A low-complexity, high-precision, strong-robustness battery state of charge estimation method and system

Abstract

The application relates to a battery state of charge estimation method and system with low complexity, high precision and strong robustness, and relates to the field of battery state of charge estimation. In order to solve the problems of high cost, poor precision and poor robustness of the existing battery state of charge estimation technology, the application is proposed. Technical points: firstly, a second-order equivalent circuit model is established through offline experiments, an offline parameter identification method is adopted, the magnitude difference between the to-be-identified model parameters and the fitted voltage is reduced, and the fitting precision is improved. The relationship between the model parameters obtained through offline parameter identification and SOC is fitted, and a third-order Gaussian fitting OCV-SOC relationship curve after adding fitting points is utilized. The real-time measured battery terminal voltage and current values of a sensor are input into an ECM model for calculating an OCV value, the calculated OCV value is subjected to variable-weight distribution sliding window filtering to smooth the curve and reduce errors, and the filtered result is fitted through an OCV-SOC relationship curve to obtain an SOC value, which is used as an observation value for subsequent Kalman filtering. A prediction value is calculated by using the ampere-hour integral method, and the prior value is used to combine the model parameters and the SOC fitting to obtain the current model parameters. Finally, Kalman filtering is performed on the two values to obtain a posteriori SOC value.

Description

Technical Field

[0001] This invention relates to the field of battery state of charge estimation technology, specifically to a low-complexity, high-precision, and robust battery state of charge estimation method and system. Background Technology

[0002] The state of charge (SOC) of a battery is a fundamental parameter representing its remaining usable capacity. Accurate SOC estimation is not only a basic requirement for estimating the driving range of electric vehicles, but also a fundamental guarantee for improving battery utilization efficiency and safety performance. Therefore, accurately obtaining the real-time SOC value of a power battery is particularly important. However, in practical applications, the SOC value cannot be directly measured and can only be estimated through external physical parameters such as voltage, current, and temperature. Therefore, accurate SOC estimation remains a challenging goal.

[0003] Currently, the main SOC estimation methods include traditional methods, battery model-based methods, data-driven methods, and various joint estimation methods.

[0004] Traditional methods mainly include two categories: the ampere-hour integration method and the open-circuit voltage method. The ampere-hour integration method starts from the definition of SOC and uses real-time measured current values ​​to estimate SOC; the open-circuit voltage method establishes the relationship between open-circuit voltage (OCV) and SOC in advance through offline experiments, and can predict the SOC value by using the OCV value under the current state of the battery.

[0005] Battery model-based State of Charge (SOC) estimation methods are typically combined with various observers and filters. State monitor-based methods aim to minimize the error between the observed and actual states through a closed-loop feedback system, ultimately treating the observed values ​​as the actual state values. State observer-based methods mainly include Luenberger observers, proportional-integral observers, sliding diaphragm observers, and nonlinear robust observers. Filter-based methods filter the state and observed values ​​to obtain the final result. Filter-based methods are widely used in online battery SOC estimation due to their low computational complexity and high accuracy. Filter-based methods mainly include Kalman filtering, particle filtering, and HIF filtering, with Kalman filtering being the most widely used.

[0006] In recent years, artificial intelligence and machine learning have developed rapidly. Data-driven SOC estimation methods have shown great potential in electric vehicle SOC estimation due to their strong nonlinear mapping capabilities, relatively simple structure, fast response speed, and model-free nature. Among them, neural network-based SOC estimation methods have been widely used due to their powerful nonlinear fitting capabilities. Currently, neural networks used for SOC estimation mainly include two types: feedforward neural networks and recurrent neural networks.

[0007] With the extensive and in-depth research, researchers have proposed various joint estimation methods after comprehensively considering the advantages and disadvantages of the aforementioned methods. Dr. Guo Xiangwei of South China University of Technology, in his doctoral dissertation, combined the ampere-hour integration method with the open-circuit voltage method, using the open-circuit voltage method to correct the accumulated error caused by current measurement deviation in the ampere-hour integration method at a specific SOC. Dr. Lu Chusheng of South China University of Technology, in his doctoral dissertation, combined the data-driven method with the open-circuit voltage method, using a battery model constructed with a neural network to calculate the OCV value, and then using the open-circuit voltage method to obtain the SOC value, realizing a simplified SOC estimation method based on a linearized equivalent circuit model. Dr. Appiah Emmanue of Southwest University of Science and Technology combined a Long Short-Term Memory Neural Network (LSTM) with the Unscented Kalman Filter (UKF) algorithm, using LSTM to simulate battery behavior parameters at different temperatures for SOC estimation, and using the UKF algorithm to further remove noise and improve the accuracy of SOC estimation. In the previous patent CN118091438A, the authors proposed a SOC estimation method based on deep learning and an improved IAKF. The method uses the SOC calculated by ampere-hour integration and the SOC estimated by deep learning as the prediction and observation values ​​of the improved intelligent adaptive Kalman filter algorithm, respectively. After filtering the two, a higher SOC estimation accuracy is obtained.

[0008] It can be seen that existing battery state-of-charge estimation techniques have the following shortcomings (i.e., areas that need to be avoided or improved):

[0009] Traditional methods: The ampere-hour integration method is a way to directly estimate the SOC value based on the definition of SOC. However, its estimation accuracy is greatly affected by the initial SOC value and the accuracy of the current sensor, and the error accumulates over time. The open-circuit voltage method, also known as the offline lookup table method, involves establishing a pre-defined correspondence between SOC and open-circuit voltage (OCV) in an offline table. When an SOC value needs to be estimated, it can be obtained from the corresponding OCV value under the current operating conditions. However, in actual operating conditions, the battery rarely reaches an equilibrium state, meaning that the OCV value cannot be directly measured.

