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

Abstract

The invention discloses a low-complexity, high-precision and high-robustness battery state of charge estimation method and system, relates to the field of battery state of charge estimation, and aims to solve the problems of high cost, to-be-improved precision, poor robustness and the like of the existing battery state of charge estimation technology. According to the technical key points, firstly, a second-order equivalent circuit model is established through an off-line experiment, an off-line parameter identification means is adopted, the magnitude difference between to-be-identified model parameters and fitting voltage is reduced, and the fitting precision is improved; and fitting the relationship between the model parameters obtained by the off-line parameter identification and the SOC, and fitting an OCV-SOC relationship curve by using the third-order Gaussian after the fitting points are added. A battery end voltage and a current value measured by a sensor in real time are input into an ECM model for calculating an OCV value, sliding window filtering of variable weight distribution is carried out on the calculated OCV value to smooth a curve and reduce errors, a filtered result is fitted through an OCV-SOC relation curve to obtain an SOC value, and the SOC value is used as an observation value of subsequent Kalman filtering. A predicted value is calculated by using an ampere-hour integral method, and a current model parameter is fitted by using the priori value in combination with a relationship between the model parameter and the SOC. And finally, Kalman filtering is carried out on the two to obtain a posterior SOC value.

Description

Technical Field

[0001] The present invention relates to the technical field of battery state of charge estimation, and in particular to a battery state of charge estimation method and system with low complexity, high precision and strong robustness. Background Art

[0002] A battery's state of charge (SOC) is a fundamental parameter that indicates the remaining available capacity. Accurately estimating SOC is not only a fundamental requirement for estimating the range of electric vehicles, but also a fundamental guarantee for improving battery efficiency and safety. Therefore, accurately obtaining the real-time SOC value of power batteries is extremely important. However, in practical applications, SOC values ​​cannot be directly measured and can only be estimated using external physical parameters such as voltage, current, and temperature. Therefore, accurate SOC estimation remains a challenging goal.

[0003] At present, 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 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 current measurement to estimate SOC. The open-circuit voltage method pre-establishes the relationship between open-circuit voltage (OCV) and SOC through offline experiments. The SOC value can be estimated based on the OCV value of the battery in its current state.

[0005] The SOC estimation method based on the battery model is usually combined with various observers and filters. The state monitor-based method is committed to minimizing the error between the observed state and the actual state through a closed-loop feedback system, and ultimately regards the observed value as the actual state value. The state observer-based methods mainly include Luenberger observer, proportional integral observer, sliding film observer and nonlinear robust observer. The filter-based method filters the state value and the observation value to obtain the final result. The filter-based method is widely used in the online estimation of battery SOC due to its low computational complexity and high accuracy. The filter-based methods mainly include Kalman filtering, particle filtering and HIF filtering, among which Kalman filtering is the most widely used.

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

[0007] As research deepens, researchers have proposed various joint estimation methods after comprehensively considering the advantages and disadvantages of the above-mentioned methods. In his doctoral thesis, Dr. Guo Xiangwei of South China University of Technology combined the ampere-hour integration method with the open-circuit voltage method, and used the open-circuit voltage method to correct the cumulative error caused by current measurement deviation in the ampere-hour integration method at a specific SOC. In his doctoral thesis, Dr. Lu Chusheng of South China University of Technology combined the data-driven method with the open-circuit voltage method, using a battery model constructed using a neural network to calculate the OCV value, and then used the open-circuit voltage method to obtain the SOC value, realizing a simple SOC estimation method based on a linearized equivalent circuit model. Dr. Appiah Emmanue of Southwest University of Science and Technology combined the long short-term memory neural network (LSTM) with the unscented Kalman filter algorithm (UKF), simulated the battery behavior parameters at different temperatures through LSTM to estimate the SOC, and used 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 improved IAKF. The SOC calculated by ampere-hour integration and the SOC estimated by deep learning were used as the prediction and observation values ​​of the improved intelligent adaptive Kalman filter algorithm, respectively. After filtering both, a higher SOC estimation accuracy was obtained.

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

[0009] Traditional method: The ampere-hour integration method is a method that directly estimates 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 will continue to accumulate over time. The open circuit voltage method, also known as the offline lookup table method, can establish a correspondence between SOC and open circuit voltage (OCV) in advance and draw an offline table. When we need to estimate the SOC value, we can get it by the corresponding OCV value under the current operating conditions. However, under actual operating conditions, the battery rarely reaches a state of equilibrium, which means that the OCV value cannot be directly measured.

