A multi-level early warning method for thermal runaway of sodium-ion battery based on virtual sensor

Abstract

This invention relates to the field of sodium-ion battery management technology, and discloses a multi-level early warning method and system for thermal runaway in sodium-ion batteries based on virtual sensors. The method includes: collecting cell operating data; recursively estimating the virtual internal temperature; predicting the surface temperature and calculating the temperature residual; calculating the deep sodium embedding and abnormal reaction risk terms based on the state of charge, ohmic internal resistance, and current; calculating the exothermic power of side reactions; recursively estimating the virtual gas production and virtual pressure; calculating the voltage residual and temperature residual; weighted summing the standardized virtual internal temperature, temperature rise rate, virtual pressure, virtual gas production, voltage residual, and temperature residual to obtain a thermal risk score; and updating the early warning level based on a multi-level state machine and outputting control commands. This invention addresses the hard carbon anode characteristics of sodium-ion batteries by introducing a deep sodium embedding risk term and a hard carbon plateau region correction term, integrating multi-dimensional information to comprehensively judge thermal risk, enabling early warning and graded protection before the surface temperature reaches a dangerous temperature.

Description

Technical Field

[0001] This invention relates to the field of sodium-ion battery management technology, and in particular to a multi-level early warning method for thermal runaway of sodium-ion batteries based on virtual sensors. Background Technology

[0002] Sodium-ion batteries have gained widespread attention in energy storage systems and electric vehicles in recent years due to their abundant resources, low manufacturing costs, and excellent low-temperature performance. However, similar to lithium-ion batteries, sodium-ion batteries also face the risk of thermal runaway under conditions such as overcharging, over-discharging, high temperatures, and internal short circuits. Early thermal runaway is typically accompanied by electrolyte decomposition, SEI film damage, and enhanced interfacial side reactions. These processes often occur inside the cell, but heat conduction to the surface exhibits a significant lag. If only surface temperature thresholds are relied upon for judgment, the system often needs to wait until heat has been conducted to the outer surface before triggering a warning, easily missing the early intervention window. Therefore, how to detect changes in the internal thermal state of the cell in advance has become a key challenge for thermal runaway early warning technology.

[0003] Existing thermal runaway early warning methods primarily rely on surface temperature sensors. In actual operation, temperature sensors are typically placed on the surface of the cell casing, near the module end plate, cold plate, or in the gaps between cells, thus providing a relatively stable reflection of external measurable temperature changes. However, in this early warning method, the surface temperature is significantly affected by the heat transfer path and cannot be directly equated to the internal temperature of the cell. When abnormal side reactions occur inside the cell, heat first accumulates within the electrode assembly, the tab region, or the local reaction area, and then is gradually conducted to the sensor location through the electrode plates, separator, electrolyte, casing, and thermal interface materials. Due to the thermal resistance and thermal capacity involved in the heat transfer process, the surface temperature response to changes in the internal heat source is usually lag-dependent. In the early stages of thermal runaway, the internal temperature may have already begun to rise, but the surface temperature may still be within the normal range. If only a fixed threshold for surface temperature is used for alarm, the system needs to wait for internal heat to be transferred to the surface before triggering protection, thus limiting the early warning time.

[0004] Voltage anomaly monitoring is another common early warning method. However, for sodium-ion batteries using hard carbon anodes, the storage process of sodium ions in hard carbon materials is simultaneously affected by adsorption, pore filling, and interlayer intercalation. Some SOC regions exhibit a clear plateau characteristic, where the open-circuit voltage changes little with SOC, making it easy to lag or inaccurately judge the cell's condition based solely on voltage changes. In high SOC regions, the anode may enter a deep sodium-intercalation state, leading to increased local sodium concentration, decreased interfacial stability, and an increased probability of side reactions. In low SOC regions, the cell may approach an over-discharge state, affecting the stability of the current collector, electrolyte, and interfacial film, and potentially introducing additional thermal risks.

[0005] Internal resistance abrupt change monitoring methods determine whether there are connection abnormalities or interface degradation in the battery cell by estimating the ohmic internal resistance online. However, changes in internal resistance are not directly equivalent to heat release from side reactions or heat accumulation. Ohmic internal resistance reflects the internal conductive path and interface state of the battery cell. An increase in internal resistance may originate from cell aging, contact abnormalities, changes in electrode structure, increased interface impedance, or loose connectors. The higher the internal resistance, the greater the ohmic heat generated under the same current, and the more pronounced the local temperature rise. The rate of change of internal resistance is used to describe abrupt changes in internal resistance. If the internal resistance increases rapidly in a short period of time, it indicates that a sudden abnormality may have occurred inside the battery cell or in the connection structure. However, there is no direct quantitative relationship between the rate of change of internal resistance and heat release from side reactions, making it difficult to use as an independent early warning criterion for thermal runaway.

[0006] Recent virtual sensor methods based on thermo-electric coupling models utilize measurable data such as current, voltage, and surface temperature to recursively estimate unmeasurable state variables such as internal temperature and gas production through thermal balance equations and equivalent circuit models, thereby identifying thermal risks in advance. However, existing models are mostly designed for lithium-ion batteries and do not fully consider the unique characteristics of sodium-ion batteries, such as the hard carbon plateau region, the risk of deep sodium embedding, and the coupling relationship between side reactions and the state of charge (SOC) range. Furthermore, most models only output a single risk indicator and lack integration with residual analysis and state machine mechanisms, making it difficult to implement interpretable and executable multi-level early warning decisions in engineering systems.

[0007] Therefore, there is an urgent need for an early warning method specifically for sodium-ion batteries that can integrate multi-dimensional information such as virtual internal temperature, side reaction exothermics, gas production, pressure, voltage residuals, and temperature residuals. Based on this, a residual-driven multi-level state machine should be established to make up for the shortcomings of existing technologies in the early identification of thermal runaway in sodium-ion batteries. Summary of the Invention

[0008] To address the technical problems in existing sodium-ion battery thermal runaway early warning methods, such as insufficient early warning time due to surface temperature response lag, difficulty in identifying deep sodium embedding risk through voltage changes in the voltage plateau region, lack of direct quantitative correlation between internal resistance monitoring and exothermic side reactions, and the fact that existing virtual sensor methods do not fully consider the characteristics of sodium-ion batteries and lack multi-level state machine mechanisms, this invention provides a multi-level early warning method and system for sodium-ion battery thermal runaway based on virtual sensors, so as to achieve early identification, multi-level early warning, and graded protection of thermal runaway.

