JP2017062191A - Battery simulation apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a battery simulation apparatus capable of highly accurately analyzing the output voltage and charge state of a battery, with a small calculation load by devising a battery model applicable to a mixed electrode battery.SOLUTION: In a battery simulation apparatus 15, for use in analyzing a battery that contains two kinds of cathode active materials (lithium manganite, lithium-nickel-manganese-cobalt oxide) in a cathode, a mixed electrode model part 18 performs: computing an applied-current ratios xand xfor each cathode active at a given clock-time t, with an assumption that a closed circuit potential φof a lithium manganite 11 is equal to a closed circuit potential φof a lithium-nickel-manganese-cobalt oxide 12 (step 1); and computing Li density c, c, c.ave, and c.aveof each of the active materials at a given clock-time t on the basis of the applied-current ratios xand xcalculated in the step 1 (step 2).SELECTED DRAWING: Figure 4

Description

  The present invention relates to a technology of a simulation apparatus that analyzes an internal state of a battery.

A battery model that analyzes the internal state of a battery and a simulation based on the battery model in order to accurately grasp changes in characteristics such as output voltage and charging rate associated with charging and discharging in batteries used in electric vehicles and hybrid vehicles A device has been proposed.
For example, Non-Patent Document 1 discloses a model (hereinafter referred to as a NEWMAN model) that is calculated in consideration of all physical quantities related to the electrode reaction, and enables high-accuracy battery internal information analysis. However, the calculation load is large, which is not preferable in terms of calculation cost.

Further, Non-Patent Document 2 discloses a model in which each of the active materials of the negative electrode and the positive electrode is considered to have the same reaction, and each electrode is represented by one active material particle (hereinafter referred to as an SP model). Has been. Although the calculation load is reduced, there is a problem that the analysis accuracy is lowered because the potential and Li concentration change in the electrolyte are ignored.
Further, Patent Document 1 discloses a model in which an electrode is represented by a single active material particle as in the SP model, and changes in potential and Li concentration in the electrolyte are taken into account, while reducing the calculation load. It is shown that a decrease in analysis accuracy is suppressed.

JP 2012-154665 A

Journal of The Electrochemical Society, 140 (6), 1526-1533 (1993) Journal of The Electrochemical Society, 151 (10), A1584-A1591 (2004)

By the way, in recent years, for example, in a lithium ion secondary battery, a battery employing a mixed electrode using a plurality of types of active materials as one electrode has been developed in order to improve output and life. Also for such a mixed electrode battery, a battery model for accurately estimating the output voltage, the charging rate and the like is required.
Although it is possible to analyze a mixed electrode battery based on the Newman model, the calculation load increases as described above, which is not preferable.

Although the calculation can be simplified in the SP model and the model of Patent Document 1, since it is considered that all the active materials have the same reaction in each electrode, characteristics of different types of active materials are output when applied to a mixed electrode battery. There is a problem that is not accurately reflected in the voltage estimation result. Moreover, since the charging rate for each active material type cannot be estimated, it is difficult to accurately estimate the charging rate.
The present invention has been made to solve such problems. The object of the present invention is to devise a battery model that can be applied to a mixed electrode battery to reduce the amount of calculation and to accurately output voltage and charge state. It is an object of the present invention to provide a battery simulation apparatus capable of analyzing the above.

  In order to achieve the above object, a battery simulation apparatus according to the present invention is a battery simulation apparatus including a plurality of types of active materials in at least one of a positive electrode and a negative electrode. Each electrode is represented by active material particles in the same manner as in the model, but in an electrode in which a plurality of types of active material particles are used, the number of types of active material particles is represented. For example, when two different types of active materials are used, they are represented by two different types of particles. The battery simulation apparatus of the present invention considers that the plurality of active material particles are connected in parallel, and assumes that the closed circuit potentials (potentials when current is applied) of the active materials are the same. A first step execution unit that calculates an applied current ratio for each of the active materials at a predetermined time, and a reaction of each of the active materials at the predetermined time based on the applied current ratio calculated in the first step execution unit And a second step execution unit for calculating a substance concentration (Li concentration).

  Preferably, the simulation apparatus further includes a charge rate calculation for each active material based on the applied current ratio and the reactant concentration, and a third step execution unit for calculating the closed circuit potential and the battery voltage. Good.

  According to the present invention, the first step execution unit calculates the applied current ratio for each active material at a predetermined time, assuming that the closed circuit potentials of a plurality of different types of active materials are the same, and executes the second step. Since the reactive material concentration of each active material at a predetermined time is calculated based on the applied current ratio, the closed circuit potential and the charging rate for each active material type are calculated based on the applied current ratio and the reactive material concentration. can do. This makes it possible to accurately estimate the output voltage and the charging rate reflecting characteristics even in a simulation method with a small calculation load in which the electrode is represented by active material particles.

