JP5737106B2 - Secondary battery state estimation device - Google Patents

Description

  The present invention relates to a state estimation device for a secondary battery. More specifically, the present invention takes into account the concentration overvoltage resulting from the concentration difference of the reactant (reaction participating species) between the positive electrode and the negative electrode, and the state of the secondary battery (SOC: State of Charge) (for example, The present invention relates to a state estimation device for a secondary battery capable of easily and accurately estimating a charging rate and the like.

  In facilities using secondary batteries, for example, the state of secondary batteries (SOC) for the purpose of preventing deterioration of secondary batteries due to overdischarge or overcharging, and effective use of power stored in secondary batteries. Is required to control charging / discharging of the secondary battery based on the result. As a typical example of equipment using such a secondary battery, a vehicle such as a hybrid vehicle (HV) or an electric vehicle (EV) provided with a motor that generates a driving force by electric power supplied from the secondary battery as a power source. Can be mentioned.

  In HV, in addition to the electric power stored in the secondary battery being used as drive power for the electric motor, the electric power generated when the electric motor is regeneratively generated at the time of deceleration or the like or a power source other than the electric motor (for example, engine Etc.), the secondary battery is charged by the generated power from the generator that generates power by the rotation. In such a power supply system, the charging rate of the secondary battery is set to a state of full charge (so that the secondary battery can accept regenerative power and can supply power to the motor as required. It is necessary to control near the middle (50 to 60%) between the state (100%) and the state of no charge (0%).

  Further, the secondary battery may be deteriorated in battery performance due to overdischarge or overcharge, and the life may be shortened. Therefore, not only in the control mode for maintaining the intermediate SOC as described above, the state estimation of the secondary battery is accurately performed from the viewpoint of grasping the charge amount of the secondary battery and suppressing excessive charge / discharge. The need to do it is high.

  On the other hand, attempts have been made to predict the thermal behavior and electrochemical behavior of lithium ion batteries using a battery model based on an electrochemical reaction equation (see, for example, Non-Patent Document 1). A technique for estimating the SOC of a secondary battery using a battery has also been developed.

  For example, in this technical field, the SOC is highly accurate in an environment where arithmetic processing capability and memory capacity are limited, such as an on-board control device (for example, ECU (Electronic Control Unit)) mounted on a vehicle or the like. A simple SOC estimation model based on the electrochemical reaction equation in Non-Patent Document 1 has been proposed (for example, see Patent Document 1).

  Further, in this technical field, the battery voltage and the battery current of the secondary battery are respectively measured as battery state quantities, and one of these battery state quantities is determined based on a battery model given in advance. A technique has been proposed for estimating the degree of increase in battery resistance of a secondary battery based on the estimated value and the measured value of one battery state quantity thus estimated from the other of the quantities (for example, (See Patent Document 2).

JP 2008-243373 A JP 2010-060406 A

"THEMAL-ELECTROCHEMICAL COUPLED MODELING OF A LITHIUM-ION CELL" by WB GU and CY Wang, ECS Proceedings Vo1.99-. 25 (1), 2000 (USA), Electrochemical Society (ECS), 2000, pp 748-762.

  As described above, in facilities using secondary batteries, for example, secondary batteries are used for the purpose of preventing deterioration of secondary batteries due to overdischarge or overcharging, and effective use of electric power stored in secondary batteries. It is required to monitor / estimate the state (SOC) of the battery and control charging / discharging of the secondary battery based on the result. In the SOC estimation model according to the prior art including Patent Document 1, the SOC is estimated using the voltage and temperature detected in the secondary battery as input values.

  By the way, the voltage detected in the secondary battery includes a voltage due to a concentration overvoltage caused by a non-uniform concentration distribution (concentration gradient) between a positive electrode and a negative electrode of a reactant (for example, lithium salt) in the electrolytic solution. Includes a descent. Therefore, in order to accurately estimate the SOC, it is necessary to consider the voltage drop due to the concentration overvoltage. However, if the voltage drop due to the concentration overvoltage is also taken into account, for example, there is a possibility that the calculation load in the on-board ECU or the like that is restricted in the arithmetic processing capacity and the memory capacity as described above becomes excessive.

  On the other hand, for example, in HV and the like that have become widespread recently, as described above, the electric power stored in the secondary battery is used as the driving power for the electric motor, and the electric motor generates regenerative power generation during deceleration. The secondary battery is charged by the generated power at the time of generation or the generated power from a generator that generates power by rotation of another power source (for example, an engine or the like). That is, in HV and the like, in secondary driving (HV driving) in which driving by an electric motor, driving by another power source, regenerative power generation of the electric motor or power generation by another power source is performed, charging and discharging of the secondary battery are relatively frequent. It is done by switching to. In such a situation where the secondary battery is alternately charged and discharged, a non-uniform concentration distribution between the positive electrode and the negative electrode of the reactant (for example, lithium salt) in the electrolytic solution as described above ( Concentration gradients) cancel each other. As a result, the concentration gradient of the reactant in the electrolyte is very small, so that the voltage drop due to the concentration overvoltage is also very small.

  Therefore, in the prior art including Patent Document 1, assuming that the concentration of the reactant in the electrolytic solution is constant, for example, calculation in an on-board ECU or the like that has a limitation in arithmetic processing capability or memory capacity as described above. A simple SOC estimation model with reduced load has been proposed, but in HV traveling, as described above, the concentration gradient of the reactants in the electrolyte is very small, which greatly affects the estimation accuracy of the SOC. Is not enough. That is, practically, the voltage drop due to the concentration overvoltage can be ignored.

  However, for example, in plug-in hybrid vehicles (PHVs) and electric vehicles (EVs) that are becoming increasingly popular in recent years, charging and discharging of secondary batteries are not frequently performed as in HV described above. Absent. In other words, in PHV, EV, etc., the secondary battery is charged over a relatively long charging period as compared to HV as described above, and the secondary battery over a relatively long period. Is discharged. Such a travel mode may be hereinafter referred to as “EV travel”.

  Therefore, in PHV, EV, etc., the amount by which the concentration gradient of the reactant in the electrolyte cancels out is smaller than that in HV, the concentration gradient increases with time, and the concentration overvoltage has a significant effect on the SOC estimation accuracy. Will be affected. In other words, in PHV, EV, etc., if the voltage drop due to the concentration overvoltage is ignored as in the prior art premised on HV running as described above, the estimation accuracy of the SOC decreases.

  Further, in HV traveling, a situation where the SOC increases and a situation where the SOC decreases occur in a confusing manner, and therefore, an error in the estimation of the SOC also occurs due to an confusing error in the direction in which the SOC increases and an error in the decreasing direction. , These cancel each other. On the other hand, in EV travel, once the secondary battery is charged (when the SOC increases), then the secondary battery discharge (SOC decrease) occurs over a relatively long period of time. As for the error, the error in the direction in which the SOC increases and the error in the direction in which the SOC decreases do not cancel each other, but the errors in the direction in which the SOC decreases are accumulated, and the errors tend to accumulate. Even in such a situation, in EV traveling, it is desired to estimate the SOC with higher accuracy than in HV traveling.

  Therefore, in this technical field, it is possible to estimate the SOC with high accuracy even during EV traveling while reducing the calculation load in an on-board ECU or the like that is limited in arithmetic processing capacity or memory capacity. There is a need for a state estimation device.

  That is, the present invention provides a state estimation device for a secondary battery capable of estimating the SOC with high accuracy even during EV traveling while reducing the calculation load in an on-board ECU or the like that is limited in arithmetic processing capability or memory capacity. One purpose is to provide

The above object of the present invention is to
First and second electrodes including an active material containing a reactive substance that contributes to an electrochemical reaction, and an ion conductor that conducts the ionized reactive substance between the first and second electrodes. A state estimation device for a secondary battery comprising:
A voltage detector for detecting a battery voltage between the first and second electrodes;
An in-electrode diffusion estimation unit that estimates the concentration distribution of the reactant according to an active material diffusion model equation that defines the concentration distribution of the reactant within the active material based on a given boundary condition;
An open-circuit voltage estimation unit that estimates the open-circuit voltage between the first and second electrodes based on the concentration of the reactant at the interface between the active material and the electrolyte estimated by the in-electrode diffusion estimation unit When,
Inter-electrode diffusion for estimating the concentration distribution of the reactant between the first and second electrodes according to an inter-electrode diffusion model equation defining the concentration distribution of the reactant between the first and second electrodes An estimation unit;
A concentration overvoltage estimation unit that estimates a concentration overvoltage based on the concentration distribution of the reactant between the first and second electrodes estimated by the interelectrode diffusion estimation unit;
The open voltage, the overvoltage calculated according to the battery current density of the secondary battery, the voltage drop generated according to the battery current density, the concentration overvoltage, and the relationship between the battery voltage. A current estimation unit for estimating a battery current density of the secondary battery according to a voltage-current relationship model equation based on an electrochemical reaction;
With
The current estimation unit includes the battery voltage detected by the voltage detector, the open circuit voltage estimated by the open circuit voltage estimation unit, the concentration overvoltage estimated by the concentration overvoltage estimation unit, and the secondary By substituting the battery parameter value into the voltage-current relationship model equation, the battery current density is calculated,
A boundary for calculating the reaction current density at the interface based on the battery current density estimated by the current estimation unit, and setting the boundary condition at the interface of the active material diffusion model equation according to the calculated reaction current density A condition setting unit;
This is achieved by a state estimation device for a secondary battery.

  Advantageous Effects of Invention According to the present invention, a state estimation device for a secondary battery capable of estimating SOC with high accuracy even during EV traveling while reducing a calculation load in an on-board ECU or the like that is limited in arithmetic processing capacity or memory capacity. Can be provided.

It is a schematic block diagram explaining the structural example of a power supply system provided with a secondary battery. It is a schematic block diagram of a secondary battery. It is a figure which shows the list of the variable and constant used in a battery model type | formula. It is a conceptual diagram explaining the outline | summary of modeling of a secondary battery based on the simplified battery model type | formula. It is a conceptual diagram showing the active material model shown by the polar coordinate. It is a conceptual diagram which shows the relationship between the terminal voltage of a secondary battery, and each average electric potential. It is a conceptual diagram explaining the temperature dependence of a diffusion coefficient. It is a conceptual diagram which shows the relationship between an open circuit voltage and local SOC. It is a block diagram explaining the schematic structure of the state estimation apparatus of a secondary battery based on the simplified battery model type | formula. It is a block diagram explaining the SOC estimation structure in the state estimation apparatus of a secondary battery based on the simplified battery model formula. It is a figure which shows the relationship between the lithium average density | concentration in an active material, and a charging rate (SOC). It is a flowchart explaining a series of processes of battery state estimation and SOC estimation by a secondary battery state estimation device based on a simplified battery model equation. It is a conceptual diagram explaining the self correction | amendment of SOC estimation error by the state estimation apparatus of a secondary battery based on the simplified battery model type | formula. It is a block diagram explaining another SOC estimation method by the state estimation apparatus of the secondary battery based on the simplified battery model formula. It is a notional waveform diagram showing the relationship between the sensor measured value of battery current and the model estimated value. It is a notional waveform figure which shows the offset error of a current sensor. 15 is a flowchart for realizing the SOC estimation process shown in FIG. 14 by a battery ECU 50. It is a block diagram explaining another SOC estimation method by the state estimation apparatus of the secondary battery based on the simplified battery model formula. 19 is a flowchart for realizing the SOC estimation process shown in FIG. 18 by a battery ECU 50. It is a schematic diagram showing the change of the density | concentration distribution of the reaction material between the positive electrode and negative electrode at the time of charging / discharging of a secondary battery. It is a schematic diagram showing the mode of accumulation | storage of the estimation error of SOC at the time of charging / discharging of a secondary battery. It is a typical graph showing the change of the voltage at the time of discharging a secondary battery in a certain current rate. It is a typical graph showing the change of the voltage of a secondary battery in the transition period immediately after starting discharge, and the relaxation period immediately after stopping discharge. It is a graph which shows transition of the monopolar electric potential with respect to the content rate of a reactive material (lithium) in olivine iron (a) and carbon (b). FIG. 24 is a graph showing changes in monopolar potential with respect to the content of the reactant (lithium) in olivine iron (a) and carbon (b). It is a schematic diagram showing the embodiment which measures density | concentration overvoltage based on the voltage (potential difference) between a reference electrode and a negative electrode. It is a schematic diagram showing the case where the position of the reference electrode is shifted to the negative electrode side in the embodiment in which the concentration overvoltage is actually measured based on the voltage (potential difference) between the reference electrode and the negative electrode.

