Secondary battery temperature prediction method and secondary battery temperature prediction device

Abstract

To provide a secondary battery temperature prediction method that can calculate the temperature of a battery cell with high accuracy for a secondary battery having a battery module.SOLUTION: A Foster-type thermal circuit is generated by converting a two- or more-stage Cauer-type thermal circuit into an equivalent circuit, and the circuit constants of the Foster-type thermal circuit are obtained. The circuit constants of the Foster-type thermal circuit are then converted into an equivalent circuit to construct a Cauer-type thermal circuit, and the temperature of the secondary battery is predicted using the constructed Cauer-type thermal circuit.SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] The present invention relates to a method for predicting the temperature of a secondary battery and a device for predicting the temperature of a secondary battery. [Background technology]

[0002] Power generation facilities using renewable energy sources such as solar and wind power are being introduced on a large scale. Battery energy storage systems (BESSs) using secondary batteries are effective for balancing the supply and demand of renewable energy. The introduction of BESSs requires predicting the degradation state of secondary batteries at the end of their useful life. Factors that contribute to secondary battery degradation include elapsed time, the magnitude of charge / discharge current, the amount of charge, and the battery temperature. The elapsed time, the magnitude of charge / discharge current, and the amount of charge are controlled by the user. In contrast, battery temperature changes automatically depending on the usage state, making it difficult for the user to control it. Therefore, the secondary battery temperature must be estimated through simulation. For example, a method for estimating the internal temperature of a secondary battery unit using a thermal circuit model has been proposed (see, for example, Patent Document 1). The battery temperature estimation method described in Patent Document 1 describes two resistors as part of a thermal circuit for estimating the internal temperature. These two resistors can be replaced with a single resistor connected in series, resulting in an equivalent circuit configuration. Therefore, the method can be considered as a single-stage RC thermal circuit with one resistor and one capacitor. When using a battery with a simple configuration, a single-stage RC thermal circuit can provide sufficient prediction results. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2018-129130 Summary of the Invention [Problem to be solved by the invention]

[0004] The method described in Patent Document 1 uses an RC thermal circuit consisting of a single stage resistor and capacitor as a thermal circuit model. However, large-scale BESSs use a complex configuration in which secondary batteries are implemented in the form of a battery module equipped with multiple battery cells. For this reason, a single stage circuit consisting of a single battery cell cannot accurately estimate temperature.

[0005] In order to solve the above-mentioned problems, the present invention provides a secondary battery temperature prediction method and a secondary battery temperature prediction device that can calculate the temperature of a battery cell with high accuracy for a secondary battery having a battery module.

[0006] The above and other objects of the present invention and novel features of the present invention will become apparent from the description of this specification and the accompanying drawings. [Means for solving the problem]

[0007] The temperature prediction method for a secondary battery of the present invention predicts the temperature of the secondary battery using a thermal circuit model. The temperature prediction method generates a Foster-type thermal circuit by converting a two- or more-stage Cauer-type thermal circuit into an equivalent circuit, and obtains the circuit constants of the Foster-type thermal circuit. Then, the circuit constants of the Foster-type thermal circuit are converted into an equivalent circuit to construct a Cauer-type thermal circuit, and the temperature of the secondary battery is predicted using the constructed Cauer-type thermal circuit.

[0008] The temperature prediction device for a secondary battery of the present invention also includes a control unit that calculates a battery temperature estimated from a thermal circuit model of the secondary battery. The control unit has a thermal calculation unit that estimates the temperature of the secondary battery using a multi-stage thermal circuit model of a Cauer-type thermal circuit. The thermal calculation unit has a Foster-type multi-stage thermal circuit model generation unit that generates a Foster-type thermal circuit from the Cauer-type thermal circuit of the secondary battery, and a circuit constant calculation unit that determines the circuit constants of the Foster-type thermal circuit based on the temperature response waveform of the secondary battery under step heat generation conditions. The thermal calculation unit also includes an equivalent circuit conversion unit that converts the circuit constants of the Foster-type thermal circuit into those of a Cauer-type thermal circuit, and a temperature estimation unit that predicts the temperature of the secondary battery using the multi-stage thermal circuit model of the Cauer-type thermal circuit. [Effects of the Invention]

[0009] According to the present invention, it is possible to provide a secondary battery temperature prediction method and a secondary battery temperature prediction device that can calculate the temperature of a battery cell with high accuracy for a secondary battery having a battery module.

[0010] Problems, configurations, and effects other than those described above will become clear from the following description of the embodiments. [Brief explanation of the drawings]

[0011] [Figure 1] This is an example of a Cauer-type thermal circuit model consisting of a two-stage RC thermal circuit. [Figure 2] This is an example of a Foster-type thermal circuit model consisting of a two-stage RC thermal circuit. [Figure 3] 10 is an example of battery temperature response data of a battery cell under step heat generation conditions. [Figure 4] 10 is a graph in which the time axis of the temperature measurement results is converted into a logarithm. [Figure 5] This is a graph in which the waveform shown in FIG. 4 is differentiated with respect to logarithmic time z on the horizontal axis. [Figure 6] It is a function of the thermal resistance r and the time constant τ obtained by deconvolution using Fourier transform. [Figure 7]1 is a flowchart for determining a Cauer-type thermal circuit and circuit constants. [Figure 8] This is a one-stage RC thermal circuit model for accuracy verification. [Figure 9] This shows the results of a temperature simulation performed under step heat generation conditions. [Figure 10] FIG. 1 is a system block diagram of a temperature prediction device for a secondary battery. [Figure 11] FIG. 2 is a functional block diagram of a control unit of the temperature prediction device for a secondary battery. [Figure 12] FIG. 2 is a diagram illustrating a functional configuration of a heat calculation unit of a control unit. [Figure 13] 10 is an example of a Cauer-type thermal circuit model used for calculations in the method for predicting the temperature of a secondary battery according to the second embodiment. [Figure 14] This is an example of a temperature history in which a test was conducted under conditions in which cyclic heating of entropy heat was applied. DETAILED DESCRIPTION OF THE INVENTION

