A Lithium Battery SOC Estimation Method Based on RC Parameter Filtering and AUKF

Abstract

The present invention discloses a method for estimating the state of charge (SOC) of a lithium battery based on resistance-capacitance parameter filtering and AUKF. This method is a method for identifying a resistance-capacitance parameter vector. This method is combined with UKF to construct an adaptive unscented Kalman filter (AUKF) algorithm for the resistance-capacitance parameter vector. Based on gain iteration, the closed-loop control of the system is increased to achieve rapid estimation of the SOC of the lithium battery. A hybrid pulse power characteristic (HPPC) experiment is carried out to establish a battery equivalent model; an intermittent constant current discharge experiment, a dynamic stress test (DST) experiment, and an experiment for estimating the SOC of the battery under aging conditions are carried out. The beneficial effect of the present invention is that it can effectively improve the applicability, convergence, and robustness of the AUKF algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium battery performance detection, and particularly to a method for estimating the state of charge (SOC) of a lithium battery based on resistance-capacitance parameter filtering and AUKF. Background Art

[0002] Accurate estimation of the state of charge (SOC) of a lithium battery helps the battery management system formulate an equalization strategy for the battery pack and extend the life of the battery pack. Research scholars at home and abroad have studied the method for estimating the SOC of a lithium battery by adjusting the initial value P of the error covariance, 0 , the noise covariance Q and R. The above-mentioned methods for estimating the SOC of a lithium battery can be divided into a parameter off-line identification method and a parameter on-line identification method. The parameter off-line identification method and the parameter on-line identification method can obtain time-invariant and time-varying resistance-capacitance parameters respectively, and improve the equivalent circuit model and the SOC estimation accuracy.

[0003] However, the existing parameter on-line identification method has the problem of lack of reasonable constraints on the resistance-capacitance parameters. At the same time, affected by the initial value of the identification strategy and the working conditions, the abnormal jitter phenomenon of the resistance-capacitance parameters is relatively serious, reducing the convergence speed of the SOC and affecting the stability of the algorithm. Summary of the Invention

[0004] The purpose of the present invention is to solve the above problems and design a method for estimating the SOC of a lithium battery based on resistance-capacitance parameter filtering and AUKF.

[0005] A method for estimating the SOC of a lithium battery based on resistance-capacitance parameter filtering and AUKF, the method includes the following contents: constructing a second-order RC lithium battery equivalent circuit model to describe the charge and discharge characteristics of the lithium battery, as Figure 2 shown. Wherein, U oc is the open-circuit voltage of the battery, I is the charge and discharge current of the battery, R L , C L are the electrochemical polarization resistance and polarization capacitance respectively, R S , C S are the concentration polarization resistance and polarization capacitance respectively, U is the terminal voltage of the battery, and R o is the equivalent internal resistance of the battery.

[0006] Set [SOC U L U S T as the state variable of the lithium battery performance, and construct a discrete state space equation:

[0007]

[0008] U = U oc (SOC) - U S -UL -R o I(k) (2)

[0009] Where: U S and U L are the terminal voltages of R S and R L respectively, τ s and τ l are the time constants of R S C S and R L C L respectively, Q c is the battery capacity, Δt is the sampling interval, and k is the discrete time.

[0010] Establish the mapping relationship between U Figure 1 in oc and SOC in Equation (1). Considering the high-order polynomial relationship and hysteresis effect between the open-circuit voltage U OC and SOC, in order to reduce the model error, use the BP neural network model to fit the non-linear relationship between U OC -SOC, as shown in Figure 3 . With a certain step size, take the mean values of SOC and the corresponding U OC during charging and discharging as the training set to obtain Equation (3).

[0011] U OC = NN bp (SOC) (3).

