Parameter-shared time-frequency domain unified simulation ECM-SPMe model and construction method thereof

Abstract

The application provides a parameter-shared time-frequency domain unified simulation ECM-SPMe model and a construction method thereof, which is constructed through the following steps: a time domain control equation of a single particle SPMe model based on liquid phase diffusion is established; under small signal disturbance conditions, each nonlinear time domain control equation is linearized at a working point; Laplace transformation is performed on the linearized equation to convert it into a frequency domain transfer function form; each frequency domain transfer function is converted into an impedance form of an RC parallel branch to establish an analytical mapping relationship between each electrochemical process in the time domain and the frequency domain RC impedance; and original explicit parameters determining the analytical mapping relationship are combined into a group of core parameters through parameter dimension reduction. The method realizes one-to-one correspondence and unified solution of the same group of parameters between the time domain SPMe model and the frequency domain ECM model, significantly reduces the model complexity and calculation cost, and at the same time retains complete physical interpretability.

Description

Technical Field

[0001] This invention belongs to the field of lithium-ion battery simulation technology, specifically involving a parameter-sharing time-frequency domain unified simulation ECM-SPMe model and its construction method. Background Technology

[0002] The charging and discharging process of lithium-ion batteries involves complex electrochemical kinetics, and accurate simulation models are crucial for battery state estimation, performance optimization, and safety management. Currently, mainstream battery simulation models fall into two main categories: one is time-domain models based on electrochemical mechanisms (such as the SPMe model), which can characterize physicochemical processes like lithium-ion diffusion and charge transfer in detail and has good mechanistic interpretability. However, when performing frequency-domain impedance analysis, it requires inputting multi-frequency sinusoidal currents and performing long-term simulations combined with Fourier transform (FFT) calculations, resulting in high time resolution requirements and enormous computational overhead. The other category is frequency-domain models based on equivalent circuits (ECM models), which can quickly solve impedance spectra, but lack clear physical mechanism support and their parameters are not interchangeable with those of time-domain models, making unified time-frequency domain analysis impossible.

[0003] In existing technologies, time-domain electrochemical models and frequency-domain equivalent circuit models are independent and have incompatible parameter systems. This necessitates the separate construction and calibration of two models in practical applications, increasing engineering complexity and reducing the efficiency and consistency of simulation analysis. Furthermore, traditional electrochemical models typically rely on numerous explicit size and material parameters, making parameter identification difficult and hindering the needs of rapid engineering applications. Therefore, there is an urgent need for a battery model and its construction method that can achieve unified time- and frequency-domain simulation, parameter sharing, and combines mechanistic interpretability with computational efficiency. Summary of the Invention

[0004] The purpose of this application is to provide a parameter-sharing time-frequency domain unified simulation ECM-SPMe model and its construction method.

[0005] The embodiments of this application can be implemented through the following technical solutions: A method for constructing a parameter-sharing time-frequency domain unified simulation ECM-SPMe model includes the following steps: S1, Establish the time-domain governing equations based on the single-particle SPMe model with liquid-phase diffusion; S2, under small-signal disturbance conditions, linearizes the operating point of each nonlinear time-domain control equation; S3. Perform a Laplace transform on the linearized equation to convert it into a frequency domain transfer function form. S4 converts the frequency domain transfer functions into the impedance form of RC parallel branches to establish an analytical mapping relationship between the time domain electrochemical processes and the frequency domain RC impedance. S5, through parameter dimensionality reduction, the original explicit parameter combination that determines the analytical mapping relationship is mapped into a set of core parameters; The core parameters are used for both dynamic voltage response simulation of the time-domain SPMe model and impedance spectrum simulation of the frequency-domain equivalent circuit ECM model.

[0006] Specifically, the single-particle SPMe model with liquid-phase diffusion decomposes the battery terminal voltage into open-circuit voltage, concentration polarization overpotential, reaction polarization overpotential, and ohmic polarization overpotential.

[0007] Specifically, the frequency domain transfer function includes the solid-phase diffusion transfer function, the liquid-phase diffusion transfer function, the electric double-layer transfer function, and the solid-liquid phase interface film transfer function.