[0012] An example of a temperature prediction device for a secondary battery and a temperature prediction method for a secondary battery according to an embodiment of the present invention will be described below with reference to the drawings. Note that the present invention is not limited to the following example. In each of the drawings described below, common components are given the same reference numerals. Furthermore, in the drawings used in this specification, identical or corresponding components are given the same reference numerals, and repeated explanations of these components may be omitted. The explanation will be given in the following order. 1. Overview of secondary battery temperature prediction method 2. Secondary Battery Temperature Prediction Method (First Embodiment) 3. Secondary battery temperature prediction device 4. Secondary Battery Temperature Prediction Method (Second Embodiment) 5. Secondary Battery Temperature Prediction Method (Third Embodiment)

[0013] 1. Overview of secondary battery temperature prediction method Before describing the embodiments of the present invention, an outline of a method for predicting the temperature of a secondary battery will be described. The battery temperature estimation method employs an algorithm in which the battery temperature is calculated sequentially using a thermal circuit created based on the thermal capacity and thermal resistance of the battery cell. The secondary batteries used in BESS are implemented in the form of battery modules with many cells, and multiple battery modules are installed on a rack, creating a hierarchical structure. Therefore, for a large-scale BESS, a single-stage thermal circuit model of a single battery cell is not sufficient. For a large-scale BESS, it is necessary to consider the heat transfer between the components that make up the battery module and rack, as well as the thermal capacity of components other than the cells.

[0014] In other words, a multi-stage (two or more stages) circuit configuration must be adopted as the thermal circuit for predicting the temperature of a BESS. For example, by adopting a circuit configuration in which the first stage is the heat capacity of the battery cell and the thermal resistance between the cell and the module, and the second stage is the heat capacity of the module and the thermal resistance of the module cooling system, the accuracy of the temperature prediction calculation for a secondary battery with a battery module can be improved.

[0015] When predicting the temperature of a BESS, it is not common to use heat transfer simulations using methods such as the finite element method to determine the circuit constants of the thermal circuit model. When predicting the temperature of a BESS, it is common to determine the circuit constants based on the results of temperature measurement tests using an actual device and then construct a thermal circuit model. When predicting the temperature of a BESS, the values ​​of heat capacity and thermal resistance are determined from the results of temperature measurement tests using an actual device, and then a thermal circuit model is constructed. The reason for this is that in many cases, it is not possible to obtain detailed information about the structure and material properties of the various components that make up the BESS, such as the batteries. This is because the various components that make up the BESS are procured from external sources.

[0016] When constructing a thermal circuit model for predicting the temperature of a BESS, if the thermal circuit is a single-stage RC thermal circuit, the circuit constants can be easily determined from the temperature measurement results. In other words, if the thermal resistance R and the circuit time constant τ are determined from the temperature measurement results, the heat capacity C can be calculated using the formula C = τ / R. However, for multi-stage RC thermal circuits with two or more stages, a method for determining the circuit constants is not yet generally known.

[0017] To perform a temperature simulation of a BESS, a multi-stage thermal circuit model must be constructed. A suitable physical model for representing heat transfer is the Cauer-type thermal circuit model shown in Figure 1. Figure 1 shows an example of a Cauer-type thermal circuit: a two-stage RC thermal circuit consisting of the first stage, which is the thermal capacity C of the battery cell and the thermal resistance R between the cell and the module, and the second stage, which is the thermal capacity C of the module and the thermal resistance R of the module cooling system. In the Cauer-type thermal circuit shown in Figure 1, the thermal resistance R1 and thermal capacity C1 on the left side form the first stage of the RC thermal circuit, and the thermal resistance R2 and thermal capacity C2 on the right side form the second stage of the RC thermal circuit. The heat generated by the battery cell (equivalent to current in an electrical analogy) is input to terminal Tm1 on the left side, and the heat is dissipated into the refrigerant from the grounded part on the right side. The temperature difference (temperature rise) between the refrigerant temperature and the battery cell temperature is calculated in section T1 (as a voltage in an electrical analogy). In the first-stage RC thermal circuit, the thermal capacity C1 represents the thermal capacity of the battery cell, and the thermal resistance R1 represents the thermal resistance between the battery cell and the battery module. In the second-stage RC thermal circuit, the thermal capacity C2 represents the thermal capacity of the battery module, and the thermal resistance R2 represents the thermal resistance between the battery module and the refrigerant.

[0018] However, the analytical solution for the Cauer-type thermal circuit shown in Figure 1 is complicated. Therefore, when using a Cauer-type thermal circuit, it is not easy to determine the circuit constants. Therefore, we create a Foster-type circuit model, which is an equivalent circuit to the desired Cauer-type circuit model. Figure 2 shows the Foster-type thermal circuit, which is an equivalent circuit conversion of the Cauer-type thermal circuit shown in Figure 1. The Foster-type thermal circuit shown in Figure 2 consists of an RC thermal circuit consisting of thermal resistance r1 and heat capacity c1, and another RC thermal circuit consisting of thermal resistance r2 and heat capacity c2, connected in series. Although the Foster-type thermal circuit shown in Figure 2 does not directly correspond to a physical model, its circuit constants [r1, c1, r2, c2] can be converted to the constants [R1, C1, R2, C2] of the Cauer-type thermal circuit shown in Figure 1. Therefore, the circuit constants are calculated using the created Foster-type thermal circuit, and the calculated circuit constants are converted into an equivalent circuit to determine the circuit constants of the target Cauer-type thermal circuit. This makes it possible to perform temperature simulation of the BESS using the Cauer-type thermal circuit.

[0019] In a multi-stage Foster-type thermal circuit, the temperature response of the entire circuit is expressed as the sum of the responses of each stage. In this case, the thermal resistance of each stage is r1, r2,... and the thermal time constants are τ1, τ2,.... If the thermal resistance r and the time constant τ are treated as continuous variables, the resistance can be written as r = f(τ) as a function of the time constant. This f is called the structure function of the thermal circuit. The structure function f represents the characteristics of the thermal circuit. Therefore, to determine the circuit constants of a multi-stage RC thermal circuit, it is sufficient to determine the structure function f.

[0020] The condition in which heat generation is zero as the initial state and a constant amount of heat is added from a certain point onwards is called step heat generation. It is known that the temperature response when step heat generation is applied to a thermal circuit is the convolution integral of the structure function f of the circuit. Therefore, the circuit constants of the Foster-type thermal circuit are determined using the following procedure, and a thermal circuit model is constructed.

