Estimation device and estimation method

Abstract

To provide an estimation device and an estimation method.SOLUTION: An estimation device includes an acquisition unit that acquires measurement results from a temperature sensor that measures the temperature at a specific location where heat generated from a power storage device is transmitted, and an observer that estimates the temperature at a place where the temperature sensor does not conduct a measurement according to the input of the measurement result.SELECTED DRAWING: Figure 4

Description

[Technical field]

[0001] The present invention relates to an estimation device and an estimation method. [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 operating a battery equipped with such an energy storage element, it is essential to monitor the temperature of the energy storage element. For example, Patent Document 1 discloses a method for monitoring the temperature of an energy storage element in which a battery cell is divided into a plurality of cell blocks, and the temperature of a cell block at a position where the temperature is not measured is estimated based on the temperature of the cell block at a temperature measurement position where the temperature is measured and the amount of heat generated in each cell block. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2009-99375 A Summary of the Invention [Problem to be solved by the invention]

[0005] However, Patent Document 1 does not disclose a calibration method for when the temperature estimated by simulation differs from the temperature measured by the sensor, making it difficult to determine whether accurate temperature estimation is possible. Furthermore, when the method disclosed in Patent Document 1 is applied to an energy storage device having multiple energy storage elements, it is necessary to provide a temperature detection means for each energy storage element in order to detect the temperature of each element, which increases manufacturing costs.

[0006] The present invention has been made in consideration of the above circumstances, and has an object to provide an estimation device and an estimation method that are capable of estimating a detailed temperature distribution while feeding back temperatures measured by a temperature sensor. [Means for solving the problem]

[0007] The estimation device includes an acquisition unit that acquires measurement results from a temperature sensor that measures the temperature at a specific location where heat generated from the power storage device is transmitted, and an observer that estimates the temperature at a location where the temperature sensor is not measuring in response to input of the measurement results.

[0008] The estimation method obtains measurement results from a temperature sensor that measures the temperature at a specific location where heat generated from the power storage device is transmitted, and inputs the measurement results to an observer that estimates the state variables based on a state equation that simulates thermal conduction in the power storage device and an observation equation that represents the relationship between the state variables in the state equation and the observation variables that can be observed by the temperature sensor, thereby estimating the temperature at locations not measured by the temperature sensor. Effect of the Invention

[0009] According to the present application, a detailed temperature distribution can be estimated while feeding back the temperature measured by the temperature sensor. [Brief description of the drawings]

[0010] [Figure 1] 1 is a schematic external view of a power storage system according to an embodiment of the present invention; [Diagram 2] FIG. 2 is a perspective view showing a configuration of an energy storage element. [Diagram 3] FIG. 2 is a block diagram showing an internal configuration of the estimation device. [Figure 4] 1 is a state variable diagram including an observer. [Diagram 5] 11 is a flowchart illustrating a procedure of an estimation process executed by the estimation device. [Figure 6] FIG. 1 is a state variable diagram including a disturbance observer. [Figure 7] FIG. 2 is a circuit diagram showing an example of an equivalent circuit model. [Figure 8] 1 is a graph showing the relationship between the concentration of absorbed lithium ions in the solid phase and the open circuit potential (OCP) in a typical positive electrode material. [Figure 9] 1 is a graph showing the relationship between lithium ion concentration and ion conductivity in an electrolyte solution. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] The estimation device includes an acquisition unit that acquires measurement results from a temperature sensor that measures the temperature at a specific location where heat generated from the power storage device is transmitted, and an observer that estimates the temperature at a location not measured by the temperature sensor in response to input of the measurement results. According to this configuration, the temperature of a location not measured by the temperature sensor can be estimated while feeding back the temperature of the location measured by the temperature sensor.

[0012] In the estimation device, the observer may estimate the temperature at a location not measured by the temperature sensor by deriving the state variable based on a state equation that simulates heat conduction in the power storage device and an observation equation that represents a relationship between a state variable in the state equation and an observation variable that can be observed by the temperature sensor. With this configuration, the temperature at a location not measured by the temperature sensor can be estimated through the state variable obtained from the observer.

[0013] In the estimation device, the observer may have an internal parameter designed so that the temperature estimated by the observer and the temperature measured by the temperature sensor become asymptotic. With this configuration, the observer can be constructed so that the temperature estimated by the observer and the temperature measured by the temperature sensor become substantially the same.

[0014] In the estimation apparatus, the temperature sensor may be provided in the power storage device, and the observer may estimate a temperature outside the power storage device based on the temperature of the power storage device measured by the temperature sensor. With this configuration, the temperature outside the power storage device can be estimated based on the temperature of the power storage device.

[0015] In the estimation device, the observer may formulate an observer gain using a Kalman filter so as to provide a robust estimation function even when there is a disturbance due to heat transfer between the power storage device and the surrounding environment. With this configuration, even when system noise and observation noise are included, it is possible to perform temperature estimation while suppressing the effects of system noise and observation noise by appropriately evaluating the observer gain of the disturbance observer using a Kalman filter.

[0016] The estimation device may be configured as a server device disposed remotely from the power storage device. With this configuration, the server device installed at a location remote from the power storage device can estimate the temperature of a location not measured by a temperature sensor, so that high-speed calculations can be performed even when a large power storage device or a large-scale energy storage device consisting of multiple power storage elements is the subject of calculation.

[0017] The estimation device may further include a calculation unit that simulates a deterioration prediction of the power storage device by using the temperature estimated by the observer. With this configuration, the accuracy of the deterioration prediction can be improved by more accurately estimating the temperature of a portion that is not measured.

[0018] In the estimation device, the simulation of the deterioration prediction of the power storage device may be a simulation based on a physical model of the power storage device. With this configuration, it is possible to simulate the deterioration of the power storage device by accurately reflecting physical phenomena inside the power storage device.

[0019] The estimation method obtains measurement results from a temperature sensor that measures the temperature at a specific location where heat generated from the power storage device is transmitted, and inputs the measurement results to an observer that estimates the state variables based on a state equation that simulates thermal conduction in the power storage device and an observation equation that represents the relationship between the state variables in the state equation and the observation variables that can be observed by the temperature sensor, thereby estimating the temperature at locations not measured by the temperature sensor. According to this configuration, the temperature of a location not measured by the temperature sensor can be estimated while feeding back the temperature of the location measured by the temperature sensor.

[0020] Hereinafter, the present invention will be described in detail with reference to the drawings showing embodiments thereof. (Embodiment 1) 1 is a schematic external view of a power storage system 10 according to the present embodiment. The power storage system 10 according to the present 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.

[0021] The estimation device 100 is, for example, disposed on the upper surfaces of the energy storage elements 200, and is a flat circuit board equipped with a circuit for estimating the temperature of the energy storage elements 200 at a predetermined time. Specifically, the estimation device 100 is connected to all the energy storage elements 200, and acquires information from each of the energy storage elements 200 to estimate the temperature of each of the energy storage elements 200 at a predetermined time.

