Battery SOC estimation method based on adaptive parameter identification

Abstract

The invention discloses a battery SOC (State of Charge) estimation method based on adaptive parameter identification, which belongs to the field of electric automobiles and comprises the following steps of: establishing a second-order Thevenin model of a battery, and analyzing the second-order Thevenin model; constructing a discrete recursion equation of the second-order Thevenin model; performing recursion on the discrete recursion equation of the second-order Thevenin model by adopting a recursive least square algorithm with a forgetting factor to obtain parameters of the second-order Thevenin model; and carrying out state-of-charge estimation, namely SOC estimation, by adopting an extended Kalman filtering algorithm to obtain optimal SOC estimation. According to the method, the second-order Thevenin model of the battery is established, the recursive least square algorithm with the forgetting factor is adopted to perform parameter identification on the second-order Thevenin model, and the extended Kalman filtering algorithm is combined to estimate the state of charge of the battery, so that SOC estimation under the condition of considering the sudden change of the charging and discharging working conditions of the battery is realized, and the estimation precision is high.

Description

Technical Field

[0001] The present invention relates to the field of electric vehicles, and particularly to a battery SOC estimation method based on adaptive parameter identification. Background Art

[0002] As a key power source of the power system of hybrid electric vehicles, the battery is crucial for the power performance, safety and driving economy of the whole vehicle system. In order to ensure good battery performance and avoid reduced life caused by over-discharge, it is necessary to manage and control the battery. Therefore, it is very important to obtain accurate battery state.

[0003] In the battery state of charge prediction methods, the SOC can be directly predicted according to the voltage, current or internal resistance of the battery. The main methods are open circuit voltage method, ampere-hour metering method and internal resistance characteristic method. The ampere-hour metering method is an open-loop prediction. Due to the existence of the integration link, as the running time of the vehicle increases, the estimation error will gradually accumulate. The open circuit voltage method and the internal resistance characteristic method have better effects only under the condition of long-term battery rest, which is not conducive to online calculation. However, the SOC estimation problem under the condition of sudden change of battery charge and discharge conditions is not considered in these prediction methods. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a battery SOC estimation method based on adaptive parameter identification with simple algorithm and high accuracy.

[0005] The technical solution of the present invention to solve the above technical problems is: a battery SOC estimation method based on adaptive parameter identification, including the following steps:

[0006] S1: Establish a second-order Thevenin model of the battery and analyze the second-order Thevenin model;

[0007] S2: Construct a discrete recurrence equation of the second-order Thevenin model;

[0008] S3: Use the recursive least squares algorithm with forgetting factor to recursively solve the discrete recurrence equation of the second-order Thevenin model to obtain the parameters of the second-order Thevenin model;

[0009] S4: Use the extended Kalman filter algorithm to perform state of charge estimation, that is, SOC estimation, to obtain the optimal SOC estimation.

[0010] In the above battery SOC estimation method based on adaptive parameter identification, in the step S1, the process of analyzing the second-order Thevenin model is:

[0011] Let be the open circuit voltage of the battery, be the internal resistance of the battery, be the electrochemical polarization resistance of the battery, is the electrochemical polarization capacitance of the battery, is the concentration polarization resistance of the battery, is the concentration polarization capacitance of the battery, is the terminal voltage of the circuit. Then, according to Kirchhoff's voltage law, the expression of the terminal voltage of the circuit is as follows:

[0012] (1)

[0013] wherein, is the terminal voltage of the electrochemical polarization loop, is the terminal voltage of the concentration polarization loop, is the current of the entire circuit loop;

[0014] For the electrochemical polarization loop and the concentration polarization loop, the expressions of the terminal voltage are as follows:

[0015] (2)

[0016] (3)

[0017] (4)

[0018] (5)

[0019] wherein, represents time, represents the relationship between the open-circuit voltage and and is the ratio of the remaining charge in the battery to the full charge capacity, is the battery capacity.

[0020] For the above battery SOC estimation method based on adaptive parameter identification, in step S1, after analyzing the second-order Thevenin model, it can be known that there is a functional relationship between the open-circuit voltage of the battery and the SOC. According to the curve for polynomial fitting, the fitting equation is as follows:

[0021] (6).

