Estimation device, estimation method, and computer program

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

[Technical field]

[0001] The present invention relates to an estimation device, an estimation method, and a computer program. [Background technology]

[0002] In recent years, energy storage elements such as lithium-ion batteries have been used in a wide range of fields, including as power sources for notebook personal computers, smartphones and other mobile terminals, renewable energy storage systems, and power sources for IoT devices.

[0003] In order to effectively utilize such secondary batteries, the behavior of the secondary battery at any time is estimated. As one method for estimating the behavior of a secondary battery, a method is known in which a Kalman filter is applied to an equivalent circuit model that represents the secondary battery by an electric circuit, and the behavior of the secondary battery, such as SOC (State Of Charge), is estimated (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2016-065828 A Summary of the Invention [Problem to be solved by the invention]

[0005] However, the method disclosed in Patent Document 1 is configured to estimate the behavior by focusing only on the terminal voltage of the storage element, and does not take into account the thermal phenomenon of the storage element. It is known that the characteristics of the storage element are strongly dependent on temperature, and the prediction accuracy of the conventional method was low. In addition, Patent Document 1 uses an equivalent circuit, and does not take into account electrochemical phenomena such as solid-liquid current, material diffusion, and electrochemical reaction that occur inside the battery. Conventionally, there has been no idea of ​​coupling electrochemical phenomena and thermal phenomena in the storage element, and it is difficult to obtain effective estimation accuracy in an actual device.

[0006] The present invention has been made in consideration of the above circumstances, and aims to provide an estimation device, an estimation method, and a computer program that take into account both the electrochemical and thermal phenomena of an energy storage element and can achieve effective estimation accuracy in an actual device. [Means for solving the problem]

[0007] The estimation device includes an acquisition unit that acquires measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, and an estimation unit that inputs the acquired measurement data to a state estimator constructed to simulate electrochemical and thermal phenomena of the storage element, and estimates the state of the storage element.

[0008] The estimation method uses a computer to acquire measurement data including the voltage of a storage element, the current flowing through the storage element, and the temperature related to the storage element, inputs the acquired measurement data to a state estimator configured to simulate electrochemical and thermal phenomena of the storage element, and estimates the state of the storage element.

[0009] The computer program causes a computer to acquire measurement data including the voltage of a storage element, the current flowing through the storage element, and the temperature related to the storage element, input the acquired measurement data to a state estimator configured to simulate electrochemical and thermal phenomena of the storage element, and execute a process to estimate the state of the storage element. Effect of the Invention

[0010] According to the above configuration, both the electrochemical phenomenon and the thermal phenomenon of the energy storage element are taken into consideration, and effective estimation accuracy can be achieved in an actual device. [Brief description of the drawings]

[0011] [Figure 1] 1 is an external view of a power storage system according to an embodiment; [Diagram 2] FIG. 2 is an exploded perspective view showing a configuration example of an energy storage element. [Diagram 3] 3 is a schematic diagram showing a configuration example of a wound electrode body. FIG. [Figure 4] FIG. 2 is a block diagram illustrating an internal configuration of an estimation device. [Diagram 5] FIG. 2 is an explanatory diagram for explaining a single particle model. [Figure 6] FIG. 2 is an explanatory diagram for explaining a coordinate system in the Fick diffusion formula. [Figure 7] 1 is a graph showing the equilibrium potential of a positive electrode. [Figure 8] 1 is a graph showing the equilibrium potential of a negative electrode. [Figure 9] 4 is a flowchart illustrating a state estimation procedure according to the first embodiment. [Figure 10] 11 is a flowchart illustrating a state estimation procedure in the second embodiment. [Figure 11] 13 is a flowchart illustrating a state estimation procedure in the third embodiment. [Figure 12] 13 is a flowchart illustrating a state estimation procedure in the fourth embodiment. [Figure 13] FIG. 2 is a circuit diagram showing an example of an equivalent circuit model. [Figure 14] 1 is a graph showing the relationship between lithium ion concentration and ion conductivity in an electrolyte solution. [Figure 15] FIG. 13 is a schematic diagram showing an example of displaying a temperature state. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] The estimation device includes an acquisition unit that acquires measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, and an estimation unit that inputs the acquired measurement data to a state estimator constructed to simulate electrochemical and thermal phenomena of the storage element, and estimates the state of the storage element. According to this configuration, the state of the energy storage element, which cannot be directly measured, can be estimated through the state variables obtained from the state estimator. In addition, since the state of the energy storage element is estimated taking into account both electrochemical phenomena and thermal phenomena, which are closely related to each other, it is possible to achieve effective estimation accuracy in an actual device.

[0013] In the estimation device, the parameters describing the electrochemical phenomenon may include an activation overvoltage of the energy storage element expressed as a function of the temperature of the energy storage element, and the parameters describing the thermal phenomenon may include a heat generation amount of the energy storage element expressed as a function of the activation overvoltage of the energy storage element. By using the activation overvoltage expressed as a function of temperature and the heat generation amount expressed as a function of the activation overvoltage as parameters, it becomes possible to estimate a state in which the electrochemical phenomenon and the thermal phenomenon of the energy storage element are coupled.

[0014] In the estimation device, the state estimator may be a nonlinear filter configured to output a state quantity related to the energy storage element when the measurement data is input. With this configuration, since a nonlinear filter is used, even if noise is present in the system or the sensor, a value closer to the true value can be calculated.

[0015] 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 nonlinear estimation algorithm, state estimation based on physical mechanisms of electrochemical and thermal phenomena can be performed even in an environment with external disturbances.

[0016] In the estimation device, the state estimator may determine the time transition of each state variable using a state equation that represents the time transition of state variables including the concentration of occluded ions in the active material particles and the temperature related to the energy storage element, determine the likelihood of the state estimation using an observation equation that represents the relationship between the state variables and the observation quantities indicated by the measurement data, and update the estimated values ​​of the state variables according to the determined likelihood of the state estimation. With this configuration, the state of the energy storage element that cannot be directly observed can be estimated in a time series manner through the state variables that are successively updated. In this embodiment, ions occluded in the active material particles (i.e., ions in the solid phase) are referred to as occluded ions.

[0017] The estimation device includes an acquisition unit that acquires measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, and an estimation unit that inputs the acquired measurement data to a state estimator constructed to simulate an equivalent electrical circuit and thermal phenomenon of the storage element, and estimates the state of the storage element. According to this configuration, the state of the energy storage element, which cannot be directly measured, can be estimated through the state variables obtained from the state estimator. In addition, since the state of the energy storage element is estimated taking into account the equivalent electric circuit and thermal phenomena that are closely related to each other, it is possible to demonstrate effective estimation accuracy in an actual device.

[0018] In the estimation device, the state estimator may include one or more equations in which a state quantity representing a characteristic of the energy storage element transitions over time due to the passage of time or current flow, and may predict deterioration of the energy storage element using an observation equation that represents a relationship between a state variable describing the state of the energy storage element and an observation quantity indicated by the measurement data. With this configuration, deterioration of the energy storage element due to the passage of time or current flow can be estimated.

[0019] The estimation method uses a computer to acquire measurement data including the voltage of a storage element, the current flowing through the storage element, and the temperature related to the storage element, inputs the acquired measurement data to a state estimator configured to simulate electrochemical and thermal phenomena of the storage element, and estimates the state of the storage element.

[0020] The computer program causes a computer to acquire measurement data including the voltage of a storage element, the current flowing through the storage element, and the temperature related to the storage element, input the acquired measurement data to a state estimator configured to simulate electrochemical and thermal phenomena of the storage element, and execute a process to estimate the state of the storage element.

[0021] Hereinafter, the present invention will be described in detail with reference to the drawings showing embodiments thereof. (Embodiment 1) 1 is an external view of a power storage system 10 according to an embodiment. The power storage system 10 according to the embodiment includes an estimation apparatus 100, power storage elements 200A-200E, and a storage case 300 that accommodates the estimation apparatus 100 and the power storage elements 200A-200E. In the present embodiment, the power storage elements 200A-200E configure a power storage device 20. In the following description, when it is not necessary to distinguish between the power storage elements 200A-200E, they will also be simply referred to as power storage element 200.

