A battery soh influencing factor analysis method

Abstract

This invention provides a method for analyzing factors affecting battery state of equilibrium (SOH). It accelerates battery aging through repeated charge-discharge cycles, obtaining battery capacity and corresponding cycle time, voltage, current, and temperature data. Based on these data, 14 characteristic factors are derived as input parameters. KL divergence, Pearson correlation coefficient, and grey relational analysis are used as evaluation indicators to quantify the correlation between these characteristic factors and capacity. A temporal convolutional network is used to individually predict the capacity of each input parameter to verify the impact of each characteristic factor on the prediction accuracy. The average of multiple prediction results is calculated as the prediction error, thus determining the magnitude of the influence of the characteristic factors affecting battery SOH. Finally, appropriate characteristic factors are selected as the dominant parameters based on actual application requirements.

Description

Technical Field

[0001] This invention belongs to the field of intelligent operation and maintenance of battery energy storage systems, and specifically relates to a method for analyzing the influencing factors of battery SOH (State of Health). Background Technology

[0002] As an important resource for flexible energy management, battery energy storage has experienced rapid development. Due to its electrochemical characteristics, batteries age continuously with increasing charge-discharge cycles. When they age to a certain extent, they can no longer operate, easily leading to malfunctions, resulting in high maintenance costs, significant safety risks, and even unpredictable consequences such as fires. To quantify the degree of battery aging, the State of Charge (SOH) has been proposed as an important parameter for battery management. Although SOH has been studied, the influencing factors have not yet been quantitatively determined. Therefore, this invention applies different correlation analysis methods to screen out the main factors affecting battery SOH, providing a reference for the safe and efficient operation of battery energy storage. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention proposes a method for analyzing factors affecting battery state of equilibrium (SOH). Based on voltage, current, and temperature, 14 characteristic factors are derived. The correlation between different characteristic factors and capacity is analyzed using three methods: KL divergence, Pearson correlation coefficient, and grey relational analysis. Furthermore, a temporal convolutional neural network is applied to analyze the impact of different characteristic factors on capacity prediction. By comparison, key characteristic factors affecting battery SOH are extracted.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for analyzing factors affecting battery state of equilibrium (SOH) is proposed. This method accelerates battery aging through repeated charge-discharge cycles, obtaining battery capacity and corresponding cycle time, voltage, current, and temperature data. Based on these data, 14 characteristic factors are derived as input parameters. KL divergence, Pearson correlation coefficient, and grey relational analysis are used as evaluation indicators to quantify the correlation between these characteristic factors and capacity. A temporal convolutional network is used to predict the capacity of each input parameter individually to verify the impact of each characteristic factor on the prediction accuracy. The average of multiple prediction results is calculated as the prediction error, thus determining the magnitude of the influence of the characteristic factors on battery SOH. Finally, appropriate characteristic factors are selected as the dominant parameters based on actual application requirements.

[0006] Furthermore, the specific characteristic factors include: 1) the time taken for each discharge cycle; 2) the current for each discharge cycle; 3) the maximum voltage, minimum voltage, average voltage, voltage difference between the maximum and minimum voltages, maximum voltage change over time, and voltage sample entropy for each discharge cycle; 4) the maximum temperature, minimum temperature, average temperature, temperature difference between the maximum and minimum temperatures, maximum temperature change over time, and temperature sample entropy for each discharge cycle; wherein the voltage sample entropy and temperature sample entropy are calculated by performing sample entropy calculations on the voltage and temperature curves for each discharge cycle.

[0007] Furthermore, when using KL divergence as the evaluation index, the average temperature value is the smallest and has the highest correlation with capacity, while the current value is the largest and has the lowest correlation with capacity. When using Pearson correlation coefficient as the evaluation index, the cycle time value is the largest and has the highest correlation with capacity, while the current value is the smallest and has the lowest correlation with capacity. When using grey relational analysis as the evaluation index, the cycle time value is the largest and has the highest correlation with capacity, while the voltage sample entropy value is the smallest and has the lowest correlation with capacity.

