A lithium ion battery dendrite growth prediction and charging safety optimization method and system based on a PF-P2D model

Abstract

The application provides a lithium ion battery dendrite growth prediction and charging safety optimization method and system based on a PF-P2D model, and belongs to the technical field of battery safety. The method directly introduces an electrolyte concentration field and a potential field into a phase field model by constructing a deep coupling framework of a macroscopic pseudo two-dimensional electrochemical model and a microscopic phase field model, so that the cross-scale simulation of lithium dendrite growth, dissolution and "dead lithium" formation in the charging process is realized. A step function driven by a potential and a modified Allen-Cahn equation are introduced, and the accumulation of dead lithium and irreversible capacity loss are dynamically quantified based on a solid phase potential difference criterion. By comparing the constant current-constant voltage and pulse charging modes, it is found that the pulse charging can reduce the maximum penetration depth of dendrites by 55%, reduce the formation amount of dead lithium by 92%, and expand the state of charge safety window by 50%. The application is completely driven by a physical mechanism and does not require experimental parameter fitting, is suitable for different material systems and charging scenes, provides a clear charging termination threshold for a battery management system, and significantly improves the fast charging safety.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of battery safety technology and multi-scale computational modeling, and relates to a method and system for predicting dendrite growth and optimizing charging safety of lithium-ion batteries based on the PF-P2D model. Background Technology

[0002] The rapid expansion of the new energy vehicle market has intensified the demand for high-performance lithium-ion batteries. Lithium-ion batteries dominate electric vehicle applications due to their superior energy density, long cycle life, and extremely low self-discharge rate. To meet consumer expectations for shorter charging times, significant efforts have been invested in developing high-power charging technologies. However, under fast-charging conditions, the significant polarization effect within lithium-ion batteries can lead to uneven lithium deposition and accelerate lithium dendrite growth. These dendritic structures are particularly concerning because metallic lithium is highly reactive: repeated charge-discharge cycles promote the continuous formation and dissolution of dendrites, often resulting in the accumulation of electrically insulating "dead lithium," thereby reducing coulombic efficiency. More critically, if dendrite growth is uncontrolled, it can puncture the separator, causing internal short circuits, and in extreme cases, even thermal runaway, posing catastrophic safety hazards. Therefore, a deep understanding of lithium dendrite kinetics is crucial for developing optimized charging schemes, which helps suppress excessive dendrite formation, reduce short-circuit risks, and improve battery safety.

[0003] Lithium dendrite growth is influenced by the complex interactions of various physicochemical factors, including temperature gradients, mechanical stress, electrolyte diffusion kinetics, and interfacial overpotential. While in-situ observation techniques (such as X-ray computed tomography, electron microscopy, and magnetic resonance imaging) have provided valuable insights into dendrite dynamics, their widespread application is limited by high cost and operational complexity. To address these shortcomings, this invention proposes a method for predicting lithium-ion battery dendrite growth and optimizing charging safety based on the PF-P2D model. This method can explore morphology-performance relationships at low cost and guide the design of battery systems that suppress dendrite formation. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method and system for predicting dendrite growth and optimizing charging safety of lithium-ion batteries based on a phase-field coupled pseudo-two-dimensional (PF-P2D) model, so as to solve the technical problems in the prior art of lacking a macro-micro cross-scale coupling model, difficulty in dynamically tracking the formation of dead lithium, and inability to quantify dendrite risk under different charging strategies, and to achieve high-precision, low-cost, and physically driven dendrite behavior prediction and charging safety optimization.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for predicting dendrite growth and optimizing charging safety in lithium-ion batteries based on the PF-P2D model, the method specifically includes the following steps: S1. Construct a PF-P2D multiscale model for lithium-ion batteries, and realize the cross-scale correlation between lithium deposition behavior and battery performance during charging by coupling macroscopic electrochemical theory and microscopic morphology dynamics. S2. Introduce a potential-driven dissolution kinetics mechanism into the model. By defining a solid phase potential difference criterion, quantify the formation and accumulation of "dead lithium" during charging and achieve dynamic tracking of irreversible capacity loss. S3. Based on the model, simulate dendrite growth behavior under different charging protocols, and quantify the impact of charging rate on dendrite morphology, dead lithium ratio and safety risks. S4. Based on the simulation results, optimize the charging strategy parameters, balance charging efficiency and battery safety by suppressing dendrite penetration depth and dead lithium accumulation, and output a safe charging protocol suitable for fast charging scenarios.

