JP2014207054A - Battery system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To precisely estimate open voltage in a current secondary battery.SOLUTION: A battery system includes a temperature sensor which detects temperature of a secondary battery (11), and a controller (30) for calculating open voltage of the secondary battery from a single pole open potential at a positive electrode and a negative electrode of the secondary battery. The controller corrects a single pole open potential by using the maintenance factor of single pole capacity at the positive electrode and the negative electrode and the fluctuation amount of battery capacity according to variation in correspondence of the average charge rate at the active material of the positive electrode and the negative electrode. The controller, when correcting the single pole open potential, uses a single pole open potential that corresponds to a detection temperature by the temperature sensor.

Description

  The present invention relates to a battery system that calculates an open potential of a secondary battery from a single electrode open potential.

The open circuit voltage of the secondary battery is expressed as a potential difference between the positive electrode open potential and the negative electrode open potential. Here, in Patent Document 1, only the local lithium concentration distribution (local SOC θ ₁ ) on the surface (interface) of the positive electrode active material is considered when specifying the positive electrode open-circuit potential. Further, when specifying the negative electrode open-circuit potential, only the local lithium concentration distribution (local SOC θ ₂ ) on the surface (interface) of the negative electrode active material is considered.

JP 2010-060384 A (paragraph [0075]) JP 2008-243373 A JP 2008-532050 A

  The positive electrode open potential and the negative electrode open potential of the secondary battery not only depend on the local SOC on the surface of the active material, but also depend on the temperature of the secondary battery. That is, when the temperature of the secondary battery changes, the positive electrode open potential and the negative electrode open potential may change even if the local SOC is the same. In this case, when calculating (estimating) the open-circuit voltage of the secondary battery from the positive electrode open-circuit potential and the negative electrode open-circuit potential, the open-circuit voltage estimation accuracy decreases.

  The battery system of the present invention includes a temperature sensor that detects the temperature of the secondary battery, and a controller that calculates the open voltage of the secondary battery from the single electrode open potential at the positive electrode and the negative electrode of the secondary battery. The controller corrects the unipolar open potential using the maintenance rate of the unipolar capacity in the positive electrode and the negative electrode and the amount of change in the battery capacity accompanying the change in the correspondence relationship between the average charge rates in the active materials of the positive electrode and the negative electrode. Here, when correcting the unipolar open potential, the unipolar open potential corresponding to the temperature detected by the temperature sensor is used.

  As the deterioration of the secondary battery proceeds, the unipolar open potential (positive electrode open potential or negative electrode open potential) changes. The change in the unipolar open-circuit potential can be defined by the maintenance rate of the unipolar capacity and the variation amount of the battery capacity. Therefore, the unipolar open-circuit potential that reflects the deterioration state of the secondary battery is calculated (estimated) by correcting the unipolar open-circuit potential while grasping the maintenance rate of the unipolar capacity and the variation amount of the battery capacity. be able to.

  Here, when correcting the unipolar open potential, the unipolar open potential according to the temperature of the secondary battery is used. Since the monopolar open potential depends on the temperature of the secondary battery, if the temperature of the secondary battery changes, the monopolar open potential also changes. Even when correcting the single electrode open potential using the maintenance rate of the single electrode capacity and the amount of battery capacity fluctuation, if the temperature of the secondary battery is not taken into consideration, the single electrode open in the deteriorated secondary battery The potential cannot be estimated with high accuracy.

  In the present invention, since the single electrode open potential according to the temperature of the secondary battery is corrected, the single electrode open potential in the deteriorated secondary battery can be accurately estimated. In addition, since the open voltage of the secondary battery can be calculated from the single electrode open potential (positive electrode open potential and negative electrode open potential), it is possible to accurately estimate the single electrode open potential, thereby opening the secondary battery after deterioration. The voltage can also be estimated with high accuracy.

  The unipolar open circuit potential is defined in relation to the average charging rate. Here, the unipolar characteristic indicating the correspondence between the unipolar open-circuit potential and the average charging rate is referred to as open-circuit potential characteristic. For this reason, when correcting the unipolar open potential, the open-circuit potential characteristic is corrected. In addition, when a unipolar open potential corresponding to the detected temperature is used, an open potential characteristic corresponding to the detected temperature is used. When the secondary battery is in the initial state, the correspondence relationship between the open-circuit potential characteristic and the temperature of the secondary battery can be specified in advance. By using this correspondence relationship, it is possible to specify the open-circuit potential characteristic corresponding to the temperature of the secondary battery.

  If the open-circuit potential characteristic is corrected, the open-circuit voltage characteristic of the secondary battery can be calculated using the corrected open-circuit potential characteristic. The open-circuit voltage characteristic is a characteristic of the secondary battery that indicates the correspondence relationship between the average charging rate and the open-circuit voltage. The open circuit voltage of the secondary battery is expressed as a potential difference between the positive electrode open potential and the negative electrode open potential. For this reason, if the open circuit potential characteristic in a positive electrode and a negative electrode is used, an open circuit voltage characteristic is computable.

  The battery system of the present invention can be provided with a current sensor that detects the current of the secondary battery. Here, regarding the current of the secondary battery, by comparing the detected current and the estimated current, it is possible to calculate the optimum solution regarding the maintenance rate of the unipolar capacity and the variation amount of the battery capacity. This optimal solution reflects the current internal state of the secondary battery.

  Specifically, when the open-circuit voltage of the secondary battery is changed from the first open-circuit voltage to the second open-circuit voltage, if the current detected by the current sensor is integrated during this period, the first current integrated value is calculated. be able to. In addition, if the open-circuit voltage characteristic is calculated from the corrected open-circuit potential characteristic, the first average charge rate corresponding to the first open-circuit voltage and the second average charge rate corresponding to the second open-circuit voltage can be calculated. .

  If the first average charging rate and the second average charging rate are calculated, based on the difference between these average charging rates, the integrated current value (until the open circuit voltage is changed from the first open circuit voltage to the second open circuit voltage) ( (Second current integrated value) can be calculated (estimated). The first current integrated value (corresponding to the detected current) and the second current integrated value (corresponding to the estimated current) are compared, and the maintenance rate of the unipolar capacity and the difference between these current integrated values are minimized. The amount of change in battery capacity can be calculated.

  The maintenance rate and fluctuation amount when the difference between the first current integration value and the second current integration value is minimum are the maintenance rate and fluctuation amount reflecting the current internal state of the secondary battery. By using the maintenance ratio and the fluctuation amount, it is possible to obtain open-circuit potential characteristics and open-circuit voltage characteristics that reflect the current internal state of the secondary battery.

  When changing the open circuit voltage from the first open circuit voltage to the second open circuit voltage, by using a temperature sensor, the temperature of the secondary battery when the first open circuit voltage is acquired and the second battery when the second open circuit voltage is acquired. The temperature of the secondary battery can be detected. Here, when calculating the first average charging rate, an open-circuit voltage characteristic corresponding to the temperature of the secondary battery when the first open-circuit voltage is acquired is used. Further, when calculating the second average charging rate, an open-circuit voltage characteristic corresponding to the temperature of the secondary battery when the second open-circuit voltage is acquired is used.

  When calculating the average charging rate corresponding to the open circuit voltage, the open circuit voltage characteristic is used. The open circuit voltage characteristic depends on the temperature of the secondary battery. That is, if the temperature of the secondary battery changes, the open circuit voltage characteristics may change. Here, if the average charging rate corresponding to the open-circuit voltage is calculated using the open-circuit voltage characteristics not considering the temperature of the secondary battery, the calculated average charging rate may deviate from the actual average charging rate. is there. That is, the average charging rate may be shifted by the amount of change in open-circuit voltage characteristics accompanying the temperature change of the secondary battery.

  According to the present invention, when calculating the average charging rate, the open-circuit voltage characteristic reflecting the influence of the temperature of the secondary battery is used, so that the calculation accuracy (estimation accuracy) of the average charging rate can be improved. it can. If the estimation accuracy of the average charging rate is improved, as described above, when calculating (estimating) the maintenance rate of the unipolar capacity and the fluctuation amount of the battery capacity, the estimation accuracy of the maintenance rate and the fluctuation amount can be improved. it can.

  The average charging rate depends on the maintenance rate of the single electrode capacity and the amount of change in battery capacity. Therefore, as described above, if the maintenance rate and the fluctuation amount are calculated (estimated), the average charging rate reflecting these calculated values (estimated values) can be calculated. Thereby, the estimation precision of an average charging rate can be improved. Here, if the average charge rate is estimated, the full charge capacity of the secondary battery can be calculated (estimated), but the estimation accuracy of the full charge capacity is improved by improving the estimation accuracy of the average charge rate. be able to.

  When calculating the full charge capacity of the secondary battery, first, the average charge rate when the SOC of the secondary battery is 100% and the average charge rate when the SOC of the secondary battery is 0% are calculated. . By calculating the difference between these average charging rates, it is possible to specify the integrated current value until the SOC of the secondary battery changes from 100% to 0%, and to calculate the full charge capacity of the secondary battery. .

