Battery model parameter identification method of forgetting recursive least square with bias compensation

Abstract

The application discloses a battery model parameter identification method based on a forgetting recursive least square method with deviation compensation, and belongs to the field of battery model parameter identification.The method comprises the following steps: S1, a second-order equivalent circuit model is established, and model parameters to be identified are determined; S2, a load end voltage and an end current at the k moment are collected in real time; S3, a lower discharge rate is used to collect a state of charge (SOC) and an open circuit voltage (OCV) of the battery, and a relationship expression of the state of charge (SOC) and the open circuit voltage (OCV) is determined through fitting; S4, a discrete regression equation used for model parameter identification is established, and model parameters are updated on line by using an end voltage value and a current input at the k moment; S5, average weighted variances of noises in the voltage and the current are calculated; and S6, the result of the recursive least square method with a forgetting factor in S4 is updated according to the average weighted variances of the voltage and the current noises obtained in S5, and identification parameters at the k moment are obtained.The application can realize the update of a parameter vector and reduce the influence of noises on the estimation accuracy of a model.

Description

Technical Field

[0001] This invention belongs to the field of battery model parameter identification, and particularly relates to a battery model parameter identification method based on the forgetting recursive least squares method with bias compensation. Background Technology

[0002] In recent years, environmental pollution and fossil fuel shortages have become increasingly serious problems. With the continuous development and utilization of new energy sources and energy storage devices, the electric vehicle industry has experienced rapid growth. Lithium-ion batteries have advantages in energy density and power density, while also possessing characteristics such as long cycle life and stable performance. Lithium-ion power batteries are one of the key components of electric vehicles. To ensure the safety and stability of electric vehicle operation, the development and application of a Battery Management System (BMS) are essential.

[0003] Accurate lithium battery models can reflect the complex working process of lithium batteries and provide a basis for state estimation in BMS (Battery Management System). Therefore, establishing accurate battery models is particularly important for BMS. Equivalent circuit models are widely used in real-world vehicle BMSs due to their simple structure, few identification parameters, and low computational complexity. In practical applications, noise interference is unavoidable during voltage and current measurements in BMS. Noise errors in system identification affect the measurement accuracy of input and output. Noise interference in sampled data not only affects parameter identification but also directly impacts the accuracy of state estimation. Existing algorithms for handling noise interference in sampled data only address noise in either current or voltage, rarely studying simultaneous noise in both current and voltage. Summary of the Invention

[0004] The purpose of this invention is to provide a battery model parameter identification method based on the forgetting recursive least squares method with bias compensation, so as to solve the technical problem that current and voltage signals are interfered with during vehicle operation.

[0005] To achieve the above objectives, the specific technical solution of the battery model parameter identification method using the forgetting recursive least squares method with bias compensation of the present invention is as follows:

[0006] Accurate estimation of lithium-ion battery models affects battery state estimation, which in turn impacts the safe operation of electric vehicles. However, due to the influence of the actual operating environment and sensor errors, the sampled signals contain random noise, leading to a decrease in model estimation accuracy. To address the problem of reduced model estimation accuracy caused by noise, this paper introduces a variable error model to estimate the average weighted variance of random noise. The bias term is obtained using the augmented parameter vector, and the variance estimation bias is compensated for in the parameter estimation results, ultimately yielding unbiased parameter estimates to improve the accuracy of the established model. The specific details are as follows:

[0007] A method for creating an equivalent circuit model based on deviation compensation is characterized by the following steps:

[0008] Step S1: Establish a second-order equivalent circuit model and determine the parameters of the model to be identified;

[0009] Step S1 includes the following steps:

[0010] Step S101: Establish a dual-polarization equivalent circuit model, such as... Figure 1 As shown, equation (1) is satisfied:

[0011] (1)

[0012] Among them, U OCV U is the battery open circuit voltage (OCV). T U1 is the terminal voltage of the battery when it is working, U2 is the polarization circuit voltage formed by R1 and C1, U2 is the polarization circuit voltage formed by R2 and C2, Q is the battery capacity, SOC represents the state estimate of the battery, I is the battery operating current, R0 is the ohmic internal resistance of the battery, R1 and C1 are the concentration polarization resistance and capacitance of the battery, and R2 and C2 are the electrochemical polarization resistance and capacitance of the battery; R0, R1, R2, C1 and C2 are the parameters to be identified in the established model.

[0013] Step S2: Use voltage and current sensors to collect the load terminal voltage and current at time k in real time;

[0014] Step S3: Collect the state of charge (SOC) and open-circuit voltage (OCV) of the battery using a lower discharge rate, and determine the relationship between the battery's SOC and OCV by fitting the formula (3).