[0006] Furthermore, in step S1, the specific method for coupling macroscopic electrochemical theory and microscopic morphology dynamics is as follows: the boundary of the phase field model is aligned with the key interface of the battery, and the electrolyte concentration field and potential field in the P2D pseudo-two-dimensional model are directly introduced into the phase field model to achieve synchronous simulation of macroscopic electrochemical environment and microscopic dendrite growth; based on the P2D pseudo-two-dimensional model framework that simultaneously considers the potential of solid phase and liquid phase, a dual potential field is introduced; wherein, the liquid phase potential is constructed by a decomposition method based on the Poisson equation.

[0007] Furthermore, the liquid phase potential is constructed using a decomposition method based on the Poisson equation, decomposing the total potential into two parts, specifically including: 1) Local perturbation potential caused by charge accumulation during dendrite reaction

[0008] variable It is a conserved order parameter used to characterize the distribution of lithium metal: " = 1 corresponds to solid lithium phase, " " = 0 represents liquid electrolyte, while values ​​in between (0 < ") represent liquid electrolyte. "<1) describes the diffusion interface between the solid and liquid phases; F is the total free energy of the system, It is the liquid phase potential; Effective conductivity is defined as = ,in and These represent the conductivity of the liquid electrolyte phase and the solid lithium metal phase, respectively. The expression is derived using an interpolation function. It reflects the dynamic change in conductivity during the phase transition; 2) Reference electrolyte potential inherited from the P2D pseudo-two-dimensional model The second part is governed by a passive Poisson equation since there are no other competing chemical reactions within the membrane region, and is located at the top boundary y= of the two-dimensional dendrite growth simulation domain. and bottom boundary y= Two Dirichlet boundary conditions are applied; the overall electrolyte potential is obtained by superimposing these two parts, as follows:

[0009]

[0010] in, and These represent the liquid phase potentials at the positive electrode / separator and negative electrode / separator boundaries in the pseudo-two-dimensional battery model, respectively; under the same physical considerations as the liquid phase electrochemical potential, the solid phase potential ( It satisfies a homogeneous Poisson equation and has two Dirichlet boundary conditions, as specifically expressed below:

[0011]

[0012]

[0013] Among them, parameters and , representing the solid-state potentials at the positive electrode / separator and negative electrode / separator interfaces respectively in the pseudo-two-dimensional battery model; in the above equations It is the effective conductivity of the solid-state potential, expressed as = ; Since the separator is located between the positive and negative electrodes, lithium ions can be continuously supplied from both sides. Furthermore, because the variation in lithium ion concentration within the separator is relatively small, and considering the size of the simulation domain and the limited impact of these factors on the overall concentration distribution, this invention assumes that the lithium ion concentration at the top and bottom boundaries of the simulation domain is equal and fixed as a constant. ).

[0014] Furthermore, in step S2, a potential-driven step function is introduced to determine the electrochemical isolation state of lithium dendrites based on the solid-phase potential difference: when the potential difference between the dendrite and the negative electrode interface exceeds a critical value, it is determined to be "dead lithium"; the volume fraction of dead lithium is calculated by integrating the phase field order parameter to achieve dynamic tracking of irreversible lithium loss during charging, as detailed below: A step function = )Introduced into the evolution equation of the phase field order parameter, considering the high conductivity of the lithium dendrite phase and the near-insulating properties of the electrolyte, the solid phase potential is used as the determining factor: when there is a significant potential difference between the dendrite and the bottom boundary of the solid phase potential, the region is considered as dead lithium. Based on the simulation objectives, the modified linear Allen-Cahn equation incorporates electrochemical reaction kinetics to characterize the dynamic phase transition process at the solid-liquid interface. Its governing equation is expressed as:

[0015] in, and Representing the interface mobility and reaction rate constant, respectively, the dual-potential well potential function is defined as follows: ,in This represents the height of the energy barrier between the solid and liquid phases; the anisotropic interfacial energy is determined by... Description, in which It is the gradient surface energy coefficient. It is the anisotropy intensity. It is an anisotropic mode, and The angle between the interface normal vector and the reference axis is represented; the second part of the equation uses the Butler-Volmer equation to describe the electrochemical reaction rate, thereby capturing the growth and dissolution behavior of lithium dendrites. and These represent the number of transferred electrons and the initial electrolyte concentration, respectively; to ensure the order parameter A smooth transition is achieved within the interval [0, 1] using a smooth interpolation function. In the equation, Due to the high conductivity of lithium metal and the relatively small size of the simulation domain, for the sake of computational simplicity, it is assumed that the solid-state potential of all lithium metal connected to the boundary of the negative electrode material in the simulation is equivalent to the solid-state potential of the graphite negative electrode and the separator interface in the battery model. The equilibrium potential represents the electrochemical reaction.

[0016] Furthermore, in step S3, the simulated different charging protocols include at least constant current. Constant voltage charging mode and pulse charging mode.

[0017] Furthermore, by comparing the simulation results of constant current-constant voltage charging mode and pulse charging mode, the effect of pulse charging on suppressing the maximum dendrite penetration depth and the amount of dead lithium formation through periodic deposition-dissolution cycles was evaluated.

[0018] Furthermore, in step S4, the optimized charging strategy parameters include charging current, charging voltage, and pulse charging parameters; the optimized safe charging protocol is used to provide a charging termination threshold for the battery management system in order to control the dendrite growth risk within a preset state of charge window.

[0019] The present invention also provides a lithium-ion battery dendrite growth prediction and charging safety optimization system based on the PF-P2D model, which adopts the method described above.

[0020] The beneficial effects of this invention are as follows: This invention proposes an innovative PF-P2D multi-scale modeling method. This method first constructs a multi-scale coupling framework to organically combine macroscopic electrochemical processes with microscopic lithium dendrite morphology evolution, accurately simulating the growth, dissolution, and "dead lithium" formation processes of lithium dendrites under fast charging conditions. Subsequently, a potential-driven dissolution kinetic mechanism and step function are introduced to achieve quantitative tracking of dead lithium formation and dynamic monitoring of irreversible lithium loss. This method can accurately reproduce the complete dynamic process of dendrite growth, dissolution, and dead lithium formation in a short time. Especially under 6C high-rate charging conditions, the SOC range covered by dendrite risk is reduced by 50% compared to traditional methods, significantly improving prediction accuracy. This method uses a physical mechanism to drive modeling, eliminating the need for experimental parameter fitting or trial-and-error methods to determine critical thresholds. Theoretically, it is applicable to different material systems and charging scenarios, providing a universal tool for designing high-safety fast charging protocols. This method achieves seamless integration of macroscopic and microscopic scales through a bidirectional data interaction mechanism. The model architecture is clear, flexible in use, and the prediction results are accurate and easy to integrate into the battery management system, providing a scientific basis for real-time optimization of charging strategies and extending battery life.

[0021] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0022] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a technical roadmap of the present invention; Figure 2 Flowchart for optimizing battery charging strategies; Figure 3 A comparison chart showing the simulation results and actual results of battery dendrite growth under constant current and constant voltage; Figure 4 This is a diagram showing the evolution of lithium dendrite growth rate and area during the charging process. Figure 5 A graph showing the evolution of lithium plating overpotential time at the anode-diaphragm interface under different constant current and constant voltage charging rates; Figure 6Rate-dependent kinetic characteristics of lithium deposition under constant current and constant voltage charging; Figure 7 Electrochemical and morphological evolution characteristics under pulse charging; Figure 8 The morphological evolution characteristics of lithium dendrites under pulse charging conditions; Figure 9 The graph shows the relationship between the lithium dendrite coverage area and the state of charge under constant current and constant voltage charging strategies and pulse charging strategies. Detailed Implementation

[0023] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0024] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0025] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the 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, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0026] Figure 1 The present invention provides a method for predicting dendrite growth and optimizing charging safety of lithium-ion batteries based on a phase-field coupling pseudo-two-dimensional model, comprising the following steps: Step 1: Construct a PF-P2D multiscale model for lithium-ion batteries. By coupling macroscopic electrochemical theory with microscopic morphology and dynamics, cross-scale correlation between lithium deposition behavior and battery performance during charging is achieved.