(Configuration of power supply system with secondary battery)
FIG. 1 is a schematic block diagram illustrating a configuration example of a power supply system including a secondary battery as described above. In the following description, the same or corresponding parts in the drawings are denoted by the same reference numerals, and the description of these parts will not be repeated in principle.

  As shown in FIG. 1, the power supply system 5 includes a secondary battery 10, a load 20, and a battery ECU 50 and a control device 60 that include an electronic control unit (ECU: Electronic Control Unit). Each ECU includes, for example, a pre-programmed predetermined sequence and a central processing unit (CPU: Central Processing Unit) (for example, a microcomputer, etc.) and a data storage device (for example, a RAM (Random Access) for executing predetermined calculations. Memory), ROM (Read Only Memory), HDD (Hard Disk Drive), and the like.

  As the rechargeable secondary battery 10, for example, a lithium ion battery is used. Since the output characteristics of a lithium ion battery vary depending on the distribution state of the concentration of reactants (for example, lithium salt) in the battery, particularly between the positive electrode and the negative electrode, the present invention can be suitably applied. An example of a secondary battery can be given. However, the secondary battery provided in the power supply system to which the state estimation device for a secondary battery according to the present invention is applied is not limited to the lithium ion battery according to the example.

  The secondary battery 10 includes a temperature sensor 30 for measuring the battery temperature Tb, a current sensor 32 for measuring an input / output current Ib (hereinafter also referred to as “battery current Ib”) of the secondary battery 10, and a positive electrode and a negative electrode. Is provided with a voltage sensor 34 for measuring a voltage Vb between terminals (hereinafter also referred to as “battery voltage Vb”).

  Electric power output from the secondary battery 10 is supplied to the load 20. For example, the load 20 can be driven by electric power output from the secondary battery 10. The load 20 can include a power generation / power feeding element (not shown) inside or outside the load 20. It is assumed that the secondary battery 10 can be charged by the charging current from the power generation / feeding element. In this specification, the value of the battery current Ib that flows when the secondary battery 10 is discharged is positive (> 0), and the value of the battery current Ib that flows when the secondary battery 10 is charged is negative (<0). .

  The battery ECU 50 determines the battery state according to the battery model that can estimate the internal state of the secondary battery 10 based on the electrochemical reaction based on the detection values from the sensor groups 30, 32, and 34 provided in the secondary battery 10. Is sequentially calculated for each predetermined period (described in detail below).

  Furthermore, the battery ECU 50 generates battery information for limiting charging / discharging of the secondary battery based on the calculated state estimated value. The battery information includes, for example, an SOC (0% to 100%) indicating a charge amount (remaining capacity) with respect to a fully charged state (100%), an input allowable power Win that is an upper limit value of charge power permitted at a certain time point, and The outputtable power Wout, which is the upper limit value of the discharge power, is included.

  The control device 60 considers the battery information obtained from the battery ECU 50 based on the operation request to the load 20 and restricts charging / discharging so that the secondary battery 10 is not overcharged or overdischarged. Twenty operation commands can be generated. For example, the control device 60 can generate an operation command for the load 20 while limiting the input / output power of the secondary battery 10 to be equal to or less than the input / output available power Win and Wout. Further, when the SOC of the secondary battery 10 becomes lower than the lower limit value, the power consumption operation by the load 20 is prohibited, or the power generation operation of the load 20 (charging operation of the secondary battery 10) is forcibly started. can do. On the contrary, when the SOC of the secondary battery 10 is equal to or higher than the upper limit value, the power generation operation of the load 20 can be forcibly prohibited.

(Configuration of secondary battery)
FIG. 2 is a schematic configuration diagram of the secondary battery as described above. Here, a lithium ion battery is adopted as an example of the secondary battery, but as described above, the secondary battery included in the power supply system to which the state estimation device for the secondary battery according to the present invention is applied is an example. However, the present invention is not limited to the lithium ion battery.

  As shown in FIG. 2, the secondary battery 10 includes a negative electrode 12, a separator 14, and a positive electrode 15. The separator 14 can be made of, for example, a resin infiltrated with an electrolytic solution, and is disposed between the negative electrode 12 and the positive electrode 15. That is, the separator 14 corresponds to an “ion conductor” in a secondary battery included in a power supply system to which the state estimation device for a secondary battery according to the present invention is applied. The horizontal coordinate x indicates the position in the thickness direction of the electrode.

Each of the negative electrode 12 and the positive electrode 15 is configured by an aggregate of spherical active materials 18. During discharge, a chemical reaction that releases lithium ions Li ⁺ and electrons e ⁻ occurs on the interface of the active material 18 of the negative electrode 12. On the other hand, a chemical reaction that absorbs lithium ions Li ⁺ and electrons e ⁻ occurs on the interface of the active material 18 of the positive electrode 15.

The negative electrode 12 is provided with a current collector 13 that absorbs electrons e ⁻ , and the positive electrode 15 is provided with a current collector 16 that emits electrons e ⁻ . The negative current collector 13 is typically made of copper, and the positive current collector 16 is typically made of aluminum. The current collector 13 is provided with a negative electrode terminal 11n, and the current collector 16 is provided with a positive electrode terminal 11p. The secondary battery 10 is charged and discharged by the exchange of lithium ions Li ⁺ through the separator 14, and a charging current Ib (<0) or a discharging current Ib (> 0) is generated.

  First, the battery model formula disclosed in Non-Patent Document 1 applied to the schematic battery model shown in FIG. 2 will be described.

(Basic battery model formula for conventional technology)
Here, a basic battery model formula applied to the schematic battery model shown in FIG. 2 will be described. Here, for the purpose of facilitating understanding of the state estimation device for a secondary battery according to the present invention, first, a basic battery model formula according to the prior art described in the above-mentioned prior art documents is first described. explain. The basic battery model formula is a battery model formula according to the prior art based on that disclosed in Non-Patent Document 1. The basic battery model formula is represented by a basic equation consisting of the following formulas (1) to (11). A list of variables and constants used in the battery model equation is shown in FIG.

  In the variables and constants in the model formulas described below, the subscript e indicates a value in the electrolytic solution, and the subscript s indicates a value in the active material. The suffix j distinguishes between the positive electrode and the negative electrode, j = 1 indicates the value at the positive electrode, and j = 2 indicates the value at the negative electrode. It should be noted that when the variables or constants at the positive electrode and the negative electrode are comprehensively described, the suffix j is omitted. In addition, the description of (t) indicating that it is a function of time, the description of (T) indicating the dependency of the battery temperature, or (θ) indicating the dependency of the local SOC θ is omitted in the specification. There is a case. Furthermore, the symbol # attached to a variable or constant represents an average value.

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

  In addition, the equation (3) is established as an equation relating to the conservation law of lithium ion concentration in the electrolytic solution. On the other hand, as an equation relating to the law of preserving lithium concentration in the active material, the diffusion equation of equation (4) and the boundary condition equation shown in equations (5) and (6) are applied. Equation (5) represents the boundary condition at the center of the active material, and equation (6) represents the boundary condition at the interface between the active material and the electrolyte (hereinafter, also simply referred to as “interface”).

Here, local SOC θ _j which is a local lithium concentration distribution at the active material interface is defined by the equation (7). C _sej in the equation (7) represents the lithium concentration at the active material interface between the positive electrode and the negative electrode, as shown in the equation (8). C _{sj, max} represents the limit lithium concentration in the active material.

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

(Simplification of basic battery model)
Although the basic equations of the above formulas (1) to (11) are disclosed in Non-Patent Document 1, these batteries are incorporated in a state estimation device that is mounted on an actual machine and estimates the state of a secondary battery online. It is extremely difficult to apply the model formula as it is because of limitations on calculation load and calculation time of the ECU (battery ECU 50). Therefore, in the state estimation device mounted on the actual machine, it has been proposed to simplify and use the battery model formula as described below.

  In simplifying the basic battery model formula, it is assumed that the electrochemical reaction in each electrode of the negative electrode 12 and the positive electrode 15 is uniform. That is, it is assumed that the reaction occurs uniformly in the x direction in each of the electrodes 12 and 15. In addition, since it is assumed that the reaction of each active material in each electrode of the negative electrode 12 and the positive electrode 15 is uniform, one active material model is handled for each of the negative electrode 12 and the positive electrode 15. As a result, the schematic structure of the secondary battery shown in FIG. 2 is modeled as shown in FIG. That is, FIG. 4 is a conceptual diagram illustrating an outline of secondary battery modeling based on a simplified battery model formula as described above.

As shown in FIG. 4, when the secondary battery is discharged, the lithium atom Li in the active material model 18n becomes lithium ion Li ⁺ due to the release of electrons e ⁻ due to the electrode reaction on the surface of the negative electrode active material model 18n. It is discharged into the electrolyte solution in the separator 14. On the other hand, in the electrode reaction in the positive electrode active material model 18p surface, electrons e are captured lithium ion Li in the electrolyte solution ^{+ -} absorb. Thereby, lithium atoms Li are taken into the positive electrode active material model 18p. A current flows from the positive electrode current collector 16 toward the negative electrode current collector 13 by the release of the lithium ions Li ⁺ from the negative electrode active material model 18n and the uptake of lithium ions Li ⁺ by the positive electrode active material model 18p.

Conversely, the two in the next time of charging the battery, the negative electrode active material model by the electrode reaction on the 18n surface captured lithium ion Li in the electrolyte solution ^+, the positive electrode active material model 18p surface lithium in the electrode reaction in the ion Li ⁺ Is released into the electrolyte. In the battery model formula, the electrode reaction on the surfaces of the active material model 18p (j = 1) and the active material model 18n (j = 2) during charge / discharge, the diffusion of lithium (diameter inside the active material models 18p and 18n) Direction), as well as the diffusion (concentration distribution) of the lithium salt in the electrolyte, and the potential distribution and temperature distribution at each site.

As shown in FIG. 5, it is assumed that the lithium concentration c _s in each of the active material models 18p and 18n does not depend on the position in the circumferential direction, and the radial coordinate r (r: from the center of each point) Distance, r _s : radius of active material). This active material model is for estimating the lithium diffusion phenomenon inside the active material due to the electrochemical reaction at the interface. Each region (N: natural number of 2 or more) divided in the radial direction ( For k = 1 to N), the lithium concentration c _{s, k} (t) is estimated according to the diffusion equation described below.

  Based on the above assumption, the above equations (1) to (6) and (8) of the basic equation in Non-Patent Document 1 are simplified, and the following equations (1 ′) to (6 ′) and (8 ′).

In the above equation (3 ′), c _ej (t) is assumed to be a constant value based on the assumption that the electrolyte concentration is invariant with time. Further, for the active material models 18n and 18p defined for each of the electrodes 12 and 15, the diffusion equations (4) to (6) are converted into the diffusion equation (4 ′) in consideration of only the distribution in the polar coordinate direction. To (6 '). Note that the lithium concentration c _sej at the active material interface in the equation (8 ′) corresponds to the lithium concentration c _si (t) in the outermost region of the N-divided region shown in FIG.

Furthermore, the equation (9) relating to the law of conservation of charge in the electrolytic solution is based on the following equation (12) by assuming that the electrochemical reaction in the electrode is uniform and the concentration of the electrolytic solution is invariant with respect to time. Simplified into an expression. That is, the potential φ _{ej of the} electrolytic solution is approximated by a quadratic function of x. Then, the average potential φ _ej # in the electrolytic solution used for calculating the overvoltage η _j # is obtained as the following formula (13) by integrating the formula (12) with the electrode thickness L _j .

For the negative electrode 12, since the following equation (14) is established from the equation (12), the potential difference between the electrolytic solution average potential φ _e2 # and the electrolytic solution potential at the boundary between the negative electrode 12 and the separator 14 is expressed by the following equation (15). Represented by an expression. Similarly, for the positive electrode 15, the potential difference between the electrolytic solution average potential φ _e1 # and the electrolytic solution potential at the boundary between the positive electrode 15 and the separator 14 is expressed by the following equation (16).

Similarly, the formula (10) related to the law of conservation of charge in the active material is simplified to the following formula (17). That is, the potential φ _sj of the active material is also approximated by a quadratic function of x. Then, the average potential φ _sj # in the active material used for calculating the overvoltage η _j # is obtained as the following formula (18) by integrating the formula (17) with the electrode thickness L _j . Therefore, the potential difference between the active material average potential φ _s1 # at the positive electrode 15 and the active material potential at the boundary between the positive electrode 15 and the current collector (current collector 16) in the positive electrode 15 is similar to the potential in the electrolytic solution. It is expressed by equation (19). Similarly, the formula (20) is established for the negative electrode 12.

