A method and system for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect.

Abstract

This invention provides a method and system for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect, comprising: designing a calendar aging experiment to obtain capacity decay data under different storage temperatures and states of charge; constructing an electrochemical-quantum tunneling coupled model, including an electrochemical state acquisition module and a quantum tunneling side reaction module, wherein the electrochemical state acquisition module is constructed based on Fick's law, charge conservation relation, and Butler-Wolmer equation, and is used to output the negative electrode stoichiometry and negative electrode potential; the quantum tunneling side reaction module calculates the tunneling side reaction current of electrons passing through the inner layer of the solid electrolyte interface film on the negative electrode surface through the quantum tunneling mechanism based on the negative electrode potential; establishing a bidirectional coupling feedback mechanism between the two modules, so that the tunneling current depends on the state variables output by the electrochemical model; obtaining model parameters based on experimental data and a heuristic parameter identification algorithm; inputting the target storage conditions, and iteratively outputting the battery capacity decay prediction results.

Description

Technical Field

[0001] This invention relates to the field of calendar aging prediction and health status assessment of batteries for electric vehicles and energy storage systems, and more specifically, to a method and system for predicting the calendar aging of lithium-ion batteries that takes into account the quantum tunneling effect. Background Technology

[0002] During long-term use, lithium-ion batteries undergo various internal side reactions, leading to a gradual decline in performance, decreased capacity, increased internal resistance, and ultimately, compromised system safety. In the actual operation of electric vehicles, the time spent parked is typically much longer than the time spent driving. During this period of static storage, batteries also experience capacity decay, a process known as calendar aging. The primary mechanism of calendar aging is the continuous growth of the solid electrolyte interphase (SEI) film on the negative electrode surface. This process consumes recyclable lithium ions within the battery, resulting in irreversible capacity loss. The calendar aging rate can vary by several times under different storage states of charge and temperatures. Therefore, accurately predicting calendar aging behavior under different storage conditions using models is crucial for optimizing battery management strategies, reducing maintenance costs, and ensuring application safety.

[0003] Methods for predicting the calendar aging of lithium-ion batteries mainly include data-driven methods and model-based methods. Data-driven methods rely on large amounts of long-term stored experimental data, establishing a mapping relationship between capacity decay and storage time, temperature, and state of charge (SOC) through statistical analysis or machine learning. However, they lack explanations of physical mechanisms, and their applicability is limited by the coverage of training data. Model-based methods can be categorized into empirical models, equivalent circuit models, and electrochemical models based on the models used. Among these, empirical models and equivalent circuit models have simple structures but poor physical interpretability. Electrochemical models, starting from the internal reaction mechanism of the battery, construct partial differential equations based on the conservation of mass and charge, which can better capture the internal electrochemical behavior of the battery and have high physical interpretability.

[0004] Currently, in calendar aging modeling based on electrochemical models, the growth of the anode SEI film is usually described using traditional side reaction kinetics or empirical film growth expressions, such as Tafel-type side reaction equations, Butler-Volmer-type negative reaction equations, and empirical film growth equations, which are collectively referred to as "traditional SEI growth description methods" below. Although the traditional Tafel / Butler-Volmer-type side reaction expression has an electrochemical kinetic basis, its description of SEI growth is usually based on the interfacial reaction rate or side reaction overpotential, without showing the microscopic transport process of electrons crossing the SEI inner layer barrier; empirical / semi-empirical film growth expressions further lack physical mechanism support. Both approaches share the following shortcomings: First, they fail to describe the driving force of SEI growth from the microscopic transport level of electrons crossing the inner SEI layer, limiting their ability to physically explain the differences in aging rates under different storage SOCs; Second, the energy barrier or reaction kinetic parameters in the models are usually set as constants, failing to establish an explicit correlation with the negative electrode potential, making it difficult to accurately reflect the impact of changes in battery state of charge on calendar aging; Third, some multiphysics coupling models introduce too many physical fields and decay mechanisms in pursuit of mechanistic completeness, resulting in a large number of parameters and extremely high computational complexity, making them difficult to deploy and apply in engineering systems.

[0005] In summary, existing technologies have not yet effectively balanced the needs for model mechanism depth, SOC-dependent explanation capabilities, and engineering feasibility. If, while preserving the electrochemical model framework, a description of SEI growth based on the microscopic transport mechanism of electrons crossing the inner SEI barrier can be introduced, it is hoped that the accuracy and physical interpretability of calendar aging predictions can be improved while controlling model complexity.

[0006] In existing calendar aging electrochemical models, the growth of the negative electrode SEI film generally adopts the traditional SEI growth description method (such as Tafel-type side reaction equation, Butler-Volmer-type side reaction equation, empirical film growth equation, etc.), without modeling from the microscopic transport level of electrons crossing the inner layer barrier of the SEI, thus having limited physical explanation ability for the differences in calendar aging rate under different storage SOC conditions.

[0007] In traditional SEI side reaction models, the potential barrier or reaction rate parameters are usually set as constants, without establishing a dynamic relationship with the negative electrode potential, and thus cannot explicitly reflect the modulation effect of battery state of charge changes on the SEI growth rate.

[0008] Some models introduce too much physical field coupling in pursuit of complete mechanism, resulting in a large number of parameters and high solution complexity, making them difficult to deploy in practical battery management systems.

[0009] Existing methods mostly focus on cyclic aging prediction, and lack a systematic engineering method chain for calendar aging scenarios, from "electrochemical state acquisition - aging rate calculation - parameter identification - lifetime prediction".

[0010] In the multiphysics coupled calendar aging model disclosed in patent application CN118211431A, the SEI growth current density adopts a diffusion-reaction joint control form, and its interface reaction term is based on Tafel kinetics (…). In this expression, the reaction rate is driven by the difference between the anode potential and the SEI equilibrium potential, but it does not establish a direct physical connection with the negative electrode potential at the level of microscopic transport of electrons across the inner potential barrier of the SEI. It lacks a causal link where potential changes modulate the barrier height and tunneling probability by altering the Fermi level. Furthermore, this model simultaneously introduces a creeping flow module and a solid mechanics module, resulting in a large number of parameters and high solution complexity, further limiting its feasibility for deployment in engineered battery management systems. Summary of the Invention

[0011] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for predicting the calendar aging of lithium-ion batteries that takes into account the quantum tunneling effect.