[0021] First, heat is generated in the battery cells that make up the BESS under step heating conditions, and the cell temperature history is measured. Next, the measured temperature history data is subjected to a deconvolution operation to obtain the thermal circuit structure function f. This makes it possible to determine the thermal resistances r1, r2,... and the thermal capacitances c1, c2,..., which are the circuit constants of the Foster-type thermal circuit. Furthermore, a Cauer-type thermal circuit model is obtained by converting the obtained Foster-type circuit into an equivalent circuit.

[0022] Figure 3 shows an example of battery temperature response data for a battery cell under step heat generation conditions. In the graph shown in Figure 3, the vertical axis represents the temperature rise rate (k / W) and the horizontal axis represents time. Under step heat generation conditions, while refrigerant is circulated through the battery module, no current is passed through the battery at time t<0, resulting in zero heat generation, and then a constant amount of heat is generated at time t≧0. An example of temperature history data for a battery cell measured under these step heat generation conditions is shown in graph 31 in Figure 3.

[0023] When the thermal model of the battery used in the measurements is represented by the two-stage RC Foster-type thermal circuit shown in Figure 2, the temperature history shown in Graph 31 is the sum of two exponential functions shown in Graphs 32 and 33 in Figure 3. Graph 32 shows the response to step heat generation by the first-stage RC thermal circuit, which includes thermal resistance r1 and heat capacity c1 shown in Figure 2. Similarly, Graph 33 shows the response to step heat generation by the second-stage RC thermal circuit, which includes thermal resistance r2 and heat capacity c2 shown in Figure 2. As shown in Figure 2, the Foster-type two-stage RC thermal circuit consists of two RC thermal circuits connected in series. Therefore, the temperature rise of the entire battery (corresponding to the voltage in the electrical model) is the sum of the temperature rises of each RC thermal circuit.

[0024] For a single-stage RC thermal circuit, an exponential function response can be obtained directly from temperature measurements. Therefore, the thermal resistance and time constant values ​​can be calculated from the resulting exponential function curve. Therefore, if the temperature response curve shown in graph 31 in Figure 3 can be separated into two exponential functions shown in graphs 32 and 33, an exponential function response can be obtained from temperature measurements for each single-stage RC thermal circuit. As a result, the circuit constants for a two-stage RC circuit can be determined from the battery cell temperature measurement results. However, the procedure for decomposing a temperature response curve into two exponential functions is not trivial. Therefore, the procedure for decomposing a temperature response curve into a sum of exponential functions using deconvolution is described below.

[0025] First, let τ1 and τ2 be the time constants of each RC thermal circuit in the Foster-type thermal circuit. In this case, the time constants can be expressed as the product of thermal resistance r and heat capacity c, i.e., τ1 = r1·c1 and τ2 = r2·c2. In this case, the temperature response (T(t)) under step heat generation conditions (heat generation amount Q at time t≧0) can be expressed as the sum of exponential functions, which are the temperature responses of each RC thermal circuit, as mentioned above. The equation that expresses this is Equation (1) below. In the case of the two-stage circuit shown in Figure 2, n=2.

[0026]

number

[0027] The following variable transformation is performed on equation (1): The temperature rise T divided by the amount of heat Q is a (=T / Q). ·Let the thermal resistance r be a function of the time constant. ·The time axis is logarithmic, so replace z=log(t) and x=log(τ).

[0028] After the above variable transformations, if we consider a, r, z, and x as continuous variables and rewrite the sum in equation (1) as an integral, we can express it as equation (2) below.

[0029]

number

[0030] The following equation (3) is obtained by differentiating both sides of equation (2) with respect to logarithmic time z.

[0031]

number

[0032] From equation (3), we can see that the derivative a' of a can be expressed as a convolution integral of the thermal resistance r. That is, it is expressed as the following equation (4). Here, w t (z)=exp{z-exp(z)} is the weight function of the convolution.

[0033]

number

[0034] Applying the convolution theorem to equation (4), we obtain the following equation (5).

[0035]

number

[0036] That is, the Fourier transform of a' is r and w t Therefore, if a' can be obtained from measurements, the Fourier transform of r can be calculated using equation (5) by applying a Fourier transform. Furthermore, by applying an inverse Fourier transform, the thermal resistance r can be obtained as a function of the time constant τ. In other words, the structure function f can be obtained as r = f(τ).

[0037] An example of applying the above calculation method to the temperature response waveform of a battery cell under the step heat generation condition shown in FIG. 3 above is shown below. Graph 31 in Figure 3 shows the temperature response waveform when the thermal resistances are r1 = 0.2 (K / W), r2 = 0.3 (K / W), and the heat capacities are c1 = 50 (J / K), c2 = 333.3 (J / K) in the Foster-type thermal circuit shown in Figure 2. The time constants are τ1 = 10 (seconds) and τ2 = 100 (seconds), respectively.

[0038] Figure 4 shows a graph in which the time axis of the temperature measurement results of graph 31 in Figure 3 is converted to a logarithm. Figure 5 shows a graph in which the waveform shown in Figure 4 is differentiated with respect to the logarithmic time z on the horizontal axis. Based on the graph shown in Figure 5, by performing deconvolution using Fourier transform according to the above equation (5), it is possible to draw the function (graph) of thermal resistance r and time constant τ shown in Figure 6. This function of thermal resistance r and time constant τ shown in Figure 6 is the structure function f of the Foster-type thermal circuit shown in Figure 2.

[0039] Two peaks can be seen in the graph of the structure function f of the Foster-type thermal circuit shown in Figure 6. Note that the waveform in Figure 6 is blunted due to processing using a finite amount of data. At each peak, the thermal resistances r1 and r2 of the RC thermal circuit are obtained on the vertical axis, and the time constants τ1 and τ2 are obtained on the horizontal axis. From the graph shown in Figure 6, the respective peaks can be read as r1 = 0.2, r2 = 0.3, τ1 = 10, and τ2 = 100. The thermal resistances r1 and r2 and time constants τ1 and τ2 read from these peaks match the input conditions for the battery cell temperature response waveform under the step heating conditions shown in Figure 3 above. Therefore, it can be seen that the two-stage RC thermal circuit constants are correctly reproduced by the above calculation.

[0040] By the above calculations, the circuit constants of the Foster-type thermal circuit shown in Figure 2 can be determined, namely, the thermal resistances r1 and r2 and the heat capacities c1 (=τ1 / r1) and c2 (=τ2 / r2). Next, the Foster-type thermal circuit is converted into an equivalent circuit to form a Cauer-type thermal circuit. At this time, the circuit constants of the Foster-type thermal circuit determined by the above calculation are converted into the circuit constants of a Cauer-type thermal circuit using the following equations (6) to (9).