FIG. 6 is a conceptual diagram showing the relationship between the terminal voltage of the secondary battery and each average potential as described above. Specifically, FIG. 6 is a conceptual diagram showing the relationship between the terminal voltage V (t) of the secondary battery and each average potential obtained as described above. As shown in FIG. 6, since the reaction current density j _j ^Li = 0 in the separator 14, the voltage drop in the separator 14 is proportional to the current density I (t), and in detail, L _s / κ _s ^eff · I (t).

Furthermore, as described above, by assuming that the electrochemical reaction in each electrode is uniform, the current density I (t) per electrode plate unit area and the reaction current density (lithium generation amount) j _j ^Li In the meantime, the following expression (21) is established.

  Accordingly, from the potential relationship shown in FIG. 6 and the above equation (21), the following equation (22) is established for the battery voltage V (t). The expression (22) is based on the potential relational expression of the expression (23) shown in FIG.

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

Then, by substituting the average potentials φ _s1 # and φ _s2 # obtained by substituting the equations (15), (16), and (25) into the equation (23), the electrochemical reaction is performed. A voltage-current relationship model formula (M1a) according to the reaction model formula is derived.

  Further, the active material models 18p and 18n in the positive electrode 15 and the negative electrode 12, respectively, according to the lithium concentration conservation law (diffusion equation) (4 ') and the boundary condition equations (5') and (6 '). The active material diffusion model formula (M2a) is obtained.

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 represents the voltage drop due to the battery current. That is, the DC pure resistance of the secondary battery is represented by the portion of Rd (T) in the equation (M1a).

In the equation (M2a), the 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 are set according to a map as shown in FIG. 7, for example, as variable parameters that are variably set with respect to the battery temperature T detected by the temperature sensor 30. As shown in FIG. 7, the diffusion coefficients D _s1 and D _s2 have a characteristic of relatively decreasing as the battery temperature decreases while relatively increasing as the battery temperature increases. Therefore, reflecting the temperature dependency, the diffusion coefficients D _s1 and D _s2 in the equation (M2a) are used as battery parameter values corresponding to the battery temperature T detected based on the detection value Tb of the temperature sensor 30. A map to be set can be created in advance.

Note that the diffusion coefficients D _s1 and D _s2 may have not only temperature dependency but also local SOC θ dependency as necessary. In this case, the diffusion coefficient D _s1 and D _s2 correspond to the detected battery temperature T and the estimated local SOC θ. Then, a two-dimensional map in which these diffusion coefficients are set as parameter values can be created in advance.

Similarly, as shown in FIGS. 8A and 8B, the open-circuit voltages U ₁ and U ₂ in the equation (M1a) are also dependent on increasing or decreasing as the local SOC θ decreases. Have Therefore, a map for setting the open-circuit voltages U ₁ and U ₂ in the equation (M1a) can be created in advance in correspondence with the estimated local SOC θ, reflecting such local SOC dependency. Incidentally, FIG. 8 (a) represents the local SOCθ dependence of open circuit voltage _{U 1} in the positive electrode (j = 1), FIG. 8 (b), the local open circuit voltage _{U 1} in the negative electrode (j = 2) It is a graph showing SOC (theta) dependence.

Furthermore, although illustration is omitted, since the exchange current densities i ₀₁ and i ₀₂ in the equation (M1a) also have a dependency on the local SOC θ and the battery temperature T, a two-dimensional map with θ and T as arguments is previously stored. It is also possible to prepare and exchange current densities i ₀₁ and i ₀₂ to be determined as battery parameter values corresponding to local SOC θ and battery temperature T at a certain time.

  Similarly, since the pure DC resistance Rd also has temperature dependence, the pure DC resistance Rd is changed to a battery corresponding to the battery temperature T detected based on the detection value Tb of the temperature sensor 30 reflecting the temperature dependence. A map to be set as a parameter value can be created in advance.

  It should be noted that the above-described various maps can be described as confirming that it can be created based on, for example, experimental results such as well-known AC impedance measurement for the secondary battery 10.

(Commonization of active material models)
In the above description, a method of using a separate active material model for each of the negative electrode 12 and the positive electrode 15 has been exemplified (see FIG. 4). Instead, an active material model common to the negative electrode 12 and the positive electrode 15 is used. It is possible to model by further reducing the calculation load by applying. In this case, since the active material models 18n and 18p of the negative electrode 12 and the positive electrode 15 are collectively handled as a single element, it is necessary to replace the equation as shown in the following equation (26). In the formula (26), the subscript j indicating the distinction between the positive electrode and the negative electrode is deleted.

As a result, the following equations (M1b) and (M2b) are obtained as models obtained by further simplifying the model equations (M1a) and (M2a). In addition, as a relational expression between the current density I (t) and the reaction current density j _j ^Li in the battery model formula using the active material model in which the positive electrode and the negative electrode are shared in this way, instead of the formula (21), the following formula is used. Equation (21 ′) is applied.

(Linear approximation of polarization voltage term)
By the way, in the above-described equation (M1a), since the arcsinh term exists in the second term on the right side representing the overvoltage, it is necessary to solve the nonlinear equation. For this reason, the calculation of equation (M1a) requires repeated calculation, which not only increases the calculation load, but also may impair the stability of the calculation. Therefore, a voltage-current relationship model expression (M1c) is obtained by first-order approximation (linear approximation) of the arcsinh term in the expression (M1a).

In the equation (M1c), as a result of 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 has dependence on the local SOC θ and the battery temperature T with respect to the exchange current densities i ₀₁ and i ₀₂ as shown in the above equation (27). Therefore, when the voltage-current relationship model equation (M1c) is used, a map that reflects the dependence on the local SOC θ and the battery temperature T for the reaction resistance Rr (θ _i , T) is preliminarily determined based on experimental results. It is necessary to create and appropriately set one of the battery parameters by referring to the map.

As a result, the above equation (M1c), which is a voltage-current relationship model equation, is obtained by using the battery voltage V (t), the battery current density I (t), and Rr (θ, T) and Rd (T), and can be expressed as a linear model equation established between the open circuit voltages U ₁ and U ₂ .

  Similarly, the following equation (M1d) can also be obtained by linearly approximating the arcsinh term of the second term on the right side of the above equation (M1b). The expression (M1d) is also expressed as a linear model expression in the same manner as the expression (M1c).

(Configuration of secondary battery state estimation device)
Next, the secondary battery is realized by a combination of any one of the voltage-current relationship models (M1a) to (M1d) and the corresponding active material diffusion model (M2a) or (M2b). The configuration of the state estimation device will be described. The state estimation device described below is basically realized by a program process by the battery ECU 50 shown in FIG.

  FIG. 9 is a schematic block diagram illustrating a schematic configuration of the state estimation device for the secondary battery based on the simplified battery model formula as described above. Each block shown in FIG. 9 is basically realized by program processing by the battery ECU 50.

  As shown in FIG. 9, state estimation device 52 includes diffusion estimation unit 100, open-circuit voltage estimation unit 110, current estimation unit 120, battery parameter value setting unit 130, and boundary condition setting unit 140.

The diffusion estimation unit 100 is based on the boundary conditions set by the boundary condition setting unit 140 according to the equations (5 ′) and (6 ′) according to the equation (M2a) or (M2b) which is an active material diffusion model equation. The lithium concentration distribution inside the active material is sequentially calculated, for example, in a differential format. Further, based on the estimated lithium concentration distribution, diffusion estimation unit 100 sets the local SOC θ according to the equation (7), with the lithium concentration in the outermost _{peripheral region} as the lithium concentration c _sej at the active material interface.

  The open-circuit voltage estimation unit 110 obtains an open-circuit voltage for each of the positive electrode and the negative electrode or an open-circuit voltage obtained by combining the positive electrode and the negative electrode according to a map reflecting the characteristics shown in FIG. In FIG. 9, these are comprehensively expressed as an open circuit voltage U (θ).

The battery parameter value setting unit 130 uses the battery model equation to be used according to the battery temperature T detected based on the detection value Tb of the temperature sensor 30 and the local SOC θ at a certain time point based on the estimation by the diffusion estimation unit 100. Set the battery parameters. As described above, the diffusion constant D _s1 , D _s2 , or D _{s of} the model equation (M2a) or (M2b) used in the diffusion estimation unit 100 is not only set according to the battery temperature T, but also the model equation DC pure resistance Rt in (M1a) to (M1d), or exchange current density i ₀₁ , i ₀₂ in model equation (M1a) or (M1b), or reaction resistance Rr in model equation (M1c) or (M1d) Etc. are set by the battery parameter value setting unit 130.

  The current estimation unit 120 is based on any of the following formulas (M3a) to (M3d) for calculating the battery current density I (t) based on the formulas (M1a) to (M1d) described above. The battery current density I (t) is calculated by substituting the open circuit voltage U (θ) estimated by 110 and the current battery voltage V (t) detected according to the detection value Vb of the voltage sensor 34.

  For example, the equation (M3a) corresponds to a solution of the equation (M1a) with respect to the battery current density I (t). When solving the equation (M3a), which is a nonlinear equation, by the Newton method or the like, an initial value of I (t) is assumed, and further, the battery voltage V (t), the open circuit voltage U (θ), and the battery parameter value are substituted. Then, I (t) can be calculated and solved by performing iterative calculation until the calculated I (t) matches the assumed I (t).

  Similarly, in the battery model equation using the equation (M1b), the battery current density I (t) can be calculated by solving the following equation (M3b) by the same method as the equation (M3a).

  Further, in the battery model expression using the linearly approximated expressions (M1c) and (M1d), the battery voltage V (t (t) is not performed in accordance with the following expressions (M3c) and (M3d) without performing an iterative calculation like a nonlinear equation. ), The open-circuit voltage U (θ), and the battery parameter value can be substituted to uniquely calculate the battery current density I (t). Thereby, the calculation load can be reduced and the stability of the calculation can be improved.

Next, the boundary condition setting unit 140 converts the calculated current density I (t) into the reaction current density (lithium generation amount) j _j ^Li according to the above formula (21) or (21 ′), The boundary conditions of the active material diffusion model formulas (M2a) and (M2b) are updated according to the formula 6 ′).

  Therefore, in the secondary battery state estimation device based on the simplified battery model formula as described above, the current based on the battery voltage V (t) based on the detection value of the voltage sensor 34 and the detection value of the temperature sensor 30. Simplified voltage-current relationship model based on the electrochemical reaction model equation while estimating based on the diffusion model equation (M2a) or (M2b) equation of the reactant (lithium) in the active material with the battery temperature T as an input By combining with the equations (M1a) to (M1d), the concentration distribution of the reactant (lithium) in the active material can be estimated, and the internal state of the secondary battery can be estimated based on this concentration distribution. As a result, it is possible to realize a battery model formula suitable for mounting on an actual machine that estimates the internal state of the secondary battery based on the electrochemical reaction while reducing the computational load by adopting a simplified electrochemical reaction model formula. it can.

(SOC estimation method 1)
In the secondary battery state estimation device based on the simplified battery model equation as described above, the charging rate (SOC) of the secondary battery 10 is further estimated based on the estimated internal state of the secondary battery. be able to.

  FIG. 10 is a block diagram illustrating the SOC estimation configuration in the secondary battery state estimation device based on the simplified battery model equation as described above.

  As shown in FIG. 10, the secondary battery state estimation device based on the simplified battery model equation further includes an average concentration calculation unit 160 and an SOC estimation unit 200.

The average concentration calculation unit 160 obtains the lithium average concentration c _save (t) in the positive electrode active material model 18p by the following equation (29). Further, SOC estimation unit 200 generates SOC estimated value SOCe for secondary battery 10 as a whole according to the following equation (30).

As described above, the lithium concentration c _{s1, k} (t) (k = 1 to N) in the formula (29) is the respective regions obtained by dividing the active material model 18p into N in the radial direction as shown in FIG. The lithium concentration is estimated by the diffusion model equation (M2a) or (M2b). ΔV _k represents the volume of each divided region, and V represents the volume of the entire active material. When the active material model is shared between the positive and negative electrodes, the average value of the lithium concentrations c _{s, k} (t) (k = 1 to N) of each region in the shared active material model is expressed by the equation (29). ), The lithium average concentration c _save (t) can be obtained.

  Here, as an example, FIG. 11 shows the relationship between the average lithium concentration in the active material of the positive electrode 15 and the estimated SOC value SOCe. As shown in FIG. 11, the SOC decreases as the average lithium concentration in the positive electrode active material increases. Accordingly, the lithium average concentration Cf when fully charged (SOC = 100%) and the lithium average concentration C0 when fully discharged (SOC = 0%) are obtained in advance, and linear interpolation is performed between the two. The SOC can be estimated according to the above equation (30).

  FIG. 12 is a flowchart for explaining a series of processes of battery state estimation and SOC estimation by a secondary battery state estimation device based on a simplified battery model equation. The series of processes shown in FIG. 12 can be called and executed in the battery ECU 50 at predetermined calculation cycles.

