JP2022054018A - Estimating device, estimating method, and computer program - Google Patents

Abstract

To provide an estimating device, an estimating method, and a computer program.SOLUTION: An estimating device comprises: an acquisition section for acquiring measured data including a voltage of an electricity storage element, a current flowing through the electricity storage element, and a temperature relating to the electricity storage element; and an estimating section that estimates a state of the electricity storage element by inputting the acquired measured data into a state estimator constructed so as to simulate electrochemical phenomena and thermal phenomena of the electricity storage element.SELECTED DRAWING: Figure 9

Description

The present invention relates to an estimation device, an estimation method, and a computer program.

In recent years, power storage elements such as lithium-ion batteries have been used in a wide range of fields such as power sources for mobile terminals such as notebook personal computers and smartphones, renewable energy storage systems, and power supplies for IoT devices.

In order to make effective use of such a secondary battery, the behavior of the secondary battery at an arbitrary time point is estimated. As one of the methods for estimating the behavior of a secondary battery, a Kalman filter is applied to an equivalent circuit model in which the secondary battery is represented by an electric circuit, and the behavior of the secondary battery such as SOC (State Of Charge) is estimated. A method is known (see, for example, Patent Document 1).

Japanese Unexamined Patent Publication No. 2016-605828

However, in the method disclosed in Patent Document 1, the behavior is estimated by focusing only on the terminal voltage of the power storage element, and the thermal phenomenon of the power storage element is not considered. It is known that the characteristics of the power storage element strongly depend on the temperature, and the prediction accuracy is low in the conventional method. Further, in Patent Document 1, an equivalent circuit is used, and electrochemical phenomena such as solid-liquid current, substance diffusion, and electrochemical reaction generated inside the battery are not taken into consideration. Conventionally, there is no idea of coupling an electrochemical phenomenon and a thermal phenomenon in a power storage element, and it is difficult to obtain effective estimation accuracy in an actual machine.

The present invention has been made in view of such circumstances, and an estimation device, an estimation method, and a computer program capable of exhibiting effective estimation accuracy in an actual machine in consideration of both the electrochemical phenomenon and the thermal phenomenon of the power storage element are provided. The purpose is to provide.

The estimation device acquires measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature related to the power storage element, and the acquired measurement data is used to obtain the electrochemical phenomenon and the thermal phenomenon of the power storage element. It is provided with an estimation unit that inputs to a state estimator constructed to simulate and estimates the state of the power storage element.

The estimation method uses a computer to acquire measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature of the power storage element, and the acquired measurement data is used as the electrochemical phenomenon and heat of the power storage element. It is input to a state estimator configured to simulate a phenomenon, and the state of the power storage element is estimated.

The computer program acquires measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature of the power storage element in the computer, and uses the acquired measurement data to obtain the electrochemical phenomenon and the thermal phenomenon of the power storage element. It is input to a state estimator configured to simulate, and a process of estimating the state of the power storage element is executed.

According to the above configuration, effective estimation accuracy can be exhibited in an actual machine in consideration of both the electrochemical phenomenon and the thermal phenomenon of the power storage element.

It is an external view of the power storage system which concerns on embodiment. It is an exploded perspective view which shows the structural example of a power storage element. It is a schematic diagram which shows the structural example of a wound electrode body. It is a block diagram explaining the internal structure of an estimation device. It is explanatory drawing explaining the single particle model. It is explanatory drawing explaining the coordinate system in the Fick diffusion type. It is a graph which shows the equilibrium potential of a positive electrode. It is a graph which shows the equilibrium potential of a negative electrode. It is a flowchart explaining the state estimation procedure in Embodiment 1. FIG. It is a flowchart explaining the state estimation procedure in Embodiment 2. It is a flowchart explaining the state estimation procedure in Embodiment 3. FIG. It is a flowchart explaining the state estimation procedure in Embodiment 4. It is a circuit diagram which shows an example of the equivalent circuit model. It is a graph which shows the relationship between the lithium ion concentration in an electrolytic solution, and an ion conductivity. It is a schematic diagram which shows the display example of a temperature state.

The estimation device acquires measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature related to the power storage element, and the acquired measurement data is used to obtain the electrochemical phenomenon and the thermal phenomenon of the power storage element. It is provided with an estimation unit that inputs to a state estimator constructed to simulate and estimates the state of the power storage element.
According to this configuration, the state of the power storage element that cannot be directly measured can be estimated through the state variables obtained from the state estimator. Further, since the state of the power storage element is estimated in consideration of both the electrochemical phenomenon and the thermal phenomenon, which are strongly related to each other, effective estimation accuracy can be exhibited in the actual machine.

In the estimation device, the parameter describing the electrochemical phenomenon includes the activation overvoltage of the power storage element expressed as a function of the temperature of the power storage element, and the parameter describing the thermal phenomenon is the activation of the power storage element. It may include the calorific value of the power storage element expressed as a function of overvoltage. By using the activation overvoltage expressed as a function of temperature and the calorific value expressed as a function of activation overvoltage as parameters, it is possible to estimate the state in which the electrochemical phenomenon and the thermal phenomenon of the power storage element are coupled. It becomes.

In the estimation device, the state estimator may be a non-linear filter configured to output a state quantity related to the power storage element when the measurement data is input. According to this configuration, since a non-linear filter is used, a value closer to the true value can be calculated even when noise is included in the system or the sensor.

In the estimation device, the nonlinear filter may include a particle filter, an ensemble Kalman filter, an extended Kalman filter, or an unscented Kalman filter. By using a non-linear estimation algorithm, it is possible to estimate the state based on the physical mechanism of electrochemical and thermal phenomena even in an environment with disturbance.

In the estimation device, the state estimator obtains the time transition of each state variable by using a state equation representing the time transition of the state variable including the concentration of the stored ion in the active material particle and the temperature of the power storage element. The likelihood of the state estimation is obtained using the observation equation representing the relationship between the state variable and the observed amount indicated by the measurement data, and the estimated value of the state variable is updated according to the obtained state estimation likelihood. May be good. According to this configuration, the state of the power storage element that cannot be directly observed can be estimated in time series through the state variables that are updated sequentially. In the present embodiment, the ions stored in the active material particles (that is, the ions in the solid phase) are referred to as occluded ions.

The estimation device uses an acquisition unit for acquiring measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature related to the power storage element, and the acquired measurement data for the equivalent electric circuit and thermal phenomenon of the power storage element. It is provided with an estimation unit that inputs to a state estimator constructed to simulate and estimates the state of the power storage element.
According to this configuration, the state of the power storage element that cannot be directly measured can be estimated through the state variables obtained from the state estimator. Further, since the state of the power storage element is estimated in consideration of the equivalent electric circuit having a strong mutual relationship and the thermal phenomenon, effective estimation accuracy can be exhibited in the actual machine.

In the estimation device, the state estimator includes one or more equations in which the state quantity representing the characteristics of the power storage element changes over time or with energization, and the state variables describing the state of the power storage element and the measurement data indicate. Deterioration of the power storage element may be predicted by using an observation equation expressing the relationship with the observed amount. According to this configuration, deterioration of the power storage element due to aging or energization can be estimated.

The estimation method uses a computer to acquire measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature of the power storage element, and the acquired measurement data is used as the electrochemical phenomenon and heat of the power storage element. It is input to a state estimator configured to simulate a phenomenon, and the state of the power storage element is estimated.

The computer program acquires measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature of the power storage element in the computer, and uses the acquired measurement data to obtain the electrochemical phenomenon and the thermal phenomenon of the power storage element. It is input to a state estimator configured to simulate, and a process of estimating the state of the power storage element is executed.

Hereinafter, the present invention will be specifically described with reference to the drawings showing the embodiments thereof.
(Embodiment 1)
FIG. 1 is an external view of the power storage system 10 according to the embodiment. The power storage system 10 according to the embodiment includes an estimation device 100, a power storage element 200A to 200E, and a storage case 300 accommodating the estimation device 100 and the power storage element 200A to 200E. In the present embodiment, the power storage device 20 is configured by the power storage elements 200A to 200E. In the following description, when it is not necessary to distinguish the power storage elements 200A to 200E, the power storage element 200 is also simply described.

The estimation device 100 is, for example, a flat plate-shaped circuit arranged on the upper surface of a plurality of power storage elements 200 and estimating the state of each power storage element 200 at a predetermined time point. Specifically, the estimation device 100 acquires measurement data including the voltage of the power storage element 200, the current flowing through the power storage element 200, and the temperature of the power storage element 200, and based on the acquired measurement data, the power storage element uses a simulation model. Estimate 200 states.

