Lithium battery SOC estimation method based on re-calibration unscented Kalman filtering

Abstract

The invention discloses a lithium battery SOC estimation method based on re-calibration unscented Kalman filtering, and the method comprises the following steps: measuring voltage data under different SOCs, and building a polynomial function relation between the SOC and an open-circuit voltage; establishing a lithium battery second-order RC equivalent circuit model; performing parameter identification on the equivalent circuit model; and estimating the SOC of the lithium battery based on the re-calibration unscented Kalman filtering. According to the method, the system is re-estimated after the state vector is updated, so that errors caused by the fact that the prediction state value is used too early for Kalman gain calculation in a traditional method can be avoided, the Kalman gain is re-estimated on the basis of the updated state vector, the real state of the system can be reflected more accurately, and the calculation accuracy of the system is improved. Therefore, the overall estimation precision of the filter is improved.

Description

Technical Field

[0001] This application belongs to the technical field of lithium batteries, and specifically relates to a method for estimating the state of charge (SOC) of lithium batteries based on re-calibrated unscented Kalman filtering. Background Art

[0002] Accurate state-of-charge (SOC) estimation is crucial for ensuring battery safety, optimizing performance, and extending the service life of battery systems. In "A Method and System for Analyzing the State of Life of Batteries Based on a Charging Integration Algorithm", a method and system for analyzing the state of life of batteries based on a charging integration algorithm are proposed. This method uses the stability of the charging cycle current to evaluate the state of life of vehicle power batteries, greatly improving efficiency. In "A Method for Estimating the State of Charge of Lithium Batteries Based on the Fusion of Data and Model Filtering", a method for estimating the state of charge of lithium batteries based on the fusion of data and model filtering is proposed. In "A SOC Estimation Method and System Combining Improved Parameter Identification and Infinite Algorithm", the recursive least squares method with a time-varying forgetting factor with limited memory is used for parameter identification, and at the same time, the adaptive unscented H-infinity filtering algorithm is combined to estimate the SOC of lithium batteries, which can accurately reflect the state information of the battery and thus accurately estimate the SOC value of the battery. The second-order RC equivalent model has relatively small computational complexity, a simple structure, and high accuracy. Unscented Kalman filtering (UKF) is a state estimation method for nonlinear systems. It samples several "sampling points" ("sigma" points) of the state distribution through unscented transformation, and calculates the predicted mean and covariance after the nonlinear propagation of the system. Then, combined with measurement update, the state is corrected. UKF avoids the linearization of the nonlinear function in the traditional extended Kalman filtering and has higher estimation accuracy and stability. This filtering method is particularly suitable for situations with noisy data and uncertain environments, and can effectively improve the accuracy and reliability of data. However, in the filtering update process, the calculation of the Kalman gain is based on the predicted prior estimate, which may contain large errors. When using it to calculate the Kalman gain, it may lead to an overly large or small gain, thus affecting the final state estimation accuracy. How to solve the above technical problems has become a challenge for the present invention. Summary of the Invention

[0003] This application provides a method for estimating the SOC of lithium batteries based on re-calibrated unscented Kalman filtering to solve the technical problem of insufficient accuracy in estimating the SOC of lithium batteries.

[0004] To solve the above technical problem, a technical solution adopted by this application is: A method for estimating the SOC of lithium batteries based on re-calibrated unscented Kalman filtering, including the following steps:

[0005] Measure the voltage data at different SOCs and establish a polynomial function relationship between SOC and open-circuit voltage;

[0006] Establish a second-order RC equivalent circuit model for lithium batteries;

[0007] Identify the parameters of the equivalent circuit model;

[0008] Based on the re-calibrated unscented Kalman filter, estimate the state of charge (SOC) of the lithium battery.

