JP7413741B2 - Storage battery data storage device, computer program and storage battery data storage method - Google Patents

Description

The present invention relates to a storage battery data storage device, a computer program, and a storage battery data storage method.

Automotive storage batteries and industrial storage batteries as emergency or critical power sources are widely used. In particular, in recent years, vehicles such as HEV (Hybrid Electric Vehicle) and EV (Electric Vehicle) have become popular. A storage battery mounted on a vehicle is repeatedly charged and discharged as the vehicle travels, and it is known that storage batteries deteriorate as a result of repeated charging and discharging.

It is difficult to diagnose the deterioration of storage batteries based on rules because the form and progression of deterioration vary depending on the usage history. Patent Document 1 discloses a system that diagnoses an internal state by using charging/discharging history as learning data.

Patent No. 4075925

However, in order to accurately diagnose internal conditions and the like using charge/discharge history data, a large amount of time-series data of the current flowing through the storage battery and time-series data of the terminal voltage of the storage battery are required. Therefore, in order to continuously and accurately estimate the state of the storage battery, it is necessary to secure resources such as a large-capacity storage device.

The present invention has been made in view of the above circumstances, and provides a storage battery data storage device, a computer program, and a storage battery data storage method that can reduce the amount of data stored to estimate the state of a storage battery. The purpose is to

The storage battery data storage device includes an acquisition unit that acquires time-series data of each of a first electric value and a second electric value of the storage battery, and a storage battery data storage device that acquires time-series data of each of a first electric value and a second electric value of the storage battery. a calculation unit that calculates a plurality of parameters that can estimate the time series data of the second electrical value in the estimation period when given the time series data of the first electrical value; and the time series data of the first electrical value and the and a storage section that stores the plurality of parameters calculated by the calculation section.

The computer program causes the computer to acquire time series data of the first electric value and the second electric value of the storage battery, and to calculate the first electric value based on the acquired first electric value and second electric value. A process of calculating a plurality of parameters that can estimate the time series data of the second electric value in the estimation period when time series data is given, and a process of calculating the time series data of the first electric value and the plurality of calculated parameters. The process of storing data in the storage unit is executed.

The storage battery data accumulation method includes acquiring time series data of each of a first electric value and a second electric value of the storage battery, and calculating the time series data of the first electric value based on the acquired first electric value and second electric value. When data is given, calculate a plurality of parameters that can estimate the time series data of the second electric value in the estimation period, and store the time series data of the first electric value and the calculated plural parameters in a storage unit. Remember.

The acquisition unit acquires time series data of each of the first electric value and the second electric value of the storage battery. The first electrical value and the second electrical value are data necessary for estimating the state of the storage battery, and can be, for example, one or the other of voltage and current during charging and discharging of the storage battery.

The calculation unit calculates a plurality of parameters. The plurality of parameters can be calculated based on the time series data of the first electric value and the second electric value, and by using the time series data of the first electric value, the original second electric value in the estimation period can be calculated. It can be a parameter that can reproduce time series data of values. Here, reproduction does not only mean exactly the same, but also means that even if a certain amount of error exists, it is sufficient that the error is within an allowable range.

The storage unit stores time-series data of the first electrical value and a plurality of calculated parameters. As a result, compared to the case where time-series data of the first electric value and second electric value of the storage battery are stored, it is only necessary to store a plurality of parameters instead of the time-series data of the second electric value. The amount of data required to estimate the state can be reduced.

The storage battery data storage device may include a discard unit that discards the time series data of the second electric value.

The discarding unit may discard the time series data of the second electrical value. The time-series data of the second electrical values can be reproduced using the time-series data of the first electrical values and the calculated parameters, so there is no need to store it. By discarding it, there is no need to reserve unnecessary storage capacity.

In the storage battery data storage device, the number of the plurality of parameters may be smaller than the number of samples of the time series data in the estimation period of the time series data of the second electric value.

The number of the plurality of parameters may be smaller than the number of samples of the time series data in the estimation period of the time series data of the second electrical value. For example, if the estimation period is 10 minutes and the sampling period of time-series data is 1 second, the number of samples of time-series data within the estimation period is 600. Assume that the number of parameters is, for example, 5 (<600), and the data size of each time series data and parameter is 4 bytes. Storing all the time-series data within the estimation period requires 2400 bytes, whereas storing parameters only requires 20 bytes. In this way, the amount of accumulated data required to estimate the state of the storage battery can be reduced.

