A Fusion Method for Estimating the State of Charge of a Lithium-Ion Battery

Abstract

The present invention discloses a fusion method for estimating the state of charge of a lithium-ion battery, comprising the following steps: establishing a second-order RC equivalent circuit model of the lithium-ion battery; obtaining the state space equation of the battery model; using an H observer with a fused sliding mode observer to estimate the battery SOC; and based on the fused estimation result, using the AdaDelta gradient descent algorithm to fine-tune the sliding mode observer matrix gain L along the gradient descent direction. ∞ By fusing a sliding mode observer in the H observer and using the AdaDelta algorithm to fine-tune the sliding mode observer gain L at all times, the present invention can improve the robustness of the algorithm in the face of initial state of charge errors, non-Gaussian distributed measurement noise, and model parameter perturbations. ∞ ​

Description

Technical Field

[0001] The present invention belongs to the technical field of lithium-ion batteries and is applied to a lithium-ion battery management system. Specifically, it relates to a modeling method for lithium iron phosphate batteries using a new OCV-SOC curve fitting method. Background Art

[0002] The state of charge (SOC) of a lithium-ion battery is one of the important bases for judging the battery state. Accurate estimation of SOC can provide effective help for setting the equalization strategy of the battery management system, which is beneficial to improving the overall service life and safety of the battery pack. However, the electrochemical reactions inside the lithium-ion battery are complex and changeable, and its SOC cannot be directly measured. It can only be estimated through certain methods based on relevant physical quantities such as voltage and current.

[0003] The extended Kalman filter is recognized in battery SOC estimation due to its high accuracy and low complexity. However, the initial state of battery operation is not fixed. When the initial SOC of the battery differs greatly from the self-defined initial state of the algorithm, the convergence speed of the algorithm is not ideal. When artificially accelerating the convergence speed by adjusting parameters, it will cause algorithm chatter. In addition, the extended Kalman filter algorithm assumes an ideal state where the process noise and observation noise are Gaussian white noise during application. However, in actual working conditions, the noise situation is complex and changeable, which has a certain impact on the algorithm accuracy. The H∞ filter makes no assumptions about the noise and has high robustness to non-Gaussian noise. The sliding mode observer has a certain ability to resist model parameter perturbations and can still estimate the SOC of the battery relatively accurately when there are deviations in the model parameters. Summary of the Invention

[0004] In view of the problems existing in the above-mentioned prior art, the present invention provides a fusion method for estimating the state of charge of a lithium-ion battery. This method improves the H∞ algorithm by integrating a sliding mode observer to enhance the robustness of the H∞ observer in the process of estimating the SOC of a lithium-ion battery.

[0005] To achieve the above object, the present invention provides the following solution: The present invention provides a fusion method for the robustness of estimating the state of charge of a lithium-ion battery, including the following steps:

[0006] Step 1: Establish a second-order RC equivalent circuit model of the lithium-ion battery: Collect open-circuit voltage data and state of charge data, and based on the equivalent circuit model, obtain battery model parameters in different states;

[0007] Step 2: Obtain the state space equation of the battery model: Based on Kirchhoff's law, through the equivalent circuit model and the battery model parameters, obtain the model state space equation;

[0008] Step 3, Fusion Estimation: Use the H∞ observer of the fusion sliding mode observer to estimate state variables such as the state of charge of the battery;

[0009] Step 4, Obtain the Gain: Based on the fusion estimation result, use the AdaDelta gradient descent algorithm to fine-tune the sliding mode observer matrix gain L along the gradient descent direction, and use this gain in the fusion estimation of the next cycle;

[0010] Preferably, in the step 3, a sliding mode observer is used to participate in the posterior estimation of the H∞ filter to correct the optimal state variable estimation value Update.

[0011] Preferably, the corrected state variable estimation value The update equation is:

[0012]

[0013] Where, H k is the H∞ algorithm gain at time k, and L k is the sliding mode observer gain fine-tuned by the gradient descent algorithm.