[0012] Identify Figure 1 the unknown RC parameters R o , R S , C S , R L , C L . Considering noise and battery aging, use FFRLS to obtain the RC parameter values; sample the voltage and current data of the lithium battery under working conditions as the input of FFRLS to obtain the online identification results of the RC parameters; take the fixed voltage and current of the battery as the input of FFRLS to obtain the offline identification results of the RC parameters; combine the two identification results, calculate the noise variance, set the gain threshold according to the change characteristics of the Kalman gain, and calculate the adaptive RC parameter vector based on the Kalman gain. The specific implementation method is as follows:

[0013] 1) Define the resistance-capacitance parameter vector based on the online identification method as X k = [R o|k R S|k C S|k R L|k C L|k T and use FFRLS to perform X​k Online identification, the recurrence formula is:

[0014]

[0015] In the formula, θ is the vector of undetermined coefficients, I e is the identity matrix of the same type, λ is the forgetting factor, are I and U from time k-2 to k, K LS is the gain coefficient, P LS is the covariance matrix.

[0016] The parameter X for online identification k may exhibit instability, jitter, negative values, etc. under complex working conditions. To ensure parameter stability, the offline identification results are introduced for parameter correction.

[0017] 2) Define the resistance-capacitance parameter vector for offline identification as to suppress X k jitter and possible outliers. According to Figure 4 the zero-state response and zero-input response of voltage and current in, calculate using FFRLS

[0018]

[0019]

[0020] 3) Add Gaussian white noise to simulate the effects of factors such as the environment and battery aging on . Define the noise term w g = [w o w rs w cs w rl w cl T , and the variance vector σ = [σ o σ rs σ cs σ rl σ cl T . Among them, w o - N(0,σ o ), w rs - N(0,σ rs ), w cs - N(0,σ cs ), w rl - N(0,σ rl ), w cl - N(0,σ cl ). Calculate the values of each element of σ using the variance calculation formula (7).

[0021] ​​

[0022] Among them: σ j and are respectively the j-th elements of σ, X k,j is the j-th element of X k ; To ensure the numerical stability of the Cholesky decomposition operation, the vector elements should be restricted

[0023] 4) According to the obtained X k , and w g , design the adaptive resistance-capacitance parameter vector X a , as shown in Equation (8), and calculate X a by combining the Kalman gain K.

[0024]

[0025] Among them, ε is the step function; γ is the gain threshold.

[0026] 5) Outlier determination. When all the output elements of X k are positive, γ takes 0.1; when the output of X k contains negative numbers, γ becomes a positive integer much larger than K.

[0027] Substitute the RC parameter vector filtering method into the UKF recursion process to construct the AUKF algorithm for lithium battery SOC estimation.

[0028] According to the nonlinear characteristics of the lithium battery output, rewrite Equations (1) and (2) as:

[0029] x k+1 = f(x k , u k , w) (9)

[0030] y k = h(x k , u k , v) (10)

[0031]

[0032] Among them: w, Q are the system process noise and its covariance; v, R are the system measurement noise and its covariance.

[0033] Based on equations (9) to (11), on the basis of the classical UKF, a resistance-capacitance parameter adaptive module is added, and the recursive Kalman gain coefficient is substituted into the resistance-capacitance parameter adaptive module to construct a Kalman gain closed-loop control, realizing the synchronous iteration of the resistance-capacitance parameter vector, improving the algorithm convergence speed and stability, and obtaining the AUKF algorithm. The recursive process is as follows:

[0034] 1) Set 2n + 1 sigma points. According to the state vector x in equation (9) k =[SOC k U L,k U S,k T For the dimension of, n takes the value of 3.

[0035]

[0036] Among them: is the mean value of SOC, U L , U S , P x is the covariance matrix of the state vector. The matrix is defined as the i-th column of the square root matrix obtained after the Cholesky decomposition of (n + λ u )P x ; λ u is the scaling factor, obtained from equation (13).

[0037] λ u =α 2 (n + k i ) - n (13)

[0038] Among them: α is a very small positive number; k i takes 0 in the case of a single state variable and 3 - n in the case of multiple state variables. In this paper, n is 3, so k i takes the value of 0.

