A battery pack state of charge estimation method considering cell inconsistency

Abstract

The application discloses a battery pack state of charge estimation method considering inconsistency of single bodies, and first establishes a battery pack inconsistency compensation model, then compensates the inconsistency degree by using virtual measurement noise, next obtains joint posterior probability of the virtual noise mean and variance and state quantity by using variational Bayesian inference, and finally realizes accurate battery pack SOC estimation by using an unscented Kalman filtering algorithm for recursion. The inconsistency compensation model of the application can reduce the influence of the inconsistency of single bodies on the SOC estimation precision while not significantly increasing the calculation amount, and has the characteristics of high estimation precision and good real-time performance.

Description

Technical Field

[0001] This invention belongs to the field of battery technology, specifically relating to a method for estimating the state of charge of a battery pack. Background Technology

[0002] The state of charge (SOC) of a battery pack reflects its remaining usable capacity and is a crucial indicator for evaluating its current performance. It is also a prerequisite for other functions such as battery balancing, safety control, and fault diagnosis, and is essential for ensuring the safety of electric vehicles and extending the cycle life of the battery pack. However, SOC is the internal state of the battery, which is usually difficult to measure directly and changes in real time due to various factors such as operating conditions, temperature, and aging. Therefore, accurate online estimation of battery SOC is extremely difficult. Especially for the battery energy storage system of electric vehicles, since the capacity and voltage provided by a single lithium-ion battery cannot meet the needs of an electric vehicle, battery packs composed of dozens to thousands of individual cells connected in series and parallel are typically required to provide energy. However, due to limitations in manufacturing processes, inconsistencies in the operating conditions of individual cells, and different aging processes, a certain degree of inconsistency is inevitable in battery packs. Ignoring these inconsistencies and treating the battery pack as a single "large cell" may severely affect the accuracy of battery pack state estimation. Performing state estimation and parameter identification for each individual cell would be computationally prohibitively complex.

[0003] Current methods for estimating the State of Charge (SOC) of power battery packs involving inconsistencies among individual cells mainly fall into three categories: methods based on large-cell models, methods based on representative-cell models, and methods based on average-difference models. Large-cell models treat the entire battery pack as a single large cell for SOC estimation, ignoring the impact of inconsistencies. Therefore, their accuracy is relatively poor, but they are the simplest and require less computation. Representative-cell models require selecting one or several representative cells and calculating their SOC to obtain the overall SOC estimate for the battery pack. However, different selection criteria for representative cells can lead to significant differences in the SOC estimates. The average-difference model first establishes an average model for all individual cells, then establishes a difference model to obtain the difference between each cell and the average model, thus obtaining the SOC estimate for each cell. This method has high accuracy, but the model is complex, computationally intensive, and real-time performance is difficult to guarantee. Therefore, achieving accurate real-time SOC estimation of the battery pack while considering consistency factors remains a pressing problem to be solved. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a method for estimating the state of charge (SOC) of a battery pack considering individual cell inconsistencies. First, an inconsistency compensation model for the battery pack is established. Then, virtual measurement noise is used to compensate for the degree of inconsistency. Next, variational Bayesian inference is used to obtain the joint posterior probability of the virtual noise mean and variance with the state variables. Finally, an unscented Kalman filter algorithm is used for recursion, ultimately achieving accurate SOC estimation of the battery pack. The inconsistency compensation model of this invention reduces the impact of individual cell inconsistencies on the accuracy of SOC estimation without significantly increasing computational load, and features high estimation accuracy and good real-time performance.

