Battery state estimation device, battery state estimation method, and battery state estimation program

Abstract

This battery state estimation device comprises: a negative electrode potential calculation unit 221 that calculates a negative electrode potential that is a difference between a liquid phase potential and a solid phase potential of a negative electrode; an equilibrium potential calculation unit 222 that calculates an alkali metal ion concentration in an electrolyte at least in the negative electrode by using an electrochemical model of a battery, and calculates an equilibrium potential of a deposition reaction of the alkali metal on the basis of the alkali metal ion concentration and the temperature of the battery; and a deposition prediction unit 223 that predicts deposition of the alkali metal in the negative electrode on the basis of a magnitude relationship between the negative electrode potential and the equilibrium potential.

Description

Battery state estimation device, battery state estimation method, and battery state estimation program

[0001] This disclosure relates to a battery state estimation device, a battery state estimation method, and a battery state estimation program.

[0002] With the widespread adoption of rechargeable batteries, their applications have expanded from consumer electronics such as PCs and other electronic devices to EVs (electric vehicles), PHEVs (plug-in hybrid vehicles), automotive starter batteries, electric assist bicycles, and industrial backup power supplies. In the future, their applications are expected to expand to power supplies for data centers used in AI generation, agricultural machinery, construction machinery, electric ships, and electric aircraft. Lithium-ion rechargeable batteries are considered suitable for these applications. Generally, lithium-ion rechargeable batteries have a higher energy density and operating voltage compared to other rechargeable batteries, making them suitable for miniaturization and high-voltage generation.

[0003] In batteries that use lithium ions as reactants in electrochemical reactions, it is known that metallic lithium can be deposited on the surface of the negative electrode. This phenomenon is called lithium deposition. Lithium deposition can lead to a decrease in battery capacity, an increase in internal resistance, and a decrease in thermal safety, so it is desirable to avoid it. In response, battery developers have been working on setting charging conditions that make lithium deposition less likely, designing batteries, and developing materials. For example, Non-Patent Literature 1 discusses the deposition potential of metallic lithium at 0V vs. Li / Li ＋ Therefore, it has been suggested that lithium deposition occurs when the negative electrode potential falls below 0V.

[0004] Japanese Patent Publication No. 2014-32826, Japanese Patent Publication No. 2020-162216, Japanese Patent Publication No. 2020-77464

[0005] Hidesato SARUWATARI et. al., “Overview and Application of Lithium Ion Battery”, Journal of the Japan Society of Applied Electromagnetics, Vol 24, No. 4 (2016), P287-292

[0006] Conditions that tend to cause the negative electrode potential to fall below 0V include high charging current and low temperature. Therefore, it is conceivable to design charging conditions through simulation that prevent the negative electrode potential from falling below 0V. However, the inventors of this invention have conducted extensive research on lithium deposition at the negative electrode and have confirmed that lithium deposition occurs even when the negative electrode potential does not fall below 0V during charging. In other words, conventional knowledge does not necessarily provide sufficient accuracy in estimating lithium deposition for further improving battery performance, and there is room for improvement in avoiding lithium deposition. Furthermore, even when alkali metals other than lithium are used as reactants, it is desirable to estimate the deposition of alkali metals with high accuracy and avoid such deposition.

[0007] This disclosure is made in light of these circumstances, and one of its purposes is to provide a technique for improving the accuracy of alkali metal deposition estimation.

[0008] To solve the above problems, one aspect of the present disclosure is a battery state estimation device for estimating the electrochemical state of a battery having a negative electrode containing an active material capable of intercalating and deintercalating alkali metal ions, and an electrolyte. This battery state estimation device includes a negative electrode potential calculation unit that calculates the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode; an equilibrium potential calculation unit that calculates the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery, and calculates the equilibrium potential of the alkali metal deposition reaction based on the alkali metal ion concentration and the temperature of the battery; and a deposition prediction unit that predicts the deposition of alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential.

[0009] Another aspect of this disclosure is a battery state estimation method for estimating the electrochemical state of a battery having a negative electrode containing an active material capable of intercalating and deintercalating alkali metal ions, and an electrolyte. This battery state estimation method includes calculating the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode; calculating the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery; calculating the equilibrium potential of the alkali metal deposition reaction based on the alkali metal ion concentration and the battery temperature; and predicting the deposition of alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential.

[0010] Another aspect of this disclosure is a battery state estimation program for estimating the electrochemical state of a battery having a negative electrode containing an active material capable of intercalating and deintercalating alkali metal ions, and an electrolyte. This battery state estimation program causes a computer to perform the following processes: calculate the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode; calculate the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery, calculate the equilibrium potential of the alkali metal deposition reaction based on the alkali metal ion concentration and the battery temperature; and predict the deposition of alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential.

[0011] Furthermore, any combination of the above components, as well as any conversion of the expressions of this disclosure between devices, systems, methods, computer programs, etc., are also valid forms of this disclosure.

[0012] According to this disclosure, the accuracy of estimating alkali metal deposition can be improved.

[0013] This is a schematic diagram illustrating a battery pack according to an embodiment. It shows the relationship between lithium ion concentration and the deposition potential of metallic lithium, and the relationship between battery temperature and the deposition potential of metallic lithium. This is a diagram showing an example of calculation results using an electrochemical model. This is a schematic diagram of a grid-divided simulation model.

[0014] The present disclosure will be described below with reference to the drawings, based on preferred embodiments. The embodiments are illustrative and not limiting, and not all features or combinations thereof described in the embodiments are necessarily essential to the present disclosure. The same or equivalent components, members, and processes shown in each drawing are denoted by the same reference numerals, and redundant descriptions are omitted where appropriate. The scale and shape of each part shown in each drawing are set for convenience to facilitate explanation and are not to be interpreted restrictively unless otherwise specified. Furthermore, where terms such as "first," "second," etc. are used in this specification or claims, unless otherwise specified, these terms do not indicate any order or importance, but are used to distinguish one configuration from another. In addition, some components that are not important for explaining the embodiments are omitted in each drawing.

[0015] Figure 1 is a schematic diagram illustrating a battery pack 1 according to an embodiment. The battery pack 1 includes a battery pack 10 and a battery management device 20. The battery pack 1 can supply power to a load 2. For example, if the load 2 is a server or storage in a data center, the battery pack 1 acts as a backup power source for the server or storage. When the battery pack 1 is installed in a mobility device such as an EV, the main load 2 is an inverter and a motor.

[0016] The charger 4 is connected to the commercial power grid 3 and converts the AC power input from the commercial power grid 3 into DC power of a predetermined voltage or current and supplies it to the battery pack 1. The charger 4 may be built into the battery pack 1.

[0017] The battery pack 10 includes a plurality of batteries E1-En connected in series. Hereinafter, batteries E1-En will be collectively referred to as battery E. The number of batteries E connected in series is determined by the specifications of load 2. Batteries E can be lithium-ion batteries, nickel-metal hydride batteries, lead-acid batteries, etc. Batteries E may be primary or secondary batteries. In this embodiment, we assume the use of lithium-ion batteries (nominal voltage: 3.6-3.7V). In the series stage of each battery E, a plurality of batteries E may be connected in parallel to increase the capacity. Each battery E has an electrode body in which a negative electrode, a separator, and a positive electrode are stacked, and an electrolyte impregnated into the electrode body. The negative electrode E contains an active material capable of intercalating and deintercalating alkali metal ions. In lithium-ion batteries, alkali metal ions are lithium ions. Since the structure of battery E is well known, it is omitted from the illustration and detailed description.

[0018] A switch SW1 is inserted into the power line connecting the battery pack 10 to the load 2 or charger 4 to switch between continuity and non-continuity with the load 2 or charger 4. A semiconductor switch or relay can be used for switch SW1.

[0019] The battery management device 20 includes a measurement unit 21 and a control unit 22. The measurement unit 21 is composed of an AFE (Analog Front End) IC or an ASIC (Application Specific Integrated Circuit). The control unit 22 is composed of a microcomputer. The microcomputer includes a CPU, RAM, ROM, and I / O. The control unit 22 may also be composed of a SoC (System on a Chip) that further includes any IC such as a GPU (Graphics Processing Unit), NPU (Neural Network Processing Unit), ASIC (Application Specific Integrated Circuit), or FPGA (Field Programmable Gate Array). In this embodiment, the control unit 22 implements the function of a battery state estimation device that estimates the electrochemical state of battery E. In other words, the control unit 22 corresponds to the battery state estimation device according to this embodiment.

[0020] The measurement unit 21 is connected to each node of the multiple series-connected batteries E1-En by multiple voltage measurement lines, and measures the voltage of each battery E by measuring the voltage between two adjacent voltage measurement lines. In other words, the measurement unit 21 functions as a voltage sensor that measures the terminal voltage between the positive terminal and the negative terminal of the battery E.