[0027] Step 2: Introduce a potential-driven dissolution kinetics mechanism into the model. By defining a solid phase potential difference criterion, quantify the formation and accumulation of "dead lithium" during charging and achieve dynamic tracking of irreversible capacity loss.

[0028] Step 3: Based on the model, simulate dendrite growth behavior under different charging protocols and quantify the impact of charging rate on dendrite morphology, dead lithium ratio and safety risks.

[0029] Step 4: Based on the simulation results, optimize the charging strategy parameters, balance charging efficiency and battery safety by suppressing dendrite penetration depth and dead lithium accumulation, and output a safe charging protocol suitable for fast charging scenarios. Figure 2 Flowchart for optimizing battery charging strategy.

[0030] In Step 1, to achieve coupling between macroscopic and microscopic models, the boundary of the phase-field model is aligned with the key interface of the battery. The electrolyte concentration and potential field from the P2D model are directly introduced into the phase-field model, enabling simultaneous simulation of the macroscopic electrochemical environment and microscopic dendrite growth. Based on the P2D framework that simultaneously considers the potentials of the solid and liquid phases, the enhanced model introduces a dual potential field.

[0031] When constructing the liquid phase potential, a decomposition method based on the Poisson equation is used to decompose the total potential into two parts: (1) Local perturbation potential caused by charge accumulation during dendrite reaction

[0032] variable It is a conserved order parameter used to characterize the distribution of lithium metal: " = 1 corresponds to solid lithium phase, " " = 0 represents liquid electrolyte, while values ​​in between (0 < ") represent liquid electrolyte. "<1) describes the diffusion interface between the solid and liquid phases. F is the total free energy of the system." It is the liquid phase potential.

[0033] Effective conductivity is defined as = ,in and These represent the conductivity of the liquid electrolyte phase and the solid lithium metal phase, respectively. The expression is derived using an interpolation function. It reflects the dynamic change in conductivity during the phase transition.

[0034] (2) Reference electrolyte potential inherited from the P2D model The second part is governed by a passive Poisson equation since there are no other competing chemical reactions within the membrane region, and is located at the top boundary y= of the two-dimensional dendrite growth simulation domain. and bottom boundary y= Two Dirichlet boundary conditions are applied. The overall electrolyte potential is obtained by superimposing these two conditions, as follows:

[0035]

[0036] in, and These represent the liquid phase potentials at the boundaries of the positive electrode / separator and negative electrode / separator in the pseudo-two-dimensional battery model, respectively. Under the same physical considerations as the liquid phase electrochemical potential, the solid phase potential ( It satisfies a homogeneous Poisson equation and has two Dirichlet boundary conditions, as specifically expressed below:

[0037]

[0038]

[0039] Among them, parameters and and represent the solid-state potentials at the positive electrode / separator and negative electrode / separator interfaces, respectively, in the pseudo-two-dimensional battery model. In the above equations, It is the effective conductivity of the solid-state potential, expressed as = 。

[0040] Since the separator is located between the positive and negative electrodes, lithium ions can be continuously supplied from both sides. Furthermore, because the variation in lithium ion concentration within the separator is relatively small, and considering the size of the simulation domain and the limited impact of these factors on the overall concentration distribution, we assume that the lithium ion concentration at the top and bottom boundaries of the simulation domain is equal and fixed as a constant. ).

[0041] In Step 2, a potential-driven step function is introduced to determine the electrochemical isolation state of lithium dendrites based on the solid-phase potential difference: when the potential difference between the dendrite and the negative electrode interface exceeds a critical value, it is determined to be "dead lithium". The volume fraction of dead lithium is calculated by integrating the phase field order parameter, realizing the dynamic tracking of irreversible lithium loss during charging, as detailed below: A step function = )This is incorporated into the evolution equation of the phase field order parameter. Considering the high conductivity of the lithium dendrite phase and the near-insulating nature of the electrolyte, the solid-state potential is used as the determining factor: when there is a significant potential difference between the dendrite and the bottom boundary of the solid-state potential, the region is considered as dead lithium.