[0010] Battery Model-Based Methods: A growing number of studies indicate that the Kalman filter appears to be the most practical method for SOC estimation in electric vehicles. The core idea of ​​the Kalman filter is to couple the Gaussian probability density of the predicted state with the observed state to obtain the optimal state estimate. Since the Kalman filter is only applicable to linear systems, and the relationship between the open-circuit voltage and SOC in the observation equation of the battery model is nonlinear, the Extended Kalman Filter (EKF) has become widely used. The core idea of ​​the EKF is to linearize the nonlinear components of the system by ignoring higher-order terms after Taylor expansion. Specifically, its application in battery SOC estimation involves linearizing the open-circuit voltage in the observation equation. However, current SOC estimation methods using the EKF generally use a first-order Taylor expansion, which suffers from significant truncation errors. Increasing the order of the Taylor expansion significantly increases the computational complexity. To circumvent this problem, the Unscented Kalman Filter (UKF) was proposed. The core idea of ​​the UKF is to replace the Taylor expansion with an unscented transformation of the sigma point to achieve a nonlinear-to-linear transformation, thereby reducing the truncation error. However, UKF faces challenges such as high computational complexity and sensitivity to initial conditions and parameter selection that need to be addressed. Meanwhile, the Kalman filter method, combined with the battery model, uses the ampere-hour integral to calculate the SOC, which is then transformed through the state transition matrix to produce a predicted value and the measured terminal voltage as the observed value. This process involves conversion errors, and due to the randomness of the errors in the measured current and terminal voltage, the predicted and observed errors may have the same sign, meaning that the predicted and observed values ​​are on the same side of the true value. This significantly reduces the Kalman filter's predictive effectiveness.

[0011] Data-driven methods use machine learning to train large amounts of data and establish a model of the input-output relationship. These methods offer significant advantages in estimating battery SOC, as they don't require a precise battery model and can handle complex nonlinear relationships. However, these methods are highly data-dependent, have limited generalization capabilities, are computationally complex, require high hardware, and are prone to underfitting or overfitting.

[0012] All of the above-mentioned joint estimation methods also have limitations. The method proposed by Dr. Guo Xiangwei, which combines ampere-hour integration with open-circuit voltage, uses the ampere-hour integration method to calculate the SOC value fitting model parameters, and then uses the model parameters to calculate the OCV value for fitting the corrected SOC value. The model parameters of this method have large errors at the uncorrected SOC and are highly dependent on the OCV calculation accuracy and the OCV-SOC curve fitting accuracy. The final core estimation step of the joint estimation method proposed by Dr. Lu Chusheng still relies on the OCV-SOC curve. Compared with Dr. Guo Xiangwei, his OCV value is calculated using a neural network model. This method avoids the problem of large errors in model parameters at the uncorrected SOC, but at the same time introduces data-driven methods with high computational complexity, high hardware requirements, and prone to underfitting or overfitting. Dr. Appiah Emmanue combined the data-driven method with the filtering method, using the LSTM network to predict the battery terminal voltage and the third-order equivalent circuit model, and using the UKF method for filtering. This method has state transfer errors and high computational complexity during the filtering process. The method proposed by the author in the previous patent can avoid state transfer errors and reduce computational complexity to a certain extent. However, due to the randomness of the errors in the measured current and terminal voltage, it cannot guarantee that the true value is located in the center of the predicted and observed values, and the optimal filtering effect cannot be achieved. At the same time, the introduction of the neural network method also has high hardware requirements, requires a large amount of training data, and is costly.

[0013] In order to solve the problems existing in the above methods, it is imperative to propose a low-complexity, high-precision and strong robust battery state of charge estimation method. Summary of the Invention

[0014] The technical problems to be solved by the present invention are:

[0015] The present invention is proposed to solve the problems of the existing battery state of charge estimation technology, such as high cost, need for improved accuracy, and poor robustness.

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

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

[0018] The terminal voltage (U t ), current value (I), and use the ampere-hour integration method to calculate the SOC prior value at the current moment;

[0019] Input the SOC priori value into the pre-fitted SOC-ECM parameter relationship curve to calculate the model parameter value at the current moment. The OCV value can be calculated by combining the model parameters with the input terminal voltage and current values.

[0020] Increase the number of measured OCV points, use the third-order Gaussian formula to fit the OCV-SOC relationship, and filter the calculated OCV value with a sliding window that changes the weight distribution to obtain the observed SOC value.

[0021] According to the given filtering parameters: state vector covariance P, predicted state covariance Q, and observed state covariance R, the Kalman filter 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 at the next moment. The above 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, the present 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 highly robust battery state-of-charge estimation method. In terms of preliminary work, the present invention first establishes a second-order equivalent circuit model (ECM) through offline experiments. A novel offline parameter identification method is used to reduce the magnitude difference between the model parameters to be identified and the fitted voltage, thereby improving fitting accuracy. The relationship between the model parameters obtained through offline parameter identification and the SOC is fitted using a sixth-order polynomial. The number of measured OCV fitting points is increased, and a third-order Gaussian fit is used to fit the OCV-SOC relationship curve. During the actual prediction process, the present invention inputs the real-time sensor-measured battery terminal voltage and current values ​​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 then fitted to the OCV-SOC relationship curve to obtain the SOC value, which serves as the observation value for the subsequent Kalman filter. The predicted value (prior value) is calculated using the ampere-hour integration method, and the current model parameters are fitted using this prior value combined with the relationship between the model parameters and the SOC. Finally, a Kalman filter is applied to both to obtain the posterior SOC value.

[0024] The advantages of the present invention are as follows:

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

[0026] 2. Add more fitting points and use a third-order Gaussian to fit the OCV-SOC relationship curve to find the balance between overfitting and underfitting and improve fitting accuracy. Classic polynomial fitting methods are suitable for SOC-OCV curve fitting, but using them to fit the OCV-SOC relationship curve will result in a more severe Runge phenomenon.