[0022] For the above battery SOC estimation method based on adaptive parameter identification, the specific process of step S2 is as follows:

[0023] S21: Taking the Laplace transform of equation (5), we have:

[0024] (7)

[0025] where s represents the s-domain, that is, the complex frequency domain of the continuous-time signal; represents the s-domain impedance of the equivalent circuit;

[0026] S22: Assume the sampling period is , is the unit delay operator, then we have:

[0027] (8)

[0028] S23: Simplify to obtain the discrete transfer function of the system, and use the bilinear transformation method to transform the discrete transfer function of the system from the s-domain to the z-domain:

[0029] (9)

[0030] In the formula, represents the impedance of the equivalent circuit in the z-domain, is the parameter to be identified. The relationship between the parameters of the second-order Thevenin model and the parameters to be identified is as follows:

[0031] (10)

[0032] S24: Let , represents the difference between the terminal voltage and the open-circuit voltage measured at the k-th time, represents the battery terminal voltage measured at the k-th time, represents the battery open-circuit voltage measured at the k-th time. Discretize Equation (9), then we have:

[0033] (11)

[0034] Among them, represents the circuit loop current measured at the k-th time, represents the voltage residual measured at the k-th time;

[0035] S25: Write Equation (11) in matrix form:

[0036] (12)

[0037] In the formula, , , represents the output quantity measured at the k-th time of the system, represents the vector of parameters to be identified measured at the k-th time, represents the matrix composed of the discrete values of the voltage difference and current measured at the k-th time, and the superscript T represents the transpose.

[0038] For the above battery SOC estimation method based on adaptive parameter identification, the specific process of the step S3 is as follows:

[0039] S31: For Equation (11), perform recursion using the recursive least squares algorithm with a forgetting factor. The recursion formula is:

[0040] (13); Where, and are the identification results of the k-th and (k + 1)-th measurements respectively, is the output of the (k + 1)-th measurement of the system, is the input of the (k + 1)-th measurement of the system, is the identity matrix, is the forgetting factor, is the forgetting factor of the k-th measurement, is the Kalman gain of the (k + 1)-th measurement, , are the error covariance matrices of the (k + 1)-th and k-th measurements respectively;

[0041] S32: Use the data and the initial identification result , the initial error covariance matrix as the initial values for iterative calculation to obtain the estimated vector of the parameters to be identified of the system. Then the second-order Thevenin model parameters can be obtained from Equation (10).

[0042] For the above battery SOC estimation method based on adaptive parameter identification, in step S31, the error covariance matrix of the k-th measurement is calculated as follows:

[0043] (14)

[0044] Where, is the diagonal weighting matrix, is the observation vector.

[0045] For the above battery SOC estimation method based on adaptive parameter identification, in step S31, the forgetting factor of the k-th measurement is calculated as follows:

[0046] (15)

[0047] Where, is the change in terminal voltage, is a constant.

[0048] For the above battery SOC estimation method based on adaptive parameter identification, the specific process of step S4 is:

[0049] S41: For the discrete nonlinear system, the discrete state-space equation is as follows:

[0050] (16)

[0051] Wherein, represents the state quantity of the k-th measurement of the system. The state quantity includes SOC, V1, and V2, , is the real number field, and n is the dimension; represents the control quantity of the k-th measurement of the system, represents the observed quantity of the k-th measurement of the system, ; represents the process noise of the (k + 1)-th measurement, represents the measurement noise of the k-th measurement. The two are uncorrelated and follow a Gaussian distribution. The covariance of the process noise of the k-th measurement is , and the covariance of the measurement noise of the k-th measurement is , and are both non-linear functions;

[0052] S42: Linearize the non-linear functions and . Use the first-order Taylor expansion to linearly approximate the non-linear system in a short interval to obtain the discrete state equation of the non-linear system. The Jacobian matrix of the k-th measurement is:

[0053] (17)

[0054] (18)

[0055] Wherein, represents the Jacobian matrix of the k-th measurement with respect to linearization, represents the Jacobian matrix of the k-th measurement with respect to linearization, z represents the system observation value, represents the system observation value of the k-th measurement;