[0021] The measurement unit 21 includes a multiplexer and an A / D converter. The multiplexer outputs the voltages of multiple batteries E1-En to the A / D converter in a predetermined order. The A / D converter converts the analog voltages input from the multiplexer into digital values. The measurement unit 21 transmits the voltage values ​​of each battery E, converted into digital values, to the control unit 22 via a serial communication interface.

[0022] The measurement unit 21 measures the current flowing through the battery pack 10. A shunt resistor Rs is connected to the power line connecting the battery pack 10 to the load 2 or charger 4. A differential amplifier (not shown) amplifies the voltage across the shunt resistor Rs and outputs it to the A / D converter in the measurement unit 21. The A / D converter converts the analog voltage indicating the current flowing through the battery pack 10, which is input from the differential amplifier, into a digital value. The measurement unit 21 transmits the digitally converted current value to the control unit 22 via a serial communication interface.

[0023] A temperature sensor T1 is installed on the surface of the battery pack 10. The temperature sensor T1 is, for example, a thermistor. The divided voltage of the temperature sensor T1 and a voltage divider resistor (not shown) is input to the measurement unit 21. The A / D converter in the measurement unit 21 converts the input analog voltage representing the temperature into a digital value. The measurement unit 21 transmits the converted digital temperature value to the control unit 22 via a serial communication interface.

[0024] The control unit 22 includes at least a negative electrode potential calculation unit 221, an equilibrium potential calculation unit 222, a deposition prediction unit 223, a measurement value acquisition unit 224, a measurement voltage difference calculation unit 225, an electrochemical model calculation unit 226, and a calibration unit 227.

[0025] The negative electrode potential calculation unit 221 calculates the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode. The equilibrium potential calculation unit 222 calculates the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery E. Then, based on the alkali metal ion concentration and the temperature of the battery, it calculates the equilibrium potential of the alkali metal deposition reaction. The deposition prediction unit 223 predicts the deposition of alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential.

[0026] In this embodiment, the negative electrode potential calculation unit 221 calculates the negative electrode potential using an electrochemical model. The equilibrium potential calculation unit 222 calculates the lithium ion concentration and the temperature of the battery E using an electrochemical model. The deposition prediction unit 223 then predicts the deposition of metallic lithium at the negative electrode. The negative electrode potential calculation unit 221, the equilibrium potential calculation unit 222, and the deposition prediction unit 223 function as state estimators that estimate the state of the battery E.

[0027] The measurement value acquisition unit 224 acquires the voltage value of each battery E, the current value flowing through the battery pack 10, and the temperature value of the battery pack 10, which are received from the measurement unit 21, as measured or observed values ​​of the battery state. In this embodiment, as an example, the temperature of the battery pack 10 is treated as the temperature of each battery E. The temperature sensor T1 may be capable of individually measuring the temperature of each battery E. In addition, multiple temperature sensors T1 may be installed on each battery E. The measured voltage difference calculation unit 225 calculates the difference between the voltage of each battery E observed in the current time step and the voltage of each battery E observed in the previous time step as a measured or observed value.

[0028] The unit time step width depends on the type of load 2 and the performance of the control unit 22, but is set to, for example, 1 second or less. The measured voltage difference calculation unit 225 outputs, for example, the smallest voltage difference, the largest voltage difference, the average value of the multiple voltage differences, or the median value of the multiple voltage differences as the measured voltage difference. Alternatively, a voltage difference processed using a statistical method may be used as the measured value. Hereinafter, the voltage measured by the voltage sensor will be referred to as the measured voltage. The temperature of the battery E measured by the temperature sensor T1 will be referred to as the measured temperature. The difference between the measured voltage measured at the current time step and the measured voltage measured at the previous time step will be referred to as the measured voltage difference.

[0029] The electrochemical model calculation unit 226 calculates the voltage and temperature of each battery E using the electrochemical model used by the negative electrode potential calculation unit 221 and the equilibrium potential calculation unit 222. The electrochemical model calculation unit 226 also calculates the difference between the voltage at the current time step and the voltage at the previous time step. The electrochemical model calculation unit 226 then obtains the calculated voltage, temperature, and difference as state estimates. Hereinafter, the voltage, temperature, and voltage difference calculated using the electrochemical model will be referred to as estimated voltage, estimated temperature, and estimated voltage difference, respectively. Note that the functions of the electrochemical model calculation unit 226 may be implemented in at least one of the negative electrode potential calculation unit 221 and the equilibrium potential calculation unit 222.

[0030] As an example, when the electrochemical model calculation unit 226 calculates the estimated voltage difference, it assumes that the open-circuit voltage at the current time step is equal to the open-circuit voltage at the previous time step, and that the concentration overvoltage at the current time step is equal to the concentration overvoltage at the previous time step, and calculates the estimated voltage difference. That is, the electrochemical model calculation unit 226 calculates the estimated voltage difference as the difference between the sum of the activation overvoltage and ohm overvoltage at the current time step and the sum of the activation overvoltage and ohm overvoltage at the previous time step.

[0031] The calibration unit 227 corrects the state estimation value obtained by the electrochemical model calculation unit 226 by using the measurement values obtained by the measurement value acquisition unit 224 and the measured voltage difference calculation unit 225. The calibration unit 227 may correct the state estimation value by using any one of a Kalman filter, an extended Kalman filter, an unscented Kalman filter, an ensemble Kalman filter, or a particle filter. A protection unit (not shown) controls, for example, the switch SW1 to be turned off when each parameter corrected by the Kalman filter exceeds a preset threshold value.

[0032] Hereinafter, the operation of the control unit 22 as the battery state estimation device will be described in detail. As described above, the inventors have confirmed that lithium deposition occurs at the negative electrode even when the negative electrode potential does not fall below 0 V during charging of the battery E. In addition, it has been confirmed that lithium deposition tends to occur when the battery E is at a low temperature. From this, it has been conceived that there is room for improvement in the estimation accuracy of lithium deposition when based on the recognition that the deposition potential of metallic lithium is uniformly 0 V.

[0033] The reason why the equilibrium potential in the reaction of lithium deposition, that is, the deposition potential of metallic lithium does not uniformly become 0 V is as follows. That is, the reaction formula: Li ⇔ Li ＋ + e － The Nernst equation in is represented by Equation (1).

[0034] In Equation (1), E ｅｑ is the equilibrium potential in the reaction of lithium deposition, E ｅｑ ０ is the standard equilibrium potential, n is the number of participating electrons, F is the Faraday constant, R is the gas constant, T is the absolute temperature, [Li ＋ is the concentration of Li ＋ [[ID=2,3]]is the concentration of Li.

[0035] In the Nernst equation, the number of participating electrons n is 1 in the case of a lithium ion battery. Also, the standard equilibrium potential E ｅｑ ０ which is the first term of the Nernst equation, often becomes more positive as the temperature of the electrode decreases. For example, the standard equilibrium potential E ｅｑ０ The voltage is defined as 0 [V] when the temperature of the lithium-ion secondary battery is the standard state of 25°C, and changes with temperature at temperatures other than 25°C, decreasing as the temperature increases. For the value of the first term of the Nernst equation, for example, a map that associates the value of the first term with the battery temperature, or a table listing the function of the value of the first term with the battery temperature may be stored in the equilibrium potential calculation unit 222, etc. The second term of the Nernst equation takes on a positive or negative value depending on the battery temperature and the lithium ion concentration in the electrolyte. From the Nernst equation, the equilibrium potential of the lithium deposition reaction should be a function of temperature and concentration. In particular, when the battery temperature becomes low enough to fall below the freezing point of the electrolyte and the electrolyte freezes, the lithium ion concentration in the electrolyte may rise rapidly due to the principle of freeze-concentration. In this case, the equilibrium potential E in the lithium deposition reaction ｅｑ The temperature rises, making precipitation reactions more likely. Freezing of the electrolyte is related to phenomena such as freezing point depression, supercooling, and supersaturation.

[0036] Therefore, the rate of increase in lithium ion concentration may be stored as a table in the equilibrium potential calculation unit 222, etc. In other words, the equilibrium potential calculation unit 222 calculates the standard equilibrium potential E of the first term of the Nernst equation. ｅｑ ０ The equilibrium potential may be calculated taking into account that it can change depending on the battery temperature. The equilibrium potential calculation unit 222, when the battery temperature is below the freezing point of the electrolyte, takes into account the increase in alkali metal ion concentration due to the principle of freezing and concentrating the electrolyte and the battery temperature to calculate the equilibrium potential E of the alkali metal deposition reaction. ｅｑ This calculates the equilibrium potential E. ｅｑ The calculation of the alkali metal ion concentration and the battery temperature are taken into account. For example, when the lithium ion concentration becomes k times (1 < k) due to freeze concentration, the equilibrium potential E of the lithium deposition reaction ｅｑ The equilibrium potential E is expressed by the following equation (1a). The equilibrium potential calculation unit 222 uses equation (1a), which is the Nernst equation that takes into account the increase in alkali metal ion concentration due to the principle of freeze concentration, to calculate the equilibrium potential E ｅｑ The following is calculated. From equation (1a), when the lithium ion concentration increases by k times due to freeze concentration, the equilibrium potential E ｅｑ It is understandable that it will rise.