In the example of FIG. 1, the location of the estimation device 100 is the upper surface of the power storage element 200. Alternatively, the arrangement location may be the side surface of the power storage element 200 or the lower surface of the power storage element 200. The shape of the estimation device 100 is also not limited to the flat plate shape. Further, the estimation device 100 is a server device located at a location away from the power storage element 200, and the above-mentioned measurement data is acquired by communication, and the state of the power storage element 200 is measured by using a simulation model based on the acquired measurement data. It may be a configuration to be estimated.

The power storage element 200 is a secondary battery such as a lithium ion secondary battery. The power storage element 200 is applied to a power source for an automobile such as an electric vehicle (EV), a hybrid electric vehicle (HEV), or a plug-in hybrid electric vehicle (PHEV), a power source for an electronic device, a power source for power storage, and the like.

FIG. 1 shows an assembled battery in which five rectangular parallelepiped power storage elements 200 are arranged in series. In the first embodiment, the number of the power storage elements 200 will be described as five. Alternatively, the number of power storage elements 200 may be one or two or more. Further, some power storage elements 200 may be connected in parallel. The power storage element 200 may be a secondary battery other than the lithium ion secondary battery.

Hereinafter, the configuration of the power storage element 200 will be described.
FIG. 2 is an exploded perspective view showing a configuration example of the power storage element 200. The power storage element 200 is configured by accommodating a flat wound electrode body 210 and an electrolyte (not shown in the figure) in a hollow rectangular parallelepiped battery case 220. The lid portion 221 of the battery case 220 is provided with a positive electrode terminal 222A and a negative electrode terminal 223A for external connection. The positive electrode terminal 222A and the negative electrode terminal 223A are electrically connected to the positive electrode current collector 222B and the negative electrode current collector 223B, respectively. As the material of the battery case 220, for example, a lightweight metal material having high thermal conductivity such as aluminum is used.

FIG. 3 is a schematic view showing a configuration example of the wound electrode body 210. The wound electrode body 210 has a sheet-shaped positive electrode 211 on which the positive electrode active material layer 211A is formed and a sheet-shaped negative electrode 212 on which the negative electrode active material layer 212A is formed, via two sheet-shaped separators 213. It is composed of overlapping and winding these. The positive electrode 211 and the negative electrode 212 are arranged so as to be offset from each other in the width direction of the sheet. A region in which the positive electrode active material layer 211A is not formed is provided at one end in the width direction of the positive electrode 211, and the positive electrode current collector 222B is bonded to this region. For the positive electrode current collector 222B, for example, an aluminum foil is used. Similarly, a region in which the negative electrode active material layer 212A is not formed is provided at the other end of the negative electrode 212 in the width direction, and the negative electrode current collector 223B is bonded to this region. For the negative electrode current collector 223B, for example, a copper foil is used.

The positive electrode active material layer 211A contains a positive electrode active material. The positive electrode active material contains secondary particles composed of aggregates of primary particles as active material particles. As the primary particles, particles of a lithium metal composite oxide are used. The lithium metal composite oxide contains lithium, oxygen, and other elements (eg, Mn, Ni, Co, Fe, Nb, W, P, Si, etc.). The elements other than lithium and oxygen may be one kind or a plurality of kinds. The positive electrode active material layer 211A may further contain a conductive auxiliary agent, a binder and the like. As the conductive auxiliary agent, for example, carbon black such as acetylene black (AB) and other carbon materials (such as graphite) are preferably used. As the binder, for example, polyvinylidene fluoride (PVDF) or the like is used.

The negative electrode active material layer 212A contains a negative electrode active material. As the negative electrode active material, for example, a carbon material such as graphite, hard carbon, or soft carbon is used. The negative electrode active material layer 212A may further contain a binder, a thickener and the like. As the binder, for example, styrene butadiene rubber (SBR) or the like is used. As the thickener, for example, carboxymethyl cellulose (CMC) or the like is used.

The separator 213 is formed of a porous resin film. As the porous resin film, a porous resin film made of a resin such as polyethylene (PE) or polypropylene (PP) can be used. The separator may be formed of a resin film having a single-layer structure, or may be formed of a resin film having a multi-layer structure of two or more layers. The separator 213 may include a heat resistant layer.

As the electrolyte housed in the battery case 220 together with the wound electrode body 210, the same electrolyte as that of a conventional lithium ion battery can be used. For example, as the electrolyte, an electrolyte in which a supporting salt is contained in an organic solvent can be used. As the organic solvent, for example, an aprotic solvent such as carbonates, esters, ethers and the like is used. As the supporting salt, for example, lithium salts such as LiPF ₆ , LiBF ₄ , and LiClO ₄ are preferably used. The electrolyte may contain, for example, various additives such as a gas generating agent, a film forming agent, a dispersant, and a thickener.

As an example of the power storage element 200, a square lithium ion battery provided with a wound electrode body 210 has been described with reference to FIGS. 2 and 3. Alternatively, the power storage element 200 may be a lithium ion battery provided with a laminated electrode body, a cylindrical lithium ion battery, a laminated lithium ion battery, or the like. Further, the power storage element 200 may be an all-solid-state lithium-ion battery using a solid electrolyte.

In the embodiment, in the estimation device 100 described below, measurement data including the voltage, current, and temperature of the power storage element 200 is acquired, and a simulation model for simulating an electrochemical phenomenon and a thermal phenomenon is performed based on the acquired measurement data. It is used to estimate the state of the power storage element 200.

FIG. 4 is a block diagram illustrating an internal configuration of the estimation device 100. The estimation device 100 is a dedicated or general-purpose computer including a calculation unit 101, a storage unit 102, an input unit 103, an output unit 104, and the like. In the example of FIG. 1, the estimation device 100 is provided on the upper surface of the power storage device 20. The estimation device 100 may be a device built in the power storage element monitoring device (BMU: Battery Management Unit) of the power storage device 20, or may be a computer such as a server installed in a remote location. When the estimation device 100 is installed in a remote location, the acquired measurement data of the power storage device 20 is transmitted to the estimation device 100 by communication.

The arithmetic unit 101 is an arithmetic circuit including a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the like. In the embodiment, the arithmetic unit 101 functions as a state estimator. The CPU included in the arithmetic unit 101 executes various computer programs stored in the ROM and the storage unit 102, and controls the operation of each of the above-mentioned hardware units to make the entire device function as the estimation device of the present application. Specifically, the arithmetic unit 101 acquires measurement data including the voltage, current, and temperature of the storage element 200, and stores electricity using a state estimator that simulates an electrochemical phenomenon and a thermal phenomenon based on the acquired measurement data. The state of the element 200 is estimated.

The arithmetic unit 101 is not limited to the above configuration, and may be any processing circuit or arithmetic circuit including a plurality of CPUs, a multi-core CPU, a GPU (Graphics Processing Unit), a microcomputer, a volatile or non-volatile memory, and the like. There may be. Further, the calculation unit 101 may have functions such as a timer for measuring the elapsed time from giving the measurement start instruction to the measurement end instruction, a counter for counting the number, and a clock for outputting the date and time information.

The storage unit 102 is a storage device such as a flash memory. Various computer programs and data are stored in the storage unit 102. The computer program stored in the storage unit 102 includes, for example, a state estimation program PG for causing the calculation unit 101 to execute an operation using a simulation model. The data stored in the storage unit 102 includes parameters used in the state estimation program PG, data temporarily generated by the calculation by the calculation unit 101, and the like. The parameters stored in the storage unit 102 include parameters such as the volume, surface area, specific heat, density of each power storage element 200, the value of heat conductance between adjacent power storage elements 200, and the heat transfer coefficient to the outside. The state estimation program PG is provided, for example, by a non-temporary recording medium M in which a computer program is readablely recorded. The recording medium M is a portable memory such as a CD-ROM, a USB memory, or an SD (Secure Digital) card. The arithmetic unit 101 reads a desired computer program from the recording medium M using a reading device (not shown in the figure), and stores the read computer program in the storage unit 102. Alternatively, the computer program may be provided by communication.

The value of thermal conductance used in the calculation of temperature estimation may change as the power storage element 200 expands. Therefore, the storage unit 102 may store a table showing the relationship between the strain value measured by the strain sensor 103E, which will be described later, and the thermal conductance value.

The value of the heat transfer coefficient used in the calculation of the temperature estimation may change depending on the air flow around the power storage device 20. Therefore, the storage unit 102 may store a table showing the relationship between the value of the flow velocity measured by the current meter 103F described later and the value of the heat transfer coefficient. Alternatively, the calculation of the heat transfer coefficient may be performed from the relational expressions that hold between the Nusselt number, the Prandtl number, and the Reynolds number.

