Systematic interval optimization method of forgetting factor in parameter identification of lithium battery equivalent circuit model

Abstract

The application discloses a systematic interval optimization method for a forgetting factor in parameter identification of a lithium battery equivalent circuit model, and belongs to the technical field of battery management. The method comprises the following steps: firstly, obtaining initial values of parameters based on a standard recursive least square method; then, selecting a plurality of forgetting factors in a preset interval, respectively performing recursive least square identification with the forgetting factors, and obtaining parameter identification sequences; then, calculating root mean square trends of the parameter sequences with respect to the forgetting factors, and determining a forgetting factor subinterval at which each parameter keeps stable convergence; finally, obtaining a common intersection of all the subintervals as an optimized interval, and taking a middle value of the optimized interval as a recommended forgetting factor. The application overcomes blindness in empirical selection, can automatically determine an optimal forgetting factor suitable for current data, and improves convergence, stability and precision of online parameter identification.

Description

Technical Field

[0001] This invention belongs to the field of battery management technology and relates to a systematic interval optimization method for forgetting factors in the identification of parameters of equivalent circuit model of lithium battery. Background Technology

[0002] As a core component of electric vehicles and energy storage systems, the accurate estimation of the states of charge (SOC) and state of health (SOH) of lithium-ion batteries relies on high-precision battery models. Thevenin equivalent circuit model is widely used due to its good balance between complexity and accuracy. Recursive least squares is one of the mainstream algorithms for online parameter identification. To track the time-varying characteristics of the battery, a forgetting factor is often introduced, forming a recursive least squares method with a forgetting factor λ.

[0003] The value of the forgetting factor λ is crucial to the identification performance. A closer λ to 1 results in stronger algorithm memory but slower tracking of parameter changes; a smaller λ provides stronger tracking but is more prone to estimation oscillations due to noise or insufficient data utilization. Currently, λ is largely determined empirically, lacking systematic guidance. When faced with different batteries, operating conditions, or variations in data quality, a fixed λ value is unlikely to maintain optimal performance, leading to decreased model accuracy and consequently affecting the reliability of battery state estimation.

[0004] Therefore, there is an urgent need for a systematic and verifiable method for optimizing the forgetting factor to automatically determine the optimal value that adapts to specific data characteristics and improve the robustness and accuracy of parameter identification. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies that rely on empirical selection of the forgetting factor, and to provide a systematic interval optimization method for the forgetting factor in the parameter identification of lithium battery equivalent circuit models. This method analyzes the overall convergence characteristics of parameter identification under different λ values, scientifically determines the common λ interval that ensures stable convergence of all model parameters, and recommends the optimal value accordingly.

[0006] In a first aspect, the present invention provides a systematic interval optimization method for the forgetting factor in the parameter identification of equivalent circuit models of lithium batteries, comprising the following steps:

[0007] S1. Collect the terminal voltage U of the lithium battery during operation. t And the load current I, to obtain timing sampling data;

[0008] S2. Establish the Thevenin equivalent circuit model of the lithium battery. The continuous state-space equation of this model is shown below:

[0009] ;

[0010] Where R0 is the ohmic internal resistance, R p It is the polarization resistance, C p It is a polarized capacitor, U p It is the polarization voltage, U oc It is the open-circuit voltage, U t I is the terminal voltage, and I is the load current. It's U p The derivative with respect to time t;

[0011] Let the sampling period be T. s Discretization using the backward Euler method yields the discrete input-output equations at time k:

[0012] ;

[0013] Where k is the discrete time index, k=1,2,…,k max k max This represents the final number of samples. Define the intermediate parameter vector to be identified. Its relationship with the original circuit parameters is as follows:

[0014] ;

[0015] This yields the standard linear equation form used for parameter identification:

[0016] ;

[0017] The data vector is defined according to the form of the standard linear equation. The system output is y(k)=U t (k);

[0018] S3. Initialize the intermediate parameter vector A small random number vector with values ​​between 0 and 1, and the covariance matrix P(0) is initialized as follows: , α∈10 3 ~10 6 ; here The identity matrix is ​​used. Subsequently, to accelerate the convergence of subsequent algorithms, a recursive least squares method with a forgetting factor λ=1 is first used to initially identify the time-series sampled data, obtaining an initial estimate of the intermediate parameter vector θ. A forgetting factor variation step size Δλ is set, generating i forgetting factor values. For each λ... i The initial estimate of the intermediate parameter vector θ obtained in step S3 The recursive least squares method yields the result corresponding to λ. i The estimated sequence of intermediate parameter vector θ k=1,2,…,k max k maxThis represents the final number of samples.