[0056] S43: Parameter initialization;

[0057] , (19)

[0058] Wherein, is the initial value of the state quantity, is the initial value of the covariance, represents the initial estimated value of the state quantity;

[0059] S44: Perform a priori estimation;

[0060] (20)

[0061] (21)

[0062] Wherein, is the prior estimate of the (k + 1)-th measurement, is the prior covariance of the (k + 1)-th measurement, is the covariance of the k-th measurement, is the posterior estimate of the k-th measurement;

[0063] S45: Calculate the Kalman gain of the (k + 1)-th measurement ;

[0064] (22)

[0065] Wherein, is the estimated value of the covariance matrix of the k-th measurement noise;

[0066] S46: Perform measurement update;

[0067] (23)

[0068] Wherein, represents the estimated value of the (k + 1)-th measurement, represents the measurement function, that is, to the mapping relationship therebetween;

[0069] S47: Perform posterior estimation;

[0070] (24)

[0071] (25)

[0072] Wherein, is the posterior estimate of the (k + 1)-th measurement, is the covariance of the (k + 1)-th measurement, represents the system observation value of the (k + 1)-th measurement.

[0073] The beneficial effects of the present invention are as follows: By establishing a second-order Thevenin model of the battery, using the recursive least squares algorithm with a forgetting factor to identify the parameters of the second-order Thevenin model, and combining the extended Kalman filter algorithm to estimate the state of charge of the battery, the SOC estimation under the condition of sudden changes in the charge and discharge conditions of the battery is realized, and the estimation accuracy is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is the flow chart of the present invention.

[0075] Figure 2 This is the equivalent circuit diagram of the second-order Thevenin model of the present invention.

[0076] Figure 3 is a curve graph.

[0077] Figure 4 This is the waveform diagram of the current signal for Test 1.

[0078] Figure 5 This is the waveform diagram of the voltage signal for Test 1.

[0079] Figure 6 This is the result graph of the terminal voltage estimation and measured value for Test 1.

[0080] Figure 7 This is the result graph of the terminal voltage estimation error for Test 1.

[0081] Figure 8 This is the result graph of the SOC estimation and measured value for Test 1.

[0082] Figure 9 This is the result graph of the SOC estimation error for Test 1.

[0083] Figure 10 This is the waveform diagram of the current signal for Test 2.

[0084] Figure 11 This is the waveform diagram of the voltage signal for Test 2.

[0085] Figure 12 This is the result graph of the terminal voltage estimation and measured value for Test 2.

[0086] Figure 13 This is the result graph of the terminal voltage estimation error for Test 2.

[0087] Figure 14 This is the result graph of the SOC estimated value and measured value for Test 2.

[0088] Figure 15 This is the result graph of the SOC estimation error for Test 2. Detailed implementation manner

[0089] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0090] As Figure 1 shown, a method for estimating the SOC of a battery based on adaptive parameter identification includes the following steps:

[0091] S1: Establish a second-order Thevenin model of the battery and analyze the second-order Thevenin model.

[0092] In the step S1, the process of analyzing the second-order Thevenin model is as follows:

[0093] As Figure 2 shown, Figure 2 in is the open-circuit voltage of the battery, is the internal resistance of the battery, is the electrochemical polarization resistance of the battery, is the electrochemical polarization capacitance of the battery, is the concentration polarization resistance of the battery, is the concentration polarization capacitance of the battery, is the circuit terminal voltage. Then, according to Kirchhoff's voltage law, the expression of the circuit terminal voltage is as follows:

[0094] (1)

[0095] In the formula, is the terminal voltage of the electrochemical polarization circuit, is the terminal voltage of the concentration polarization circuit, is the current of the entire circuit loop;

[0096] For the electrochemical polarization circuit and the concentration polarization circuit, the expressions of the terminal voltage are as follows:

[0097] (2)

[0098] (3)

[0099] (4)

[0100] (5)

[0101] In the formula, represents time, represents the relationship between the open-circuit voltage and and is the ratio of the remaining charge in the battery to the full charge capacity, is the battery capacity.

