Evaluation device, evaluation method, and program

Abstract

To evaluate an energy storage device with improved accuracy.SOLUTION: An evaluation device disclosed herein is an evaluation device that performs evaluation of an energy storage device having a positive electrode and a negative electrode, and includes a control unit that performs evaluation of the energy storage device using a transmission line model that includes electronic resistances in the positive electrode and the negative electrode, ionic resistances, and charge transfer resistances that include a reaction resistance and a film resistance, which are obtained by differentiating a function of overvoltage η and current I and depend on the current I.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] This specification discloses an evaluation device, an evaluation method, and a program.

Background Art

[0002] Conventionally, as a method for evaluating a lithium secondary battery as a power storage device, a three-dimensional porous electrode model (3D-PEM), which is a transmission line model considering the influence of a three-dimensional battery structure, has been proposed for the purpose of evaluating the internal resistance (see, for example, Patent Document 1, Non-Patent Document 1, etc.). Since the transmission line model replaces a complex reaction in the battery with a simple circuit diagram, it is possible to evaluate the internal resistance at high speed compared to a so-called battery simulation using a continuum model that solves the time evolution of the reaction in the battery.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Non-Patent Documents

[0004]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, in the evaluation methods of Patent Document 1 and Non-Patent Document 1, since a simplified circuit diagram is used, the evaluation accuracy is not sufficient, and it has been required to further improve the evaluation accuracy.

[0006] The present disclosure has been made in view of such problems, and the main object thereof is to provide a novel evaluation apparatus, an evaluation method, and a program capable of evaluating a power storage device with higher accuracy.

Means for Solving the Problems

[0007] As a result of intensive studies to achieve the above object, the present inventors have found that when introducing the current dependency in a region where the interfacial resistance strongly depends on the charge transfer resistance, the evaluation accuracy can be further improved to evaluate a power storage device, and thus the invention disclosed in this specification has been completed.

[0008] That is, the evaluation apparatus of the present disclosure is an evaluation apparatus that executes evaluation of a power storage device including a positive electrode and a negative electrode, a control unit that executes evaluation of the power storage device using a transmission line model including electron resistance, ion resistance, charge transfer resistance including reaction resistance and film resistance obtained by differentiating a function of overvoltage η and current I, which are in the positive electrode and the negative electrode, and that depends on current I, and includes the above.

[0009] The evaluation method of the present disclosure is an evaluation method that executes evaluation of a power storage device including a positive electrode and a negative electrode, a step of executing evaluation of the power storage device using a transmission line model including electron resistance, ion resistance, charge transfer resistance including reaction resistance and film resistance obtained by differentiating a function of overvoltage η and current I, which are in the positive electrode and the negative electrode, and that depends on current I, and includes the above.

[0010] The program of the present disclosure causes one or more computers to implement the steps of the above-described evaluation method.

Effects of the Invention

[0011] In the evaluation device, evaluation method, and program of the present disclosure, it is possible to evaluate a power storage device with higher accuracy. The reason for obtaining such an effect is presumed as follows. For example, in a transmission line model, inside the electrode of a power storage device, there is a two-layer circuit structure consisting of an ion conduction medium part where ions with a corresponding resistance being an ion resistance flow and a solid part where electrons with a corresponding resistance being an electron resistance flow. Also, since the carrier of the current switches from ions to electrons due to the electrode reaction, the ion resistance and the electron resistance are connected by an interfacial resistance. Conventionally, for the sake of simplifying the circuit, this interfacial resistance has been modeled as a transmission line model in which the charge transfer resistance of the interfacial resistance is approximated by a constant independent of the discharge current. However, the internal resistance depends on the current, for example, at the start of discharge, and there may be an error in the internal resistance between the experiment and the battery simulation. In the present disclosure, by introducing a reaction resistance dependent on the current and a film resistance independent of the current into the charge transfer resistance and applying it to the transmission line model, the evaluation accuracy can be further improved.

Brief Description of the Drawings

[0012]

Figure 1

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Embodiments for Carrying Out the Invention

[0013] (Evaluation Device) Embodiments of the evaluation device disclosed in this specification will be described below with reference to the drawings. FIG. 1 is a schematic explanatory diagram showing an example of the evaluation device 20. FIG. 2 is an explanatory diagram showing an example of the structure of the power storage device 10. FIG. 3 is an explanatory diagram showing an example of a three-dimensional electrode model, FIG. 3A is a conceptual diagram of a three-dimensional battery in which the positive and negative electrodes are not flat plates, and FIG. 3B is a circuit diagram considering the structure of FIG. 3A. FIG. 4 is a schematic diagram of the electrode reaction in a three-dimensional battery structure. The evaluation device 20 may be configured, for example, as a device that evaluates the internal resistance of the power storage device 10 by calculation.