[0019] The recursive steps of the recursive least squares method are as follows:

[0020] Calculate the prior error:

[0021] ;

[0022] Calculate the gain vector:

[0023] ;

[0024] Update parameter estimates:

[0025] ;

[0026] Update the covariance matrix:

[0027] ;

[0028] Among them, e i (k) represents the prior error at time k; Let y(k) be the data vector at time k; y(k) = U t (k) represents the system output at time k; K i (k) is the gain vector at time k; Let θ be the estimated vector of the intermediate parameter θ at time k;

[0029] P is the intermediate parameter estimation vector at time k-1; i (k) is the covariance matrix at time k, P i (k-1) is the covariance matrix at time k-1, P i (k) In the formula " " is the identity matrix

[0030] S4. Estimating the sequence of intermediate parameter vectors for each i. Using the parameter relationships defined in step S2, the true circuit parameter sequence {R} is obtained through inverse solving. 0i (k)},{R pi (k)},{C pi (k)},{U oci (k)}, and calculate the root mean square (RMS) value of each parameter sequence respectively. R0 (i) RMS Rp (i) RMS Cp (i) RMS Uoc(i), the calculation formula is as follows:

[0031]

[0032] ;

[0033] ;

[0034] ;

[0035] Where, k max This represents the final number of samples.

[0036] S5, Draw RMS R0 (i) RMS Rp (i) RMS Cp (i) RMS Uoc (i) The curves that vary with i are used to determine the i-th sub-intervals for each parameter to remain stable and convergent, and then the λ corresponding to each parameter remaining stable and convergent is calculated. i Sub-interval; take the final preferred interval [λ] L ,λ H The median value of λ is used as the recommended optimal forgetting factor. optional This is used for the final online parameter identification, where , This interval represents the range of values ​​for the forgetting factor that allows all circuit parameters to maintain stable convergence simultaneously; where λ is... R0L , λ R0H Let λ be the minimum and maximum values ​​of λ when R0 converges, respectively. RpL , λ RpH R respectively p The minimum and maximum values ​​of λ at convergence, λ CpL , λ CpH C p The minimum and maximum values ​​of λ at convergence, λ UocL , λ UocH U oc The minimum and maximum values ​​of λ at convergence.

[0037] In some embodiments of the present invention, in step S3, the forgetting factor λ i Generated by the following formula:

[0038] λ i =1-(i-1)×Δλ;

[0039] Where i = 1, 2, ..., N, and the value of Δλ ranges from 0.001 to 0.005.

[0040] In some embodiments of the present invention, the inverse solution is specifically performed using the parameter relationship defined in step S2 as follows:

[0041] Calculate the time constant τ i (k):

[0042] ;

[0043] Calculate circuit parameters:

[0044] ;

[0045] Here, for each i, R 0i (k), R pi (k), C pi (k), U oci (k), τ i (k) represents the ohmic internal resistance, polarization internal resistance, polarization capacitance, open-circuit voltage, and polarization time constant at time k. , , , The parameter vectors θ at time k are respectively i The estimated values ​​of the four intermediate parameters.

[0046] In some embodiments of the present invention, the basis for determining stable convergence is that, within the interval, the root mean square of the parameter is lower than a preset threshold and the curve is smooth without sudden increases.

[0047] In some embodiments of the present invention, the criterion for "maintaining stable convergence" is: the root mean square corresponding to the parameter is lower than a preset threshold.