[0102] After analyzing the second-order Thevenin model, it can be seen that there is a functional relationship between the open-circuit voltage of the battery and SOC; as Figure 3 shown, according to curve for polynomial fitting, the fitting equation is obtained as follows:

[0103] (6).

[0104] S2: Construct a discrete recurrence equation for the second-order Thevenin model.

[0105] The specific process of the said step S2 is as follows:

[0106] S21: Perform Laplace transform on Equation (5), and we get:

[0107] (7)

[0108] Where s represents the s-domain, that is, the complex frequency domain of the continuous-time signal; represents the s-domain impedance of the equivalent circuit;

[0109] S22: Assume that the sampling period is , is the unit delay operator, then we have:

[0110] (8)

[0111] S23: Substitute Equation (8) into Equation (7), and simplify to obtain the discrete transfer function of the system. To ensure the consistency of system stability before and after the transformation, the bilinear transformation method is used to transform the discrete transfer function of the system from the s-domain to the z-domain:

[0112] (9)

[0113] In the formula, represents the z-domain impedance of the equivalent circuit, is the parameter to be identified. The relationship between the second-order Thevenin model parameters and the parameters to be identified is as follows:

[0114] (10)

[0115] S24: Let , represents the difference between the terminal voltage and the open-circuit voltage of the kth measurement, represents the battery terminal voltage of the kth measurement, represents the battery open-circuit voltage of the kth measurement. Discretize Equation (9), then we have:

[0116] (11)

[0117] Where, represents the circuit loop current of the kth measurement, represents the voltage residual of the kth measurement;

[0118] S25: Write Equation (11) in matrix form:

[0119] (12)

[0120] In the formula, , , represents the output of the k-th measurement of the system, represents the vector of parameters to be identified in the k-th measurement, represents the matrix composed of the discrete values of the voltage difference and current in the k-th measurement, and the superscript T represents the transpose.

[0121] S3: Use the recursive least squares algorithm with a forgetting factor to recursively calculate the discrete recursive equation of the second-order Thevenin model to obtain the parameters of the second-order Thevenin model.

[0122] The recursive least squares has the advantages of being easy to implement and having high accuracy, but problems such as "data saturation" will occur as the amount of data increases during the identification process. To prevent the "data saturation" problem, a forgetting factor is introduced in the recursive least squares algorithm to determine the weight of data update, and the convergence speed and tracking speed are affected by the forgetting factor.

[0123] The specific process of step S3 is as follows:

[0124] S31: For equation (11), use the recursive least squares algorithm with a forgetting factor for recursion, and the recursive formula is:

[0125] (13); In the formula, and are the identification results of the k-th and (k + 1)-th measurements respectively, is the output of the (k + 1)-th measurement of the system, is the input of the (k + 1)-th measurement of the system, is the identity matrix, is the forgetting factor, is the forgetting factor of the k-th measurement, is the Kalman gain of the (k + 1)-th measurement, 、 are the error covariance matrices of the (k + 1)-th and k-th measurements respectively;

[0126] The error covariance matrix of the k-th measurement is calculated as follows:

[0127] (14)

[0128] In the formula, is the diagonal weighting matrix, is the observation vector.

[0129] The forgetting factor of the k-th measurement is calculated as follows:

[0130] (15)

[0131] Wherein, is the change in terminal voltage, is a constant.

[0132] S32: Substitute the data and the initial identification result , the initial error covariance matrix into Equation (13) for calculation to obtain the estimated vector of the parameters to be identified of the system , and then substitute into Equation (10) to obtain the parameters of the second-order Thevenin model , , , , .

[0133] S4: Use the extended Kalman filter algorithm for state of charge estimation, i.e., SOC estimation, to obtain the optimal SOC estimation.