The input unit 103 includes an interface for connecting various sensors. The sensors connected to the input unit 103 include a voltage sensor 103A that measures the voltage of the power storage element 200, a current sensor 103B that measures the current flowing through the power storage element 200, and a temperature sensor that measures the temperature (element temperature) of the power storage element 200. The 103C includes a temperature sensor 103D that measures the ambient temperature (environmental temperature) of the power storage element 200.

The voltage sensor 103A is an existing voltage sensor, and measures the voltage between terminals of the power storage element 200 in time series. The calculation unit 101 of the estimation device 100 acquires voltage data measured by the voltage sensor 103A at any time through the input unit 103.

The current sensor 103B is an existing sensor such as a current transformer and a Hall effect type current sensor, and measures the current flowing through the power storage element 200 in time series. The calculation unit 101 of the estimation device 100 acquires current data measured by the current sensor 103B at any time through the input unit 103.

The temperature sensor 103C is an existing sensor such as a thermocouple or a thermistor, and measures the temperature (element temperature) of the power storage element 200 in time series. The calculation unit 101 of the estimation device 100 acquires temperature data measured by the temperature sensor 103C at any time through the input unit 103. In the present embodiment, the power storage element 200 to be measured is a part of the five power storage elements 200A to 200E included in the power storage device 20 (for example, the power storage element 200E). The number of power storage elements 200 to be measured may be one, or may be two to four. That is, when the number of power storage elements 200 is N (N is an integer of 2 or more), the power storage elements 200 to be measured are appropriately installed in the range of 1 to (N-1). The temperature sensor 103C is arranged, for example, on the upper surface of the power storage element 200. Alternatively, the temperature sensor 103C is arranged on the side surface or the lower surface of the power storage element 200.

The temperature sensor 103D is an existing sensor such as a thermocouple or a thermistor, and measures the ambient temperature (environmental temperature) of the power storage element 200 in time series. The calculation unit 101 of the estimation device 100 acquires temperature data measured by the temperature sensor 103D at any time through the input unit 103.

A strain sensor 103E that detects the magnitude of strain of the power storage element 200 may be connected to the input unit 103. The strain sensor 103E is an existing sensor using a strain gauge type load cell or the like. The strain sensor 103E is provided for each of the power storage elements 200.

A current meter 103F that measures the flow of air around the power storage device 20 may be connected to the input unit 103. The current meter 103F is an existing measuring device such as a flow meter. The current meter 103F is installed at an appropriate place around the power storage device 20.

The output unit 104 includes an interface for connecting an external device. An example of an external device is a display device (not shown) such as a liquid crystal display. Alternatively, the external device may be a terminal device (not shown) such as a computer or smartphone used by the user. The calculation unit 101 outputs the estimation result of the state of the power storage device 20 from the output unit 104 to the external device. The estimation device 100 may include a notification unit such as an LED lamp or a buzzer in order to notify the user of the estimation result of the state of the power storage device 20.

Hereinafter, the content of the arithmetic processing executed by the estimation device 100 will be described.
In the embodiment, the electrochemical phenomenon of the power storage element 200 is described by a single particle model, and the heat phenomenon is described by a heat transfer equation. The single particle model and the heat transfer equation are each rewritten into a state space model, and then rewritten into an expansion system equation in which both are coupled. The estimation device 100 estimates the state of the power storage element 200 by solving the equation of the expansion system using the state estimator. In the following, (A) a state space model using a single particle model, (B) a state space model using a heat transfer equation, (C) an expansion system equation, and (D) a state estimation using an expansion system equation. Each will be described in turn.

(A) State-space model using a single particle model FIG. 5 is an explanatory diagram illustrating a single particle model. The Newman model is known as a physical model showing the charge / discharge behavior of a lithium ion battery. The Newman model regards a battery as consisting of three spatial regions: a negative electrode porous body, a separator, and a positive electrode porous body, and (1) solid phase potential distribution, (2) liquid phase potential distribution, and (3) liquid phase concentration (lithium). The ion concentration) distribution and (4) the solid-phase occluded lithium ion concentrations of the positive electrode and the negative electrode are solved while considering the charge transfer reaction resistance and the equilibrium potential at the solid-liquid interface.

The five main equations solved in the Newman model are the Nernst-Plank equation, the Fick diffusion equation, the charge conservation equation, the Nernst equation, the SOC-OCP relational equation, and the Butler-Volmer equation. Here, the Nernst-Plank equation represents the diffusion / migration of lithium ions in the electrolytic solution. The Fick diffusion formula represents the molecular diffusion of occluded lithium ions in the solid phase of the active material particles. The charge-saving formula represents electron conduction in active material particles. The Nernst equation and the SOC-OCP relational equation represent the equilibrium potential at the solid-liquid interface. SOC (State Of Charge) is an index showing a state of charge in which a full charge is 1 and a complete discharge is 0. OCP (Open Circuit Potential) is an equilibrium potential difference between a liquid phase and a solid phase when there is a redox reaction, and is usually expressed as a relative value with respect to a reference electrode as a reference.

The Newman model is the most successful physical model of lithium-ion batteries due to its physical precision and extensive usage record. However, since the calculation element is finely divided in the energization direction of the battery to be calculated, the calculation load is high and it is not suitable for online processing. Therefore, in the embodiment, a single particle model (Single-Particle Model) which is a simplification of the Newman model is used. In the single particle model, the calculation load of the Newman model can be significantly reduced by assuming that the active material particles of the positive electrode and the negative electrode are all in the same state.

Since the single particle model is a group of ordinary differential equations obtained by removing the space differential from the Newman model, which is a group of partial differential equations including the space derivative and the time derivative, it is easy to bring it into the state space model described later. .. For details on the single particle model, see, for example, "Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior, Meng Guo, Godfrey Sikha, and Ralph E. White, Journal of The Electrochemical Society, 158 (2) 122-132 (2011). ) ”And so on.

FIG. 6 is an explanatory diagram illustrating a coordinate system in the Fick diffusion equation. In the single particle model, the positive electrode active material particles are represented as one particle. Let the radius of the positive electrode active material particles be R _p (m). Typically, 0.1 μm <R _p <10 μm. The diffusion of occluded lithium ions is solved by the radial Fick diffusion equation in spherical coordinates. As a coordinate axis, consider the r _p axis with the center of the sphere as the origin. Let c _p be the concentration of occluded lithium ions in the positive electrode active material particles. The dimension of c _p is mol / m ³ , which is a function of the position r and the time t. r _p = 0 represents the center of the positive electrode active material particles. r _p = R _p is the position of the outermost periphery of the positive electrode active material particles, and represents the solid-liquid interface (that is, the place where the charge transfer reaction occurs).

The radial Diffusion equation in spherical coordinates is as shown in Equation 1. D _p is the diffusion coefficient m ² / s of the occluded lithium ion in the positive electrode active material particles. D _p may be a function of r _p or c _p , or may be a function of temperature T, but is expressed as a constant in the formula for simplification.

Equation 2 shows the difference equation when the sphere is evenly divided in the radial direction in order to calculate the diffusion of occluded lithium ions. As an example, the number of divisions is 5. In FIG. 6, the points divided into _five are shown as r ₁ , r ₂ , ..., R 5 in order from the surface of the sphere. r ₁ represents the outermost surface of the sphere (ie, the solid-liquid interface), and r ₅ represents the center of the sphere. Let Δr _p be the distance between adjacent computational elements. In FIG. 6, an example in which the sphere is evenly divided into five in the radial direction is shown, but the number of divisions may be other than 5, and may be unevenly divided.

Here, c _{p and i} represent the concentration of the stored lithium ion in the split element i, Δc _{p and i} represent the change in the concentration of the stored lithium ion in the split element i, and Δt represents the time step of the calculation. In Equation 2, the central difference was used as the difference method. Alternatively, other difference methods such as forward difference and backward difference may be used.

At i = 5, the number 2 is as follows due to the symmetry.

On the outermost surface (i = 1) of the positive electrode active material particles, there is an inflow and outflow of occluded lithium ions due to a charge transfer reaction. Assuming that the volume of the positive electrode is V _p (m ³ ), the volume ratio of the active material particles is ε _{s, p} , and the number of active material particles in the positive electrode is n _p .

Therefore, the total active material particle surface area _Sp (m ² ) is represented by the equation 5.

At this time, the reaction current density I _reac (A / m ² ) on the surface of the active material particles is represented by the equation 6. Here, I (A) is the current flowing through the battery, and 0 <I when discharging.

Assuming that the valence of the reaction is z and the Faraday constant is F (C / mol), the amount of inflow and outflow of stored lithium ions J _p (mol / m ² s) is

Therefore, the difference equation of the occluded lithium ion at i = 1 is represented by the equation 8.

Similarly, the difference equation of the occluded lithium ion at i = 2 to 5 can be summarized as the number 9.

By performing the time difference using the forward Euler method, the following equation tens is obtained. Here, the subscripts k and k + 1 are natural numbers representing time steps.

