Storage battery management method and battery management system

Abstract

To reduce a calculation load on a processor while estimating an SOC of a storage battery with high accuracy.SOLUTION: A positive electrode active material includes: a rich phase in which charge carriers are high in content; a poor phase in which charge carriers are low in content; and a two-phase coexistence phase in which the rich phase and the poor phase coexist. A method of managing a battery 10 includes, in a multi-particle model in which a plurality of particles each distinguished by a particle number indicating a reaction sequence of the positive electrode active material represents the positive electrode active material, assuming that charge carriers are equal in content among one or more particles belonging to each of the rich phase, the poor phase, and the two-phase coexistence phase, a step of calculating overvoltage of each of the particles for each of the phases; a step of calculating reaction current density on the basis of the overvoltage for each of the phases; and a step of estimating an SOC of a storage battery on the basis of the reaction current density in each of the phases.SELECTED DRAWING: Figure 16

Description

[Technical field]

[0001] The present disclosure relates to a storage battery management method and a battery management system. [Background technology]

[0002] Techniques have been proposed to improve the accuracy of estimating the SOC (State Of Charge) of a storage battery. Non-Patent Documents 1 and 2 disclose techniques for estimating the SOC of a storage battery having a positive electrode containing lithium iron phosphate by applying a many particle model (MPM). The multi-particle model is a model that formulates electrochemical phenomena related to SOC estimation by expressing the active material contained in the electrode (positive electrode active material in Non-Patent Documents 1 and 2) as a large number of particles. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2018-169398 A [Non-patent literature]

[0004] [Non-Patent Document 1] Hiroki Kondo, Tsuyoshi Sasaki, Pallab Barai and Venkat Srinivasan. Comprehensive Study of the Polarization Behavior of LiFePO4 Electrodes Based on a Many-Particle Model. Journal of The Electrochemical Society, Volume 165, Number 10 Published 6 July 2018. [Non-Patent Document 2] Tsuyoshi Sasaki, Yoshio Ukyo and Petra Novak. Memory effect in a lithium-ion battery. Nature materials, Volume 12, June 2013. Summary of the Invention [Problem to be solved by the invention]

[0005] By adopting the multi-particle model, the estimation accuracy of SOC can be improved compared to the single-particle model. On the other hand, the computational load on the processor may be increased. More specifically, in the multi-particle model, variables are used for each particle, so it is necessary to secure a memory capacity of (number of particles) x (memory usage per particle). Therefore, for example, when several thousand particles are used, the memory usage may become excessively large, and as a result, the computational load on the processor may become excessively large. This problem is particularly noticeable when a computation processing device with limited computational resources (such as an on-board ECU (Electronic Control Unit) or a mobile terminal) is used.

[0006] The present disclosure has been made to solve the above problems, and one of the objectives of the present disclosure is to reduce the computational load on a processor while estimating the SOC of a storage battery with high accuracy. [Means for solving the problem]

[0007] A method for managing a storage battery according to an aspect of the present disclosure includes managing a storage battery having a positive electrode containing a positive electrode active material by a processor. The positive electrode active material has a plurality of phases in which the content of charge carriers in the positive electrode active material is different from one another. The plurality of phases include a rich phase having a high content of charge carriers, a poor phase having a low content of charge carriers, and a two-phase coexistence phase in which the rich phase and the poor phase coexist. The management method includes first to third steps in a multi-particle model that expresses the positive electrode active material by a plurality of particles distinguished by particle numbers indicating a reaction sequence of the positive electrode active material, on the assumption that the content of charge carriers is equal between one or more particles belonging to each of the rich phase, poor phase, and two-phase coexistence phase. The first step is a step of calculating an overvoltage of each of the plurality of phases by the processor based on the measured voltage of the storage battery, the measured current of the storage battery, and the open-circuit potential of the particles belonging to the phase. The second step is a step of calculating a reaction current density of each of the plurality of phases by the processor based on the overvoltage. The third step is estimating, by the processor, the SOC of the battery based on the reaction current density of each of the multiple phases.

[0008] In the above method, the SOC of the storage battery can be estimated with high accuracy by using a multi-particle model. In addition, by assuming that the content of charge carriers is equal between particles belonging to each phase, the rich phase, the poor phase, and the two-phase coexistence phase, the overvoltage (and the reaction current density based on the overvoltage) of all particles belonging to each phase is calculated collectively. This reduces the calculation load on the processor compared to the case where the overvoltage (and the reaction current density) is calculated separately for each particle. Therefore, the above method reduces the calculation load on the processor while estimating the SOC of the storage battery with high accuracy. Effect of the Invention

[0009] According to the present disclosure, it is possible to estimate the SOC of a storage battery with high accuracy while reducing the computational load. [Brief description of the drawings]

[0010] [Figure 1]1 is a diagram illustrating a schematic overall configuration of a vehicle equipped with a battery management system according to an embodiment of the present disclosure. [Diagram 2] FIG. 2 is a perspective view illustrating an example of a cell configuration. [Diagram 3] FIG. 2 is a diagram showing an example of the configuration of an electrode body. [Figure 4] FIG. 2 is a diagram showing the relationship between the lithium composition and the open circuit potential of a positive electrode active material in a lithium iron phosphate ion battery, assuming that the positive electrode active material is a single particle. [Diagram 5] FIG. 1 is a conceptual diagram for explaining a multi-particle model. [Figure 6] 10 is a flowchart showing a procedure for SOC estimation processing using a comparison model. [Figure 7] FIG. 2 is a conceptual diagram for explaining the reaction sequence in a comparative model. [Figure 8] FIG. 1 is a conceptual diagram for explaining how each particle undergoes a phase transition in a comparative model. [Figure 9] FIG. 13 is a conceptual diagram for explaining the current flowing through each particle in the comparative model. [Figure 10] FIG. 1 is a first conceptual diagram for explaining a difference between a comparative model and a simplified model. [Figure 11] FIG. 11 is a second conceptual diagram for explaining the difference between the comparative model and the simplified model. [Figure 12] FIG. 11 is a third conceptual diagram for explaining the differences between the comparative model and the simplified model. [Figure 13] FIG. 11 is a diagram for contrasting the concept of multi-particle phase transitions between the comparative model and the simplified model. [Figure 14] FIG. 1 is a diagram for explaining a phase transition of multiparticulates accompanying the discharge of a battery. [Figure 15] FIG. 1 is a diagram for explaining a phase transition of multiparticulates accompanying charging of a battery. [Figure 16] 5 is a flowchart showing a first example of a processing procedure of an SOC estimation process using a simple model in the present embodiment. [Figure 17]10 is a flowchart showing a second example of a processing procedure of an SOC estimation process using a simple model in the present embodiment. [Figure 18] FIG. 13 is a conceptual diagram for explaining barcoding of variables. [Figure 19] FIG. 11 is a diagram for explaining a first additional rule. [Figure 20] FIG. 11 is a diagram for explaining the second and third additional rules. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. In the drawings, the same or corresponding parts are denoted by the same reference characters, and the description thereof will not be repeated.

[0012] In the following, a configuration in which the battery management system (BMS) according to the present disclosure is mounted on a hybrid electric vehicle (HEV), more specifically, a plug-in hybrid electric vehicle (PHEV), will be described as an example. However, the battery management system according to the present embodiment is applicable to all vehicles equipped with a storage battery for driving. That is, the battery management system according to the present embodiment may also be mounted on an electric vehicle (BEV: Battery Electric Vehicle), a fuel cell vehicle (FCEV: Electric Vehicle Electric Vehicle), and the like. Furthermore, the use of the battery management system according to the present disclosure is not limited to vehicles, and may be, for example, stationary.

