C rate) are obtained, the four groups of data are respectively substituted into the initial model for approximate fitting, the fitting result can refer to table 1, and table 1 is a numerical list of each constant coefficient in the initial model of the working voltage of the 20Ah hard shell battery cell.

TABLE 1

Coefficient of constant	a1	a2	a3	h1
					Numerical value	1.04×10¹⁰	-1.46×10^-01	-1.04×10^-01	3.01×10^-6
Coefficient of constant	b1	b2	b3	h2
					Numerical value	6.20×10^-03	-8.00×10^-02	-4.17×10^-03	2.55×10^-04
Coefficient of constant	g1	g2	g3	h3
					Numerical value	4.14×10⁺¹¹	1.41×10^-05	-1.96×10^-02	1.11×10^-02
Coefficient of constant	d1	d2	f1	f2
					Numerical value	1.77×10^-01	-7.80×10^-02	1.83×10⁺⁰⁴	1.24

Specifically, fig. 4 to 7 are schematic diagrams of a target curve and a real voltage curve obtained based on each constant coefficient and the initial model in table 1. Fig. 4 is a schematic diagram of a target curve and a real voltage curve of a 20Ah hard shell battery cell in an embodiment of the present invention when a 20A operating current (1C rate) is in a charging state, fig. 5 is a schematic diagram of a target curve and a real voltage curve of a 20Ah hard shell battery cell in an embodiment of the present invention when a 100A operating current (5C rate) is in a charging state, fig. 6 is a schematic diagram of a target curve and a real voltage curve of a 20Ah hard shell battery cell in an embodiment of the present invention when a 20A operating current (1C rate) is in a discharging state, and fig. 7 is a schematic diagram of a target curve and a real voltage curve of a 20Ah hard shell battery cell in an embodiment of the present invention when a 100A operating current (5C rate) is in a discharging state.

As shown in fig. 4 to 7, the target curve is curve 1, and the real voltage curve is curve 2. As shown in fig. 4 to 7, the curve 1 and the curve 2 approach each other infinitely, and even overlap each other. That is, the target curve can accurately characterize the true voltage curve of the 20Ah hard shell cell at different operating currents and operating conditions.

Based on this, the specific values of the constant coefficients in table 1 are substituted into the initial model, so as to obtain the model for obtaining the operating voltage of the 20Ah hard shell battery core. Therefore, in the practical application process, the working voltage and the working current of the 20Ah hard shell battery cell can be obtained by substituting the working voltage and the working current into the obtaining model.

And secondly, generating an acquisition model of the working voltage of the 12Ah PHEV cell.

Specifically, the 12Ah PHEV cell is a cell with a cell rated capacity of 12Ah in a new energy vehicle (PHEV).

First, an equivalent operating circuit of the 12Ah PHEV cell is obtained, and the circuit structure thereof is the same as that of the equivalent operating circuit shown in fig. 2.

Then, according to the equivalent working circuit, an initial model of the working voltage of the 12Ah PHEV cell is obtained. Specifically, when the operating state of the battery cell is the charging state, the initial model of the battery cell operating voltage is as follows:

in the embodiment of the present invention, the physical meanings and expressions of the various items in the initial model are the same as those in the first embodiment, and are not described herein again. Based on this, the above-mentioned electric core operating voltage U_tEach part of the initial model in (1) contains constant coefficients of unknown values.

And then, acquiring working data such as working voltage, working current and working time of the 12Ah PHEV cell.

Specifically, in the embodiment of the invention, the working condition voltage curve of the 12Ah PHEV cell is used as the real working data. At this time, the remaining capacity SOC of the 12Ah PHEV cell can be obtained by fig. 8. Fig. 8 is a schematic diagram of the working data of the 12Ah PHEV cell collected in the embodiment of the present invention, where a curve 1 in fig. 8 is a curve of the remaining capacity and the working time of the 12Ah PHEV cell, and a curve 2 is a curve of the working current and the working time of the 12Ah PHEV cell. A curve of the relationship between the remaining capacity and the open-circuit voltage of the 12Ah PHEV cell is shown in fig. 9, and at this time, the open-circuit voltage of the 12Ah PHEV cell may be obtained according to the curve relationship.

In the embodiment of the invention, a relation curve of the working voltage changing along with the working time is acquired based on the acquired working voltage and the working time, namely a real voltage curve of the 12Ah PHEV cell is acquired.