[0015] (3)

[0016] Where V is the OCV value of the battery, and n is the fitting order. These are the fitting coefficients. This refers to the battery's SOC (State of Charge).

[0017] Step S3 includes the following steps:

[0018] Step S301: The methods used to estimate the SOC of the battery are mainly divided into one of the following: ampere-hour integration, deep learning method, and extended Kalman filter.

[0019] The ampere-hour integration method is selected to estimate the battery's state of charge (SOC).

[0020] (2)

[0021] Where I(k) is the current value at time k, and t is the total time.

[0022] Step S302: To obtain the relationship between OCV and SOC, fully charge the battery and discharge it using the C / 20 method, recording the OCV value according to different SOC values; use formula (3) to obtain the relationship between OCV and SOC:

[0023] (3)

[0024] Where V is the OCV value of the battery, and n is the fitting order. These are the fitting coefficients. This refers to the battery's SOC (State of Charge).

[0025] Step S4: Establish a discrete regression equation for model parameter identification. Using the terminal voltage value and current input at time k, update the model parameters online using the recursive least squares method with a forgetting factor.

[0026] Step S4 includes the following steps:

[0027] Step S401: Construct the discrete domain regression equation for model identification:

[0028] (4)

[0029] in, Let k be the parameter vector to be identified. , Let be the observation matrix at time k. ;

[0030] Step S402: Construct the identification parameter vector:

[0031] (5)

[0032] in, ; The value is C1. The value is C2;

[0033] Step S403: Identify the model parameter vector online using the least squares method with a forgetting factor:

[0034] Initialize the error covariance P and the parameter identification vector θ;

[0035] Online acquisition of voltage and current data to determine the input of the model at time k. And output y(k), calculate the estimation error:

[0036] (6)

[0037] In the formula, This is the parameter vector without considering bias compensation.

[0038] Update system gains:

[0039] (7)

[0040] Parameter vector without considering bias compensation:

[0041] (8)

[0042] Update error covariance:

[0043] (9)

[0044] Wherein, λ is the forgetting factor, and the value of λ generally ranges from 0.95 to 1.

[0045] Step S5: Calculate the average weighted variance of noise in voltage and current.

[0046] Step S5 includes the following steps:

[0047] Step S501, Calculation of the error criterion function:

[0048] (10)

[0049] Step S502: Obtain the new augmented parameter vector:

[0050] Will

[0051] (11)

[0052] The denominator is augmented with a value of 0, i.e. , θ6=0, and we obtain the new augmented parameter vector, as shown in formula (12):

[0053] (12)

[0054] In the formula, , , , , All of these are intermediate coefficients estimated online using the recursive least squares method, and their expressions are shown in formula (5);

[0055] Step S503: Introduce auxiliary vectors ,in ;

[0056] Step S504: Convert the system error covariance matrix P into matrix form.

[0057] (13)

[0058] Step S505: Thus, the equation for solving the average weighted variance parameter is obtained.

[0059] (14)

[0060] In the formula, and (k) are the parameter vectors estimated by the recursive least squares algorithm with forgetting factor, i.e., a in formula (12). T (k)=a LS (k),b T (k)=b LS (k), where This is the average weighted variance parameter for voltage and current.

[0061] Step S6: Based on the average weighted variance of voltage and current noise obtained in step S5, update the result of the recursive least squares method with forgetting factor in step S4, and then obtain the identification parameters at time k.

[0062] Step S6 includes the following:

[0063] Step S601: Update the result of the recursive least squares method with forgetting factor in step S4 using formula (15):

[0064] (15)

[0065] In the formula, , , For the bias term of parameter estimation, Variance of current noise and voltage noise variance The vector formed; The average weighted variance of the current measurement noise; This represents the average variance of the voltage measurement noise.

[0066] The battery model parameter identification method using the forgetting recursive least squares method with bias compensation of the present invention has the following advantages: When noise occurs simultaneously in voltage and current, the bias compensation method calculates the average variance of the two random noises, thereby updating the parameter vector and reducing the impact of noise on the model estimation accuracy. The use of a dual-polarized lithium battery equivalent circuit model, compared to a first-order equivalent circuit model, reflects the charge transfer and diffusion processes of the battery, further improving the battery estimation accuracy. Attached Figure Description

[0067] Figure 1 This is the equivalent circuit model of the dual-polarized lithium battery in this invention.

[0068] Figure 2 This refers to the estimated terminal voltage value of the UDDS (Urban Dynamometer Driving Schedule) in this invention.

[0069] Figure 3 This refers to the prediction error of the UDDS operating condition terminal voltage estimate in this invention.