  The reaction-related substance moves between the positive electrode and the negative electrode, whereby the secondary battery is charged and discharged. The reaction participating substance is a substance that participates in the charge / discharge reaction of the secondary battery. For example, when the secondary battery is a lithium ion secondary battery, the reaction participating substance is lithium ion. Here, the average charging rate is represented by a ratio between the maximum concentration of the reaction-participating substance in the active material and the average concentration of the reaction-participating substance in the current active material. Inside the active material, the concentration distribution (concentration variation) of the reaction participating substance may occur due to the influence of diffusion of the reaction participating substance. In consideration of this concentration distribution, it is preferable to use the average concentration of the reaction-participating substance.

It is a figure which shows the structure of a battery system. It is the schematic which shows the structure of a secondary battery. It is a figure which shows the change characteristic of the open circuit voltage with respect to the change of local SOC. It is a figure which shows the change of the monopolar open circuit potential accompanying the reduction | decrease of monopolar capacity | capacitance. It is a figure explaining the correspondence shift of the composition between a positive electrode and a negative electrode. It is a figure explaining the correspondence shift of the composition by deterioration. It is a figure which shows the relationship between a positive electrode open potential and the negative electrode open potential after deterioration. It is a flowchart which shows the search process of a degradation parameter. It is a flowchart which shows the search process of a degradation parameter. It is a figure which shows the open circuit voltage characteristic computed for every battery temperature. It is a figure which shows the open circuit voltage characteristic calculated without considering battery temperature.

  Examples of the present invention will be described below.

  A battery system that is Embodiment 1 of the present invention will be described with reference to FIG. FIG. 1 is a diagram illustrating a configuration of a battery system. The battery system of the present embodiment can be mounted on a vehicle.

  The battery system of this embodiment includes an assembled battery 10. The assembled battery 10 includes a plurality of unit cells 11 connected in series. As the cell 11, a secondary battery such as a nickel metal hydride battery or a lithium ion battery can be used. The unit cell 11 has a power generation element housed in a battery case. The power generation element is an element that performs charging and discharging, and can be composed of a positive electrode plate, a negative electrode plate, and a separator disposed between the positive electrode plate and the negative electrode plate. The separator contains an electrolytic solution. Here, a solid electrolyte may be used instead of the separator.

  The number of unit cells 11 constituting the assembled battery 10 can be appropriately set based on the required output of the assembled battery 10 and the like. In this embodiment, all the unit cells 11 constituting the assembled battery 10 are connected in series, but a plurality of unit cells 11 connected in parallel may be included in the assembled battery 10.

  The monitoring unit 21 detects the voltage value of the assembled battery 10 or detects the voltage value Vb of each unit cell 11. The monitoring unit 21 outputs the detection result to the controller 30. The current sensor 22 detects the current value Ib flowing through the assembled battery 10 and outputs the detection result to the controller 30. In the present embodiment, a positive value is used as the current value Ib when the assembled battery 10 is discharged, and a negative value is used as the current value Ib when the assembled battery 10 is charged.

  In the present embodiment, the current sensor 22 is provided in the positive electrode line PL connected to the positive electrode terminal of the assembled battery 10, but the present invention is not limited to this. That is, the current sensor 22 only needs to be able to detect the current value Ib flowing through the assembled battery 10. For example, the current sensor 22 can be provided in the negative electrode line NL connected to the negative electrode terminal of the assembled battery 10.

  The temperature sensor 23 detects the temperature Tb of the assembled battery 10 (unit cell 11) and outputs the detection result to the controller 30. The number of temperature sensors 23 can be set as appropriate. By using a plurality of temperature sensors 23, it is possible to accurately detect the temperatures of the single cells 11 arranged at different positions. The controller 30 has a memory 30a, and the memory 30a stores various information for the controller 30 to perform predetermined processing. In the present embodiment, the memory 30 a is built in the controller 30, but the memory 30 a may be provided outside the controller 30.

  A system main relay SMR-B is provided in the positive electrode line PL, and the system main relay SMR-B is switched between on and off by receiving a control signal from the controller 30. A system main relay SMR-G is provided in the negative electrode line NL, and the system main relay SMR-G is switched between on and off by receiving a control signal from the controller 30.

  System main relay SMR-P and current limiting resistor 24 are connected in parallel to system main relay SMR-G. System main relay SMR-P is switched between on and off by receiving a control signal from controller 30. The current limiting resistor 24 is used to suppress the inrush current from flowing when the assembled battery 10 is connected to the inverter 31.

  When the assembled battery 10 is connected to the inverter 31, the controller 30 switches the system main relay SMR-B from off to on and switches the system main relay SMR-P from off to on. Thereby, the discharge current of the assembled battery 10 can be passed through the current limiting resistor 24.

  Next, the controller 30 switches the system main relay SMR-G from off to on and switches the system main relay SMR-P from on to off. Thereby, the connection between the assembled battery 10 and the inverter 31 is completed, and the battery system shown in FIG. 1 is in an activated state (Ready-On). On the other hand, when the connection between the assembled battery 10 and the inverter 31 is cut off, the controller 30 switches the system main relays SMR-B and SMR-G from on to off. Thereby, the battery system shown in FIG. 1 is in a stopped state (Ready-Off).

  Information about on / off of the ignition switch of the vehicle is input to the controller 30. Here, when the ignition switch is switched from OFF to ON, the controller 30 switches the battery system shown in FIG. 1 from the stopped state to the activated state. When the ignition switch is switched from on to off, the controller 30 switches the battery system shown in FIG. 1 from the activated state to the stopped state.

  The inverter 31 converts the DC power from the assembled battery 10 into AC power, and outputs the AC power to the motor / generator 32. As the motor generator 32, for example, a three-phase AC motor can be used. The motor / generator 32 receives AC power from the inverter 31 and generates kinetic energy for driving the vehicle. By transmitting the kinetic energy generated by the motor / generator 32 to the wheels, the vehicle can be driven.

  When the vehicle is decelerated or stopped, the motor / generator 32 converts kinetic energy generated during braking of the vehicle into electric energy (AC power). The inverter 31 converts the AC power generated by the motor / generator 32 into DC power and outputs the DC power to the assembled battery 10. Thereby, the assembled battery 10 can store regenerative electric power.

  In the present embodiment, the assembled battery 10 is connected to the inverter 31, but this is not a limitation. Specifically, a booster circuit can be provided in the current path of the assembled battery 10 and the inverter 31. The booster circuit can step up the output voltage of the assembled battery 10 or step down the output voltage from the inverter 31 to the assembled battery 10.

  In this embodiment, the full charge capacity of the secondary battery 11 that changes with the deterioration of the secondary battery (unit cell) 11 is estimated. First, a battery model used in the full charge capacity estimation process will be described below. If this battery model is used, the internal state of the secondary battery 11 can be estimated. In the following description, a lithium ion secondary battery is used as the secondary battery 11.

  FIG. 2 is a diagram for explaining the outline of the internal configuration of the secondary battery 11 expressed by a battery model. In FIG. 2, the secondary battery 11 includes a positive electrode 121, a negative electrode 122, and a separator 123. The separator 123 is provided between the positive electrode 121 and the negative electrode 122, and can be formed of, for example, a resin. The electrolytic solution penetrates into the separator 123.

  The positive electrode 121 includes a current collector plate 121a and an aggregate of spherical positive electrode active materials 121b. The current collecting plate 121a can be formed of aluminum, for example. The negative electrode 122 includes a current collector plate 122a and an aggregate of spherical negative electrode active materials 122b. The current collector plate 122a can be formed of, for example, copper.

As shown in FIG. 2, when the secondary battery 11 is discharged, a chemical reaction is performed on the interface of the negative electrode active material 122b to release lithium ions (corresponding to a reaction participating substance) Li ⁺ and electrons e ⁻ . On the other hand, a chemical reaction that absorbs lithium ions Li ⁺ and electrons e ⁻ is performed on the interface of the positive electrode active material 121b. When the secondary battery 11 is charged, a reaction opposite to the above-described chemical reaction is performed on the interface between the negative electrode active material 122b and the positive electrode active material 121b. Thus, the state of charge of the secondary battery 11 depends on the lithium concentration distribution inside the positive electrode active material 121b and the negative electrode active material 122b.

  In this embodiment, a case where a lithium ion secondary battery is used as the secondary battery 11 will be described. However, the present invention is not limited to this. For example, when a nickel metal hydride battery is used as the secondary battery 11, protons are used as a reaction participating substance. The reaction participating substance is a substance that participates in the charge / discharge reaction of the secondary battery 11.

The DC resistance when viewed rechargeable battery 11 to the macro (called DC resistance R _a), include pure resistance R _d and reaction resistance R _r. The pure resistance R _d is a pure electrical resistance against the movement of the electron e ⁻ in the negative electrode 122 and the positive electrode 121, and the reaction resistance R _r is equivalent when a reaction current is generated at the interface between the active materials 121b and 122b. It is a charge transfer resistance that acts as an electrical resistance. The diffusion of lithium in the interior of the active material 121b, 122b is governed by the diffusion coefficient _{D s.}

  In this embodiment, considering that the influence of the electric double layer capacitor at normal temperature is small, a battery model is constructed that ignores this influence. Here, the battery model is defined as a model per unit electrode plate area of the electrode (the positive electrode 121 or the negative electrode 122). By using a model per unit plate area of the electrode, this model can be generalized to the design capacity.