[0009] The technical solution of the present invention is as follows: (I) Methodology A multi-level early warning method for thermal runaway of sodium-ion batteries based on virtual sensors includes the following steps: S1: Data acquisition, acquiring the terminal voltage, current, surface temperature and ambient temperature of the battery cell, and obtaining the state of charge of the battery cell; S2: Virtual internal temperature recursion, based on the heat balance equation, using the virtual internal temperature at the current sampling moment, the current, terminal voltage, open circuit voltage, surface temperature and side reaction exothermic power to calculate the virtual internal temperature at the next sampling moment; Specifically, the virtual internal temperature is calculated recursively using the following formula: This is the equivalent heat capacity of the battery. This represents the virtual internal temperature. For time; For current; This is the open-circuit voltage; Terminal voltage; The equivalent heat transfer coefficient; Surface temperature; This refers to the exothermic power of the side reaction; This indicates the observable heat sources during the charging and discharging process, including the effects of ohmic heat and polarization heat. This indicates heat dissipation from the interior to the surface; The sampling period; The virtual internal temperature at the next sampling time; The virtual internal temperature at the current sampling moment; The surface temperature at the current sampling moment; Furthermore, the difference between the terminal voltage and the open-circuit voltage can be decomposed into an ohmic voltage drop and a polarization voltage: in, The internal resistance is ohmic; Polarization voltage; The corresponding observable electrothermal power is decomposed into ohmic thermal power and polarization thermal power: in, To provide observable electrothermal power; It is the ohmic thermal power; This represents the polarization thermal power.

[0010] S3: Surface temperature prediction and residual calculation; using the virtual internal temperature, measured surface temperature and ambient temperature at the current sampling time, predict the surface temperature at the next sampling time, and calculate the temperature residual between the predicted surface temperature and the measured surface temperature. Specifically, the predicted surface temperature is calculated using the following formula: in, Surface temperature; Internal temperature; The thermal diffusion time constant from the interior to the surface; Ambient temperature; The surface heat dissipation time constant to the environment; To predict the surface temperature at the next sampling time, The measured surface temperature at the current sampling time. The virtual internal temperature at the current sampling moment. The ambient temperature at the current sampling time. The sampling period; Furthermore, for multiple temperature measuring points, the predicted surface temperature at each measuring point is corrected using a position correction factor: in, For the first Predict surface temperature at individual measurement points; For the first The position correction amount of each measuring point; the position correction amount is obtained by fitting thermal simulation, bench test or historical operating data based on the heat transfer path, heat dissipation conditions and thermal coupling relationship between the measuring point position and the battery cell. Furthermore, the temperature consistency between adjacent measuring points is calculated using the following formula: in, For the k-th measuring point and the... Temperature difference between measuring points; The measured temperature at the k-th measuring point; For the first Measured temperature at each measuring point.

[0011] S4: Calculation of deep sodium embedding and abnormal reaction risk items. Based on the current state of charge, ohmic internal resistance, internal resistance change rate and current, combined with the hard carbon platform region identification results, the deep sodium embedding and abnormal reaction risk items are calculated. Specifically, the risk items for deep sodium embedding and abnormal reactions are calculated according to the following formula: in, Risks include deep sodium intercalation and abnormal reactions; It is a logical function; For bias terms; For SOC; The internal resistance is ohmic; This represents the absolute value of the rate of change of internal resistance. For current; to The corresponding factor weights; Risk weights for hard carbon platform regions; Used to describe the risk contribution of high SOC areas; Used to describe the risk contribution of low SOC regions; Furthermore, the hard carbon platform region correction term is calculated according to the following formula: in, Risk correction item for hard carbon platform area; This represents the absolute value of the slope of the open-circuit voltage with respect to the state of charge (SOC). The slope scale of the plateau region; Furthermore, the rate of change of the ohmic internal resistance is obtained by the difference between adjacent sampling points: in, The ohmic internal resistance at the current sampling time; The internal resistance of the ohm at the previous sampling time; Furthermore, the ohmic internal resistance is processed using exponential smoothing: in, The smoothed ohmic internal resistance; This is the internal resistance smoothing coefficient; The smoothed rate of change of internal resistance is: S5: Calculation of exothermic power of side reaction: The exothermic power of side reaction is calculated based on the current internal temperature, the depth of sodium embedding and the risk of abnormal reaction, and the effective start-up temperature of side reaction. Specifically, the exothermic power of the side reaction is calculated according to the following formula: in, This refers to the exothermic power of the side reaction; The pre-exothermic factor; It is the activation energy of the reaction; It is the gas constant; Internal temperature; Risks include deep sodium intercalation and abnormal reactions; This is the temperature at which the side reaction begins. This is the temperature smoothing coefficient; This is the effective initiation temperature for side reactions; Furthermore, the effective side reaction initiation temperature is calculated according to the following formula: in, As to the degree of health loss; This represents the increase in ohmic internal resistance relative to its initial value; , , This is the corresponding correction factor; Furthermore, the exothermic power of the side reaction is limited: in, This represents the exothermic power of the side reaction after limiting. This represents the upper limit of the exothermic power of the side reaction.

[0012] S6: Virtual gas production and virtual pressure are calculated recursively based on the heat release power of the side reaction; and virtual pressure is calculated recursively based on the virtual gas production and internal temperature. Specifically, the virtual gas production is calculated using the following formula: in, This is a virtual gas production figure; The coefficient of heat release and gas production per unit; This refers to the exothermic power of the side reaction; This is the gas diffusion or release coefficient; The virtual gas production at the next sampling time; This represents the virtual gas production at the current sampling moment. Virtual pressure is derived using the following formula: in, For virtual pressure; It is the gas constant; Internal temperature; This is the equivalent cavity volume; This represents the gas production rate; This is the pressure relief coefficient; Due to external pressure; Virtual pressure for the next sampling time; Virtual pressure at the current sampling moment; The virtual gas production rate at the current sampling moment; Furthermore, the cumulative risk of gas production is calculated using the following formula: in, The risk of gas production accumulating within the time window; This serves as a window for gas production risk statistics. For the first in the window Virtual gas production rate at any given time; Furthermore, the module-level virtual gas generation risk is calculated using the following formula: in, Risk of virtual gas generation at the module level; This refers to the number of individual units within the module. The spatial propagation weight of the m-th unit; This represents the virtual gas production of the m-th individual unit. Furthermore, the risk of accumulated stress is calculated using the following formula: in, Risk of accumulating pressure within the time window; This serves as a window for stress and risk statistics; For the first in the window The rate of increase in pressure at any given moment.

[0013] S7: Voltage residual and temperature residual calculation: The voltage residual is obtained by comparing the measured terminal voltage with the predicted terminal voltage, and the temperature residual is obtained by comparing the measured surface temperature with the predicted surface temperature. Specifically, the voltage residual and temperature residual are standardized: in, For voltage residual; This refers to the temperature residual. For standardized voltage residuals; Standardized temperature residuals; The voltage residual is the metric. The temperature residual scale; To prevent small constants with a denominator of zero; Furthermore, the residual duration is calculated according to the following rules: in, The duration for which the residual exceeds the threshold; Standardized residual threshold; For standardized residual signals; The sampling period.

[0014] S8: Thermal risk score calculation, which calculates the standardized virtual internal temperature, internal temperature rise rate, virtual pressure, virtual gas production, voltage residual and temperature residual by weighted summation and then obtains the thermal risk score through a logic function mapping. Specifically, the thermal risk score is calculated using the following formula: Assess thermal risk rating; to The corresponding indicator weights; For standardized voltage residuals; Standardized temperature residuals; To standardize the internal temperature; To standardize the internal temperature rise rate; To standardize virtual pressure; To standardize virtual gas production; The standardized components are as follows: in, , , , For the corresponding scale parameters; For reference temperature; Internal temperature; This refers to the internal temperature rise rate; For virtual pressure; This is a virtual gas production figure; Furthermore, the contribution of each risk component is calculated according to the following formula: in, Contribution to the j-th risk component; For the j-th standardized input component; Let j be the weight.

