Method for determining the degree of degradation of a secondary battery, device for determining the degree of degradation of a secondary battery, and program

Abstract

To quickly determine the degradation of secondary batteries. [Solution] The system includes means for obtaining an approximation formula by approximating a voltage curve, which is either a charging curve or a discharge curve, or either a charging curve or a discharge curve, that shows the voltage v(t) across the secondary battery as a function of time t, measured during either charging or discharging of the secondary battery, or a current curve, which is either a charging curve or a discharge curve, or either a charging curve or a discharge curve, or either a charging curve or a discharge curve, or either a current I(t) across the secondary battery as a function of time t, measured during either charging or discharging of the secondary battery, and means for estimating the degree of degradation of the secondary battery from the approximation formula.

Description

[Technical Field]

[0001] This invention relates to a method for determining the degree of degradation of a secondary battery, a secondary battery degradation determination device, and a program for determining the degree of degradation of a secondary battery. [Background technology]

[0002] The rapid electrification of vehicles in recent years has led to an increase in demand for rechargeable batteries for vehicles. Along with this increase in demand for rechargeable batteries, the need for their reuse is also growing.

[0003] When a vehicle is scrapped, the secondary battery is removed from the vehicle and its degradation is assessed. If the assessment determines that the secondary battery is reusable, it is rebuilt and reused in the second-hand market.

[0004] One technique for determining the degradation of secondary batteries involves estimating the degree of battery degradation from the voltage values ​​or the nth derivative values ​​of either the charging voltage when a constant current is passed through the secondary battery, or the discharge voltage when the power supply is disconnected from the secondary battery, or both (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Patent No. 7528148 [Overview of the project] [Problems that the invention aims to solve]

[0006] However, when using the technology disclosed in Patent Document 1, there is a problem in that it takes a considerable amount of time to determine the optimal explanatory variables for multivariate analysis.

[0007] This invention has been made in view of the circumstances described above. The object of this invention is to provide a secondary battery degradation degree determination method, a secondary battery degradation degree determination device, and a program that can determine the degradation of a secondary battery in a short amount of time. [Means for solving the problem]

[0008] To achieve the above-mentioned objective, the secondary battery degradation determination method of this invention comprises an approximation formula acquisition step of obtaining an approximation formula by approximating a voltage curve which is either a charging curve or a discharge curve, or both, that shows the voltage v(t) across the terminals of the secondary battery with respect to time t, and the voltage curve which is either a charging curve or a discharge curve, and an approximation formula of obtaining an approximation formula, and a degradation degree estimation step of estimating the degradation degree of the secondary battery from the approximation formula.

[0009] Furthermore, the secondary battery degradation determination device of this invention comprises an approximation formula acquisition means for obtaining an approximation formula by approximating a charging curve or discharge curve that shows the voltage v(t) across the terminals of the secondary battery as a function of time t, and a degradation degree estimation means for estimating the degradation degree of the secondary battery from the approximation formula.

[0010] Furthermore, the program of this invention causes a computer to function as an approximation formula acquisition means, which approximates a charging curve or discharge curve showing the voltage v(t) across the terminals of a secondary battery as a function of time t, and obtains an approximation formula, and as a degradation degree estimation means, which estimates the degree of degradation of the secondary battery from the approximation formula. [Effects of the Invention]

[0011] According to the secondary battery degradation determination method, secondary battery degradation determination device, and program of this invention, the degradation of a secondary battery can be determined in a short time. [Brief explanation of the drawing]

[0012] [Figure 1] This is a schematic diagram illustrating a secondary battery degradation level determination system. [Figure 2] This is a schematic diagram to explain electrical discharge. [Figure 3] Figure (1) shows the relationship between the measured Q value and the estimated Q value. [Figure 4] It is a diagram (2) showing the relationship between the measured Q value and the estimated Q value. [Figure 5] It is a diagram showing the test results of the selected explanatory variables. [Figure 6] It shows a histogram of the error obtained by subtracting the estimated Q value from the measured Q value. [Figure 7] It is a diagram showing the verification results of the model. [Figure 8] It is a diagram showing an example of a voltage curve when a popularization machine is used. [Figure 9] It is a diagram showing another example of a voltage curve when a popularization machine is used. [Figure 10] It is the measured voltage curve (1). [Figure 11] It is the measured voltage curve (2). [Figure 12] It is a diagram showing the difference between the measured voltage curve and the approximate formula. [Figure 13] It is a schematic diagram showing the relationship between the charging curve of the measured voltage curve and the approximate curve obtained by approximating this charging thymus. [Figure 14] It is a schematic diagram for explaining the correction step. [Figure 15] It is a schematic diagram for explaining another example of the secondary battery degradation degree determination system. [Figure 16] It is a schematic diagram for explaining the parallel measurement of a plurality of secondary batteries. [Figure 17] It is the calculation result of the noise of each secondary battery. [Figure 18] It is 3σ calculated from the noise waveform of each secondary battery. [Figure 19] It shows a histogram of the error of the secondary battery. [Figure 20] It shows 3σ of the histogram of the error of the secondary battery.

Embodiments for Carrying Out the Invention

[0013] The embodiments of this invention will be described below with reference to the figures, but the shapes, sizes, and arrangements of each component are only shown in a general manner to the extent that the invention can be understood. Furthermore, preferred configuration examples of this invention will be described below, but the numerical conditions and other details are merely examples. Therefore, this invention is not limited to the following embodiments, and many changes or modifications can be made to achieve the effects of this invention without departing from the scope of the configuration of this invention.

[0014] This section primarily describes the process of determining the degree of degradation of secondary batteries used in electric vehicles or hybrid vehicles. However, this invention is not limited to secondary batteries for vehicles and can be applied to determining the degree of degradation of various types of reusable secondary batteries.

[0015] Traditionally, when a vehicle is scrapped, the secondary battery is removed and sent to a remanufacturing company. At the remanufacturing company, the battery's degradation level is assessed. If the assessment determines that the battery is reusable, it is remanufactured and used in the used vehicle market. A secondary battery degradation assessment system is used, for example, in such a remanufacturing company.

