An adaptive charge estimation method for lithium-ion batteries based on initial value compensation unscented Kalman filter algorithm

Abstract

A lithium-ion battery adaptive charge estimation method based on an initial value compensation unscented Kalman filter algorithm comprises the following steps: step 1, selecting an equivalent circuit model; step 2, using an augmented vector method to process the initial value of the state, unknown order and unknown parameters, processing noise by an iterative method, and updating an adaptive fractional-order unscented Kalman filter algorithm; step 3, adaptively estimating the covariance matrix of the noise according to the proposed unscented Kalman filter algorithm with initial value compensation, and then estimating the SOC value of the lithium-ion battery. The present invention provides a method for designing an adaptive fractional-order unscented Kalman filter based on initial value compensation. Compared with an adaptive fractional-order unscented Kalman filter algorithm without initial value compensation and when the noise covariance matrix is ​​known, this method effectively improves the SOC estimation accuracy of the lithium-ion battery and improves the adaptive ability of the SOC estimation of the lithium-ion battery under different working conditions.

Description

Technical Field

[0001] The present invention relates to the field of lithium-ion battery algorithms, and in particular to a lithium-ion battery adaptive charge estimation method based on an initial value compensated unscented Kalman filter algorithm. Background Art

[0002] With the rapid development of electric vehicles, the management and control technology of automotive power batteries has gradually become a research hotspot. Among them, the SOC of lithium-ion batteries is one of the important parameters of the battery management system. Accurately estimating the battery SOC can effectively prevent lithium batteries from being overcharged or over-discharged, thereby extending the service life of lithium-ion batteries.

[0003] In the process of SOC estimation, due to the interference of external factors such as temperature and noise, the estimation accuracy of SOC is easily reduced. Therefore, the Kalman filter algorithm is selected to achieve state space description by establishing a battery model, and then the Kalman filter algorithm is used for state estimation. This method is an autoregressive data processing algorithm. Its core idea is to make the optimal estimate of the state of the dynamic system in the sense of the least mean square, so the estimation accuracy is relatively high.

[0004] As an algorithm that removes interference data and obtains high-quality estimation results, the adaptive Kalman filter algorithm can estimate the open circuit voltage of the battery pack based on the discharge test data of the battery pack and achieve effective estimation of SOC. Its advantage is that it can obtain the minimum variance estimation of SOC by recursive method based on the collected voltage and current, thereby solving the problems of inaccurate initial SOC estimation and error accumulation. Improving the accuracy of SOC estimation is the key to ensuring the safety and reliability of electric vehicles and the efficient use of energy. Summary of the invention

[0005] The purpose of the present invention is to solve the current situation that the SOC estimation accuracy of lithium-ion batteries is not high and the adaptability is not strong. In order to improve the SOC estimation accuracy of lithium-ion batteries and enhance the adaptability to actual working conditions, the present invention provides a lithium-ion battery adaptive charge estimation method based on an initial value compensation unscented Kalman filter algorithm. The technical solution is as follows:

[0006] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A lithium-ion battery adaptive charge estimation method based on an initial value compensated unscented Kalman filter algorithm comprises the following steps:

[0008] Step 1, setting the equivalent circuit model;

[0009] Step 2, using the augmented vector method to process the initial state value, unknown order and unknown parameters, processing the noise through the iterative method, and updating the adaptive fractional-order unscented Kalman filter algorithm;

[0010] Step 3, adaptively estimating the covariance matrix of the noise according to the proposed unscented Kalman filter algorithm with initial value compensation, and then estimating the SOC value of the lithium-ion battery;

[0011] Step 4, the SOC estimation of the lithium-ion battery is performed for the noise adaptive fractional-order unscented Kalman filter algorithm with initial value compensation, and compared with the adaptive fractional-order unscented Kalman filter algorithm without initial value compensation and with known noise covariance, to obtain the accuracy comparison curve of the lithium-ion battery SOC estimation.