[0015] S9: Multi-level state machine update: Based on the previous warning level, the thermal risk score, the rate of change of the risk score, the virtual pressure, and the virtual gas production, update the current warning level and output a warning signal or control command. Specifically, the status escalation rules are as follows: in, The current warning level; This is a recoverable abnormal state; This is an irreversible side reaction state; This is a precursor to thermal runaway; This is a state of thermal runaway; to Thresholds for different levels of risk scoring; The residual duration threshold; This is the cumulative risk threshold for gas production; This is the threshold for accumulated stress risk. The threshold for the dangerous rate of temperature rise; Furthermore, the downgrade rules include hysteresis conditions: in, This is the next higher warning level; The downgrade threshold corresponding to the current level; The period during which the risk remains within a safe range; Set a time threshold for downgrading; Precursor states of thermal runaway and thermal runaway state Downgrading requires the following conditions to be met simultaneously: in, This is the safe threshold for gas production; This is the pressure safety threshold.

[0016] (II) System Solution This invention also provides a multi-level early warning system for thermal runaway of sodium-ion batteries based on virtual sensors, comprising: The data acquisition module is used to collect the terminal voltage, current, surface temperature and ambient temperature of the battery cell in real time, and to obtain the state of charge of the battery cell. The virtual internal temperature estimation module is used to calculate the virtual internal temperature at the next sampling moment based on the heat balance equation, using the virtual internal temperature at the current sampling moment, the current, the terminal voltage, the open circuit voltage, the surface temperature, and the exothermic power of the side reaction. The surface temperature prediction and residual calculation module is used to predict the surface temperature at the next sampling time using the virtual internal temperature, the measured surface temperature and the ambient temperature at the current sampling time, and to calculate the temperature residual between the predicted surface temperature and the measured surface temperature. The risk term calculation module is used to calculate the risk terms of deep sodium embedding and abnormal reaction based on the current state of charge, ohmic internal resistance, rate of change of internal resistance and current, combined with the hard carbon platform region identification results. The side reaction exothermic calculation module is used to calculate the side reaction exothermic power based on the current internal temperature, the sodium embedding depth and the abnormal reaction risk item, and the effective start temperature of the side reaction. The virtual state quantity estimation module is used to recursively calculate the virtual gas production based on the exothermic power of the side reaction; and to recursively calculate the virtual pressure based on the virtual gas production and the internal temperature. The voltage residual calculation module is used to compare the measured terminal voltage with the predicted terminal voltage to obtain the voltage residual. The thermal risk scoring module is used to obtain a thermal risk score by weighted summation of standardized virtual internal temperature, internal temperature rise rate, virtual pressure, virtual gas production, voltage residual, and temperature residual, and then mapping the sum through a logic function. The multi-level state machine module is used to update the current warning level based on the previous warning level, the thermal risk score, the rate of change of the risk score, the virtual pressure, and the virtual gas production, and output a warning signal or control command. The execution module is used to perform at least one of the following operations based on the warning signal or control command: current limiting operation, power reduction operation, enhanced cooling operation, fault cell isolation operation, or shutdown protection operation.

[0017] (III) Control Strategy Scheme Furthermore, the execution module implements different control strategies based on the warning level: When the warning level is a recoverable abnormal state (S1), perform power reduction operation or start cooling enhancement operation; When the warning level is an irreversible side reaction state (S2), flow limiting operation is performed and cooling is enhanced; When the warning level is pre-thermal runaway state (S3), the faulty cell is isolated and the highest level of cooling is initiated. When the warning level is thermal runaway (S4), a shutdown protection operation is performed and the circuit is disconnected.

[0018] (iv) Equipment Scheme The present invention also provides a multi-level early warning device for thermal runaway of sodium-ion batteries, including the above-mentioned system, wherein the device is integrated into a vehicle battery pack, an energy storage power station cabinet or a power storage system.

[0019] (v) Application Plan The present invention also provides the application of the above method in a battery management system (BMS) or energy storage monitoring system (EMS), wherein the method is used for early warning of thermal runaway of sodium-ion batteries and controls the actuator to perform protective actions when thermal risk is detected.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Early warning time This invention, by constructing a virtual internal temperature thermal balance model and a surface temperature hysteresis observation model, can identify changes in the internal thermal state before the surface temperature reaches a dangerous temperature, significantly advancing the early warning time for thermal runaway and buying valuable time for emergency response.

[0021] 2. Comprehensive judgment from multiple dimensions This invention integrates multi-dimensional information such as virtual internal temperature, internal temperature rise rate, virtual pressure, virtual gas production, voltage residual, and temperature residual, and makes a comprehensive judgment through a thermal risk scoring model. This avoids the limitations of a single temperature threshold or voltage threshold and improves the accuracy and reliability of early warning.

[0022] 3. Specifically designed for sodium-ion batteries This invention addresses the characteristics of hard carbon anodes in sodium-ion batteries by introducing deep sodium intercalation and abnormal reaction risk terms, as well as hard carbon plateau region correction terms. This overcomes the shortcomings of existing methods in early warning of thermal runaway in sodium-ion batteries and significantly improves the adaptability to sodium-ion batteries.

[0023] 4. Multi-level state machine enables hierarchical early warning This invention employs a residual-driven multi-level state machine, which classifies early warning levels based on indicators such as thermal risk score, residual duration, gas production accumulation risk, and pressure accumulation risk. The warning levels are progressively upgraded from recoverable abnormal state to thermal runaway state, providing a clear and executable protection strategy for BMS / EMS.

[0024] 5. Highly explainable This invention, by calculating the contribution of each risk component, can identify the main sources of thermal risk scoring, providing maintenance personnel with clear directions for anomaly location and handling, and improving the practicality of engineering applications.

[0025] 6. Clear hierarchical control strategy This invention sets differentiated control strategies for different warning levels, from power reduction and enhanced cooling to isolation of faulty cells and shutdown protection, achieving graded response and avoiding the problems of over-protection or under-protection.

[0026] 7. Wide range of applications This invention can be integrated into vehicle battery packs, energy storage power station cabinets, or power storage systems, and has broad application prospects and commercial value. Attached Figure Description

[0027] Figure 1 This is a process flow diagram of the present invention. Detailed Implementation

[0028] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below with reference to specific embodiments.

[0029] Example 1: Model Building

[0030] This embodiment provides a method for constructing a multi-level early warning model for thermal runaway of sodium-ion batteries based on virtual sensors. The method includes the construction of the following modules: virtual internal temperature thermal balance model, surface temperature hysteresis observation model, deep sodium embedding and abnormal reaction risk terms, side reaction exothermic power calculation, virtual gas production calculation, virtual pressure calculation, voltage residual and temperature residual calculation, thermal risk scoring, residual-driven multi-level state machine, and training loss and risk monotonic constraints.

