Lithium battery charge state estimation method considering lithium dendrite influence

Abstract

The invention relates to a lithium battery state estimation technology, and discloses a lithium battery state-of-charge estimation method considering lithium dendrite influence, and the technical scheme is that the method comprises the following steps: segmenting and mapping nonlinear characteristics of terminal voltage and model resistance-capacitance parameters through an ALO algorithm; establishing an optimization equivalent model based on the model and the Huber loss of the actually measured terminal voltage as a fitness function, and obtaining a global parameter identification method; then, a self-adaptive interpolation algorithm is introduced to carry out linear pseudo interpolation on the parameters, and dynamic response characteristic compensation is achieved; finally, based on a strong tracking algorithm, a fading factor is introduced to correct an SOC estimation error covariance matrix, estimation residual vector orthogonality is achieved, and the capacity state sudden change tracking capacity is improved. And a noise self-adaptive mechanism is adopted to dynamically adjust the process and measure noise covariance parameters, so that the robustness of the algorithm is enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium battery state of charge estimation, and in particular to a lithium battery state of charge estimation method taking into account the influence of lithium dendrites. Background Art

[0002] Lithium battery state of charge (SOC) estimation, a key indicator in battery management systems, is crucial for electric vehicle safety management, charge and discharge control, and energy management. Lithium dendrite growth can pierce the separator, forming micro-shorts and increasing the ohmic internal resistance (R0). Simultaneously, lithium dendrite accumulation exacerbates the unevenness of electrode surface reactions, causing dynamic changes in polarization resistance and capacitance. Traditional parameter identification methods generally fail to incorporate the dynamic mutations caused by lithium dendrites into their models. Simulations based on fixed or slowly changing parameters result in poor SOC estimation accuracy.

[0003] Considering the complexity of battery dynamics and noise interference, research on achieving high-precision SOC estimation has focused on improving adaptive filtering algorithms and multi-time-scale modeling. To address the non-stationary nature of process noise caused by the nonlinear, time-varying characteristics of power batteries, researchers have introduced adaptive Kalman filtering algorithms to positively optimize the calculation of the SOC estimation noise covariance matrix. While this extended Kalman filtering algorithm can achieve online SOC estimation, it introduces a delay effect during the estimation process, reducing the robustness of SOC estimation under dynamic conditions.

[0004] Therefore, those skilled in the art are in urgent need of an SOC estimation method that can enhance the robustness of the SOC estimation system against changes in the internal structure of the battery caused by lithium dendrite growth and non-Gaussian measurement noise uncertainty factors. Summary of the Invention

[0005] The purpose of the present invention is to solve the above problems and design a method for estimating the state of charge of a lithium battery taking into account the influence of lithium dendrites.

[0006] The technical solution of the present invention to achieve the above-mentioned purpose is a method for estimating the state of charge of a lithium battery considering the influence of lithium dendrites, the method comprising the following steps:

[0007] Step 1: Use the ALO (Ant Lion Algorithm) to segmentally map the nonlinear characteristics of the terminal voltage and the model's resistance and capacitance parameters, establish an optimization equivalent model based on the Huber loss function of the model and the measured terminal voltage as the fitness function, find the optimal parameter set of the lithium battery model, and obtain the optimal impedance parameters with the minimum Huber loss function;

[0008] Step 2: Use the extended Kalman filter (EKF) algorithm to build an SOC estimation algorithm based on the optimal parameter set of the lithium battery model;

[0009] Step 3: Introduce an adaptive interpolation algorithm to perform linear pseudo-interpolation on the parameters to achieve dynamic response characteristic compensation;

[0010] Step 4: Introduce a fading factor to obtain an improved strong tracking extended Kalman filter algorithm (AISTAEKF), and modify the SOC estimation algorithm based on the improved strong tracking extended Kalman filter algorithm to enhance the robustness of the SOC estimation algorithm;

[0011] The improved strong tracking extended Kalman filter algorithm is mainly used to correct the SOC estimation error covariance matrix, achieve orthogonality of the estimated residual vector, improve the capacity state mutation tracking capability, adopt a noise adaptive mechanism, dynamically adjust the process and measurement noise covariance parameters, and enhance the robustness of the algorithm.

[0012] The ALO (Ant Lion Optimizer) algorithm in step 1 can simulate the global search ability of an ant lion group during foraging behavior, adaptively adjust the inertia weight and elastic boundary contraction parameters to fit the nonlinear characteristics of the battery voltage and the model resistance and capacitance parameters, and gradually approach the optimal solution by constructing a fitness function to obtain the optimal parameter set of the lithium battery model;

[0013] Among them, the lithium battery current I t As the input quantity of ant movement, the terminal voltage As the output quantity, the model terminal voltage and the measured terminal voltage U t The Huber loss is used as the fitness function. Considering the differences in battery internal resistance and polarization capacitance at different SOC stages (high, medium, and low), three parameter identification states are set. Parameter optimization and error correction are performed in stages to obtain the optimal values of model parameters R0, R1, R2, C1, and C2.