[0039] 2) The mean weight W i m and the variance weight W i c of the sigma sampling points are set as

[0040]

[0041]

[0042] Among them: β is a hyperparameter reflecting the high-order state historical information.

[0043] 3) Input the Kalman gain K k at time k into the resistance-capacitance parameter adaptive module to construct a closed-loop feedback, and calculate X at time k in combination with equation (8)​a 。

[0044]

[0045] 4) Optimize the time update process of the sigma sampling points, and substitute X a into Equation (9) to obtain the mean and variance of the one-step predicted state vector as follows:

[0046]

[0047] 5) Update the sampling points of the predicted value of the state vector to

[0048]

[0049] 6) Optimize the measurement update process of the sigma sampling points, and substitute X a into Equation (10) to obtain the mean, variance and covariance of the one-step predicted measurement vector as follows:

[0050]

[0051] 7) Calculate the Kalman gain, state estimation and covariance matrix at time k+1, where x k+1 = [SOC k+1 U L,k+ 1 U S,k+1 ] T 。

[0052]

[0053] Beneficial effects

[0054] A lithium battery SOC estimation method based on RC parameter filtering and AUKF fabricated by using the technical solution of the present invention has the following advantages:

[0055] 1. Use the offline identification results of RC parameters to correct the online identification results, calculate the noise variance, and combine the Kalman gain threshold to implement RC parameter filtering, and construct the AUKF algorithm to achieve rapid estimation of the lithium battery SOC;

[0056] 2. The AUKF algorithm has good convergence, robustness and effectiveness when estimating the lithium battery SOC, and gives the selection range of the gain threshold. The maximum error of the SOC estimation after the AUKF algorithm converges is less than 1%. Description of the drawings

[0057] Figure 1 is a flowchart of a lithium battery SOC estimation method based on RC parameter filtering and AUKF according to the present invention;

[0058] Figure 2is the equivalent circuit model of the lithium battery described in the present invention;

[0059] Figure 3 is the BP neural network diagram described in the present invention;

[0060] Figure 4 is the voltage parameter curve diagram described in the present invention;

[0061] Figure 5 is the physical diagram of the lithium battery test platform described in the present invention;

[0062] Figure 6 is the comparison diagram of HPPC experimental data described in the present invention;

[0063] Figure 7 is the U OC -SOC charge and discharge relationship curve diagram;

[0064] Figure 8 is the current waveform diagram described in the present invention;

[0065] Figure 9 is the time series diagram of online identification of R L and C L ;

[0066] Figure 10 is the SOC estimation diagram under the intermittent constant current discharge condition described in the present invention;

[0067] Figure 11 is the Kalman gain change trend diagram described in the present invention;

[0068] Figure 12 is the P 0 variable convergence experiment comparison diagram;

[0069] Figure 13 is the Q variable convergence experiment comparison diagram described in the present invention;

[0070] Figure 14 is the R variable convergence experiment comparison diagram described in the present invention;

[0071] Figure 15 is the γ variable convergence experiment comparison diagram described in the present invention;

[0072] Figure 16 is the DST experimental current waveform diagram described in the present invention;

[0073] Figure 17 is the SOC estimation experimental data diagram with an initial value of 0.2 described in the present invention;

[0074] Figure 18 is the SOC estimation experimental data diagram with an initial value of 0.5 described in the present invention;

[0075] Figure 19 is the outlier schematic diagram of C S and R S in the present invention;

[0076] Figure 20 is the time series diagram of R S and C S in the present invention;

[0077] Figure 21 is the SOC estimation diagram when there is outlier perturbation in the present invention;

[0078] Figure 22 is the external characteristic curve diagram of the battery in the present invention;

[0079] Figure 23 is the capacity change curve diagram in the present invention;

[0080] Figure 24 is the SOC estimation diagram of the aged battery in the present invention;

[0081] Figure 25 is the U oc -SOC data analysis table;

[0082] Figure 26 is the offline parameter identification table in the present invention; Detailed implementation manners

[0083] Embodiment

[0084] Taking a 18650 type ternary lithium battery with a rated capacity of 1800 mAh, a maximum voltage of 4.2 V, and a cut-off voltage of 2.5 V as the experimental object. Design HPPC experiment, DST experiment, intermittent constant current discharge experiment, and cyclic aging lithium battery SOC estimation experiment.

