Lithium battery residual capacity estimation method based on coupled hyperbolic-parabolic partial differential system

Abstract

The invention discloses a lithium battery residual capacity estimation method based on a coupled hyperbolic-parabolic partial differential system, and the method comprises the following steps: S1, building a lithium battery mathematical model based on the coupled hyperbolic-parabolic partial differential system based on the parameter data of a lithium battery measured through an experiment, describing an electrolyte ion conduction mechanism, and calculating the residual capacity of the lithium battery; therefore, the lithium ion intercalation and deintercalation processes are simulated; s2, solving the lithium battery mathematical model by adopting a finite difference method to obtain a lithium ion concentration change formula; s3, calculating a residual capacity estimation value of the lithium battery based on the lithium ion concentration change formula obtained in S2; and S4, comparing the residual capacity estimation value obtained in S3 with the initial estimation value, if the difference between the two exceeds a preset threshold value, returning to the step S3, starting a calibration program, adjusting related parameters and recalculating until the difference between the two does not exceed the threshold value, and outputting the current residual capacity estimation value as the residual capacity of the lithium battery. According to the lithium battery residual capacity estimation method based on the coupled hyperbolic-parabolic partial differential system, the mathematical model of the coupled hyperbolic-parabolic partial differential system is provided based on the internal reaction process of the lithium battery, the residual capacity is calculated by using the accurate simulation result of the model on the internal physical and chemical process of the lithium battery, the calculation precision is high, and the calculation efficiency is high. And the method has real-time performance.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium batteries, in particular to estimation of the remaining capacity of a lithium battery, and in particular to a method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system. Background Art

[0002] With the rapid development of electric vehicles, energy storage, and other fields, battery packs, as core components of electric vehicles and energy storage systems, have garnered widespread attention both within and outside the industry. Their performance and safety directly determine the efficiency, reliability, and service life of the entire system. In the electric vehicle sector, battery pack capacity is a key indicator of range and power performance. Higher battery capacity means longer vehicle range, reduced charging times, and a better user experience.

[0003] Data-driven methods are suitable for solving strong nonlinear problems and mainly include neural network algorithms, support vector machines, fuzzy controllers, and other methods. These methods establish nonlinear relationships by integrating sample data. For example, a direct mapping relationship model between battery current, voltage, temperature, and state of charge (SOC) is used to train the model with data and then use it to estimate SOC. This type of method does not need to consider the internal electrochemical characteristics of the battery, has strong fitting capabilities, and high estimation accuracy. However, it requires a large amount of data to train the model, has harsh application conditions, is highly dependent on prior data, and is computationally intensive.

[0004] Model-based SOC estimation methods achieve SOC prediction by establishing an accurate battery model and employing advanced state estimation algorithms. The Kalman filter family of algorithms has become a research focus due to its optimal estimation properties. This approach uses a state equation to describe the system's dynamic characteristics, integrates observed data through measurement equations, and employs iterative computation to achieve optimal state estimation. To address the nonlinear characteristics of battery systems, researchers have proposed various improved algorithms: the Extended Kalman Filter (EKF) addresses nonlinearities through a first-order Taylor expansion, the Unscented Kalman Filter (UKF) uses an unscented transformation to enhance nonlinearity handling, and the Quadrature Kalman Filter (QKF) achieves higher-precision estimation based on deterministic sampling and Gaussian integration. The UKF still suffers from covariance matrix instability when estimating high-dimensional states. The QKF exhibits accuracy advantages in high-dimensional state estimation, but its computational complexity is relatively high. Current research still faces challenges such as model mismatch caused by battery aging and numerical stability in high-dimensional state estimation, necessitating a better balance between computational accuracy and real-time performance. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: in order to solve the technical problems of model mismatch and numerical stability of high-dimensional state estimation caused by battery aging in the prior art, the present invention provides a lithium battery remaining capacity estimation method based on a coupled hyperbolic-parabolic partial differential system. Based on the internal reaction process of the lithium battery, a mathematical model of the coupled hyperbolic-parabolic partial differential system is proposed. The model is used to accurately simulate the physical and chemical processes inside the lithium battery to infer the remaining capacity, with high calculation accuracy and real-time performance.