[0008] Specifically, the core parameters include: solid-phase diffusion time constant. Liquid phase diffusion ratio Liquid phase diffusion time constant Positive electrode electrochemical reaction polarization coefficient Effective capacitance of the positive double layer Negative electrode electrochemical reaction polarization coefficient Effective capacitance of negative double layer SEI film effective conductivity SEI film effective capacitance CEI membrane effective conductivity CEI film effective capacitance Ohmic internal resistance .

[0009] Specifically, the parameter dimensionality reduction is based on the mechanism grouping of each electrochemical process. The geometric size parameters, material parameters and kinetic parameters of solid-phase diffusion, liquid-phase diffusion, electric double layer and solid-liquid phase interface film are combined and mapped to obtain a set of core parameters.

[0010] Furthermore, the combined mapping includes: Based on the radius of active particles and solid-phase diffusion system The combined mapping is obtained; From electrochemical reaction constant active particle radius The combined mapping is obtained; By double-layer capacitor Specific surface area of ​​active particles Electrode area Electrode thickness The combined mapping is obtained; Based on the conductivity of the SEI film Electrode thickness Electrode area Specific surface area The combined mapping is obtained; SEI film capacitor Electrode thickness Electrode area Specific surface area The combined mapping is obtained; Based on the conductivity of CEI film Electrode thickness Electrode area Specific surface area The combined mapping is obtained; CEI film capacitor Electrode thickness Electrode area Specific surface area The combined mapping is obtained; It is obtained by mapping the combination of electrolyte resistance, current collector resistance and contact resistance.

[0011] Specifically, the impedance form of the RC parallel branch is as follows: Solid-phase diffusion: ; Liquid phase diffusion: ; Double layer: ; Solid-liquid phase interface film: , ; in, , and These represent the equivalent impedance, equivalent resistance, and equivalent time constant of solid-phase diffusion, respectively. , and These represent the equivalent impedance, equivalent resistance, and equivalent time constant for liquid-phase diffusion, respectively. , and These represent the impedance, resistance, and time constant of the double layer, respectively. , and These represent the impedance, resistance, and time constant of the SEI film, respectively. , and These represent the impedance, resistance, and time constant of the CEI film, respectively. Angular frequency, It is the imaginary unit.

[0012] Furthermore, the analytical mapping relationship between each electrochemical process and the frequency domain RC impedance includes: From the solid-phase diffusion time constant Correction coefficients for OCV fitting Lithium intercalation rate of positive electrode Positive electrode capacity Analysis confirmed. Equal to the solid-phase diffusion time constant ; From the liquid phase diffusion ratio Liquid phase lithium ion concentration Analysis confirmed. Equal to the liquid phase diffusion time constant ; Electrochemical reaction polarization coefficient Positive and negative battery capacity Surface lithium intercalation rate Liquid phase lithium ion concentration Analysis confirmed. Due to double layer resistance and double-layer effective capacitance Analysis confirmed; Effective conductivity of SEI film and the thickness of the SEI film Analysis confirmed. SEI film resistance and SEI film effective capacitance Analysis confirmed; Effective conductivity of CEI membrane and the thickness of the CEI film Analysis confirmed. From CEI film resistance and CEI film effective capacitance Analysis confirmed.

[0013] Specifically, the total impedance expression for the frequency domain equivalent circuit model is: .

[0014] A time-frequency domain unified simulation ECM-SPMe model with shared parameters includes: The time-domain SPMe model is used to receive the input current and solve the time-domain control equations based on a set of core parameters, outputting the dynamic time-domain response of the battery terminal voltage. The frequency domain ECM model is used to receive frequency signals and calculate the frequency domain impedance based on the same set of core parameters, outputting the impedance spectrum. The set of core parameters includes the 12 core parameters mentioned above, and each electrochemical polarization process in the time-domain SPMe module has a one-to-one analytical mapping relationship with each RC parallel branch in the frequency-domain ECM module.