[0014] The power storage device 10 includes, for example, a hybrid capacitor, a pseudo electric double layer capacitor, an alkali metal secondary battery such as lithium or sodium, an alkali metal ion battery, an air battery, and the like. Among these, as the power storage device 10, a lithium secondary battery, particularly a lithium ion secondary battery is preferable. Here, the power storage device 10 will be mainly described as being a lithium ion secondary battery. The power storage device 10 may include, for example, a positive electrode 12, a negative electrode 15, and an ion conductive medium 18 interposed between the positive electrode 12 and the negative electrode 15. The ion conductive medium 18 may be composed of, for example, an electrolytic solution and a separator containing the electrolytic solution. Alternatively, the ion conductive medium 18 may be a solid electrolyte interposed between the positive electrode 12 and the negative electrode 15. The positive electrode 12 includes a current collector 14 and a positive electrode active material layer 13 formed on one surface of the current collector 14. The positive electrode active material layer 13 may contain a positive electrode active material and, if necessary, may further contain a conductive material and a binder. Examples of the positive electrode active material include sulfides containing a transition metal element, composite oxides containing lithium and a transition metal element, and phosphate compounds containing iron. The positive electrode active material has, for example, a basic composition formula of Li (1-x) MnO2 (0 < x < 1, etc., the same hereinafter) or Li (1-x) Mn2O4 and other lithium manganese composite oxides, a basic composition formula of Li (1-x) CoO2 and other lithium cobalt composite oxides, a basic composition formula of Li (1-x) NiO2 and other lithium nickel composite oxides, a basic composition formula of Li (1-x) Ni a Co b Mn cLithium nickel cobalt manganese composite oxides such as O2 (a + b + c = 1) can be used. In addition, examples of the positive electrode active material include lithium iron phosphate. Note that the "basic composition formula" means that other elements may be included. The negative electrode 15 includes a current collector 17 and a negative electrode active material layer 16 formed on one surface of the current collector 17. The negative electrode active material layer 16 contains a negative electrode active material and may further contain a conductive material and a binder as necessary. Examples of the negative electrode active material may include metallic lithium and its alloys, carbon materials, composite oxides containing lithium, and the like. The negative electrode active material includes, for example, lithium, lithium alloys, inorganic compounds such as tin compounds, carbon materials capable of occluding and releasing lithium ions, composite oxides containing a plurality of elements, conductive polymers, and the like. Examples of the carbon materials include cokes, glassy carbons, graphites, non-graphitizable carbons, pyrolytic carbons, carbon fibers, and the like. Among these, graphites such as artificial graphite and natural graphite are preferred. Examples of the composite oxides include lithium titanium composite oxides and lithium vanadium composite oxides. The separator may contain, for example, an electrolytic solution in which a supporting salt is dissolved. Examples of the supporting salt include lithium salts such as LiPF6 and LiBF4. Solvents for the electrolytic solution include, for example, carbonates, esters, ethers, nitriles, furans, sulfolanes, and dioxolanes, and these can be used alone or in combination. Specifically, examples of the carbonates include cyclic carbonates such as ethylene carbonate, propylene carbonate, vinylene carbonate, butylene carbonate, and chloroethylene carbonate, and chain carbonates such as dimethyl carbonate, ethyl methyl carbonate, diethyl carbonate, ethyl-n-butyl carbonate, methyl-t-butyl carbonate, di-i-propyl carbonate, and t-butyl-i-propyl carbonate. Further, as the ion conduction medium 18, a solid ion conductive polymer, an inorganic solid electrolyte, a mixed material of an organic polymer electrolyte and an inorganic solid electrolyte, or an inorganic solid powder bound by an organic binder can be used.

[0015] The evaluation device 20 is a device that evaluates the power storage device 10 having the positive electrode 12 and the negative electrode 15. This evaluation device 20 may, for example, evaluate the internal resistance, cell energy, etc. of the power storage device 10 having a predetermined battery structure including the distributions of the positive electrode 12 and the negative electrode 15 using the transmission line model 24. The evaluation device 20 includes a control unit 21, a storage unit 22, an input device 38, and a display device 39. The control unit 21 is configured as a microprocessor centered on a CPU and controls the entire device. The storage unit 22 is configured as a large-capacity storage device such as an HDD, for example, and stores an evaluation program 23, a transmission line model 24, etc. The input device 38 includes a mouse, a keyboard, etc. that perform various inputs. The display device 39 displays a screen and is, for example, a liquid crystal display.

[0016] The control unit 21 executes the evaluation of the power storage device 10 using the transmission line model 24 including the electronic resistance 27, the ionic resistance 28, and the interfacial resistance 29 including the charge transfer resistance 30 at the positive electrode 12 and the negative electrode 15. The transmission line model 24 is constructed as a model considering the influence of the three-dimensional battery structure for the purpose of evaluating the internal resistance of the power storage device 10. This transmission line model 24 is a three-dimensional porous electrode model (3D-PEM) that replaces the complex reactions in the battery with a simple circuit diagram, and it is possible to execute the evaluation of the power storage device 10 such as the internal resistance at high speed compared with the so-called battery simulation using a continuum model that solves the time evolution of the reactions in the battery. This evaluation device 20 may be configured to evaluate the internal resistance immediately after discharge where the contribution of the diffusion resistance is low. In the evaluation in this region, since the interfacial resistance 29 greatly depends on the charge transfer resistance 30, the interfacial resistance 29 can be approximated to the charge transfer resistance 30 and applied to the transmission line model 24 for handling. Here, by reflecting the current-dependent reaction resistance 31 and the film resistance 32 in the charge transfer resistance 30, the internal resistance can be evaluated with higher evaluation accuracy.

[0017] As shown in FIG. 3, the transmission line model 24 has a structure in which the positive electrode 12 and the negative electrode 15 are blocked, and an electronic resistance 27, an interfacial resistance 29, and an ionic resistance 28 are connected to each block. This transmission line model 24 is defined as a two-layer circuit in which an electronic resistance 27 is connected between each block for the solid part through which electrons conduct, and an ionic resistance 28 is connected between each block for the ionic conductive medium part through which ions conduct. The electronic resistance 27 and the ionic resistance 28 are connected by an interfacial resistance 29 so that the movement of ions and electrons is switched by an electrode reaction. Further, the transmission line model 24 has a structure in which it is connected by an ionic resistance 28 between the positive electrode block 25 and the negative electrode block 26 separated by the ionic conductive medium 18. As shown in FIG. 4, this transmission line model 24 includes a charge transfer resistance 30 in which a reaction resistance 31 and a film resistance 32 are connected in series. In the transmission line model 24, black circles or white circles within the divided elements represent the centers of the respective elements, and the centers of the elements are connected by resistances. Since this model models a porous electrode, the inside of the electrode has a two-layer circuit structure of an ionic conductive medium part through which ions corresponding to the ionic resistance flow and a solid part through which electrons corresponding to the electronic resistance flow. Also, since the current carrier switches from ions to electrons due to the electrode reaction, the ionic resistance 28 and the electronic resistance 27 are connected by the interfacial resistance 29. So far, in 3D-PEM, the internal resistance of the battery cell has been evaluated using three types of resistances: the electronic resistance 27, the ionic resistance 28, and the interfacial resistance 29. However, there was concern that the error was large compared to the internal resistance evaluated by experiments and continuum models. For this reason, in the evaluation device 20, a reaction resistance 31 that depends on the current is introduced into the 3D-PEM.