[0037]

[0038] Furthermore, the Butler-Volmer equation, which expresses the relationship between reaction rate and activation overpotential, is represented by equation (2).

[0039] In equation (2), I is the current, S is the reaction surface area of ​​the electrode, and k ｃ k is the oxidation reaction rate constant. ａ is the reduction reaction rate constant, α is the transfer coefficient, n is the number of electrons involved (1 in the case of lithium-ion batteries), F is the Faday constant, R is the gas constant, T is the absolute temperature, [Li ＋ ] is Li in the electrolyte ＋ The concentration of η is the activation overpotential.

[0040] The activation overpotential η is expressed by equation (3): η = φ ｓ -φ ｌ -E ｅｑ (3) In equation (3), φ ｓ φ is the solid-phase potential. ｌ E is the liquid phase potential. ｅｑ V is the equilibrium potential in the lithium deposition reaction. Also, the negative electrode potential V is... ａ is, V ａ = φ ｓ -φ ｌ That is the case.

[0041] In equation (2), k ｃ exp(αnFη / RT) represents the dissolution reaction rate of metallic lithium. Also, k ａ exp{(1-α)nFη / RT} represents the deposition reaction rate of metallic lithium. Therefore, the negative electrode potential when the lithium deposition reaction is in equilibrium in the electrolyte is the potential at which I = 0 in the Butler-Volmer equation. On the other hand, if lithium deposition occurs at a negative electrode potential of 0V, then I should be 0 when η = 0V. However, when η is 0, the Butler-Volmer equation becomes I = S(k ｃ -k ａ [Li ＋ ]) and the right-hand side is not 0. From this, we can see that the negative electrode potential of 0V is not necessarily the deposition potential of metallic lithium.

[0042] The inventors conceived that the accuracy of lithium deposition estimation can be improved by changing the deposition potential of metallic lithium, which is an indicator for estimating lithium deposition, according to the current flowing through battery E and the temperature of battery E. Here, the current and the deposition potential of metallic lithium are not directly related. On the other hand, as the current increases, the lithium ion concentration in the electrolyte at the negative electrode increases. Therefore, the lithium ion concentration in the electrolyte was used to calculate the deposition potential of metallic lithium. In other words, the deposition potential of metallic lithium is a two-variable function of lithium ion concentration and battery temperature. Also, the negative electrode potential V ａ We define that metallic lithium is deposited when the solid phase potential falls below the deposition potential of metallic lithium. ｓ , liquid phase potential φ ｌ , and negative electrode potential V ａ It has been confirmed that this value fluctuates during actual operation of the machine and during simulation calculations, depending on factors such as current, temperature, and lithium ion concentration in the electrolyte.

[0043] For example, as shown in Figure 2, it is conceivable to employ a function such that the deposition potential of metallic lithium increases as the lithium ion concentration in the electrolyte increases, and decreases as the temperature increases. Figure 2 is a schematic diagram showing the relationship between lithium ion concentration and the deposition potential of metallic lithium, and the relationship between the battery temperature and the deposition potential of metallic lithium. The lithium ion concentration may be calculated using an activity coefficient to correct for activity. Alternatively, instead of a function, the deposition potential of metallic lithium may be determined using a map that correlates the deposition potential of metallic lithium with the reaction field temperature and the lithium ion concentration in the electrolyte. Such functions and maps can be pre-set and stored based on experiments and simulations conducted by the designer.

[0044] Here, the negative electrode potential can be calculated from the voltage sensor's measurement. The reaction field temperature, i.e., the battery temperature, can be measured with a temperature sensor. However, there is no practical method for measuring the lithium ion concentration in the electrolyte. Therefore, at least for the lithium ion concentration in the electrolyte, it is necessary to use an estimated value calculated using the electrochemical model described later. In this embodiment, the negative electrode potential and temperature are also obtained using the electrochemical model. The electrochemical model will be described in detail below.

[0045] First, we will explain the solid-phase diffusion of lithium ions using an electrochemical model and the calculation of the solid-phase potentials of the positive and negative electrodes. The solid-phase diffusion of lithium ions in the positive and negative electrode active materials can be obtained by solving the diffusion equation shown in equation (4). This solid-phase diffusion equation may also be calculated considering the diffusion distribution in each component by using a computational grid, which will be described later.

[0046] In equation (4), C ｓ is the lithium ion concentration in the solid phase of the negative and positive electrodes, t is the time, and D is the lithium ion concentration in the solid phase of the negative and positive electrodes. ｓ r is the diffusion coefficient of lithium ions within the solid phases of the negative and positive electrodes, and r is the radial distance between the active material particles of the positive and negative electrodes.

[0047] When R is the radius of the active material particles of the positive and negative electrodes, the material flux Jr of lithium ions at the position where r = R, i.e., at the outermost edge of the active material particles, is expressed by equation (5). In equation (5), D ｓ The diffusion coefficient of lithium ions in the solid phase of the negative and positive electrodes is C. ｓ r is the lithium ion concentration in the solid phase of the negative and positive electrodes, and r is the radial distance between the active material particles of the positive and negative electrodes.

[0048] In the electron-conducting parts such as the positive electrode active material, negative electrode active material, and current collector foil, Ohm's law regarding electron conduction is applied.

[0049] In equation (6), i ｓ σ is the solid-phase current density, i.e., the electron current density. ｓΦ is the solid-phase electronic conductivity. ｓ x is the solid-phase potential, and x is the position in the thickness direction of the battery.

[0050] solid phase current density i ｓ i is the reaction current density per unit volume. ｖ It can be expressed by the differential equation (7) using .

[0051] In equation (7), x is the position in the thickness direction of the battery.

[0052] Based on the above calculations, the solid-phase diffusion of lithium ions and the solid-phase potentials Φ of the positive and negative electrodes are determined. ｓ It is possible to calculate this.

[0053] Next, we will explain how to calculate the lithium ion concentration and liquid phase potential in the liquid phase using an electrochemical model. The lithium ion concentrations in the electrolyte portions of the negative electrode, positive electrode, and separator can be obtained by solving the Nernst-Planck equation, which is represented by equation (8). In equation (8), N is the ion flux, D ｌ c is the diffusion coefficient of ions. ｌ θ is the ion concentration, z is the ion valence, u is the ion mobility, F is the Faraday constant, Φ ｌ x is the liquid phase potential, and x is the position in the thickness direction of the battery. Diffusion coefficient D ｌ The mobility u takes on different values ​​depending on the structure of the gaps in the negative electrode, positive electrode, and separator.

[0054] The outflow rate R of the ion flux can be expressed by equation (9), using the lithium ion flux at the outermost periphery of the active material particles described above, and the specific surface area per unit volume a of the positive and negative electrodes. Note that a takes different values ​​for the positive and negative electrodes. Also, R is usually 0 in a separator.

[0055] In equation (9), N is the ion flux, x is the position in the thickness direction of the battery, R is the outflow rate of the ion flux, a is the specific surface area per unit volume of the positive and negative electrodes, Jr is the mass flux of lithium ions, z is the valence of the ions, F is the Faday constant, i ｖ This is the reaction current density per unit volume.

[0056] liquid phase current density i ｌ And from Ohm's law, the liquid phase potential Φ ｌ This can be obtained by solving equations (10) and (11).

[0057] In equation (10), i ｌ is the liquid phase current density, z is the valence of the ions, F is the Faraday constant, and N is the ion flux.

[0058] In equation (11), σ ｌ x is the ionic conductivity of the liquid phase, and it takes different values ​​for the negative electrode, positive electrode, and separator. x is the position in the thickness direction of the battery.

[0059] liquid phase current density i ｌ i is the reaction current density per unit volume. ｖ It can be expressed by the differential equation (12) using .

[0060]

[0061] Using the above formula, the lithium ion concentration and liquid phase potential in the liquid phase can be calculated.

[0062] Next, we will explain the analysis of the reactions occurring between the negative and positive electrodes using an electrochemical model. The reactions occurring between the solid and liquid phases at the negative and positive electrodes can be obtained by solving the Butler-Volmer equation, represented by equation (13).