[0008] Furthermore, the KL divergence calculation includes the following steps:

[0009] Let p(x) and q(x) represent the probabilities of two processes, then the KL distance is:

[0010]

[0011] Therefore, the KL divergence between p(x) and q(x) is:

[0012] D(p,q)=δ(p,q)+δ(q,p) (2)

[0013] The KL divergence is a measure of the angle between the probability distributions of two processes. The larger the value, the greater the difference; conversely, the smaller the difference, the smaller the difference. When the two probability distributions are exactly the same, the value is 0.

[0014] When finding the signal X = {x1, x2, ..., x3} n} and the signal Y = {y1, y2, ..., y3} n When calculating the KL divergence between x and q, assume that the probability distributions are p(x) and q(x), respectively.

[0015] First, calculate the probability distribution of signal X using a nonparametric estimation method:

[0016]

[0017] In the formula, p(x) is the probability density function after kernel density estimation; h is a given positive number, called the window width or smoothing parameter; K(·) is the kernel function, commonly the Gaussian kernel function; and n is the number of samples.

[0018]

[0019] Where u is the expected value;

[0020] Similarly, the probability distribution q(x) of signal Y is obtained;

[0021] Substitute p(x) and q(x) into formula (1) to solve for the KL distance (p,q) and (q,p) between signals X and Y, and then use formula (2) to calculate the KL divergence value D(p,q).

[0022] Furthermore, the calculation of the Pearson correlation coefficient includes the following steps:

[0023] The Pearson correlation coefficient is used to measure the degree of linear correlation between two variables:

[0024]

[0025] In the formula, Let X and Y be the expected values ​​of variables X and Y, respectively.

[0026] Where -1 ≤ γ ≤ 1; its properties are as follows:

[0027] When γ > 0, it indicates a positive correlation between the two variables; when γ < 0, it indicates a negative correlation between the two variables.

[0028] When γ = 0, it indicates that the two variables have no linear correlation.

[0029] When |γ|=1, it indicates that the two variables are perfectly linearly related, that is, they have a functional relationship.

[0030] When 0 < |γ| < 1, it indicates that there is a certain degree of linear correlation between the two variables; and the closer |γ| is to 1, the stronger the linear relationship between the two variables; the closer |γ| is to 0, the weaker the linear correlation between the two variables.

[0031] Furthermore, the calculation of the grey relational degree includes the following steps:

[0032] Assume a reference sequence X1 and a comparison sequence X k They are represented as follows:

[0033]

[0034] In the formula, n is the sample size, x1(n) and x k (n) represents sample data.

[0035] Initialize X1 and X k To reduce the differences in parameters across dimensions:

[0036]

[0037] Assume ξ i (h) represents Y1 and Y k The grey relational coefficient at time h is then:

[0038]

[0039] |Y1(h)-Y k (h)|+ρm k axm h ax|Y1(h)-Y k (h)|

[0040] In the formula, ρ is the resolution coefficient;

[0041] Get Y0 and Y k The grey relational degree is:

[0042]

[0043] In the formula, i = 1, 2, ..., n; h = 1, 2, ..., Q, where Q is the time value.

[0044] Furthermore, the construction of the temporal convolutional network includes:

[0045] (1) Temporal convolutional network modeling is used to establish a mapping relationship between the input sequence and the output sequence, so that the actual output y0,…,y T And the predicted output y′0,…,y′ T Minimize the error loss between them:

[0046] Suppose the given input sequence is x0,…,x T The expected predicted output is y0,…,y T The relationship between the predicted output and the input sequence is as follows:

[0047] (y0′,…,y′ T )=f(x0,…,x T (12)

[0048] In the formula, y t Only the input sequence x0,…,x at time t and before is considered. t Related to, and with future input x t ,…,x T Irrelevant;

[0049] (2) Expand causal convolution, specifically:

[0050]

[0051] In the formula, F(i) represents the expression for the sequence x0,…,x TThe convolution result of the i-th element; h(j) is the filter, also called the convolution kernel; d is the scaling factor, when d=1 it is a standard causal convolution; x(i-dj) represents the convolution direction, that is, only convolution operation on past data;

[0052] (3) Add residual blocks:

[0053] Assuming the input of the residual block is x and the output is o, after linear transformation and mapping through the activation function, we obtain formula (14):

[0054] o=Activation(x+Γ(x)) (14)

[0055] In the formula, Activation(·) is the activation function, and Γ(x) is the relational function of x.