[0012] The lithium-ion battery calendar aging prediction method considering quantum tunneling effect provided by the present invention includes: Step 1: Design a calendar aging experiment. The calendar aging experiment includes a performance reference experiment on a fresh battery to obtain the basic electrochemical parameters of the battery, and a calendar aging matrix experiment with different temperatures and different storage states of charge to obtain capacity decay data over storage time. Step 2: Construct an electrochemical-quantum tunneling coupling model, which includes an electrochemical state acquisition module and a quantum tunneling side reaction module. The electrochemical state acquisition module is used to output the negative electrode stoichiometry and negative electrode potential. The quantum tunneling side reaction module calculates the tunneling side reaction current of electrons passing through the inner layer of the solid electrolyte interphase (SEI) membrane on the negative electrode surface based on the negative electrode potential through the quantum tunneling mechanism. Step 3: Establish a bidirectional coupling feedback mechanism between the quantum tunneling side reaction module and the electrochemical state acquisition module: In the positive coupling direction, the negative electrode stoichiometry and negative electrode potential output in real time by the electrochemical state acquisition module are used as inputs to the quantum tunneling side reaction module. The negative electrode stoichiometry is used to modulate the electron supply density, and the negative electrode potential is used to modulate the tunneling barrier height through the Fermi level; In the negative feedback direction, the growth amount of the SEI film is calculated based on the tunneling side reaction current. The growth amount of the SEI film causes at least one of the following physical quantities to be updated: increased film thickness, increased film resistance, loss of active lithium, and decreased negative electrode porosity. The updated film parameters and / or transport parameters are fed back to the electrochemical state acquisition module, forming a physically self-consistent closed-loop coupling. Step 4: Based on experimental data and heuristic parameter identification algorithms, obtain the model parameters of the electrochemical-quantum tunneling coupling model; Step 5: Based on the electrochemical-quantum tunneling coupling model, input the target storage conditions and perform open-loop iterative simulation. Within each time step, sequentially execute electrochemical state acquisition, tunneling side reaction current calculation, SEI growth and feedback update, and temperature correction, and gradually output the battery capacity decay curve with storage time. When the battery capacity decays to the specified health state threshold, record the corresponding storage time, which is the calendar lifetime prediction value.

[0013] Preferably, the quantum tunneling secondary reaction module calculates the Fermi level of the negative electrode material based on the negative electrode potential, as expressed by:

[0014] in, The Fermi level of the negative electrode material. This represents the Fermi level in the fully lithium-intercalated state, where e is the electron charge. The negative electrode potential is output in real time by the electrochemical state acquisition module; The voltage-dependent tunneling barrier attenuation coefficient is calculated based on the Fermi level, and the expression is as follows:

[0015] Where α(t) is the barrier decay coefficient, and U is the electronic energy level in the inner shell of the SEI. Here, m is the reduced Planck constant, and m is the electron mass. The electron tunneling probability is calculated based on the barrier attenuation coefficient, and the expression is as follows:

[0016] Where P(t) is the electron tunneling probability, As the pre-factor, The current thickness of the SEI inner layer. It is an exponential function; The tunneling side reaction current of SEI growth is calculated based on the electron tunneling probability, and the calculation formula is as follows:

[0017] in, For tunneling side reaction current, This term characterizes the effect of the degree of lithium intercalation in the negative electrode on the modulation of the density of electrons participating in tunneling. Where F is the negative electrode stoichiometric coefficient and F is the Faraday constant. For carbon density, The molar mass of carbon. Frequency for electron tunneling attempts; The tunneling secondary reaction current is used as the SEI growth current, replacing the traditional SEI growth description method, and coupled to the negative electrode interface current balance or state update equation.

[0018] Preferably, the complete expression for the prefactor is:

[0019] in, For the simplified wave vector parameters, Use the reference energy barrier constant; in scenarios with low parameter sensitivity, Simplify and treat it as a constant.

[0020] Preferably, the identification and dynamic updating of the negative electrode state quantity is achieved through the following state identification link: After disassembling a fresh battery, assemble positive and negative coin cells. Obtain the negative electrode OCP curve by low-rate charge-discharge test and establish a mapping benchmark from stoichiometry to potential. Based on the pseudo open-circuit voltage test of the fresh battery full cell, identify the initial positive and negative electrode stoichiometry boundaries. In the calendar aging matrix experiment, after each capacity calibration test, the battery is subjected to a pseudo open circuit voltage test to obtain the full battery pseudo open circuit voltage curve under the current aging state. The pseudo-open circuit voltage curve of the current aging state is fitted with the OCP curve of the positive and negative electrode half-cell to identify the current stoichiometric boundary of the positive and negative electrodes. The offset of the stoichiometric boundary reflects the degree of loss of active lithium and active material. In the zero-current static calendar aging scenario, the negative electrode potential is directly obtained from the OCP curve table; when covering mixed operating conditions, the negative electrode potential is output in real time by the reduced-order electrochemical model.

[0021] Preferably, the growth amount of the SEI film is calculated based on the tunneling side reaction current, and the growth rate of the SEI inner layer thickness is... The following equation gives the explicit meaning:

[0022] in, This refers to the thickness of the SEI inner layer, where t is the unit of time. The molar mass of the SEI product is... The density of the SEI product is given by factor 2, which reflects the stoichiometric relationship of two moles of electrons transferred for every mole of lithium ions consumed in the SEI formation reaction; the corresponding cumulative thickness is... ,in, The initial inner SEI thickness, It is the integral of the SEI inner layer thickness growth rate from the initial time 0 to the current time t, representing the total amount of newly generated SEI inner layer thickness since the start of aging. It is an integral variable; the increase in the thickness of the inner SEI layer leads to an exponential decay in the tunneling probability, giving the electrochemical-quantum tunneling coupling model an intrinsic self-limiting characteristic.