[0031] 1. Virtual internal temperature thermal balance model Virtual internal temperature is used to describe the internal thermal state of a battery cell. During operation, heat generated by the cell first accumulates in the electrodes, separator, electrolyte, and local reaction areas, and then gradually transfers to the casing surface through thermal conduction paths. Due to thermal resistance and capacity between the cell's interior and surface, the surface temperature response to internal thermal changes exhibits a certain lag. Early abnormal heat release in thermal runaway typically occurs inside the cell. If only surface temperature thresholds are relied upon for judgment, the system often needs to wait until heat is conducted to the outer surface before triggering an early warning, potentially missing early intervention opportunities. To detect changes in the internal thermal state of the cell in advance, the model introduces virtual internal temperature as a recursive state variable. Virtual internal temperature cannot be directly measured by conventional sensors, but it can be estimated by combining operational data and thermal balance relationships. The model continuously updates the internal thermal state using information such as current, terminal voltage, open-circuit voltage, surface temperature, and heat release from side reactions, ensuring that early warning judgments no longer rely solely on surface temperature changes.

[0032] The thermal equilibrium relationship of the virtual internal temperature is as follows: in, This is the equivalent heat capacity of the battery. This represents the virtual internal temperature. For time; For current; This is the open-circuit voltage; Terminal voltage; The equivalent heat transfer coefficient; Surface temperature; This represents the exothermic power of the side reaction. This indicates the observable heat sources during the charging and discharging process, including the effects of ohmic heat and polarization heat. This indicates heat dissipation from the interior to the surface; This indicates the additional heat generated by abnormal side reactions.

[0033] Under normal charging and discharging conditions, the internal temperature of a battery cell is mainly affected by both the current heat source and the heat dissipation process. When the cell is in a stable operating state, internal heat generation and external heat dissipation gradually reach equilibrium, and the virtual internal temperature change is relatively gradual. If abnormal side reactions occur inside the cell, the additional heat release will cause... As the surface temperature increases, internal heat begins to accumulate rapidly. Since it takes time for heat to transfer to the surface, the virtual internal temperature usually shows an upward trend earlier than the surface temperature, thus serving as an important input for early identification of thermal runaway.

[0034] In BMS or EMS, the running data is input according to the sampling period, so the continuous model needs to be written in discrete recursive form: in, The sampling period; The virtual internal temperature at the next sampling time; The virtual internal temperature at the current sampling moment; The surface temperature at the current sampling moment; This represents the exothermic power of the side reaction at the current sampling moment.

[0035] The discrete recursive form is suitable for embedding in battery management systems, energy storage monitoring systems, or bench testing systems. Within each sampling period, the system reads data such as current, voltage, state of charge (SOC), and surface temperature, and calculates a new virtual internal temperature using a thermal model. The sampling period is determined by the data refresh rate; a higher sampling rate allows the model to track rapid thermal changes more effectively. At lower sampling rates, the recursive results become more dependent on parameter calibration and filtering. Different systems only need to adjust the sampling interval according to their specific requirements. The basic structure of the thermal equilibrium model does not need to be changed. If the convention for the current direction changes, only the current sign needs to be standardized, and the recursive relationship can still remain consistent.

[0036] To make the heat source term easier to explain, the difference between the terminal voltage and the open-circuit voltage can be decomposed into ohmic voltage drop and polarization voltage drop: in, The internal resistance is ohmic; This is the polarization voltage.

[0037] The corresponding observable electrothermal power is written as: in, To provide observable electrothermal power; It is the ohmic thermal power; This represents the polarization thermal power.

[0038] Equations (1-2) and (1-3) allow the model to further distinguish between different sources of electrothermal heat. Ohmic heat is mainly related to the current magnitude and internal resistance level; it may increase significantly when the cell ages, contact resistance increases, or temperature conditions deteriorate. Polarization heat is mainly related to electrochemical reaction processes, diffusion processes, and concentration gradient changes; it is more likely to increase under high-rate charge / discharge, low-temperature operation, or deteriorating cell consistency. Calculating the two types of heat sources separately helps determine the source of temperature rise and facilitates subsequent differentiation from side reaction exothermic reactions. If the system cannot estimate the polarization voltage in real time, it can also be directly used... As a comprehensive heat source term, it reduces the complexity of online calculations.

[0039] Open-circuit voltage can be obtained by looking up a table or fitting data based on SOC, temperature, and health status. in, For open-circuit voltage, look up a table or fit a function; For SOC; Surface temperature; It indicates a healthy state.

[0040] Open-circuit voltage is a crucial foundation for calculating electrothermal power. In practical applications, open-circuit voltage is affected by state of charge (SOC), temperature, and aging conditions. As the number of battery cycles increases, polarization characteristics and internal resistance levels change, and the open-circuit voltage curve may also shift. Therefore, when building a model, an open-circuit voltage mapping relationship can be established based on different temperature ranges, different SOC ranges, and different health states to improve the accuracy of heat source estimation. If data conditions are limited, an initial model can be built using the OCV curve of the same type of cell, and then corrected by combining operational data. Equivalent heat capacity Equivalent heat transfer coefficient The open-circuit voltage curve and polarization parameters can be obtained by fitting publicly available test data, bench data of the same type of cell, thermal simulation data, or normal operation data. The equivalent heat capacity reflects the rate of temperature change after the cell absorbs heat; the larger the value, the slower the internal temperature change. The equivalent heat transfer coefficient reflects the combined ability of the cell's internal structure to dissipate heat to the surface and the surface to the environment, and is affected by the cell structure, casing material, installation method, and cooling conditions. During parameter calibration, current, voltage, and temperature data from normal charge and discharge processes can be used to keep the error between the model-calculated temperature and the measured surface temperature within a reasonable range. If complete thermal abuse data of the target sodium-ion battery is lacking, the heat capacity and heat transfer parameters can be calibrated first using normal charge and discharge data. Then, combined with publicly available thermal runaway curves, accelerated calorimetry test results, or thermal simulation results, initial settings for side reaction-related parameters can be made. Subsequently, parameters can be further corrected through small-sample bench experiments or playback of operational data, ensuring that the model maintains stable output under different rates, ambient temperatures, and SOC conditions. The virtual internal temperature, internal temperature rise rate, ohmic thermal power, polarization thermal power, and side reaction exothermic input obtained from equations (1) to (1-4) can be further used for surface temperature hysteresis correction, side reaction exothermic estimation, and thermal risk scoring. When the virtual internal temperature continues to rise and the temperature rise rate is significantly higher than the normal operating level, the system can consider that there is an abnormal heat accumulation risk inside the cell. If this is accompanied by enhanced side reaction exothermics, a hysteresis rise in surface temperature, or abnormal voltage fluctuations, the thermal risk score should be increased accordingly, thereby providing a basis for early warning, power limiting, enhanced cooling, and system shutdown protection.