[0056] Beneficial effects:

[0057] This invention can analyze the main influencing factors on SOH from different algorithmic perspectives, thereby providing options and references for accurate SOH assessment under different operating scenarios. Attached Figure Description

[0058] Figure 1 A schematic diagram of expanding the causal convolution structure of TCN;

[0059] Figure 2 This is a diagram illustrating the battery capacity.

[0060] Figure 3 A schematic diagram of the time for each discharge cycle;

[0061] Figure 4 This is a schematic diagram of the current.

[0062] Figure 5 This is a schematic diagram of voltage-related parameter 1;

[0063] Figure 6 This is a schematic diagram of voltage-related parameters 2;

[0064] Figure 7 This is a schematic diagram of temperature-related parameters 1;

[0065] Figure 8 This is a schematic diagram of temperature-related parameters 2. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0067] The battery SOH influencing factor analysis method of the present invention includes the following steps:

[0068] Step 1: Calculate the KL divergence:

[0069] KL divergence, also known as relative entropy, measures the difference between the probability distributions of two processes. Let p(x) and q(x) represent the probabilities of the two processes, then the KL distance is:

[0070]

[0071] Therefore, the KL divergence between p(x) and q(x) is:

[0072] D(p,q)=δ(p,q)+δ(q,p) (2)

[0073] The KL divergence is a measure of the angle between the probability distributions of two processes. The larger the value, the greater the difference; conversely, the smaller the value, the smaller the difference. When the two probability distributions are exactly the same, the value is 0.

[0074] When finding the signal X = {x1, x2, ..., x3} n} and the signal Y = {y1, y2, ..., y3} n When calculating the KL divergence between x and q, assume the probability distributions are p(x) and q(x), respectively.

[0075] First, the probability distribution of signal X is calculated. This invention uses a non-parametric estimation method to solve for the probability distribution:

[0076]

[0077] In the formula, p(x) is the probability density function after kernel density estimation; h is a given positive number, called the window width or smoothing parameter; K(·) is the kernel function, commonly the Gaussian kernel function. n is the number of samples.

[0078]

[0079] Where u is the expected value.

[0080] Similarly, the probability distribution q(x) of signal Y can be obtained;

[0081] Substitute p(x) and q(x) into formula (1) to solve for the KL distance (p,q) and (q,p) between signals X and Y, and then use formula (2) to calculate the KL divergence value D(p,q).

[0082] Step 2: Calculate the Pearson correlation coefficient:

[0083] Pearson correlation coefficient is widely used to measure the degree of linear correlation between two variables:

[0084]

[0085] In the formula, Let X and Y be the expected values ​​of variables X and Y, respectively.

[0086] Where -1 ≤ γ ≤ 1. Its properties are as follows:

[0087] When γ > 0, it indicates a positive correlation between the two variables; when γ < 0, it indicates a negative correlation between the two variables.

[0088] When γ = 0, it indicates that there is no linear correlation between the two variables.

[0089] When |γ|=1, it indicates that the two variables are perfectly linearly related, that is, they have a functional relationship.

[0090] When 0 < |γ| < 1, it indicates that there is a certain degree of linear correlation between the two variables. The closer |γ| is to 1, the stronger the linear relationship between the two variables; the closer |γ| is to 0, the weaker the linear correlation between the two variables.

[0091] Step 3: Calculate the grey relational degree:

[0092] Grey relational analysis assesses the relationship between different curves by analyzing their geometric proximity; the higher the proximity, the stronger the correlation.