[0009] Furthermore, a method for establishing a second-order RC equivalent circuit model of a lithium battery includes:

[0010] Based on Equation (1), define the SOC of the lithium-ion battery as the ratio of its actual remaining capacity to the rated capacity; where Equation (1) is:

[0011]

[0012] where Q n is the rated capacity of the battery, t 0 is the initial time, t 1 is the current time, and I is the battery load current;

[0013] Based on Equation (2), construct the transfer function of the second-order RC equivalent circuit model of the lithium battery; where Equation (2) is:

[0014]

[0015] where U oc is the open-circuit voltage, and the terminal voltage is U; U 1 , U 2 respectively represent the voltages of the two resistor-capacitor circuits, R omc represents the ohmic internal resistance of the battery; R 1 and R 2 are the circuit resistances, C 1 and C 2 are the circuit capacitances.

[0016] Furthermore, a method for identifying the parameters of the equivalent circuit model includes:

[0017] Based on Equation (3), discretize the transfer function; where Equation (3) is:

[0018] U(t) - U oc (t) = a 1 [U(t - 1) - U oc (t - 1)] + a 2 [U(t - 2) - U oc (t - 2)] + b 0 I(t) + b 1 I(t - 1) + b 2 I(t - 2) + v(t) (3);

[0019] where a 1, a 2 , b 0 , b 1 and b 2 are the parameters of the equivalent circuit model;.

[0020] Let y(t) = U(t) - U oc (t), and based on Equation (4), obtain the parameter identification model; where Equation (4) is:

[0021]

[0022] Among them, θ = [a 1 , a 2 , b 0 , b 1 , b 2 T, and identify each element in θ through the recursive Bayesian algorithm.

[0023] Furthermore, based on Equation (5), define the discrete form of the battery SOC; Equation (5) is:

[0024]

[0025] Based on Equation (6), obtain the state equation and measurement equation of the second-order RC equivalent circuit model; where Equation (6) is:

[0026]

[0027] Among them, X k and Y k are the state vector and measurement vector at time k respectively, u k is the system input at time k, f(.) and h(.) are non-linear functions, w k and v k are the process noise and measurement noise respectively, both of which are Gaussian white noise, and Q and R are the corresponding process noise covariance matrix and measurement noise covariance matrix;

[0028] Based on Equation (7), obtain the state space equation for estimating the lithium battery SOC; where Equation (7) is:

[0029]

[0030] Furthermore, a method for estimating the lithium battery SOC based on re-calibrated unscented Kalman filtering includes:

[0031] Based on several sampling points ("sigma" points) of the state distribution sampled by the unscented transform, obtain the predicted values of the state mean and state covariance;

[0032] Calculate the Kalman gain based on the mean of the predicted measurement values, the covariance matrix, and the observation information covariance matrix;

[0033] Update the state vector based on the Kalman gain and the state mean;

[0034] Perform an unscented transformation based on the predicted value of the state covariance and the state vector to obtain the updated state vector and the predicted measurement values;

[0035] Repeat the above steps. When the trace of the updated state covariance matrix is not greater than the trace of the predicted value of the state covariance matrix, retain the update result; otherwise, perform a fallback operation.

[0036] The beneficial effects of this application are as follows:

[0037] 1. By re - estimating the system after updating the state vector, this application can avoid the errors caused by calculating the Kalman gain using the predicted state value too early in the traditional method. Therefore, re - estimating the Kalman gain based on the updated state quantity can more accurately reflect the true state of the system, thereby improving the overall estimation accuracy of the filter.

[0038] 2. In the standard Kalman filter, after state update, the covariance matrix sometimes shows inappropriate results (for example, the trace of the covariance matrix increases, indicating a deterioration in estimation accuracy). Adding a fallback step can retain the update only when it is confirmed that the updated state improves the estimation accuracy, which can effectively avoid the instability of the filter caused by inaccurate updates and make the filter more robust in the face of noise or uncertainty. Description of the Drawings

[0039] Figure 1 is a schematic flowchart of an embodiment of the lithium - battery SOC estimation method based on re - calibrated unscented Kalman filtering of this application;