[0048] In some embodiments of the present invention, for RMS R0 (i) RMS Rp (i) RMS Cp (i) RMS Uoc (i) The preset thresholds are 0.05Ω, 0.2Ω, 1500F and 4V respectively.

[0049] The beneficial effects of this invention are as follows:

[0050] 1. Systematic and objective: Through data-driven analysis, the optimal range is systematically determined. The method is objective and reproducible, reducing reliance on experience.

[0051] 2. Global optimality: Seek the common intersection of the convergence intervals of all parameters to ensure that the recommended values ​​can take into account the overall recognition performance of the model and achieve global stable convergence.

[0052] 3. Improve identification accuracy and robustness: The λ value selected by this method can effectively balance the algorithm's memory and tracking capabilities, reduce parameter oscillations, and improve the convergence speed, stability, and accuracy of online identification of Thevenin model parameters.

[0053] 4. High versatility: This method is applicable to lithium batteries of different models and under different operating conditions, providing a reliable tool for adaptive tuning of model parameters of battery management system (BMS). Attached Figure Description

[0054] These and / or other aspects and advantages of the present invention will become apparent and readily understood from the following description of preferred embodiments taken in conjunction with the accompanying drawings, in which:

[0055] Figure 1 This is a schematic diagram of the Thevenin equivalent circuit model of a lithium battery;

[0056] Figure 2 This is a flowchart of the systematic optimization method and parameter identification for forgetting factors;

[0057] Figure 3 It is the number of times the root mean square parameter R0 changes with the forgetting factor. The curve of change;

[0058] Figure 4 It is parameter R p The number of times the root mean square changes with the forgetting factor The curve of change;

[0059] Figure 5 It is parameter C p The number of times the root mean square changes with the forgetting factor The curve of change;

[0060] Figure 6 It is parameter U oc The number of times the root mean square changes with the forgetting factor The curve of change;

[0061] Figure 7 This is a comparison curve (partial view) of the estimated terminal voltage and the experimental value when the optimal forgetting factor is used.

[0062] Figure 8 It is the estimation error curve of the terminal voltage when sampling the optimal forgetting factor;

[0063] Figure 9 It is the R0 convergence curve obtained by using the optimal forgetting factor.

[0064] Figure 10 R is obtained by using the optimal forgetting factor. p Convergence curve;

[0065] Figure 11 C is obtained by using the optimal forgetting factor. p Convergence curve;

[0066] Figure 12 U is obtained by using the optimal forgetting factor. oc Change curve;

[0067] Figure 13 When using a non-optimal forgetting factor (λ=0.9625), C p Divergence curve. Detailed Implementation

[0068] The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings. In this specification, the same or similar reference numerals indicate the same or similar components. The following description of the embodiments of the present invention with reference to the accompanying drawings is intended to explain the overall inventive concept of the present invention and should not be construed as a limitation thereof.

[0069] A systematic interval optimization method for forgetting factors in lithium battery equivalent circuit model parameter identification includes the following steps:

[0070] S1. Data Acquisition: Acquire the terminal voltage U of the lithium battery during operation. t And the timing sampling data of the load current I.

[0071] S2. Model Establishment and Discretization: Establishing a model as follows... Figure 1 The Thevenin equivalent circuit model of a lithium battery is shown. The continuous state-space equations of this model are:

[0072] (1)

[0073] Where R0 is the ohmic internal resistance, R p It is the polarization resistance, C p It is a polarized capacitor, U p It is the polarization voltage, U oc It is the open-circuit voltage, U t I is the terminal voltage, and I is the load current. It's U p The derivative with respect to time t. Let the sampling period be T. s Discretization using the backward Euler method yields the discrete input-output equations at time k:

[0074] (2)

[0075] Where k is the discrete time index, k=1,2,…,k max k max This represents the final number of samples. Define the intermediate parameter vector to be identified. (The "T" in the upper right corner is the transpose operator), and its relationship with the original circuit parameters is as follows:

[0076] (3)

[0077] This yields the standard linear equation form used for parameter identification:

[0078] (4)

[0079] Accordingly, a data vector is defined as The system output is y(k)=U t (k).

