Lithium battery fractional order model parameter identification method

Abstract

The invention discloses a lithium battery fractional order model parameter identification method, and belongs to the technical field of battery modeling and parameter identification. According to the method, the zero input response characteristic of a fractional order circuit in the standing stage is fully utilized, an analytic solution of the fractional order circuit is deduced based on Caputo fractional order differential definition, a key attenuation section in a voltage response curve is extracted, an identification target function in a closed form is constructed, and the identification accuracy of the fractional order circuit is improved. And efficient and accurate estimation of parameters such as fractional order, time constant and resistance in the model is realized. Compared with a traditional parameter identification technology depending on metaheuristic methods such as particle swarm optimization (PSO) and a genetic algorithm (GA), the method has the advantages that the calculation complexity is greatly reduced, the operation time is greatly shortened, and the stability and repeatability of the identification process are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of battery modeling and parameter identification, and particularly relates to a parameter identification method for a lithium battery fractional-order model. Background Art

[0002] With the rapid development of electric vehicles and energy storage systems, lithium batteries have become a key energy source due to their high energy density, long cycle life, and environmental friendliness. As the core monitoring and control system for lithium batteries, the performance of the battery management system (BMS) depends on a high-precision battery model. The traditional integer-order equivalent circuit model (IOM) simulates the polarization behavior of the battery through multiple RC branches. It has the characteristics of simple structure and efficient computation and is widely used in BMS. However, the electrochemical processes within lithium batteries have complex characteristics such as multi-scale, nonlinear, and history-dependent. As a result, the IOM modeling accuracy is insufficient under dynamic conditions, making it difficult to accurately describe the battery's medium-frequency impedance response.

[0003] In recent years, the Fractional-Order Model (FOM), by introducing a constant phase element (CPE) to replace an ideal capacitor, has become an important development direction in the field of battery modeling, enabling a more reasonable description of the dynamic behavior of batteries, especially the impedance characteristics in the mid-frequency region. However, parameter identification of the FOM faces many challenges:

[0004] Many parameters and strong coupling: FOM contains multiple parameters such as fractional order, time constant, resistance, etc., which are coupled with each other, increasing the difficulty of identification.

[0005] High computational complexity: Existing methods (such as particle swarm optimization (PSO) and genetic algorithms (GA)) rely on numerical optimization and global search, which takes a long time to calculate and is difficult to meet the needs of online applications.

[0006] Insufficient stability and repeatability: Traditional methods are prone to falling into local optimal solutions, the identification results are greatly affected by the initial values, and the stability is poor.

[0007] To address the above issues, an efficient, stable and physically clear parameter identification method is urgently needed to improve the practicality of FOM in BMS. Summary of the Invention

[0008] To solve the above technical problems, the present invention provides a parameter identification method for a lithium battery fractional-order model. This method does not rely on complex numerical optimization, but directly constructs an error function based on the analytical expression of the battery's zero-input response, thereby achieving efficient and robust fitting of fractional-order parameters.

[0009] To achieve the above object, the present invention adopts the following technical solutions:

[0010] A method for identifying parameters of a lithium battery fractional-order model, the method comprising:

[0011] Step 1: Based on the Caputo fractional differential definition, an n-order fractional equivalent circuit model for lithium batteries is constructed;

[0012] Step 2: During the battery rest phase, obtain the zero-input response voltage curve and extract the voltage data of the key attenuation section as the experimental data required for parameter identification;

[0013] Step 3: Based on the analytical solution of the fractional-order equivalent circuit model, the Mittag-Leffler function is used to express the zero-input response, and an objective function is constructed to describe the error between the experimental data and the predicted value of the fractional-order equivalent circuit model;

[0014] Step 4: Use the trust region reflection method to perform nonlinear least squares fitting on the objective function to identify the parameters of the fractional order model.

[0015] Furthermore, in step 1, the n-order fractional-order equivalent circuit model includes n series-connected fractional-order branches and a constant resistor connected in series with the n series-connected fractional-order branches. , each fractional-order branch is connected by a resistor R i It is connected in parallel with the constant phase element CPE.