[0010] Battery Model-Based Approaches: Increasing research suggests that Kalman filtering appears to be the most practical method for estimating the State of Charge (SOC) of electric vehicles. The core idea of ​​Kalman filtering is to couple the Gaussian probability density of the predicted state with the observed state to obtain the optimal state estimate. Since Kalman filtering is only applicable to linear systems, and the relationship between open-circuit voltage and SOC in the observation equations of a battery model is nonlinear, the Extended Kalman Filter (EKF) has been widely used. The core idea of ​​EKF is to linearize the nonlinear part of the system by ignoring higher-order terms after Taylor expansion. In battery SOC estimation, this specifically manifests as linearizing the open-circuit voltage value in the observation equations. However, current SOC estimations using EKF generally employ first-order Taylor expansions, resulting in significant truncation errors. This is because increasing the order of the Taylor expansion greatly increases computational complexity. To avoid this problem, the Unscented Kalman Filter (UKF) was proposed. The core idea of ​​UKF is to use an unscented transformation at the sigma point to replace the Taylor expansion to achieve a nonlinear-to-linear conversion, thereby reducing the magnitude of the truncation error. However, UKF suffers from high computational complexity and sensitivity to initial conditions and parameter selection, issues that need to be addressed. Meanwhile, the Kalman filter method combined with a battery model uses ampere-hour integration to calculate the State of Charge (SOC), which is then transformed by a state transition matrix to obtain a predicted value, while the measured terminal voltage is used as the observed value. This process contains transformation errors, and due to the randomness of the measured current and terminal voltage errors, the prediction error and the observation error may have the same sign, meaning the predicted and observed values ​​are on the same side of the true value. This significantly reduces the predictive effectiveness of the Kalman filter.

[0011] Data-driven methods, which use machine learning to train on large amounts of data and build a model of the relationship between input and output, offer significant advantages in estimating battery state of charge (SOC) without requiring a precise battery model and in handling complex nonlinear relationships. However, these methods are highly dependent on data, have limited generalization ability, high computational complexity, demanding hardware, and are prone to underfitting or overfitting.

[0012] All of the aforementioned joint estimation methods have limitations. Dr. Guo Xiangwei's method, combining ampere-hour integration and open-circuit voltage, uses ampere-hour integration to calculate the SOC value and fit the model parameters. Then, the OCV value is calculated using these model parameters to fit and correct the SOC value. This method suffers from significant errors in the model parameters at the uncorrected SOC and is highly dependent on the accuracy of OCV calculation and OCV-SOC curve fitting. Dr. Lu Chusheng's joint estimation method still relies on the OCV-SOC curve in its core estimation step. Compared to Dr. Guo Xiangwei's method, his OCV value is calculated using a neural network model, avoiding the problem of large errors in the model parameters at the uncorrected SOC. However, this method introduces the high computational complexity of data-driven methods, high hardware requirements, and a tendency to underfit or overfit. Dr. Appiah Emmanue combines data-driven methods with filtering methods, using an LSTM network to predict the battery terminal voltage and a third-order equivalent circuit model, and then uses the UKF method for filtering. This method suffers from state transition errors during filtering and has high computational complexity. The method proposed by the author in the previous patent can avoid state transition errors and reduce computational complexity to a certain extent. However, due to the randomness of the measurement current and terminal voltage errors, it cannot be guaranteed that the true value is in the middle of the prediction and observation, and the optimal filtering effect cannot be achieved. At the same time, the introduction of neural network methods also has high hardware requirements, requires a large amount of training data, and is costly.

[0013] To address the problems of the aforementioned methods, it is imperative to propose a low-complexity, high-precision, and robust method for estimating the state of charge of batteries. Summary of the Invention

[0014] The technical problem to be solved by this invention is:

[0015] This invention is proposed to address the problems of high cost, insufficient accuracy, and poor robustness in existing battery state of charge estimation technologies.

[0016] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0017] The present invention provides a low-complexity, high-precision, and robust method for estimating the state of charge of a battery, comprising:

[0018] The terminal voltage (U) is obtained based on the initial SOC value and sensor measurements. t The current value (I) is calculated using the ampere-hour integration method to obtain the SOC prior value at the current moment;

[0019] By inputting the prior SOC value into the pre-fitted SOC-ECM parameter relationship curve, the model parameter value at the current time can be calculated. The OCV value can be calculated by combining the model parameter with the input terminal voltage and current values.

[0020] Increase the number of measured OCV points, fit the OCV-SOC relationship using the third-order Gaussian formula, and then substitute the calculated OCV values ​​into the sliding window filter with different weights to obtain the observed SOC values.

[0021] Based on the given filtering parameters: state vector covariance P, predicted state covariance Q, and observed state covariance R, Kalman filtering is applied to filter the predicted and observed SOC values ​​to obtain the posterior estimated SOC value, which is then used as the initial SOC value for the next time step. This process is repeated until the iteration ends.

[0022] The present invention has the following beneficial technical effects:

[0023] To address the problems of the aforementioned methods, this invention combines the ampere-hour integration method, the open-circuit voltage method, and the Kalman filter algorithm to propose a low-complexity, high-precision, and robust method for estimating the state of charge (SOC) of a battery. In terms of preliminary work, this invention first establishes a second-order equivalent circuit model (ECM) through offline experiments. A novel offline parameter identification method is employed to reduce the magnitude difference between the model parameters to be identified and the fitted voltage, thereby improving the fitting accuracy. The relationship between the model parameters obtained from the offline parameter identification and SOC is fitted using a sixth-order polynomial, and the number of measured OCV fitting points is increased to fit the OCV-SOC relationship curve using a third-order Gaussian. In the actual prediction process, this invention inputs the real-time measured battery terminal voltage and current values ​​from sensors into the ECM model to calculate the OCV value. The calculated OCV value is then subjected to an improved sliding window filter to smooth the curve and reduce errors. The filtered result is fitted to the OCV-SOC relationship curve to obtain the SOC value, which serves as the observation value for subsequent Kalman filtering. The predicted values ​​(prior values) are calculated using the ampere-hour integral method, and the current model parameters are fitted using these prior values ​​in conjunction with the relationship between the model parameters and the SOC. Finally, Kalman filtering is applied to both to obtain the posterior SOC value.

[0024] The advantages of this invention are as follows:

[0025] 1. A novel offline parameter identification method is adopted to reduce the magnitude difference between the parameters of the model to be identified and the fitted voltage, thereby improving the fitting accuracy.