In the storage battery data storage device, the first electric value may be a current when the storage battery is discharged, and the second electric value may be a voltage when the storage battery is discharged.

When the storage battery is discharging, the first electrical value may be a current, and the second electrical value may be a voltage. That is, when the storage battery is discharging, time-series data of the voltage (terminal voltage) of the storage battery during discharging can be estimated by using time-series data of current values and a plurality of parameters.

In the storage battery data storage device, the first electrical value may be a voltage when charging the storage battery, and the second electrical value may be a current when charging the storage battery.

When the storage battery is being charged, the first electrical value may be a voltage, and the second electrical value may be a current. That is, when the storage battery is being charged, time-series data of the current (charging current) of the storage battery during charging can be estimated by using time-series data of voltage values and a plurality of parameters.

In the storage battery data storage device, the calculation unit may calculate parameters of an equivalent circuit of the storage battery as the plurality of parameters.

The calculation unit may calculate parameters of an equivalent circuit of the storage battery as the plurality of parameters. An equivalent circuit (also referred to as an equivalent circuit model) is an equivalent circuit that represents the terminal voltage of a storage battery. For example, as shown in FIG. Resistance R0, which corresponds to physical resistance, etc. and is connected in series to the voltage source; resistance R1, R2, which corresponds to interfacial charge transfer resistance and diffusion impedance, etc., and electric double layer capacitance, which is connected in parallel to each of resistors R1 and R2. It is composed of a combination of capacitors C1, C2, etc.

To calculate the parameters of the equivalent circuit, for example, when the storage battery is discharging, the equivalent current is This can be done by repeatedly adjusting the parameters so that the error between the calculated voltage value and the time series data (calculated voltage waveform) calculated by the parameters of the equivalent circuit when the current flows is minimized. Similarly, when the storage battery is charging, the time series data (actual current waveform) of the actual measured current value when the voltage represented by the time series data is applied, and when the equivalent voltage is applied This can be done by repeatedly adjusting the parameters so that the error between the calculated current value and the time series data (calculated current waveform) calculated by the parameters of the equivalent circuit of is minimized.

The storage battery data storage device may include a determination unit that determines the state of the storage battery based on the parameters of the equivalent circuit calculated by the calculation unit.

The determination unit may determine the state of the storage battery based on the parameters of the equivalent circuit calculated by the calculation unit. For example, the degree of deterioration may be determined based on the magnitude of the internal resistance (the magnitude of the difference from the initial value).

In the storage battery data storage device, the acquisition unit may acquire time-series data of an on-vehicle storage battery.

The acquisition unit may acquire time-series data of an on-vehicle storage battery. For example, even if connected cars become popular and the amount of data acquired from in-vehicle storage batteries increases explosively, it is possible to reduce the amount of data required to estimate the state of the storage battery.

According to the present invention, it is possible to reduce the amount of accumulated data necessary for estimating the state of a storage battery.

FIG. 1 is a diagram showing the concept of a storage battery data storage system according to the present embodiment. It is a diagram showing the configuration of a server. It is a diagram showing an example of an equivalent circuit of a storage battery. It is a figure showing an example of a current waveform of a storage battery. FIG. 3 is a diagram showing an example of a voltage waveform of a storage battery. It is a figure which shows the process of the server at the time of discharge of a storage battery. It is a figure which shows the process of the server at the time of charging a storage battery. It is a diagram showing the configuration of a storage battery DB. It is a figure which shows the example of state determination of a storage battery. 3 is a flowchart illustrating an example of a server processing procedure.

Embodiments of the present invention will be described below based on the drawings. FIG. 1 is a diagram showing the concept of a storage battery data storage system according to this embodiment. The storage battery data storage system includes a server 50 as a storage battery data storage device. The server 50 is connected to the roadside device 20 via the communication network 1. A storage battery 11 and a communication device 12 are mounted on the vehicle 10 (for example, a connected car). The storage battery 11 may be a lead acid battery, a lithium ion battery, or another secondary battery. The communication device 12 includes a storage unit (not shown) that temporarily stores time-series data obtained by measuring the voltage, current, temperature, etc. of the storage battery 11 at a predetermined sampling period, and a storage unit (not shown) that stores the time-series data stored in the storage unit. A communication unit (not shown) is provided for transmitting the information to the outside. The time-series data includes measured values such as voltage, current, and temperature, as well as the time at which they were measured.