[0006] The technical solution adopted by the present invention to solve its technical problems is: a method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system, comprising the following steps: S1. Based on experimentally measured parameter data of the lithium battery, a mathematical model of the lithium battery based on the coupled hyperbolic-parabolic partial differential system is established to describe the electrolyte ion conduction mechanism, thereby simulating the lithium ion insertion and deinsertion process; S2. The mathematical model of the lithium battery is solved using a finite difference method to obtain a formula for the change of lithium ion concentration; S3. Based on the lithium ion concentration change formula obtained in S2, an estimated value of the remaining capacity of the lithium battery is calculated; S4. The estimated value of the remaining capacity obtained in S3 is compared with the preliminary estimated value. If the difference between the two exceeds a preset threshold, the method returns to step S3, starts a calibration program, adjusts relevant parameters and recalculates until the difference between the two does not exceed the threshold, and outputs the current estimated value of the remaining capacity as the remaining capacity of the lithium battery.

[0007] The present invention is based on a method for estimating the remaining capacity of a lithium battery using a coupled hyperbolic-parabolic partial differential system. The invention proposes a mathematical model of the coupled hyperbolic-parabolic partial differential system, uses a finite difference method to solve the constructed mathematical model of the coupled hyperbolic-parabolic partial differential system, and uses the model-simulated capacity estimation to accurately simulate the physical and chemical processes inside the lithium battery to infer the remaining capacity, thereby ensuring calculation accuracy and real-time performance.

[0008] Furthermore, the mathematical model of the lithium battery based on the coupled hyperbolic-parabolic partial differential system in step S1 is as follows:

[0009]

[0010] Among them: It represents the rate of change of lithium ion concentration c with time t; Based on the classic Fick diffusion law, it describes the diffusion of lithium ions driven by concentration gradient; D is the diffusion coefficient of lithium ions in a specific medium; is the second-order partial derivative of the lithium ion concentration c with respect to the spatial position x; The effect of the electrochemical reaction on the electrode surface on the lithium ion concentration is taken into account; F is the Faraday constant; j represents the amount of charge carried by each mole of electrons; is the reaction current density of the negative electrode; is the reaction current density of the positive electrode.

[0011] Furthermore, the process of solving the lithium battery mathematical model using the finite difference method in step S2 is as follows:

[0012] In the time dimension Discretize using the forward difference format: in Indicates that at the nth time step, node x i The lithium ion concentration at , Δt is the time step;

[0013] In the spatial dimension, the lithium battery is divided into N grid nodes with equal spacing along its length, and the position of each node is recorded as x i , where i = 0, 1, 2, ..., N, and the grid spacing is Here L represents the length of the lithium battery. For the key variables in the model: lithium ion concentration c(x, t) and electrode potential φ(x, t), discrete values ​​are taken at these grid nodes, that is, Indicates that at the nth time step, the lithium x at the node i ion concentration, represents the electrode potential at the corresponding node and time;

[0014] Second-order spatial partial derivative with respect to lithium ion concentration The discretization of is carried out using the central difference format, and its discrete expression is:

[0015]

[0016] Convert all terms involving spatial partial derivatives in the model into algebraic combinations of node values ​​to obtain the discretized lithium ion concentration equation:

[0017]

[0018] For the lithium battery model, the boundary conditions are:

[0019]

[0020] Special treatment is also required in the discretization process. At the negative boundary x=0, the virtual node method is used to introduce a virtual node x -1 , according to the central difference format, we have:

[0021]

[0022] According to the boundary conditions, we can get:

[0023]

[0024] Substitute the value of this virtual node into the discrete equation to ensure that the boundary conditions are accurately met;