  The voltage value V of the secondary battery 11 is represented by the following formula (1).

  In the above formula (1), the battery current I indicates a current value per unit electrode plate area. That is, the battery current I is a value obtained by dividing the current value Ib detected by the current sensor 22 by the electrode plate area S of the electrode (the positive electrode 121 or the negative electrode 122). Hereinafter, “current” and “estimated current” used in the battery model are currents per unit electrode plate area unless otherwise specified.

The open circuit voltage OCV is expressed as a potential difference between the positive electrode open potential U ₁ and the negative electrode open potential U ₂ . The positive electrode opening potential U ₁ depends on the battery temperature T and the local SOC θ ₁ of the positive electrode active material 121b. The local SOC is a local lithium concentration distribution on the surface (interface) of the positive electrode active material 121b and is expressed as θ. Here, the value related to the positive electrode is expressed as a subscript “1”, and the value related to the negative electrode 122 is expressed as a subscript “2”. The characteristic of the secondary battery 11 showing the correspondence between the open circuit voltage OCV and the local SOC θ is referred to as an open circuit voltage characteristic.

The negative electrode open-circuit potential U ₂ depends on the battery temperature T and the local SOC θ ₂ of the negative electrode active material 122b. The local SOC θ ₂ is a local lithium concentration distribution on the surface (interface) of the negative electrode active material 122b. In the battery model of this example, the aggregate of the positive electrode active materials 121b in the positive electrode 121 is regarded as one spherical positive electrode active material 121b, and the aggregate of the negative electrode active materials 122b in the negative electrode 122 is regarded as one spherical negative electrode active material. 122b.

When the secondary battery 11 is in the initial state, the correspondence relationship between the positive electrode opening potential U ₁ , the local SOC θ _1, and the battery temperature T can be obtained in advance by experiments or the like. This correspondence relationship can be expressed as a map or a function, and information regarding this correspondence relationship can be stored in the memory 30a. FIG. 3 shows a correspondence (map) between the positive electrode open-circuit potential U ₁ and the local SOC θ _{1 at} a specific battery temperature T. The correspondence relationship between the positive electrode opening potential U ₁ and the local SOC θ ₁ shown in FIG. 3 is provided for each battery temperature T. Here, the characteristic of the positive electrode 121 showing the correspondence between the positive electrode open-circuit potential U ₁ and the local SOC θ ₁ is referred to as an open-circuit potential characteristic.

If the local SOC θ ₁ and the battery temperature T are specified, the positive electrode open potential U ₁ can be calculated by using the above-described correspondence. As the battery temperature T, the temperature Tb of the secondary battery 11 detected by the temperature sensor 23 is used. The initial state is a state in which the secondary battery 11 is not deteriorated, and can be a state immediately after the secondary battery 11 is manufactured, for example.

Further, if the correspondence relationship (map or function) between the negative electrode opening potential U ₂ , the local SOC θ ₂ and the battery temperature T is obtained in advance by experiments or the like, the local SOC θ ₂ and the battery temperature T can be specified to open the negative electrode it is possible to calculate the potential U _2. FIG. 3 shows the correspondence (map) between the negative electrode open-circuit potential U ₂ and the local SOC θ _{2 at} a specific battery temperature T. The correspondence relationship between the negative electrode open-circuit potential U ₂ and the local SOC θ ₂ shown in FIG. 3 is provided for each battery temperature T. Here, the characteristic of the negative electrode 122 showing the correspondence between the negative electrode open-circuit potential U ₂ and the local SOC θ ₂ is referred to as an open-circuit potential characteristic.

Here, as the battery temperature T, the temperature Tb of the secondary battery 11 detected by the temperature sensor 23 is used. Further, information regarding the correspondence relationship between the negative electrode open-circuit potential U ₂ , the local SOC θ _2, and the battery temperature T can be stored in the memory 30a.

DC resistance _{R a} shown in the equation (1) is locally SOC [theta] _1, it depends on the theta ₂ and the battery temperature T. For this reason, when the secondary battery 11 is in the initial state, the correspondence relationship (map or function) of the DC resistance R _a , the local SOC θ ₁ , θ ₂ and the battery temperature T can be obtained in advance by experiments or the like. . Using this relationship by identifying the local SOC [theta] _1, theta ₂ and the battery temperature T, it is possible to calculate the DC resistance R _a. As the battery temperature T, the temperature Tb of the secondary battery 11 detected by the temperature sensor 23 is used. Information regarding the correspondence relationship between the direct current resistance R _a , the local SOCs θ ₁ and θ ₂ and the battery temperature T can be stored in the memory 30a.

The local SOC θ _i (i = 1, 2) is defined by the following formula (2).

In the above formula (2), c _{se, i} is an average lithium concentration at the interface between the active materials 121b and 122b, and c _{s, i, max} is a limit lithium concentration in the active materials 121b and 122b. In the active materials 121b and 122b handled as a spherical model, the lithium concentration cs _{, i} has a distribution in the radial direction of the active materials 121b and 122b. That is, the lithium concentration distribution inside the active materials 121b and 122b is defined by the diffusion equation of the polar coordinate system shown in the following formula (3).

In the above formula (3), D _{s, i} is a diffusion coefficient of lithium in the active materials 121b and 122b. Since the diffusion coefficient D _{s, i} depends on the battery temperature T, the correspondence (map or function) between the diffusion coefficient D _{s, i} and the battery temperature T is determined by experiments using the secondary battery 11 in the initial state. It can be obtained in advance. This correspondence relationship is obtained for each of the diffusion coefficients D _{s, 1} , D _{s, 2} , and by using this correspondence relationship, by specifying the battery temperature T, the diffusion coefficients D _{s, 1} , D _{s, 2} are obtained. Each can be calculated.

As the battery temperature T, the temperature Tb of the secondary battery 11 detected by the temperature sensor 23 is used. Information regarding the correspondence between the diffusion coefficient D _{s, i} and the battery temperature T can be stored in the memory 30a. Generally, the diffusion coefficient D _{s, i} tends to increase as the battery temperature T increases. In other words, the diffusion coefficient D _{s, i} tends to decrease as the battery temperature T decreases.

  The boundary conditions of the diffusion equation shown in the above equation (3) are set as the following equations (4) and (5).

  The above formula (4) indicates that the concentration gradient at the center of the spherical active materials 121b and 122b is zero. The above formula (5) indicates that the lithium concentration at the interface between the active materials 121b and 122b changes in accordance with the entry and exit of lithium at the interface between the active materials 121b and 122b.

In the above formula (5), r _{s, i} is the radius of the active material 121b, 122b, ε _{s, i} is the volume fraction of the active material 121b, 122b, and as _{, i} is the electrode 121, It is the surface area of the active materials 121b and 122b per unit volume of 122. These values r _{s, i} , ε _{s, i} , a _{s, i} are determined from the results measured by various electrochemical measuring methods. F is a Faraday constant.

J ^Li shown in the above formula (5) is the amount of lithium produced per unit volume / time. For simplicity, assuming that the reactions in the thickness direction of the electrodes 121 and 122 are uniform, the lithium generation amount j ^Li can be calculated based on the following formula (6). In the following formula (6), L ₁ and L ₂ are the thicknesses of the electrodes 121 and 122, and I is a battery current.

  By using the voltage value Vb of the secondary battery 11 as an input value and solving the equations (1) to (6) simultaneously, it is possible to estimate the internal state of the secondary battery 11 while calculating the estimated current. . For example, the SOC (State of Charge) of the secondary battery 11 can be estimated while calculating the estimated current. The SOC is the ratio of the current charge capacity to the full charge capacity.

The process of estimating the SOC of the secondary battery 11 is repeatedly performed at a predetermined cycle and is executed by the controller 30. The controller 30 calculates the local SOC θ _i (θ ₁ and θ ₂ ) of the active materials 121b and 122b based on the lithium concentration distribution c _{se, i} at the previous calculation. If the local SOC θ _i is calculated and the battery temperature Tb is detected, for example, by using the map shown in FIG. 3, the controller 30 causes the positive electrode open-circuit potential U ₁ and the negative electrode corresponding to the battery temperature Tb and the local SOC θ _i to be detected. it is possible to calculate the open-circuit potential U _2. Then, the controller 30, as a potential difference of the positive electrode open-circuit potential _{U 1} and the negative electrode open-circuit potential _{U 2,} it is possible to calculate the open circuit voltage OCV.

On the other hand, calculates the local SOC [theta] _i, by detecting the battery temperature Tb, the controller 30, the local SOC [theta] _i, using a correspondence relationship between battery temperature Tb and the DC resistance _{R a,} calculating the DC resistance _{R a} Can do. The controller 30, by substituting the open circuit voltage OCV and DC resistance R _a was calculated as described above, the detected by the monitoring unit 21 secondary battery 11 and the voltage value Vb to the following equation (7), the secondary battery 11 estimated currents I _te can be calculated.