[0042] Based on the simulation objectives, the modified linear Allen-Cahn equation incorporates electrochemical reaction kinetics to characterize the dynamic phase transition process at the solid-liquid interface. Its governing equation can be expressed as:

[0043] in, and These represent the interface mobility and the reaction rate constant, respectively. The double-well potential function is defined as follows: ,in This represents the height of the energy barrier between the solid and liquid phases. The anisotropic interfacial energy is determined by... Description, in which It is the gradient surface energy coefficient. It is the anisotropy intensity. It is an anisotropic mode, and This represents the angle between the interface normal vector and the reference axis. The second part of the equation uses the Butler-Volmer equation to describe the electrochemical reaction rate, thereby capturing the growth and dissolution behavior of lithium dendrites. and These represent the number of electrons transferred and the initial electrolyte concentration, respectively. To ensure the order parameter... A smooth transition is achieved within the interval [0, 1] using a smooth interpolation function. In the equation, Due to the high conductivity of lithium metal and the relatively small size of the simulation domain, for the sake of computational simplicity, it is assumed that the solid-state potential of all lithium metal connected to the boundary of the negative electrode material in the simulation is equivalent to the solid-state potential of the graphite negative electrode and the separator interface in the battery model. The equilibrium potential represents the electrochemical reaction. It is worth noting that this model is based on the following assumptions: (1) all reactions except lithium deposition and stripping are ignored; (2) the electrolyte and electrode materials are considered to be isotropic; and (3) the system operates under isothermal conditions.

[0044] Example: In this embodiment, a simulation experimental platform was built to simulate lithium dendrite growth under various charging conditions, and the simulation data was used to describe the method in detail. In COMSOL, an innovative multi-scale field-coupled pseudo-two-dimensional model was constructed to accurately simulate lithium dendrite growth and the electrochemical-thermal coupling behavior of the battery. First, the overall architecture of the model was designed, organically combining the phase-field method with pseudo-two-dimensional electrode theory to form a comprehensive model capable of simultaneously capturing microscopic morphological evolution and macroscopic performance changes. Next, using publicly available battery experimental datasets, key parameters in the model, such as electrode material properties, electrolyte conductivity, and diffusion coefficient, were identified and set through optimization algorithms to ensure the accuracy and reliability of the model. Subsequently, the electrochemical model and the thermal model were constructed in the COMSOL environment. The electrochemical model solves the charge and mass conservation equations and electrode reaction kinetic equations based on P2D theory, while the thermal model describes the heat generation and conduction processes inside the battery. Through a clever coupling mechanism, the heat generation term in the electrochemical process is used as the input to the thermal model, while the temperature calculated by the thermal model is fed back to the electrochemical model, achieving bidirectional coupling between electrochemical and thermal behavior. In the single-cell model verification and optimization stage, the model was comprehensively verified using independent experimental data. Based on the verification results, necessary adjustments were made to the model parameters and structure to improve the model's prediction accuracy. In-depth simulation analysis of battery pack performance under different operating conditions was also conducted, providing strong theoretical support for the optimized design of battery systems. A comparison of the dendrite growth simulation results under constant current / constant voltage charging and pulse charging conditions with real-world scenarios shows that the simulation model established in this invention has a smaller error. The comparison results are as follows: Figure 3 As shown.

[0045] The embodiments of the present invention take the simulated battery above as an example, and the specific charging strategy optimization process includes the following steps: Step 1: Collect the voltage U and temperature T of each battery in the battery pack at a frequency of 1Hz, and determine their values.

[0046] Step 2: Calculate the relative entropy of the median values ​​of each battery voltage and temperature in real time using a sliding window of length 100. The results are as follows: Figure 4 and Figure 5 As shown.

[0047] Step 3: Perform DBSCAN cluster analysis on the calculated relative entropies of voltage and temperature. The DBSCAN algorithm uses two parameters: neighborhood radius. and minimum sample point In this example, voltage and temperature are taken as... They are 0.42 and 1.5 respectively, while All values ​​are set to 2. The battery pack's fault characteristics are analyzed based on the clustering results, such as... Figure 6 and Figure 7 As shown.

