JP2014120200A - Battery system, and method for estimating lithium concentration distribution - Google Patents

Abstract

PROBLEM TO BE SOLVED: To highly accurately estimate a lithium concentration distribution in an active material, when the temperature of a lithium ion secondary battery decreases.SOLUTION: A battery system comprises: a temperature sensor (203) for detecting the temperature of a lithium ion secondary battery (1); and a controller (300) for calculating a lithium concentration distribution in spherical active material models (141b, 142b) included in the lithium ion secondary battery. In a state where the active material models are divided into a plurality of regions in a radial direction, the controller calculates a lithium concentration distribution showing the lithium concentration in each of the regions, using a diffusion equation. The controller makes the division number (Ninc) of the regions in the case where a detected temperature obtained by the temperature sensor is below a threshold level larger than the division number (Nref) of the regions in the case where the detected temperature is above the threshold level.

Description

  The present invention relates to a technique for estimating a lithium concentration distribution in an active material of a lithium ion secondary battery.

  In patent document 1, the lithium concentration distribution in the active material model included in the lithium ion secondary battery is calculated by defining a battery model. Specifically, the active material model is divided into N pieces in the radial direction of the active material model regarded as a sphere, and each divided region in the active material model is obtained by using a diffusion equation (diffusion model equation). In other words, the lithium concentration distribution in the active material model is calculated.

JP 2008-243373 A

  In patent document 1, the number N when dividing an active material model is uniquely set. Here, when the temperature of the lithium ion secondary battery decreases, the diffusion coefficient used in the diffusion equation decreases, and the diffusion of lithium in the active material model is likely to be limited. At this time, if the number N for dividing the active material model is uniquely set, it becomes difficult to grasp the lithium concentration distribution in the active material model.

  A battery system according to a first invention of the present application includes a temperature sensor that detects a temperature of a lithium ion secondary battery, and a controller that calculates a lithium concentration distribution in a spherical active material model included in the lithium ion secondary battery. . In a state where the active material model is divided into a plurality of regions in the radial direction, the controller calculates a lithium concentration distribution indicating a lithium concentration in each region using a diffusion equation. Further, the controller sets the number of divisions of the region when the temperature detected by the temperature sensor is lower than the threshold to be larger than the number of divisions of the region when the detected temperature is higher than the threshold.

  If the number of divisions of the active material model is increased, the active material model can be subdivided, and the lithium concentration of each subdivided region can be calculated. As a result, it becomes easier to grasp the lithium concentration distribution inside the active material model. Here, when the temperature of the lithium ion secondary battery is higher than the threshold value, the diffusion coefficient used in the diffusion equation tends to increase, and if the number of divisions of the active material model is increased, the stability of the diffusion equation cannot be secured. End up.

  Therefore, in the first invention of the present application, when the temperature of the lithium ion secondary battery is lower than the threshold value, a division number larger than the division number used when the temperature of the lithium ion secondary battery is higher than the threshold value is set. Yes. As described above, since the diffusion of lithium in the active material model is likely to be limited when the temperature of the lithium ion secondary battery is decreased, the lithium concentration distribution in the active material model is increased by increasing the number of divisions of the active material model. It becomes easy to grasp.

  If the lithium concentration distribution inside the active material model is calculated, the lithium concentration at the interface of the active material model can be calculated based on this lithium concentration distribution. The reaction resistance and diffusion resistance that define the internal resistance of the lithium ion secondary battery depend on the lithium concentration at the interface of the active material model. Therefore, by calculating the lithium concentration at the interface, the reaction resistance of the lithium ion secondary battery and Each diffusion resistance can be specified.

  If the reaction resistance and the diffusion resistance can be specified, the internal resistance of the lithium ion secondary battery can be specified by combining these resistance components. According to the first invention of the present application, as described above, the lithium concentration distribution in the active material model can be easily grasped. Therefore, when calculating the lithium concentration at the interface from the lithium concentration distribution, the lithium concentration at the interface is accurately determined. It can be estimated well. If the lithium concentration at the interface can be estimated with high accuracy, the reaction resistance and diffusion resistance depending on the lithium concentration at the interface can also be estimated with high accuracy. Accordingly, the internal resistance of the lithium ion secondary battery including the reaction resistance and the diffusion resistance can be estimated with high accuracy.

  If the internal resistance of the lithium ion secondary battery can be specified, the open circuit voltage of the lithium ion secondary battery can be calculated. That is, the open circuit voltage of the lithium ion secondary battery can be calculated by subtracting the amount of voltage change associated with the internal resistance from the closed circuit voltage of the lithium ion secondary battery. Here, since the open circuit voltage and the SOC (State of Charge) have a correspondence relationship, the SOC corresponding to the open circuit voltage can be specified by using this correspondence relationship.

  As described above, according to the first invention of the present application, since the internal resistance of the lithium ion secondary battery can be estimated with high accuracy, the open circuit voltage of the lithium ion secondary battery can also be calculated with high accuracy. Accordingly, it is possible to improve the estimation accuracy of the SOC corresponding to the open circuit voltage.

  When calculating the lithium concentration distribution in the active material model using the diffusion equation, boundary conditions at the center and interface of the active material model can be set. If the boundary conditions are set in this way, the lithium concentration in each region included in the active material model can be calculated by using the diffusion equation.

  The threshold value to be compared with the detected temperature can be set as appropriate based on the diffusion coefficient used in the diffusion equation. As the diffusion coefficient increases, the number of divisions of the active material model cannot be increased in order to ensure the stability of the diffusion equation. On the other hand, if the diffusion coefficient decreases, the stability of the diffusion equation can be ensured even if the number of divisions of the active material model is increased. Based on this point, the threshold value can be set as appropriate. Here, the diffusion coefficient used in the diffusion equation when the detection temperature is lower than the threshold value is smaller than the diffusion coefficient used in the diffusion equation when the detection temperature is higher than the threshold value.

  The threshold value to be compared with the detected temperature can include a first threshold value and a second threshold value that is higher than the first threshold value. Here, when the SOC of the lithium ion secondary battery is included in a predetermined range apart from 0% and 100%, the number of divisions when the detected temperature is lower than the second threshold is determined, and the detected temperature is lower than the second threshold. It can be made larger than the number of divisions when it is high. On the other hand, when the SOC of the lithium ion secondary battery is out of the predetermined range, the number of divisions when the detected temperature is lower than the first threshold is made larger than the number of divisions when the detected temperature is higher than the first threshold. be able to.

  The diffusion coefficient used in the diffusion equation also depends on the SOC of the lithium ion secondary battery. Specifically, the diffusion coefficient increases as the SOC of the lithium ion secondary battery approaches 0% and 100%. Further, when the SOC of the lithium ion secondary battery is included in the predetermined range, the diffusion coefficient is difficult to increase. In other words, the diffusion coefficient when the SOC is included in the predetermined range is smaller than the diffusion coefficient when the SOC is out of the predetermined range. For this reason, when the SOC is included in the predetermined range, the stability of the diffusion equation can be ensured even if the threshold value to be compared with the detected temperature is shifted to the high temperature side.

  Therefore, when the SOC of the lithium ion secondary battery is included in the predetermined range, the division number is changed with the second threshold as a reference. On the other hand, when the SOC of the lithium ion secondary battery is out of the predetermined range, the number of divisions can be changed based on the first threshold value. When the SOC of the lithium ion secondary battery is included in the predetermined range, the reference for switching the number of divisions is changed from the first threshold value to the second threshold value, thereby ensuring the stability of the diffusion equation and dividing the active material model. Conditions (temperature range) that can increase the number can be expanded.