[0041]

number

[0042] The above calculations yield the Cauer-type thermal circuit shown in Figure 1, which is a thermal model that corresponds to the physical values ​​of thermal resistance and heat capacity. Then, by using the obtained Cauer-type thermal circuit and circuit constants, the temperature of the secondary battery can be estimated by simulation.

[0043] 2. Secondary Battery Temperature Prediction Method (First Embodiment) Next, a method for predicting the temperature of a secondary battery according to this embodiment will be described. The amount of heat generated by a secondary battery (Q) is expressed as the Joule heat generated (Q P ) and entropy heat release (Q S ) is the sum of

[0044]

number

[0045] For this reason, when predicting the temperature of a secondary battery, first the amount of Joule heat generation is calculated from the battery's internal resistance and current. Next, the amount of entropy heat generation is calculated from the current, temperature, and entropy heat generation coefficient (∂E / ∂T: temperature dependence of electromotive force) as shown in the following equation (11). The entropy heat generation coefficient depends on the battery's state of charge (SOC: Status of Charge).

[0046]

number

[0047] Furthermore, in predicting the temperature of the secondary battery, the temperature and flow rate of the coolant supplied from the chiller to the battery module are calculated. The temperature of the battery is then calculated from the total value of the calculated Joule heat generation amount and entropy heat generation amount, and the temperature and flow rate of the coolant.

[0048] When calculating the battery temperature from the Joule heat generation amount, entropy heat generation amount, and the temperature and flow rate of the refrigerant, a Cauer-type thermal circuit, which is an equivalent circuit conversion of the Foster-type thermal circuit, and the converted circuit constants, as explained in the overview of the temperature prediction method above, are used.

[0049] FIG. 7 shows a Cauer-type thermal circuit and a flowchart for determining the circuit constants. First, battery temperature response data measured under step heat generation conditions is obtained (step S10). The battery temperature response obtained by the measurement is, for example, a temperature response curve such as graph 31 shown in FIG. Next, the normalized temperature response curve is differentiated with respect to logarithmic time (step S11). This normalization is performed in the same manner as in deriving a(z) in equation (2) above. The graph in FIG. 4 is the result of normalizing graph 31 shown in FIG. 3. Then, a(z) is differentiated with respect to logarithmic time to derive a'(z) in equation (3). The graph in FIG. 5 is the result of differentiating the graph in FIG. 4 with respect to logarithmic time. Next, a'(z) in equation (3) is deconvoluted to obtain the structure function r=f(τ) (step S12). a'(z) in equation (3) is obtained by deconvoluting r and w shown in equation (5) according to the convolution theorem. t Therefore, by deconvolving a'(z) using the Fourier transform, the structure function r=f(τ) of the thermal resistance r and the time constant τ is obtained. The structure function r=f(τ) of the thermal resistance r and the time constant τ obtained by the Fourier transform is shown in the graph in Figure 6. Next, the combination of r and c is determined from the peak of the structure function r = f(τ) (step S13). As shown in the graph in Figure 6, two peaks are read from the waveform. Then, the thermal resistances r1 and r2 of the RC thermal circuit are determined from the vertical axis of each peak, and the time constants τ1 and τ2 are determined from the horizontal axis. Furthermore, the thermal capacities c1 and c2 are calculated from the thermal resistances r1 and r2 and the time constants τ1 and τ2. Next, the RC thermal circuits are connected in series (step S14). That is, a two-stage Foster-type thermal circuit is constructed by connecting in series an RC thermal circuit (first stage) having thermal resistance r1, time constant τ1, and heat capacity c1 determined from the waveform peak, and an RC thermal circuit (second stage) having thermal resistance r2, time constant τ2, and heat capacity c2. Next, the constructed Foster-type thermal circuit is converted into an equivalent circuit to construct a Cauer-type thermal circuit (step S15). Here, the thermal resistances r1 and r2 and the time constants τ1 and τ2 in the Foster-type thermal circuit are converted into the circuit constants of the Cauer-type thermal circuit using equations (6) to (9). This constructs a Cauer-type thermal circuit that directly corresponds to the physical model of the secondary battery. With the above processing, the flowchart shown in FIG. 7 is completed. Furthermore, the temperature of the secondary battery is calculated by inputting the current value into a Cauer-type thermal circuit that uses the circuit constants determined by the processing of the flowchart shown in FIG.

[0050] We verified the accuracy of temperature estimation using a multi-stage thermal circuit for the secondary battery temperature calculated using the above method. In verifying accuracy, we compared the temperature estimation results calculated using the above method with those of a single-stage RC thermal circuit model shown in Figure 8. In a one-stage RC thermal circuit model, the circuit constants are determined from the temperature response waveform under step heat generation conditions. When determining the circuit constants, first determine the value of thermal resistance R (= T / Q) from the temperature rise result (T) at the point when the temperature has converged to a steady state and the amount of heat generated by the battery cell (Q). Next, the time constant τ is set to the time when the temperature has reached 63.2% of the converged value, and the thermal capacity C is determined using C = τ / R. This gives the thermal resistance R and thermal capacity C, which are the circuit constants of the one-stage RC thermal circuit model.

[0051] Following the above procedure, a single-stage RC thermal circuit was determined from the temperature response waveform of graph 31 in FIG. 3. The calculated circuit constants were R = 0.5 and C = 157.2 (τ = 49.7). Using this thermal model, a temperature simulation was performed under the same step heat generation conditions as graph 31 in FIG. 3, resulting in graph 91 shown by the solid line in FIG. 9. Also in FIG. 9, the calculation results for the two-stage RC thermal circuit model are shown by graph 92 shown by the dashed line. Graph 92 represents temperatures calculated using the temperature prediction method according to the above-described embodiment. Therefore, graph 92 reproduces the circuit constants of the first and second stages of the Cauer-type thermal circuit model in the two-stage RC thermal circuit. Therefore, there is no error between graph 92 and graph 31 in FIG. 3.