[0015] The embodiments of this application provide a parameter-sharing time-frequency domain unified simulation ECM-SPMe model and its construction method, which have at least the following beneficial effects: (1) Achieve unified simulation in time and frequency domains: By establishing a parameter sharing mechanism between the SPMe model and the ECM model, the same set of core parameters can simultaneously support time-domain dynamic response simulation and frequency-domain impedance spectrum analysis, thus solving the problem of time-frequency domain separation in traditional models; (2) Significantly reduce computational costs: Frequency domain simulation does not require time domain integration and steady-state waiting. The impedance response is solved directly by analytical methods. The computation time is linearly related to the number of frequency points, which greatly improves the simulation efficiency. (3) It combines mechanism interpretability and engineering efficiency: Based on the SPMe model, it retains the accurate characterization of core electrochemical processes such as lithium-ion diffusion and charge transfer, while achieving efficient calculation through the ECM equivalent impedance structure; (4) Unified representation of low-dimensional parameters: The model parameters are simplified to 12 core shared parameters through the parameter dimensionality reduction strategy, which eliminates the dependence on explicit size parameters, reduces the difficulty of parameter identification, and is suitable for practical engineering applications; (5) Applicable to battery state analysis and parameter identification in multiple scenarios: It can be widely used in the analysis of multiple scenarios such as state estimation, performance optimization, and fault diagnosis of lithium-ion batteries, providing technical support for the full life cycle management of batteries. Attached Figure Description

[0016] Figure 1 The flowchart shows the method for constructing the parameter-sharing time-frequency domain unified simulation ECM-SPMe model according to the embodiments of this application; Figure 2 A comparison chart of the Nyquist curves of the time-domain FFT calculation results and the frequency-domain ECM analysis results; Detailed Implementation The present application will now be further described based on preferred embodiments and with reference to the accompanying drawings.

[0017] To address the problems mentioned in the background section, this application provides a parameter-sharing time-frequency domain unified simulation ECM-SPMe model and its construction method, such as... Figure 1As shown, based on the SPMe electrochemical model as the physical basis, through small-signal linearization and Laplace transform, the time-domain control equation is transformed into a frequency-domain transfer function, and further each frequency-domain transfer function is converted into the impedance form of a parallel RC branch to establish an analytical mapping relationship between each electrochemical process in the time domain and the frequency-domain RC impedance. Finally, a set of core parameters that can be used for both time-domain and frequency-domain simulations is obtained through mechanism grouping and dimension reduction.

[0018] The specific implementation process of each step is described in detail below.

[0019] <S1. Establish the time-domain control equation based on the single-particle SPMe model with liquid-phase diffusion> The charge and discharge process of a lithium-ion battery can be essentially described as the insertion and extraction of lithium ions in the active particles of the positive and negative electrodes, as well as the migration and diffusion process in the electrolyte. To reduce the model complexity while ensuring the integrity of the main electrochemical mechanisms, this method uses the single-particle model with liquid-phase diffusion (Single Particle Model with Electrolyte, SPMe) as the physical basis for unified modeling.

[0020] This model characterizes the solid-phase diffusion behavior inside the entire electrode with a single equivalent active particle, and further introduces a liquid-phase concentration gradient to describe the mass transfer process in the electrolyte, thereby effectively characterizing the main kinetic processes of the lithium-ion battery. Based on this, the battery terminal voltage can be decomposed into four components in the time domain: open-circuit voltage, concentration polarization overpotential, reaction polarization overpotential, and ohmic polarization overpotential, and the time-domain control equation is established accordingly.