[0013] [Embodiment Mode] <Overall composition> 1 is a diagram illustrating a schematic overall configuration of a vehicle equipped with a battery management system according to an embodiment of the present disclosure. The vehicle 900 includes a battery management system 100. The battery management system 100 is a battery pack, and includes a battery 10, a monitoring unit 20, a system main relay (SMR) 30, and a battery ECU (Electronic Control Unit) 40. The vehicle 900 further includes an inlet 91, a power conversion device 92, a charging relay 93, a power control unit (PCU) 94, a motor generator 95, a power transmission gear 96, driving wheels 97, and an integrated ECU 98.

[0014] The battery 10 stores power for driving the motor generator 95 and supplies the power to the motor generator 95 via the PCU 94. The battery 10 is charged by receiving the generated power via the PCU 94 when the motor generator 95 generates power. The battery 10 is an assembled battery including one or more battery modules. Each of the one or more battery modules includes a plurality of cells 50. Each of the cells 50 is a lithium-ion secondary battery. The configuration of the cells 50 will be described with reference to FIGS. 2 and 3.

[0015] The monitoring unit 20 includes various sensors for monitoring the state of the battery 10. Specifically, the monitoring unit 20 includes a voltage sensor 201, a current sensor 202, and a temperature sensor 203. The voltage sensor 201 detects the voltage V of the battery 10 (each cell). The current sensor 202 detects the current I charged to and discharged from the battery 10. The temperature sensor 203 detects the temperature T of the battery 10. Each sensor outputs a signal indicating the detection result to the battery ECU 40.

[0016] The SMR 30 is provided on a power line connecting the battery 10 and the PCU 94. When the SMR 30 is closed, charging and discharging of the battery 10 is possible.

[0017] The battery ECU 40 includes a processor 401 and a memory 402. The processor 401 is an arithmetic processing device such as a CPU (Central Processing Unit) or an MPU (Micro Processing Unit). The memory 402 is a storage device including a ROM (Read Only Memory) and a RAM (Random Access Memory). The memory 402 stores a system program including an OS (Operating System), a control program including computer-readable codes required for control calculations, and various parameters for managing the battery 10. The processor 401 realizes various processes by reading out the system program, the control program, and the parameters, expanding them in the memory 402, and executing them. In this embodiment, the main process executed by the processor 401 is a process of estimating the SOC (State Of Charge) of the battery 10 (each cell in the assembled battery). This process will be described in detail later.

[0018] The inlet 91 is configured to be capable of connecting, via a mechanical coupling, a charging connector (not shown) provided at the tip of a charging cable. By connecting the inlet 91 and the charging connector, an electrical connection is established between the charging equipment (not shown) and the vehicle 900. In addition, it becomes possible for an integrated ECU 98 of the vehicle 900 and a control device (not shown) of the charging equipment to exchange various signals.

[0019] The power conversion device 92 is, for example, an AC / DC converter. The power conversion device 92 converts AC power supplied from a charging facility via a charging cable into DC power for charging the battery 10.

[0020] The charging relay 93 is electrically connected to a power line connecting the SMR 30 and the PCU 94. When the charging relay 93 is closed and the SMR 30 is closed, power transmission between the inlet 91 and the battery 10 is enabled.

[0021] The PCU 94 is electrically connected between the SMR 30 and the motor generator 95. The PCU 94 includes a converter and an inverter (neither of which are shown), and drives the motor generator 95 in accordance with a command from the integrated ECU 98.

[0022] The motor generator 95 is an AC rotating electric machine, for example a permanent magnet type synchronous motor having a rotor with a permanent magnet embedded therein. The output torque of the motor generator 95 is transmitted to drive wheels 97 through a power transmission gear 96 to drive the vehicle 900. Furthermore, the motor generator 95 generates electricity using the rotational force of the drive wheels 97 when braking the vehicle 900. The generated electricity by the motor generator 95 is converted by the PCU 94 into charging electricity for the battery 10.

[0023] The integrated ECU 98 includes a processor 981 and a memory 982. The processor 981 executes various controls for controlling the vehicle 900 to a desired state, based on signals received from various sensors and programs and maps stored in the memory 982. For example, the integrated ECU 98 controls the charging and discharging of the battery 10 by controlling the PCU 94 in cooperation with the battery ECU 40.

[0024] <Cell configuration> FIG. 2 is a perspective view that shows a schematic example of the configuration of the cell 50. FIG. 2 shows a see-through view of the inside of the cell 50. In this example, the cell 50 is a sealed rectangular battery. The shape of the cell 50 may be, for example, a cylindrical shape. Alternatively, the cell 50 may be a cell that constitutes a bipolar stacked battery pack. The cell 50 includes an electrode body 60, a battery case 70, and an electrolyte 80. The battery case 70 includes a positive electrode terminal 71 and a negative electrode terminal 72.

[0025] The electrode body 60 has an outer shape of, for example, a flattened rectangular parallelepiped. The electrode body 60 is housed in the battery case 70 such that the long sides of the flattened rectangular parallelepiped extend in the long side direction of the battery case 70. The battery case 70 may be made of, for example, a metal such as an aluminum (Al) alloy. The battery case 70 may be, for example, a pouch such as an Al laminate film. The electrolyte 80 is injected into the battery case 70 and impregnates the electrode body 60. The liquid level of the electrolyte 80 is indicated by a dashed line.

[0026] Fig. 3 is a diagram showing an example of the configuration of an electrode assembly 60. With reference to Fig. 2 and Fig. 3, the electrode assembly 60 is formed by alternately stacking and winding positive electrodes 1 and negative electrodes 2 with a separator 3 sandwiched therebetween. Fig. 3 shows an exploded view of the electrode assembly in the middle of winding.

[0027] Positive electrode 1 is in a sheet form and includes a positive electrode current collector 11 and a positive electrode mixture layer 12. Positive electrode current collector 11 is electrically connected to a positive electrode terminal 71. Positive electrode current collector 11 can be, for example, an aluminum (Al) foil, an Al alloy foil, or the like.

[0028] In this example, the positive electrode mixture layer 12 is formed on both the front and back surfaces of the positive electrode current collector 11. However, the positive electrode mixture layer 12 may be formed only on the front surface (either one surface) of the positive electrode current collector 11. The positive electrode mixture layer 12 includes a positive electrode active material 121 (see FIG. 5), a conductive material (not shown), and a binder (not shown). The positive electrode active material 121 is a two-phase coexisting material described later, for example, iron phosphate (LiFePO4). Two or more types of positive electrode active materials may be used in combination. The conductive material may include at least one selected from the group consisting of carbon black (acetylene black, etc.), vapor grown carbon fiber (VGCF), carbon nanotubes (CNT), and graphene flakes. The binder may include, for example, at least one selected from the group consisting of carboxymethyl cellulose (CMC), styrene butadiene rubber (SBR), polyvinylidene fluoride (PVdF), and polytetrafluoroethylene (PTFE).

[0029] The negative electrode 2 is in a sheet shape and includes a negative electrode current collector 21 and a negative electrode mixture layer 22. The negative electrode current collector 21 is electrically connected to a negative electrode terminal 72. The negative electrode current collector 21 may be, for example, a copper (Cu) foil.