[0052] As shown in FIG. 9 , a difference exists between solid-line graph 91, in which circuit constants are set based on a single-stage RC thermal circuit, and dashed-line graph 92, in which circuit constants for each stage are set based on a two-stage RC thermal circuit. The maximum difference between graph 91 and graph 92 is 0.046 (K / W), which is 9% of the temperature rise in steady state. As described above, when the thermal model is set as a single-stage RC thermal circuit model, the predicted temperature of the secondary battery obtained by temperature simulation has a large error compared to the actual temperature of the secondary battery or when set as a two-stage RC thermal circuit model. Therefore, by creating a thermal circuit model according to the temperature prediction method of the present embodiment described above, it is possible to improve the accuracy of predicting the battery temperature of a battery module equipped with a large number of battery cells.

[0053] In the above example of secondary battery temperature prediction, the input data is the temperature response of a two-stage RC thermal circuit. However, for secondary batteries such as BESSs that are actually implemented, it may be difficult to determine in advance how many stages the thermal model should have. Even in this case, by following the temperature prediction method of this embodiment, it is possible to determine an appropriate number of stages in the thermal circuit by counting the peaks of the differential value of the structure function. As a result, an optimal thermal circuit model can be constructed for secondary battery temperature prediction.

[0054] 3. Temperature Prediction Device for Secondary Battery Next, the configuration of a temperature prediction device for a secondary battery that can implement the above-mentioned temperature prediction method for a secondary battery will be described. Fig. 10 shows a system block diagram of the temperature prediction device for a secondary battery. The temperature prediction device for a secondary battery 1 shown in Fig. 10 includes a control unit 100, a storage unit 50, and a communication unit 60, which are all connected to a bus 70.

[0055] The control unit 100 is a calculation unit that includes a CPU 101, a ROM 102, and a RAM 103, each of which is connected to a bus 70, and that controls the temperature prediction device 1 in an integrated manner. The CPU 101 reads out program code of software that realizes each function according to this embodiment from the ROM 102, expands it into the RAM 103, and executes it. Variables, parameters, etc. that arise during the calculation processing of the CPU 101 are temporarily written to the RAM 103, and these variables, parameters, etc. are read out by the CPU 101 as appropriate. Also, an MPU may be used instead of the CPU 101.

[0056] The storage unit 50 is configured, for example, with an HDD, SSD, or non-volatile memory. The storage unit 50 stores an OS, various parameters, and programs for operating the temperature prediction device 1. The ROM 102 and storage unit 50 record programs and data necessary for the CPU 101 to operate, and are used as an example of a computer-readable, non-transitory storage medium that stores programs executed by the temperature prediction device 1. The storage unit 50 also stores externally acquired secondary battery temperature data (temperature history data, battery temperature response data, etc.), RC thermal circuits (Cauer-type thermal circuits, Foster-type thermal circuits), and calculated thermal circuit circuit constants.

[0057] The communication unit 60 transmits and receives various data to and from information devices (e.g., client devices). The communication unit 60 is configured with a NIC (Network Interface Card), a modem, etc. The communication unit 60 also transmits and receives various data to and from information devices such as servers and client devices. The communication unit 60 also receives signals from temperature sensors arranged in secondary batteries constituting a BESS, etc., or in secondary batteries for measurement, etc., and transmits the signals to the control unit 100. The control unit 100 stores the temperature data acquired from the communication unit 60 in the memory unit 50.

[0058] [Configuration of the control unit of semiconductor manufacturing equipment] Next, a functional configuration of the control unit 100 of the secondary battery temperature prediction device 1 will be described. Fig. 11 shows a functional block diagram of the control unit 100. As shown in Fig. 2, the control unit 100 has a Joule heat generation calculation unit 110, an entropy heat generation calculation unit 120, a chiller model 130, a heat calculation unit 150, and an output unit 140.

[0059] Each functional component of the control unit 100 performs the various processes described in the above-mentioned method for predicting the temperature of a secondary battery. The specific processing method is the same as that described in the above-mentioned embodiment of the method for predicting the temperature of a secondary battery. Therefore, in the following description, overlapping explanations will be omitted. The Joule heat generation calculation unit 110 calculates the amount of Joule heat generation (Q P ) is calculated. The entropy heat generation calculation unit 120 calculates the entropy heat generation amount (Q S ) is calculated. The chiller model 130 calculates the temperature and flow rate of the coolant supplied from the chiller to the battery module.

[0060] The thermal calculation unit 150 determines circuit constants to configure a thermal circuit model of a multi-stage thermal circuit, and predicts the temperature of the secondary battery. The thermal calculation unit 150 also outputs data on the estimation result of the temperature of the secondary battery to the output unit 140. 12 shows the functional configuration of the thermal calculation unit 150. The thermal calculation unit 150 includes a Cauer-type multistage thermal circuit model generation unit 151, a Foster-type multistage thermal circuit model generation unit 152, a temperature response waveform acquisition unit 153, a circuit constant calculation unit 154, an equivalent circuit conversion unit 155, and a temperature estimation unit 156.

[0061] The Cauer-type multistage thermal circuit model generation unit 151 generates a Cauer-type thermal circuit, which is a physical model corresponding to a secondary battery constituting a BESS or the like. Furthermore, the Cauer-type multistage thermal circuit model generation unit 151 generates a Cauer-type multistage thermal circuit model for predicting the temperature of a secondary battery by acquiring the circuit constants of the Cauer-type thermal circuit obtained by converting the circuit constants of the Foster-type thermal circuit into an equivalent circuit. For example, the Cauer-type multistage thermal circuit model generation unit 151 generates a Cauer-type multistage thermal circuit using a two-stage RC thermal circuit as shown in FIG. 1 or a Cauer-type multistage thermal circuit using a two-stage RC thermal circuit as shown in FIG. 13 (described later). Furthermore, the Cauer-type multistage thermal circuit model generation unit 151 generates a Cauer-type multistage thermal circuit model used for predicting the temperature of a secondary battery by using the circuit constants of the Cauer-type thermal circuit converted using the above equations (6) to (9) based on the circuit constants of the Foster-type thermal circuit.

[0062] The Foster-type multistage thermal circuit model generation unit 152 generates a Foster-type thermal circuit from a Cauer-type thermal circuit. For example, the Foster-type multistage thermal circuit model generation unit 152 generates a Foster-type circuit model using a two-stage RC thermal circuit shown in Fig. 2, which is an equivalent circuit to the Cauer-type circuit model shown in Fig. 1. The Foster-type multistage thermal circuit model generation unit 152 also generates a Foster-type circuit model, which is an equivalent circuit to the Cauer-type multistage thermal circuit shown in Fig. 13, which will be described later.