  As shown in FIG. 12, the battery ECU 50 acquires the battery voltage V (t) based on the detected value Vb of the voltage sensor 34 in step S100, and based on the detected value Tb of the temperature sensor 30 in step S110. The battery temperature T at that time is acquired.

  Further, in step S120, battery ECU 50 calculates local SOC θ based on the lithium concentration on the surface of the active material, based on the lithium concentration distribution obtained in the previous calculation by the diffusion model equation (M2a) or (M2b). .

  Then, in step S130, the battery ECU 50 obtains the open circuit voltage U (θ) value from the local SOC θ for each of the negative electrode 12 and the positive electrode 15 or in common with the positive and negative electrodes, for example, by referring to the map according to the characteristics shown in FIG. calculate. That is, the process executed in step S130 corresponds to the function of open-circuit voltage estimation unit 110 in FIG.

  Further, in step S140, the battery ECU 50 sets the battery parameter value set according to the battery voltage V (t), the open circuit voltage U (θ), and the battery temperature T by the function of the current estimation unit 120 shown in FIG. Based on the above, an estimated value of the battery current density I (t) is calculated according to any one of the voltage-current relationship model formulas (M1a) to (M1d).

Further, in step S150, the battery ECU 50 calculates the reaction current density (lithium generation amount) j _j ^Li from the estimated battery current density I (t) based on the formula (21) or (21 ′). At the same time, the boundary condition (active material interface) at the active material interface of the diffusion model equation (M2a) or (M2b) is set using the calculated reaction current density. That is, the process executed in step S150 corresponds to the function of the boundary condition setting unit 140 in FIG.

  In step S160, the battery ECU 50 calculates the lithium concentration distribution in the set active material model for each of the negative electrode 12 and the positive electrode 15 or in common to the positive and negative electrodes according to the diffusion equation model (M2a) or (M2b). The lithium concentration estimated value in each region is updated. That is, the process executed in step S160 corresponds to the function of the diffusion estimation unit 100 in FIG. As described above, the lithium concentration in the outermost divided region calculated at this time is used to calculate the local SOC θ on the active material surface when the next calculation is executed.

  As a further process, in step S170, the battery ECU 50 can estimate the charging rate (SOC) of the entire secondary battery 10 based on the internal state of the secondary battery obtained in steps S100 to S160.

For example, in step S170, the lithium average concentration c _save is calculated based on the lithium concentration distribution in the active material determined in step S160, and the secondary based on the lithium average concentration c _save determined in step S171. Step S172 for calculating the charging rate of the battery. The process executed in step S171 corresponds to the function of the average concentration calculation unit 160 in FIG. 10, and the process executed in step S172 corresponds to the process by the SOC estimation unit 200 in FIG.

  As described above, according to the secondary battery charge estimation device based on the simplified battery model equation, the battery voltage V (t) is input and the battery current (battery current density I (t)) is estimated. Based on this, the internal state of the secondary battery is estimated. For this reason, as described below with reference to FIG. 13, even if a model error occurs, it has a self-correcting function.

  FIG. 13 is a conceptual diagram illustrating the self-correction of the SOC estimation error by the secondary battery state estimation device based on the simplified battery model equation as described above. As understood from the battery model (M1a) equation and the like, a polarization voltage ΔV as shown in FIG. 13 is generated between the battery voltage V (t) of the secondary battery 10 and the open circuit voltage OCV during charging. . As can be understood from the linearly approximated equations (M1c) and (M1d), this polarization voltage ΔV is a value corresponding to the battery current density I.

Therefore, if a calculation error occurs in the battery model and the open circuit voltage is estimated to be too small with respect to the true value, OCV (estimated value) <OCV (true value) and SOC (estimated value) <SOC (true value). The polarization voltage ΔV (estimated value)> ΔV (true value). Accordingly, the battery current density I (t) is excessively estimated with respect to the true value. As a result, the reaction current density j _j ^Li is also excessively estimated by the equation (21) or (21 ′), and therefore, the SOC increase amount is excessively estimated in the next calculation cycle. The error will be self-correcting. Similarly, even when the open circuit voltage is excessively estimated with respect to the true value, the model error related to the SOC can be corrected in the opposite direction.

  In other words, in the secondary battery charge estimation device based on the simplified battery model formula, the model estimation error once generated can be self-corrected in the next and subsequent calculations, so that the battery model error is not integrated. The internal state and the charging rate (SOC) of the secondary battery can be accurately estimated.

(SOC estimation method 2)
An example of a method for estimating the charging rate (SOC) of the secondary battery 10 based on the internal state of the secondary battery estimated in the secondary battery state estimation device based on the simplified battery model formula is described above. However, the method for estimating the charging rate (SOC) of the secondary battery 10 is not limited to the above, and the charging rate (SOC) of the secondary battery 10 can also be estimated by other methods.

  FIG. 14 is a block diagram for explaining another SOC estimation method by the secondary battery state estimation device based on the simplified battery model equation.

  As shown in FIG. 14, in the SOC estimation method, a secondary battery state estimation device based on a simplified battery model equation includes an offset estimation unit 170, a current integration unit 180, and an SOC estimation unit 210. Comprising.

  Based on the battery current density I (t) estimated by the current estimator 120 and the battery current Ib (t) measured by the current sensor 32, the offset estimator 170 calculates the current sensor 32 according to the following equation (31). An offset error Iof is calculated. The model battery current Im (t) in the equation (31) is obtained by multiplying the battery current density I (t) estimated by the current estimation unit 120 and the electrode surface area. As shown in the equation (31), the offset estimation unit 170 integrates the deviation between the model battery current Im (t) and the battery current Ib (t) measured by the current sensor 32, and integrates the integrated value. By dividing by the time Tm, the current offset error Iof is calculated.

  Then, the calculation unit 175 obtains the corrected battery current Ibc (t) by subtracting the offset error Iof estimated by the offset estimation unit 170 from the battery current Ib (t) detected by the current sensor 32.

  Current integrating unit 180 obtains integrated value ΣIbc of corrected battery current Ibc (t) calculated by computing unit 175. Then, SOC estimation unit 210 obtains SOC change amount ΔSOCi based on integrated value ΣIbc of corrected battery current Ibc (t) according to the above equation (32). The SOC change amount ΔSOCi indicates the change amount of SOC from the previous SOC estimation calculation to the time point. Further, according to the above equation (33), SOC estimation unit 210 determines the current time according to the sum of SOC estimated value SOCe (0) at the time of the previous estimation calculation and SOC change amount ΔSOCi obtained by equation (32). An estimated SOC value SOCe is calculated.

  Here, as described in the introduction, for example, in HV driving in which driving by an electric motor or driving by another power source in HV or the like, regenerative power generation of the motor or power generation by another power source is performed, the secondary battery is charged. In addition, the discharge is switched relatively frequently. In such a situation where the secondary battery is alternately charged and discharged, as shown in FIG. 15, the current estimation error by the battery model generally does not include an offset component. If it integrates over a period, it will approach 0. On the other hand, as shown in FIG. 16, since the offset error of the current sensor 32 is maintained at a constant value, the deviation between the battery current Ib (t), which is a sensor measurement value, and the model estimated value Im (t) is , It always has a constant DC component. Therefore, the offset error Iof of the current sensor 32 can be calculated by the calculation in the offset estimation unit 170 based on the above equation (31).

  FIG. 17 is a flowchart for realizing the SOC estimation process shown in FIG. 14 by battery ECU 50. The SOC estimation process as described above is realized by replacing step S170 in FIG. 12 with steps S173 to S175 shown in FIG.

  As shown in FIG. 17, in step S173, the battery ECU 50 determines the battery current model estimate value Im (t) based on the battery current density I (t) obtained by inputting the battery voltage V (t) by the battery model. The offset error Iof is calculated by integrating the deviation from the sensor value Ib (t) by the current sensor 32. That is, the process executed in step S173 corresponds to the function of the offset estimation unit 170 in FIG.

  Further, in step S174, the battery ECU 50 calculates the corrected battery current Ibc (t) by correcting the sensor value Ib (t) using the offset error Iof. The processing executed in step S174 corresponds to the function of the calculation unit 175 in FIG.

  Then, in step S175, battery ECU 50 calculates secondary battery charging rate estimated value SOCe based on the integration of corrected battery current Ibc (t). That is, the process executed in step S175 corresponds to the functions of current integrating unit 180 and SOC estimating unit 210 in FIG.

  According to the SOC estimation method by the secondary battery state estimation device based on the simplified battery model formula described above, the offset error is detected based on the battery model formula, and based on the current integration from which the offset error is removed. The charging rate (SOC) of the secondary battery 10 can be accurately estimated.

(SOC estimation method 3)
FIG. 18 is a block diagram for explaining yet another SOC estimation method by the secondary battery state estimation device based on the simplified battery model formula.

  As shown in FIG. 18, in the SOC estimation method, the secondary battery state estimation device based on the simplified battery model equation is the SOC estimation unit 200 described with respect to the SOC estimation method 1 with reference to FIG. 10. And SOC estimation unit 210 # based on current integration, and SOC estimation unit 220 that generates a final SOC estimated value SOCe by combining the SOC estimation results of both.

  As in SOC estimation method 1, SOC estimation unit 200 follows the internal state estimation of the secondary battery based on the simplified battery model equation, and calculates the SOC model estimated value SOCm based on the average lithium concentration in the active material. presume. Since this detail is the same as that described in FIG. 10, the description thereof will not be repeated.

  On the other hand, SOC estimation unit 210 # obtains SOC change amount ΔSOCi between SOC estimation calculation cycles based on the integration of battery current Ib (t) measured by current sensor 32.

  Note that the SOC estimation unit 210 # is based on the offset error estimation of the current sensor 32 based on the battery model and the integration of the corrected battery current Ibc (t) corrected for the offset error, as described with reference to FIG. Without being limited to the configuration for obtaining the SOC change amount ΔSOCi, the SOC change amount ΔSOCi may be obtained by integrating the battery current Ib (t) measured by the current sensor 32. However, it is more desirable that the SOC estimation unit 210 shown in FIG. 14 is configured to be used as the SOC estimation unit 210 # in FIG. 18 because the SOC change amount ΔSOCi can be accurately obtained by the effect of offset error correction. .

  The SOC estimating unit 220 calculates a final SOC estimated value SOCe based on the following equation (34).

  In the above equation (34), the SOC estimated value SOCe is obtained by multiplying the previous SOC estimated value SOCe (0) by the SOC change amount ΔSOCi based on the current integration and the gain k1, the SOC model estimated value SOCm, and the previous SOC. It is obtained by the sum of the difference from the estimated value SOCe (0) and the term multiplied by the gain k2.

  For gains k1 and k2, k1> k2 (for example, gain k1 = 1.0 and gain k2 <1.0) combined current integration and battery model internal state estimation. SOC estimation can be performed. As described above, for the short-term SOC change estimation, the highly reliable SOC change ΔSOCi is reflected with a small time constant, and the model estimated value SOCm reflecting the internal state change of the secondary battery is reflected with a relatively large time constant. By reflecting, not only the short-term SOC estimation error but also the SOC estimation error caused by the long-term battery use can be eliminated.

Alternatively, the gains k1 and / or k2 may be changed according to the battery state. For example, it is desirable to mainly perform SOC estimation based on current integration by reducing the gain k2 at a low temperature when the accuracy of the battery model is reduced or when charging / discharging a large battery current. In particular, in the voltage-current relationship model expressions (M1c) and (M1d), the absolute value of the I (t) / {2L _j a _sj i _oj (θ, T)} term is a predetermined value by linear approximation of the arcsinh term. If it becomes above, the error of a battery model type will increase. That is, when the battery temperature T at which the exchange current density i _ej (θ, T) decreases when the current is large (| I (t) | >> 0) and the absolute value of the above term increases, the battery model increases. The error increases. Therefore, in such a case, for example, by setting k2 = 0 and stopping the SOC estimation by the battery model, it is possible to prevent the estimation error of the charging rate (SOC) of the secondary battery 10 from being increased due to the battery model error. it can.

  FIG. 19 is a flowchart for realizing the SOC estimation process shown in FIG. 18 by battery ECU 50.

  As shown in FIG. 19, the battery ECU 50 performs steps S171, S172 #, S173, S174, S175 #, and S176 shown in FIG. 19 in place of step S170 in FIG. SOC estimation can be performed.

As shown in FIG. 19, after the process in step S171 (similar to FIG. 12), the battery ECU 50 determines the model SOC in step S172 # from the lithium average concentration c _save obtained in step S171 as in step S172. Estimated value SOCm is calculated.