[0018] Note that it is necessary to note that the interfacial resistance 29 is connected between the node of the electronic resistance and the node of the ionic resistance on the same coordinates in FIG. 3A. For a lithium-ion battery that uses, for example, an electrolytic solution, since the electrolytic solution penetrates into the porous electrode, in order to handle it accurately, the positive electrode and the negative electrode in FIG. 3A need to represent a structure in which the electrode part and the part of the electrolytic solution that has penetrated are intricately intertwined at the micro level (see, for example, FIG. 4). Since it is difficult to handle it as it is, in this model, the specific structural information, for example, the information on the interface between the electrode solid and the electrolytic solution is eliminated, and an approximation is made that the electrolytic solution and the electrode material exist on the same space on average at a specified ratio. Note that the mainstream continuum models of lithium-ion batteries, including the above-mentioned reference documents such as Patent Document 1 and Non-Patent Document 1, also handle it in the same way. Under that approximation, the coordinates of the center (node) of each element in FIG. 3A are the coordinates of the actual battery (real space coordinates), but the nodes for ionic resistance and the nodes for electronic resistance connected by the interfacial resistance in FIG. 3B represent the same coordinates in real space. That is, both the nodes for ions and the nodes for electrons represent the same corresponding nodes in FIG. 3A. Note that the interface between the electrode part and the electrolytic solution part is defined by the area (and resistivity) of the interface between the electrolytic solution and the electrode averaged within the element, and since that information is averaged, it is not shown in FIG. 3A.

[0019] The 3D-PEM extends the transmission line model (TLM) used in the analysis of porous electrodes in a normal flat-plate facing structure disclosed, for example, in Reference 1 (Ogihara et al., J. Electrochem. Soc., 159, A1034 (2012)). In 3D-PEM, first, as shown in Fig. 3A, the three-dimensional battery is divided into elements, and an equivalent circuit is created by connecting the centers of those elements with resistors as shown in Fig. 3B. Here, by dividing the elements to reflect the structural features, it becomes possible to evaluate the internal resistance considering the effect of the three-dimensional structure of the electrode. Here, these divided elements are also referred to as electrode elements. In a porous electrode used in a general lithium-ion battery or the like, the electrolyte penetrates into the electrode, and reactions occur within the electrode. To represent this, in the transmission line model 24, two types of circuits, an electron resistance (resistance of the solid part inside the electrode) represented by thin lines and an ion resistance (resistance of the liquid part inside the electrode) represented by thick lines, are arranged within the electrode and connected by an interface resistance represented by a square. Here, the content of the interface resistance varies depending on the phenomenon to be modeled and the purpose of the analysis (internal resistance evaluation or impedance analysis). For example, when evaluating the internal resistance assuming only a charge transfer reaction, it becomes a charge transfer resistance.

[0020] So far, in 3D-PEM, the internal resistance of the battery cell has been evaluated using three types of resistances: electron resistance, ion resistance, and charge transfer resistance (as the interface resistance). However, since the charge transfer resistance, which originally depends on the discharge current, was approximated as a constant ignoring its contribution, there is concern that the error becomes large compared to the internal resistance evaluated by experiments or continuum models, especially when the reaction resistance at the electrode / electrolyte interface is large. Therefore, the charge transfer resistance was improved to be current-dependent. When evaluating the internal resistance R inter 3D-PEM using 3D-PEM, the ion resistance R ion and the electron resistance R e are required. The ion resistance R ct and the electron resistance R ion connecting electrode elements of the same type (e.g., between positive electrodes) e, and the resistance between the same current collector elements is evaluated by the following formula (1). Here, ρ is the ionic resistivity ρ ion or the electronic resistivity ρ e represents, and l and a represent the length and cross-sectional area of the resistance connecting the centers of the two electrode elements.

[0021] The ionic resistance at the positive / negative electrode interface is defined by the following formula (2). Here, s is the thickness of the separator, ρ ion pos , ρ ion neg , and ρ ion sep represent the ionic resistivities of the positive electrode, negative electrode, and separator, respectively. Here, ρ ion pos , ρ ion neg , and ρ ion sep are affected by the properties of the electrode and separator such as the curvature, and it should be noted that they are different from the ionic resistivity of the bulk electrolyte. The charge transfer resistance is defined as in the following formula (4). Here, ρ ct area and A reac represent the reaction resistivity (Ωcm 2 ) and the reaction surface area at the interface between the active material and the electrolyte in the electrode. Assume that the reaction surface area can be calculated as in the following formula (3). Here, V is the volume of one electrode element excluding the volume of the separator, and c is a constant that converts the reaction surface area and the electrode volume. By substituting formula (3) into formula (4), formula (5) is obtained. Here, ρ ct (=ρ ct area / c) is called the charge transfer resistivity, and its unit is Ωcm 3 . From the above, the ionic resistivity ρ ion , the electronic resistivity ρ e , and the charge transfer resistivity ρ ctIf it is obtained as a material parameter, the internal resistance can be evaluated. For further details on 3D-PEM, refer to the literature (Miyamoto et al., iScience, 23, 101317(2020).) and its Supplemental Information. In this reference, ρ ct is a constant and does not depend on the current.

[0022] Figure 4 shows a schematic diagram of the electrode reaction in a three-dimensional battery. Figure 4 shows a comb structure, which is one type of three-dimensional battery, and an enlarged view of the negative electrode / separator interface. Note that the left and right comb teeth represent the positive and negative electrodes, respectively, and the white region between the positive and negative electrodes is the separator. In a lithium-ion battery, a porous electrode is usually used. As shown in the enlarged view, the electrode region consists of a region of a composite electrode containing an active material and a region of an electrolyte solution, and the electrode reaction occurs at the interface. In addition, graphite, which is widely used as the negative electrode of a lithium-ion battery, has a low charge / discharge potential. Therefore, it is known that a film (Solid electrolyte interphase: SEI) is formed at the interface between the electrode and the electrolyte solution by the reduction decomposition of the electrolyte solution during the first charge. It is also known that a film may be formed at the interface between the positive electrode and the electrolyte solution. Focusing on the reaction in the negative electrode region during charge and discharge, during charging, lithium ions in the electrolyte solution reach the electrode surface, receive electrons there, and then are inserted into the electrode active material. On the other hand, during discharging, lithium existing in the electrode active material loses electrons on the electrode surface and is released as ions into the electrolyte solution. Considering that the film is passed through when the electrode active material and the electrolyte solution go back and forth during both charging and discharging, the interface resistance R ct of the electrode / electrolyte solution can be modeled as a series connection of a reaction resistance and a film resistance as shown in the following equation (6). Here, R reac and R film are the reaction resistance and the film resistance, respectively.