  The second invention of the present application is an estimation method for estimating a lithium concentration distribution inside a spherical active material model included in a lithium ion secondary battery. Here, in a state where the active material model is divided into a plurality of regions in the radial direction, a lithium concentration distribution indicating the lithium concentration in each region can be calculated using a diffusion equation. When calculating the lithium concentration distribution, the temperature of the lithium ion secondary battery is detected, and the number of divisions of the region when the detection temperature is lower than the threshold is greater than the number of divisions of the region when the detection temperature is higher than the threshold Also make it bigger. Also in the second invention of the present application, the same effect as that of the first invention of the present application can be obtained.

It is a figure which shows the structure of a battery system. It is a figure which shows the structure of a part of battery system. It is a figure which shows the structure of an equalization circuit. It is the schematic which shows the structure of a secondary battery. It is a figure which shows the list of variables etc. which are used with a battery model type | formula. It is a conceptual diagram explaining a battery model. It is a conceptual diagram which shows the active material model shown by the polar coordinate. It is a figure which shows the relationship between the terminal voltage of a secondary battery, and various average electric potential. It is a figure explaining the temperature dependence of a diffusion coefficient. It is a figure explaining the SOC dependence of a diffusion coefficient. It is a figure which shows the relationship between an open circuit voltage (positive electrode) and local SOC. It is a figure which shows the relationship between an open circuit voltage (negative electrode) and local SOC. It is the schematic which shows the structure of the battery state estimation part provided in the inside of a controller. It is a flowchart which shows the process of a battery state estimation part. It is a figure explaining the conditions (temperature and SOC) which switch the division | segmentation number of an active material model. It is a flowchart which shows the process which sets the division | segmentation number of an active material model. It is a conceptual diagram which shows an active material model when the division | segmentation number is switched. It is a figure which shows the lithium concentration of each area | region when an active material model is divided | segmented into three area | regions. It is a figure which shows the lithium concentration of each area | region when an active material model is divided | segmented into five area | regions.

  Examples of the present invention will be described below.

  FIG. 1 is a diagram showing the configuration of the battery system of this example. The battery system shown in FIG. 1 can be mounted on a vehicle. Vehicles include HV (Hybrid Vehicle), PHV (Plug-in Hybrid Vehicle), and EV (Electric Vehicle).

  The HV includes other power sources such as an internal combustion engine or a fuel cell in addition to an assembled battery described later as a power source for running the vehicle. In PHV, an assembled battery can be charged using power from an external power source in HV. The EV includes only an assembled battery, which will be described later, as a power source of the vehicle, and can charge the assembled battery by using power supply from an external power source. The external power source is a power source (for example, commercial power source) provided separately from the vehicle outside the vehicle.

  The assembled battery 100 includes a plurality of secondary batteries 1 connected in series. As the secondary battery 1, a lithium ion secondary battery can be used. The number of secondary batteries 1 can be appropriately set based on the required output of the assembled battery 100 and the like. The assembled battery 100 can also include a plurality of secondary batteries 1 connected in parallel. The monitoring unit (voltage sensor) 201 detects the inter-terminal voltage of the assembled battery 100 or detects the inter-terminal voltage Vb of each secondary battery 1. The monitoring unit 201 outputs the detection result to the controller 300.

  The current sensor 202 detects the current Ib flowing through the assembled battery 100 and outputs the detection result to the controller 300. Here, the discharge current Ib is a positive value, and the charging current Ib is a negative value. The temperature sensor 203 detects the temperature Tb of the assembled battery 100 and outputs the detection result to the controller 300. By using the plurality of temperature sensors 203, it becomes easy to detect the temperature Tb of the secondary batteries 1 arranged at different positions.

  The controller 300 includes a memory 300a, and the memory 300a stores various types of information for the controller 300 to perform predetermined processing (for example, processing described in the present embodiment). In this embodiment, the memory 300a is built in the controller 300, but the memory 300a can be provided outside the controller 300.

  A system main relay SMR-B is provided on the positive electrode line PL connected to the positive electrode terminal of the assembled battery 100. System main relay SMR-B is switched between ON and OFF by receiving a control signal from controller 300. A system main relay SMR-G is provided on the negative electrode line NL connected to the negative electrode terminal of the assembled battery 100. System main relay SMR-G is switched between on and off by receiving a control signal from controller 300.

  A system main relay SMR-P and a current limiting resistor 204 are connected in parallel to the system main relay SMR-G. System main relay SMR-P and current limiting resistor 204 are connected in series. System main relay SMR-P is switched between ON and OFF by receiving a control signal from controller 300.

  The current limiting resistor 204 is used for suppressing an inrush current from flowing through the capacitor 205 when the assembled battery 100 is connected to a load (specifically, an inverter 205). Capacitor 205 is connected to positive electrode line PL and negative electrode line NL, and is used to smooth voltage fluctuations between positive electrode line PL and negative electrode line NL.

  When connecting the assembled battery 100 to the inverter 206, the controller 300 first switches the system main relay SMR-B from off to on and switches the system main relay SMR-P from off to on. As a result, a current flows through the current limiting resistor 204.

  Next, the controller 300 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 100 and the inverter 205 is completed, and the battery system shown in FIG. 1 is in a start-up state (Ready-On). Information about on / off of the ignition switch of the vehicle is input to the controller 300, and the controller 300 activates the battery system shown in FIG. 1 in response to the ignition switch switching from off to on.

  On the other hand, when the ignition switch is switched from on to off, the controller 300 switches the system main relays SMR-B and SMR-G from on to off. Thereby, the connection between the assembled battery 100 and the inverter 206 is cut off, and the battery system shown in FIG. 1 enters a stopped state (Ready-Off).

  The inverter 206 converts the DC power from the assembled battery 100 into AC power and outputs the AC power to the motor / generator 207. As the motor generator 207, for example, a three-phase AC motor can be used. Motor generator 207 receives AC power from inverter 206 and generates kinetic energy for running the vehicle. The kinetic energy generated by the motor / generator 207 is transmitted to the wheels so that the vehicle can run.

  When the vehicle is decelerated or stopped, the motor / generator 207 converts kinetic energy generated during braking of the vehicle into electric energy (AC power). The inverter 206 converts AC power generated by the motor / generator 207 into DC power, and outputs the DC power to the assembled battery 100. Thereby, the assembled battery 100 can store regenerative electric power.

  In the present embodiment, the assembled battery 100 is connected to the inverter 206, but the present invention is not limited to this. Specifically, a booster circuit can be provided in the current path between the assembled battery 100 and the inverter 206. By using the booster circuit, the output voltage of the assembled battery 100 can be boosted. The booster circuit can step down the output voltage from the inverter 206 to the assembled battery 100.

  As shown in FIG. 2, the monitoring unit 201 includes voltage monitoring ICs (Integrated Circuits) 201a corresponding to the number of secondary batteries 1 constituting the assembled battery 100, and each voltage monitoring IC 201a includes each secondary battery. 1 is connected in parallel. The voltage monitoring IC 201a detects the voltage Vb of the secondary battery 1 and outputs the detection result to the controller 300. In addition, an equalization circuit 208 is connected in parallel to each secondary battery 1, and the equalization circuit 208 is used to equalize the voltage or SOC (State of Charge) in the plurality of secondary batteries 1. It is done. The SOC indicates the ratio of the current charge capacity to the full charge capacity. The operation of the equalization circuit 208 is controlled by the controller 300.