[0014] The process of constructing the SOC estimation algorithm in step 2 is as follows:

[0015] First, the discretized space equation of the battery system is constructed, and then the SOC estimation iteration is implemented based on the EKF algorithm, and finally the prior estimate and posterior estimate of the error covariance matrix of the battery system state quantity are obtained.

[0016] The process of achieving dynamic response characteristic compensation in step three is based on an adaptive interpolation method of pseudo-measurement values of interpolation factors of a finite state machine model, calculating nonlinear indicators of a state transfer function and a measurement function, and compensating for accumulated errors.

[0017] The process of correcting the SOC estimation algorithm based on the improved strong tracking extended Kalman filter algorithm in step three is based on the strong tracking filter (STF) theory, introduces a fading factor, corrects the filter weights based on dynamic voltage and current fluctuations, adjusts the error covariance matrix, designs a strong tracking extended Kalman filter (STEKF) algorithm, and corrects the error covariance matrix and residual covariance matrix of the SOC estimation algorithm to solve the problem of decreased SOC estimation accuracy caused by changes in lithium battery capacity.

[0018] The process of enhancing the robustness of the SOC estimation algorithm in step 3 is as follows:

[0019] Based on the noise adaptive mechanism, the stability of the SOC estimation algorithm is maintained by introducing the forgetting factor and adaptive estimation.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] 1. This application uses the ALO algorithm to identify the time-varying parameters of the second-order equivalent circuit model of lithium batteries in segments; considering that the voltage hysteresis response causes the actual terminal voltage change to be unable to be accurately predicted by the linearized state transition function, according to the nonlinear index n z 、n l And the interpolation factor r is introduced at different stages of SOC to solve the linearization error accumulation in the SOC estimation process;

[0022] 2. This application introduces a gradual elimination factor to correct the SOC estimation error covariance matrix to address the capacity fluctuations caused by lithium dendrites, thereby improving the ability to track sudden changes in capacity state. At the same time, a noise adaptive mechanism is adopted to dynamically adjust the process and measurement noise covariance parameters to address the problem of large SOC estimation errors caused by fixed noise covariance parameters under complex operating conditions due to the time-varying nature of sensor noise.

[0023] 3. This application conducts comparative analysis of different estimation methods based on the experimental data of voltage and current capacity under HPPC and DST working conditions measured in the laboratory. The results show that:

[0024] 1) Based on the ALO algorithm, under HPPC conditions, compared with the KF, FFRLS, and GA algorithms, the average error of the predicted lithium battery terminal voltage decreased by 33.79%, 77.25%, and 82.43%, respectively; the mean absolute error decreased by 17.8%, 62.12%, and 54.44%, respectively; and the root mean square error decreased by 27.37%, 78.07%, and 69.69%, respectively. Under DST conditions, the average error, mean absolute error, and root mean square error of the predicted battery terminal voltage decreased by 61.83%, 40.21%, and 45.78%, respectively, indicating that the ALO algorithm has excellent model parameter identification performance;

[0025] 2) Considering lithium dendrite growth, the SOC estimation model based on the AISTAEKF algorithm demonstrates that, under HPPC conditions, the average error of SOC estimation decreases by 91.67%, 83.87%, and 50%, respectively, compared to the EKF, AEKF, and STAEKF algorithms; the root mean square error decreases by 90%, 80.87%, and 45%, respectively. Under DST conditions, the average error decreases by 92.31%, 67.57%, and 42.86%, and the root mean square error decreases by 90.8%, 78.44%, and 42.5%, respectively. Under different conditions, the maximum average error of SOC estimation based on the AISTAEKF algorithm is less than 1.2%, demonstrating that the AISTAEKF algorithm has excellent SOC estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a flow chart of a method for estimating the state of charge of a lithium battery taking into account the influence of lithium dendrites according to the present invention;

[0027] Figure 2 is the interpolation number table of the present invention;

[0028] Figure 3 This is a terminal voltage error table identified by each algorithm under the HPPC working condition described in the present invention;

[0029] Figure 4 It is the terminal voltage error table for parameter identification under the DST working condition described in the present invention;

[0030] Figure 5 is a flow chart of the ALO algorithm of the present invention;

[0031] Figure 6 is a diagram of parameter identification results according to the present invention;

[0032] Figure 7 It is a structural diagram of the finite state machine (three states) of the present invention;

[0033] Figure 8 It is a flow chart of SOC estimation based on AISTAEKF algorithm according to the present invention;

[0034] Figure 9 This is a diagram of the experimental equipment of Example 1 of the present invention;

[0035] Figure 10 This is a comparison chart of the terminal voltage verification results of various algorithms under HPPC conditions in Example 1 of the present invention;

