A method for controlling sodium-ion battery cells based on in-situ expansion force monitoring

Abstract

This invention discloses a method for regulating sodium-ion battery cells based on in-situ expansion force monitoring, relating to the field of battery expansion force regulation. The method includes: applying an initial constraint force to a battery cell containing a specific cathode material and performing charge-discharge cycles to generate a characteristic spectrum reflecting the change in expansion force with electrochemical state, and extracting key features from the spectrum characterizing the accumulation trend of irreversible expansion force; identifying the critical electrochemical window corresponding to the phase transition of the cathode material during charge-discharge based on the key features, and formulating a differentiated current control strategy; cycling under various different initial constraint force conditions, and determining a target constraint force based on the increase in irreversible expansion force after each cycle; and synergistically applying the differentiated current control strategy and the target constraint force to the battery pack. This solution can achieve a precise balance between suppressing the source of irreversible volume growth and structural constraint in sodium-ion batteries throughout the entire charge-discharge cycle.

Description

Technical Field

[0001] This invention relates to the field of battery expansion force regulation, and in particular to a method for regulating sodium-ion battery cells based on in-situ expansion force monitoring. Background Technology

[0002] Sodium-ion batteries are rapidly gaining commercial application in electrochemical energy storage systems and low-speed electric vehicles due to their significant advantages, including high resource abundance, low cost, and excellent safety characteristics. However, during charge-discharge cycles, the active materials in these batteries undergo intrinsic lattice volume changes due to the continuous insertion and extraction of sodium ions. This, coupled with complex behaviors such as side reactions at the electrode-electrolyte interface and trace gas escape, results in continuous and irreversible structural expansion forces within the cell. If these expansion forces are not effectively controlled, they will trigger a series of chain reactions, including accelerated battery capacity decay and electrode structural instability. Therefore, accurately understanding and actively controlling the evolution of expansion forces in sodium-ion batteries during service is a key technological step in improving their electrochemical lifespan and operational safety.

[0003] In existing methods, optimizing battery charging strategies typically relies on complex cyclic experiments with multiple pre-set parameter conditions. The optimal strategy is then selected by comparing the final expansion performance under different combinations of charging rates, voltage ranges, and cutoff conditions. This approach is not only time-consuming and resource-intensive, but the resulting strategies often only apply to specific electrochemical systems, lacking an understanding of the underlying mechanisms of timing and intensity of regulation. Furthermore, determining the optimal preload required for battery pack structural design currently employs numerical simulation, using multiphysics models to iteratively calculate stress distribution and deformation under different preloads. However, each modification to design parameters necessitates restarting the entire simulation process, resulting in high computational costs. Additionally, the simplification of boundary conditions such as interface contact states and material expansion constitutive relationships in the simulation model can lead to significant discrepancies between predicted results and actual mechanical responses. Therefore, based on these challenges, this invention proposes a sodium-ion battery cell regulation method based on in-situ expansion force monitoring. Summary of the Invention

[0004] To address the aforementioned issues, the present invention aims to provide a sodium-ion battery cell regulation method based on in-situ expansion force monitoring. This method identifies the mechanical abrupt change window of specific electrode materials during charging and discharging and dynamically matches differentiated current control strategies. Simultaneously, it combines optimal constraint force determination methods aimed at minimizing irreversible expansion increments to achieve efficient and source-based suppression of sodium-ion battery expansion force, thereby simultaneously improving cycle life and volume stability within an engineering-feasible framework.

[0005] To achieve the above objectives, this invention provides a sodium-ion battery cell control method based on in-situ expansion force monitoring. First, under constant gap constraint conditions, a battery cell containing a specific cathode material is charged and discharged. Real-time expansion force data is simultaneously acquired, and a time-expansion force characteristic spectrum is constructed. From this spectrum, key mechanical features such as the non-monotonic expansion force peak induced by phase transition and irreversible baseline drift are extracted. Based on these features, the critical electrochemical state window for phase transition is identified, and a differentiated current control strategy is formulated accordingly. Within this window, a significantly reduced charging current compared to the conventional stage is applied to mitigate the mechanical impact of the phase transition. Simultaneously, cyclic testing is conducted under various initial constraint force levels. The dual optimization objectives are minimizing the expansion force amplitude in a single cycle and the irreversible baseline rise after multiple cycles, thus solving for the target constraint force that balances structural constraints and ion transport requirements. Finally, the aforementioned differentiated current strategy and the optimal constraint force are synergistically applied to the battery pack to form a coupled control closed loop that jointly suppresses irreversible expansion from both the electrochemical process and the external mechanical boundary. The effectiveness of the scheme is verified by comparing the long-cycle capacity retention rate and volume expansion rate of the battery pack before and after the control.

[0006] In a first aspect, the present invention provides a method for regulating sodium-ion battery cells based on in-situ expansion force monitoring, comprising: An initial constraint force is applied to a battery cell containing a specific cathode material and a charge-discharge cycle is performed. In-situ expansion force data is acquired simultaneously, a characteristic spectrum reflecting the change of expansion force with electrochemical state is generated, and key features characterizing the accumulation trend of irreversible expansion force in the characteristic spectrum are extracted. Based on the key features, the critical electrochemical window corresponding to the phase transition of the cathode material during charging and discharging is identified, and a differentiated current control strategy is formulated according to the window, that is, charging with a current lower than that in the conventional stage within the critical electrochemical window to mitigate the mechanical impact induced by the phase transition. Cycling under various initial constraint conditions, a target constraint is determined based on the increase in irreversible expansion force after each cycle. This constraint is defined as the optimal mechanical boundary that minimizes the effect of ion diffusion obstruction while suppressing cell structure relaxation. The differentiated current control strategy and the target constraint are applied to the battery pack in a coordinated manner to form a coupled control mechanism that suppresses irreversible volume growth of the cells.