[0025] At the positive electrode boundary x=L, a virtual node x is introduced. N+1 , the formula for the change of lithium ion concentration can be obtained:

[0026] Furthermore, in step S3, the model parameters are corrected according to the real-time temperature of the lithium battery by using the pre-established temperature and parameter relationship model;

[0027] The relationship between the lithium ion diffusion coefficient D and temperature T can be approximately described by the Arrhenius formula:

[0028]

[0029] Where D0 is the pre-exponential factor, E is the activation energy, and R is the gas constant;

[0030] For the reaction rate constant k, establish a functional relationship with temperature:

[0031]

[0032] Among them, k0 is the pre-exponential factor, E k is the activation energy of the reaction rate constant.

[0033] Furthermore, in step S3, measured data is collected by sensors installed on the lithium battery, and the measured data is fed back into the mathematical model of the lithium battery.

[0034] Furthermore, in step S3, the residual capacity is estimated by using the accurate simulation results of the physical and chemical processes inside the lithium battery using the lithium battery mathematical model.

[0035] Furthermore, in step S3, a coupled hyperbolic-parabolic partial differential system model is solved by a numerical method to obtain the distribution of lithium ion concentration at various locations inside the battery over time under given charge and discharge conditions, as well as the dynamic evolution of the electrode potential;

[0036] The model is discretized using the finite difference method:

[0037] In the spatial dimension, the lithium battery is abstracted into a one-dimensional model and divided into equal intervals along its main lithium ion transmission direction to obtain N grid nodes, which are denoted as x i , where i = 0, 1, 2, ..., N, the grid spacing Here L represents the length of the lithium battery; the key variables in the model, lithium ion concentration c(x, t) and electrode potential φ(x, t), are all discretely valued at these grid nodes, that is, Indicates that at the nth time step, node x i The lithium ion concentration at represents the electrode potential at the corresponding node and time;

[0038] In the time dimension, the appropriate time advancement format is selected to discretize the lithium ion concentration change formula. Under the explicit Euler format, the equation Can be organized as:

[0039]

[0040] Furthermore, in step S4, the threshold is set to ΔQ, and the estimated remaining capacity is Q remain (t), the preliminary estimate is Q ah (t), then the judgment condition is:

[0041] |Q remain (t)-Q ah (t)|>ΔQ

[0042] When this condition is met, start the calibration procedure, adjust the relevant parameters and recalculate until the following conditions are met:

[0043] |Q remain (t)-Q ah (t)|≤ΔQ

[0044] Finally, the remaining capacity Q that meets the conditions is output remain (t) is the remaining capacity of the lithium battery.

[0045] Furthermore, in step S4, a preliminary estimated value is obtained by using the ampere-hour integration method.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] 1. The present invention is based on a method for estimating the remaining capacity of a lithium battery using a coupled hyperbolic-parabolic partial differential system. In terms of lithium battery state estimation, due to strong nonlinearity, multi-parameter coupling, and time lag, a coupled hyperbolic-parabolic partial differential system is constructed to estimate the SOC of the lithium battery. Based on the internal reaction process of the lithium battery, a mathematical model of the coupled hyperbolic-parabolic partial differential system is proposed. The model uses the accurate simulation results of the internal physical and chemical processes of the lithium battery to infer the remaining capacity, with high calculation accuracy and real-time performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The present invention will be further described below with reference to the accompanying drawings and examples.

[0049] Figure 1 The figure is a flow chart of the method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system according to the present invention. DETAILED DESCRIPTION

[0050] The present invention will now be described in further detail with reference to the accompanying drawings, which are simplified schematic diagrams that illustrate the basic structure of the present invention in a schematic manner.

