A lithium battery state-of-charge estimation method based on adaptive dual-fusion Kalman filtering

Abstract

This invention belongs to the field of state estimation technology and relates to a lithium battery state of charge estimation method based on adaptive dual-fusion Kalman filtering. The method includes: constructing an equivalent circuit model; obtaining battery parameters based on the equivalent circuit model; obtaining battery measurement values ​​and measurement estimates based on the battery parameters; using a corresponding Kalman filter to estimate the battery state of charge based on the absolute value of the error between the measurement values ​​and the measurement estimates, and obtaining the battery state of charge estimate; and obtaining the battery state of charge estimation result based on the battery state of charge estimate. This invention combines the advantages and disadvantages of both EKF and XKF filters, employing different estimation schemes at different times, which can improve estimation efficiency while ensuring accuracy.

Description

Technical Field

[0001] This invention belongs to the field of battery state estimation technology, and particularly relates to a method for estimating the state of charge of lithium batteries based on adaptive dual-fusion Kalman filtering. Background Technology

[0002] With the continuous depletion of fossil fuels, environmental pollution and other issues have received increasing attention. Electric vehicles are a relatively energy-efficient and environmentally friendly mode of transportation, leading to greater focus on their production and sales. The power battery, as a crucial power source for electric vehicles, is one of the most important components. The safety of the power battery has become paramount, requiring constant monitoring of its operating temperature, current, and voltage. The device that continuously monitors and manages the power battery is the Battery Management System (BMS). Through its interface, users can clearly view information such as the battery's current operating temperature, state of charge, and remaining lifespan, while managing the charging and discharging of the battery. It can also help users determine if the battery system is faulty and requires maintenance. Therefore, the quality of the battery management system directly impacts the efficiency and safety of electric vehicles. The performance of the power battery pack, as the power source of electric vehicles, has always been a key research focus. Electric vehicle batteries need to operate within a reasonable voltage, current, and temperature range. Therefore, effective management of the electric battery in electric vehicles is essential. The level of the battery management system largely determines the performance of the power battery pack. Therefore, a real-time, efficient battery management system is crucial. The power battery, as a crucial power source for electric vehicles, is one of the most important components. Through extensive research, lithium-ion battery state-of-charge (SOC) estimation based on equivalent circuit models has become possible. Firstly, experiments have been conducted to determine the relevant lithium-ion battery's SOC. Currently, numerous filtering algorithms have been developed to improve the computational accuracy of this method. These algorithms include extended Kalman filtering, unscented Kalman filtering, capacitive Kalman filtering, and their many variants. From a mathematical perspective, these schemes still retain some problems related to nonlinear systems. For example, extended Kalman filtering struggles with slow convergence and is prone to getting trapped in local errors. Furthermore, while these algorithms undoubtedly contribute to improved accuracy, the overall computational efficiency of the estimation scheme is reduced, which is detrimental to the operation of the vehicle system and the information exchange between the vehicle and cloud platforms. Therefore, there is an urgent need for a lithium-ion battery SOC estimation method based on adaptive dual-fusion Kalman filtering. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a lithium battery state of charge estimation method based on adaptive dual-fusion Kalman filtering, which can improve the estimation accuracy of SOC.

[0004] This invention provides a method for estimating the state of charge of lithium batteries based on adaptive dual-fusion Kalman filtering, including:

[0005] Construct an equivalent circuit model;

[0006] Based on the equivalent circuit model, battery parameters are obtained;

[0007] Based on the battery parameters, obtain the battery measurement value and the measurement estimate value;

[0008] Based on the absolute value of the error between the measured value and the estimated value, the corresponding Kalman filter is used to estimate the battery state of charge.

[0009] Based on the estimated battery state of charge, the battery state of charge estimation result is obtained.

[0010] Optionally, based on the equivalent circuit model, obtaining battery parameters includes:

[0011] The battery parameters of the equivalent circuit model are obtained by using the least squares method, wherein the battery parameters include: battery internal resistance, voltage, capacity and charge / discharge efficiency.