[0021] (1) Time-domain control equation of open-circuit voltage The open-circuit voltage of a lithium-ion battery is determined by the difference between the open-circuit potentials of the positive and negative electrodes. As shown in the following equation (1), the open-circuit potentials of the positive and negative electrodes are only related to the lithium intercalation rate on the surface of the active particles, and the surface lithium intercalation rate is affected by the solid-phase diffusion process. Specifically, the open-circuit voltage can be expressed as: (1) where is the open-circuit potential of the positive electrode, is the open-circuit potential of the negative electrode, and both are determined by the lithium-ion concentration ratio on the surface of the active particles and are physical quantities related only to the material properties; and are the lithium intercalation rates (i.e., lithium-ion concentration ratios) on the surfaces of the positive and negative electrodes, respectively, and are defined as: (2) where and are the lithium-ion concentrations on the surfaces of the positive and negative active particles, respectively; and Here, represents the maximum lithium-ion concentration of the active particles in the positive and negative electrodes, respectively, which can be calculated from the corresponding capacities of the positive and negative electrodes using the following formula: (3) in, It is the thickness of the electrode sheet. It is the electrode area. F It is Faraday's constant. It is the volume fraction of solid-phase active material. n and p These represent the negative and positive terminals of the battery, respectively. The values ​​for the positive and negative electrodes are related to the total capacity of the battery as follows: (4) in, Q This refers to the total capacity of the lithium-ion battery. Dy This represents the range of lithium intercalation rate of the positive electrode active particles. Dx This represents the range of lithium intercalation rate of the negative electrode active particles. The lithium intercalation rate of the active particles is related to the state of charge (SOC) of the battery. SOC The relationship is as follows: (5) in, and Represent SOC The corresponding average lithium insertion rates of the positive and negative electrodes and They represent the initial lithium insertion rates of the positive and negative electrodes corresponding to 100% SOC, respectively, combined with equations (1) and (5). and as well as and It can be obtained by fitting the measured open-circuit voltage curve.

[0022] Due to the influence of solid-phase diffusion, the relationship between the surface lithium intercalation rate and the average lithium intercalation rate of the particles is as follows: (6) in, and These represent the changes in lithium intercalation rates of the positive and negative electrode active particles, respectively. This involves solving for the solid-phase diffusion process within the lithium-ion battery. Solid-phase diffusion describes the diffusion process of lithium ions within the active particles and is typically described using Fick's second law. However, using a three-parameter parabolic equivalent calculation can effectively simplify the calculation process. After simplification... and It can be calculated using the following formula (7): (7) Among them, dynamic items and Satisfies the first-order differential equation: (8) in, It is an externally applied current; , representing the solid-phase diffusion time constant. Let be the radius of the spherical active particle. Let be the solid-phase diffusion coefficient; for simplicity, assume that the solid-phase diffusion time constants of the positive and negative electrodes are equal, i.e. .

[0023] By combining the above equations, the open-circuit voltage can be dynamically calculated in the time domain.

[0024] (2) Time-domain governing equations of concentration polarization overpotential The concentration polarization overpotential is caused by the uneven lithium-ion concentration along the electrode direction and can be calculated by the following formula: (9) in, R The molar gas constant, T Absolute temperature This represents the lithium-ion transference number. This represents the equilibrium concentration of lithium ions in the liquid phase. It is the change in liquid phase lithium ion concentration at the boundary between the positive and negative electrode current collectors, achieved through simplification of the liquid phase diffusion formula. It can be calculated by the following formula: (10) in, This is the liquid phase diffusion ratio. is the liquid phase diffusion time constant.

[0025] (3) Time-domain governing equation of reaction polarization overpotential The reactive polarization overpotential is caused by the charge transfer impedance during the electrochemical reaction process. Its dynamic characteristics are mainly controlled by the charge-discharge effect of the double layer on the electrode surface. Therefore, it is modeled based on the double layer theory.

[0026] First, the average lithium-ion flux density can be measured by an externally applied current. I Perform approximate calculations: (11) in, The specific surface area of ​​the active particles is expressed as a percentage of the volume fraction of the active substance. and particle radius The relationship is: (12) Residual charge density inside the electric double layer Calculated by integral from the non-Radar current flow density: (13) in, This is the Faraday current, the current involved in the electrochemical reaction, given by the Butler-Volmer equation: (14) in, The exchange current density is given by R, where R is the molar gas constant and T represents the temperature. It is the electrochemical reaction constant. It refers to the concentration of lithium ions in the liquid phase. It is the reaction polarization overpotential; The relationship between the reaction polarization overpotential and the residual charge density is as follows: (15) in, It is a double-layer capacitor.