[0085] According to the "Freedom CAR Battery Test Manual", conduct standard HPPC experiment to establish an equivalent circuit model; design intermittent constant current discharge experiment, and verify the convergence of the designed algorithm according to the absolute error lower than 2%; conduct DST working condition experiment to verify the stability of the algorithm; conduct cyclic aging lithium battery SOC estimation experiment to verify the effectiveness and accuracy of full life cycle SOC estimation based on AUKF algorithm under the condition that the external characteristics of the lithium battery change.

[0086] The experimental equipment is as Figure 5 shown, including a high-performance battery detection platform and a thermostatic and humidistatic chamber. Keep the constant temperature at 26 °C, and the sampling interval is 0.5 s.

[0087] 1. HPPC Experiment and Analysis

[0088] Charge the battery to the maximum voltage of 4.2V and discharge it to the cut-off voltage of 2.5V to conduct the HPPC experiment, as Figure 6 shown. The corresponding U oc -SOC discrete values during discharge and charge are obtained respectively, as shown in Table 1.

[0089] Construct the U oc -SOC mapping relationship according to Table 1, as Figure 7 shown. According to Figure 2 , use the SOC and the corresponding U OC mean value as the training set to construct a BP neural network, and the fitting maximum relative error is 0.1%. Use polynomial fitting as shown in Equation (21), and the maximum relative error is 0.3%. The results show that using the neural network algorithm for U oc -SOC relationship fitting has higher accuracy.

[0090] U OC = 0.9748SOC 5 - 5.533SOC 4 + 9.803SOC 3

[0091] - 6.654SOC 2 + 2.35SOC + 3.24 (21)

[0092] Based on Figure 7 the data, with a step size of 0.1SOC, combine Equation (5) and Equation (6) to offline identify the time-invariant resistance-capacitance parameters, and use the parameter mean value as the effective value of the identification result, as shown in Table 2.

[0093] 2. Convergence experiment and analysis under intermittent constant current discharge conditions

[0094] In the SOC estimation experiment, set a control group to compare with the AUKF combined with the RC parameter vector filtering method:

[0095] 1) Control group 1: Use the UKF algorithm with the online identification result of RC parameters;

[0096] 2) Control group 2: Use the UKF algorithm with the offline identification result of RC parameters.

[0097] Set the initial SOC of the lithium battery discharge to 0.9 and the terminal SOC to 0.6. The battery terminal voltage is measured by a high-precision sensor built into the experimental equipment. The discharge is intermittently static for 1 hour to ensure that the internal temperature of the battery is fully dissipated and reduce the influence of temperature noise on the experimental results. The intermittent constant current discharge current waveform is as Figure 8 shown. Some of the online identification results of RC parameters are as Figure 9 shown.

[0098] The convergence of the SOC estimation is observed through the approximation process of the state variable to the true value. The same P, 0 , Q, and R are selected for Control Group 1, Control Group 2, and AUKF. The results are as Figure 10 shown.

[0099] According to Figure 10 , when performing SOC estimation in Control Group 1, it converges after 300 s, with a relatively low convergence speed, and the maximum error after convergence is less than 1%. In Control Group 2, it quickly approaches the true value within the interval [0 s, 50 s], but the maximum error of SOC is greater than 2% within the interval [50 s, 1250 s], and the convergence performance is poor. When performing SOC estimation based on the AUKF algorithm, it converges within 50 s, and the maximum error of SOC after convergence is less than 1%. The results show that when estimating SOC using the AUKF algorithm, the convergence speed is higher than that of Control Group 1, and the accuracy is higher than that of Control Group 2.