[0134] The specific process of the said step S4 is as follows:

[0135] S41: For a discrete nonlinear system, the discrete state equation in the state space is as follows:

[0136] (16)

[0137] Wherein, represents the state quantity of the k-th measurement of the system, and the state quantity includes SOC, V1, and V2, , is the real number field, and n is the dimension; represents the control quantity of the k-th measurement of the system, represents the observed quantity of the k-th measurement of the system, ; represents the process noise of the (k + 1)-th measurement, represents the measurement noise of the k-th measurement, and the two are uncorrelated and follow a Gaussian distribution. The covariance of the process noise of the k-th measurement is , and the covariance of the measurement noise of the k-th measurement is , and are both nonlinear functions;

[0138] S42: Linearize the nonlinear functions and , use the Taylor first-order expansion to linearly approximate the nonlinear system in a short interval, and substitute the expanded first-order terms into Equation (4) and Equation (5) to obtain the discrete state equation of the nonlinear system. The Jacobian matrix of the k-th measurement is:

[0139] (17)

[0140] (18)

[0141] Among them, represents the linearized Jacobian matrix for the k-th measurement of represents the linearized Jacobian matrix for the k-th measurement of z represents the system observation value, and

[0142] S43: Parameter initialization;

[0143] , (19)

[0144] In the formula, is the initial value of the state quantity, is the initial covariance value, represents the initial estimated value of the state quantity;

[0145] S44: Perform a priori estimation;

[0146] (20)

[0147] (21)

[0148] In the formula, is the a priori estimation for the (k + 1)-th measurement, is the a priori covariance for the (k + 1)-th measurement, is the covariance for the k-th measurement, is the a posteriori estimation for the k-th measurement;

[0149] S45: Calculate the Kalman gain for the (k + 1)-th measurement ;

[0150] (22)

[0151] Among them, is the estimated value of the covariance matrix of the k-th measurement noise;

[0152] S46: Perform measurement update;

[0153] (23)

[0154] Among them, represents the estimated value of the (k + 1)-th measurement, represents the measurement function, that is to The mapping relationship between;

[0155] S47: Perform posterior estimation;

[0156] (24)

[0157] (25)

[0158] Wherein, Is the posterior estimation of the (k + 1)-th measurement, Is the covariance of the (k + 1)-th measurement, Represents the system observation value of the (k + 1)-th measurement.

[0159] The present invention conducts experiments on a computing device with a CPU main frequency of 3.6 GHz and a memory of 16 GB, and uses MATLAB2022 for battery model parameter identification and battery SOC estimation simulation experiments. To avoid accidental factors in the experiments, different test data are selected for simulation.

[0160] The electromotive force of the battery corresponding to different SOCs is different, and it is difficult to obtain the electromotive force. Usually, the open-circuit voltage is used to approximate the battery electromotive force. For the same battery at a certain temperature V OC There is a corresponding relationship with SOC. Table 1 shows the battery Curve calibration data.

[0161]

[0162] Select an 11th-order polynomial fitting to obtain the function relationship between V OC And SOC as follows:

[0163]

[0164] The coefficients in the formula are shown in Table 2:

[0165]

[0166] The current and voltage signals of the test 1 data are respectively as Figure 4 And Figure 5 Shown. The current is positive from 0 to 9999 s, and the battery is in the discharge state. When the time t = 10000 s, the current ends the discharge state and becomes an open-circuit state; when t = 20000 s, the battery changes from the open-circuit state to the charging state. The battery has similar changes at t = 25000 s, 30000 s, 40000 s, 50000 s, 55000 s, 60000 s, 70000 s, 80000 s, 85000 s states. Figure 5Correspondingly, during the battery charging time interval, the battery terminal voltage measurement value increases, the discharge interval terminal voltage decreases, and during the battery open circuit interval, the terminal voltage remains basically unchanged. The slight change is due to the discharge phenomenon in the R1C1 circuit and the R2C2 circuit causing a small change in the terminal voltage. , ,in Represents the 5th-order unit matrix. Simulation is performed in MATLAB, and the experimental results are as follows Figures 6 - 9 shown.

[0167] The parameter R s Substitute the estimated results of R1, R2, C1, and C2 into equations (4) and (5) to calculate V T The estimation results of battery parameters and SOC using the general least squares algorithm RLS combined with the extended Kalman filter EKF are as follows: Figures 6 - 9 As shown. The estimated V T and the actual measured V T By comparison, the estimation accuracy of the terminal voltage can reflect the estimation accuracy of each parameter.