Up to this point, the diffusion of stored lithium ions in the positive electrode active material particles has been described, but the same equation holds for the diffusion of stored lithium ions in the negative electrode active material particles. However, for diffusion in the negative electrode active material particles, it is only necessary to change the subscript p to n and reverse the amount of occluded lithium ions on the surface of the active material particles.

The sum of the total amount of stored lithium ions (mol) in the positive electrode active material particles and the total amount of stored lithium ions (mol) in the negative electrode active material particles is constant unless a side reaction is considered. Assuming that the total amount of stored lithium ions charged in the initial stage of production is N _tot (mol), N _tot is represented by the following number 11.

Since N _tot is a constant, one character can be erased from c _{p, 5} to c _{p, 1} and c _{n, 1} to c _{n, 5} . For example, solving the number 11 for c _{n, 5} gives the number 12.

In the equation 12, c _{p, 1} to c _{p, 5} and c _{n, 1} to c _{n, 4} are state variables. To simplify the description, the coefficients of each state variable are expressed as _{an5, p1} to _{an5, p5} and _{an5, n1} to _{an5, n4} , and the constant term is expressed as f _{n, 5} . 13 is obtained.

The same equation as the number 10 representing the concentration of occluded lithium ions in the positive electrode active material particles, the number 10 representing the concentration of occluded lithium ions in the negative electrode active material particles, and the number 13 solved for c _{n, 5} are combined into one. When collectively described in a matrix format, the following number 14 is obtained. Here, u = 1.

The value of each component of the matrix shown in Eq. 14 is given by Eq. 15 and Eq. 16. The value of the component not given a value by the equations 15 and 16 is zero.

Next, the observation equation will be described.
The occluded lithium ion concentration in the active material particles shown in the number 14 and the like cannot be directly measured. The value that can be measured is, for example, the voltage between the terminals of the positive and negative electrodes. The voltage V is determined by the following equation.

Here, OCP _p (c _{p, 1} ) is the equilibrium potential of the positive electrode and is a function of the occluded lithium ion concentration c _{p, 1} at the solid-liquid interface of the positive electrode active material particles. OCP _n (c _{n, 1} ) is the equilibrium potential of the negative electrode as described above, and is a function of the occluded lithium ion concentration c _{n, 1} at the solid-liquid interface of the negative electrode active material particles. R _ohm is a voltage drop (ohm overvoltage) due to ohmic resistance in the electron conduction section and the ion conduction section. R _ohm may be a function of temperature T. η _{act, p} (cp _{, 1} , I) is the activation overvoltage at the solid-liquid interface of the positive electrode active material particles, and the occluded lithium ion concentration c _{p, 1} , current I at the solid-liquid interface of the positive electrode active material particles. , And a non-linear function of temperature T. η _{act, n} (c _{n, 1} , I) is the activation overvoltage at the solid-liquid interface of the negative electrode active material particles, and the occluded lithium ion concentration c _{n, 1} and the current I at the solid-liquid interface of the negative electrode active material particles. , And a non-linear function of temperature T. That is, the observed voltage V is the occluded lithium ion concentration c _{p, 1} at the solid-liquid interface of the positive electrode active material particles, the occluded lithium ion concentration c _{n, 1} at the solid-liquid interface of the negative electrode active material particles, and the current I. It is a complex non-linear function of temperature T.

Hereinafter, each item on the right side of the equation 17 will be described.
FIG. 7 is a graph showing the equilibrium potential of the positive electrode, and FIG. 8 is a graph showing the equilibrium potential of the negative electrode. The horizontal axis of FIG. 7 represents the occluded lithium ion concentration c _{p, 1} at the solid-liquid interface of the positive electrode active material particles, and the vertical axis represents the equilibrium potential OCP _p (c _{p, 1} ) of the positive electrode. The horizontal axis of FIG. 8 represents the occluded lithium ion concentration c _{n, 1} at the solid-liquid interface of the negative electrode active material particles, and the vertical axis represents the equilibrium potential OCP _n (c _{n, 1} ) of the negative electrode. The graphs of FIGS. 7 and 8 show that the equilibrium potentials of the positive and negative electrodes are a non-linear function of the occluded lithium ion concentration at the solid-liquid interface. The equilibrium potential is theoretically a function of temperature, but in practice the effect of temperature can be ignored.

The ohm resistance R _ohm (Ω) of the entire battery is represented by the equation 18.

Here, R _{s and pos} represent the electron resistance (Ω) of the solid phase of the positive electrode, R _{s and neg} represent the electronic resistance (Ω) of the solid _phase of the negative electrode, and RI represents the ion resistance (Ω) of the electrolytic solution. Each resistance may be determined by the shape dimension, the solid phase volume fraction, the tortuosity, and the physical properties of the material. Ohmic resistance is often considered to be largely unaffected by temperature, but may be a function of temperature.

The activation overvoltage η _{act, p} of the positive electrode is expressed by the Butler-Volmer equation of the number 19.

Here, I is the current (A), Sp is the total active material particle surface area (m ² ), ip ₀ is the exchange current density (A / m ² ), α is the transition coefficient, _n is the number of involved electrons, and F is Faraday. The constant (C / mol), η _{act, p} is the activation overvoltage (V) of the positive electrode, R is the gas constant (J / (K · mol)), and T is the temperature (K). It is known that the exchange current density ip 0 is a function of the occluded lithium ion concentration c _{p , 1} at the solid-liquid interface of the positive electrode active material particles. As shown in Equation 19, the activation overvoltage η _{act, p} of the positive electrode is a complicated nonlinear function of the occluded lithium ion concentration c _{p, 1} , the current I, and the temperature T at the solid-liquid interface of the positive electrode active material particles. Although the specific formula is not specified, the activation overvoltage η _{act, n} of the negative electrode is the same as the activation overvoltage η _{act, p} of the positive electrode.

So far, (A) has described an example of a single particle model, but this is only described as an example. Other models may be used as long as they adequately represent the characteristics of the battery. If the computational load is not a problem, the Newman model may be used.

(B) State space model using the heat transfer equation The heat transfer equation of the power storage device 20 shown in FIG. 1 is represented by the equation 20.

Here, T ₁ to T ₅ , S ₁ to S ₅ , Q ₁ to Q ₅ , and h ₁ to h ₅ are the temperature (K), surface area (m ² ), and calorific value (W) of the power storage elements 200A to 200E, respectively. ), Heat transfer coefficient to the outside (W / m ² / K). k _ij represents the thermal conductance (W / K) between the i-th power storage element 200 (for example, the power storage element 200A) and the j-th power storage element 200 (for example, the power storage element 200B). ρ, C _p , and V represent the density (kg / m ³ ), specific heat (J / kg / K), and volume (m ³ ) of the power storage element 200. In the embodiment, the density, specific heat, and volume of each power storage element 200 are common, but the density, specific heat, and volume of each power storage element 200 may be set individually. T ₀ represents the environmental temperature (K).

The left side of the number 20 represents the amount of heat used to raise the temperature of the power storage element 200. The term including the thermal conductance k _ij on the right side represents the thermal conduction based on the temperature difference between the adjacent power storage elements 200. The term including the heat transfer coefficients h ₁ to h ₅ on the right side represents heat dissipation from the power storage element 200 to the outside, and is a negative value when heat dissipation is generated. The term including _Q1 to _Q5 represents the heat generation of the power storage device 20. Factors of heat generation include Joule heat and reaction heat due to energization.

In the following, parameters other than T ₁ to T ₅ will be described as constant values (time-invariant). Alternatively, the time variation of parameters other than T ₁ to T ₅ may be considered. Even if the time change of parameters other than T ₁ to T ₅ is taken into consideration, the same calculation method is established.

When the time derivative in the number 20 is rewritten by the time difference and arranged, the following number 21 is obtained.

Here, k represents a time step and is a natural number. α is (ρC _p V / Δt) ^-1 .

Next, in order to represent the number 21 as a matrix, the state vector x _T (k), the vector b _T , and the matrix _AT are defined by the following number 22.

Here, a _T11 = 1-α (S ₁ h ₁ + k ₁₂ ), a _T22 = 1-α (k ₁₂ + k ₂₃ + S ₂ h ₂ ), a _T33 = 1-α (k ₂₃ + k ₃₄ + S ₃ h ₃ ) ), A _T44 = 1-α (k ₃₄ + k ₄₅ + S ₄ h ₄ ), a _T55 = 1-α (k ₄₅ + S ₅ h ₅ ). Further, a _T12 = a _T21 = αk ₁₂ , a _T23 = a _T32 = αk ₂₃ , a _T34 = a _T43 = αk ₃₄ , a _T45 = a _T54 = αk ₄₅ , and the others are 0.