[0030] In this example, the negative electrode mixture layer 22 is formed on both the front and back surfaces of the negative electrode current collector 21. However, the negative electrode mixture layer 22 may be formed only on the front surface (either one surface) of the negative electrode current collector 21. The negative electrode mixture layer 22 includes a negative electrode active material 221 and a binder (not shown). The negative electrode active material 221 may be, for example, a carbon-based negative electrode active material such as natural graphite, graphitizable carbon, or non-graphitizable carbon, or may be an alloy-based negative electrode active material containing silicon (Si), tin (Sn), or the like. As the binder, a material that can be used as a binder contained in a positive electrode active material layer is used.

[0031] The separator 3 is a strip-shaped film. The separator 3 is disposed between the positive electrode 1 and the negative electrode 2, and electrically insulates the positive electrode 1 from the negative electrode 2. The material of the separator 3 may be, for example, a porous film made of a polyolefin resin such as polyethylene (PE) or polypropylene (PP), or a polyamide resin such as nylon or aromatic polyamide (aramid), or a woven or nonwoven fabric made of polypropylene, polyethylene terephthalate (PET), methylcellulose, or the like.

[0032] The electrolyte 80 includes at least a lithium (Li) salt and a solvent. The Li salt is a supporting electrolyte dissolved in the solvent. The Li salt may be, for example, LiPF6. The solvent is aprotic. The solvent may be, for example, a mixture of a cyclic carbonate and a chain carbonate. In addition to the Li salt and the solvent, the electrolyte 80 may further include a known functional additive.

[0033] <Lithium composition vs. OCP> FIG. 4 is a diagram showing the relationship between the lithium composition and the open circuit potential (OCP) of the positive electrode active material in a lithium iron phosphate ion battery, assuming that the positive electrode active material is a single particle. The horizontal axis represents the lithium composition in the positive electrode active material. The lithium composition is Li x The x (0≦x≦1) indicates the lithium content in FePO4. The lithium composition corresponds to the "charge carrier content" according to the present disclosure. The vertical axis represents the OCP of the positive electrode active material. The same applies to FIG. 12 described later.

[0034] The lithium composition-OCP curve shown in FIG. 4 has a maximum point and a minimum point, each of which is a spinodal point. In general, when a lithium iron phosphate ion battery is charged and discharged, a Li-rich phase, a Li-poor phase, and a two-phase coexistence phase exist in the positive electrode active material. The Li-rich phase is a region having a higher lithium composition than the maximum point (x=0.95 in this example) of the lithium composition-OCP curve. The Li-poor phase is a region having a lower lithium composition than the minimum point (x=0.05 in this example) of the lithium composition-OCP curve. The Li-rich phase and the Li-poor phase are solid solution phases. The two-phase coexistence phase is a region located between the Li-rich phase and the Li-poor phase, where the Li-rich phase and the Li-poor phase coexist.

[0035] Between the two spinodal points (maximum and minimum), the OCP of the positive electrode active material decreases roughly in proportion to the decrease in the lithium composition x. In this example, the voltage difference between the two spinodal points is about 20 mV. The average voltage of the two spinodal points (the equilibrium voltage of the two coexisting phases) V ave is approximately 3.43 V. In an actual lithium iron phosphate battery, the positive electrode active material contains multiple particles, so a flat lithium composition-OCP curve is observed between x = 0.05 and x = 0.95.

[0036] <Multi-particle model> In this embodiment, a multi-particle model (MPM) is employed to estimate the SOC of the battery 10.

[0037] 5 is a conceptual diagram for explaining the multi-particle model. In the single-particle model, the positive electrode active material is typically represented as one particle, and the negative electrode active material is typically represented as one particle.

[0038] In contrast, the multi-particle model is a model that assumes that the positive electrode is composed of a large number (N pieces) of spherical particles that are electronically and ionically connected to each other, taking into account the polarization behavior of the lithium iron phosphate positive electrode. In the multi-particle model, the positive electrode active material 121 is represented diagrammatically as multiple particles. The negative electrode active material 221 is represented diagrammatically as one particle in this example, but the negative electrode active material 221 can also be represented as multiple particles.

[0039] 5 shows the state of the battery 10 during charging. When the battery 10 is charged, lithium ions (Li + ) is released, while lithium ions are inserted into the negative electrode active material 221. At this time, a current (applied current I app ) flows. Although not shown, when the battery 10 is discharged, the direction of the current is opposite to that shown in FIG.

[0040] By using the multi-particle model, the estimation accuracy of the SOC can be improved compared to the case of using the one-particle model. On the other hand, the computation load of the processor 401 may be large. More specifically, in the multi-particle model, variables are used for each particle. Also, several thousand particles are required to maintain the smoothness of the computation results between particles in the multi-particle model. Furthermore, since the SOC may vary between cells, it is desirable to estimate the SOC for each cell 50. Then, in order to obtain smooth computation results for all cells, it is necessary to secure a memory capacity equivalent to (memory usage per particle) x (several thousand particles) x (tens of cells). Therefore, the usage of the memory 402 may become excessively large, and as a result, the computation load of the processor 401 may become excessively heavy. This problem is particularly noticeable when computation resources are limited, such as in the on-board battery ECU 40.

[0041] Therefore, in this embodiment, a simplified multi-particle model is adopted to reduce the computation load of the processor 401. This model is simply referred to as a "simplified model". On the other hand, the non-simplified multi-particle model is referred to as a "comparison model". In the following, in order to facilitate understanding of the simplified model, first, the SOC estimation process using the comparison model will be described. For details of the comparison model, refer to Patent Document 1.

[0042] <Comparative Model> FIG. 6 is a flowchart showing the procedure of the SOC estimation process using the comparison model. In this example, the SOC estimation process is performed for each cell. A cell that is the target of the SOC estimation process is referred to as a "target cell." The SOC estimation process is performed repeatedly. The value in the current SOC estimation process (current value) is represented by (t), and the value in the previous SOC estimation process (previous value) is represented by (t-1). Step is abbreviated as S.

[0043] In S901, the processor obtains from the sensor or reads from the memory 402 various variables (parameters) used in the current SOC estimation process.

[0044] In S902, the processor calculates a voltage V'(t) to be input to the comparison model according to equation (1).

number

[0045] In equation (1), V(t) is the current value of the closed circuit voltage (CCV) of the target cell measured by the voltage sensor. I(t) is the current value of the current measured by the current sensor. Rd is the DC resistance of the target cell (the impedance component associated with the movement of lithium ions and electrons between the positive and negative electrodes). dVc(t) is the current value of the salt concentration overpotential caused by the concentration gradient of lithium ions between the positive and negative active materials, and is calculated according to equation (2). α and β are coefficients suitably determined by prior experiments or simulations.

number

[0046] In the multi-particle model, it is necessary to set the reaction sequence, that is, the order of particles involved in the reaction (intercalation / deintercalation of lithium ions) among the multi-particles. In an actual storage battery, various factors may be related to the reaction sequence. Specific examples of factors include the distance from the current collector foil to the positive electrode active material, the distance from the current collector terminal to the positive electrode active material, and the particle size of the positive electrode active material. In the comparative model described in Patent Document 1, the reaction sequence is determined by the particle size following a log-normal distribution (see FIG. 1(c) in Patent Document 1).