[0036] Figure 11 This is a comparison diagram of the lithium battery terminal voltage based on various algorithms under the DST working condition in Example 1 of the present invention;

[0037] Figure 12This is a comparison chart of lithium battery SOC estimation based on various algorithms under HPPC conditions in Example 1 of the present invention;

[0038] Figure 13 This is a comparison diagram of SOC estimation based on various algorithms under the DST operating condition in Example 1 of the present invention;

[0039] Figure 14 This is a comparison table of SOC estimation errors of various algorithms under the HPPC working condition described in the present invention;

[0040] Figure 15 This is a comparison table of SOC estimation errors of various algorithms under the DST working condition described in the present invention;

[0041] Figure 16 , is the second-order RC equivalent circuit model diagram of the present invention. DETAILED DESCRIPTION

[0042] The present invention will be described in detail below in conjunction with the accompanying drawings:

[0043] Considering the complex electrochemical polarization and concentration polarization phenomena in the lithium battery during the charging and discharging process, and under conditions such as fast charging or overcharging, lithium dendrites are easy to grow at the negative electrode, destroying the battery structure, piercing the diaphragm, and changing the internal current concentration distribution, the electrochemical polarization resistor R1, capacitor C1, concentration polarization resistor R2 and capacitor C2 are introduced to establish a second-order RC model to capture the dynamic characteristics of the battery, such as Figure 16 As shown. Among them, U oc and U are the battery open circuit voltage and terminal voltage respectively, I is the battery charge and discharge current, and R0 is the ohmic internal resistance.

[0044] The circuit time domain equation can be obtained from Kirchhoff's law:

[0045]

[0046] Where: U1 and U2 are the pressure differences across R1 and R2 respectively; τ1 and τ2 are R1C1 and R2C2 respectively.

[0047] A typical 18650 lithium battery was selected as the research object, with a rated capacity of 2Ah and a voltage range of [2.5V, 4.2V]. The OCV and SOC of lithium batteries have a relatively stable nonlinear relationship. The functional relationship between OCV and SOC at a fixed measurement point considering the voltage hysteresis effect is calculated using the static method and a 7th-order polynomial fit:

[0048] OCV=-47.15C 7 +186.6C 6 -292.5C 5

[0049] +227.8158C4 -89.0C 3 +15.1C 2

[0050] -0.01C+3.38(2).

[0051] A method for estimating the state of charge of lithium batteries considering the influence of lithium dendrites, such as Figure 1-15 As shown, the method includes the following steps:

[0052] Step 1: Based on Ohm's law, the lithium battery voltage and current parameters are determined as state variables, indirectly representing the dynamic changes in internal resistance and polarization capacitance. The ALO (Ant Lion Optimizer) algorithm simulates the global search capabilities of ant lion colonies during foraging behavior. It adaptively adjusts the inertia weight and elastic boundary contraction parameters to fit the nonlinear characteristics of the battery voltage and the model's resistance and capacitance parameters. By constructing a fitness function, it gradually approaches the optimal solution.

[0053] Lithium battery current I t As the input quantity of ant movement, the terminal voltage As the output quantity, the model terminal voltage and the measured terminal voltage U t The Huber loss is used as the fitness function, and the differences in battery internal resistance and polarization capacitance at different SOC stages (high, medium, and low) are considered. Three parameter identification states are set, and parameter optimization and error correction are performed in stages to obtain the optimal values of model parameters R0, R1, R2, and C1, C2. The equivalent model parameter identification flow chart is shown in the figure. Figure 5 shown.

[0054] 1) Initialize the equivalent model parameter set X = [R0R1R2C1C2] and the optimal parameter set X best The total number of iterations is set to 50, the maximum number of iterations is set to 100, and the model parameter set is randomly generated, where R0∈[0.001,1], R1, R2∈[0.001,0.1], C1, C2∈[0,2000]. The fitness value of the optimal parameter set is initially set to 0.001, the initial parameter adjustment value Δx is set to 0.01, and the fitness value change within 50 iterations is less than 1×10 -8 Or when the maximum number of iterations reaches 500, the algorithm terminates.

[0055] 2) Determine the optimal parameter set X of the equivalent model best The parameter with the best fitness in the initialized model parameter set X is taken as the optimal parameter to form X best. In view of the internal resistance fluctuation and terminal voltage delay caused by the growth of lithium dendrites, the different changing rules of parameters such as battery internal resistance and polarization capacitance at different SOC stages are considered. In the high SOC stage (80-100%), the internal resistance of the battery is low and changes smoothly, the polarization capacitance is relatively stable, the lithium dendrites grow slowly, and the influence on the parameters is small; in the medium SOC stage (20-80%), the internal resistance and polarization capacitance are affected by the growth of lithium dendrites, the fluctuation increases, and the parameter changes are nonlinear; in the low SOC stage (0-20%), the internal resistance rises sharply, the polarization capacitance fluctuates greatly, the lithium dendrites grow fast, and the parameter changes are complex and drastic. Therefore, the Huber loss function is used and different threshold parameters are introduced in segments to classify the errors between the model terminal voltage and the actual terminal voltage, calculate the comprehensive loss value, and characterize the degree of fitting of the battery model parameters.