[0063] In equation (13), i ｖ is the reaction current density per unit volume, a is the specific surface area per unit volume, i ０ θ is the exchange current density, α is the transfer coefficient, n is the number of reaction electrons, F is the Faday constant, R is the gas constant, and T is the temperature. Also, η is the activation overpotential, and as shown in equation (3) above, η = φ ｓ -φ ｌ -E ｅｑ，ｉ It is represented by φ. ｓ φ is the solid-phase potential. ｌ E is the liquid phase potential. ｅｑ，ｉ This is the equilibrium potential in the lithium ion insertion and removal reaction.

[0064] equilibrium potential Ｅｅｑ，ｉThis is a function of the lithium ion concentration at the outermost periphery of the active material particles (i.e., r=R), which is generally calculated using solid-phase diffusion, and can be expressed by equation (14).

[0065] In equation (14), E ｅｑ，ｉ C is the equilibrium potential in lithium ion insertion and removal reactions. ｓ This represents the lithium ion concentration within the solid phase of the negative and positive electrodes.

[0066] Generally, equilibrium potential E ｅｑ，ｉ This is the slope of the function represented by equation (15).

[0067] Next, we will explain how to calculate the heat generated by a battery, that is, the battery temperature, using an electrochemical model. The heat generated by a battery includes heat generated due to resistance, as shown in equation (16), and heat generated due to chemical reactions, as shown in equation (17).

[0068] In equation (16), Q ｉｒ This represents the amount of heat generated, corresponding to the Joule thermal volume density, and heat is generated during both charging and discharging, meaning the value is positive. Also, i ｌ Φ is the liquid phase current density. ｌ is the liquid phase potential, i ｓ φ is the solid-phase current density. ｓ i is the solid phase potential. ｖ η is the reaction current density per unit volume, and η is the activation overpotential.

[0069] In equation (17), Q ｒ This is the amount of heat generated from the entropy heat-generating volume density, and the heat generation and heat dissipation switch between charging and discharging. Also, i ｖ is the reaction current density per unit volume, T is the absolute temperature, and E ｅｑ，ｉ This is the equilibrium potential in the lithium ion insertion and removal reaction.

[0070] The battery temperature may also be calculated by considering the heat generation distribution in each component using the computational grid described later. However, it is also possible to treat the battery as a single temperature point and calculate its representative temperature. In this case, the heat transfer formula shown in equation (18) can be used.

[0071] In Equation (18), ρ is the mass density, C ｐ is the volume specific heat, V ｏｌ is the volume of the battery, T is the representative temperature of the battery, t is the time, Q ｉｒ is the heat generation amount shown in Equation (16), Q ｒ is the heat generation amount shown in Equation (17), the integral is the volume integral over the battery volume, h is the heat transfer coefficient, S is the surface area of the battery, T ０ is the temperature outside the battery.

[0072] By using the electrochemical model described above, for example, calculation results as shown in FIG. 3 can be obtained. FIG. 3 is a diagram showing an example of the calculation results using the electrochemical model. Therefore, the negative electrode potential calculation unit 221 can calculate the negative electrode potential V ａ . Further, the equilibrium potential calculation unit 222 can calculate the lithium ion concentration in the electrolytic solution at the negative electrode and the temperature of the battery using the electrochemical model. Then, the equilibrium potential calculation unit 222 uses a two-variable function or a map of the lithium ion concentration and temperature with respect to the precipitation potential of metallic lithium, in other words, the equilibrium potential E ｅｑ to calculate the equilibrium potential E ｅｑ from the calculated lithium ion concentration and temperature.

[0073] Then, the precipitation prediction unit 223 determines the magnitude relationship between the negative electrode potential V ａ and the equilibrium potential E ｅｑ , and determines that metallic lithium precipitates when the negative electrode potential V ａ is less than or equal to the equilibrium potential E ｅｑ . Alternatively, the precipitation prediction unit 223 may determine that metallic lithium precipitates when the negative electrode potential V ｅｑ falls below a threshold value obtained by adding a predetermined margin to the equilibrium potential E ａ . When the precipitation prediction unit 223 predicts the precipitation of metallic lithium, the control unit 22 suppresses the decrease of the negative electrode potential V ａ or executes protection control to increase the negative electrode potential V ａ above the equilibrium potential E ｅｑ in order to avoid or suppress lithium precipitation. As the protection control, for example, the equilibrium potential E ｅｑ<Negative potential V ａ You may also use a charging current value that results in the equilibrium potential E ｅｑ <Negative potential V ａ The maximum charging current value among the resulting charging current values ​​may be used for charging. The battery state estimation device according to this disclosure can be used to calculate the maximum charging current value. Another example of protective control is the equilibrium potential E ｅｑ <Negative potential V ａ The battery temperature may be adjusted to achieve this. Examples of such temperature adjustment include raising the battery temperature using a heater or other heating device, or maintaining the battery above a predetermined temperature using a known temperature control mechanism. This "predetermined temperature" is, for example, the melting point of the electrolyte. The control unit 22, as a battery state estimation device, can also predict deposition for alkali metals other than lithium using a similar method.

[0074] Next, we will explain the computational grid used when calculating each parameter using the electrochemical model. Figure 4 is a schematic diagram of the grid-divided simulation model. In this embodiment, the equilibrium potential calculation unit 222 divides the negative electrode into multiple computational grids M and calculates the lithium ion concentration in each computational grid. In other words, the equilibrium potential calculation unit 222 calculates the positional distribution of lithium ion concentration using a grid-divided simulation model (Newman model). Then, using this positional distribution, the equilibrium potential E ｅｑ Calculate.

[0075] For example, as shown in Figure 4, the equilibrium potential calculation unit 222 divides the negative electrode into five parts in the thickness direction, that is, in the stacking direction of the negative electrode, separator, and positive electrode, and generates five computational grids M (mesh, elements). Then, in each computational grid M, the lithium ion concentration c ｌ The following is calculated. The battery temperature may also be calculated in each computational grid M. This improves the accuracy of lithium deposition estimation compared to using a zero-dimensional model that does not consider the lithium ion concentration and temperature distribution in the thickness direction of the negative electrode. Note that the number of computational grids M is not limited to five and can be set as appropriate. The number of computational grids M is two or more, for example, five to ten.

[0076] The deposition prediction unit 223 may predict lithium deposition based on the location in the negative electrode where lithium deposition is most likely to occur. For example, the deposition prediction unit 223 may use the negative electrode potential V in each computational grid M as a reference. ａ and equilibrium potential E ｅｑ Lithium deposition can also be predicted based on the smallest difference among the differences. That is, the negative electrode potential V in each computational grid M of the negative electrode. ａ and equilibrium potential E ｅｑ The battery is designed and controlled so that the minimum difference within that range is greater than zero. This makes it possible to more reliably avoid the occurrence of lithium deposition.

[0077] Furthermore, the battery state estimation device of this embodiment calculates various values ​​for the separator and positive electrode using a lumped-parameter model. Generating multiple computational grids M for the separator and positive electrode would increase the computation time, which could be detrimental to performing real-time calculations in line with the actual operation of the device. Also, when estimating lithium deposition during charging at the negative electrode, the detailed distribution of various values ​​at the separator and positive electrode is not important. Therefore, a simulation model is used in which only the negative electrode is meshed, and a simulation model is used in which the separator and positive electrode are assumed to be uniform in the thickness direction. This makes it possible to improve the estimation accuracy of lithium deposition at the negative electrode while suppressing redundancy in the estimation time.

[0078] Examples of values ​​that can be calculated using a lumped-parameter model for the separator and positive electrode include resistance and overvoltage. For example, if the thickness of the positive electrode is x ｐｏｓ , the thickness of the separator is x ｓｅｐ , the positive electrode's ohm resistance is R Ｏｈｍ，ｐｏｓ The reaction resistance of the positive electrode is R. ａｃｔ，ｐｏｓ The ohm resistance of the separator is R Ｏｈｍ，ｓｅｐ , the positive electrode ohm overvoltage η Ｏｈｍ，ｐｏｓ , the ohm overvoltage of the separator is R Ｏｈｍ，ｓｅｐ , the reaction overpotential of the positive electrode is η ａｃｔ，ｐｏｓ If I is the total current flowing through the battery, then equations (19) to (23) hold. Using these equations, the overvoltages of the separator and the positive electrode can be determined without compromising the accuracy of the positional distribution in the calculation of various quantities at the negative electrode.