[0047] Figure 7 is a conceptual diagram for explaining the reaction sequence in the comparative model. In the multi-particle model in which the reaction sequence is determined by the particle diameter, all particles are assumed to be spherical. Therefore, the radius of the jth particle (j is a natural number that distinguishes particles from each other) is defined as r j Then, the surface area S of the jth particle j =4πr j and the volume of the jth particle, V j =4πr j 3 / 3. j = 1 to N.

[0048] Particle surface area S j is a parameter for expressing the reaction area of ​​the positive electrode active material. j is a parameter for expressing the capacity of the positive electrode active material. j / V j ) corresponds to the reaction area / capacity of the positive electrode active material. The smaller the particle diameter, the larger the surface area / volume of the particle, and therefore the easier it is for the lithium composition to change. The easier it is for the lithium composition to change, the higher the reaction sequence and the smaller the particle number is assigned. Therefore, the particle with particle number = 1 has the highest reaction sequence, and the particle with particle number = N has the lowest reaction sequence.

[0049] As the target cell is charged and discharged, the multiple particles undergo phase transitions in order from the particles with the highest reaction order (particles with the lowest particle number).

[0050] Figure 8 is a conceptual diagram for explaining how each particle undergoes a phase transition in the comparative model. For simplicity, an example with a total particle number of N = 10 is shown here. Originally, all particles belonged to the Li-rich phase, but as the target cell was charged, particles with particle numbers j = 1 and 2 underwent a phase transition through the two-phase coexistence phase to the Li-poor phase, and particles with particle numbers j = 3 to 5 underwent a phase transition to the two-phase coexistence phase. In this way, all particles are treated separately in the comparative model.

[0051] The phase to which each of the 10 particles belongs depends on the lithium composition x of the particle. j The lithium composition of the particle is expressed as x j Once this is determined, the open circuit potential of the particle, U, is calculated according to the lithium composition-OCP curve. j is determined.

[0052] FIG. 9 is a conceptual diagram for explaining the current flowing through each particle in the comparative model. In the comparative model, the applied current I app is the lithium composition of each particle x j Overvoltage η according to j The current distributed to the jth particle is assumed to be the reaction current density i j It is described using:

[0053] Referring again to FIG. 6 , in S903, the processor calculates an overvoltage η j Specifically, the processor calculates the open circuit potential U of the jth particle from the voltage V' calculated for each particle according to the above-mentioned formulas (1) and (2). j By subtracting , the particle's overvoltage η j Calculate the overvoltage η j is the difference between the CCV of the target cell and the OCV (Open Circuit Voltage) of the particle.

number

[0054] In equation (3), the open circuit potential U j is the lithium composition x j The function is calculated based on the lithium composition vs. OCP curve shown in FIG. 8. More specifically, the processor calculates the lithium composition from the previous value x j The open circuit potential corresponding to (t-1) is U j It is calculated as follows.

[0055] In S904, the processor calculates the overvoltage η j Based on the reaction current density i j More specifically, the reaction current density i j is calculated according to the Butler-Volmer equation (4): Oj is the exchange current density, which is a predetermined value depending on the particle number. F is the Faraday constant. R is the gas constant. T is the temperature measured by the temperature sensor.

number

[0056] In S905, the processor calculates the reaction current density i of each of the plurality of particles calculated in S903. j and the surface area S of the particle j The reaction current I flowing through the jth particle is j (see formula (5)).

number

[0057] In S906, the processor calculates the reaction current I j The product of this and the period Δt of the SOC estimation process (the time between the current SOC estimation process and the previous SOC estimation process) is the capacity Q of the jth particle. jThe processor divides the divided value by the previous value (x j (t-1)) is added to the current value of the lithium composition of the particle x j (t) (see formula (6)). Formula (6) is the lithium composition x j is the reaction current I j This indicates that the change is proportional to the amount of charge.

number

[0058] In S907, the processor calculates each lithium composition x j The SOC of the target cell is estimated by calculating a weighted average according to the lithium composition x of the particle for each particle. j and the volume of the particle V j (corresponding to the capacity) and add up the multiplied values ​​for all particles. The processor then divides the sum by the total volume of all particles (corresponding to the total capacity) (see equation (7)). This calculates the so-called "center of gravity" of all particles in the lithium composition-OCP curve, and this center of gravity corresponds to the SOC of the target cell.

number

[0059] In S908, the processor determines whether the SOC of all cells has been estimated. If there are any cells whose SOC has not been estimated (NO in S908), the processor returns to S901 and executes the processes of S901 to S907 for the next cell. When the SOC estimation of all cells is completed (YES in S908), the processor ends the process.

[0060] <Simple model> Next, the simplified model in this embodiment will be described in comparison with a comparative model.

[0061] FIG. 10 is a first conceptual diagram for explaining the difference between the comparative model and the simple model. As mentioned above, in the comparative model, multiple particle sizes are set. In contrast, in the simple model, all particles are set to have the same particle size. That is, the reaction area and volume of all particles are equal to each other. However, they have in common that the particles higher in the reaction sequence are assigned smaller particle numbers.

[0062] FIG. 11 is a second conceptual diagram for explaining the difference between the comparative model and the simplified model. In the comparative model, the lithium composition x j is calculated (see formula (6) above). In contrast, in the simplified model, three particle groups corresponding to the three phases are assumed, and the lithium composition is calculated for each particle group. Below, a more detailed explanation will be given using an example with 10 particles as in FIG. 8. Note that variables related to the Li-poor phase are marked with p, variables related to the two-phase coexistence phase are marked with c, and variables related to the Li-rich phase are marked with r.

[0063] Figure 12 is a third conceptual diagram for explaining the difference between the comparative model and the simplified model. In the comparative model, all particles are considered separately. In the example shown in Figure 8 for the comparative model, the particles belonging to the Li-poor phase are particles with particle numbers j = 1, 2, the particles belonging to the two-phase coexistence phase are particles with j = 3, 4, 5, and the particles belonging to the Li-rich phase are particles with j = 6, 7, 8, 9, 10.

[0064] In contrast, in the simplified model, particles belonging to the same phase among the three phases are considered to be a single particle group. In other words, the multi-particles are divided into a particle group belonging to the Li-poor phase, a particle group belonging to the two-phase coexistence phase, and a particle group belonging to the Li-rich phase. Each of the three particle groups is represented by the minimum (Min) and maximum (Max) particle numbers of the particles contained in that particle group. In the example shown in FIG. 12, the particle group belonging to the Li-poor phase is represented by Min=1 and MAX=2. The particle group belonging to the two-phase coexistence phase is represented by Min=3 and Max=5. The particle group belonging to the Li-rich phase is represented by Min=6 and Max=10.

[0065] Each of the three particle groups may be expressed by the number of particles belonging to the particle group. According to this embodiment, even if the multi-particle model includes several thousand particles, the variables for expressing these particles (minimum and maximum values ​​of particle numbers or particle numbers) can be reduced to less than 100.

[0066] Figure 13 is a diagram for comparing the concept of multi-particle phase transition between the comparative model and the simplified model. Figure 13 illustrates the situation of the target cell at SOC 50% during charging.

[0067] In the comparative model, the reaction current density i j Based on the reaction current Ij according to the lithium composition x j (In this example, x4 to x7) are calculated (see formulas (5) and (6) above).

[0068] In contrast, the following conditions are set in the simplified model. All particles included in the particle group belonging to the two-phase coexistence phase have a common value for the lithium composition. This value is a representative value of the lithium composition in the two-phase coexistence phase and is fixed in advance. In this example, the particle group belonging to the two-phase coexistence phase and represented by Min=4 and Max=7 has a lithium composition x c = 0.50.