  For example, when the controller 300 determines that the voltage of a specific secondary battery 1 is higher than the voltages of other secondary batteries 1 based on the output of the voltage monitoring IC 201a, the controller 300 is equivalent to the specific secondary battery 1. Only the specific secondary battery 1 is discharged by operating only the control circuit 208. Thereby, only the voltage of the specific secondary battery 1 falls, and it can align with the voltage of the other secondary battery 1.

  A specific configuration (example) of the equalization circuit 208 will be described with reference to FIG. FIG. 3 is a circuit diagram showing the configuration of the secondary battery 1 and the equalization circuit 208.

  The equalization circuit 208 includes a resistor 208a and a switch element 208b. The switch element 208b is switched between ON and OFF in response to a control signal from the controller 300. When the switch element 208b is switched from OFF to ON, a current flows from the secondary battery 1 to the resistor 208a, and the secondary battery 1 can be discharged. Thereby, the voltage of each secondary battery 1 can be adjusted, and the voltage in the some secondary battery 1 can be equalized.

  In this embodiment, the equalization circuit 208 and the voltage monitoring IC 201a are provided for each secondary battery 1, but this is not restrictive. For example, when a plurality of secondary batteries 1 constituting the assembled battery 100 are divided into a plurality of battery blocks, an equalization circuit 208 and a voltage monitoring IC 201a can be provided for each battery block. Each battery block includes a plurality of secondary batteries 1 connected in series, and the assembled battery 100 is configured by connecting the plurality of battery blocks in series. The voltage monitoring IC 201a detects the voltage of the corresponding battery block, and the equalization circuit 208 discharges the corresponding battery block. Each battery block can also include a plurality of secondary batteries 1 connected in parallel.

  In order to perform the equalization process with high accuracy, it is preferable to perform the equalization process based on the OCV (Open Circuit Voltage) of the secondary battery 1. In the plurality of secondary batteries 1 constituting the assembled battery 100, the SOC may vary. The full charge capacity of the secondary battery 1 decreases as the deterioration of the secondary battery 1 proceeds, and variations in the full charge capacity occur according to variations in the deterioration of the plurality of secondary batteries 1. . In addition, the charge capacity of the secondary battery 1 may be reduced due to self-discharge or the like, but the amount of charge capacity reduction may be different among the plurality of secondary batteries 1. As a result, SOC variation occurs in the plurality of secondary batteries 1.

  When the SOC variation occurs, it is preferable to reduce the SOC variation in order to continue using the secondary batteries 1 in an equivalent state. If a plurality of secondary batteries 1 are continuously used in different states, only a specific secondary battery 1 may be easily deteriorated. Here, since the SOC of the secondary battery 1 has a corresponding relationship with the OCV of the secondary battery 1, in order to reduce the variation in the SOC, the variation in the OCV may be reduced. For this reason, if OCV in the some secondary battery 1 is acquired and equalization processing is performed based on these OCV, the variation in SOC can be reduced.

  Next, the battery model used in the present embodiment will be described. FIG. 4 is a schematic diagram showing the configuration of the secondary battery 1. A coordinate axis x shown in FIG. 4 indicates a position in the thickness direction of the electrode.

  The secondary battery 1 includes a positive electrode 141, a negative electrode 142, and a separator 143. The separator 143 is located between the positive electrode 141 and the negative electrode 142 and contains an electrolytic solution. The positive electrode 141 has a current collecting plate 141 a made of aluminum or the like, and the current collecting plate 141 a is electrically connected to the positive electrode terminal 11 of the secondary battery 1. The negative electrode 142 includes a current collector plate 142 a made of copper or the like, and the current collector plate 142 a is electrically connected to the negative electrode terminal 12 of the secondary battery 1.

Each of the negative electrode 142 and the positive electrode 141 is composed of an aggregate of spherical active materials 142b and 141b. When the secondary battery 1 is discharged, a chemical reaction that releases lithium ions Li ⁺ and electrons e ⁻ is performed on the interface of the active material 142 b of the negative electrode 142. In addition, a chemical reaction that absorbs lithium ions Li ⁺ and electrons e ⁻ is performed on the interface of the active material 141 b of the positive electrode 141. The secondary battery 1 is charged and discharged by the exchange of lithium ions Li ⁺ between the negative electrode 142 and the positive electrode 141, and a charging current Ib (Ib <0) or a discharging current Ib (Ib> 0) is generated.

  The basic battery model formula used in this embodiment is represented by a basic equation consisting of the following formulas (1) to (11). FIG. 5 shows a list of variables and constants used in the battery model equation.

  Regarding the variables and constants in the model formula described below, the subscript e indicates a value in the electrolytic solution, and s indicates a value in the active material. The subscript j distinguishes between the positive electrode and the negative electrode. When j is 1, the value at the positive electrode is indicated. When j is 2, the value at the negative electrode is indicated. When the variables or constants in the positive electrode and the negative electrode are described comprehensively, the suffix j is omitted. In addition, the notation (t) indicating that it is a function of time, the notation (T) indicating the dependency of the battery temperature, the (θ) indicating the dependency of the local SOC θ, and the like are indicated in the specification. Sometimes omitted. The symbol # attached to a variable or constant represents an average value.

  The above formulas (1) and (2) are formulas indicating an electrochemical reaction in the electrode (active material), and are called Butler-Volmer formulas.

  The following formula (3) is established as a formula for the conservation law of lithium ion concentration in the electrolytic solution. As an equation relating to the law of conservation of lithium concentration in the active material, a diffusion equation of the following equation (4) and boundary condition equations shown in the following equations (5) and (6) are applied. The following formula (5) represents the boundary condition at the center of the active material, and the following formula (6) represents the boundary condition at the interface between the active material and the electrolyte (hereinafter also simply referred to as “interface”).

The local SOC θ _j that is a local lithium concentration distribution (concentration distribution) at the interface of the active material is defined by the following formula (7). C _sej in the following formula (7) indicates the lithium concentration at the active material interface between the positive electrode and the negative electrode, as shown in the following formula (8). c _{sj, max} indicates the limit lithium concentration in the active material.

The following equation (9) is established as an equation relating to the charge conservation law in the electrolytic solution, and the following equation (10) is established as an equation relating to the charge conservation law in the active material. As an electrochemical reaction formula at the active material interface, the following formula (11) indicating the relationship between the current density I (t) and the reaction current density j _j ^Li is established.

  The battery model formula represented by the basic equations of the above formulas (1) to (11) can be simplified as described below. The simplification of the battery model formula can reduce the calculation load and the calculation time.

  It is assumed that the electrochemical reaction in each of the negative electrode 142 and the positive electrode 141 is uniform. That is, it is assumed that the reaction in the x direction occurs uniformly in each of the electrodes 142 and 141. Further, since it is assumed that the reactions in the plurality of active materials 142b and 141b included in the electrodes 142 and 141 are uniform, the active materials 142b and 141b of the electrodes 142 and 141 are handled as one active material model. Thereby, the structure of the secondary battery 1 shown in FIG. 4 can be modeled into the structure shown in FIG.