Specifically, the communication device 12 uses, for example, a mobile phone network (for example, LTE [Long Term Evolution], 4G, 3G, etc.) or a wireless LAN (for example, WiFi, etc.), Time series data can be transmitted to the server 50 together with the storage battery ID. Furthermore, the communication device 12 can transmit time-series data together with the storage battery ID to the roadside device 20 using ITS (Intelligent Transport System) wireless. The roadside device 20 can transmit the received storage battery ID and time series data to the server 50. Note that although one vehicle 10 is shown in FIG. 1, there may be a large number of vehicles 10. In this way, the server 50 can acquire (receive) a large amount of time-series data on the storage batteries 11 from a large number of vehicles 10.

FIG. 2 is a diagram showing the configuration of the server 50. The server 50 includes a control section 51 that controls the entire server, a communication section 52, a storage section 53, a parameter calculation section 54, a determination section 55, and a storage battery DB 56. The storage battery DB 56 may be incorporated into a data server separate from the server 50. The control unit 51 can be configured with a CPU, ROM, RAM, etc.

The communication unit 52 has a communication function between the vehicle 10 and the roadside device 20. The communication unit 52 can acquire the storage battery ID and time series data of the storage battery 11 mounted on the vehicle 10 directly from the vehicle 10 or via the roadside device 20. The time series data includes time series data of the voltage, current, and temperature of the storage battery 11. Further, the time series data may include physical quantities (eg, SOC, SOH, etc.) that can be calculated based on voltage, current, temperature, and the like. The communication unit 52 can acquire time-series data of each of the first electric value and the second electric value of the storage battery 11. Here, the first electrical value and the second electrical value are data necessary for estimating the state of the storage battery 11, and can be, for example, one and the other of the voltage and current during charging and discharging of the storage battery 11. . The time series data acquired via the communication unit 52 may be stored in the storage unit 53.

The storage unit 53 can be configured with a flash memory, a hard disk, or the like.

The parameter calculation unit 54 can calculate a plurality of parameters. The plurality of parameters are parameters that can be calculated based on the time-series data of the first electric value and the second electric value, and by using the time-series data of the first electric value within the required estimation period, The parameter can be used to reproduce the time-series data of the original second electric value during the estimation period. Here, reproduction does not only mean exactly the same, but also means that even if a certain amount of error exists, it is sufficient that the error is within an allowable range.

The control unit 51 calculates the time-series data of the first electric value and the plurality of parameters calculated by the parameter calculation unit 54 from among the time-series data of the first electric value and the second electric value acquired via the communication unit 52. It can be stored in the storage battery DB 56. That is, the control unit 51 does not need to store time-series data of the second electrical value that can be estimated based on the time-series data of the first electrical value and the plurality of calculated parameters. The control unit 51 may discard the time series data of the second electric value. The time-series data of the second electrical values can be reproduced using the time-series data of the first electrical values and the calculated parameters, so there is no need to store it.

As a result, compared to the case where time-series data of each of the first electric value and the second electric value of the storage battery is stored, it is only necessary to store a plurality of parameters instead of the time-series data of the second electric value. The amount of data required to estimate the state of the data can be reduced. Further, by discarding the time-series data of the second electrical values, there is no need to secure unnecessary storage capacity.

In particular, even if connected cars become widespread and the amount of data acquired from the in-vehicle storage battery 11 increases explosively, the amount of data required to estimate the state of the storage battery 11 can be reduced.

The parameter calculation unit 54 may calculate parameters of an equivalent circuit of the storage battery 11.

FIG. 3 is a diagram showing an example of an equivalent circuit of the storage battery 11. The equivalent circuit (also referred to as an equivalent circuit model) is an equivalent circuit that represents the impedance of the storage battery 11. For example, as shown in FIG. and a capacitor (in FIG. 3, a parallel circuit of resistor R1 and capacitor C1, and a parallel circuit of resistor R2 and capacitor C2) are connected in series. Note that the number of parallel circuits of resistors and capacitors may be one instead of two, or may be three or more.