[0080] S3. Obtaining Initial Parameter Estimates: To accelerate the convergence of subsequent algorithms, the standard recursive least squares method (i.e., setting the forgetting factor λ=1) is first used to initially identify the data from step S1. Initialize the parameter estimation vector. (usually set as a zero vector or a small random number vector) and the covariance matrix P(0) (usually set as...) Where α is a large number, such as 10 3 ~10 6 ; here (This is an identity matrix). Subsequently, iterative calculations are performed using the recursive least squares formula to obtain a stable set of initial parameter estimates. .

[0081] S4. Systematic Forgetting Factor Test: Set a step size Δλ for the change of the forgetting factor (e.g., 0.0025). Generate a series of decreasing forgetting factor values ​​using the following formula.

[0082] λ i =1-(i-1)×Δλ (where i=1,2,…,N) (5)

[0083] For each λ i The result obtained in step S3 Using the initial values, run the complete recursive least squares algorithm with a forgetting factor. The recursive steps of this algorithm are as follows:

[0084] Calculate the prior error:

[0085] (6)

[0086] Calculate the gain vector:

[0087] (7)

[0088] Update parameter estimates:

[0089] (8)

[0090] Update the covariance matrix:

[0091] (9)

[0092] Among them, e i (k) represents the prior error at time k; Let y(k) be the data vector at time k; y(k) = U t (k) represents the system output at time k; K i (k) is the gain vector at time k; This is the intermediate parameter estimation vector at time k;

[0093] P is the intermediate parameter estimation vector at time k-1; i (k) is the covariance matrix at time k, P i (k-1) is the covariance matrix at time k-1, P i (k) In the formula " " is the identity matrix;

[0094] The corresponding λ is obtained through recursion. i intermediate parameter vector estimation sequence k=1,2,…,k max k max This represents the final number of samples.

[0095] S5. Inverse circuit parameters: Estimation sequence of intermediate parameter vectors for each i.

[0096] (in Using the parameter relationships defined in step S2, the true circuit parameter sequence {R} is obtained through inverse solving. 0i (k)},{R pi (k)},{C pi (k)},{U oci (k)}. First, calculate the time constant τ. i (k):

[0097] (10)

[0098] Then calculate the circuit parameters:

[0099] (11)

[0100] Here, for each i (i=1,2,…,N), R 0i (k), R pi (k), C pi (k), U oci (k), τ i (k) represents the ohmic internal resistance, polarization internal resistance, polarization capacitance, open-circuit voltage, and polarization time constant at time k. , , , The parameter vectors θ at time k are respectively i The estimated values ​​of the four intermediate parameters.

[0101] This yields {R} corresponding to the number of changes i of each forgetting factor. 0i (k)},{R pi (k)},{C pi (k)},{U oci (k)} sequence.

[0102] S6. Calculate the root mean square (RMS) value to assess stability: To quantify the volatility of parameter estimates under different values ​​of i, calculate the root mean square (RMS) value for each parameter series. R0 (i) RMS Rp (i) RMS Cp (i) RMS Uoc (i), the calculation formula is as follows:

[0103] (12)

[0104] (13)

[0105] (14)

[0106] (15)

[0107] Where, k max This represents the final number of samples.

[0108] S7. Determine the convergence subintervals for each parameter: Plot the RMS. R0 (i) RMS Rp (i) RMS Cp (i) RMS Uoc (i) The curves that vary with i are used to determine the i-th sub-intervals for each parameter to remain stable and convergent, and then the λ corresponding to each parameter remaining stable and convergent is calculated. i Subinterval. The criterion for stable convergence is: within this interval, the root mean square of the parameter is below a preset threshold and the curve is smooth without sudden increases. Let the convergence subinterval of parameter X be [λ]. XL ,λXH ], where X∈{R0, R p C p U oc}

[0109] S8. Determine the common optimal interval: Find the common intersection of all convergent subintervals of the parameters, which serves as the final optimal interval [λ] for the forgetting factor. L ,λ H ],in , This interval represents the range of forgetting factor values ​​that ensures all circuit parameters remain stable and convergent simultaneously.