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] Furthermore, the deposition prediction unit 223 measures the negative electrode potential V at multiple points in the in-plane direction perpendicular to the stacking direction of the negative electrode, separator, and positive electrode. ａ and equilibrium potential E ｅｑ Lithium deposition may be predicted based on the smallest difference among the differences between the two. For example, in the case of a battery equipped with a cylindrical wound electrode body, the distribution of various quantities within the electrode surface is considered in the in-plane direction perpendicular to the stacking direction of the negative electrode, separator, and positive electrode, that is, in the direction of extension of the electrode surface, assuming that the electrode body is unfolded in a planar state. In particular, as the size of the battery increases, in other words, as the area of ​​the electrode surface increases, the variation in lithium ion concentration in the electrolyte within the electrode surface tends to increase. Therefore, the negative electrode potential V at multiple points in the in-plane direction is considered. ａ and equilibrium potential E ｅｑ The battery is designed and controlled so that the minimum difference within the given range is greater than zero. This makes it possible to more reliably avoid the occurrence of lithium deposition. The shape of the battery is not particularly limited and may have a flattened wound electrode body, a stacked electrode body, or be a bipolar battery.

[0085] Next, we will explain the comparative calibration of the electrochemical model. By mounting the electrochemical model used by the battery state estimation device onto an actual device, performing real-time calculations, and calibrating the calculation results by comparing them with sensor-acquired values, the accuracy of lithium deposition estimation can be further improved. The electrochemical model can be incorporated into a system that monitors operating batteries, such as batteries E installed in EVs or batteries E in energy storage plants. This monitoring system is also called a BMU (Battery Management Unit). The following explanation is in accordance with the method for observing the battery state in an operating device and the method for correcting the numerical values ​​in the electrochemical model based on the observed values, as described in Japanese Patent Application No. 2024-169387, filed earlier by this applicant.

[0086] The following describes the observation of battery status in an operational device. The quantity observed is, for example, the battery temperature T. ｋ Battery voltage V ｋ , the voltage difference ΔV of the battery during current fluctuations ＩＲ，ｋ These are the three. Battery temperature T ｋ The voltage of the battery is measured by the temperature sensor T1. ｋ This is measured by a voltage sensor. The voltage difference ΔV during current fluctuations. ＩＲ，ｋ As shown in equation (24), the battery voltage V measured at the current time step k is ｋ And the battery voltage V measured in the previous time step (k-1) ｋ－１ That is the difference.

[0087] ΔV ＩＲ，ｋ = V ｋ -V ｋ－１ (24)

[0088] Therefore, in the battery state estimation device according to this embodiment, the observed value vector y ｏｂｓ ｋ This is given by equation (25). Hereafter, vectors will be shown in bold except within the equations.

[0089]

[0090] Here, the battery voltage V at time step k. ｋ This is expressed by equation (26). V ｋ =OCV(SOC) ｋ ) -ηaｃｔ，ｋ -η ｏｈｍ，ｋ -η Ｄｉｆｆ，ｋ (26) In equation (26), OCV (SOC ｋ ) is the open-circuit potential (OCP) corresponding to the State of Charge (SOC) at time step k, η ａｃｔ，ｋ η is the activation overpotential at time step k. ｏｈｍ，ｋ η is the ohmic overvoltage at time step k. Ｄｉｆｆ，ｋ This is the concentration overvoltage at time step k.

[0091] Overall activation overvoltage η of the battery ａｃｔ This is the activation overpotential η of the positive electrode. ａｃｔ，ｐ and the activation overpotential η of the negative electrode ａｃｔ，ｎ It is the sum of and is expressed by equation (27).

[0092]

[0093] Activation overpotential η of the positive electrode ａｃｔ，ｐ This is obtained using the Butler-Volmer equation, which is shown in equation (28).

[0094] In equation (28), α is the transfer coefficient, R is the gas constant, T is the temperature, i ｐ０ This is the exchange current density of the positive electrode.

[0095] Temperature T is a variable that changes during the temperature calculation process. The exchange current density i of the positive electrode. ｐ０ This parameter represents the activity of the electrode. The lithium ion concentration C is located at the outermost surface of the active material particles, i.e., at the interface between the active material particles and the electrolyte. ｐ，５，ｋ It is often expressed as a function of C. ｐ，５，ｋ As will be explained in detail later, this represents the lithium ion concentration at the outermost coordinate when the distance from the center to the outer edge of the sphere in the single-particle model is divided into five equal parts. By solving equation (28) using, for example, Newton's method, the activation overpotential η of the positive electrode at current I can be obtained. ａｃｔ，ｐ We find the activation overpotential η of the positive electrode at current I by solving equation (28). ａｃｔ，ｐ For convenience, we will write the process of finding this as shown in equation (29).

[0096]

[0097] The same equations as (28) and (29) hold true at the negative electrode. Activation overpotential η of the negative electrode ａｃｔ，ｎ This can be expressed as equation (30) by replacing the subscript p with the subscript n.

[0098]

[0099] The total ohm overvoltage η of the battery ｏｈｍ R is the sum of the ohm resistances. ｏｈｍ It is the product of and the current I, and is expressed by equation (31).

[0100] η ｏｈｍ = R ｏｈｍ I (31)

[0101] The sum of the ohm resistances R ｏｈｍ R is the positive electrode electron conduction resistance. ｐｓ , positive electrode ion conduction resistance R ｐＬ , separator ion conduction resistance R ｓＬ , negative electrode electron conduction resistance R ｎｓ , and the negative electrode ion conduction resistance R ｎＬ The sum of the five types of resistances is sufficient and can be expressed by equation (32). The subscripts ps are taken from the positive electrode and the solid electron conductor, pL from the positive electrode and the liquid ion conductor, sL from the separator and the liquid ion conductor, ns from the negative electrode and the solid electron conductor, and nL from the negative electrode and the liquid ion conductor.

[0102] R ｏｈｍ = R ｐｓ +R ｐＬ +R ｓＬ +R ｎｓ +R ｎＬ (32)

[0103] The activation overvoltage η of the entire battery shown in equation (27) ａｃｔ And the ohm overvoltage η of the entire battery shown in equation (31) ｏｈｍ When these are discretized in time, we obtain equations (33) and (34), respectively.

[0104] η ｏｈｍ，ｋ = Rｏｈｍ u ｋ (34)

[0105] In equations (33) and (34), u ｋ = I, that is, u ｋ is the current I at time step k. The activation overvoltage and ohmic overvoltage are overvoltages that arise when current flows; in other words, if no current is flowing, both the activation overvoltage and ohmic overvoltage are 0.

[0106] Battery-wide concentration overvoltage η Ｄｉｆｆ，ｋ η is expressed by equation (35). Ｄｉｆｆ，ｋ = η ｐ，Ｄｉｆｆ (C ｐ，ａｖｅ，ｋ , C ｐ，５，ｋ ) - η n，Ｄｉｆｆ (C n，ａｖｅ，ｋ , C n，５，ｋ ) (35)

[0107] η ｐ，Ｄｉｆｆ，ｋ η is the concentration overpotential of the positive electrode and is expressed by equation (36). ｎ，Ｄｉｆｆ，ｋ η is the concentration overpotential at the negative electrode and is expressed by equation (37). ｐ，Ｄｉｆｆ，ｋ =OCP ｐ (C ｐ，ａｖｅ，ｋ ) - OCP ｐ (C ｐ，５，ｋ ) (36) η ｎ，Ｄｉｆｆ，ｋ =OCP ｎ (C ｎ，ａｖｅ，ｋ ) - OCP ｎ (C ｎ，５，ｋ ) (37) In equation (36), OCP ｐ (C ｐ ) is the open-circuit potential of the positive electrode. In equation (37), OCP ｎ (C ｎ ) is the open-circuit potential of the negative electrode.

[0108] The concentration overpotential in positive electrode active material particles is due to the distribution of lithium ion concentration within the active material particles. The average lithium ion concentration within the positive electrode active material particles is defined by equation (38) (continuous equation) or equation (39) (discrete equation).

[0109]

[0110]

[0111] OCP of the positive electrode and lithium ion concentration C within the positive electrode active material particles ｐ The relationship is as follows: That is, the relationship between the open-circuit potential of the active material particles of the positive and negative electrodes and the lithium ion concentration is generally a downward-sloping curve. Lithium ion concentration C at the interface between the active material particles of the positive electrode and the electrolyte. ｐ，５，ｋ And the average lithium ion concentration C within the active material particles of the positive electrode. ｐ，ａｖｅ，ｋ When there is a difference, the difference in open-circuit potential corresponding to the difference in lithium ion concentration between the two is the concentration overpotential η. ｐ，Ｄｉｆｆ，ｋ That is the case.

[0112] Since OCV cannot be measured directly, it is estimated using SOC estimation by current integration and an SOC-OCV map. SOC estimation by current integration can be performed using equation (40) or equation (41). Equation (41) is the time-discretized form of equation (40).