[0022] The estimation device 100 is a flat circuit disposed, for example, on the upper surface of the plurality of energy storage elements 200, and estimates the state of each energy storage element 200 at a predetermined point in time. Specifically, the estimation device 100 acquires measurement data including the voltage of the energy storage element 200, the current flowing through the energy storage element 200, and the temperature related to the energy storage element 200, and estimates the state of the energy storage element 200 using a simulation model based on the acquired measurement data.

[0023] In the example of Fig. 1, the estimation device 100 is disposed on the upper surface of the energy storage element 200. Alternatively, the estimation device 100 may be disposed on a side surface or a lower surface of the energy storage element 200. The shape of the estimation device 100 is not limited to a flat plate. Furthermore, the estimation device 100 may be a server device located away from the energy storage element 200, and may be configured to acquire the above-mentioned measurement data through communication and estimate the state of the energy storage element 200 using a simulation model based on the acquired measurement data.

[0024] The energy storage device 200 is a secondary battery such as a lithium ion secondary battery. The energy storage device 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 electronic devices, a power source for power storage, and the like.

[0025] FIG. 1 shows a battery pack in which five rectangular parallelepiped energy storage elements 200 are arranged in series. In the first embodiment, the number of energy storage elements 200 is described as five. Alternatively, the number of energy storage elements 200 may be one, or two or more. Furthermore, some of the energy storage elements 200 may be connected in parallel. The energy storage elements 200 may be secondary batteries other than lithium ion secondary batteries.

[0026] The configuration of energy storage element 200 will be described below. 2 is an exploded perspective view showing a configuration example of the energy storage element 200. The energy storage element 200 is configured by housing a flat-shaped wound electrode body 210 and an electrolyte (not shown) in a hollow rectangular parallelepiped battery case 220. A positive electrode terminal 222A and a negative electrode terminal 223A for external connection are provided on a lid 221 of the battery case 220. The positive electrode terminal 222A and the negative electrode terminal 223A are electrically connected to a positive electrode current collector 222B and a negative electrode current collector 223B, respectively. The material of the battery case 220 is, for example, a metal material that is lightweight and has high thermal conductivity, such as aluminum.

[0027] FIG. 3 is a schematic diagram showing a configuration example of the wound electrode body 210. The wound electrode body 210 is configured by stacking a sheet-shaped positive electrode 211 on which a positive electrode active material layer 211A is formed and a sheet-shaped negative electrode 212 on which a negative electrode active material layer 212A is formed, with two sheet-shaped separators 213 in between, and winding them. The positive electrode 211 and the negative electrode 212 are arranged in a state where they are shifted from each other in the width direction of the sheet. At one end in the width direction of the positive electrode 211, a region where the positive electrode active material layer 211A is not formed is provided, and a positive electrode current collector 222B is joined to this region. For example, aluminum foil is used for the positive electrode current collector 222B. Similarly, at the other end in the width direction of the negative electrode 212, a region where the negative electrode active material layer 212A is not formed is provided, and a negative electrode current collector 223B is joined to this region. For example, copper foil is used for the negative electrode current collector 223B.

[0028] The positive electrode active material layer 211A includes a positive electrode active material. The positive electrode active material includes secondary particles consisting of aggregates of primary particles as active material particles. The primary particles are made of lithium metal composite oxide particles. The lithium metal composite oxide includes lithium, oxygen, and other elements (e.g., Mn, Ni, Co, Fe, Nb, W, P, Si, etc.). The elements other than lithium and oxygen may be one type or multiple types. The positive electrode active material layer 211A may further include a conductive assistant, a binder, etc. As the conductive assistant, for example, carbon black such as acetylene black (AB) or other carbon materials (e.g., graphite) are preferably used. As the binder, for example, polyvinylidene fluoride (PVDF) or the like is used.

[0029] The negative electrode active material layer 212A includes a negative electrode active material. For example, a carbon material such as graphite, hard carbon, or soft carbon is used as the negative electrode active material. The negative electrode active material layer 212A may further include a binder, a thickener, or the like. For example, styrene butadiene rubber (SBR) or the like is used as the binder. For example, carboxymethyl cellulose (CMC) or the like is used as the thickener.

[0030] 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.

[0031] The electrolyte housed in the battery case 220 together with the wound electrode body 210 may be the same as that used in conventional lithium ion batteries. For example, an electrolyte containing a supporting salt in an organic solvent may be used. As the organic solvent, for example, aprotic solvents such as carbonates, esters, and ethers are used. As the supporting salt, for example, lithium salts such as LiPF6, LiBF4, and LiClO4 are suitably used. The electrolyte may contain various additives such as a gas generating agent, a film forming agent, a dispersing agent, and a thickening agent.

[0032] 2 and 3, a square lithium ion battery including a wound electrode body 210 has been described as an example of the energy storage element 200. Alternatively, the energy storage element 200 may be a lithium ion battery including a stacked electrode body, or may be a cylindrical lithium ion battery, a laminated lithium ion battery, or the like. Furthermore, the energy storage element 200 may be an all-solid-state lithium ion battery that uses a solid as the electrolyte.

[0033] In an embodiment, in the estimation device 100 described below, measurement data including the voltage, current, and temperature of the storage element 200 is acquired, and the state of the storage element 200 is estimated based on the acquired measurement data using a simulation model that simulates electrochemical and thermal phenomena.

[0034] FIG. 4 is a block diagram for explaining the 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 incorporated in a 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.

[0035] The calculation unit 101 is an arithmetic circuit including a central processing unit (CPU), a read only memory (ROM), a random access memory (RAM), and the like. In the embodiment, the calculation unit 101 functions as a state estimator. The CPU included in the calculation unit 101 executes various computer programs stored in the ROM or the storage unit 102, and controls the operation of each of the above-mentioned hardware components, thereby causing the entire device to function as the estimation device of the present application. Specifically, the calculation unit 101 acquires measurement data including the voltage, current, and temperature of the energy storage element 200, and estimates the state of the energy storage element 200 based on the acquired measurement data using a state estimator that simulates electrochemical and thermal phenomena.

[0036] The calculation unit 101 is not limited to the above configuration, and may be any processing circuit or calculation circuit including multiple CPUs, a multi-core CPU, a GPU (Graphics Processing Unit), a microcomputer, a volatile or non-volatile memory, etc. The calculation unit 101 may also have functions such as a timer that measures the elapsed time from when a measurement start instruction is given to when a measurement end instruction is given, a counter that counts numbers, and a clock that outputs date and time information.

[0037] 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 programs stored in the storage unit 102 include, for example, a state estimation program PG for causing the calculation unit 101 to execute calculations using a simulation model. The data stored in the storage unit 102 include parameters used in the state estimation program PG, data temporarily generated by calculations 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, and density of each storage element 200, the value of thermal conductance between adjacent storage elements 200, and the heat transfer rate to the outside. The state estimation program PG is provided, for example, by a non-transient recording medium M on which the computer program is recorded in a readable manner. The recording medium M is a portable memory such as a CD-ROM, a USB memory, or an SD (Secure Digital) card. The calculation 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 telecommunications.

[0038] The thermal conductance value used in the calculation of temperature estimation may change due to expansion of the energy storage element 200. For this reason, the storage unit 102 may store a table indicating the relationship between the value of the thermal conductance and the value of the strain measured by a strain sensor 103E described later.

[0039] 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. For this reason, the storage unit 102 may store a table indicating the relationship between the value of the heat transfer coefficient and the value of the flow velocity measured by a flow meter 103F described later. Alternatively, a calculation may be performed to calculate the heat transfer coefficient from a relational expression that holds among the Nusselt number, the Prandtl number, and the Reynolds number.

[0040] 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 energy storage element 200, a current sensor 103B that measures the current flowing through the energy storage element 200, a temperature sensor 103C that measures the temperature of the energy storage element 200 (element temperature), and a temperature sensor 103D that measures the temperature around the energy storage element 200 (environmental temperature).

[0041] Voltage sensor 103A is an existing voltage sensor, and measures in time series the voltage between the terminals of energy storage element 200. Calculation unit 101 of estimation device 100 acquires, via input unit 103, data on the voltage measured by voltage sensor 103A as needed.

[0042] Current sensor 103B is an existing sensor such as a current transformer or a Hall effect current sensor, and measures in time series the current flowing through energy storage element 200. Calculation unit 101 of estimation device 100 acquires, via input unit 103, data on the current measured by current sensor 103B as needed.