[0022] The location of the estimation device 100 is not limited to the top surface of the energy storage element 200. Alternatively, the estimation device 100 may be located on the side surface of the energy storage element 200 or on the bottom surface of the energy storage element 200. The shape of the estimation device 100 is also not particularly limited. Furthermore, the estimation device 100 may be a server device located away from the energy storage element 200, and may acquire information from sensors (sensors 103A to 103D shown in FIG. 3) through communication. Many of the formulas described in this specification are simple, and when the energy storage element is a small energy storage element 200 as in the embodiment, an inexpensive arithmetic processing device is sufficient. When a larger energy storage element is the calculation target or a large-scale energy storage device consisting of multiple energy storage elements, the calculation load increases and the arithmetic processing speed decreases. In such a case, it may be possible to perform high-speed processing by transferring the sensor acquisition value to a server device located away from the energy storage element through communication and performing the arithmetic processing in the server device.

[0023] The energy storage element 200 is a secondary battery such as a lithium ion secondary battery. The energy storage element 200 is applied to a power source for an automobile such as an electric vehicle (EV), a hybrid electric vehicle (HEV), or a plug-in hybrid electric vehicle (PHEV), a power source for electronic devices, a power source for power storage, etc. In Fig. 1, five rectangular energy storage elements 200 are arranged in series to configure a battery pack.

[0024] The number of the energy storage elements 200 is not limited to five. For example, the number of the energy storage elements 200 may be one, or two or more. Furthermore, some of the energy storage elements 200 may be connected in parallel. Furthermore, the energy storage elements 200 may be secondary batteries other than lithium ion secondary batteries. Furthermore, the same principle applies not only to secondary batteries, but also to all devices that have a heat-generating portion (e.g., power modules, primary batteries, fuel cells, electronic circuit boards, switchboards, etc.).

[0025] The configuration of energy storage element 200 will be described in detail below, assuming that energy storage element 200 is a liquid-based lithium-ion battery. Fig. 2 is a perspective view showing the configuration of energy storage element 200. Specifically, Fig. 2 shows the configuration in a state where a main body portion of container 210 is separated from energy storage element 200.

[0026] 2, the energy storage element 200 includes a container 210, a positive electrode terminal 220, and a negative electrode terminal 230. Inside the container 210, a positive electrode current collector 240, a negative electrode current collector 250, and two electrode bodies 261, 262 are housed.

[0027] In addition to the above components, a spacer disposed inside the container 210, a gasket disposed around the terminals, a gas exhaust valve for releasing pressure when the pressure inside the container 210 increases, an insulating film for encasing the electrode bodies 261, 262, etc. may be disposed. An electrolyte is enclosed inside the container 210, but is not shown. The type of electrolyte is not particularly limited as long as it does not impair the performance of the energy storage element 200, and various electrolytes can be selected. As an example of a different energy storage element 200, a solid exhibiting ionic conductivity (e.g., an ion-conductive polymer or an ion-conductive ceramic) may be used instead of the electrolyte in the liquid-based lithium ion battery.

[0028] The container 210 is a box-shaped member having plate-like side walls 211-214 and a bottom wall 215 that constitute the container body, and a plate-like lid 216 that closes the opening of the container body. The material of the container 210 can be, for example, a weldable metal such as stainless steel, aluminum, or an aluminum alloy, or a resin.

[0029] The electrode bodies 261 and 262 are two electricity storage elements (power generation elements) that include a positive electrode plate, a negative electrode plate, and a separator and can store electricity. That is, the two electrode bodies, the electrode body 261 and the electrode body 262, are arranged side by side in the direction of the Y axis shown in FIG.

[0030] Here, the positive electrode plate of the electrode body 261, 262 is a positive electrode active material layer formed on a positive electrode base material layer which is a long strip-shaped current collector foil made of aluminum, aluminum alloy, etc. The negative electrode plate is a negative electrode active material layer formed on a negative electrode base material layer which is a long strip-shaped current collector foil made of copper, copper alloy, etc. The separator can be, for example, a microporous sheet made of resin or a nonwoven fabric. The current collector foil can be appropriately made of known materials such as nickel, iron, stainless steel, titanium, baked carbon, conductive polymer, conductive glass, and Al-Cd alloy.

[0031] The electrode bodies 261 and 262 are formed by stacking electrode plates. That is, the electrode bodies 261 and 262 are formed by winding layers arranged so that a separator is sandwiched between a positive electrode plate and a negative electrode plate. Specifically, the electrode bodies 261 and 262 are wound with a positive electrode plate and a negative electrode plate shifted from each other in the direction of the winding axis (a virtual axis parallel to the X-axis shown in FIG. 2) via a separator. In addition, at the outermost periphery of each of the electrode bodies 261 and 262, only the separator, which does not interpose either a positive electrode plate or a negative electrode plate, is wound one or two times in a double-layered state to ensure insulation. In this embodiment, an oval shape is illustrated as the cross-sectional shape of the electrode bodies 261 and 262. Alternatively, the cross-sectional shape of the electrode bodies 261 and 262 may be an ellipse shape or the like.

[0032] As the positive electrode active material used in the positive electrode active material layer, any known material can be used as long as it is a positive electrode active material capable of absorbing and releasing lithium ions. For example, LiMPO 4 , LiMSiO 4 , LiMBO 3 (M is one or more transition metal elements selected from Fe, Ni, Mn, Co, etc.), polyanion compounds such as LiMn 2 O 4 yaLiMn 1.5 Ni 0.5 O 4 Spinel-type lithium manganese oxides such as LiMO 2(M is one or more transition metal elements selected from Fe, Ni, Mn, Co, etc., and includes lithium-excess composite oxides) and the like can be used.

[0033] As the negative electrode active material used in the negative electrode active material layer, any known material can be used as long as it is a negative electrode active material capable of absorbing and releasing lithium ions. For example, as the negative electrode active material, lithium metal, lithium alloys (lithium-silicon, lithium-aluminum, lithium-lead, lithium-tin, lithium-aluminum-tin, lithium-gallium, Wood's alloy, and other lithium metal-containing alloys), as well as alloys capable of absorbing and releasing lithium, carbon materials (e.g., graphite, non-graphitizable carbon, easily graphitizable carbon, low-temperature fired carbon, amorphous carbon, etc.), silicon oxides, metal oxides, lithium metal oxides (Li 4 Ti 5 O 12 etc.), polyphosphate compounds, or, commonly called conversion anodes, Co 3 O 4 or Fe 2 Examples of the metal include compounds of transition metals such as P and elements of Groups 14 to 16.

[0034] The positive electrode terminal 220 is an electrode terminal electrically connected to the positive electrode plates of the electrode bodies 261, 262, and the negative electrode terminal 230 is an electrode terminal electrically connected to the negative electrode plates of the electrode bodies 261, 262. The positive electrode terminal 220 and the negative electrode terminal 230 are attached to the cover body 216. The positive electrode terminal 220 and the negative electrode terminal 230 are formed of, for example, aluminum or an aluminum alloy.