[0016] Furthermore, the impedance expression of the constant phase element is:

[0017] ,

[0018] Where s represents the complex variable in the Laplace transform domain, represents the order of the i-th constant phase element, represents the constant term of the i-th constant phase element, i represents the i-th constant phase element;

[0019] Battery terminal voltage Expressed as:

[0020] ,

[0021] Where, It indicates the open circuit voltage of the battery after a long period of rest, and SOC indicates the state of charge. represents the voltage of the i-th constant phase element.

[0022] Furthermore, in step 2, the key attenuation section is the voltage attenuation section in the static phase after the pulse current ends.

[0023] Furthermore, in step 3, based on the fractional-order differential equation defined by Caputo, the zero-input response analytical solution of the fractional-order model is derived:

[0024] ,

[0025] Where, represents the fractional differential of the i-th constant phase element, represents the voltage value of the i-th fractional-order branch at time t;

[0026] The time domain analytical solution is:

[0027] ,

[0028] represents the power of time, which is a characteristic of fractional-order systems. represents the initial voltage, that is, the voltage on the i-th fractional-order branch at t=0, represents the Mittag-Leffler function;

[0029] By superimposing the analytical solutions of n parallel fractional-order branches, the zero-input response voltage expression of the complete system is obtained:

[0030] ,

[0031] Where, represents the time constant, defined as =R i , used to control the response speed of the i-th fractional-order branch, I pulse Indicates pulse current.

[0032] Furthermore, the initial guess values ​​and constraint boundaries of the parameters are set, and the parameter vector to be identified is defined as:

[0033] .

[0034] Furthermore, in step 3, the objective function is a mean square error function between the experimental data and the model prediction value.

[0035] Furthermore, the method is applicable to any type of lithium-ion batteries.

[0036] In a second aspect, the present invention provides an electronic device comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for identifying parameters of a lithium battery fractional-order model.

[0037] In a third aspect, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the aforementioned method for identifying parameters of a fractional-order lithium battery model.

[0038] The beneficial effects of the present invention are:

[0039] Compared with traditional parameter identification techniques that rely on meta-heuristic methods such as particle swarm optimization (PSO) and genetic algorithm (GA), the present invention constructs the objective function based on the analytical solution of the fractional-order model and combines it with efficient nonlinear least squares optimization (such as the trust region reflective method), which greatly reduces the computational complexity and running time, and significantly improves the stability and repeatability of the identification process.

[0040] The present invention utilizes Caputo fractional-order differential theory and the analytical solution of the Mittag-Leffler function to ensure that the model is highly consistent with the actual dynamic characteristics of the battery, while retaining the physical interpretability of parameters (such as polarization resistance and time constant), facilitating subsequent SOC estimation and health status analysis. It has a good iterative structure and physical interpretability, and is particularly suitable for embedded battery management systems (BMS) with high requirements for model accuracy and computational efficiency.

[0041] This method only requires extracting the zero-input response decay segment after the pulse current ends, completing parameter identification through short-term excitation, reducing experimental difficulty and data acquisition costs. By using constrained optimization boundaries and trust region reflection methods, the parameters are ensured to converge within a reasonable range, improving the repeatability and reliability of the identification results. The method is applicable to different temperatures, SOCs, and battery aging states.

[0042] In addition, the present invention does not rely on a specific battery type or positive electrode material and can be adapted to a variety of lithium-ion batteries (such as lithium iron phosphate, ternary lithium, etc.). The proposed analytical identification framework has good versatility and can be extended to modeling and online monitoring tasks of various battery types and complex working conditions. It has broad engineering application value and industrialization prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the second-order fractional equivalent circuit model;

[0044] Figure 2 Schematic diagram of the HPPC test current-voltage curve and zero-input response section. DETAILED DESCRIPTION

[0045] The present invention will be further described below with reference to the accompanying drawings and examples.