[0007] Furthermore, the specific cathode material is sodium iron sulfate cathode material. The differentiated current control strategy is based on the non-monotonic decrease characteristic of the material after the expansion force reaches a local peak at the end of charging and the higher expansion force peak characteristic induced by the reverse phase transition during the discharge stage. The charging current is reduced within the critical electrochemical window of the phase transition to mitigate the mechanical impact caused by the reverse phase transition.

[0008] Furthermore, the key features include that the expansion force of the sodium iron sulfate cathode material shows a non-monotonic decreasing trend after reaching a local peak during the charging phase, and that the expansion force reaches a second peak higher than the peak during the charging phase during the discharging phase, accompanied by a continuous rise in the irreversible expansion force baseline after the end of the discharge.

[0009] Furthermore, the differentiated current control strategy is configured to charge with a stepped or continuously decreasing current within the critical electrochemical window to delay and reduce the generation of the second peak.

[0010] Furthermore, the step of identifying the critical electrochemical window corresponding to the phase transition includes: The acquired expansion force data is differentiated to obtain the rate of change of expansion force over time, and the voltage range corresponding to the moment when the rate of change changes sign is determined as the critical electrochemical window for the phase transition of the cathode material.

[0011] Furthermore, the step of determining the target constraint includes: The difference between the maximum and minimum expansion force in a single cycle under each initial constraint condition is obtained, as well as the irreversible increase in the minimum expansion force after multiple cycles. Using minimizing the difference and the irreversible growth as dual optimization indicators, the target constraint is selected from a variety of different initial constraint conditions. This constraint ensures that the battery cell simultaneously satisfies the dual conditions of controllable reversible expansion component and suppressed irreversible structural evolution during cycling.

[0012] Furthermore, under the same differentiated current control strategy, the capacity retention rate and volume expansion rate were obtained after multiple cycles at multiple different initial constraint force levels. The target constraint force is determined from the initial constraint force level by using the simultaneous satisfaction of the highest capacity retention rate and the lowest volume expansion rate as screening criteria.

[0013] It should be noted that, as described above, specific implementation methods for determining the target constraint force are provided from two dimensions: mechanical response characteristics and electrochemical performance. These two are not mutually exclusive substitutes, but rather constitute a complementary closed-loop verification logic within the coupled control mechanism. In practical applications, the optimal range with mechanical equilibrium potential can be quickly screened from a predefined constraint force set based on the expansion force characteristic spectrum, using minimizing the single-cycle expansion force amplitude and the irreversible baseline rise after multiple cycles as dual optimization indicators. Subsequently, candidate constraint force levels falling within this optimal range are subjected to cyclic testing under the same differentiated current control strategy. Capacity retention rate and volume expansion rate are used as the final screening criteria to determine the target constraint force that enables the cell to simultaneously meet the highest capacity retention rate and the lowest volume expansion rate. When the initial screening results based on mechanical characteristics conflict with the final screening results based on electrochemical performance, the electrochemical performance indicators are prioritized as the final decision-making basis for the target constraint force, thereby ensuring that the determined constraint force has optimal comprehensive performance under real long-cycle service conditions.

[0014] Furthermore, the method applies an initial constraint force to a simulated module composed of multiple identical battery cells connected in parallel, obtains the total expansion force characteristic spectrum of the simulated module under in-situ conditions, and performs differential analysis with the characteristic spectrum of a single battery cell of the same type. Based on the degree of nonlinear growth of peak expansion force caused by superposition effect, the method determines the required enhanced constraint stiffness at the module level to achieve mechanical boundary mapping from a single battery cell to the module.

[0015] Furthermore, the expansion force monitoring adopts a constant gap mode, that is, the initial gap of the clamp used to apply the constraint force is kept constant during the charge and discharge test, so as to ensure that the expansion force data directly reflects the actual stress generated by the intrinsic volume change of the material and eliminates the measurement error introduced by external clamping relaxation.

[0016] Secondly, a sodium-ion battery cell control system based on in-situ expansion force monitoring is also provided, the system being based on the method described in the first aspect above, comprising: The mechanical constraint and sensing module, which includes an integrated tooling fixture and force sensing components, is used to apply a precisely settable initial constraint force to the battery cell and to acquire expansion force signals in real time in constant gap mode. The electrochemical control module is used to execute a charge and discharge program on the battery cell according to a preset differentiated current control strategy, which automatically performs current derating within the critical electrochemical window. The core computing module is used to generate time-expansion force characteristic spectrum in real time, execute expansion force trend analysis and phase transition window identification algorithm, calculate the target constraint force according to dual optimization index, and finally send control commands to the mechanical constraint and sensing module and the electrochemical regulation module.

[0017] This invention proposes a sodium-ion battery cell control method based on in-situ expansion force monitoring. First, under constant gap constraint conditions, charge-discharge cycles are performed on a battery cell containing a specific cathode material, simultaneously collecting in-situ expansion force data and constructing a time-expansion force characteristic spectrum. Key mechanical features characterizing the accumulation trend of irreversible expansion force are extracted from this spectrum. Based on these features, the critical electrochemical window corresponding to the phase transition of the cathode material during charge-discharge is identified, and a differentiated current control strategy is formulated accordingly. Within this window, a significantly reduced charging current compared to the conventional stage is applied to mitigate the mechanical impact caused by the phase transition. Simultaneously, cycle tests are conducted under various initial constraint force levels, with the dual optimization objectives of minimizing the expansion force amplitude in a single cycle and the irreversible baseline rise after multiple cycles. The target constraint force that balances structural constraints and ion transport requirements is then determined. Finally, the differentiated current strategy and the optimal constraint force are synergistically applied to the battery pack, and the capacity retention rate and volume expansion rate after long-cycle testing are compared to verify and optimize the control parameters.