[0100] Analyze the relationship between the changing trend of the Kalman gain and the SOC convergence speed. The change of the Kalman gain within [0 s, 300 s] is intercepted as shown in Figure 11 . According to the principle of the Kalman filtering algorithm, the larger the Kalman gain, the faster the convergence speed. Within [0 s, 50 s], the average Kalman gains of AUKF, Control Group 2, and Control Group 1 are 0.51, 0.5, and 0.42 respectively. Therefore, the AUKF algorithm for estimating SOC has better convergence.

[0101] Different P 0 , Q, and R affect the convergence speed and accuracy of the algorithm, and also have an impact on the changing trend of the Kalman gain. Repeat the experiment by changing P 0 , Q, and R. The results are shown in Figures 12 - 14 respectively.

[0102] From Figure 12 (a) and (b), it can be seen that increasing P 0 can improve the convergence speed of the SOC estimation. There is an overshoot in Control Group 2, and the maximum error after convergence is greater than 2%. The maximum error after convergence in Control Group 1 is less than 1%, but the convergence speed is slow. The convergence speed of AUKF is higher than that of Control Group 1, and the maximum error after convergence is less than 1%.

[0103] From Figure 13 (a), (b) and Figure 14 (a), (b), it can be seen that decreasing Q and R can improve the convergence speed of the SOC estimation. When estimating SOC based on AUKF, it is higher than the convergence speed of Control Group 1 and the estimation accuracy of Control Group 2, and the maximum error after convergence is less than 1%.

[0104] From Figure 12 (c), (d), Figure 13 (c), (d) and Figure 14 (c), (d), it can be seen that changing P 0, Q, and R do not affect the final convergence interval of the AUKF Kalman gain. After 200 s, the Kalman gain converges to the range of [0.05, 0.2], and the gain threshold γ can be adjusted within the range of [0.05, 0.2]. As Figure 15 shown, the convergence curves of the SOC estimation values when the γ values are 0.05, 0.1, 0.15, and 0.2 respectively. After convergence, the maximum error is lower than 1%. Among them, when γ is 0.1 or 0.15, the convergence can be completed within 100 s; when γ is 0.2, the convergence can be completed within 130 s; when γ is 0.05, the convergence can be completed within 160 s. By adjusting the γ value, the convergence performance of the AUKF-estimated SOC can be changed.

[0105] 3. Robustness experiments and analysis under DST conditions

[0106] Design DST experiments to simulate complex conditions. The initial discharge SOC is set to 0.7, and the initial value of the state variable SOC is set to 0.2 to verify the robustness of the SOC estimation. Set the current waveform as Figure 16 shown, and the SOC estimation results are as Figure 17 shown.

[0107] According to Figure 17 , the control group 2 completed convergence after 350 s. After convergence, the maximum SOC error was greater than 2%, and the average error was higher than 1%; the control group 1 completed convergence before 200 s. After convergence, the maximum SOC error was lower than 1%. AUKF converged within 200 s at a convergence speed higher than that of the control group 1, and the maximum SOC error after convergence was lower than 1%.

[0108] Considering the randomness of the initial value of the state variable SOC, change the initial value of the state variable SOC to 0.5, as Figure 18 shown. The control group 2 can quickly approach the true value and complete convergence within 100 s, but there is overshoot, and the average error after convergence is greater than 1.5%, and the maximum error is greater than 2%. The control group 1 completed convergence within 150 s. After convergence, the maximum SOC error was less than 1%. AUKF, on the other hand, completed convergence within 100 s, with a maximum error less than 1%. It estimated SOC with a convergence speed higher than that of the control group 1 and the accuracy of the control group 2, and had good comprehensive performance.

[0109] As Figure 19 (a) and (b) shown, in the early stage of online parameter identification, R S and C S showed numerical jitter, and the amplitudes exceeded 500 F and 0.05 Ω respectively. Moreover, R S and C S showed abnormal negative values around the 10th s. The jitter and abnormal values led to the divergence of the RC link and a non-positive semi-definite matrix that could not be processed by Cholesky decomposition.