The controller 30 calculates the lithium generation amount j ^Li by substituting the estimated current I _te calculated from the equation (7) into the battery current I shown in the equation (6). The controller 30 calculates the lithium concentration distribution inside the active materials 121b and 122b by solving the diffusion equation of the above equation (3) using this lithium generation amount j ^Li as the boundary condition of the above equation (5). be able to. Here, the diffusion coefficient D _s to be used in the diffusion _equation, as the _i, diffusion coefficient D _s, by using the correspondence between the _i and the battery temperature, the diffusion coefficient corresponds to the temperature Tb detected by the temperature sensor 23 D _{s , I} are used.

When solving the diffusion equation of the above equation (3), the lithium concentration distribution c _{s, i, k} (t + Δt) inside the active material 121b, 122b is updated using the diffusion equation discretized by time and position. Here, Δt is a calculation cycle, and k is a position when the active materials 121b and 122b are discretized in the radial direction. In addition, since the method of discretizing a diffusion equation with time and position is well-known, detailed description is abbreviate | omitted.

If the lithium concentration distribution c _{s, k} inside the active material 121b, 122b is calculated, the average lithium concentration c _save inside the active material 121b, 122b can be calculated. The average lithium concentration c _save is an average value of the lithium concentrations c _{s, k} inside the active materials 121b, 122b. Specifically, the average lithium concentration c _save can be calculated based on the following formula (8). In the following formula (8), N is the number of divisions when the active materials 121b and 122b are discretized in the radial direction.

If the correspondence relationship (map or function) between the average lithium concentration c _save and the SOC of the secondary battery 11 is obtained in advance, the SOC corresponding to the average lithium concentration c _save can be calculated (estimated). Here, information on the correspondence relationship between the average lithium concentration c _save and the SOC can be stored in the memory 30a.

  The open-circuit voltage and full charge capacity of the secondary battery 11 change according to the deterioration of the secondary battery 11. For this reason, when estimating the open circuit voltage or the full charge capacity of the secondary battery 11, it is necessary to consider the deterioration of the secondary battery 11. In the present embodiment, changes in open-circuit voltage characteristics and full charge capacity due to deterioration of the secondary battery 11 are modeled as two phenomena that are considered to occur inside the secondary battery 11.

The first phenomenon is a decrease in single electrode capacity at the positive electrode 121 and the negative electrode 122, and the second phenomenon is a correspondence shift in composition between the positive electrode 121 and the negative electrode 122. Here, the mismatch in composition means that the correspondence in average lithium concentration c _save in the positive electrode active material 121b and the negative electrode active material 122b is shifted. Further, in each of the active materials 121b and 122b, when the ratio of the average lithium concentration c _{save to} the limit lithium concentration c _{s, i, max} is the average charging rate, the correspondence between the compositions is between the positive electrode 121 and the negative electrode 122. This means that the correspondence of the average charging rate is shifted.

Here, the relationship of the single electrode open potential with respect to the composition of each of the positive electrode 121 and the negative electrode 122 does not change even when the secondary battery 11 deteriorates. That is, even if the secondary battery 11 is deteriorated, the relationship between the local SOC θ _i and the open potential U _i shown in FIG. 3 is maintained.

FIG. 4 is a schematic diagram showing a change in unipolar open potential with a decrease in unipolar capacitance. 4, Q_L1 and Q_H11 on the positive electrode single electrode capacity axis represent capacities respectively corresponding to local SOCs θ _L1 and θ _H1 shown in FIG. 3 in the initial state of the secondary battery 11. Similarly, Q_L2 in anode monopolar volume axis and Q_H21, in the initial state of the secondary battery 11, represents the local SOC [theta] _L2, capacitance respectively corresponding to theta _H2 shown in FIG.

The “decrease in single electrode capacity” represents a decrease in lithium acceptance capacity in each of the positive electrode 121 and the negative electrode 122. This represents a phenomenon such as a decrease in active material that functions effectively for charging and discharging in each electrode. In the positive electrode 121, the reduction in ability to receive lithium, the capacity corresponding to local SOC [theta] _H1 drops Q_H12 from Q_H11. Similarly, also in the negative electrode 122, the capacity | capacitance corresponding to local SOC (theta) _H2 falls from Q_H21 to Q_H22 by the fall of the capability of accepting lithium.

On the other hand, even if the secondary battery 11 deteriorates, the relationship between the local SOC θ ₁ and the positive electrode open potential U ₁ does not change. Therefore, when the relationship between the local SOC θ ₁ and the positive electrode open potential U ₁ is converted into the relationship between the positive electrode capacity and the positive electrode open potential, a curve showing the relationship between the positive electrode capacity and the positive electrode open potential as shown in FIG. The secondary battery 11 is contracted as the secondary battery 11 deteriorates. The solid line shown in FIG. 4, at the time when the rechargeable battery 11 is in the initial state, indicating the change in the positive electrode open-circuit potential U ₁₁ for positive electrode capacity. Further, one-dot chain line shown in FIG. 4, at the time when the rechargeable battery 11 is in a deteriorated state, shows a variation of positive electrode open-circuit potential U ₁₂ for positive electrode capacity.

Similarly, when the relationship between the local SOC θ ₂ and the negative electrode open potential U ₂ is converted into the relationship between the negative electrode single electrode capacity and the negative electrode open potential, the curve showing the relationship between the negative electrode capacity and the negative electrode open potential is The battery 11 contracts as the battery 11 deteriorates. The solid line shown in FIG. 4, at the time when the rechargeable battery 11 is in the initial state, indicating the change of the negative electrode open-circuit potential U ₂₁ for negative electrode capacity. Further, one-dot chain line shown in FIG. 4, at the time when the rechargeable battery 11 is in a deteriorated state, indicating the change of the negative electrode open-circuit potential U ₂₂ for negative electrode capacity

  FIG. 5 is a schematic view showing a shift in composition correspondence between positive and negative electrodes. “Miscellaneous compositional correspondence” corresponds to the amount of variation in battery capacity in the present invention. When the set of the positive electrode 121 and the negative electrode 122 is used as the secondary battery 11, the combination of the positive electrode composition and the negative electrode composition is Represents that the secondary battery 11 is deviated from the initial state. Here, the composition of the positive electrode is an average charging rate inside the positive electrode active material 121b, and the composition of the negative electrode is an average charging rate inside the negative electrode active material 122b.

The curve showing the relationship between the composition (average charge rate inside the active material) θ _i and the open circuit potential U _i is the same as the curve shown in FIG. Here, as the deterioration of the secondary battery 11 proceeds, the negative electrode composition axis shifts by Δθ _{2 in the} direction of decreasing the positive electrode composition. As a result, the curve indicating the relationship between the negative electrode composition θ ₂ and the negative electrode open-circuit potential U ₂ is also shifted by Δθ _{2 in the} direction in which the positive electrode composition θ ₁ decreases. Here, the solid line shown in FIG. 5, at the time when the rechargeable battery 11 is in the initial state, indicating the change of the negative electrode open-circuit potential U ₂₁ for the negative electrode composition. Further, one-dot chain line shown in FIG. 5, at the time when the rechargeable battery 11 is in a deteriorated state, indicating the change of the negative electrode open-circuit potential U ₂₂ for the negative electrode composition.

The composition of the negative electrode 122 corresponding to the composition θ _{1fix of the} positive electrode 121 is θ _{2fix_ini} in the initial state of the secondary battery 11, but becomes θ _2fix after the secondary battery 11 is deteriorated. As an example of the cause of such a compositional deviation, for example, a case where lithium ions released from the positive electrode 121 during charging become a by-product or the like and are not taken into the negative electrode 122 can be considered. In FIG. 5, the negative electrode composition θ _{L2 is set} to 0, which means a state in which all lithium in the negative electrode 122 has been removed.

  In this example, the above-described two phenomena are introduced by introducing three parameters (referred to as deterioration parameters) of “positive electrode capacity retention rate”, “negative electrode capacity retention rate”, and “positive and negative electrode composition correspondence deviation capacity” into the battery model. Is modeled. Specifically, the three deterioration parameters are estimated, and the battery model is corrected using the estimated deterioration parameters, so that the open-circuit voltage characteristic on the battery model is adapted to the open-circuit voltage characteristic of the secondary battery 11 after deterioration. Or the full charge capacity of the secondary battery 11 after deterioration can be estimated.

  First, a method for modeling the above-described two phenomena will be specifically described.

The capacity maintenance rate of a single electrode (positive electrode 121 or negative electrode 122) is expressed by dividing the deteriorated single electrode capacity by the initial single electrode capacity. Here, it is assumed that the deterioration of the secondary battery 11 causes the single electrode capacity after deterioration to decrease by a predetermined amount from the single electrode capacity in the initial state. At this time, the positive electrode capacity retention ratio k ₁ is expressed by the following formula (9).

Similarly, the negative electrode capacity retention ratio k ₂ is represented by the following formula (10).