[0051] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", "axial", "radial", "circumferential" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, features defined as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0052] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0053] like Figure 1 A method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system comprises the following steps:

[0054] S1. Based on experimentally measured lithium battery parameter data, a mathematical model of lithium batteries based on a coupled hyperbolic-parabolic partial differential system is established to describe the electrolyte ion conduction mechanism and thus simulate the lithium ion insertion and deinsertion process;

[0055] S2. Use the finite difference method to solve the mathematical model of the lithium battery and obtain the formula for the change of lithium ion concentration;

[0056] S3. Calculate the estimated remaining capacity of the lithium battery based on the lithium ion concentration change formula obtained in S2;

[0057] S4. Compare the remaining capacity estimate obtained in S3 with the preliminary estimate. If the difference between the two exceeds a preset threshold, return to step S3, start the calibration program, adjust the relevant parameters and recalculate until the difference between the two does not exceed the threshold. Output the current remaining capacity estimate as the remaining capacity of the lithium battery.

[0058] During the model building phase, experimental data under various temperature and charge / discharge rates are collected to obtain the required lithium battery parameters. The lithium ion insertion and deinsertion processes and the electrolyte ion conduction mechanism are simulated. A coupled hyperbolic-parabolic partial differential system is constructed using electrochemical principles and partial differential modeling theory. During the model solution phase, numerical methods are used to discretize time and space. Simultaneously, the coupled hyperbolic-parabolic partial differential system is solved, taking into account boundary conditions, to obtain the required algebraic array. A real-time detection and correction mechanism is introduced, and the solution is finally achieved using an iterative algorithm. During the remaining capacity estimation phase, this paper simulates the changes in lithium ion concentration during charge and discharge, deriving the dynamic evolution of the electrode potential and obtaining a model estimate. The ampere-hour integral method estimate is used as the standard value. If the difference between the two values ​​is greater than a given threshold, a calibration procedure is initiated, and the relevant parameters are adjusted and the calculation is repeated. If the difference is less than the threshold, the current model estimate is output as the remaining capacity estimate.

[0059] The model is established based on a coupled hyperbolic-parabolic partial differential system:

[0060] In the microscopic world of lithium-ion battery charging and discharging, lithium ions shuttle back and forth between the lattices of the positive and negative electrode materials. Their diffusion behavior is not a simple uniform linear motion but is influenced by the interactions of multiple factors, such as the material's crystal structure, temperature, and electric field strength. Simultaneously, electrochemical reactions occur on the electrode surfaces, where lithium ions combine or separate with electrons, following a complex rhythm described by the Butler-Volmer kinetic equation. The reaction rate is closely linked to subtle changes in lithium ion concentration and electrode potential. Furthermore, the electrolyte, as a medium for lithium ion transport, must ensure smooth ion migration while maintaining electroneutrality. Parameters such as the ion transference number and conductivity dynamically regulate the charge balance of the entire battery system. This paper aims to obtain basic parameters for model development by analyzing the lithium ion insertion and deintercalation processes in lithium-ion batteries and the electrolyte's ion conductivity. Subsequently, experimental data is collected under various conditions, such as charge and discharge rates, to provide more accurate parameters for model development. The proposed modeling theory is then combined with electrochemical principles to develop a lithium battery model.

[0061] Lithium battery parameter collection: Collaborative collection of temperature and SOC parameters: The experimental environment chamber controls the temperature (e.g., gradients from -20°C to 50°C), while the battery testing system simultaneously controls the charge and discharge rate and SOC (e.g., 0%, 20%, 50%, 100%). An electrochemical workstation or data acquisition module records voltage, current, temperature, impedance, and other parameters in real time, comprehensively capturing battery characteristic data under different temperature-rate-SOC combinations. For example, data related to battery cycle stability and thermal runaway risk at high temperatures (50°C), high rates (2C), and high SOC (80%) can be studied. Real-time online monitoring and data acquisition: Leveraging a battery management system and customized data acquisition equipment, voltage, current, temperature, SOC, and other data are collected in real time during actual battery application scenarios. Data is transmitted to a host computer via the CAN bus and wireless communications, accumulating battery data under different operating conditions and environmental conditions over time for analysis of battery state changes during actual use.