[0016] The degree of degradation of a rechargeable battery is usually expressed as the ratio Q1 / Q0 × 100 (%) of the full charge capacity Q0 (Ah) of a new rechargeable battery to the full charge capacity Q1 (Ah) of a used rechargeable battery, or as the full charge capacity Q1 (Ah) of the used battery. Here, the full charge capacity Q0 (Ah) of a new rechargeable battery and the full charge capacity Q1 (Ah) of a used rechargeable battery may also be simply expressed as the full charge capacity Q (Ah).

[0017] Here, the full charge capacity Q (Ah) is given by Q = It (Ah) when the battery is fully charged, discharged with a constant current I (A), and the time t (h) until it is completely discharged is measured. This measurement method is called precision measurement.

[0018] Precise measurements allow for the accurate determination of the full charge capacity Q(Ah). However, precise measurements have the drawback of being time-consuming. Two methods exist for estimating the full charge capacity Q(Ah) in a short time: one using alternating current (AC) and the other using direct current (DC).

[0019] The method using alternating current is called electrochemical impedance spectroscopy (EIS) and has been used for a long time. However, EIS has not been able to achieve good accuracy after accuracy verification, due to reasons such as the time-dependent changes in battery parameters and the fact that the effects of stray impedance in the transmission line, which is unique to alternating current, cannot be ignored.

[0020] Therefore, this invention employs a method that uses direct current.

[0021] The secondary battery degradation determination system will be explained with reference to Figure 1. Figure 1 is a schematic diagram illustrating the secondary battery degradation determination system.

[0022] The secondary battery degradation determination system 10 includes a voltage curve acquisition device 100 and a secondary battery degradation determination device 200.

[0023] The voltage curve acquisition device 100 acquires a measured voltage curve showing the measured voltage v(t) across the secondary battery 300 with respect to time t. The voltage curve acquisition device 100 includes, for example, a constant current power supply 110, a switch 120, and a voltage sensor 130.

[0024] The constant current power supply 110 is a power source that supplies a constant current to the secondary battery 300 to be evaluated. The current supplied from the constant current power supply 110 is sent to the secondary battery 130 via the switch 120.

[0025] Switch 120 is provided to enable switching between charging and discharging the secondary battery 300. When charging the secondary battery 300, switch 120 is switched to the ON state, electrically connecting the constant current power supply 110 and the secondary battery 300 to supply a constant current to the secondary battery 300. On the other hand, when discharging the secondary battery 300, switch 120 is switched to the OFF state, disconnecting the constant current power supply 110 and the secondary battery 300, thereby cutting off the current to the secondary battery 300. Voltage sensor 130 measures the voltage across the terminals of the secondary battery 300.

[0026] Furthermore, it is not necessary to use expensive constant current power supply 110 and voltage sensor 130 in this invention. Expensive voltage sensors (high-end models) have high resolution, and when using high-end models, the resolution of the measured voltage can be kept to around several tens (nV). In contrast, the present invention can use inexpensive voltage sensors (common models) with low resolution, for example, a resolution of about 10 (mV) to 30 (mV).

[0027] Furthermore, the voltage sensor 130 acquires the measured voltage at each sampling interval Δt. The sampling interval Δt is, for example, 0.1 seconds.

[0028] In this invention, the degree of degradation is determined from the voltage curve obtained during charging (charging curve) or the voltage curve obtained during discharging (discharge curve), so it is not necessary to measure the time from full charge to complete discharge. It is sufficient to have measurement values ​​that are enough to obtain an approximate curve. For example, a charging time of 120 seconds and a discharge time of 60 seconds can be used. Note that both the charging curve and the discharge curve may be used as the voltage curve, or only one of the charging curve or the discharge curve may be used. A voltage curve that includes both charging and discharging is also called a charge-discharge curve.

[0029] The voltage curve obtained by the voltage curve acquisition device 100 is sent to the secondary battery degradation determination device 200.

[0030] The secondary battery degradation determination device 200 has an input unit 210, an output unit 220, a storage unit 230, and a control unit 240.

[0031] The input unit 210 consists of input devices such as keyboards and mice, and wired or wireless receiving devices from the internet, etc. The output unit 220 is a device that outputs information to the outside, and consists of display devices such as liquid crystal panels or display devices, printing devices such as printers, and wired or wireless transmitting devices to the internet, etc. The input unit 210 and the output unit 220 are collectively referred to as the input / output unit.

[0032] The memory unit 230 is a storage device such as RAM, ROM, hard disk drive, and non-volatile memory. For example, the control unit 240 reads and executes a program stored in ROM to perform a predetermined process. The result of this process is temporarily stored in RAM and finally stored in the hard disk drive, etc. Here, a hard disk drive is used as an example, but a solid-state drive (SSD), flash memory, CD, DVD, BD may be used instead of a hard disk drive, or a combination of these may be used. Alternatively, online storage connected via the internet may be used.

[0033] The control unit 240 controls the entire secondary battery degradation determination device 200. The control unit 240 reads and executes a program stored in the storage unit 230, such as a ROM, thereby realizing the various functional means described later.

[0034] This secondary battery degradation determination device 200, which comprises an input unit 210, an output unit 220, a storage unit 230, and a control unit 240, can be configured using any suitable electronic computer, such as a personal computer.

[0035] The voltage curve acquisition device 100 and the secondary battery degradation determination device 200 may or may not be directly connected. For example, the voltage curve acquired by the voltage curve acquisition device 100 may be sent to the secondary battery degradation determination device 200 via the internet or other means, or it may be stored on a recording medium such as a USB memory stick, CD, or DVD and read by the secondary battery degradation determination device 200.

[0036] The secondary battery degradation determination method performed by the secondary battery degradation determination device 200 has the following steps.

[0037] First, in the approximation formula acquisition step, the approximation formula acquisition means 242, which is provided in the secondary battery degradation degree determination device 200, approximates the charging curve or the discharging curve to acquire an approximation formula.

[0038] As an approximation formula, a higher-order polynomial, such as a quadratic polynomial, can be used. However, the approximation formula is not limited to higher-order polynomials; any suitable formula can be used.