[0070] Figure 4 This is the estimated terminal voltage value for the HPPC (Hybrid Pulse Power Characterization) operating condition of this invention.

[0071] Figure 5 This refers to the prediction error of the HPPC operating condition terminal voltage estimate in this invention.

[0072] Figure 6 The present invention relates to the voltage variation under HPPC operating conditions.

[0073] Figure 7 The HPPC operating current variation of this invention

[0074] Figure 8 This is the voltage variation curve of the UDDS under operating conditions according to the present invention.

[0075] Figure 9 This is the current variation curve of the UDDS under operating conditions according to the present invention.

[0076] Figure 10 This is a flowchart of a battery model parameter identification method based on the bias-compensated forgetting recursive least squares method according to the present invention. Detailed Implementation

[0077] To better understand the purpose, structure, and function of this invention, the following description, in conjunction with the accompanying drawings, provides a more detailed account of the battery model parameter identification method based on the forgetting recursive least squares method with bias compensation.

[0078] To address the issue of reduced model estimation accuracy caused by noise, this paper introduces a variable error model to estimate the average weighted variance of random noise. The bias term is obtained using the augmented parameter vector, and the variance estimation bias is compensated for in the parameter estimation results, ultimately yielding unbiased estimates of the parameters to improve the accuracy of the established model.

[0079] Example:

[0080] When Gaussian white noise with a standard deviation of 0.1A and 0.01V is added to the test battery data, the following results are observed:

[0081] Figure 2 and Figure 4 The figures show the terminal voltage estimation results of the three estimation methods under UDDS and HPPC operating conditions, respectively. Figure 3 and Figure 5 The figures compare the terminal voltage errors under UDDS and HPPC operating conditions. It is clear from the figures that the BCFFRLS (Bias Compensated Forgetting Factor Recursive Least Square) method has a smaller and more stable terminal voltage estimation error, while the FFRLS (Forgetting Factor Recursive Least Squares) and offline methods have larger and more dispersed terminal voltage estimation errors, especially during periods of rapid voltage change, where the influence of noise exacerbates the error fluctuations. Table 1 compares the modeling performance of different methods.

[0082] Table 1. Comparison of modeling performance under different methods

[0083]

[0084] Under the UDDS operating conditions, the MAE (Mean Absolute Error) of offline identification and FFRLS are 27.2 mV and 22.5 mV, respectively, and the RMSE (Root Mean Squared Error) are 39.7 mV and 27.8 mV, respectively, while the MAE and RMSE of the BCFFRLS algorithm are 16.7 mV and 20.8 mV, respectively. Under the same initial conditions and operating conditions, compared with offline identification and FFRLS, the BCFFRLS algorithm reduces MAE by 10.5 mV and 5.8 mV, respectively, corresponding to an improvement in prediction accuracy of 38% and 25%, respectively; and reduces RMSE by 18.9 mV and 7 mV, respectively, corresponding to an improvement in prediction accuracy of 47.6% and 25.1%, respectively, thus improving the accuracy of model parameter identification. Similarly, analyzing the modeling performance of different methods under the HPPC operating conditions shown in Table 1 yields basically consistent results, which will not be elaborated further here.

[0085] First, voltage and current data under HPPC conditions were tested to perform offline parameter identification and operating condition verification of the battery. A pulse test was performed every 5% SOC. Figure 6 and Figure 7 The figures show the battery voltage and current curves under HPPC operating conditions.

[0086] Secondly, considering the significant voltage and current variations in lithium-ion batteries during actual operation, the algorithm was validated using the UDDS operating condition. For example... Figure 8 and Figure 9 These represent the voltage and current under UDDS operating conditions, respectively.

[0087] The battery voltage and current data obtained from the test are introduced into Gaussian white noise, and the noise-added values ​​are substituted into the algorithm experiment for testing. The input is the current, and the output is the predicted voltage of the battery.

[0088] To address the impact of random noise interference on the accuracy of model parameter identification and battery model precision under two complex operating conditions—UDDS and HPPC—this paper proposes the BCFFRLS parameter identification algorithm. This algorithm considers the average weighted variance of random noise and compensates for variance estimation bias in the parameter estimation results. The algorithm is then used to identify parameters for the established dual-polarization model. Compared to offline identification, BCFFRLS overcomes the limitation that offline identification fails to update model parameters in real time according to battery temperature and aging status. Compared to traditional FFRLS, BCFFRLS can overcome the adverse effects of random noise on parameter identification accuracy, especially under complex operating conditions. The model parameter identification results show that, in terms of parameter identification accuracy, under the UDDS condition, BCFFRLS, compared with offline identification and FFRLS, reduced MAE (Mean Absolute Error) by 10.5 mV and 5.8 mV, respectively, corresponding to an improvement in prediction accuracy of 38% and 25%, respectively. RMSE (Root Mean Squared Error) decreased by 8.9 mV and 7 mV, respectively, corresponding to an improvement in prediction accuracy of 47.6% and 25.1%, respectively, significantly improving parameter identification accuracy and model precision.