  In the battery model shown in FIG. 6, the electrode reaction on the surfaces of the active material model 141b (j = 1) and the active material model 142b (j = 2) can be modeled. Further, in the battery model shown in FIG. 6, it is possible to model the diffusion (diameter direction) of lithium inside the active material models 141b and 142b and the diffusion (concentration distribution) of lithium ions in the electrolytic solution. Furthermore, potential distribution and temperature distribution can be modeled in each part of the battery model shown in FIG.

As shown in FIG. 7, the lithium concentration c _s inside each of the active material models 141b and 142b can be expressed as a function on the coordinate r in the radial direction of the active material models 141b and 142b. r is the distance from the center of the active material models 141b and 142b to each point, and r _s is the radius of the active material models 141b and 142b. Here, it is assumed that there is no position dependency in the circumferential direction of the active material models 141b and 142b.

The active material models 141b and 142b shown in FIG. 7 are used to estimate the lithium diffusion phenomenon inside the active material due to the electrochemical reaction at the interface. The lithium concentration c _{s, k} (t) is estimated according to the diffusion equation described later for each region (k = 1 to N) divided into N (N: natural number of 2 or more) in the radial direction of the active material models 141b and 142b. Is done. Here, the lithium concentration distribution in the active material is obtained by the lithium concentrations c _{s, k} (t) in a plurality of N-divided regions.

  According to the battery model shown in FIG. 6, the basic equations (1) to (6) and (8) can be expressed by the following equations (1 ') to (6') and (8 ').

In the above equation (3 ′), it is assumed that c _ej (t) is a constant value by assuming that the concentration of the electrolytic solution does not change with time. For the active material models 141b and 142b, the diffusion equations (4) to (6) are transformed into diffusion equations (4 ′) to (6 ′) considering only the distribution in the polar coordinate direction. In the above formula (8 ′), the lithium concentration c _{sej at} the interface of the active material corresponds to the lithium concentration c _sj (t) in the outermost region of the N-divided region shown in FIG.

The above formula (9) relating to the law of conservation of electric charge in the electrolysis solution is simplified to the following formula (12) using the above formula (3 ′). That is, the potential φ _{ej of the} electrolytic solution is approximated as a quadratic function of x. The average potential φ _ej # in the electrolytic solution used for calculating the overvoltage η _j # is obtained by the following formula (13) obtained by integrating the following formula (12) with the electrode thickness L _j .

For the negative electrode 142, the following formula (14) is established based on the following formula (12). Therefore, the potential difference between the electrolyte average potential φ _e2 # and the electrolyte potential at the boundary between the negative electrode 142 and the separator 143 is expressed by the following equation (15). For the positive electrode 141, the potential difference between the electrolyte average potential φ _e1 # and the electrolyte potential at the boundary between the positive electrode 141 and the separator 143 is expressed by the following formula (16).

The above formula (10) relating to the law of conservation of charge in the active material can also be simplified to the following formula (17). That is, the potential φ _sj of the active material is also approximated as a quadratic function of x. The average potential φ _sj # in the active material used for calculating the overvoltage η _j # is obtained by the following formula (18) obtained by integrating the following formula (17) with the electrode thickness L _j . Therefore, with respect to the positive electrode 141, the potential difference between the active material average potential φ _s1 # and the active material potential at the boundary between the active material model 141b and the current collector plate 141a is expressed by the following formula (19). Similarly, the following formula (20) is established for the negative electrode 142.

FIG. 8 shows the relationship between the terminal voltage V (t) of the secondary battery 1 and each average potential obtained as described above. In FIG. 8, since the reaction current density j _j ^Li is 0 in the separator 143, the voltage drop at the separator 143 is proportional to the current density I (t), and L _s / κ _s ^eff · I (t) Become.

In addition, by assuming that the electrochemical reaction in each electrode is uniform, the current density I (t) per unit area of the electrode plate and the reaction current density (lithium generation amount) j _j ^Li are as follows. Formula (21) is materialized.

  Based on the potential relationship shown in FIG. 8 and the above equation (21), the following equation (22) is established for the battery voltage V (t). The following equation (22) is based on the potential relational equation of equation (23) shown in FIG.

Next, an average overvoltage η # (t) is calculated. ^Assuming that j _j ^Li is constant and the charge / discharge efficiency is the same in the Butler-Bolmer relational expression and α _aj and α _cj are 0.5, the following equation (24) is established. The average overvoltage η # (t) is obtained by the following equation (25) by inversely transforming the following equation (24).

The average potentials φ _s1 and φ _s2 are obtained using FIG. 8, and the obtained values are substituted into the above equation (22). Further, the average overvoltages η ₁ # (t) and η ₂ # (t) obtained from the above equation (25) are substituted into the above equation (23). As a result, a voltage-current relationship model formula (M1a) according to the electrochemical reaction model formula is derived based on the formulas (1 ′), (21) and the formula (2 ′).

  The active material diffusion model equation (M2a) for the active material models 141b and 142b is obtained by the above equation (4 ′) and boundary condition equations (5 ′) and (6 ′) which are the lithium concentration conservation law (diffusion equation). .

The first term on the right side of the model formula (M1a) represents the open circuit voltage (OCV) determined by the concentration of the reactant (lithium) on the active material surface, and the second term on the right side represents the overvoltage (η ₁ # −η ₂ #), And the third term on the right side indicates a voltage drop due to current flowing in the secondary battery. That is, the DC pure resistance of the secondary battery 10 is represented by Rd (T) in the formula (M2a).

In the formula (M2a), diffusion coefficients D _s1 and D _s2 used as parameters for defining the diffusion rate of lithium as a reactant have temperature dependence. Therefore, the diffusion coefficients D _s1 and D _s2 can be set using, for example, the map shown in FIG. The map shown in FIG. 9 can be acquired in advance. In FIG. 9, the battery temperature Tb on the horizontal axis is the temperature acquired using the temperature sensor 203. As shown in FIG. 9, the diffusion coefficients D _s1 and D _s2 decrease as the battery temperature Tb decreases. In other words, the diffusion coefficients D _s1 and D _s2 increase as the battery temperature Tb increases.

Regarding the diffusion coefficients D _s1 and D _s2 , not only the dependency of the temperature Tb but also the dependency of the local SOC θ may be considered. Here, the diffusion coefficients D _s1 and D _s2 and the local SOC θ have the relationship shown in FIG. In FIG. 10, the vertical axis represents the local SOC θ, and the horizontal axis represents the diffusion coefficients D _s1 and D _s2 . As shown in FIG. 10, as the local SOCθ approaches 0%, the diffusion coefficient D _s1, D _s2 along with rises, the more local SOCθ approaches 100%, the diffusion coefficient D _s1, D _s2 is increased. On the other hand, when the local SOC θ is between 0% and 100%, the diffusion coefficients D _s1 and D _s2 decrease. In this case, if a map showing the relationship between the battery temperature Tb, the local SOC θ and the diffusion coefficients D _s1 and D _s2 is prepared in advance, the diffusion coefficients D _s1 and D _s2 corresponding to the battery temperature Tb and the local SOC θ are specified. Can do.

  The open circuit voltage U1 included in the equation (M1a) decreases as the local SOC θ increases as shown in FIG. 11A. Further, the open circuit voltage U2 increases as the local SOC θ increases as shown in FIG. 11B. If the maps shown in FIGS. 11A and 11B are prepared in advance, the open circuit voltages U1 and U2 corresponding to the local SOC θ can be specified.