[0014] Preferably, the formula for fine-tuning L by the gradient descent algorithm in the step 4 is:

[0015] s k = ρs k-1 +(1 - ρ)*g k

[0016]

[0017] L k = L k-1 - m k

[0018] Δx k = ρΔx k-1 +(1 - ρ)*m k *m k

[0019] Where, g k is the partial derivative value of the error with respect to L at time k; ρ is a hyperparameter, and its value range is generally 0.9 to 0.99; ε is a relatively small parameter.

[0020] The present invention discloses the following technical effects:

[0021] Compared with the prior art, the present invention provides a fusion method for estimating the state of charge of a lithium-ion battery. This method fuses the sliding mode observer control in the H∞ algorithm and fine-tunes the sliding mode observer gain through the gradient descent algorithm, improving the convergence speed of the algorithm in the presence of SOC initial value errors and enhancing the algorithm's ability to suppress complex noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0023] Figure 1 It is a schematic flowchart of a fusion method for estimating the state of charge of a lithium-ion battery disclosed in the present invention.

[0024] Figure 2 It is a second-order RC equivalent circuit model of a lithium-ion battery.

[0025] Figure 3 It is the current of the United States Federal Urban Driving Schedule at 25°C.

[0026] Figure 4-1 、 4-2 They are respectively the SOC estimation results and estimation error diagrams of two algorithms (H∞ algorithm, sliding mode observer algorithm SMO, and the H∞ algorithm with a combined sliding mode observer proposed in the present invention) when the initial SOC is accurate and no noise is added to the voltage signal under the United States Federal Urban Driving Schedule at 25°C.

[0027] Figure 5-1 、 5-2 They are respectively the SOC estimation results and estimation error diagrams of two algorithms (H∞ algorithm, sliding mode observer algorithm SMO, and the H∞ algorithm with a combined sliding mode observer proposed in the present invention) when the initial SOC is inaccurate and no noise is added to the voltage signal under the United States Federal Urban Driving Schedule at 25°C.

[0028] Figure 6-1 、 6-2 They are respectively the SOC estimation results and estimation error diagrams of two algorithms (H∞ algorithm, sliding mode observer algorithm SMO, and the H∞ algorithm with a combined sliding mode observer proposed in the present invention) when the initial SOC is inaccurate and non-Gaussian distributed noise is added to the voltage signal under the United States Federal Urban Driving Schedule at 25°C. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood, however, that the present invention can be implemented in various forms, and some exemplary and non-limiting embodiments presented in the accompanying drawings and described below are not intended to limit the present invention to the specific embodiments described.

[0030] See Figure 1 , Figure 1 A fusion method for estimating the state of charge of a lithium-ion battery according to an embodiment of the present invention includes the following steps:

[0031] Step 1: Establish a second-order RC equivalent circuit model of the lithium-ion battery: Collect open-circuit voltage data and state-of-charge data, and based on the equivalent circuit model, obtain battery model parameters under different states.

[0032] The second-order RC equivalent circuit model of the lithium-ion battery in Step 1 is as Figure 2 shown, which is composed of a controlled voltage source, two RC links, and an ohmic internal resistance R0 connected in series. The controlled voltage source represents the open-circuit voltage of the battery, and the RC links (R1, C1, R2, C2) are the polarization internal resistance and polarization content, used to simulate the electrochemical polarization and concentration polarization of the battery, and the battery ohmic internal resistance is used to simulate the ohmic polarization process of the battery.

[0033] Step 1 is specifically implemented according to the following steps:

[0034] Step 1.1: The static method discharges the fully charged battery intermittently at a constant rate and allows it to rest fully (at intervals of 10% SOC) to obtain the open-circuit voltage U oc and SOC data;

[0035] Step 1.2: Use the least squares method to fit the relationship between the open-circuit voltage U oc and SOC, and use a 9th-order polynomial U oc = a1*SOC 9 + a2*SOC 8 + a3*SOC 7 + a4*SOC 6 + a5*SOC 5 + a6*SOC 4 + a7*SOC 3 + a8*SOC 2 + a9*SOC + a 10 to perform the fitting and obtain the functional relationship between the open-circuit voltage U oc and SOC;

[0036] Step 1.3: Calculate the ohmic internal resistance by dividing the sudden change voltage value at the moment of the battery pulse discharge by the sudden change current value;