[0039] Next, in the degradation degree estimation step, the degradation degree estimation means 244 of the secondary battery degradation degree determination device 200 estimates the degradation degree of the secondary battery from the approximate formula obtained in the approximate formula acquisition step.

[0040] The degree of degradation of secondary batteries can be estimated using methods such as machine learning or multiple regression analysis. Here, as an example, we will explain an example using multiple regression analysis with the coefficients of an approximation formula as explanatory variables. Furthermore, the measured charge-discharge curve is used as the voltage curve, and a fourth-degree polynomial is used as the approximation formula. Note that multivariate analysis may be used instead of machine learning.

[0041] In the voltage curve acquisition device 100, charging was performed with a constant current of 2.5(A) for 120 seconds, and the charging curve was obtained by measuring the voltage across the battery terminals during that time. In addition, in the voltage curve acquisition device 100, the battery terminals were opened, and natural discharge was performed for 62 seconds, and the discharge curve was obtained by measuring the voltage across the battery terminals during that time.

[0042] Furthermore, any of the three types of discharge methods—natural discharge, constant current discharge, and constant load discharge—can be used to obtain the discharge curve. Figure 2 is a schematic diagram illustrating the three types of discharge. Figure 2(A) shows natural discharge, Figure 2(B) shows constant current discharge, and Figure 2(C) shows constant load discharge. Note that the constant current power supply is not shown in Figures 2(A) to (C).

[0043] In the natural discharge shown in Figure 2(A), discharge occurs by stopping the supply of a constant current to the secondary battery 300. In the constant current discharge shown in Figure 2(B), discharge occurs by stopping the supply of a constant current to the secondary battery 300 and operating the switch 310 to allow a constant current to flow from the secondary battery 300 to the variable resistor 321. In the constant load discharge shown in Figure 2(C), discharge occurs by stopping the supply of a constant current to the secondary battery 300 and operating the switch 310 to allow a constant current to flow from the secondary battery 300 to the non-variable, so-called fixed resistor 322.

[0044] The acquired voltage curves, or charge-discharge curves, are divided into two regions each, creating a total of four regions. Each of these four regions is approximated by a fourth-degree polynomial. For the charge curve, there are two regions: from 5 seconds after the start of charging to 35 seconds after, and from 35 seconds after the start of charging to 120 seconds after (end of charging). Similarly, for the discharge curve, there are two regions: from 2 seconds after the start of discharging to 32 seconds after, and from 32 seconds after the start of discharging to 62 seconds after (end of discharging). The number of regions and other settings can be arbitrarily and suitably determined. Here, we will explain the case where three regions are used, excluding the region from 32 seconds after the start of discharging to 62 seconds after (end of discharging).

[0045] The approximate formulas for the three regions from 5 seconds after the start of charging to 35 seconds after, from 35 seconds after the start of charging to 120 seconds after (end of charging), and from 2 seconds after the start of discharging to 32 seconds after, are given by the following equations (1.1) to (1.3).

[0046]

number

[0047] Since there are 5 variables for each of the 3 domains, there are a total of 15 a i , b i , c i A multivariate analysis was performed with (i=0, 1, 2, 3, 4) as the explanatory variables and the measured value of the full charge capacity Q as the dependent variable.

[0048] Alternatively, when acquiring the voltage value at a specific time t, a small time interval Δs (usually 1 to 2 s) may be used to obtain a regression curve from measured values ​​in the time domain t-Δs≦t≦t+Δs which includes time t, and then the voltage value at time t may be obtained from this regression curve.

[0049] Furthermore, while a fourth-degree polynomial was used as the approximation here, the method is not limited to this. Therefore, a lower-degree polynomial, a higher-degree polynomial, or even a formula other than a polynomial may be used.

[0050] Alternatively, two or more approximation formulas can be used, for example, both a cubic polynomial and a quartic polynomial. In this case, for each domain, nine explanatory variables can be used: four variables for the cubic polynomial and five variables for the quartic polynomial. In this case as well, formulas other than polynomials can be used.

[0051] In this study, the total number of secondary batteries measured (hereinafter also referred to as the number of data points) N was 874. Of these, half, 437 data points, were used for modeling, and the remaining 437 data points were used for verification.

[0052] Figure 3 shows the results of a model in which the measured full charge capacity Q value (measured Q value; hereinafter sometimes simply referred to as Q) is plotted on the horizontal axis and the estimated full charge capacity Q value (estimated Q value; hereinafter sometimes simply referred to as Q') is plotted on the vertical axis. Figure 3 is a diagram showing the relationship between the measured Q value and the estimated Q value. In Figure 3, the measured Q value is shown on the horizontal axis and the estimated Q value is shown on the vertical axis.

[0053] As shown in Figure 3, the dispersion of the points is arc-shaped, which is not a good result. This is because the model has some nonlinearity. The curve obtained by regression of the data shown in Figure 2 using the equation A·lnQ+B, with the measured Q value as x and the estimated Q value as y, is shown as curve I in Figure 3.

[0054] Therefore, instead of using the measured Q value, we performed multivariate analysis with A·lnQ+B as the dependent variable, and from the estimated Q value (Q'), we obtained Q'=e (Q―B) / A This was done. The results of the modeling at this time are shown in Figure 4. Comparing Figure 4 with Figure 3, it can be seen that the nonlinearity has been eliminated to some extent.

[0055] Here, A·lnQ+B was used because its inverse function is easy to find, but generally, a regression curve represented by a single-valued function y=f(Q) for which an inverse function exists is also possible. However, the function y=f(Q) is a single-valued function for which only one y can be found for each Q. Let y=f(Q) be, for example, a monotonically increasing y=α0+α1·Q+α2·Q 2 +α3·Q 3 A cubic polynomial like this would also be acceptable.

[0056] After selecting explanatory variables such that the significance probability is within 0.05 and the VIF (Variance Inglation Factor) does not exceed 10, the prediction formula for Q is given by the following equation (2).

[0057]

number

[0058] The results of the test for the selected explanatory variables are shown in Figure 5. Here, VIF indicates the severity of multicollinearity, which is a situation in multiple regression analysis where two or more explanatory variables have a high degree of linear relationship. A VIF of 10 or higher indicates a problem of multicollinearity.