[0023] Preferably, the temperature dependence of the model parameters is described by the Arrhenius equation, and the method for correcting the temperature for the quantum tunneling current is as follows: calculate the tunneling current at a reference temperature. Then, the value is corrected to the actual temperature using the Arrhenius factor:

[0024] in, R is the activation energy for the SEI growth reaction, and R is the gas constant. T(t) is the reference temperature, and T(t) is the actual temperature.

[0025] Preferably, the acquisition of model parameters based on experimental data and heuristic parameter identification algorithms specifically includes: After disassembling the fresh battery, assemble the positive and negative electrode coin cells to obtain the open circuit potential curves of the positive and negative electrodes; use scanning electron microscopy to measure the particle radius of the positive and negative electrode materials; measure the physical parameters of electrode thickness, area, and volume fraction of active material. Heuristic algorithms are applied to identify key parameters in the electrochemical model. Current, voltage, and temperature data obtained from performance tests under fresh conditions are used as inputs, and voltage error is used as the optimization target to obtain electrochemical sub-model parameters. The key parameters include solid-phase diffusion coefficient, reaction kinetic parameters, and liquid-phase diffusion coefficient. Using the calendar aging capacity decay curves under different storage SOC and temperature conditions as the objective function, a heuristic optimization algorithm is used to jointly identify the key parameters of the quantum tunneling side reaction module, including the fully lithium-intercalated Fermi level, the electronic energy level in the inner SEI layer, the initial inner SEI thickness, the effective tunneling area, and the activation energy of the SEI growth reaction.

[0026] Preferably, the reverse feedback direction also causes a decrease in the negative electrode porosity, and the rate of change is:

[0027] in, The negative porosity, The negative electrode porosity isolation factor. The cumulative SEI film thickness is represented by t, which is a unit of time. The updated negative electrode porosity is fed back to the electrochemical state acquisition module, affecting the equivalent liquid phase transport parameters.

[0028] Preferably, the anode transfer coefficient and the cathode transfer coefficient are respectively denoted as... and In the electrochemical state acquisition module, the coupling relationship between overpotential and the lithium-ion concentration on the solid surface and the lithium-ion concentration in the liquid phase is described by the Butler-Wolmer equation:

[0029]

[0030] in, Let x be the lithium-ion current density at the current position x and time t. Let F be the exchange current density, η be the interfacial overpotential, R be the gas constant, T be the temperature, and k be the reaction rate kinetic constant. This represents the lithium-ion concentration on the surface of the active material particles. This refers to the lithium-ion concentration in the liquid electrolyte. This represents the maximum lithium-ion concentration of the active material particles.

[0031] The lithium-ion battery calendar aging prediction system considering quantum tunneling effect provided by the present invention includes: The electrochemical state acquisition module is used to output the negative electrode stoichiometry and negative electrode potential; The quantum tunneling side reaction calculation module has its input end connected to the output end of the electrochemical state acquisition module. It is used to receive the negative electrode stoichiometry and the negative electrode potential, and calculate the tunneling side reaction current of electrons passing through the inner layer of the solid electrolyte interphase (SEI) membrane on the negative electrode surface based on the negative electrode potential through the quantum tunneling mechanism. An aging state update and feedback module, whose input is connected to the output of the quantum tunneling side reaction calculation module, is used to receive the tunneling side reaction current and calculate the update amount of SEI film thickness and active lithium loss based on the tunneling side reaction current; the output of the aging state update and feedback module is connected to the input of the electrochemical state acquisition module, and is used to feed back the updated film parameters and / or transmission parameters to the electrochemical state acquisition module to correct the state quantity output by the electrochemical state acquisition module; The prediction output module is used to iteratively call the electrochemical state acquisition module, the quantum tunneling side reaction calculation module, and the aging state update and feedback module to gradually output the battery capacity decay prediction results within the target storage period.

[0032] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention uses quantum tunneling mechanism to replace the traditional SEI growth description method within the framework of electrochemical model to model SEI film growth. It establishes an explicit dependence of SEI growth rate on negative electrode potential from the microscopic transport level of electrons crossing the SEI inner layer barrier, which helps to explain the difference in calendar aging rate under different storage SOCs. (2) In the specific implementation, the tunneling barrier parameter is calculated in relation to the negative electrode potential, so that the model can distinguish the aging rate difference under different storage charge states. Compared with the fixed SOC processing method in the existing tunneling aging model, the model has a wider range of applicable working conditions. (3) The present invention establishes a two-way coupling feedback mechanism between the quantum tunneling side reaction module and the electrochemical state acquisition module: the calculation of the tunneling current depends on the stoichiometry and potential output by the electrochemical model, and the SEI thickening caused by tunneling in turn corrects the membrane parameters and transport parameters, forming a closed-loop coupling with strong physical self-consistency. (4) The model has an inherent self-limiting characteristic. The thickening of the SEI naturally leads to an exponential decrease in the tunneling probability and a slowdown in the aging rate, without the need to introduce an additional empirical decay factor. (5) This invention establishes a complete state identification link from “fresh battery OCP calibration - pseudo open circuit voltage tracking test during calendar aging - stoichiometric number identification and update - negative electrode potential real-time output”, so that the quantum tunneling side reaction module can obtain reliable input state quantities throughout the aging process, ensuring the engineering operability of the prediction method; (6) Compared with the calendar aging model that introduces strong coupling of multiple physics fields, this invention retains the ability of the electrochemical model framework to estimate the internal state variables of the battery without significantly increasing the complexity, thus taking into account both the depth of mechanism and engineering feasibility. Attached Figure Description

[0033] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 A flowchart of the overall process for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect; Figure 2 This is a diagram showing the bidirectional coupling data flow of the electrochemical-quantum tunneling coupling model. Figure 3 This is a schematic diagram of the microscopic energy bands for electron tunneling at the negative electrode-SEI inner layer interface. Detailed Implementation

[0034] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0035] Example 1 This invention provides a method for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect, including: aging experiment design, electrochemical-quantum tunneling coupling model construction, model parameter determination, and calendar aging prediction.