[0069] The lithium composition is the same for all particles in the Li-poor phase. p x p is the x in the two-phase coexistence phase c Unlike x, x is a variable that is not fixed. The same is true for the Li-rich phase. The lithium composition of the particles belonging to the Li-rich phase is x r It is written as follows.

[0070] In addition, in the simplified model, the number of particles moving between the three phases is calculated using the reaction current in each phase. The reaction currents in the Li-poor phase, the two-phase coexistence phase, and the Li-rich phase are respectively defined as I p ,I c ,Ir The sum of the three reaction currents and the applied current I app The following relationship holds between (see equation (8)):

number

[0071] Reaction current I p ,I c ,I r Each of these can be calculated as follows. Taking the Li-poor phase as an example, the reaction current I p is calculated, for example, according to formula (9). Note that the p at the bottom right of the summation symbol means that all particles belonging to the Li-poor phase are included.

number

[0072] Alternatively, since the relationship in equation (10) also holds, the reaction conductivities (described later) can be summed up as if they were one particle to produce a reaction current I p may be calculated, where S is the particle surface area common to all particles.

number

[0073] The reaction current I obtained in this way p ,I c ,I r changes the lithium composition as follows. Here again, using the Li-poor phase as an example, the change in the lithium composition of the Li-poor phase, Δx p is calculated as shown in equation (11). Q p represents the capacity of the Li-poor phase.

number

[0074] In the simplified model, the capacity of each of the three particle groups is equal to the sum of the capacities of the particles contained in that group. The capacity of each of the three particle groups is proportional to the number of particles contained in that group. Therefore, the capacity of a particle group increases as the number of particles contained in the group increases. If the number of particles belonging to the Li-poor phase is n p and the capacity (common) of each particle is denoted as q, then Q p =n p ×q.

[0075] Change in lithium composition in the Li-poor phase Δx p The previous value of the lithium composition of the Li-poor phase, x p By adding to (t-1), the lithium composition of the Li-poor phase is now x p (t) is calculated (see equation (12)).

number

[0076] Here, the lithium composition of the Li-poor phase is x p (t) never crosses the boundary between the Li-poor phase and the two-phase coexistence (x=0.05 in this example). Particles corresponding to a change in lithium composition beyond the boundary move from the Li-poor phase to the two-phase coexistence.

[0077] The capacity change corresponding to the change in lithium composition beyond the boundary value is (x p -0.05) × n p × q. On the other hand, when Δn[p→c] particles move from the boundary value of the Li-poor phase (x=0.05) to the two-phase coexistence phase (x=0.5), the capacitance change is expressed as (0.5-0.05)×Δn[p→c]×q. These two capacitance changes are equal to each other (see equation (13)).

number

[0078] Solving equation (13) for the number of particles Δn[p→c] moving from the Li-poor phase to the two-phase coexistence phase, Δn[p→c] is expressed as equation (14).

number

[0079] Thus, the lithium composition of the particles belonging to the Li-poor phase changes continuously until it reaches the boundary value of the Li-poor phase (x = 0.05). The lithium composition of the particles belonging to the Li-poor phase does not change beyond 0.05. When the lithium composition reaches the boundary value of the Li-poor phase, the reaction current I p A number of particles proportional to Δn moves from the Li-poor phase to the two-phase coexistence phase. Here, we have used the example of movement from the Li-poor phase to the two-phase coexistence phase, but the number of particles moving between each phase, Δn, can be calculated in the same way for movement from the two-phase coexistence phase to the Li-poor phase, from the Li-rich phase to the two-phase coexistence phase, and from the two-phase coexistence phase to the Li-rich phase.

[0080] The reaction conductivity of each of the three particle groups is the sum of the reaction conductivity of the particles contained in that particle group. The reaction conductivity of the jth particle is the reaction resistance (R ct,j ) The reciprocal of the reaction resistance of each of the three particle groups is the sum of the reciprocals of the reaction resistances of the particles contained in that particle group. Therefore, as the number of particles contained in a particle group increases, the reaction resistance of that particle group decreases.

[0081] <Phase transition> The manner in which the multiparticulate undergoes a phase transition according to the above-described simplified model will now be described in more detail for each of charging and discharging of the battery 10.

[0082] Fig. 14 is a diagram for explaining the phase transition of the multi-particles accompanying the discharge of the battery 10. Fig. 14 shows a schematic diagram of how the phase to which the multi-particles belong changes when the battery 10 is monotonically discharged from SOC 100% to SOC 0%.

[0083] At an SOC of 100%, all particles belong to the Li-poor phase. When discharging of the battery 10 is started, the particles transition from the smallest particle number shown at the bottom of the figure to the Li-rich phase via the two-phase coexistence phase. As the SOC decreases to 80%, 30%, and 0%, the number of particles belonging to the Li-poor phase decreases, while the number of particles belonging to the Li-rich phase increases. Note that since the positive electrode has a surplus capacity (so-called reserve capacity) that is rechargeable but not charged, even at an SOC of 0%, not all particles belong to the Li-rich phase, and some particles remain in the Li-poor phase and the two-phase coexistence phase.

[0084] As mentioned above, the particles belonging to each phase are identified by the minimum and maximum particle numbers of the particles belonging to that phase. For example, at SOC 80%, the particles belonging to the two-phase coexistence phase are identified by the minimum (Min) = p and maximum (Max) = q of the particle numbers. The particles belonging to the Li-rich phase are identified by Min = 1 and Max = p-1, and the particles belonging to the Li-poor phase are identified by Min = q+1 and Max = N.

[0085] Fig. 15 is a diagram for explaining the phase transition of the multi-particles accompanying the charging of the battery 10. Fig. 15 shows a schematic diagram of how the phase to which the multi-particles belong changes when the battery 10 is monotonically charged from SOC 0% to SOC 100%.

[0086] At 0% SOC, most particles, except for those corresponding to the reserve capacity, belong to the Li-rich phase. When charging of the battery 10 begins, the particles change from the smallest particle number to the Li-poor phase via the two-phase coexistence phase. As the SOC increases to 20%, 70%, and 100%, the particles belonging to the Li-rich phase decrease while the particles belonging to the Li-poor phase increase.

[0087] <Processing flow> Fig. 16 is a flowchart showing a first example of a processing procedure of SOC estimation processing using a simple model in this embodiment. The processing shown in this flowchart (and the processing shown in the flowchart in Fig. 17 described later) is executed when a predetermined condition is satisfied (for example, at predetermined intervals). Each step is realized by software processing by the battery ECU 40 (processor 401), but may also be realized by hardware (electrical circuitry) arranged in the battery ECU 40.

[0088] In this embodiment, the SOC estimation process is also performed for each “target cell.” However, the SOC estimation process may be performed for the entire battery, or may be performed for each of a plurality of cells (for example, for each battery module).

[0089] In S101, the battery ECU 40 acquires various variables necessary for the current SOC estimation process from the sensors. The battery ECU 40 also reads from the memory 402 the previous values ​​of the variables necessary for the current SOC estimation process.