[0063] The temperature response waveform acquisition unit 153 acquires the temperature response waveform of the battery measured under the step heating conditions. The function of the temperature response waveform acquisition unit 153 corresponds to the processing of step S10 in the flowchart shown in FIG. The circuit constant calculation unit 154 determines the circuit constants of the Foster-type thermal circuit based on the temperature response waveform. The function of this circuit constant calculation unit 154 corresponds to the processing of steps S11 to S14 in the flowchart shown in FIG. 8. Specifically, the circuit constant calculation unit 154 performs calculation processing to determine the circuit constants of the Foster-type thermal circuit from the temperature response waveform. The circuit constant calculation unit 154 acquires a graph (function formula) in which the time axis of the temperature measurement result is logarithmically converted from the temperature response waveform shown in FIG. 3 acquired by the temperature response waveform acquisition unit 153, and a graph (function formula) in which the waveform of FIG. 4 is differentiated with respect to the logarithmic time z on the horizontal axis shown in FIG. 5. Then, the circuit constant calculation unit 154 calculates the structure function f of the Foster-type thermal circuit shown in FIG. 6 by a deconvolution operation. Furthermore, the circuit constant calculation unit 154 obtains the thermal resistances r1 and r2 and the time constants τ1 and τ2 from the structural function f of the Foster-type thermal circuit, and determines the circuit constants of the Foster-type thermal circuit, i.e., the thermal resistances r1 and r2 and the heat capacities c1 (=τ1 / r1) and c2 (=τ2 / r2). The equivalent circuit conversion unit 155 converts the circuit constants of the Foster-type thermal circuit into those of the Cauer-type thermal circuit. The function of this equivalent circuit conversion unit 155 corresponds to the processing of step S15 in the flowchart shown in FIG.

[0064] The temperature estimation unit 156 predicts the temperature of the secondary battery using a multi-stage thermal circuit model of a Cauer-type thermal circuit. For example, the temperature estimation unit 156 predicts the temperature of the secondary battery using the multi-stage thermal circuit model configured in the Cauer-type multi-stage thermal circuit model generation unit 151. The temperature estimation unit 156 performs a temperature simulation using the configured Cauer-type multi-stage thermal circuit model, the heat generation amounts calculated by the Joule heat generation calculation unit 110 and the entropy heat generation calculation unit 120, and the temperature and flow rate of the refrigerant calculated by the chiller model 130. Then, the temperature estimation unit 156 estimates the temperature of the secondary battery from the results of the temperature simulation.

[0065] The output unit 140 outputs data on the estimation result of the temperature of the secondary battery to the outside of the temperature prediction device 1 for a secondary battery via the communication unit 60, etc. For example, the data on the estimation result of the temperature of the secondary battery is output to the memory unit 50 and stored in the memory unit 50. The output unit 140 also outputs the data to a display device connected to the temperature prediction device 1 for a secondary battery, a server connected via a network, etc.

[0066] 4. Secondary Battery Temperature Prediction Method (Second Embodiment) Next, a second embodiment of a temperature prediction method for a secondary battery will be described. The temperature prediction method for a secondary battery of the second embodiment predicts the temperature of a secondary battery having multiple battery cells in one module. Note that the temperature prediction method for a secondary battery of the second embodiment differs from the temperature prediction method for a secondary battery of the first embodiment described above only in the method for determining a thermal circuit model. Therefore, only the differences from the temperature prediction method for a secondary battery of the first embodiment described above will be described below, and a description of similar configurations will be omitted. Furthermore, the temperature prediction device can apply a similar configuration by changing the determination of the thermal circuit model of the multi-stage thermal circuit in the thermal calculation unit to processing in accordance with the temperature prediction method of the second embodiment.

[0067] FIG. 13 shows a thermal circuit used for calculations in the method for predicting the temperature of a secondary battery according to the second embodiment. In the method for predicting the temperature of a secondary battery, a thermal model is constructed for multiple battery cells. FIG. 13 shows a Cauer-type thermal circuit. The Cauer-type thermal circuit shown in FIG. 13 is a two-stage RC thermal circuit having a first battery cell 11 and a second battery cell 12 in the first stage and a module 20 in the second stage. The first battery cell 11 has a heat capacity of C 11 , and the thermal resistance R between the first battery cell 11 and the module 20 11 It has an RC thermal circuit. The second battery cell 12 has a heat capacity of C 12 , and the thermal resistance R between the second battery cell 12 and the module 20 12 It has an RC thermal circuit. Module 20 has a thermal capacity of C 20 , and the thermal resistance R between the module 20 and ground. 20It has an RC thermal circuit.

[0068] In the Cauer-type thermal circuit shown in FIG. 13 , as in the first embodiment described above, a Foster-type circuit model, which is an equivalent circuit to the Cauer-type circuit model, is created, and circuit constants are calculated using the Foster-type thermal circuit. Then, the calculated circuit constants of the Foster-type thermal circuit are converted into an equivalent circuit to determine the circuit constants of the target Cauer-type thermal circuit. Calculation of the circuit constants using the Foster-type thermal circuit and conversion of the circuit constants of the Foster-type thermal circuit into an equivalent circuit of the Cauer-type thermal circuit can be performed in the same way as in the first embodiment described above. This allows temperature simulation of a secondary battery to be performed using the Cauer-type thermal circuit.

[0069] In the configuration shown in FIG. 13, which has two battery cells in the first stage and a module in the second stage, the structure function f 11 and the structure function f 12 For example, the temperature measurement results of graph 31 shown in FIG. 3 are measured for the temperature between the first battery cell 11 and the module 20, and the temperature between the second battery cell 12 and the module 20. Then, a graph shown in FIG. 4 in which the time axis of the temperature measurement results is converted into a logarithm, and a graph shown in FIG. 5 in which the waveform of FIG. 4 is differentiated with respect to the logarithmic time z on the horizontal axis are obtained. Furthermore, the structure function f of the Foster-type thermal circuit between the first battery cell 11 and the module 20 shown in FIG. 6 is obtained. 11 and the structure function f of the Foster-type thermal circuit formed by the second battery cell 12 and the module 20. 12 and are calculated by a deconvolution operation.