[0027] 3. The OCV value calculated using the model parameters is subjected to sliding window filtering with variable weight distribution to smooth the OCV curve, reduce the fluctuation error and avoid the occurrence of error accumulation.

[0028] 4. Compared to classic model-based SOC estimation methods, this approach eliminates the need to fit the SOC-OCV curve to calculate the observed terminal voltage, thus avoiding both fitting errors and state transition errors. Both the predicted and observed values ​​are SOC values, reducing computational complexity while eliminating nonlinearities and avoiding truncation errors.

[0029] 5. The observed value is the SOC value fitted by the open-circuit voltage method. When the current sensor deviates (assuming a discharge condition, the current sensor measurement result is biased), the SOC value calculated by the ampere-hour integration method is lower than the true SOC value. However, the OCV value calculated by the model is higher than the true OCV value, which corresponds to the observed SOC value being higher than the true SOC value. This ensures that the true SOC value lies between the observed and predicted values, greatly enhancing the estimation accuracy and robustness of the filtering algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is the overall flow chart of the algorithm of the present invention; Figure 2 It is a flow chart of the algorithm of the present invention; Figure 3 Response diagram of the model, in which: a is the second-order ECM model diagram, b is the current excitation and voltage response diagram; Figure 4 is the polarization voltage curve after treatment; Figure 5 This is the exponential fitting effect diagram at 100% SOC at 25℃;

[0031] Figure 6 The comparison chart of the OCV calculation accuracy before and after filtering under the DST working condition at 15°C is shown in the figure: (a) is OCV, (b) is error; Figure 7 The comparison chart of the OCV value calculation accuracy before and after filtering under FUDS working conditions at 25°C is shown in the figure: (a) is OCV, (b) is error; Figure 8 This is a comparison chart of the OCV value calculation accuracy before and after filtering for the US06 operating condition at 35°C. In the figure: (a) is OCV, (b) is error;

[0032] Figure 9 This is a comparison chart of the second-order, third-order polynomial fitting and second-order Gaussian fitting effects at 15°C. Figure 10 This is a comparison chart of the second-order, third-order polynomial fitting and second-order Gaussian fitting effects at 25°C. Figure 11 Comparison of the fitting results of second-order and third-order polynomials and second-order Gaussian at 35°C;

[0033] Figure 12The battery SOC performance diagram estimated by the open circuit voltage method under DST conditions at 15°C, where: (a) is SOC, (b) is error; Figure 13 The performance diagram of battery SOC estimation using the open circuit voltage method under FUDS operating conditions at 25°C, where (a) is SOC and (b) is error. Figure 14 The battery SOC performance diagram estimated by the open circuit voltage method under US06 operating conditions at 35°C, where (a) is SOC and (b) is error.

[0034] Figure 15 The battery SOC performance diagram is estimated by the actual open circuit voltage under DST conditions at 15°C. In the figure: (a) is SOC, (b) is error; Figure 16 The battery SOC performance diagram estimated by the actual open circuit voltage under FUDS working conditions at 25°C, in which: (a) is SOC, (b) is error; Figure 17 The battery SOC performance diagram is estimated by the actual open circuit voltage of the US06 operating condition at 35°C. In the figure: (a) is SOC, (b) is error;

[0035] Figure 18 Comparison of the OCV calculation accuracy before and after filtering after updating the filtering formula for the DST condition at 15°C. In the figure: (a) is OCV, (b) is error; Figure 19 Comparison of the OCV calculation accuracy before and after filtering after updating the filtering formula for the FUDS working condition at 25°C. In the figure: (a) is OCV, (b) is error; Figure 20 Comparison of OCV calculation accuracy before and after filtering after updating the filtering formula for the US06 operating condition at 35°C. In the figure: (a) is OCV, (b) is error;

[0036] Figure 21 The second-order and third-order Gaussian fitting effects are shown after adding fitting points at 15°C. Figure 22 This is the second-order and third-order Gaussian fitting effect diagram after adding fitting points at 25℃. Figure 23 The second-order and third-order Gaussian fitting effects after adding fitting points at 35°C;

[0037] Figure 24 The open circuit voltage method for estimating battery SOC performance after optimization for DST conditions at 15°C. In the figure: (a) is SOC, (b) is error; Figure 25 The open circuit voltage method for estimating battery SOC performance after optimization of FUDS operating conditions at 25°C. In the figure: (a) is SOC, (b) is error; Figure 26 The open circuit voltage method is optimized for the US06 operating condition at 35°C to estimate the battery SOC performance. In the figure: (a) is the SOC, and (b) is the error.