Exchange current densities i ₀₁ and i ₀₂ included in formula (M1a) have a dependency on local SOC θ and battery temperature Tb. Therefore, if a map showing the relationship between the exchange current densities i ₀₁ and i ₀₂ , the local SOC θ and the battery temperature Tb is prepared in advance, the exchange current densities i ₀₁ and i ₀₂ are specified from the local SOC θ and the battery temperature Tb. Can do.

  The DC pure resistance Rd has temperature dependence. Therefore, if a map showing the relationship between DC pure resistance Rd and battery temperature Tb is prepared in advance, DC pure resistance Rd can be specified from battery temperature Tb. In addition, about the map mentioned above, it can create based on experimental results, such as the well-known alternating current impedance measurement regarding the secondary battery 1. FIG.

  The battery model shown in FIG. 6 can be further simplified. Specifically, a common active material model can be used as the active material of the electrodes 142 and 141. By treating the active material models 141b and 142b shown in FIG. 6 as one active material model, the following equation (26) can be replaced. In the following formula (26), the suffix j indicating the distinction between the positive electrode 141 and the negative electrode 142 is omitted.

The model formulas (M1a) and (M2a) can be expressed by the following formulas (M1b) and (M2b). In the battery model using one active material model, the following formula (21 ′) is applied instead of the above formula (21) as the relational expression of the current density I (t) and the reaction current density j _j ^Li. The

  The following equation (M1c) is obtained by first-order approximation (linear approximation) of the arcsinh term in the above equation (M1a). By performing linear approximation in this way, it is possible to reduce the calculation load and the calculation time.

In the above formula (M1c), as a result of the linear approximation, the second term on the right side is also represented by the product of the current density I (t) and the reaction resistance Rr. The reaction resistance Rr is calculated from the exchange current densities i ₀₁ and i ₀₂ depending on the local SOC θ and the battery temperature Tb, as shown in the above equation (27). Therefore, when the above formula (M1c) is used, a map showing the relationship between the local SOC θ, the battery temperature Tb, and the exchange current densities i ₀₁ and i ₀₂ may be prepared in advance. According to the above formula (M1c) and the above formula (27), the above formula (28) is obtained.

  If the arcsinh term of the second term on the right side in the above equation (M1b) is linearly approximated, the following equation (M1d) is obtained.

  The above formula (M1b) can be expressed as the following formula (M1e).

  The above formula (M1e) is expressed by the following formula (M1f) by performing linear approximation.

  Next, a configuration for estimating the state of the secondary battery using the battery model formula described above will be described. FIG. 12 is a schematic diagram showing the internal configuration of the controller 300. The battery state estimation unit 310 includes a diffusion estimation unit 311, an open circuit voltage estimation unit 312, a current estimation unit 313, a parameter setting unit 314, and a boundary condition setting unit 315. In the configuration shown in FIG. 12, battery state estimation section 310 calculates current density I (t) by using formula (M1f) and formula (M2b).

  In this embodiment, the current density I (t) is calculated using the above formula (M1f), but the present invention is not limited to this. Specifically, the current density I (t) is calculated based on any combination of the above formula (M1a) to the above formula (M1e) and the above formula (M2a) or the above formula (M2b). Can do.

  The diffusion estimation unit 311 calculates the lithium concentration distribution inside the active material based on the boundary condition set by the boundary condition setting unit 315 using the above formula (M2b). The boundary condition is set based on the above formula (5 ') or the above formula (6'). Diffusion estimation unit 311 calculates local SOC θ based on the calculated lithium concentration distribution using equation (7). Diffusion estimation unit 311 outputs information on local SOC θ to open circuit voltage estimation unit 312.

  The open circuit voltage estimation unit 312 specifies the open circuit voltages U1 and U2 of the electrodes 142 and 141 based on the local SOC θ calculated by the diffusion estimation unit 311. Specifically, the open circuit voltage estimation unit 312 can identify the open circuit voltages U1 and U2 by using the maps shown in FIGS. 11A and 11B. The open circuit voltage estimation unit 312 can calculate the open circuit voltage of the secondary battery 1 based on the open circuit voltages U1 and U2. The open circuit voltage of the secondary battery 1 is obtained by subtracting the open circuit voltage U2 from the open circuit voltage U1.

Parameter setting unit 314 sets parameters used in the battery model equation according to battery temperature Tb and local SOC θ. The temperature Tb detected by the temperature sensor 203 is used as the battery temperature Tb. The local SOC θ is acquired from the diffusion estimation unit 311. Parameters set by the parameter setting unit 314 include the diffusion constant D _{s in} the above formula (M2b), the current density i ₀ in the above formula (M1f), and the DC resistance Rd.

The current estimation unit 313 calculates (estimates) the current density I (t) using the following formula (M3a). The following formula (M3a) is a formula obtained by modifying the above formula (M1f). In the following formula (M3a), the open circuit voltage U (θ, t) is the open circuit voltage U (θ) estimated by the open circuit voltage estimation unit 312. The voltage V (t) is the battery voltage Vb acquired using the monitoring unit 201. Rd (t) and i ₀ (θ, T, t) are values set by the parameter setting unit 314.

  Note that even when any one of the above formulas (M1a) to (M1e) is used, the current density I (t) can be calculated by the same method as the above formula (M3a). .

The boundary condition setting unit 315 calculates the reaction current density (lithium generation amount) j _j ^Li from the current density I (t) calculated by the current estimation unit 313 using the above formula (21) or the above formula (21 ′). calculate. Then, the boundary condition setting unit 315 updates the boundary condition in the equation (M2b) using the equation (6 ′).

  Next, the process of the battery state estimation part 310 is demonstrated using the flowchart shown in FIG. The process shown in FIG. 13 is executed at a predetermined cycle.

  In step S101, the battery state quantity estimation unit 310 acquires the voltage (battery voltage) Vb of the secondary battery 1 based on the output of the monitoring unit 201. In addition, in step S102, the battery state quantity estimation unit 310 acquires the temperature (battery temperature) Tb of the secondary battery 1 based on the output of the temperature sensor 203.

  In step S103, battery state estimation unit 310 (diffusion estimation unit 311) calculates local SOC θ based on the lithium concentration distribution at the time of the previous calculation using equation (M2b). In step S104, battery state estimation unit 310 (open circuit voltage estimation unit 312) calculates open circuit voltage U (θ) from local SOC θ obtained in step S103.

  In step S105, the battery state estimation unit 310 (current estimation unit 313) calculates (estimates) the current density Im (t) using the above formula (M1f). For the estimated current density Im (t), the battery voltage Vb, the open circuit voltage U (θ) obtained in step S103, and the parameter value set by the parameter setting unit 314 are substituted into the above equation (M3a). Can be obtained.

In step S106, the battery state estimation unit 310 (boundary condition setting unit 315) calculates a reaction current density (lithium generation amount) j _j ^Li from the estimated current density I (t) obtained in step S105. Moreover, the battery state estimation part 310 (boundary condition setting part 315) sets the boundary condition (active material interface) in the active material interface of said Formula (M2b) using the calculated reaction current density.