[0005] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0006] Step 1: Treat the battery pack as a single battery and establish an equivalent battery model;

[0007] A second-order RC network was selected as the equivalent circuit model of the battery. The various parameters of the battery model were identified through HPPC experiments on the hybrid pulse power characteristics of the battery, including the battery's ohmic internal resistance R0, the two polarization resistors R1 and R2, and the two polarization capacitors C1 and C2. The battery terminal voltage after resting was collected as the open-circuit voltage U. oc Calibrate the relationship curve between open-circuit voltage and SOC;

[0008] Step 2: Establish an inconsistency compensation model and construct the system state equation and measurement equation;

[0009] The state-space equations for the inconsistency compensation model are shown below:

[0010]

[0011] Where k represents time; x k The system state variable x at time k k =[SOC k U 1,k U 2,k ] T SOC k U represents the state of charge of the battery at time k. 1,k U 2,k These represent the terminal voltages of the two RC loops at time k; w k This represents process noise, which follows a zero-mean covariance of Q. k Gaussian distribution; y k This represents the system observation value at time k, here it is the terminal voltage measurement value U. k ξ k =h * (x k )+v k, representing the system's virtual measurement noise, used to compensate for inconsistencies in measurement noise h. * (x k ) and the original system measurement noise v k The sum, treating it as a whole for calculation, ξ k The mean and covariance are both unknown, and its mean is expressed as... It indicates that its covariance is expressed as express;

[0012] f(·) and h(·) represent the nonlinear state transfer function and observation function, respectively, and their expressions are as follows:

[0013]

[0014] h(·)=U k =U OC (SOC k )-U 1,k -U 2,k -I k R0

[0015] Among them, I k R0 is the charging and discharging current of the battery pack, R1 and R2 represent the polarization resistances in the two loops, τ1 = R1C1 and τ2 = R2C2 represent the time constants of the two RC loops in the model, and U k This is the terminal voltage value at time k, which is also the output value of the model. η is the Coulomb efficiency, Δt is the sampling period, and Q... max U is the rated capacity of the battery. OC (SOC k The curve shows the relationship between the battery open-circuit voltage and the state of charge (SOC).

[0016] Step 3: Approximate the posterior distribution of the system state and the mean and variance of the virtual measurement noise using variational Bayesian inference. This leads to the state estimation result, where y 1:k This represents all measurements from the beginning to time k;

[0017] Step 3-1: Derive the original joint posterior probability distribution using the Bayesian filtering algorithm;

[0018] Based on the Chapman-Kolmogorov equation, the joint predicted distribution of the system state, virtual noise mean, and variance is obtained:

[0019]

[0020] Using the measured values ​​at the next time step and the aforementioned predicted probability distribution, the posterior distribution of the joint probability can be recursively obtained using Bayes' theorem:

[0021]

[0022] Step 3-2: Approximate the joint posterior probability using variational Bayesian inference;

[0023] According to variational Bayesian inference, the product of three marginal distributions approximates the joint posterior probability distribution, as shown below:

[0024]

[0025] Step 3-3: Obtain the characteristics of the three marginal distributions by minimizing the KL divergence;

[0026] The marginal distributions are obtained by minimizing the KL divergence of the product of the true joint posterior distribution and the three marginal distributions. q x (x k They are respectively:

[0027]

[0028]

[0029]

[0030] in,

[0031]

[0032]

[0033]

[0034] That is, assuming the mean of the virtual measurement noise follows a mean of variance is Gaussian distribution, It is its variance adjustment coefficient; the variance of the virtual measurement noise follows an inverse gamma distribution; assuming it is a diagonal matrix, it is expressed as... d is the dimension of the measurement variable. These are the two parameters of the inverse gamma distribution; These are the mean and variance of the state variables;

[0035] Through derivation and calculation, we obtain:

[0036] logq x (x k ) follows a mean of m k Covariance is P k * The Gaussian distribution of is given by the recurrence relation as follows:

[0037]

[0038]

[0039] Follows the mean η k The variance is The Gaussian distribution of is given by the recurrence relation as follows:

[0040]

[0041]

[0042] The sum of the products of d new independent Inv-Gamma distributions gives the parameters of the new Inv-Gamma distribution:

[0043]

[0044]

[0045] Based on the properties of the Inv-Gamma distribution, the estimated value of the measurement noise variance is:

[0046]

