Storage battery management method and battery management system

Abstract

The positive electrode active material includes a rich phase in which the content of charge carriers is high, a lean phase in which the content of charge carriers is low, and a two-phase coexisting phase in which the rich phase and the lean phase coexist. In a multi-particle model in which a positive electrode active material is represented by a plurality of particles distinguished by a particle number representing a reaction sequence of the positive electrode active material, the management method assumes that the charge carrier content between one or more particles belonging to a rich phase, a lean phase, and a two-phase coexistence phase is equal to each other, and on the basis of this, the charge carrier content between the particles belonging to the phase is determined to be equal to the charge carrier content between the particles belonging to the two-phase coexistence phase. Comprises: a step for calculating the overvoltage of the particle for each of a plurality of phases; a step for calculating a reaction current density on the basis of the overvoltage for each of the plurality of phases; and a step for estimating the SOC of the storage battery on the basis of the reaction current density of each of the plurality of phases.

Description

Technical Field

[0001] The present invention relates to a battery management method and a battery management system. Background Art

[0002] A technique for improving the estimation accuracy of the SOC (State Of Charge) of a storage battery is proposed. 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.) and non-patent document 2 (Tsuyoshi Sasaki, Yoshio Ukyo and Petra Novak. Memory effect in a lithium-ion battery. Nature materials, Volume 12, June 2013.) disclose a technique for estimating the SOC of a storage battery having a positive electrode containing lithium iron phosphate by applying a multi-particle model (MPM: Many Particle Model). The multi-particle model is a model that formulates electrochemical phenomena related to SOC estimation by expressing an active material contained in an electrode (positive electrode active material in Non-Patent Documents 1 and 2) using a plurality of particles. Summary of the invention

[0003] By adopting a multi-particle model, the estimation accuracy of SOC can be improved compared to a single-particle model. On the other hand, the computational load of the processor may increase. In more detail, in a multi-particle model, since variables are used for each particle, it is necessary to ensure a memory capacity of (number of particles) × (memory usage for each particle). Therefore, for example, when thousands of particles are used, the memory usage will be too large, and as a result, the computational load of the processor may be too large. This issue is particularly prominent when using a computing processing device with limited computing resources (vehicle-mounted ECU (Electronic Control Unit), portable terminal, etc.).

[0004] The present disclosure has been made to solve the above-mentioned problems, and one of the objects of the present disclosure is to estimate the SOC of a battery with high accuracy while reducing the calculation load of a processor.

[0005] A battery management method according to an aspect of the present disclosure manages a battery having a positive electrode containing a positive electrode active material through a processor. The positive electrode active material has a plurality of phases in which the contents of charge carriers in the positive electrode active material are different from each other. The plurality of phases include a rich phase with a large content of charge carriers, a poor phase with a small content of charge carriers, and a two-phase coexistence phase in which a rich phase and a poor phase coexist. The management method assumes that the contents of charge carriers between one or more particles belonging to the phase are equal to each other in each phase of the rich phase, the poor phase, and the two-phase coexistence phase in a multi-particle model in which the positive electrode active material is represented by a plurality of particles distinguished by particle numbers representing the reaction sequence of the positive electrode active material, and includes the first step to the third step on this basis. The first step is a step in which, for each of the plurality of phases, the overvoltage of the particle is calculated by the processor based on the measured voltage of the battery, the measured current of the battery, and the open potential of the particle belonging to the phase. The second step is a step in which, for each of the plurality of phases, the reaction current density is calculated by the processor based on the overvoltage. The third step is a step of estimating the SOC of the battery by the processor based on the reaction current density of each of the plurality of phases.

[0006] In the above method, by using a multi-particle model, the SOC of the battery can be estimated with high accuracy. In addition, it is assumed that the content of charge carriers between particles belonging to each phase is equal, so that the overvoltage (and the reaction current density based on the overvoltage) of all particles belonging to each phase are calculated at once. As a result, compared with the case where the overvoltage (and the reaction current density) are calculated separately for each particle, the calculation load of the processor can be reduced. Therefore, according to the above method, the SOC of the battery can be estimated with high accuracy while reducing the calculation load of the processor. The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 This is a diagram schematically showing the overall configuration of a vehicle equipped with a battery management system according to an embodiment of the present disclosure. Figure 2 It is a perspective view schematically showing an example of a single body structure. Figure 3 It is a diagram showing an example of the structure of an electrode body. Figure 4This is a diagram showing the relationship between the lithium content and the open potential of the positive electrode active material when the positive electrode active material is assumed to be a single particle in a lithium iron phosphate lithium ion battery. Figure 5 This is a conceptual diagram used to illustrate the multi-particle model. Figure 6 : is a flowchart showing the processing procedure of the SOC estimation process using the comparison model. Figure 7 This is a conceptual diagram used to illustrate the reaction sequence in the comparison model. Figure 8 This is a conceptual diagram for explaining the manner of phase transition of each particle in the comparative model. Fig. 9 This is a conceptual diagram for explaining the current flowing in each particle in the comparative model. Fig.10 This is a first conceptual diagram for explaining the difference between the comparative model and the simplified model. Fig.11 This is a second conceptual diagram for explaining the difference between the comparative model and the simplified model. Fig.12 This is a third conceptual diagram for explaining the difference between the comparative model and the simplified model. Fig.13 This diagram compares the way of considering phase transition of multiple particles between the comparative model and the simplified model. Fig.14 This is a diagram for explaining phase transition of multi-particles accompanying battery discharge. Fig.15 This is a diagram for explaining phase transition of multi-particles accompanying battery charging. Fig.16 This is a flowchart showing a first example of the processing procedure of the SOC estimation process using the simple model in the present embodiment. Fig.17 1 is a flowchart showing a second example of the processing procedure of the SOC estimation process using the simple model in the present embodiment. Fig.18 This is a conceptual diagram for explaining the barcoding of variables. Fig.19 This is a diagram for explaining the first additional rule. Fig. 20 It is a diagram for explaining the second and third additional rules. DETAILED DESCRIPTION

[0008] Hereinafter, the embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. In addition, the same reference numerals are given to the same or corresponding parts in the drawings, and their description will not be repeated.

[0009] In the following, the battery management system (BMS: Battery Management System) involved in the present disclosure is described by taking the configuration of a hybrid vehicle (HEV: Hybrid Electric Vehicle), more specifically a plug-in hybrid vehicle (PHEV: Plug-in Hybrid Electric Vehicle) as an example. However, the battery management system involved in the present embodiment can be applied to all vehicles equipped with batteries for driving. That is, the battery management system involved in the present embodiment can also be installed in electric vehicles (BEV: Battery Electric Vehicle), fuel cell vehicles (FCEV: Fuel Cell Vehicle Electric Vehicle), etc. Moreover, the use of the battery management system involved in the present disclosure is not limited to vehicles, and can also be used for fixed placement, for example.