[0036] The first step is to design a calendar aging experiment. In this invention, the battery needs to undergo a performance reference experiment in its fresh state to obtain the battery's basic electrochemical parameters. The battery performance reference experiment includes a pseudo open-circuit voltage test, a mixed pulse power test, and charge-discharge tests at different rates. In addition, after disassembling the fresh battery, coin cells with positive and negative electrodes are assembled to obtain the open-circuit potential curves (OCP curves) of the positive and negative electrodes; physical parameters such as electrode thickness, area, and active material volume fraction are measured; and the particle radius of the positive and negative electrode materials is measured using scanning electron microscopy and other methods.

[0037] Design a calendar aging matrix experiment with different temperatures and storage SOCs. After charging or discharging the batteries to the specified SOC level, store them under constant temperature conditions. Perform capacity calibration tests periodically to obtain data on capacity changes over storage time. Perform pseudo-open-circuit voltage tests periodically to obtain changes in the pseudo-open-circuit voltage curve during aging, which is used to identify parameters such as electrochemical stoichiometry after aging.

[0038] The second step is to construct an electrochemical-quantum tunneling coupling model. In this model, quantitative mathematical relationships are built based on the following fundamental physicochemical processes. This invention uses an electrochemical state acquisition module to obtain the negative electrode stoichiometry and negative electrode potential. This module can be implemented using a reduced-order electrochemical model; in a typical calendar aging scenario (zero-current static storage), it can be further simplified to an OCP lookup table and Coulomb conservation update scheme. The general scheme of the reduced-order electrochemical model is described first, followed by the quantum tunneling mechanism.

[0039] Based on Fick's law, charge conservation, and the Butler-Volmer equation, a sub-model is constructed to calculate the internal voltage components and terminal voltage of the battery.

[0040] The lithium-ion insertion / extraction and solid-phase diffusion processes are represented by Fick's second law in the radial dimension of the spherical particles of the active material:

[0041] in, ( (This refers to lithium ions at different time dimensions) (s) Spatial dimension (m) and the inner radius dimension of spherical active particles Concentration distribution on (m), ( ) is the diffusion coefficient of lithium ions in the active material.

[0042] The overpotential is coupled with the lithium-ion concentration at the solid surface and the lithium-ion concentration in the liquid phase, and the relationship is described by the Butler-Wolmer equation:

[0043]

[0044] In the formula, (V) represents the interface overpotential. The gas constant is (K) represents temperature. The reaction rate kinetic constant is ( ) represents the exchange current density. ( The concentration of lithium ions on the surface of the active material particles is denoted as . ( () represents the lithium-ion concentration in the liquid electrolyte. and These are the anodic transfer coefficient and the cathodic transfer coefficient, respectively.

[0045] The lithium ion concentration distribution in the electrolyte phase is described by Fick's second law:

[0046] in, This represents the integral of the electrolyzed liquid. ( ) represents the specific surface area of ​​the active material. ( () represents the equivalent liquid-phase lithium-ion diffusion coefficient. denoted as ion transport number.

[0047] Based on the boundary conditions, the original governing equations are... By integrating along the direction to obtain the liquid phase potential difference, and combining all voltage components, the terminal voltage can be calculated.

[0048] in, and These are the open-circuit potentials of the positive and negative terminals, respectively. and These are the overpotentials at the positive and negative electrodes, respectively. For the liquid phase potential difference, (Ω) represents the lumped DC impedance.

[0049] In a typical calendar aging scenario (zero-current static storage), the above reduced-order electrochemical model can be further simplified to an OCP lookup table and coulomb conservation update scheme: the concentration distribution within the particles tends to be uniform, and the stoichiometry of the negative electrode... The potential of the negative electrode is directly updated by Coulomb conservation, and the potential of the negative electrode is directly obtained from the table by looking up the OCP curve. This simplified approach significantly reduces computational load and is suitable for engineering applications involving purely static calendar aging.

[0050] On the negative electrode side, unlike traditional methods, the side reactions of SEI film growth in this invention are no longer described using traditional SEI growth methods (such as the Tafel equation), but are calculated based on the quantum tunneling mechanism. While traditional Tafel / Butler-Volmer type side reaction expressions have an electrochemical kinetic basis, their description of SEI growth is usually based on interfacial reaction rates or side reaction overpotentials, failing to explicitly characterize the microscopic transport process of electrons crossing the inner SEI barrier. This invention explicitly models this microscopic electron transport process as a core pre-construction mechanism and forms a bidirectional feedback loop with the negative electrode state variables.

[0051] The SEI film consists of a dense inner layer and a loose outer layer. The inner SEI layer is insulating to electrons, but when its thickness is on the nanometer scale, electrons can penetrate this barrier through quantum tunneling to reach the SEI / electrolyte interface, reducing solvent molecules and allowing the SEI to continue growing. The microscopic energy band diagram of this tunneling process is shown below. Figure 3 As shown.

[0052] In a specific implementation of this invention, the tunneling barrier parameter is calculated in relation to the negative electrode potential, rather than using the fixed energy barrier treatment method in existing tunneling aging models. Existing energy-based tunneling aging models (such as Li et al., Chen et al., etc.) use a fixed energy barrier. As an input parameter, this energy barrier is treated as a constant and does not change with the battery's state of charge (SOC), which is typically assumed to be a constant value (e.g., 0.5). In this invention, the Fermi level of the negative electrode material is represented as the Fermi level of the fully lithium-intercalated state. With the current negative electrode potential The difference ( ), which reduces the tunnel barrier attenuation coefficient It becomes a real-time function of the negative electrode potential:

[0053] The effect of this implementation is: negative electrode potential When the SOC increases (corresponding to low SOC), As the negative electrode potential increases, the tunneling probability decreases, and the SEI growth rate is suppressed; conversely, when the negative electrode potential decreases (corresponding to high SOC), the tunneling probability increases, and SEI growth accelerates. This potential dependence allows the model to distinguish the differences in aging rates under different storage SOC conditions.

[0054] The present invention calculates the tunneling side reaction current of SEI growth based on the following steps.

[0055] (a) Calculation of the Fermi level based on the negative electrode potential. The electrochemical state acquisition module outputs the negative electrode stoichiometric parameters in real time. and negative electrode potential Calculation of the Fermi level of the negative electrode material based on the negative electrode potential:

[0056] in, The Fermi level in the fully lithium-intercalated state. Let be the electron charge. This equation shows that the negative electrode potential dynamically changes the Fermi level with the stoichiometric coefficient, thereby modulating the tunneling barrier height.