[0056] Among them, the fitness function fit is:

[0057]

[0058] Among them, Hδ(a) represents the Huber loss function, which is defined as follows:

[0059]

[0060] in, U t and are the measured terminal voltage and model terminal voltage of the battery at time t, respectively. δ is the threshold parameter of the Huber loss function, which is used to distinguish small errors from large errors between the terminal voltage fitting value and the actual value. In this application, δ1, δ2, and δ3 are taken as 0.0005, 0.001, and 0.002, corresponding to the threshold parameters of the Huber loss function at the high, medium, and low SOC stages, respectively.

[0061] 3) According to formula (5), the parameter set and parameter adjustment amount Δx update its position X new The position of each set of parameters is compared with the reference optimal parameter set to update the optimal reference set so that the calculated fitness function fit is optimal. In each round of iteration, the global optimal parameter set is adjusted by updating the reference optimal parameter set to find the optimal parameter set that makes the model terminal voltage and the measured terminal voltage U t The parameter combination with the smallest Huber loss function.

[0062] X new =X+Δx·D (5)

[0063] Where X is the current parameter value and D represents a random direction vector in the range of [-1, 1].

[0064] 4) According to the current number of iterations, use formula (6) to gradually reduce the parameter adjustment amount Δx to achieve the transition from global search to local search and solve the balance problem between global exploration and local development. Adjust the model parameter set X and the battery model optimal parameter set X best The search boundary is set to ensure movement within the boundary and prevent crossing the boundary.

[0065]

[0066] Among them, k is the current iteration number, k max is the maximum number of iterations.

[0067] Find the optimal parameter set of the lithium battery model and obtain the optimal impedance parameter with the minimum Huber loss function, and then the optimal impedance parameter identification of the lithium battery second-order model can be realized. Based on the ALO algorithm, the parameter identification results under HPPC and DST conditions are as follows: Figure 6 shown.

[0068] In step two, the extended Kalman filter (EKF) algorithm predicts the state-space equation of the linear system using the ampere-hour integration method. Measurement feedback is performed using the open-circuit voltage method to obtain the observation equation of the linear system. Based on a second-order RC equivalent circuit model, the EKF algorithm can obtain the SOC based on model parameters such as resistance and capacitance, as well as measured voltage and current data.

[0069] Assume that the battery system state quantity, input parameters, and observation quantity at time k are x k 、u k 、z k , the state equation and measurement equation are f(x k ,u k )、h(x k ,u k ), then the discretized space equation of the battery system is

[0070] x k =f(x k-1 ,u k-1 )+ω k-1

[0071] ≈A k-1 x k-1 +B k-1 u k-1 +ω k-1 (7)

[0072] z k =h(x k ,u k )+v k ≈C k x k +D k +vk (8)

[0073] in,

[0074]

[0075] D k =I k R k ;x k =[SOC k U 1,k U 2，k ] T ;

[0076] Among them, ω k is the process noise; v k To measure noise.

[0077] The iterative process of SOC estimation based on the EKF algorithm is as follows:

[0078] (1) Variable initialization

[0079]

[0080] (2) The iterative process is:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] Where: and are the prior estimate and the posterior estimate of the system state at time k respectively; K is the Kalman filter gain; and are the prior estimate and the posterior estimate of the error covariance matrix of the system state quantity at time k respectively.

[0087] Step 3: The EKF algorithm in Equation (7) lacks high-order terms, ignoring the step-wise increase in the ohmic internal resistance of the lithium battery equivalent circuit model parameters and the delayed response of voltage to changes in current direction. To address the accumulated EKF linearization errors, an adaptive interpolation method for pseudo-measurement values of interpolation factors based on a finite state machine model is proposed. This method calculates the nonlinear indicators of the state transfer function and measurement function to compensate for the accumulated errors.

[0088] Aiming at the problem that the voltage hysteresis response caused by the internal current distribution of lithium batteries leads to the problem that the actual terminal voltage change cannot be accurately predicted by the linearized state transfer function, in order to quantify the nonlinearity of lithium battery SOC estimation, the linearization error ε of the state transfer function is defined according to formula (7): z and nonlinear index n z They are:

[0089]

[0090]

[0091] According to formula (8), the linearization error ε of the measurement function is defined as l and nonlinear index n l They are:

[0092]

[0093]

[0094] Where, ε z and ε l They represent the errors in the linearization process of the state transfer function f(x) and the measurement function h(x); n z and n l is the linearization error; ε z and ε l The noise covariance matrix Q k and R k Nonlinear indicators after processing.