[0048] Step 1: Based on the battery's initial state (e.g., SOC, temperature) and target charging requirements, set the initial charging current and voltage parameters. Simultaneously, use the Dendrite PF-P2D model to simulate the lithium dendrite growth trend under different charging conditions, providing a theoretical basis for subsequent dynamic parameter adjustments.

[0049] Step 2: During charging, the charging current is dynamically adjusted based on real-time battery status feedback. Specifically, when the model predicts an increased risk of lithium dendrite growth (such as reaching a specific overpotential threshold), the charging current is automatically reduced to slow down dendrite growth; conversely, when the prediction shows that dendrite growth is suppressed, the charging current can be appropriately increased to shorten the charging time.

[0050] Step 3: Introduce a pulse charging mode. By periodically inserting short rest periods, a dynamic balance between lithium deposition and dissolution is achieved. This periodic current interruption helps alleviate internal battery polarization, reduces the tip effect of lithium dendrites, and thus inhibits further dendrite growth. Simultaneously, the Dendrite PF-P2D model is used to evaluate the impact of different pulse parameters on dendrite growth, and the pulse charging strategy is optimized to achieve the best suppression effect.

[0051] By comparing dendrite growth results under different charging modes, the study shows that as the charging rate increases from 2C to 6C, the growth kinetics of lithium dendrites exhibit a highly nonlinear pattern. The maximum dendrite growth increases by approximately 4806%, and the proportion of residual dead lithium rises from 0% to 24.55%, while the total charging time only decreases by 55%. This highlights the significant trade-off between charging efficiency and safety. Most notably, comparative analysis shows that pulse charging demonstrates superior performance by controlling the deposition-dissolution cycle. While maintaining comparable charging efficiency, it reduces the maximum dendrite penetration depth by 55%, effectively reducing the risk of internal short circuits caused by dendrite penetration. The results are as follows... Figure 4 — Figure 9 As shown.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting dendrite growth and optimizing charging safety in lithium-ion batteries based on the PF-P2D model, characterized in that, The method specifically includes the following steps: S1. Construct a PF-P2D multiscale model for lithium-ion batteries, and realize the cross-scale correlation between lithium deposition behavior and battery performance during charging by coupling macroscopic electrochemical theory and microscopic morphology dynamics. S2. Introduce a potential-driven dissolution kinetics mechanism into the model. By defining a solid phase potential difference criterion, quantify the formation and accumulation of "dead lithium" during charging and achieve dynamic tracking of irreversible capacity loss. S3. Based on the model, simulate dendrite growth behavior under different charging protocols, and quantify the impact of charging rate on dendrite morphology, dead lithium ratio and safety risks. S4. Based on the simulation results, optimize the charging strategy parameters, balance charging efficiency and battery safety by suppressing dendrite penetration depth and dead lithium accumulation, and output a safe charging protocol suitable for fast charging scenarios.

2. The method for predicting dendrite growth and optimizing charging safety of lithium-ion batteries based on the PF-P2D model according to claim 1, characterized in that, In step S1, the specific method for coupling macroscopic electrochemical theory and microscopic morphology dynamics is as follows: the boundary of the phase field model is aligned with the key interface of the battery, and the electrolyte concentration field and potential field in the P2D pseudo-two-dimensional model are directly introduced into the phase field model; based on the P2D pseudo-two-dimensional model framework that simultaneously considers the potentials of the solid and liquid phases, a dual potential field is introduced; wherein, the liquid phase potential is constructed by a decomposition method based on the Poisson equation.