[0043] The temperature sensor 103C is an existing sensor such as a thermocouple or a thermistor, and measures the temperature (element temperature) of the energy storage element 200 in a time series manner. The calculation unit 101 of the estimation device 100 acquires data of the temperature measured by the temperature sensor 103C through the input unit 103 at any time. In this embodiment, the energy storage element 200 to be measured is a part (for example, the energy storage element 200E) of the five energy storage elements 200A to 200E included in the energy storage device 20. The energy storage element 200 to be measured may be one, or may be two to four. That is, when the number of energy storage elements 200 is N (N is an integer equal to or greater than 2), the energy storage elements 200 to be measured are appropriately installed in the range of 1 to (N-1). The temperature sensor 103C is disposed on the upper surface of the energy storage element 200, for example. Alternatively, the temperature sensor 103C is disposed on the side surface or the lower surface of the energy storage element 200.

[0044] Temperature sensor 103D is an existing sensor such as a thermocouple or a thermistor, and measures in time series the temperature (environmental temperature) around power storage element 200. Calculation unit 101 of estimation device 100 acquires, via input unit 103, data on the temperature measured by temperature sensor 103D as needed.

[0045] A strain sensor 103E that detects the magnitude of strain of the energy storage element 200 may be connected to the input unit 103. The strain sensor 103E is an existing sensor that uses a strain gauge type load cell or the like. The strain sensor 103E is provided for each of the energy storage elements 200.

[0046] A flow meter 103F that measures the flow of air around the power storage device 20 may be connected to the input unit 103. The flow meter 103F is an existing measuring device such as a flow meter. The flow meter 103F is installed at an appropriate location around the power storage device 20.

[0047] The output unit 104 includes an interface for connecting an external device. An example of the 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 a smartphone used by a user. The calculation unit 101 outputs the estimation result of the state of the power storage device 20 to the external device from the output unit 104. The estimation device 100 may include a notification unit such as an LED lamp or a buzzer to notify the user of the estimation result of the state of the power storage device 20.

[0048] The details of the calculation process executed by the estimation device 100 will be described below. In the embodiment, the electrochemical phenomenon of the energy storage element 200 is described by a single particle model, and the thermal 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 augmented system equation that couples the two. The estimation device 100 estimates the state of the energy storage element 200 by solving the augmented system equation using a state estimator. Below, (A) a state space model using a single particle model, (B) a state space model using a heat transfer equation, (C) an augmented system equation, and (D) state estimation using an augmented system equation will be described in order.

[0049] (A) State space model using single particle model Figure 5 is an explanatory diagram explaining the single particle model. The Newman model is known as a physical model that shows the charge / discharge behavior of lithium-ion batteries. The Newman model considers a battery to consist of three spatial regions: a negative electrode porous body, a separator, and a positive electrode porous body, and solves (1) solid-phase potential distribution, (2) liquid-phase potential distribution, (3) liquid-phase concentration (lithium ion concentration) distribution, and (4) solid-phase occluded lithium ion concentration of the positive and negative electrodes, while also taking into account the charge transfer reaction resistance and equilibrium potential at the solid-liquid interface.

[0050] The 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 equation, and the Butler-Volmer equation. Here, the Nernst-Plank equation represents the diffusion and migration of lithium ions in the electrolyte. The Fick diffusion equation represents the molecular diffusion of absorbed lithium ions in the solid phase of the active material particles. The charge conservation equation represents the electronic conduction in the active material particles. The Nernst equation and the SOC-OCP equation represent the equilibrium potential at the solid-liquid interface. SOC (State Of Charge) is an index that represents the state of charge, with full charge being 1 and full discharge being 0. OCP (Open Circuit Potential) is the equilibrium potential difference between the liquid phase and the solid phase when there is an oxidation-reduction reaction, and is usually expressed as a relative value to the reference electrode that serves as the standard.

[0051] The Newman model is the most successful physical model of lithium-ion batteries due to its physical sophistication and extensive use. However, since the calculation elements of the battery to be calculated are finely divided in the current flow direction, the calculation load is high and it is not suitable for online processing. Therefore, in the embodiment, a single-particle model that is a simplified version of the Newman model is used. The single-particle model can significantly reduce the calculation load of the Newman model by assuming that the active material particles of the positive and negative electrodes are all in the same state.

[0052] The single-particle model is a group of ordinary differential equations that removes spatial differentials under appropriate assumptions from the Newman model, which is a group of partial differential equations that include spatial and time differentials, and is therefore easy to introduce into the state space model described below. Details of the single-particle model are described, for example, in "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)".

[0053] FIG. 6 is an explanatory diagram for explaining the coordinate system in the Fick diffusion equation. In the single particle model, the positive electrode active material particle is represented as one particle. The radius of the positive electrode active material particle is R p (m). Typically, 0.1 μm <R p The diffusion of the absorbed lithium ions is solved by the radial Fick diffusion equation in spherical coordinates. The coordinate axis is r p Consider the axis. The concentration of absorbed lithium ions in the positive electrode active material particles is c p Let us assume that p The dimension is mol / m 3 and is a function of position r and time t. p = 0 represents the center of the positive electrode active material particle. p =R pis the outermost position of the positive electrode active material particle, and represents the solid-liquid interface (i.e., the location where the charge transfer reaction occurs).

[0054] The radial Fick diffusion equation in spherical coordinates is given by Equation 1. D p is the diffusion coefficient m of the absorbed lithium ion in the positive electrode active material particle 2 / s. D p is r p Or p It may be a function of or a function of temperature T, but in the formula, it is written as a constant for simplicity.

[0055]

number

[0056] To calculate the diffusion of absorbed lithium ions, the difference equation when the sphere is divided evenly in the radial direction is shown in Equation 2. As an example, the number of divisions is 5. In Figure 6, the 5 division points are shown as r1, r2, ..., r5 from the surface of the sphere. r1 represents the outermost surface of the sphere (i.e., the solid-liquid interface), and r5 represents the center of the sphere. The distance between adjacent calculation elements is Δr p Although an example in which the sphere is divided into five equal parts in the radial direction is shown in Fig. 6, the number of divisions may be other than five, and the sphere may be divided unequally.

[0057]

number

[0058] where c p,i is the concentration of absorbed lithium ions in the division element i, Δc p,i represents the change in concentration of absorbed lithium ions in the division element i, and Δt represents the time step of the calculation. In Equation 2, central difference is used as the difference method. Alternatively, other difference methods such as forward difference and backward difference may be used.

[0059] For i=5, by symmetry, number 2 becomes:

[0060]

number

[0061] At the outermost surface (i=1) of the positive electrode active material particle, the absorbed lithium ions flow in and out due to the charge transfer reaction. The volume of the positive electrode is V p (m 3 ), and the active material particle volume ratio is ε s,p , the number of active material particles in the positive electrode is n p If we assume that

[0062]

number

[0063] Therefore, the total active material particle surface area S p (m 2 ) is represented by the number 5.

[0064]

number

[0065] At this time, the reaction current density I reac (A / m 2 ) is expressed by the following equation 6. Here, I(A) is the current flowing through the battery, and when discharging, it is 0 <Iとする。

[0066]

number

[0067] If the reaction valence is z and the Faraday constant is F (C / mol), the amount of absorbed lithium ions flowing in and out, J p (mol / m 2 s) is

[0068]

number

[0069] Therefore, the difference equation for the absorbed lithium ions at i=1 is expressed by Equation 8.

[0070]

number

[0071] Similarly, the differential equation for the absorbed lithium ions when i=2 to 5 can be summarized as shown in Equation 9.

[0072]

number

[0073] By performing time differencing using the forward Euler algorithm, we obtain the following equation (10), where the subscripts k and k+1 are natural numbers that represent the time step.

[0074]

number

[0075] So far, we have described the diffusion of absorbed lithium ions in positive electrode active material particles, but the same formula also applies to the diffusion of absorbed lithium ions in negative electrode active material particles. However, for diffusion in negative electrode active material particles, all you need to do is change the subscript p to n and reverse the flow of absorbed lithium ions into and out of the active material particle surface.

[0076] The sum of the total amount (mol) of absorbed lithium ions in the positive electrode active material particles and the total amount (mol) of absorbed lithium ions in the negative electrode active material particles is constant unless side reactions are taken into consideration. tot (mol), N tot is expressed by the following equation (11).

[0077]

number

[0078] N tot Since is a constant, c p,5 ~c p,1 and c n,1 ~c n,5 For example, you can change the number 11 to c n,5 Solving for this, we obtain number 12.