[0110] Here λ R0L , λ R0H Let λ be the minimum and maximum values ​​of λ when R0 converges, respectively.

[0111] λ RpL , λ RpH R respectively p The minimum and maximum values ​​of λ at convergence.

[0112] λ CpL , λ CpH C respectively p The minimum and maximum values ​​of λ at convergence.

[0113] λ UocL , λ UocH U oc The minimum and maximum values ​​of λ at convergence.

[0114] S9. Recommend the optimal forgetting factor: Take the final optimal interval [λ]. L ,λ H The median value of λ is used as the recommended optimal forgetting factor. optional This is used for the final online parameter identification. The calculation formula is:

[0115] (16)

[0116] The overall process of the method of the present invention is as follows: Figure 2 As shown.

[0117] Simulation was performed using MATLAB software. A discharge experiment was conducted on a lithium-ion battery, and the terminal voltage U was measured at each discharge stage. t Load current I. Using FFRLS for parameter identification, plot the ohmic internal resistance R0 and polarization internal resistance R... p Polarization capacitor C p and open-circuit voltage U oc The root mean square of the four parameters The curve λ of the number of transformations i decreases from 1, with Δλ = 0.0025. The waveform obtained from the simulation is as follows. Figure 3-13 As shown. For Figure 3-13 Let's analyze each of the graphs.

[0118] Figure 3 This is the curve showing the change of the root mean square of parameter R0 with the forgetting factor *i*. Figure 3 It can be seen that when the number of changes in the forgetting factor i increases from 1, the RMS value of R0 does not change much, decreasing from 0.0347Ω to 0.0339Ω, indicating that the identification results of R0 have good convergence, and the convergence interval of R0 is i≥1.

[0119] Figure 4 This is the curve showing the root mean square of parameter Rp as a function of the number of times the forgetting factor i changes. From... Figure 4 It can be seen that R p The trend of RMS value changing with the number of times the forgetting factor changes, i. Within the range of 2 ≤ i ≤ 36, R... p The RMS value remained consistently low, and the curve was flat, indicating that R... p The convergence is good within this interval. The convergence interval of Rp is 2≤i≤36.

[0120] Figure 5 For parameter C p Number of times the root mean square changes with the forgetting factor The curve showing the change. From Figure 5 It can be seen that C p The trend of RMS value changing with the number of times the forgetting factor i changes. Within the range of i ≤ 14, C p The RMS value remained consistently low, and the curve was flat, indicating that C p It converges well within this interval, C p The interval of convergence is 1≤i≤14.

[0121] Figure 6 For parameter U oc The curve showing the change of the root mean square (RMS) with the number of times the forgetting factor (i) changes. Figure 6 It can be seen that when the number of changes in the forgetting factor i ≥ 2, U oc The RMS value is small and remains relatively stable, indicating that U at this time oc The identification results show good convergence. When the number of changes in the forgetting factor i=1, the RMS value increases sharply, indicating that U oc The identification results show a divergence. oc The interval of convergence is i≥2.

[0122] Depend on Figures 3-6It can be seen that the intersection of the number of changes in the forgetting factor i is 2≤i≤14, and the corresponding convergence interval of the forgetting factor is 0.9975≤λ≤0.9675, that is, λ L =0.9675, λ H =0.9975. λ is calculated using formula (16). optional =0.9825.

[0123] Figure 7 This is a partial plot showing the comparison between the estimated and experimental terminal voltage values ​​when using the optimal forgetting factor. Figure 7 Observation shows that the two curves highly overlap, with only subtle differences that are difficult to discern with the naked eye in localized areas. This indicates that the model parameters identified using the recommended forgetting factor can accurately reproduce the dynamic external characteristics of the battery.

[0124] Figure 8 The curve showing the estimation error of the terminal voltage when sampling the optimal forgetting factor. Figure 8 The error between the estimated and experimental terminal voltage values ​​is shown. As can be seen from the figure, the error curve fluctuates around zero, with the maximum absolute error not exceeding 0.003V and the relative error less than 0.1%. The error does not show a significant trend shift, indicating that the model does not have a systematic bias and the identification accuracy meets the requirements of engineering applications.