  On the other hand, after the processing in steps S173 and S174 (similar to FIG. 17), battery ECU 50 determines in step S175 # the SOC change amount ΔSOCi within the SOC estimation calculation execution period based on the integration of correction current value Ibc (t). Is calculated. As described above, the calculation of the SOC change amount ΔSOCi in step S175 # can also be performed by integrating the measured value Ib (t) by the current sensor 32 without the correction of the offset error Iof.

  Further, in step S176, battery ECU 50 determines an equation (SOC) based on previous SOC estimated value SOCe (0), model SOC estimated value SOCm obtained in step S172, and SOC change amount ΔSOCi obtained in step S175 #. 34), the current SOC estimated value SOCe is calculated.

  With the above configuration, for the short-term SOC change estimation, the SOC estimation by reliable current integration and the SOC estimation by the battery model formula reflecting the internal state change of the secondary battery are appropriately combined. Thus, the charging rate (SOC) of the secondary battery can be accurately estimated.

(First embodiment of the present invention)
As described above, in the state estimation device for the secondary battery based on the battery model formula according to the conventional technique, the current battery based on the battery voltage V (t) based on the detection value of the voltage sensor 34 and the detection value of the temperature sensor 30. Simplified voltage-current relationship model equations (M1a) to (M1d) according to the diffusion model equations (M2a) and (M2b) of the reactant (lithium) in the active material and the electrochemical reaction model equation with the temperature T as an input ), The concentration distribution of the reactant (lithium) in the active material can be estimated, and the internal state of the secondary battery can be estimated based on this concentration distribution. Moreover, the charging rate (SOC) of the secondary battery 10 can be further estimated based on the estimated internal state of the secondary battery.

  However, in the state estimation device for the secondary battery based on the battery model formula according to the above-described prior art, the SOC estimation model simplified by assuming that the concentration of the reactant (eg, lithium salt) in the electrolytic solution is constant. Is used. That is, in the state estimation device of the secondary battery based on the battery model formula according to the prior art, due to the concentration overvoltage caused by the non-uniform concentration distribution (concentration gradient) of the reactant in the electrolyte between the positive electrode and the negative electrode. Voltage drop is not considered.

  As described at the beginning, in HV and the like, in HV traveling in which driving by an electric motor, driving by another power source, regenerative power generation of the motor or power generation by another power source is performed, charging and discharging of the secondary battery are performed. It is performed by switching relatively frequently. In such a situation where the secondary battery is alternately charged and discharged, the non-uniform concentration distribution (concentration gradient) between the positive electrode and the negative electrode of the reactant in the electrolytic solution as described above cancels out. Since the concentration gradient of the reactant in the electrolyte is very small, the voltage drop due to the concentration overvoltage is also very small (see FIG. 20 (a)). Therefore, in such a situation where the secondary battery is alternately charged and discharged, even if the voltage drop due to the concentration overvoltage is not taken into account, the SOC estimation accuracy or the like is not greatly affected.

However, as described above, in PHV, EV, etc., the secondary battery is charged over a relatively long charging period and over a relatively long period compared to HV as described above. EV running is performed in which the secondary battery is discharged. During EV traveling, the concentration gradients of the reactants in the electrolyte solution do not cancel each other as in HV traveling, and the concentration gradient increases with time (time t advances to t ₀ , t ₁ , t ₂ , t ₃ ). The concentration overvoltage greatly affects the SOC estimation accuracy (see FIG. 20B).

  Further, regarding the error in the estimation of the SOC, in the HV traveling, the SOC increases because the situation where the SOC increases and the situation where the SOC decreases center around a predetermined SOC center value (for example, 50%). A direction error and a decreasing direction error occur in a confusing manner and cancel each other (see FIG. 21A). On the other hand, in EV travel, once the secondary battery is charged (when the SOC increases), then the secondary battery discharge (SOC decrease) occurs over a relatively long period of time. That is, in EV travel, the SOC gradually decreases from the SOC at the start of EV travel (start SOC, for example, 90%) to the SOC at the end of EV travel (end SOC, for example, 10%). go. Therefore, as for the error in the estimation of the SOC, the error in the direction in which the SOC increases and the error in the direction in which the SOC decreases do not cancel each other, but the errors in the direction in which the SOC decreases are accumulated, and the errors are likely to accumulate (see FIG. 21 (b)). Even in such a situation, in EV traveling, it is desired to estimate the SOC with higher accuracy than in HV traveling.

  As described above, in this technical field, it is possible to estimate the SOC with high accuracy even during EV traveling while reducing the calculation load in an on-board ECU or the like that is limited in arithmetic processing capacity or memory capacity. There is a need for a secondary battery state estimation device. That is, in this technical field, based on a new battery model formula that takes into account the voltage drop due to concentration overvoltage caused by non-uniform concentration distribution (concentration gradient) between the positive electrode and negative electrode of the reactant in the electrolyte. A state estimation device for a secondary battery is required.

When the concentration overvoltage (Δφ _e ) is taken into consideration, the above-described voltage-current relationship model equations (M1a) to (M1d) are expressed by the following voltage-current relationship model equations (M1a ′) to (M1d ′), respectively. It is necessary to replace with.

  Further, as described above, the voltage-current relationship model equation (M1c) is replaced with the equation (M1c ′), so that the above-described voltage-current relationship model equation (28) is also expressed by the following (28 ′) It needs to be replaced by the formula.

  Furthermore, the above-described equations (M3a) to (M3d) for calculating the battery current density I (t) also need to be replaced with the following equations (M3a ′) to (M3d ′), respectively.

As described above, the concentration overvoltage (Δφ _e ) caused by the non-uniform concentration distribution (concentration gradient) between the positive electrode and the negative electrode of the reactant in the electrolytic solution is expressed by the voltage-current relationship model equation (M1a ′) to (M1a ′) to ( By incorporating it into the equations (M1d ′) and (M3a ′) to (M3d ′), the internal state and SOC of the secondary battery can be estimated with higher accuracy.

By the way, the concentration overvoltage (Δφ _e ) can be estimated from the concentration distribution (Δc _e ) between the positive electrode and the negative electrode of a reactant (for example, lithium salt) in the electrolytic solution. The concentration distribution (Δc _e ) between the positive electrode and the negative electrode of the reactant can be estimated based on, for example, the following formulas (51) and (52).

On the other hand, for example, by a real machine evaluation, a correspondence relationship between the concentration distribution (Δc _e ) and the concentration overvoltage (Δφ _e ) is obtained, and based on this relationship, the concentration overvoltage (Δφ _e ) is calculated from the concentration distribution (Δc _e ). Can be estimated. The correspondence relationship between the concentration distribution (Δc _e ) and the concentration overvoltage (Δφ _e ) can be determined in advance as a map such as a data table or as a function such as a regression equation.

That is, the state estimation device for a secondary battery according to the first embodiment of the present invention includes:
First and second electrodes including an active material containing a reactive substance that contributes to an electrochemical reaction, and an ion conductor that conducts the ionized reactive substance between the first and second electrodes. A state estimation device for a secondary battery comprising:
A voltage detector for detecting a battery voltage between the first and second electrodes;
An in-electrode diffusion estimation unit that estimates the concentration distribution of the reactant according to an active material diffusion model equation that defines the concentration distribution of the reactant within the active material based on a given boundary condition;
An open-circuit voltage estimation unit that estimates the open-circuit voltage between the first and second electrodes based on the concentration of the reactant at the interface between the active material and the electrolyte estimated by the in-electrode diffusion estimation unit When,
Inter-electrode diffusion for estimating the concentration distribution of the reactant between the first and second electrodes according to an inter-electrode diffusion model equation defining the concentration distribution of the reactant between the first and second electrodes An estimation unit;
A concentration overvoltage estimation unit that estimates a concentration overvoltage based on the concentration distribution of the reactant between the first and second electrodes estimated by the interelectrode diffusion estimation unit;
The open voltage, the overvoltage calculated according to the battery current density of the secondary battery, the voltage drop generated according to the battery current density, the concentration overvoltage, and the relationship between the battery voltage. A current estimation unit for estimating a battery current density of the secondary battery according to a voltage-current relationship model equation based on an electrochemical reaction;
With
The current estimation unit includes the battery voltage detected by the voltage detector, the open circuit voltage estimated by the open circuit voltage estimation unit, the concentration overvoltage estimated by the concentration overvoltage estimation unit, and the secondary By substituting the battery parameter value into the voltage-current relationship model equation, the battery current density is calculated,
A boundary for calculating the reaction current density at the interface based on the battery current density estimated by the current estimation unit, and setting the boundary condition at the interface of the active material diffusion model equation according to the calculated reaction current density A condition setting unit;
It is a state estimation apparatus of a secondary battery.

As described above, in the state estimation device for a secondary battery according to the present embodiment, the concentration overvoltage (Δφ _e ) is calculated from the concentration distribution (Δc _e ) between the positive electrode and the negative electrode of the reactant (for example, lithium salt). And using the voltage-current relationship model formulas (M1a ′) to (M1d ′) and (M3a ′) to (M3d ′) in which the concentration overvoltage (Δφ _e ) is incorporated, the secondary battery The internal state and SOC can be estimated with higher accuracy.

(Second embodiment of the present invention)
By the way, for example, similarly to the equation (M1a) which is a voltage-current relationship model equation according to the prior art, in the above-described voltage-current relationship model equation (M1a ′) equation, the arcsinh term is the second term on the right-hand side representing the overvoltage. Therefore, it is necessary to solve the nonlinear equation. For this reason, the calculation of the expression (M1a ′) requires repeated calculation, which not only increases the calculation load, but also may impair the stability of the calculation. Therefore, as described at the beginning, for example, in order to reduce the calculation load in an on-board ECU or the like that is limited in arithmetic processing capacity or memory capacity, the arcsinh term in the equation (M1a ′) is linearly approximated (linear approximation). It is desirable to use the voltage-current relationship model equation (M1c ′). Similarly, for the expression (M1b ′), it is desirable to use the expression (M1d ′) obtained by linearly approximating the arcsinh term of the second term on the right side.

That is, the state estimation device for a secondary battery according to the second embodiment of the present invention includes:
A state estimation device for a secondary battery according to the first embodiment of the present invention, comprising:
The voltage-current relationship model equation is obtained by subtracting the product of the model battery current and the reaction resistance and the product of the model battery current and the DC pure resistance from the open-circuit voltage and adding the concentration overvoltage to the battery voltage. Consisting of a linear approximation formula showing
It is a state estimation apparatus of a secondary battery.

As described above, in the secondary battery state estimation device according to the present embodiment, linearly approximated voltage-current relationship model equations (for example, (M1c ′) equation and (M1d ′) equation) are used. The battery current density I (t) is uniquely determined by substituting the battery voltage V (t), the open circuit voltage U (θ), the concentration overvoltage (Δφ _e ), and the battery parameter value without performing the iterative calculation as described above. Can be calculated. Further, the model battery current Im (t) can be obtained by multiplying the battery current density I (t) thus calculated by the electrode surface area. Thereby, it is possible to reduce the calculation load and improve the stability of the calculation.

(Third embodiment of the present invention)
By the way, as described above, for example, diffusion coefficients D _s1 and D _s2 , exchange current densities i ₀₁ and i ₀₂ , DC pure resistance Rd, etc. used as parameters for defining the diffusion rate of the reactant (for example, lithium) are the temperature. Has dependency. Therefore, it is desirable to set these parameter values as variable parameters that are variably set with respect to the battery temperature T detected by the temperature sensor 30.

That is, the state estimation device for a secondary battery according to the third embodiment of the present invention is:
A state estimation device for a secondary battery according to any one of the first and second embodiments of the present invention,
A temperature detector for detecting a battery temperature of the secondary battery;
A parameter value setting unit for variably setting the parameter value according to at least the battery temperature;
Further comprising
The parameter value setting unit further variably sets a parameter value representing a diffusion rate in the active material diffusion model formula according to at least the battery temperature.
It is a state estimation apparatus of a secondary battery.

  As described above, in the state estimation device for a secondary battery according to the present embodiment, the parameter value setting unit can variably set the parameter value according to at least the battery temperature. Can be set to a value corresponding to the battery temperature T. As a result, in the secondary battery state estimation device according to this embodiment, the internal state and SOC of the secondary battery can be estimated with higher accuracy. Note that the correspondence between the value of the parameter having temperature dependency and the battery temperature T can be created in advance as a map such as a data table, for example.

(Fourth embodiment of the present invention)
In addition, the parameter value setting unit can set a parameter having dependency on factors other than the battery temperature T (for example, local SOC θ) to a value corresponding to the plurality of factors.

That is, the state estimation device for a secondary battery according to the fourth embodiment of the present invention is:
A state estimation device for a secondary battery according to the third embodiment of the second embodiment of the present invention, comprising :
The parameter value setting unit includes the reaction resistance and the pure DC resistance according to the concentration of the reactant at the interface estimated by the in- electrode diffusion estimation unit and the battery temperature detected by the temperature detector. Set to variable,
It is a state estimation apparatus of a secondary battery.