[0038] Figure 27The patented low-complexity, high-precision, and robust method for estimating battery SOC performance under 15°C DST conditions is shown in the figure: (a) is SOC, and (b) is error; Figure 28 The patented low-complexity, high-precision, and robust method for estimating battery SOC performance under 25°C FUDS conditions is shown in the figure: (a) is SOC, and (b) is error; Figure 29 The patented low-complexity, high-precision, and robust method for estimating battery SOC performance under 35°C US06 operating conditions is used. In the figure: (a) is SOC, and (b) is error. DETAILED DESCRIPTION

[0039] Give Attachment Figure 1-29 The implementation of a low-complexity, high-precision, and highly robust battery state-of-charge estimation method and system of the present invention is described as follows:

[0040] like Figure 1 The figure shows the overall flow chart of the algorithm. The input values ​​in the figure are the initial SOC value and the terminal voltage (U t ), current value (I), and the ampere-hour integration method can be used to calculate the SOC priori value at the current moment. The SOC priori value is input into the pre-fitted SOC-ECM parameter relationship to obtain the model parameter value at the current moment. The OCV value can be calculated by combining the model parameters with the input terminal voltage and current values; the number of measured OCV points is increased, and the OCV-SOC relationship is fitted using the third-order Gaussian formula. The calculated OCV value is filtered with a sliding window with improved weight distribution and then brought into the relationship to obtain the observed SOC value (the calculated OCV value is filtered with a sliding window and then brought into the pre-fitted Gaussian fitting OCV-SOC curve to obtain the observed SOC value). Given the filtering parameters, state vector covariance: P; predicted state covariance: Q; observed state covariance: R. Apply Kalman filtering to filter the predicted and observed SOC values ​​to obtain the posterior estimated SOC value, which is used as the initial SOC value at the next moment. Repeat the above process until the iteration ends.

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

[0042] The mathematical model establishment process of this model has been detailed, so it will not be deduced in detail here. The discretized battery model expression is shown in Equation (1). Where k represents the parameter value at time k; Δt is the unit of 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 is the maximum available capacity of the battery; η is the battery charge and discharge efficiency.

[0043]

[0044] The model parameters of ECM can be identified through the HPPC experimental test curve, such as Figure 3 The figure shows the pulse current excitation applied to the battery and the corresponding voltage change curve. d is the discharge current, I c 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] According to the equivalent circuit model, when the battery discharge is completed, 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:

[0046]

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

[0048]

[0049] At this point, the least squares fitting method based on exponential terms can be used to solve the dual-polarization ECM model parameters. The specific process is as follows:

[0050] (1) Selection of fitting interval:

[0051] Considering that the polarization voltage expression after the discharge is simpler and more in line with the exponential fitting situation, this interval is selected to fit the model parameters, that is, the depolarization process (t2-t3) interval after the discharge is completed is used to fit the model parameters;

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

[0053]

[0054] Considering that R1 and R2 are both of very small magnitude, it is easy to see from the image that although the difference between U5 and U6 is small, its magnitude is large, and it is easy to see that U t It is increasing, indicating that the polarization voltage is decreasing. If we directly select the U5 to U6 interval on the image for fitting, the magnitude difference will be too large and the fitting accuracy will decrease. In order to reduce the magnitude difference and conform to the trend of polarization voltage change, we choose to subtract the subsequent U from the U5 to U6 interval data. t The stable value and take its opposite. The image is as follows Figure 4 As shown. Image vertical coordinate U t ' is the polarization voltage after treatment.

[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, it is easy to obtain the general form of exponential fitting:

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

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

[0059] observe Figure 5 It is not difficult to find that the fitting effect is better after polarization voltage treatment. The calculated correlation coefficient squared (R-square) value of the fitting reaches 0.9969, and the root mean square error (RMSE) value is as low as 0.0001, further indicating the high accuracy of the fitting.

[0060] The model parameter values ​​at each SOC point obtained by the above method are fitted with a 6th-order polynomial to obtain the ECM model parameter-SOC value relationship expression.

[0061] The process of SOC estimation based on OCV value is:

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

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

[0064] Based on formula (1), the OCV value calculation formula is as follows:

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

[0066] If the OCV value calculated by the ECM model is used directly for SOC estimation without filtering, the estimation result will have large fluctuations. The invention adopts the sliding window filtering method for filtering, and the formula is shown in formula (7). L This is the window size of the smoothing filter.

[0067]

[0068] The present invention selects 15℃ DST working condition, 25℃ FUDS working condition, and 35℃ US06 working condition to compare the OCV value calculation accuracy before and after filtering under different smoothing filter window sizes. The real OCV value is obtained by fitting a 6th-order polynomial through the aforementioned OCV test experiment, which corresponds to the fitting relationship between ECM parameters and SOC. Figure 6 、 7 , 8, and the specific numerical results are shown in Table 1.

[0069] Table 1 Different M under various working conditions L OCV calculation error before and after smoothing filtering

[0070]

[0071] By 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 has large fluctuations, and can only reduce the maximum error of the OCV value calculation under some working conditions, while the RMSE value is generally too large; when the smoothing filter window size is 15, although the RMSE value is reduced under some working conditions, it will greatly increase the maximum error of the OCV value calculation. In comprehensive analysis, the comprehensive performance of the OCV value calculation is best when the smoothing filter window size is 10, that is, M L =10.

[0072] (2) OCV-SOC relationship fitting:

[0073] The SOC estimation based on OCV value, namely the open circuit voltage method, establishes the corresponding relationship between SOC and OCV in advance and directly obtains the estimated SOC value based on the OCV value under the current operating conditions. However, unlike fitting the SOC-OCV curve, when fitting the OCV-SOC curve, if a polynomial fit is used, a large error will occur. In this invention, the second-order Gaussian fitting method is pre-selected for fitting, and the fitting formula is as follows:

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

[0075] Among them, a1, b1, c1, a2, b2, and c2 are the parameters to be solved. When using a high-order polynomial to fit the SOC-OCV relationship, a serious Runge phenomenon will occur, resulting in serious distortion. Therefore, the present invention selects 15°C, 25°C, and 35°C to compare the second-order and third-order polynomial fitting with the second-order Gaussian fitting effect. Figure 9 、 10 , 11. It's easy to see from the figures that the second-order polynomial fit is inaccurate, while the third-order polynomial fit exhibits Runge's phenomenon. Compared to the polynomial fit, the second-order Gaussian fit provides a better fit. However, the OCV-SOC curve fit accuracy is poorer at 15°C than at 25°C and 35°C.