[0110] As Figure 20As shown, when jitter and outliers occur, AUKF can avoid perturbations, and R S has an amplitude less than 0.035Ω within [0s, 100s], and C S is less than 100F within [0s, 100s], and R S and C S have no abnormal negative values. At this time, SOC is estimated based on AUKF, as Figure 21 shown. It converges within 100s, and the maximum error after convergence is less than 1%, with good stability.

[0111] In summary, the AUKF algorithm adaptively obtains the resistance-capacitance parameters of the system equation according to the actual working conditions, converges quickly, achieves high precision, and meets the high-robustness requirements under complex working conditions.

[0112] 4. Effectiveness Experiment and Analysis under Battery Aging

[0113] After 0 and 300 charge-discharge cycles of the lithium battery, the voltage characteristics of the HPPC experiment are as Figure 22 shown. After 300 cycles of aging, the external characteristics of the lithium battery change, the terminal voltage decreases, and the maximum voltage difference exceeds 0.3V. To verify the effectiveness of the AUKF algorithm for SOC estimation of lithium batteries, a DST working condition experiment is designed under battery aging.

[0114] Set the initial discharge SOC to 0.7 and the initial value of the state variable SOC estimation to 0.4, and correct Q using the capacity change curve measured by the experimental instrument c to eliminate the influence of the discharge rate on the SOC estimation result. As Figure 23 shown, the capacity ratio represents the ratio of the current capacity to the maximum capacity. After 300 cycles, Q c is 0.9 times the maximum capacity. The SOC estimation result is as Figure 24 shown.

[0115] It can be seen from Figure 24 that battery aging exacerbates the estimation error of control group 2. The average error after convergence exceeds 2%, and the maximum error exceeds 2.5%. The maximum SOC estimation error of control group 1 and the AUKF algorithm is less than 1%, but the AUKF algorithm completes convergence 20s earlier than control group 1.

[0116] It should be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or device comprising said element.