[0012] Beneficial effects of the present invention:

[0013] The present invention adopts the above method, which effectively improves the SOC estimation accuracy of the lithium-ion battery and improves the adaptability of the SOC estimation of the lithium-ion battery under different working conditions, compared with the adaptive fractional-order unscented Kalman filtering algorithm without initial value compensation and when the noise covariance matrix is ​​known. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flow chart of the present invention.

[0015] Figure 2 It is the equivalent circuit model diagram of the present invention.

[0016] Figure 3 This is a schematic diagram of the SOC estimation curve of a lithium-ion battery with a nominal capacity of 2.5 Ah under the conditions of 20° C. and 0.5C in Example 1.

[0017] Figure 4 This is a schematic diagram of the SOC estimation curve of a lithium-ion battery with a nominal capacity of 2.2 Ah under the conditions of 20° C. and 0.5C in Example 1. DETAILED DESCRIPTION

[0018] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments.

[0019] The abbreviations involved in the present invention have the following meanings:

[0020] SOC: state of charge;

[0021] OCV: open circuit voltage;

[0022] CPE: Constant Phase Element;

[0023] GL: Grünwald-Letnikov.

[0024] A lithium-ion battery adaptive charge estimation method based on an initial value compensated unscented Kalman filter algorithm comprises the following steps:

[0025] Step 1, setting the equivalent circuit model;

[0026] Step 1-1) selecting a model containing a CPE element, wherein the model containing a CPE element includes an ideal voltage source, representing an open circuit voltage OCV, and an ohmic internal resistance R, a polarization resistor R1, and a polarization capacitor C1, reflecting a transient response of the battery;

[0027] Step 1-2) According to GL difference, the discretized state equation and output equation of the lithium-ion battery are obtained.

[0028] The expression formula of the system discretization state equation and output equation of the lithium-ion battery in the step 1-2) is:

[0029]

[0030] z(t)=h(x(t),I(t),θ)+v(t),

[0031] In the formula, is the Sigmoid function, w s (t) is the original process noise of the system. According to the equivalent circuit model, the parameters are set as θ3=R, α is the fractional order, η is the Coulomb efficiency, C b is the nominal capacity of the battery, I(t) is the current, u1(t) is the polarization voltage, C1 is the polarization capacitance, z(t) is the system measurement equation, w(t) is the process noise, v(t) is the measurement noise, and the measurement equation h(x(t), I(t), θ) satisfies

[0032]

[0033] Where b0, b1, b2, b3, b4, b5 are real numbers.

[0034] Step 2, using the augmented vector method to process the initial state value, unknown order and unknown parameters, processing the noise through the iterative method, and updating the adaptive fractional-order unscented Kalman filter algorithm;

[0035] Step 2-1) Set the variables related to the initial state value x1(0) ε,τ=1,2,3…are positive parameters;

[0036] Step 2-2) Process the initial state value and unknown order and parameters by augmented vector method to obtain the augmented equation of the system;

[0037] Step 2-3) Take the σ point and process the nonlinear function of the system through untraceable transformation;

[0038] Step 2-4) According to the unscented transformation, the prediction and update equations of the adaptive fractional-order unscented Kalman filter algorithm are obtained.

[0039] The expression formula of the system augmented equation in step 2-2) is:

[0040] η(k)=[x T (k),x0(k),β(k),θ T (k)] T ,

[0041]

[0042] In the formula, θ (k) = [θ1, θ2, θ3, θ4] T , w0(k-1), w β (k-1) and w θ (k-1) are the noises related to the initial value x0(k), fractional order α and parameter θ(k) respectively. also, satisfy Q is the process noise covariance matrix of the system, Q0,Q β ,Q θ are the noise covariance matrices of the initial state value, unknown fractional order and unknown parameters respectively, and T is the sampling period.

[0043] The expression formula of the σ point in the steps 2-3) is:

[0044]

[0045]

[0046] In the formula, is the predicted value of the augmented state, is an estimate of the augmented state based on the unscented transformation, is a matrix The i-th row of is a very small positive number, and κ=3-n.