[0047] Thus, the statistical characteristics of the mean and variance of the virtual noise are derived;

[0048] Step 4: Combining variational Bayesian inference with unscented Kalman filtering, a method based on variational Bayesian unscented Kalman filtering is proposed to estimate the battery pack SOC under inconsistent conditions; the specific steps are as follows:

[0049] Step 4-1: Initialize system parameters, including variational Bayesian initial parameters, system initial state, and covariance: x0, m0, P0, η0, κ0, α i,0 β i,0 ;

[0050] Step 4-2: Prediction Step;

[0051] 1) Unscented transformation, calculate the sigma point and corresponding weights:

[0052]

[0053]

[0054] Among them, W i c and W i m Here, λ represents the weighting coefficients for the state mean and covariance, d is the dimension of the state variables, and λ is the weighting coefficient for the state variables. x For a composite coefficient, 0 <ax <1,b x =2;

[0055] 2) Calculate the predicted values ​​of the state variables and the predicted value of the state covariance:

[0056]

[0057]

[0058]

[0059] 3) Calculate the predicted values ​​of the variational Bayes parameters:

[0060] α k|k-1,i =μα k-1|k-1,i

[0061] β k|k-1,i =μβ k-1|k-1,i

[0062] η k|k-1 =η k-1|k-1 +1

[0063]

[0064] Step 4-3: Update step; implemented through N iterations, including the following steps:

[0065] Step 4-3-1: Initialization, let α k|k,i =α k|k-1,i +1, for n = 0: N-1, iterate through the following steps:

[0066] Step 4-3-2: Calculate the predicted measurement value;

[0067] First of all, regarding Perform another unscented transformation to obtain the sigma point under one-step prediction:

[0068]

[0069] The predicted measurement values ​​are then calculated as follows:

[0070]

[0071]

[0072] Step 4-3-3: Variational Bayesian iterative process;

[0073] 1) Calculate the covariance P of the predicted measurement. yy and the cross-covariance P between predicted measurements and state vectors xy :

[0074]

[0075]

[0076] 2) Calculate the Kalman gain, state estimate, and covariance:

[0077]

[0078]

[0079]

[0080] 3) Calculate the virtual noise mean η and the parameter β of the inverse gamma distribution of the virtual noise variance:

[0081]

[0082]

[0083] Step 4-3-4: Iterate through steps 4-3-2 to 4-3-3 until the parameters converge or the maximum number of iterations is reached;

[0084] Step 4-3-5: Convert the converged estimate η k|k , x k|k P k|k This value is used as the final estimate at time k and fed into step 4-2 to continue filtering at subsequent times until the state estimate at each time is completed.

[0085] Preferably, N is 2 to 10.

[0086] The beneficial effects of this invention are as follows:

[0087] This invention establishes an inconsistency compensation model that utilizes virtual measurement noise to compensate for battery pack inconsistencies. Simultaneously, it combines variational Bayesian inference with unscented Kalman filtering to estimate the battery pack's state of charge (SOC). Experimental results show that the inconsistency compensation model can reduce the impact of individual cell inconsistencies on SOC estimation accuracy without significantly increasing computational load, exhibiting high estimation accuracy and good real-time performance. Attached Figure Description

[0088] Figure 1 The flowcharts for the present invention are as follows: (a) Overall steps of the inconsistent battery pack SOC estimation method, and (b) Flowchart of the variational Bayesian unscented Kalman filter algorithm.

[0089] Figure 2 This is a second-order RC equivalent circuit model according to an embodiment of the present invention.

[0090] Figure 3 This is the SOC estimation of the battery pack under UDDS conditions when SOC0 = 0.7 in an embodiment of the present invention.

[0091] Figure 4 This refers to the SOC error of the battery pack under UDDS conditions when SOC0 = 0.7 in an embodiment of the present invention. Detailed Implementation

[0092] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0093] In this embodiment, a battery pack is composed of six 18650 lithium batteries connected in series. After 150 cycles of aging, the battery pack is subjected to operational condition testing. Experimental data are obtained through capacity testing, HPPC operational condition testing, UDDS operational condition testing, and NEDC operational condition testing.