[0095] When n z <<1 and n l When ≤ 1, the system dynamic characteristics can be regarded as quasi-linear and no interpolation processing is required; otherwise, according to the joint nonlinear index calculated in real time, pseudo-measurements are added between consecutive sampling points to increase the sampling frequency and reduce the nonlinearity of the coupling between state prediction and observation. The adaptive interpolation strategy is designed as follows:

[0096] 1) Calculate the nonlinear index n according to formulas (15)-(18) z and n l .

[0097] 2) Based on n z and n l, the degree to which the state equation and measurement equation deviate from the linear assumption is obtained. Considering that the capacity decay rate of lithium batteries in different SOC ranges affects the battery's linear performance, at high SOC, the battery has sufficient available capacity, a smooth release process, slow capacity decay, and high linearity. In the medium SOC range, the available capacity gradually decreases, the release process is interfered by various factors, the capacity decay rate accelerates, and the linearity decreases. At low SOC, the available capacity drops significantly, the release becomes difficult, the capacity decay intensifies, and the battery exhibits obvious nonlinear characteristics. Based on the SOC variation trend, three linearity states are set: State 1 corresponds to an SOC of 80-100%, at which point the linearity is high, with an interpolation factor of r = 1, thresholds U1 = 0.25, and D1 = 0.10; State 2 corresponds to an SOC of 20-80%, with r = 3, U2 = 0.45, and D2 = 0.20; State 3 corresponds to an SOC of 0-20%, at which point the linearity is low, with r = 5, U3 = 0.65, and D3 = 0.30. In the state transition logic, when any indicator exceeds the current state U i When both indicators are lower than D i This mechanism can dynamically adapt to the nonlinear changes of lithium batteries, especially when the SOC is low, inserting more pseudo-measurements can compensate for nonlinear errors.

[0098] Figure 7 In, n zi and n li Represent the nonlinear indicators of the state equation and the measurement equation respectively. When any state threshold is selected, ensure that U i >D i , and the interpolation factor satisfies the higher state corresponding to the larger interpolation factor, that is, r i+1 >r i .

[0099] 3) To balance the estimation accuracy and computation time, the nonlinear index is compared with the threshold of the corresponding state to determine the current state. When any nonlinear index corresponding to state i exceeds the upper threshold U i When the two nonlinear indicators of state i are both lower than the lower threshold D i When , the state machine returns to the previous state i-1. According to the number of interpolations of the finite state machine in the four states, Figure 2 shown.

[0100] 4) Between two adjacent voltage and current sampling measurements of the lithium battery, r pseudo-measurements are added based on linear interpolation. After determining the adaptive interpolation of the measurement values, the adaptive interpolation extended Kalman filter (AIEKF) algorithm is derived through the EKF algorithm to perform SOC estimation.

[0101] Step 4: Lithium dendrites change the internal electrical parameters and electrode structure, resulting in disordered lithium ion transmission. In the early stage, the degree of lithium ion transmission disorder is not high, and the change of noise statistical characteristics is relatively slow and small in amplitude, and it is stable in a relatively fixed state; during the charge and discharge process, lithium dendrites grow, lithium ion transmission is greatly disturbed, and the difference in voltage change under different charge and discharge rates increases, the actual capacity decreases, and the noise mean fluctuates. The system model based on the linearization of the EKF algorithm fixes the noise parameters, and the growth of lithium dendrites causes the battery to be highly nonlinear and time-varying. The noise statistical characteristics no longer meet the assumptions of the EKF algorithm. Therefore, based on the strong tracking filter (STF) theory, a fading factor is introduced, the filter weights are corrected based on dynamic voltage and current fluctuations, the error covariance matrix is adjusted, and the strong tracking extended Kalman filter (STEKF) algorithm is designed to solve the problem of decreased SOC estimation accuracy caused by changes in lithium battery capacity.

[0102] The fading factor is introduced in formula (11) to adjust the prior error covariance matrix in real time

[0103]

[0104] Where μ k is the suboptimal fading factor and μ k >1.

[0105]

[0106] in,

[0107]

[0108]

[0109]

[0110]

[0111] Where V k is the residual covariance matrix, λ is the forgetting factor, which takes a value of (0, 1), and this application takes λ = 0.95; β is the weakening factor, and this application takes β = 1.2.

