A SOC calibration algorithm based on Kalman filter multi-sensor fusion

Abstract

This invention belongs to the field of state control and control optimization application technology for complex systems, and particularly relates to a SOC calibration algorithm based on Kalman filter multi-sensor fusion. The algorithm includes constructing a lithium battery circuit model, lithium battery model identification, Kalman filter multi-sensor fusion SOC calibration, and improving the accuracy of multi-sensor fusion Kalman filtering. This invention considers the charging and discharging characteristics of the lithium battery model, the complexity of battery internal parameter identification, and the complexity of the Kalman algorithm. It proposes a Kalman filter multi-sensor fusion SOC calibration that takes into account process noise and measurement noise, ensuring accurate SOC. This can improve user experience, extend battery life, ensure safety, and optimize energy management. This invention utilizes the cloud platform of the BMS to define and analyze data, adjust the parameter matrix of the battery model and the covariance of the sensors, and still maintain SOC accuracy even under sensor aging conditions.

Description

Technical Field

[0001] This invention belongs to the field of state control and control optimization application technology for complex systems, and particularly relates to a SOC calibration algorithm based on Kalman filter multi-sensor fusion. Background Technology

[0002] The State of Charge (SOC) of a power battery is a crucial parameter, often displayed as a core parameter on instruments in practical applications. This allows users to intuitively understand the remaining charge and health status of the battery pack, and provides important information for rational charging and discharging and the development of optimal energy management strategies. Due to the complexity of the internal reactions during battery charging and discharging, and the strong time-varying nonlinearity of batteries in practical applications due to the influence of operating conditions and environmental factors, overcharging and over-discharging can easily occur, leading to reduced driving range and safety hazards. Therefore, real-time and accurate estimation of the power battery's SOC value has significant theoretical and engineering value for extending battery life, improving battery safety and reliability, and enhancing the overall performance of electric vehicles. A battery is a complex chemical device with strong nonlinear characteristics; SOC cannot be directly measured by sensors and can only be estimated indirectly using model-based algorithms.

[0003] Currently, the main problems in estimating the SOC of lithium batteries are low accuracy, noise interference, and the inability to guarantee algorithm accuracy after sensor aging. Summary of the Invention

[0004] This invention addresses the technical problems existing in SOC calibration by proposing a SOC calibration algorithm based on Kalman filter multi-sensor fusion that is rationally designed, simple in method, theoretically sound, and capable of solving interference problems while maintaining accuracy even under sensor aging conditions.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: a SOC calibration algorithm based on Kalman filter multi-sensor fusion, comprising the following steps:

[0006] S1. Construct a circuit model for the lithium battery, choosing a second-order RC model. The mathematical equations of the circuit are:

[0007] (1),

[0008] Where R0 represents the ohmic internal resistance of the battery, U0 represents the battery terminal voltage, and U ocv The voltage U1 represents the open-circuit voltage of the battery. Voltage U1, resistance R1, and capacitance C1 represent the electrochemical polarization effect of the lithium battery. Voltage U2, resistance R2, and capacitance C2 represent the concentration difference polarization effect of the lithium battery.

[0009] S2. Lithium battery model identification: The polarization circuit section is subjected to a Laplace transform separately to obtain the transfer function of the polarization component.

[0010] (2),

[0011] Where U(s) is the total polarization voltage, I(s) is the total polarization current, R1 and R2 are resistors, and C1 and C2 are capacitors, HPPC and U are tested under different temperatures and different rates. ocv The experiment used the MATLAB system identification toolbox to identify the ohmic internal resistance R0 and the resistances R1, R2 and capacitances C1, C2 of the two polarization effects at different SOCs under different temperature and rate charge / discharge conditions of the lithium battery model, and obtained the SOC-OCV curve.

[0012] SOC calibration using S3 and Kalman filtering multi-sensor fusion, the mathematical equations for discrete and continuous lithium batteries, and the solutions to the differential equations for electrochemical polarization effect voltage U1 and concentration difference polarization effect voltage U2 are:

[0013] (3),

[0014] in (x=1,2) represents the polarization voltage, resistance, and capacitance, U i Let I(t) represent the initial voltage of the polarization effect, and let I(t) represent the current as a function of time. When time t is very small, I(t) approaches region I, which simplifies to:

[0015] (4),

[0016] The further polarization voltage equation (4) is discretized as follows:

[0017] (5),

[0018] Where k represents time, Ux(k) represents the voltage at time k, Ux(k-1) represents the voltage at time k-1, I(k-1) represents the current at time k-1, Ts is the discrete sampling time, and the state equation of the SOC is:

[0019] (6),

[0020] Where Ccap represents the lithium battery capacity, SOC represents the remaining charge, and the unit is Ah. Equation (6) is discretized as follows:

[0021] (7),

[0022] Where k represents time, and using the SOC-OCV curve, Uocv in equation (1) can be transformed into:

[0023] (8),

[0024] Where focv represents the SOC-OCV curve, the discrete state space of the battery model can be obtained from equations (6), (7) and (8) as follows:

[0025] (9),

[0026] Where x(k)=[U1(k) U2(k) SOC(k)]T represents the current system state at time k, with state variables being polarization voltages U1, U2, and SOC, respectively; y(k) represents the current system output, i.e., battery terminal voltage U0(k); u(k) represents the previous system input, i.e., I(k); w(k-1)~(0, Q) and v(k-1)~(0, R) represent the previous noise, representing process noise and measurement noise, respectively; Q and R represent the covariance matrices of process noise and measurement noise, respectively; and A represents the system matrix with values... B represents the input matrix, and the value is... C represents the output matrix, and the value is... , Let R represent the partial derivative, D represent the transfer matrix with a value of R0, and Kalman filtering is used to perform data fusion and SOC calibration on the output of the discretized lithium battery circuit model. Kalman filtering includes two processes: prediction and correction, which are repeated cyclically.

[0027] S4. Improved accuracy of multi-sensor fusion and Kalman filtering, supporting all-weather, all-condition operation of BMS. Utilizes the BMS cloud platform to define and analyze data, and adjust the parameter matrix of the battery model and the covariance of the sensors.

[0028] Preferably, the prediction process of the Kalman filter in step S3 includes the following steps:

[0029] S311. Set the initial posterior estimate, posterior estimate covariance, process covariance matrix Q, and unit voltage measurement noise R. c Total pressure unit measurement noise R s ;

[0030] S312, Update Prior Estimation Update According to equation (10), the system input u k-1 and posterior estimation To achieve this, equation (10) is:

[0031] (10),

[0032] in, It is the posterior estimate after Kalman filtering, and also the result after Kalman fusion localization. It is a priori estimation. It is the covariance matrix of the posterior estimate. It is the covariance matrix estimated a priori;

[0033] S313. Update the prior covariance matrix according to equation (10). .

[0034] Preferably, the Kalman filter correction process in step S3 includes the following steps:

[0035] S321. Calculate the Kalman gain according to equation (11), which is:

[0036] (11),

[0037] in, Let C be the gain and C be the output matrix. Let R be the prior covariance matrix. c For individual cell voltage measurement noise and R s The noise level is measured for the total pressure unit.

[0038] S322. Obtain voltage information of individual lithium battery cells measured by two sensors;

[0039] S323. Update the posterior estimate according to equation (12). This is an estimate of the SOC, used for SOC calibration, and equation (12) is:

[0040] (12),

[0041] in, ) represents the position of the element in the prior estimate, focv is the SOC-OCV curve, and U c and U s The voltage that can be obtained by a single unit, u k-1 Input for the system;

[0042] S324. Update the posterior estimate according to equation (13). At this point, one Kalman filter cycle is completed. The next cycle begins from S322 and repeats. Equation (13) is:

[0043] (13),

[0044] Where I is the identity matrix, To update the posterior estimate, Let be the prior covariance matrix.

[0045] As a preferred option, when the number of sensors is increased, equations (12) and (13) can be easily modified to achieve more sensor fusion.

[0046] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0047] This invention presents a State of Charge (SOC) calibration algorithm based on Kalman filter multi-sensor fusion. Considering the complexity of the lithium battery's charge-discharge characteristics, internal parameter identification, and the Kalman algorithm itself, this invention proposes a Kalman filter multi-sensor fusion SOC calibration method. It takes into account process noise and measurement noise, ensuring accurate SOC, which can improve user experience, extend battery life, ensure safety, and optimize energy management. This invention utilizes the cloud platform of the Battery Management System (BMS) to define and analyze data, adjusting the parameter matrix of the battery model and the covariance of the sensors, maintaining SOC accuracy even under sensor aging conditions. Attached Figure Description

[0048] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 A flowchart of a SOC calibration algorithm based on Kalman filter multi-sensor fusion is provided for an embodiment of the present invention;

[0050] Figure 2 A lithium battery circuit model diagram provided for an embodiment of the present invention;

[0051] Figure 3 A polarization circuit model diagram provided for an embodiment of the present invention;

[0052] Figure 4 This is a state-space transition diagram of a lithium battery provided in an embodiment of the present invention. Detailed Implementation

[0053] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0054] Numerous specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and therefore the invention is not limited to the specific embodiments disclosed in the following specification.