[0113] In equation (40), SOC(t) is the SOC at time t, SOC ｉｎｉｔ I is the SOC (State of Charge) at the start of power application, FCC (Full Charge Capacity) is the full charge capacity and is a quantity with the dimension of electric quantity, and I is the current.

[0114] SOC ｋ＋１ = SOC ｋ +I / FCCΔt (41) In equation (41), the subscript k is a natural number representing the time step due to time discretization, and Δt is the time step size of the time step due to time discretization.

[0115] After estimating the State of Charge (SOC), the OCV corresponding to the estimated SOC is estimated by referring to the battery's SOC-OCV curve. The battery's SOC-OCV curve is created in advance based on characteristic tests conducted by the battery manufacturer and is registered in the ROM within the control unit 22 at the time of shipment.

[0116] The State of Control (SOC) can be estimated based on current pattern data that should flow through the battery. The current pattern data is created in advance by the designer and stored in the ROM of the control unit 22. The current pattern data is used as basic data for estimating the battery state through simulation and is created according to the type of load 2. The current pattern data may be a periodic sine wave, square wave, triangular wave, or sawtooth wave, or it may be an irregular current pattern generated randomly. Alternatively, it may be a current pattern generated by the designer based on measured data of the load 2. Furthermore, the current pattern does not have to be one prepared in advance; the current value actually applied to the load 2 during operation may be used.

[0117] The OCV corresponding to the estimated SOC can be expressed by equation (42) or equation (43). Equation (43) is the time-discretized form of equation (42).

[0118] OCV=OCV(SOC) (42) OCV ｋ =OCV(SOC) ｋ ) (43)

[0119] Voltage difference ΔV ＩＲ，ｋ This can be rewritten from equations (24) and (26) as equation (44).

[0120] ΔV ＩＲ，ｋ = V ｋ -V ｋ－１ =OCV(SOC) ｋ )-OCV(SOC ｋ－１ ) - (η ａｃｔ，ｋ -η ａｃｔ，ｋ－１ ) - (η ｏｈｍ，ｋ -η ｏｈｍ，ｋ－１ ) - (η Ｄｉｆｆ，ｋ -η Ｄｉｆｆ，ｋ－１ ) (44)

[0121] Here, if Δt is sufficiently small, more specifically, if the change in current I at Δt is sufficiently small with respect to FCC, then OCV (SOC ｋ ) and OCV (SOC ｋ－１ ) can be considered to have the same value, η Ｄｉｆｆ，ｋ and η Ｄｉｆｆ，ｋ－１ These can also be considered to have the same value. Therefore, equation (44) can be simplified to equation (45).

[0122] ΔV ＩＲ，ｋ = V ｋ -V ｋ－１ = -(η) ａｃｔ，ｋ -η ａｃｔ，ｋ－１ ) - (η ｏｈｍ，ｋ -η ｏｈｍ，ｋ－１ ) (45)

[0123] During current fluctuations, the activation overpotential η ａｃｔ，ｋ and Ohm overvoltage η ｏｈｍ,k It fluctuates without time delay or wasted time, and the battery voltage difference value ΔV ＩＲ，ｋ Because it is fast and can measure directly with a voltage sensor, it is possible to accurately determine the difference between the estimated value and the measured value.

[0124] The observed vector y derived from the estimation calculation ｋ This is given by equation (46).

[0125] V in equation (46) ｋ From equation (26), ΔV ＩＲ，ｋ These can be calculated from equation (45). T ｋ This can be derived from equation (47).

[0126]

[0127] Equation (47) is the time-discretized form of equation (48).

[0128] In equations (47) and (48), ρ is the density of the battery [kg / m³]. ３ ], V ｏｌ is the volume of the battery [m³ ３ ], Cp is the specific heat of the battery [J / kg / K], I is the current [A], T is the temperature of the battery [K], OCV is the open-circuit voltage [V], and h is the heat transfer coefficient [W / m]. ２ / K], S is the surface area of ​​the battery [m ２ ], T ０ η is the outside temperature [K], η ｏｈｍ η is the Ohm overvoltage [V], η ａｃｔ η is the activation overpotential [V], η Ｄｉｆｆ This is the concentration overpotential [V].

[0129] Equation (48) is a common equation in thermal engineering used to calculate the temperature of a battery. The terms on the left side of equation (48) represent the temperature rise. The first term on the right side of equation (48) represents the amount of heat generated due to the flow of current. The second term on the right side of equation (48) represents the entropy heat generated due to the flow of current. The third term on the right side of equation (48) represents the heat dissipation to the outside due to heat transfer. Although not shown in equation (48), radiative heat transfer may also be considered.

[0130] Outside temperature T ０ If the battery pack 1 is equipped with an ambient temperature sensor for measuring ambient temperature, the value obtained from the ambient temperature sensor can be used. If an ambient temperature sensor is not installed, for example, the average temperature of the area where the battery pack 1 is used will be used. Temperature T ｋ The initial value is set to, for example, room temperature. ｋ When updated by a Kalman filter or similar, it may be set to an arbitrary value (for example, 300K at room temperature). When the current I changes, the ohmic overpotential and activation overpotential change and affect the amount of heat generated, but the concentration overpotential does not affect the amount of heat generated.

[0131] By adjusting the numerical values ​​in the electrochemical model according to the difference between equation (25) and equation (46), it is possible to estimate lithium deposition with high accuracy. A Kalman filter can be used as a method of adjustment. There are several methods, such as nonlinear Kalman filters, ensemble Kalman filters, and particle filters, but since the observation equation is nonlinear, using a particle filter provides the highest accuracy.

[0132] The following describes how to modify the battery state estimate using a particle filter. Note that nonlinear Kalman filters, ensemble Kalman filters, and fragrance-free Kalman filters are described in detail, for example, in Chapter 7 of "Fundamentals of Kalman Filters," by Shuichi Adachi and Ichiro Maruta, first edition October 1, 2012, Tokyo Denki University Press, ISBN: 9784501328900, and the battery state estimate can be modified using a procedure similar to that for particle filters.

[0133] For example, equations (26), (33), (34), (35), (41), (43), (45), (47), (49), and (50) are used as equations to construct the particle filter. Equations (49) and (50) are expressed as follows:

[0134]

[0135]

[0136] Equations (49) and (50) are explained below. In the single-particle model used for overpotential estimation, the sphere is divided into np computational elements for discretization. Here, we will explain assuming np = 5. Let r1 be the coordinate of the center of the sphere and r5 be the coordinate of the outer edge of the sphere, and define coordinates r1 to r5 that are equally spaced in the radial direction of the sphere. The interval between computational elements, Δrp, is given by Δrp = rp / (np - 1). Note that the intervals between each computational element do not need to be equal; for example, they may change in a geometric progression.

[0137] Lithium ion concentration C of the active material particles in the positive electrode ｐ The distribution of can be expressed by equation (51). For i ≠ 1 and 5, discretization results in equation (52). Here, discretization is performed using central differences in the position direction and forward differences in time. Here, the subscript i represents the position (i = 1 to 5), and the subscript k is a natural number representing the time step due to the discretization of time.

[0138]

[0139] In equations (51) and (52), D ｓ，ｐ This is the diffusion coefficient of lithium ions in the positive electrode active material particles.

[0140] Since i=1 is the center of the sphere, it exhibits symmetry, and discretization yields equation (53).

[0141]

[0142] At i=5, since it is the outer periphery of the active material particle, we consider that a charge transfer reaction occurs, resulting in equation (54).

[0143] In equation (54), I is the total current flowing through the battery, and S is the total current flowing through the battery. ｐ is the total reaction area of ​​the positive electrode active material particles, z is the valence of the reaction (z = 1 for a typical lithium-ion battery), and F is the Faday constant.

[0144] The equations shown in equations (52), (53), and (54) can be combined into a matrix to obtain equation (55) or equation (49). Equation (49) is a simplified notation of equation (55). Current I is defined as positive for discharge and negative for charge.

[0145]

[0146] To simplify things, if we rearrange only the case where i = 3 in equation (52), we get equation (56).

[0147]

[0148] Compared with the coefficient of the third column of the matrix, D ｐ，３１ = 0, D ｐ，３２ This is expressed by equation (57), D ｐ，３３ This is expressed by equation (58), D ｐ，３４ This is expressed by equation (59), D ｐ，３５ = 0, b ｐ３ = 0.

[0149]

[0150]

[0151]

[0152] column vector b ｐｉ The components are, ｐ５ It is 0 except for b. ｐ５ b is expressed by equation (60). ｐ５ = zFΔt / S ｐ (60)

[0153] Equations (55) and (49) represent the diffusion phenomenon and concentration distribution of lithium ions in the positive electrode active material particles. The diffusion phenomenon and concentration distribution of lithium ions in the negative electrode active material particles can be derived in the same way as equations (49), (51) to (55), and can be expressed by equations (60) and (50). Note that in the negative electrode, the subscript p is replaced with the subscript n.