In the above formulas (9) and (10), Q 1 _—ini and Q 2 _—ini are the positive electrode capacity and the negative electrode capacity in the initial state, and can be obtained in advance by experiments or the like. ΔQ ₁ and ΔQ ₂ are reduction amounts of the single electrode capacity in the positive electrode 121 and the negative electrode 122.

On the other hand, a deviation capacity corresponding to the positive and negative electrode composition corresponding to the relative deviation amount (Δθ ₂ shown in FIG. 5) between the positive electrode composition axis and the negative electrode composition axis is represented by ΔQ _s .

FIG. 6 is a schematic diagram for explaining a correspondence deviation between positive and negative electrode compositions due to deterioration. After the secondary battery 11 is deteriorated, the capacity when the negative electrode composition θ ₂ is 1 is a value obtained by subtracting the amount of decrease in negative electrode capacity (ΔQ ₂ ) from the initial negative electrode capacity (Q 2 — _ini ). Further, the positive and negative electrode composition correspondence deviation capacity ΔQ _s is a capacity corresponding to the deviation amount Δθ ₂ of the negative electrode composition axis with respect to the positive electrode composition axis. Thereby, the relationship of following formula (11) is materialized.

  The above equation (11) can be converted into the following equation (12).

The negative electrode composition in the initial state corresponding to the positive electrode composition θ _{1fix_ini} in the initial state is _defined as θ _{2fix_ini} . Further, when the composition deviation due to deterioration of the secondary battery 11 occurs, the negative electrode composition corresponding to positive electrode composition theta _1fix and _θ 2fix. Here, the positive electrode composition θ _{1fix_ini} in the initial state is _used as a reference for deviation. That is, the positive electrode composition θ _{1fix_ini} and the positive electrode composition θ _1fix are _assumed to be equal to each other.

When a relative composition correspondence shift occurs between the positive and negative electrodes due to deterioration of the secondary battery 11, the positive electrode composition θ _1fix and the negative electrode composition θ _2fix are expressed by the following formulas (13) and (14).

  The meaning of the above formula (14) will be described.

After the secondary battery 11 is deteriorated, the amount of lithium released from the positive electrode 121 when the positive electrode composition θ ₁ changes (decreases) from 1 to θ _1fix is the change in the positive electrode composition (1-θ _1fix ). It is expressed as a value obtained by multiplying the single electrode capacity (k ₁ × Q _{1 —ini} ) of the positive electrode 121. _Assuming that all of the lithium released from the positive electrode 121 is occluded in the negative electrode 122, the single electrode capacity (after degradation) of the negative electrode 122 is “k ₂ × Q _{2 —ini} ”, and therefore the negative electrode composition θ _2fix is _expressed by the following formula (15 ).

Here, when the secondary battery 11 is deteriorated, there is a relative composition correspondence difference (Δθ ₂ ) between the positive and negative electrodes. _Therefore, the negative electrode composition θ _2fix after the deterioration is the negative electrode composition θ _represented by the above formula (15). A value obtained by subtracting the shift amount Δθ ₂ from _2fix . According to the above formulas (11) and (12), the shift amount Δθ ₂ can be expressed by using the positive and negative electrode composition corresponding shift capacity ΔQ _s . Therefore, the negative electrode composition θ _2fix after deterioration can be expressed by the above formula (14).

In the battery model of this example, the decrease in single electrode capacity is reflected in the electrode thickness L _i and the volume fraction ε _{s, i} of the active material as shown in the following formulas (16) to (19).

In the above formulas (16) and (17), L ₁₀ and L ₂₀ are the thicknesses of the positive electrode 121 and the negative electrode 122 in the initial state, and can be obtained in advance by experiments or the like. In the above formulas (18) and (19), ε _s0,1 and ε _s0,2 are the volume fractions of the positive electrode active material 121b and the negative electrode active material 122b when the secondary battery 11 is in the initial state. Etc. can be obtained in advance.

  The open circuit voltage OCV when the capacity of the single electrode is reduced and the relative composition correspondence between the positive and negative electrodes is shifted is calculated from the following equation (20).

  Here, when the secondary battery 11 is in an energized state or immediately after switching from an energized state to a non-energized state, a concentration distribution of lithium is present inside the active materials 121b and 122b. The lithium concentration at the interface between 121b and 122b does not match the average lithium concentration inside the active materials 121b and 122b.

  On the other hand, when the open circuit voltage OCV is calculated, the secondary battery 11 is in a sufficiently relaxed state, and no lithium concentration distribution is generated in the active materials 121b and 122b. That is, the lithium concentration at the interface between the active materials 121b and 122b is equal to the average lithium concentration inside the active materials 121b and 122b.

Here, when the average charging rates θ 1 _ave and θ 2 _ave are defined as shown in the following formula (21), the open circuit voltage OCV is expressed by the above formula (20). In the following formula (21), c _{save, i} is the average lithium concentration inside the active material 121b, 122b.

As shown in the equation (20), open circuit voltage OCV includes a positive electrode open-circuit potential _{U 1} identified from the average charging rate theta _1Ave inside of the positive electrode active material 121b, the average charging rate in the interior of the negative electrode active material _122b θ 2ave It expressed as a potential difference between the anode open-circuit potential U ₂ specified from. Here, as described above, the positive electrode opening potential U ₁ is specified in consideration of not only the average charging rate θ _1ave but also the battery temperature T. Similarly, the negative electrode open-circuit potential U ₂ is specified in consideration of not only the average charging rate θ _2ave but also the battery temperature T.

Between the average charging rates θ 1 _ave and θ 2 _ave , the relationship represented by the following formula (22) is established.

  Λ shown in the above equation (22) is defined by the following equation (23).

Figure 7 is a diagram for explaining a relationship that holds between the average charging rate theta _1Ave and the negative electrode active average charging rate of the material inside theta _2Ave inside the positive electrode active material. In FIG. 7, it is _assumed that the positive electrode composition θ _1fix and the negative electrode composition θ _2fix correspond to each other. Moreover, all lithium released from the negative electrode 122 positive electrode 121 by absorbing, together with the negative electrode composition changes to theta _2Ave from theta _2Fix, positive electrode composition is assumed that changes theta _1Ave from theta _1fix.

  Since the amount of change of lithium in the positive electrode 121 is equal to the amount of change of lithium in the negative electrode 122, the following equation (24) is established from the equations (16) to (19) and (21).

  By solving the above equation (24), the above equations (22) and (23) are established.

As described above, the average charging rates θ 1 _ave and θ 2 _ave are calculated, and by detecting the battery temperature Tb, the open-circuit voltage OCV when the unipolar capacity decreases and the composition correspondence between the positive and negative electrodes is shifted is obtained. Can be calculated. That is, the average charging rate theta _1Ave, be calculated theta _2Ave, based on the relationship shown in FIG. 3, the average charging rate theta _1Ave, the open-circuit potential _U 1, _{U 2} corresponding to theta _2Ave be calculated. Then, if the potential difference between the open circuit potentials U ₁ and U ₂ is calculated, the change characteristic of the open circuit voltage OCV (referred to as open circuit voltage characteristic) can be calculated.

The average charging rate _θ 1ave, θ 2ave, as shown in the equation (22), is associated with the positive electrode composition theta _1fix and negative electrode composition _θ 2fix. As shown in the above formula (14), the negative electrode composition θ _2fix includes a positive electrode capacity retention ratio k ₁ , a negative electrode capacity retention ratio k _2, and a positive and negative electrode composition-compatible shift capacity ΔQ _s . Therefore, the average charge rates θ 1 _ave and θ 2 _ave can be estimated by estimating the positive electrode capacity retention rate k ₁ , the negative electrode capacity retention rate k _2, and the positive and negative electrode composition corresponding deviation capacity ΔQ _s . If the average charging rates θ 1 _ave and θ 2 _ave are estimated, the open circuit voltage OCV can be estimated as described above.

  Next, a method for calculating the full charge capacity of the secondary battery 11 when the single electrode capacity is reduced and the composition correspondence between the positive and negative electrodes is shifted will be described.

Using the above equation (20), calculates a positive electrode composition theta _{1_0} when the positive electrode composition theta _{1_100} when the SOC is 100%, and the SOC is 0%. Specifically, first, an open circuit voltage when the SOC is 100% is V _100, and an open circuit voltage when the SOC is 0% is V ₀ . Here, the open circuit voltage OCV (θ _1, θ ₂₎ is a positive electrode composition theta ₁ is a positive electrode composition theta _{1_100} becomes satisfying _{V 100,} open circuit voltage OCV (θ _1, θ ₂₎ is a positive electrode composition theta ₁ which satisfies V ₀ positive The composition becomes θ _{1 — 0} .

As described above, the open-circuit voltage OCV shown in the above formula (20) is estimated by estimating the positive electrode capacity retention rate k ₁ , the negative electrode capacity retention rate k _2, and the positive and negative electrode composition-corresponding deviation capacity ΔQ _s . For this reason, the positive electrode compositions θ _{1 — 100} and θ _{1 — 0 depend on} the positive electrode capacity retention rate k ₁ , the negative electrode capacity retention rate k _2, and the positive and negative electrode composition corresponding deviation capacity ΔQ _s .