[0041] 2. Surface temperature hysteresis observation model Surface temperature is the most common thermal safety monitoring signal in battery systems. In actual operation, temperature sensors are usually placed on the surface of the cell casing, near the module end plate, cold plate, or in the gaps between cells, and can relatively stably reflect changes in external measurable temperature. However, surface temperature is significantly affected by the heat transfer path and cannot be directly equated to the internal temperature of the cell. When abnormal side reactions occur inside the cell, heat first accumulates inside the electrode assembly, in the tab area, or in the local reaction area, and then is gradually conducted to the sensor location through the electrode sheet, separator, electrolyte, casing, and thermal interface materials. Due to the thermal resistance and heat capacity involved in the heat transfer process, the response of surface temperature to changes in internal heat sources is usually lag-dependent. In the early stages of thermal runaway, the internal temperature may have already begun to rise, but the surface temperature may still be within the normal range. If only a fixed threshold for surface temperature is used for alarm, the system needs to wait for internal heat to be transferred to the surface before triggering protection, which limits the warning time. To improve early identification capability, the model uses a virtual internal temperature to calculate and predict the surface temperature, and compares the predicted value with the measured value to form a temperature residual. The temperature residual reflects the degree of inconsistency between the internal thermal state and the externally observed temperature. When internal heat accumulates abnormally, the predicted surface temperature will change in advance, while the measured surface temperature will respond subsequently. The difference between the two can provide supplementary information for thermal risk assessment.

[0042] Surface temperature hysteresis relationship writing: in, Surface temperature; Internal temperature; The thermal diffusion time constant from the interior to the surface; Ambient temperature; Let be the time constant for heat dissipation from the surface to the environment. Describe the process of heat conduction from the inside to the surface. When the internal temperature is higher than the surface temperature, heat is transferred from the inside of the cell to the outside, causing the surface temperature to rise. The larger the value, the slower the process of internal heat transfer to the surface, and the more delayed the surface temperature response. Describes the heat dissipation process from the surface to the environment. When the surface temperature is higher than the ambient temperature, the battery cell releases heat outward through natural convection, forced cooling, cold plate heat exchange, or the module structure. The larger the value, the weaker the external heat dissipation capacity and the slower the surface temperature drops.

[0043] Discrete recursive form writing: in, To predict the surface temperature at the next sampling time, The measured surface temperature at the current sampling time. The virtual internal temperature at the current sampling moment. The ambient temperature at the current sampling time. The sampling period is defined as follows. Within each sampling period, the system calculates the predicted surface temperature for the next moment based on the current virtual internal temperature, the measured surface temperature, and the ambient temperature. If the predicted surface temperature is consistently higher than the measured surface temperature, it indicates that the internal thermal state change may precede the external temperature response. If both the predicted and measured values ​​increase simultaneously, it indicates that internal heat generation has gradually transferred to the surface. If the measured surface temperature increases abnormally, but the virtual internal temperature does not change synchronously, further judgment is needed based on the sensor status, installation location, and surrounding heat sources.

[0044] For multiple temperature measurement points, the model can be modified to include measurement point location corrections: in, For the first Predict surface temperature at individual measurement points; For the first Position correction amount for each measuring point.

[0045] The placement of temperature measuring points within a battery pack or module is not entirely uniform. These points may be located on the main surface of the cell, near the tabs, on the module casing, near the cold plate, between cells, or near air ducts. The heat transfer paths, heat dissipation conditions, and thermal coupling relationships differ at these locations. Therefore, the temperature response speed and amplitude may vary when the internal thermal state of the same cell is transferred to different measuring points. The area near the tabs is typically more susceptible to current concentration and connection impedance, while the area near the cold plate is more affected by the cooling system. The location between cells may better reflect changes in thermal coupling between adjacent cells. (Position correction amount) It can be obtained through thermal simulation, bench testing, or fitting of historical operating data. Thermal simulation can be used to analyze the heat transfer path and temperature distribution at different measuring points, bench testing can be used to obtain the actual temperature response under different operating conditions, and operating data can be used to continuously correct position deviations. When the system has only a single surface temperature sensor, the position correction can be set to zero, and the model degenerates into a single-measuring-point surface temperature prediction form.

[0046] Temperature consistency between adjacent measuring points can be written as: in, For the first The measuring point and the first Temperature difference between measuring points; For the first Measured temperature at each measuring point; For the first Measured temperature at each measuring point.

[0047] Temperature differences between adjacent measuring points can be used to determine the spatial distribution characteristics of thermal anomalies. If multiple adjacent measuring points rise synchronously, it indicates that heat may have already spread within the module, and the thermal risk has a spatial propagation trend. If the temperature at a certain measuring point rises significantly while the temperatures at adjacent measuring points remain stable, factors such as sensor offset, loose installation, abnormal sampling, poor local contact, or interference from external heat sources need to be considered. If the temperature rise rate at a certain measuring point is relatively fast, and adjacent measuring points subsequently also show a temperature rise, it indicates that the local thermal anomaly may be spreading to the surrounding area. In subsequent thermal risk scoring, temperature residuals, measuring point temperature differences, and temperature rise slopes can serve as important inputs. Temperature residuals reflect the deviation between the predicted thermal state and the measured thermal state, measuring point temperature differences reflect the spatial consistency of the thermal anomaly, and temperature rise slopes reflect the rate of change of the thermal state. Using these three types of information in combination can reduce the risk of misjudgment caused by a single temperature threshold and improve the sensitivity and reliability of early identification of thermal runaway.

[0048] 3. Risks of deep sodium embedding and abnormal reactions The thermal safety mechanism of sodium-ion batteries differs from that of lithium-ion batteries. For sodium-ion batteries using hard carbon anodes, the storage process of sodium ions in hard carbon materials is simultaneously affected by adsorption, pore filling, and interlayer intercalation. A distinct plateau characteristic appears in some SOC regions, where the open-circuit voltage changes little with SOC, making it easy to lag or inaccurately judge the cell state solely based on voltage changes. In high SOC regions, the anode may enter a deep sodium-intercalation state, leading to increased local sodium concentration, decreased interface stability, and an increased probability of side reactions. In low SOC regions, the cell may approach an over-discharge state, affecting the stability of the current collector, electrolyte, and interface film, potentially introducing additional thermal risks. Besides extreme SOC regions, factors such as abnormal ohmic internal resistance, high-current operating conditions, abrupt changes in internal resistance, and enhanced polarization all increase the likelihood of abnormal heat release. To better reflect the characteristics of sodium-ion batteries, the model introduces deep sodium intercalation and abnormal reaction risk terms to describe the degree to which side reactions are triggered or amplified under different operating conditions.

[0049] Writing basic risk items: in, Risks include deep sodium intercalation and abnormal reactions; It is a logical function; For bias terms; For SOC; The internal resistance is ohmic; This represents the absolute value of the rate of change of internal resistance. For current; to The corresponding factor weights. This is used to describe the risk contribution of the high SOC region. When the SOC is high, the degree of sodium intercalation in the negative electrode increases, raising the likelihood of local overintercalation, interfacial instability, and enhanced side reactions. This is used to describe the risk contribution in the low SOC region. When the SOC is low, the cell may be close to a deep discharge state, increasing the risks associated with interface film structure, current collector stability, and electrolyte side reactions. This is achieved by simultaneously introducing... and The model can account for anomalies in both the high-end and low-end regions. Ohmic internal resistance. This reflects the internal conductive path and interface state of the battery cell. Increased internal resistance may stem from cell aging, abnormal contact, changes in electrode structure, increased interface impedance, or loose connections. Higher internal resistance results in greater ohmic heat generation under the same current, and more pronounced localized temperature rise. The rate of change of internal resistance... This term describes sudden changes in internal resistance. If the internal resistance increases rapidly within a short period, it indicates a potential sudden anomaly within the cell or its connection structure, and the risk factor needs to be increased accordingly. Current square term. This term describes the thermal risks under high-current operating conditions. High current significantly increases ohmic heat and also enhances polarization effects, making local potential shifts and concentration accumulation more pronounced. When conditions such as low temperature, high state of charge (SOC), and high-rate charge / discharge are combined, high current is more likely to induce local side reactions or amplify existing anomalies.