[0062] Using a coupled hyperbolic-parabolic partial differential system, this system is a universal system, and its mathematical model can be described as follows:

[0063]

[0064] Where v(x, t) represents a parabolic partial differential system, u(x, t) represents a hyperbolic partial differential system, ∈ and λ are coupling constants, and ∈, λ>0, and the function q(x, y) represents the coupling kernel.

[0065] The evolution of the coupled partial differential system is as follows. At x = 1, a control input U(t) acts on the equation u(x, t). Then, at the boundary x = 0, u(x, t) combines with the unstable diffusion equation v(x, t). The internal state v(x, t) of the diffusion equation is coupled to the equation u(x, t) through the kernel function q(x, y).

[0066] Considering the hyperbolic-parabolic partial differential system and its corresponding initial and boundary conditions, the following boundary controller is designed:

[0067]

[0068] in and is the solution of the coupled hyperbolic-parabolic partial differential system. Based on the existing solution method, we can obtain:

[0069]

[0070] Where F(x) is a step function, is a solution to a Goursat-type problem and satisfies the following conditions:

[0071]

[0072] This article applies the above general model specifically to the reaction process of lithium batteries, aiming to comprehensively describe key physical and chemical processes such as the transport behavior of lithium ions inside the lithium battery and the electrochemical reactions on the electrode surface, and to characterize the dynamic characteristics of the lithium battery during the charging and discharging process through a set of interrelated equations.

[0073] Combining the theoretical basis of the above research with the internal reaction process of lithium batteries, the mathematical model of lithium batteries based on the coupled hyperbolic-parabolic partial differential system is as follows:

[0074]

[0075] in represents the rate of change of lithium-ion concentration c over time t. From a physical perspective, it reflects the increase or decrease in lithium-ion concentration per unit time at any location within the lithium-ion battery, directly reflecting the dynamic changes in the entire system. During charging, as lithium ions are released from the positive electrode and migrate to the negative electrode, the lithium-ion concentration at the corresponding location changes, and this term tracks this concentration change over time.

[0076] The classic Fick diffusion law describes the diffusion of lithium ions driven by a concentration gradient. D is the diffusion coefficient of lithium ions in a specific medium (electrode material or electrolyte), and its magnitude depends on factors such as the material's microstructure and temperature. is the second-order partial derivative of the lithium-ion concentration c with respect to the spatial position x, which characterizes the spatial unevenness of the concentration and the curvature of the change. When the second-order derivative of the concentration in a certain area is not zero, it means that there is a concentration gradient in that area, and lithium ions will diffuse from the high-concentration area to the low-concentration area to tend to a uniform distribution. The influence of electrochemical reaction on the electrode surface on lithium ion concentration is considered.

[0077] F is Faraday's constant, and j represents the charge carried by each mole of electrons, which serves to relate current density to the amount of substance. is the reaction current density of the negative electrode; is the reaction current density of the positive electrode, k in the formula n is the negative electrode reaction rate constant, k p is the negative electrode reaction rate constant, is the overpotential of the electrode, is the equilibrium potential of the electrode. The difference between the two reflects the net flux of lithium ions due to electrochemical reactions at the electrode-electrolyte interface. During charging, electrochemical reactions at the positive electrode cause lithium ions to escape from the positive electrode and enter the electrolyte, while reactions at the negative electrode cause lithium ions to embed into the negative electrode. This imbalance in electrode reactions causes lithium ions to redistribute throughout the battery system, affecting the lithium ion concentration at various locations. This term quantifies this effect.

[0078] Numerical solution of the model:

[0079] Given the high complexity of the mathematical model for the coupled hyperbolic-parabolic partial differential system, finding an analytical solution is extremely challenging. Therefore, a numerical solution becomes the inevitable choice. Among the many numerical methods available, this paper chooses the finite difference method to solve the model. This method discretizes continuous space and time, transforming the partial differential equation into a system of algebraic equations, which can then be solved using an iterative algorithm.