In the embodiment of the invention, the obtained working data of the 12Ah PHEV cell are substituted into the initial model at 25 ℃ for approximate fitting, the fitting result can refer to table 2, and table 2 is a numerical value list of each constant coefficient in the initial model of the working voltage of the 12Ah PHEV cell.

TABLE 2

Coefficient of constant	a1	a2	a3	h1
					Numerical value	5.75×10⁺⁰¹	-1.15	-4.10×10^-02	9.92×10^-1
Coefficient of constant	b1	b2	b3	h2
					Numerical value	3.53×10⁺⁰⁴	-7.68×10^-3	-1.21×10^-1	4.45×10^-2
Coefficient of constant	g1	g2	g3	h3
					Numerical value	1.06×10⁺⁷	2.73×10^-01	-6.02×10^-4	1.67×10^-02
Coefficient of constant	d1	d2	f1	f2
					Numerical value	1.53×10^-04	-9.25×10^-02	2.36×10⁺⁰⁴	6.87×10^-01

Specifically, fig. 10 is a schematic diagram of a target curve and a real voltage curve obtained based on each constant coefficient and the initial model in table 2. Fig. 10 is a schematic diagram of a target curve and a real voltage curve of a 12Ah PHEV cell in the embodiment of the present invention, where as shown in fig. 10, curve 1 is the target curve of the 12Ah PHEV cell, and curve 2 is the real voltage curve of the 12Ah PHEV cell. As shown in fig. 10, the curve 1 and the curve 2 approach infinitely, the error between the two curves is small, and the target curve can accurately represent the real voltage curve of the 12Ah PHEV cell.

Based on this, the specific values of the constant coefficients in table 2 are substituted into the initial model, so as to obtain the acquisition model of the working voltage of the 12Ah PHEV cell. Therefore, in the practical application process, the working voltage of the hardware battery cell can be obtained by substituting the working voltage and the working current into the obtaining model only by obtaining the working voltage and the working current of the battery cell.

EXAMPLE III

The embodiment of the invention provides a cell voltage obtaining method. Referring to fig. 11, a schematic flow chart of a cell voltage obtaining method according to an embodiment of the present invention is shown in fig. 11, where the method includes:

and S1101, collecting the working data of the battery cell.

Specifically, the working data includes: operating current and operating time.

And S1102, acquiring the working voltage of the battery cell by using the acquisition model of the working voltage of the battery cell based on the working data.

It should be noted that, in the embodiment of the present invention, when S1102 is executed, the acquired work data of the battery cell is substituted into the acquisition model of the battery cell work voltage, so as to obtain the battery cell work voltage.

In a specific implementation process, the obtaining model of the cell operating voltage may be the obtaining model provided in the first embodiment.

Example four

Based on the cell model generation method provided in the first embodiment, embodiments of an apparatus for implementing the steps and methods in the first embodiment of the present invention are further provided.

Fig. 12 is a functional block diagram of a cell model generation apparatus according to an embodiment of the present invention. As shown in fig. 12, the apparatus includes:

the first obtaining unit 121 is configured to obtain an equivalent operating circuit of the battery cell, where the equivalent operating circuit includes: a concentration polarization circuit;

the second obtaining unit 122 is configured to obtain an initial model of the cell operating voltage according to the equivalent operating circuit, where the initial model includes a constant coefficient of an unknown value;

the acquisition unit 123 is configured to acquire working data of the battery cell, where the working data includes: working time, working current and working voltage;

the processing unit 124 is configured to perform approximation fitting processing on the working data based on the initial model to obtain a numerical value of each constant coefficient in the initial model;

and a third obtaining unit 125, configured to obtain an obtaining model of the cell operating voltage according to the value of each constant coefficient and the initial model.

Specifically, in the embodiment of the present invention, the equivalent operating circuit further includes: the circuit comprises an open-circuit voltage source, a first resistor, a capacitor and a second resistor;

the capacitor is connected in parallel with the second resistor.

Based on the above equivalent operating circuit, the second obtaining unit 122 is configured to:

according to the equivalent working circuit, respectively obtaining the partial pressure of a first resistor, the partial pressure of a second resistor, the partial pressure of a concentration polarization element and an open-circuit voltage, wherein the open-circuit voltage is the voltage of an open-circuit voltage source, and the partial pressure of the first resistor, the partial pressure of the second resistor and the partial pressure of the concentration polarization element contain constant coefficients of unknown values;

and generating an initial model of the cell working voltage according to the open-circuit voltage, the partial voltage of the first resistor, the partial voltage of the second resistor and the partial voltage of the concentration polarization element.