[0047] The prediction and update equations of the adaptive fractional-order unscented Kalman filter algorithm in step 2-4) are expressed as follows:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] In the formula, They represent the measured prediction and the predicted value of the augmented state of the system respectively, and represents the prediction error matrix. η(k) is the augmented vector with respect to the initial value, unknown order and unknown parameters, z (i) (k|k-1)=h(η (i) (k|k-1),I(k)). is the system measurement noise covariance matrix, the noise covariance matrix Q w (k-1) satisfies F (i) (k-1|k-1)=f(η (i) (k-1|k-1),I(k-1)),f(η (i) (k-1|k-1),I(k-1)) is a nonlinear function of the system based on the unscented transformation.

[0057] g(η(k-1),I(k-1))=[J(k-1),β(k-1),θ(k-1)] T ,

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] Augmentation Vector Γ(·) is the gamma function, weight W i (c) =Wi (m) ,i=1,2,…,2n, is a parameter that contains prior information about the distribution. For the normal distribution, is the best. K(k), and P(k|k) are the Kalman gain matrix, the estimated value of the augmented state, and the estimation error matrix, respectively.

[0064] Step 3, adaptively estimating the covariance matrix of the noise according to the proposed unscented Kalman filter algorithm with initial value compensation, and then estimating the SOC value of the lithium-ion battery;

[0065] Step 3-1) Based on an adaptive fractional-order unscented Kalman filter algorithm with initial value compensation when the noise is known, the covariance matrix of the noise is adaptively estimated to obtain an adaptive noise covariance equation;

[0066] Step 3-2) using the adaptive noise covariance equation, updating the filter equation of the adaptive fractional-order unscented Kalman filter algorithm with initial value compensation when the partial noise covariance matrix is ​​adaptive;

[0067] Step 3-3) Select lithium-ion batteries with different nominal capacities under different working conditions for experiments.

[0068] The expression formula of the adaptive noise covariance in step 3-1) is:

[0069]

[0070]

[0071] In the formula, yes The estimated value of It's Q w The estimated value of (k-1) is and satisfy:

[0072]

[0073] Where P 11 (k|k) and P 11 (kj|kj) is the matrix formed by the first row to the second row and the first column to the second column of P(k|k) and P(kj|kj), respectively. x(k) is the first two rows of η(k). K1(k)∈R 2 , K2(k)∈R, K3(k)∈R, K4(k)∈R 4 ,

[0074]

[0075] ,

[0076]

[0077]

[0078] The expression formula of the partial update equation in step 3-2) is:

[0079]

[0080]

[0081] Step 4, the noise adaptive fractional-order unscented Kalman filter algorithm with initial value compensation is used to estimate the SOC of the lithium-ion battery, and compared with the adaptive fractional-order unscented Kalman filter algorithm without initial value compensation and with known noise covariance, to obtain an accuracy comparison curve of the SOC estimation of the lithium-ion battery.

[0082] Implementation example:

[0083] Under the working conditions of 20℃ and 0.5C, 18650 lithium-ion batteries with nominal capacities of 2.2Ah and 2.5Ah were selected for experiments. First, the thermostat was adjusted to 20℃, and after standing for 30 minutes, the battery was fully charged at a rate of 0.5C and stood for 30 minutes, and then discharged at the same rate. The actual capacities of the batteries were obtained to be 2.0505Ah and 2.3691Ah respectively. The open circuit voltage experiment was continued to obtain the OCV-SOC function. The SOC was set to 2%, 5%, 10%, 15%, ..., 95%, 98% for testing, and the interval time was 3 minutes. By fitting the data using the least square method, the fitting function coefficients of the 2.2Ah battery are b0=3.0225, b1=1.9419, b2=-1.2786, b3=0.4292, b4=-0.0045, b5=-0.1523; the fitting function coefficients of the 2.5Ah battery are b0=4.2004, b1=-1.6281, b2=2.3015, b3=-0.7413, b4=0.0061, b5=0.2676. Finally, fully charge the battery again, let it stand for 30 minutes, and then discharge it at a constant current rate of 0.5C to 80% of the test capacity, and let it stand for 30 minutes. Then continue to discharge at 10% of the test capacity until 20% of the capacity remains, and let it stand for 10 minutes.