[0026] 2. Increase the number of fitting points and use a third-order Gaussian fitting method to fit the OCV-SOC relationship curve to find the balance point between overfitting and underfitting, thereby improving the fitting accuracy. The classic polynomial fitting method is suitable for SOC-OCV curve fitting, but using it to fit the OCV-SOC relationship curve will result in a more severe Runge phenomenon.

[0027] 3. The OCV values ​​calculated using model parameters are subjected to a sliding window filter with variable weight allocation to smooth the OCV curve, reduce fluctuation errors, and avoid error accumulation.

[0028] 4. Compared to classic model-based SOC estimation methods, this approach eliminates the need to fit SOC-OCV curves to calculate the observed voltage value, avoiding both fitting errors and state transition errors. Since both the predicted and observed values ​​are SOC values, computational complexity is reduced while eliminating nonlinear components and truncation errors.

[0029] 5. The observed value is the SOC value fitted by the open-circuit voltage method. When the current sensor deviates (assuming discharge conditions, the current sensor measurement result is too large), the SOC value calculated by the ampere-hour integration method is less than the true SOC value, while the OCV value calculated by the model is greater than the true OCV value. This corresponds to the observed SOC value being greater than the true SOC value, ensuring that the true SOC value is between the observed and predicted values, which greatly enhances the estimation accuracy and robustness of the filtering algorithm. Attached Figure Description

[0030] Figure 1 This is the overall flowchart of the algorithm of this invention; Figure 2 This is a flowchart of the algorithm of this invention; Figure 3 The model's response diagrams are shown in the figure: a is the second-order ECM model diagram, and b is the current excitation and voltage response diagram. Figure 4 The result is a graph of the polarization voltage after processing. Figure 5 The graph shows the exponential fitting effect at 100% SOC at 25℃.

[0031] Figure 6 The figure shows a comparison of the calculation accuracy of OCV values ​​before and after filtering under DST conditions at 15℃. In the figure: (a) is OCV, and (b) is the error. Figure 7 The figure shows a comparison of the calculation accuracy of OCV values ​​before and after filtering under FUDS operating conditions at 25℃. In the figure: (a) is OCV, and (b) is the error. Figure 8 The figure shows a comparison of the calculation accuracy of OCV values ​​before and after filtering under the US06 operating condition at 35℃. In the figure: (a) is OCV, and (b) is the error.

[0032] Figure 9 This is a comparison of the fitting results of second-order and third-order polynomials and the second-order Gaussian at 15℃. Figure 10 This is a comparison of the fitting results of second-order and third-order polynomials with that of second-order Gaussian at 25℃. Figure 11 A comparison of the fitting effects of second-order and third-order polynomials with second-order Gaussian at 35℃.

[0033] Figure 12The figure shows the battery SOC performance estimated by the open-circuit voltage method under DST conditions at 15℃. In the figure: (a) is SOC, (b) is error. Figure 13 The figure shows the battery SOC performance estimated by the open-circuit voltage method under FUDS conditions at 25℃. In the figure: (a) is SOC, (b) is error. Figure 14 The figure shows the battery SOC performance estimated by the open-circuit voltage method under the US06 operating condition at 35℃. In the figure: (a) is SOC, (b) is error.

[0034] Figure 15 The figure shows the battery SOC performance estimated by the actual open-circuit voltage under DST conditions at 15℃. In the figure: (a) is SOC, (b) is error. Figure 16 The figure shows the battery SOC performance estimated by the actual open-circuit voltage under FUDS conditions at 25℃. In the figure: (a) is SOC, (b) is error. Figure 17 The figure shows the battery SOC performance estimated by the actual open-circuit voltage under the US06 operating condition at 35℃. In the figure: (a) is SOC, (b) is error.

[0035] Figure 18 A comparison of the calculation accuracy of OCV values ​​before and after filtering for the DST operating condition at 15℃ is shown in the figure. In the figure, (a) is OCV and (b) is error. Figure 19 A comparison of the calculation accuracy of OCV values ​​before and after filtering for the FUDS operating condition at 25℃ is shown in the figure. In the figure, (a) is OCV and (b) is error. Figure 20 A comparison of the calculation accuracy of OCV values ​​before and after filtering for the US06 operating condition at 35℃ is shown in the figure. In the figure, (a) is OCV and (b) is error.

[0036] Figure 21 The images show the second- and third-order Gaussian fitting results after adding fitting points at 15℃. Figure 22 The images show the second- and third-order Gaussian fitting results after adding fitting points at 25℃. Figure 23 The fitting results of second-order and third-order Gaussian after adding fitting points at 35℃ are shown in the figure.

[0037] Figure 24 The open-circuit voltage method optimized for DST conditions at 15℃ is used to estimate the battery SOC performance. In the figure: (a) is SOC, (b) is error. Figure 25 The open-circuit voltage method optimized for FUDS conditions at 25℃ is used to estimate the battery SOC performance. In the figure: (a) is SOC, (b) is error. Figure 26 The open-circuit voltage method optimized for US06 operating conditions at 35℃ is used to estimate the battery SOC performance. In the figure: (a) is SOC, and (b) is error.