[0018] The proposed method can suppress the generation and accumulation of irreversible expansion forces in sodium-ion batteries during cycle service by combining electrochemical process regulation and external mechanical boundary constraints, thereby weakening the driving forces leading to capacity decay and structural instability at the source. Specifically, by accurately identifying the phase transition window based on in-situ mechanical characteristic spectra and applying differentiated current regulation, the severe mechanical response caused by the reverse phase transition during discharge can be effectively delayed and alleviated, significantly reducing the accumulation rate of irreversible expansion forces. The optimal constraint force determined by dual optimization indicators can effectively constrain electrode volume changes while avoiding increased ion transport resistance due to excessive confinement, enabling the cell to maintain a stable low internal resistance state and high reversible capacity during long cycles. This collaborative control mechanism enables the battery pack to achieve a balance between high capacity retention and low volume expansion rate after long-term service. Furthermore, since the setting of control parameters does not rely on empirical trial and error or offline simulation, but rather on a closed-loop mechanism of in-situ mechanical feature analysis and performance feedback correction to continuously approach the optimal solution, it has the ability to adapt to different cathode material systems, different battery pack configurations, and multi-cell parallel modules. At the same time, it can also provide the battery management system with a dynamic calibration basis for safety boundaries based on in-situ mechanical signals, and realize early mechanical warning of the structural integrity loss threshold under extreme working conditions.

[0019] Beneficial effects By implementing the sodium-ion battery cell control method based on in-situ expansion force monitoring provided by the present invention, the following technical effects are achieved: (1) The counterintuitive mechanical characteristic of sodium ferric sulfate cathode material, which shows a non-monotonic decrease after the expansion force reaches a local peak at the end of charging, is used as an in-situ criterion for identifying phase transitions during charging and discharging. This method can accurately pinpoint the key voltage range that contributes most significantly to irreversible expansion without relying on off-site characterization or long-term experimental calibration, providing a clearly physical triggering condition for subsequent differentiated current regulation, and significantly improving the targeting and response accuracy of the regulation strategy.

[0020] (2) A dual evaluation system is proposed, which uses the difference between the maximum and minimum expansion forces in a single cycle to characterize the reversible expansion component, and the continuous increase in the minimum expansion force after multiple cycles to characterize the rate of irreversible expansion accumulation. This system is used as the objective function for optimizing the initial constraint force. This method can achieve an optimal balance between effectively constraining electrode volume deformation and avoiding diffusion obstruction due to excessive constraint, enabling the cell to maintain both low internal resistance and high structural stability during long-term cycling. This suppresses irreversible capacity decay from the root level of mechanical boundary design.

[0021] (3) This study revealed that the expansion force after multiple cells are connected in parallel is not a simple linear sum, but exhibits a nonlinear growth of peak expansion force. A method was established to qualitatively reveal the growth trend of peak expansion force caused by the superposition effect by comparing the in-situ expansion force characteristic spectra of single cells and parallel modules, thus providing guidance for the design of module constraint stiffness. This method can predict and compensate for the expansion force amplification effect caused by the coupling of multiple cells during the module structure design stage, effectively avoiding module structure fatigue failure due to insufficient constraint, while preventing the unnecessary weight increase caused by excessive reinforcement, thereby achieving a balance between lightweight and high reliability at the system level.

[0022] (4) A coupled control closed-loop mechanism with in-situ expansion force monitoring data as the hub was constructed. This mechanism achieves synchronous linkage between electrochemical process control and external mechanical boundary constraints by synergistically applying a differentiated current control strategy based on the mechanical characteristics of phase transition and a target constraint force determined based on dual optimization indices to the battery pack. Under this synergistic mechanism, the differentiated current strategy provides reduced fatigue stress to the constraint interface by mitigating the mechanical impact of the phase transition stage, while the optimal constraint force ensures the reproducibility of the current control effect by maintaining a stable geometric boundary. The two reinforce each other, enabling the battery pack to achieve a balance between high capacity retention and low volume expansion rate after long-term service. Attached Figure Description

[0023] To make the above-described sodium-ion battery cell control method based on in-situ expansion force monitoring of the present invention more obvious and understandable, the accompanying drawings used in the specific embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0024] Figure 1 A schematic diagram showing the time-expansion force of a single charge-discharge test of sodium ferric sulfate cathode material; Figure 2 This diagram illustrates the time-expansion force of a single charge-discharge test after modifying the charging strategy for sodium ferric sulfate cathode material. Figure 3 A schematic diagram showing the cyclic test time and expansion force under a preload of 25 kPa; Figure 4 A schematic diagram showing the cyclic test time and expansion force under a preload of 50 kPa; Figure 5 A schematic diagram showing the cyclic test time and expansion force under a preload of 75 kPa; Figure 6 A schematic diagram showing the cycle retention rate of the battery pack; Figure 7 This diagram illustrates the volume expansion rate of the battery pack after cycling. Detailed Implementation

[0025] Example 1: This embodiment provides a sodium-ion battery cell control method based on in-situ expansion force monitoring. This method is implemented through an in-situ monitoring system jointly constructed by an integrated tooling fixture, an expansion force data acquisition box, a host computer, and battery charging and discharging equipment.

[0026] First, the battery cell containing sodium ferric sulfate cathode material is clamped onto an integrated fixture. An initial constraint force is applied to the cell and locked in place, maintaining a constant gap operation mode. This ensures the initial gap of the fixture remains constant throughout the charge-discharge test, allowing the acquired expansion force data to directly reflect the actual stress magnitude caused by the intrinsic volume change of the material, eliminating measurement errors introduced by external clamping slack. After applying the initial constraint force, a pressure holding operation is performed until the pressure reading on the data acquisition box no longer changes, ensuring a stable mechanical contact state between the cell and the fixture. This lays the foundation for the accuracy and repeatability of subsequent test data. The data acquisition box reads the real-time expansion force signal through a host computer. Simultaneously, the cell is connected to the charge-discharge equipment, and an electrochemical cycle test is performed according to a preset charge-discharge program, synchronously recording multi-dimensional data such as time, voltage, and expansion force, thereby generating data such as... Figure 1 The time-expansion force characteristic spectrum is shown.