Using the representation of the discrete space equation of state, Equation 22 can be described as follows: However, it is assumed that the control signal u _T ^k == 1.

The observation equation is expressed as the equation 24. The t in the upper right represents transposition. More generally, the direct term is added to the right side, but in the case of heat transfer, the representative time is larger than the calculation time, so it can be ignored in many cases.

In the observation equation of Eq. 24, the scalar observation value y _T ^k was used. Alternatively, there may be multiple observations. CT is an observation vector (or observation matrix) whose element is the measured element _temperature . For example, when measuring only the temperature of the fifth power storage element 200, the observation vector is represented by the equation 25.

(C) Expansion system equations In the following, the expansion system equations are obtained by coupling the state space model derived using the electrochemical single particle model and the state space model derived using the heat transfer equation. Derived.

The number 26 is obtained by adding a disturbance term to the stored lithium ion concentration shown in the number 14. If the disturbance has a normal distribution (ie, Gaussian noise), an unscented Kalman filter or an ensemble Kalman filter can be used. If the disturbance is not normally distributed, a particle filter can be used. The disturbance may be expressed by a random number.

In the following, the number 26 may be abbreviated as the number 27.

When the battery module consists of five cells, the occluded lithium ion concentration is defined for each of the five cells, so the equation of state of the single particle model is composed of five equations as shown in Equation 28. Since it would be redundant to describe all these equations, in the embodiment, only a single particle model of one battery will be described.

By adding a disturbance term to the temperature shown in Equation 23, Equation 29 is obtained. If the disturbance has a normal distribution (ie, Gaussian noise), an unscented Kalman filter or an ensemble Kalman filter can be used. If the disturbance is not normally distributed, a particle filter can be used. The disturbance may be expressed by a random number.

In the following, the number 29 may be abbreviated as the number 30.

The above-mentioned number 26 and number 27 deal with the stored lithium ion concentration, and the number 29 and the number 30 deal with the temperature of the power storage element 200. It is possible to calculate both as independent variables, but in reality they are related to each other.

For example, temperature-related electrochemical parameters include diffusion coefficients D _p and D _n of occluded lithium ions and activation overvoltages of positive and negative electrodes η _{act, p} , η _{act, n} . The mass diffusivity D _p of the occluded lithium ion in the positive electrode active material particles appearing in the number 1 or the like is a function of temperature, and is set based on the results of experimental data and first-principles calculation. The same applies to the diffusion coefficient D _n of the occluded lithium ions in the negative electrode active material particles. The activation overvoltages η _{act, p} , η _{act, n} of the positive electrode and the negative electrode appearing in the number 17 and the like are also functions of temperature, and an Arenius type function with respect to temperature such as the Butler-Volmer equation is used.

The calorific value is mentioned as a relation from electrochemical to temperature. Since the calorific value of the battery is (current) × (overvoltage), it is expressed as the number 31.

The final equation of state in which electrochemistry and heat transfer are coupled is expressed as in equation 32.

Since the mathematical formula becomes complicated when all the terms are described, the number 32 is expressed by using the function f of the nonlinear transformation according to the convention. In the number 32, the vector without the lower right subscript represents a vector containing all the electrochemical variables and the temperature variables.

Since the observed amount is the temperature and the voltage between terminals, the observation equation is expressed as the number 33.

In observation, if the disturbance has a normal distribution (that is, Gaussian noise), an unscented Kalman filter or an ensemble Kalman filter can be used. If the disturbance is not normally distributed, a particle filter can be used. The disturbance may be expressed by a random number.

(D) State estimation using the equation of the expansion system The estimation device 100 according to the first embodiment uses a particle filter and is a time series model represented by the state equation of the number 32 and the observation equation of the number 33. The update is sequentially calculated and the state of the power storage element 200 is estimated.

Hereinafter, the procedure of the process executed by the estimation device 100 will be described.
FIG. 9 is a flowchart illustrating a state estimation procedure according to the first embodiment. The arithmetic unit 101 of the estimation device 100 gives an initial value of k = 1 (step S101). The calculation unit 101 may give a temporary value preset as the initial value of the voltage and the current of the power storage element 200, and give the environmental temperature as the initial value of the temperature.

Next, the arithmetic unit 101 generates N particles for each state variable (step S102). Here, a number of about ¹⁰² to ¹⁰⁶ is usually used for N.

Next, the arithmetic unit 101 generates a random number corresponding to v _k for i = 1, 2, ..., N (step S103).

The calculation unit 101 updates the state of the particles to the state of the particles in the next time step by executing the calculation based on the number 34 for all N particles (step S104).

The calculation unit 101 acquires the sensor outputs of the voltage sensor 103A, the current sensor 103B, and the temperature sensors 103C and 103D through the input unit 103 (step S105), and for all N particles, the particle weight P is based on the observation equation. Calculate _k ⁽ⁱ⁾ (step S106). The particle weight is the probability (likelihood) that the observed value y _k is observed when the state vector x _k of the particle i is obtained, and is described by the following equation.

The calculation unit 101 normalizes the particle weight P _k ⁽ⁱ⁾ calculated in step S106 based on the following equation (step S107).

The calculation unit 101 calculates a vector obtained by taking a weighted average of the weight of the particles and the state vector as an estimated value by the particle filter (step S108). The arithmetic expression is as shown in Equation 37. By this calculation, an estimated value of the stored lithium ion concentration and the temperature in each storage element 200 can be obtained.

The calculation unit 101 determines whether or not to calculate the next time step (step S109). The calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the preset time step has been reached. Alternatively, the calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the state of the power storage element 200 has reached a preset state. When the next time step is not calculated (S109: NO), the calculation unit 101 ends the process according to this flowchart.

When calculating the next time step (S109: YES), the arithmetic unit 101 resamples (stratified sampling) the particles for estimation of the next time step (step S110). The arithmetic unit 101 may determine the state vector in the time step k + 1 by assuming that the state vector x _k ⁽ⁱ⁾ in the time step k is restored and extracted in proportion to p _k ⁽ⁱ⁾ . After resampling the particles, the calculation unit 101 returns the process to step S104 and continues the calculation in the next time step k + 1.

As described above, the arithmetic unit 101 of the estimation device 100 can estimate the occluded lithium ion concentration and temperature of each storage element 200 at each time step. The calculation unit 101 may estimate various physical quantities in the power storage element 200 such as SOC, OCP, and activation overvoltage based on the estimated storage lithium ion concentration and temperature.

In the first embodiment, a configuration for estimating a state variable using a particle filter has been described. The particle filter is a filter method for a state-space model having non-linearity and non-Gaussian property, and can target a more general state-space model without assuming linearity or Gaussian property. Further, the particle filter has a relatively simple algorithm and can be easily implemented in the estimation device 100.

(Embodiment 2)
In the second embodiment, a state estimation algorithm using an ensemble Kalman filter will be described. That is, the estimation device 100 in the second embodiment sequentially calculates the time update of the time series model represented by the state equation of the number 32 and the observation equation of the number 33 by using the ensemble Kalman filter, and determines the state of the power storage element 200. presume.

FIG. 10 is a flowchart illustrating a state estimation procedure according to the second embodiment. The arithmetic unit 101 of the estimation device 100 gives an initial value of k = 1 (step S121). The calculation unit 101 may give a temporary value preset as the initial value of the voltage and the current of the power storage element 200, and give the environmental temperature as the initial value of the temperature. Let the variances of the disturbance term v _k in the equation of state and the disturbance term w _k in the observation equation be Q _k and R _k , respectively.

Next, the arithmetic unit 101 generates N particles for each state variable (step S122). Here, a number of about ¹⁰² to ¹⁰⁶ is usually used for N.

Next, the arithmetic unit 101 generates a random number corresponding to v _k for i = 1, 2, ..., N (step S123). It is assumed that v _k follows a normal distribution and the variance is known.

The calculation unit 101 updates the state of the particles to the state of the particles in the next time step by executing the calculation based on the number 38 for all N particles (step S124).

The calculation unit 101 calculates the difference between the state vector of each particle of i = 1, 2, ..., N and the average value of the state vector of all particles (step S125), and calculates the state quantity predicted value for all the particles. The covariance matrix P _k is calculated (step S126). The covariance matrix P _k is represented by the number 39.

The calculation unit 101 acquires the sensor outputs of the voltage sensor 103A, the current sensor 103B, and the temperature sensors 103C, 103D through the input unit 103 (step S127). The acquired sensor output gives the observed value y _k ⁱ of each particle in the time step k.

The calculation unit 101 calculates the observation error r _k ⁱ in the time step k of the i-th particle (step S128). Here, w _k is an observation disturbance. The observation error r _k ⁱ is represented by the number 40.