[0125] Figure 9 The R0 convergence curve is obtained by using the optimal forgetting factor. Figure 9 The results show that the ohmic internal resistance R0 converges rapidly to near a stable value in the initial identification phase, and then fluctuates smoothly within a small range without significant drift or divergence. This indicates that the recommended forgetting factor λ... optional With the value of 0.9825, the identification of R0 exhibits good fast convergence and steady-state stability.

[0126] Figure 10 R obtained by using the optimal forgetting factor p Convergence curve. (From...) Figure 10 It can be seen that the polarization internal resistance R p Similarly, it converged rapidly in the initial sampling phase with small fluctuations, validating the recommended forgetting factor λ. optional For R p Effectiveness of identification.

[0127] Figure 11 C obtained by using the optimal forgetting factor p Convergence curve. (From...) Figure 11 It can be seen that the polarization capacitance C p The sampling converged rapidly in the initial stage with small fluctuations, validating the recommended forgetting factor λ. optional For C p Effectiveness of identification

[0128] Figure 12 U obtained by using the optimal forgetting factor oc Convergence curve. (From...) Figure 12 It can be seen that the open-circuit voltage U oc The identification results converged rapidly in the early stages of identification, and decreased as the number of samplings increased, which is consistent with the actual engineering situation and further verifies the reliability of the identification results.

[0129] Figures 7 to 12 Together, they show that the recommended forgetting factor λ selected using the method in this paper... optional =0.9825, which enables all four circuit parameters of the Thevenin model to converge quickly to stable values, while the estimated terminal voltages conform to actual engineering conditions. This verifies the effectiveness of the proposed forgetting factor selection method.

[0130] Figure 13 When using a non-optimal forgetting factor (λ=0.9625), C p Divergence curve. (From...) Figure 13 It can be seen that when the number of samplings k=61, C p The estimated value suddenly jumped to an abnormally large value (far exceeding the reasonable range), and although it subsequently decreased, it had lost its physical meaning. This phenomenon is related to... Figure 5 The observed RMS peak at i=16, i.e., λ=0.9625, is in perfect agreement, confirming that C under this forgetting factor... p The identification did indeed diverge. This also indirectly proves the correctness of the proposed method's method of determining the convergence interval by analyzing the curve of RMS changing with the number of times the forgetting factor (i) changes—if the traditional empirical method is used and λ=0.9625 is mistakenly selected, it will directly lead to identification failure.

[0131] While some embodiments of the present general inventive concept have been shown and described, those skilled in the art will understand that changes may be made to these embodiments without departing from the principles and spirit of the present general inventive concept, the scope of which is defined by the claims and their equivalents.