[0012] Optionally, obtaining battery measurement values ​​and measurement estimates based on the battery parameters includes:

[0013] Initialize the state parameters and battery equivalent circuit model in the battery parameters, and obtain the initial state parameters;

[0014] The error covariance is initialized based on the initialization state parameters.

[0015] Based on the initialized error covariance, obtain the battery measurement estimate.

[0016] Optionally, based on the absolute value of the error between the measured value and the estimated value, a corresponding Kalman filter is used to estimate the battery state of charge, including:

[0017] Determine whether the absolute value of the error between the measured value and the estimated value is greater than a first voltage threshold. If it is not greater, use an extended Kalman filter for estimation; if it is greater, use an exogenous Kalman filter for iterative estimation.

[0018] Optionally, an extended Kalman filter is used for estimation to obtain the battery state-of-charge estimate, including:

[0019] The battery parameters are estimated a priori to obtain the a priori estimates.

[0020] Update the Kalman gain based on the prior estimate;

[0021] Based on the updated Kalman gain, update the posterior error covariance and obtain the current error covariance;

[0022] Based on the current error covariance, obtain the estimated state of charge of the battery.

[0023] Optionally, the current error covariance may also be used to initialize the error covariance at the next time step.

[0024] Optionally, an exogenous Kalman filter can be used for estimation to obtain the battery state-of-charge estimate, including:

[0025] Establish the observation equations and state equations for the battery;

[0026] Based on the observation equation and the state equation, a priori estimation is performed to obtain the priori estimated value;

[0027] Based on the prior estimates, the Kalman gain, posterior error covariance, and state estimates are updated.

[0028] Based on the updated information, determine whether the absolute value of the error between the battery measurement value and the measurement estimate value is greater than the second voltage threshold. If it is not greater than the second voltage threshold, perform local iteration; otherwise, directly obtain the error covariance.

[0029] Based on the error covariance, the estimated state of charge of the battery is obtained.

[0030] Optionally, performing local iterations includes:

[0031] S1, Corrected noise covariance;

[0032] S2. Update the Kalman gain matrix based on the corrected noise covariance;

[0033] S3. Update the posterior error covariance based on the updated Kalman gain matrix;

[0034] S4. Repeat steps S1-S3 until the absolute value of the error between the battery measurement value and the measurement estimate value is less than the preset value, then stop the iteration.

[0035] Optionally, the observation equation is:

[0036]

[0037] The state equation is:

[0038]

[0039] Where, x k+1 and x k L represents the system's state variables at times k+1 and k, respectively. kLet v be the system input at time k. k ~(0,Q k );w k ~(0,R k ), R k and Q k Representing the measurement noise covariance and process noise covariance respectively, y k Represents the measured state variables, A, B, C, and D are the system matrices, Φ k θ represents the system's data variables. k Let a1, a2, a3, a4, and a5 represent the system's parameter variables, a1, a2, a3, a4, and a5 be the corresponding constant coefficients, y(k) be the system's output at time k, y(k-1) be the system's output at time k-1, y(k-2) be the system's output at time k-2, l(k-1) be the system's input at time k-1, and l(k-2) be the system's input at time k-2.

[0040] Optionally, the method for obtaining the battery state of charge estimation result based on the battery state of charge estimation value is as follows:

[0041]

[0042] U d,k =f(SOC) k )-U 1,k -U 2,k -R0I k +w k

[0043] in, Let represent the state variables of the model; time constants τ1 = R1C1, τ2 = R2C2; R1 represents the activation polarization resistance, R2 represents the concentration polarization resistance, C1 represents the activation polarization capacitance, C2 represents the concentration polarization capacitance, and η is the coulombic efficiency; Q N The maximum usable capacity of the battery at the current temperature; I k-1 f(SOC) represents the current at time k-1; k ) represents the open-circuit voltage U oc Functional relationship with state of charge (SOC); SOC k U represents the state of charge at time k; 1,k U is the electrochemical polarization voltage at time k; 2,k V is the concentration polarization voltage at time k, Δt is the time step, and v k Let R0 be the Gaussian process noise at time k, and I be the internal resistance of the battery. k Let w be the current measured at time k. k For the Gaussian measurement noise at time k, U d,k Let be the battery terminal voltage calculated at time k.