The calculation unit 101 calculates the Kalman gain K _k in the time step k (step S129). The Kalman gain K _k is represented by the number 41.

The calculation unit 101 calculates the estimated value x _k ⁽ⁱ⁾ _hat of the i-th particle (step S130). The estimated value x _k ⁽ⁱ⁾ _hat is represented by the number 42. That is, the arithmetic unit 101 corrects the first predicted value of the number 38 by using the observation error r _k ⁱ of the number 40 and the Kalman gain K _k of the number 41.

The calculation unit 101 calculates the average value x _k _hat of each particle (step S131). The average value x _k _hat of each particle represents the state vector estimated value obtained by the ensemble Kalman filter, and is calculated by the following equation.

The estimated value (mean value x _k _hat of each particle) obtained by the number 43 includes an estimated value of the occluded lithium ion concentration and the temperature of each power storage element 200. The calculation unit 101 determines whether or not to calculate the next time step (step S132). The calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the preset time step has been reached. Alternatively, the calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the state of the power storage element 200 has reached a preset state.

When calculating the next time step (S132: YES), the calculation unit 101 returns the process to step S124 and executes the calculation in the next time step k + 1. When the next time step is not calculated (S132: NO), the calculation unit 101 ends the process according to this flowchart.

The estimation device 100 in the second embodiment estimates a state variable using an ensemble Kalman filter. The ensemble Kalman filter is a filter method for a state-space model having non-linearity and non-Gaussian property, and can target a more general state-space model. The ensemble Kalman filter has a relatively simple algorithm and can be easily implemented in the estimation device 100.

(Embodiment 3)
In the third embodiment, a state estimation algorithm using an extended Kalman filter will be described. That is, the estimation device 100 in the third embodiment sequentially calculates the time update of the time series model represented by the state equation of the number 32 and the observation equation of the number 33 by using the extended Kalman filter, and determines the state of the power storage element 200. presume.

FIG. 11 is a flowchart illustrating a state estimation procedure according to the third embodiment. The arithmetic unit 101 of the estimation device 100 gives an initial value of k = 1 (step S141). The calculation unit 101 may give a temporary value preset as the initial value of the voltage and the current of the power storage element 200, and give the environmental temperature as the initial value of the temperature. Let the variances of the disturbance term v _k in the equation of state and the disturbance term w _k in the observation equation be Q _k and R _k , respectively. Assume an initial variance-covariance matrix P.

The calculation unit 101 calculates the pre-state estimated value x ⁻ _{k + 1} _ hat by the following equation (step S142).

The arithmetic unit 101 derives the Jacobian determinant of the nonlinear transformation f by the following procedure (step S143). For example, when the nonlinear transformation f is expressed as the number 46 for the three-component vector represented by the number 45, the Jacobian is calculated by the number 47. The arithmetic unit 101 may derive the Jacobian in advance and store it in the storage unit 102.

The arithmetic unit 101 calculates the prior error covariance matrix P ⁻ _{k + 1} by the following equation (step S144). Here, the state transition matrix _Ak is represented by the equation 49.

The calculation unit 101 calculates the Kalman gain g _k (step S145). The Kalman gain g _k is represented by the number 50. Here, c _k ^T is represented by the number 51.

The calculation unit 101 acquires the sensor outputs of the voltage sensor 103A, the current sensor 103B, and the temperature sensors 103C, 103D through the input unit 103 (step S146). The acquired sensor output gives the observed value y _k in the time step k.

The calculation unit 101 calculates the post-state estimated value x _{k + 1} _hat and the post-error covariance matrix P _k by the following equations (step S147).

The estimated value (posterior state estimated value x _{k + 1} _hat) obtained by the number 52 includes an estimated value of the occluded lithium ion concentration and the temperature of each power storage element 200. The calculation unit 101 determines whether or not to calculate the next time step (step S148). The calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the preset time step has been reached. Alternatively, the calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the state of the power storage element 200 has reached a preset state.

When calculating the next time step (S148: YES), the calculation unit 101 returns the process to step S142 and executes the calculation in the next time step k + 1. When the next time step is not calculated (S148: NO), the calculation unit 101 ends the process according to this flowchart.

The estimation device 100 in the third embodiment estimates a state variable using an extended Kalman filter. The extended Kalman filter is a method that enables the application of a Kalman filter by linearly approximating a nonlinear model near a representative value such as an average value. The extended Kalman filter has a small calculation load and can be realized by an inexpensive device.

(Embodiment 4)
In the fourth embodiment, a state estimation algorithm using an unscented Kalman filter will be described. That is, the estimation device 100 in the fourth embodiment uses the unscented Kalman filter to sequentially calculate the time update of the time series model represented by the equation of state of equation 32 and the observation equation of equation 33, and the state of the power storage element 200. To estimate.

FIG. 12 is a flowchart illustrating a state estimation procedure according to the fourth embodiment. The arithmetic unit 101 of the estimation device 100 gives an initial value of k = 1 (step S161). The calculation unit 101 may give a temporary value preset as the initial value of the voltage and the current of the power storage element 200, and give the environmental temperature as the initial value of the temperature. Let the variances of the disturbance term v _k in the equation of state and the disturbance term w _k in the observation equation be Q _k and R _k , respectively. Assume an initial variance-covariance matrix P.

The calculation unit 101 generates a calculation point called a sigma point by using the estimated value x ⁻ _k obtained in a certain calculation step and the variance-covariance matrix P _k (step S162). When the generated (2n + 1) sigma points are numbered like the number 53, the j (j is an integer satisfying −n ≦ j ≦ n) th sigma point is expressed as the number 54.

However, sig (j) is a function that gives -1 when j <0, 0 when j = 0, and +1 when 0 <j. κ is a positive adjustment parameter.

The weight w _j of each sigma point is w _j = κ / 2 (n + κ) when j ≠ 0, and w ₀ = κ / (n + κ) when j = 0.

The arithmetic unit 101 updates the states of all sigma points, the pre-state estimated values, and the pre-error covariance matrix as in the following equation (step S163).

Since the calculation unit 101 has updated the pre-state estimated value and the pre-error covariance matrix, the sigma point is recalculated by the following equation (step S164).

The calculation unit 101 updates the observation sigma point according to the following equation (step S165).

The calculation unit 101 calculates the pre-observed estimated value y ⁻ _{k + 1} _ hat by the following equation (step S166).

The arithmetic unit 101 calculates the covariance matrix P ^- _{yy, k + 1} of the prior observation error by the following equation (step S167).

The arithmetic unit 101 calculates the covariance matrix P ^- _{xy, k + 1} of the prior state / observation error by the following equation (step S168).

The calculation unit 101 calculates the Kalman gain g _k by the following equation (step S169).

The calculation unit 101 acquires the sensor outputs of the voltage sensor 103A, the current sensor 103B, and the temperature sensors 103C, 103D through the input unit 103 (step S170). The acquired sensor output gives the observed value y _{k +} 1 in the time step k + 1.

The arithmetic unit 101 multiplies the Kalman gain g _k by the difference between the observed value y _{k + 1} and the pre-observed estimated value y ⁻ _{k + 1} _ hat to estimate the state in the time step k + 1 (step S171).

The arithmetic unit 101 calculates the covariance matrix P _{k + 1} of the post-observation error by the following equation (step S172).

The post-observation estimated value (x _{k + 1} _hat) obtained by the number 62 includes an estimated value of the occluded lithium ion concentration and the temperature of each storage element 200. The calculation unit 101 determines whether or not to calculate the next time step (step S173). The calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the preset time step has been reached. Alternatively, the calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the state of the power storage element 200 has reached a preset state.

When calculating the next time step (S173: YES), the calculation unit 101 returns the process to step S162 and executes the calculation in the next time step k + 1. When the next time step is not calculated (S173: NO), the calculation unit 101 ends the process according to this flowchart.

The estimation device 100 in the fourth embodiment estimates the short-circuit resistance by using an unscented Kalman filter. The unscented Kalman filter provides a plurality of sample points called sigma points around the mean value, and estimates the covariance matrix based on these statistical properties. Fragrance-free Kalman filters perform better than extended Kalman filters in the problem of strong non-linearity.

(Embodiment 5)
In the fifth embodiment, a configuration in which the electrochemical phenomenon of the power storage element 200 is represented by an equivalent circuit model will be described.

FIG. 13 is a circuit diagram showing an example of an equivalent circuit model. The equivalent circuit model of the power storage element 200 is often represented by a combination of a resistor, a capacitance component, and a voltage source as shown in FIG. 13, for example.

In FIG. 13, R ₀ is an ohm resistance component, R ₁ is a positive electrode reaction resistance component, C ₁ is a positive electrode capacitance component, R ₂ is a negative electrode reaction resistance component, C ₂ is a negative electrode capacitance component, and E _eq is an open circuit. Voltage (OCV: Open Circuit Voltage). However, FIG. 13 is an example, and there is no limitation on the combination of series and parallel, and the number and types of electric circuit elements.