[0027] The unique expansion force evolution behavior of sodium ferric sulfate cathode material during charging and discharging can be clearly identified from this characteristic spectrum. This behavior contains key mechanical characteristics closely related to the phase transition of the material. In the early charging stage, as sodium ions are extracted from the cathode material, the crystal lattice undergoes volume changes, and the expansion force shows a monotonically increasing trend, reaching a local peak. Subsequently, in the later charging stage, the expansion force does not continue to increase; instead, it shows a non-monotonic decreasing trend. This counterintuitive mechanical characteristic corresponds to the starting point of the two-phase transition in the sodium ferric sulfate cathode material within this voltage range. The transformation of the crystal structure from one phase to another is accompanied by significant volume contraction, resulting in a change in expansion force from increasing to decreasing. In the subsequent discharging stage, as sodium ions are reinserted into the cathode material lattice, the expansion force rises again, generating a second expansion force peak. The peak value of this discharge expansion force peak is higher than the peak value reached in the charging stage. This is because the reverse phase transition during discharge is accompanied by more intense volume expansion. As the discharge continues until the end, the expansion force gradually decreases. However, after each cycle, the baseline level of the irreversible expansion force does not return to the initial state, but shows a continuous upward trend. This characterizes the cumulative effect of the irreversible evolution of the material structure during the cycle.

[0028] Based on in-depth analysis of the expansion force characteristic spectrum, this method can accurately pinpoint the critical electrochemical window corresponding to the phase transition of sodium ferric sulfate cathode material during charging—that is, the voltage range where the expansion force changes from its peak to a decrease—without relying on in-situ characterization methods or long-term experimental calibration. Based on this window identification, a differentiated current control strategy is formulated: constant current charging is performed using a standard rate current within the normal voltage range; when the charging voltage enters the critical window, the charging current is reduced to a level lower than the previous stage current value, and constant current charging is performed in a step-wise or continuous derating manner until the charging cutoff voltage is reached, after which constant voltage charging is switched to constant voltage charging, until the current decays to a preset cutoff threshold and charging is terminated. By applying a significantly reduced charging current compared to the normal stage within this phase transition window, the mechanical impact caused by the phase transition can be effectively mitigated, and the severe expansion force peak caused by the reverse phase transition during the discharge stage can be delayed and weakened. This reduces the accumulation rate of irreversible expansion force from the perspective of electrochemical process regulation. The characteristic spectrum after modifying the charging strategy is shown below. Figure 2 As shown.

[0029] In parallel with the construction of the aforementioned differentiated current control strategy, this method also needs to determine the target constraints in the battery pack structural design. Under multiple different initial constraint levels, cyclic tests are performed on sodium iron sulfate cathode material cells, and in-situ expansion force data for each cycle are collected simultaneously. Figure 3An illustrative example is shown of the cycle test time-expansion force curves under a low initial constraint force level and a conventional charging strategy. It can be observed that the expansion force continues to increase with the number of cycles, indicating that the constraint force condition is insufficient to effectively suppress the accumulation of irreversible expansion. Figure 4 and Figure 5 The results of cyclic testing under different initial constraint conditions and differentiated charging strategies are presented. The expansion force behavior under different initial constraint conditions is decoupled and analyzed. The difference between the maximum and minimum expansion force in a single cycle characterizes the reversible expansion component, reflecting the intrinsic elastic volume change caused by ion insertion / extraction during a single charge-discharge cycle. The cumulative rate of irreversible expansion is characterized by the sustained rise of the minimum expansion force relative to the initial baseline after multiple cycles, reflecting the sustained contribution of irreversible processes such as permanent deformation of the electrode structure, accumulation of interfacial by-reaction products, and gas generation to the expansion force. Minimizing the reversible expansion amplitude and minimizing the irreversible baseline rise are used as dual optimization objectives. Target constraint forces that simultaneously satisfy these dual conditions are selected from a predefined set of constraint forces. The optimal constraint force falls within a moderate equilibrium range: if the constraint force is too small, it cannot effectively suppress the volume changes of the electrode material during cycling, leading to structural relaxation of the cell, ineffective constraint of irreversible volume growth, and deterioration of both cycle life and safety; if the constraint force is too large, the external mechanical confinement will compress the ion transport channels, hindering the normal diffusion of sodium ions at the electrode-electrolyte interface and within the bulk material, resulting in increased polarization, decreased capacity utilization, and performance deterioration that further increases expansion force. Therefore, determining this optimal constraint force essentially seeks a balance between the structural mechanical constraints of the cell and the mechanical requirements of ion transport, ensuring that the cell simultaneously meets the dual conditions of controllable reversible expansion and suppressed irreversible structural evolution during long-term cycling. This effectively constrains electrode volume changes while avoiding increased ion transport resistance due to excessive confinement, maintaining a stable low internal resistance state and high reversible capacity in the cell.

[0030] Applying the aforementioned differentiated current control strategy in conjunction with the target constraint to the battery pack constitutes a coupled regulation mechanism. Under this synergistic mechanism, electrochemical process regulation reduces the mechanical impact amplitude of the phase transition stage from the perspective of charge-discharge regime, delaying the accumulation of irreversible expansion; external mechanical constraints suppress structural relaxation and volume growth of the cell from the perspective of mechanical boundaries, while maintaining the unobstructed ion diffusion channels. The two regulation methods complement and reinforce each other: the differentiated current strategy provides a smaller reversible amplitude for the external constraint, reducing fatigue stress at the constraint interface; the optimal constraint provides a stable geometric boundary for the differentiated current strategy, ensuring the reproducibility of the regulation effect. Ultimately, this achieves source suppression of the irreversible expansion force of sodium-ion batteries, enabling the battery pack to possess excellent comprehensive performance of high capacity retention and low volume expansion rate after long-term service. Figure 6 and Figure 7 The figures show the long-cycle capacity retention rate and volume expansion rate of the battery pack after adopting the synergistic control scheme of this embodiment. As can be seen from the figures, the battery pack can still maintain a high capacity retention rate and a low volume expansion rate after long-cycle operation, thus verifying the synergistic effect of the coupled control mechanism on delaying capacity decay and suppressing structural deformation compared with the single control method.