It is a schematic block diagram of the battery analyzed by the simulation method and apparatus which concern on embodiment of this invention. It is a conceptual diagram of the simulation method of the battery which concerns on this embodiment. It is a list of variables and constants used in the battery model formula. It is a block diagram explaining the structure of the battery simulation apparatus which concerns on this embodiment. It is a graph which shows an example of transition of the closed circuit potential of a mixed positive electrode at the time of constant current discharge in the battery concerning this embodiment. It is a graph which shows an example of transition of the charging rate of each active material in a mixed positive electrode at the time of carrying out constant current discharge in the battery concerning this embodiment. It is a graph for demonstrating the difference of the response with respect to the applied current at the time of carrying out the linear approximation of the theoretical formula of the overvoltage by a charge transfer reaction.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is a schematic configuration diagram of a battery 1 analyzed by a simulation method and apparatus according to an embodiment of the present invention.
As shown in FIG. 1, a battery 1 analyzed by the simulation method and apparatus of the present embodiment is a chargeable / dischargeable secondary battery, for example, a lithium ion secondary battery. The battery 1 includes a positive electrode 2, a negative electrode 3, and a separator 4 in a container filled with an electrolytic solution, and charging / discharging is possible by moving lithium ions between the positive electrode 2 and the negative electrode 3.

The electrolyte is a non-aqueous electrolyte having lithium ion conductivity, and is used in various states such as liquid, gel, and solid.
The separator 4 is formed into a film shape, for example, with a resin or the like, and allows movement of lithium ions while preventing a short circuit due to contact between the positive electrode 2 and the negative electrode 3.
The positive electrode 2 includes a positive electrode current collector 5 formed of, for example, a plate-like or foil-like metal (aluminum or the like). The positive electrode 2 includes a positive electrode active material together with a binder and a conductive auxiliary material. The positive electrode active material includes two types of lithium metal oxides such as lithium manganate 11 (Li _1-x Mn ₂ O ₄ ) and lithium nickel manganese cobalt oxide 12 (Li _1-y Ni _1/3 Mn _1/3 Co). _1/3 O ₂ ) is used.

The negative electrode 3 includes a negative electrode current collector 6 made of, for example, a plate-like or foil-like metal (copper or the like). The negative electrode 3 includes a negative electrode active material 13 together with a binder and a conductive auxiliary material. For the negative electrode active material 13, for example, a carbon-based material such as graphite or amorphous carbon is used.
As described above, the battery 1 of the present embodiment employs two types of lithium manganate 11 and lithium nickel manganese cobalt oxide 12 as the positive electrode active material.

Note that the positive electrode current collector 5 and the negative electrode current collector 6 of the battery 1 are connected via an electric load 7 to form an electric circuit.
The battery simulation apparatus according to the present embodiment is a simulation apparatus that can analyze the charge / discharge characteristics of the battery 1 that employs such two types of positive electrode active materials, that is, a so-called mixed electrode battery.

FIG. 2 is a conceptual diagram of a battery simulation method according to this embodiment. Note that the arrows described in FIG. 2 indicate the flow of applied current during discharge (actually, the flow of Li ions that are driven by applying a current and chemically react with the active material).
In the simulation method according to the present embodiment, as the battery model, a model is used in which the positive electrode is represented by different types of active material particles and they are considered to be connected in parallel. As shown in FIG. 2, the battery 1 having two types of positive electrode active materials (lithium manganate 11 and lithium nickel manganese cobalt oxide 12) has an amount of Li proportional to the applied current I and lithium manganate 11. The lithium nickel manganese cobalt oxide 12 is divided and reacted so that the closed circuit potentials of the respective active materials are equal.

  In the simulation method according to the present embodiment, the characteristics of the battery 1 are calculated and analyzed by the following theoretical formula. However, according to the SP model and prior patent 1, only one-dimensional reaction in the electrode stacking direction is considered, and it is assumed that the same reaction occurs in all active material particles of the same type (having the same composition formula) at each electrode. To do. Fig. 3 shows a list of variables and constants used in the theoretical formula.

The battery cell voltage V _cell is obtained as a difference between the positive electrode potential φ _p and the negative electrode potential φ _n as shown in the following formula (1).