[0027] By combining the above equations, we can obtain the time-domain governing equation for the reactive polarization overpotential.

[0028] (4) Ohmic polarization overpotential Ohmic polarization overpotential is caused by various ohmic impedances within the battery, mainly including: the SEI film impedance and CEI film impedance on the surfaces of the positive and negative electrode active particles, the bulk resistance of the positive and negative electrode materials, the electrolyte ionic conductivity impedance, and the contact resistance between the current collector and the electrode tabs. Traditional models typically use a lumped parameter. A unified representation of all the above Ohmic contributions: (16) To further improve the physical interpretability of the model, this method models the impedance characteristics of the SEI and CEI films separately. Ignoring diffusion within the thin films, the current densities across the SEI and CEI films are simultaneously driven by the electric field and influenced by the capacitor charging and discharging effect. Their governing equations are expressed as follows: (17) in, , and These represent the conductivity of the SEI film, the voltage drop across its terminals, and the capacitance, respectively. The thickness of the SEI film; , and represent the conductivity, voltage drop across, and capacitance of the CEI film, respectively. , The thickness is the CEI film thickness.

[0029] Combining the voltage drops of the two types of membranes and the contributions of the ohmic internal resistance, the total ohmic polarization overpotential can be expressed as: (18) Based on the above open-circuit voltage and each polarization overpotential, the total expression of the battery terminal voltage is: (19) <S2, under small-signal perturbation conditions, linearize the operating point of each nonlinear time-domain control equation> (1) Solid-phase diffusion linearization (taking the positive electrode as an example) There is a complex nonlinear relationship between the open-circuit potential and the surface lithium intercalation rate. Existing research fits it in the form of a high-order polynomial, making it difficult to directly perform linearization. Therefore, this paper uses the following expression to describe the relationship between the two: (20) where is the reference potential constant, is the correction coefficient for OCV fitting.

[0030] Under small-signal perturbation conditions, decompose the surface lithium intercalation rate near the steady-state operating point: (21) where is the average lithium intercalation rate at the steady-state operating point, is the small perturbation with respect to this equilibrium point, satisfying . Then Equation (20) can be written as: (22) Perform a first-order Taylor expansion of the logarithmic term at : (23) where (24) Therefore, Equation (23) can be deduced as: (25) Substitute Equation (25) into Equation (20) to further obtain the open-circuit potential perturbation expression caused by the perturbation : (26); (2) Liquid-phase diffusion linearization To establish a small-signal impedance model, linearize Equation (9) near the equilibrium operating point. Since the perturbation in electrochemical impedance analysis is small and satisfies: , therefore, a first-order Taylor expansion can be performed on the logarithmic term: (27) Then it expands at to (28) Since , further derivative is taken: (29) Therefore, , substituting it into Equation (9) gives: (30) (3) Double-layer linearization By combining Equations (13) and (15), the dynamic differential equation of the double-layer overpotential is obtained: (31) Since the Faraday current satisfies the B-V process, for establishing the small-signal impedance model, the B-V equation is linearized near the equilibrium point. Since the EIS excitation signal is small and satisfies , thus the first-order Taylor expansion can be carried out for the exponential term: (32) Let , then: (33) Substitute Equation (33) into Equation (14): (34) After arrangement, we get: (35) Substitute Equation (35), Equation (11), and Equation (12) into Equation (31), and after arrangement, the linear differential equation can be obtained: (36); (4) Solid-liquid interface film linearization Since the control equations of the SEI film and the CEI film (Equation 17) are linear ordinary differential equations without non-linear terms, further small-signal linearization is not required, and the Laplace transform can be directly carried out to obtain its frequency-domain impedance expression.