[0094] like Figure 1 As shown, the battery pack state-of-charge estimation method based on variational Bayesian unscented Kalman filtering under inconsistency conditions includes the following steps:

[0095] 1. A second-order RC model is selected as the battery equivalent circuit model, such as... Figure 2 As shown. Through battery hybrid pulse power characteristic (HPPC) experiments, the parameters of the battery model were identified, yielding a set of parameter values: R0 = 0.5076Ω, R1 = 0.1592Ω, R2 = 1.8595Ω, C1 = 818.8974F, C2 = 8.7859 × 10⁻⁶. 4 F, and by obtaining the open-circuit voltage values ​​under different SOC conditions, the OCV-SOC curve is fitted and expressed as:

[0096] U oc = -515.59 × SOC 8 +1.9340×10 3 ×SOC 7 -2.8640×10 3 ×SOC 6 +2.1254×10 3 ×SOC 5

[0097] -852.62×SOC 4 +217.23×SOC 3 -53.08×SOC 2 +13.399×SOC 1 +19.935

[0098] 2. Establish an inconsistency compensation model and construct the system state equation and measurement equation. Using virtual noise compensation technology, an additive non-zero mean measurement noise is added to the original state-space equations to compensate for the impact of battery pack inconsistencies. Therefore, the battery pack SOC estimation problem with inconsistencies is transformed into a battery pack SOC estimation problem with uncertain measurement errors.

[0099] The state-space equations of the large battery compensation model are shown below:

[0100]

[0101] Where k represents time; x k The system state variable x at time k k =[SOC k U 1,k U 2,k ] T SOC k U represents the state of charge of the battery at time k. 1,k U 2,k These represent the terminal voltages of the two RC loops at time k; w k This represents process noise, which follows a zero-mean covariance of Q. k Gaussian distribution; y k This represents the system observation value at time k, here it is the terminal voltage measurement value U. k ξ k =h * (x k )+v k , representing the system's virtual measurement noise, is the measurement noise h used to compensate for inconsistencies. * (x k ) and the original system measurement noise v k The sum. Treat it as a whole and calculate ξ. k The mean and covariance are both unknown, and its mean is expressed as... It indicates that its covariance is expressed as express.

[0102] f(·) and h(·) represent the nonlinear state transfer function and observation function, respectively, and their expressions are as follows:

[0103]

[0104] h(·)=U k =U OC (SOC k )-U 1,k -U 2,k -I k R0

[0105] Among them, Ik R0 is the charging and discharging current of the battery pack, R1 and R2 represent the polarization resistances in the two loops, τ1 = R1C1 and τ2 = R2C2 represent the time constants of the two RC loops in the model, and U k This is the terminal voltage value at time k, which is also the output value of the model. η is the Coulomb efficiency, Δt is the sampling period, and Q... max U is the rated capacity of the battery. OC (SOC k () represents the battery open-circuit voltage.

[0106] 3: Use variational Bayesian inference to approximate the posterior distribution of the system state and the mean and variance of virtual measurement noise.

[0107] Variational Bayesian inference is used to approximate the posterior distributions of the system state and the mean and variance of the virtual measurement noise. Here, all measurements are taken from the beginning to time k, thus yielding the state estimation result.

[0108] 3-1: The original joint posterior probability distribution is derived using the Bayesian filtering algorithm. According to the Chapman-Kolmogorov equation, the joint predicted distribution of the system state, the mean of the virtual noise, and its variance can be obtained:

[0109]

[0110] Based on the measured values ​​at the next time step and the aforementioned predicted probability distribution, the posterior distribution of the joint probability can be recursively derived using Bayes' theorem:

[0111]

[0112] 3-2 Approximate the joint posterior probability through variational Bayesian inference.