The full charge capacity Q _d per unit electrode plate area after deterioration is calculated by the following equation (25).

The electrode thickness L ₁ and the volume fraction ε _{s, 1} shown in the above equation (25) depend on the positive electrode capacity retention rate k ₁ as shown in the above equations (16) and (18). Therefore, also depends on positive electrode capacity maintenance rate k ₁ full charge capacity Q _d.

The fully charged capacity Q _{d_all} after deterioration is calculated based on the following equation (26). In the following formula (26), S is an electrode plate area.

Next, a method for estimating the positive electrode capacity retention rate k ₁ , the negative electrode capacity retention rate k _2, and the positive and negative electrode composition correspondence deviation capacity ΔQ _s will be described. In this embodiment, when the open circuit voltage OCV of the secondary battery 11 is changed by a predetermined value, the measured current integrated value (corresponding to the first current integrated value) ΔAh_i and the estimated current integrated value (second current integrated value) during this period are changed. By comparing ΔAh_m (corresponding to the value), the positive electrode capacity retention rate k ₁ , the negative electrode capacity retention rate k _2, and the positive and negative electrode composition corresponding deviation capacity ΔQ _s are estimated.

FIG. 8 and FIG. 9 are flowcharts showing processing for estimating the positive electrode capacity retention rate k ₁ , the negative electrode capacity retention rate k _2, and the positive and negative electrode composition-corresponding deviation capacity ΔQ _s . The processing shown in FIGS. 8 and 9 is executed by the controller 30 at a predetermined cycle.

  In step S <b> 101, the controller 30 detects the temperature Tb_a of the secondary battery 11 based on the output of the temperature sensor 23. Further, the controller 30 estimates an open circuit voltage (corresponding to a first open circuit voltage) OCV_a. Here, the open circuit voltage OCV_a is calculated based on the following equation (27). The following formula (27) is a modification of the above formula (1).

In the above equation (27), Vb is a voltage value of the secondary battery 11 detected by the monitoring unit 21, I is an estimated current, and _Ra is a DC resistance. The estimated current I and DC resistance _Ra are calculated using the battery model described above. Specifically, the estimated current I is calculated based on the above equation (6). Calculating a local SOCθ _1, θ _2, by detecting the battery temperature T, local SOCθ _1, θ _2, by using the correspondence between the battery temperature T and DC resistance _{R a,} and calculates the DC resistance _{R a} be able to.

  Note that the open circuit voltage OCV_a of the secondary battery 11 can be calculated after confirming that the secondary battery 11 is in the relaxed state. Here, as a determination condition that the secondary battery 11 is in the relaxed state, for example, the maximum concentration difference in the lithium concentration in the active material is equal to or less than a predetermined concentration difference, and the current value (absolute value) Ib is A condition that the value is equal to or less than a predetermined value can be set.

  In step S <b> 102, the controller 30 detects the current value Ib flowing through the secondary battery 11 based on the output of the current sensor 22. In step S103, the controller 30 calculates the measured current integrated value ΔAh_i based on the current value Ib detected in the process of step S102. That is, by integrating the current value Ib, a current integrated value ΔAh_i as an actual measurement value is calculated.

  In step S104, the controller 30 determines whether or not to end the current integration for estimating the deterioration parameter. The determination as to whether or not to end the current integration is made by, for example, the SOC (SOC_s) of the secondary battery 11 when the current integration is started and the SOC (SOC_e) of the secondary battery 11 when the current integration is ended. This can be done by determining whether they are different from each other. That is, when SOC_s and SOC_e are different from each other, it can be determined that the current integration for estimating the deterioration parameter is terminated.

  When it is determined that the current integration is to be terminated, it can be confirmed that the secondary battery 11 is in a relaxed state. As a determination condition that the secondary battery 11 is in a relaxed state, for example, the maximum concentration difference in lithium concentration in the active material is equal to or less than a predetermined concentration difference, and the current value (absolute value) Ib is equal to or less than a predetermined value. Can be set.

  Here, since the estimated SOC (SOC_s, SOC_e) includes an estimation error, it can be determined that the current integration is terminated when the SOC ranges including the estimation error are different from each other. When it is determined that the current integration is to be terminated, the controller 30 performs the process of step S105. On the other hand, when determining that the current integration is not finished, the controller 30 returns to the process of step S102.

  In step S105, the controller 30 calculates the open circuit voltage (corresponding to the second open circuit voltage) OCV_b of the secondary battery 11 based on the above equation (27). The open circuit voltage OCV_b is a value different from the open circuit voltage OCV_a, and the open circuit voltage OCV of the secondary battery 11 can be changed from the open circuit voltage OCV_a to the open circuit voltage OCV_b by at least one of charging and discharging of the secondary battery 11. . The method for estimating the open circuit voltage OCV_b is the same as the method for estimating the open circuit voltage OCV_a.

  In step S <b> 105, the controller 30 detects the temperature Tb_b of the secondary battery 11 based on the output of the temperature sensor 23. Here, the battery temperature Tb_b may be different from the battery temperature Tb_a detected in the process of step S101. For example, when the secondary battery 11 is energized, the temperature Tb of the secondary battery 11 may increase, or the temperature Tb of the secondary battery 11 may change depending on the environmental temperature of the secondary battery 11. In this case, the battery temperatures Tb_a and Tb_b may be different from each other.

  In step S106, the controller 30 performs a search process for calculating the optimum solution of the degradation parameter. The degradation parameter search process will be described with reference to the flowchart shown in FIG.

In step S201, the controller 30 sets the upper limit value Delta] Q _{s_h} and a lower limit value Delta] Q _{S_L} of the positive and negative electrodes discrepancy capacity Delta] Q _s. The upper limit value ΔQ _{s_h} and the lower limit value ΔQ _{s_l} are a search range for the deviation capacity ΔQ _s corresponding to the positive and negative electrode compositions. In the first search process, the upper limit value ΔQ _{s_h} and the lower limit value ΔQ _{s_l} are set to predetermined values.

When the upper limit value ΔQ _{s_h} and the lower limit value ΔQ _{s_l} are set, the upper limit value ΔQ _{s_h} and the lower limit value ΔQ _{s_l} can be set on the assumption of the deterioration state of the secondary battery 11. For example, since the secondary battery 11 is likely to deteriorate with the passage of time, if the correspondence relationship between the elapsed time and the deterioration state is obtained in advance by experiments or the like, the deterioration state corresponding to the current time is estimated. be able to. The elapsed time can be the time from when the secondary battery 11 is used for the first time, and the elapsed time can be measured using a timer. If the deterioration state of the secondary battery 11 is estimated, the upper limit value ΔQ _{s_h} and the lower limit value ΔQ _{s_l} can be set based on the deterioration state.

In step S202, the controller 30 calculates a candidate value ΔQ _{s_e} of the positive and negative electrode composition corresponding displacement capacity ΔQ _s within the set upper limit value ΔQ _{s_h} and lower limit value ΔQ _{s_l} (within the search range). For example, the controller 30 can calculate an intermediate value between the upper limit value ΔQ _{s_h} and the lower limit value ΔQ _{s_l} as the candidate value ΔQ _{s_e} .

In step S203, the controller 30, the candidate value Delta] Q _{S_E} calculated in the processing in step S202, calculates a positive electrode capacity maintenance rate _{k 1} and negative electrode capacity maintenance rate _{k 2.} Here, the correspondence (map or function) between the positive and negative electrode composition correspondence deviation capacity ΔQ _s and the positive electrode capacity maintenance rate k ₁ , and the correspondence relationship between the positive and negative electrode composition correspondence deviation capacity ΔQ _s and the negative electrode capacity maintenance factor k ₂ (map or function). ) Can be obtained in advance by experiments or the like. Information regarding these correspondences can be stored in the memory 30a. By using these correspondences, the positive electrode capacity retention rate k ₁ and the negative electrode capacity retention rate k ₂ can be calculated by specifying the positive and negative electrode composition correspondence deviation capacity ΔQ _s .

In step S204, the controller 30 calculates an open-circuit voltage characteristic using the deterioration parameters ΔQ _s , k ₁ , k ₂ calculated in the processes of steps S202, S203. This open-circuit voltage characteristic is an open-circuit voltage characteristic when the temperature Tb of the secondary battery 11 is Tb_a.

Here, if the single electrode capacity retention ratios k ₁ and k ₂ are specified, the electrode thicknesses L ₁ and L ₂ can be calculated based on the above formulas (16) and (17), and the above formula (18). ) And (19), the active material volume fraction ε _{s, 1} , ε _{s, 2} can be calculated. If the electrode thickness and the active material volume fraction are calculated, λ shown in the above equation (23) can be calculated.

If the deterioration parameters ΔQ _s , k ₁ , k ₂ are specified, the positive electrode composition θ _1fix and the negative electrode composition θ _2fix can be calculated based on the above formulas (13) and (14). By calculating λ shown in the above equation (23) and calculating the positive electrode composition θ _1fix and the negative electrode composition θ _2fix , the average charging rates θ _1ave and θ _2ave can be estimated based on the above equation (22). . If the average charging rates θ 1 _ave and θ 2 _ave are estimated, the open-circuit voltage characteristics of the secondary battery 11 can be calculated as described above.