[0023] In 3D-PEM, as shown in equation (5), since R ct = ρ ct / V, R reac and R filmSimilarly, it can be written as equations (7) and (8). Here, ρ reac and ρ film represent the reaction resistivity and the film resistivity respectively, and from equations (5) to (8), ρ ct =ρ reac +ρ film is derived. Therefore, if ρ reac and ρ film are determined, ρ ct is determined, so it becomes possible to evaluate the internal resistance with 3D-PEM. The method for determining ρ film is, for example, as shown in J. Electrochem. Soc., 143, 1890 (1996). As material physical property parameters, the film resistance ρ film area per unit reaction surface area is given as a constant. Using this, R film can be written as in equation (9) by the same discussion as in equations (3) to (5). Solving this equation for ρ film results in equation (10), and if the ratio of V and A reac is known, ρ film can be obtained. As an example, when assuming that the active material is an aggregate of spheres with radius r s , A reac =3ε s V / r s , so equation (11) is obtained. Here, ε s is the volume ratio of the solid in the electrode. ρ film is a constant and does not depend on the current.

[0024] ρ reac As a method for determining ρ reacSince it is obtained by differentiating the overvoltage η with respect to the interfacial current I, Equation (15) is obtained. Here, the current I flowing through the electrode / electrolyte interface is, according to the law of conservation of current, the charge / discharge current I ext which is consistent with, and the exchange current I0 can be written as I0 = i0A reac using this fact. From the correspondence with Equation (7), Equation (16) is obtained. Assuming that the active material is spherical, ρ film by the same discussion as above, Equation (17) can be obtained. Equations (15) and (16) depend on the current I ext therefore, the reaction resistivity ρ reac , that is, ρ ct can be defined in a current-dependent form. Note that when the asymmetric parameter α is not 0.5, or when the relationship between the interfacial current I and the overvoltage η is not expressed by the Butler-Volmer equation, ρ reac may not be analytically obtained. However, even in such cases, by evaluating the current I with respect to the overvoltage η and calculating the reciprocal of its numerical differentiation, ρ reac can be obtained. An example of such a calculation will be described in detail later (Figure 11). Note that a general method for evaluating the reaction resistivity ρreac is to obtain the resistance after linearly approximating Equation (12) or Equation (13) of the Butler-Volmer equation. Assuming that the active material is spherical, Equation (18) is obtained. In Equation (18), LFA means low field assumption, and ρ reac LFA is a constant independent of current.

[0025]

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[0026]

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[0027] In the evaluation device 20, based on the above definition, the control unit 21 uses a transmission line model 24 including an electron resistance 27, an ion resistance 28, and an interface resistance 29 in the positive electrode 12 and the negative electrode 15 to execute the evaluation of the power storage device 10. This evaluation device 20 is assumed to evaluate the power storage device 10, for example, in a region where the interface resistance 29 depends on the charge transfer resistance 30. In this transmission line model 24, an evaluation is executed with the charge transfer resistance 30 including a reaction resistance 31 and a film resistance 32, which are obtained by differentiating the function of the overvoltage η with respect to the current I for the power storage device 10 and depend on the current I, as the interface resistance 29. The transmission line model 24 may include a charge transfer resistance 30 in which the reaction resistance 31 and the film resistance 32 are connected in series. As shown in FIG. 3, the transmission line model 24 may have a structure in which the positive electrode 12 and the negative electrode 15 are blocked and the electron resistance 27, the ion resistance 28, and the charge transfer resistance 30 as the interface resistance 29 are connected to each block. This transmission line model 24 is defined as a two-layer circuit in which the electron resistance 27 is connected between the blocks for the solid part through which electrons conduct, and the ion resistance 28 is connected between the blocks for the ion conductive medium part through which ions conduct. It may have a structure in which the ion resistance 28 and the electron resistance 27 are connected by the charge transfer resistance 30 so that the movement of ions and electrons is switched by the electrode reaction. Further, the power storage device 10 includes an ion conductive medium 18 between the positive electrode 12 and the negative electrode 15, and the transmission line model 24 may have a structure in which the positive electrode block 25 and the negative electrode block 26 separated by the ion conductive medium 18 are connected by the ion resistance 28. With such a structure, while defining a relatively simple structure, the accuracy of the evaluation result can be further improved.

[0028] In this transmission line model 24, the reaction resistance 31 is preferably defined by the Butler-Volmer equation. The Butler-Volmer equation is an equation for one-step one-electron transfer and is suitable for performing a continuum simulation of the power storage device 10. Further, in the reaction resistance 31, the asymmetric parameter α of the Butler-Volmer equation may be set to 0.5. When the asymmetric parameter α is 0.5, the redox reaction is estimated equally, and further, since the formula expansion when differentiating the function of the overvoltage η and the current I can be made easier, it is preferable. The Butler-Volmer equation is the above formula (12), and when α = 0.5, it becomes formula (13). Further, the reaction resistance 31 obtained by expanding this is formula (15). The film resistance 32 may be the resistance value per reaction surface area. Further, the film resistance 32 may be obtained by assuming that the active material contained in the positive electrode 12 and / or the negative electrode 15 is an aggregate of spheres. When the active material is a sphere, the film resistance 32 can be expressed by substituting formula (11) into the above formula (9).

[0029] (Evaluation method) Next, the processing of the evaluation device 20 of the present embodiment configured in this way, particularly the evaluation method executed by the evaluation device 20, will be described. This evaluation method is a method for evaluating the power storage device 10. This evaluation method may be, for example, a method for evaluating the internal resistance, cell energy, etc. of the power storage device 10 using the transmission line model 24 for a power storage device 10 having a predetermined battery structure including the distributions of the positive electrode and the negative electrode. This evaluation method includes a step of evaluating the power storage device 10 using the transmission line model 24 including the electron resistance 27, the ion resistance 28, and the interface resistance 29 in the positive electrode 12 and the negative electrode 15. In this transmission line model 24, the charge transfer resistance 30 including the reaction resistance 31 and the film resistance 32 obtained by differentiating the function of the overvoltage η and the current I with respect to the power storage device 10 and depending on the current I is evaluated as the interface resistance 29. Note that the transmission line model 24 and the formulas used for the evaluation use the contents of the power storage device 10 described above, and the detailed description thereof is omitted here.