[0010] [Implementation Method] <Overall composition> Figure 1 1 is a diagram schematically showing the overall structure of a vehicle equipped with a battery management system according to an embodiment of the present disclosure. A vehicle 900 is provided with a battery management system 100. The battery management system 100 includes a battery 10 as a battery pack, a monitoring unit 20, a system main relay (SMR: System Main Relay) 30, and a battery ECU (Electronic Control Unit) 40. The vehicle 900 also includes an inlet 91, a power conversion device 92, a charging relay (CHR) 93, a power control unit (PCU: Power Control Unit) 94, an electric generator (MG) 95, a power transmission gear 96, a drive wheel 97, and an integrated ECU 98.

[0011] The battery 10 stores electric power for driving the electric generator 95, and supplies the electric power to the electric generator 95 through the PCU 94. When the electric generator 95 generates electric power, the battery 10 receives the generated electric power through the PCU 94 and is charged. The battery 10 is a battery pack including one or more battery modules. Each of the one or more battery modules includes a plurality of cells 50. Each cell 50 is a lithium ion secondary battery. Figure 2 and Figure 3 The structure of the single body 50 will be described.

[0012] 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 for charging and discharging the battery 10. The temperature sensor 203 detects the temperature T of the battery 10. Each sensor outputs a signal indicating its detection result to the battery ECU 40.

[0013] The SMR 30 is provided on a power line connecting the battery 10 and the PCU 94. When the SMR 30 is closed, the battery 10 can be charged and discharged.

[0014] The battery ECU 40 includes a processor 401 and a memory 402. The processor 401 is a calculation 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). In the memory 402, a system program including an OS (Operating System), a control program including a computer-readable code required for control calculations, and various parameters for managing the battery 10 are stored. The processor 401 implements various processes by reading out the system program, the control program, and the parameters, expanding them onto the memory 402, and executing them. In the present embodiment, the main process performed by the processor 401 is, for example, a process for estimating the SOC (State Of Charge) of the battery 10 (each cell in the battery pack). This process will be described in detail later.

[0015] The inlet 91 is configured to be able to connect a charging connector (not shown) provided at the front end of the charging cable with mechanical connection. The inlet 91 is connected to the charging connector to ensure electrical connection between the charging device (not shown) and the vehicle 900. In addition, the integrated ECU 98 of the vehicle 900 and the control device (not shown) of the charging device can exchange various signals.

[0016] Power conversion device 92 is, for example, an AC / DC converter and converts AC power supplied from a charging device via a charging cable into DC power for charging battery 10 .

[0017] 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 can be performed.

[0018] 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.

[0019] The motor generator 95 is an AC rotating electric machine, for example, a permanent magnet type synchronous motor having a rotor in which a permanent magnet is embedded. The output torque of the motor generator 95 is transmitted to the drive wheel 97 through the power transmission gear 96, so that the vehicle 900 travels. In addition, the motor generator 95 generates electricity using the rotational force of the drive wheel 97 when the vehicle 900 is braked. The generated power of the motor generator 95 is converted into charging power for the battery 10 by the PCU 94.

[0020] 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 while coordinating with the battery ECU 40.

[0021] <Single body composition> Figure 2 It is a perspective view schematically showing an example of the structure of the single body 50 . Figure 2 , a perspective view of the interior of a cell 50 is shown. In this example, the cell 50 is a sealed square battery. The shape of the cell 50 may also be, for example, cylindrical. Alternatively, the cell 50 may also be a cell constituting 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 terminal 71 and a negative terminal 72.

[0022] The electrode body 60 has an outer shape of, for example, a flat rectangular parallelepiped. The electrode body 60 is housed in the battery case 70 in a manner such that the long sides of the flat rectangular parallelepiped extend along the long side direction of the battery case 70. The battery case 70 may be made of a metal such as an aluminum (Al) alloy. The battery case 70 may also be a package such as an Al laminated film. The electrolyte 80 is injected into the battery case 70 to impregnate the electrode body 60. The liquid level of the electrolyte 80 is shown by a single dotted line.

[0023] Figure 3 is a diagram showing an example of the structure of the electrode body 60. Figure 2 and Figure 3 The electrode body 60 is formed by alternately stacking and winding positive electrodes 1 and negative electrodes 2 with separators 3 interposed therebetween. Figure 3 An exploded view of the winding process is shown in FIG.

[0024] The positive electrode 1 is in a sheet shape and includes a positive electrode current collector 11 and a positive electrode composite material layer 12. The positive electrode current collector 11 is electrically connected to a positive electrode terminal 71. The positive electrode current collector 11 may be, for example, an aluminum (Al) foil, an Al alloy foil, or the like.

[0025] In this example, the positive electrode composite material layer 12 is formed on both the front and back surfaces of the positive electrode current collector 11. However, the positive electrode composite material layer 12 may be formed only on the surface (either side) of the positive electrode current collector 11. The positive electrode composite material layer 12 includes a positive electrode active material 121 (see Figure 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, such as lithium iron phosphate (LiFePO4). Two or more positive electrode active materials may also be used in combination. The conductive material may include, for example, at least one selected from carbon black (acetylene black, etc.), vapor grown carbon fiber (VGCF), carbon nanotubes (CNT) and graphene sheets. The binder may include, for example, at least one selected from carboxymethyl cellulose (CMC), styrene butadiene rubber (SBR), polyvinylidene fluoride (PVdF) and polytetrafluoroethylene (PTFE).

[0026] The negative electrode 2 is in a sheet shape and includes a negative electrode current collector 21 and a negative electrode composite material 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.

[0027] In this example, the negative electrode composite material layer 22 is formed on both the surface and the back of the negative electrode collector 21. However, the negative electrode composite material layer 22 can also be formed only on the surface (either side) of the negative electrode collector 21. The negative electrode composite material layer 22 includes a negative electrode active material 221 and a binder (not shown). The negative electrode active material 221 can be, for example, a carbon-based negative electrode active material such as natural graphite, easily graphitized carbon, and non-graphitized carbon, or an alloy-based negative electrode active material containing silicon (Si), tin (Sn), etc. The binder uses a material that can be used as a binder contained in the positive electrode active material layer.

[0028] The separator 3 is a strip-shaped film. The separator 3 is disposed between the positive electrode 1 and the negative electrode 2 to electrically insulate the positive electrode 1 from the negative electrode 2. The material of the separator 3 may be, for example, a porous film made of polyolefin resins such as polyethylene (PE) and polypropylene (PP), or a polyamide resin such as nylon and aromatic polyamide (aramid), or a woven or non-woven fabric made of polypropylene, polyethylene terephthalate (PET), methyl cellulose, or the like.