  The open-circuit voltage characteristics of the secondary battery 11 are calculated from the positive electrode open potential and the negative electrode open potential shown in FIG. 3, and the open potential corresponding to the battery temperature Tb_a is used as the positive electrode open potential and the negative electrode open potential. By using the positive electrode open potential and the negative electrode open potential corresponding to the battery temperature Tb_a, it is possible to calculate (estimate) the open-circuit voltage characteristics reflecting the influence of the battery temperature Tb_a, and to improve the estimation accuracy of the open-circuit voltage characteristics. it can.

In step S205, the controller 30 calculates an average charging rate (corresponding to the first average charging rate) _{θ1_a} corresponding to the open-circuit voltage OCV_a using the open-circuit voltage characteristic calculated in the process of step S204. The open circuit voltage OCV_a is a value calculated in the process of step S101 shown in FIG. Open-circuit voltage characteristics, in order to show the open circuit voltage OCV and the average charging rate theta ₁ correspondence, it is possible to calculate the average charging rate theta _{1_a} corresponding to open voltage OCV_a.

In step S206, the controller 30 calculates an open-circuit voltage characteristic using the deterioration parameters ΔQ _s , k ₁ , k ₂ calculated in the processes of steps S202, S203. This open-circuit voltage characteristic is an open-circuit voltage characteristic when the temperature Tb of the secondary battery 11 is Tb_b. The process of step S206 is the same as the process of step S204. Here, when the open circuit voltage characteristic is calculated by the process of step S206, the open circuit potential corresponding to the battery temperature Tb_b is used as the positive electrode open potential and the negative electrode open potential. By using the positive electrode open potential and the negative electrode open potential corresponding to the battery temperature Tb_b, it is possible to calculate (estimate) the open circuit voltage characteristic reflecting the influence of the battery temperature Tb_b, and to improve the estimation accuracy of the open circuit voltage characteristic. it can.

In step S207, the controller 30 calculates an average charging rate (corresponding to the second average charging rate) _{θ1_b} corresponding to the open circuit voltage OCV_b using the open circuit voltage characteristic calculated in the process of step S206. The open circuit voltage OCV_b is a value calculated by the process of step S105 shown in FIG. Open-circuit voltage characteristics, in order to show the open circuit voltage OCV and the average charging rate theta ₁ correspondence, it is possible to calculate the average charging rate theta _{unit 1_b} corresponding to open voltage OCV_b.

In step S208, the controller 30, the average charging rate theta _{1_a} calculated in the processing in step S205, on the basis of the average charging rate theta _{unit 1_b} calculated in the processing in step S207, calculates an estimated current integrated value DerutaAh_m. The estimated current integrated value ΔAh_m is a current integrated value (estimated value) calculated on the battery model while the open circuit voltage of the secondary battery 11 changes from OCV_a to OCV_b. The controller 30 can calculate the estimated current integrated value ΔAh_m based on the following equation (28).

In the above formula (28), S is the electrode area, and F is the Faraday constant. The electrode thickness L ₁ is calculated from the above equation (16) that depends on the positive electrode capacity retention rate k ₁ , and the active material volume fraction ε _{s, 1} is the above equation (18) that depends on the positive electrode capacity retention rate k _1. Is calculated from

  In step S209, the controller 30 compares the estimated current integrated value ΔAh_m calculated in the process of step S208 with the actually measured current integrated value ΔAh_i calculated in the process of step S103 shown in FIG. Specifically, the controller 30 determines whether or not the measured current integrated value ΔAh_i is larger than the estimated current integrated value ΔAh_m. Here, when the measured current integrated value ΔAh_i is larger than the estimated current integrated value ΔAh_m, the controller 30 performs the process of step S210. When the measured current integrated value ΔAh_i is smaller than the estimated current integrated value ΔAh_m, the controller 30 The process of step S211 is performed.

In step S210, the controller 30 sets the candidate value ΔQ _{s_e} calculated in the process of step S202 as the upper limit value ΔQ _{s_h} of the positive and negative electrode composition correspondence deviation capacity ΔQ _s in the next search process. Thereby, in the next search process, the search range is narrowed to the range of the upper limit value ΔQ _{s_e} and the lower limit value ΔQ _{s_l} .

In step S211, the controller 30 sets the candidate value ΔQ _{s_e} calculated in step S202 as the lower limit value ΔQ _{s_l} of the positive and negative electrode composition-corresponding deviation capacity ΔQ _s in the next search process. Thereby, in the next search process, the search range is narrowed to the range of the upper limit value ΔQ _{s_h} and the lower limit value ΔQ _{s_e} .

In step S212, the controller 30 determines whether or not the upper limit value Delta] Q _{s_h} and a lower limit value Delta] Q difference _{s_l} (ΔQ _{s_h -ΔQ s_l)} is smaller than the threshold value Delta] Q _{s_min.} The value of the threshold ΔQ _{s_min} can be set as appropriate, and information regarding the threshold ΔQ _{s_min} can be stored in the memory 30a. The closer the upper limit value ΔQ _{s_h} and the lower limit value ΔQ _{s_l} are to each other, the _narrower the search range becomes, and the positive and negative electrode composition correspondence deviation capacity ΔQ _s becomes easier to specify. For this reason, the threshold value ΔQ _{s_min} can be appropriately set so that the positive and negative electrode composition-corresponding displacement capacity ΔQ _s can be easily specified.

When the difference between the upper limit value Delta] Q _{s_h} and a lower limit value Delta] Q _{S_L} is smaller than the threshold value Delta] Q _{s_min,} controller 30 terminates the process shown in FIG. At this time, the candidate value ΔQ _{s_e} calculated in the process of step S202 is determined as the positive and negative electrode composition corresponding deviation capacity ΔQ _s in the current secondary battery 11. Moreover, single electrode capacity maintenance rate _k 1, _{k 2} corresponding to the candidate value Delta] Q _{S_E} is determined as a single electrode capacity maintenance rate _k 1, _{k 2} in the current of the secondary battery 11.

When the difference between the upper limit value Delta] Q _{s_h} and a lower limit value Delta] Q _{S_L} is greater than the threshold Delta] Q _{s_min,} controller 30 returns to the processing in step S202. In the process of step S202, the candidate value ΔQ _{s_e} is calculated in the narrowed search range (range of the upper limit value ΔQ _{s_h} and the lower limit value ΔQ _{s_l} ).

In the process shown in FIG. 9, the positive and negative electrode composition correspondence deviation capacity (candidate value) ΔQ _{s_e} is calculated, and the positive electrode capacity maintenance rate k ₁ and the negative electrode capacity maintenance rate k ₂ are calculated from the candidate value ΔQ _{s_e.} It is not limited to. That is, candidate values can be set for at least one of the positive and negative electrode composition-corresponding deviation capacity ΔQ _s , the positive electrode capacity retention rate k _1, and the negative electrode capacity retention rate k ₂ .

Specifically, instead of setting the positive and negative electrode composition correspondence deviation capacity (candidate value) ΔQ _{s_e} , a candidate value can be set for one of the positive electrode capacity retention ratio k ₁ and the negative electrode capacity retention ratio k ₂ . In this case, similar to the process shown in FIG. 9, until the difference of the estimated current integrated value ΔAh_m and measured current integrated value ΔAh_i is minimized, search one of the positive electrode capacity maintenance rate k ₁ and negative electrode capacity maintenance rate k ₂ do it.

For example, when setting the candidate values of the positive electrode capacity maintenance rate k ₁ can be determined in advance by experiments or the like of correspondence between the positive electrode capacity maintenance rate k ₁ and negative electrodes discrepancy capacity Delta] Q _s (map or function) . As a result, it is possible to calculate the positive and negative electrode composition corresponding deviation capacity ΔQ _s corresponding to the positive electrode capacity maintenance rate (candidate value) k ₁ . Further, if the deviation capacity ΔQ _s corresponding to the positive / negative electrode composition is calculated, the correspondence relationship (map or function) between the negative electrode capacity retention ratio k ₂ and the deviation capacity ΔQ _s corresponding to the positive / negative electrode composition is obtained in advance by experiments or the like. The negative electrode capacity retention ratio k ₂ corresponding to the positive and negative electrode composition correspondence deviation capacity ΔQ _s can be calculated.

On the other hand, candidate values can be set for each of the positive and negative electrode composition-corresponding deviation capacity ΔQ _s , the positive electrode capacity retention ratio k _1, and the negative electrode capacity retention ratio k ₂ . Even if the candidate value is set in this way, the estimated current integrated value ΔAh_m can be calculated by the processing in steps S204 to S208. If the estimated current integrated value ΔAh_m is calculated, the positive and negative electrode composition corresponding deviation capacity ΔQ _s , the positive electrode capacity retention rate k ₁ and the negative electrode capacity maintenance rate k until the difference between the estimated current integrated value ΔAh_m and the measured current integrated value ΔAh_i is minimized. ₂ may be searched for.