It is known that the charge / discharge characteristics of the power storage element 200 represented by a lithium ion battery are strongly affected by temperature and SOC. SOC is an abbreviation for State Of Charge, and represents a fully charged state as 100% and a fully discharged state as 0%. In the following, it is assumed that the open circuit voltage (OCV) is a function of SOC, and R ₀ to R ₂ and C ₁ to C ₂ are functions of temperature. At this time, the equation of state is represented by the number 64, and the observation equation is represented by the number 65.

Here, Δt is a time step, Cap is the full charge capacity (C) of the power storage element 200, and ^uk = I (current).

Here, OCV (SOC) is a non-linear function of SOC.

The equation of state, which represents the voltage of the equivalent circuit, plus the disturbance is expressed by the equation 66.

The equation of state of heat transfer plus disturbance is expressed by the equation 67.

Here, Q included in the vector b _T of the number 67 is a calorific value, and is expressed as follows.

From these equations of state and observation equations, equations of state and observations of the expansion system similar to those of equations 32 and 33 can be obtained. Subsequent calculation procedures are the same as those of the first to fourth embodiments, and the calculation unit 101 of the estimation device 100 uses a particle filter, an ensemble Kalman filter, an extended Kalman file, and an unscented Kalman filter to form the power storage element 200. The voltage and temperature can be estimated.

In the fifth embodiment, the open circuit voltage (OCV) is a function of SOC, and R ₀ to R ₂ and C ₁ to C ₂ are functions of temperature. Alternatively, the open circuit voltage may be a function of SOC and temperature, and R ₀ to R ₂ and C ₁ to C ₂ may be a function of temperature and SOC.

(Embodiment 6)
In the sixth embodiment, an embodiment in which the deterioration of the battery is further considered in the single particle model will be described. By using the estimation device 100, more precise deterioration prediction simulation can be performed even when based on limited temperature information. Specifically, by using the temperature estimated by the estimation device 100 as the temperature included in the known deterioration prediction formula, more precise deterioration prediction becomes possible. In particular, in a storage battery system in which an assembled battery in which a plurality of cells are connected in series is used, the performance of the cell with large deterioration has a great influence on the performance of the entire storage battery system. It is very useful to make a more precise prediction of deterioration using the estimated temperature.

It is known that the deterioration behavior of a battery is strongly affected by temperature. A more accurate simulation can be performed by accurately considering the temperature, but in reality, the observable quantity is limited, and there is a problem that the simulation based only on the sensor measured quantity is inferior in accuracy. By performing temperature correction by this method and making the temperature information more accurate, the accuracy of deterioration prediction can be improved.

There are very few models that take electrochemical phenomena into consideration when simulating battery deterioration prediction. For example, "International Publication No. 2017/016966: A method for estimating the current open circuit voltage curve of a battery" discloses a method of deriving deterioration due to a decrease in charge carriers (deterioration due to so-called capacitance imbalance) by numerical calculation. Has been done. The method disclosed in this patent document has the disadvantage that it cannot be used while energized and the battery must be stopped. Further, it is known that the mechanism of battery deterioration is not limited to the decrease of charge carriers (capacity imbalance), which is insufficient to cover a wide range of battery deterioration.

In addition to this, as a method using machine learning, for example, "Japanese Patent Laid-Open No. 2019-168453: Deterioration Estimator, Computer Program, and Deterioration Estimating Method" exists. In this method, the calculation process is performed by machine learning, it is difficult to obtain physical consideration, and it is difficult to reflect it in the product design.

In the sixth embodiment, deterioration prediction simulation is performed using the single particle model described in the present specification based on the concept of the patent document “Japanese Patent Application No. 2019-064218: development support device, development support method, and computer program”. Describes how to execute.

Battery deterioration mechanisms represented by lithium-ion batteries include at least (1) isolation of active material particles, (2) decrease in charge carriers, (3) increase in electrical resistance, and (4) conductivity in electrolytic solutions. It is known that there are four types of decline. These deterioration mechanisms contribute in combination to change the charge / discharge characteristics of the battery, causing a decrease in capacity.

Temperature is one of the most important factors that determine the rate of progress of these deteriorations. Therefore, it is important to grasp the temperature precisely from the viewpoint of deterioration prediction. The estimation device 100 can determine the rate of progress of deterioration, assuming that it has a temperature dependence based on, for example, an Arrhenius-type reaction rate equation. Alternatively, the estimation device 100 may determine the rate of progression of deterioration based on any other function of temperature. It is known that deterioration includes aging deterioration (sometimes called calendar deterioration) that deteriorates over time and energization deterioration that deteriorates due to energization, and it has been confirmed by experiments that both are functions of temperature. Has been done.

The first deterioration mechanism is the isolation of active material particles. Isolation of the active material particles proceeds mainly at the positive electrode during discharge, but it may occur at the time of current suspension or during discharge, and it may occur at the negative electrode. In the sixth embodiment, it is assumed that the isolation of the active material particles occurs only in the positive electrode during discharge for simplification, but other cases can be easily expanded by the same equation expansion.

The calculation unit 101 of the estimation device 100 calculates the speed at which the isolation of the positive electrode active material particles progresses based on the time difference equation of the number 69.

Ε _{s, p} in the number 69 is the volume ratio of the positive electrode active material particles contained in the numbers 4 to 6, 8, 10 and 15. Isolation of the positive electrode active material particles is expressed as a decrease in the volume ratio of the positive electrode active material particles. k _{0 and iso} are constants of the progress rate of isolation of positive electrode active material particles with time, and a function of temperature is used. The function may be, for example, an Arrhenius-type exponential function, or any other function. k _{1 and iso} are constants of the progress rate of isolation of positive electrode active material particles by energization, and functions of temperature and current are used. α _iso is an arbitrary constant. In many cases, k _{0, iso} may be 0, but k _{1, iso} is a positive value and increases monotonically with temperature. In other words, the isolation of the positive electrode active material does not proceed when there is no energization, and the isolation of the positive electrode active material tends to proceed at higher temperatures when there is energization. In addition to this, various variants can be considered, such as an expression whose right side contains ε _{s, p} itself, and a function of other state variables. Since a non-linear filter is used, any equation may be used.

The second degradation mechanism is the reduction of charge carriers. The decrease in charge carriers is also called the capacity imbalance. In this phenomenon, the charge carriers that pass between the positive electrode and the negative electrode during charging and discharging decrease due to side reactions on the electrode surface.

The arithmetic unit 101 of the estimation device 100 calculates the decrease in charge carriers based on the two equations described in Equation 70.

The b _n1 of the number 70 is the same as the coefficient in the number 16, and the current I in the number 16 is replaced with (I + δ). δ is the rate of decrease of the charge carrier. This equation shows that the occluded lithium ion concentration c _{n, 1} at the solid-liquid interface of the negative electrode active material particles decreases due to factors other than the change in the occluded lithium ion concentration due to the charging and discharging of the battery. Note that the current I flowing through the battery takes both positive and negative values, whereas δ is a positive value. N _tot of the number 70 is the total amount of occluded lithium ions of the positive and negative electrodes, and is the same as that described in the numbers 11 and 12.

K _{0, imb} of the number 71 is the rate of decrease of the stored lithium ion concentration with time, and a function of temperature is used. The function may be, for example, an Arrhenius-type exponential function, or any other function. k _{1 and imb} are constants of the progress rate of the occluded lithium ion concentration by energization, and the function of temperature and current is used. α _imb is an arbitrary constant. In most cases, k _{0, imb} and k _{1, imb} are positive values and increase monotonically with temperature. In addition to this, various variants can be considered, such as the right-hand side being a function of other state variables. Since a non-linear filter is used, any equation may be used.

The third deterioration mechanism is an increase in electrical resistance. The causes of the increase in electrical resistance can be further classified into peeling between the current collector foil and the electrode, breakage of the conduction path of the conductive auxiliary agent, formation of a resistor film, and the like. These are described in the patent document "Japanese Patent Application No. 2019-064218: Development Support Device, Development Support Method, and Computer Program". The decrease in conductivity in the electrolytic solution, which is the fourth deterioration mechanism, is similar to the increase in electrical resistance, and will be dealt with together.

The calculation unit 101 of the estimation device 100 calculates the speed at which the electric resistance of the battery increases based on the time difference equation of the number 72.