As described above, in the state estimation device for the secondary battery according to the present embodiment, the reaction resistance is determined not only by the battery temperature but also by the concentration of the reactant at the interface by the parameter value setting unit. Since the DC pure resistance can be variably set, the internal state and SOC of the secondary battery can be estimated with higher accuracy. In addition, as in this embodiment, when trying to set a parameter having dependency on factors other than the battery temperature T according to the plurality of factors, the relationship between the plurality of factors and the parameter value is set. A multidimensional map (for example, a two-dimensional map) can be created in advance.

(Fifth embodiment of the present invention)
As described above, in the state estimation device for a secondary battery according to the present invention, the concentration overvoltage (Δφ _e ) is calculated from the concentration distribution (Δc _e ) between the positive electrode and the negative electrode of the reactant (for example, lithium salt). By using the voltage-current relationship model expressions (M1a ′) to (M1d ′) and (M3a ′) to (M3d ′), which are estimated and the concentration overvoltage (Δφ _e ) is incorporated, the secondary battery The internal state and SOC can be estimated with higher accuracy. Further, the correspondence relationship between the concentration distribution (Δc _e ) and the concentration overvoltage (Δφ _e ) can be obtained by, for example, actual machine evaluation or the like, and is determined in advance as a map such as a data table or as a function such as a regression equation, for example. I can keep it.

By the way, the concentration overvoltage (Δφ _e ) due to the non-uniform concentration distribution (concentration gradient) between the positive electrode and the negative electrode of the reactant in the electrolytic solution can be expressed by the following equation (41).

Therefore, based on the above equation (41), the concentration overvoltage (Δφ _e ) is calculated from the concentration distribution (Δc _e ) between the positive electrode and the negative electrode of the reactant in the electrolyte, and is substituted into the voltage-current relationship model equation. Thus, the battery current density of the secondary battery can be estimated. However, practically, if a function including a logarithm is calculated as in the above equation (41), the calculation load increases. On the other hand, as described above, the correspondence relationship between the concentration distribution (Δc _e ) and the concentration overvoltage (Δφ _e ) can be determined in advance as a map such as a data table, for example. However, since the concentration distribution (Δc _e ) and the concentration overvoltage (Δφ _e ) have a dependency on the battery temperature T, it is necessary to create these correspondences as a two-dimensional map. This may lead to an increase in memory capacity.

Accordingly, if the correspondence relationship between the concentration distribution (Δc _e ) and the concentration overvoltage (Δφ _e ) can be a simplified function, for example, calculation in an on-board ECU or the like that is restricted in arithmetic processing capacity or memory capacity. This is desirable because the concentration overvoltage (Δφ _e ) can be calculated from the concentration distribution (Δc _e ) using the function without increasing the load or the required memory capacity.

  Therefore, assuming that the voltage drop due to DC resistance in the electrolyte and the concentration overvoltage are independent of each other, the following equation (44) is derived from the following equation (42) which is a difference equation based on the above equation (41). Can do.

From the above equation (44), the concentration overvoltage (Δφ _e ) can be expressed by the following equation (45) as a function of the concentration (c _e ) of the reactant (eg, lithium salt) in the electrolyte.

Further, the equation (45) is modified as follows, and the concentration overvoltage (Δφ _e ) is expressed as the following equation (46) which is a function of the concentration distribution (Δc _e ).

The logarithm is still included in the equation (46). Therefore, the equation (46) is linearly approximated, and the concentration overvoltage (Δφ _e ) is expressed as the following equation (47) which is a linear approximation equation of the concentration distribution (Δc _e ).

According to the equation (47), the concentration overvoltage (Δφ _e ) is expressed as a linear function of the concentration distribution (Δc _e ). Therefore, the concentration overvoltage (Δφ _e ) can be easily calculated from the concentration distribution (Δc _e ) based on the above equation (47). For example, the calculation can be performed by an onboard ECU or the like that is limited in arithmetic processing capacity or memory capacity. The internal state and SOC of the secondary battery can be estimated with higher accuracy in consideration of the concentration overvoltage (Δφ _e ) without increasing the load and the required memory capacity.

That is, the state estimation device for a secondary battery according to the fifth embodiment of the present invention is:
A state estimation device for a secondary battery according to any one of the first to fourth embodiments of the present invention,
The concentration overvoltage estimation unit is derived from a model equation representing a relationship between a concentration of the reactant in the ion conductor and a potential of the ion conductor, and the reactant between the first and second electrodes. The concentration overvoltage is estimated from the concentration distribution of the reactant based on the linear approximation of the relational expression between the concentration distribution and the concentration overvoltage.
It is a state estimation apparatus of a secondary battery.

As described above, in the state estimation device for a secondary battery according to the present embodiment, the concentration overvoltage estimation unit is configured to perform the reaction based on a linear approximation of a relational expression between the concentration distribution of the reactant and the concentration overvoltage. Estimate the concentration overvoltage from the concentration distribution of the substance. Therefore, the concentration overvoltage (Δφ _e ) can be easily calculated from the concentration distribution (Δc _e ) without increasing the calculation load and the required memory capacity. Even with a limited on-board ECU or the like, the internal state and SOC of the secondary battery can be estimated with higher accuracy in consideration of the concentration overvoltage (Δφ _e ).

(Sixth embodiment of the present invention)
As described above, in the state estimation device for a secondary battery according to the present invention, the concentration overvoltage (Δφ _e ) is calculated from the concentration distribution (Δc _e ) between the positive electrode and the negative electrode of the reactant (for example, lithium salt). By using the voltage-current relationship model expressions (M1a ′) to (M1d ′) and (M3a ′) to (M3d ′), which are estimated and the concentration overvoltage (Δφ _e ) is incorporated, the secondary battery The internal state and SOC can be estimated with higher accuracy. Also, to estimate the concentration overpotential ([Delta] [phi _e) from the density distribution (.DELTA.c _e) is a correspondence between the density distribution and (.DELTA.c _e) and concentration overpotential ([Delta] [phi _e), for example, be determined in advance by the actual evaluation, etc. The correspondence relationship thus obtained can be determined in advance as a map such as a data table or as a function such as a regression equation.

Here, a method for obtaining the correspondence between the concentration distribution (Δc _e ) and the concentration overvoltage (Δφ _e ) by actual machine evaluation will be described with reference to FIG. FIG. 22 is a schematic graph showing a change in voltage when the secondary battery is discharged at a certain current rate as described above. In FIG. 22, the solid line represents the measured voltage (terminal voltage).

First, when the discharge is started at time t ₁ , the inter-terminal voltage decreases from V ₁ to V ₂ as shown by a portion surrounded by a dotted ellipse in the graph of FIG. This voltage drop is due to the DC resistance and reaction resistance of the secondary battery. Thereafter, the inter-terminal voltage does not maintain a constant voltage as shown by the broken line in the graph of FIG. 22, but gradually decreases from V ₂ to V ₃ as shown by the solid curve. . This voltage drop is caused by the diffusion phenomenon of the reactive substance (for example, lithium) in the active material constituting the electrode of the secondary battery and the ionic conductor (for example, electrolyte) that conducts the ionized reactive substance between the electrodes. This is due to the diffusion phenomenon of the reactants. Strictly speaking, it includes the influence of a decrease in the open circuit voltage (OCV) accompanying the discharge, but it is negligibly small in the discussion here.

As described above, the voltage between the terminals of the secondary battery is a concentration overvoltage (corresponding to the portion (a) in the graph of FIG. 22) resulting from the concentration distribution of the reactant in the active material as the discharge continues. And the concentration overvoltage (corresponding to the portion (b) in the graph of FIG. 22) due to the concentration distribution of the reactant in the ion conductor. Thus, the drop in the voltage between the terminals accompanying the continuation of discharge includes not only the concentration distribution of the reactant in the ion conductor but also the contribution due to the concentration distribution of the reactant in the active material. Therefore, the concentration overvoltage (Δφ _e ) cannot be known only by observing such a drop in voltage between terminals.

  By the way, the diffusion phenomenon of the reaction material in the active material depends on the potential of the electrode formed by the active material. In addition, among materials used as the active material, there is a material in which the electrode potential is constant (flat potential) even if the content of the reactant is changed in a specific region of the content of the reactant. Hereinafter, the region of the content of the reactant in which the electrode potential is constant even when the content of the reactant is changed may be referred to as “potential flat region”. In an electrode using such a material having a potential flat region as an active material, as long as the content of the reactant in the active material corresponds to the potential flat region, charging and discharging may proceed (accordingly, the active material The electrode potential is constant (even if the content of the reactant in the chamber changes). Specific examples of the material having such a potential flat region include olivine-type lithium iron phosphate (hereinafter simply referred to as “olivine iron”), carbon, and the like.

  FIG. 24 is a graph showing changes in monopolar potential with respect to the content of the reactant (lithium) in olivine iron (a) and carbon (b). As shown in FIG. 24A, in the electrode using olivine iron as the active material, the monopolar potential increases as the lithium content in the olivine iron in the active material decreases as a whole. However, in the region surrounded by the dotted line (potential flat region), the unipolar potential is constant even when the lithium content changes. In addition, as shown in FIG. 24B, in an electrode using carbon as an active material, the monopolar potential decreases overall as the lithium content in the carbon in the active material decreases. However, in the region surrounded by the dotted line, the monopolar potential is constant even when the lithium content changes.

  By using a material having a flat potential region as described above as the active material constituting the electrode of the secondary battery, at least partly due to the concentration distribution of the reactants in the active material as the discharge continues Thus, it is possible to configure a battery that does not generate a concentration overvoltage (corresponding to the portion (a) in the graph of FIG. 22). More specifically, when discharging the battery in a region where the potentials of the positive electrode and the negative electrode of the battery are both flat with respect to the change in the content of the reactant, the potential drop between the terminals as the discharge continues Does not include the concentration overvoltage (corresponding to the portion (a) in the graph of FIG. 22) due to the concentration distribution of the reactant in the active material, and is attributed to the concentration distribution of the reactant in the ion conductor. Only the concentration overvoltage (corresponding to the portion (b) in the graph of FIG. 22) is included. That is, in such a battery, the concentration overvoltage resulting from the concentration distribution of the reactant in the ion conductor can be measured by measuring the drop in potential between the terminals as the discharge continues.

On the other hand, the concentration distribution (Δc _e ) between the positive electrode and the negative electrode of the reactant (eg, lithium salt) is calculated based on the following formulas (51) and (52), for example, as described above. The correspondence relationship between the concentration overvoltage (Δφ _e ) and the concentration distribution (Δc _e ) resulting from the concentration distribution of the reactant in the ion conductor obtained as described above, for example, as a map such as a data table, Alternatively, it can be determined in advance as a function such as a regression equation.

That is, the state estimation device for a secondary battery according to the sixth embodiment of the present invention is:
A state estimation device for a secondary battery according to any one of the first to fourth embodiments of the present invention,
Each of the active materials included in the first and second electrodes has a potential flat region that is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of material
The concentration overvoltage estimation unit is a concentration overvoltage caused by the reactant measured in a state where potential flat regions of active materials included in the first and second electrodes overlap when discharging or charging the secondary battery, The concentration distribution of the reactant between the first and second electrodes in the same state, estimated according to an interelectrode diffusion model equation that defines the concentration distribution of the reactant between the first and second electrodes. And, based on the correspondence relationship, a concentration overvoltage is estimated from the concentration distribution of the reactant.
It is a state estimation apparatus of a secondary battery.

As described above, in the state estimation device for a secondary battery according to this embodiment, the potential flat region of the active material included in the first electrode when the secondary battery is discharged or charged, and the first The potential flat region included in the active material included in the second electrode overlaps at least partially. Therefore, in the state where these potential flat regions overlap, the electrode potential of neither the first electrode nor the second electrode changes. Therefore, in this state, the change in the voltage between the terminals accompanying the continuation of the discharge or the charge of the secondary battery can be regarded as being caused only by the concentration overvoltage resulting from the concentration distribution of the reactant in the ion conductor. it can. Thereby, in the state estimation apparatus of the secondary battery which concerns on this embodiment, the density | concentration overvoltage itself resulting from the density | concentration distribution of the reactant in the ion conductor can be actually measured. Further, by using the concentration overvoltage actually measured and the concentration distribution between the electrodes of the reactant obtained as described above, the correspondence between the concentration distribution (Δc _e ) and the concentration overvoltage (Δφ _e ) It can be determined in advance as a map such as a data table or as a function such as a regression equation.