[0030] A method for evaluating the internal resistance of a battery cell using 3D-PEM will be described. In the evaluation apparatus 20, the internal resistance of the battery cell is evaluated by the following process. Hereinafter, it is assumed that the electrode active material is composed of spheres of the same radius r s For the sake of argument, it is assumed that the electrode (the entire positive or negative electrode) is composed of spheres of radius r reac As a result, the ratio of the volume V to the reaction surface area A s of the electrode (the entire positive or negative electrode) is r s / 3ε s Here, ε (1) The electronic resistivity (ρ e [Ωcm]) and the ionic resistivity (ρ ion [Ωcm]) are obtained from the effective electronic conductivity and the effective ionic conductivity. This calculation method is detailed in Miyamoto et al., Cell Rep. Phys. Sci., 2, 100504 (2021). (2) Given material property parameters (for example, r s [m], ε s , and ρ film area [Ωm 2 ) in Table 1 described later are substituted into Equation (11) to obtain ρ film [Ωm 3 or Ωcm 3 . (3) Given material property parameters (for example, the exchange current density i0 and the exchange current I0) and the set discharge current I ext etc. are substituted into Equation (16) to obtain ρ reac [Ωm 3 or Ωcm 3 . (4) The charge transfer resistivity ρ ct [Ωm 3 or Ωcm 3 is obtained by ρ ct =ρ film +ρ reac . (5) The distances between the centers of each element in Fig. 3B and the cross-sectional area perpendicular thereto are known, and ρ e and ρ ionSince it is known, the ionic resistance R that connects between the centers of each element can be calculated using Equation (1) or the like. ion [Ω], or R e [Ω]) can be calculated. Also, the interfacial resistance R ct is the charge transfer resistance [Ω] within the scope of the present disclosure, while the R within each element ct [Ω] can be obtained by Equation (5) using ρ ct and the volume of each element.

[0031] As a result, the resistance connecting between the centers of all the elements in FIG. 3B could be determined. Once the resistance between the centers of the elements in FIG. 3B is determined, the internal resistance can be evaluated by a standard method such as the loop current method or the node voltage method (Reference: Circuit Analysis by Graph Theory by Kenshi Hukuto, Morikita Publishing Co., Ltd. (2014)). Since the internal resistance is the resistance between the current collector foil on the positive electrode side and the current collector foil on the negative electrode side in FIG. 3A, for example, when using the node voltage method, if the potentials V1 and V2 (FIG. 3B) of the nodes connected to the external power supply are obtained, the internal resistance can be evaluated by using Kirchhoff's second law or the like.

[0032] In the evaluation apparatus 20 and the evaluation method of the present embodiment described above, the power storage device can be evaluated with higher accuracy. The reason for obtaining such an effect is presumed as follows. For example, in the transmission line model 24, inside the electrode of the power storage device 10, it has a two-layer circuit structure of an ion conduction medium portion through which ions with an ionic resistance 28 flow and a solid portion through which electrons with an electronic resistance 27 flow. Also, since the current carrier switches from ions to electrons due to the electrode reaction, the ionic resistance 28 and the electronic resistance 27 are connected by the interfacial resistance 29. Conventionally, this interfacial resistance 29 has been modeled by approximating the charge transfer resistance 30 of the interfacial resistance 29 as a constant independent of the discharge current in order to simplify the circuit. However, at the start of discharge or the like, the internal resistance depends on the current, and there may be an error in the internal resistance between the experiment and the battery simulation. In the present disclosure, by introducing a reaction resistance 31 that depends on the current and a film resistance 32 that does not depend on the current into the charge transfer resistance 30 and applying it to the transmission line model 24, the evaluation accuracy can be further improved.

[0033] Note that the present disclosure is not limited to the above-described embodiments at all, and it goes without saying that the present disclosure can be implemented in various modes as long as it belongs to the technical scope of the present disclosure.

[0034] For example, in the above-described embodiments, the present disclosure has been described as an evaluation apparatus and an evaluation method, but it is not particularly limited thereto, and it may be a program for executing the evaluation method. This program causes one or a plurality of computers to realize each step of the above-described evaluation method. This program may be recorded on a computer-readable recording medium (for example, a hard disk, ROM, FD, CD, DVD, etc.), may be distributed from one computer to another computer via a transmission medium (a communication network such as the Internet or a LAN), or may be transferred in any other form.

[0035] The present disclosure may be any of the following [1] to

[17] . [1] An evaluation apparatus for evaluating a power storage device including a positive electrode and a negative electrode, a control unit that executes the evaluation of the power storage device using a transmission line model including an electron resistance, an ion resistance, a charge transfer resistance including a reaction resistance and a film resistance obtained by differentiating a function of an overvoltage η and a current I with respect to the current I, which depends on the current I, in the positive electrode and the negative electrode; An evaluation apparatus comprising the same. [2] The evaluation apparatus according to [1], wherein the transmission line model includes the charge transfer resistance in which the reaction resistance and the film resistance are connected in series. [3] The evaluation apparatus according to [1] or [2], wherein the transmission line model has a structure in which the positive electrode and the negative electrode are blocked and the electron resistance, the ion resistance, and the charge transfer resistance are connected to each block. [4] The transmission line model is defined as a two-layer circuit in which the electron resistance is connected between blocks for the solid part through which electrons conduct, and the ion resistance is connected between blocks for the ion-conducting medium part through which ions conduct, and has a structure in which the ion resistance and the electron resistance are connected by the charge transfer resistance so that the movement of ions and electrons is switched by an electrode reaction, the evaluation apparatus according to [3]. [5] The power storage device includes an ion-conducting medium between the positive electrode and the negative electrode. The transmission line model has a structure in which it is connected by the ion resistance between a positive electrode block and a negative electrode block separated by the ion-conducting medium, the evaluation apparatus according to [3] or [4]. [6] The transmission line model has the reaction resistance obtained from the Butler-Volmer equation introduced therein, the evaluation apparatus according to any one of [1] to [5]. [7] The transmission line model has the reaction resistance introduced using an equation in which the asymmetric parameter α of the Butler-Volmer equation is set to 0.5, the evaluation apparatus according to [6]. [8] The transmission line model has the film resistance introduced by assuming that the active material contained in the positive electrode and / or the negative electrode is an aggregate of spheres, the evaluation apparatus according to any one of [1] to [7]. [9] An evaluation method for performing evaluation of a power storage device including a positive electrode and a negative electrode, performing the evaluation of the power storage device using a transmission line model including a charge transfer resistance including an electron resistance, an ion resistance, a reaction resistance and a film resistance that are obtained by differentiating a function of the overvoltage η and the current I with respect to the electron resistance and the ion resistance in the positive electrode and the negative electrode and that depend on the current I. An evaluation method including this.