[0050] Logical functions By compressing the multi-factor weighted results to a finite range, the risk term is kept within a stable interval, facilitating subsequent coupling with the side reaction exothermic power model. Its form can be written as: When the input risk factors are weak Approaching low values; when extreme SOC, increased internal resistance, sudden internal resistance changes, or high current factors occur simultaneously. It will rise rapidly.

[0051] The hard carbon plateau region can be identified by the slope of the OCV-SOC curve: in, Risk correction item for hard carbon platform area; This represents the absolute value of the slope of the open-circuit voltage with respect to the state of charge (SOC). This is the slope scale for the plateau region.

[0052] When the slope of the OCV-SOC curve is small Approaching zero, A voltage level close to a high level indicates that the cell is in a voltage plateau region. At this point, the voltage change's responsiveness to SOC (State of Charge) weakens, and errors are more likely to accumulate when the BMS (Battery Management System) estimates SOC solely based on terminal voltage or open-circuit voltage. If the plateau region simultaneously experiences increased internal resistance, enhanced polarization, or abnormal temperature rise, voltage stability may mask the risks of deep sodium intercalation and side reactions; therefore, it is necessary to increase the relevant risk weights. When the slope of the OCV-SOC curve is large... A decrease indicates that voltage is more sensitive to changes in SOC, and the SOC state is more easily identified through voltage changes. At this point, the impact of plateau region corrections on risk terms weakens, and the model mainly relies on factors such as SOC, internal resistance, current, and temperature rise to determine the risk of abnormal reactions.

[0053] Writing the risk item after incorporating the hard carbon platform region correction: in, This represents the risk weight for the hard carbon plateau region. When the cell is in the high SOC plateau region, if the current is large or the internal resistance increases simultaneously, the risk of deep sodium embedding will be further amplified. When the cell is in the low SOC plateau region, if there is a sudden change in internal resistance or abnormal temperature rise, the risk of over-discharge-related side reactions will also increase. The plateau region correction term can compensate for the insufficient identification caused by the insignificant voltage change, allowing the model to maintain risk sensitivity in the region with weak voltage response.

[0054] The rate of change of the ohmic internal resistance can be obtained by the difference between adjacent sampling points: in, The ohmic internal resistance at the current sampling time; The ohmic internal resistance at the previous sampling time is given.

[0055] To reduce the impact of sampling noise on the rate of change of internal resistance, ohmic internal resistance can be smoothed exponentially. in, The smoothed ohmic internal resistance; This is the internal resistance smoothing coefficient.

[0056] Smoothing coefficient This determines the model's response speed to changes in internal resistance. When the resistance is large, the model is more sensitive to changes in the current internal resistance, making it suitable for capturing sudden anomalies, but it is also more susceptible to noise. When the resistance is relatively small, the internal resistance curve is smoother, making it suitable for long-term trend tracking, but the response to sudden changes will be slower. In engineering applications, an appropriate smoothing coefficient can be selected based on the sampling frequency, current excitation intensity, and internal resistance estimation method.

[0057] After smoothing, the rate of change of internal resistance can be further written as: Inputting the smoothed rate of change of internal resistance into equation (3-2) can reduce noise false triggering and improve the stability of risk terms. When the internal resistance increases slowly and continuously, the model tends to judge it as an increase in aging or heat accumulation risk; when the internal resistance changes rapidly in a short period of time, the model will regard it as a sudden anomaly and increase the risk level of side reactions. The risk terms of deep sodium embedding and abnormal reactions are finally entered into the side reaction exothermic power model to adjust the intensity of side reactions at the same internal temperature. When in the high-risk SOC region, hard carbon platform region, internal resistance abnormal region, or high current region, As the temperature increases, the exothermic side reaction term also increases. If the cell simultaneously experiences a rise in virtual internal temperature, an accelerated rate of temperature rise, a sudden change in internal resistance, and an increased risk of plateau region, the system should increase its thermal risk score and take preventative measures such as current limiting, power reduction, enhanced cooling, or shutdown protection.

[0058] 4. Calculation of exothermic power from side reactions Thermal runaway typically develops gradually. Initially, localized side reactions intensify within the cell, followed by sustained heat accumulation, further increasing the internal temperature and accelerating the side reaction rate. This may be accompanied by increased gas production, pressure rise, diaphragm contraction, interfacial membrane damage, and electrolyte decomposition. In the early stages, surface temperature changes may not be significant, but internal side reactions have already begun consuming active materials and electrolyte, releasing additional heat. As the internal temperature rises, the exothermic process gradually accelerates, creating a positive feedback loop between heat accumulation and enhanced reaction. The exothermic power of the side reactions is not only related to the internal temperature but is also affected by the state of charge (SOC), the risk of deep sodium embedding, the hard carbon plateau region, the degree of cell aging, abnormal internal resistance, and high-current operating conditions. At the same internal temperature, if the cell is in a high SOC region, a low SOC abnormality region, an internal resistance abrupt change region, or a high-rate operating region, side reactions are more easily triggered, and the exothermic intensity increases. Therefore, the model incorporates the temperature exponential term, risk modulation term, and side reaction initiation term into the exothermic power calculation to describe the development process of side reactions from weak to strong.

[0059] Writing the exothermic power of a side reaction: in, This refers to the exothermic power of the side reaction; The pre-exothermic factor; It is the activation energy of the reaction; It is the gas constant; Internal temperature; Risks include deep sodium intercalation and abnormal reactions; This is the temperature at which the side reaction begins. This is the temperature smoothing coefficient.

[0060] The higher the temperature, the larger the exponential term, and the higher the exothermic power of the side reaction. When the temperature approaches the side reaction initiation region, the smoothing term ensures a continuous change in the exothermic power of the side reaction from weak to strong, avoiding abrupt changes near the threshold. The deep sodium intercalation and abnormal reaction risk terms are used to distinguish between ordinary high-temperature operating conditions and high electrochemical risk operating conditions.

[0061] To reflect the effects of aging, SOC, and internal resistance anomalies on the side reaction start-up temperature, an effective start-up temperature can be defined: in, This is the effective initiation temperature for side reactions; As to the degree of health loss; This represents the increase in ohmic internal resistance relative to its initial value; , , This corresponds to a correction factor. When the degree of cell aging increases, the ohmic internal resistance rises, or the risk of abnormal reactions increases, side reactions may begin to significantly intensify at lower internal temperatures. Aging leads to changes in the structure of active materials, thickening of the interfacial film, electrolyte consumption, and increased impedance, making the cell more sensitive to thermal disturbances. Increased internal resistance increases ohmic heat power, making localized temperature concentrations more likely. Risk Item A higher temperature indicates that the battery cell is in an operating range where abnormal reactions are more likely to occur, therefore the effective start-up temperature needs to be lowered.