[0070] As a result, the structure function f 11 From the thermal resistance r 11 ,r 20 , time constant τ 11 ,τ 20 Similarly, the structure function f of the Foster-type thermal circuit formed by the second battery cell 12 and the module 20 is obtained.12 From the thermal resistance r 12 ,r 20 , time constant τ 12 ,τ 20 Then, the circuit constant of the Foster-type thermal circuit formed by the first battery cell 11 and the module 20, that is, the thermal resistance r 11 ,r 20 and heat capacity c 11 (=τ 11 / r 11 ),c 20 (=τ 20 / r 20 ) can be determined. In addition, the circuit constant of the Foster-type thermal circuit formed by the second battery cell 12 and the module 20, i.e., the thermal resistance r 12 ,r 20 and heat capacity c 12 (=τ 12 / r 12 ),c 20 (=τ 20 / r 20 ) can be determined.

[0071] Furthermore, the thermal resistance r of the circuit constant of the Foster type thermal circuit was calculated. 11 ,r 12 ,r 20 , heat capacity c 11 ,c 12 ,c 20 is converted into the circuit constants of the Cauer thermal circuit using the above equations (6) to (9). As a result, the Cauer thermal circuit shown in Figure 13, which is a thermal model corresponding to the physical values ​​of thermal resistance and heat capacity, is obtained.

[0072] The Cauer type thermal circuit shown in Figure 13 is 11 The heat generation amount of the first battery cell 11 is measured at the terminal Tm 12 The heat generation amount of the second battery cell 12 is input from the above. As a result of the simulation using the thermal circuit, the temperature of the first battery cell 11 is calculated as T11, and the temperature of the second battery cell 12 is calculated as T12. As described above, the temperature prediction method for a secondary battery according to the second embodiment can accurately predict the temperature of a battery cell even when the amount of heat generated by each of the battery cells is different or when the thermal characteristics (heat capacity, thermal resistance) of the battery cells are different from one another. As a result, it is possible to improve the accuracy of predicting the temperature of a secondary battery having a battery module equipped with many battery cells.

[0073] 5. Secondary Battery Temperature Prediction Method (Third Embodiment) Next, a third embodiment of the temperature prediction method for a secondary battery will be described. The temperature prediction method for a secondary battery of the third embodiment differs from the temperature prediction method for a secondary battery of the first embodiment described above only in the method for acquiring battery temperature response data of the battery cell under step heat generation conditions. Therefore, only the differences from the temperature prediction method for a secondary battery of the first embodiment described above will be described below, and a description of similar configurations will be omitted. Furthermore, the temperature prediction device can apply a similar configuration by changing the determination of the thermal circuit model of the multi-stage thermal circuit in the thermal calculation unit to processing in accordance with the temperature prediction method of the third embodiment.

[0074] To generate heat, a secondary battery is charged and discharged. However, secondary batteries are used within a specific range of state of charge (SOC) (0% to 100% at most). If a secondary battery continues to be charged or discharged, the state of charge will reach a limit (upper or lower limit of SOC) and further charging or discharging will no longer be possible.

[0075] Therefore, to obtain battery temperature response data for a battery cell under step heat generation conditions, a secondary battery must be subjected to repeated charging and discharging tests. However, as shown in Equation (11) above, the entropic heat of a battery is proportional to the current. Therefore, the sign of the entropic heat is reversed during charging and discharging. In other words, if entropic heat is a heat-generating condition during charging, discharging at the same SOC and current value results in entropic heat absorption. Therefore, even if a test is conducted under conditions where Joule heat is dominant, cyclic heat occurs when switching between charging and discharging, resulting in repeated heat generation and absorption due to entropic heat. Therefore, when obtaining battery temperature response data in a charge / discharge test, the amount of heat generated fluctuates due to entropic heat, making it difficult to maintain a constant amount of heat.

[0076] In Figure 14, the solid line 142 shows an example of the temperature history of a test conducted under conditions in which cyclic entropy heat is applied. The temperature history shown in Figure 14 is an example in which the battery is repeatedly charged and discharged from time 0 to generate heat, and then power is stopped at time 600 and cooled to a steady state. Also in Figure 14, the dashed line 141 shows an ideal temperature curve under step heat generation conditions in which a constant amount of heat is generated.

[0077] As shown in Figure 14, the solid line 142, to which the cyclic heat of entropy is added, represents a temperature history with fine fluctuations caused by fluctuations in the amount of heat generated by the battery. With temperature history data from heating from time 0 to 600, where the amount of heat generated fluctuates finely, it is difficult to determine the circuit constants of the thermal circuit model using a method similar to the temperature prediction method of the first embodiment. For this reason, in the example of Figure 14, the temperature history from cooling after time 600 is used to analyze the circuit constants of the thermal circuit model.

[0078] In the example of the temperature history shown in Fig. 14, the temperature change indicated by the solid line 142 due to repeated charging and discharging approaches a periodic state fluctuating above and below 0.5 K / W as the time approaches 600 seconds. In other words, the battery temperature response data of the battery cell under the step heat generation condition is considered to have reached a quasi-steady state close to the temperature saturation indicated by the dashed line 141 in Fig. 14 at 600 seconds.

[0079] Therefore, when determining the circuit constants of the thermal circuit model, the battery cell temperature response data under the step heat generation condition is acquired from the time when the quasi-steady state is reached, i.e., from 600 seconds onwards. Acquisition of this temperature history data from 600 seconds onwards corresponds to step S10 in the flowchart shown in Figure 7 above.

[0080] The acquired temperature history data from 600 seconds onward is then processed to enable normalization of the temperature response curve and differentiation in logarithmic time. First, the origin of the temperature history data from time 0 to 600 is shifted to the 600-second position. That is, the temperature response curve shown in FIG. 14 is translated in the x-axis direction so that time 600 corresponds to time 0. Next, the temperature scale in the y-axis direction is inverted up and down around 0.25 K / W. This creates a temperature response curve profile similar to graph 31 shown in FIG. 3 from the temperature response curve shown in FIG. 14. This operation allows for the acquisition of a temperature history similar to that obtained when heating with a constant calorific value. The circuit constants of the thermal circuit model can then be determined using a method similar to that of the temperature prediction method of the first embodiment described above, i.e., steps S10 to S15 of the flowchart shown in FIG. 7.

[0081] As described above, even when it is difficult to generate a certain amount of heat in the secondary battery, by determining the circuit constants of the thermal circuit model according to this embodiment, it is possible to measure the temperature history during cooling from a quasi-steady state and determine the thermal circuit constants. Therefore, it is possible to predict the temperature of the secondary battery using the acquired battery cell temperature response data, as in the first and second embodiments.