[0090] In S102, the battery ECU 40 calculates the input voltage V' to the simplified model according to equation (15). The salt concentration overvoltage dVc(t) in equation (15) is calculated according to equation (16). The calculation methods are the same as those in the comparative model (see equations (1) and (2)).

number

[0091] In S103, the battery ECU 40 calculates the overvoltage η of each particle group. More specifically, the battery ECU 40 calculates a common overvoltage η for all particle groups belonging to the two-phase coexistence phase according to the formula (17). c Calculate U in equation (17). c is the representative value of the lithium composition in the two-phase coexistence phase, x c (=0.50) and is a fixed value.

number

[0092] In addition, the battery ECU 40 calculates the overvoltage η p Calculate U in equation (18). p is the previous value of the common lithium composition in the Li-poor phase, x p (t-1) is the open circuit potential, which is a variable value. p (t-1) is calculated in S110 described later. The battery ECU 40 also calculates the overvoltage η r Calculate.

number

[0093] In S104, the battery ECU 40 calculates the reaction current Ic for the entire particle group belonging to the two-phase coexistence phase (the total value of the reaction currents of all particles belonging to the two-phase coexistence phase) according to the formula (20). O is determined to be smaller as the particle number increases (i.e., the reaction sequence is lower). For example, the exchange current density decreases linearly as the particle number increases (i Oj =1 / R O ×j). By reference to such a predefined relationship, the exchange current density can be set.

number

[0094] Similarly, for the entire particle group belonging to the Li-poor phase and the entire particle group belonging to the Li-rich phase, the battery ECU 40 calculates the reaction current I p ,I r Calculate.

number

[0095] In S105, the battery ECU 40 calculates the applied current I flowing through the target cell by taking the sum of the reaction currents of the respective phases calculated in S104. app (see equation (23)).

number

[0096] In S106, the battery ECU 40 detects the applied current I app The current SOC value SOC(t) of the target cell is estimated by dividing by the battery capacity C of the target cell and adding the result to the previous SOC value SOC(t-1) of the target cell (see equation (24)).

number

[0097] In S107, the battery ECU 40 calculates the number of particles Δn that undergo a phase transition between the three phases based on the reaction currents Ip, Ic, and Ir of the respective phases. That is, the battery ECU 40 calculates the number of particles Δn[r→c] that undergo a phase transition from the Li-rich phase to the two-phase coexistence phase, the number of particles Δn[c→p] that undergo a phase transition from the two-phase coexistence phase to the Li-poor phase, the number of particles Δn[p→c] that undergo a phase transition from the Li-poor phase to the two-phase coexistence phase, and the number of particles Δn[c→r] that undergo a phase transition from the two-phase coexistence phase to the Li-rich phase. These calculation methods have been described in detail using equations (9) to (14), and therefore will not be described again here.

[0098] Then, the battery ECU 40 identifies which particles belong to which phase based on the calculated particle number Δn. As described above, each of the three particle groups can be expressed by the minimum (Min) and maximum (Max) particle numbers of the particles included in the particle group. Furthermore, the battery ECU 40 determines the current value n of the number of particles belonging to each phase. c (t),n p (t),n r (t) is calculated (see formulas (25) to (27)). The number of particles can be used in the process of S206 described later.

number

[0099] In S108, the battery ECU 40 calculates the lithium composition x of the entire particle group belonging to the Li-poor phase. p The reaction current I calculated in S104 is added to the previous value of p The product of this and the SOC estimation process period Δt is the capacity (total capacity of the Li poor phase) Q p The lithium composition x of the entire particle group is calculated by adding the value divided by p The current value of is calculated (see equation (28)). The same process is performed for the Li-rich phase (see equation (29)). However, x p If (t)>0.05 then x p (t)=0.05. p If (t)<0.95 then x p (t)=0.95. These values ​​are used in the process of S103 in the next SOC estimation process (see equations (18) and (19)).

number

[0100] In S109, the battery ECU 40 determines whether the SOC of all cells has been estimated. If there are any cells whose SOC has not been estimated (NO in S109), the battery ECU 40 returns the process to S101 and executes the processes of S101 to S108 for the next cell. When the SOC estimation of all cells is completed (YES in S109), the battery ECU 40 ends the process.

[0101] 17 is a flowchart showing a second example of the processing procedure of the SOC estimation processing using the simple model in the present embodiment. The processing of S201 to S204 is similar to the processing of S101 to S104 in the first example (see FIG. 16), and therefore description thereof will not be repeated.

[0102] In S205, the battery ECU 40 calculates the lithium composition x p ,x r These processes are similar to those in S108 (see equations (28) and (29)).

[0103] In S206, the battery ECU 40 estimates the SOC of the target cell based on the lithium composition x of each of the three phases. More specifically, the battery ECU 40 multiplies the lithium composition x of each phase by the number of particles n contained in that phase, and adds the products for the three phases. Then, the battery ECU 40 divides the above sum by the total number of particles N (see equation (30)). This allows the position of the center of gravity of all the particles to be calculated, and the position of the center of gravity can be used as the SOC of the target cell.

number

[0104] The subsequent processes of S207 and S208 are similar to the processes of S107 and S109 in the first example.

[0105] In the first example of the procedure for SOC estimation (see FIG. 16), although the error is not as large as the accumulated error of the detected values ​​of various sensors (voltage sensor, current sensor, etc.), there is a concern that numerical calculation errors may be accumulated. In contrast, the second example of the procedure for SOC estimation (see FIG. 17) is less susceptible to the accumulation of numerical calculation errors than the first example. This is because, for example, when the error becomes large during charging and the estimated SOC becomes higher than the actual SOC (true value), feedback is obtained in the following manner: the estimated OCV increases; the overvoltage η is reduced; the estimated current is reduced below the actual current; and the rate of increase of the estimated SOC becomes slower than the rate of increase of the actual SOC, and the estimated SOC approaches the true value.

[0106] As described above, in this embodiment, the particles belonging to the two-phase coexistence phase are regarded as a lump of particles, and the particle group is a representative common lithium composition x c(=0.50) as a fixed value. In addition, the particles belonging to the Li-poor phase are considered as a group of particles, and the particles belonging to the Li-rich phase are considered as a group of particles, and these particle groups also have a common lithium composition x p ,x r Then, the open circuit potential U of all particles is calculated collectively for each phase, and the overvoltage η (and hence the reaction current density i) is also calculated collectively. This makes it possible to reduce the number of variables for expressing the particles, compared to a comparison model in which all particles are handled separately. Therefore, according to this embodiment, it is possible to reduce the calculation load on the battery ECU 40 (processor 401) while estimating the SOC of the battery 10 with high accuracy using the multi-particle model.

[0107] [Variations] <Barcoding> When the battery 10 is repeatedly charged and discharged, in other words, when the battery 10 is repeatedly switched between charging and discharging, the number of variables representing particles belonging to the two-phase coexistence phase (pairs of variables with maximum and minimum particle numbers) increases, which may result in a situation that the inventors call "barcoding" of the variables.

[0108] Figure 18 is a conceptual diagram for explaining barcoding of variables. The particle number increases toward the top in the figure. Therefore, in the following, the transition of a particle with a large particle number is also referred to as a transition from the "upper side", and the transition of a particle with a small particle number is also referred to as a transition from the "lower side".

[0109] First, assume a situation where all particles belong to the Li-poor phase and the SOC is 100% (see Fig. 18(A)). When the target cell is discharged from this situation, the particles belonging to the Li-poor phase transition from the bottom through the two-phase coexistence phase to the Li-rich phase (see Fig. 18(B)). In this example, the target cell is discharged until the SOC reaches 0% (see Fig. 18(C)). At this time, some particles remain in the Li-poor phase and the two-phase coexistence phase.