[0046] The present invention provides a method for identifying parameters of a lithium battery fractional-order model, comprising the following steps:

[0047] Step 1: Based on the Caputo fractional differential definition, construct an n-order fractional equivalent circuit model for lithium batteries (such as Figure 1 An n-order fractional-order equivalent circuit model (FOM) is given; the model contains n series-connected fractional-order branches and a constant resistor in series with the n series-connected fractional-order branches. , all fractional-order branches are connected by resistors R i It is connected in parallel with a constant phase element (CPE), where the impedance expression of the constant phase element is:

[0048] ,

[0049] Where s represents the complex variable in the Laplace transform domain, represents the order of the i-th constant phase element, represents the constant term of the i-th constant phase element, i represents the i-th constant phase element;

[0050] Battery terminal voltage It can be expressed by the following equation:

[0051] ,

[0052] Where, It indicates the open circuit voltage of the battery after a long period of rest, and SOC indicates the state of charge. Represents the voltage of the i-th constant phase element; open circuit voltage It can be obtained by fitting a fifth-order polynomial:

[0053] .

[0054] At multiple different SOC points, a constant pulse current I with an amplitude of ±5 A and a duration of not less than 10 s is applied. pulse Then let it stand for 60 seconds and record the corresponding battery voltage response curve U t (t).

[0055] Step 2: During the battery rest phase, obtain the zero input response voltage curve and extract the voltage data of the key attenuation section as the experimental data required for parameter identification; intercept the voltage attenuation section of the rest phase after the pulse current ends from the battery voltage response curve, that is, the zero input response phase, i.e. Figure 2 The T4 to T5 stage is used as experimental data for parameter identification.

[0056] Step 3: Based on the analytical solution of the fractional-order equivalent circuit model, the Mittag-Leffler function is used to express the zero-input response, and an objective function is constructed to describe the error between the experimental data and the predicted value of the fractional-order equivalent circuit model;

[0057] Based on the fractional-order differential equation defined by Caputo, the analytical solution of the zero-input response of the fractional-order model is derived:

[0058] ,

[0059] Where, represents the fractional differential of the i-th constant phase element, It represents the voltage value of the i-th fractional-order branch at time t, representing the attenuation process of the capacitor voltage on this branch.

[0060] Transformed into the time domain analytical solution:

[0061] ,

[0062] represents the power of time, which is a characteristic of fractional-order systems. represents the initial voltage, that is, the voltage on the i-th fractional-order branch at t=0, which is often used to represent the initial state in zero-input response; it is determined by the pulse current as: ;

[0063] represents the Mittag-Leffler function, which is a special function commonly used in the analytical solution of fractional-order systems and is defined as:

[0064] ,

[0065] x represents the independent variable of the Mittag–Leffler function, represents the gamma function;

[0066] Furthermore, the Mittag–Leffler function is calculated using the following truncation strategy:

[0067] .

[0068] By superimposing the analytical solutions of n parallel fractional-order branches, the zero-input response voltage expression of the complete system is obtained:

[0069] ,

[0070] Where, represents the time constant, defined as =R i , in seconds (s), is used to control the response speed of the i-th fractional-order branch.

[0071] Set the initial guess value of the parameter and the constraint boundary, and define the parameter vector to be identified as:

[0072] ,

[0073] Performing HPPC experiment at a certain SOC point, we get Figure 2 Data snippet of zero input response The specific operation is as follows: To perform parameter identification, the voltage response segment for identification must first be constructed. In practice, a constant current excitation experiment can be used to excite the battery at multiple SOC points, collecting voltage response data. The natural decay segment after the excitation is removed is then extracted as the identification input, as shown in Figure 2.

[0074] The extracted natural decay segment corresponds to the zero-input response of the system, and its theoretical expression is given by the analytical solution above. The voltage response data at multiple moments and the analytical model expression form a nonlinear least squares fitting problem. The optimization objective function can be written as follows to construct the following objective function to minimize the mean square error between the experimental data and the model prediction value:

[0075] ,

[0076] Where k represents the kth sampling point in the time series, and N represents the total number of voltage sampling points used for fitting.