[0037] Step 1.4: Through the formula Obtain the electrochemical polarization time constant τ1 and the concentration polarization time constant τ2; through the formula Obtain the electrochemical polarization internal resistance R1 and the concentration polarization resistance R2. The ratio of the electrochemical polarization time constant τ1 to the electrochemical polarization internal resistance R1 is the first polarization capacitance C1, and the ratio of the concentration polarization time constant τ2 to the concentration polarization internal resistance R2 is the second polarization capacitance C2; where U1 is the terminal voltage of the first RC link, U2 is the terminal voltage of the second RC link, U oc Is the open-circuit voltage of the battery, I is the working current of the battery, and U is the terminal voltage of the battery;

[0038] Step 1.5: Execute Step 1.3 to Step 1.4 according to different states of charge to obtain battery model parameters under different states of charge.

[0039] Step 2: Obtain the state space equation of the battery model: Based on Kirchhoff's law, through the equivalent circuit model and the battery model parameters, obtain the model state space equation.

[0040] The model state space equation established in Step 2 includes a state equation and an observation equation, as follows:

[0041]

[0042] U k = U oc,k - U 1,k - U 2,k - R0I k + v k

[0043] where T is the sampling period, w k is the process noise, v k is the measurement noise, C N is the rated capacity of the battery, soc represents the state of charge of the battery, and k represents the number of iterative calculation steps at the current moment.

[0044] The state space equation can be simplified to:

[0045] x k = Ax k-1 + BI k-1 + w k-1

[0046] U k = U oc,k - U 1,k - U 2,k - R0I k + v k

[0047] where,

[0048] Step 3: Estimate state variables such as the state of charge of the battery using an H∞ observer with a fusion sliding mode observer.

[0049] Step 3 is specifically implemented according to the following steps:

[0050] Step 3.1: Perform a first-order Taylor expansion of the model observation equation near the estimated value of the state variable, and linearize the system by using first-order approximation and ignoring the remaining high-order terms:

[0051] U k = Cx k - I k R0 + v k + m

[0052]

[0053] where m is the error generated by the first-order Taylor expansion and can be ignored; C is the output matrix of the state variable;

[0054] Step 3.2: Set the initial value of the state variable x0, the initial value of the state error covariance P0, and the initial values of the process noise covariance Q and the measurement noise covariance R;

[0055] Step 3.3: According to the SOC of the battery at this time, combine the battery model parameter table obtained in Step 1 for different SOCs, and look up the battery model parameters in the table. For the SOC values that are not within the corresponding relationship, use the rounding method to obtain the parameter values corresponding to the adjacent SOCs for substitution;

[0056] Step 3.4: Update the measurement matrix: is the estimated terminal voltage value at time k - 1, U oc,k-1 is the open-circuit voltage value at time k - 1, U 1,k-1 is the terminal voltage value of the first RC link at time k - 1, U 2,k-1 is the terminal voltage value of the second RC link at time k - 1;

[0057] Step 3.5: H∞ gain: H k = P k-1 (I - θSP k-1 + C T R -1 CP k-1 ) -1 C T R -1 , H k is the H∞ filter gain at time k, δ is the filter parameter, and generally taken as 0.1;

[0058] One-step prediction of the state variable: Among them, is the optimal estimated value of the state variable at time k of the state variable, I k-1 is the working current at time k-1, is the optimal estimated value of the state variable at time k-1;

[0059] Step 3.6, Prediction error covariance matrix: P k = AP k-1 (I - θSP k-1 + C T R -1 CP k-1 )A T + Q, P k-1 is the error covariance at time k-1, A T is the transpose of matrix A, P k is the error covariance at time k;

[0060] Step 4, Obtain the gain: Based on the prior estimation result, the formula for fine-tuning the gain L of the sliding mode observer matrix using the AdaDelta algorithm along the gradient descent direction is:

[0061] s k = ρs k-1 + (1 - ρ)*g k

[0062]

[0063] L k = L k-1 - m k

[0064] Δx k = ρΔx k-1 + (1 - ρ)*m k * m k

[0065] Among them, g k is the partial derivative value of the error matrix at time k with respect to L; ρ is a hyperparameter, and its value range is generally 0.9 to 0.99; ε is a relatively small parameter.