[0031] <S3. Perform the Laplace transform on the linearized equation to convert it into the form of a frequency-domain transfer function> (1) Solid-phase diffusion transfer function Since Equation (7) consists of a dynamic term and an instantaneous term, and the electrochemical impedance spectrum focuses on the steady-state sinusoidal response, the transient term can be ignored, that is ; The Laplace transform of Equation (8) gives: (37) Substitute Equation (37) into Equation (26), and let , to obtain the expression for the solid-phase diffusion impedance in the frequency domain: (38) (2) Liquid-phase diffusion transfer function Perform the Laplace transform on Equations (10) and (30), and calculate the liquid-phase diffusion impedance, to obtain: (39) (3) Double-layer transfer function Perform the time Laplace transform on Equation (36): (40) Let , to obtain the following expression for the double-layer impedance: (41); (4) Solid-liquid interface membrane transfer function Perform the Laplace transform on Equation (17) to obtain: (42) Rearrange it into an impedance expression: (43); <S4. Convert each frequency-domain transfer function into the impedance form of an RC parallel branch to establish an analytical mapping relationship between each electrochemical process in the time domain and the RC impedance in the frequency domain> (1) Solid-phase diffusion RC impedance form and analytical mapping relationship , That is, the equivalent resistance of solid-phase diffusion is analytically determined by the solid-phase diffusion time constant , the correction coefficient fitted from OCV, the lithium intercalation rate of the positive electrode, and the positive electrode capacity ; among which, except , other parameters can be determined when the battery model and SOC are determined; The equivalent time constant is equal to the solid-phase diffusion time constant .

[0032] (2) Liquid-phase diffusion RC impedance form and analytical mapping relationship , That is, the equivalent resistance of liquid-phase diffusion From the liquid phase diffusion ratio Lithium-ion transference number Liquid phase lithium-ion equilibrium concentration Analysis confirmed; Its equivalent time constant With liquid phase diffusion time constant equal.

[0033] (3) Forms and analytical mapping relationships of double-layer RC impedance , That is, the resistance of the double layer Electrochemical reaction polarization coefficient Liquid phase lithium-ion equilibrium concentration Surface lithium intercalation rate Positive and negative electrode capacity Analysis confirmed; Its time constant Due to double layer resistance and double-layer effective capacitance Analysis confirmed.

[0034] (4) The form of RC impedance of solid-liquid phase interface film and analytical mapping relationship , That is, the resistance of the solid-liquid phase intersecting SEI film. Effective conductivity of SEI film and the thickness of the SEI film The time constant is determined analytically. SEI film resistance and SEI film effective capacitance Analysis confirmed; Resistance of solid-liquid phase cross-linked CEI film Effective conductivity of CEI membrane and the thickness of the CEI film The time constant is determined analytically. From CEI film resistance and CEI film effective capacitance Analysis confirmed.

[0035] In summary, by connecting the various physical sub-modules in series in the frequency domain, the following complete impedance expression is obtained: (44) Through the above derivation, this method successfully establishes a unified analytical mapping between the time-domain electrochemical model and the frequency-domain equivalent circuit model. Key kinetic processes such as solid-phase diffusion, liquid-phase diffusion, charge transfer, and interfacial films are all uniformly represented as impedance structures of equivalent parallel RC circuits, and the equivalent resistance and capacitance parameters can be directly obtained analytically from the corresponding electrochemical mechanism parameters.

[0036] <S5, reduce the dimensionality of parameters to combine the original explicit parameter group determining the analytical mapping relationship into a set of core parameters> Furthermore, this application proposes a parameter dimensionality reduction strategy based on mechanism grouping: Mechanistically combine and analytically map the geometric size parameters (such as particle radius, electrode thickness, electrode area), material parameters (such as solid-phase diffusion coefficient, reaction constant, membrane conductivity), and kinetic parameters (such as exchange current density, double-layer capacitance) involved in each of the aforementioned electrochemical processes, thereby eliminating the strong dependence of traditional electrochemical models on explicit size parameters. Through this dimensionality reduction strategy, this model only requires 12 core parameters , and can simultaneously complete the time-domain voltage response simulation and the frequency-domain impedance spectrum simulation.

[0037] Specifically, the combined mapping relationships of the 12 core parameters are summarized in Table 1 as follows: Table 1 Through the above parameter dimensionality reduction strategy based on mechanism grouping, dozens of physical parameters in the original electrochemical model that are difficult to directly measure are streamlined into 12 lumped parameters with clear physical meanings, eliminating the strong dependence on explicit size parameters and significantly reducing the complexity of parameter identification.