[0113] Based on the fundamental idea of ​​variational Bayes, the final posterior joint probability distribution can be approximated using three easily tractable marginal distributions, as shown below:

[0114]

[0115] 3-3 The properties of the three marginal distributions are obtained by minimizing the KL divergence.

[0116] The Kullback-Leibler divergence between two distributions is typically used to measure whether they are consistent. Therefore, the marginal distributions can be obtained by minimizing the KL divergence of the product of the true joint posterior distribution and the three marginal distributions. q x (x k They are respectively:

[0117]

[0118]

[0119]

[0120]

[0121] in,

[0122]

[0123] That is, assuming the mean of the virtual measurement noise follows a mean of variance is Gaussian distribution, This is its variance adjustment coefficient. The variance of the virtual measurement noise follows an Inv-Gamma distribution. Assuming it is a diagonal matrix, it can be represented as... d is the dimension of the measurement variable. These are the two parameters of the inverse gamma distribution.

[0124] These are the mean and variance of the state variables.

[0125] Through derivation and calculation, we can obtain:

[0126] logq x (x k ) follows a mean of m k Covariance is P k * The Gaussian distribution, with the recurrence formula as follows:

[0127]

[0128]

[0129] Follows the mean η k The variance is The Gaussian distribution, with the recurrence formula as follows:

[0130]

[0131]

[0132] The sum of the products of d new independent Inv-Gamma distributions gives the parameters of the new Inv-Gamma distribution:

[0133]

[0134]

[0135] Based on the properties of the Inv-Gamma distribution, the estimated value of the measurement noise variance is...

[0136]

[0137] Therefore, the statistical characteristics of the mean and variance of the virtual noise can be derived.

[0138] 4: Using variational Bayesian unscented Kalman filtering to estimate the state of charge (SOC) of the battery pack.

[0139] 4-1: Initialize system parameters. The initial system state and covariance are: x0 = [0.7, 0, 0] T P0 = [1 0 0; 00.1 0; 0 0 0.1], the system noise covariance is Q0, and the diagonal is 4 × 10⁻⁶. -4 A diagonal matrix.

[0140] The initial values ​​for the variational Bayesian iteration are: η0 = 0.001, κ0 = 0.01, α i,0 =1000, β i,0 =1, measurement noise variance adjustment coefficient μ = 0.76, variational Bayes iteration number N = 10.

[0141] Unscented transformation correlation coefficient initialization: dimensionality of state variables d = 3

[0142] Parameters required to calculate the sigma point: b x =2,a x =0.02,λ x =a 2 ×dd

[0143] 4-2: Prediction Step

[0144] Unscented transformation. Calculate the sigma points and their corresponding weights.

[0145]

[0146]

[0147] 2) Calculate the predicted values ​​of the state variables and the predicted values ​​of the state covariance.

[0148]

[0149]

[0150]

[0151] 3) Calculate the predicted values ​​of the variational Bayes parameters.

[0152] α k|k-1,i =μα k-1|k-1,i

[0153] β k|k-1,i =μβ k-1|k-1,i

[0154] η k|k-1 =η k-1|k-1 +1

[0155]

[0156] 4-3: Update Step. This is achieved through N iterations (N is typically 2-10), and mainly includes the following steps:

[0157] 4-3-1: Setting the initial values ​​of variational Bayes parameters: The initial values ​​for iterating the state variables are... as well as α k|k,i =α k|k-1,i +1. The number of iterations is n = 0:N-1.

[0158] 4-3-2: Calculate the predicted measurement value.

[0159] First of all, regarding Perform another unscented transformation to obtain the sigma point under one-step prediction:

[0160]

[0161] The predicted measurement values ​​are then calculated as follows:

[0162]

[0163]

[0164] 4-3-3: Variational Bayesian Iterative Process.

[0165] 1) Calculate the covariance P of the predicted measurement. yy and the cross-covariance P between predicted measurements and state vectors xy :

[0166]

[0167]

[0168] 2) Calculate the Kalman gain, state estimate, and covariance.