[0035] The positive electrode current collector 240 is a member having conductivity and rigidity, which is electrically connected (joined) to the positive electrode terminal 220 and the positive electrode plate of the electrode bodies 261, 262. The negative electrode current collector 250 is a member having conductivity and rigidity, which is electrically connected (joined) to the negative electrode terminal 230 and the negative electrode plate of the electrode bodies 261, 262. The positive electrode current collector 240 and the negative electrode current collector 250 are fixed to the lid body 216. The positive electrode current collector 240 is made of aluminum or an aluminum alloy, etc., like the positive electrode base layer. The negative electrode current collector 250 is made of copper or a copper alloy, etc., like the negative electrode base layer.

[0036] The configuration of the estimation device 100 will be described below. 3 is a block diagram showing the internal configuration of the estimation device 100. The estimation device 100 includes a calculation unit (estimation unit) 101, a storage unit 102, an input unit 103, and an output unit 104.

[0037] The calculation unit 101 is an arbitrary calculation circuit including a microcomputer, a volatile or non-volatile memory, etc. The microcomputer controls the operation of each hardware unit according to a computer program stored in advance in the memory, and causes the entire device to function as the estimation device of the present application. Specifically, the calculation unit 101 performs calculations to estimate the temperature of each energy storage element 200 based on a heat balance model of each energy storage element 200 expressed using an element temperature and an environmental temperature. Here, the element temperature indicates the temperature of the energy storage element 200 measured by a temperature sensor 103A described later. The environmental temperature indicates the outside air temperature of the energy storage device 20 (i.e., the temperature of the space in which the energy storage device 20 is placed). Note that a method of estimating the temperature of each energy storage element 200 without measuring the environmental temperature will be described later in the second embodiment.

[0038] In this embodiment, the calculation unit 101 is an arbitrary calculation circuit including a microcomputer, a volatile or non-volatile memory, etc. Alternatively, the calculation unit 101 may be configured with a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), etc.

[0039] The storage unit 102 is a storage device such as a flash memory. The storage unit 102 stores data necessary for calculation of temperature estimation of each energy storage element 200. For example, the storage unit 102 includes data such as the volume, surface area, specific heat, and density of each energy storage element 200, the value of thermal conductance between adjacent energy storage elements 200, and the coefficient of heat transfer to the outside.

[0040] 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 the strain sensor 103C described later.

[0041] 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 showing the relationship between the value of the heat transfer coefficient and the value of the flow velocity measured by a flow meter 103D 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.

[0042] The input unit 103 includes an interface for connecting various sensors. The sensors connected to the input unit 103 include a temperature sensor 103A that measures the temperature (element temperature) of the energy storage element 200. The temperature sensor 103A is an existing sensor such as a thermocouple or a thermistor. 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 devices 20 is N (N is an integer of 2 or more), the energy storage elements 200 to be measured are appropriately installed in the range of 1 to (N-1). The temperature sensor 103A is arranged on the upper surface of the energy storage device 20, for example. Alternatively, the temperature sensor 103A is arranged on the side surface or the lower surface of the energy storage device 20.

[0043] A temperature sensor 103B that measures an environmental temperature of the power storage device 20 may be connected to the input unit 103. The temperature sensor 103B is an existing sensor such as a thermocouple or a thermistor. The temperature sensor 103B may be installed at an appropriate location on the power storage device 20, or may be installed at an appropriate location in the surrounding area. When the estimation device 100 includes a communication interface that communicates with an external device, the information on the environmental temperature may be acquired through communication, instead of acquiring the information on the environmental temperature from the temperature sensor 103B.

[0044] A strain sensor 103C that detects the magnitude of strain of the energy storage element 200 may be connected to the input unit 103. The strain sensor 103C is an existing sensor that uses a strain gauge type load cell or the like. The strain sensor 103C is provided for each of the energy storage elements 200.

[0045] A flow meter 103D that measures the flow of air around the power storage device 20 may be connected to the input unit 103. The flow meter 103D is an existing measuring device such as a flow meter. The flow meter 103D is installed at an appropriate location around the power storage device 20.

[0046] The output unit 104 includes an interface for connecting an external device. The output unit 104 outputs the temperature estimation result of each energy storage element 200, which is the calculation result of the calculation unit 101, to the external device. The external device connected to the output unit 104 is, for example, a management device that manages the state of the energy storage device 20, or a control device that controls the operation of the energy storage device 20. Alternatively, the external device connected to the output unit 104 may be a control device of a mobile terminal or an electric vehicle that operates with power supplied from the energy storage device 20. The external device may calculate the state of charge (SOC), state of health (SOH), etc. of the energy storage device based on the temperature estimation result of the estimation device 100. The external device may control the operation of the energy storage device 20 according to the temperature estimation result of the estimation device 100.

[0047] The details of the calculation process executed by the estimation device 100 will be described below. The estimation device 100 estimates the temperature of each of the storage elements 200A-200E using a heat balance model that takes into account the element temperature measured for some of the storage elements 200 (e.g., 200E) among the multiple storage elements 200 (200A-200E) that constitute the storage device 20 and the environmental temperature of the storage device 20.

[0048] The heat balance model of each of power storage elements 200A-200E is expressed by a heat transfer equation, and for example, the following equation 1 is used.

[0049]

number

[0050] Here, T 1 ~T 5 , S 1 ~S 5 , Q 1 ~Q 5 , h 1 ~h 5 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 Alternatively, the values ​​of density, specific heat, and volume may be set individually for each of the energy storage elements 200A to 200E. 0 represents the environmental temperature (K), and t represents time (s).

[0051] The left side of the formula 1 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 the thermal conduction based on the temperature difference between adjacent energy storage elements 200, 200. 1 ~h 5The term including Q represents heat dissipation from the energy storage element 200 to the outside, and is a negative value when heat dissipation is occurring. 1 ~Q 5 The term including represents heat generation in the electricity storage device 20. Causes of heat generation include Joule heat and reaction heat due to current flow.

[0052] The calculation unit 101 calculates the thermal conductance k ij The calculation may be performed using a preset value as the value of , or may be performed using a value that is changed according to the distortion of the energy storage element 200. In the latter case, the value of the thermal conductance corresponding to the distortion of the energy storage element 200 may be read from a table that specifies the relationship between the distortion of the energy storage element 200 and the thermal conductance.

[0053] The calculation unit 101 calculates the heat transfer coefficient h 1 ~h 5 The calculation may be performed using a preset value as the value of , or using a value that varies depending on the flow velocity of the surrounding fluid. In the latter case, the value of the heat transfer coefficient corresponding to the flow velocity of the surrounding fluid may be read from a table that defines the relationship between the flow velocity and the heat transfer coefficient.

[0054] By rewriting the time differential on the left side of equation 1 using the time difference, we obtain the following equation 2.