[0110] Next, the target cell is charged from SOC 0% to SOC 90% via SOC 20% (see Figures 18(D) and 18(E)). Then, the particles belonging to the Li-rich phase transition from the bottom through the two-phase coexistence phase to the Li-poor phase. At this time, particles different from the particles that transitioned to the two-phase coexistence phase by the first discharge belong to the two-phase coexistence phase by the first charge. In other words, the particles belonging to the two-phase coexistence phase are divided into two particle groups.

[0111] Next, the target cell is discharged from SOC 90% to SOC 10% via SOC 80% (see Fig. 18(F) and Fig. 18(G)). Then, the particles belonging to the Li-poor phase again transition from the bottom to the Li-rich phase via the two-phase coexistence phase. As a result, the particles belonging to the two-phase coexistence phase are divided into three particle groups.

[0112] Similarly, the target cell is charged from SOC 10% to SOC 80% (see FIG. 18(H)). As a result, the particles belonging to the Li-rich phase transition from the bottom to the Li-poor phase through the two-phase coexistence phase. As a result, the particles belonging to the two-phase coexistence phase are divided into four particle groups.

[0113] Finally, the target cell is discharged from SOC 80% to SOC 20% (see FIG. 18(I)). This causes the particles belonging to the Li-poor phase to transition from the bottom (particles with small particle numbers) to the Li-rich phase via the two-phase coexistence phase. As a result, the particles belonging to the two-phase coexistence phase are divided into five particle groups.

[0114] In this way, every time the charging and discharging of the target cell is switched, some particles remain in the two-phase coexistence phase, and the particle group consisting of particles belonging to the two-phase coexistence phase increases. In the case of FIG. 18, each of the particle groups belonging to the two-phase coexistence phase is expressed as a thin line, so that it looks like a barcode. Since such barcoding means an increase in the variables representing the particles belonging to the two-phase coexistence phase, it is desirable to avoid barcoding from the viewpoint of reducing the computational load of the battery ECU 40. Therefore, in this modified example, three additional rules are set in order to avoid barcoding and thereby reduce the computational load of the battery ECU 40.

[0115] <Additional rules> FIG. 19 is a diagram for explaining the first additional rule. The first additional rule imposes a condition on the generation of a variable expressing a particle group belonging to a two-phase coexistence phase. More specifically, when the charge / discharge of the target cell is switched, if the number of particles in the solid solution phase to which the particles were transferred immediately before is equal to or greater than the reference value REF, the generation of a new variable is permitted. On the other hand, if the number of particles in the solid solution phase to which the particles were transferred immediately before is less than the reference value REF, the generation of a new variable is prohibited. Here, the solid solution phase to which the particles were transferred immediately before is the phase (i.e., the lowest phase) to which the particles are transferred when the charge / discharge of the target cell is switched, and is a Li-rich phase when the target cell is charged and a Li-poor phase when the target cell is discharged. The reference value REF can be set arbitrarily, but in this example, it is 50% (REF=N / 2) of the total particle number N.

[0116] To explain using the example shown in Figure 19, (1) when the number of particles in the Li-rich phase, which is the bottom solid solution phase, is equal to or greater than the reference value REF (see the upper diagram), it is considered that when the target cell is switched from discharging to charging, the particles belonging to the Li-rich phase transition from the bottom through the two-phase coexistence phase to the Li-poor phase. This is the same idea as that explained in Figure 18, and a new variable is generated to represent the two-phase coexistence phase.

[0117] In contrast, (2) when the number of particles in the Li-rich phase is less than the reference value REF (see the figure below), when the target cell is switched from discharging to charging, it is considered that the upper particles (particles with larger particle numbers) among the particles belonging to the two-phase coexistence phase will transition to the Li-poor phase in order, replacing the lower particles (particles with smaller particle numbers) among the particles belonging to the Li-rich phase. It is also considered that the upper particles from the Li-rich phase will transition to the two-phase coexistence phase in order.

[0118] In this way, when the charge and discharge of the target cell are switched, (1) a new variable is generated only when the condition that the number of particles of the solid solution phase from which the particles are transferred is equal to or greater than the reference value REF is satisfied. This means that (1A) when the target cell is switched from charge to discharge, a new variable is generated only when the target cell has a sufficient SOC change and has been continuously charged before the switching, or (1B) when the target cell is switched from discharge to charge, a new variable is generated only when the target cell has a sufficient SOC change and has been continuously discharged before the switching.

[0119] On the other hand, (2) when the above condition is not satisfied (when the number of particles of the solid solution phase from which the particles are transferred is less than the reference value REF), the movement of the particles is considered as follows. (2A) When the target cell is switched from charging to discharging, if the charging of the target cell before the switching did not involve a large change in SOC, no variable is generated. Also, (2B) when the target cell is switched from discharging to charging, if the discharging of the target cell before the switching did not involve a large change in SOC, no variable is generated. In short, when the charging and discharging of the target cell are frequently switched, it is considered that the particles belonging to the two-phase coexistence phase return to the solid solution phase they belonged to before the switching.

[0120] In this case, the "number of particles" belonging to the solid solution phase is used for the explanation. The "capacity" of the solid solution phase is proportional to the number of particles belonging to the solid solution phase. Therefore, the number of particles can be interpreted as the capacity. The reference value REF is the capacity equivalent to SOC50% of the target cell.

[0121] FIG. 20 is a diagram for explaining the second and third additional rules. The second additional rule is based on the first additional rule, and is intended to reliably reduce the number of variables for expressing particles belonging to the two-phase coexistence phase and quickly eliminate the two-phase coexistence phase. More specifically, a condition is imposed that the current Ic due to the phase transition from the top two-phase coexistence phase (the two-phase coexistence phase to which the particle with the largest particle number belongs) to the solid solution phase is greater than the current Iout due to the particles undergoing phase transition from the two-phase coexistence phase and a current value determined according to the particle number change Δn between the phases due to the most recent charge and discharge (see formula (31)). Note that the right side of formula (31) corresponds to the "set value" according to the present disclosure.

number

[0122] An example shown in FIG. 20 will be used for explanation. Assume a situation in which a target cell that was recently discharged is being charged. The numbers of particles in the seven phases are represented as p to v. The current due to particles that undergo a phase transition from the two-phase coexistence phase with the particle number s generated by the past discharge is represented as Is. The current due to particles that undergo a phase transition from the two-phase coexistence phase with the particle number u generated by the most recent charge is represented as Iu. The sum of the absolute values ​​of these two currents is |Iout| in equation (31), that is, the total value (absolute value) of the current due to particles that undergo a phase transition from the two-phase coexistence phase (|Iout|=|Is|+|Iu|).

[0123] According to the first additional rule, a new variable is generated when the particle number change due to the most recent charging of the target cell, that is, the number of particles Δn=v that have undergone a phase transition from the Li-rich phase due to the charging of the target cell, becomes equal to or greater than a reference value. The second additional rule is to actively cause the particles to undergo a phase transition from the top two-phase coexistence phase (in this example, the two-phase coexistence phase with particle number s) to zero before generating a new variable. Specifically, the current Is due to particles undergoing a phase transition from the two-phase coexistence phase with particle number s to the Li-poor phase is determined to satisfy formula (32). Note that the current due to the particles undergoing a phase transition is proportional to the reaction current density of the particles, so the right side of formula (32) is determined based on the product of the reaction current density of the particles belonging to the two-phase coexistence phase and the number of particles (u+v) that have undergone a phase transition from the Li-rich phase. By applying formula (32) according to the first additional rule, the particle number s is reliably set to zero before the condition for allowing the creation of a new variable is established.

number

[0124] In this way, by considering that the current corresponding to the previous particle number change flows from the two-phase coexistence phase to the solid solution Li-poor phase before a new variable is generated, the top two-phase coexistence phase can be quickly eliminated. Note that, when the particle number (u+v) of the solid solution phase approaches the reference value REF with the charging of the target cell, if the two-phase coexistence phase with particle number s remains, it is preferable to assume that all the current (Iout) flows from the two-phase coexistence phase with particle number s.