As shown in FIG. 2, when two types of active materials (where lithium manganate is j = 1 and lithium nickel manganese cobalt oxide is j = 2) are used for the positive electrode, It is assumed that they are connected in parallel. Therefore, the electrode potential φ _i (i = p (positive electrode), n (negative electrode)) is described by the closed circuit potential of the active material as shown in the following equation (2).

Here, it is considered that the applied current is divided between the two types of active materials so that the closed circuit potentials of the respective active materials are the same. When the applied current ratio (current division ratio) at the positive electrode is x _{p, j} , there is a relationship of the following formula (3) between j _{p, j} . Since the negative electrode is one type of active material, the applied current ratio is not defined.

x _{p, j} satisfies the following formula (4).

Since each of the active materials such as the positive electrode active material and the negative electrode active material has a unique Li composition-potential profile, the open circuit potential U _{i, j} of the active material is expressed by the following equation (5): It has the surface Li concentration c _{i, j, surf} of the active material as an argument.

Here, the Li concentration c _{i, j} (r, t) in the active material follows the following equation (6) when the active material is regarded as particles having a radius R _{i, j} . The boundary condition is Equation (7).

The surface Li concentration c _{i, j, surf} and the average concentration c.ave _{i, j} of the active material are defined by the following equations (8) and (9).

Here, considering equation (3), c _{i, j, surf} has x _{i, j} × I as an argument.
The overvoltage η _{i, j} due to the charge transfer reaction of each active material is obtained by the following equation (10). Here, considering equation (3), η _{i, j} has x _{i, j} × I, c _{i, j, surf} as arguments.

When the voltage change due to the DC resistance is written as ΔV _{i, j} (= FR _{d, i, j} j _{i, j} ), ΔV _{i, j} has x _{i, j} × I as an argument _, considering equation (3). . From the above, if the argument of each term is clearly described, Equation (2) can be rewritten to Equation (11) for the positive electrode.

Here, since the equations (4) and (11) change with the passage of time, the following equation (12) and (13) can be written, where t is the time from the start of the simulation. However, in the following formula development, the electrolyte potential φ _{e, p} is omitted because it is common to both sides.

X _{p, 1} and x _{p, 2} can be obtained by simultaneous equations (12) and (13), but as described above, c _{p, j, surf} itself has x _{p, j} as an argument. It is difficult to directly solve the equations (12) and (13). Therefore, in actual simulation, in order to calculate x _{p, j} (t _k ) at a certain time t _k , c _{p, j, surf} (t _k ) ≈ focusing on the point where Li diffusion in the active material is slow An approximation is introduced as c _{p, j, surf} (t _k-1 ). By introducing the above approximation, the equation (12) at the time t _k can be changed to the following equation (14).

In the simulation method according to the present embodiment, first, as step 1, the applied current ratio x _{p, j} (t) at time t (= t _k ) is expressed by the above equations (13) and (14). Seek together.
Next, in step 2, the applied current ratio x _{p, j} (t) calculated in step 1 is substituted into the above equation (3), and c _{p, j, surf} (t) is calculated from equations (6) to (9). C.ave _{p, j} (t) is obtained.
Further, in step 3, x _{p, j} (t) and c _{p, j, surf} (t) calculated in steps 1 and 2, the electrolyte potential φ _{e, p} separately calculated from the method of Non-Patent Document 1, etc., The positive electrode potential φ _p is obtained by substituting the Li concentration c _{e, p} in the electrolytic solution into the equation (11). Similarly, the negative electrode potential φ _n is obtained at each time with j = 1. In this way, φ _p and φ _n that change over time are obtained, and the battery cell voltage V _cell can be obtained from equation (1).

Further, from c _{p, j, surf} (t) and c.ave _{p, j} (t) calculated in step 2, the surface charge rate SOC _{p, j, surf} , which is the local charge rate of the active material surface, The average charging rate SOC.ave _{p, j of the} substance is obtained from the following equations (15) and (16).

As described above, in the simulation method according to the present embodiment, the applied current ratio of the two active materials in the positive electrode is calculated for each elapsed time, and the characteristics of the two active materials are accurately reflected in the simulation result. As a result, the cell voltage V _{cell of the} battery using the mixed electrode and the charging rates SOC _{i, j, surf} and SOC.ave _{i, j of} each active material type can be accurately estimated and analyzed.
Further, since each of the two active materials in the positive electrode is calculated assuming that the same reaction occurs in all the active materials of the same type as in the SP model, it can be analyzed by calculation with a small load.