[0112] The STEKF decision criterion depends on the combination of equivalent circuit model parameters, system state transition equations, measurement equations, and noise statistical characteristics, and cannot detect parameters alone. When the sensor is continuously disturbed and generates large noise, the innovation sequence increases. After being processed by STEKF, the covariance matrix will be amplified, resulting in an increase in the Kalman gain to improve the confidence in the observed value. However, in this case, the equivalent circuit model parameters and noise characteristics of the battery in different charge and discharge stages are significantly different. It is difficult to reflect the true state of the battery under lithium dendrite growth and complex changes in different charge and discharge stages only relying on a fixed decision criterion. At the same time, the sensor noise should be estimated in real time and adjusted online. Therefore, based on the noise adaptive mechanism, by introducing forgetting factors α and β, adaptively estimate R k and Q k . The larger α and β are, the larger the initial value weights of R k and Q k are, and the better the estimation stability when the battery state changes gently can be maintained; the smaller the adaptive estimation weights of R k and Q k are, the more capable of quickly tracking the internal resistance mutation caused by lithium dendrite growth and the non-stationary characteristics of the terminal voltage observation noise. Among them, R k and Q k are respectively expressed as

[0113]

[0114] In the formula: K K is the Kalman gain; the values of α and β are (0, 1].

[0115] The flow chart of the lithium battery SOC estimation algorithm based on AISTAEKF is as Figure 8 shown. The steps are as follows:

[0116] 1) Initialize the lithium battery SOC state quantity and the error covariance matrix according to Equation (9).

[0117] 2) Calculate the nonlinear indexes n z and n l through Equations (15)-(18), determine the interpolation factor r in combination with different SOC intervals, and linearly insert r values between adjacent measurement values.

[0118] 3) Estimate the lithium battery SOC using Equation (10), combined with the strong tracking algorithm; adjust the prior error covariance matrix through Equations (20)-(24). At the same time, after correcting the Q and R matrices using Equation (25), correct the SOC state estimation value using Equations (12)-(14).

[0119] 4) After completing a strong tracking process in step 3), if i < r + 1, repeat step 3) to continue the strong tracking process and further optimize the SOC estimation result.

[0120] 5) Determine whether the SOC estimation process is complete. If not, repeat steps 2) through 3) to continue estimating and optimizing. If complete, output the final SOC estimation result.

[0121] Example 1;

[0122] The rated capacity of the lithium battery is 2000mAh, and the upper and lower cut-off voltages are 4.2V and 2.5V respectively. The HPPC and DST working condition experiments are designed at a constant temperature of 25℃, with a sampling interval of 1s. Among them, the lithium battery HPPC experiment is charged to a cut-off voltage of 4.2V at a constant current of 1C, and then discharged at a constant rate of 0.25C at intervals of 10% after standing for 1h until the voltage drops to the lowest cut-off voltage. The DST experiment is carried out in sequence with a current rate of 0.25C, 0.5C, and 1C, and the cycle operation is carried out until the power drops to 0. The experimental equipment is as follows: Figure 9 shown.

[0123] An equivalent model resistance and capacitance parameter identification scheme is designed under HPPC and DST working conditions, and the identification accuracy and convergence speed of the equivalent model parameters for SOC estimation based on the ALO algorithm are verified.

[0124] 1) Under HPPC conditions, the equivalent circuit model parameter identification results based on traditional FFRLS, genetic algorithm (GA), Kalman filter (KF) and ALO algorithm are compared and analyzed;

[0125] 2) Under DST conditions, the parameter identification results based on the traditional FFRLS algorithm and the ALO algorithm are compared and analyzed.

[0126] Under HPPC conditions, the test duration is set to 60,000 seconds, and the terminal voltage and error based on the four algorithms are compared. Figure 10 As shown, and the error analysis is as follows Figure 3 .

[0127] Depend on Figure 10 and Figure 3 As can be seen, under HPPC operating conditions, the mean absolute error and root mean square error of the terminal voltage when performing model parameter identification based on the traditional FFRLS algorithm and GA algorithm are both higher than those of the ALO algorithm and KF algorithm. Moreover, compared with the model parameter identification scheme of the KF algorithm, the SOC estimation accuracy based on the ALO algorithm, which considers the nonlinear parameter changes during the lithium battery charging and discharging process and its global search capability, is higher, with the mean error, mean absolute error, and root mean square error decreasing by 33.79%, 17.8%, and 27.37%, respectively. The results show that under HPPC operating conditions, the ALO algorithm can effectively capture the step-like increase in ohmic internal resistance during the lithium battery charging and discharging process, reducing the error between the model terminal voltage and the actual terminal voltage.

[0128] Under DST conditions, the test duration is set to 14000s. The terminal voltage and error comparison of the equivalent circuit model based on the ALO algorithm and the FFRLS algorithm are as follows: Figure 11 As shown, the error analysis is as follows Figure 4 .