[0154]

[0155] column vector b ｎｉ The components are, ｎ５ It is 0 except for b. ｎ５ b is expressed by equation (61). ｎ５ = -zFΔt / S ｎ (61)

[0156] In equations (55) and (60), the lithium ion concentration C at the outermost periphery of the active material particle, i.e., at the interface between the active material particle and the electrolyte. ｐ，５，ｋ , C ｎ，５，ｋ These are values ​​related to the activation overpotential and concentration overpotential mentioned above.

[0157] For example, the state vector x is an equation used to construct a particle filter. ｋ This is determined as shown in equation (62).

[0158]

[0159] Regarding the time evolution of the state vector in equation (46), the system noise v ｋ The state equation when is added is described using a general function F as shown in equation (63). The system noise may be normal noise or irregular noise, but the noise distribution is known or can be assumed. Function F is a symbol that collectively describes equations (26), (33), (34), (35), (41), (43), (45), (47), (49), and (50).

[0160]

[0161] For the system model in equation (63), the observation model y ｋ This is written as in equation (64). In the observation model, the observation noise w ｋ It is assumed that this is added to the observed quantity. In this embodiment, since all observed quantities are simply the values ​​of the state vector, the observation model is linear, but for generality, it is described using the function H.

[0162]

[0163] Also, the state vector xｋ Given the observed value y ｏｂｓ ｋ Let P be the probability of obtaining the system noise v. ｋ The probability P can serve as a tuning parameter to ensure stable computation.

[0164] The following describes the procedure for implementing particle filtering.

[0165] In procedure (1), N particles are generated, and the state vector x is determined for each of them. ｎ ｋ This provides the initial values. The superscript n represents the particle's serial number (1 ≤ n ≤ N). In this embodiment, the state vector at time step k also requires the values ​​at time step (k-1) for some variables. Initially, the values ​​at time step k and the values ​​at time step (k-1) should be the same.

[0166] In step (2), random numbers are used to determine the system noise v of each of the N particles. ｎ ｋ Generates.

[0167] In step (3), using the values ​​generated in steps (1) and (2), the state vector x at time step (k-1) is obtained by equation (63). ｎ ｋ－１ and system noise v ｎ ｋ From this, the state vector x of each of the N particles at the next time step ｎ ｋ The following is calculated. At this stage, the state vector is a provisional value before filtering.

[0168] In step (4), the weight of the nth particle is expressed by equation (65).

[0169] In equation (65), the right-hand side is the state vector x ｎ ｋ If obtained, the observed value y ｏｂｓ ｋ This represents the probability P of obtaining [the desired result].

[0170] In step (5), the weights of all particles obtained in step (4) are normalized. The normalized particle weight pｎ ｋ This is expressed by equation (66).

[0171]

[0172] In step (6), the state vectors of the n particles are averaged by the particle weights, and the state vectors are updated as shown in equation (67).

[0173] In equation (67), the state vector on the left side has a different value from the state vector in equation (63), and is a value filtered using the observed values.

[0174] In step (7), for example, the value of the right-hand side of equation (46) may be estimated from the observation vector shown in equation (64) based on equation (67). Alternatively, (ΔV in the state vector of equation (67) ＩＲ，ｋ ,V ｋ ,T ｋ ) can be used as the value on the right side of equation (46).

[0175] The above describes the difference in battery voltage ΔV during current fluctuations. ＩＲ The calculation and the correction process for the estimated battery state were explained. In this regard, the correction process for the estimated battery state may be performed only when the current value changes. That is, u ｋ ≠u ｋ－１ The battery state estimate may be corrected only in this case.

[0176] Also, when the current is interrupted, u ｋ = 0 and u ｋ－１ Since ≠ 0, in this case the activation overvoltage and ohm overvoltage at time step (k-1) are both 0. Therefore, equation (45) can be rewritten as equation (68) and further simplified. In this case, more accurate battery state estimation becomes possible.

[0177] ΔV ＩＲ，ｋ = V ｋ -V ｋ－１ = V ｋ = -η ａｃｔ，ｋ -η ｏｈｍ，ｋ (68)

[0178] Although not mentioned in the above explanation, a certain time delay may occur in the activation overpotential response due to the capacitive component at the solid-liquid interface. Therefore, it may be preferable to set the time step size used for battery state estimation in the embodiment to be larger than the time constant determined by the activation overpotential and the capacitance at the solid-liquid interface.

[0179] As described above, according to this embodiment, the deposition potential of metallic lithium, that is, the equilibrium potential of the deposition reaction of metallic lithium, is determined from a function or map of the lithium ion concentration in the electrolyte and temperature, and metallic lithium is predicted to precipitate when the negative electrode potential falls below the deposition potential of metallic lithium. This improves the accuracy of estimating metallic lithium deposition. Furthermore, it is also possible to improve the accuracy of estimating deposition for alkali metals other than lithium.

[0180] The embodiments of this disclosure have been described in detail above. The embodiments described above are merely examples of how to implement this disclosure. The content of the embodiments does not limit the technical scope of this disclosure, and many design changes, such as changes, additions, and deletions of components, are possible as long as they do not depart from the spirit of the invention as defined in the claims. A new embodiment with design changes will have the combined effects of both the embodiment and the variation. In the embodiments described above, the content in which such design changes are possible is emphasized with notations such as "of this embodiment" or "in this embodiment," but design changes are also permitted even if there are no such notations. Furthermore, any combination of components included in each embodiment is also valid as an embodiment of this disclosure. The hatching applied to the cross-section in the drawings does not limit the material of the object to which the hatching is applied.

[0181] In the embodiment described above, an example was explained in which the battery state estimation device is implemented in the control unit 22 within the battery pack 1. However, the battery state estimation device may also be implemented in a cloud server installed in a data center or in a company's own server installed in its own facility. In that case, the control unit 22 within the battery pack 1 transmits the voltage values ​​of each battery E1-En, the current values ​​flowing through the battery pack 10, and the temperature values ​​of the battery pack 10, received from the measurement unit 21, to the cloud server or the company's own server via wireless or wired communication. In this case, a more precise electrochemical model can be used.

[0182] When the control unit 22, which acts as a battery state estimation device, performs the above-described protection control, that is, when the control unit 22 is at the equilibrium potential E ｅｑ <Negative potential V ａ Set the charging current value so that the equilibrium potential E ｅｑ <Negative potential V ａ Adjusting the battery temperature to achieve the negative electrode potential V ａ Equilibrium potential E ｅｑ When instructing the execution of more advanced control, the battery state estimation device can be interpreted as further comprising a protection control unit that performs the protection control described above. Furthermore, a battery state estimation device comprising a protection control unit can be interpreted as a charge / discharge control device that controls the charging and discharging of the battery. Also, the battery state estimation method can be interpreted as a battery control method, and the battery state estimation program can be interpreted as a battery control program.