[10] The transmission line model includes the charge transfer resistance in which the reaction resistance and the film resistance are connected in series, the evaluation method according to [9].

[11] The transmission line model has a structure in which the positive electrode and the negative electrode are blocked and the electron resistance, the ion resistance, and the charge transfer resistance are connected to each block, the evaluation method according to [9] or

[10] .

[12] The transmission line model is defined as a two-layer circuit in which the electron resistance is connected between blocks for the solid part through which electrons conduct, and the ion resistance is connected between blocks for the ion-conductive medium part through which ions conduct, and has a structure in which the ion resistance and the electron resistance are connected by the charge transfer resistance so that the movement of ions and electrons is switched by an electrode reaction, the evaluation method according to

[11] .

[13] The power storage device includes an ion-conductive medium between the positive electrode and the negative electrode, The transmission line model has a structure in which it is connected by the ion resistance between the positive electrode block and the negative electrode block separated by the ion-conductive medium, the evaluation method according to

[11] or

[12] .

[14] The transmission line model has the reaction resistance obtained from the Butler-Volmer equation introduced therein, the evaluation method according to any one of [9] to

[13] .

[15] The transmission line model has the reaction resistance introduced using an equation with the asymmetric parameter α of the Butler-Volmer equation set to 0.5, the evaluation method according to

[14] .

[16] The transmission line model has the film resistance introduced by assuming that the active material contained in the positive electrode and / or the negative electrode is an aggregate of spheres, the evaluation method according to any one of [9] to

[15] .

[17] A program that causes one or more computers to implement the steps of the evaluation method according to any one of [9] to

[16] .

Example

[0036] Hereinafter, an example in which the evaluation method and evaluation device of the present disclosure are specifically examined will be described as an experimental example.

[0037] (Evaluation conditions) To evaluate the effects of the present invention, for a three-dimensional lithium-ion battery, the error in the internal resistance evaluated by 3D-PEM with respect to the internal resistance evaluated from the discharge calculation of the continuum model was evaluated. Furthermore, as reported in Reference 1 (Miyamoto et al., Cell Rep. Phys. Sci., 2, 100504 (2021)), by using the internal resistance of this 3D-PEM as one of the characteristic quantities, a model for predicting the energy, which is an important characteristic of the 3D battery, can be created. Therefore, the accuracy of the energy prediction model was also evaluated. Regarding the materials to be used, a first battery with a combination of lithium iron phosphate (LFP) and lithium titanate (LTO) as the positive electrode active material and a second battery with graphite as the negative electrode active material were used. The electrolyte was a polymer electrolyte obtained by mixing a solution of LiPF6 dissolved in a (EC + DMC) solvent mixed at a volume ratio of 1:2 at a concentration of 1.0 M with a polymer. These material property parameters are summarized in Tables 1 to 3. (1-x) Ni a Mn b Co c O2 (NMC532: a = 0.5, b = 0.3, c = 0.2) and a second battery with graphite as the negative electrode active material were used.

[0038] FIG. 5 is an explanatory diagram of an example of structure generation conditions for generating a three-dimensional battery structure. FIG. 6 is an explanatory diagram of the three-dimensional battery structure generated using the structure generation conditions. This FIG. 5 shows the structure generation conditions when the 3D battery structure of FIG. 6 is generated by an Automatic geometry generator. As shown in FIG. 5, the dimensions of the three-dimensional battery are 3000 μm × 600 μm × 3000 μm, and the design resolution of the structure is 50 × 10. Inside this cell, the volume ratio of the positive and negative electrodes is 5:5, and only within the dotted frame is considered as the design freedom. The lower half is determined by periodicity, that is, the structure of the upper half is copied. The rectangular parallelepiped on the left represents the positive electrode, and the rectangular parallelepiped on the right represents the negative electrode. Also, the positive and negative electrodes are separated by a separator, and its thickness is set to 20 μm. The current collector foil is installed on the side surface, and its area is length × depth = 3000 μm × 3000 μm). Here, the structure shown in FIG. 6 was taken as the calculation target. These are one of the 50,000 structures generated using an Automatic geometry generator under the calculation conditions of FIG. 5 in Non-Patent Document 1.

[0039] Also, as the calculation conditions for the continuum simulation, the temperature was set to T = 298K. Regarding the discharge current, the reference current I ext = 3.16 mA / cm 2 is referred to as 1C Ref. and for the three-dimensional battery composed of LFP / LTO, simulations were performed at 1C Ref. -4C Ref. (where 4C Ref. represents a current amount 4 times that of 1C Ref. ). Also, for the three-dimensional battery composed of NMC532 / Graphite, simulations were performed at 1C Ref. -4C Ref. . The resistance parameters of 3D-PEM were calculated from the material parameters in Tables 1 to 3 (and ρ reac is the discharge current), and the values are summarized in Tables 4 to 5. Regarding the calculation conditions of other continuum models and the creation method of the energy prediction model, refer to the results described later and Reference 1.