[0038] Figure 27The patented method for estimating battery SOC performance under 15℃ DST conditions is a low-complexity, high-precision, and robust method. In the figure: (a) represents SOC, and (b) represents error. Figure 28 The patented method for estimating battery SOC performance under 25℃ FUDS conditions is a low-complexity, high-precision, and robust method. In the figure: (a) represents SOC, and (b) represents error. Figure 29 The low-complexity, high-precision, and robust method proposed in the US06 patent is used to estimate the SOC performance of the battery under the 35℃ operating condition. In the figure, (a) is SOC and (b) is error. Detailed Implementation

[0039] to attach Figure 1-29 The implementation of a low-complexity, high-precision, and robust battery state-of-charge estimation method and system according to the present invention is described below:

[0040] like Figure 1 The diagram shows the overall algorithm flowchart. The input values ​​are the initial SOC value and the terminal voltage (U) measured by the sensor. t The SOC prior value at the current moment can be calculated using the ampere-hour integration method, given the current value (I). Inputting the SOC prior value into the pre-fitted SOC-ECM parameter relationship yields the model parameter values ​​at the current moment. Using the model parameters combined with the input terminal voltage and current values, the OCV value can be calculated. Increasing the number of measured OCV points and fitting the OCV-SOC relationship using a third-order Gaussian formula, then applying an improved weighted sliding window filter to the calculated OCV value, and finally substituting it into the pre-fitted Gaussian-fitted OCV-SOC curve, yields the observed SOC value. Given the filtering parameters: state vector covariance: P; predicted state covariance: Q; observed state covariance: R. Applying Kalman filtering to the predicted and observed SOC values ​​yields the posterior estimated SOC value, which is used as the initial SOC value for the next moment. This process is repeated until the iteration ends.

[0041] The second-order ECM model is established as follows: Figure 2 As shown, U ocv Indicates the open-circuit voltage of the battery; U t R represents the terminal voltage applied to the load terminals by the battery; I represents the current in the circuit, and this patent specifies that the discharge current is positive; R0 represents the ohmic internal resistance in the battery; R1 represents the activation polarization resistor; and R2 represents the concentration polarization resistor.

[0042] The mathematical modeling process for this model has been detailed and will not be elaborated here. The discretized battery model expression is shown in equation (1). Where k represents the parameter value at time k; Δt is the unit time interval; τ1 and τ2 represent the activation and concentration polarization time constants, respectively, and their values ​​are the polarization resistance-capacitance product; Q n η represents the maximum usable capacity of the battery; η represents the battery charge / discharge efficiency.

[0043]

[0044] The model parameters of ECM can be identified through HPPC experimental test curves, such as Figure 3 The figure shows the pulse current excitation applied to the battery and the corresponding voltage change curve. This invention specifies that the discharge current is positive, as shown in Figure I. d I is the discharge current. c U is the charging current; U0 is the initial terminal voltage, and U1 to U4 correspond to the terminal voltages at times t1 to t4, respectively.

[0045] Based on the equivalent circuit model, at the instant the battery discharge ends, the equivalent RC circuit corresponds to a first-order zero-input response. According to the three-element method of first-order linear circuit analysis, it is easy to obtain:

[0046]

[0047] Then, the activation polarization and concentration polarization voltages of the battery after discharge time t are respectively:

[0048]

[0049] At this point, the parameters of the bipolar ECM model can be solved using the least squares fitting method with the exponential term as the basis. The specific process is as follows:

[0050] (1) Selection of fitting interval:

[0051] Considering that the polarization voltage expression after the discharge is more convenient and better fits the exponential fitting situation, this interval is selected to fit the model parameters, that is, the interval of depolarization process (t2-t3) after the discharge is completed to fit the model parameters.

[0052] observe Figure 3 It is not difficult to observe that a rapid voltage step (U2-U5) occurs at time t2, which is caused by the influence of the ohmic internal resistance R0. Since the effect of pure internal resistance is transient, we can easily solve for the ohmic internal resistance at this time:

[0053]

[0054] Considering that R1 and R2 are both of a very small order of magnitude, it is easy to see from the graph that although the difference between U5 and U6 is small, its magnitude is large, and it is easy to see that U t The increasing value indicates that the polarization voltage is decreasing. If we directly select the U5 to U6 interval from the image for fitting, the magnitude difference would be too large, leading to a decrease in fitting accuracy. To reduce the magnitude difference and conform to the trend of polarization voltage change, we choose to subtract the subsequent U from all data in the U5 to U6 interval. t Find the stable value and take its inverse. The resulting image is as follows: Figure 4 As shown. Image ordinate U t This refers to the polarization voltage after processing.

[0055] (2) Exponential fitting based on least squares method:

[0056] Since the fitting interval does not include the ohmic internal resistance R0 and the data has been processed to the same order of magnitude, the general form of exponential fitting can be easily obtained:

[0057] U t '=ae bx +ce dx (5)

[0058] Where a, b, c, and d are the parameters to be solved.

[0059] observe Figure 5 It is easy to see that the fitting effect is better after polarization voltage processing. Calculations show that the correlation coefficient square (R-square) of the fitting reaches 0.9969; the root mean square error (RMSE) is as low as 0.0001, further indicating that the fitting accuracy is high.

[0060] By fitting the model parameter values ​​at each SOC point obtained by the above method with a 6th-order polynomial, the relationship expression between ECM model parameters and SOC values ​​can be obtained.

[0061] The process of SOC estimation based on OCV values ​​is as follows:

[0062] (1) OCV value calculation and filtering:

[0063] Under actual operating conditions of electric vehicles, the battery rarely reaches an equilibrium state due to polarization. This means that the OCV value cannot be directly measured. Therefore, this invention uses an ECM model to calculate the OCV value.

[0064] Based on equation (1), the formula for calculating the OCV value can be obtained as follows:

[0065] U ocv (k)=U t (k)+I(k)R0+U1(k)+U2(k) (6)

[0066] If the OCV value calculated using the ECM model is used directly for SOC estimation without filtering, the estimation result will fluctuate significantly. This paper employs a sliding window filtering method, as shown in equation (7). Where M... L This refers to the window size for smoothing filtering.

[0067]

[0068] This invention compares the calculation accuracy of OCV values ​​before and after filtering under different smoothing filter window sizes, using 15℃ DST, 25℃ FUDS, and 35℃ US06 operating conditions. The actual OCV values ​​are obtained through 6th-order polynomial fitting in the aforementioned OCV test experiments, corresponding to the fitting relationship between ECM parameters and SOC. The comparison of OCV value calculation accuracy before and after filtering is as follows: Figure 6 , 7 As shown in Figures 8 and 8, the specific numerical results are shown in Table 1.