[0044] Compared with the prior art, the present invention has the following advantages and technical effects:

[0045] This invention, considering the absolute value of the difference between the measured and estimated voltages, improves the accuracy of State of Charge (SOC) estimation by incorporating an additional function into the error update. Simultaneously, by combining the advantages and disadvantages of EKF and XKF filters and employing different estimation schemes at different time periods, it can improve estimation efficiency while maintaining accuracy. This is of great significance for estimating and controlling the overall battery state, fully utilizing battery capacity, and improving the information transmission efficiency of the vehicle-to-cloud platform. Attached Figure Description

[0046] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0047] Figure 1 This is a schematic diagram of the second-order RC equivalent circuit model of a lithium-ion battery according to an embodiment of the present invention;

[0048] Figure 2 This is a flowchart of a lithium battery state-of-charge estimation method based on adaptive dual-fusion Kalman filtering, according to an embodiment of the present invention. Detailed Implementation

[0049] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0050] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0051] This invention proposes a method for estimating the state of charge (SOC) of lithium batteries based on adaptive dual-fusion Kalman filtering, such as... Figure 2 As shown, the specific steps include:

[0052] like Figure 1 As shown, construct the equivalent circuit model;

[0053] Battery parameters are obtained based on the equivalent circuit model;

[0054] Based on battery parameters, obtain battery measurement values ​​and measurement estimates;

[0055] Based on the absolute value of the error between the measured value and the estimated value, the corresponding Kalman filter is used to estimate the battery state of charge.

[0056] Based on the battery state of charge estimate, the battery state of charge estimate result is obtained.

[0057] Specifically, such as Figure 1 As shown, an equivalent model is established, where U oc R0 represents the open-circuit voltage of the battery, and U represents the internal resistance in ohms. d I represents the battery terminal voltage, C1 represents the load current, R1 represents the battery activation polarization voltage, C2 represents the activation polarization capacitor, R2 represents the activation polarization resistor, U2 represents the battery concentration polarization voltage, C2 represents the concentration polarization capacitor, and R2 represents the concentration polarization resistor.

[0058] based on Figure 1 Based on the equivalent circuit model, the continuous-time state-space equations of the battery are established as follows:

[0059]

[0060] Furthermore, based on the equivalent circuit model, the battery parameters are obtained as follows:

[0061] The battery parameters of the equivalent circuit model are obtained by using the least squares method. The battery parameters include the battery's internal resistance, voltage, capacity, and charge / discharge efficiency.

[0062] Specifically, parameter identification: taking recursive least squares method with forgetting factor as an example.

[0063] The basic calculation formula is as follows:

[0064] y k =Φ k θ k +ξ k #(2)

[0065] Among them, y k Φ represents the system's output variable. k θ represents the system's data variables. k ξ represents the system's parameter variables. k It is fixed zero-mean white noise. The system identification method is as shown in formula (3):

[0066]

[0067] Where λ is the forgetting factor, and its value generally ranges from 0.95 to 1, K Ls,k It is the algorithm gain, P Ls,k

[0068] It is the error covariance matrix of the state estimation, P Ls,k-1 Let be the error covariance matrix at time k-1. Let Φ be the transpose matrix of the data variables at time k. Ls,k Let θ be the matrix of data variables at time k. Ls,k For parameter estimation at time k, θ Ls,k-1 For parameter estimation at time k-1, K Ls,k Let be the Kalman gain at time k. For equation (1)

[0069] Performing a Laplace transform, we get:

[0070]

[0071] Its transfer function is:

[0072]

[0073] U oc R0 represents the open-circuit voltage of the battery, and U represents the internal resistance in ohms. d Represents the battery terminal voltage, I represents the load current, and C represents the load current. pa R represents the activation polarization capacitance value. pa C represents the activation polarization resistance value. pc R represents the concentration polarization capacitance value. pc This indicates the concentration polarization resistance value.