[0066] Step 5, Fusion estimation: Use the H∞ observer of the fusion sliding mode observer to estimate the state of charge of the battery.

[0067] Step 5 is specifically implemented according to the following steps:

[0068] Step 5.1, Execute Step 3.1.

[0069] Step 5.2, Set the initial value x0 of the state variable, the initial value P0 of the state error covariance, and the initial values of the process noise covariance Q and the measurement noise covariance R.

[0070] Step 5.3: Calculate the battery model parameters according to the state of charge (SOC) of the current battery.

[0071] Step 5.4: Execute Step 3.4.

[0072] Step 5.5: Execute Step 3.5.

[0073] Step 5.6: Execute Step 3.6.

[0074] Step 5.7: Execute Step 4.

[0075] Step 5.8: Loop through Steps 5.3 to 5.7 to estimate the state of charge of the lithium-ion battery in real time.

[0076] To verify the effect of estimating the SOC of the present invention, a ternary lithium-ion battery NCR18650B with a rated capacity of 3.4 Ah produced by Panasonic Corporation was used as the research object for a simulated working condition experiment. The simulated working condition was the Federal Urban Driving Schedule (FUDS) at 25°C, and the charge and discharge currents were as Figure 3 shown. From Figure 4-1 , 4-2 , 5-1, and 5-2, it can be seen that when there is no noise interference, the estimation accuracy and convergence speed of the H∞ algorithm of the fusion sliding mode observer are better than those of the sliding mode observer and the H∞ observer. From Figure 6-1 , 6-2 , it can be seen that after adding mixed Gaussian distribution noise to the voltage signal, the estimation accuracy and convergence speed of the H∞ observer of the fusion sliding mode observer are still better than those of the two basic algorithms. Generally speaking, the H∞ observer of the fusion sliding mode observer has good robustness in the face of non-Gaussian distribution measurement noise and SOC initial value errors.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A fusion method for estimating the state of charge of a lithium-ion battery, characterized in that, The method mainly includes the following steps: Step 1: Establish a second-order RC equivalent circuit model of the lithium-ion battery: Collect open-circuit voltage and current data under the parameter identification condition, and identify the battery model parameters under different state of charge based on the equivalent circuit model; Step 2: Obtain the state-space equation of the battery model: Based on Kirchhoff's law, discretize the s-domain model of the equivalent circuit model to obtain the state-space equation of the battery model; Step 3: Fusion estimation: Use the H∞ observer of the fusion sliding mode observer to estimate state variables such as the state of charge of the battery; Step 4: Obtain the gain: Based on the fusion estimation result, use the AdaDelta gradient descent algorithm to fine-tune the sliding mode observer matrix gain L along the gradient descent direction, and use this gain in the fusion estimation of the next cycle; The formula for fine-tuning the sliding mode observer matrix gain L along the gradient descent direction of the error matrix using the AdaDelta algorithm is: s k = ρs k-1 +(1 - ρ)*g k L k = L k-1 - m k △x k = ρ△x k-1 +(1 - ρ)*m k *m k where g k is the partial derivative of the error at time k with respect to L; ρ is a hyperparameter with a value range of 0.9 to 0.99; ε is a small parameter.

2. The fusion method for estimating the state of charge of a lithium-ion battery according to claim 1, characterized in that In step 3, the H∞ observer of the fusion sliding mode observer is used to estimate the state of charge of the battery.

3. A fusion method for estimating the state of charge of a lithium-ion battery according to claim 2, characterized in that, In step 3, a sliding mode observer is used to participate in the posterior estimation of the H∞ observer to correct the estimated value of the optimal state variable Update.

4. A fusion method for estimating the state of charge of a lithium-ion battery according to claim 3, characterized in that The estimated value of the optimal state variable after correction The update equation is as follows: Among them, H k is the H∞ observer gain at time k, and L k is the sliding mode observer gain fine-tuned by the gradient descent algorithm, is the estimated terminal voltage value at time k-1.

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