[0093] Assume a reference sequence X1 and a comparison sequence X k They are represented as follows:

[0094]

[0095] In the formula, n is the sample size, x1(n) and x k (n) represents sample data.

[0096] Initialize X1 and X k To reduce the differences in parameters across dimensions:

[0097]

[0098] Assume ξ i (h) represents Y1 and Y k The grey relational coefficient at time h is then:

[0099]

[0100] |Y1(h)-Y k (h)|+ρm k axm h ax|Y1(h)-Y k (h)|

[0101] In the formula, ρ is the resolution coefficient;

[0102] Get Y0 and Y k The grey relational degree is:

[0103]

[0104] In the formula, i = 1, 2, ..., n; h = 1, 2, ..., Q. Q is the time value.

[0105] Step 4: Construct a temporal convolutional network:

[0106] Temporal Convolution Networks (TCNs) employ structures such as enlarged causal convolutions and residual blocks, enabling them to extract features from large time series samples and perform predictions. Furthermore, they effectively address the performance degradation problem of deep networks during training. Their construction includes the following steps:

[0107] (1) TCN modeling:

[0108] Suppose the given input sequence is x0,…,x T The expected predicted output is y0,…,y T The relationship between the predicted output and the input sequence is as follows:

[0109] (y0′,…,y′ T )=f(x0,…,x T (12)

[0110] In the formula, y t Only the input sequence x0,…,x at time t and before is considered. t Related to, and with future input x t ,…,x T Irrelevant. TCN modeling aims to establish a mapping relationship between the input sequence and the output sequence, with the goal of making the actual outputs y0,…,y... T And the predicted output y′0,…,y′ T The error loss between them is minimized.

[0111] (2) Enlarging causal convolution:

[0112] Compared to recurrent neural networks, models using causal convolutions do not use recurrent connections, allowing time-series data to be input in parallel, resulting in faster network training speeds and unique advantages in training large-sample time series. However, standard causal convolutions require stacking many network layers or using large convolutional kernels to increase the receptive field of neurons in the neural network when processing large-sample time series. To address this, TCN employs Dilated Causal Convolution (DCC) to increase the receptive field without significantly increasing computational cost. DCC is a convolution operation that performs a step-by-step operation on the input sequence, specifically:

[0113]

[0114] In the formula, F(i) represents the expression for the sequence x0,…,x T The convolution result of the i-th element; h(j) is the filter, also called the convolution kernel; d is the scaling factor, when d=1 it is a standard causal convolution. x(i-dj) represents the convolution direction, that is, only convolution operation is performed on past data.

[0115] The structure of DCC is as follows: Figure 1 As shown, compared with standard causal convolution, DCC can make the output y as related to the input x as much as possible with the same number of network layers; the multi-layer stacking principle of DCC can enable deep learning networks to achieve a very large receptive field with fewer network layers; the convolution kernel can perform sliding operations on the input data, which enables TCN to handle variable-length inputs and continuously calculate and output new prediction values ​​as the model input data is updated.

[0116] (3) Add residual blocks:

[0117] Residual blocks are mainly used to address the degradation problem in deep learning networks. Their core idea is to introduce a "skip connection" operation that skips one or more layers. Assuming the input of the residual block is x and the output is o, after a linear transformation and mapping through an activation function, formula (14) is obtained. Since residuals are never zero in practice, stacked layers in deep learning networks can always learn new features, meaning the learning performance of deep networks will not degrade.

[0118] o=Activation(x+Γ(x)) (14)

[0119] In the formula, Activation(·) is the activation function, and Γ(x) is the relational function of x.

[0120] In summary, using a network structure combining residual blocks and DCC in TCN modeling can effectively improve the feature learning ability and robustness of the TCN model. The invention will be explained in detail below with specific examples.