[0069] Table 1. Different M values ​​under various operating conditions L OCV calculation error before and after smoothing filtering

[0070]

[0071] Observing the above charts and comparing the OCV calculation error values ​​under various smoothing filter window sizes, it is not difficult to find that when the smoothing filter window size is 5, the calculated OCV value still fluctuates significantly. It only reduces the maximum error in OCV calculation under certain operating conditions, while the RMSE value is generally large. When the smoothing filter window size is 15, although the RMSE value decreases under certain operating conditions, it significantly increases the maximum error in OCV calculation. In summary, the best overall performance for OCV calculation is achieved when the smoothing filter window size is 10, i.e., M... L =10.

[0072] (2) Fitting of OCV-SOC relationship:

[0073] SOC estimation based on OCV values, also known as the open-circuit voltage method, directly derives the estimated SOC value from the OCV value under the current operating condition by establishing a pre-established correspondence between SOC and OCV. However, unlike fitting the SOC-OCV curve, fitting the OCV-SOC curve using polynomial fitting will result in significant errors. Therefore, this invention pre-selects a second-order Gaussian fitting method for fitting, with the following fitting formula:

[0074] SOC=a1*exp(-((OCV-b1) / c1)^2)+a2*exp(-((OCV-b 2) / c2)^2)

[0075] Where a1, b1, c1, a2, b2, and c2 are the parameters to be solved. When fitting the SOC-OCV relationship using higher-order polynomials, severe Runge's phenomenon occurs, leading to significant distortion. Therefore, this invention compares the fitting effects of second-order and third-order polynomials with those of second-order Gaussian at temperatures of 15℃, 25℃, and 35℃. Figure 9 , 10 As shown in Figure 11, it is easy to see from the graph that the fitting accuracy of the second-order polynomial is insufficient, while the third-order polynomial fitting exhibits Runge's phenomenon. Compared to polynomial fitting, the second-order Gaussian fitting has a better fitting effect. However, compared to the 25℃ and 35℃ environments, the OCV-SOC curve fitting accuracy is poor at 15℃.

[0076] (3) Correction of filtering formula and fitting method

[0077] This invention selects the 15℃ DST condition, 25℃ FUDS condition, and 35℃ US06 condition respectively to verify the accuracy of SOC estimation using the open-circuit voltage method. The estimation results are as follows: Figure 12 , 13 As shown in Figures 1 and 14, the specific numerical results are shown in Table 2.

[0078] It is easy to see from the charts that when using the open-circuit voltage method to estimate the battery SOC alone, even without applying the initial SOC deviation and current measurement deviation (this invention directly uses the ampere-hour integral to calculate the SOC value, that is, the real SOC value under the condition of no current error to update the ECM parameters for OCV calculation), there is still a large error, which cannot meet the estimation accuracy requirements.

[0079] Table 2. Error values ​​for SOC estimation using the open-circuit voltage method under various operating conditions.

[0080]

[0081] The reasons for the large errors in the above estimation methods are investigated, and two possibilities are found: 1. Insufficient accuracy in calculating OCV values ​​based on the ECM model; 2. Insufficient accuracy in second-order Gaussian fitting. Comparing Tables 1 and 2, it is easy to see that the SOC estimation error is smallest in the 35℃ US06 condition due to the higher accuracy of the filtered OCV. This proves that the large errors in the above estimation methods are related to the accuracy of OCV value calculation. Similarly, although the 15℃ DST condition has excellent OCV calculation accuracy, its poor second-order Gaussian fitting accuracy still results in a large error in SOC estimation. This proves that insufficient second-order Gaussian fitting accuracy is also a major reason for the large errors in the above estimation algorithms. To further verify this hypothesis, this invention directly substitutes the actual OCV values ​​into the second-order Gaussian fitting formula for each condition to test the SOC estimation performance. The estimation results are as follows: Figure 15 , 16 As shown in Figures 1 and 17, the specific numerical results are shown in Table 3.

[0082] Observing the charts, it is easy to see that directly using the actual OCV value for estimation can significantly reduce the SOC estimation bias, but a large estimation bias still exists. Furthermore, since the second-order Gaussian fitting accuracy is worst at 15℃, its corresponding estimation error is the largest. This proves that the large error in the SOC estimation method based on the open-circuit voltage method is caused by both insufficient accuracy in OCV value calculation and insufficient accuracy in second-order Gaussian fitting.

[0083] Table 3. Error values ​​for estimating SOC based on actual open-circuit voltage.

[0084]

[0085] To address the two types of problems mentioned above, this invention employs two processing methods: adjusting the data weights within the smoothing filter window and increasing the number of OCV value measurement points while improving the Gaussian fitting order, and then refitting the OCV-SOC relationship. Specific analysis follows:

[0086] observe Figure 6 , 7 It is not difficult to observe that as the size of the smoothing filter window increases, the RMSE value of the estimation result continuously decreases (only the DST condition at 15℃ is an isolated case, where the RMSE increases due to the excessive maximum error value in the later stage of the smoothing filter), while the maximum error of the estimation result continuously increases, and all occur in the later stage of the estimation. The observed formula is SOC=a1*exp(-((OCV-b1) / c1)^2)+a2*exp(-((OCV-b1) / c1)^2) 2)It is not difficult to see that increasing the smoothing filter window can effectively reduce the fluctuation of OCV value calculation, thereby reducing the RMSE value. However, since subsequent filtering results are always affected by preceding data and the weights of data within the smoothing window are all the same, increasing the smoothing filter window in this case will exacerbate the error accumulation phenomenon. To address this problem, this invention introduces a weight allocation for the data within the smoothing window, reducing the weight of preceding data and increasing the weight of subsequent data, thereby reducing error accumulation. The updated smoothing filter formula is shown in the following equation.

[0087]

[0088] Where M L Still taking 10, α and β are selected through trial and error; in this invention, they are chosen to be 0.5 and 1.5, respectively. The filtering result is then introduced using the updated filtering formula. Figure 18 , 19 As shown in Figures 20 and 20, the specific numerical results are shown in Table 4.

[0089] Observing the charts, it is easy to see that after introducing the updated smoothing filter formula, although the RMSE value calculated by OCV increases slightly under some operating conditions, the ME value decreases significantly. This proves the effectiveness of the updated smoothing filter formula.