[0079]

number

[0080] In the formula 12, c p,1 ~c p,5 and c n,1 ~c n,4 are state variables. For simplicity, we use the coefficients of each state variable as n5,p1 ~a n5,p5 and a n5,n1 ~a n5,n4 and the constant term is f n,5 Then, we obtain the following equation (13).

[0081]

number

[0082] A formula similar to the formula 10 representing the concentration of absorbed lithium ions in the positive electrode active material particles, a formula similar to the formula 10 representing the concentration of absorbed lithium ions in the negative electrode active material particles, and c n,5 Putting the solutions of (13) together in matrix form gives us (14), where u=1.

[0083]

number

[0084] The value of each element of the matrix shown in Equation 14 is given by Equation 15 and Equation 16. The value of elements for which values ​​are not given by Equation 15 and Equation 16 is zero.

[0085]

number

[0086]

number

[0087] Next, the observation equation will be described. The concentration of absorbed lithium ions in the active material particles, as shown in Equation 14, cannot be measured directly. The only value that can be measured is, for example, the voltage between the positive and negative terminals. The voltage V is determined by the following formula:

[0088]

number

[0089] Here, OCP p (c p,1 ) is the equilibrium potential of the positive electrode, and the concentration of absorbed lithium ions at the solid-liquid interface of the positive electrode active material particles c p,1 It is a function of OCP. n (c n,1 ) is the equilibrium potential of the negative electrode, as already mentioned, and the concentration of absorbed lithium ions at the solid-liquid interface of the negative electrode active material particles c n,1 It is a function of R ohm is the voltage drop (ohmic overvoltage) due to the ohmic resistance in the electronic and ionic conductive parts. R ohm may be a function of temperature T. η act,p (c p,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, and 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 absorbed lithium ion concentration c n,1 , current I, and temperature T. In other words, the observed voltage V is a nonlinear function of the concentration of absorbed lithium ions c p,1, the concentration of absorbed lithium ions at the solid-liquid interface of the negative electrode active material particles c n,1 , current I, and temperature T.

[0090] Each term on the right side of equation 17 will be explained below. 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 is the occluded lithium ion concentration c p,1 The vertical axis represents the equilibrium potential OCP of the positive electrode. p (c p,1 ) The horizontal axis of FIG. 8 represents the occluded lithium ion concentration c n,1 The vertical axis represents the equilibrium potential OCP of the negative electrode. n (c n,1 7 and 8 show that the equilibrium potentials of the positive and negative electrodes are nonlinear functions of the concentration of absorbed lithium ions at the solid-liquid interface. Theoretically, the equilibrium potential is also a function of temperature, but in practice the effect of temperature can be ignored.

[0091] The ohmic resistance across the battery, R ohm (Ω) is expressed by the number 18.

[0092]

number

[0093] Here, R s,pos is the electronic resistance of the positive electrode solid phase (Ω), R s,neg is the electronic resistance of the negative electrode solid phase (Ω), R I represents the ionic resistance (Ω) of the electrolyte. The resistance of each may be determined by the geometry, solid volume fraction, tortuosity, and material properties. The ohmic resistance can often be considered to be largely independent of temperature, but may also be a function of temperature.

[0094] Positive electrode activation overpotential η act,p is expressed by the Butler-Volmer formula in equation 19.

[0095]

number

[0096] where I is the current (A) and S p is the total active material particle surface area (m 2 ), i p0 is the exchange current density (A / m 2 ), α is the transfer coefficient, n is the number of electrons involved, F is the Faraday constant (C / mol), η act,p is the activation overpotential of the positive electrode (V), R is the gas constant (J / (K mol)), and T is the temperature (K). The exchange current density i p0 is the concentration of absorbed lithium ions at the solid-liquid interface of the positive electrode active material particles, c p,1 As shown in Equation 19, the activation overpotential of the positive electrode, η act,p is the concentration of absorbed lithium ions at the solid-liquid interface of the positive electrode active material particles, c p,1 , current I, and temperature T are complex nonlinear functions. Although no specific formula is given, the activation overvoltage η act,n Regarding the activation overvoltage of the positive electrode, η act,p is the same as:

[0097] Up to this point, an example of the single particle model has been described in (A), but this is only one example. Other models may be used as long as they adequately represent the characteristics of the battery. If the computational load is not an issue, the Newman model may be used.

[0098] (B) State space model using the heat transfer equation The heat transfer equation of the electricity storage device 20 shown in FIG.

[0099]

number

[0100] Here, T1 to T5, S1 to S5, Q1 to Q5, and h1 to h5 are the temperatures (K) and surface areas (m 2 ), heat generation (W), heat transfer rate to the outside (W / m 2 / K).ij ρ, C represents the thermal conductance (W / K) between the i-th energy storage element 200 (e.g., the energy storage element 200A) and the j-th energy storage element 200 (e.g., the energy storage element 200B). p , V is the density of the energy storage element 200 (kg / m 3 ), specific heat (J / kg / K), volume (m 3 In the embodiment, the density, specific heat, and volume of each energy storage element 200 are common, but the density, specific heat, and volume of each energy storage element 200 may be set individually. T0 represents the environmental temperature (K).

[0101] The left side of the formula 20 represents the amount of heat used to increase the temperature of the energy storage element 200. The thermal conductance k ij The term including represents thermal conduction based on the temperature difference between adjacent energy storage elements 200. The term including heat transfer coefficients h1 to h5 on the right side represents heat dissipation from the energy storage elements 200 to the outside, and takes a negative value when heat dissipation occurs. The term including Q1 to Q5 represents heat generation in the energy storage device 20. Causes of heat generation include Joule heat and reaction heat due to current flow.

[0102] In the following description, parameters other than T1 to T5 are assumed to be constant (time-invariant). Alternatively, time changes in parameters other than T1 to T5 may be considered. Even if time changes in parameters other than T1 to T5 are considered, the same calculation method is valid.

[0103] By rewriting the time differential in equation 20 using the time difference and rearranging it, we obtain the following equation 21.

[0104]

number

[0105] Here, k is the time step and is a natural number. α is (ρC p V / Δt) -1 It is.

[0106] Next, to express Eq. 21 as a matrix, we use the state vector x T (k), vector bT , matrix A T is defined by the following equation (22).

[0107]

number

[0108] Here, a T11 =1-α(S1h1+k 12 ), a T22 =1-α(k 12 +k 23 +S2h2), a T33 =1-α(k 23 +k 34 +S3h3), a T44 =1-α(k 34 +k 45 +S4h4), a T55 =1-α(k 45 +S5h5). Also, 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 0 otherwise.

[0109] Using the discrete space state equation representation, Equation 22 can be written as follows, where the control signal u T k ==1.

[0110]

number

[0111] The observation equation is expressed as in Equation 24. The upper right suffix t indicates transposition. More generally, a direct term is added to the right hand side, but in the case of heat transfer, the representative time is larger than the calculation time, so it can often be ignored.

[0112]

number

[0113] In the observation equation of Equation 24, the scalar observation y T k Alternatively, there may be multiple observations. T is an observation vector (or observation matrix) having elements each representing a measured element temperature. For example, when measuring the temperature of only the fifth energy storage element 200, the observation vector is expressed as in Equation 25.

[0114]

number

[0115] (C) Equation of the expanded system In the following, an equation of the expanded system is derived by coupling a state space model derived using a single particle model of electrochemistry and a state space model derived using a heat transfer equation.

[0116] By adding a disturbance term to the occluded lithium ion concentration shown in Equation 14, Equation 26 is obtained. If the disturbance has a normal distribution (i.e., it is Gaussian noise), an unscented Kalman filter or an ensemble Kalman filter can be used. If the disturbance does not have a normal distribution, a particle filter can be used. The disturbance can be expressed by a random number.

[0117]

number

[0118] In the following, formula 26 may be simplified and written as formula 27.

[0119]

number

[0120] When a battery module is composed of five cells, the concentration of absorbed lithium ions is defined for each of the five cells, and therefore the state equation of the single particle model is composed of five equations as shown in Equation 28. Since describing all of these equations would be redundant, in the embodiment, only the single particle model of one battery is described.