[0074] Perform a bilinear transformation on equation (5), and let The discretized transfer function is obtained as follows:

[0075]

[0076] Where a1, a2, a3, a4, and a5 are the corresponding constant coefficients, and the difference equation is obtained from formula (6):

[0077] y(k)=U OC (k)-U t (k)=a1y(k-1)+a2y(k-2)+a3l(k)+a4l(k-1)+a5l(k-2)#

[0078] Where y(k) is the system output and l(k) is the system input.

[0079] The identifiable battery model is:

[0080]

[0081] Furthermore, based on battery parameters, obtaining battery measurements and estimated values ​​includes:

[0082] Initialize the state parameters and battery equivalent circuit model in the battery parameters, and obtain the initial state parameters;

[0083] The error covariance is initialized based on the initialization state parameters.

[0084] Based on the initialized error covariance, obtain the battery measurement estimate.

[0085] Specifically, the battery measurements are obtained through actual measurements, typically real-time data acquired by sensors during battery operation. The initialization of noise and error covariance reflects the initial uncertainty of the system. The initialization phase usually uses empirical values ​​or a large initial covariance to represent significant uncertainty about the initial state. In subsequent time steps, the error covariance is updated based on the Kalman gain.

[0086] More specifically, state initialization: initializing the parameters x0, P0, and R0 in the algorithm.

[0087]

[0088] R0 = 200

[0089] Furthermore, based on the absolute value of the error between the measured value and the estimated value, a corresponding Kalman filter is used for estimation to obtain the battery state of charge estimate, including:

[0090] Determine whether the absolute value of the error between the measured value and the estimated value is greater than the first voltage threshold. If it is not greater, use extended Kalman filtering for estimation; if it is greater, use exogenous Kalman filtering for iterative estimation.

[0091] Specifically, the absolute value of the error between the estimated and measured values ​​is used to adaptively determine whether to perform iterations. m is set as the first voltage error threshold, m = 0.01V. If... Then, iteration is unnecessary; an extended Kalman filter (EKF) can be used to improve computational efficiency. If This indicates that the error exceeds the threshold and an exogenous Kalman filter (XKF) is required.

[0092] Furthermore, an extended Kalman filter is used for estimation to obtain the battery state-of-charge estimate, including:

[0093] Perform prior estimation of battery parameters and obtain prior estimate values;

[0094] Update the Kalman gain based on prior estimates;

[0095] Based on the updated Kalman gain, update the posterior error covariance and obtain the current error covariance;

[0096] Based on the current error covariance, obtain the estimated value of the battery state of charge.

[0097] Specifically, prior estimation of state and prior estimation of state covariance:

[0098]

[0099] in This represents the prior estimate of the state variables at time k. This represents the prior estimate of the state variables at time k-1; P represents the estimated value of the measured state quantity at time k; k-1 , Let represent the posterior estimated covariance at time k-1 and the prior estimated covariance at time k, respectively. Q represents the estimated state quantity at time k; F and H represent the state transition matrices; Q represents the estimated state quantity at time k. k-1 and R k-1 These are the process noise covariance and measurement noise covariance at time k-1, respectively.

[0100] Revised estimate:

[0101]

[0102] Update Kalman gain:

[0103]

[0104] Updated posterior estimate of covariance:

[0105]

[0106] in P represents the posterior estimate of the state variable at time k; k K represents the posterior estimated covariance at time k; E is the identity matrix; K k The Kalman gain at time k for this scheme.

[0107] Furthermore, the current error covariance also needs to participate in the initialization of the error covariance at the next time step.