[0055] In practice, accurate battery level display allows users to better understand the remaining usage time of their device, thus enabling them to better plan their usage. For example, in mobile devices, users can decide when to charge based on accurate battery level information, avoiding sudden shutdowns or malfunctions due to misjudged battery levels. The stability and performance of devices and systems may be related to the battery's state of charge (SOC). Accurate SOC information helps the system better allocate and manage resources, resulting in more stable and smoother performance. For lithium batteries, overcharging or over-discharging can affect their lifespan; accurate SOC calibration can reduce the risk of overcharging and over-discharging, helping to extend battery life. In some cases, inaccurate battery SOC can lead to unexpected device malfunctions, such as allowing high-performance operation when the battery is low, potentially causing overload and danger. Accurate SOC information helps the system more intelligently control charging behavior, avoiding frequent charging or overcharging, thereby improving battery efficiency. In summary, the significance of lithium battery SOC calibration lies in ensuring the accuracy of battery level display, improving user experience, extending battery life, ensuring safety, and optimizing energy management. This is a crucial step in ensuring normal device operation and user satisfaction. However, current lithium battery SOC estimation methods suffer from low accuracy, noise interference, and inconsistent algorithm accuracy after sensor aging. To address these issues, this invention proposes a SOC calibration algorithm based on Kalman filter multi-sensor fusion, such as... Figure 1 , Figure 2 As shown, firstly, considering the complexity of the model satisfying the charging and discharging characteristics of lithium batteries, the complexity of identifying internal battery parameters, and the complexity of the Kalman algorithm, a second-order RC model is chosen to construct the circuit model of the lithium battery. The mathematical equations of the circuit are:

[0056] (1),

[0057] Where R0 represents the ohmic internal resistance of the battery, U0 represents the battery terminal voltage, and U ocv U1 represents the open-circuit voltage of the battery. Voltage U1, resistance R1, and capacitance C1 represent the electrochemical polarization effect of the lithium battery. Voltage U2, resistance R2, and capacitance C2 represent the concentration difference polarization effect of the lithium battery.

[0058] Next, the lithium battery model was identified, and the polarization circuit section was subjected to a Laplace transform separately, such as... Figure 3 As shown, the transfer function of the polarization part is obtained:

[0059] (2),

[0060] Where U(s) is the total polarization voltage, I(s) is the total polarization current, R1 and R2 are resistors, and C1 and C2 are capacitors, HPPC and U are tested under different temperatures and different rates.ocv The experiment used the MATLAB system identification toolbox to identify the ohmic internal resistance R0 and the resistances R1, R2 and capacitances C1, C2 of the two polarization effects at different SOCs under different temperature and rate charge / discharge conditions of the lithium battery model, and obtained the SOC-OCV curve.

[0061] Then, using Kalman filtering and multi-sensor fusion for SOC calibration, the solutions to the differential equations for the discrete and continuous lithium battery mathematical equations, the electrochemical polarization effect voltage U1, and the concentration difference polarization effect voltage U2 are:

[0062] (3),

[0063] in (x=1,2) represents the polarization voltage, resistance, and capacitance, U i Let I(t) represent the initial voltage of the polarization effect, and let I(t) represent the current as a function of time. When time t is very small, I(t) approaches region I, which simplifies to:

[0064] (4),

[0065] The further polarization voltage equation (4) is discretized as follows:

[0066] (5),

[0067] Where k represents time, Ux(k) represents the voltage at time k, Ux(k-1) represents the voltage at time k-1, I(k-1) represents the current at time k-1, Ts is the discrete sampling time, and the state equation of the SOC is:

[0068] (6),

[0069] Where Ccap represents the lithium battery capacity, SOC represents the remaining charge, and the unit is Ah. Equation (6) is discretized as follows:

[0070] (7),

[0071] Where k represents time, and using the SOC-OCV curve, Uocv in equation (1) can be transformed into:

[0072] (8),

[0073] Where focv represents the SOC-OCV curve, such as Figure 4 As shown, the discrete state space of the battery model can be obtained from equations (6), (7) and (8) as follows:

[0074] (9),

[0075] Where x(k)=[U1(k) U2(k) SOC(k)]T represents the current system state at time k, with state variables being polarization voltages U1, U2, and SOC, respectively; y(k) represents the current system output, i.e., battery terminal voltage U0(k); u(k) represents the previous system input, i.e., I(k); w(k-1)~(0, Q) and v(k-1)~(0, R) represent the previous noise, representing process noise and measurement noise, respectively; Q and R represent the covariance matrices of process noise and measurement noise, respectively; and A represents the system matrix with values... B represents the input matrix, and the value is... C represents the output matrix, and the value is... , Let R denote the partial derivative, and D denote the transfer matrix with a value of R0.

[0076] Considering that the BMS board collects the individual cell voltage and total voltage of each lithium battery, and that each cell can yield at least two voltages (Uc and Us), based on the established lithium battery circuit model, a multi-sensor Kalman filter can be used to fuse the individual cell voltages to estimate the lithium battery's State of Charge (SOC). The Kalman filter mainly involves two processes: prediction and correction, which are repeated cyclically. The prediction process of the Kalman filter is as follows:

[0077] Set the initial posterior estimate, posterior estimate covariance, process covariance matrix Q, and unit voltage measurement noise R. c Total pressure unit measurement noise R s Update prior estimates According to equation (10), the system input u k-1 and posterior estimation To achieve this, equation (10) is:

[0078] (10),

[0079] in, It is the posterior estimate after Kalman filtering, and also the result after Kalman fusion localization. It is a priori estimation. It is the covariance matrix of the posterior estimate. It is the prior estimated covariance matrix; the prior covariance matrix is ​​updated according to equation (10). .

[0080] Considering that the Kalman filter correction process first requires obtaining the Kalman gain, then correcting the Kalman filter based on the Kalman gain, and finally completing the prediction correction, this process is repeated cyclically. The Kalman filter correction process is as follows:

[0081] The Kalman gain is calculated according to equation (11), which is:

[0082] (11),

[0083] in, Let C be the gain and C be the output matrix. Let R be the prior covariance matrix. c For individual cell voltage measurement noise and R s To measure the noise of the total voltage cell; obtain the voltage information of the lithium battery cell measured by the two sensors; update the posterior estimate according to equation (12), This is an estimate of the SOC, used for SOC calibration, and equation (12) is:

[0084] (12),

[0085] in For the position of the element in the prior estimate, focv is the SOC-OCV curve, U c and U s The voltage that can be obtained by a single unit, u k-1 The system input is used; the posterior estimate is updated according to equation (13), at which point one Kalman filtering cycle is completed. The next cycle begins from the second step, and the cycle repeats. Equation (13) is:

[0086] (13),

[0087] Where I is the identity matrix, To update the posterior estimate, Let be the prior covariance matrix.

[0088] Finally, the accuracy of multi-sensor fusion and Kalman filtering is improved. This invention supports all-weather, all-condition operation of the BMS. However, over time, the parameter matrix of the battery model will change, and sensor aging will also increase the measurement covariance. To address this, the cloud platform of the BMS is used to define and analyze the data, adjust the parameter matrix of the battery model and the covariance of the sensors, and still ensure SOC accuracy under sensor aging conditions. In addition, when the number of sensors is increased, equations (12) and (13) can be easily modified to achieve more sensor fusion.