[0059] Figure 6 shows a histogram of the error obtained by subtracting the estimated Q value from the measured Q value. The distribution of the errors is approximately a normal distribution, indicating that the estimation was performed correctly.

[0060] The remaining 437 data points, which were not used in the modeling process, were used to validate the model using multiple regression analysis.

[0061] Figure 7 shows the results of the model validation. In Figure 7, the measured Q value is shown on the horizontal axis, and the estimated Q value using equation (2) above is shown on the vertical axis. When approximated as a straight line using the least squares method, the coefficient of determination R2 is 0.921, which is good.

[0062] In this invention's secondary battery degradation determination system, the voltage curve is approximated by a higher-order polynomial, and the coefficients of this higher-order polynomial are used directly as explanatory variables. Therefore, the process of selecting the optimal explanatory variables is unnecessary, and the required time is significantly shorter compared to the technology disclosed in Patent Document 1, which requires a long time due to the process of selecting explanatory variables.

[0063] Furthermore, since higher-order polynomials contain information corresponding to the absolute values ​​and infinite-order derivatives of all voltage values ​​in the time domain under consideration, there is no information loss. In contrast, as mentioned above, the technology disclosed in Patent Document 1 has limitations in the computation time of the explanatory variables, so there is no guarantee that the optimal explanatory variables are selected.

[0064] To obtain a voltage curve, using an expensive power supply and voltmeter (high-end equipment) can achieve a resolution of tens of nanometers (nV). However, the resolution of most commonly available equipment (common equipment) is only tens of millivolts (mV). High-end equipment can only be purchased by a limited number of businesses, and the vast majority of private rebuild companies that wish to measure battery degradation own common equipment.

[0065] There is a difference of about 1000 times or more in resolution between entry-level and high-end models. An example of a voltage curve when using an entry-level model is shown in Figure 8. Figure 8 shows the measured values ​​of the discharge curve of a certain secondary battery over time 10 ≤ t(s) ≤ 60, and an approximate curve using a cubic polynomial, using an entry-level model commonly used in the private sector.

[0066] In this example, the measured resolution of the discharge curve is approximately 1.25 mV. Although the graph appears stepped due to the low resolution, it can be seen that it is well approximated by the cubic polynomial.

[0067] Figure 9 shows another example of a voltage curve of a battery obtained using an on-board test of an automobile. In an on-board test of an automobile, information about the battery is obtained via terminals such as the OBD2 terminal without removing the secondary battery from the automobile. Figure 9 shows the measured value of the discharge curve of a certain secondary battery over time 10 ≤ t(s) ≤ 50, obtained by an on-board test of an automobile using the vehicle's power supply and voltmeter, and an approximate curve using a quartic polynomial.

[0068] In the example shown in Figure 9, the resolution of the measured values ​​of the discharge curve is approximately 25 mV. Although the graph appears stepped due to the low resolution, it can be seen that it is well approximated by the quartic polynomial.

[0069] In this secondary battery degradation determination system, the voltage curve is approximated by a higher-order polynomial, and the coefficients of this higher-order polynomial are used directly as explanatory variables. Therefore, even when using a general-purpose device with lower resolution compared to a high-end device, secondary battery degradation can be determined.

[0070] Figures 10 and 11 show the measured voltage curves. Figure 11 is an enlarged view of the area around 0(s) to 70(s) in Figure 10.

[0071] Figure 10 appears normal at first glance. However, looking at Figure 11, which is an enlarged view of a part of Figure 10, we can see that there are regions around t=11.2 seconds and t=50.2 seconds where the voltage remains constant for an unnaturally long time compared to other areas. This is thought to be because, when charging the secondary battery, if the voltage supplied from the constant current power supply 110 is fixed to the electrodes of the secondary battery 300 with clips, slight vibrations or an oxide film that forms between the electrode terminals and the clips cause the clips and electrodes to be in a non-contact state for a very short time during charging.

[0072] In fact, based on the inventors' experience with this invention, when a clip is used to connect a cable to the battery's electrodes, almost all charge and discharge data shows discontinuities of 2 to 3 points in the data.

[0073] When this non-contact state occurs, it becomes impossible to accurately estimate the degradation of the secondary battery.

[0074] Therefore, in this secondary battery degradation determination system, the secondary battery degradation determination device 200 can be configured to include a correction means 246. In this case, after obtaining an approximate formula, a correction step can be performed to detect and correct the non-contact state.

[0075] In this correction step, first, the correction means 246 of the secondary battery degradation determination device 200 takes the difference between the measured voltage curve and the approximation formula. Figure 12 shows this difference. Figure 12 shows that, in addition to the points around t=11.2 seconds and t=50.2 seconds shown in Figure 11, a non-contact state also occurred around t=99 seconds.

[0076] Figure 13 is a schematic diagram showing the relationship between the charging curve among the measured voltage curves and the approximate curve obtained by approximating this charging curve. In Figures 13(A) and (C), the charging curve is shown as a solid line and the approximate curve as a dotted line, while Figures 13(B) and (D) show the difference between the charging curve and the approximate curve. Furthermore, Figures 13(A) and (B) show the case where no contact occurs, and Figures 13(C) and (D) show the case where no contact occurs.

[0077] As shown in Figures 13(A) and (C), this measured voltage curve is flat during the sampling interval Δt. Furthermore, when the approximation formula closely approximates the voltage curve, the approximation curve intersects the flat region of the voltage curve, often near its center.

[0078] The approximate curve obtained by approximating the charging curve from the measured voltage curve is a monotonically increasing function. Therefore, as shown in Figure 13(B), the difference obtained by subtracting the approximation formula from the charging curve from the measured voltage curve takes a positive value at a certain sampling time ts, gradually decreases until the next sampling time ts+Δt, and becomes 0 around the midpoint of the next sampling time, i.e., around ts+Δt / 2. Then it continues to decrease until just before the next sampling time ts+Δt, and finally becomes a negative value. Furthermore, at the next sampling time ts+Δt, the value increases in a stepwise manner and becomes a positive value. In this way, the difference between the charging curve and the approximation formula takes a positive value at a certain sampling time, continues to decrease towards the next sampling time, and takes a negative value just before the next sampling time. This is repeated at the sampling interval Δt.