[0090] Table 4. Updated Smoothing Filter OCV Calculation Error Values

[0091]

[0092] Increasing the number of fitting points can effectively improve fitting accuracy; however, it also carries the risk of overfitting. To find the optimal balance between overfitting and underfitting, this invention re-performs the OCV test experiment, calibrating the OCV value every 5% SOC and attempting to further increase the Gaussian fitting order to enhance its nonlinear fitting ability, ultimately making the fitting result closer to the true distribution. The effects of second-order and third-order Gaussian fitting at various temperatures after increasing the number of fitting points are shown below. Figure 2-21 As shown in Figures 2-22 and 2-23.

[0093] contrast Figure 21 , 22 23 and Figure 9 , 10It is not difficult to see from the fitting accuracy of 11 that adding fitting points and using third-order Gaussian fitting can further improve the fitting accuracy. Therefore, this invention subsequently chooses to add fitting points and apply third-order Gaussian to fit the OCV-SOC relationship. It should be noted that: at 25℃, if second-order Gaussian is used for fitting after adding fitting points, the fitting accuracy is lower than before adding fitting points, indicating that overfitting has occurred in this case. Conversely, at 15℃, the fitting accuracy is significantly improved by adding fitting points and using second-order Gaussian fitting compared to before adding fitting points. After analysis, it is not difficult to see that the fitting accuracy is low before adding fitting points, so no overfitting occurs after adding fitting points.

[0094] Overfitting occurs because the quality of newly added data points is insufficient. (Comparison) Figure 10 , 11 It is difficult to find in points 22 and 23 that even after adding fitting points at 35℃, the second-order Gaussian fitting still has high fitting accuracy. This is because the data measurement quality is better at 35℃ (the optimal operating temperature of this battery is around 35℃), so the addition of fitting points will not cause overfitting.

[0095] After optimization using the two methods described above, the results of SOC estimation using the open-circuit voltage method under various operating conditions are as follows: Figure 24 , 25 As shown in Figures 26 and 26, the specific numerical results are shown in Table 5.

[0096] Observing the above charts, it is easy to see that the optimized open-circuit voltage method significantly improves the estimation accuracy of SOC value compared to the unoptimized method under the 15℃ and 25℃ conditions. Under the 35℃ condition, the improvement is not significant because the OCV calculation accuracy and OCV-SOC relationship fitting accuracy were already high before optimization. However, there is still considerable room for improvement in the SOC estimation accuracy under the above temperature conditions. At the same time, analysis reveals that this method has poor robustness. When there is a deviation between the sensor's measured current and terminal voltage, it directly affects the OCV calculation accuracy, which in turn affects the SOC estimation accuracy. The decrease in SOC estimation accuracy directly affects the ECM parameter solution accuracy, ultimately impacting the OCV calculation accuracy. This situation will continuously accumulate SOC estimation deviations, leading to divergence in the estimated value. To enhance the algorithm's robustness and avoid such phenomena, this invention will introduce a Kalman filter algorithm in subsequent steps.

[0097] Table 5. Optimized Open-Circuit Voltage Method for Estimating SOC under Various Operating Conditions

[0098]

[0099] Based on the above analysis, it is clear that even with improved filtering methods that modify the OCV value calculated by ECM and by using a more accurate third-order Gaussian fitting method to fit the OCV-SOC relationship after adding fitting points, the SOC estimation using the open-circuit voltage method alone still suffers from significant estimation bias. In contrast, SOC estimation based on the extended Kalman filter is widely used due to its better robustness, but it is prone to divergence in the later stages of estimation, and its computational complexity, involving matrix operations, is greater than that of the open-circuit voltage method. To address this, this invention introduces the idea of ​​dimensionality reduction of the state equation and updates the Kalman filter formula, combining the strengths of both methods. Unlike the classic EKF algorithm based on the ECM model, this invention uses the SOC value calculated by the ampere-hour integration method as the predicted value of the filtering algorithm, and the SOC value calculated by the open-circuit voltage method as the observed value of the filtering algorithm. In this case, the three-dimensional state equation of the traditional battery is simplified to one dimension, and the calculation of the polarization voltage value is no longer included in the state equation, thus avoiding the deviation of the predicted SOC value from the observed U. t The value conversion process simplifies computational complexity while increasing the accuracy of SOC estimation. The overall algorithm flow is as follows: Figure 1 As shown in the figure, the input values ​​are the initial SOC value and the terminal voltage and current values ​​measured by the sensor. The prior SOC value at the current moment can be calculated using the ampere-hour integration method. Inputting the prior SOC value into the pre-fitted SOC-second-order ECM parameter relationship yields the model parameter values ​​at the current moment. Using the model parameters combined with the input terminal voltage and current values, the OCV value can be calculated. After applying a variable-weight sliding window filter to the calculated OCV value, it is substituted into the pre-fitted third-order Gaussian-fitted OCV-SOC curve to obtain the observed SOC value. Kalman filtering is then applied to the predicted and observed SOC values ​​to obtain the posterior estimated SOC value, which is used as the initial SOC value for the next moment. This process is repeated until the iteration ends.

[0100] The updated Kalman filter formula is given below:

[0101] SOCpre(k)=SOC(k-1)-ηI(k-1) / (3600Q n )

[0102] Ppre = P + Q

[0103] SOC_ECM(k)=f(OCV_ECM_L(k))

[0104] K = (P + Q)(P + Q + R) -1

[0105] SOC(k)=SOCpre(k)+K(SOC_ECM(k)-SOCpre(k))

[0106] P = P + QK(P + Q) = (P + Q)(1 - K)

[0107] Where SOCpre(k) represents the prior SOC value at time k, SOC(k-1) represents the posterior SOC value at the previous time, η is the battery charge / discharge efficiency, and Q... n Here, K represents the battery capacity, OCV_ECM_L(k) represents the OCV value calculated by ECM at time k and then smoothed and filtered, f is the third-order Gaussian fitting formula after adding fitting points, and SOC_ECM(k) represents the SOC value obtained by the open-circuit voltage method at time k. At this point, the Kalman parameters have special physical meanings. Ppre can be considered the square of the SOC estimation error generated by the ampere-hour integration method, Q corresponds to the square of the SOC estimation error caused by the current sensor error, R is the square of the estimation error of the SOC value output by the open-circuit voltage method, and P corresponds to the square of the overall error. The P value can also be understood as the square of the error caused by the inaccuracy of the initial SOC value when calculating the SOC by the ampere-hour integration method at the next time step.