[0040] Figure 2 is an equivalent model of a second - order RC circuit in an embodiment of the lithium - battery SOC estimation method based on re - calibrated unscented Kalman filtering of this application;

[0041] Figure 3 is a flowchart of re - calibrated unscented Kalman filtering in an embodiment of the lithium - battery SOC estimation method based on re - calibrated unscented Kalman filtering of this application;

[0042] Figure 4 is Figure 1 a schematic flowchart of an embodiment of step S4 in

[0043] Figure 5In Embodiment 1 of the present application, under the FUDS working condition, it is a comparison curve graph of the SOC predicted by the SOC estimation method based on RUKF, the SOC predicted only using the UKF algorithm, and the true SOC.

[0044] Figure 6 In Embodiment 2 of the present application, under the DST working condition, it is a comparison curve graph of the SOC predicted by the SOC estimation method based on RUKF, the SOC predicted only using the UKF algorithm, and the true SOC. Detailed implementation manners

[0045] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with specific embodiments.

[0046] Many specific details are set forth in the following description in order to provide a thorough understanding of the present invention. However, the present invention may be implemented in other ways different from those described herein. Therefore, the present invention is not limited by the limitations of the specific embodiments disclosed in the following specification.

[0047] Refer to Figure 1 , Figure 1 It is a schematic flow chart of an embodiment of the lithium battery SOC estimation method based on re-calibrated unscented Kalman filter of the present application. The method includes the following steps:

[0048] Step S1. Measure the voltage data at different SOCs and establish a polynomial function relationship between SOC and open-circuit voltage.

[0049] Specifically, use a battery measurement instrument, apply a constant load current, record the battery terminal voltage and load current, intermittently return to the open-circuit state, and measure the voltage data at different SOCs. Through polynomial fitting, establish a function relationship between SOC and open-circuit voltage (OCV).

[0050] Step S2. Establish a second-order RC equivalent circuit model of the lithium battery.

[0051] Specifically, refer to Figure 2 , establish a second-order RC equivalent circuit model, which consists of a parallel structure of R1 and C1, and a parallel structure of R2 and C2 to reflect the complex chemical reactions and dynamic characteristics inside the battery. Uoc is the open-circuit voltage, and the terminal voltage is U; U1 and U2 respectively represent the voltages of the two resistor-capacitor loops, and Romc represents the ohmic internal resistance of the battery; define the SOC of the lithium-ion battery as the ratio of its actual remaining capacity to the rated capacity, which is expressed as:

[0052]

[0053] Among them, Q n is the rated capacity of the battery, t 0 is the initial moment, t1 is the current moment, and I is the battery load current;

[0054] The transfer function of the established lithium battery equivalent circuit can be expressed according to Kirchhoff's law as:

[0055]

[0056] where U oc is the open-circuit voltage, and the terminal voltage is U; U 1 , U 2 respectively represent the voltages of two resistor-capacitor loops, R omc represents the ohmic internal resistance of the battery; R 1 and R 2 are circuit resistances, C 1 and C 2 are circuit capacitances.

[0057] Step S3. Perform parameter identification on the equivalent circuit model.

[0058] Specifically, based on formula (3), discretize the transfer function; where formula (3) is:

[0059] U(t) - U oc (t) = a 1 [U(t - 1) - U oc (t - 1)] + a 2 [U(t - 2) - U oc (t - 2)] + b 0 I(t) + b 1 I(t - 1) + b 2 I(t - 2) + v(t) (3);

[0060] where a 1 , a 2 , b 0 , b 1 and b 2 are the parameters of the equivalent circuit model;.

[0061] Let y(t) = U(t) - U oc (t), and based on formula (4), obtain the parameter identification model; where formula (4) is:

[0062]

[0063] where θ = [a 1 , a 2 , b 0 , b 1 , b 2 T, and identify each element in θ through the recursive Bayesian algorithm.

[0064] Step S4. Perform lithium battery SOC estimation based on the re-calibrated unscented Kalman filter.