3. The method for predicting dendrite growth and optimizing charging safety of lithium-ion batteries based on the PF-P2D model according to claim 2, characterized in that, The liquid phase potential is constructed using a decomposition method based on the Poisson equation, decomposing the total potential into two parts, specifically including: 1) Local perturbation potential caused by charge accumulation during dendrite reaction variable It is a conserved order parameter used to characterize the distribution of lithium metal: " = 1 corresponds to the solid lithium phase," = 0 represents a liquid electrolyte, while values ​​in between describe the diffusion interface between the solid and liquid phases; F is the total free energy of the system. It is the liquid phase potential; Effective conductivity is defined as = ,in and These represent the conductivity of the liquid electrolyte phase and the solid lithium metal phase, respectively. The expression is derived using an interpolation function. It reflects the dynamic change in conductivity during the phase transition; 2) Reference electrolyte potential inherited from the P2D pseudo-two-dimensional model Governed by a passive term of the Poisson equation, and at the top boundary y= in the two-dimensional dendrite growth simulation domain. and bottom boundary y= Two Dirichlet boundary conditions are applied; the overall electrolyte potential is obtained by superimposing these two parts, as follows: in, and These represent the liquid phase potentials at the positive electrode / separator and negative electrode / separator boundaries in the pseudo-two-dimensional battery model, respectively; under the same physical considerations as the liquid phase electrochemical potential, the solid phase potential ( It satisfies a homogeneous Poisson equation and has two Dirichlet boundary conditions, as specifically expressed below: Among them, parameters and , representing the solid-state potentials at the positive electrode / separator and negative electrode / separator interfaces respectively in the pseudo-two-dimensional battery model; in the above equations It is the effective conductivity of the solid-state potential, expressed as = .

4. The method for predicting dendrite growth and optimizing charging safety of lithium-ion batteries based on the PF-P2D model according to claim 3, characterized in that, In step S2, a potential-driven step function is introduced to determine the electrochemical isolation state of lithium dendrites based on the solid-phase potential difference: when the potential difference between the dendrite and the negative electrode interface exceeds a critical value, it is determined to be "dead lithium"; the volume fraction of dead lithium is calculated by integrating the phase field order parameter to achieve dynamic tracking of irreversible lithium loss during charging, as detailed below: A step function = ) Introduced into the evolution equation of the phase field order parameter, considering the high conductivity of the lithium dendrite phase and the near-insulating properties of the electrolyte, the solid phase potential is used as the determining factor: when there is a significant potential difference between the dendrite and the bottom boundary of the solid phase potential, the region is considered as dead lithium. Based on the simulation objectives, the modified linear Allen-Cahn equation incorporates electrochemical reaction kinetics to characterize the dynamic phase transition process at the solid-liquid interface. Its governing equation is expressed as: in, and Representing the interface mobility and reaction rate constant, respectively, the dual-potential well potential function is defined as follows: ,in This represents the height of the energy barrier between the solid and liquid phases; the anisotropic interfacial energy is determined by... Description, in which It is the gradient surface energy coefficient. It is the anisotropy intensity. It is an anisotropic mode, and The angle between the interface normal vector and the reference axis is represented; the second part of the equation uses the Butler-Volmer equation to describe the electrochemical reaction rate, thereby capturing the growth and dissolution behavior of lithium dendrites. and These represent the number of transferred electrons and the initial electrolyte concentration, respectively; to ensure the order parameter A smooth transition is achieved within the interval [0, 1] using a smooth interpolation function. In the equation, Due to the high conductivity of lithium metal and the relatively small size of the simulation domain, it is assumed that the solid-state potential of all lithium metals connected to the boundary of the negative electrode material in the simulation is equivalent to the solid-state potential of the graphite negative electrode and the separator interface in the battery model. The equilibrium potential represents the electrochemical reaction.

5. The method for predicting dendrite growth and optimizing charging safety of lithium-ion batteries based on the PF-P2D model according to claim 4, characterized in that, In step S3, the simulated different charging protocols include at least constant current. Constant voltage charging mode and pulse charging mode.

6. The method for predicting dendrite growth and optimizing charging safety of lithium-ion batteries based on the PF-P2D model according to claim 5, characterized in that, By comparing simulation results from constant current-constant voltage charging mode and pulse charging mode, the effect of pulse charging on suppressing the maximum dendrite penetration depth and the amount of dead lithium formation through periodic deposition-dissolution cycles is evaluated.

7. The method for predicting dendrite growth and optimizing charging safety of lithium-ion batteries based on the PF-P2D model according to claim 6, characterized in that, In step S4, the optimized charging strategy parameters include charging current, charging voltage, and pulse charging parameters; the optimized safe charging protocol is used to provide a charging termination threshold for the battery management system in order to control the risk of dendrite growth within a preset state of charge window.

8. A lithium-ion battery dendrite growth prediction and charging safety optimization system based on the PF-P2D model, characterized in that, The system employs the method as described in any one of claims 1 to 7.

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