[0080] In the time dimension Discretize using the pre-difference format:

[0081]

[0082] in Indicates that at the nth time step, node x i is the lithium ion concentration at , and Δt is the time step.

[0083] In the spatial dimension, the lithium battery is divided into N grid nodes with equal spacing along its length, and the position of each node is recorded as x i , where i = 0, 1, 2, ..., N, and the grid spacing is Here L represents the length of the lithium battery. For the key variables in the model: lithium ion concentration c(x,t) and electrode potential φ(x,t), discrete values ​​are taken at these grid nodes, that is, Indicates that at the nth time step, the lithium x at the node i ion concentration, represents the electrode potential at the corresponding node and time.

[0084] Second-order spatial partial derivative with respect to lithium ion concentration The discretization of is carried out using the central difference format, and its discrete expression is:

[0085]

[0086] This central difference format has second-order accuracy and can more accurately approximate the true second-order derivative, reducing discretization errors. Through a similar discretization method, all terms involving spatial partial derivatives in the model are converted into algebraic combinations of node values, and the discretized lithium ion concentration equation is obtained:

[0087]

[0088] After completing the spatial and temporal discretization, the boundary conditions need to be properly handled. For the lithium battery model, the boundary conditions are:

[0089]

[0090] Special treatment is also required in the discretization process. At the negative boundary x = 0, the virtual node method is used for processing. A virtual node x is introduced. -1 , according to the central difference format, we have:

[0091]

[0092] According to the boundary conditions, we can get:

[0093]

[0094] In this way, during actual calculations, the value of this virtual node can be substituted into the discrete equation to ensure that the boundary conditions are accurately met.

[0095] Similarly, at the positive boundary x = L, a virtual node x is introduced. N+1 , through similar derivation, the formula for the change of lithium ion concentration can be obtained:

[0096]

[0097] To further improve the accuracy of remaining capacity estimation, this paper introduces a real-time monitoring and correction mechanism. During actual battery operation, sensors installed on the battery's exterior collect real-time data on battery voltage, current, temperature, and other parameters, and feed this data back into the model.

[0098] The initial parameters of the model are adjusted in real time using measured data. Temperature has a significant impact on the performance of lithium batteries. When the temperature rises, the diffusion coefficient of lithium ions generally increases, and the reaction rate constant may also change. Based on the real-time temperature value collected by the temperature sensor, the model parameters such as the lithium ion diffusion coefficient and reaction rate constant are corrected using a pre-established temperature-parameter relationship model. The relationship between the lithium ion diffusion coefficient D and temperature T can be approximately described by the Arrhenius formula:

[0099]

[0100] Where D0 is the pre-exponential factor, E is the activation energy, and R is the gas constant. In practical applications, the values ​​of D0 and E can be obtained by fitting the experimental data, and then the corrected diffusion coefficient D can be calculated based on the real-time temperature T. n and the cathode reaction rate constant k p ), the functional relationship with temperature can also be established:

[0101]

[0102] Among them, k0 is the pre-exponential factor, E k is the activation energy of the reaction rate constant. After these parameters are determined through experimental fitting, the reaction rate constant can be corrected according to the real-time temperature.

[0103] Capacity estimation based on model simulation:

[0104] The core of this method is to use the model to accurately simulate the physical and chemical processes within the lithium battery to estimate the remaining capacity. First, a coupled hyperbolic-parabolic partial differential system model is solved numerically to obtain the distribution of lithium ion concentration at various locations within the battery over time under given charge and discharge conditions, as well as the dynamic evolution of the electrode potential. This process involves multiple complex steps:

[0105] The model is discretized using the finite difference method. In terms of spatial dimension, the lithium battery is abstracted into a one-dimensional model and divided into N grid nodes along its main lithium ion transmission direction (usually assumed to be the length direction of the battery), which is equidistant. i , where i = 0, 1, 2, ..., N, the grid spacing Here L represents the length of the lithium battery. For the key variables in the model, lithium ion concentration c(x,t) and electrode potential φ(x,t), they are all discretely valued at these grid nodes, that is, Indicates that at the nth time step, node x i The lithium ion concentration at Indicates the electrode potential at the corresponding node and time. In the time dimension, select an appropriate time advancement format, such as the explicit Euler format, to discretize the lithium ion concentration change formula. In the explicit Euler format, the equation Can be organized as:

[0106]

[0107] Compare the estimated remaining capacity calculated based on the above formula with the preliminary estimate obtained by a simple method such as the ampere-hour integration method (estimating the remaining capacity based on the integration of real-time current over time). If the difference between the two exceeds the set threshold, it means that there may be errors in the model or the battery performance has fluctuated. In this case, the model needs to be recalibrated. Let the set threshold be ΔQ and the remaining capacity calculated based on the model be Q remain (t), the remaining capacity estimated by the ampere-hour integration method is Q ah (t), then the judgment condition is:

[0108] |Q remain (t)-Q ah (t)|>ΔQ

[0109] When this condition is met, start the calibration procedure, adjust the relevant parameters and recalculate until the following conditions are met:

[0110] |Q remain (t)-Q ah (t)|≤ΔQ

[0111] Finally, the remaining capacity Q that meets the conditions is output remain (t) is the remaining capacity of the model.

[0112] In summary, the present invention is based on a method for estimating the remaining capacity of a lithium battery using a coupled hyperbolic-parabolic partial differential system. Based on the internal reaction process of the lithium battery, a mathematical model of the coupled hyperbolic-parabolic partial differential system is proposed. The model accurately simulates the internal physical and chemical processes of the lithium battery to estimate the remaining capacity, with high calculation accuracy and real-time performance.

[0113] The above description is intended to serve as a guide for the preferred embodiments of the present invention. Based on the above description, relevant personnel are fully capable of making various changes and modifications without departing from the technical scope of the present invention. The technical scope of the present invention is not limited to the contents of the specification and must be determined according to the scope of the claims.

Claims

1. A method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system, characterized in that: The following steps are involved: S1. Based on experimentally measured lithium battery parameter data, a mathematical model of lithium batteries based on a coupled hyperbolic-parabolic partial differential system is established to describe the electrolyte ion conduction mechanism and thus simulate the lithium ion insertion and deinsertion process; S2. Use the finite difference method to solve the mathematical model of the lithium battery and obtain the formula for the change of lithium ion concentration; S3. Calculate the estimated remaining capacity of the lithium battery based on the lithium ion concentration change formula obtained in S2; S4. Compare the remaining capacity estimate obtained in S3 with the preliminary estimate. If the difference between the two exceeds a preset threshold, return to step S3, start the calibration program, adjust the relevant parameters and recalculate until the difference between the two does not exceed the threshold. Output the current remaining capacity estimate as the remaining capacity of the lithium battery.

2. The method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system according to claim 1, wherein: The mathematical model of the lithium battery based on the coupled hyperbolic-parabolic partial differential system in step S1 is as follows: Among them: It represents the rate of change of lithium ion concentration c with time t; Based on the classic Fick diffusion law, it describes the diffusion of lithium ions driven by concentration gradient; D is the diffusion coefficient of lithium ions in a specific medium; is the second-order partial derivative of the lithium ion concentration c with respect to the spatial position x; The effect of the electrochemical reaction on the electrode surface on the lithium ion concentration is taken into account; F is the Faraday constant; j represents the amount of charge carried by each mole of electrons; is the reaction current density of the negative electrode; is the reaction current density of the positive electrode.