[0040] Table 1 summarizes the physical property parameters of the composite electrodes when LFP and LTO are used as active materials. In addition to these parameters, the open circuit potential (OCP) of LFP and LTO is required, and the functions in Reference 2: J. Appl. Electrochem., 47, 281 (2017), and Reference 3: J. Electrochem. Soc., 155, A253 (2008) were used. Table 2 summarizes the physical property parameters of the composite electrodes when NMC532 and Graphite are used as active materials. In addition to these parameters, the OCP of NMC532 and Graphite is required, and the functions in Reference 4: J. Electrochem. Soc., 166, A1412 (2019), and Reference 5: J. Power Sources, 185, 1398 (2008) were used. Table 3 summarizes the physical property parameters of the electrolyte (LiPF6 / 1EC2DMC and PVdF-HFP). In addition to these parameters, a function of conductivity is required, and the function in Reference 6: J. Electrochem. Soc., 143, 1890 (1996) was used. Table 4 summarizes the resistance parameters of the 3D-PEM when the positive and negative active materials are LFP and LTO, respectively. Here, the ionic resistivity of the separator was set to 348.07 [Ωcm]. Table 5 summarizes the resistance parameters of the 3D-PEM when the positive and negative active materials are NMC532 and Graphite, respectively. Here, the ionic resistivity of the separator was set to 584.70 [Ωcm]. Table 6 summarizes the comparison of the internal resistance depending on the current amount of the battery composed of LFP and LTO as the positive and negative active materials. C rate is xC Ref. = x × 3.16 [mA / cm 2 . Also, LFA is the result when Equation (18), that is, ρ reac does not depend on the external current. Table 7 summarizes the comparison of the internal resistance depending on the current amount of the battery composed of NMC532 and Graphite as the positive and negative active materials. C rate is xC Ref. = x × 3.16 [mA / cm 2 . Also, LFA is Equation (18), that is, ρ reacThis is the result when it does not depend on the external current.

[0041] (Accuracy of the energy prediction model) Using the internal resistance calculated using the present disclosure as one of the feature quantities, a model for predicting the energy of a three-dimensional battery was created by principal component regression, and its accuracy was evaluated. This regression model was created according to the procedure for creating a regression model when the positive and negative electrode volume ratios are 5:5 in Reference 1, and its performance evaluation method also follows the procedure of this document. The differences between the regression model creation method of this document and the present study are the following two points. (1) The internal resistance evaluated by 3D-PEM used as a feature quantity is calculated by the present invention. (2) As a feature quantity representing one structure, in addition to the 14 types of values described in Reference 1, the distance between each node defined in FIG. 3A and the counter electrode node at the shortest distance, and the average, variance, and standard deviation of the square thereof were added. These values were obtained by evaluating the distance between each node defined in FIG. 3A and the counter electrode node at the shortest distance and its squared value for all nodes of the positive and negative electrodes, and calculating the average, variance, and standard deviation thereof.

[0042] Figure 7 is a diagram showing the result of energy prediction at 1C of a three-dimensional battery structure composed of LFP and LTO. Figure 8 is a diagram showing the result of energy prediction at 4C of a three-dimensional battery structure composed of LFP and LTO. In Figures 7 and 8, True energy represents the energy evaluated by the continuum model, and predicted energy represents the energy predicted by the regression model. The black diamonds represent the training data, and the circles represent the test data. This regression model was created according to the method for generating the regression model when the positive and negative electrode volume ratios are 5:5 in Reference 1, and the accuracy evaluation method also follows this document. The difference in the generation of this regression model for this document is that the internal resistance used as one of the feature quantities is obtained from the present invention, and in addition to the feature quantities used in Reference 1, the average value, variance, and standard deviation of the minimum value of the distance between the counter electrode nodes in Figure 3A and its square value are newly added as feature quantities. Also, the number of training data at 4C is 49 instead of 50 in the document. This is because the calculation of the continuum model of one structure failed, so that point was excluded. Also, R 2 (train.), R 2 (test), and N PC are the coefficient of determination in the training data, the coefficient of determination in the test data, and the number of principal components used in the principal component regression model, respectively. As shown in Figures 7 and 8, it was found that a highly accurate prediction model with an R 2 value of 0.955 or more was obtained for both the training data and the test data at both 1C and 4C current rates.

[0043] Figure 9 is a diagram showing the result of energy prediction at 1C of a three-dimensional battery structure composed of NMC532 and graphite. Figure 10 is a diagram showing the result of energy prediction at 4C of a three-dimensional battery structure composed of NMC532 and graphite. Except that both regression models in Figure 9A and Figure 10B use the 50 structures described in Reference 1 as training data, the generation method and its performance evaluation method are the same as those in Figures 7 and 8. As shown in Figures 9 and 10, here too, similar to Figures 7 and 8, the R 2It has been clarified that an extremely high-precision prediction model with a value of 0.988 or more has been created.

[0044] (Comparison of internal resistance) Next, the internal resistance (R ext ) of the 3D-PEM that depends on the current I inter 3D-PEM was compared with the internal resistance (R inter CM ) at the initial stage of discharge evaluated from the corresponding continuum model. Here, the reason for using the internal resistance at the initial stage of discharge as the comparison target is that at the initial stage of discharge, there is no resistance caused by diffusion resistance (not considered in this 3D-PEM), so the I ct dependency of the interfacial resistance R ext can be clearly evaluated. Note that R inter CM can be calculated by dividing the overvoltage of the battery at the very beginning of the simulation (the difference between the open-circuit voltage and the actual battery voltage) by I ext . The evaluated three-dimensional battery structure is shown in Fig. 6.

[0045] (Results of the first battery with LFP and LTO as the positive and negative electrode active materials) The current dependency of the internal resistance of the three-dimensional battery was evaluated when the positive and negative electrode active materials were LFP and LTO, respectively (Table 6). From the values of ρ reac of the positive and negative electrodes when the C rate in this table is 1-4, it was confirmed that ρ reac decreases as the current amount increases. That is, it was confirmed that ρ reac changes depending on the external current amount. Subsequently, the internal resistance R inter 3D-PEM of the battery evaluated by 3D-PEM was compared with the internal resistance R inter CM at the initial stage of discharge evaluated by the continuum model, and it was found that the two were in good agreement. When evaluated by LFA, since the R inter 3D-PEM in Equation (17) has a large error of 200 Ω or more with respect to the value of the continuum model, the effectiveness of the present disclosure could be confirmed.

[0046] (Results of a battery composed of NMC532 and Graphite as the positive and negative electrode active materials) The current dependence of the internal resistance of a three-dimensional battery was evaluated when the positive and negative electrode active materials were NMC532 and Graphite, respectively (Table 7). Similar to Table 6, it was confirmed how ρ reac changes with the external current amount, and R inter 3D-PEM showed that the error with respect to R inter CM was smaller for the present invention compared to the case of LFA. From the comparison between Table 6 and Table 7, it was found that when the positive and negative electrode active materials are NMC532 and Graphite, the current dependence of ρ reac is small. However, since such dependence depends on reaction resistance, material concentration, particle radius, volume ratio of solid components in the composite electrode, etc., it was speculated that it is difficult to predict in advance. Therefore, it was speculated that this disclosure, which enables internal resistance evaluation for any material system without the need for such prior consideration, is particularly important for material exploration.