[0129] Depend on Figure 11 and Figure 4 As can be seen, under DST conditions, the initial characteristics of the equivalent circuit model parameter identification based on the ALO algorithm are relatively stable compared to FFRLS. Although the model parameter acquisition converges relatively slowly and has relatively low accuracy, the impact on the long-term parameter identification results is minimal. After 200 seconds, the model parameter acquisition converges faster, and the parameter identification accuracy is higher. This is because the initial lithium dendrite growth is slow, which has limited impact on key parameters such as internal resistance and polarization capacitance. The initial characteristics are relatively stable and change more gradually. The traditional FFRLS algorithm is more adaptable to stationary data, quickly tracking parameter changes and maintaining stability. The ALO algorithm, on the other hand, focuses on global search, initially exploring a larger parameter space, with more random factors and jitter between [0s and 200s]. As the number of iterations increases, the ALO algorithm gradually focuses on the optimal solution region. After 200 seconds, it establishes the advantage of global search, approaches the true parameters, and effectively captures the long-term dynamics of lithium batteries. The mean absolute error, mean error, and root mean square error decrease by 40.21%, 61.83%, and 45.78%, respectively. The results show that the lithium battery equivalent circuit model parameter identification method based on the ALO algorithm has higher identification accuracy under long-term and complex working conditions.

[0130] A comparison scheme for lithium-ion battery SOC estimation based on four algorithms, namely EKF, AEKF, STAEKF and AISTAEKF, is designed to verify the effectiveness of SOC estimation based on AISTAEKF.

[0131] According to the terminal voltage and current parameters of the lithium battery, the SOC estimation and error based on the four algorithms under HPPC conditions are as follows: Figure 12 As shown, the error comparison is Figure 14 .

[0132] Depend on Figure 12 and Figure 14 It can be seen that the comparative analysis of SOC estimation under HPPC conditions:

[0133] 1) HPPC operating conditions involve complex current pulse variations, and lithium battery capacity fluctuates to a certain extent. The EKF algorithm is characterized by a linear approximation process. When mapping SOC, especially at the transition between pulse charge and discharge, SOC estimation exhibits a significant delay, resulting in significant error peaks. The average error and root mean square error reached 0.6% and 0.44%, respectively.

[0134] 2) Under HPPC operating conditions, the rapid changes in lithium battery current produce strong nonlinear time-varying characteristics. The SOC estimation model based on the AEKF algorithm can perform online adaptive adjustments to the covariance of noise and measurement noise, but it cannot adapt to the complex nonlinear changes within the battery and its adaptive capability is limited. Compared with the EKF SOC estimation, its mean error and root mean square error are slightly lower, reducing by 0.31% and 0.23% respectively; however, the improvement in SOC estimation accuracy is not significant during high current pulses.

[0135] 3) Under HPPC conditions, the STAEKF-based SOC estimation, by introducing a fading factor to adjust the filter gain, is able to strongly track the actual battery SOC variation characteristics and cope with sudden changes in battery state performance under pulse current interference. However, the cumulative error will still gradually increase during the continuous pulse charge and discharge process. The average error is controlled within 0.1%, and the root mean square error is approximately 0.08%.

[0136] 4) Under HPPC operating conditions, the SOC model based on the AISTAEKF algorithm features adaptive, strong tracking, and an integral strategy. By correcting model linearization errors and noise estimation errors, it addresses error accumulation and noise mean fluctuations. Whether during a single pulse or a continuous pulse sequence, including high-current pulse intervals with significant battery polarization effects and when current direction frequently switches, it effectively tracks dynamic SOC changes and suppresses error generation and accumulation. Its mean error and root mean square error are as low as 0.05% and 0.044% respectively.

[0137] Set the DST working conditions of the lithium battery charge and discharge process with different amplitudes and durations, and compare the SOC estimation and error based on different algorithms. Figure 13 As shown, the error analysis is as follows Figure 15 shown.

[0138] Depend on Figure 13 and Figure 15 It can be seen that the comparative analysis of SOC estimation under DST conditions:

[0139] (1) The DST operating condition involves charge and discharge phases of varying magnitudes and durations, resulting in frequent and complex changes. The EKF algorithm's dependence on the accuracy and noise characteristics of the battery model is prominent, making it unable to adapt to such dynamic and frequently changing operating conditions. Especially during rapid charge and discharge transitions, its linearization limitations cause the SOC estimate to lag behind the true value, resulting in significant deviations. The average error and root mean square error reach 15.6% and 7.5%, respectively.

[0140] (2) In DST conditions, although the EKF algorithm has the ability to adaptively adjust the noise and measurement noise covariance, its adaptive adjustment effect is limited by the highly nonlinear performance of lithium batteries. In particular, when a long period of low-current discharge is followed by a sudden high-current charge, factors such as the polarization effect and internal resistance change within the battery are intertwined, resulting in the AEKF algorithm's SOC estimation being unable to keep up with the actual value changes in a timely manner. Although its average error and root mean square error have dropped to 3.7% and 3.2% respectively, which is a certain improvement compared to the EKF algorithm, the estimation accuracy under complex conditions still needs to be improved.