3. The method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system according to claim 2, wherein: The process of solving the lithium battery mathematical model using the finite difference method in step S2 is as follows: In the time dimension Discretize using the forward difference format: in Indicates that at the nth time step, node x i The lithium ion concentration at , Δt is the time step; In the spatial dimension, the lithium battery is divided into N grid nodes with equal spacing along its length, and the position of each node is recorded as x i , where i = 0, 1, 2, ..., N, and the grid spacing is Here L represents the length of the lithium battery. For the key variables in the model: lithium ion concentration c(x, t) and electrode potential φ(x, t), discrete values ​​are taken at these grid nodes, that is, Indicates that at the nth time step, the lithium x at the node i ion concentration, represents the electrode potential at the corresponding node and time; Second-order spatial partial derivative with respect to lithium ion concentration The discretization of is carried out using the central difference format, and its discrete expression is: Convert all terms involving spatial partial derivatives in the model into algebraic combinations of node values ​​to obtain the discretized lithium ion concentration equation: For the lithium battery model, the boundary conditions are: Special treatment is also required in the discretization process. At the negative boundary x=0, the virtual node method is used to introduce a virtual node x -1 , according to the central difference format, we have: According to the boundary conditions, we can get: Substitute the value of this virtual node into the discrete equation to ensure that the boundary conditions are accurately met; At the positive electrode boundary x=L, a virtual node x is introduced. N+1 , the formula for the change of lithium ion concentration can be obtained:

4. The method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system according to claim 2, wherein: In step S3, the model parameters are corrected according to the real-time temperature of the lithium battery using the pre-established temperature and parameter relationship model; The relationship between the lithium ion diffusion coefficient D and temperature T can be approximately described by the Arrhenius formula: Where D0 is the pre-exponential factor, E is the activation energy, and R is the gas constant; For the reaction rate constant k, establish a functional relationship with temperature: Among them, k0 is the pre-exponential factor, E k is the activation energy of the reaction rate constant.

5. The method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system according to claim 4, wherein: In step S3, the measured data is collected by the sensor installed on the lithium battery, and the measured data is fed back into the mathematical model of the lithium battery.

6. The method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system according to claim 2, wherein: In step S3, the remaining capacity is estimated by using the accurate simulation results of the physical and chemical processes inside the lithium battery using the lithium battery mathematical model.

7. The method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system according to claim 6, wherein: In step S3, a coupled hyperbolic-parabolic partial differential system model is solved by a numerical method to obtain the distribution of lithium ion concentration at various locations inside the battery over time under given charge and discharge conditions, as well as the dynamic evolution of the electrode potential; The model is discretized using the finite difference method: In the spatial dimension, the lithium battery is abstracted into a one-dimensional model and divided into equal intervals along its main lithium ion transmission direction to obtain N grid nodes, which are denoted as x i , where i = 0, 1, 2, ..., N, the grid spacing Here L represents the length of the lithium battery; the key variables in the model, lithium ion concentration c(x, t) and electrode potential φ(x, t), are all discretely valued at these grid nodes, that is, Indicates that at the nth time step, node x i The lithium ion concentration at represents the electrode potential at the corresponding node and time; In the time dimension, the appropriate time advancement format is selected to discretize the lithium ion concentration change formula. Under the explicit Euler format, the equation Can be organized as:

8. The method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system according to claim 7, wherein: In step S4, the threshold is set to ΔQ, and the estimated remaining capacity is Q remain (t), the preliminary estimate is Q ah (t), then the judgment condition is: |Q remain (t)-Q ah (t)|>ΔQ When this condition is met, start the calibration procedure, adjust the relevant parameters and recalculate until the following conditions are met: |Q remain (t)-Q ah (t)|≤ΔQ Finally, the remaining capacity Q that meets the conditions is output remain (t) is the remaining capacity of the lithium battery.

9. The method for estimating the remaining capacity of a lithium battery based on a coupled hyperbolic-parabolic partial differential system according to claim 8, wherein: In step S4, a preliminary estimated value is obtained by the ampere-hour integration method.

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