[0125] The third additional rule is to combine the solid solution phases separated into multiple parts, based on the second additional rule. Figure 20(C) shows a situation in which the discharge of the target cell continues from the situation shown in Figure 20(B), and the capacity of the Li-rich phase with a smaller particle number reaches the reference capacity Cref. In this example, before the combination, the Li-poor phase is separated into three parts and the Li-rich phase is separated into two parts above the two-phase coexistence phase (see the dashed-dotted frame). In this case, three pairs of variables are required to represent the Li-poor phase, and two pairs of variables are required to represent the Li-rich phase.

[0126] According to the third additional rule, Li-poor phases are combined with each other, and Li-rich phases are combined with each other (see FIG. 20(D)). As a result, even after the combination, the Li-poor phases are separated into two, but the Li-rich phases are combined into one. Therefore, the number of variables representing the Li-poor phases is reduced from three pairs to two pairs, and the number of variables representing the Li-rich phases is reduced to one pair. This reduces the computational load on the processor 401.

[0127] The embodiments disclosed herein should be considered to be illustrative and not restrictive in all respects. The scope of the present disclosure is defined by the claims, not by the description of the embodiments described above, and is intended to include all modifications within the meaning and scope of the claims. [Explanation of symbols]

[0128] 1 positive electrode, 2 negative electrode, 3 separator, 10 battery, 11 positive electrode current collector, 12 positive electrode composite layer, 20 monitoring unit, 21 negative electrode current collector, 22 negative electrode composite layer, 50 cell, 60 electrode body, 70 battery case, 71 positive electrode terminal, 72 negative electrode terminal, 80 electrolyte, 91 inlet, 92 power conversion device, 93 charging relay, 95 motor generator, 96 power transmission gear, 97 driving wheel, 100 battery management system, 121 positive electrode active material, 201 voltage sensor, 202 current sensor, 203 temperature sensor, 221 negative electrode active material, 40 battery ECU, 401 processor, 402 memory, 900 vehicle, 98 integrated ECU, 981 processor, 982 memory.

Claims

1. A method for managing a storage battery, the method comprising: managing a storage battery having a positive electrode including a positive electrode active material by a processor, the method comprising: The positive electrode active material has a plurality of phases each having a different content of charge carriers in the positive electrode active material, the plurality of phases include a rich phase having a high content of the charge carriers, a poor phase having a low content of the charge carriers, and a two-phase coexistence phase in which the rich phase and the poor phase coexist, The management method is a multi-particle model that expresses the positive electrode active material by a plurality of particles that are distinguished by particle numbers that indicate a reaction sequence of the positive electrode active material, and assumes that the contents of the charge carriers are equal between one or more particles that belong to each of the rich phase, the poor phase, and the two-phase coexistence phase, calculating an overvoltage of a particle belonging to each of the plurality of phases by the processor based on a measured voltage of the battery, a measured current of the battery, and an open circuit potential of the particle belonging to the phase; calculating, by the processor, a reaction current density for each of the plurality of phases based on the overpotential; and estimating, by the processor, a SOC of the battery based on the reaction current density of each of the plurality of phases.

2. In the multi-particle model, Between the particles belonging to the two coexisting phases, the content of the charge carriers is a predetermined fixed value, The method for managing a storage battery according to claim 1 , wherein the content of the charge carriers between the particles belonging to the rich phase and between the particles belonging to the poor phase is a variable value that changes depending on the reaction current density.

3. 3. The method of claim 2, wherein the multi-particle model includes, as variables for expressing the plurality of particles, a minimum value and a maximum value of the particle numbers of the particles belonging to the two-phase coexistence phase, or a number of particles belonging to the two-phase coexistence phase.

4. The method of claim 3 , wherein the number of variables is less than 100. .

5. The multi-particle model defines a reaction sequence of the positive electrode active material based on reaction resistances of the plurality of particles, The method for managing a storage battery according to any one of claims 1 to 4, wherein a difference in reaction resistance between particles having consecutive particle numbers among the plurality of particles is smaller than a predetermined value.

6. The method for managing a storage battery according to any one of claims 1 to 4, wherein the multi-particle model assumes that the plurality of particles have equal particle diameters, thereby causing the plurality of particles to have equal reaction areas and capacities.

7. The step of calculating the overvoltage includes, for each of the plurality of phases, calculating the open-circuit potential from the charge carrier content by referring to a relationship between the charge carrier content and the open-circuit potential; The storage battery management method according to any one of claims 1 to 4, further comprising a step of calculating the overvoltage based on a salt concentration overvoltage caused by a concentration gradient of the charge carrier in addition to the measured voltage, the measured current, and the open-circuit potential.

8. The step of estimating the SOC of the storage battery includes: multiplying, for each of the plurality of phases, the reaction current density in that phase by the number of particles belonging to that phase by the surface area of ​​the particles belonging to that phase; calculating an applied current flowing through the storage battery by adding the multiplied values ​​for the plurality of phases; The method for managing a storage battery according to any one of claims 1 to 4, further comprising the step of estimating a current value of the SOC of the storage battery by adding a value obtained by dividing the applied current by a battery capacity of the storage battery to a previous value of the SOC of the storage battery.

9. The step of estimating the SOC of the storage battery includes: calculating a content of the charge carriers in each of the plurality of phases by multiplying the reaction current density in that phase by a surface area of ​​particles belonging to that phase by a time elapsed since a previous estimation of the SOC of the storage battery; multiplying, for each of the plurality of phases, the charge carrier content by the number of particles belonging to that phase; Adding the multiplied values ​​for the multiple phases; The method for managing a storage battery according to any one of claims 1 to 4, further comprising a step of estimating an SOC of the storage battery by dividing the sum by a total number of particles in the plurality of particles.

10. The multi-particle model is a method for determining whether a particle belonging to a first phase, which is one of the rich phase and the poor phase, transitions to a second phase, which is the other, due to charging and discharging of the storage battery, and then when charging and discharging of the storage battery are switched, It is assumed that when the number of particles belonging to the second phase exceeds a reference value, the particles belonging to the second phase undergo a phase transition to the first phase via the two-phase coexistence phase; 5. The method for managing a storage battery according to claim 1, wherein when the number of particles belonging to the second phase falls below the reference value, it is assumed that the particles belonging to the two-phase coexistence phase return to the first phase.

11. the multi-particle model sets a current flowing when returning a particle belonging to the two-phase coexistence phase to the first phase to a value greater than a set value; 11. The method for managing a storage battery according to claim 10, wherein the set value is determined based on a product of a reaction current density of particles belonging to the two-phase coexistence phase and a number of particles that have transitioned from the first phase to the second phase before switching between charging and discharging of the storage battery.

12. The method for managing a storage battery according to claim 11, wherein the multi-particle model combines at least a portion of the two or more particle groups when particles belonging to the rich phase or the poor phase are separated into two or more particle groups.

13. A battery management system comprising the processor according to any one of claims 1 to 4.

Images