More specifically, the resistance R0 represents, for example, the electrical resistance of the alloy member, the resistances R1 and R2 represent, for example, the interfacial charge transfer resistance and the diffusion impedance, and the capacitors C1 and C2 represent, for example, the electrical resistance of the alloy member. Represents layer capacitance. The resistance R0 corresponds to the internal resistance of the storage battery 11, and its value tends to increase as the storage battery 11 deteriorates. The parallel circuit of a resistor and a capacitor is a parameter expressing a transient phenomenon inside the storage battery 11.

FIG. 4 is a diagram showing an example of a current waveform of the storage battery 11. In the figure, the vertical axis represents current, and the horizontal axis represents time. FIG. 5 is a diagram showing an example of the voltage waveform of the storage battery 11. In the figure, the vertical axis shows voltage and the horizontal axis shows time. The time series data of current values and voltage values is time series data of numerical values obtained by measuring the current waveform and voltage waveform as shown in the figure at a predetermined sampling period (for example, 1 second, etc.). 4 and 5 may be, for example, charging/discharging patterns when the vehicle 10 is traveling at a relatively constant speed without sudden acceleration or sudden deceleration. Conversely, the current waveform and voltage waveform change depending on the driving state of the vehicle 10 (acceleration, deceleration, idling, high-speed driving, etc.).

For example, when the storage battery 11 is discharging, the parameters of the equivalent circuit are calculated by calculating the equivalent current with respect to the time series data (actually measured voltage waveform) of the actually measured voltage value when the current represented by the time series data flows. This can be done by repeatedly adjusting the parameters so that the error between the calculated voltage value and the time series data (calculated voltage waveform) calculated by the parameters of the equivalent circuit when the voltage is flowing is minimized. Similarly, when the storage battery 11 is being charged, an equivalent voltage is applied to the time series data (actually measured current waveform) of the measured current value when the voltage represented by the time series data is applied. This can be done by repeatedly adjusting the parameters so that the error between the calculated current value and the time series data (calculated current waveform) calculated using the parameters of the current equivalent circuit is minimized.

The equivalent circuit model to be set and the method for calculating parameters include, for example, a method of fitting an equivalent circuit model that takes into account positive and negative electrode potentials and polarization resistance so that the residual difference between the actual measured value and the calculated value is minimized, A known method such as a fitting method using the Gauss-Newton method or the Levenberg-Marquardt method may be used for a higher-order exponential function model.

FIG. 6 is a diagram showing the processing of the server 50 when the storage battery 11 is discharged. The periods T and T+1 are estimated periods, and may be, for example, 10 minutes, but may be adjusted as appropriate depending on the state of charging and discharging and the state of the storage battery 11. For example, if the current or voltage of the storage battery 11 fluctuates largely, the estimation period may be shortened, and if the current or voltage of the storage battery 11 fluctuates little, the estimation period may be lengthened. Furthermore, the estimation period may be shortened as the degree of deterioration of the storage battery 11 progresses. As shown in FIG. 6, during the estimation period T, the acquired time-series data is assumed to be voltages V1, V2, ..., Vn and currents I1, I2, ..., In. Let Ve, R0, R1, C1, R2, and C2 be parameters calculated from time-series data of voltage values and current values within the estimation period T. These parameters are those illustrated in FIG.

When the estimation period T is a discharge time, the server 50 may store the currents I1, I2, ..., In and the calculated parameters Ve, R0, R1, C1, R2, C2 within the estimation period T in the storage battery DB 56. can. Further, the server 50 may discard the voltages V1, V2, . . . , Vn.

As described above, when the storage battery 11 is discharging, the first electrical value to be stored may be a current, and the second electrical value that can be discarded may be a voltage. In other words, even if the time series data of voltage values is discarded, the time series data of the voltage (terminal voltage) of the storage battery 11 during discharge can be estimated (reproduced) by using the time series data of current values and a plurality of parameters. can do.

FIG. 7 is a diagram showing the processing of the server 50 when charging the storage battery 11. As shown in FIG. 7, during the estimation period T, the acquired time-series data is assumed to be voltages V1, V2, . . . , Vn and currents I1, I2, . Let Ve, R0, R1, C1, R2, and C2 be parameters calculated from time-series data of voltage values and current values within the estimation period T. These parameters are those illustrated in FIG.