[0029] The electrolyte 80 contains at least a lithium (Li) salt and a solvent. The Li salt is a supporting electrolyte dissolved in a 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. The electrolyte 80 may also contain a known functional additive in addition to the Li salt and the solvent.

[0030] <Lithium composition and OCP> Figure 4 This is a graph showing the relationship between the lithium content and the open circuit potential (OCP) of the positive electrode active material in a lithium iron phosphate battery assuming that the positive electrode active material is a single particle. The horizontal axis represents the lithium content in the positive electrode active material. The lithium content refers to the Li x The lithium content x in FePO4 (0≤x≤1). The lithium component corresponds to the "charge carrier content" involved in the present disclosure. The vertical axis represents the OCP of the positive electrode active material. Fig.12 Same.

[0031] Figure 4 The lithium composition-OCP curve shown has a maximum point and a minimum point which are inflection points, respectively. Usually, when a lithium iron phosphate 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 lithium component higher 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 lithium component lower 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.

[0032] Between the two inflection points (maximum point and minimum point), the OCP of the positive electrode active material decreases roughly in proportion to the decrease in the lithium component x. In this example, the voltage difference between the two inflection points is about 20mV. The average voltage of the two inflection points (equilibrium voltage of the two-phase coexistence phase) V ave It is about 3.43 V. In an actual lithium iron phosphate ion battery, since the positive electrode active material includes a plurality of particles, a flat lithium composition-OCP curve is observed between x=0.05 and x=0.95.

[0033] <Multi-particle model> In the present embodiment, a multi-particle model (MPM) is used to estimate the SOC of the battery 10 .

[0034] Figure 5 : is a conceptual diagram for explaining the multi-particle model. In the single-particle model, the positive electrode active material is schematically represented as a single particle, and the negative electrode active material is schematically represented as a single particle.

[0035] In contrast, the multi-particle model refers to a model in which the positive electrode is assumed to be composed of multiple (N) spherical particles connected to each other electronically and ionically, 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 schematically represented as multiple particles. The negative electrode active material 221 is schematically represented as a single particle in this example, but the negative electrode active material 221 can also be represented as multiple particles.

[0036] also, Figure 5 FIG. 1 shows the charging state of the battery 10. When the battery 10 is charged, lithium ions (Li + ) are extracted from the positive electrode active material 121, while lithium ions are inserted into the negative electrode active material 221. At this time, a current (applied current I described later) flows through the battery 10. app ). Although not shown in the figure, when the battery 10 is discharged, the direction of the current is Figure 5 The directions shown are opposite.

[0037] By using a multi-particle model, the estimation accuracy of SOC can be improved compared to the case of using a single-particle model. On the other hand, the computational load of the processor 401 may increase. In more detail, in the multi-particle model, variables are used for each particle. In addition, thousands of particles are required to maintain the smoothness of the computational results between particles in the multi-particle model. Moreover, the SOC may fluctuate between cells, so it is desirable to estimate the SOC for each cell 50. In this way, in order to obtain smooth computational results for all cells, it is necessary to ensure a memory capacity equivalent to (memory usage for each particle) × (thousands of particles) × (tens of cells). Therefore, the usage of the memory 402 will be too large, and as a result, the computational load of the processor 401 may be too heavy. This issue is particularly significant in a case where computing resources are limited, such as in a vehicle-mounted battery ECU 40.

[0038] Therefore, in this embodiment, in order to reduce the computational load of the processor 401, a simplified multi-particle model is used. This model is 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 the understanding of the simplified model, the SOC estimation process using the comparison model is first described. For details about the comparison model, please refer to Japanese Patent Publication No. 2018-169398.

[0039] <Compare Models> Figure 6This is a flowchart showing the processing sequence of the SOC estimation process using the comparison model. In this example, the SOC estimation process is executed for each monomer. The monomer that is the execution object of the SOC estimation process is denoted as the "object monomer". The SOC estimation process is repeatedly executed. (t) represents the value in the current SOC estimation process (this value), and (t-1) represents the value in the previous SOC estimation process (previous value). Step S is abbreviated.

[0040] In S901 , the processor obtains from the sensor or reads from the memory 402 various variables (parameters) used in the current SOC estimation process.

[0041] In S902, the processor calculates the voltage V'(t) to be input to the comparison model according to equation (1). V′(t)=V(t)-I(t)·R d -dV c (t)…(1)

[0042] In formula (1), V(t) is the current value of the closed circuit voltage (CCV (Closed Circuit Voltage)) 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 electrode and the negative electrode). dVc(t) is the current value of the salt concentration overvoltage caused by the concentration gradient of lithium ions between the positive electrode active material and the negative electrode active material, and is calculated according to formula (2). α and β are coefficients appropriately set by prior experiments or simulations. dV c (t) = (1-α) dV c (t-1)+β·I(t)…(2)

[0043] In the multi-particle model, it is required to set the reaction sequence, that is, the order of particles participating in the reaction (embedding / de-embedding of lithium ions) in the multi-particles. In actual storage batteries, the reaction sequence may be related to various factors. Specific examples of factors include the distance from the collector foil to the positive electrode active material, the distance from the 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 set according to the particle size that follows the log-normal distribution (see Patent Document 1). Figure 1 (c)).

[0044] Figure 7 This is a conceptual diagram for explaining the reaction sequence in the comparison model. In the multi-particle model in which the reaction sequence is set according to the particle size, it is assumed that all particles are spherical. Therefore, when the radius of the jth particle (j is a natural number used to distinguish particles from each other) is set to r jIn the case of j =4πr j , the volume V of the jth particle j =4πr j 3 / 3. j=1~N.

[0045] The surface area of ​​the particle S j It is a parameter used to express the reaction area of ​​the positive electrode active material. The volume V of the particle j It is a parameter used to express the capacity of the positive electrode active material. The surface area / volume (S j / V j ) corresponds to the reaction area / capacity of the positive electrode active material. The smaller the particle size, the larger the surface area / volume of the particle, so the lithium composition is easier to change. The particles with easier lithium composition change have higher reaction sequences and are assigned smaller particle numbers. Therefore, the particle with particle number = 1 has the highest reaction sequence, and the particle with particle number = N has the lowest reaction sequence.

[0046] Accompanying the charge and discharge of the target cell, a plurality of particles undergo phase transition in order from particles with a high reaction sequence (particles with a small particle number).

[0047] Figure 8 This is a conceptual diagram for explaining the phase transition of each particle in the comparison model. Here, for simplicity, an example of a total number of particles N = 10 is shown. All particles originally belong to the Li-rich phase, but with the charging of the target monomer, the particles with particle numbers j = 1 and 2 phase transition to the Li-poor phase via the two-phase coexistence phase, and the particles with particle numbers j = 3 to 5 phase transition to the two-phase coexistence phase. In this way, in the comparison model, all particles are treated separately.