[0121]

number

[0122] By adding the disturbance term to the temperature shown in Equation 23, we obtain Equation 29. If the disturbance has a normal distribution (i.e., it is Gaussian noise), we can use the unscented Kalman filter or the ensemble Kalman filter. If the disturbance does not have a normal distribution, we can use a particle filter. The disturbance can be represented by a random number.

[0123]

number

[0124] In the following, number 29 may be abbreviated as number 30.

[0125]

number

[0126] The above-mentioned formulas 26 and 27 deal with the absorbed lithium ion concentration, and formulas 29 and 30 deal with the temperature of the energy storage element 200. Although it is possible to calculate the two as independent variables, in reality, the two are interrelated with each other.

[0127] For example, the temperature-related electrochemical parameter is the diffusion coefficient D of the absorbed lithium ion. p ,D n and the activation overvoltage η of the positive and negative electrodes act,p ,η act,n The diffusion coefficient D of the absorbed lithium ions in the positive electrode active material particles shown in the formula 1 isp is a function of temperature and is set based on experimental data and the results of first-principles calculations. The diffusion coefficient D of the absorbed lithium ions in the negative electrode active material particles n The same is true for the activation overvoltage η of the positive and negative electrodes shown in Equation 17. act,p ,η act,n is also a function of temperature, and an Arrhenius-type function for temperature, such as the Butler-Volmer equation, is used.

[0128] The amount of heat generated can be seen as a relation between electrochemistry and temperature. The amount of heat generated by a battery is (current) x (overvoltage), and can be expressed as follows:

[0129]

number

[0130] The final equation of state coupling electrochemistry and heat transfer is expressed as shown in Equation 32.

[0131]

number

[0132] Since the formula would be complicated if all terms were written, we follow the convention and use the nonlinear transformation function f in Equation 32. In Equation 32, the vector without a subscript at the bottom right represents a vector that includes all electrochemical variables and temperature variables.

[0133] Since the observables are the temperature and the terminal voltage, the observation equation is expressed as shown in Equation 33.

[0134]

number

[0135] In the observation, if the disturbance has a normal distribution (i.e., Gaussian noise), the unscented Kalman filter or the ensemble Kalman filter can be used. If the disturbance does not have a normal distribution, the particle filter can be used. The disturbance can be represented by a random number.

[0136] (D) State estimation using the equations of the augmented system The estimation device 100 according to the first embodiment utilizes a particle filter to sequentially calculate time updates of a time series model represented by the state equation of Expression 32 and the observation equation of Expression 33, and estimates the state of the energy storage element 200.

[0137] The procedure of the process executed by the estimation device 100 will be described below. 9 is a flowchart illustrating a state estimation procedure in the first embodiment. The calculation unit 101 of the estimation device 100 provides an initial value of k=1 (step S101). The calculation unit 101 may provide provisional values ​​set in advance as initial values ​​of the voltage and current of the energy storage element 200, and may provide the environmental temperature as an initial value of the temperature.

[0138] Next, the calculation unit 101 generates N particles for each state variable (step S102). Here, N is 10 2 ~10 6 A degree of accuracy is usually used.

[0139] Next, the calculation unit 101 calculates v for i=1, 2, ..., N. k A random number corresponding to (step S103) is generated.

[0140] The calculation unit 101 executes the calculation based on Equation 34 for all N particles, thereby updating the states of the particles to the states of the particles in the next time step (step S104).

[0141]

number

[0142] 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 calculates particle weights P k (i) (Step S106). The weight of a particle is calculated by the state vector x k When we obtain the observed value y k is the probability (likelihood) of observing and is described by the following equation:

[0143]

number

[0144] The calculation unit 101 calculates the particle weight P k (i) is normalized based on the following equation (step S107).

[0145]

number

[0146] The calculation unit 101 calculates a vector obtained by taking a weighted average of the particle weights and the state vector as an estimated value by the particle filter (step S108). The calculation formula is as shown in Equation 37. By this calculation, the estimated values ​​of the absorbed lithium ion concentration and temperature in each energy storage element 200 are obtained.

[0147]

number

[0148] 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 a 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 energy storage element 200 has reached a preset state. If the next time step is not to be calculated (S109: NO), the calculation unit 101 ends the processing according to this flowchart.

[0149] When the next time step is to be calculated (S109: YES), the calculation unit 101 resamples (stratified sampling) the particles for estimating the next time step (step S110). k (i) HAp k (i) Then, the state vector at time step k+1 can be determined by assuming that the particles are resampled in proportion to the state vector at time step k+1. After resampling the particles, the calculation unit 101 returns the process to step S104 and continues the calculation at the next time step k+1.

[0150] As described above, the calculation unit 101 of the estimation device 100 can estimate, at each time step, the absorbed lithium ion concentration and temperature of each energy storage element 200. The calculation unit 101 may estimate various physical quantities of the energy storage element 200, such as the SOC, OCP, and activation overvoltage, based on the estimated absorbed lithium ion concentration and temperature.

[0151] In the first embodiment, a configuration for estimating state variables using a particle filter has been described. The particle filter is a filter method targeted at state space models having nonlinearity and non-Gaussianity, and can be targeted at more general state space models without assuming linearity or Gaussianity. In addition, the particle filter has a relatively simple algorithm and can be easily implemented in the estimation device 100.

[0152] (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 uses the ensemble Kalman filter to sequentially calculate time updates of a time series model represented by the state equation of Expression 32 and the observation equation of Expression 33, and estimates the state of the energy storage element 200.

[0153] FIG. 10 is a flowchart illustrating a state estimation procedure in the second embodiment. The calculation unit 101 of the estimation device 100 provides an initial value of k=1 (step S121). The calculation unit 101 provides provisional values ​​set in advance as initial values ​​of the voltage and current of the energy storage element 200, and provides the environmental temperature as an initial value of the temperature. The disturbance term v in the state equation is k and the disturbance term w in the observation equation k The variance of each is Q k and R k Let us assume that.

[0154] Next, the calculation unit 101 generates N particles for each state variable (step S122). Here, N is 10 2 ~10 6 A degree of accuracy is usually used.

[0155] Next, the calculation unit 101 calculates v for i=1, 2, ..., N. k A random number corresponding to v is generated (step S123). k is assumed to follow a normal distribution and the variance is known.

[0156] The calculation unit 101 executes the calculation based on Equation 38 for all N particles, thereby updating the states of the particles to the states of the particles in the next time step (step S124).

[0157]

number

[0158] The calculation unit 101 calculates the difference between the state vector of each particle (i=1, 2, . . . , N) and the average value of the state vectors of all the particles (step S125), and calculates the covariance matrix P k (Step S126) The covariance matrix P k is expressed by the number 39.

[0159]

number

[0160] 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 S127). The acquired sensor outputs are the observed values ​​y k i Gives.

[0161] The calculation unit 101 calculates the measurement error r k i (Step S128). Here, w k is the observed disturbance. The observation error r k i is represented by the number 40.

[0162]

number

[0163] The calculation unit 101 calculates the Kalman gain K at time step k. k (Step S129). The Kalman gain K k is expressed by the number 41.

[0164]

number

[0165] The calculation unit 101 calculates the estimated value x of the i-th particle. k (i)_hat is calculated (step S130). k (i) _hat is expressed by Equation 42. That is, the calculation unit 101 converts the initial predicted value of Equation 38 into the observation error r k i and the Kalman gain K k and are used to correct it.

[0166]

number

[0167] The calculation unit 101 calculates the average value x of each particle. k _hat is calculated (step S131). The average value x k _hat represents the state vector estimate obtained by the ensemble Kalman filter and is calculated by the following equation.

[0168]

number

[0169] The estimated value obtained by Eq. 43 (average value of each particle x k _hat) includes estimated values ​​of the absorbed lithium ion concentration and temperature of each energy 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 a 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 energy storage element 200 has reached a preset state.

[0170] If the next time step is to be calculated (S132: YES), the calculation unit 101 returns the process to step S124 and executes the calculation at the next time step k+1. If the next time step is not to be calculated (S132: NO), the calculation unit 101 ends the process according to this flowchart.

[0171] The estimation device 100 in the second embodiment estimates state variables using an ensemble Kalman filter. The ensemble Kalman filter is a filter method targeted at state space models having nonlinearity and non-Gaussianity, and can be targeted at more general state space models. The ensemble Kalman filter has a relatively simple algorithm and can be easily implemented in the estimation device 100.