When the estimation period T is charging, the server 50 may store the voltages V1, V2, ..., Vn and the calculated parameters Ve, R0, R1, C1, R2, C2 within the estimation period T in the storage battery DB 56. can. Further, the server 50 may discard the currents I1, I2, . . . , In.

As described above, when the storage battery 11 is being charged, the first electrical value to be stored may be a voltage, and the second electrical value that can be discarded may be a current. That is, even if the time series data of current values is discarded, by using the time series data of voltage values and a plurality of parameters, the time series data of the current of the storage battery 11 during charging can be estimated (reproduced). .

The number of parameters (6 in the examples of FIGS. 6 and 7) is the number of samples of time series data in the estimation period T of the time series data of the second electrical value (n in the examples of FIGS. 6 and 7) It may be less. For example, if the estimation period T is 10 minutes and the sampling period of time series data is 1 second, the number of samples of time series data within the estimation period is 600. Assume that the number of parameters is, for example, 6 (<600), and the data size of each time series data and parameter is 4 bytes. While 2400 bytes are required to store all the time series data within the estimation period, 24 bytes are required to store the parameters. In this way, the amount of accumulated data necessary for estimating the state of the storage battery 11 can be reduced.

FIG. 8 is a diagram showing the configuration of the storage battery DB 56. The storage battery DB 56 is composed of items such as period (estimated period), charging/discharging, and data to be accumulated, as shown in FIG. 8 for each storage battery 11. The estimable data does not represent data stored in the storage battery DB 56, but represents data that can be estimated (reproduced) from accumulated data as necessary. For example, when the period T1 is charging, the data to be accumulated can be time-series data of the voltage during the period T1 and equivalent circuit parameters. When the period T2 is a discharge, the data to be accumulated can be time-series data of the current during the period T2 and equivalent circuit parameters. The same applies to other periods. In this way, based on the data accumulated during periods T1, T2, ..., time-series data of current during charging and time-series data of voltage during discharge can be estimated as necessary without storing them. .

The time-series data recorded in the storage battery DB 56 and the estimated (reproduced) time-series data are used together with other time-series data (e.g., temperature) to estimate the state of the storage battery 11 (e.g., SOC, SOH, etc.). Can be used.

FIG. 9 is a diagram showing an example of determining the state of the storage battery 11. In the figure, the vertical axis shows the internal resistance of the storage battery 11, and the horizontal axis shows time. The determining unit 55 may determine the state of the storage battery 11 based on the parameters of the equivalent circuit calculated by the parameter calculating unit 54. For example, the degree of deterioration may be determined based on the magnitude of the internal resistance (the magnitude of the difference from the initial value). In the example of FIG. 9, if the difference between the calculated internal resistance value and the initial internal resistance value (internal resistance when the storage battery 11 is new) exceeds a threshold value, it can be determined that the storage battery 11 has deteriorated.

FIG. 10 is a flowchart showing an example of the processing procedure of the server 50. For convenience, the main body of processing will be described as the control unit 51 below. The control unit 51 acquires time-series data of the voltage and current of the storage battery 11 from the vehicle 10 (S11), and specifies the charging/discharging switching time point based on the acquired time-series data (S12).

For example, the control unit 51 determines whether the charging period or the discharging period is shorter than the length of the estimated period from the oldest to the newest date and time (S13). When the charging period or discharging period is short, there is no large difference between the number of samples of time-series data of voltage or current values and the number of parameters, and parameters are used instead of time-series data of voltage or current values. This is because even if the information is stored, it may not be possible to reduce the storage capacity.

If the charging period or discharging period is shorter than the length of the estimation period (YES in S13), the control unit 51 stores time-series data of voltage and current within the charging period or discharging period in the storage battery DB 56 (S14), The processing from step S13 onwards is continued. When the charging period or the discharging period is not shorter than the length of the estimated period (NO in S13), the control unit 51 determines whether the period (estimated period) is a charging period (S15).

If the period is a charging period (YES in S15), the control unit 51 calculates equivalent circuit parameters based on the time series data of voltage and current within the charging period (S16), The time series data and the calculated equivalent circuit parameters are stored in the storage battery DB 56, the time series data of the current within the charging period is discarded (S17), and the process of step S18 described later is performed.