[0062] When the aging process is advanced, the internal resistance is high, or the model is in a high-risk SOC region, the effective start-up temperature decreases, and the model becomes more sensitive to side reactions. Using the effective start-up temperature, the exothermic power of the side reactions is written as: Battery cells in good health and The effective starting temperature is close to the base starting temperature. Cells that are severely aged or have abnormal internal resistance, The lower the temperature, the earlier the model will identify the increasing trend of exothermic side reactions. For sodium-ion batteries, if the cell is located in a hard carbon plateau region and carries the risk of deep sodium intercalation, Increasing the temperature will also lower the effective start-up temperature, making the heat dissipation power more sensitive to changes in internal temperature.

[0063] To prevent an unbounded increase in heat release power due to a single abnormal sampling, a limiting process can be added: in, This represents the exothermic power of the side reaction after limiting. This represents the upper limit of the exothermic power of the side reaction.

[0064] The upper limit of exothermic power can be determined based on cell capacity, material system, thermal abuse experiments, ARC testing, accelerated calorimetry data, or thermal simulation results. Cells with larger capacities can have a higher upper limit of exothermic power, while cells with poor thermal stability or high aging levels can have their upper limit trigger range appropriately lowered. Limiting does not alter the trend of exothermic side reactions; it is only used to limit the excessive impact of abnormal inputs on the recursive model, making the model output more stable.

[0065] The limited exothermic power of the side reaction is incorporated into the virtual internal temperature recursive model, directly affecting the internal temperature estimation at the next sampling time. Meanwhile, It can also be used to calculate virtual gas production, which can be used to estimate the degree of side reaction accumulation. When If the temperature continues to rise, accompanied by an increase in virtual internal temperature, a faster rate of temperature rise, an expansion of surface temperature residual, or an abnormal increase in internal resistance, it indicates that thermal risks are accumulating inside the battery cell. The system should increase the thermal risk score and implement measures such as current limiting, power reduction, enhanced cooling, isolation of faulty battery cells, or shutdown protection in advance.

[0066] 5. Calculation of virtual gas production Early thermal runaway is typically accompanied by electrolyte decomposition, SEI film damage, enhanced interfacial side reactions, and gas generation. As internal side reactions continue, heat release and gas production often develop simultaneously. The exothermic reaction raises the internal temperature, which in turn further promotes electrolyte decomposition and interfacial film instability, leading to increased gas generation. As gas production accumulates, the internal pressure of the cell may gradually increase, potentially triggering the opening of the pressure relief valve, casing bulging, eruption, or overheating of adjacent cells. In practical energy storage systems, equipping each cell with a gas sensor would increase cost, wiring complexity, and system maintenance difficulty. Gas sensors are also affected by installation location, ventilation path, environmental disturbances, and response time, making it difficult to directly reflect the early gas production process within a cell. Therefore, the model sets the gas production rate as a virtual state variable and uses the exothermic power of the side reactions for recursive estimation. In this way, even without gas sensors, the gas production trend can be obtained based on the thermal state and the intensity of side reactions, providing supplementary information for thermal risk assessment.

[0067] Writing the virtual gas production change relationship: in, This is a virtual gas production figure; The coefficient of heat release and gas production per unit; This refers to the exothermic power of the side reaction; This is the gas diffusion or release coefficient.

[0068] Discrete form writing: in, The virtual gas production at the next sampling time; This represents the virtual gas production at the current sampling moment. Within each sampling period, the system calculates the gas production increase based on the current exothermic power of the side reaction, and then calculates the diffusion or release attenuation based on the current virtual gas production. If the exothermic effect of the side reaction continues to increase, the increase term will be greater than the attenuation term, and the virtual gas production will gradually increase. If the exothermic effect of the side reaction weakens, and release or diffusion becomes dominant, the virtual gas production will gradually decrease. Through continuous recursion, the model can describe the process of gas production risk accumulating and decaying over time.

[0069] Writing virtual gas production rates: in, This represents the virtual gas production rate. When... This indicates that the current gas production growth caused by the exothermic side reaction is stronger than gas diffusion or release, and the virtual gas production is in the accumulation stage. When the rate of increase in gas production slows down, diffusion or venting becomes dominant, and the virtual gas production begins to decline. Compared to observing the virtual gas production rate alone, the gas production rate can reflect whether the side reaction is increasing earlier.

[0070] Short-term gas production rate fluctuations may arise from model errors, load disturbances, or parameter deviations. To identify sustained gas production processes, cumulative gas production risk can be defined: in, The risk of gas production accumulating within the time window; This serves as a window for gas production risk statistics. For the first in the window The gas production rate at any given time. The above formula only accumulates the forward gas production rate, highlighting the continuous gas production growth process. When a short-term disturbance causes the gas production rate to rise occasionally but then quickly fall back, the accumulated value within the window will not increase significantly. When the side reaction continues to intensify and causes continuous gas production, It will increase rapidly over time. (Statistical window) The settings can be adjusted based on the sampling period, module thermal inertia, and early warning sensitivity. With a shorter window, the model is more sensitive to sudden gas production; with a longer window, the model focuses more on the risk of continuous accumulation.

[0071] In a modular scenario, the virtual gas production of a single unit can be used to generate module-level gas production risk through spatial propagation weights. in, Risk of virtual gas generation at the module level; This refers to the number of individual units within the module. The spatial propagation weight of the m-th unit; Let m be the virtual gas production of the m-th cell.

[0072] Spatial propagation weights are used to describe the impact of gas generation from different individual cells on the overall risk of the module. Cells located at the module center, with poor ventilation paths, weak heat dissipation, or close to critical connection components can be assigned higher weights. Cells located at the edge, with better ventilation or shorter venting paths can be assigned lower weights. Weights can be determined based on cell location, module housing structure, cell spacing, pressure relief direction, air duct layout, cooling plate location, and gas diffusion path. If the virtual gas generation of a cell increases, and the temperature rise slope of adjacent cells also increases, it indicates that the thermal risk may have spread from the cell interior to the module space. If the virtual gas generation of multiple adjacent cells increases synchronously, the module-level gas generation risk should increase significantly. If only a single cell's virtual gas generation increases briefly, while the internal temperature, temperature rise rate, surface temperature residual, and adjacent cell states do not change synchronously, a review based on sensor data quality and model parameter stability is necessary. Virtual gas generation, virtual gas generation rate, and cumulative gas generation risk can be included in the thermal risk score along with virtual internal temperature, side reaction exothermic power, surface temperature residual, and internal resistance change rate. Gas production-related parameters are mainly used to describe the degree of side reaction accumulation, temperature-related parameters are mainly used to describe the degree of heat accumulation, and electrical parameter-related parameters are mainly used to describe the degree of electrochemical anomalies. By combining multiple types of information, the system can identify the development process from abnormal exothermic reaction to gas production accumulation earlier, and provide a basis for current limiting, power reduction, enhanced cooling, module isolation, and shutdown protection.