[0057] (b) Calculate the voltage-dependent tunneling barrier parameters. Barrier attenuation coefficient. Depends on the current Fermi level (i.e., depends on the negative electrode potential):

[0058] in, These are the electronic energy levels in the inner shell of the SEI. To reduce Planck's constant, Electron mass. Negative electrode potential. When the SOC is elevated (low SOC), As the number of tunnels increases, the probability of tunneling decreases dramatically.

[0059] (c) Calculate the electron tunneling probability:

[0060] in, The current thickness of the SEI inner layer. The pre-factor is the barrier parameter. The function. This invention preserves the complete expression of the prefactor in its implementation:

[0061] in, For the simplified wave vector parameters, Use the reference energy barrier constant. In scenarios with low parameter sensitivity, It can also be simplified to constant treatment.

[0062] (d) Calculate the tunneling side reaction current of SEI growth:

[0063] in, This term characterizes the modulation effect of the degree of lithium intercalation in the negative electrode on the density of electrons participating in tunneling. This tunneling side reaction current replaces the SEI growth current in the traditional SEI growth description method and is coupled to the negative electrode interface current balance or state update equation.

[0064] This invention establishes a bidirectional coupling feedback between the quantum tunneling side reaction module and the electrochemical state acquisition module, achieving a physically self-consistent closed-loop coupling. The positive coupling direction is: the electrochemical model outputs the negative electrode stoichiometry in real time. and negative electrode potential This serves as the input to the quantum tunneling side reaction module. The stoichiometric coefficients are obtained through... The modulation electron supply density, the potential through the Fermi level Modulating the tunneling barrier height. Reverse feedback direction: Calculating SEI growth based on tunneling secondary reaction current.

[0065] SEI accumulation will cause the following physical quantity updates: SEI Inner Layer Thickness Increase: Based on the tunneling side reaction current, the growth rate of SEI inner layer thickness is explicitly given by the following equation:

[0066] in, (g / mol) represents the molar mass of the SEI product. ( ) represents the density of the SEI product. (C / mol) is the Faraday constant, and factor 2 reflects the stoichiometric relationship of two moles of electrons transferred for every mole of lithium ions consumed in the SEI formation reaction. This equation incorporates the tunneling side reaction current. This is directly related to the physical thickness increment of the SEI, forming a complete conversion chain from tunneling current to film thickness update in a bidirectional coupled feedback. The corresponding cumulative thickness is... ,in This represents the initial inner SEI thickness.

[0067] Increased membrane resistance: Increased thickness of the SEI inner layer leads to increased membrane resistance. The increased and updated membrane resistance is fed back into the electrochemical model, affecting the calculation of the negative electrode overpotential.

[0068] Active lithium loss: Lithium ions consumed during SEI growth irreversibly withdraw from the reaction, resulting in a reduction in the battery's usable capacity and a corresponding update of the stoichiometric coefficients.

[0069] The above three factors constitute the main axis of the feedback. Furthermore, when using a reduced-order electrochemical model, increasing the SEI thickness may also lead to a decrease in the negative electrode porosity. This, in turn, affects the equivalent liquid phase transport parameters and can be incorporated as an optional feedback path.

[0070] This bidirectional coupling mechanism gives the model an intrinsic self-limiting characteristic: SEI thickening → tunneling probability exponentially decreases → aging rate naturally slows down → SEI growth rate further decreases, forming a negative feedback loop.

[0071] The temperature dependence of the model parameters can be described by the Arrhenius formula:

[0072] For the affected parameter values, Reference temperature The value of the parameter under (K), (J / mol) represents the activation energy parameter, describing the degree to which the corresponding parameter is affected. In this invention, the quantum tunneling current is also subject to temperature correction. The tunneling current is calculated at a reference temperature. Then, the value is corrected to the actual temperature using the Arrhenius factor:

[0073] This design achieves a fusion of voltage-driven (quantum tunneling mechanism) and temperature-driven (thermal activation mechanism).

[0074] The third step is to obtain model parameters based on experimental data and heuristic parameter identification algorithms.

[0075] (1) Acquisition and fusion of multi-dimensional experimental data: By disassembling fresh batteries and assembling positive and negative electrode coin cells, the open-circuit potential curves of the positive and negative electrodes were obtained. Combined with the precise measurement of physical parameters such as electrode thickness, area, and volume fraction of active material, basic data were provided for the model. The particle radius of the positive and negative electrode materials was accurately measured by means of scanning electron microscopy, and the microstructural characteristics were combined with macroscopic performance testing to achieve fine calibration of model parameters.

[0076] (2) Electrochemical sub-model parameter identification: Heuristic algorithms (such as genetic algorithms and particle swarm optimization algorithms) are applied to identify key parameters (such as solid-phase diffusion coefficient, reaction kinetic parameters, liquid-phase diffusion coefficient, etc.) in the electrochemical model. Current, voltage, and temperature data obtained from performance tests under fresh conditions are used as inputs, and voltage error is used as the optimization target to obtain the electrochemical sub-model parameters.

[0077] (3) Identification of quantum tunneling aging parameters: Using the calendar aging capacity decay curves under different storage SOC and temperature conditions as the objective function, a heuristic optimization algorithm is used to jointly identify the key parameters of the quantum tunneling side reaction module, including the fully lithium-intercalated Fermi level. SEI inner electron level Initial inner SEI thickness Effective tunnel area SEI growth activation energy wait.

[0078] (4) Identification and dynamic updating of negative electrode state quantities: The quantum tunneling side reaction module of the present invention uses negative electrode stoichiometry... and negative electrode potential The reliable acquisition of these two state variables throughout the calendar aging process is crucial to the operability of the method. This invention establishes the following state identification chain: (4a) Fresh Battery OCP Benchmark Calibration: After disassembling a fresh battery, assemble the positive and negative coin cells and perform charge-discharge tests at low rates (such as C / 20 or lower) to obtain the OCP curves of the positive and negative electrodes respectively. and The OCP curve forms a baseline for mapping stoichiometry to potential. Simultaneously, based on the pseudo-open-circuit voltage test of a fresh full-cell battery, the initial stoichiometric boundaries between the positive and negative electrodes are identified. , , , .