[0117] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that those skilled in the art of the present technology may make to some parts thereof all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A lithium battery SOC estimation method based on RC parameter filtering and AUKF, characterized in that, the method comprises the following steps: Step 1, construct a second-order RC lithium battery equivalent circuit model to describe the charging and discharging characteristics of the lithium battery. Among them, U oc is the open-circuit voltage of the battery, I is the charging and discharging current of the battery, R L , C L are the electrochemical polarization resistance and polarization capacitance respectively, R S , C S are the concentration polarization resistance and polarization capacitance respectively, U is the terminal voltage of the battery, R o is the equivalent internal resistance of the battery, set [SOC U L U S T as the state variable of the lithium battery performance, and construct the discrete state-space equation:​ U = U oc (SOC) - U S -U L -R o I(k) (2) Where: U S and U L are the terminal voltages of R S and R L respectively, τ s and τ l are the time constants R S C S and R L C L respectively, Q c is the battery capacity, Δt is the sampling interval, and k is the discrete time; Step 2: Identify the unknown RC parameters R o , R S , C S , R L , C L in the second-order RC lithium battery equivalent circuit model. Use FFRLS to obtain the RC parameter values. Sample the voltage and current data of the lithium battery under the working conditions as the input of FFRLS to obtain the online identification result of the RC parameters. Then, use the fixed voltage and current of the battery as the input of FFRLS to obtain the offline identification result of the RC parameters. Combine the two identification results, calculate the noise variance, set the gain threshold according to the change characteristics of the Kalman gain, and thus obtain the adaptive RC parameter vector calculated based on the Kalman gain; Step three, substituting the RC parameter vector filtering method into the UKF recursion process to construct the AUKF algorithm for lithium battery SOC estimation. According to the non-linear characteristics of the lithium battery output, rewrite equations (1) and (2) as: x k+1 = f(x k , u k , w) (9) y k = h(x k , u k , v) (10) where: w and Q are the system process noise and its covariance; v and R are the system measurement noise and its covariance. From equations (9) to (11), on the basis of the classical UKF, add an RC parameter adaptive module, and substitute the recursive Kalman gain coefficient into the RC parameter adaptive module to construct a Kalman gain closed-loop control to obtain the AUKF algorithm. The recursion process is as follows: 1) Set 2n + 1 sigma points. According to the state vector x in Equation (9) k = [SOC k U L,k U S,k T For the dimension, n takes the value of 3​ Wherein: is the mean of SOC and U L and U S , P x is the covariance matrix of the state vector, and the matrix is defined as the i-th column of the square root matrix obtained after Cholesky decomposition of (n + λ u )P x ; λ u is the scaling factor, obtained from Equation (13). λ u = α 2 (n + k i ) - n (13) where: α is a very small positive number; k i is 0 in the case of a single state variable and 3 - n in the case of multiple state variables, where n is 3, so k i takes the value of 0 2) Mean weight W of sigma sampling points i m and variance weight W i c Set to where: β is a hyperparameter reflecting the high-order state historical information, 3) Input the Kalman gain K at time k k into the resistance-capacitance parameter adaptive module, construct a closed-loop feedback, and calculate X at time k in combination with Equation (8) a , 4) Optimize the time update process of the sigma sampling points, and substitute X a into Equation (9), and the mean and variance of the one-step predicted state vector are obtained as follows: 5) Update the sampling points of the predicted value of the state vector as: 6) Optimize the measurement update process of the sigma sampling points, and substitute X a into Equation (10) to obtain the mean, variance, and covariance of the one-step predicted measurement vector as follows: 7) Calculate the Kalman gain, state estimate, and covariance matrix at time k+1, where x k+1 = [SOC k+1 U L,k+1 U S,k+1 T ,​ The mapping relationship between U in the established second-order RC lithium battery equivalent circuit model and SOC in Equation (1), and the BP neural network model is used to fit the non-linear relationship between U oc -SOC. With a certain step size, the charging and discharging means of SOC and the corresponding U OC are used as the training set to obtain Equation (3). OC ​ U OC = NN bp (SOC) (3); The specific implementation of calculating the adaptive RC parameter vector based on the Kalman gain obtained in step two is as follows: 1) Define the resistance-capacitance parameter vector based on the online identification method as X k = [R o|k R S|k C S|k R L|k C L|k T , and use FFRLS to perform online identification of X k . The recurrence formula is as follows:​ where θ is the vector of undetermined coefficients, I e is an identity matrix of the same type, λ is the forgetting factor, are I and U from time k - 2 to time k, K LS is the gain coefficient, P LS is the covariance matrix, Parameter X for online identification k Under complex working conditions, instability, jitter, negative values, etc. may occur. To ensure the stability of the parameters, the offline identification results are introduced for parameter correction. 2) Define the resistance-capacitance parameter vector for offline identification as Suppress X k jitter and possible outliers, calculated using FFRLS 3) Define the noise term w g = [w o w rs w cs w rl w cl T , and the variance vector σ = [σ o σ rs σ cs σ rl σ cl T , where w o ~N(0, σ o ), w rs ~N(0, σ rs ), w cs ~N(0, σ cs ), w rl ~N(0, σ rl ), w cl ~N(0, σ cl ). Calculate the values of each element of σ according to the variance calculation formula (7).​​ Where: σ j and are the j-th elements of σ and respectively, and X k,j is the j-th element of X k . To ensure the numerical stability of the Cholesky decomposition operation, the vector elements should be restricted 4) According to the obtained X k , and w g , design the adaptive resistance-capacitance parameter vector X a , as shown in Equation (8), and calculate X a , where ε is the step function; γ is the gain threshold, 5) When X k When all output elements are positive, γ takes 0.1; when X k When the output contains negative numbers, γ becomes a positive integer much larger than K.

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