[0108] Analysis of the specific implementation process and advantages of the algorithm of this invention:

[0109] The flowchart of the specific algorithm implementation is as follows: Figure 2 As shown in the figure, U t I and T represent terminal voltage, current, and temperature, respectively. f_i(), i=1,2,…,5 correspond to the polynomial fitting formulas of ECM parameters R0, R1, C1, R2, C2, where the C matrix is ​​the coefficient matrix of the original observation equation in formula (2-5). OCV_ECM(k) is the OCV value calculated by the ECM model at time k.

[0110] In terms of advantages, when the current sensor deviates, assuming a discharge condition and the measurement result is too large, according to the ampere-hour integral calculation formula, the predicted SOCpre value is too small, and according to the OCV_ECM calculation formula, the calculated OCV_ECM value is too large. (Observation...) Figure 2-21 It is easy to see from the Gaussian fitting curves in 2-22 and 2-23 that the calculated SOC_ECM value will be too large at this point. This ensures that when the current sensor measurement deviates, the true SOC value lies between the predicted and observed SOC values, which conforms to the default probability density coupling form of Kalman filtering, increasing the accuracy and robustness of the filtering algorithm's SOC estimation. Furthermore, since the filtering algorithm in this invention uses SOC values ​​for both prediction and observation, it does not involve state transitions between prediction and observation, thus avoiding errors in the state transition process. The model equations do not contain the nonlinear part of the SOC-OCV fitting curve, therefore Taylor expansion is unnecessary, avoiding truncation errors and significantly reducing real-time computational complexity.

[0111] Algorithm performance verification based on dynamic working conditions:

[0112] To verify the accuracy and robustness of the proposed low-complexity SOC estimation algorithm, this invention applied a 1.2-fold current deviation to the measured data under the operating conditions of 15℃ DST, 25℃ FUDS, and 35℃ US06, and set an initial SOC deviation of 10% for algorithm performance verification. The SOC estimation results under the three operating conditions are as follows: Figure 27 , 28 As shown in Figure 29, the specific numerical results are shown in Table 6 (ME values ​​do not include the initial SOC deviation).

[0113] Observing the charts, it is easy to see that the algorithm proposed in this invention can converge quickly when faced with an initial applied 10% SOC deviation, and even with a 20% current deviation, the algorithm still maintains high estimation accuracy. This proves that the method proposed in this invention has high accuracy and robustness.

[0114] Table 6. Error values ​​of low-complexity SOC estimation algorithm under various operating conditions.

[0115]

[0116] Algorithm computational complexity and runtime efficiency analysis:

[0117] The low-complexity SOC estimation algorithm proposed in this invention reduces the computational dimensionality and complexity, and eliminates complex matrix operations, thereby improving the algorithm's running efficiency. This paper verifies the computation time of the proposed method on a 64-bit computer. The single-operation time of the proposed method is less than 5μs, which is 24.2% shorter than the classic EKF algorithm, fully meeting the requirements of BMS operation.

[0118] Key points and areas to be protected in this invention:

[0119] 1. A novel offline parameter identification method is adopted to reduce the magnitude difference between the parameters of the model to be identified and the fitted voltage, thereby improving the fitting accuracy.

[0120] 2. Improve fitting accuracy by using a third-order Gaussian fitting method with added fitting points to fit the OCV-SOC relationship curve. Classical polynomial fitting methods are suitable for SOC-OCV curve fitting, but using them to fit the OCV-SOC relationship curve will result in significant Runge's phenomenon.

[0121] 3. The OCV values ​​calculated using model parameters are subjected to sliding window filtering by changing the numerical weights within the window, which smooths the OCV curve, reduces fluctuation errors, and avoids error accumulation.

[0122] 4. Compared to classic model-based SOC estimation methods, this approach eliminates the need to fit SOC-OCV curves to calculate the observed voltage value, avoiding both fitting errors and state transition errors. Since both the predicted and observed values ​​are SOC values, computational complexity is reduced while eliminating nonlinear components and truncation errors.

[0123] 5. The observed value is the SOC value fitted by the open-circuit voltage method. When the current sensor deviates (assuming discharge conditions, the current sensor measurement result is too large), the SOC value calculated by the ampere-hour integration method is less than the true SOC value, while the OCV value calculated by the model is greater than the true OCV value. This corresponds to the observed SOC value being greater than the true SOC value, ensuring that the true SOC value is between the observed and predicted values, which greatly enhances the estimation accuracy and robustness of the filtering algorithm.

[0124] Matters not covered in this invention are common knowledge.

[0125] The above examples are merely illustrative of the technical concept and workflow of this invention, intended to enable those skilled in the art to understand and implement the invention, and should not be construed as limiting the scope of protection of this invention. For those skilled in the art, other variations or modifications can be made based on the above description; it is impossible to exhaustively list all possible implementations here. All equivalent changes or modifications made to the technical solution of this invention should be included within the scope of protection of this invention.