[0172] (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 uses an extended Kalman filter to sequentially calculate time updates of a time series model represented by a state equation of Expression 32 and an observation equation of Expression 33, and estimates a state of the energy storage element 200.

[0173] FIG. 11 is a flowchart illustrating a state estimation procedure in the third embodiment. The calculation unit 101 of the estimation device 100 provides an initial value of k=1 (step S141). The calculation unit 101 provides provisional values ​​set in advance as initial values ​​of the voltage and current of the energy storage element 200, and provides the environmental temperature as an initial value of the temperature. The disturbance term v in the state equation is k and the disturbance term w in the observation equation k The variance of each is Q k and R k Assume that the initial variance-covariance matrix P is

[0174] The calculation unit 101 calculates a prior state estimate x - k+1 _hat is calculated by the following formula (step S142).

[0175]

number

[0176] The calculation unit 101 derives the Jacobian matrix of the nonlinear transformation f by the following procedure (step S143). For example, for a three-component vector expressed by Expression 45, when the nonlinear transformation f is expressed as Expression 46, the Jacobian is calculated by Expression 47. The calculation unit 101 may derive the Jacobian in advance and store it in the storage unit 102.

[0177]

number

[0178]

number

[0179]

number

[0180] The calculation unit 101 calculates the a priori error covariance matrix P - k+1 is calculated by the following equation (step S144). Here, the state transition matrix A k is expressed by the number 49.

[0181]

number

[0182]

number

[0183] The calculation unit 101 calculates the Kalman gain g k (Step S145). The Kalman gain g k is expressed by the number 50, where c k T is expressed by the number 51.

[0184]

number

[0185]

number

[0186] 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 S146). The acquired sensor outputs are the observed value y k Gives.

[0187] The calculation unit 101 calculates the ex-post state estimate x k+1 _hat, and the posterior error covariance matrix P k is calculated by the following formula (step S147).

[0188]

number

[0189] The estimate obtained by Equation 52 (posterior state estimate x k+1 _hat) includes estimated values ​​of the absorbed lithium ion concentration and temperature of each energy 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 a 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 energy storage element 200 has reached a preset state.

[0190] If the next time step is to be calculated (S148: YES), the calculation unit 101 returns the process to step S142 and executes the calculation at the next time step k+1. If the next time step is not to be calculated (S148: NO), the calculation unit 101 ends the process according to this flowchart.

[0191] The estimation device 100 in the third embodiment estimates state variables by 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.

[0192] (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 time updates of a time series model represented by the state equation of Expression 32 and the observation equation of Expression 33, and estimates the state of the energy storage element 200.

[0193] FIG. 12 is a flowchart illustrating a state estimation procedure in the fourth embodiment. The calculation unit 101 of the estimation device 100 provides an initial value of k=1 (step S161). The calculation unit 101 provides provisional values ​​set in advance as initial values ​​of the voltage and current of the energy storage element 200, and provides the environmental temperature as an initial value of the temperature. The disturbance term v in the state equation is k and the disturbance term w in the observation equation k The variance of each is Q k and R k Assume that the initial variance-covariance matrix P is

[0194] The calculation unit 101 calculates an estimated value x obtained in a certain calculation step. - k and the variance-covariance matrix P k Using the formula, calculation points called sigma points are generated (step S162). If the generated (2n+1) sigma points are numbered as in Formula 53, the j-th sigma point (j is an integer satisfying -n≦j≦n) is expressed as in Formula 54.

[0195]

number

[0196]

Number

[0197] 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.

[0198] The weight w of each sigma point j is set to w j = κ / 2(n + κ) when j ≠ 0, and w0 = κ / (n + κ) when j = 0.

[0199] The arithmetic unit 101 updates the states, prior state estimates, and prior error covariance matrices of all sigma points as follows (step S163).

[0200]

Number

[0201] Since the arithmetic unit 101 has updated the prior state estimate and the prior error covariance matrix, it recalculates the sigma points according to the following equation (step S164).

[0202]

Number

[0203] The arithmetic unit 101 updates the observed sigma points according to the following equation (step S165).

[0204]

Number

[0205] The arithmetic unit 101 calculates the prior observation estimate y - k+1 _hat according to the following equation (step S166).

[0206]

Number

[0207] The calculation unit 101 calculates the covariance matrix P - yy,k+1 is calculated by the following formula (step S167).

[0208]

number

[0209] The calculation unit 101 calculates the covariance matrix P - xy,k+1 is calculated by the following formula (step S168).

[0210]

number

[0211] The calculation unit 101 calculates the Kalman gain g k is calculated by the following formula (step S169).

[0212]

number

[0213] 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 S170). The acquired sensor outputs are the observed value y k+1 Gives.

[0214] The calculation unit 101 calculates the Kalman gain g k Let y be the observed value k+1 and the prior observation estimate y - k+1 _hat is multiplied by the difference to perform state estimation at time step k+1 (step S171).

[0215]

number

[0216] The calculation unit 101 calculates the covariance matrix P k+1 is calculated by the following formula (step S172).

[0217]

number

[0218] The posterior observation estimate (x k+1 _hat) includes estimated values ​​of the absorbed lithium ion concentration and temperature of each energy 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 a 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 energy storage element 200 has reached a preset state.

[0219] If the next time step is to be calculated (S173: YES), the calculation unit 101 returns the process to step S162 and executes the calculation at the next time step k+1. If the next time step is not to be calculated (S173: NO), the calculation unit 101 ends the process according to this flowchart.

[0220] The estimation device 100 in the fourth embodiment estimates the short-circuit resistance by using an unscented Kalman filter. The unscented Kalman filter estimates a covariance matrix based on a plurality of sample points called sigma points around a mean value and their statistical properties. The unscented Kalman filter shows better performance than the extended Kalman filter in problems with strong nonlinearity.

[0221] (Embodiment 5) In the fifth embodiment, a configuration in which the electrochemical phenomenon of energy storage element 200 is represented by an equivalent circuit model will be described.

[0222] 13 is a circuit diagram showing an example of an equivalent circuit model. The equivalent circuit model of the energy storage element 200 is often expressed by a combination of resistors, capacitance components, and a voltage source as shown in FIG.

[0223] In Fig. 13, R0 is the ohmic resistance component, R1 is the positive electrode reaction resistance component, C1 is the positive electrode capacitance component, R2 is the negative electrode reaction resistance component, C2 is the negative electrode capacitance component, E eq is the open circuit voltage (OCV). However, Fig. 13 is merely an example, and there is no restriction on the combination of series and parallel, or the number and types of electric circuit elements.

[0224] It is known that the charge / discharge characteristics of the energy storage element 200, which is typified by a lithium ion battery, are strongly affected by temperature and SOC. SOC is an abbreviation for State Of Charge, with a fully charged state being expressed as 100% and a fully discharged state being expressed as 0%. In the following, it is assumed that the open circuit voltage (OCV) is a function of SOC, and R0 to R2 and C1 to C2 are functions of temperature. In this case, the state equation is expressed by Equation 64, and the observation equation is expressed by Equation 65.

[0225]

number

[0226] Here, Δt is the time step, Cap is the full charge capacity (C) of the storage element 200, and u k =I (current).

[0227]

number

[0228] Here, OCV(SOC) is a nonlinear function of SOC.

[0229] The equation of state that expresses the voltage of the equivalent circuit plus the disturbance is expressed by equation 66.

[0230]

number

[0231] The equation of state for heat transfer plus a disturbance is expressed by equation 67.

[0232]

number

[0233] Here, the vector b T The Q included in is the amount of heat generated, and is expressed as follows:

[0234]

number

[0235] From these state equations and observation equations, state equations and observation equations of an expanded system similar to those in Expressions 32 and 33 can be obtained. The subsequent calculation procedures are similar to those in the first to fourth embodiments, and the calculation unit 101 of the estimation device 100 can estimate the voltage, temperature, and the like of the storage element 200 using a particle filter, an ensemble Kalman filter, an extended Kalman file, or an unscented Kalman filter.

[0236] In the fifth embodiment, the open circuit voltage (OCV) is a function of the SOC, and R0 to R2 and C1 to C2 are functions of the temperature. Alternatively, the open circuit voltage may be a function of the SOC and the temperature, and R0 to R2 and C1 to C2 may be functions of the temperature and the SOC.