[0079] Thus, when acquiring the charging curve, if no non-contact state occurs, the difference changes significantly from negative to positive at each sampling interval Δt. On the other hand, if a non-contact state occurs at a certain time, as shown in Figure 13(D), the difference does not change significantly from negative to positive at a given sampling time, and continues to decrease until the contact state returns. Therefore, whether or not a non-contact state has occurred can be determined by whether or not there is a large change in the difference around the sampling time.

[0080] Figure 14 is a schematic diagram illustrating the correction steps. If a non-contact state occurs (see Figure 14(A)), data from the time when no significant change in the difference was observed is deleted, and the data from that time onward is shifted forward by a predetermined time interval Δt' (see Figure 14(B)). This predetermined time interval Δt' is given, for example, as a constant multiple of the sampling interval Δt. Note that Figure 14 shows the case where Δt' = 1 × Δt. This is performed for each non-contact state, and the corrected voltage curve is used as the measured voltage curve for subsequent processing.

[0081] While an example of a charging curve was shown here, the same principle applies to a discharge curve. In the case of a discharge curve, the increase or decrease in the difference is the opposite of that in a charging curve.

[0082] Furthermore, while we have described examples of determining the degree of degradation from the voltage curve obtained during charging (charging curve) or the voltage curve obtained during discharging (discharging curve), the method is not limited to these examples.

[0083] A current curve acquisition device may be used instead of a voltage curve acquisition device. An example of using a current curve acquisition device will be explained with reference to Figure 15. Figure 15 is a schematic diagram of a secondary battery degradation determination system equipped with a current curve acquisition device. The current curve acquisition device 101 equipped in the secondary battery degradation determination system 11 includes, for example, a constant voltage power supply 111, a switch 120, and a current sensor 131. During charging, the current curve acquisition device 101 applies a constant voltage to both ends of the secondary battery 300 and acquires the measured current curve as a charging curve. In the case of a discharge curve, the application of the constant voltage is stopped and the current from the secondary battery 300 is measured. After acquiring the current curve, the process can be carried out in the same way as when using the voltage curve as described above, and the voltage curve can be replaced with the current curve, so a detailed explanation is omitted.

[0084] Referring to Figure 16, we will now explain the case of measuring multiple secondary batteries in parallel. Figure 16 is a schematic diagram illustrating the parallel measurement of multiple secondary batteries. Figure 16(A) is a schematic diagram of the arrangement of secondary batteries. Figure 16(B) is an enlarged view of the dashed line portion of Figure 16(A). The battery measurement jig used here can measure a total of 28 secondary batteries in parallel. For each secondary battery, the terminal that contacts the positive electrode of the secondary battery and the terminal that contacts the negative electrode of the secondary battery are connected by cables to a DMM (Digital Multimeter) that measures the voltage. Note that noise countermeasures have been taken for the constant current power supply and the DMM itself, so noise is likely to be generated by hardware other than the constant current power supply and DMM.

[0085] Now, the cable connecting the secondary battery and the DMM is a normal single wire without any shielding measures. Also, assume that the wires coming out of the electrodes of the secondary battery are randomly bundled and wired up to the DMM.

[0086] Now, assume that the secondary batteries are separated by δ each, and the lengths of the cables from each battery to the DMM are sufficiently long. Also, assume that one terminal of each battery is located on the x-axis. At this time, the x-coordinate of the terminal of the k-th battery can be given by k×δ.

[0087] When the voltage at coordinate x is Es, the voltage at the reference coordinate origin (x = 0) is Ese -x Thus, when the voltage of the k-th secondary battery is Es, the absolute value of the potential at the reference is Ese -k×δ given by. Here, ε = e -δ Then, Ese -k×δ = Esε k is.

[0088] For example, when the voltage at the terminal of the 4th secondary battery (x = 4δ) is Es, the voltage at the position corresponding to the terminal of the 3rd secondary battery (x = 3δ) is Esε, the voltage at the position corresponding to the terminal of the 2nd battery (x = 2δ) is Esε 2 , the voltage at the position corresponding to the terminal of the 1st battery (x = δ) is Esε 3 , and the absolute value of the potential at the reference (x = 0) is Esε 4 is.

[0089] Now, let the cable connected to the k-th battery be Line-k. When Line-k is divided into sections every distance δ, assume that in that section, the voltage noise from all the cables parallel to Line-k is superimposed. Here, the k-th section is the section between the k-th secondary battery and the k - 1-th secondary battery, and the 0th secondary battery indicates the reference coordinate origin (x = 0). Also, the voltage of the k-th section indicates the voltage at the x-coordinate corresponding to the terminal of the k - 1-th secondary battery.

[0090] The noise in the k-th interval is obtained, for example, by superimposing a coefficient A (0 < A ≤ 1) multiplied by the voltage of the k-th interval. Here, for simplicity, it is described with A = 1.

[0091] Here, the following equation (3) is defined.

[0092]

Number

[0093] Line-1 exists only in the first interval. Also, in the first interval, Line-1 to n exist. Therefore, the noise of Line-1 is obtained by adding the noise Esε caused by Line-1 in the first interval and the noise of Line-2 to n other than Line-1 (Esε 2 ~Esε n ), and is given by the following equation (4).

[0094]

Number

[0095] Next, Line-2 exists in the first interval and the second interval. The noise S1 in the first interval is the same as that of Line-1. Also, in the second interval, Line-2 to n exist. Therefore, the noise of Line-2 in the second interval is obtained by adding the noise Esε caused by Line-2 in the second interval and the noise of Line-3 to n other than Line-2 (Esε 2 ~Esε nー1 ), and is given by the following equation (5).

[0096]

Number

[0097] As a result, the noise of Line-2 is obtained by adding the noise S1 in the first interval and the noise S2 in the second interval, resulting in S1 + S2.

[0098] Similarly, the noise in the k-th interval is given by equation (3) above, and the noise of Line-k is given by S1 + S2 + ... + Sk.