[0031] Example 2: This embodiment extends the in-situ expansion force monitoring and control system constructed in the previous embodiments to multiple operating scenarios, such as comparative evaluation of cathode material systems and characterization of the mechanical behavior of multi-cell parallel modules, forming a universally applicable method for in-situ expansion force monitoring and analysis of sodium-ion batteries under multiple operating conditions.

[0032] First, a standardized in-situ expansion force testing device and method is provided. This device includes an integrated fixture, battery charging / discharging equipment, and an expansion force data acquisition box. The battery cell is locked in place by the integrated fixture to provide a controllable initial constraint force. The data acquisition box connects to the fixture and reads real-time expansion force data from a host computer. After the battery cell is connected to the charging / discharging equipment, a charge-discharge cycle test is performed according to a preset program. This standardized process yields a time-expansion force variation curve, i.e., an in-situ expansion force characteristic spectrum. Based on the mechanical characteristics implied in this spectrum, the behavior of the battery cell under different operating conditions can be analyzed in depth.

[0033] In the first type of application, this embodiment uses the in-situ expansion force monitoring method to compare and evaluate different cathode material systems, providing an efficient basis for material selection based on mechanical dimensions. Three types of cells were selected: layered oxide materials, sodium iron pyrophosphate and sodium iron sulfate from polyanionic materials, and hard carbon anodes. These cells were clamped in an integrated fixture and subjected to the same initial constraint force. After sufficient pressure holding to achieve mechanical equilibrium, the same charge-discharge cycle procedure was executed. By analyzing their respective time-expansion force characteristic spectra, in-situ and rapid identification of the structural evolution characteristics of different cathode materials can be achieved. The expansion force of the layered oxide cathode material shows a monotonically increasing trend during charging and a monotonically decreasing trend during discharging. The extraction and insertion of sodium ions during charging and discharging exhibits a single-phase continuous reaction, thus the expansion force change shows a monotonic characteristic. The maximum expansion force change amplitude and the cumulative amount of irreversible expansion force in each cycle are relatively small, indicating good structural stability. Sodium iron pyrophosphate cathode material exhibits two expansion force peaks during charge and discharge, with the peak being higher during the charging phase. This reflects the involvement of multiple single-phase reactions in the charge and discharge process, accompanied by multiple sodium ion rearrangement processes. Multiple sodium sites and different sodium ion diffusion barriers may induce lattice strain of varying degrees at different stages. Its maximum expansion force variation and average irreversible expansion force increment per cycle are the smallest among several cathode materials, demonstrating excellent cycle stability. Sodium iron sulfate cathode material exhibits a unique expansion force curve morphology. During the charging phase, the expansion force first rises to a local peak and then decreases. During the discharging phase, the expansion force rises again, producing an expansion force peak higher than the charging peak, before decreasing. This material undergoes a two-phase transition within a specific voltage range, accompanied by significant volume contraction and expansion, thus generating characteristic expansion force peaks. Its maximum expansion force variation and average irreversible expansion force increment per cycle are significantly greater than the previous two types of materials, and the minimum expansion force continuously increases with the number of cycles, indicating a high degree of irreversible structural evolution. The lateral comparison of the aforementioned characteristic spectra shows that layered oxide materials exhibit relatively simple expansion force behavior due to their single-phase continuous reaction. Sodium iron pyrophosphate materials show minimal overall irreversible expansion due to their multi-step single-phase reaction. However, sodium iron sulfate cathode materials, due to the clear two-phase transition during charging and discharging accompanied by significant non-monotonic expansion force characteristics and a higher irreversible baseline drift rate, exhibit expansion force behavior that is far more sensitive to electrochemical process parameters than the other two types of materials. This characteristic makes it more suitable to employ an electrochemical control method based on identifying the critical window of phase transition using in-situ expansion force characteristic spectra and matching it with a differentiated current control strategy for sodium iron sulfate cathode materials. By reducing the charging current within this critical window to directly intervene in the mechanical impact during the phase transition process, the high tendency for irreversible expansion accumulation can be suppressed at its source. In contrast, simple mechanical boundary constraints or conventional charging strategies have limited effectiveness in controlling this type of expansion behavior dominated by intrinsic phase transitions.

[0034] In the second type of application, this embodiment extends the in-situ expansion force monitoring method to the mechanical behavior characterization of a multi-cell parallel system using sodium iron sulfate cathode material, to simulate the superposition effect of expansion force based on this material in actual battery modules during service. Cells of the same specification, with sodium iron sulfate cathode and hard carbon anode, were selected and tested in three configurations: single cell, two cells in parallel, and three cells in parallel. All configurations were clamped in an integrated fixture and subjected to the same initial constraint force. After voltage stabilization, the same charge-discharge cycle program was executed, and the in-situ expansion force data of each configuration was recorded simultaneously. Comparative analysis of the expansion force characteristic spectra of a single cell and modules with different numbers of parallel cells revealed that the increase in expansion force after parallel connection of sodium iron sulfate cells is not a simple linear summation, but rather exhibits a non-linear and significant increase in peak expansion force with increasing number of parallel cells. The expansion force generated by each cell is superimposed, and the more parallel cells are connected, the more significant the superposition effect. The maximum expansion force increases significantly with increasing number of parallel cells, but the minimum expansion force does not decrease with increasing number of parallel cells. This discovery reveals that a mechanical coupling amplification effect also exists in the parallel system of multi-cell sodium iron sulfate cathode materials. Furthermore, because the expansion force amplitude and irreversible baseline drift of sodium iron sulfate cathode material in a single cycle are higher than those of other cathode materials, the absolute amplitude of the superposition effect in its parallel system is correspondingly larger, posing higher requirements for the design of the module constraint structure. Based on this understanding, in the battery pack structure design stage for sodium iron sulfate cathode cells, the nonlinear growth trend of the peak expansion force caused by the superposition effect can be evaluated through differential analysis based on the in-situ expansion force characteristic spectrum of a single cell and the number of parallel cells. This provides a more realistic reference for simulating the actual stress state at the module level, and the required enhanced constraint stiffness of the module can be determined based on this trend, achieving a mapping of mechanical boundary conditions from single cell to module level. This method can effectively avoid fatigue failure and cycle life degradation of the module structure due to insufficient constraint, while preventing ineffective weight increase and volume expansion due to excessive reinforcement, achieving a balance between lightweight and high reliability at the system level.