[0237] (Embodiment 6) In the sixth embodiment, an example in which battery deterioration is further considered in the single particle model will be described. By using the estimation device 100, a more precise deterioration prediction simulation is possible even when based on limited temperature information. Specifically, by using the temperature estimated by the estimation device 100 for the temperature included in a known deterioration prediction formula, a more precise deterioration prediction is possible. In particular, in a storage battery system using a battery pack formed by connecting a plurality of single cells in series, the performance of a highly deteriorated single cell has a significant impact on the performance of the entire storage battery system, so that it is very useful to perform a more precise deterioration prediction using a temperature estimation value obtained from the estimation device 100.

[0238] It is known that the degradation behavior of batteries is strongly affected by temperature. More accurate simulations can be performed by accurately considering temperature, but in reality, there is a problem that the observable quantities are limited, and simulations based only on sensor measurements are less accurate. By performing temperature correction using this method and making the temperature information more accurate, the accuracy of degradation predictions can be improved.

[0239] There are very few models that take into account electrochemical phenomena in battery degradation prediction simulations. For example, "International Publication No. 2017 / 016966: Method for Estimating the Current Open Circuit Voltage Curve of a Battery" discloses a method for deriving degradation due to a decrease in charge carriers (so-called deterioration due to capacity imbalance) by numerical calculation. The method disclosed in this patent document has the disadvantage that it cannot be used while electricity is flowing and requires the battery to be stopped. In addition, it is known that the mechanism by which a battery deteriorates is not limited to a decrease in charge carriers (capacity imbalance), and the method is insufficient to cover a wide range of battery deterioration.

[0240] In addition, as a method using machine learning, for example, there is "JP Patent Publication No. 2019-168453: Deterioration Estimation Apparatus, Computer Program, and Deterioration Estimation Method." In this method, the calculation process is performed by machine learning, and it is difficult to obtain physical considerations and to reflect them in product design.

[0241] In embodiment 6, based on the concept of patent document "Patent Application No. 2019-064218: Development support apparatus, development support method, and computer program," a method for performing a degradation prediction simulation using the single particle model described in this specification is described.

[0242] It is known that there are at least four types of degradation mechanisms in batteries, such as lithium-ion batteries: (1) isolation of active material particles, (2) reduction of charge carriers, (3) increase in electrical resistance, and (4) decrease in conductivity in the electrolyte. The combined contribution of these degradation mechanisms causes changes in the charge / discharge characteristics of the battery, resulting in a decrease in capacity.

[0243] Temperature is a particularly important factor in determining the rate of deterioration. Therefore, precise understanding of temperature is also important from the viewpoint of deterioration prediction. The estimation device 100 can determine the rate of deterioration assuming that the rate of deterioration has temperature dependency based on, for example, an Arrhenius-type reaction rate equation. Alternatively, the estimation device 100 may determine the rate of deterioration based on any other function of temperature. It is known that there are two types of deterioration: time-related deterioration (sometimes called calendar deterioration), which occurs due to the passage of time, and current-related deterioration, which occurs due to the passage of current, and it has been confirmed through experiments that both are functions of temperature.

[0244] The first deterioration mechanism is the isolation of active material particles. The isolation of active material particles mainly progresses in the positive electrode during discharging, but it may also occur when the current is stopped or during discharging, or it may also occur in the negative electrode. In the sixth embodiment, for the sake of simplicity, it is assumed that the isolation of active material particles occurs only in the positive electrode during discharging, but it can be easily extended to other cases by similar formula development.

[0245] 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 Equation 69.

[0246]

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[0247] ε in the number 69 s,p is the volume ratio of the positive electrode active material particles included in the numbers 4 to 6, 8, 10, and 15. The 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,iso is a constant of the rate of the isolation of the positive electrode active material particles over time, and is a function of temperature. The function may be, for example, an Arrhenius-type exponential function or any other function. 1,iso is a constant for the rate at which the positive electrode active material particles become isolated due to current flow, and is a function of temperature and current. iso is an arbitrary constant. In many cases, k 0,iso can be set to 0, but k 1,iso is a positive value and increases monotonically with temperature. In other words, when no current is applied, the isolation of the positive electrode active material does not progress, and when current is applied, the higher the temperature, the more likely the isolation of the positive electrode active material progresses. In addition, when the right side of ε s,p Various modifications are possible, such as an equation including itself, a function of other state variables, etc. Since a nonlinear filter is used, any equation may be used.

[0248] The second degradation mechanism is the reduction in charge carriers. The reduction in charge carriers is also called capacity imbalance. This phenomenon occurs when the charge carriers that travel between the positive and negative electrodes during charging and discharging are reduced due to side reactions on the electrode surfaces.

[0249] The calculation unit 101 of the estimation device 100 calculates the reduction in charge carriers based on the two equations described in Equation 70.

[0250]

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[0251] Number 70 b n1is the same as the coefficient in equation 16, and the current I in equation 16 is replaced with (I + δ). δ is the rate of charge carrier reduction. This equation is expressed as the concentration of absorbed lithium ions c n,1 This shows that the charge / discharge current is reduced by factors other than the change in the concentration of absorbed lithium ions that accompanies the charging and discharging of the battery. Note that while the current I flowing through the battery can be either positive or negative, δ is a positive value. tot is the total amount of absorbed lithium ions in the positive and negative electrodes, and is the same as that described in Equations 11 and 12.

[0252]

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[0253] k in the number 71 0,imb is the rate of decrease in the concentration of absorbed lithium ions over time, and is a function of temperature. The function may be, for example, an Arrhenius-type exponential function or any other function. 1,imb is a constant for the rate of change in the concentration of absorbed lithium ions due to current flow, and is a function of temperature and current. imb is an arbitrary constant. In many cases, k 0,imb and k 1,imb is a positive value and increases monotonically with temperature. In addition, various other variations are possible, such as the right-hand side being a function of other state variables. Since a nonlinear filter is used, any formula may be used.

[0254] The third degradation mechanism is an increase in electrical resistance. The causes of increased electrical resistance can be classified in more detail as peeling between the current collecting foil and the electrode, breakage of the conductive path of the conductive additive, and formation of a resistor film. These are described in the patent document "Patent Application No. 2019-064218: Development Support Device, Development Support Method, and Computer Program." The fourth degradation mechanism, a decrease in the conductivity of the electrolyte, is similar to an increase in electrical resistance and will be treated together.

[0255] The calculation unit 101 of the estimation device 100 calculates the rate at which the electrical resistance of the battery increases based on the time difference equation of Equation 72.

[0256]

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[0257] R in Number 72 ohm is the total ohmic resistance of the battery in equation (17), R ohm where I is the current I flowing through the battery in numbers 6, 8, 10, and 17. k 0,ohm is a constant for the rate of increase in ohmic resistance over time, and is a function of temperature. The function may be, for example, an Arrhenius-type exponential function, or any other function. 1,ohm is a constant for the rate at which the ohmic resistance increases due to current flow, and is a function of temperature and current. α is an arbitrary constant. In many cases, k 0,ohm and k 1,ohm is a positive value and increases monotonically with temperature. ohm Various modifications are possible, such as an equation including itself, a function of other state variables, etc. Since a nonlinear filter is used, any equation may be used.

[0258] Equations 73 to 75 are the equations obtained by adding disturbance terms to the above equations.

[0259]

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[0260]

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[0261]

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[0262] where v εs,p is the disturbance of the positive electrode active material particle volume ratio, vδ is the disturbance term for the rate of decrease in the concentration of absorbed lithium ions, v ohm is the disturbance term for the rate of increase in the ohmic resistance. By adding Equation 73 to Equation 75, which consider these disturbance terms, to Equation 32, in other words, ε s,p , N tot , R ohm Now we create a new state variable vector x k By adding this to the battery degradation mechanism, it becomes possible to estimate the battery state.

[0263] (Embodiment 7) In the seventh embodiment, the diffusion coefficient D of the absorbed lithium ions in the positive electrode active material particles s,p and the diffusion coefficient D of the absorbed lithium ions in the negative electrode active material particles s,n We will explain how to estimate these values. These values ​​are difficult to measure, and are known to change from moment to moment as deterioration progresses, so they cannot be obtained easily. Therefore, these diffusion coefficients may be included in the state variables and estimated.

[0264] Assuming that the diffusion coefficient of the absorbed lithium ions in the active material particles does not change with time, a time evolution equation such as the following equation (76) is formulated.