[0108] Furthermore, the observation equations and state equations of the battery are established;

[0109] Based on the observation equation and the state equation, prior estimation is performed to obtain the prior estimate value;

[0110] The Kalman gain, posterior error covariance, and state estimate are updated based on the prior estimates.

[0111] Based on the updated information, determine whether the absolute value of the error between the battery measurement value and the measurement estimate value is greater than the second voltage threshold. If it is not greater than the second voltage threshold, perform local iteration; otherwise, directly obtain the error covariance.

[0112] Based on the error covariance, the estimated state of charge of the battery is obtained.

[0113] Furthermore, S1, corrected noise covariance;

[0114] S2. Update the Kalman gain matrix based on the corrected noise covariance;

[0115] S3. Update the posterior error covariance based on the updated Kalman gain matrix;

[0116] S4. Repeat steps S1-S3 until the absolute value of the error between the battery measurement value and the measurement estimate value is less than the preset value, then stop the iteration.

[0117] Specifically, establish the observer: establish the observation equation and the state equation of the battery (Equation 8):

[0118] Observation equation:

[0119]

[0120] Where: x k+1 and x k These represent the system's state variables at times k+1 and k, respectively; k Input for the system; v k ~(0,Q k );w k ~(0,R k ), R k and Q k These represent the measurement noise covariance and the process noise covariance, respectively; y k This represents the measured state quantity. A, B, C, and D are the system matrices.

[0121] State prior estimation and state covariance prior estimation:

[0122]

[0123] in This represents the prior estimate of the state variables at time k. This represents the prior estimate of the state variables at time k-1; P represents the estimated value of the measured state quantity at time k; k-1 , Let represent the posterior estimated covariance at time k-1 and the prior estimated covariance at time k, respectively. Q represents the estimated state quantity at time k; F and H represent the state transition matrices; Q represents the estimated state quantity at time k. k-1 and R k-1 These are the process noise covariance and measurement noise covariance at time k-1, respectively.

[0124] (1) Set n as the second voltage error threshold, n = 0.02V.

[0125] like Then IXKF degenerates into XKF scheme, and step (3) is executed directly.

[0126] like This indicates that the error exceeds the threshold and the accuracy needs to be improved. Step (2) needs to be executed first, and then step (3) needs to be executed.

[0127] (2) Iterative update:

[0128]

[0129] After step (2) is completed, proceed to step (3).

[0130] (3) Kalman gain matrix:

[0131]

[0132] Error covariance correction:

[0133]

[0134] System status correction:

[0135]

[0136] Furthermore, the method for establishing a discrete state-space model of the battery and solving for the SOC based on the second-order RC equivalent circuit model of the battery and Kirchhoff's laws is as follows:

[0137]

[0138] U d,k =f(SOC) k )-U 1,k -U 2,k -R0I k +w k

[0139] in, Let represent the state variables of the model; time constants τ1 = R1C1, τ2 = R2C2; R1 represents the activation polarization resistance, R2 represents the concentration polarization resistance, C1 represents the activation polarization capacitance, C2 represents the concentration polarization capacitance, and η is the coulombic efficiency; Q N The maximum usable capacity of the battery at the current temperature; I k-1 f(SOC) represents the current at time k-1; k ) represents the open-circuit voltage U oc Functional relationship with state of charge (SOC); SOC k U represents the state of charge at time k;1,k U is the electrochemical polarization voltage at time k; 2,k V is the concentration polarization voltage at time k, Δt is the time step, and v k Let R0 be the Gaussian process noise at time k, and I be the internal resistance of the battery in the second-order equivalent circuit of the battery. k Let w be the current measured at time k. k For the Gaussian measurement noise at time k, U d,k Let be the battery terminal voltage calculated at time k.