Claims

1. A low-complexity, high-precision, and robust method for estimating the state of charge of a battery, characterized in that, The method includes: The terminal voltage U is obtained based on the initial SOC value and sensor measurements. t The current value I is used to calculate the prior value of SOC at the current moment using the ampere-hour integration method; By inputting the prior SOC value into the pre-fitted SOC-ECM parameter relationship curve, the model parameter value at the current moment can be calculated. The OCV value can be calculated by combining the model parameter with the input terminal voltage and current values. Increase the number of measured OCV points, fit the OCV-SOC relationship using the third-order Gaussian formula, and then substitute the calculated OCV values ​​into the sliding window filter with different weights to obtain the observed SOC values. Based on the given filtering parameters: state vector covariance P, predicted state covariance Q, and observed state covariance R, Kalman filtering is applied to filter the predicted and observed SOC values ​​to obtain the posterior estimated SOC value, which is used as the initial SOC value for the next time step. The above process is repeated until the iteration ends. The discretized second-order ECM model expression for the battery is shown in equation (1): (1) Among them, U ocv Indicates the open-circuit voltage of the battery; U t R represents the terminal voltage applied to the load by the battery; I represents the current in the circuit, with the discharge current being positive; R0 represents the ohmic internal resistance of the battery; R1 represents the activation polarization resistor; R2 represents the concentration polarization resistor; k represents the parameter value at time k. The unit is a time interval; , These represent the activation and concentration polarization time constants, respectively, and their values ​​are the product of polarization resistance and capacitance. This represents the maximum usable capacity of the battery. Improve battery charging and discharging efficiency; The model parameters of the ECM can be identified through HPPC experimental test curves, namely, the pulse current excitation applied to the battery and the corresponding voltage change curves; the discharge current is specified as positive, where I... d I is the discharge current. c U is the charging current; U0 is the initial terminal voltage; Based on the equivalent circuit model, at the instant the battery discharge ends, the equivalent RC circuit is equivalent to a first-order zero-input response. According to the three-element method of first-order linear circuit analysis, it is easy to obtain: (2) Then, the activation polarization and concentration polarization voltages of the battery after discharge time t are respectively: (3) The parameters of the second-order ECM model are solved using the least squares fitting method with the exponential term as the basis. The specific process is as follows: (1) Selection of fitting interval: The polarization voltage expression after discharge follows an exponential fitting pattern. The t2-t3 interval of the depolarization process after discharge is selected to fit the model parameters. At time t2, a rapid voltage step U2-U5 occurs, which is caused by the ohmic internal resistance R0. The ohmic internal resistance at this time can be calculated as follows: (4) Choose to subtract the subsequent U from all data in the U5 to U6 interval. t The stable value is then taken as its negative to obtain the processed polarization voltage. (2) Exponential fitting based on least squares method: Since the fitting interval does not include the ohmic internal resistance R0 and the data has been processed to the same order of magnitude, the general form of exponential fitting is obtained: (5) Where a, b, c, and d are the parameters to be solved; By performing a 6th-order polynomial fitting on the ECM model parameter values ​​at each SOC point obtained by the above method, the relationship between ECM model parameters and SOC values ​​can be obtained.

2. The low-complexity, high-precision, and robust battery state-of-charge estimation method according to claim 1, characterized in that, The specific process of SOC estimation based on OCV values ​​in the method is as follows: (1) Calculation and filtering of OCV value: Due to the polarization effect under actual operating conditions of electric vehicles, the battery rarely reaches an equilibrium state, and the OCV value cannot be directly measured. Therefore, the OCV value is calculated using an ECM model. Based on equation (1), the formula for calculating the OCV value can be obtained as follows: (6) The sliding window filtering method is adopted for filtering, and the formula is shown in equation (7), where That is, the window size for smoothing filtering; (7) (2) Fitting of OCV-SOC relationship: A second-order Gaussian fitting method is pre-selected for fitting, and the fitting formula is as follows: SOC = a1*exp(-((OCV-b1) / c1)^2) + a2*exp(-((OCV-b 2) / c2)^2) Where a1, b1, c1, a2, b2, and c2 are the parameters to be solved; (3) Correction of filtering formula and fitting method Two processing methods were employed to refit the OCV-SOC relationship: adjusting the data weights within the smoothing filter window and increasing the number of OCV measurement points while raising the Gaussian fitting order. The details are as follows: By introducing weight allocation to the data within the smoothing window, decreasing the weight of preceding data and increasing the weight of subsequent data, error accumulation is reduced. The updated smoothing filter formula is shown below: (8) Where M L Take 10, , The values ​​were selected through trial and error, and were 0.5 and 1.

5. We selected additional fitting points and applied a third-order Gaussian to fit the OCV-SOC relationship, while controlling the addition of new fitting points to prevent overfitting.

3. The low-complexity, high-precision, and robust battery state-of-charge estimation method according to claim 2, characterized in that: The SOC value obtained by filtering the OCV value calculated using the ECM model and then substituting it into the Gaussian fitting formula is used as the observation value for Kalman filtering. The SOC value calculated using the ampere-hour integration method is used as the predicted value for Kalman filtering. The two are then filtered together using the following filtering formula: predict: (9) (10) Observation: (11) renew: (12) (13) (14) in SOC represents the prior SOC value at time k, and SOC(k-1) represents the posterior SOC value at the previous time. For battery charging and discharging efficiency, represents the battery capacity, K represents the Kalman gain; f is the second-order Gaussian fitting formula in equation (6); Ppre can be regarded as the square of the SOC estimation error generated by the ampere-hour integration method, Q corresponds to the square of the SOC estimation error caused by the current sensor error, R is the square of the estimation error of the SOC value output by the open-circuit voltage method, P corresponds to the square of the overall error, and P is the square of the error caused by the inaccuracy of the initial SOC value when the ampere-hour integration method calculates the SOC at the next moment.

4. The low-complexity, high-precision, and robust battery state-of-charge estimation method according to claim 3, characterized in that, When the current sensor deviates, assuming a discharge condition, the predicted SOCpre value is too small according to the ampere-hour integral calculation formula, and the calculated OCV_ECM value is too large according to the OCV_ECM calculation formula. Since OCV_ECM is positively correlated with the observed SOC value, the calculated observed SOC value is too large. This ensures that when the current sensor measurement deviates, the true SOC value is between the predicted and observed SOC values, increasing the accuracy and robustness of the SOC estimation by the filtering algorithm.

5. A low-complexity, high-precision, and robust battery state-of-charge estimation system, characterized in that: The system has a program module corresponding to the steps of any one of claims 1-4, and executes the steps in the low-complexity, high-precision, and robust battery state-of-charge estimation method when it is run.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the low-complexity, high-precision, and robust battery state-of-charge estimation method according to any one of claims 1-4.

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