  In step S107, the battery state estimation unit 310 (diffusion estimation unit 311) calculates the lithium concentration distribution inside the active material model using the above formula (M2b), and updates the estimated value of the lithium concentration in each region. . Here, the lithium concentration (updated value) in the outermost peripheral divided region is used to calculate the local SOC θ in step S103 when the process shown in FIG. 13 is performed next time.

  According to the process shown in FIG. 13, the battery current (battery current density I (t)) can be estimated using the battery voltage Vb as an input, and the internal state of the secondary battery 1 can be estimated based on this.

  In this embodiment, when the lithium concentration distribution in the active material models 141b and 142b is calculated, the number of active material models 141b and 142b divided in the radial direction according to the temperature Tb and SOC of the secondary battery 1 ( The number of divisions N is changed. Specifically, in consideration of the relationship shown in FIGS. 9 and 10, when the diffusion coefficient Ds decreases, the division number N is increased.

  FIG. 14 shows the setting contents of the division number N according to the temperature Tb and the SOC of the secondary battery 1. In FIG. 14, the horizontal axis indicates the battery temperature Tb, and the vertical axis indicates the SOC of the secondary battery 1. The battery temperature Tb can be acquired using the temperature sensor 203. Further, as the SOC of the secondary battery 1, the SOC estimated before (for example, immediately before) the lithium concentration distribution estimation process can be used.

  The first threshold value Tb_th1 shown in FIG. 14 is set based on the relationship shown in FIG. When the battery temperature Tb is higher than the first threshold Tb_th1, the diffusion coefficient Ds is likely to increase as shown in FIG. In this case, the reference value Nref is set as the division number N. On the other hand, when the battery temperature Tb is lower than the first threshold value Tb_th1, the diffusion coefficient Ds tends to decrease as shown in FIG. In this case, a value Ninc larger than the reference value Nref is set as the division number N. The first threshold value Tb_th1 can be appropriately set based on the behavior of the diffusion coefficient Ds according to the battery temperature Tb.

  Further, even when the battery temperature Tb is higher than the first threshold value Tb_th1, when the SOC of the secondary battery 1 is between the first threshold value SOC_th1 and the second threshold value SOC_th2, the battery temperature Tb reaches the second threshold value Tb_th2. Sets the division number Ninc as the division number N. Here, the second threshold value SOC_th2 is higher than the first threshold value SOC_th1. As shown in FIG. 10, when the SOC of the secondary battery 1 is between the first threshold value SOC_th1 and the second threshold value SOC_th2, the diffusion coefficient Ds tends to decrease.

  Accordingly, even if the battery temperature Tb is higher than the first threshold value Tb_th1, the division number N is set to a value Ninc that is larger than the reference value Nref. However, when the battery temperature Tb becomes higher than the second threshold value Tb_th2, the diffusion coefficient Ds tends to increase. Therefore, until the battery temperature Tb reaches the second threshold value Tb_th2, the division number Ninc is set as the division number N. ing. Further, when the battery temperature Tb is higher than the second threshold value Tb_th2, the reference value Nref is set as the division number N.

  The division number Nref can be set as appropriate based on the stability conditions of the diffusion model equations (M2a) and (M2b). As described with reference to FIG. 9, the diffusion coefficient Ds depends on the battery temperature Tb, and the diffusion coefficient Ds increases as the battery temperature Tb increases. As described with reference to FIG. 10, the diffusion coefficient Ds depends on the SOC of the secondary battery 1, and the diffusion coefficient Ds increases as the SOC of the secondary battery 1 approaches 0% or 100%. Become.

  When the diffusion coefficient Ds increases, depending on the value of the division number N, the solution of the diffusion model equations (M2a) and (M2b) becomes unstable, and it becomes difficult to specify the lithium concentration distribution. That is, if the value of the division number N is increased in a state where the diffusion coefficient Ds is increased, the solution of the diffusion model equations (M2a) and (M2b) becomes unstable, and it is difficult to specify the lithium concentration distribution. turn into. Therefore, the division number Nref is set in consideration of the stability of the diffusion model equations (M2a) and (M2b).

  The division number Ninc only needs to be larger than the division number Nref, and a specific value of the division number Ninc can be set as appropriate. Here, if the division number Ninc is too large, the calculation load when calculating the lithium concentration distribution becomes high. Therefore, the division number Ninc can be set in consideration of this point.

  As shown in FIG. 9, the diffusion coefficient Ds decreases as the battery temperature Tb decreases. As shown in FIG. 10, the diffusion coefficient Ds decreases as the SOC of the secondary battery 1 increases from 0% or 100%. In this way, in the state where the diffusion coefficient Ds is lowered, the stability of the diffusion model equations (M2a) and (M2b) can be ensured even if the number of divisions N is increased. Therefore, in this embodiment, the division number N is increased in consideration of the diffusion coefficient Ds.

  When the division number N is increased, it becomes easier to grasp the lithium concentration distribution in the active material models 141b and 142b. That is, if the division number N is increased, the inside of the active material models 141b and 142b can be subdivided. In each subdivided region, the lithium concentration is determined using the diffusion model equations (M2a) and (M2b). Can be estimated. Thereby, it is possible to accurately grasp the lithium concentration distribution inside the active material models 141b and 142b.

  If the lithium concentration distribution inside the active material models 141b and 142b can be grasped with high accuracy, the lithium concentration at the surface (interface) of the active material models 141b and 142b can be calculated with high accuracy. The internal resistance of the secondary battery 1 includes a reaction resistance and a diffusion resistance. The reaction resistance is resistance when a chemical reaction that absorbs lithium ions and electrons or a chemical reaction that releases lithium ions and electrons is performed at the interface between the active material models 141b and 142b. The diffusion resistance is a resistance when lithium diffuses in the active material models 141b and 142b.

  The reaction resistance depends on the lithium concentration at the interface between the active material models 141b and 142b. For this reason, if a map showing the correspondence between the reaction resistance and the lithium concentration (interface) is obtained in advance by experiments or the like, the reaction resistance according to the lithium concentration (interface) can be specified. As described above, if the lithium concentration at the interface between the active material models 141b and 142b can be accurately estimated, the reaction resistance can also be accurately estimated.

  On the other hand, the diffusion resistance depends on the difference (lithium concentration difference) between the lithium concentration (interface) and the average lithium concentration in the active material models 141b and 142b. For this reason, if a map showing the correspondence between the diffusion resistance and the lithium concentration difference is obtained in advance by experiments or the like, the diffusion resistance corresponding to the lithium concentration difference can be specified. As described above, if the lithium concentration at the interface between the active material models 141b and 142b can be estimated with high accuracy, the diffusion resistance can also be estimated with high accuracy.

Here, the average lithium concentration c _save can be calculated based on the lithium concentration distribution by using the following formula (29).

As shown in FIG. 7, the lithium concentration c _{s1, k} (t) (k = 1 to N) shown in the above formula (29) is the lithium concentration in each region obtained by dividing the active material models 141b and 142b into N parts in the radial direction. The concentration is estimated by the diffusion model equations (M2a) and (M2b). ΔVk indicates the volume of each divided region, and V indicates the volume of the entire active material. Moreover, when the active material model in the positive electrode and the negative electrode is made common, the average value of the lithium concentration c _{s, k} (t) (k = 1 to N) in each region in the common active material model is By obtaining in the same manner as the above equation (29), the average lithium concentration c _save (t) can be obtained.