[0084] The experimental parameters are set as follows: sampling period T = 4s, Q0 = 0.00003, Q β =0.002, Q θ=diag(0.0001,0.001,0.00003,1 / 7920000),ε=1.2,τ=0.1. Define when k≤T m hour, When k>T m hour, and As shown in the above formula, the parameter ε is set R =0.002,ε Q =0.0005. In order to prevent divergence in the early parameter identification stage, T is set in the noise adaptation stage. m =1800. In addition, in order to evaluate the algorithm, the error index is defined as

[0085]

[0086] Where M+1 is the number of sampled data and r(k) is the reference value.

[0087] The noise adaptive fractional-order unscented Kalman filter algorithm with initial value compensation is used to estimate the SOC of lithium-ion batteries, and then compared with the adaptive fractional-order unscented Kalman filter algorithm without initial value compensation and with known noise covariance. Based on the error index, the error data obtained by the two algorithms for SOC estimation of 2.2Ah lithium-ion batteries are 0.0654 and 0.0807 respectively, and the error data obtained for SOC estimation of 2.5Ah lithium-ion batteries are 0.0523 and 0.1155 respectively, and the accuracy comparison curve can be obtained. The results of 20℃, 0.5C, and 2.5Ah are as follows: Figure 3 As shown, the results at 20℃, 0.5C, 2.2Ah are as follows Figure 4 As shown, the noise adaptive fractional-order unscented Kalman filter algorithm based on initial value compensation has better estimation accuracy for the SOC of lithium-ion batteries than the estimation effect when there is no initial value compensation and the noise covariance is known.

Claims

1. A lithium-ion battery adaptive charge estimation method based on an initial value compensated unscented Kalman filter algorithm, characterized in that: The steps include: Step 1, setting the equivalent circuit model; Step 2, using the augmented vector method to process the initial state value, unknown order and unknown parameters, processing the noise through the iterative method, and updating the adaptive fractional-order unscented Kalman filter algorithm; Step 2-1) Set the variables related to the initial state value x1(0) ε,τ=1,2,3…are positive parameters; Step 2-2) Process the initial state value and unknown order and parameters by augmented vector method to obtain the augmented equation of the system; The expression formula of the system augmented equation in step 2-2) is: η(k)=[x T (k),x0(k),β(k),θ T (k)] T , In the formula, θ(k)=[θ1, θ2, θ3, θ4] T , w0(k-1), w β (k-1) and w θ (k-1) are the noises about the initial value x0(k), fractional order α and parameter θ(k); in addition, satisfy Q is the process noise covariance matrix of the system, Q0,Q β ,Q θ are the noise covariance matrices of the initial state value, unknown fractional order and unknown parameters, respectively, and T is the sampling period; Step 2-3) Take the σ point and process the nonlinear function of the system through untraceable transformation; The expression formula of σ point is: In the formula, is the predicted value of the augmented state, is an estimate of the augmented state based on the unscented transformation, is a matrix The i-th row of is a very small positive number, and κ=3-n; Step 2-4) According to the unscented transformation, the prediction and update equations of the adaptive fractional-order unscented Kalman filter algorithm are obtained; the expression formula of the prediction and update equations of the adaptive fractional-order unscented Kalman filter algorithm is: In the formula, They represent the measured prediction and the predicted value of the augmented state of the system respectively, and represents the prediction error matrix; η(k) is the augmented vector with respect to the initial value, unknown order and unknown parameters, z (i) (k|k-1)=h(η (i) (k|k-1),I(k)); is the system measurement noise covariance matrix, the noise covariance matrix Q w (k-1) satisfies F (i) (k-1|k-1)=f(η (i) (k-1|k-1),I(k-1)),f(η (i) (k-1|k-1),I(k-1)) is a nonlinear function of the system based on the unscented transformation. g(η(k-1),I(k-1))=[J(k-1),β(k-1),θ(k-1)] T , Augmentation Vector Γ(·) is the gamma function, weight W i (c) =W i (m) ,i=1,2,…,2n, is a parameter that contains prior information about the distribution. For the normal distribution, is optimal; K(k), and P(k|k) are the Kalman gain matrix, the estimated value of the augmented state, and the estimation error matrix, respectively; Step 3, adaptively estimating the covariance matrix of the noise according to the proposed unscented Kalman filter algorithm with initial value compensation, and then estimating the SOC value of the lithium-ion battery; Step 4, the SOC estimation of the lithium-ion battery is performed for the noise adaptive fractional-order unscented Kalman filter algorithm with initial value compensation, and compared with the adaptive fractional-order unscented Kalman filter algorithm without initial value compensation and with known noise covariance, to obtain the accuracy comparison curve of the lithium-ion battery SOC estimation.