[0038] To clearly show the unified mapping relationship of this model in the time domain and the frequency domain, Table 2 systematically summarizes the working principles, related core parameters, time-domain control equations, and frequency-domain RC impedance forms of each electrochemical process.

[0039] Table 2 Example 1 This example is used to verify the effectiveness of the proposed ECM-SPMe model in unified simulation in the time domain and the frequency domain, and two methods of time-domain dynamic simulation and frequency-domain analytical calculation are used for comparative verification respectively.

[0040] To ensure the comparability of the time-domain and frequency-domain results, 51 frequency points uniformly distributed logarithmically are selected, and the selected frequency range is Hz to Hz. This range covers the low-frequency region dominated by solid-phase diffusion, the mid-frequency region dominated by charge transfer, and the high-frequency region dominated by the solid-liquid interface membrane effect, and can comprehensively characterize the multi-scale kinetic characteristics of the battery.

[0041] In the time-domain simulation, a sinusoidal excitation current signal corresponding to each frequency point is constructed and input into the SPMe time-domain model to calculate the dynamic response of the terminal voltage. After the system reaches steady state, a Fast Fourier Transform (FFT) is performed on the input and output signals to extract the amplitude and phase information at each frequency point, and then the frequency domain response of each electrochemical process and the total impedance is calculated. Because low-frequency signals have longer periods, multiple complete periods need to be covered to ensure the accuracy of the spectrum calculation, resulting in a significant increase in simulation time as the frequency decreases. In frequency domain simulation, based on identical parameters, the corresponding frequency points are directly input, and the constructed ECM frequency domain model is used to analytically solve for solid-phase diffusion impedance, liquid-phase diffusion impedance, charge transfer impedance, interface film impedance, and total impedance spectrum. This method does not require time-domain integration or waiting for a steady-state process, and the calculation time is linearly related to the number of frequency points, with extremely low calculation time per point.

[0042] During the simulation, the time-domain model and the frequency-domain model used the exact same set of parameters to ensure the consistency and fairness of the comparison results. The specific values ​​are listed in Table 3.

[0043] Table 3 The Nyquist plots are compared between the time-domain FFT calculation results and the frequency-domain ECM analytical results, such as... Figure 2 As shown in the figure. The results show that the two methods have good consistency across the entire frequency band, verifying that the proposed ECM-SPMe model can achieve unified time-frequency domain simulation based on the same set of parameters.

[0044] The specific embodiments of this application have been described in detail above. For those skilled in the art, several improvements and modifications can be made to this application without departing from the principle of this application, and these improvements and modifications also fall within the protection scope of the claims of this application.

Claims

1. A method for constructing a parameter-sharing time-frequency domain unified simulation ECM-SPMe model, characterized in that, Includes the following steps: S1, Establish the time-domain governing equations based on the single-particle SPMe model with liquid-phase diffusion; S2, under small-signal disturbance conditions, linearizes the operating point of each nonlinear time-domain control equation; S3. Perform a Laplace transform on the linearized equation to convert it into a frequency domain transfer function form. S4 converts the frequency domain transfer functions into the impedance form of RC parallel branches to establish an analytical mapping relationship between the time domain electrochemical processes and the frequency domain RC impedance. S5, through parameter dimensionality reduction, the original explicit parameter combination that determines the analytical mapping relationship is mapped into a set of core parameters; The core parameters are used for both dynamic voltage response simulation of the time-domain SPMe model and impedance spectrum simulation of the frequency-domain equivalent circuit ECM model.

2. The method according to claim 1, characterized in that, The single-particle SPMe model with liquid-phase diffusion decomposes the battery terminal voltage into open-circuit voltage, concentration polarization overpotential, reaction polarization overpotential, and ohmic polarization overpotential.

3. The method according to claim 1, characterized in that, The frequency domain transfer function includes the solid-phase diffusion transfer function, the liquid-phase diffusion transfer function, the electric double layer transfer function, and the solid-liquid phase interface film transfer function.