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

[0077] The present invention selects 15℃ DST working condition, 25℃ FUDS working condition and 35℃ US06 working condition to verify the accuracy of SOC estimation by open circuit voltage method. The estimation results are as follows: Figure 12 、 13 , 14, and the specific numerical results are shown in Table 2.

[0078] It is not difficult to find out from the chart that when the open circuit voltage method is used alone to estimate the battery SOC, even if the initial SOC deviation and current measurement deviation are not applied (the present invention directly uses the ampere-hour integral to calculate the SOC value, that is, the real SOC value in the absence of current error updates the ECM parameters for OCV calculation), there is still a large error, which cannot meet the estimation accuracy requirements.

[0079] Table 2 Error values ​​of SOC estimated by open circuit voltage method under various working conditions

[0080]

[0081] The reasons why the above estimation method has large errors are now explored, and analysis shows that there are two possibilities: 1. The calculation accuracy of the OCV value based on the ECM model is insufficient; 2. The second-order Gaussian fitting accuracy is insufficient. Comparing Table 1 and Table 2, it is not difficult to find that due to the high accuracy of the OCV after filtering under the 35℃ US06 working condition, the SOC estimation error in its corresponding Table 2 is the smallest, which proves that the large error in the above estimation method is related to the accuracy of the OCV value calculation. Similarly, although the 15℃ DST working condition has excellent OCV calculation accuracy, due to its poor fitting accuracy when performing second-order Gaussian fitting, there is still a large error when performing SOC estimation, which proves that the insufficient second-order Gaussian fitting accuracy is also the main reason for the large error in the above estimation algorithm. In order to further verify the conjecture, the present invention directly brings the real OCV value into the second-order Gaussian fitting formula under each working condition to test the SOC estimation performance at this time. The estimation results are as follows. Figure 15 、 16 , 17, and the specific numerical results are shown in Table 3.

[0082] Looking at the chart, it's easy to see that directly using the actual OCV value for estimation significantly reduces SOC estimation bias, but significant bias still exists. Furthermore, since the second-order Gaussian fit accuracy is the worst at 15°C, the corresponding estimation error is the largest. This demonstrates that the significant error in the open-circuit voltage-based SOC estimation method is caused by both insufficient OCV calculation accuracy and insufficient second-order Gaussian fit accuracy.

[0083] Table 3 SOC error estimated by real open circuit voltage

[0084]

[0085] To solve the above two problems, the present invention adopts two processing methods: adjusting the data weight within the smoothing filter window; increasing the OCV value measurement points and improving the Gaussian fitting order, and refitting the OCV-SOC relationship. The specific analysis is as follows:

[0086] observe Figure 6 、 7 , 8 It is not difficult to find that with the increase of the smoothing filter window size, the RMSE value of the estimation result continues to decrease (only the 15℃ DST condition is an exception. The increase in RMSE here is due to the excessive maximum error value in the late stage of smoothing filter), while the maximum error of the estimation result continues to increase, and all occurs in the late stage of estimation. Observation formula SOC=a1*exp(-((OCV-b1) / c1)^2)+a2*exp(-((OCV-b 2)It's not difficult to find that increasing the smoothing filter window can effectively reduce fluctuations in OCV value calculations, thereby lowering the RMSE value. However, since subsequent filtering results are always affected by the preceding data and the weights of the data within the smoothing window are consistent, increasing the smoothing filter window in such cases will exacerbate the error accumulation phenomenon. To address this issue, the present invention introduces a weight distribution for the data within the smoothing window, reducing the weight of the preceding data and increasing the weight of the subsequent data, thereby reducing error accumulation. The updated smoothing filter formula is shown below.

[0087]

[0088] Among them, M L Still taking 10, α and β are selected by trial and error, and the present invention selects 0.5 and 1.5. The filtering result of the updated filtering formula is introduced Figure 18 、 19 , 20, and the specific numerical results are shown in Table 4.

[0089] It is not difficult to observe the chart and find that after introducing the updated smoothing filter formula, although the RMSE value of the OCV calculation 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] Properly increasing the number of fitting points can effectively improve the fitting accuracy, but it also faces the risk of overfitting. In order to find the best balance between overfitting and underfitting, the present invention re-performed the OCV test experiment, calibrated the OCV value at every 5% SOC interval, and tried to further increase the Gaussian fitting order to enhance its nonlinear fitting ability, and finally make the fitting result closer to the real distribution. After increasing the fitting points, the second-order Gaussian fitting and third-order Gaussian fitting effects at each temperature are shown as follows: Figure 2-21 , 2-22, and 2-23.