  As described above, if the reaction resistance and the diffusion resistance are estimated, the internal resistance of the secondary battery 1 can be calculated. If the division number N is increased, the reaction resistance and the diffusion resistance can be estimated with high accuracy, so that the internal resistance of the secondary battery 1 can also be estimated with high accuracy. It is known that the internal resistance of the secondary battery 1 increases as the temperature of the secondary battery 1 decreases. For this reason, it is necessary to accurately estimate the internal resistance of the secondary battery 1 as the temperature of the secondary battery 1 decreases.

  Processing for estimating the internal resistance and SOC of the secondary battery 1 will be described with reference to the flowchart shown in FIG. The process shown in FIG. 15 is executed by the controller 300 and is performed at a predetermined cycle.

  In step S201, the controller 300 acquires (measures) the temperature Tb of the secondary battery 1 based on the output of the temperature sensor 203. In step S202, the controller 300 determines whether or not the previously estimated SOC of the secondary battery 1 is included in the range of the first threshold SOC_th1 and the second threshold SOC_th2. Here, when the SOC of the secondary battery 1 is included in the range of the first threshold value SOC_th1 and the second threshold value SOC_th2, the controller 300 performs the process of step S203.

  On the other hand, when the SOC of the secondary battery 1 is outside the range of the first threshold value SOC_th1 and the second threshold value SOC_th2, the controller 300 performs the process of step S206. Specifically, when the SOC of the secondary battery 1 is lower than the first threshold SOC_th1, or when the SOC of the secondary battery 1 is higher than the second threshold SOC_th2, the controller 300 performs the process of step S206. .

  In step S203, the controller 300 determines whether or not the battery temperature Tb acquired in the process of step S201 is lower than the second threshold Tb_th2. Here, when the battery temperature Tb is lower than the second threshold value Tb_th2, the controller 300 performs the process of step S204, and when the battery temperature Tb is higher than the second threshold value Tb_th2, the controller 300 performs the process of step S205. .

  In step S204, the controller 300 sets the division number Ninc as the division number N when calculating the lithium concentration distribution. In step S205, the controller 300 sets the division number Nref as the division number N when calculating the lithium concentration distribution.

  When the process proceeds from step S202 to step S206, the controller 300 determines whether or not the battery temperature Tb acquired in step S201 is lower than the first threshold Tb_th1. Here, when the battery temperature Tb is lower than the first threshold value Tb_th1, the controller 300 performs the process of step S207. When the battery temperature Tb is higher than the first threshold value Tb_th1, the controller 300 performs the process of step S208. .

  In step S207, the controller 300 sets the division number Ninc as the division number N when calculating the lithium concentration distribution. In step S208, the controller 300 sets the division number Nref as the division number N when calculating the lithium concentration distribution.

  In step S209, the controller 300 uses the diffusion model equations (M2a) and (M2b) under the division number N (Nref or Ninc) set in any of steps S204, S205, S207, and S208. The lithium concentration distribution inside the material models 141b and 142b is calculated, or the lithium concentration at the interface between the active material models 141b and 142b is calculated.

  In step S210, the controller 300 estimates the internal resistance of the secondary battery 1 based on the calculation result of step S209. The method for estimating the internal resistance of the secondary battery 1 is as described above. In step S <b> 211, the controller 300 estimates the SOC of the secondary battery 1 based on the internal resistance of the secondary battery 1. The SOC estimation method is as described above.

  According to the process shown in FIG. 15, as shown in FIG. 16, the division number N when calculating the lithium concentration distribution according to the SOC of the secondary battery 1 and the battery temperature Tb is the division number Nref and the division number Ninc. Switch between. By switching the division number N in this way, it is possible to improve the estimation accuracy of the lithium concentration distribution associated with increasing the division number N while ensuring the stability of the diffusion model equations (M2a) and (M2b). .

  The lithium concentration distribution when the division number N is set to the division number Nref and the lithium concentration distribution when the division number N is set to the division number Ninc are calculated using diffusion model equations (M2a) and (M2b), respectively. be able to. On the other hand, the lithium concentration distribution when the division number Ninc is set can also be calculated based on the lithium concentration distribution when the division number Nref is set.

  For example, FIG. 17 shows lithium concentrations C3 [0] to C3 [2] in the regions D0 to D2 when the active material models 141b and 142b are divided into three regions D0 to D2. In the example illustrated in FIG. 17, “3” is set as the division number Nref. The region D0 includes the centers of the active material models 141b and 142b. The region D1 is adjacent to the region D0 and is located closer to the interface side of the active material models 141b and 142b than the region D0. The region D2 is adjacent to the region D1 and includes the interface between the active material models 141b and 142b.

  In FIG. 17, the active material models 141b and 142b are divided into three regions D0 to D2 so that the volumes of the regions D0 to D2 are equal to each other. Since the volumes of the regions D0 to D2 are equal, the widths of the regions D0 to D2 in the radial direction of the active material models 141b and 142b are different from each other. The lithium concentrations C3 [0] to C3 [2] of the regions D0 to D2 can be calculated based on the diffusion model equations (M2a) and (M2b).

  When the division number N is increased from the state shown in FIG. 17, for example, the active material models 141b and 142b can be divided as shown in FIG. In FIG. 18, the active material models 141b and 142b are divided into five regions D0 to D4. In the example illustrated in FIG. 18, “5” is set as the division number Ninc.

  The region D0 includes the centers of the active material models 141b and 142b. The region D1 is adjacent to the region D0 and is located closer to the interface side of the active material models 141b and 142b than the region D0. The region D2 is adjacent to the region D1, and is located closer to the interface side of the active material models 141b and 142b than the region D1. The region D3 is adjacent to the region D2, and is located closer to the interface side of the active material models 141b and 142b than the region D2. The region D4 is adjacent to the region D3 and includes an interface between the active material models 141b and 142b.

  The volumes of the regions D0 to D4 are equal to each other. Since the volumes of the regions D0 to D4 are equal, the widths of the regions D0 to D4 in the radial direction of the active material models 141b and 142b are different from each other. When calculating the lithium concentrations C5 [0] to C5 [4] of the regions D0 to D4, the lithium concentrations C3 [0] to C3 [2] shown in FIG. 17 can be used.

  Specifically, the lithium concentrations C5 [0] to C5 [4] of the regions D0 to D4 can be calculated based on the following formula (30).

  According to the above formula (30), the lithium concentrations C3 [0] to C3 [2] can be converted into the lithium concentrations C5 [0] to C5 [4]. On the other hand, if the above formula (30) is modified, the lithium concentrations C5 [0] to C5 [4] can be converted into the lithium concentrations C3 [0] to C3 [2]. Thus, when the lithium concentrations C5 [0] to C5 [4] are first calculated based on the diffusion model equations (M2a) and (M2b), the lithium concentration C3 is calculated from the lithium concentrations C5 [0] to C5 [4]. [0] to C3 [2].

  According to the example shown in FIGS. 17 and 18, the division number N is switched between “3 (Nref)” and “5 (Ninc)”, but is not limited thereto. That is, as described above, the division numbers Nref and Ninc can be set as appropriate, and the division number Ninc only needs to be larger than the division number Nref. Even if the division numbers Nref and Ninc are appropriately set, by using a conversion formula similar to the above equation (30), the lithium concentration in each region when the division number Nref is set and the division number Ninc are set. The lithium concentration in each region can be converted into each other.