[0168] Figure 6 In, V T -RLS represents the V estimated by the least squares (RLS) method in Test 1 T Curve, V T -Measurement indicates V in test 1 T Measurement curve, V T -AFFRLS represents the V estimated by the adaptive least squares method (AFFRLS) for the forgetting factor in test 1. T curve. Figure 7 In Figure 1, RLS represents the voltage error curve corresponding to the least squares method in test 1, and AFFRLS represents the voltage error curve corresponding to the forgetting factor adaptive least squares method in test 1. Figure 8 In the figure, SOC-RLS represents the SOC curve estimated by the least squares method in test 1, SOC-RLSAFF represents the SOC curve estimated by the forgetting factor adaptive least squares method in test 1, and SOC-Measurement represents the SOC measurement curve in test 1. Figure 9 In the figure, AFFRLS represents the SOC error corresponding to the forgetting factor adaptive least squares method in test 1, and RLS represents the SOC error curve corresponding to the least squares method in test 1.

[0169] from Figure 6It can be seen that at several moments when the battery operating conditions change, the error of the terminal voltage is relatively large, indicating that when the battery operating conditions change, the parameter estimation of the ordinary least squares algorithm fluctuates greatly, and the maximum error reaches 9.3789V. Even at the moment of sudden change in the battery state, the estimation error of the terminal voltage by the AFFRLS algorithm proposed in the present invention does not exceed 0.1V, greatly reducing the transient error of the terminal voltage estimation at the moment of sudden change in the battery state. In other time periods, when the battery state remains unchanged, the least squares algorithm has good estimation effect, and the terminal voltage estimation error remains within 0.2V, as Figure 7 shown. In the time interval when the battery state remains unchanged, the estimation error of the voltage by the AFFRLS algorithm is less than 0.0439V, indicating that this algorithm can not only improve the dynamic performance, but also improve the estimation accuracy in the steady state. Based on the parameter estimation, EKF is applied for SOC estimation, and the estimation results are as Figure 8 , Figure 9 shown. At several special moments of sudden change in the battery state, the parameter estimation error is relatively large, and the SOC estimation error suddenly increases; in the time interval when the battery state remains unchanged, the parameter estimation effect is good, but the SOC estimation error is poor. However, since the algorithm proposed in the present invention combines the EKF algorithm for SOC estimation based on accurate parameter identification, the SOC estimation effect is very good, and the estimation error basically remains within 2.3%.

[0170] Taking the maximum error to represent the dynamic performance of the estimation algorithm and RMSE to represent the estimation accuracy of the algorithm, Table 3 lists the error situations of the terminal voltage and SOC estimated by the RLS-EKF and AFFRLS-EKF algorithms.

[0171]

[0172] As can be seen from Table 3, the maximum error (Max Error) of the AFFRLS-EKF algorithm for estimating battery parameters is less than that of the RLS-EKF algorithm, indicating that the dynamic performance of the proposed algorithm is significantly improved. The estimation accuracy of the proposed algorithm for VT is improved by about 20% compared with RLS-EKF, and the estimation accuracy for SOC is improved by about 37.5%.

[0173] The simulation data of Test 2 uses a 18650 lithium battery as the test object, and the obtained test current and voltage signals are respectively as Figure 10 and Figure 11 shown. The algorithm proposed in the present invention is verified by simulation with other algorithms, and the simulation results are as Figures 12 - 15 shown.

[0174] Figure 12 In, V T -RLS represents the voltage curve estimated by the least squares method in Test 2, V T-Measurement represents the voltage measurement curve in Test 2, V T -AFFRLS represents the voltage curve obtained by the forgetting factor adaptive least squares estimation in Test 2. Figure 13 In, RLS represents the voltage error curve corresponding to the least squares method in Test 2, and AFFRLS represents the voltage error curve corresponding to the forgetting factor adaptive least squares method in Test 2. Figure 14 In, SOC-RLS represents the SOC curve obtained by the least squares estimation in Test 2, SOC-AFFRLS represents the SOC curve obtained by the forgetting factor adaptive least squares estimation in Test 2, and SOC-Measurement represents the SOC measurement curve in Test 2. Figure 15 In, RLS represents the error result graph obtained by the least squares estimation in Test 2, and AFFRLS represents the error result graph obtained by the forgetting factor adaptive least squares estimation in Test 2.