[0121] Battery capacity is a simple and clear indicator of battery aging, but in actual operation, capacity is not easily measured directly. This invention uses a lithium battery, charged at a constant current of 1.5A at room temperature. When the voltage reaches 4.2V, charging is switched to constant voltage until the charging current drops to 20mA. Then, it is discharged at a constant current of 2A until the voltage drops to 2.5V. This repeated charge-discharge cycle accelerates battery aging. The obtained battery capacity data is as follows: Figure 2 As shown. Then, starting with easily measurable time, voltage, current, and temperature, more indirect health indicators are extracted to enrich the model's input parameters. Specifically, they are divided into the following four categories, totaling 14 feature factors, such as... Figures 3 to 8 The following are shown: 1) Time taken for each discharge cycle; 2) Current for each discharge cycle; 3) Maximum voltage, minimum voltage, average voltage, voltage difference between maximum and minimum voltage, maximum voltage change over time, and voltage sample entropy for each discharge cycle; 4) Maximum temperature, minimum temperature, average temperature, temperature difference between maximum and minimum temperature, maximum temperature change over time, and temperature sample entropy for each discharge cycle. The voltage and temperature sample entropy are calculated by performing sample entropy calculations on the voltage and temperature curves for each discharge cycle.

[0122] Since the changing trends of the above 14 characteristic factors are different, in order to analyze the correlation between different characteristic factors and capacity, this invention uses KL divergence, Pearson correlation coefficient, and grey relational analysis for quantification. As shown in Table 1, when using KL divergence as the evaluation index, the average temperature value is the smallest and has the highest correlation with capacity, while the current value is the largest and has the lowest correlation with capacity. When using Pearson correlation coefficient as the evaluation index, the cycle time value is the largest and has the highest correlation with capacity, while the current value is the smallest and has the lowest correlation with capacity. When using grey relational analysis as the evaluation index, the cycle time value is the largest and has the highest correlation with capacity, while the voltage sample entropy value is the smallest and has the lowest correlation with capacity. To verify the impact of each characteristic factor on the accuracy of capacity prediction, capacity prediction was performed separately based on TCN, and the average of six prediction results was taken as the prediction error, which is the root mean square error, as shown in Table 1. The top five factors with high prediction accuracy are cycle time -> average voltage -> voltage sample entropy -> temperature sample entropy -> current value. This shows that correlation evaluation indicators can reflect the importance of different characteristic factors to a certain extent. The Pearson correlation coefficient and TCN prediction results are quite similar, mainly focusing on the characteristic factors with the highest importance ranking. Therefore, different methods yield different main characteristic factors affecting battery SOH, and the appropriate dominant parameters should be selected according to the actual application requirements.

[0123] Table 1. Relationship between different characteristic factors and SOH

[0124]

[0125] To better predict SOH using neural network algorithms, this invention primarily employs the prediction results of TCN. Since different feature factors have varying impacts on capacity, the errors in capacity prediction for each of the five feature factors—cycle time, average voltage, voltage sample entropy, temperature sample entropy, and current value—are all around 10% or less when used individually. Therefore, these five feature factors with smaller errors are selected as input parameters for the subsequent neural network to improve the adaptability of the prediction algorithm and the reliability of the prediction results.