[0035] Example 3: This embodiment is a preferred implementation of the method described in Example 1 on a sodium ferric sulfate cathode material battery cell.

[0036] The in-situ expansion force acquisition box was connected to the tooling fixture, and real-time expansion force data was read from the host computer. The NFS (sodium ferric sulfate) battery cell was locked using the integrated tooling fixture, and an initial preload of 50 kPa was applied. The pressure was maintained for 30 minutes until the pressure displayed on the data acquisition box no longer changed, ensuring the accuracy of the experimental data. The working mode was set to constant gap mode, and the sampling frequency was set to 30 seconds. The battery cell was connected to the charging and discharging equipment for charging and discharging tests. Constant current charging was performed at a rate of 0.5C in the 2.5V to 4.1V range, and constant current charging at a rate of 0.2C in the 4.1V to 4.2V range. After reaching 4.2V, constant voltage charging was switched, and charging was stopped when the current was less than 0.05C. The battery cell was allowed to stand for 30 minutes at the end of each charging and discharging stage. Relevant test data were recorded, obtaining cyclic test data and in-situ expansion force test data. The test data was processed into a time-expansion force change curve. The battery cell was assembled using an initial preload of 50 kPa, and cyclic tests were performed using the above charging strategy to obtain the following results: Figure 6 The cycle life of the battery pack shown is 300 cycles and Figure 7 The battery expansion rate data shown is defined as the ratio of the increase in battery pack thickness after cycling to the battery pack thickness before cycling. After 300 cycles at 0.5C at room temperature, the battery pack retained 98.33% of its capacity, and the post-cycle expansion rate was 0.38%.

[0037] In contrast, this embodiment also shows a control scheme that does not employ this method. The in-situ expansion force acquisition box is connected to a tooling fixture, and real-time expansion force data is read by a host computer. The NFS cell is locked using an integrated tooling fixture, and an initial preload of 25 kPa is applied. The pressure is maintained for 1 hour until the pressure displayed on the data acquisition box no longer changes. The operating mode is set to constant gap mode, and the sampling frequency is set to 60 seconds. The cell is connected to a charging and discharging device for charging and discharging tests. Charging is performed at a constant current of 0.5C throughout the 2.5V to 4.2V range, and the cell is left to stand for 30 minutes at the end of each charging and discharging stage. Relevant test data is recorded and processed into a time-expansion force change curve. The cell is then assembled into a pack using an initial preload of 25 kPa, and a cyclic test is performed using the aforementioned conventional charging strategy to obtain the following results: Figure 6 The cycle life of the battery pack shown is 300 cycles and Figure 7 The battery expansion rate data is shown. In the control scheme, the battery pack retains only 88.83% of its capacity after 300 cycles, and the battery expansion rate is as high as 8.68%. The above comparison shows that the differentiated charging strategy and the optimal constraint force synergistic control scheme adopted in this embodiment have improved both the cycle retention rate and volume expansion rate, two key indicators.

[0038] Example 4: This embodiment demonstrates an alternative implementation scheme based on Embodiment 3, adjusting the starting voltage point of the phase transition critical window. The in-situ expansion force acquisition box is connected to a fixture, and real-time expansion force data is read by a host computer. The NFS cell is locked using an integrated fixture, and an initial preload of 50 kPa is applied. The pressure is maintained for 30 minutes until the pressure displayed on the data acquisition box no longer changes, ensuring the accuracy of the experimental data. The operating mode is set to constant gap mode, and the sampling frequency is set to 60 seconds. The cell is connected to a charging and discharging device for charge and discharge testing. Constant current charging is performed at a rate of 0.5C in the 2.5V to 4.15V range, and constant current charging at a rate of 0.2C in the 4.15V to 4.2V range. After reaching 4.2V, constant voltage charging is switched, and charging is stopped when the current is less than 0.05C. The cell is left to stand for 30 minutes at the end of each charging and discharging stage. Relevant test data are recorded, obtaining cyclic test data and in-situ expansion force test data. The test data is processed into a time-expansion force change curve. The battery cells were assembled using an initial preload of 50 kPa, and cycle tests were performed using the aforementioned charging strategy to obtain the following results: Figure 6 The cycle life of the battery pack shown is 300 cycles and Figure 7 The battery expansion rate data are shown. After 300 cycles at 0.5C at room temperature, the battery pack retained 96.98% of its capacity and expanded by 2.52%. Compared with Example 3, adjusting the current-drop initiation voltage from 4.1V to 4.15V resulted in a slight decrease in cycle retention and a significant increase in expansion rate. This result indicates that accurate identification of the phase transition critical window has a significant impact on the control effect, further confirming the necessity of accurately determining this window through in-situ expansion force characteristic spectrum.

[0039] The supplementary mechanism explains the quantitative relationship between the magnitude of the expansion rate change and the 0.05V shift in the current-drop initiation voltage. As described in Example 1, the anomalous characteristic of the expansion force of the sodium ferric sulfate cathode material changing from increasing to decreasing at the end of charging corresponds to the starting point of its phase transition. This phase transition occurs within a very narrow voltage range, accompanied by significant lattice volume contraction, and the expansion force is highly sensitive to voltage changes within this window. When the current-drop initiation voltage is adjusted from 4.1V to 4.15V, this 0.05V shift covers a considerable portion of the phase transition window, causing the cell to continue charging at the conventional 0.5C rate during the voltage range where the phase transition is most intense. The rapid extraction of sodium ions during this stage exacerbates the non-equilibrium distortion of the lattice structure, and the resulting mechanical shock not only directly increases the amplitude of the expansion force in a single cycle but also accelerates the accumulation of irreversible structural damage over multiple cycles. It should be noted that the expansion rate increase shown in Example 4 is the cumulative result after 300 cycles. Although the irreversible expansion increment caused by window offset in a single cycle seems small, it is eventually manifested as a several-fold increase in expansion rate after continuous accumulation and amplification over hundreds of cycles. This characteristic is consistent with the conclusion that the expansion behavior of sodium ferric sulfate cathode material is highly sensitive to the phase transition window. From a quantitative perspective, this further confirms the necessity of accurately locking the current reduction initiation voltage point based on the in-situ expansion force characteristic spectrum. A window identification deviation on the order of 0.05V can have a significant impact on the stability of the long-cycle structure.