  If the said Formula (30) is used, the conversion process between lithium concentration C3 [0] -C3 [2] and lithium concentration C5 [0] -C5 [4] can be performed easily. That is, when the division number N is set to 3 and when the division number N is set to 5, compared to the case where the lithium concentration is calculated using the diffusion model equations (M2a) and (M2b), The calculation load when calculating the lithium concentration can be reduced.

  In the present embodiment, as described above, when the temperature of the secondary battery 1 decreases, specifically, when the battery temperature Tb is lower than the first threshold Tb_th1, the secondary number 1 is increased by increasing the division number N. The internal resistance of the battery 1 can be estimated with high accuracy. If the internal resistance of the secondary battery 1 can be calculated, the SOC of the secondary battery 1 can be estimated. Specifically, since SOC and OCV are in a correspondence relationship, if this correspondence relationship is obtained in advance by experiments or the like, the SOC corresponding to this OCV is identified by identifying the OCV of secondary battery 1. be able to.

  The OCV of the secondary battery 1 can be calculated based on the following formula (31).

  CCV (Closed Circuit Voltage) is a voltage value of the secondary battery 1 detected by the monitoring unit 201 when the secondary battery 1 is energized. I is a current value flowing through the secondary battery 1, and the current value I can be detected by the current sensor 202. R is the internal resistance of the secondary battery 1.

  As described above, the internal resistance R of the secondary battery 1 can be calculated from the reaction resistance and the diffusion resistance. For this reason, if the voltage value CCV and the current value I are detected, the OCV of the secondary battery 1 can be calculated. If the OCV of the secondary battery 1 is calculated, the SOC corresponding to the OCV can be specified using the correspondence relationship between the SOC and the OCV. As described above, if the internal resistance R of the secondary battery 1 can be accurately estimated, the OCV and SOC of the secondary battery 1 can be accurately estimated.

  If the SOC of the secondary battery 1 can be estimated, the equalization process can be performed based on the variation in the SOC of the plurality of secondary batteries 1 as described above. As described above, if the estimation accuracy of the SOC when the secondary battery 1 is in the low temperature state is improved, the equalization process can be performed with high accuracy.

  Moreover, if the SOC of the secondary battery 1 is estimated, the full charge capacity FCC of the secondary battery 1 can be calculated based on the following formula (32).

  In the above equation (32), ΣI is an integrated current value during charging or discharging of the secondary battery 1, and integrating the current value detected by the current sensor 202 during charging or discharging. It is obtained by doing. SOC_s is the SOC of the secondary battery 1 when charging or discharging starts, and SOC_e is the SOC of the secondary battery 1 when charging or discharging ends. As described above, if the estimation accuracy of the SOC when the secondary battery 1 is in a low temperature state is improved, the estimation accuracy of the full charge capacity FCC can be improved.

  According to the present embodiment, the division number N is switched between the division numbers Nref and Ninc based on the SOC of the secondary battery 1 and the battery temperature Tb, but is not limited thereto. Specifically, the division number N can be switched between the division numbers Nref and Ninc based only on one of the SOC of the secondary battery 1 and the battery temperature Tb.

  As described with reference to FIG. 14, when the battery temperature Tb is lower than the first threshold value Tb_th1, the division number N is set to the division number Ninc regardless of the SOC of the secondary battery 1. For this reason, for example, the division number N can be set based only on the battery temperature Tb. Similarly, when the battery temperature Tb is higher than the second threshold value Tb_th2, the division number N is set to the division number Ninc regardless of the SOC of the secondary battery 1. For this reason, for example, the division number N can be set based only on the battery temperature Tb.

  In the present embodiment, the division number N is switched between the two division numbers Nref and Ninc based on the SOC of the secondary battery 1 and the battery temperature Tb, but the present invention is not limited to this. Specifically, the division number N can be switched between three or more division numbers. Here, when switching between three or more division numbers, the division number N can be increased as the battery temperature Tb decreases.

1: secondary battery, 100: assembled battery, 201: monitoring unit, 201a: voltage monitoring IC,
202: current sensor, 203: temperature sensor, 204: current limiting resistor,
205: capacitor, 206: inverter, 207: motor / generator,
208: equalization circuit, 208a: resistance, 208b: switch element,
300: Controller, 300a: Memory,
141: positive electrode, 141a: current collector plate, 141b: active material, 142: negative electrode,
142a: current collector plate, 142b: active material, 143: separator, 11: positive electrode terminal,
12: Negative terminal 310: Battery state estimation unit, 311: Diffusion estimation unit,
312: Open circuit voltage estimation unit, 313: Current estimation unit, 314: Parameter setting unit,
315: Boundary condition setting part

Claims (8)

A temperature sensor for detecting the temperature of the lithium ion secondary battery;
In a state where the spherical active material model included in the lithium ion secondary battery is divided into a plurality of regions in the radial direction, a controller that calculates a lithium concentration distribution indicating a lithium concentration in each region using a diffusion equation; Have
The controller makes the number of divisions of the region when the temperature detected by the temperature sensor is lower than a threshold larger than the number of divisions of the region when the detected temperature is higher than the threshold. system. The controller is
Based on the lithium concentration distribution, the lithium concentration at the interface of the active material model is calculated,
2. The battery system according to claim 1, wherein the internal resistance of the lithium ion secondary battery is calculated by specifying a reaction resistance and a diffusion resistance corresponding to a lithium concentration at the interface. The controller is
Using the calculated internal resistance, calculate the open circuit voltage of the lithium ion secondary battery,
The battery system according to claim 2, wherein the SOC corresponding to the calculated open circuit voltage is specified using the correspondence relationship between the open circuit voltage and the SOC.   4. The controller according to claim 1, wherein the controller sets boundary conditions at a center and an interface of the active material model, and calculates the lithium concentration distribution by using the diffusion equation. The battery system described.   The diffusion coefficient used in the diffusion equation when the detection temperature is lower than the threshold value is smaller than the diffusion coefficient used in the diffusion equation when the detection temperature is higher than the threshold value. The battery system according to any one of 1 to 4. The threshold value includes a first threshold value and a second threshold value higher than the first threshold value,
The controller is
When the SOC of the lithium ion secondary battery is included in a predetermined range apart from 0% and 100%, the number of divisions when the detected temperature is lower than the second threshold is set to the detected temperature being the second Greater than the number of divisions when higher than the threshold,
When the SOC of the lithium ion secondary battery is out of the predetermined range, the number of divisions when the detected temperature is lower than the first threshold is set to the division number when the detected temperature is higher than the first threshold. The battery system according to claim 1, wherein the battery system is larger than the number of divisions.   The diffusion coefficient used in the diffusion equation when the SOC of the lithium ion secondary battery is included in the predetermined range is used in the diffusion equation when the SOC of the lithium ion secondary battery is out of the predetermined range. The battery system according to claim 6, wherein the battery system has a smaller diffusion coefficient. An estimation method for estimating a lithium concentration distribution inside a spherical active material model included in a lithium ion secondary battery,
In a state where the active material model is divided into a plurality of regions in the radial direction, the diffusion concentration equation is used to calculate the lithium concentration distribution indicating the lithium concentration in each region,
The temperature of the lithium ion secondary battery is detected, and the number of divisions of the region when the detected temperature is lower than a threshold is made larger than the number of divisions of the region when the detected temperature is higher than the threshold. An estimation method characterized by that.