[0093] contrast Figure 21 、 22 , 23 and Figure 9 、 10, it is not difficult to find that the fitting accuracy of 11 can be further improved by using the third-order Gaussian fitting after adding the fitting points. Therefore, the present invention subsequently chooses to add fitting points and applies the third-order Gaussian to fit the OCV-SOC relationship. It should be noted that if the second-order Gaussian is used for fitting after adding the fitting points in the 25°C environment, the fitting accuracy is lower than before the fitting points are added, which indicates that overfitting has occurred in this case. In contrast, the fitting accuracy is greatly improved after adding the fitting points in the 15°C environment compared to before the fitting points are added. After analysis, it is not difficult to know that this is because the fitting accuracy is low when the fitting points are not added in the previous order, so there is no overfitting after adding the fitting points.

[0094] The overfitting phenomenon is caused by insufficient quality of the newly added fitting point data. Figure 10 、 11 , 22, and 23 are difficult to find. Even if the second-order Gaussian fitting is continued with adding fitting points at 35°C, the fitting accuracy is still relatively high. This is because the data measurement quality is better at 35°C (the optimal operating temperature of this battery is around 35°C), so the newly added fitting points will not cause overfitting.

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

[0096] It is not difficult to find out from the above charts that the open circuit voltage method after optimization under 15℃ and 25℃ working conditions has greatly improved the estimation accuracy of the SOC value compared with that before optimization. The improvement under 35℃ working conditions is not significant because the OCV calculation accuracy and the OCV-SOC relationship fitting accuracy are both high before optimization. However, there is still a lot of room for improvement in the SOC estimation accuracy under the above temperature conditions. At the same time, it is not difficult to find out from the analysis that the robustness of this method is poor. When the sensor measures the current and terminal voltage and there is a deviation, it will directly affect the OCV calculation accuracy, and then affect the SOC estimation accuracy. The decrease in SOC estimation accuracy will directly affect the ECM parameter solution accuracy, and ultimately react to the OCV calculation accuracy. Such situations will continue to accumulate SOC estimation deviations, resulting in divergence of the estimated value. In order to enhance the robustness of the algorithm and avoid the occurrence of such phenomena, the present invention will subsequently introduce the Kalman filter algorithm.

[0097] Table 5 SOC estimation error values ​​of the optimized open circuit voltage method under various working conditions

[0098]

[0099] According to the above analysis, it is not difficult to know that even if the OCV value calculated by ECM is improved by the filtering method, and the OCV-SOC relationship is fitted with a third-order Gaussian with higher accuracy after adding fitting points, there is still a large SOC estimation deviation when the open circuit voltage method is used alone for SOC estimation. In comparison, SOC estimation based on extended Kalman filtering is widely used because of its good robustness, but the estimation results are prone to divergence in the later stage of estimation, and it involves matrix operations, and the computational complexity is greater than the open circuit voltage method. In response to this phenomenon, the present invention introduces the idea of ​​dimensionality reduction of the state equation and updates the Kalman filter formula to complement the two methods. Different from the classic EKF algorithm based on the ECM model, the present 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 above-mentioned open circuit voltage method as the observed value of the filtering algorithm. At this time, the three-dimensional state equation of the traditional battery is simplified to one dimension, and the state equation no longer contains the calculation of the polarization voltage value, thereby avoiding the predicted SOC value to the observed U t The conversion process of the value simplifies the calculation complexity and increases the accuracy of SOC estimation. The overall process of the algorithm 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 SOC prior value at the current moment can be calculated using the ampere-hour integration method. The SOC prior value is input into the pre-fitted SOC-second-order ECM parameter relationship to obtain the model parameter value at the current moment. The OCV value can be calculated using the model parameters combined with the input terminal voltage and current values. The calculated OCV value is filtered with a variable weight sliding window and then brought into the pre-fitted third-order Gaussian fitting OCV-SOC curve to obtain the observed SOC value. The predicted and observed SOC values ​​are filtered using a Kalman filter to obtain the posterior estimated SOC value, which is used as the initial SOC value at the next moment. The above process is repeated until the iteration ends.

[0100] The updated Kalman filter formula is given as follows:

[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 moment, η is the battery charge and discharge efficiency, Q n represents the battery capacity, K represents the Kalman gain, OCV_ECM_L(k) represents the smoothed OCV value calculated by the ECM at time k, f represents the third-order Gaussian fit formula after adding the fitting points, and SOC_ECM(k) represents the SOC value calculated by the open-circuit voltage method at time k. The Kalman parameters here have special physical meanings. Ppre can be considered the square of the SOC estimation error caused by the ampere-hour integration method, Q corresponds to the square of the SOC estimation error caused by current sensor error, R is the square of the estimated SOC value output by the open-circuit voltage method, and P corresponds to the square of the overall error. P can also be understood as the square of the error caused by the inaccurate initial SOC value when the ampere-hour integration method is used to calculate the SOC at the next moment.