[0055]

number

[0056] Here, k is a natural number that represents the time step, and Δt represents the time step size (s) of the calculation.

[0057] By rearranging Equation 2, we obtain Equation 3 below.

[0058]

number

[0059] Here, α=(ρC p V / Δt) -1 It is.

[0060] Next, in order to express Equation 3 in a matrix, the state vector x(k), vector b, and matrix A are defined by Equation 4 below.

[0061]

number

[0062] Here, a 11 =1-α(k 12 +S 1 h 1 ), a 22 =1-α(k 12 +k 23 +S 2 h 2 ), a 33 =1-α(k 23 +k 34 +S 3 h 3 ), a 44 =1-α(k 34 +k 45 +S 4 h 4 ), a 55 =1-α(k 45 +S 5 h 5 ) Also, a 12 =a 21 =αk 12 , a 23 =a 32 =αk 23 , a 34 =a 43 =αk 34 , a 45 =a 54 =αk 45 and 0 otherwise.

[0063] The discrete space state equation including the above state vector x(k) as a state variable is expressed as follows: Here, u(k)=1 may be used.

[0064]

number

[0065] The observation equation is expressed as in Equation 6. The upper right-hand side 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.

[0066]

number

[0067] In the observation equation of formula 6, a scalar observation value y(k) is used as the observation variable. Alternatively, there may be multiple observation values. Here, C is an observation vector (or observation matrix) whose elements are the element temperatures measured by temperature sensor 103A. For example, when measuring only the temperature of the fifth storage element 200, the observation vector is expressed as in formula 7 below.

[0068]

number

[0069] Equation 5 is a state equation that simulates heat conduction in the power storage device 20, and Equation 6 is an observation equation that represents the relationship between a state variable in the state equation and an observation variable that can be observed by the temperature sensor 103A.

[0070] In this embodiment, temperature estimation is performed using an observer corresponding to a real system represented by the state equation of Expression 5 and the observation equation of Expression 6.

[0071] FIG. 4 is a state variable diagram including an observer. The observer O1 corresponding to the real system represented by the state equation of Equation 5 and the observation equation of Equation 6 is represented by the discrete space state equation shown in Equation 8 and the observation equation shown in Equation 9. -1 represents a delayer by z-transformation, and I represents the unit matrix.

[0072]

number

[0073]

number

[0074] The parameters A, b, c and control input u(k) are the same in the real system and the observer O1, but the state variables and observed variables are different. If there is a difference between the state variable x(k) in the real system and the state variable x_hat(k) of the observer O1, it indicates that there is a difference between the actual measurement and the simulation model. Therefore, feedback is used to correct the behavior of the observer O1. The feedback gain (observer gain) is set to L. L is a vertical vector having the same dimension as x(k). The discrete space state equation with the observer gain added is expressed by the following equation 10.

[0075]

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[0076] In this case, the difference in the observed variables between the actual system and the observer O1 at the (k+1) step is expressed as follows:

[0077]

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[0078] Here, x_hat(k+1)-x(k+1) and x_hat(k)-x(k) represent the difference between the real system and the observer O1, while the matrix (A-LC T It is known that if the real parts of the eigenvalues ​​of the matrix (A-LC) are all negative, the error approaches zero. TBy using an observer O1 whose observer gain is designed so that the real parts of the eigenvalues ​​of (k) are all negative, it is possible to make the state variable x_hat(k) obtained from the observer O1 coincide with the state variable x(k) in the real system. Since the state variable x(k) in the real system represents the temperature in each of the storage elements 200A-200E as shown in Expression 4, it is possible to estimate the temperature of a location not measured by the temperature sensor 103A (for example, the temperature on the storage elements 200A-200D) through the state variable x_hat(k) of the observer O1.

[0079] The estimation process performed by the estimation device 100 will be described below. 5 is a flowchart illustrating the procedure of the estimation process executed by the estimation device 100. The calculation unit 101 of the estimation device 100 reads out numerical values ​​such as physical property values ​​and boundary conditions from the storage unit 102 (step S101), and sets a discrete space state equation and an observation equation representing the real system, and a discrete space state equation and an observation equation representing the observer O1 (step S102).

[0080] Next, the calculation unit 101 acquires the measurement result by the temperature sensor 103A through the input unit 103 (step S103).

[0081] The calculation unit 101 executes calculations based on the acquired measurement results, the discrete equations and observation equations representing the set real system, and the discrete equations and observation equations representing the observer O1 (step S104), and acquires an estimate of the temperature through the state variable x_hat(x) included in the state equation of the observer O1 (step S105). By repeatedly executing these measurements and calculation processes in real time at the same time as the actual machine is operating, it is possible to estimate the unmeasured temperature, i.e., the potential state variable.

[0082] As described above, in this embodiment, by using the observer O1, the temperature of other locations (e.g., energy storage elements 200A to 200D) can be estimated while feeding back the difference between the temperature measured at a specific location (e.g., energy storage element 200E) to which heat generated from the energy storage device 20 is transmitted and the estimated temperature at that location.

[0083] In this embodiment, the temperatures of energy storage elements 200A to 200D are estimated based on the temperature and the amount of heat absorption and generation measured for energy storage element 200E. The amount of heat absorption and generation may include not only the amount of heat absorption and generation in the electrode portions but also the amount of heat generation in members electrically connecting the energy storage elements (not shown in FIG. 1, for example, an electrical connection member such as a bus bar connecting positive terminal 220 of energy storage element 200A and negative terminal 230 of energy storage element 200B).

[0084] In addition, in this embodiment, an example has been shown in which all state variables x(k) are estimated using only one observation value of the scalar observation value y(k). Alternatively, even if there are multiple observation values, all state variables can be estimated using a similar calculation method. Furthermore, although the state vector x(k) has been described as one state quantity for one power storage device, the power storage device may be divided into multiple regions to take into account three-dimensional temperature distribution, or the temperatures of electrical connection members such as positive and negative terminals and bus bars may be included in the state vector x(k), and temperature estimation is possible using exactly the same logic.

[0085] (Embodiment 2) In the second embodiment, a configuration will be described in which temperature estimation is performed taking into consideration the exchange of heat between the power accumulation device 20 and the surrounding environment. The overall configuration of the system, and the internal configurations of the power storage device 20 and the estimation apparatus 100 are similar to those in the first embodiment, and therefore description thereof will be omitted.

[0086] The heat conduction equation of the power storage device 20 is expressed as follows.

[0087]

number

[0088] Here, ρ, C p , V is the density of the electricity storage device 20 (kg / m 3 ), specific heat (J / kg / K), volume (m 3 ) T represents the temperature (K) of the power storage device 20, and T 0 represents the temperature of the surrounding environment, t is time (s), and h is the heat transfer coefficient (W / m 2 / K), and S is the surface area of ​​the electricity storage device 20 (m 2 ), and Q represents the amount of heat generated by the electricity storage device 20 (W).