(Seventh embodiment of the present invention)
By the way, in the above description regarding the method for measuring the concentration overvoltage caused by the concentration distribution of the reactant in the ion conductor in the secondary battery to which the state estimation device for the secondary battery according to this embodiment is applied, The description has been given with particular attention to the voltage drop between terminals in the transition period immediately after the start of discharge. However, considering the influence on the drop in voltage between terminals due to the change in reaction resistance that occurs during the charging and discharging of the secondary battery, the measurement of the concentration overvoltage due to the concentration distribution of the reactant in the ion conductor is It is more desirable to carry out in the relaxation period immediately after stopping charging and discharging of the secondary battery.

Here, the above will be described again with reference to FIG. FIG. 23 is a schematic graph showing changes in the voltage of the secondary battery in the transition period immediately after the start of discharge and the relaxation period immediately after the discharge is stopped, as described above. As shown in FIG. 23, first, when the discharge at time t ₁ is started, the terminal voltage is reduced from V ₁ to V _2. This voltage drop is due to the DC resistance and reaction resistance of the secondary battery. Thereafter, the inter-terminal voltage does not maintain a constant voltage at V ₂ as indicated by the broken line in the graph of FIG. 23, but instead of the solid line included in the region T surrounded by the dotted line in the graph of FIG. As shown by the curve, it continues to drop gradually from V ₂ to V ₃ .

In general, the voltage drop is caused by a diffusion phenomenon of a reactive substance (for example, lithium) in an active material constituting an electrode of a secondary battery, and an ion conductor (for example, conducting the ionized reactive substance between the electrodes) This is due to the diffusion phenomenon of the reactant in the electrolyte solution. Further, when the electrode is formed of an active material having a flat potential region as in the sixth embodiment of the present invention, the contribution of concentration overvoltage caused by the diffusion phenomenon of the reactive material in the active material in the voltage drop. Can be eliminated. However, the period corresponding to the solid curve included in the region T (that is, the period from the time t ₁ to the time t ₂ in the graph of FIG. 23) is the period during which the discharge of the secondary battery proceeds (transition period). In this period, the drop in the voltage between the terminals includes the influence of the change in reaction resistance accompanying the progress of discharge.

Then, when the discharge at time t ₂ is stopped, the terminal voltage rises from V ₃ to V _4. This voltage rise is also due to the DC resistance and reaction resistance of the secondary battery. Thereafter, the inter-terminal voltage continues to gradually increase from V ₄ to V ₁ as shown by the solid curve included in the region R surrounded by the dotted line in the graph of FIG. In the discussion here, the influence of the decrease in the open circuit voltage (OCV) caused by the discharge is considered to be negligible.

The above voltage increase is also generally caused by a diffusion phenomenon of a reactive substance (for example, lithium) in an active material constituting an electrode of a secondary battery, and an ion conductor that conducts the ionized reactive substance between the electrodes ( This is due to, for example, the diffusion phenomenon of the reactant in the electrolyte). In addition, when the electrode is formed of an active material having a potential flat region as in the sixth embodiment of the present invention, the contribution of concentration overvoltage due to the diffusion phenomenon of the reaction material in the active material due to the voltage increase. Can be eliminated. Moreover, the period corresponding to the solid curve included in the region R (i.e., the period of time t ₂ after in the graph of FIG. 23), the discharge of the secondary battery is a period that has been stopped (relaxation period), The change in the inter-terminal voltage during this period does not include the influence of the change in reaction resistance accompanying the progress of discharge.

  That is, if the contribution of the concentration overvoltage due to the diffusion phenomenon of the reactant in the active material can be eliminated, any increase in the inter-terminal voltage during this period will conduct the ionized reactant between the electrodes. It can be considered that it originates in the diffusion phenomenon of the reactive substance in an ionic conductor (for example, electrolyte solution). In this way, taking into consideration the effect on the drop in voltage between terminals due to the change in reaction resistance that occurs during charging and discharging of the secondary battery, measurement of concentration overvoltage due to concentration distribution of reactants in the ion conductor It is more desirable to carry out in the relaxation period immediately after stopping the charging or discharging of the secondary battery, not in the transition period in which charging or discharging of the secondary battery is in progress.

That is, the state estimation device for a secondary battery according to the seventh embodiment of the present invention is:
A state estimation device for a secondary battery according to any one of the first to fourth embodiments of the present invention,
Each of the active materials included in the first and second electrodes has a potential flat region that is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of material
The concentration overvoltage estimation unit has an active material included in the first and second electrodes during a period from when the discharge or charging of the secondary battery is stopped until the battery voltage of the secondary battery is stabilized. In the same state estimated according to an interelectrode diffusion model formula that defines the concentration overvoltage due to the reactant measured in the state where the potential flat regions overlap and the concentration distribution of the reactant between the first and second electrodes Estimating a concentration overvoltage from the concentration distribution of the reactant based on a correspondence relationship with the concentration distribution of the reactant between the first and second electrodes;
It is a state estimation apparatus of a secondary battery.

  As described above, in the state estimation device for a secondary battery according to the present embodiment, during the period until the battery voltage of the secondary battery is stabilized after the discharge or charging of the secondary battery is stopped (that is, In the relaxation period) and in a state where the potential flat regions of the active materials included in the first and second electrodes overlap, by measuring the change in the voltage between the terminals of the secondary battery, the concentration by the reactant Measure the overvoltage. This eliminates not only the effect of concentration overvoltage caused by the diffusion phenomenon of the reactant in the active material, but also the influence of the change in reaction resistance that occurs during the charging and discharging of the secondary battery. The concentration overvoltage due to can be measured more accurately. In the state estimation device for a secondary battery according to the present embodiment, the correspondence relationship between the concentration overvoltage due to the reactant thus obtained and the concentration distribution of the reactant between the electrodes is obtained in advance, and the correspondence Since the concentration overvoltage is estimated from the concentration distribution of the reactant based on the relationship, the estimation accuracy of the concentration overvoltage can be further increased.

(Eighth embodiment of the present invention)
Incidentally, in an actual secondary battery, both of the active materials included in the first and second electrodes are not necessarily made of a material having a potential flat region. In reality, carbon, which is a kind of material having a flat potential region, is often used as the active material contained in the negative electrode. However, as the active material contained in the positive electrode, for example, materials that have almost no potential flat region such as cobalt, nickel, and manganese are widely used. In addition, even if both of the active materials included in the first and second electrodes are made of a material having a potential flat region, these active materials are used during the transition period and relaxation period of the secondary battery charging and discharging. It is not always possible to achieve a state in which both of the materials fall into the potential flat region at the same time (the potential flat regions of these active materials overlap).

  Therefore, the present inventors have intensively studied to find a method capable of actually measuring the concentration overvoltage caused by the concentration distribution of the reactant in the ion conductor for the secondary battery as described above, As shown in FIG. 25, in a secondary battery in which at least one of the active materials included in the first and second electrodes is made of a material having a potential flat region, the first electrode in the ion conductor and Based on the voltage (potential difference) between the reference electrode and an electrode containing an active material made of a material having a potential flat region, a reference electrode is further arranged at a position intermediate to the second electrode. It has been found that the concentration overvoltage resulting from the concentration distribution of the reactant in the conductor can be measured. FIG. 25 is a schematic diagram showing an embodiment in which the concentration overvoltage is actually measured based on the voltage (potential difference) between the reference electrode and the negative electrode. Naturally, the active material contained in the positive electrode has a flat potential. When it has a region, the concentration overvoltage may be measured based on the voltage (potential difference) between the reference electrode and the positive electrode.

  Specifically, as described above, the reference electrode is disposed just in the middle of the first and second electrodes, and the factors that influence the moving distance of the reactant in the electrodes (for example, electrode thickness and porosity) Are equal between the first and second electrodes, a voltage between an electrode including an active material made of a material having a flat potential region (hereinafter also referred to as “potential flat electrode”) and a reference electrode The concentration overvoltage between the first electrode and the second electrode can be obtained by doubling the concentration overvoltage between the potential flat electrode and the reference electrode measured based on (potential difference).

That is, the state estimation device for a secondary battery according to the eighth embodiment of the present invention is:
A state estimation device for a secondary battery according to any one of the first to fourth embodiments of the present invention,
A potential flat region in which at least one of the active materials included in the first and second electrodes is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of a material having
A reference electrode is further disposed at an intermediate position between the first electrode and the second electrode in the ion conductor;
The concentration overvoltage estimation unit is configured to provide a potential difference between the reference electrode and an electrode including the active material made of a material having the potential flat region in a state corresponding to the potential flat region when the secondary battery is discharged or charged. And the first and second states in the same state estimated according to an interelectrode diffusion model equation defining a concentration distribution of the reactants between the first and second electrodes. A concentration overvoltage is estimated from the concentration distribution of the reactant based on the correspondence relationship with the concentration distribution of the reactant between the second electrodes.
It is a state estimation apparatus of a secondary battery.

(Ninth embodiment of the present invention)
In addition, as described above with reference to FIG. 23, when the influence on the drop in voltage between terminals due to the change in reaction resistance that occurs during the charging or discharging of the secondary battery is considered, the reaction in the ion conductor It is more desirable to measure the concentration overvoltage due to the concentration distribution of the substance in the relaxation period immediately after stopping the charging or discharging of the secondary battery, not in the transient period in which charging or discharging of the secondary battery is in progress. . This is also true for embodiments that utilize a reference pole as described above.

Therefore, the state estimation device for a secondary battery according to the ninth embodiment of the present invention provides:
A state estimation device for a secondary battery according to any one of the first to fourth embodiments of the present invention,
A potential flat region in which at least one of the active materials included in the first and second electrodes is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of a material having
A reference electrode is further disposed at an intermediate position between the first electrode and the second electrode in the ion conductor;
The concentration overvoltage estimation unit has the potential flat region in a state corresponding to the potential flat region in a period from when the discharge or charging of the secondary battery is stopped until the battery voltage of the secondary battery becomes stable. A concentration overvoltage due to the reactant estimated based on a potential difference between the electrode including the active material made of a material and the reference electrode, and a concentration distribution of the reactant between the first and second electrodes. Based on the correspondence relationship with the concentration distribution of the reactants between the first and second electrodes in the same state estimated according to the interelectrode diffusion model equation to be defined, the concentration overvoltage is calculated from the concentration distribution of the reactants. presume,
It is a state estimation apparatus of a secondary battery.

(Tenth embodiment of the present invention)
By the way, in the embodiment using the reference electrode, as described above, it is assumed that the reference electrode is disposed just between the first and second electrodes. However, in reality, it is possible that the arrangement position of the reference electrode is shifted from exactly the middle between the first and second electrodes. On the other hand, the concentration overvoltage required in the embodiment using the reference electrode has a large dependence on the arrangement position of the reference electrode. For example, when the active material of the negative electrode is an electrode including an active material having a voltage flat region, when the reference electrode is disposed closer to the negative electrode than the position between the positive electrode and the negative electrode (see FIG. 26). ), The concentration overvoltage between the reference electrode and the negative electrode is underestimated. In addition, for example, it is also affected by battery reaction spots caused by temperature distribution between the positive electrode and the negative electrode.

  As described above, in the secondary battery having a general configuration that is actually used, both of the active materials included in the first and second electrodes have a potential flat region, and these potential flat regions are It may be difficult to satisfy the condition of at least partial overlap. In the embodiment using the reference electrode as a countermeasure against such a situation, it is necessary to strictly control the arrangement position of the reference electrode as described above.

  In view of this situation, the present inventors have intensively studied to find out a method capable of accurately and reliably measuring the concentration overvoltage due to the reactant. As a result, a symmetric cell (symmetry cell) employing the same material having a potential flat region as an active material contained in both the first and second electrodes is created, and this is used for actually measuring the concentration overvoltage. It has been found that by using it as a secondary battery, the concentration overvoltage due to the reactant can be measured accurately and reliably.

That is, the state estimation device for a secondary battery according to the tenth embodiment of the present invention is:
A state estimation device for a secondary battery according to any one of the first to fourth embodiments of the present invention,
Each of the active materials included in the first and second electrodes has a potential flat region that is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of the same material
The concentration overvoltage estimation unit is a concentration overvoltage caused by the reactant measured in a state where potential flat regions of active materials included in the first and second electrodes overlap when discharging or charging the secondary battery, The concentration distribution of the reactant between the first and second electrodes in the same state, estimated according to an interelectrode diffusion model equation that defines the concentration distribution of the reactant between the first and second electrodes. And, based on the correspondence relationship, a concentration overvoltage is estimated from the concentration distribution of the reactant.
It is a state estimation apparatus of a secondary battery.