[0183] The embodiments may be specified by the items described below. [Item 1] A battery state estimation device (22) for estimating the electrochemical state of a battery (E) having a negative electrode containing an active material capable of intercalating and deintercalating alkali metal ions, and an electrolyte, comprising: a negative electrode potential calculation unit (221) that calculates the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode; an equilibrium potential calculation unit (222) that calculates the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery (E), and calculates the equilibrium potential of the alkali metal deposition reaction based on the alkali metal ion concentration and the temperature of the battery (E); and a deposition prediction unit (223) that predicts the deposition of alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential. [Item 2] The equilibrium potential calculation unit (222) divides the negative electrode into a plurality of computational grids (M) and calculates the alkali metal ion concentration in each computational grid (M), as described in Item 1, the battery state estimation device (22). [Item 3] The equilibrium potential calculation unit (222) calculates the equilibrium potential by taking into account that the standard equilibrium potential of the first term of the Nernst equation may change depending on the temperature of the battery (E), as described in Item 2, the battery state estimation device (22). [Item 4] The equilibrium potential calculation unit (222) calculates the equilibrium potential by taking into account the increase in alkali metal ion concentration due to the principle of freeze-concentration of the electrolyte and the temperature of the battery (E) when the temperature of the battery (E) is below the freezing point of the electrolyte, as described in Item 3, the battery state estimation device (22). [Item 5] The equilibrium potential calculation unit (222) calculates the equilibrium potential using the Nernst equation that takes into account the increase in alkali metal ion concentration due to the principle of freeze-concentration, as described in Item 4, the battery state estimation device (22). [Item 6] The deposition prediction unit (223) predicts deposition based on the minimum difference between the negative electrode potential and the equilibrium potential in each computational grid (M), as described in Item 2, the battery state estimation device (22). [Item 7] The battery (E) has a separator and a positive electrode, and the battery state estimation device (22) calculates various values ​​of the separator and positive electrode using a lumped-parameter model, as described in any of Items 2 to 6, the battery state estimation device (22).[Item 8] The battery (E) has a negative electrode, a separator, and a positive electrode stacked together, and the deposition prediction unit (223) predicts deposition based on the minimum difference among the differences between the negative electrode potential and the equilibrium potential at multiple points in the in-plane direction perpendicular to the stacking direction of the negative electrode, separator, and positive electrode, the battery state estimation device (22) according to any of Items 1 to 7. [Item 9] The negative electrode potential calculation unit (221) calculates the negative electrode potential using an electrochemical model, the equilibrium potential calculation unit (222) calculates the temperature using an electrochemical model, the battery state estimation device (22) further comprises: a measurement value acquisition unit (224) that acquires the measured voltage measured by a voltage sensor for the voltage between the terminals of the battery (E) and the measured temperature measured by a temperature sensor for the temperature of the battery (E) as measured values, a measured voltage difference calculation unit (225) that calculates the measured voltage difference, which is the difference between the measured voltage measured at the current time step and the measured voltage measured at the previous time step, as a measured value, an electrochemical model calculation unit (226) that calculates the voltage and temperature using an electrochemical model, and also calculates the difference between the voltage at the current time step and the voltage at the previous time step, and acquires the calculated voltage, temperature, and difference as state estimation values, and a calibration unit (227) that corrects the state estimation values ​​using the measured values. A battery state estimation device (22) according to any of the first to eighth items. [Item 10] A battery state estimation device (22) according to the ninth item, wherein the calibration unit (227) corrects the estimated state value using any of the following: a Kalman filter, a nonlinear Kalman filter, a fragrance-free Kalman filter, an ensemble Kalman filter, or a particle filter. [Item 11] A battery state estimation method for estimating the electrochemical state of a battery (E) having a negative electrode containing an active material capable of intercalating and deintercalating alkali metal ions, and an electrolyte, comprising: calculating the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode; calculating the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery (E); calculating the equilibrium potential of the alkali metal deposition reaction based on the alkali metal ion concentration and the temperature of the battery (E); and predicting the deposition of alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential.[Item 12] A battery state estimation program for estimating the electrochemical state of a battery (E) having a negative electrode containing an active material capable of intercalating and deintercalating alkali metal ions, and an electrolyte, the program causing a computer to perform the following steps: calculate the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode; calculate the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery (E), and calculate the equilibrium potential of the alkali metal deposition reaction based on the alkali metal ion concentration and the temperature of the battery (E); and predict the deposition of alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential. [Item 13] A battery state estimation device (22) according to any one of items 1 to 10, further comprising a protection control unit that instructs the execution of a control to raise the negative electrode potential above the equilibrium potential when the deposition prediction unit (223) predicts that alkali metal will be deposited. [Item 14] A battery state estimation method according to Item 11, further comprising controlling the charging current value and adjusting the temperature of the battery (E) so that the negative electrode potential exceeds the equilibrium potential when the prediction predicts the deposition of alkali metals. [Item 15] A battery state estimation program according to Item 12, further comprising causing a computer to perform a process that controls the charging current value and adjusts the temperature of the battery (E) so that the negative electrode potential exceeds the equilibrium potential when the prediction predicts the deposition of alkali metals.

[0184] This disclosure can be used in a battery state estimation device, a battery state estimation method, and a battery state estimation program.

[0185] 22 Control unit, 221 Negative electrode potential calculation unit, 222 Equilibrium potential calculation unit, 223 Deposition prediction unit, 224 Measurement value acquisition unit, 225 Measurement voltage difference calculation unit, 226 Electrochemical model calculation unit, 227 Calibration unit, E Battery.

Claims

1. A battery state estimation device for estimating the electrochemical state of a battery having a negative electrode containing an active material capable of intercalating and deintercalating alkali metal ions, and an electrolyte, comprising: a negative electrode potential calculation unit that calculates the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode; an equilibrium potential calculation unit that calculates the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery, and calculates the equilibrium potential of the alkali metal deposition reaction based on the alkali metal ion concentration and the temperature of the battery; and a deposition prediction unit that predicts the deposition of the alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential.

2. The battery state estimation device according to claim 1, wherein the equilibrium potential calculation unit divides the negative electrode into a plurality of calculation grids and calculates the alkali metal ion concentration in each calculation grid.

3. The battery state estimation device according to claim 2, wherein the equilibrium potential calculation unit calculates the equilibrium potential taking into account that the standard equilibrium potential of the first term of the Nernst equation may change depending on the temperature of the battery.

4. The battery state estimation device according to claim 3, wherein the equilibrium potential calculation unit calculates the equilibrium potential by taking into account the increase in alkali metal ion concentration due to the principle of freeze-concentration of the electrolyte and the temperature of the battery when the temperature of the battery is below the freezing point of the electrolyte.

5. The battery state estimation device according to claim 4, wherein the equilibrium potential calculation unit calculates the equilibrium potential using the Nernst formula which takes into account the increase in alkali metal ion concentration due to the principle of freeze-concentration.

6. The battery state estimation device according to claim 2, wherein the deposition prediction unit predicts the deposition based on the minimum difference among the differences between the negative electrode potential and the equilibrium potential in each computational grid.

7. The battery has a separator and a positive electrode, and the battery state estimation device calculates various values ​​of the separator and the positive electrode using a lumped-parameter model, as described in any one of claims 2 to 6.

8. The battery state estimation device according to any one of claims 2 to 6, wherein the battery has the negative electrode, separator, and positive electrode stacked, and the deposition prediction unit predicts the deposition based on the minimum difference among the differences between the negative electrode potential and the equilibrium potential at multiple points in an in-plane direction perpendicular to the stacking direction of the negative electrode, separator, and positive electrode.

9. The battery state estimation device according to any one of claims 1 to 6, further comprising: a negative electrode potential calculation unit that calculates the negative electrode potential using the electrochemical model; an equilibrium potential calculation unit that calculates the temperature using the electrochemical model; a battery state estimation device that further comprises: a measurement value acquisition unit that acquires a measured voltage measured by a voltage sensor for the voltage between the terminals of the battery, and a measured temperature measured by a temperature sensor for the temperature of the battery, as measured values; a measured voltage difference calculation unit that calculates a measured voltage difference, which is the difference between the measured voltage measured at the current time step and the measured voltage measured at the previous time step, as a measured value; an electrochemical model calculation unit that calculates the voltage and the temperature using the electrochemical model, and also calculates the difference between the voltage at the current time step and the voltage at the previous time step, and acquires the calculated voltage, the temperature, and the difference as state estimation values; and a calibration unit that corrects the state estimation values ​​using the measured values.

10. The battery state estimation device according to claim 9, wherein the calibration unit corrects the state estimation value using one of the following: a Kalman filter, a nonlinear Kalman filter, a fragrance-free Kalman filter, an ensemble Kalman filter, or a particle filter.

11. A method for estimating the electrochemical state of a battery having a negative electrode containing an active material capable of intercepting and deintercepting alkali metal ions, and an electrolyte, comprising: calculating the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode; calculating the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery; calculating the equilibrium potential of the alkali metal deposition reaction based on the alkali metal ion concentration and the temperature of the battery; and predicting the deposition of the alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential.

12. A battery state estimation program for estimating the electrochemical state of a battery having a negative electrode containing an active material capable of intercepting and deintercepting alkali metal ions, and an electrolyte, wherein the program causes a computer to perform the following steps: calculate the negative electrode potential, which is the difference between the liquid phase potential and the solid phase potential of the negative electrode; calculate the alkali metal ion concentration in the electrolyte at least at the negative electrode using an electrochemical model of the battery, and calculate the equilibrium potential of the alkali metal deposition reaction based on the alkali metal ion concentration and the temperature of the battery; and predict the deposition of the alkali metal at the negative electrode based on the relative magnitudes of the negative electrode potential and the equilibrium potential.

13. The battery state estimation device according to any one of claims 1 to 6, further comprising a protection control unit that instructs the execution of a control to raise the negative electrode potential above the equilibrium potential when the deposition prediction unit predicts that the alkali metal will precipitate.

14. The battery state estimation method according to claim 11, further comprising controlling the charging current value and adjusting the temperature of the battery so that the negative electrode potential exceeds the equilibrium potential when the prediction predicts the deposition of the alkali metal.

15. The battery state estimation program according to claim 12, further comprising causing a computer to perform a process to control the charging current value and adjust the temperature of the battery so that the negative electrode potential exceeds the equilibrium potential when the prediction predicts that the alkali metal will precipitate.

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