[0099] Figure 17 shows the calculation results for the noise of each battery using the above formula. On the other hand, Figure 18 shows the 3σ calculated from the noise waveform of each battery. The noise waveform of each battery does not necessarily follow a normal distribution, but it was calculated for convenience. As shown in Figure 18, the value of 3σ is smallest for the secondary battery closest to the DMM, and the value of 3σ increases sequentially as you move away from the DMM.

[0100] Comparing Figure 17 and Figure 18, the increase in both is linear and similar. From this, it can be concluded that the noise in each secondary battery shown in Figure 18 is likely being generated in the cables within the jig.

[0101] Such systematic errors can be removed using time series analysis. Here, we will explain an example using the Auto Regressive Integrated Moving Average (ARIMA) model. The ARIMA model is expressed as ARIMA(P, d, q) using three parameters: p, d, and q. p is the autoregressive (AR) parameter and indicates the order of the autoregressive component. d is used to remove nonstationarity of the data and indicates the number of times the difference is taken. q indicates the order of the moving average (MA) component.

[0102] The ARIMA(P,d,q) time series formulation is based on the Box-Jenkins method. The Box-Jenkins method consists of four steps: identification, estimation, diagnostic check, and prediction. In the identification step, it is assessed whether the time series is stationary. If the time series is not stationary, the number of differences required to make it stationary is assessed. Next, difference data is generated for use in the diagnostic plot. The parameters of the ARIMA model for the data are identified from the autocorrelation and partial autocorrelation.

[0103] In the estimation step, the data is used to train the model's parameters (coefficients).

[0104] The diagnostic check step evaluates the fitted model in relation to the available data and checks for areas where the model can be improved. In particular, it checks for overfitting and calculates residuals.

[0105] After the model is created, the prediction step involves using that model to predict values.

[0106] Here, stationarity refers to the property that the statistical characteristics (mean, variance, autocorrelation, etc.) of time series data remain constant over time. Specifically, stationarity has the following characteristics:

[0107] 1. The average is constant regardless of time: This means that the "center" of the data does not change over time. In other words, the average value at one point in time is the same as the average value at another point in time.

[0108] 2. The variance is constant regardless of time: This means that the "variability" of the data does not change over time. In other words, the variance at one point in time is the same as the variance at another point in time.

[0109] 3. Autocovariance (or autocorrelation) is constant over time: This indicates that the relationship between two points in time depends only on lag, and not on time itself.

[0110] While the original purpose of the ARIMA model is to stabilize the original time series data and predict future data, here we focus on the fact that the ARIMA model can be used to remove systematic errors contained in the original data.

[0111] For example, when measuring multiple batteries in parallel, if there is a systematic error in the original data, the randomness of the measurement is eliminated, and the accuracy of estimating the capacity Q deteriorates. Therefore, it is preferable to eliminate systematic errors as much as possible.

[0112] The ARIMA model separates the true trend from other errors in time series data. This method extracts the true trend from time series data. Typically, users only need the true trend, and errors are assumed to be only random errors, so errors themselves were not given much thought. In contrast, the inventors of this invention noticed that errors include both systematic and random errors, and realized that by separating the errors, the problematic systematic errors could be automatically eliminated. Therefore, this method utilizes the functionality of the ARIMA model.

[0113] The Box-Jenkins method removes the trend using the d-th order difference, and the parameters p, d, and q of ARIMA(p, d, q) are determined from the autocorrelation function (ASF) and partial autocorrelation function (PACF), and the coefficients are estimated using methods such as the maximum likelihood method.

[0114] The residuals of the original time series data and ARIMA(p, d, q) must be white noise. Methods for confirming that the data is white noise include correlograms and the Ljing-Box test. A correlogram is a representation of the correlation function ρn between a given time series and a time series shifted by n times, viewed as a function of n. n This is also called the autocorrelation function (ACF). The k-th order partial autocorrelation function (PACF) is an indicator that shows the influence of only k of the time difference. If both the ACF and PACF fall within the confidence limits, the time series data can be judged as white noise.

[0115] The error of 28 batteries set in a jig was examined. The time series data of the charging waveform of each battery for 10 ≤ t ≤ 120 was fitted to ARIMA(p, d, q) = ARIMA(10, 1, 10).

[0116] Figure 19 shows the error histogram for the 28th secondary battery, which is the furthest from the DMM among the 28 batteries. As shown in Figure 19, the error histogram has the shape of a normal distribution. From this, it can be seen that the true voltage value is the center of the normal distribution, i.e., the mean value, and therefore the true voltage value can be determined by finding the mean value.

[0117] Figure 20 shows the 3σ histogram of errors for 28 secondary batteries. In Figure 20, the errors in the configuration example of this invention, with systematic errors removed by the ARIMA model, are shown in black, while the prior art, with systematic errors not removed, is shown in white.

[0118] In prior art, even the first secondary battery, which is closest to the DMM, has a 3σ of approximately 28 μV, and the 3σ increases as the distance from the DMM increases.

[0119] In contrast, in the configuration example of this invention, the 3σ value is generally within 25, although there are some secondary batteries where the 3σ value exceeds 30, regardless of the distance of the secondary battery from the DMM. Thus, it can be seen that by removing systematic errors using the ARIMA model, the noise is reduced and the performance is independent of the distance from the DMM.

Claims

1. An approximation formula acquisition step involves approximating a voltage curve, which is either a charging curve or a discharge curve, or both, that shows the voltage v(t) across the secondary battery as a function of time t, measured during either the charging or discharging of the secondary battery, or both, to obtain an approximation formula. A degradation estimation step in which the degree of degradation of the secondary battery is estimated from the aforementioned approximation formula, Equipped with, The aforementioned step of estimating the degree of deterioration is: The coefficients of the aforementioned approximation formula are applied to a model obtained by multivariate analysis or machine learning to estimate the full charge capacity. Method for determining the degree of deterioration of a secondary battery.