Claims

1. A systematic interval optimization method for forgetting factors in the parameter identification of lithium battery equivalent circuit models, characterized in that, Includes the following steps: S1. Collect the terminal voltage U of the lithium battery during operation. t And the load current I, to obtain timing sampling data; S2. Establish the Thevenin equivalent circuit model of the lithium battery. The continuous state-space equation of this model is shown below: ； Where R0 is the ohmic internal resistance, R p It is the polarization resistance, C p It is a polarized capacitor, U p It is the polarization voltage, U oc It is the open-circuit voltage, U t I is the terminal voltage, and I is the load current. It's U p The derivative with respect to time t; Let the sampling period be T. s Discretization using the backward Euler method yields the discrete input-output equations at time k: ； Where k is the discrete time index, k=1,2,…,k max k max This represents the final number of samples. Define the intermediate parameter vector to be identified. Its relationship with the original circuit parameters is as follows: ； This yields the standard linear equation form used for parameter identification: ； The data vector is defined according to the form of the standard linear equation. The system output is y(k)=U t (k); S3. Initialize the intermediate parameter vector as a small random number vector with values ​​between 0 and 1, and initialize the covariance matrix P(0) as... , α∈10 3 ~10 6 ; here The identity matrix is ​​used. Subsequently, to accelerate the convergence of subsequent algorithms, a recursive least squares method with a forgetting factor λ=1 is first used to initially identify the time-series sampled data, obtaining an initial estimate of the intermediate parameter vector θ. A forgetting factor variation step size Δλ is set, generating i forgetting factor values. For each λ... i Using the initial estimate of the intermediate parameter vector θ obtained in step S3 as the initial value, the recursive least squares method is run to obtain the value corresponding to λ. i The estimated sequence of intermediate parameter vector θ k=1,2,…,k max k max This represents the final number of samples. The recursive steps of the recursive least squares method are as follows: Calculate the prior error: ； Calculate the gain vector: ； Update parameter estimates: ； Update the covariance matrix: ； Among them, e i (k) represents the prior error at time k; Let y(k) be the data vector at time k; y(k) = U t (k) represents the system output at time k; K i (k) is the gain vector at time k; Let θ be the estimated vector of the intermediate parameter θ at time k; P is the intermediate parameter estimation vector at time k-1; i (k) is the covariance matrix at time k, P i (k-1) is the covariance matrix at time k-1, P i (k) In the formula " " is the identity matrix; S4. Estimating the sequence of intermediate parameter vectors for each i. By using the parameter relationships defined in step S2, the true circuit parameter sequence {R} is obtained through inverse solving. 0i (k)},{R pi (k)},{C pi (k)},{U oci (k)}, and calculate the root mean square (RMS) value of each parameter sequence respectively. R0 (i) RMS Rp (i) RMS Cp (i) RMS Uoc (i), the calculation formula is as follows: ； ； ； ； Where, k max This represents the final number of samples. S5. Draw RMS R0 (i) RMS Rp (i) RMS Cp (i) RMS Uoc (i) The curves that vary with i are used to determine the i-th sub-intervals for each parameter to remain stable and convergent, and then the λ corresponding to each parameter remaining stable and convergent is calculated. i Sub-interval; take the final preferred interval [λ] L ,λ H The median value of λ is used as the recommended optimal forgetting factor. optional This is used for the final online parameter identification, where , This interval represents the range of values ​​for the forgetting factor that allows all circuit parameters to maintain stable convergence simultaneously; where λ is... R0L , λ R0H Let λ be the minimum and maximum values ​​of λ when R0 converges, respectively. RpL , λ RpH R respectively p The minimum and maximum values ​​of λ at convergence, λ CpL , λ CpH C p The minimum and maximum values ​​of λ at convergence, λ UocL , λ UocH U oc The minimum and maximum values ​​of λ at convergence.

2. The method according to claim 1, characterized in that, In step S3, the forgetting factor λ i Generated by the following formula: l i =1-(i-1)×Δλ; Where i = 1, 2, ..., N, and the value of Δλ ranges from 0.001 to 0.

005.

3. The systematic interval optimization method according to claim 1, characterized in that, The inverse solution is performed using the parameter relationships defined in step S2 as follows: Calculate the time constant τ i (k): ； Calculate circuit parameters: ； Here, for each i, R 0i (k), R pi (k), C pi (k), U oci (k), τ i (k) represents the ohmic internal resistance, polarization internal resistance, polarization capacitance, open-circuit voltage, and polarization time constant at time k. , , , The parameter vectors θ at time k are respectively i The estimated values ​​of the four intermediate parameters.

4. The systematic interval optimization method according to claim 1, characterized in that, The basis for determining stable convergence is that within this interval, the root mean square of the parameter is lower than a preset threshold and the curve is stable without sudden increases.

5. The systematic interval optimization method according to claim 1, characterized in that, The criterion for maintaining stable convergence is: the root mean square of the parameter is lower than a preset threshold.

6. The systematic interval optimization method according to claim 5, characterized in that, For RMS R0 (i) RMS Rp (i) RMS Cp (i) RMS Uoc (i) The preset thresholds are 0.05Ω, 0.2Ω, 1500F and 4V respectively.

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