[0140] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for estimating the state of charge of a lithium battery based on adaptive dual-fusion Kalman filtering, characterized in that, include: Construct an equivalent circuit model; Based on the equivalent circuit model, battery parameters are obtained; Based on the equivalent circuit model, the battery parameters are obtained as follows: The battery parameters of the equivalent circuit model are obtained by using the least squares method, wherein the battery parameters include: battery internal resistance, voltage, capacity and charge / discharge efficiency; Based on the battery parameters, obtain the battery measurement value and the measurement estimate value; Based on the battery parameters, obtaining the battery measurement values ​​and measurement estimates includes: Initialize the state parameters and battery equivalent circuit model in the battery parameters, and obtain the initial state parameters; The error covariance is initialized based on the initialization state parameters. Based on the initialized error covariance, obtain the battery measurement estimate; Based on the absolute value of the error between the measured value and the estimated value, the corresponding Kalman filter is used to estimate the battery state of charge. Based on the absolute value of the error between the measured value and the estimated value, a corresponding Kalman filter is used to estimate the battery state of charge, including: Determine whether the absolute value of the error between the measured value and the estimated value is greater than the first voltage threshold. If it is not greater, use extended Kalman filtering for estimation; if it is greater, use exogenous Kalman filtering for iterative estimation. The extended Kalman filter is used for estimation to obtain the battery state of charge estimate, including: The battery parameters are estimated a priori to obtain the a priori estimates. Update the Kalman gain based on the prior estimate; Based on the updated Kalman gain, update the posterior error covariance and obtain the current error covariance; Based on the current error covariance, obtain the estimated value of the battery state of charge; The current error covariance also needs to participate in the initialization of the error covariance at the next time step; The exogenous Kalman filter is used for estimation to obtain the battery state-of-charge estimate, which includes: Establish the observation equations and state equations for the battery; Based on the observation equation and the state equation, a priori estimation is performed to obtain the priori estimated value; Based on the prior estimates, the Kalman gain, posterior error covariance, and state estimates are updated. Based on the updated information, determine whether the absolute value of the error between the battery measurement value and the measurement estimate value is greater than the second voltage threshold. If it is not greater than the second voltage threshold, perform local iteration; otherwise, directly obtain the error covariance. Based on the error covariance, the estimated state of charge of the battery is obtained; Local iteration includes: S1, Corrected noise covariance; S2. Update the Kalman gain matrix based on the corrected noise covariance; S3. Update the posterior error covariance based on the updated Kalman gain matrix; S4. Repeat steps S1-S3 until the absolute value of the error between the battery measurement value and the measurement estimate value is less than the preset value, then stop the iteration. Based on the estimated battery state of charge, the battery state of charge estimation result is obtained.

2. The lithium battery state-of-charge estimation method based on adaptive dual-fusion Kalman filtering according to claim 1, characterized in that, The observation equation is: The state equation is: in, and These represent the system's state variables at times k+1 and k, respectively. Let k be the system input at time k. ; , and These represent the measurement noise covariance and the process noise covariance, respectively. Representing the measured state variables, A, B, C, and D are system matrices. Represents the system's data variables. Represents the system's parameter variables. , , , , For the corresponding constant coefficients, The output of the system at time k is... The output of the system at time k-1, The output of the system at time k-2, The input to the system at time k-1, This represents the system input at time k-2.

3. The lithium battery state-of-charge estimation method based on adaptive dual-fusion Kalman filtering according to claim 1, characterized in that, The method for obtaining the battery state of charge estimation result based on the battery state of charge estimation value is as follows: in, , represents the state variables of the model; time constant ; Indicates the activation polarization resistance. Indicates concentration polarization resistance. Indicates the activation polarization capacitor. Indicates concentration polarization capacitance. For Coulomb efficiency; This represents the maximum usable capacity of the battery at the current temperature. This represents the current at time k-1; Indicates open circuit voltage Functional relationship with state of charge (SOC); The state of charge at time k; Let k be the electrochemical polarization voltage at time k; Let k be the concentration polarization voltage at time k. For time step, The noise is the Gaussian process noise at time k. This refers to the battery's internal resistance. Let be the current measured at time k. For the Gaussian measurement noise at time k, Let be the battery terminal voltage obtained by calculation at time k.

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