2. The model acquisition step is provided before the aforementioned approximation formula acquisition step. The model acquisition step includes a model acquisition approximation formula acquisition step, which approximates a voltage curve that is either a charging curve or a discharge curve, or both, that shows the voltage v(t) across the secondary battery as a function of time t, measured during either charging or discharging of the secondary battery, and acquires an approximation formula for model acquisition. The model generation step involves generating the model by performing machine learning or multiple regression analysis using the coefficients of the aforementioned model acquisition approximation formula as explanatory variables and the measured full charge capacity as the dependent variable. A method for determining the degree of degradation of a secondary battery according to claim 1, comprising:

3. To obtain the voltage v(t) across the terminals of a secondary battery with respect to time t, a regression curve is obtained for the interval including time t, and v(t) is obtained from the regression curve. A method for determining the degree of degradation of a secondary battery according to claim 1.

4. An approximation formula acquisition step involves approximating the current curve, which is either a charging curve or a discharge curve, or both, that show the current I(t) flowing through the secondary battery as a function of time t, measured during either the charging or discharging of the secondary battery, and obtaining an approximation formula. A degradation estimation step in which the degree of degradation of the secondary battery is estimated from the aforementioned approximation formula, Equipped with, The aforementioned step of estimating the degree of deterioration is: A method for determining the degree of degradation of a secondary battery, which involves applying the coefficients of the aforementioned approximation formula to a model obtained by multivariate analysis or machine learning to estimate the full charge capacity.

5. After the aforementioned approximation formula acquisition step, The steps include taking the difference between the measured charging curve or the discharge curve and the approximation formula, The steps include determining whether the difference is discontinuous at each sampling period Δt of the measured charging curve or the discharging curve, If the discontinuity does not occur after a predetermined time interval Δt' from the time of discontinuity, the data for the time after the predetermined time interval Δt' from the time of discontinuity is deleted, and the data for the time after the deleted data is shifted by the predetermined time interval Δt'. The modification step includes having, After the correction step, the approximation formula acquisition step is performed again. A method for determining the degree of degradation of a secondary battery according to any one of claims 1 to 4.

6. Before the step of obtaining the approximation formula, A step of performing a time-series analysis on the measured charging curve or the discharge curve and removing systematic errors. A method for determining the degree of degradation of a secondary battery according to any one of claims 1 to 4.

7. An approximation formula acquisition means for approximating a voltage curve, which is either a charging curve or a discharge curve, or both, that shows the voltage v(t) across the terminals of a secondary battery as a function of time t, measured during either the charging or discharging of the secondary battery, or both, and obtaining an approximation formula. Degradation estimation means for estimating the degree of degradation of the secondary battery from the aforementioned approximation formula, Equipped with, The aforementioned degradation degree estimation means is The coefficients of the aforementioned approximation formula are applied to a model obtained by multivariate analysis or machine learning to estimate the full charge capacity. Secondary battery deterioration degree determination device.

8. moreover, Equipped with a model acquisition means, The aforementioned model acquisition means is A means for obtaining an approximate formula for model acquisition, which approximates a voltage curve that is either a charging curve or a discharge curve, or both, showing the measured voltage v(t) across the terminals of a secondary battery as a function of time t, and obtains an approximate formula for model acquisition. A model generation means that generates the model by performing machine learning or multiple regression analysis using the coefficients of the aforementioned model acquisition approximation formula as explanatory variables and the measured full charge capacity as the dependent variable, and A secondary battery degradation degree determination device according to claim 7, comprising:

9. To obtain the voltage v(t) across the terminals of a secondary battery with respect to time t, a regression curve is obtained for the interval including time t, and v(t) is obtained from the regression curve. The secondary battery degradation degree determination device according to claim 7.

10. An approximation formula acquisition means for approximating a current curve, which is either a charging curve or a discharge curve, or both, that shows the current I(t) flowing through a secondary battery as a function of time t, measured during either the charging or discharging of a secondary battery, or both, and obtaining an approximation formula, Degradation estimation means for estimating the degree of degradation of the secondary battery from the aforementioned approximation formula, Equipped with, The aforementioned degradation degree estimation means is The coefficients of the aforementioned approximation formula are applied to a model obtained by multivariate analysis or machine learning to estimate the full charge capacity. Secondary battery deterioration degree determination device.

11. moreover, A means for taking the difference between the measured charging curve or the discharge curve and the approximation formula, Means for determining whether the difference is discontinuous at each sampling period Δt of the measured charging curve or the discharging curve, If the data does not become discontinuous after a predetermined time interval Δt' from the time of discontinuity, the means include deleting the data from the time of discontinuity after the predetermined time interval Δt', and shifting the data from a time later than the time of the deleted data by the predetermined time interval Δt'. Equipped with a modification means having A secondary battery degradation degree determination device according to any one of claims 7 to 10.

12. moreover, Means for performing time-series analysis on the measured charging curve or the discharge curve and removing systematic errors. A secondary battery degradation degree determination device according to any one of claims 7 to 10, comprising:

13. Computer An approximation formula acquisition means for approximating a voltage curve, which is either a charging curve or a discharge curve, or both, that shows the voltage v(t) across the terminals of a secondary battery as a function of time t, measured during either the charging or discharging of the secondary battery, or both, and obtaining an approximation formula. Degradation estimation means for estimating the degree of degradation of the secondary battery from the aforementioned approximation formula, and make it work The aforementioned degradation degree estimation means is The coefficients of the aforementioned approximation formula are applied to a model obtained by multivariate analysis or machine learning to estimate the full charge capacity. program.

14. Furthermore, the computer is used as a means of acquiring models. The aforementioned model acquisition means is A means for obtaining an approximate formula for model acquisition, which approximates a voltage curve that is either a charging curve or a discharge curve, or both, showing the measured voltage v(t) across the terminals of a secondary battery as a function of time t, and obtains an approximate formula for model acquisition. A model generation means that generates the model by performing machine learning or multiple regression analysis using the coefficients of the aforementioned model acquisition approximation formula as explanatory variables and the measured full charge capacity as the dependent variable, and Equipped with The program according to claim 13.

15. To obtain the voltage v(t) across the terminals of a secondary battery with respect to time t, a regression curve is obtained for the interval including time t, and v(t) is obtained from the regression curve. The program according to claim 13.