[0175] From Figures 12 - 15 It can be seen that at t = 1545 s and t = 3478 s, the charge and discharge state of the battery changes, and the absolute value of the battery terminal voltage estimation error is relatively large at t = 1545 s and t = 3478 s, which are 0.2512 V and 0.2013 V respectively. Except for the initial moment, the error at other moments does not exceed 0.1 V. The absolute value of the estimated error of the battery SOC reaches the maximum at t = 1545 s, and the peak value of the absolute value of the error is 0.6552. Followed by t = 3478 s, the absolute value of the error is 0.5541.

[0176] When the parameter identification takes into account the change of the battery charge and discharge conditions, except for the initial moment, the absolute value of the battery terminal voltage estimation error is relatively large at t = 1545 s and t = 3478 s, which are 0.2314 V and 0.1718 V respectively. Except for the initial moment, the error at other moments does not exceed 0.1 V. The absolute value of the estimated error of the battery SOC reaches the maximum at t = 1545 s, and the peak value of the absolute value of the error is 0.4794 V. Followed by t = 3478 s, the absolute value of the error is 0.4611.

[0177] Based on the data of Test 2, the estimation error results of the two algorithms for the terminal voltage and battery SOC are shown in Table 4.

[0178]

[0179] It can be seen from Table 4 that the maximum error of the AFFRLS-EKF algorithm for estimating battery parameters is less than that of the RLS-EKF algorithm. The estimation accuracy of the algorithm proposed in the present invention for VT is higher than that of the RLS-EKF, and the estimation accuracy for SOC is also significantly improved.

Claims

1. A battery SOC estimation method based on adaptive parameter identification, characterized in that, It includes the following steps: S1: Establish a second-order Thevenin model of the battery and analyze the second-order Thevenin model; S2: Construct a discrete recurrence equation of the second-order Thevenin model; S3: Use the recursive least squares algorithm with a forgetting factor to recurse the discrete recurrence equation of the second-order Thevenin model to obtain the parameters of the second-order Thevenin model; S4: Use the extended Kalman filter algorithm for state of charge estimation, i.e., SOC estimation, to obtain the optimal SOC estimation.

2. The battery SOC estimation method based on adaptive parameter identification according to claim 1, wherein, In the step S1, the process of analyzing the second-order Thevenin model is as follows: Let be the open - circuit voltage of the battery, be the internal resistance of the battery, be the electrochemical polarization resistance of the battery, be the electrochemical polarization capacitance of the battery, be the concentration polarization resistance of the battery, be the concentration polarization capacitance of the battery, be the terminal voltage of the circuit. Then, according to Kirchhoff's voltage law, the expression of the terminal voltage of the circuit is as follows: （1）； Wherein, is the terminal voltage of the electrochemical polarization circuit, is the terminal voltage of the concentration polarization circuit, is the current of the entire circuit loop; For the electrochemical polarization circuit and the concentration polarization circuit, the terminal voltage expression is as follows: （2）； （3）； （4）； （5）； Wherein, represents time, represents the relationship between the open-circuit voltage and therebetween, is the ratio of the remaining power in the battery to the full charge capacity, is the battery capacity.

3. The battery SOC estimation method based on adaptive parameter identification according to claim 2, characterized in that, In the step S1, after analyzing the second-order Thevenin model, it can be known that there is a functional relationship between the open-circuit voltage of the battery and the SOC. According to the curve for polynomial fitting, the fitting equation is as follows: （6）。 4. The battery SOC estimation method based on adaptive parameter identification according to claim 3, wherein The specific process of the step S2 is as follows: S21: Perform a Laplace transform on Equation (5), and we have: （7）； where s represents the s-domain, i.e., the complex frequency domain of the continuous-time signal; represents the s-domain impedance of the equivalent circuit; S22: Assume that the sampling period is , is the unit delay operator, then we have: （8）； S23: Simplify to obtain the system discrete transfer function, and use the bilinear transformation method to transform the system discrete transfer function from the s-domain to the z-domain: （9）； In the formula, represents the equivalent circuit impedance in the z-domain, are the parameters to be identified. The relationship between the second-order Thevenin model parameters and the parameters to be identified is as follows: （10）； S24: Let , denote the difference between the terminal voltage and the open-circuit voltage of the k-th measurement, denote the battery terminal voltage of the k-th measurement, denote the battery open-circuit voltage of the k-th measurement. Discretizing Equation (9), we have: （11）； Among them, represents the circuit loop current of the k-th measurement, represents the voltage residual of the k-th measurement; S25: Write Equation (11) in matrix form: （12）； wherein, , , represents the output of the k-th measurement of the system, represents the vector of parameters to be identified in the k-th measurement, represents the matrix composed of the discrete values of the voltage difference and current in the k-th measurement, and the superscript T represents the transpose.