[0082] In the above-described embodiments, the temperature of a secondary battery is predicted using a two-stage RC thermal circuit, but this can also be applied to a configuration with three or more stages of battery modules. For example, by setting n in the above-described formula (1) to 3 or more, a thermal circuit model and its circuit constants can be obtained by applying the method described in the above overview and in each embodiment. Then, using this thermal circuit model and circuit constants, it is possible to predict the temperature of a secondary battery having a battery module equipped with a large number of battery cells.

[0083] Furthermore, the present invention is not limited to the above-described embodiments, and various modifications are possible. For example, the above-described embodiments have been described in detail to clearly explain the present invention, and the present invention is not necessarily limited to embodiments including all of the described configurations. Furthermore, it is possible to replace part of the configuration of one embodiment with the configuration of another embodiment. It is also possible to add the configuration of another embodiment to the configuration of one embodiment. It is also possible to delete part of the configuration of each embodiment, or to add or replace other configurations. [Explanation of symbols]

[0084] 1 Temperature prediction device, 11 First battery cell, 12 Second battery cell, 20 Module, 31, 32, 33, 91, 92 Graph, 50 Memory unit, 60 Communication unit, 70 Bus, 100 Control unit, 101 CPU, 102 ROM, 103 RAM, 110 Joule heat generation calculation unit, 120 Entropy heat generation calculation unit, 130 Chiller model, 140 Output unit, 141 Dashed line, 142 Solid line, 150 Thermal calculation unit, 151 Cauer type multi-stage thermal circuit model generation unit, 152 Foster type multi-stage thermal circuit model generation unit, 153 Temperature response waveform acquisition unit, 154 Circuit constant calculation unit, 155 Equivalent circuit conversion unit, 156 Temperature estimation unit, 600 Time, C1, c1, C2, c2, c11, c12 Heat capacity, f11, f12 Structure function, R1, r1, R2, r2, R11, r11, R12, r12, R20 Thermal resistance, Tm1, Tm11, Tm12 Terminal

Claims

1. A method for predicting a temperature of a secondary battery, comprising: Using a thermal circuit model including a Foster-type thermal circuit obtained by converting a two or more stage Cauer-type thermal circuit into an equivalent circuit, the circuit constants of the Foster-type thermal circuit are obtained; converting the circuit constants of the Foster-type thermal circuit into an equivalent circuit to construct a Cauer-type thermal circuit; The temperature of the secondary battery is predicted using the constructed Cauer-type thermal circuit. A method for predicting the temperature of a secondary battery.

2. In obtaining the circuit constants of the Foster-type thermal circuit, A temperature response curve of the secondary battery measured under step heating conditions is obtained; Differentiating the normalized temperature response curve with respect to logarithmic time; The structure function f is obtained by deconvolution from the differentiated equation. The circuit constants are obtained from the peak of the structure function f. The method for predicting the temperature of a secondary battery according to claim 1 .

3. In obtaining the circuit constants from the peak of the structure function f, The thermal resistance r in the multi-stage RC thermal circuit is calculated from the peak of the structure function f. １ , thermal resistance r ２ , time constant τ １ , and the time constant τ ２ Determine The thermal resistance r １ , the thermal resistance r ２ , the time constant τ １ , and the time constant τ ２ From the above, the heat capacity c １、 heat capacity c ２ Calculate The thermal resistance r １ , the time constant τ １ , the heat capacity c １ an RC thermal circuit having the thermal resistance r ２ , the time constant τ ２ , the heat capacity c ２ and an RC thermal circuit having the same are connected in series to construct a Foster type thermal circuit. The method for predicting the temperature of a secondary battery according to claim 2 .

4. In predicting the temperature of the secondary battery using the constructed Cauer-type thermal circuit, Calculate the amount of Joule heat generated from the battery's internal resistance and current, Calculate the entropy heat generation amount from the current, temperature, and entropy heat generation coefficient, Calculating the temperature and flow rate of a refrigerant supplied from a chiller to the secondary battery; The temperature of the secondary battery is calculated from the Cauer-type thermal circuit, the Joule heat generation amount, the entropy heat generation amount, and the temperature and flow rate of the coolant. The method for predicting the temperature of a secondary battery according to claim 1 .

5. In obtaining a temperature response curve of the secondary battery measured under step heating conditions, Obtain the temperature history after the time when the temperature of the secondary battery reaches a quasi-steady state under step heat generation conditions. The method for predicting the temperature of a secondary battery according to claim 2 .

6. A method for predicting the temperature of a secondary battery using a pre-constructed two or more stage thermal circuit model, As the thermal circuit model, the circuit constants of the Foster type thermal circuit are obtained from a Foster type thermal circuit obtained by converting a two or more stage Cauer type thermal circuit into an equivalent circuit, and a Cauer type thermal circuit constructed by converting the circuit constants of the Foster type thermal circuit into an equivalent circuit is used. A method for predicting the temperature of a secondary battery.

7. a control unit that calculates a battery temperature estimated from a thermal circuit model of the secondary battery; the control unit has a thermal calculation unit that estimates a temperature of the secondary battery using a multi-stage thermal circuit model of a Cauer type thermal circuit, The thermal calculation part is a Foster-type multistage thermal circuit model generation unit that generates a Foster-type thermal circuit from the Cauer-type thermal circuit of the secondary battery; a circuit constant calculation unit that determines a circuit constant of the Foster-type thermal circuit based on a temperature response waveform under step heat generation conditions of the secondary battery; an equivalent circuit conversion unit that converts the circuit constants of the Foster-type thermal circuit into the circuit constants of the Cauer-type thermal circuit; a temperature estimation unit that estimates the temperature of the secondary battery using a multi-stage thermal circuit model of the Cauer-type thermal circuit. Temperature prediction device for secondary batteries.

8. The control unit includes a Joule heat generation calculation unit that calculates the amount of Joule heat generation from the internal resistance and the current; an entropy heat generation calculation unit that calculates the amount of entropy heat generation from the current, temperature, and entropy heat generation coefficient; a chiller model that calculates the temperature and flow rate of the coolant supplied from the chiller to the battery; The thermal calculation unit predicts the temperature of the secondary battery using the Joule heat generation calculation unit, the entropy heat generation calculation unit, the chiller model, and the multi-stage thermal circuit model of the Cauer-type thermal circuit. The temperature prediction device for a secondary battery according to claim 7 .

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