Specifically, in the embodiment of the present invention, when the working state of the battery cell is the charging state, the initial model of the battery cell working voltage is as follows:

U_t＝U_oc+U₁+U₂-U₃

U_t＝U_oc-U₁-U₂+U₃

In a specific implementation process, the second obtaining unit 122 is specifically configured to:

the partial pressure of the concentration polarization element is obtained by the following formula:

wherein, U₃Represents the partial pressure of the concentration polarization element, and oc represents the polarization coefficient, wherein oc is d1 × SOC^d2And τ represents a transition time, wherein,

b is the first coefficient, g1 × I^g2×e^g3×T，E_aIs a second coefficient representing diffusion activation energy, E_a＝f1×SOC^f2Where SOC denotes a remaining battery capacity of the cell, T denotes an operation time of the cell, I denotes an operation current of the cell, T denotes an operation temperature, R denotes an ideal gas constant, F denotes a faraday constant, n denotes an amount of a substance, and d1, d2, g1, g2, g3, F1, and F2 are all constant coefficients.

obtaining the voltage division of the second resistor through the following formula:

wherein, U₂The voltage division of the second resistor is represented, I represents the working current of the battery cell, t represents the working time of the battery cell, and R₂Is the resistance value of the second resistor, wherein R₂＝b1×SOC^b2×e^b3×TC is the capacitance of the capacitor, h1 × SOC^h2×e^h3×TB1, b2, b3, h1, h2 and h3 are constant coefficients, T represents the operating temperature, and SOC represents the residual capacity of the battery cell.

obtaining the voltage division of the first resistor through the following formula:

U₁＝I×R₁

wherein, U₁The partial voltage of the first resistor is represented, I represents the working current of the battery cell, and R represents₁Is the resistance value of the first resistor, wherein R₁＝a1×SOC^a2×e^a3×TA1, a2 and a3 are all constant coefficients, T represents the operating temperature, and SOC represents the remaining capacity of the battery cell.

In a specific implementation process, the second obtaining unit 122 is further specifically configured to:

when the working state of the battery cell is the charging state, acquiring the residual electric quantity of the battery cell by the following formula:

therein, SOC₀Indicates the initial electric quantity of the cell, C₀For the rated capacity of the battery cell, I represents the working current of the battery cell, and t represents the working time of the battery cell.

Specifically, in the embodiment of the present invention, the processing unit 124 is specifically configured to:

In this embodiment of the present invention, the third obtaining unit 125 is specifically configured to:

and substituting the obtained numerical values of the constant coefficients into the initial model to obtain an obtaining model of the working voltage of the battery cell.

Since each unit in the present embodiment can execute the method shown in fig. 1, reference may be made to the related description of fig. 1 for a part of the present embodiment that is not described in detail.

EXAMPLE five

Based on the cell voltage obtaining method provided in the third embodiment, embodiments of an apparatus for implementing the steps and the method in the third embodiment of the present invention are further provided.

Fig. 13 is a functional block diagram of a cell voltage obtaining apparatus according to an embodiment of the present invention. As shown in fig. 13, the apparatus includes:

the collecting unit 131 is configured to collect working data of the battery cell, where the working data includes: operating current and operating time;

the obtaining unit 132 is configured to obtain the cell operating voltage by using an obtaining model of the cell operating voltage based on the operating data. The model for obtaining the cell operating voltage is obtained by using the method for generating the cell model according to any one of the manners described in the first embodiment.

Since each unit in the present embodiment can execute the method shown in fig. 11, reference may be made to the related description of fig. 11 for a part of the present embodiment that is not described in detail.

EXAMPLE six

In the cell model generation method provided in the first embodiment and the cell voltage acquisition method provided in the third embodiment, a battery management system is provided in an embodiment of the present invention.

Please refer to fig. 14, which is a functional block diagram of a battery management system according to an embodiment of the present invention. As shown in fig. 14, the battery management system includes:

the cell model generation device 141 in any of the above-described implementation manners; and the number of the first and second groups,

the cell voltage obtaining device 142 is described above.

For parts of the present embodiment not described in detail, reference may be made to the description of fig. 1 and 11.

It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.

In the embodiments provided in the present invention, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions in actual implementation, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.

The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.