  As described above, in the state estimation device for a secondary battery according to the present embodiment, a symmetry cell that employs the same material having a potential flat region as an active material included in both the first and second electrodes. During the discharge or charging of the symmetry cell, the content of the reactant in the active material contained in the first and second electrodes corresponds to the potential flat region, and the voltage between the terminals of the symmetry cell is By measuring the change, the concentration overvoltage due to the reactant is measured. As a result, not only the effect of concentration overvoltage caused by the diffusion phenomenon of reactants in the active material, but also the effect of changes in reaction resistance during the charging and discharging of secondary batteries and the influence of unevenness of battery reactions. The concentration overvoltage caused by the reactant can be measured reliably and accurately. In the state estimation device for a secondary battery according to the present embodiment, the correspondence relationship between the concentration overvoltage due to the reactant thus obtained and the concentration distribution of the reactant between the electrodes is obtained in advance, and the correspondence Since the concentration overvoltage is estimated from the concentration distribution of the reactant based on the relationship, the estimation accuracy of the concentration overvoltage can be further improved.

  In the present embodiment, as described above, both of the active materials contained in the first and second electrodes have the electrode potential constant even when the content of the reactant changes. It consists of the same material which has an electric potential flat area | region which is an area | region of content rate. The configuration of such a symmetry cell is different from the configuration of a secondary battery actually used. However, as described above, the factors that affect the moving distance of the reactant in the electrode between the active material of the secondary battery actually used and the active material in the symmetry cell (for example, electrode thickness, porosity, etc.) ) Are equivalent, it can be considered that the concentration overvoltage actually measured in the symmetry cell is equal to the concentration overvoltage in the secondary battery actually used.

(Eleventh embodiment of the present invention)
In addition, as described above with reference to FIG. 23, when the influence on the drop in voltage between terminals due to the change in reaction resistance that occurs during the charging or discharging of the secondary battery is considered, the reaction in the ion conductor It is more desirable to measure the concentration overvoltage due to the concentration distribution of the substance in the relaxation period immediately after stopping the charging or discharging of the secondary battery, not in the transient period in which charging or discharging of the secondary battery is in progress. . This is also true for embodiments utilizing a symmetry cell as described above.

Therefore, the state estimation device for a secondary battery according to the eleventh embodiment of the present invention provides:
A state estimation device for a secondary battery according to any one of the first to fourth embodiments of the present invention,
Each of the active materials included in the first and second electrodes has a potential flat region that is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of the same material
The concentration overvoltage estimation unit has an active material included in the first and second electrodes during a period from when the discharge or charging of the secondary battery is stopped until the battery voltage of the secondary battery is stabilized. The same state estimated according to the concentration overvoltage due to the reactant measured in the state where the potential flat regions overlap, and the interelectrode diffusion model equation defining the concentration distribution of the reactant between the first and second electrodes A concentration overvoltage is estimated from the concentration distribution of the reactant based on a correspondence relationship between the concentration distribution of the reactant between the first and second electrodes in
It is a state estimation apparatus of a secondary battery.

  As described above, the state estimation device for a secondary battery according to the present invention can be applied to other secondary batteries other than the lithium ion battery without particularly limiting the type of load. For example, in a nickel metal hydride battery, the concentration distribution of protons as reactants (reaction participating species) inside the active material is calculated by a diffusion equation, and the open circuit voltage is defined as a function of protons on the active material surface. The state estimation device for a secondary battery according to the invention can be similarly applied.

  Further, a secondary battery state of charge (SOC) estimation device is obtained by combining the concentration distribution estimation of the reactants by the secondary battery state estimation device described above and the SOC estimation method other than that described in this specification. The points that can be realized are also described in a confirming manner.

  Furthermore, the various embodiments disclosed above are merely examples, and the present invention should not be construed as being limited to these embodiments. The scope of the present invention is defined by the terms of the claims, and should be understood to include any modifications within the scope and meaning equivalent to the terms of the claims.

  DESCRIPTION OF SYMBOLS 5 ... Power supply system, 10 ... Secondary battery, 11p ... Positive electrode terminal, 11n ... Negative electrode terminal, 12 ... Negative electrode, 13 ... Negative electrode current collector, 14 ... Separator, 15 ... Positive electrode, 16 ... Positive electrode current collector, 18p ... Positive electrode active material Model, 18p ... Negative electrode active material model, 19 ... Electric double layer capacitor, 20 ... Load, 30 ... Temperature sensor, 32 ... Current sensor, 34 ... Voltage sensor, 50 ... Battery ECU, 52 ... State estimation device, 60 ... Control device , 100 ... diffusion estimation unit, 110 ... open circuit voltage estimation unit, 120 ... current estimation unit, 125 ... current calculation unit, 130 ... battery parameter value setting unit, 140 ... boundary condition setting unit, 160 ... average concentration calculation unit, 170 ... Offset estimation unit, 175... Arithmetic unit, 180... Current integration unit, and 200, 210, 210 #, 220.

Claims (12)

First and second electrodes including an active material containing a reactive substance that contributes to an electrochemical reaction, and an ion conductor that conducts the ionized reactive substance between the first and second electrodes. A state estimation device for a secondary battery comprising:
A voltage detector for detecting a battery voltage between the first and second electrodes;
An in-electrode diffusion estimation unit that estimates the concentration distribution of the reactant according to an active material diffusion model equation that defines the concentration distribution of the reactant within the active material based on a given boundary condition;
An open-circuit voltage estimation unit that estimates the open-circuit voltage between the first and second electrodes based on the concentration of the reactant at the interface between the active material and the electrolyte estimated by the in-electrode diffusion estimation unit When,
Inter-electrode diffusion for estimating the concentration distribution of the reactant between the first and second electrodes according to an inter-electrode diffusion model equation defining the concentration distribution of the reactant between the first and second electrodes An estimation unit;
A concentration overvoltage estimation unit that estimates a concentration overvoltage based on the concentration distribution of the reactant between the first and second electrodes estimated by the interelectrode diffusion estimation unit;
The open voltage, the overvoltage calculated according to the battery current density of the secondary battery, the voltage drop generated according to the battery current density, the concentration overvoltage, and the relationship between the battery voltage. A current estimation unit for estimating a battery current density of the secondary battery according to a voltage-current relationship model equation based on an electrochemical reaction;
With
The current estimation unit includes the battery voltage detected by the voltage detector, the open circuit voltage estimated by the open circuit voltage estimation unit, the concentration overvoltage estimated by the concentration overvoltage estimation unit, and the secondary By substituting the battery parameter value into the voltage-current relationship model equation, the battery current density is calculated,
A boundary for calculating the reaction current density at the interface based on the battery current density estimated by the current estimation unit, and setting the boundary condition at the interface of the active material diffusion model equation according to the calculated reaction current density A condition setting unit;
Secondary battery state estimation device. The state estimation device for a secondary battery according to claim 1,
The voltage-current relationship model equation is obtained by subtracting the product of the model battery current and the reaction resistance and the product of the model battery current and the DC pure resistance from the open-circuit voltage and adding the concentration overvoltage to the battery voltage. Consisting of a linear approximation formula showing
Secondary battery state estimation device. The state estimation device for a secondary battery according to claim 1 ,
A temperature detector for detecting a battery temperature of the secondary battery;
A parameter value setting unit for variably setting the parameter value according to at least the battery temperature;
Further comprising
The parameter value setting unit further variably sets a parameter value representing a diffusion rate in the active material diffusion model formula according to at least the battery temperature.
Secondary battery state estimation device.   The state estimation device for a secondary battery according to claim 2,
  A temperature detector for detecting a battery temperature of the secondary battery;
  A parameter value setting unit for variably setting the parameter value according to at least the battery temperature;
Further comprising
  The parameter value setting unit further variably sets a parameter value representing a diffusion rate in the active material diffusion model formula according to at least the battery temperature.
Secondary battery state estimation device. The state estimation device for a secondary battery according to claim 4 ,
The parameter value setting unit includes the reaction resistance and the pure DC resistance according to the concentration of the reactant at the interface estimated by the in- electrode diffusion estimation unit and the battery temperature detected by the temperature detector. Set to variable,
Secondary battery state estimation device. The state estimation device for a secondary battery according to any one of claims 1 to 5 ,
The concentration overvoltage estimation unit is derived from a model equation representing a relationship between a concentration of the reactant in the ion conductor and a potential of the ion conductor, and the reactant between the first and second electrodes. The concentration overvoltage is estimated from the concentration distribution of the reactant based on the linear approximation of the relational expression between the concentration distribution and the concentration overvoltage.
Secondary battery state estimation device. The state estimation device for a secondary battery according to any one of claims 1 to 5 ,
Each of the active materials included in the first and second electrodes has a potential flat region that is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of material
The concentration overvoltage estimation unit is a concentration overvoltage caused by the reactant measured in a state where potential flat regions of active materials included in the first and second electrodes overlap when discharging or charging the secondary battery, The concentration distribution of the reactant between the first and second electrodes in the same state, estimated according to an interelectrode diffusion model equation that defines the concentration distribution of the reactant between the first and second electrodes. And, based on the correspondence relationship, a concentration overvoltage is estimated from the concentration distribution of the reactant.
Secondary battery state estimation device. The state estimation device for a secondary battery according to any one of claims 1 to 5 ,
Each of the active materials included in the first and second electrodes has a potential flat region that is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of material
The concentration overvoltage estimation unit has an active material included in the first and second electrodes during a period from when the discharge or charging of the secondary battery is stopped until the battery voltage of the secondary battery is stabilized. The same state estimated according to the concentration overvoltage due to the reactant measured in the state where the potential flat regions overlap, and the interelectrode diffusion model equation defining the concentration distribution of the reactant between the first and second electrodes A concentration overvoltage is estimated from the concentration distribution of the reactant based on a correspondence relationship between the concentration distribution of the reactant between the first and second electrodes in
Secondary battery state estimation device. The state estimation device for a secondary battery according to any one of claims 1 to 5 ,
A potential flat region in which at least one of the active materials included in the first and second electrodes is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of a material having
A reference electrode is further disposed at an intermediate position between the first electrode and the second electrode in the ion conductor;
The concentration overvoltage estimation unit is configured to provide a potential difference between the reference electrode and an electrode including the active material made of a material having the potential flat region in a state corresponding to the potential flat region when the secondary battery is discharged or charged. And the first and second states in the same state estimated according to an interelectrode diffusion model equation defining a concentration distribution of the reactants between the first and second electrodes. A concentration overvoltage is estimated from the concentration distribution of the reactant based on the correspondence relationship with the concentration distribution of the reactant between the second electrodes.
Secondary battery state estimation device. The state estimation device for a secondary battery according to any one of claims 1 to 5 ,
A potential flat region in which at least one of the active materials included in the first and second electrodes is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of a material having
A reference electrode is further disposed at an intermediate position between the first electrode and the second electrode in the ion conductor;
The concentration overvoltage estimation unit has the potential flat region in a state corresponding to the potential flat region in a period from when the discharge or charging of the secondary battery is stopped until the battery voltage of the secondary battery becomes stable. A concentration overvoltage due to the reactant estimated based on a potential difference between the electrode including the active material made of a material and the reference electrode, and a concentration distribution of the reactant between the first and second electrodes. Based on the correspondence relationship with the concentration distribution of the reactants between the first and second electrodes in the same state estimated according to the interelectrode diffusion model equation to be defined, the concentration overvoltage is calculated from the concentration distribution of the reactants. presume,
Secondary battery state estimation device. The state estimation device for a secondary battery according to any one of claims 1 to 5 ,
Each of the active materials included in the first and second electrodes has a potential flat region that is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of the same material
The concentration overvoltage estimation unit is a concentration overvoltage caused by the reactant measured in a state where potential flat regions of active materials included in the first and second electrodes overlap when discharging or charging the secondary battery, The concentration distribution of the reactant between the first and second electrodes in the same state, estimated according to an interelectrode diffusion model equation that defines the concentration distribution of the reactant between the first and second electrodes. And, based on the correspondence relationship, a concentration overvoltage is estimated from the concentration distribution of the reactant.
Secondary battery state estimation device. The state estimation device for a secondary battery according to any one of claims 1 to 5 ,
Each of the active materials included in the first and second electrodes has a potential flat region that is a region of the content of the reactant in which the electrode potential is constant even when the content of the reactant changes. Made of the same material
The concentration overvoltage estimation unit has an active material included in the first and second electrodes during a period from when the discharge or charging of the secondary battery is stopped until the battery voltage of the secondary battery is stabilized. The same state estimated according to the concentration overvoltage due to the reactant measured in the state where the potential flat regions overlap, and the interelectrode diffusion model equation defining the concentration distribution of the reactant between the first and second electrodes A concentration overvoltage is estimated from the concentration distribution of the reactant based on a correspondence relationship between the concentration distribution of the reactant between the first and second electrodes in
Secondary battery state estimation device.

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