[0089] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments for application in other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A SOC calibration algorithm based on Kalman filter multi-sensor fusion, characterized in that, Includes the following steps: S1. Construct a circuit model for the lithium battery, choosing a second-order RC model. The mathematical equations of the circuit are: (1)， Where R0 represents the ohmic internal resistance of the battery, U0 represents the battery terminal voltage, and U ocv The voltage U1 represents the open-circuit voltage of the battery. Voltage U1, resistance R1, and capacitance C1 represent the electrochemical polarization effect of the lithium battery. Voltage U2, resistance R2, and capacitance C2 represent the concentration difference polarization effect of the lithium battery. S2. Lithium battery model identification: The polarization circuit section is subjected to a Laplace transform separately to obtain the transfer function of the polarization component. (2)， Where U(s) is the total polarization voltage, I(s) is the total polarization current, R1 and R2 are resistors, and C1 and C2 are capacitors, HPPC and U are tested under different temperatures and different rates. ocv The experiment used the MATLAB system identification toolbox to identify the ohmic internal resistance R0 and the resistances R1, R2 and capacitances C1, C2 of the two polarization effects at different SOCs under different temperature and rate charge / discharge conditions of the lithium battery model, and obtained the SOC-OCV curve. SOC calibration using S3 and Kalman filtering multi-sensor fusion, the mathematical equations for discrete and continuous lithium batteries, and the solutions to the differential equations for electrochemical polarization effect voltage U1 and concentration difference polarization effect voltage U2 are: (3)， in x=1,2, representing polarization voltage, resistance, and capacitance, U i Let I(t) represent the initial voltage of the polarization effect, and let I(t) represent the current as a function of time. When time t is very small, I(t) approaches I, which simplifies to: (4)， The further polarization voltage equation (4) is discretized as follows: (5)， Where k represents time, Ux(k) represents the voltage at time k, Ux(k-1) represents the voltage at time k-1, I(k-1) represents the current at time k-1, Ts is the discrete sampling time, and the state equation of the SOC is: (6)， Where Ccap represents the lithium battery capacity, SOC represents the remaining charge, and the unit is Ah. Equation (6) is discretized as follows: (7)， Where k represents time, and using the SOC-OCV curve, Uocv in equation (1) can be transformed into: (8)， Where focv represents the SOC-OCV curve, the discrete state space of the battery model can be obtained from equations (6), (7) and (8) as follows: (9)， Where x(k) = [U1(k) U2(k) SOC(k)] T The system state at time k is represented by the polarization voltages U1 and U2 and the state of charge (SOC). y(k) represents the system output at the current time, i.e., the battery terminal voltage U0(k) and u(k). Let ) represent the system input at the previous time step, w(k-1) represent the process noise at time step k-1, which follows a Gaussian distribution with a mean of 0 and a covariance matrix of Q, respectively; v(k-1) represent the measurement noise at time step k-1, which follows a Gaussian distribution with a mean of 0 and a covariance matrix of R; and A represent the system matrix with a value of . B represents the input matrix, and the value is... C represents the output matrix, and the value is... , Let represent the partial derivative, D represent the transfer matrix, and the value is the ohmic internal resistance R0 of the battery. The output of the discretized lithium battery circuit model is fused and calibrated using Kalman filtering. Kalman filtering includes two processes: prediction and correction, which are repeated cyclically. S4. Improved accuracy of multi-sensor fusion and Kalman filtering, supporting all-weather, all-condition operation of BMS. Utilizes the BMS cloud platform to define and analyze data, and adjust the parameter matrix of the battery model and the covariance of the sensors.

2. The SOC calibration algorithm based on Kalman filter multi-sensor fusion according to claim 1, characterized in that, The prediction process of the Kalman filter in step S3 includes the following steps: S311. Set the initial posterior estimate, posterior estimate covariance, process covariance matrix Q, and unit voltage measurement noise R. c Total pressure unit measurement noise R s ; S312, Update Prior Estimation Update According to equation (10), the system input u k-1 and posterior estimation To achieve this, equation (10) is: (10)， in, It is the posterior estimate after Kalman filtering, and also the result after Kalman fusion localization. It is a priori estimation. It is the covariance matrix of the posterior estimate. It is the covariance matrix estimated a priori; S313. Update the prior covariance matrix according to equation (10). .

3. The SOC calibration algorithm based on Kalman filter multi-sensor fusion according to claim 2, characterized in that, The correction process of the Kalman filter in step S3 includes the following steps: S321. Calculate the Kalman gain according to equation (11), which is: (11)， in, Let C be the gain and C be the output matrix. Let R be the prior covariance matrix. c For individual cell voltage measurement noise and R s The noise level is measured for the total pressure unit. S322. Obtain voltage information of individual lithium battery cells measured by two sensors; S323. Update the posterior estimate according to equation (12). This is an estimate of the SOC, used for SOC calibration, and equation (12) is: (12)， in, , represents the position of the element in the prior estimate, focv is the SOC-OCV curve, U c and U s The voltage that can be obtained by a single unit, u k-1 Input for the system; S324. Update the posterior estimate according to equation (13). At this point, one Kalman filter cycle is completed. The next cycle begins from S322 and repeats. Equation (13) is: (13)， Where I is the identity matrix, To update the posterior estimate, Let be the prior covariance matrix.

4. The SOC calibration algorithm based on Kalman filter multi-sensor fusion according to claim 3, characterized in that, When the number of sensors is increased, equations (12) and (13) can be easily modified to achieve more sensor fusion.

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