FIG. 4 is a block diagram illustrating the configuration of the battery simulation device 15 according to the present embodiment. As shown in FIG. 4, the battery system includes a data input unit 14 and a battery simulation device 15.
The data input unit 14 has a data table at a predetermined time t acquired in advance with an actual battery, and sends the applied current I and the battery temperature T at each time to the battery simulation device 15. Alternatively, the applied current I and the battery temperature T may be measured from an actual battery using a current sensor and a temperature sensor (not shown), and the data may be sent online to the battery simulation apparatus.

The battery simulation device 15 corresponds to the simulation device of the present invention, and includes a battery model unit 16 and a battery state estimation unit 17. The battery model unit 16 includes a mixed electrode model unit 18 and an electrolytic solution model unit 19 based on the above simulation method.
The mixed electrode model unit 18 corresponds to a first step execution unit of the present invention that executes Step 1 of the above-described simulation method and a second step execution unit of the present invention that executes Step 2, and the applied current ratio x _{i, j} and Li concentration (reactant concentration) c _{i, j, surf} and c.ave _{i, j} for each active material type are calculated based on the input values from the data input unit 14. Further, the electrolytic solution model unit 19 calculates the Li concentration c _{e, i} and the potential φ _{e, p} in the electrolytic solution in each electrode based on Non-Patent Document 1 and the like.

The battery state estimation unit 17 corresponds to a third step execution unit of the present invention that executes Step 3 of the above-described simulation method, and based on the physical quantity estimated by the battery model unit 16, the charge rate and output for each active material type Calculate the voltage. As described above, when the analysis is performed online, it is possible to estimate the charging rate for each active material type online.
FIG. 5 is a graph showing an example of the transition of the positive electrode potential φ _p when the battery 1 of this embodiment is discharged at a constant current. The solid line is an actual measurement value, and the broken line is an estimation by the simulation method using the invention model of this embodiment. The value and the alternate long and short dash line are values estimated by an SP model (considering the influence of the electrolytic solution) in which two types of positive electrode active materials are regarded as one active material. This graph shows the results with two types of current values.

As shown in FIG. 5, in the simulation method according to the present embodiment, the positive electrode potential φ _p that changes (decreases) over time can be estimated with higher accuracy than the estimated value based on the SP model.
FIG. 6 is a graph showing an example of the transition of the surface charge rate SOC _{p, j, surf} for each type of active material when the battery 1 of the present embodiment is subjected to constant current discharge, where the solid line is lithium manganate 11 and the broken line is The lithium nickel manganese cobalt oxide 12 is represented.

As shown in FIG. 6, in the simulation method according to the present embodiment, it is possible to estimate the charge rate of the active material that changes based on the characteristics of each active material over time. The charge rate of each type of active material is information that cannot be estimated by the SP model in which all the active materials are represented by one active material particle or the Patent Document 1 model.
FIG. 7 explains the difference in response to the applied current when the theoretical formula (10) of the overvoltage due to the charge transfer reaction is linearly approximated. In this embodiment, when calculating the applied current ratio x _{i, j} , the overvoltage η _{i, j} due to the charge transfer reaction is handled in a non-linear manner with respect to the applied current I in the calculation formula (10). As shown in FIG. 7, when the linear approximation is performed, an error from the theory increases when the applied current I is large. Therefore, the simulation method according to the present embodiment enables accurate simulation over a wider current range than calculating the applied current ratio x _{i, j} by linearly approximating η _{i, j} .

  In addition, this invention is not limited to the said embodiment. For example, in the above embodiment, the simulation method is applied to a mixed battery in which two types of electrode active materials are used for the positive electrode, but mixing in which more than two types of electrode active materials are used for one electrode. It can also be applied to batteries. Moreover, it is applicable also to mixed batteries other than the lithium ion secondary battery which uses active materials other than a lithium compound.

1 battery 2 positive electrode 3 negative electrode 11 lithium manganate (active material)
12 Lithium nickel manganese cobalt oxide (active material)
15 Battery simulation device (simulation device)
17 Battery state estimation unit (third step execution unit)
18 Mixed electrode model part (first step execution part, second step execution part)

Claims (2)

A battery simulation apparatus including a plurality of types of active materials in at least one of a positive electrode and a negative electrode,
A first step execution unit that calculates an applied current ratio for each of the plurality of active materials at a predetermined time assuming that the electrode is represented by a plurality of types of active material particles and that the closed circuit potential of each of the active materials is the same. When,
A second step execution unit that calculates the reactant concentration of each of the active materials at the predetermined time based on the applied current ratio calculated in the first step execution unit;
A battery simulation apparatus comprising:   The simulation apparatus further includes a third step execution unit for calculating a charging rate of each active material based on the applied current ratio and the concentration of the reactant, and calculating the closed circuit potential and the battery voltage. The battery simulation device according to claim 1.

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