[0079] (4b) Pseudo-open-circuit voltage tracking test during aging process: In the calendar aging matrix experiment, after each capacity calibration test, the battery is tested at a low rate to obtain the pseudo-open-circuit voltage curve of the full battery under the current aging state.

[0080] (4c) Stoichiometric Number Identification and Update: The pseudo-open-circuit voltage curve of the current aging state is fitted with the OCP curves of the positive and negative electrode half-cells to identify the current stoichiometric number boundaries of the positive and negative electrodes. The offset of the stoichiometric number boundaries reflects the degree of active lithium loss (LLI) and active material loss (LAM). The identified negative electrode stoichiometric number... Update to the value under the current aging state.

[0081] (4d) Real-time output of negative electrode potential: Under the calendar aging (zero current static) scenario, the concentration distribution within the negative electrode particles tends to be uniform, and the negative electrode potential is directly given by looking up the table from the OCP curve: When covering mixed operating conditions, The output is generated in real time by the reduced-order electrochemical model.

[0082] The above-mentioned link ensures that the quantum tunneling side reaction module can obtain experimentally corrected input state quantities throughout the aging process, making the prediction method engineering feasible rather than just theoretical calculation.

[0083] The fourth step is calendar aging prediction. Based on the constructed electrochemical-quantum tunneling coupling model, initial battery parameters and target storage conditions (storage SOC level, ambient temperature) are input, and the model performs open-loop iterative simulation: within each time step, electrochemical state acquisition, tunneling side reaction current calculation, SEI growth and feedback update, and temperature correction are executed sequentially, gradually outputting the battery capacity decay curve with storage time. When the battery capacity decays to a specified SOH threshold (e.g., 80%), the corresponding storage time is recorded as the predicted calendar lifetime value of the battery under that condition.

[0084] Overall design as Figure 1 As shown. Figure 1 The overall method flow of this invention is demonstrated, presented in four steps: First, a calendar aging experiment is designed to acquire data; second, an electrochemical-quantum tunneling coupling model is constructed, in which the electrochemical state acquisition module outputs the negative electrode stoichiometry and potential, and the quantum tunneling side reaction module calculates the SEI growth side reaction current based on these (replacing the traditional SEI growth description method), and the SEI thickening is fed back to the electrochemical state acquisition module through membrane parameters and transport parameters to form a closed loop; third, model parameters are identified based on experimental data; and fourth, storage conditions are input to predict calendar aging.

[0085] Figure 2 This demonstrates the bidirectional coupling between the electrochemical state acquisition module and the quantum tunneling side reaction module. Forward coupling: The electrochemical state acquisition module outputs stoichiometric coefficients. and electric potential These parameters drive the electron supply density and barrier height in the quantum tunneling sub-reaction module, respectively. Reverse feedback: The SEI growth output from the quantum tunneling sub-reaction module updates the film parameters, transport parameters, and related state variables. The SEI thickness simultaneously feeds back to suppress the tunneling probability, forming a self-limiting negative feedback loop.

[0086] Figure 3 This demonstrates the quantum tunneling process of electrons crossing the inner barrier of the SEI (Self-Electro-Insulator). The Fermi level of the anode material is also shown. With negative electrode potential Dynamic changes determine the effective height of the potential barrier. and attenuation coefficient High SOC (low )hour As the SOC increases, the effective height of the potential barrier decreases, the tunneling probability increases, and SEI growth accelerates; low SOC (high The opposite is true for SEI inner layer thickness. The barrier width is such that its increase leads to an exponential decrease in the tunneling probability, reflecting the self-limiting characteristic of the model.

[0087] The present invention has the following alternative: 1. Alternatives to the electrochemical state acquisition module: The main scheme obtains the negative electrode state variables through a reduced-order electrochemical model (Fick's law and Butler-Wolmer equation), which can be simplified to an OCP lookup table and Coulomb conservation scheme in typical calendar aging (zero current) scenarios. Alternative schemes include the Extended Single Event Model (ESPM), the Single Event Model (SPM), or direct input of the measured negative electrode potential.

[0088] 2. Temperature Correction Alternative: The main solution uses the Arrhenius factor to correct the tunneling current. An alternative solution is to use a thermal resistance network temperature sub-model to calculate the internal temperature field of the battery, or directly input the measured temperature value.

[0089] 3. Algorithm Algorithm Alternatives: The main solution can employ particle swarm optimization. Alternative solutions include genetic algorithms, Nelder-Mead simplex methods, or gradient descent methods.

[0090] Simplified substitution of tunneling probability pre-factor: pre-factor in the master scheme It includes a complete expression related to the barrier parameters. When parameter sensitivity is low, it can be... Simplify the process to treat it as a constant to reduce the amount of computation.

[0091] Example 2 This invention provides a method for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect, comprising the following steps: 1) Experimental Phase. Fresh batteries were disassembled and assembled into coin cells. The positive and negative electrode materials were tested, including thickness measurement, area measurement, porosity measurement, and particle radius measurement. Simultaneously, performance reference experiments were conducted on the fresh batteries, including pseudo-open circuit voltage testing, hybrid pulse power testing, and charge-discharge experiments at different rates, to obtain the changes in battery impedance with temperature and SOC. A calendar aging matrix experiment was designed: storage temperatures of 5°C, 25°C, and 45°C, and storage SOCs of 20%, 50%, 80%, and 100%. Capacity calibration and pseudo-open circuit voltage tests were performed every 30 days, with a total experimental duration of no less than 360 days.

[0092] 2) State identification link establishment. Charge and discharge tests were performed on the positive and negative coin cells at a C / 20 rate to obtain the positive electrode OCP curve. and negative electrode OCP curve Based on the C / 20 pseudo-open circuit voltage test data of a fresh full cell, the pseudo-open circuit voltage curve of the full cell is fitted by superimposing the positive and negative electrode OCP curves to identify the initial stoichiometric boundaries. , , , The pseudo-open-circuit voltage test data after each 30-day capacity calibration are used to identify and update the stoichiometric boundaries using the same method, tracking the evolution of active lithium loss and active material loss. The negative electrode potential, under static conditions, changes from... It is given directly as the real-time input to the quantum tunneling side reaction module.