[0089] For simplification, the present embodiment shows a heat conduction equation for the power storage device 20. Alternatively, similarly to the first embodiment, a heat conduction equation may be written for each of the power storage elements 200A to 200E constituting the power storage device 20.

[0090] By modifying Equation 12, Equation 13 is obtained. Here, T is the temperature of the power storage device 20, and is, for example, the temperature measured by the temperature sensor 103A. The second term on the right side represents heat absorption and heat due to Joule heating or electrochemical reaction heat, and is a value that can be calculated using the internal resistance, reaction heat, current flow, and the like. That is, the second term on the right side can be treated as a known value. The third term on the right side is a term that represents the influence of the temperature of the surrounding environment, and is an unknown value. The third term on the right side includes not only heat dissipation from the power storage device 20 to the outside, but also heat conduction from the storage case 300 and the like.

[0091]

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[0092] In this embodiment, a state equation is written with the second term on the right side of Equation 13 as the control input and the third term as the disturbance. When Equation 13 is simplified, it is expressed as Equation 14.

[0093]

number

[0094] Here, A=-hS / ρC p V, B=1 / ρC p V, D=hS / ρC p V, u=Q, d=T 0 In equation 14, u represents the control input, and d represents the disturbance. B, u, D, and d can be set arbitrarily. In equation 14, A, B, and D are scalars, but they can also be written as vectors.

[0095] The rate of change of the disturbance is sufficiently slow compared to the speed of calculation processing, particularly in the case of a thermal problem, so the first-order time derivative of the disturbance may be set to zero.

[0096] The observation equation is expressed by equation 15.

[0097]

number

[0098] Here, y represents an observation value and C represents an observation matrix, but for the time being, y and C are treated as scalars.

[0099] When the state vector x is defined by Equation 16, the state equation is expressed as Equation 17.

[0100]

number

[0101]

number

[0102] The temperature T of the power storage device 20 is measured by the temperature sensor 103A, while the temperature T of the surrounding environment is 0 Since we do not measure, the observation equation of Equation 15 can be rewritten in the form of Equation 18 below using the state vector x.

[0103]

number

[0104] When each component of Equation 17 is discretized, it is expressed as Equation 19.

[0105]

number

[0106] If we write number 19 collectively, it can be expressed as number 20.

[0107]

number

[0108] Here, A e = 1-AΔt, D e = DΔt, B e =BΔt. Similarly, when equation (18) is discretized, it is expressed as equation (21).

[0109]

number

[0110] In this embodiment, temperature estimation is performed using an observer corresponding to a real system represented by the state equation of Mathematical Expression 20 and the observation equation of FIG.

[0111] 6 is a state variable diagram including a disturbance observer. If it is assumed that the systems expressed by Equations 20 and 21 are observable, the state equation and the observation equation of the disturbance observer O2 are expressed by Equations 22 and 23, respectively.

[0112]

number

[0113]

number

[0114] where x and y denote the observer estimates, and L e represents the observer gain. Observer gain L e is the matrix (A e -L e C e ) is an asymptotically stable matrix, i.e., the matrix (A e -L e C e ) should be set appropriately so that the real parts of the eigenvalues ​​of the matrix (A e -L e C e By using a disturbance observer O2 whose observer gain is designed so that the real parts of the eigenvalues ​​of d_hat(k) are all negative, the state variable T_hat(k) obtained from the disturbance observer O2 can be made to match the state variable x(k) in the actual system. In this case, the estimation device 100 can estimate the temperature outside the power storage device 20 through d_hat(k) obtained from the disturbance observer O2.

[0115] When the value of d, which is a disturbance term, indicates an abnormal value (when it indicates a large value), the estimation device 100 can estimate that the outside of the power storage device 20 is in a high temperature state. The estimation device 100 may compare the value of d obtained from the disturbance observer O2 with a preset threshold value, and when the value of d is higher than the threshold value, may notify information that the outside of the power storage device 20 is in a high temperature state via the output unit 104.

[0116] In this embodiment, one disturbance in the power storage device 20 is estimated by one observation value. Alternatively, any number of variables may be used. For example, the estimation device 100 may estimate q disturbances (p is an integer equal to or greater than 1) by using r observation values ​​(r is an integer equal to or greater than 1) in p power storage devices 20 (p is an integer equal to or greater than 1). For example, when p=5, an equation similar to Equation 2 is used as the heat conduction equation of each power storage device 20. Also, in Equation 17, the state vector x may be a (p+q)×1 vertical vector, A may be a p×p matrix, the scalar 1 may be replaced with a q×q unit matrix, and B may be a p×1 vertical vector. Furthermore, in Equation 18, y may be an r×1 vertical vector, and c may be an r×p matrix.

[0117] The estimation device 100 may estimate a plurality of disturbances (temperatures outside the power storage device 20) and display the estimated temperatures outside the power storage device 20 in a mapped form as a function of position.

[0118] According to the method of the second embodiment, the temperature of the surrounding environment can be estimated, which makes it possible to omit, for example, the temperature sensor 103B that measures the temperature of the surrounding environment.

[0119] The estimation device 100 may compare the estimated temperature of the surrounding environment with the measured value of the temperature sensor 103B and determine the validity of the measured value of the temperature sensor 103B. Although there is usually only one temperature sensor 103B for measuring the temperature of the surrounding environment for the power storage system 10, the temperature is not necessarily the same over the entire outer surface of the power storage system 10. Therefore, if the measured value of the temperature sensor 103B is an inappropriate value (for example, the temperature is measured in an area with a lower temperature than the surroundings), the calculation of the observer may calculate a temperature that is different from the actual condition. By using the method of the second embodiment, the temperature can be estimated while verifying the validity of the temperature of the surrounding environment used in the calculation of the observer.

[0120] (Embodiment 3) In the third embodiment, temperature estimation in the case where system noise and observation noise are included will be described. The overall configuration of the system, the internal configuration of the power storage device 20, and the estimation device 100 are the same as those of the first embodiment, and the description thereof will be omitted. In addition, in the description of the third embodiment, the equation of the disturbance observer described in the second embodiment (i.e., the equation with the subscript e in the system parameter) is used. e A, C e By replacing with C, the same theory holds true in the first embodiment.

[0121] In the third embodiment, the influence of noise is suppressed using a Kalman filter. The discrete space state equation and observation equation including the system noise w(k) and the observation noise v(k) are expressed by the following Expressions 24 and 25, respectively.

[0122]

number

[0123]

number

[0124] Here, the observer gain L of the disturbance observer using the Kalman filter is e is expressed by the following equation 26: where V represents the covariance matrix of the system noise, and W represents the covariance matrix of the observation noise.

[0125]

number

[0126] Observer Gain L e is derived via the Riccatti equation based on the LQ (Linear Quadratic) control theory that minimizes an objective function expressed by a quadratic form. The matrix P in Equation 26 is expressed as a solution that satisfies the following Riccatti equation.