[0048] Which phase do the 10 particles belong to? The lithium composition x of the particles j If the lithium content of the particle is x j Determine, then according to the lithium composition-OCP curve, as the open potential U of the particle j Sure.

[0049] Fig. 9 : This is a conceptual diagram for explaining the current flowing in each particle in the comparative model. In the comparative model, it is assumed that the applied current I flowing in the target single body app As the lithium content x of each particle j The corresponding overvoltage η j and distributed to multiple particles. Using the reaction current density i j To describe the current assigned to the jth particle.

[0050] Refer again Figure 6In S903, the processor calculates the overvoltage η of each of the multiple particles. j Specifically, the processor subtracts the open potential U of the jth particle from the voltage V' calculated according to the above equations (1) and (2) for each particle. j , from which the overvoltage η of the particle is calculated j (Refer to formula (3)). Overvoltage η j It refers to the difference between the CCV of the target cell and the OCV (Open Circuit Voltage) of the particle. η j (t) = V′(t)-U j (x j (t-1))…(3)

[0051] In formula (3), the open potential U j Is the lithium component x j The function is based on Figure 8 More specifically, the processor calculates the previous value x of the lithium content in the lithium content-OCP curve. j The open potential corresponding to (t-1) is taken as U j .

[0052] In S904, the processor calculates the overvoltage η for each particle based on the overvoltage η calculated in S903. j Calculate the reaction current density i j In more detail, the reaction current density i j It is calculated according to the following Butler-Volmer equation (4). Oj is the exchange current density, which is a value preset according to the particle number. F is the Faraday constant. R is the gas constant. T is the temperature measured by the temperature sensor.

[0053] In S905, the processor calculates the reaction current density i of each of the plurality of particles calculated in S903. j The surface area S of the particle j The product of the reaction current I flowing in the jth particle is calculated. j (Refer to formula (5)). I j (t) = S j ·i j (t)…(5)

[0054] In S906, the processor calculates the reaction current I in S905. jThe product of the cycle Δt of the SOC estimation process (the time between the current SOC estimation process and the previous SOC estimation process) and the capacity Q of the jth particle is divided by j The processor calculates the division value and the previous value of the lithium content of the particle (x j The value obtained by adding the value of (t-1)) is taken as the current value x of the lithium content of the particle. j (t) (See formula (6)). Formula (6) shows that the lithium component x j Only the change with the reaction current I j The case of proportional quantities (charge amounts).

[0055] In S907, the processor calculates the lithium composition x calculated in S906. j The SOC of the target cell is estimated by taking the corresponding weighted average. More specifically, the processor calculates the lithium content x of the particle for each particle. j The volume V of the particle j The processor then multiplies the volume of all particles by the volume of the particles (equivalent to the total capacity) and adds the multiplied values ​​for all particles. The processor then divides the added value by the total volume of all particles (equivalent to the total capacity) (see formula (7)). Thus, the so-called "center of gravity position" of all particles in the lithium component-OCP curve is calculated, and the center of gravity position is equivalent to the SOC of the target monomer.

[0056] In S908, the processor determines whether the SOC of all cells has been estimated. If there are cells whose SOC has not been estimated (No in S908), the processor returns the process 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.

[0057] <Simple Model> Next, the simplified model in this embodiment will be described in comparison with a comparative model.

[0058] Fig.10 This is the first conceptual diagram for explaining the difference between the comparative model and the simplified model. As mentioned above, multiple particle sizes are set in the comparative model. In contrast, in the simplified model, all particles are set to have equal particle sizes. That is, the reaction area and capacity of all particles are equal to each other. However, it is common that particles with higher reaction sequences are assigned smaller particle numbers.

[0059] Fig.11 This is a second conceptual diagram for explaining the difference between the comparative model and the simplified model. In the comparative model, the lithium component x is calculated for each particle.j (See the above formula (6)). In contrast, in the simplified model, three particle groups corresponding to the three phases are assumed, and the lithium content is calculated for each particle group. Figure 8 Similarly, an example based on 10 particles is used for further description. In addition, variables related to the Li-poor phase are denoted by p, variables related to the two-phase coexistence phase are denoted by c, and variables related to the Li-rich phase are denoted by r.

[0060] Fig.12 This is the third conceptual diagram used to explain the difference between the comparative model and the simplified model. In the comparative model, all particles are considered separately. Figure 8 In the example shown, particles belonging to the Li-poor phase are particles with particle numbers j=1 and 2, particles belonging to the two-phase coexistence phase are particles with j=3, 4, and 5, and particles belonging to the Li-rich phase are particles with j=6, 7, 8, 9, and 10.

[0061] In contrast, in the simplified model, particles belonging to the same phase in the three phases are considered to be a group of particles. In other words, multiple particles are divided into a group of particles belonging to the Li-poor phase, a group of particles belonging to the two-phase coexistence phase, and a group of particles belonging to the Li-rich phase. Each of the three particle groups is represented by the minimum value (Min) and the maximum value (Max) of the particle number of the particles contained in the particle group. Fig.12 In the example shown, 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.

[0062] In addition, each of the three particle groups can be represented by the number of particles belonging to the particle group. According to this embodiment, even if the multi-particle model contains thousands of particles, the variables used to represent these particles (the minimum and maximum values ​​of the particle numbers or the number of particles) can be reduced to less than 100.

[0063] Fig.13 This diagram compares the way of considering phase transition of multiple particles between the comparative model and the simplified model. Fig.13 50% SOC during charging of the target cell is exemplified in FIG.

[0064] In the comparison model, each particle is separated from each other based on the reaction current density i j The corresponding reaction current Ij is used to calculate the lithium content x j (In this example, x4 to x7) (refer to the above equations (5) and (6)).

[0065] 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 as the lithium component. This value is a representative value of the lithium component in the two-phase coexistence phase and is fixed in advance. In this example, the particle group belonging to the two-phase coexistence phase represented by Min=4 and Max=7 has a lithium component x c =0.50.

[0066] The lithium component is also common to all particles included in the particle group belonging to the Li-poor phase. This lithium component is denoted as x p .x p Different from x in the two-phase coexistence phase c , which is a variable value that is not fixed. The same is true for the Li-rich phase. The lithium component of the particle group belonging to the Li-rich phase is denoted by x r .

[0067] Furthermore, 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 of the Li-poor phase, the two-phase coexistence phase, and the Li-rich phase are respectively denoted as I p ,I c ,I r The sum of the three reaction currents and the applied current I flowing in the target cell app The following relationship holds (see formula (8)). I app =I p +I c +I r …(8)

[0068] Reaction current I p ,I c ,I r Each can be calculated as follows. Taking the Li-poor phase as an example, the reaction current I p For example, it is calculated according to Formula (9). In addition, p at the lower right of the sum symbol means that all particles belonging to the Li-poor phase are taken as the object. I p =∑ p I j …(9)

[0069] Alternatively, the relationship of formula (10) also holds true, so the reaction current I can be calculated as for a single particle by summing up the reaction conductivity (described later). p . S is the particle surface area common to all particles.