[0169]

[0170]

[0171]

[0172] 3) Calculate the virtual noise mean η and the parameter β of the inverse gamma distribution of the virtual noise variance.

[0173]

[0174]

[0175] 4-3-4: Iterate through steps 4-3-2 to 4-3-3 until the maximum number of iterations is reached.

[0176] 4-3-5: The converged parameter η k|k , x k|k P k|k As the final estimate at time k, it is fed into step 4-2 to continue filtering for subsequent times until the state estimate for each time is completed.

[0177] Simulation results: The estimated SOC of the battery pack is as follows Figure 3 , Figure 4 As shown. Figure 3 The graph shows the SOC estimation results of the battery pack under UDDS conditions. The circular icon curve represents the true SOC value calculated by the ampere-hour integration method, the star icon curve represents the SOC estimation result obtained by using the large battery model and applying unscented Kalman filtering, and the square icon curve represents the SOC estimation result obtained by using the inconsistency compensation model and applying variational Bayesian unscented Kalman filtering. Figure 4 This relates to the SOC estimation errors of the traditional large-cell method and the VBUKF inconsistency compensation model method proposed in this invention. Figure 3 and Figure 4 It can be seen that the method proposed in this invention is closer to the true value and has a smaller SOC error, while the ordinary large battery model shows a significant increasing trend in SOC error in the later stages of discharge. This indicates that the method proposed in this invention can significantly reduce the impact of cell inconsistency on the accuracy of SOC estimation, resulting in higher estimation accuracy.