[0047] (Method for numerically obtaining ρ reac ) ρ reac will be obtained numerically instead of using the analytical formula (16), and the method will be described below. In this example, the ρ Ref. at 1C Ref. and 4C reac of LFP in Table 6 will be obtained step by step. In that case, the relational expression between the interfacial current I and the overvoltage η used when deriving formula (16) is formula (13). First, I is plotted against η using formula (13). Figure 11 is a relational diagram plotting the interfacial current I against the overvoltage η. In this example, for formula (13), plot points were obtained using the material parameters of LFP (I0 = 7.06×10 -5 [A]) and a temperature of T = 298K. Specific plot points are the data at 1C Ref. and 4C Ref. in Table 6. Also, the dashed line is the tangent at these points. The numerical differentiation of the interfacial current I with respect to the overvoltage η (approximate dI / dη) shall be obtained using the standard central difference method with points on the left and right of the specific point. From Figure 11, when the interfacial current I is at 1CRef. and 4C Ref. for the discharge current I ext search for the overvoltage η that matches. Note that the discharge current I ext matching the interface current I is based on the current conservation law. Also, since the area of the current collector foil in this example (Figure 6) is 0.09 cm 2 , for example, 1C in Figure 11 Ref. of I ext = 0.000284 [A] becomes 3.16 [mA / cm 2 . Next, numerically differentiate the data points corresponding to the found 1C Ref. and 4C Ref. (dI / dη). Figure 11 shows the results calculated using the standard central difference method using the data of the points to the left and right of a specific circle. Next, the reciprocal of dI / dη is R reac [Ω]. That is, when dI / dη = 6.1716×10 -3 , R reac = 1 / (6.1716×10 -3 ) = 162.03 [Ω]. Next, use Equation (7) to obtain ρ reac [Ω] from R reac . In the case of Figure 6, since the volume of the positive electrode is 2.2518×10 -9 [m 3 , the ρ Ref. for 1C reac is 0.3649 [Ωcm 3 , and the ρ Ref. for 4C reac is 0.1011 [Ωcm 3 . These values match the values obtained by the analytical formula (16) in Table 6. Thus, in the case of this method, an analytical formula such as Equation (16) is not necessary, and as long as I can be plotted against η as in Figure 11, ρ reac can be obtained without defining the asymmetric parameter α to 0.5. On the other hand, the merits of using the analytical formula (16) are the following two points. The first is that it is simpler than the numerical solution method, and the second is that the value is accurate. Note that in this example, although the values match in the number of digits shown, the numerical solution method is an approximate formula and it is necessary to note that there are errors included.

[0048]

Table 1

[0049]

Table 2

[0050]

Table 3

[0051]

Table 4

[0052]

Table 5

[0053]

Table 6

[0054]

Table 7

[0055] Note that the evaluation device, evaluation method, and program disclosed in this specification are not limited to the above-described embodiments at all, and it goes without saying that they can be implemented in various modes as long as they belong to the technical scope of the present disclosure.

Industrial Applicability

[0056] The evaluation device, evaluation method, and program disclosed in this specification can be used in the technical field of evaluating the characteristics of power storage devices.

Description of Reference Numerals

[0057] 10 Energy storage device, 12 Positive electrode, 13 Positive electrode active material layer, 14 Current collector, 15 Negative electrode, 16 Negative electrode active material layer, 17 Current collector, 18 Ion conductive medium, 20 Evaluation device, 21 Control unit, 22 Memory unit, 23 Evaluation program, 24 Transmission line model, 25 Positive electrode block, 26 Negative electrode block, 27 Electronic resistance, 28 Ion resistance, 29 Interface resistance, 30 Charge transfer resistance, 31 Reaction resistance, 32 Film resistance, 38 Input device, 39 Display device.

Claims

1. An evaluation device for evaluating a power storage device having a positive electrode and a negative electrode, comprising: a control unit that performs evaluation of the power storage device using a transmission line model including an electron resistance, an ion resistance, a charge transfer resistance including a reaction resistance and a film resistance that are obtained by differentiating a function of the overvoltage η and the current I and that depend on the current I, in the positive electrode and the negative electrode; An evaluation device comprising:

2. The evaluation device according to claim 1, wherein the transmission line model includes the charge transfer resistance in which the reaction resistance and the film resistance are connected in series.

3. The evaluation device according to claim 1 or 2, wherein the transmission line model has a structure in which the positive electrode and the negative electrode are blocked and the electron resistance, the ion resistance, and the charge transfer resistance are connected to each block.

4. The evaluation device according to claim 3, wherein the transmission line model is defined as a two-layer circuit in which the electron resistance is connected between the blocks for the solid portion through which electrons conduct, and the ion resistance is connected between the blocks for the ion conductive medium portion through which ions conduct, and has a structure in which the ion resistance and the electron resistance are connected by the charge transfer resistance so that the movement of ions and electrons is switched by an electrode reaction.

5. The power storage device includes an ion conductive medium between the positive electrode and the negative electrode, The evaluation device according to claim 3, wherein the transmission line model has a structure in which the positive electrode block and the negative electrode block separated by the ion conductive medium are connected by the ion resistance.

6. The evaluation device according to claim 1 or 2, wherein the reaction resistance obtained from the Butler-Volmer equation is introduced into the transmission line model.

7. The evaluation device according to claim 6, wherein the reaction resistance is introduced using an equation in which the asymmetric parameter α of the Butler-Volmer equation is set to 0.

5.

8. The evaluation device according to claim 1 or 2, wherein the film resistance assuming that the active material contained in the positive electrode and / or the negative electrode is an aggregate of spheres is introduced into the transmission line model.

9. An evaluation method for evaluating a power storage device having a positive electrode and a negative electrode, comprising: performing evaluation of the power storage device using a transmission line model including an electron resistance, an ion resistance, a charge transfer resistance including a reaction resistance and a film resistance that are obtained by differentiating a function of the overvoltage η and the current I and that depend on the current I, in the positive electrode and the negative electrode; An evaluation method comprising:

10. A program that causes one or more computers to implement the steps of the evaluation method according to Claim 9.

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