[0108] Specific implementation process and superiority analysis of the algorithm of the present invention:

[0109] The specific algorithm implementation flow chart is given below: Figure 2 As shown in the figure, U t Where I, T represent the terminal voltage, current, and temperature, respectively. f_i(), i = 1, 2, …, 5, corresponds to the polynomial fitting formulas for the ECM parameters R0, R1, C1, R2, and C2, respectively. 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 superiority, when the current sensor deviates, it is assumed that it is a discharge condition and the measurement result is too large. According to the ampere-hour integral calculation formula, the predicted SOCpre value at this time is too small. According to the OCV_ECM calculation formula, the OCV_ECM calculated value is too large at this time. Figure 2-21 It is not difficult to find from the Gaussian fitting curves in 2-22 and 2-23 that the observed SOC_ECM calculated value will be too large at this time. This ensures that when the current sensor measurement deviates, the true SOC value is between the predicted and observed SOC values, which conforms to the default probability density coupling form of the Kalman filter and increases the accuracy and robustness of the SOC estimation of the filtering algorithm. At the same time, since the predicted and observed values ​​of the filtering algorithm in the invention are both SOC values, there is no state transition between the predicted and observed values, thereby avoiding errors in the state transition process; there is no nonlinear part of the SOC-OCV fitting curve in the model equation, so there is no need to perform Taylor expansion, which avoids truncation errors while greatly reducing the complexity of real-time calculations.

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

[0112] In order to verify the accuracy and robustness of the proposed low-complexity SOC estimation algorithm, the present invention applies a 1.2-fold current deviation to the measured data under 15°C DST, 25°C FUDS, and 35°C US06 operating conditions, and sets a 10% initial SOC deviation to verify the algorithm performance. The SOC estimation results under the three operating conditions are shown in Figure 2. Figure 27 、 28 , 29, and the specific numerical results are shown in Table 6 (the ME value does not include the initial SOC deviation).

[0113] The graph shows that the proposed algorithm converges quickly with an initial 10% SOC deviation, and maintains high estimation accuracy even with a 20% current deviation. This demonstrates the high accuracy and robustness of the proposed method.

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

[0115]

[0116] Analysis of algorithm computational complexity and operating efficiency:

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

[0118] The key points and points to be protected of the present invention are:

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

[0120] 2. Use a third-order Gaussian with additional fitting points to fit the OCV-SOC curve to improve fitting accuracy. Classical polynomial fitting methods are suitable for SOC-OCV curve fitting, but will exhibit a more severe Runge phenomenon when used to fit the OCV-SOC curve.

[0121] 3. The OCV value calculated using the model parameters is subjected to sliding window filtering by changing the numerical weight within the window to smooth the OCV curve, reduce the fluctuation error and avoid error accumulation.

[0122] 4. Compared to classic model-based SOC estimation methods, this approach eliminates the need to fit the SOC-OCV curve to calculate the observed terminal voltage, thus avoiding both fitting errors and state transition errors. Both the predicted and observed values ​​are SOC values, reducing computational complexity while eliminating nonlinearities and avoiding truncation errors.

[0123] 5. The observed value is the SOC value fitted by the open-circuit voltage method. When the current sensor deviates (assuming a discharge condition, the current sensor measurement result is biased), the SOC value calculated by the ampere-hour integration method is lower than the true SOC value, while the OCV value calculated by the model is higher than the true OCV value. This corresponds to the observed SOC value being higher than the true SOC value. This ensures that the true SOC value lies between the observed and predicted values, greatly enhancing the estimation accuracy and robustness of the filtering algorithm.

[0124] Matters not covered by the present invention are known technologies.

[0125] The above-mentioned implementation examples are merely for the purpose of illustrating the technical concept and workflow of the present invention in detail. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not possible to enumerate all implementation methods here. Any equivalent variations or modifications made based on the technical solution of the present invention are intended to fall within the scope of protection of the present invention.

Claims

1. A low-complexity, high-precision, and robust battery state-of-charge estimation method, characterized in that: The method comprises: The terminal voltage (U t ), current value (I), and use the ampere-hour integration method to calculate the SOC prior value at the current moment; Input the SOC priori value into the pre-fitted SOC-ECM parameter relationship curve to calculate the model parameter value at the current moment. The OCV value can be calculated by combining the model parameters with the input terminal voltage and current values. Increase the number of measured OCV points, use the third-order Gaussian formula to fit the OCV-SOC relationship, and filter the calculated OCV value with a sliding window that changes the weight distribution to obtain the observed SOC value. According to the given filtering parameters: state vector covariance P, predicted state covariance Q, and observed state covariance R, the Kalman filter 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 at the next moment. The above process is repeated until the iteration ends.