[0093] 3) Model Construction Stage. Based on the experimental battery being studied, an electrochemical-quantum tunneling coupling model is constructed. In this embodiment, the electrochemical state acquisition module employs a simplified scheme of OCP lookup and coulomb conservation updates under the calendar aging (zero current resting) scenario, resulting in a more uniform concentration within the particles, with the negative electrode potential directly provided by the OCP curve. When covering mixed operating conditions, a reduced-order electrochemical model scheme can be used. The quantum tunneling side reaction module calculates the Fermi level, barrier parameters, and tunneling probability sequentially based on the negative electrode stoichiometry and potential output by the electrochemical state acquisition module, and then calculates the tunneling side reaction current of SEI growth. The thickness change caused by SEI growth leads to increased film resistance and loss of active lithium, which is fed back to the electrochemical state acquisition module, forming a closed loop.

[0094] 4) Model Parameter Calibration Stage. Based on battery performance reference experiments under fresh conditions, and combined with parameter identification algorithms such as particle swarm optimization, electrochemical sub-model parameters (solid-phase diffusion coefficient, reaction kinetic constant, liquid-phase diffusion coefficient, etc.) are obtained. Based on calendar aging capacity decay data under multiple SOC and temperature conditions, the parameters of the quantum tunneling side reaction module (Fermi level) are jointly identified. electronic energy levels Initial SEI inner layer thickness Effective area ,activation energy ).

[0095] 5) Calendar Aging Prediction Stage. Input the target storage conditions (storage SOC level, ambient temperature). Starting from the initial state of a fresh battery, the model iteratively executes the following steps at time steps: electrochemical state acquisition → tunneling side reaction current calculation → SEI growth and feedback update → temperature correction. The output is the capacity decay curve over storage time, until the specified SOH threshold is reached, and the calendar lifetime prediction value is obtained.

[0096] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0097] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A lithium-ion battery calendar aging prediction method considering quantum tunneling effect, characterized in that, include: Step 1: Design a calendar aging experiment. The calendar aging experiment includes a performance reference experiment on a fresh battery to obtain the basic electrochemical parameters of the battery, and a calendar aging matrix experiment with different temperatures and different storage states of charge to obtain capacity decay data over storage time. Step 2: Construct an electrochemical-quantum tunneling coupling model, which includes an electrochemical state acquisition module and a quantum tunneling side reaction module. The electrochemical state acquisition module is used to output the negative electrode stoichiometry and negative electrode potential. The quantum tunneling side reaction module calculates the tunneling side reaction current of electrons passing through the inner layer of the solid electrolyte interphase (SEI) membrane on the negative electrode surface based on the negative electrode potential through the quantum tunneling mechanism. Step 3: Establish a bidirectional coupling feedback mechanism between the quantum tunneling side reaction module and the electrochemical state acquisition module: In the positive coupling direction, the negative electrode stoichiometry and negative electrode potential output in real time by the electrochemical state acquisition module are used as inputs to the quantum tunneling side reaction module. The negative electrode stoichiometry is used to modulate the electron supply density, and the negative electrode potential is used to modulate the tunneling barrier height through the Fermi level; In the negative feedback direction, the growth amount of the SEI film is calculated based on the tunneling side reaction current. The growth amount of the SEI film causes at least one of the following physical quantities to be updated: increased film thickness, increased film resistance, loss of active lithium, and decreased negative electrode porosity. The updated film parameters and / or transport parameters are fed back to the electrochemical state acquisition module, forming a physically self-consistent closed-loop coupling. Step 4: Based on experimental data and heuristic parameter identification algorithms, obtain the model parameters of the electrochemical-quantum tunneling coupling model; Step 5: Based on the electrochemical-quantum tunneling coupling model, input the target storage conditions and perform open-loop iterative simulation. Within each time step, sequentially execute electrochemical state acquisition, tunneling side reaction current calculation, SEI growth and feedback update, and temperature correction, and gradually output the battery capacity decay curve with storage time. When the battery capacity decays to the specified health state threshold, record the corresponding storage time, which is the calendar lifetime prediction value.

2. The method for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect according to claim 1, characterized in that, The quantum tunneling secondary reaction module calculates the Fermi level of the negative electrode material based on the negative electrode potential, and the expression is: in, The Fermi level of the negative electrode material. This represents the Fermi level in the fully lithium-intercalated state, where e is the electron charge. The negative electrode potential is output in real time by the electrochemical state acquisition module; The voltage-dependent tunneling barrier attenuation coefficient is calculated based on the Fermi level, and the expression is as follows: Where α(t) is the barrier decay coefficient, and U is the electronic energy level in the inner shell of the SEI. Here, m is the reduced Planck constant, and m is the electron mass. The electron tunneling probability is calculated based on the barrier attenuation coefficient, and the expression is as follows: Where P(t) is the electron tunneling probability, As the pre-factor, The current thickness of the SEI inner layer. It is an exponential function; The tunneling side reaction current of SEI growth is calculated based on the electron tunneling probability, and the calculation formula is as follows: in, For tunneling side reaction current, This term characterizes the effect of the degree of lithium intercalation in the negative electrode on the modulation of the density of electrons participating in tunneling. Where F is the negative electrode stoichiometric coefficient and F is the Faraday constant. For carbon density, The molar mass of carbon. Frequency for electron tunneling attempts; The tunneling secondary reaction current is used as the SEI growth current, replacing the traditional SEI growth description method, and coupled to the negative electrode interface current balance or state update equation.

3. The method for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect according to claim 2, characterized in that, The complete expression for the prefactor is: wherein, is the simplified wave vector parameter, is the reference energy barrier constant; in the scenario where the parameter sensitivity is low, will be simplified as a constant processing. is simplified as a constant processing.