[0127]

number

[0128] As described above, in the third embodiment, even when system noise and observation noise are included, the observer gain L of the disturbance observer using the Kalman filter is e By appropriately evaluating, it becomes possible to estimate the temperature using an observer while suppressing the effects of system noise and observation noise.

[0129] An application example of temperature estimation will be described below.

[0130] (Application example 1) An equivalent circuit model is well known as a mathematical model that represents the electrical characteristics of an energy storage element 200, typically a lithium ion battery. Fig. 7 is a circuit diagram showing an example of the 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, for example, as shown in Fig. 7.

[0131] R in Figure 7 0 is the ohmic resistance component, R 1 is the reaction resistance component of the positive electrode, C 1 is the capacitance component of the positive electrode, R 2 is the reaction resistance component of the negative electrode, C 2 is the capacitance component of the negative electrode, E eq is the open circuit voltage (OCV). However, Fig. 7 is an example, and there is no limitation on the combination of series and parallel, or the number and types of electric circuit elements.

[0132] It is known that the charge and discharge characteristics of the energy storage element 200, which is typically a lithium-ion battery, are strongly affected by temperature and SOC. SOC is an abbreviation for State Of Charge, where a fully charged state is expressed as 100% and a completely discharged state is expressed as 0%. 0 ~R 2 , C 1 ~C 2 , E eq The components of R are expressed as a bivariate function of SOC and temperature. 0 ~R 2 , C 1 ~C2 , E eq The relationship between the value of and the SOC and temperature may be a value obtained in advance.

[0133] In addition to the estimation device 100, the energy storage system 10 may hold a mathematical model of the energy storage element 200. The mathematical model of the energy storage element 200 includes information on the open circuit potential and internal impedance of the energy storage element 200, and indicates the relationship between current and voltage. The mathematical model of the energy storage element 200 is used as a state estimator (also called an observer) of the energy storage element 200 and for future prediction.

[0134] Use of estimation device 100 enables precise and accurate temperature estimation of each storage element 200, which is expected to result in more accurate characteristic values ​​for each element in the equivalent circuit and improved accuracy in simulation of charge and discharge characteristics.

[0135] (Application example 2) As a battery model other than the equivalent circuit, for example, the model disclosed in the non-patent document "Comparison of Modeling Predictions with Experimental Data from Plastic Lithium Ion Cells, M. Doyle, TF Fuller and J. Newman, Journal of The Electrochemical Society, 143 (6), 1890-1903 (1996)" may be used. This model is a physical model of a battery (particularly a lithium ion battery) called the Newman model.

[0136] In the Newman model, it is assumed that the positive and negative electrodes are made up of multiple uniformly sized active material particles arranged side by side. The quantities to be solved are the potential of the active material particles (solid-phase potential), the potential of the electrolyte (liquid-phase potential), the ion concentration of the electrolyte, and the molecular diffusion of the absorbed lithium ions in the active materials of the positive and negative electrodes. These quantities are solved while taking into account the equilibrium potential at the solid-liquid interface, the activation overpotential determined by the Butler-Volmer equation, and stoichiometry, and relating them to each other. The Newman model is described by the Nernst-Planck equation, the charge conservation equation, the diffusion equation, the Butler-Volmer equation, and the Nernst equation, which are explained below.

[0137] The Nernst-Planck equation is an equation for solving ion migration and ion diffusion in an electrolyte or a porous electrode, and is expressed by the following equation.

[0138]

number

[0139] Here, σ l,eff is the liquid phase conductivity (S / m), φ l is the liquid phase potential (V), R is the gas constant (J / (K mol)), T is the temperature (K), F is the Faraday constant (C / mol), f is the activity coefficient, c l is the ion concentration of the electrolyte (mol / m 3 ), t + is the cation transport number, i tot is the reaction current density per volume. The liquid phase effective conductivity σ l,eff is the apparent conductivity in the porous medium, and is the ratio of the bulk conductivity of the liquid phase to the solid phase volume fraction ε s It is often expressed as a function of

[0140] The charge conservation equation represents electronic conduction in a porous electrode or a current collector, and is expressed by the following equation:

[0141]

number

[0142] Here, φ s is the solid-state potential (V), σ s is the solid-phase conductivity (S / m), i tot is the reaction current density per volume (A / m 3 ) The solid phase refers to the electron conducting part.

[0143] The diffusion equation is an equation that represents the diffusion of absorbed lithium ions in active material particles, and is expressed by the following formula.

[0144]

number

[0145] where c s is the concentration of absorbed lithium ions in the solid phase (mol / m 3 ), t is time (s), D s is the diffusion coefficient of the absorbed lithium ions in the active material particles (m 2 / s). D s may be a function of the occluded lithium ions in the active material particles, the electrode composition, the SOC (State Of Charge), or the temperature.

[0146] The Butler-Volmer equation expresses the activation overvoltage in the charge transfer reaction that occurs at the interface between the active material particles and the electrolyte, while the Nernst equation expresses the equilibrium potential E eq are defined as follows:

[0147]

number

[0148] where i loc is the reaction current density (A / m 2 ), i 0 is the exchange current density (A / m 2 ), α a ,α c is the transfer coefficient, η is the activation overpotential (V), E eq is the equilibrium potential (V), E 0 is the standard equilibrium potential (V), n is the number of electrons involved, a0 is the oxidant concentration, a R is the reducing agent concentration (mol / m 3 ).

[0149] Equation 32 shows the relation between the concentration of absorbed lithium ions in the solid phase on the surface of the active material particle and the absorbed lithium ion flux involved in the charge transfer reaction. 0 represents the radius of the active material particle (m), and J s is the flux of absorbed lithium ions (mol / m 2 s). In other words, J s is the amount of absorbed lithium ions lost or generated by the charge transfer reaction per unit area and unit time.

[0150]

number

[0151] Number 33 is the flux of absorbed lithium ions, J s and reaction current density i loc This is an equation that expresses the relationship between

[0152]

number

[0153] Equation 34 expresses the reaction current density i loc and the reaction current density per volume i tot This is the equation that expresses the relationship between S v is the specific surface area per unit volume (m 2 / m 3 ) S v is the radius of the active material particle, r 0 It may be a function of

[0154]

number

[0155] FIG. 8 is a graph showing the relationship between the concentration of absorbed lithium ions in the solid phase of a typical positive electrode material and the open circuit potential (OCP). θ is a dimensionless number defined by the formula 35, and the absorbed lithium ion concentration c s It is a function of c smax is the concentration of absorbed lithium ions (mol / m) in the solid phase at the end of discharge (= at the minimum voltage) when the battery is manufactured, that is, when the battery has not deteriorated at all (i.e., at the 0th cycle). 3 ) On the other hand, c smin is the concentration of absorbed lithium ions (mol / m) in the solid phase at the beginning of discharge (= at the upper limit voltage = at full charge) when the battery is manufactured, that is, when the battery has not deteriorated at all (i.e., at the 0th cycle). 3 When fully charged, it is c s =c smin So θ=0.0, and at the end of the discharge, c s =c smax Therefore, θ = 1.0, and therefore θ changes on average from 0.0 to 1.0 as the battery discharges. In this way, the open circuit potential OCP of the positive electrode is expressed as a function of the positive electrode θ. In the same way, the open circuit potential OCP of the negative electrode is also expressed as a function of the negative electrode θ. Note that at the negative electrode, θ = 1.0 at the beginning of discharge and θ = 0.0 at the end of discharge.