2. The low-complexity, high-precision, and strong-robust battery state-of-charge estimation method according to claim 1, characterized in that: The discretized battery second-order ECM model expression is shown in formula (1): Among them, U ocv Indicates the open circuit voltage of the battery; U t represents the terminal voltage applied by the battery to both ends of the load; I represents the current in the circuit, and the discharge current is positive; R0 represents the ohmic internal resistance in the battery; R1 represents the activation polarization resistance; R2 represents the concentration polarization resistance; k represents the parameter value at time k; Δt is the unit of time interval; τ1 and τ2 represent the activation and concentration polarization time constants, respectively, and their values ​​are the product of polarization resistance and capacitance; Q n is the maximum available capacity of the battery; η is the battery charge and discharge efficiency; The model parameters of ECM can be obtained by identifying the HPPC experimental test curve, that is, the pulse current excitation applied to the battery and the corresponding voltage change curve; the present invention stipulates that the discharge current is positive, where I d is the discharge current, I c is the charging current; U0 is the initial terminal voltage; According to the equivalent circuit model, when the battery discharge is completed, 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: Then the battery activation polarization and concentration polarization voltages after discharge at time t are: The least squares fitting method based on the exponential term is used to solve the parameters of the second-order ECM model. The specific process is as follows: (1) Selection of fitting interval: The polarization voltage expression after discharge is consistent with the exponential fitting situation, and the depolarization process (t2-t3) after discharge is selected to fit the model parameters; At time t2, a rapid voltage step (U2-U5) occurs, which is caused by the influence of the ohmic internal resistance R0. Solve for the ohmic internal resistance at this time: Select to subtract all subsequent U from the data in the interval U5 to U6 t The stable value and its opposite are taken to obtain the polarization voltage U after treatment. t ' (2) Exponential fitting based on least squares method: Since the fitting interval does not include the ohmic internal resistance R0 and the data have been processed to the same order of magnitude, the general form of the exponential fitting is obtained: The t '=ae bx +this dx (5) Among them, a, b, c, and d are the parameters to be solved; The ECM model parameter values ​​at each SOC point obtained by the above method are fitted with a 6th-order polynomial to obtain the relationship between the ECM model parameters and the SOC value.

3. The low-complexity, high-precision, and highly robust battery state-of-charge estimation method according to claim 1, characterized in that: The specific process of SOC estimation based on OCV value in the method is as follows: (1) OCV value calculation and filtering: Due to the influence of polarization under the actual operating conditions of electric vehicles, the battery rarely reaches a balanced state. The OCV value cannot be directly measured. The ECM model is used to calculate the OCV value: Based on formula (1), the OCV value calculation formula is as follows: U ocv (k)=U t (k)+I(k)R0+U1(k)+U2(k) (6) The sliding window filtering method is used for filtering, and the formula is shown in formula (7), where M L That is the window size of the smoothing filter; (2) OCV-SOC relationship fitting: The 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) Among them, a1, b1, c1, a2, b2, and c2 are the parameters to be solved; (3) Modification of filtering formula and fitting method Two processing methods are adopted: adjusting the data weight within the smoothing filter window, increasing the OCV value measurement points and improving the Gaussian fitting order, and refitting the OCV-SOC relationship. The details are as follows: A weight distribution is introduced for the data in the smoothing window, reducing the weight of the preceding data and increasing the weight of the following data, thereby reducing the error accumulation. The updated smoothing filter formula is shown below. Among them, M L Still taking 10, α and β are selected by trial and error and are chosen as 0.5 and 1.5; Choose to add fitting points and apply third-order Gaussian to fit the OCV-SOC relationship, and control the newly added fitting points to avoid overfitting.

4. The low-complexity, high-precision, and highly robust battery state-of-charge estimation method according to claim 3, characterized in that: The OCV value calculated by the ECM model is filtered and then brought into the Gaussian fitting formula to obtain the SOC value as the observation value of the Kalman filter. The SOC value calculated by the ampere-hour integration method is used as the Kalman filter prediction value. Both are filtered. The filtering formula is as follows: Prediction: SOCpre(k)=SOC(k-1)-ηI(k-1) / (3600Q n )(9) Ppre=P+Q (10) Observation: SOC_ECM(k) = f(OCV_ECM_L(k)) (11) Update: K = (P + Q) (P + Q + R) -1 (12) SOC(k)=SOCpre(k)+K(SOC_ECM(k)-SOCpre(k)) (13) P=P+QK(P+Q)=(P+Q)(1-K) (14) Where SOCpre(k) represents the prior SOC value at time k, SOC(k-1) represents the posterior SOC value at the previous moment, η is the battery charge and discharge efficiency, Q n represents the battery capacity, K represents the Kalman gain; f is the second-order Gaussian fitting formula in formula (6); Ppre can be regarded as the square value of the SOC estimation error generated by the ampere-hour integration method, Q corresponds to the square value of the SOC estimation error caused by the current sensor error, R is the square value of the estimation error of the SOC value output by the open circuit voltage method, and P corresponds to the square value of the overall error. The P value is the square value of the error caused by the inaccurate initial SOC value when the ampere-hour integration method is used to calculate the SOC at the next moment.

5. The low-complexity, high-precision, and strong-robustness battery state-of-charge estimation method according to claim 4, characterized in that: When the current sensor deviates, assuming it is a discharge condition, according to the ampere-hour integral calculation formula, the predicted SOCpre value at this time is too small. According to the OCV_ECM calculation formula, the OCV_ECM calculated value is too large at this time, and OCV_ECM is positively correlated with the SOC observation value, so the observed SOC value is calculated 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 of the filtering algorithm.

6. The low-complexity, high-precision, and strong-robustness battery state-of-charge estimation method according to claim 5, characterized in that: The predicted and observed values ​​of the filtering algorithm in the method are both SOC values, and no state transition between the predicted and observed values ​​is involved; there is no nonlinear part of the SOC-OCV fitting curve in the model equation; Avoid state transfer errors and nonlinear stage errors.

7. A low-complexity, high-precision, and robust battery state-of-charge estimation system, characterized by: The system has a program module corresponding to the steps of any one of claims 1 to 6, and executes the steps of the low-complexity, high-precision, and strong robust battery state of charge estimation method during operation.

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

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