[0070] The reaction current I calculated in this way p ,I c ,I rThe lithium content is changed as follows. Here, the lithium-poor phase is used as an example to explain the change in the lithium content of the Li-poor phase Δx. p Calculate as in formula (11). p Represents the capacity of the Li-poor phase.

[0071] In addition, 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 the particle group. The capacity of each of the three particle groups is proportional to the number of particles contained in the particle group. Therefore, as the number of particles contained in the particle group increases, the capacity of the particle group becomes larger. If the number of particles belonging to the Li-poor phase is represented by n p , let the capacity (common) of each particle be q, then Q p =n p ×q.

[0072] By calculating the change Δx of the lithium content in the Li-poor phase p The previous value x of the lithium content of the Li-poor phase p (t-1) is added to calculate the current value x of the lithium content of the Li-poor phase p (t)(refer to formula (12)). x p (t) = x p (t-1)+Δx p …(12)

[0073] Here, the current value x of the lithium content of the Li-poor phase is p (t) does not exceed the boundary value between the Li-poor phase and the dual-phase coexistence phase (x=0.05 in this example). Particles corresponding to the change in lithium content exceeding the boundary value move from the Li-poor phase to the dual-phase coexistence phase.

[0074] The capacity change corresponding to the change in lithium content exceeding the critical value is expressed as (x p -0.05)×n p ×q. On the other hand, the capacity change 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) is expressed as (0.5-0.05)×Δn[p→c]×q. These two capacity changes are equal to each other (see formula (13)). (x p -0.05)*n p *q=(0.5-0.05)*Δn[p→c]*q…(13)

[0075] When equation (13) is solved for the number of particles Δn[p→c] that migrate from the Li-poor phase to the two-phase coexistence phase, Δn[p→c] is expressed as equation (14).

[0076] In this way, the lithium content of 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 content of particles belonging to the Li-poor phase does not change by more than 0.05. When the lithium content reaches the boundary value of the Li-poor phase, the reaction current I p Here, the movement from the Li-poor phase to the two-phase coexistence phase is used as an example for explanation, but the number of moving particles Δn between each phase can also be calculated in the same way for the movement from the two-phase coexistence phase to the Li-poor phase, the movement from the Li-rich phase to the two-phase coexistence phase, and the movement from the two-phase coexistence phase to the Li-rich phase.

[0077] In addition, the reaction conductivity of each of the three particle groups is the sum of the reaction conductivity of the particles included in the 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 the particle group. Therefore, as the number of particles contained in the particle group increases, the reaction resistance of the particle group becomes lower.

[0078] <Phase Transition> How the multiparticles undergo phase transition based on the above-described simplified model will be described in more detail, divided into charging and discharging of the battery 10 .

[0079] Fig.14 This is a diagram for explaining phase transition of multi-particles accompanying discharge of the battery 10 . Fig.14 , it is schematically shown how the phases to which the multiparticles belong change when the battery 10 is simply discharged from SOC 100% to SOC 0%.

[0080] At SOC 100%, all particles belong to the Li-poor phase. When the discharge of battery 10 begins, starting from the particles with smaller particle numbers shown below in the figure, they transfer to the Li-rich phase via the two-phase coexistence phase in sequence. 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. In addition, since the positive electrode has residual capacity that can be charged but is not charged (the so-called reserved capacity), even at SOC 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.

[0081] As mentioned above, the multiple particles belonging to each phase are determined by the minimum and maximum values ​​of the particle numbers of the particles belonging to the phase. For example, at SOC 80%, the particle group belonging to the two-phase coexistence phase is determined by the minimum value (Min) = p and the maximum value (Max) = q of the particle number. The particle group belonging to the Li-rich phase is determined by Min = 1 and Max = p-1, and the particle group belonging to the Li-poor phase is determined by Min = q+1 and Max = N.

[0082] Fig.15 It is a diagram for explaining the phase transition of the multi-particles accompanying the charging of the battery 10 . Fig.15 , it is schematically shown how the phases to which the multi-particles belong change when the battery 10 is simply charged from SOC 0% to SOC 100%.

[0083] At SOC0%, except for particles with a reserved capacity, almost all particles belong to the Li-rich phase. When the battery 10 starts to charge, starting from the particles with a small particle number, they change to the Li-poor phase through the two-phase coexistence phase. As the SOC rises to 20%, 70%, and 100%, the number of particles belonging to the Li-rich phase decreases, while the number of particles belonging to the Li-poor phase increases.

[0084] <Processing Flow> Fig.16 1 is a flowchart showing a first example of the processing sequence of the SOC estimation process using the simplified model in this embodiment. The process shown in this flowchart (and the process described later) Fig.17 The processing shown in the flowchart of ) is executed when a preset condition is met (for example, each preset cycle). Each step is implemented by software processing performed by the battery ECU 40 (processor 401), but can also be implemented by hardware (circuitry) configured in the battery ECU 40.

[0085] In the present embodiment, the SOC estimation process is also executed for each “target cell.” However, the SOC estimation process may be executed for the entire battery or for each of a plurality of cells (for example, each battery module).

[0086] In S101 , the battery ECU 40 acquires various variables necessary for the current SOC estimation process from sensors and reads out previous values ​​of the variables necessary for the current SOC estimation process from the memory 402 .

[0087] 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 method is the same as that of the comparative model (see equations (1) and (2)). V′(t)=V(t)-I(t)·Rd -dV c (t)…(15) dV c (t) = (1-α) dV c (t-1)+β·I(t)…(16)

[0088] In S103, the battery ECU 40 calculates the overvoltage η of each particle group. More specifically, the battery ECU 40 calculates the common overvoltage η for all particle groups belonging to the two-phase coexistence phase according to equation (17): c U in formula (17) c It refers to the open potential corresponding to the representative value xc (=0.50) of the lithium component in the two-phase coexistence phase and is a fixed value. η c =V′(t)-U c (x c )…(17)

[0089] In addition, the battery ECU 40 calculates the overvoltage η according to equation (18) for the entire particle group belonging to the Li-lean phase. p U in formula (18) p It refers to the previous value x of the lithium component common to the Li-poor phase p The open potential corresponding to (t-1) is a variable value. p (t-1) is calculated in S110 described later. The battery ECU 40 also calculates the overvoltage η according to the formula (19) for the entire particle group belonging to the Li-rich phase. r . η p =V′(t)-U p (x p (t-1))…(18) η r =V′(t)-U r (x r (t-1))…(19)

[0090] In S104, the battery ECU 40 calculates the reaction current Ic of the entire particle group belonging to the two-phase coexistence phase (the total value of the reaction current of all particles belonging to the two-phase coexistence phase) according to equation (20). O It is set that the larger the particle number (i.e., the lower the reaction sequence), the smaller it is. For example, as the particle number increases, the exchange current density decreases linearly (i Oj =1 / R O ×j). By referring to such a preset relationship, the exchange current density can be set.