2. The method for adaptive charge estimation of lithium-ion batteries based on initial value compensation unscented Kalman filter algorithm according to claim 1, characterized in that: In the step 1, the specific method is: Step 1-1) selecting a model containing a CPE element, wherein the model containing a CPE element includes an ideal voltage source, representing an open circuit voltage OCV, and an ohmic internal resistance R, a polarization resistor R1, and a polarization capacitor C1, reflecting a transient response of the battery; Step 1-2) According to GL difference, the discretized state equation and output equation of the lithium-ion battery are obtained.

3. The method for adaptive charge estimation of lithium-ion batteries based on initial value compensation unscented Kalman filter algorithm according to claim 2, characterized in that: The expression formula of the system discretization state equation and output equation of the lithium-ion battery in the step 1-2) is: z(t)=h(x(t),I(t),θ)+v(t), In the formula, is the Sigmoid function, w s (t) is the original process noise of the system. According to the equivalent circuit model, the parameters are set as θ3=R, α is the fractional order, η is the Coulomb efficiency, C b is the nominal capacity of the battery, I(t) is the current, u1(t) is the polarization voltage, C1 is the polarization capacitance, z(t) is the system measurement equation, w(t) is the process noise, v(t) is the measurement noise, and the measurement equation h(x(t), I(t), θ) satisfies Where b0, b1, b2, b3, b4, b5 are real numbers.

4. The method for adaptive charge estimation of lithium-ion batteries based on initial value compensation unscented Kalman filter algorithm according to claim 1, characterized in that: In the step 3, the specific method is: Step 3-1) Based on an adaptive fractional-order unscented Kalman filter algorithm with initial value compensation when the noise is known, the covariance matrix of the noise is adaptively estimated to obtain an adaptive noise covariance equation; Step 3-2) using the adaptive noise covariance equation, updating the filter equation of the adaptive fractional-order unscented Kalman filter algorithm with initial value compensation when the partial noise covariance matrix is ​​adaptive; Step 3-3) Select lithium-ion batteries with different nominal capacities under different working conditions for experiments.

5. The method for adaptive charge estimation of lithium-ion batteries based on initial value compensation unscented Kalman filter algorithm according to claim 4, characterized in that: The expression formula of the step 3-1) adaptive noise covariance equation is: In the formula, yes The estimated value of It's Q w The estimated value of (k-1) is and satisfy: Where P 11 (k|k) and P 11 (kj|kj) is the matrix formed by the first row to the second row and the first column to the second column of P(k|k) and P(kj|kj), respectively. x(k) is the first two rows of η(k). K1(k)∈R 2 , K2(k)∈R, K3(k)∈R, K4(k)∈R 4 , ， 6. The method for adaptive charge estimation of lithium-ion batteries based on initial value compensation unscented Kalman filter algorithm according to claim 4, characterized in that: The expression formula of the partial update equation of step 3-2) is:

Images