In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, or in a form of hardware plus a software functional unit.

The integrated unit implemented in the form of a software functional unit may be stored in a computer readable storage medium. The software functional unit is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) or a Processor (Processor) to execute some steps of the methods according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims

1. A method for generating a cell model, the method comprising:

obtaining an obtaining model of the working voltage of the battery cell according to the numerical value of each constant coefficient and the initial model;

the equivalent operating circuit further includes: the circuit comprises an open-circuit voltage source, a first resistor, a capacitor and a second resistor;

the capacitor is connected with the second resistor in parallel;

obtaining an initial model of the cell operating voltage according to the equivalent operating circuit, including:

2. The method of claim 1,

when the working state of the battery cell is a charging state, the initial model of the working voltage of the battery cell is as follows:

U_t＝U_oc+U₁+U₂-U₃

U_t＝U_oc-U₁-U₂+U₃

wherein, U_tPresentation instrumentThe cell operating voltage U_ocRepresents the open circuit voltage, U, of the cell₁Representing the divided voltage of said first resistance, U₂Representing the voltage division, U, of said second resistance₃Representing the partial pressure of the concentration polarization member.

3. The method of claim 1, wherein obtaining the divided voltage of the concentration polarization element according to the equivalent operating circuit comprises:

4. The method of claim 1, wherein obtaining the divided voltage of the second resistor according to the equivalent operating circuit comprises:

obtaining the voltage division of the second resistor by the following formula:

5. The method of claim 1, wherein obtaining the divided voltage of the first resistor according to the equivalent operating circuit comprises:

obtaining the voltage division of the first resistor by the following formula:

U₁＝I×R₁

6. The method according to claim 3 or 4 or 5,

wherein the content of the first and second substances,SOC₀represents the initial electric quantity of the battery cell, C₀For the rated capacity of the battery cell, I represents the working current of the battery cell, and t represents the working time of the battery cell.

7. The method of claim 1, wherein performing an approximate fitting process on the working data based on the initial model to obtain values of constant coefficients in the initial model comprises:

8. The method of claim 1, wherein obtaining the model of obtaining the cell operating voltage according to the value of each constant coefficient and the initial model comprises:

9. A cell voltage acquisition method is characterized by comprising the following steps:

acquiring the cell working voltage by using an acquisition model of the cell working voltage based on the working data; the model for obtaining the cell operating voltage is obtained by the cell model generation method according to any one of claims 1 to 8.

10. A cell model generation apparatus, comprising:

a third obtaining unit, configured to obtain an obtaining model of the cell working voltage according to the value of each constant coefficient and the initial model;

the capacitor is connected with the second resistor in parallel;

the second obtaining unit is configured to:

11. The apparatus of claim 10,

U_t＝U_oc+U₁+U₂-U₃

U_t＝U_oc-U₁-U₂+U₃

12. The apparatus according to claim 10, wherein the second obtaining unit is specifically configured to:

b is the first coefficient, g1 × I^g2×e^g3×T，E_aIs a second coefficient representing diffusion activation energy, E_a＝f1×SOC^f2SOC represents the residual capacity of the battery cell, T represents the working time of the battery cell, I represents the working current of the battery cell, T represents the working temperature, R is an ideal gas constant, and F is a methodThe larth constant, n is the amount of substance, and d1, d2, g1, g2, g3, f1 and f2 are all constant coefficients.

13. The apparatus according to claim 10, wherein the second obtaining unit is specifically configured to:

obtaining the voltage division of the second resistor by the following formula:

14. The apparatus according to claim 10, wherein the second obtaining unit is specifically configured to:

obtaining the voltage division of the first resistor by the following formula:

U₁＝I×R₁

15. The apparatus according to claim 12, 13 or 14, wherein the second obtaining unit is further specifically configured to:

16. The apparatus according to claim 10, wherein the processing unit is specifically configured to:

17. The apparatus according to claim 10, wherein the third obtaining unit is specifically configured to:

18. A cell voltage acquisition apparatus, comprising:

the acquisition unit is used for acquiring the cell working voltage by utilizing an acquisition model of the cell working voltage based on the working data; the model for obtaining the cell operating voltage is obtained by the cell model generation method according to any one of claims 1 to 8.

19. A battery management system, characterized in that the battery management system comprises:

the cell model generation apparatus of any of claims 10 to 17; and the number of the first and second groups,

the cell voltage acquisition apparatus of claim 18.