[0141] (3) Under DST conditions, the STAEKF algorithm introduces a fading factor to correct the state estimation error covariance matrix. When the SOC is 80-100%, based on the relatively high linearity of lithium batteries in this range, the fading factor can better adjust the filter gain and effectively achieve the SOC change trend tracking effect. When the SOC is 20-80%, as the charge and discharge current magnitude and direction change frequently, the growth of lithium dendrites affects the fading factor, and the adjustment ability of the error covariance matrix is limited to a certain extent, resulting in a gradual increase in the estimation error. In the SOC range of 0-20%, the internal resistance fluctuates greatly, the multiple charge and discharge rates switch rapidly and the amplitude changes greatly, and the fading factor cannot quickly adjust the error covariance matrix to adapt to the changes. Its average error and root mean square error are approximately 2.1% and 1.2% respectively. In summary, although the SOC estimation based on the STAEKF algorithm can make a certain rapid response to high SOC and medium SOC state mutations, the continuous fluctuation causes the accumulation of uncertainties, and strong tracking characteristics are difficult to effectively achieve. In particular, the estimation error will increase in the stage where the charge and discharge rates switch rapidly and the amplitude changes greatly.

[0142] (4) Under DST conditions, the SOC estimation effect based on the AISTAEKF algorithm is the best. During the long-term stable charge and discharge phase of the lithium battery, the AISTAEKF algorithm calculates the change of SOC through an integral strategy, which can improve the accuracy of SOC estimation. During short-term drastic changes in operating conditions, especially when the lithium battery suddenly switches from high-current discharge to low-current charging, the AISTAEKF algorithm monitors the residual information in real time; uses an adaptive mechanism to dynamically adjust the filter gain, and combines strong tracking characteristics to quickly correct the state prediction equation and measurement update equation. Its average error and root mean square error can be controlled below 1.2% and 0.69%, respectively. In summary, the parameter weight adjustment of the SOC estimation model based on the AISTAEKF algorithm can redistribute the degree of dependence on historical data and current measurement data; the introduction of a gradual fading factor to continue the state estimation error covariance matrix correction can enhance the tracking ability of the sudden state and effectively suppress the generation of errors.

[0143] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Any changes that may be made to certain parts thereof by those skilled in the art all reflect the principles of the present invention and fall within the scope of protection of the present invention.

Claims

1. A method for estimating the state of charge of a lithium battery considering the influence of lithium dendrites, characterized in that: The method comprises the following steps: Step 1: Use the Ant Lion algorithm to segmentally map the nonlinear characteristics of the terminal voltage and the model's resistance and capacitance parameters, establish an optimization equivalent model with the Huber loss function as the fitness function, and find the optimal parameter set for the lithium battery model; Step 2: Using the extended Kalman filter algorithm to construct the SOC estimation algorithm based on the optimal parameter set of the lithium battery model; Step 3: Introduce an adaptive interpolation algorithm to perform linear pseudo-interpolation on the parameters to achieve dynamic response characteristic compensation; Step 4: Introduce a fading factor to obtain an improved strong tracking extended Kalman filter algorithm. Based on the improved strong tracking extended Kalman filter algorithm, the SOC estimation algorithm is corrected and the robustness of the SOC estimation algorithm is enhanced.

2. The method for estimating the state of charge of a lithium battery considering the influence of lithium dendrites according to claim 1, characterized in that: In the step 1, the inertia weight and the elastic boundary contraction parameter are adaptively adjusted by the ant lion algorithm, and the optimal parameter set of the lithium battery model is obtained by constructing a fitness function.

3. The method for estimating the state of charge of a lithium battery considering the influence of lithium dendrites according to claim 1, characterized in that: The process of constructing the SOC estimation algorithm in step 2 is as follows: First, the discretized space equation of the battery system is constructed, and then the SOC estimation iteration is implemented based on the EKF algorithm, and finally the prior estimate and posterior estimate of the error covariance matrix of the battery system state quantity are obtained.

4. The method for estimating the state of charge of a lithium battery considering the influence of lithium dendrites according to claim 1, wherein: The process of achieving dynamic response characteristic compensation in step three is based on an adaptive interpolation method of pseudo-measurement values of interpolation factors of a finite state machine model, calculating nonlinear indicators of a state transfer function and a measurement function, and compensating for accumulated errors.

5. The method for estimating the state of charge of a lithium battery considering the influence of lithium dendrites according to claim 1, characterized in that: The process of correcting the SOC estimation algorithm based on the improved strong tracking extended Kalman filter algorithm in step 3 is as follows: Based on the strong tracking filter theory, the fading factor is introduced, the error covariance matrix is adjusted, and a strong tracking extended Kalman filter algorithm is designed. The error covariance matrix and residual covariance matrix of the SOC estimation algorithm are corrected.

6. A method for estimating the state of charge of a lithium battery considering the influence of lithium dendrites according to claim 5, characterized in that: The process of enhancing the robustness of the SOC estimation algorithm in step 3 is as follows: Based on the noise adaptive mechanism, the stability of the SOC estimation algorithm is maintained by introducing the forgetting factor and adaptive estimation.

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