Claims

1. A method for estimating the state of charge (SOC) of a battery pack considering individual cell inconsistencies, characterized in that, Includes the following steps: Step 1: Treat the battery pack as a single battery and establish an equivalent battery model; A second-order RC network was selected as the equivalent circuit model of the battery. The various parameters of the battery model were identified through HPPC experiments on the hybrid pulse power characteristics of the battery, including the battery's ohmic internal resistance R0, the two polarization resistors R1 and R2, and the two polarization capacitors C1 and C2. The battery terminal voltage after resting was collected as the open-circuit voltage U. oc Calibrate the relationship curve between open-circuit voltage and SOC; Step 2: Establish an inconsistency compensation model and construct the system state equation and measurement equation; The state-space equations for the inconsistency compensation model are shown below: Where k represents time; x k The system state variable x at time k k =[SOC k U 1,k U 2,k ] T SOC k U represents the state of charge of the battery at time k. 1,k U 2,k These represent the terminal voltages of the two RC loops at time k; w k This represents process noise, which follows a zero-mean covariance of Q. k Gaussian distribution; y k This represents the system observation value at time k, here it is the terminal voltage measurement value U. k ξ k =h * (x k )+v k , representing the system's virtual measurement noise, used to compensate for inconsistencies in measurement noise h. * (x k ) and the original system measurement noise v k The sum, treating it as a whole for calculation, ξ k The mean and covariance are both unknown, and its mean is expressed as... It indicates that its covariance is expressed as express; f(·) and h(·) represent the nonlinear state transfer function and observation function, respectively, and their expressions are as follows: h(·)=U k =U OC (SOC k )-IN 1,k -IN 2,k -AND k R0 Among them, I k R0 is the charging and discharging current of the battery pack, R1 and R2 represent the polarization resistances in the two loops, τ1 = R1C1 and τ2 = R2C2 represent the time constants of the two RC loops in the model, and U k It is the terminal voltage value at time k, which is also the output value of the model; η is the coulomb efficiency, Δt is the sampling period, and Q... max U is the rated capacity of the battery. OC (SOC k The curve shows the relationship between the battery open-circuit voltage and the state of charge (SOC). Step 3: Approximate the posterior distribution of the system state and the mean and variance of the virtual measurement noise using variational Bayesian inference. This leads to the state estimation result, where y 1:k This represents all measurements from the beginning to time k; Step 3-1: Derive the original joint posterior probability distribution using the Bayesian filtering algorithm; Based on the Chapman-Kolmogorov equation, the joint predicted distribution of the system state, virtual noise mean, and variance is obtained: Using the measured values ​​at the next time step and the predicted probability distribution mentioned above, the posterior distribution of the joint probability can be recursively obtained according to Bayes' theorem: Step 3-2: Approximate the joint posterior probability using variational Bayesian inference; According to variational Bayesian inference, the product of three marginal distributions approximates the joint posterior probability distribution, as shown below: Step 3-3: Obtain the characteristics of the three marginal distributions by minimizing the KL divergence; The marginal distributions are obtained by minimizing the KL divergence of the product of the true joint posterior distribution and the three marginal distributions. q x (x k They are respectively: in, That is, assuming the mean of the virtual measurement noise follows a mean of variance is Gaussian distribution, It is its variance adjustment coefficient; the variance of the virtual measurement noise follows an inverse gamma distribution; assuming it is a diagonal matrix, it is expressed as... d is the dimension of the measurement variable. These are the two parameters of the inverse gamma distribution; These are the mean and variance of the state variables; Through derivation and calculation, we obtain: logq x (x k ) follows a mean of m k Covariance is P k * The Gaussian distribution of is given by the recurrence relation as follows: Follows the mean η k The variance is The Gaussian distribution of is given by the recurrence relation as follows: The sum of the products of d new independent Inv-Gamma distributions gives the parameters of the new Inv-Gamma distribution: Based on the properties of the Inv-Gamma distribution, the estimated value of the measurement noise variance is: Thus, the statistical characteristics of the mean and variance of the virtual noise are derived; Step 4: Combining variational Bayesian inference with unscented Kalman filtering, a method based on variational Bayesian unscented Kalman filtering is proposed to estimate the battery pack SOC under inconsistent conditions; the specific steps are as follows: Step 4-1: Initialize system parameters, including variational Bayesian initial parameters, system initial state, and covariance: x0, m0, P0, η0, κ0, α i,0 β i,0 ; Step 4-2: Prediction Step; 1) Unscented transformation, calculate the sigma point and corresponding weights: Among them, W i c and W i m Here, λ represents the weighting coefficients for the state mean and covariance, d is the dimension of the state variables, and λ is the weighting coefficient for the state variables. x For a composite coefficient, 0 x <1,b x =2;​ 2) Calculate the predicted values ​​of the state variables and the predicted value of the state covariance: 3) Calculate the predicted values ​​of the variational Bayes parameters: a k|k-1,i =ma k-1|k-1,i b k|k-1,i =mv k-1|k-1,i or k|k-1 =the k-1|k-1 +1 Step 4-3: Update step; implemented through N iterations, including the following steps: Step 4-3-1: Initialization, let α k|k,i =α k|k-1,i +1, for n = 0: N-1, iterate through the following steps: Step 4-3-2: Calculate the predicted measurement value; First of all, regarding Perform another unscented transformation to obtain the sigma point under one-step prediction: The predicted measurement values ​​are then calculated as follows: Step 4-3-3: Variational Bayesian iterative process; 1) Calculate the covariance P of the predicted measurement. yy and the cross-covariance P between predicted measurements and state vectors xy : 2) Calculate the Kalman gain, state estimate, and covariance: 3) Calculate the virtual noise mean η and the parameter β of the inverse gamma distribution of the virtual noise variance: Step 4-3-4: Iterate through steps 4-3-2 to 4-3-3 until the parameters converge or the maximum number of iterations is reached; Step 4-3-5: Convert the converged estimate η k|k , x k|k P k|k This value is used as the final estimate at time k and fed into step 4-2 to continue filtering at subsequent times until the state estimate at each time is completed.

2. The method for estimating the state of charge of a battery pack considering the inconsistency of individual cells according to claim 1, characterized in that, The value of N is 2 to 10.

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