[0091] Similarly, the battery ECU 40 also calculates the reaction current I according to equations (21) and (22) for the entire particle group belonging to the Li-lean phase and the entire particle group belonging to the Li-rich phase. p ,I r .

[0092] In S105, the battery ECU 40 calculates the applied current I flowing in the target cell by obtaining the sum of the reaction currents of the respective phases calculated in S104. app (Refer to formula (23)). I app =I p +I c +I r …(twenty three)

[0093] In S106, the battery ECU 40 applies an applied current I flowing in the target cell. app The value obtained by dividing by the battery capacity C of the target cell is added to the previous value SOC(t-1) of the SOC of the target cell, thereby estimating the current value SOC(t) of the SOC of the target cell (see equation (24)).

[0094] In S107, the battery ECU 40 calculates the number of particles Δn that undergo phase transition between the three phases based on the reaction currents Ip, Ic, and Ir of each phase. That is, the battery ECU 40 calculates the number of particles Δn[r→c] that undergo phase transition from the Li-rich phase to the two-phase coexistence phase, the number of particles Δn[c→p] that undergo phase transition from the two-phase coexistence phase to the Li-lean phase, the number of particles Δn[p→c] that undergo phase transition from the Li-lean phase to the two-phase coexistence phase, and the number of particles Δn[c→r] that undergo phase transition from the two-phase coexistence phase to the Li-rich phase. The calculation methods have been described in detail using equations (9) to (14), so they will not be repeated here.

[0095] Then, the battery ECU 40 determines which particle belongs to which phase based on the calculated particle number Δn. As described above, each of the three particle groups can be represented by the minimum value (Min) and the maximum value (Max) of the particle number of the particles included in the particle group. Furthermore, the battery ECU 40 calculates the current value n of the number of particles belonging to each phase. c (t), n p (t), n r (t) (See equations (25) to (27)). The number of particles can be used in the process of S206 described later. n c (t) = nc (t-1)+Δn[r→c]-Δn[c→p]+Δn[p→c]-Δn[c→r]…(25) n p (t)=np(t-1)+Δn[c→p]-Δn[p→c]…(26) n r (t) = n r (t-1)+Δn[c→r]-Δn[r→c]…(27)

[0096] In S108, the battery ECU 40 calculates the lithium content x of the entire particle group belonging to the Li-poor phase. p The previous value and the reaction current I calculated in S104 p The product of the cycle Δt of the SOC estimation process and the capacity (total capacity of the lean Li phase) Q p The values ​​obtained are added together to calculate the lithium content x of the entire particle group. p The current value of (refer to formula (28)). The same treatment is performed on the Li-rich phase (refer to formula (29)). However, in x p When (t)>0.05, x is set p (t) = 0.05. p When (t) < 0.95, 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)).

[0097] In S109, the battery ECU 40 determines whether the SOC of all cells has been estimated. If there are 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.

[0098] Fig.17 1 is a flowchart showing a second example of the processing procedure of the SOC estimation process using the simplified model in the present embodiment. The processes of S201 to S204 are similar to the processes of S101 to S104 in the first example (see Fig.16 ) are the same, so the description will not be repeated.

[0099] In S205, the battery ECU 40 calculates the lithium composition x of the entire particle group belonging to the Li-lean phase and the entire particle group belonging to the Li-rich phase. p 、x rThese processes are the same as the processes of S108 (refer to equations (28) and (29)).

[0100] 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 adds the value obtained by multiplying the lithium composition x of each phase by the number of particles n contained in the phase for the three phases. Then, the battery ECU 40 divides the above-mentioned added value by the total number of particles N (refer to formula (30)). Thus, the center of gravity position of all particles is calculated, so the center of gravity position can be used as the SOC of the target cell.

[0101] The subsequent processing of S207 and S208 is the same as the processing of S107 and S109 in the first example.

[0102] In the first example of the processing sequence of the SOC estimation process (refer to Fig.16 ), although the accumulated error of the detection values ​​of various sensors (voltage sensor, current sensor, etc.) is not as large, it is possible that the numerical calculation error is accumulated. In contrast, the second example of the processing order of the SOC estimation process (refer to 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 larger during charging and the estimated SOC becomes higher than the actual SOC (true value), the estimated OCV increases - the overvoltage η decreases - the estimated current decreases compared to the actual current - the estimated SOC rises slower than the actual SOC rise, and the estimated SOC is close to the true value.

[0103] As described above, in this embodiment, particles belonging to the two-phase coexistence phase are treated as a group of particles, and it is considered that the particle group has a common lithium component x that is representative of the two-phase coexistence phase. c In addition, the particles belonging to the Li-poor phase are treated as a group of particles, and the particles belonging to the Li-rich phase are treated as a group of particles, and it is assumed that these particle groups also have a common lithium component x p 、x r . In this way, the open potential U of all particles is calculated for each phase, and thus the overvoltage η (and thus the reaction current density i) is also calculated. As a result, compared with the comparison model in which all particles are treated separately, the variables used to represent the particles can be reduced. Therefore, according to this embodiment, the use of the multi-particle model can reduce the computational load of the battery ECU 40 (processor 401) while estimating the SOC of the battery 10 with high accuracy.

[0104] [Modifications] <Barcoding> If the battery 10 is repeatedly charged and discharged, in other words, if the battery 10 is switched between charging and discharging for many times, the variable representing the particles belonging to the two-phase coexistence phase (the variable of the maximum and minimum particle number pairs) will increase. This may result in what the inventors call "barcoding" of the variables.

[0105] Fig.18 This is a conceptual diagram for explaining the barcoding of variables. The closer to the top of the diagram, the larger the particle number. Therefore, below, the transfer of particles with large particle numbers is also referred to as transfer from the "upper side", and the transfer of particles with small particle numbers is also referred to as transfer from the "lower side".

[0106] First, assume that all particles are in the Li-poor phase and the SOC is 100% (see Fig.18 (A)). When the subject monomer is discharged from this state, the particles belonging to the Li-poor phase sequentially transfer from the bottom side through the two-phase coexistence phase to the Li-rich phase (refer to Fig.18 (B)) In this example, the target cell is discharged until the SOC reaches 0% (refer to Fig.18 (C)). At this time, some particles remain in the Li-poor phase and the two-phase coexistence phase.