[0126] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing factors affecting the state of harm (SOH) of a battery, characterized in that, Battery aging is accelerated by repeated charge-discharge cycles, and battery capacity, corresponding cycle time, voltage, current and temperature data are obtained. Based on the cycle time, voltage, current and temperature data, 14 characteristic factors are derived as input parameters, and KL divergence, Pearson correlation coefficient and grey relational degree are used as evaluation indicators to quantify the correlation between characteristic factors and capacity. Based on the temporal convolutional network, the input parameters are predicted separately to verify the impact of each feature factor on the accuracy of capacity prediction. The average value of multiple prediction results is taken as the prediction error, thereby obtaining the influence of the feature factors affecting the battery SOH. Finally, the corresponding feature factors are selected as the dominant parameters according to the actual application requirements. The specific characteristic factors include: 1) the time taken for each discharge cycle; 2) the current for each discharge cycle; 3) the maximum voltage, minimum voltage, average voltage, voltage difference between the maximum and minimum voltages, maximum voltage change over time, and voltage sample entropy for each discharge cycle; 4) the maximum temperature, minimum temperature, average temperature, temperature difference between the maximum and minimum temperatures, maximum temperature change over time, and temperature sample entropy for each discharge cycle; wherein the voltage sample entropy and temperature sample entropy are calculated by performing sample entropy calculations on the voltage and temperature curves for each discharge cycle. When KL divergence is used as the evaluation index, the average temperature value is the smallest and has the highest correlation with capacity, while the current value is the largest and has the lowest correlation with capacity. When Pearson correlation coefficient is used as the evaluation index, the cycle time value is the largest and has the highest correlation with capacity, while the current value is the smallest and has the lowest correlation with capacity. When grey relational analysis is used as the evaluation index, the cycle time value is the largest and has the highest correlation with capacity, while the voltage sample entropy value is the smallest and has the lowest correlation with capacity. The construction of the temporal convolutional network includes: (1) Temporal convolutional network modeling is used to establish a mapping relationship between the input sequence and the output sequence, so that the actual output... and predicted output Minimize the error loss between them: Suppose the given input sequence is The expected predicted output is The relationship between the predicted output and the input sequence is as follows: (12) In the formula, Only with time and the previous input sequence Related to future input Irrelevant; (2) Expand causal convolution, specifically: (13) In the formula, For the sequence The Middle The convolution result of 1 element; For filters, also known as convolution kernels; As an expansion factor, when The time was a standard causal volume; Indicates the convolution direction, meaning that the convolution operation is performed only on past data; (3) Add residual blocks: Assume the input of the residual block is The output is After linear transformation and mapping through the activation function, formula (14) is obtained: (14) In the formula, For activation function, for The relational function.

2. The method for analyzing factors affecting SOH of a battery according to claim 1, characterized in that, The KL divergence calculation includes the following steps: set up , Let the probabilities of the two processes be represented, then the KL distance is: (1) And thus obtain , The KL divergence between them is: (2) The KL divergence is a measure of the angle between the probability distributions of two processes. The larger the value, the greater the difference; conversely, the smaller the difference, the smaller the difference. When the two probability distributions are exactly the same, the value is 0. When seeking signals and signal When considering the KL divergence between the pairs of probabilities, assume the probability distributions are as follows: , ; First, calculate the signal. The probability distribution is obtained by using a nonparametric estimation method: ， (3) In the formula, The probability density function after kernel density estimation; A given positive number is called the window width or smoothing parameter; The kernel function is denoted by n, commonly the Gaussian kernel function; n is the number of samples. (4) Where u is the expected value; Similarly, the signal is obtained probability distribution ; Will , Substitute into formula (1) to solve for the signal. and KL distance and The KL divergence value is then calculated using formula (2). .

3. The method for analyzing factors affecting SOH of a battery according to claim 1, characterized in that, The calculation of the Pearson correlation coefficient includes the following steps: The Pearson correlation coefficient is used to measure the degree of linear correlation between two variables: (5) In the formula, , Variables , Expected value; in Its properties are as follows: when When the two variables are positively correlated, it indicates that they are positively correlated. When the two variables are negatively correlated; when When, it indicates that there is no linear correlation between the two variables; when When the expression is true, it indicates that the two variables are perfectly linearly related, that is, they have a functional relationship. when When , it indicates that there is a certain degree of linear correlation between the two variables; and The closer the value is to 1, the stronger the linear relationship between the two variables. The closer a value is to 0, the weaker the linear correlation between the two variables.

4. The method for analyzing factors affecting SOH of a battery according to claim 1, characterized in that, The calculation of the grey relational degree includes the following steps: Assuming a reference sequence and comparison sequences They are represented as follows: (6) (7) In the formula, For the sample size, and All data are sample data; initialization and To reduce the differences in parameters across dimensions: (8) (9) assumed for and exist The grey relational coefficient at time t is then: (10) In the formula, The resolution coefficient; get and The grey relational degree is: (11) In the formula, ; Q is the time value.

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