4. The lithium-ion battery calendar aging prediction method considering quantum tunneling effect according to claim 3, characterized in that, The identification and dynamic updating of the negative electrode state variables are achieved through the following state identification link: After disassembling a fresh battery, assemble positive and negative coin cells. Obtain the negative electrode OCP curve by low-rate charge-discharge test and establish a mapping benchmark from stoichiometry to potential. Based on the pseudo open-circuit voltage test of the fresh battery full cell, identify the initial positive and negative electrode stoichiometry boundaries. In the calendar aging matrix experiment, after each capacity calibration test, the battery is subjected to a pseudo open circuit voltage test to obtain the full battery pseudo open circuit voltage curve under the current aging state. The pseudo-open circuit voltage curve of the current aging state is fitted with the OCP curve of the positive and negative electrode half-cell to identify the current stoichiometric boundary of the positive and negative electrodes. The offset of the stoichiometric boundary reflects the degree of loss of active lithium and active material. In the zero-current static calendar aging scenario, the negative electrode potential is directly obtained from the OCP curve table; when covering mixed operating conditions, the negative electrode potential is output in real time by the reduced-order electrochemical model.

5. The method for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect according to claim 4, characterized in that, The amount of growth of the SEI film is calculated based on the tunneling side reaction current, and the growth rate of the inner layer thickness of the SEI is explicitly given by the equation: in, This refers to the thickness of the SEI inner layer, where t is the unit of time. The molar mass of the SEI product is... The density of the SEI product is given by factor 2, which reflects the stoichiometric relationship of two moles of electrons transferred for every mole of lithium ions consumed in the SEI formation reaction; the corresponding cumulative thickness is... ,in, The initial inner SEI thickness, It is the integral of the SEI inner layer thickness growth rate from the initial time 0 to the current time t, representing the total amount of newly generated SEI inner layer thickness since the start of aging. It is an integral variable; the increase in the thickness of the inner SEI layer leads to an exponential decay in the tunneling probability, giving the electrochemical-quantum tunneling coupling model an intrinsic self-limiting characteristic.

6. The method for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect according to claim 5, characterized in that, The temperature dependence of the model parameters is described by the Arrhenius equation, and the method for correcting the temperature for the quantum tunneling current is as follows: calculate the tunneling current at a reference temperature. Then, the value is corrected to the actual temperature using the Arrhenius factor: in, R is the activation energy for the SEI growth reaction, and R is the gas constant. T(t) is the reference temperature, and T(t) is the actual temperature. 7.The lithium-ion battery calendar aging prediction method considering quantum tunneling effect according to claim 6, wherein, The acquisition of model parameters based on experimental data and heuristic parameter identification algorithms specifically includes: After disassembling the fresh battery, assemble the positive and negative electrode coin cells to obtain the open circuit potential curves of the positive and negative electrodes; use scanning electron microscopy to measure the particle radius of the positive and negative electrode materials; measure the physical parameters of electrode thickness, area, and volume fraction of active material. Heuristic algorithms are applied to identify key parameters in the electrochemical model. Current, voltage, and temperature data obtained from performance tests under fresh conditions are used as inputs, and voltage error is used as the optimization target to obtain electrochemical sub-model parameters. The key parameters include solid-phase diffusion coefficient, reaction kinetic parameters, and liquid-phase diffusion coefficient. Using the calendar aging capacity decay curves under different storage SOC and temperature conditions as the objective function, a heuristic optimization algorithm is used to jointly identify the key parameters of the quantum tunneling side reaction module, including the fully lithium-intercalated Fermi level, the electronic energy level in the inner SEI layer, the initial inner SEI thickness, the effective tunneling area, and the activation energy of the SEI growth reaction. 8.The lithium-ion battery calendar aging prediction method considering quantum tunneling effect according to claim 1, wherein, The reverse feedback direction also causes a decrease in the negative electrode porosity, and the rate of change is: in, The negative porosity, The negative electrode porosity isolation factor. The cumulative SEI film thickness is represented by t, which is a unit of time. The updated negative electrode porosity is fed back to the electrochemical state acquisition module, affecting the equivalent liquid phase transport parameters.

9. The method for predicting the calendar aging of lithium-ion batteries considering the quantum tunneling effect according to claim 1, characterized in that, The anodic transfer coefficient and the cathode transfer coefficient are respectively denoted as... and In the electrochemical state acquisition module, the coupling relationship between overpotential and the lithium-ion concentration on the solid surface and the lithium-ion concentration in the liquid phase is described by the Butler-Wolmer equation: in, Let x be the lithium-ion current density at the current position x and time t. Let F be the exchange current density, η be the interfacial overpotential, R be the gas constant, T be the temperature, and k be the reaction rate kinetic constant. This refers to the lithium-ion concentration on the surface of the active material particles. This refers to the lithium-ion concentration in the liquid electrolyte. This represents the maximum lithium-ion concentration of the active material particles.

10. A lithium-ion battery calendar aging prediction system considering the quantum tunneling effect, characterized in that, The lithium-ion battery calendar aging prediction method considering quantum tunneling effect according to any one of claims 1 to 9 includes: The electrochemical state acquisition module is used to output the negative electrode stoichiometry and negative electrode potential; The quantum tunneling side reaction calculation module has its input end connected to the output end of the electrochemical state acquisition module. It is used to receive the negative electrode stoichiometry and the negative electrode potential, and calculate the tunneling side reaction current of electrons passing through the inner layer of the solid electrolyte interphase (SEI) membrane on the negative electrode surface based on the negative electrode potential through the quantum tunneling mechanism. An aging state update and feedback module, whose input is connected to the output of the quantum tunneling side reaction calculation module, is used to receive the tunneling side reaction current and calculate the update amount of SEI film thickness and active lithium loss based on the tunneling side reaction current; the output of the aging state update and feedback module is connected to the input of the electrochemical state acquisition module, and is used to feed back the updated film parameters and / or transmission parameters to the electrochemical state acquisition module to correct the state quantity output by the electrochemical state acquisition module; The prediction output module is used to iteratively call the electrochemical state acquisition module, the quantum tunneling side reaction calculation module, and the aging state update and feedback module to gradually output the battery capacity decay prediction results within the target storage period.

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