[0040] Example 5: This embodiment demonstrates an alternative implementation scheme based on Embodiment 3, adjusting the initial constraint force level. The in-situ expansion force acquisition box is connected to a fixture, and real-time expansion force data is read by a host computer. The NFS cell is locked using an integrated fixture, and an initial preload of 75 kPa is applied. The pressure is maintained for 30 minutes until the pressure displayed on the data acquisition box no longer changes, ensuring the accuracy of the experimental data. The operating mode is set to constant gap mode, and the sampling frequency is set to 60 seconds. The cell is connected to a charging and discharging device for charging and discharging tests. Constant current charging is performed at a rate of 0.5C in the 2.5V to 4.1V range, and constant current charging at a rate of 0.2C in the 4.1V to 4.2V range. After reaching 4.2V, constant voltage charging is switched, and charging is stopped when the current is less than 0.05C. The cell is left to stand for 30 minutes at the end of each charging and discharging stage. Relevant test data are recorded, obtaining cyclic test data and in-situ expansion force test data. The test data is processed into a time-expansion force change curve. The battery cells were assembled using an initial preload of 75 kPa, and cycle tests were performed using the aforementioned charging strategy to obtain the following results. Figure 6 The cycle life of the battery pack shown is 300 cycles and Figure 7The battery expansion rate data is shown. After 300 cycles at 0.5C at room temperature, the battery pack maintained a capacity retention of 95.93% and an expansion rate of 3.28%. Compared with Example 3, increasing the initial preload from 50 kPa to 75 kPa resulted in a certain decrease in cycle retention and an increase in expansion rate. This result indicates that excessive external constraint may weaken the control benefits by compressing ion transport channels, verifying the mechanism analysis that the optimal constraint force needs to achieve a moderate balance between structural constraint and ion transport. This result is consistent with... Figure 5 The trend reflected by the cyclic test time-expansion force curve under higher constraint is consistent.

[0041] Example 6: This embodiment demonstrates an alternative implementation scheme based on Embodiment 3, adjusting the derating range of the charging current within the critical window. The in-situ expansion force acquisition box is connected to a fixture, and real-time expansion force data is read by a host computer. The NFS cell is locked using an integrated fixture, and an initial preload of 50 kPa is applied. The pressure is maintained for 30 minutes until the pressure displayed on the data acquisition box no longer changes, ensuring the accuracy of the experimental data. The operating mode is set to constant gap mode, and the sampling frequency is set to 60 seconds. The cell is connected to a charging and discharging device for charging and discharging tests. Constant current charging is performed at a rate of 0.5C in the 2.5V to 4.1V range, and constant current charging at a rate of 0.3C in the 4.1V to 4.2V range. After reaching 4.2V, constant voltage charging is switched, and charging is stopped when the current is less than 0.05C. The cell is left to stand for 30 minutes at the end of each charging and discharging stage. Relevant test data are recorded, obtaining cyclic test data and in-situ expansion force test data. The test data is processed into a time-expansion force change curve. The battery cells were assembled using an initial preload of 50 kPa, and cycle tests were performed using the aforementioned charging strategy to obtain the following results: Figure 6 The cycle life of the battery pack shown is 300 cycles and Figure 7 The battery expansion rate data is shown. After 300 cycles at 0.5C at room temperature, the battery pack retained 97.02% of its capacity and expanded by 1.52%. Compared to Example 3, adjusting the charging current within the critical window from 0.2C to 0.3C slightly reduced the cycle retention rate, but the expansion rate remained at a low level. This indicates that applying a significantly reduced charging current within the critical window compared to the conventional stage is a key means of suppressing irreversible expansion, and the specific extent of the current derating can be appropriately selected based on actual application requirements while ensuring the control effect.

[0042] To further separate the independent contributions of the differentiated charging strategy and the target constraint to performance, a cross-comparative analysis is conducted using the above embodiments. Comparing Embodiment 3 (50kPa + differentiated charging, 0.2C derating) with Embodiment 5 (75kPa + differentiated charging, 0.2C derating), both employ the same differentiated charging strategy, differing only in the initial constraint. The cycle retention rate changes from 98.33% to 95.93%, and the expansion rate changes from 0.38% to 3.28%. This difference can be attributed to the change in the single factor of constraint, indicating that 50kPa is closer to the optimal mechanical boundary than 75kPa, and excessive constraint will lead to performance degradation. Comparing Embodiment 3 with Embodiment 6 (50kPa + differentiated charging, 0.3C derating), both have the same constraint, differing only in the derating magnitude within the critical window. The cycle retention rate decreases slightly from 98.33% to 97.02%, and the expansion rate increases from 0.38% to 1.52%. This difference reflects the independent impact of the current derating degree on performance in the charging strategy. Furthermore, using the control scheme (25 kPa + 0.5C conventional charging throughout, retention rate 88.83%, expansion rate 8.68%) without employing this method as a benchmark, when only the constraint force is optimized from 25 kPa to 50 kPa while maintaining the conventional charging strategy, considering the severe insufficiency of constraint force reflected in the control scheme and the significant impact of individual constraint force changes on performance in Example 5, it can be reasonably inferred that constraint force optimization can bring about a certain improvement. Similarly, when only the charging strategy is changed from conventional charging to differentiated charging while maintaining a 25 kPa constraint force, performance improvement can also be expected. Example 3 achieved the best overall performance (retention rate 98.33%, expansion rate 0.38%) when both optimizations were implemented simultaneously, thus confirming that the differentiated charging strategy and the target constraint force are not simply superimposed, but rather achieve a performance level that cannot be reached by a single means through synergistic coupling. The two reinforce each other and together constitute a coupled control mechanism to suppress irreversible expansion.