_Rohm in the number 72 is the ohmic resistance _Rohm of the entire battery included in the number 17, and I is the current I flowing through the battery included in the numbers 6, 8, 10 and 17. k _{0, ohm} is a constant of the progress rate of the increase of ohm resistance with time, and a function of temperature is used. The function may be, for example, an Arrhenius-type exponential function, or any other function. k _{1, ohm} is a constant of the progress rate of the increase of ohm resistance due to energization, and a function of temperature or current is used. α is an arbitrary constant. In most cases, k _{0, ohm} and k _{1, ohm} are positive values and increase monotonically with temperature. In addition to this, various variants can be considered, such as an expression whose right side contains R _ohm itself, and a function of other state variables. Since a non-linear filter is used, any equation may be used.

The equations obtained by adding the disturbance term to the above equations are numbers 73 to 75.

Here, v _{εs and p} are disturbances of the positive electrode active material particle volume ratio, v _δ is a disturbance term of the decrease rate of the stored lithium ion concentration, and v _ohm is a disturbance term of the ohm resistance increase rate. By adding the numbers 73 to 75 considering these disturbance terms to the number 32, in other words, by adding ε _{s, p} , N _tot , and R _ohm to the state variable vector x _k of the number 32, the battery It is possible to estimate the state in consideration of the deterioration mechanism.

(Embodiment 7)
In the seventh embodiment, a method of estimating the mass diffusivity D _{s, p} of the stored lithium ions in the positive electrode active material particles and the diffusivity D _{s, n} of the stored lithium ions in the negative electrode active material particles will be described. It is known that these values are difficult to measure and change from moment to moment as the deterioration progresses, and cannot be easily obtained. Therefore, these diffusion coefficients may be included in the state variables for estimation.

Assuming that the diffusion coefficient of the occluded lithium ion in the active material particles does not change with time, a time evolution equation such as Eq. 76 is established.

v _{Ds, p} and v _{Ds, n} are disturbance terms. By newly adding these equations to the state variable vector xk of the number 32, the diffusion _coefficient of the occluded lithium ion in the active material particles can be estimated.

(Embodiment 8)
In the eighth embodiment, an embodiment in which the deterioration of the battery is further considered in the equivalent circuit model will be described. In the sixth embodiment, the method of predicting deterioration based on the single particle model has been described, but in the eighth embodiment, the deterioration prediction method based on the equivalent circuit model described in the fifth embodiment will be described.

The calculation unit 101 of the estimation device 100 calculates the speed at which the deterioration of the equivalent circuit element progresses based on the time difference equation of the number 77.

R ₀ and the like in the number 77 are the circuit constants shown in the numbers 64, 65 and 13. k _{0 and} R 0 are constants of the rate of deterioration of R ₀ over time, and a function of temperature is used. The function may be, for example, an Arrhenius-type exponential function, or any other function. k _{1 and} R 0 are constants of the rate of deterioration of R ₀ due to energization, and functions of temperature and current are used. α _R0 is an arbitrary constant. In addition to this, various variants can be considered, such as an expression whose right side contains R ₀ itself, and a function of other state variables. Since a non-linear filter is used, any equation may be used. The same applies to constants other than R ₀ , R ₁ to C ₂ . Alternatively, a more complicated equivalent circuit may be defined, and R ₃ , R ₄ ..., C ₃ , C ₄ ... may be defined separately.

The deterioration prediction model based on the single particle model described in the sixth embodiment and the deterioration prediction model based on the equivalent circuit model described in the eighth embodiment may be used in combination. For example, the model of the decrease in the stored lithium ions (capacitive balance deviation) of the sixth embodiment is used for the deterioration of the equilibrium potential E _eq in the equivalent circuit model, and the equivalent circuit is used for the internal resistance. It's okay.

The equation obtained by adding the disturbance term to the number 77 is the number 78.

v _R0 is a disturbance term of _R0 , and the others are the same. By adding the number 78 considering these disturbance terms to the number 32, in other words, by adding R ₀ , R ₁ , R ₂ , C ₁ , and C ₂ to the state variable vector x _k of the number 32, the battery It is possible to estimate the state in consideration of the deterioration of the equivalent circuit element.

Hereinafter, application examples will be described.

(Application example 1)
The digital twin of the power storage device 20 may be constructed by using the estimation device 100. Digital twin refers to a technology that collects the state of a product that actually exists (temperature, current, voltage, etc.), the surrounding environment, the usage status, etc. in real time, and builds a simulation model of the same state as the reality on a computer. .. In the digital twin, the simulation model is constantly updated based on the values measured by the sensors, and the same state as the actual product can be reproduced on the computer in almost real time. If this mechanism is used, when an abnormality occurs in a real product, it is immediately reflected in the simulation model, and if the simulation model is analyzed, the cause of the abnormality may be identified. Further, since the behavior of the latent variable that cannot be directly measured can be known from the sensor value, it is possible to predict or prevent the failure.

Further, the estimation device 100 generates information such as preventive maintenance such as parts replacement, feedback to product development, replacement timing prediction, timely maintenance, and proposal of a more efficient operation method based on the estimation result. The generated information may be output from the output unit 104.

Furthermore, since the simulation model can take charge of the analysis and analysis of the cause of failure, which was conventionally performed by specialized employees, a cost reduction effect can be expected.

(Application example 2)
The estimation device 100 may graphically display the estimated state of the power storage element 200 in real time. FIG. 15 is a schematic diagram showing a display example of a temperature state. In the example of FIG. 15, an example in which the temperature of the outer surface of the power storage device 20 is three-dimensionally displayed graphically is shown. Each time the estimation device 100 estimates the temperature state of each power storage element 200, the estimation device 100 generates a distribution map showing the temperature distribution, and outputs the generated distribution map to the display device 150. In this way, the estimation device 100 can graphically display the temperature of the outer surface of the power storage device 20 on the display device 150 in real time. The display device 150 is connected to, for example, the output unit 104 of the estimation device 100. Alternatively, the estimation device 100 may be configured to include the display device 150.

The graphics display may be performed at the request of the user or may be performed at the request of the maintenance personnel. By displaying it graphically, the temperature state of the power storage device 20 can be intuitively grasped, and an abnormality can be detected at an early stage. Alternatively, the estimation device 100 may graphically display the estimated electrochemical state of the power storage device 20.

The embodiments disclosed this time should be considered to be exemplary in all respects and not restrictive. The scope of the present invention is indicated by the scope of claims, not the above-mentioned meaning, and is intended to include all modifications within the meaning and scope equivalent to the scope of claims.

10 Power storage system 20 Power storage device 100 Estimator 101 Calculation unit 102 Storage unit 103 Input unit 103A Voltage sensor 103B Current sensor 103C Temperature sensor 103D Temperature sensor 104 Output unit 200 Power storage element M Recording medium PG State estimation program

Claims (9)

An acquisition unit that acquires measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature of the power storage element.
An estimation device including an estimation unit that inputs the acquired measurement data to a state estimator constructed to simulate the electrochemical phenomenon and thermal phenomenon of the power storage element and estimates the state of the power storage element. The parameter describing the electrochemical phenomenon includes the activation overvoltage of the power storage element expressed as a function of the temperature of the power storage element.
The estimation device according to claim 1, wherein the parameter describing the thermal phenomenon includes the calorific value of the energy storage element represented as a function of the activation overvoltage of the energy storage element. The estimator according to claim 1 or 2, wherein the state estimator is a nonlinear filter configured to output a state quantity related to the power storage element when the measurement data is input. The estimation device according to claim 3, wherein the non-linear filter includes a particle filter, an ensemble Kalman filter, an extended Kalman filter, or an unscented Kalman filter. The state estimator is
The time transition of each state variable is obtained by using the equation of state representing the time transition of the state variable including the concentration of the occluded ion in the active material particle and the temperature related to the power storage element.
The likelihood of state estimation is obtained using the observation equation that expresses the relationship between the state variable and the observed amount indicated by the measured data.
The estimation device according to any one of claims 1 to 4, wherein the estimated value of the state variable is updated according to the likelihood of the obtained state estimation. An acquisition unit that acquires measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature of the power storage element.
An estimation device including an estimation unit that inputs the acquired measurement data to an equivalent electric circuit of the power storage element and a state estimator constructed to simulate a thermal phenomenon, and estimates the state of the power storage element. The state estimator is
It includes one or more equations in which the state quantity representing the characteristics of the power storage element changes with time or with energization.
1. The estimation device described. Using a computer,
Acquisition of measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature of the power storage element,
An estimation method in which the acquired measurement data is input to a state estimator configured to simulate the electrochemical phenomenon and the thermal phenomenon of the power storage element, and the state of the power storage element is estimated. On the computer
Acquisition of measurement data including the voltage of the power storage element, the current flowing through the power storage element, and the temperature of the power storage element,
A computer program for inputting acquired measurement data to a state estimator configured to simulate an electrochemical phenomenon and a thermal phenomenon of the power storage element, and executing a process of estimating the state of the power storage element.

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