[0156]

number

[0157] The above is a general explanation of the Newman model. For example, the transport number t + If ≒ 1.0, the second term on the right hand side of the first equation of Equation 2 can be ignored. In this case, the liquid phase current is calculated using Ohm's law. Since highly nonlinear terms can be ignored, the calculation load can be reduced while improving calculation stability.

[0158] The Butler-Volmer equation was used to express the activation overpotential in the charge transfer reaction, but the Tafel equation may be used instead. Furthermore, it may be given in the form of any table data. The exchange current density may be a function of the concentration of absorbed lithium ions in the electrode, the electrode composition, the SOC, or the temperature. The diffusion equation of the charge carriers in the solid phase described in Equation 4 may be omitted when the effect of the concentration overpotential can be ignored or when it is desired to reduce the calculation load.

[0159] By imparting temperature dependency to the reaction resistance equation (i.e., the Butler-Volmer equation), ion conductivity, ion diffusion coefficient, diffusion coefficient of absorbed lithium ions in the active material, or other physical property values ​​in this model, and by providing the temperature estimation value obtained from the estimation device 100 as an input condition to the Newman model simulation, it becomes possible to perform a precise simulation of charge and discharge characteristics.

[0160] Alternatively, a single-particle model may be used in which the electrode is represented by a single active material particle. For the single-particle model, for example, see the model disclosed in the non-patent document "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)". The single-particle model is a model that simplifies the above-mentioned Newman model and assumes that the active material particles constituting the positive and negative electrodes are all the same. By giving temperature dependency to the reaction resistance equation (i.e., the Butler-Volmer equation), ion conductivity, ion diffusion coefficient, diffusion coefficient of absorbed lithium ions in the active material, or other physical property values ​​in the model, and by providing the temperature estimation value obtained from the estimation device 100 as an input condition to the simulation of the single-particle model, a precise charge / discharge characteristic simulation is possible.

[0161] Alternatively, a polynomial model expressing the open circuit voltage OCV and the internal resistance as a power function of temperature and SOC may be used. For the polynomial model, for example, refer to the model disclosed in the non-patent document "Modeling the Dependence of the Discharge Behavior of a Lithium-Ion Battery on the Environmental Temperature, Ui Seong Kim, Jaeshin Yi, Chee Burm Shin, Taeyoung Han, and Seongyong Park, Journal of The Electrochemical Society, 158 (5) 611-618 (2011)". By providing the temperature estimate value described in the embodiment as an input condition to the simulation of the polynomial model, a precise charge and discharge characteristic simulation is possible.

[0162] Alternatively, if the model represents the characteristics of the energy storage element 200 and requires input of temperature, the estimation device 100 can be used to perform a precise simulation of the charge and discharge characteristics.

[0163] (Application example 3) By using the estimation device 100, it is possible to estimate the temperature distribution in the power storage device 20. Appropriate cooling conditions and heating conditions may be determined based on the estimated temperature distribution. The cooling and heating conditions may be, for example, air volume, air direction, and air temperature in the case of air cooling, and refrigerant flow rate and refrigerant temperature in the case of water cooling. Feedback control such as PID control and on / off control may be used as a method for determining the conditions.

[0164] (Application example 4) By using the estimation device 100, it is possible to estimate abnormal heating of the energy storage element 200. The estimated temperature of the energy storage element 200 may be an abnormal value (in many cases, an abnormal value is a value higher than normal). Since such an energy storage element 200 may be in an abnormal state due to an internal short circuit or the like, it is desirable to immediately take measures such as disconnecting the circuit.

[0165] (Application example 5) By using the estimation device 100, a more precise deterioration prediction simulation can be performed even when based on limited temperature information. Specifically, by using the temperature estimated by the estimation device 100 for the temperature included in a known deterioration prediction formula, a more precise deterioration prediction can be performed. In particular, in a storage battery system using a battery pack in which a plurality of unit cells are connected in series, the performance of a unit cell with a large degree of deterioration has a significant impact on the performance of the entire battery system, so that it is very useful to perform a more precise deterioration prediction using the temperature estimated value obtained by the estimation device 100.

[0166] 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 are limited observables, and simulations based only on sensor measurements tend to be less accurate. By performing temperature correction using this method and making temperature information more accurate, the accuracy of degradation predictions can be improved.

[0167] As a method for more accurate deterioration prediction, it is possible to consider performing deterioration calculations using historical data based on actually observed quantities such as current, voltage, and temperature, which have been corrected using the temperature observer of the present application.

[0168] 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 changes the charge / discharge characteristics of the battery, causing a decrease in capacity.

[0169] 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 by 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 deteriorates over time, and cycle deterioration, which deteriorates according to the number of cycles, and it has been confirmed through experiments that both are functions of temperature.

[0170] The estimation device 100 may simulate the deterioration of the power storage device 20 based on the determined deterioration progression rate. As a deterioration prediction method, for example, the method disclosed in Patent Document "Japanese Patent Application No. 2019-064218: Development Support Apparatus, Development Support Method, and Computer Program" may be used.

[0171] For example, the calculation unit 101 of the estimation device 100 calculates the rate at which the electrical resistance increases, that is, the rate at which the electrical conductivity decreases, using the following formula 36 or 37.

[0172]

number

[0173] where r cycle,res represents the rate at which the electrical conductivity decreases with the number of cycles (S / m / number of cycles). Typically, r cycle,res <0. 0,res is the reaction rate constant, e.g., a function of the number of cycles. E a0,res represents the activation energy of cycle degradation (J / mol) and is a coefficient that represents the effect of temperature. i is the current density (A / m 2 ) where || represents an absolute value. In cases where the number of cycles cannot be clearly defined, such as in the case of batteries for electric vehicles, an equation that does not express the number of cycles may be used, for example by using a constant reaction rate.

[0174]

number

[0175] where r t,res is the rate at which the electrical conductivity decreases over time (S / m / s). Typically, r t,res <0. 1,res is the reaction rate constant, e.g., a function of time. Alternatively, k 1,res may be defined by any function based on experimental data. a1,res represents the activation energy of degradation over time (J / mol) and is a coefficient that represents the effect of temperature. Δt is the elapsed time (s). The rate at which electrical conductivity decreases is the sum of Equation 36 and Equation 37.

[0176] The calculation unit 101 of the estimation device 100 calculates the rate at which the isolation of the active material particles progresses using Equation 38 or Equation 39.