[0107] Next, the target cell is charged from SOC0% to SOC20% to SOC90% (refer to Fig.18 (D) and Fig.18 (E)). In this way, the particles belonging to the Li-rich phase are transferred from the bottom to the Li-poor phase via the two-phase coexistence phase. At this time, particles different from the particles transferred to the two-phase coexistence phase by the first discharge become particles belonging 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.

[0108] Next, the target cell is discharged from SOC 90% to SOC 10% via SOC 80% (refer to Fig.18 (F) and Fig.18 (G)). In this way, the particles belonging to the Li-poor phase are transferred to the Li-rich phase again from the bottom through the two-phase coexistence phase. As a result, the particles belonging to the two-phase coexistence phase are divided into three particle groups.

[0109] Similarly, the target cell is charged from SOC 10% to SOC 80% (refer to Fig.18 (H)). As a result, the particles belonging to the Li-rich phase sequentially transfer from the bottom side through the two-phase coexistence phase to the Li-poor phase. As a result, the particles belonging to the two-phase coexistence phase are divided into four particle groups.

[0110] Finally, the target cell is discharged from SOC 80% to SOC 20% (refer to Fig.18(I)). As a result, the particles belonging to the Li-poor phase sequentially transfer from the lower side (particles with smaller particle numbers) through the two-phase coexistence phase to the Li-rich phase. As a result, the particles belonging to the two-phase coexistence phase are divided into five particle groups.

[0111] In this way, each time the charge and discharge of the target cell are switched, a part of the particles remain in the two-phase coexistence phase, and the particle group consisting of particles belonging to the two-phase coexistence phase increases. Fig.18 In the case of such a diagram, the plurality of particle groups belonging to the two-phase coexistence phase are each expressed as thin lines, which looks like a barcode. Such barcoding means that the variables expressing the particles belonging to the two-phase coexistence phase increase, so from the perspective of reducing the calculation load of the battery ECU 40, it is desirable to avoid barcoding. Therefore, in this modified example, in order to avoid barcoding and thereby reduce the calculation load of the battery ECU 40, three additional rules are set.

[0112] <Additional rules> Fig.19 This is a diagram for explaining the first additional rule. The first additional rule adds conditions to the generation of variables representing a particle group belonging to a two-phase coexistence phase. In more detail, when the charge and discharge of the target monomer are switched, if the number of particles of the target solid solution phase to which the particles have just transferred before the switch is greater than the reference value REF, the generation of new variables is allowed. On the other hand, when the number of particles of the target solid solution phase to which the particles have just transferred is less than the reference value REF, the generation of new variables is prohibited. Here, the target solid solution phase to which the particles have just transferred refers to the phase that becomes the transfer source of the particles accompanying the switching of the charge and discharge of the target monomer (i.e., the lowermost phase), which is a Li-rich phase when the target monomer is charged and a Li-poor phase when the target monomer is discharged. The reference value REF can be set arbitrarily, but in this example it is 50% of the total number of particles N (REF = N / 2).

[0113] use Fig.19 The example shown in FIG. 1 is used to illustrate that (1) when the number of particles of the bottom solid solution phase, i.e., the Li-rich phase, is greater than the reference value REF (see the figure above), it is considered that as the target monomer switches from discharge to charge, the particles belonging to the Li-rich phase sequentially transfer from the bottom side to the Li-poor phase via the two-phase coexistence phase. This is consistent with Fig.18 The consideration method is the same as that already explained in , and new variables are generated to represent the two-phase coexistence phase.

[0114] On the other hand, (2) when the number of particles in the above-mentioned Li-rich phase is less than the reference value REF (see the figure below), it is considered that with the switching of the target monomer from discharge to charge, the particles on the upper side (particles with large particle numbers) among the particles belonging to the two-phase coexistence phase are replaced by the particles on the lower side (particles with small particle numbers) among the particles belonging to the Li-rich phase and are sequentially transferred to the Li-poor phase. In addition, it is considered that from the Li-rich phase, the particles on the upper side are also sequentially transferred to the two-phase coexistence phase.

[0115] In this way, when the charge and discharge of the target cell are switched, (1) a new variable is generated only when the number of particles in the solid solution phase that is the transfer source of the particles is greater than the reference value REF. 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 before the switch and has been continuously charged, 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 before the switch and has been continuously discharged.

[0116] On the other hand, (2) when the above conditions do not hold (when the number of particles in the solid solution phase that is the transfer source of the particles is less than the reference value REF), the movement of the particles is considered to be as follows. (2A) When the object monomer is switched from charging to discharging, no variable is generated when the charging of the object monomer before the switching is not accompanied by a significant SOC change. In addition, (2B) when the object monomer is switched from discharging to charging, no variable is generated when the discharge of the object monomer before the switching is not accompanied by a significant SOC change. In short, when the charging and discharging of the object monomer are frequently switched, it is considered that the particles belonging to the two-phase coexistence phase will return to the solid solution phase to which they belonged before the switching.

[0117] In addition, here, the "number of particles" belonging to the solid solution phase is used for 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 also be replaced by capacity. The reference value REF becomes the capacity equivalent to SOC50% of the target cell.

[0118] Fig. 20 It is a diagram for explaining the second and third additional rules. The second additional rule is based on the first additional rule and is used to effectively reduce the variables used to represent particles belonging to the two-phase coexistence phase and quickly eliminate the two-phase coexistence phase. In more detail, the following conditions are added: the current Ic based on 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 based on the particles that undergo phase transition from the two-phase coexistence phase and the current value determined based on the change Δn in the number of particles between the phases of the most recent charge and discharge (refer to formula (31)). In addition, the right side of formula (31) is equivalent to the "set value" involved in the present disclosure.

[0119] use Fig. 20 The example shown is used for explanation. Assume that a target cell that has been recently discharged is charged. The number of particles in the seven phases is represented by p to v. Is represents the current of particles transferred from the two-phase coexistence phase based on the number of particles s generated by the past discharge. Iu represents the current of particles transferred from the two-phase coexistence phase based on the number of particles u generated by the most recent charge. The sum of the absolute values ​​of these two currents is |Iout| in formula (31), that is, the total value (absolute value) of the current based on the particles transferred from the two-phase coexistence phase (|Iout| = |Is| + |Iu|).

[0120] According to the first additional rule, when the number of particles accompanying the most recent charging of the object monomer changes, that is, the number of particles Δn=v transferred from the Li-rich phase accompanying the charging of the object monomer becomes greater than the reference value, a new variable is generated. The second additional rule is that before generating a new variable, the particles are actively phase-transferred from the top two-phase coexistence phase (in this case, the two-phase coexistence phase with a particle number s) so that the particles belonging to the two-phase coexistence phase are 0. Specifically, the current Is of the particles transferred from the two-phase coexistence phase to the Li-poor phase based on the particle number s is set to satisfy equation (32). In addition, the current of the particles based on the phase transfer is proportional to the reaction current density of the particles, so the right side of equation (32) is set based on the product of the reaction current density of the particles belonging to the two-phase coexistence phase and the number of particles transferred from the Li-rich phase (u+v). By applying equation (32) according to the second additional rule, the particle number s is effectively made 0 until the conditions for allowing the generation of new variables are met.