5. The battery SOC estimation method based on adaptive parameter identification according to claim 4, characterized in that The specific process of the step S3 is as follows: S31: For Equation (11), use the recursive least squares algorithm with a forgetting factor to recurse, and the recurrence formula is: （13）； Wherein, and are the identification results of the k-th and (k + 1)-th measurements respectively, is the output of the (k + 1)-th measurement of the system, is the input of the (k + 1)-th measurement of the system, is the identity matrix, is the forgetting factor, is the forgetting factor of the k-th measurement, is the Kalman gain of the (k + 1)-th measurement, and are the error covariance matrices of the (k + 1)-th and k-th measurements respectively; S32: Use the data and the initial identification result , and the initial error covariance matrix as the initial values for iterative calculation to obtain the estimated vector of the parameters to be identified for the system , and then the parameters of the second-order Thevenin model can be obtained from Equation (10).

6. The battery SOC estimation method based on adaptive parameter identification according to claim 5, wherein In the step S31, the error covariance matrix of the k-th measurement is calculated as follows: （14）； In the formula, is a diagonal weighting matrix, is an observation vector.

7. The battery SOC estimation method based on adaptive parameter identification according to claim 5, characterized in that In the step S31, the forgetting factor of the k-th measurement is calculated as follows: （15）； In the formula, is the change in terminal voltage, is a constant.

8. The battery SOC estimation method based on adaptive parameter identification according to claim 5, characterized in that The specific process of the step S4 is as follows: S41: For the discrete nonlinear system, the discrete state-space equation is as follows: （16）； In the formula, represents the state quantity of the k-th measurement of the system. The state quantity includes SOC, V1, and V2. , is the real number field, and n is the dimension; represents the control quantity of the k-th measurement of the system, represents the observed quantity of the k-th measurement of the system, ; represents the process noise of the (k + 1)-th measurement, represents the measurement noise of the k-th measurement. The two are uncorrelated and follow a Gaussian distribution. The covariance of the process noise of the k-th measurement is , and the covariance of the measurement noise of the k-th measurement is , and are both non-linear functions; S42: For the non-linear function and perform linearization processing, use the first-order Taylor expansion to linearly approximate the non-linear system in a short interval, and obtain the discrete state equation of the non-linear system. The Jacobian matrix for the k-th measurement is as follows: （17）； （18）； Among them, represents the k-th measurement pair linearized Jacobian matrix, represents the k-th measurement pair linearized Jacobian matrix, z represents the system observation value, represents the system observation value of the k-th measurement; S43: Initialize the parameters; ， （19）； In the formula, is the initial value of the state quantity, is the initial value of the covariance, represents the initial estimated value of the state quantity; S44: Perform a priori estimation; （20）； （21）； wherein, is the prior estimate of the (k + 1)-th measurement, is the prior covariance of the (k + 1)-th measurement, is the covariance of the k-th measurement, is the posterior estimate of the k-th measurement; S45: Calculate the Kalman gain for the (k + 1)-th measurement ; （22）； wherein, is the estimated covariance matrix of the k-th measurement noise; S46: Perform measurement update; （23）； Among them, represents the estimated value of the (k + 1)-th measurement, represents the measurement function, that is, to the mapping relationship between them; S47: Perform a posteriori estimation; （24）； （25）； wherein, is the posterior estimate of the (k + 1)-th measurement, is the covariance of the (k + 1)-th measurement, represents the system observation value of the (k + 1)-th measurement.

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