[0177]

number

[0178] where r cycle,iso represents the rate at which the isolation of active material particles progresses with the number of cycles (1 / number of cycles). Typically, r cycle,iso <0. 0,iso is the reaction rate constant, e.g., a function of the number of cycles. E a0,iso represents the activation energy of cycle degradation (J / mol) and is a coefficient that represents the effect of temperature. i is the current density (A / m 2 In cases where the number of cycles cannot be clearly defined, such as in the case of batteries for electric vehicles, an equation that does not express the number of cycles may be used, for example by using a constant reaction rate.

[0179]

number

[0180] where rt,iso represents the rate at which the isolation of active material particles progresses over time (1 / s). Typically, r t,iso <0. 1,iso is the reaction rate constant, e.g., a function of time. Alternatively, k 1,iso may be defined by any function based on experimental data. a1,iso represents the activation energy of degradation over time (J / mol) and is a coefficient that represents the effect of temperature. Δt is the elapsed time (s). The rate at which isolation progresses is the sum of Equation 38 and Equation 39.

[0181] The third degradation mechanism is the decrease in charge carriers involved in charging and discharging. The degradation mechanism caused by the decrease in charge carriers is a phenomenon in which ions in the electrolyte are lost due to a side reaction on the surface of the electrode during charging.

[0182] A third degradation mechanism is known to be accelerated in lithium-ion batteries both with age and with cycling. During charging, Li + +e - +6C+P→xLiC 6 +(1-x)Li SEI As shown in the reaction equation, in addition to the main reaction in which Li is produced (ideally x=1), Li SEI A by-product is generated. P is the substance that is the source of the by-product. Here, x:(1-x) is the stoichiometric ratio of the main reaction:side reaction, but usually (1-x) / x<<1, and the stoichiometric coefficient of the side reaction is very small. The number of lithium ions lost from the electrolyte is calculated by multiplying the stoichiometric coefficient of the side reaction by the current density and the surface area of ​​the electrode, and dividing the result by the Faraday constant. To express this mechanism, the number of Li ions lost in the liquid phase is calculated by multiplying the stoichiometric coefficient of the side reaction by the current density and the surface area of ​​the electrode, and dividing the result by the Faraday constant. + The amount of loss is J Li+ (mol / m 2 s), the amount of Li flowing into the solid phase J Li (mol / m 2 s), J Li =xJ Li+ This can be done as follows.

[0183] x is the upper limit SOC max and lower limit SOCmin , temperature T, and current density i. For example, it may be a function as described in Equation 40. h is an arbitrary function determined to fit the experimental data. Note that 0.0≦x≦1.0.

[0184]

number

[0185] Side reactions occur even when there is no current flowing, other than when charging, but this is based on actual measurement data and is calculated based on the rate of lithium ion loss r Li as a function of time (r Li = g(t)). A function proportional to the square root of time t is often used as the function g. The function g may further include a factor related to temperature. The rate at which the charge carriers involved in charging and discharging decrease is J Li+ andr Li It becomes the sum of.

[0186] As the fourth deterioration mechanism, the decrease in the conductivity of the electrolyte will be described. The deterioration mechanism due to the decrease in the conductivity of the electrolyte is mainly the decrease in the conductivity due to the disappearance of the charge carrier. The disappearance of the charge carrier mainly occurs when a resistor film is formed on the surface of the active material particles.

[0187] It is known that the lithium ions in the electrolyte are reduced when the charge and discharge are repeated. The conductivity of the electrolyte is a function of the lithium ion concentration, and is generally maximum at the time of initial manufacture, but is known to decrease with the decrease in the lithium ion concentration. FIG. 9 is a graph showing the relationship between the lithium ion concentration in the electrolyte and the ionic conductivity. The horizontal axis of the graph shown in FIG. 9 indicates the lithium ion concentration in the electrolyte, and the vertical axis indicates the ionic conductivity. The relationship between the lithium ion concentration in the electrolyte and the ionic conductivity is often as shown in FIG. 9. The calculation unit 101 of the estimation device 100 can calculate the rate of decrease in the conductivity using functions similar to Equation 36 and Equation 37.

[0188] (Application example 6) Q described in Equation 1 to Equation 4 1 ~Q 5 The value of may be calculated based on the battery model described in (Application Example 1) and (Application Example 2).

[0189] 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.

[0190] For example, the power storage device 20 may be a module in which a plurality of cells are connected in series, a bank in which a plurality of modules are connected in series, a domain in which a plurality of banks are connected in parallel, or the like. When the power storage device 20 is a bank configured with a plurality of modules, the estimation device 100 may acquire temperatures measured for some of the modules as element temperatures, and estimate the temperatures of each of the power storage elements 200 including the temperatures of modules that are not measured (the temperatures of each module in this example). Similarly, when the power storage device 20 is a domain configured with a plurality of banks, the estimation device 100 may acquire temperatures measured for some of the banks as element temperatures, and estimate the temperatures of each of the power storage elements 200 including the temperatures of banks that are not measured (the temperatures of each bank in this example). [Explanation of symbols]

[0191] 10 Energy Storage System 20 Energy storage devices 100 Estimator 101 Arithmetic section 102 Storage section 103 Input section 103A Temperature Sensor 103B Temperature Sensor 103C Strain Sensor 103D current meter 104 Output section 200 Energy storage element

Claims

1. an acquisition unit that acquires a measurement result from a temperature sensor that measures a temperature at a specific location to which heat generated from the power storage device is transmitted; an observer that estimates temperatures at locations not measured by the temperature sensor by deriving state variables based on a state equation that simulates heat conduction in the power storage device and an observation equation that represents a relationship between state variables in the state equation and observation variables that can be observed by the temperature sensor in response to an input of the measurement results; An estimation device comprising:

2. The observer has an internal parameter designed so that the temperature estimated by the observer and the temperature measured by the temperature sensor become asymptotic. The estimation device according to claim 1 .

3. the temperature sensor is provided in the power storage device, The observer estimates a temperature outside the power storage device based on a temperature of the power storage device measured by the temperature sensor. The estimation device according to claim 1 or 2.

4. The observer has an observer gain formulated by a Kalman filter. The estimation device according to any one of claims 1 to 3.

5. A server device that is disposed remotely from the power storage device The estimation device according to any one of claims 1 to 4.

6. a calculation unit that simulates a deterioration prediction of the power storage device by using the temperature estimated by the observer; The estimation device according to any one of claims 1 to 5, comprising:

7. The simulation of the deterioration prediction of the power storage device is a simulation based on a physical model of the power storage device. The estimation device according to claim 6.

8. Obtaining a measurement result from a temperature sensor that measures a temperature at a specific point where heat generated from the power storage device is transmitted; The temperature at a location not measured by the temperature sensor is estimated by inputting the measurement results to an observer that estimates a state variable based on a state equation that simulates heat conduction in the power storage device and an observation equation that represents a relationship between a state variable in the state equation and an observation variable that can be observed by the temperature sensor. The estimation method is carried out by a computer.

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