[0089] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for identifying battery model parameters using a bias-compensated forgetting recursive least squares method, characterized in that, Includes the following steps: Step S1: Establish a second-order equivalent circuit model and determine the parameters of the model to be identified; Step S2: Use voltage and current sensors to collect the load terminal voltage and current at time k in real time; Step S3: Collect the state of charge (SOC) and open-circuit voltage (OCV) of the battery using a lower discharge rate, and determine the relationship between the battery's SOC and OCV by fitting the formula (3). （3） Where V is the OCV value of the battery, and n is the fitting order. These are the fitting coefficients. Battery SOC; Step S3 includes the following steps: Step S301: The method used to estimate the SOC of the battery is one of the following: ampere-hour integration, deep learning method, or extended Kalman filter. The ampere-hour integration method is selected to estimate the battery's state of charge (SOC). （2） Where I(k) is the current value at time k, and t is the total time; Step S302: To obtain the relationship between OCV and SOC, fully charge the battery and discharge it using the C / 20 method, recording the OCV value according to different SOC values; use formula (3) to obtain the relationship between OCV and SOC: （3） Where V is the OCV value of the battery, and n is the fitting order. These are the fitting coefficients. Battery SOC; Step S4: Establish a discrete domain regression equation for model parameter identification. Using the terminal voltage value and current input at time k, update the model parameters online using the recursive least squares method with a forgetting factor. Step S5: Calculate the average weighted variance of noise in voltage and current; Step S5 includes the following steps: Step S501, Calculation of the error criterion function: （10） Step S502: Obtain the new augmented parameter vector: Will （11） The denominator is augmented with a value of 0, i.e. θ6=0, resulting in a new augmented parameter vector, as shown in formula (12): （12） Step S503: Introduce auxiliary vectors ,in ; Step S504: Convert the system error covariance matrix P into matrix form. （13） Step S505: Thus, the equation for solving the average weighted variance parameter is obtained. （14） In the formula, and (k) are the parameter vectors estimated by the recursive least squares algorithm with forgetting factor, i.e., a in formula (12). T (k)=a LS (k),b T (k)=b LS (k), where The average weighted variance parameters of voltage and current Step S6: Based on the average weighted variance of voltage and current noise obtained in step S5, update the result of the recursive least squares method with forgetting factor in step S4, and then obtain the identification parameters at time k.

2. The battery model parameter identification method using the forgetting recursive least squares method with deviation compensation according to claim 1, characterized in that, Step S1 includes the following steps: Step S101: Establish a dual-polarization equivalent circuit model that satisfies equation (1): （1） Among them, U OCV U is the battery open-circuit voltage. T U1 is the terminal voltage of the battery when it is working, U2 is the polarization circuit voltage formed by R1 and C1, U2 is the polarization circuit voltage formed by R2 and C2, Q is the battery capacity, SOC represents the state estimate of the battery, I is the battery operating current, R0 is the ohmic internal resistance of the battery, R1 and C1 are the concentration polarization resistance and capacitance of the battery, and R2 and C2 are the electrochemical polarization resistance and capacitance of the battery; R0, R1, R2, C1 and C2 are the parameters to be identified in the established model.

3. The battery model parameter identification method using the forgetting recursive least squares method with deviation compensation according to claim 2, characterized in that, Step S4 includes the following steps: Step S401: Construct the discrete domain regression equation for model identification: （4） in, Let k be the parameter vector to be identified. , Let be the observation matrix at time k. ; Step S402: Construct the identification parameter vector: （5） in, ; The value is C1. The value is C2; Step S403: Identify the model parameter vector online using the least squares method with a forgetting factor: Initialize the error covariance P and the parameter identification vector θ; Online acquisition of voltage and current data to determine the input of the model at time k. And output y(k), calculate the estimation error: （6） In the formula, This is the parameter vector without considering bias compensation; Update system gains: （7） Parameter vector without considering bias compensation: （8） Update error covariance: （9） Wherein, λ is the forgetting factor, and the value of λ generally ranges from 0.95 to 1.

4. The battery model parameter identification method using the forgetting recursive least squares method with deviation compensation according to claim 1, characterized in that, Step S6 includes the following: Step S601: Update the result of the recursive least squares method with forgetting factor in step S4 using formula (15): （15） In the formula, , , This is the deviation term for parameter estimation.

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