[0065] Specifically, for the defined SOC of electricity in step S2, its discrete form is:

[0066]

[0067] Based on formula (6), obtain the state equation and measurement equation of the second-order RC equivalent circuit model; where, the formula (6) is:

[0068]

[0069] where, X k and Y k are the state vector and measurement vector at time k respectively, u k is the system input at time k, f(.) and h(.) are non-linear functions, w k and v k are the process noise and measurement noise respectively, both being Gaussian white noise, and Q and R are the corresponding process noise covariance matrix and measurement noise covariance matrix.

[0070] Establish the state space equation for lithium battery SOC estimation:

[0071]

[0072] Refer to Figures 3-4 , step S4 includes:

[0073] Step S41. Based on the unscented transform to sample a number of sampling points ("sigma" points) of the state distribution, obtain the predicted values of the state mean and state covariance.

[0074] Specifically, during the filtering process, first sample a number of sampling points ("sigma" points) of the state distribution through the unscented transform, and the sampling points ("sigma" points) after the system non-linear propagation are δ i,k|k-1 , and calculate the predicted values of the state mean and state covariance.

[0075]

[0076] where, is the predicted value of the state estimate at time k obtained based on the information at time k-1, and are the weight parameters of the unscented transform, P k|k-1 is the predicted value of the state covariance, and Q k is the process noise covariance matrix.

[0077] Step S42. Calculate the Kalman gain based on the mean and covariance matrix of the predicted measurement values and the covariance matrix of the observation information.

[0078] Specifically, based on formulas (10)-(14), calculate the mean of the predicted measurement values and the covariance matrix P xy,k|k-1 、P y,k|k-1 and the covariance matrix S of the observation information k|k-1 for update, and calculate the Kalman gain K:

[0079]

[0080] S k|k-1 =P xy,k|k-1 +R k (13);

[0081]

[0082] Step S43. Update the state vector based on the Kalman gain and the state mean.

[0083] Specifically, update the state vector to obtain the updated state vector

[0084]

[0085] Step S44. Perform an unscented transform based on the predicted value of the state covariance and the state vector to obtain the updated state vector and the measured value of the state covariance P k|k .

[0086] Specifically, to prevent the introduction of a state update with poor effects, recalibrate the filtering parameters, and perform an unscented transform again according to the already calculated P k|k-1 to obtain the updated state vector and the predicted measurement value. On this basis, further calculate according to the information at time k:

[0087] S k|k =P xy,k|k +P k (16);

[0088]

[0089] Step S45.

[0090] If tr(P k|k ) > tr(P k|k-1 ), it means that this update is unhelpful and a rollback operation is required to roll back the state vector and the measured value of the error covariance matrix to the values at the previous moment:

[0091]

[0092] P k|k = P k|k-1 (20);

[0093] Repeat the above steps and continuously iterate this filtering process to achieve accurate estimation of the battery SOC.

[0094] Refer to Figure 5 , the research object of this embodiment is the Panasonic lithium-ion battery NCR-18650B, with a rated voltage of 3.7V and a capacity of 3400 mAh. First, the battery is charged in a constant current charging mode (0.5C) until the cut-off voltage is reached, and the battery is allowed to stand for a period of time to reach a fully charged state. In Example 1, the lithium battery operates under the FUDS working condition and data is collected. The FUDS (Federal Urban Driving Schedule) working condition is a test method used to simulate the battery performance under urban driving conditions and is often used to evaluate the performance of lithium batteries during actual driving. The application of the FUDS working condition in lithium battery testing is very extensive because it can more realistically reflect the usage of the battery during actual urban driving, which is particularly important for evaluating the battery performance of electric vehicles and hybrid vehicles.

[0095] The results show that the lithium battery SOC estimation method based on re-calibrated unscented Kalman filtering has high accuracy, and the predicted SOC error is significantly lower than other methods, having certain engineering value.