[0121] In this way, it is considered that before generating a new variable, the current corresponding to the particle number change just now flows from the two-phase coexistence phase to the solid solution phase, thereby being able to quickly eliminate the top two-phase coexistence phase. In addition, when the particle number (u+v) of the solid solution phase approaches the reference value REF accompanying the charging of the target monomer and a two-phase coexistence phase with a particle number s remains, it is preferably assumed that all currents (Iout) flow from the two-phase coexistence phase with a particle number s.

[0122] The third additional rule is based on the second additional rule and combines the separated solid solutions. Fig. 20 (C) shows the Fig. 20The condition shown in (B) is a condition where the discharge of the object monomer continues and the capacity of the Li-rich phase with a small particle number reaches the reference capacity Cref. In this example, before the combination, the Li-poor phase is separated into three and the Li-rich phase is separated into two (see the single-point dashed frame) above the two-phase coexistence phase. 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.

[0123] According to the third additional rule, Li-poor phases are bonded to each other, and Li-rich phases are bonded to each other (refer to Fig. 20 (D)). Thus, although the Li-poor phase is also separated into two after the combination, the Li-rich phase is combined into one. Therefore, the variables used to represent the Li-poor phase are reduced from three pairs to two pairs, and the variables used to represent the Li-rich phase are reduced to one pair. Therefore, the computational load of the processor 401 can be reduced. Although the embodiments of the present invention have been described, it should be understood that the embodiments disclosed this time are illustrative and non-restrictive in all aspects. The scope of the present invention is indicated by the claims, and it is intended to include all modifications within the meaning and scope equivalent to the claims.

Claims

1. A method for managing a battery, wherein a processor manages a battery having a positive electrode containing a positive electrode active material, wherein: The positive electrode active material has a plurality of phases having different contents of charge carriers in the positive electrode active material. The plurality of phases include a rich phase having a relatively large content of the charge carrier, a lean phase having a relatively small content of the charge carrier, and a two-phase coexistence phase in which the rich phase and the lean phase coexist. The management method, in a multi-particle model representing the positive electrode active material using a plurality of particles distinguished by particle numbers representing the reaction sequence of the positive electrode active material, assumes that the contents of the charge carriers in one or more particles belonging to each of the rich phase, the poor phase, and the two-phase coexistence phase are equal to each other, and on this basis, includes: For each of the plurality of phases, the processor calculates an overvoltage of the particle based on the measured voltage of the battery, the measured current of the battery, and the open potential of the particle belonging to the phase; For each of the plurality of phases, based on the overvoltage, the processor calculates a reaction current density; and The step of estimating the SOC of the battery by the processor based on the reaction current density of each of the plurality of phases.

2. The battery management method according to claim 1, wherein: In the multi-particle model, Between the particles belonging to the two-phase coexistence phase, the charge carrier content is a predetermined fixed value, In between particles belonging to the rich phase and between particles belonging to the lean phase, the contents of the charge carriers are variable values ​​that vary according to the reaction current density.

3. The battery management method according to claim 2, wherein: In the multi-particle model, as variables for expressing the plurality of particles, there are included the minimum and maximum values ​​of the particle numbers of particles belonging to the two-phase coexistence phase or the number of particles belonging to the two-phase coexistence phase.

4. The battery management method according to claim 3, wherein: The number of said variables is less than 100.

5. The battery management method according to any one of claims 1 to 4, wherein: In the multi-particle model, the reaction sequence of the positive electrode active material is set according to the reaction resistance of the plurality of particles. A difference in reaction resistance between particles having consecutive particle numbers among the plurality of particles is smaller than a predetermined value.

6. The battery management method according to any one of claims 1 to 4, wherein: In the multi-particle model, it is assumed that the plurality of particles have the same particle diameter, and thus the plurality of particles have the same reaction area and capacity.

7. The battery management method according to any one of claims 1 to 4, wherein: The step of calculating the overvoltage, for each of the plurality of phases, comprises the following steps: By referring to the relationship between the content of the charge carrier and the open potential, the open potential is calculated according to the content of the charge carrier; The overvoltage is calculated based on the salt concentration overvoltage caused by the concentration gradient of the charge carriers in addition to the measurement voltage, the measurement current, and the open potential.

8. The battery management method according to any one of claims 1 to 4, wherein: The step of estimating the SOC of the battery comprises the following steps: For each phase of the plurality of phases, multiplying the reaction current density in the phase, the number of particles belonging to the phase, and the surface area of ​​the particles belonging to the phase; By adding the multiplied values ​​for the plurality of phases, an applied current flowing in the battery is calculated, The current value of the SOC of the battery is estimated by adding a value obtained by dividing the applied current by the battery capacity of the battery to a previous value of the SOC of the battery.

9. The battery management method according to any one of claims 1 to 4, wherein: The step of estimating the SOC of the battery comprises the following steps: For each of the plurality of phases, calculating the charge carrier content in the phase by multiplying the reaction current density in the phase, the surface area of ​​particles belonging to the phase, and the time elapsed since the last estimation of the SOC of the battery; For each phase of the plurality of phases, multiplying the charge carrier content by the number of particles belonging to the phase; summing the multiplication values ​​with respect to the plurality of phases; By dividing the added value by the total number of the plurality of particles, the SOC of the battery is estimated.

10. The battery management method according to any one of claims 1 to 4, wherein: In the multi-particle model, after particles belonging to a first phase, which is one of the rich phase and the lean phase, are transferred to a second phase, which is the other phase, accompanying charge and discharge of the battery, when charge and discharge of the battery are switched, Assuming that when the number of particles belonging to the second phase exceeds a reference value, the particles belonging to the second phase transfer to the first phase via the two-phase coexistence phase, It is assumed that when the number of particles belonging to the second phase is lower than the reference value, particles belonging to the two-phase coexistence phase return to the first phase.

11. The battery management method according to claim 10, wherein: In the multi-particle model, the current flowing when returning the particles belonging to the two-phase coexistence phase to the first phase is set to be larger than a set value, The set value is determined based on the product of the reaction current density of particles belonging to the two-phase coexistence phase and the number of particles transferred from the first phase to the second phase before switching between charge and discharge of the storage battery.

12. The battery management method according to claim 11, wherein: In the multi-particle model, when particles belonging to the rich phase or the lean phase are separated into two or more particle groups, at least a part of the two or more particle groups are combined with each other. 13 . A battery management system comprising the processor according to claim 1 .

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