4. The method according to claim 1, characterized in that, The core parameters include: solid-phase diffusion time constant. Liquid phase diffusion ratio Liquid phase diffusion time constant Positive electrode electrochemical reaction polarization coefficient Effective capacitance of the positive double layer Negative electrode electrochemical reaction polarization coefficient Effective capacitance of negative double layer SEI film effective conductivity SEI film effective capacitance CEI membrane effective conductivity CEI film effective capacitance Ohmic internal resistance .

5. The method according to claim 1, characterized in that, The parameter dimensionality reduction is based on the mechanism grouping of each electrochemical process. The geometric, material, and kinetic parameters of solid-phase diffusion, liquid-phase diffusion, electric double layer, and solid-liquid interface film are combined and mapped to obtain a set of core parameters.

6. The method according to claim 5, characterized in that, The combined mapping includes: Based on the radius of active particles and solid-phase diffusion system The combined mapping is obtained; From electrochemical reaction constant active particle radius The combined mapping is obtained; By double-layer capacitor Specific surface area of ​​active particles Electrode area Electrode thickness The combined mapping is obtained; Based on the conductivity of the SEI film Electrode thickness Electrode area Specific surface area The combined mapping is obtained; SEI film capacitor Electrode thickness Electrode area Specific surface area The combined mapping is obtained; Based on the conductivity of CEI film Electrode thickness Electrode area Specific surface area The combined mapping is obtained; CEI film capacitor Electrode thickness Electrode area Specific surface area The combined mapping is obtained; It is obtained by mapping the combination of electrolyte resistance, current collector resistance and contact resistance.

7. The method according to claim 1, characterized in that, The impedance form of the RC parallel branch is as follows: Solid-phase diffusion: ; Liquid phase diffusion: ; Double layer: ; Solid-liquid phase interface film: , ; in, , and These represent the equivalent impedance, equivalent resistance, and equivalent time constant of solid-phase diffusion, respectively. , and These represent the equivalent impedance, equivalent resistance, and equivalent time constant for liquid-phase diffusion, respectively. , and These represent the impedance, resistance, and time constant of the double layer, respectively. , and These represent the impedance, resistance, and time constant of the SEI film, respectively. , and These represent the impedance, resistance, and time constant of the CEI film, respectively. Angular frequency, It is the imaginary unit.

8. The method according to claim 7, characterized in that, The analytical mapping relationships between various electrochemical processes and frequency domain RC impedance include: From the solid-phase diffusion time constant Correction coefficients for OCV fitting Lithium intercalation rate of positive electrode Positive electrode capacity Analysis confirmed. Equal to the solid-phase diffusion time constant ; From the liquid phase diffusion ratio Liquid phase lithium ion concentration Analysis confirmed. Equal to the liquid phase diffusion time constant ; Electrochemical reaction polarization coefficient Positive and negative battery capacity Surface lithium intercalation rate Liquid phase lithium ion concentration Analysis confirmed. Due to double layer resistance and double-layer effective capacitance Analysis confirmed; Effective conductivity of SEI film and the thickness of the SEI film Analysis confirmed. SEI film resistance and SEI film effective capacitance Analysis confirmed; Effective conductivity of CEI membrane and the thickness of the CEI film Analysis confirmed. From CEI film resistance and CEI film effective capacitance Analysis confirmed.

9. The method according to claim 7, characterized in that, The total impedance expression for the frequency domain equivalent circuit model is: 。 10. A time-frequency domain unified simulation ECM-SPMe model with shared parameters, characterized in that, include: The time-domain SPMe model is used to receive the input current and solve the time-domain control equations based on a set of core parameters, outputting the dynamic time-domain response of the battery terminal voltage. The frequency domain ECM model is used to receive frequency signals and calculate the frequency domain impedance based on the same set of core parameters, outputting the impedance spectrum. The set of core parameters includes the 12 parameters described in claim 5, and each electrochemical polarization process in the time-domain SPMe module has a one-to-one analytical mapping relationship with each RC parallel branch in the frequency-domain ECM module.

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