If the period is not a charging period (NO in S15), the control unit 51 determines whether the period (estimated period) is a discharging period (S18). If the period is a discharge period (YES at S18), the control unit 51 calculates equivalent circuit parameters based on the time series data of voltage and current within the discharge period (S19), and calculates the current during the discharge period. The time series data and the calculated equivalent circuit parameters are stored in the storage battery DB 56, the time series data of the voltage within the discharge period is discarded (S20), and the process of step S21 described later is performed.

If the period is not a discharge period (NO in S18), the control unit 51 determines whether there is another estimation period (an estimation period with a newer date and time) (S21), and if there is another estimation period (YES in S21). ), the processing from step S15 onwards is continued. If there is no other estimation period (NO in S21), the control unit 51 ends the process.

The server 50 can also be realized using a computer equipped with a CPU (processor), ROM, RAM, and the like. By loading a computer program (recordable on a recording medium) that defines the processing procedure shown in FIG. can be realized.

As described above, according to the present embodiment, the equivalent circuit parameters are calculated based on the time series data of voltage values and the time series data of current values necessary for estimating the state of the storage battery. By saving equivalent circuit parameters instead of time-series data or time-series data of current values, it is possible to estimate the state of the storage battery as needed by saving a smaller amount of data than before, and the storage resource It is possible to store the data necessary for highly accurate state estimation without being restricted by. Furthermore, since a larger number of samples of data can be stored in a resource with the same storage capacity, it is possible to estimate the storage battery with higher accuracy.

In addition, since the charging and discharging behavior of storage batteries can be stored with a smaller amount of data, it is possible to use machine learning (for example, neural networks) on large amounts of learning data. It is expected that this will enable more accurate state estimation.

In the above-described embodiment, a storage battery installed in a vehicle has been described, but the present embodiment can be applied not only to a storage battery installed in a vehicle but also to a stationary storage battery.

1 communication network 10 vehicle 11 storage battery 12 communication device 20 roadside device 50 server 51 control unit 52 communication unit 53 storage unit 54 parameter calculation unit 55 determination unit 56 storage battery DB

Claims (10)

an acquisition unit that acquires time series data of each of the first electric value and the second electric value of the storage battery;
Based on the first electric value and the second electric value acquired by the acquisition unit, time-series data of the second electric value in the estimation period can be estimated when the time-series data of the first electric value is given. a calculation unit that calculates multiple parameters;
A storage battery data storage device comprising: a storage unit that stores time-series data of the first electrical value and a plurality of parameters calculated by the calculation unit in place of the time-series data of the second electrical value. The storage battery data storage device according to claim 1, further comprising a discard unit that discards the time series data of the second electric value. 3. The storage battery data storage device according to claim 1, wherein the number of the plurality of parameters is smaller than the number of samples of the time series data of the second electrical value during the estimation period. The first electric value is a current when the storage battery is discharged,
The storage battery data storage device according to any one of claims 1 to 3, wherein the second electrical value is a voltage when the storage battery is discharged. The first electric value is a voltage when charging the storage battery,
The storage battery data storage device according to any one of claims 1 to 4, wherein the second electric value is a current when charging the storage battery. The calculation unit is
The storage battery data storage device according to any one of claims 1 to 5, wherein parameters of an equivalent circuit of the storage battery are calculated as the plurality of parameters. The storage battery data storage device according to claim 6, further comprising a determination unit that determines the state of the storage battery based on the parameters of the equivalent circuit calculated by the calculation unit. The acquisition unit includes:
The storage battery data storage device according to any one of claims 1 to 7, wherein the storage battery data storage device acquires time-series data of an on-vehicle storage battery. to the computer,
A process of acquiring time series data of each of the first electric value and the second electric value of the storage battery;
Based on the acquired first electrical value and second electrical value, a plurality of parameters that can estimate the time-series data of the second electrical value in the estimation period when the time-series data of the first electrical value is given. The calculation process and
A computer program that executes a process of storing a plurality of calculated parameters in a storage unit in place of the time series data of the first electrical value and the time series data of the second electrical value . Obtain time series data of each of the first electric value and the second electric value of the storage battery,
A plurality of parameters that can estimate time-series data of the second electrical value in an estimation period when time-series data of the first electrical value is given, based on the acquired first electrical value and second electrical value. Calculate,
A storage battery data storage method, wherein a plurality of calculated parameters are stored in a storage unit in place of the time-series data of the first electrical value and the time-series data of the second electrical value .

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