[0265]

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[0266] v Ds,p and v Ds,n is the disturbance term. These equations are newly transformed into the state variable vector x k By adding this to the above, the diffusion coefficient of the occluded lithium ions in the active material particles can be estimated.

[0267] (Embodiment 8) In the eighth embodiment, an embodiment in which battery deterioration is further considered in the equivalent circuit model will be described. In the sixth embodiment, a method for predicting deterioration based on a single particle model was described, but in the eighth embodiment, a method for predicting deterioration based on the equivalent circuit model described in the fifth embodiment will be described.

[0268] The calculation unit 101 of the estimation device 100 calculates the rate at which the deterioration of the equivalent circuit elements progresses based on the time difference equation of Equation 77.

[0269]

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[0270] R0 in Equation 77 is the circuit constant described in Equation 64, Equation 65 and FIG. 0,R0 is a constant for the rate of deterioration of R0 over time, and is a function of temperature. The function may be, for example, an Arrhenius-type exponential function, or any other function. k 1,R0 is a constant for the rate of degradation of R0 due to current flow, and is a function of temperature and current. R0 is an arbitrary constant. In addition to this, various other variations are possible, such as the right-hand side being an equation including R0 itself, or being a function of other state variables. Since a nonlinear filter is used, any equation may be used. The same applies to the constants other than R0, R1 to C2. Alternatively, a more complicated equivalent circuit may be specified, and R3, R4... and C3, C4... may be defined separately.

[0271] 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 together. For example, the equilibrium potential E eq For the deterioration of the battery, the model of the decrease in the stored lithium ions (capacity imbalance) in the sixth embodiment is used, and for the internal resistance, an equivalent circuit is used. For example, any combination may be used according to convenience.

[0272] Adding a disturbance term to equation (77) gives equation (78).

[0273]

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[0274] v R0is the disturbance term for R0, and the others are the same. By adding Equation 78, which considers these disturbance terms, to Equation 32, in other words, R0, R1, R2, C1, and C2 are newly added to the state variable vector x k By adding this to the battery equivalent circuit elements, it becomes possible to estimate the state of the battery while taking into account the deterioration of the battery equivalent circuit elements.

[0275] Application examples are described below.

[0276] (Application example 1) The estimation device 100 may be used to construct a digital twin of the power storage device 20. A digital twin refers to a technology that collects the state (temperature, current, voltage, etc.) of a product that actually exists, the surrounding environment, the usage situation, etc. in real time, and constructs a simulation model on a computer that is the same as the real state. In a digital twin, the simulation model is constantly updated based on values ​​measured by sensors, and the same state as the real product can be reproduced on a computer in almost real time. By using this mechanism, when an abnormality occurs in the real product, it is reflected in the simulation model immediately, and by analyzing the simulation model, it is possible to identify the cause of the abnormality. Furthermore, since it is possible to know the behavior of latent variables that cannot be directly measured from sensor values, it is possible to predict or prevent failures before they occur.

[0277] In addition, the estimation device 100 may generate information based on the estimation results, such as preventive maintenance such as part replacement, feedback for product development, prediction of replacement timing, timely maintenance, and suggestions for more efficient operation methods, and output the generated information from the output unit 104.

[0278] Furthermore, since the analysis and diagnosis of failure causes, which was previously performed by specialized employees, can now be performed by the simulation model, cost reduction effects can also be expected.

[0279] (Application example 2) The estimation device 100 may graphically display the estimated state of the energy storage element 200 in real time. FIG. 15 is a schematic diagram showing an example of display of the temperature state. In the example of FIG. 15, an example of a three-dimensional graphical display of the temperature of the outer surface of the energy storage device 20 is shown. The estimation device 100 generates a distribution diagram showing the temperature distribution every time the temperature state of each energy storage element 200 is estimated, and outputs the generated distribution diagram to the display device 150. In this way, the estimation device 100 can graphically display the temperature of the outer surface of the energy storage device 20 in real time on the display device 150. 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.

[0280] The graphical display may be performed in response to a request from a user or a request from a maintenance personnel. By displaying the graphical display, the temperature state of the power storage device 20 can be intuitively understood and anomalies can be detected early. Alternatively, the estimation device 100 may display the estimated electrochemical state of the power storage device 20 in graphical form.

[0281] The embodiments disclosed herein are illustrative in all respects and should not be considered as limiting. The scope of the present invention is defined by the claims, not by the above meaning, and is intended to include all modifications within the meaning and scope of the claims. [Explanation of symbols]

[0282] 10 Energy Storage System 20 Energy storage devices 100 Estimator 101 Arithmetic section 102 Storage section 103 Input section 103A Voltage Sensor 103B Current Sensor 103C Temperature Sensor 103D Temperature Sensor 104 Output section 200 Energy storage element M Recording medium PG state estimation program

Claims

1. an acquisition unit that acquires measurement data including a voltage of a storage element, a current flowing through the storage element, and a temperature related to the storage element; an estimation unit that inputs the acquired measurement data into a state estimator that is constructed to simulate an electrochemical phenomenon and a thermal phenomenon of the energy storage element, and estimates a state of the energy storage element; Equipped with The state estimator determining a time transition of each state variable using a state equation expressing a time transition of a state variable including a concentration of occluded ions in the active material particles and a temperature related to the energy storage element; calculating a likelihood of a state estimation using an observation equation that represents a relationship between the state variables and an observation amount indicated by the measurement data; The estimated values ​​of the state variables are updated according to the likelihood of the obtained state estimation. Estimation device.

2. The parameters describing the electrochemical phenomenon include an activation overvoltage of the storage element expressed as a function of the temperature of the storage element; The parameters describing the thermal phenomenon include the amount of heat generated by the storage element expressed as a function of the activation overvoltage of the storage element. The estimation device according to claim 1 .

3. The state estimator is a nonlinear filter configured to output a state quantity related to the storage element when the measurement data is input. The estimation device according to claim 1 or 2.

4. The nonlinear filter includes a particle filter, an ensemble Kalman filter, an extended Kalman filter, or an unscented Kalman filter. The estimation device according to claim 3 .

5. an acquisition unit that acquires measurement data including a voltage of a storage element, a current flowing through the storage element, and a temperature related to the storage element; an estimation unit that inputs the acquired measurement data into a state estimator that is constructed to simulate an equivalent electric circuit and a thermal phenomenon of the storage element, and estimates a state of the storage element; Equipped with The state estimator determining a time transition of each state variable using a state equation expressing a time transition of a state variable including a concentration of occluded ions in the active material particles and a temperature related to the energy storage element; calculating a likelihood of a state estimation using an observation equation that represents a relationship between the state variables and an observation amount indicated by the measurement data; The estimated values ​​of the state variables are updated according to the likelihood of the obtained state estimation. Estimation device.

6. The state estimator The state quantity representing the characteristic of the energy storage element includes one or more equations in which the state quantity changes over time or due to current flow, Deterioration of the storage element is predicted using an observation equation that represents a relationship between a state variable describing a state of the storage element and an observation amount indicated by the measurement data. The estimation device according to any one of claims 1 to 5.

7. The computer Acquiring measurement data including a voltage of a storage element, a current flowing through the storage element, and a temperature related to the storage element; An estimation method for estimating a state of the energy storage element by inputting acquired measurement data to a state estimator configured to simulate an electrochemical phenomenon and a thermal phenomenon of the energy storage element, comprising: The state estimator determining a time transition of each state variable using a state equation expressing a time transition of a state variable including a concentration of occluded ions in the active material particles and a temperature related to the energy storage element; calculating a likelihood of a state estimation using an observation equation that represents a relationship between the state variables and an observation amount indicated by the measurement data; The estimated values ​​of the state variables are updated according to the likelihood of the obtained state estimation. Estimation method.

8. On the computer, Acquiring measurement data including a voltage of a storage element, a current flowing through the storage element, and a temperature related to the storage element; The acquired measurement data is input to a state estimator configured to simulate electrochemical and thermal phenomena of the energy storage element, and a state of the energy storage element is estimated. A computer program for executing a process, The state estimator determining a time transition of each state variable using a state equation expressing a time transition of a state variable including a concentration of occluded ions in the active material particles and a temperature related to the energy storage element; calculating a likelihood of a state estimation using an observation equation that represents a relationship between the state variables and an observation amount indicated by the measurement data; The estimated values ​​of the state variables are updated according to the likelihood of the obtained state estimation. Computer program.

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