[0043] Regarding the cross-example comparison of the significant increase in expansion rate (1.52%) compared to Example 3 (0.38%), while the capacity retention rate showed a smaller difference, the following supplementary explanation is provided. The expansion behavior of the sodium ferric sulfate cathode material within the phase transition critical window is extremely sensitive to the charging current. The irreversible accumulation of expansion force mainly stems from structural damage within this window, rather than simple capacity loss. In Example 6, after increasing the charging current within the critical window from 0.2C to 0.3C, the derating rate decreased from 60% to 40%, and the mechanical impact during the phase transition stage increased accordingly. Although the irreversible volume increase per cycle was still negligible, after 300 cycles, it resulted in a several-fold increase in the expansion rate. Simultaneously, the capacity retention rate was controlled by multiple factors, remaining within a relatively stable performance range within the derating range of 0.2C to 0.3C, where the capacity decay caused by a slight increase in current was not significant. This asymmetric response characteristic precisely indicates that the expansion rate is much more sensitive to the degree of current derating within the critical window than the capacity retention rate, thus further confirming the necessity of applying sufficient current derating within the phase transition window to suppress irreversible expansion. The specific magnitude of the current derating can be appropriately selected based on the comprehensive requirements of expansion rate and charging speed in practical applications.

Claims

1. A method for controlling sodium-ion battery cells based on in-situ expansion force monitoring, characterized in that, include: An initial constraint force is applied to a battery cell containing a specific cathode material and a charge-discharge cycle is performed. In-situ expansion force data is acquired simultaneously, a characteristic spectrum reflecting the change of expansion force with electrochemical state is generated, and key features characterizing the accumulation trend of irreversible expansion force in the characteristic spectrum are extracted. Based on the key features, the critical electrochemical window corresponding to the phase transition of the cathode material during charging and discharging is identified, and a differentiated current control strategy is formulated according to the window, that is, charging with a current lower than that in the conventional stage within the critical electrochemical window. Cycling under various initial constraint conditions, a target constraint is determined based on the increase in irreversible expansion force after each cycle. This constraint is defined as the optimal mechanical boundary that minimizes the effect of ion diffusion obstruction while suppressing cell structure relaxation. The differentiated current control strategy and the target constraint are applied to the battery pack in a coordinated manner to form a coupled control mechanism that suppresses irreversible volume growth of the cells.

2. The method according to claim 1, characterized in that: The specific cathode material is sodium iron sulfate cathode material. The differentiated current control strategy is based on the non-monotonic decrease characteristic of the material after the expansion force reaches a local peak at the end of charging and the higher expansion force peak characteristic induced by the reverse phase transition during the discharge stage. The charging current is reduced within the critical electrochemical window of the phase transition to mitigate the mechanical impact caused by the reverse phase transition.

3. The method according to claim 2, characterized in that: The key features include that the expansion force of the sodium iron sulfate cathode material reaches a local peak during the charging phase and then shows a non-monotonic decreasing trend, and that the expansion force reaches a second peak higher than the peak during the charging phase during the discharging phase, accompanied by a continuous rise in the irreversible expansion force baseline after the end of the discharge.

4. The method according to claim 1, characterized in that: The differentiated current control strategy is configured to charge the device with a stepped or continuously decreasing current within the critical electrochemical window.

5. The method according to claim 1, characterized in that, The steps for identifying the critical electrochemical window corresponding to the phase transition include: The acquired expansion force data is differentiated to obtain the rate of change of expansion force over time, and the voltage range corresponding to the moment when the rate of change changes sign is determined as the critical electrochemical window for the phase transition of the cathode material.

6. The method according to claim 1, characterized in that, The steps for determining the target constraint include: The difference between the maximum and minimum expansion force in a single cycle under each initial constraint condition is obtained, as well as the irreversible increase in the minimum expansion force after multiple cycles. Using minimizing the difference and the irreversible growth as dual optimization indicators, the target constraint is selected from a variety of different initial constraint conditions. This constraint ensures that the battery cell simultaneously satisfies the dual conditions of controllable reversible expansion component and suppressed irreversible structural evolution during cycling.

7. The method according to claim 1, characterized in that: Under the same differentiated current control strategy, the capacity retention rate and volume expansion rate were obtained after multiple cycles at multiple different initial constraint force levels. The target constraint force is determined from the initial constraint force level by using the simultaneous satisfaction of the highest capacity retention rate and the lowest volume expansion rate as screening criteria.

8. The method according to claim 1, characterized in that: The method applies an initial constraint force to a simulated module composed of multiple identical battery cells connected in parallel, obtains the total expansion force characteristic spectrum of the simulated module under in-situ conditions, and performs differential analysis with the characteristic spectrum of a single battery cell of the same type. Based on the degree of nonlinear growth of peak expansion force caused by superposition effect, the required enhanced constraint stiffness at the module level is determined.

9. The method according to claim 1, characterized in that: The expansion force monitoring is performed in a constant gap mode, that is, the initial gap of the fixture used to apply the constraint force is kept constant during the charge and discharge test.

10. A sodium-ion battery cell control system based on in-situ expansion force monitoring, characterized in that: The system is implemented based on the method described in any one of claims 1-9: The system includes: The mechanical constraint and sensing module, which includes an integrated tooling fixture and force sensing components, is used to apply a precisely settable initial constraint force to the battery cell and to acquire expansion force signals in real time in constant gap mode. The electrochemical control module is used to execute a charge and discharge program on the battery cell according to a preset differentiated current control strategy, which automatically performs current derating within the critical electrochemical window. The core computing module is used to generate time-expansion force characteristic spectrum in real time, execute expansion force trend analysis and phase transition window identification algorithm, calculate the target constraint force according to dual optimization index, and finally send control commands to the mechanical constraint and sensing module and the electrochemical regulation module.

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