[0077] Step 4: Use the trust region reflection method to perform nonlinear least squares fitting on the objective function to identify the parameters of the fractional order model.

[0078] The Trust-Region Reflective Method is used to solve the nonlinear least squares problem and obtain the optimal identification parameters. The parameters identified by this method can be applied to online BMS scenarios such as battery SOC estimation, voltage prediction, internal resistance monitoring, and health status assessment.

[0079] Furthermore, the method is applicable to any type of lithium-ion battery and is not limited to a specific cathode material system.

[0080] In a second aspect, the present invention provides an electronic device comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method for identifying parameters of a lithium battery fractional-order model.

[0081] In a third aspect, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the aforementioned method for identifying parameters of a fractional-order lithium battery model.

[0082] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A lithium battery fractional order model parameter identification method, characterized in that: The method comprises: Step 1: Based on the Caputo fractional differential definition, an n-order fractional equivalent circuit model for lithium batteries is constructed; Step 2: During the battery rest phase, obtain the zero-input response voltage curve and extract the voltage data of the key attenuation section as the experimental data required for parameter identification; Step 3: Based on the analytical solution of the fractional-order equivalent circuit model, the Mittag-Leffler function is used to express the zero-input response, and an objective function is constructed to describe the error between the experimental data and the predicted value of the fractional-order equivalent circuit model; Step 4: Use the trust region reflection method to perform nonlinear least squares fitting on the objective function to identify the parameters of the fractional order model.

2. The method for identifying parameters of a lithium battery fractional-order model according to claim 1, wherein: In step 1, the n-order fractional-order equivalent circuit model includes n series-connected fractional-order branches and a constant resistor connected in series with the n series-connected fractional-order branches. , each fractional-order branch is connected by a resistor R i It is connected in parallel with the constant phase element CPE.

3. The method for identifying parameters of a lithium battery fractional-order model according to claim 2, wherein: The impedance expression of the constant phase element is: ， Where s represents the complex variable in the Laplace transform domain, represents the order of the i-th constant phase element, represents the constant term of the i-th constant phase element, i represents the i-th constant phase element; Battery terminal voltage Expressed as: ， Where, It indicates the open circuit voltage of the battery after a long period of rest, and SOC indicates the state of charge. represents the voltage of the i-th constant phase element.

4. The method for identifying parameters of a lithium battery fractional-order model according to claim 1, wherein: In step 2, the key attenuation section is the voltage attenuation section in the static phase after the pulse current ends.

5. The method for identifying parameters of a lithium battery fractional-order model according to claim 3, wherein: In step 3, based on the fractional-order differential equation defined by Caputo, the zero-input response analytical solution of the fractional-order model is derived: ， Where, represents the fractional differential of the i-th constant phase element, represents the voltage value of the i-th fractional-order branch at time t; The time domain analytical solution is: ， represents the power of time, which is a characteristic of fractional-order systems. represents the initial voltage, that is, the voltage on the i-th fractional-order branch at t=0, represents the Mittag-Leffler function; By superimposing the analytical solutions of n parallel fractional-order branches, the zero-input response voltage expression of the complete system is obtained: ， Where, represents the time constant, defined as =R i , used to control the response speed of the i-th fractional-order branch, I pulse Indicates pulse current.

6. The method for identifying parameters of a lithium battery fractional-order model according to claim 5, wherein: Set the initial guess value of the parameter and the constraint boundary, and define the parameter vector to be identified as: 。 7. The method for identifying parameters of a lithium battery fractional-order model according to claim 1, wherein: In step 3, the objective function is a mean square error function between the experimental data and the model prediction value.

8. The method for identifying parameters of a lithium battery fractional-order model according to claim 1, wherein: The method is applicable to any type of lithium-ion batteries.

9. An electronic device, characterized in that: include: one or more processors; a memory for storing one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the lithium battery fractional-order model parameter identification method according to any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that Executable instructions are stored thereon, and when the instructions are executed by the processor, the processor can implement the lithium battery fractional-order model parameter identification method described in any one of claims 1-8.

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