16. Computer An approximation formula acquisition means for approximating a current curve, which is either a charging curve or a discharge curve, or both, that shows the current I(t) flowing through a secondary battery as a function of time t, measured during either the charging or discharging of a secondary battery, and obtaining an approximation formula, and Degradation degree estimation means for estimating the degree of degradation of the secondary battery from the aforementioned approximation formula. To make it function as, The aforementioned degradation degree estimation means is The coefficients of the aforementioned approximation formula are applied to a model obtained by multivariate analysis or machine learning to estimate the full charge capacity. program.

17. Computers, further, A means for taking the difference between the measured charging curve or the discharge curve and the approximation formula, Means for determining whether the difference is discontinuous at each sampling period Δt of the measured charging curve or the discharging curve, If the data does not become discontinuous after a predetermined time interval Δt' from the time of discontinuity, the means include deleting the data from the time of discontinuity after the predetermined time interval Δt', and shifting the data from a time later than the time of the deleted data by the predetermined time interval Δt'. Modification means having A program according to any one of claims 13 to 16 that functions as such.

18. Computers, further, Means for performing time-series analysis on the measured charging curve or the discharge curve and removing systematic errors. A program according to any one of claims 13 to 16 that functions as such.

19. An approximation formula acquisition step involves approximating a voltage curve, which is either a charging curve or a discharge curve, or both, that shows the voltage v(t) across the terminals of the secondary battery as a function of time t, measured during either the charging or discharging of the secondary battery, and obtaining two or more approximation formulas. A degradation degree estimation step in which the degree of degradation of the secondary battery is estimated from two or more of the aforementioned approximation formulas, Equipped with, The aforementioned step of estimating the degree of deterioration is: The coefficients of two or more of the aforementioned approximation formulas are applied to a model obtained by multivariate analysis or machine learning to estimate the full charge capacity. Furthermore, the model acquisition step is provided before the approximation formula acquisition step. The model acquisition step includes a model acquisition approximation formula acquisition step, which approximates a voltage curve that is either a charging curve or a discharge curve, or both, that shows the voltage v(t) across the secondary battery as a function of time t, measured during either charging or discharging of the secondary battery, to obtain two or more model acquisition approximation formulas, A model generation step involves generating the model by performing machine learning or multiple regression analysis using the coefficients of two or more of the aforementioned model acquisition approximation formulas as explanatory variables and the measured full charge capacity as the dependent variable. A method for determining the degree of degradation of a secondary battery, comprising the following components.

20. An approximation formula acquisition means for obtaining two or more approximation formulas by approximating the voltage curve, which is either a charging curve or a discharge curve, or both, that shows the voltage v(t) across the terminals of a secondary battery as a function of time t, measured during either the charging or discharging of the secondary battery, and the voltage curve, which is either a charging curve or a discharge curve, or both. Degradation degree estimation means for estimating the degree of degradation of the secondary battery from two or more of the aforementioned approximation formulas, Equipped with, The aforementioned degradation degree estimation means is The coefficients of two or more of the aforementioned approximation formulas are applied to a model obtained by multivariate analysis or machine learning to estimate the full charge capacity. moreover, Equipped with a model acquisition means, The aforementioned model acquisition means is A means for obtaining an approximate formula for model acquisition, which approximates a voltage curve that is either a charging curve or a discharge curve, or both, showing the measured voltage v(t) across the terminals of a secondary battery as a function of time t, and obtains two or more approximate formulas for model acquisition. A model generation means generates the model by performing machine learning or multiple regression analysis using the coefficients of two or more of the aforementioned model acquisition approximation formulas as explanatory variables and the measured full charge capacity as the dependent variable. A secondary battery degradation degree determination device equipped with the following features.

21. Computer An approximation formula acquisition means for obtaining two or more approximation formulas by approximating either or both of the charging curve and the discharging curve, which show the voltage v(t) across the terminals of a secondary battery as a function of time t, measured during either or both of the charging and discharging of a secondary battery, Degradation degree estimation means for estimating the degree of degradation of the secondary battery from two or more of the aforementioned approximation formulas, and make it work The aforementioned degradation degree estimation means is The coefficients of two or more of the aforementioned approximation formulas are applied to a model obtained by multivariate analysis or machine learning to estimate the full charge capacity. Furthermore, the computer is used as a means of acquiring models. The aforementioned model acquisition means is A means for obtaining an approximate formula for model acquisition, which approximates a voltage curve that is either a charging curve or a discharge curve, or both, showing the measured voltage v(t) across the terminals of a secondary battery as a function of time t, and obtains two or more approximate formulas for model acquisition. A model generation means generates the model by performing machine learning or multiple regression analysis using the coefficients of two or more of the aforementioned model acquisition approximation formulas as explanatory variables and the measured full charge capacity as the dependent variable. A program equipped with these features.

22. A model acquisition approximation formula acquisition step involves approximating the voltage curve, which is either a charging curve or a discharge curve, or both, that show the voltage v(t) across the terminals of a secondary battery as a function of time t, measured during either the charging or discharging of the secondary battery, and acquiring an approximation formula for model acquisition. The model generation step involves generating a model by performing machine learning or multiple regression analysis using the coefficients of the aforementioned model acquisition approximation formula as explanatory variables and the measured full charge capacity as the dependent variable. Required model acquisition steps A method for determining the degree of degradation of a secondary battery.

23. A means for obtaining an approximate formula for model acquisition, which approximates a voltage curve that is either a charging curve or a discharge curve, or both, showing the measured voltage v(t) across the terminals of a secondary battery as a function of time t, and obtains an approximate formula for model acquisition. A model generation means generates a model by performing machine learning or multiple regression analysis using the coefficients of the aforementioned model acquisition approximation formula as explanatory variables and the measured full charge capacity as the dependent variable. Model acquisition method provided A secondary battery degradation degree determination device having the following features.

24. Computers, A means for obtaining an approximate formula for model acquisition, which approximates a voltage curve that is either a charging curve or a discharge curve, or both, showing the measured voltage v(t) across the terminals of a secondary battery as a function of time t, and obtains an approximate formula for model acquisition. A model generation means generates a model by performing machine learning or multiple regression analysis using the coefficients of the aforementioned model acquisition approximation formula as explanatory variables and the measured full charge capacity as the dependent variable. Model acquisition method provided A program that makes it function as such.

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