[0096] Refer to Figure 6 , the research object of this embodiment is the Panasonic lithium-ion battery NCR-18650B, with a rated voltage of 3.7V and a capacity of 3400 mAh. In Example 2, the lithium battery operates under the DST working condition and data is collected. DST (Dynamic Stress Test) is a dynamic stress test method used to evaluate the comprehensive performance of the battery under actual usage conditions.

[0097] The results show that under the DST working condition, the lithium battery SOC estimation method based on re-calibrated unscented Kalman filtering has high accuracy, and the predicted SOC error is significantly lower than other methods, having certain engineering value.

[0098] The above are only the embodiments of the present application, and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present application, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present application.

Claims

1. A lithium battery SOC estimation method based on a recalibrated unscented Kalman filter, characterized in that: The following steps are involved: Measure the voltage data under different SOCs and establish a polynomial function relationship between SOC and open circuit voltage; Establish a second-order RC equivalent circuit model for lithium batteries; Performing parameter identification on the equivalent circuit model; Lithium battery SOC estimation is performed based on the recalibrated unscented Kalman filter.

2. The method according to claim 1, characterized in that: The method for establishing a second-order RC equivalent circuit model of a lithium battery comprises: Based on formula (1), the SOC of a lithium-ion battery is defined as the ratio of its actual remaining capacity to its rated capacity; wherein formula (1) is: Among them, Q n is the rated capacity of the battery, t0 is the initial time, t1 is the current time, and I is the battery load current; Based on formula (2), the transfer function of the second-order RC equivalent circuit model of the lithium battery is constructed; wherein the formula (2) is: Among them, U oc is the open circuit voltage, the terminal voltage is U; U1 and U2 represent the voltages of the two resistor and capacitor loops, respectively. omc represents the ohmic internal resistance of the battery; R1 and R2 are circuit resistances, and C1 and C2 are circuit capacitances.

3. The method according to claim 1, characterized in that The method for performing parameter identification on the equivalent circuit model comprises: Based on formula (3), the transfer function is discretized; wherein the formula (3) is: U(t)-U oc (t)=a1[U(t-1)_U oc (t-1)]+a2[U(t-2)-U oc (t-2)]+b0I(t)+b1I(t-1)+b2I(t-2)+v(t) (3); Wherein, a1, a2, b0, b1 and b2 are parameters of the equivalent circuit model; Let y(t) = U(t) - U oc (t), based on formula (4), obtain the parameter identification model; wherein, the formula (4) is: in, θ=[a1,a2,b0,b1,b2]T, and identify each element in θ through the recursive Bayesian algorithm.

4. The method according to claim 2, characterized in that: The method according to claim 2, characterized in that Based on formula (5), the discrete form of battery SOC is defined; the formula (5) is: Based on formula (6), the state equation and measurement equation of the second-order RC equivalent circuit model are obtained; wherein the formula (6) is: Among them, X k and Y k are the state vector and measurement vector at time k, u k is the system input at time k, f(.) and h(.) are nonlinear functions, and w k and v k are process noise and measurement noise, respectively, both are Gaussian white noise, Q and R are the corresponding process noise covariance matrix and measurement noise covariance matrix; Based on formula (7), the state space equation for lithium battery SOC estimation is obtained; wherein, the formula (7) is:

5. The method according to claim 1, characterized in that The method for estimating the SOC of a lithium battery based on a recalibrated unscented Kalman filter comprises: Based on the unscented transformation, a number of sampling points of the sampling state distribution are sampled to obtain the predicted values ​​of the state mean and the state covariance; Calculate the Kalman gain based on the mean and covariance matrix of the predicted measurement values ​​and the covariance matrix of the observed information; Based on the Kalman gain and the state mean, updating a state vector; Based on the predicted value of the state covariance and the state vector, an unscented transformation is performed to obtain an updated state vector and the predicted measurement value; Repeat the above steps, and when the trace of the updated state covariance matrix is ​​not greater than the trace of the predicted value of the state covariance matrix, retain the update result; otherwise, perform a rollback operation.

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