By performing the processing shown in FIG. 9, the difference capacity ΔQ _s corresponding to the positive and negative electrode compositions when the difference between the estimated current integrated value ΔAh_m and the measured current integrated value ΔAh_i is minimized is specified, and the actual internal state of the secondary battery 11 It is possible to estimate the deviation capacity ΔQ _s corresponding to the positive and negative electrode compositions reflecting the above. That is, it is possible to improve the estimation accuracy of the positive and negative electrode composition-corresponding deviation capacity ΔQ _s . If the estimation accuracy of the positive and negative electrode composition correspondence deviation capacity ΔQ _s is improved, the estimation accuracy of the single electrode capacity maintenance rates k ₁ and k ₂ can also be improved.

According to the present embodiment, since the open circuit voltage characteristics corresponding to the battery temperatures Tb_a and Tb_b are calculated, the average charging rates θ _{1 — a} and θ 1 — _b corresponding to the open circuit voltages OCV_a and OCV_b can be calculated with high accuracy. As shown in FIG. 10, the open-circuit voltage characteristics may not match depending on the battery temperatures Tb_a and Tb_b.

In the present embodiment, when calculating the average charging rate θ1_a, the average charging rate θ1_a corresponding to the open-circuit voltage _{OCV_a} is calculated using the open-circuit voltage characteristics corresponding to the battery temperature Tb_a. Further, when calculating the average charging rate θ _{1_b} , the average charging rate θ _{1_b} corresponding to the open circuit voltage _{OCV_b} is calculated using the open circuit voltage characteristic corresponding to the battery temperature Tb_b.

Here, when the average charging rates θ _{1 — a} and θ 1 — _b corresponding to the open circuit voltages OCV_a and OCV_b are calculated, only one open circuit voltage characteristic (solid line) shown in FIG. 11 is calculated unless the battery temperature Tb is taken into consideration. The In the example shown in FIG. 11, it is assumed that the open-circuit voltage characteristic (solid line) matches the open-circuit voltage characteristic at the battery temperature Tb_b shown in FIG. When the open circuit voltage characteristic shown in FIG. 11 is used, the average charging rate θ 1 — _b corresponding to the open circuit voltage OCV_b can be estimated with high accuracy.

However, the average charging rate theta ₁ of estimation accuracy corresponding to the open circuit voltage OCV_a may decrease. When the open-circuit voltage characteristic at the battery temperature Tb_a is indicated by a dotted line shown in FIG. 11, the average charging rate θ 1 — _a1 calculated from the open-circuit voltage characteristic indicated by the solid line and the average charging rate θ calculated from the open-circuit voltage characteristic indicated by the dotted line _{1_a2} and is deviated only minute Δθ _1. When the deviation amount Δθ ₁ occurs, the deviation amount Δθ ₁ is included in the estimated current integrated value ΔAh_m when the estimated current integrated value ΔAh_m is calculated based on the above equation (28).

Along with this, the accuracy when searching (estimating) the positive and negative electrode composition correspondence deviation capacity ΔQ _s is lowered. If the estimation accuracy of the positive and negative electrode composition correspondence deviation capacity ΔQ _s decreases, the estimation accuracy of the single electrode capacity retention ratios k ₁ and k ₂ also decreases. Deterioration parameter Delta] Q _s, the estimation accuracy of the _{k 1,} k ₂ is reduced, when estimating the full charge capacity Q _d by using equation (25), decreases also the estimation accuracy of the full charge capacity Q _d.

FIG. 11 shows the case where the open circuit voltage characteristic indicated by the solid line matches the open circuit voltage characteristic at the battery temperature Tb_b, but the open circuit voltage characteristic does not match the open circuit voltage characteristic at the battery temperatures Tb_a and Tb_b. There is also. In this case, the open-circuit voltage OCV_a, average charging rate theta _{1_a} corresponding to OCV_b, θ _{1_b} is, the average charging rate theta _{1_a} in the actual secondary battery 11, deviates from the theta _{unit 1_b,} deterioration parameter Delta] Q _{s, k 1} , K ₂ and the full charge capacity Q _d are estimated less accurately.

When the open-circuit voltage characteristic calculated without considering the battery temperature matches the open-circuit voltage characteristic at the battery temperature Tb_a, the average charge rate θ 1 — _b corresponding to the open-circuit voltage _{OCV_b} is the actual secondary battery. 11 is deviated from the average charging rate θ 1 — _{b in FIG} . Along with this, the estimation accuracy of the degradation parameters ΔQ _s , k ₁ , k ₂ and the full charge capacity Q _d decreases.

According to the present embodiment, as described above, the average charging rates θ _{1 — a} and θ 1 — _b can be accurately estimated in consideration of the battery temperatures Tb_a and Tb_b. Therefore, the degradation parameters ΔQ _s , k ₁ , k ₂ can be estimated with high accuracy, and the estimation accuracy of the full charge capacity Q _d can be improved. If the full charge capacity Q _d is continuously estimated, the transition of the full charge capacity Q _d can be grasped. Here, by calculating the full charge capacity _{Q D_ini} when secondary battery 11 is in the initial state, the current ratio between the full charge capacity _{Q D_now} in the secondary battery 11 (after deterioration) _(Q d_now _/ Q d_ini) Thus, it is possible to grasp the deterioration state of the secondary battery 11. As the deterioration of the secondary battery 11 progresses, the full charge capacity of the secondary battery 11 decreases, and the ratio (Q _{d_now} / Q _{d_ini} ) decreases below 1 accordingly.

10: assembled battery, 11: single battery (secondary battery), 121: positive electrode, 121a: current collector,
121b: positive electrode active material, 122: negative electrode, 122a: current collector, 122b: negative electrode active material,
123: Separator, 21: Monitoring unit, 22: Current sensor, 23: Temperature sensor,
24: current limiting resistor, 30: controller, 30a: memory, 31: inverter,
32: Motor generator, PL: Positive line, NL: Negative line,
SMR-B, SMR-G, SMR-P: System main relay

Claims (8)

A temperature sensor for detecting the temperature of the secondary battery;
The open circuit voltage of the secondary battery is calculated from the single electrode open potential at the positive electrode and the negative electrode of the secondary battery, the maintenance rate of the single electrode capacity at the positive electrode and the negative electrode, and the average of the active materials of the positive electrode and the negative electrode A controller that corrects the unipolar open-circuit potential using a variation amount of the battery capacity that accompanies a change in the correspondence relationship of the charging rate, and
The battery system according to claim 1, wherein the controller uses the unipolar open potential according to a temperature detected by the temperature sensor when correcting the unipolar open potential.   The controller corrects an open-circuit potential characteristic indicating a correspondence relationship between the average charge rate and the single-pole open potential using the maintenance rate of the single-pole capacity and the variation amount of the battery capacity. The battery system according to 1.   The controller uses the correspondence relationship between the open-circuit potential characteristic and the temperature of the secondary battery specified in advance using the secondary battery in an initial state, and the detected temperature is corrected as the open-circuit potential characteristic. The battery system according to claim 2, wherein the open-circuit potential characteristic corresponding to is used.   4. The battery system according to claim 2, wherein the controller calculates an open-circuit voltage characteristic indicating a correspondence relationship between the average charging rate and the open-circuit voltage using the corrected open-circuit potential characteristic. Having a current sensor for detecting the current of the secondary battery;
The controller is
Calculating a first current integrated value obtained by integrating the current detected by the current sensor until the open circuit voltage of the secondary battery changes from the first open circuit voltage to the second open circuit voltage;
Using the calculated open-circuit voltage characteristics, a first average charge rate corresponding to the first open-circuit voltage and a second average charge rate corresponding to the second open-circuit voltage are calculated,
From a difference between the first average charging rate and the second average charging rate, a second current integrated value which is a current integrated value until the open circuit voltage changes from the first open circuit voltage to the second open circuit voltage is determined. Calculate
5. The maintenance rate of the unipolar capacity and the fluctuation amount of the battery capacity when the difference between the first current integrated value and the second current integrated value is minimized are calculated. Battery system. The controller is
When calculating the first average charging rate, using the open-circuit voltage characteristics corresponding to the detected temperature when the first open-circuit voltage is acquired,
The battery system according to claim 5, wherein when calculating the second average charging rate, the open-circuit voltage characteristic corresponding to the detected temperature when the second open-circuit voltage is acquired is used. The average charging rate changes according to the maintenance rate of the single electrode capacity and the amount of fluctuation of the battery capacity,
The controller uses the difference between the average charging rate when the SOC of the secondary battery is 100% and the average charging rate when the SOC of the secondary battery is 0% to use the secondary battery. The battery system according to claim 5 or 6, wherein a full charge capacity of the battery is calculated. The secondary battery is charged and discharged according to the movement of the reaction-participating substance between the positive electrode and the negative electrode,
The average charge rate is represented by a ratio between a maximum concentration of the reaction-participating substance in the active material and a current average concentration of the reaction-participating substance in the active material. 8. The battery system according to any one of 7.