[0073] 6. Virtual pressure calculation Gas production causes pressure changes within the cell, casing, or localized spaces of the module. In the early stages of thermal runaway, electrolyte decomposition, interfacial film disruption, and enhanced side reactions continuously generate gas. The accumulation of gas within the cell or localized spaces of the module leads to increased pressure. This increased pressure further increases the risk of casing bulging, pressure relief valve opening, eruption, and impact on adjacent cells. Therefore, pressure changes can serve as an important auxiliary signal for early-stage thermal runaway. In low-cost BMS and large-scale energy storage systems, pressure sensors are typically difficult to deploy on a per-cell basis. On the one hand, a large number of cells increases hardware costs and wiring complexity; on the other hand, the installation location of pressure sensors is limited by structural space and may be affected by sealing issues, vibration, aging, and environmental disturbances during long-term operation. To reduce reliance on pressure sensors, the model sets pressure as a virtual state variable and recursively estimates it based on the virtual gas production rate, virtual internal temperature, equivalent cavity volume, and pressure relief parameters.

[0074] Writing about hypothetical stress changes: in, For virtual pressure; It is the gas constant; Internal temperature; This is the equivalent cavity volume; This represents the gas production rate; This is the pressure relief coefficient; Due to external pressure.

[0075] The higher the gas production rate, the faster the pressure rises; the higher the internal temperature, the more obvious the gas expansion effect; the smaller the equivalent cavity volume, the more sensitive the pressure is to gas production; the larger the pressure relief coefficient, the weaker the pressure accumulation.

[0076] Discrete form writing: in, Virtual pressure for the next sampling time; Virtual pressure at the current sampling moment; This represents the virtual gas production rate at the current sampling moment.

[0077] Writing about the rate of increase in virtual stress: in, For the virtual pressure growth rate. When This indicates that the pressure increase from gas production and thermal expansion is stronger than the pressure reduction due to pressure relief, and the pressure is in the accumulation phase. When the pressure increases, it indicates that depressurization, diffusion, or reduced gas production has caused the pressure to begin to drop. Compared to observing virtual pressure alone, the rate of pressure increase can reflect whether the gas production process is accelerating earlier.

[0078] Writing about the risks of accumulating stress: in, Risk of accumulating pressure within the time window; This serves as a window for stress and risk statistics.

[0079] If the system is equipped with a small number of module-level pressure sensors, the equivalent cavity volume can be corrected using the measured pressure. and pressure relief coefficient If the system is not equipped with a pressure sensor, the virtual pressure can still be obtained recursively from the gas production rate and internal temperature. The virtual pressure, pressure growth rate, and pressure accumulation risk, along with the virtual gas production, temperature residual, and voltage residual, are incorporated into the thermal risk scoring and state machine.

[0080] 7. Calculation of voltage residual and temperature residual Residuals are used to detect anomalous changes that are difficult to explain by the basic electrothermal model. During normal battery operation, terminal voltage and surface temperature change with current, state of charge (SOC), ambient temperature, and heat dissipation conditions. These changes can usually be explained by the equivalent circuit model and thermal model. If there is a long-term deviation between measured and predicted values, it indicates that the cell condition, connection status, heat transfer conditions, or side reaction processes may have deviated from the normal range. Voltage residuals can be used to identify voltage sags, sudden changes in internal resistance, connection anomalies, internal short circuits, polarization anomalies, or anomalous side reactions. Temperature residuals can be used to identify localized heating, temperature sensor offset, heat transfer parameter drift, cooling anomalies, or enhanced side reactions. By comparing predicted and measured values, the model can distinguish between normal load disturbances and persistent anomalous risks.

[0081] Voltage residuals and temperature residuals are written as follows: in, For voltage residual; This is the measured voltage; Predict voltage for the model; This refers to the temperature residual. This is the measured surface temperature; Predict surface temperature for the model. When A consistently large value indicates that the terminal voltage change cannot be fully explained by SOC, ohmic voltage drop, and polarization voltage. If the measured voltage is significantly lower than the predicted voltage, it may correspond to voltage slump, increased connection impedance, partial short circuit, or enhanced side reactions. If the measured voltage is significantly higher than the predicted voltage, it may correspond to model parameter deviation, SOC estimation error, sampling synchronization error, or inconsistency in current direction convention. A consistently high temperature indicates that the surface temperature change cannot be fully explained by the internal temperature recursion and heat transfer hysteresis model. If the measured temperature is higher than the predicted temperature, there may be a local heat source, abnormal contact near the sensor, insufficient cooling, or heat diffusion from adjacent cells. If the measured temperature is lower than the predicted temperature, it may be due to poor sensor adhesion, enhanced cooling, deviation in heat transfer parameters, or an overestimation of the internal temperature.

[0082] The predicted terminal voltage can be obtained from the equivalent circuit model: in, For predicting terminal voltage; The open-circuit voltage corresponding to SOC and temperature; For ohmic voltage drop; This is the polarization voltage.

[0083] The polarization voltage can be recursively derived using a first-order RC model: in, The polarization time constant; This is the polarization resistor.

[0084] To facilitate the inclusion of signals with different dimensions in risk scoring, the residuals can be standardized: in, For standardized voltage residuals; Standardized temperature residuals; The voltage residual is the metric. The temperature residual scale; To prevent small constants with zero denominators, standardization eliminates the dimensional differences between voltage and temperature, making the residual signal easier to calculate together with risk components such as virtual internal temperature, virtual pressure, and virtual gas production. and The scale parameter can be obtained from statistical analysis of normal operating data or set based on engineering experience. If the system is operating under high noise conditions, the scale parameter can be appropriately increased to reduce the impact of short-term disturbances on the risk score.

[0085] Residual duration writing: in, The duration for which the residual exceeds the threshold; Standardized residual threshold; This is for the standardized residual signal.

[0086] Short-term residuals may originate from sudden load changes, sampling noise, communication delays, or environmental disturbances; persistent residuals are more likely to correspond to real anomalies. The residual amplitude, residual duration, and consistency between the residual and virtual gas production, virtual pressure, and internal temperature rise all affect the thermal risk score.

[0087] 8. Heat Risk Score Thermal risk scoring integrates virtual internal temperature, internal temperature rise rate, virtual pressure, virtual gas production, voltage residual, and temperature residual into a single risk index. A single temperature threshold is prone to lag, a single voltage threshold is easily affected by load disturbances, and a single internal resistance threshold is insufficient to determine whether side reactions have accumulated. A comprehensive scoring system can improve the stability and interpretability of early warnings.

[0088] Writing a basic thermal risk score: in, Assess thermal risk rating; to The corresponding indicator weights; Internal temperature; This refers to the internal temperature rise rate; For virtual pressure; This is a virtual gas production figure; This is the absolute value of the voltage residual; This represents the absolute value of the temperature residual.

[0089] To reduce the impact of dimensional differences on scoring, standardized risk components can be defined: in, To standardize the internal temperature; To standardize the internal temperature rise rate; To standardize virtual pressure; To standardize virtual gas production; For reference temperature; , , , For the corresponding scale parameters.

[0090] Standardized risk score writing: Writing the rate of change of thermal risk score: in, This is the thermal risk score for the previous sampling time.

[0091] To enhance interpretability, the contribution of each risk component can be calculated: in, Contribution to the j-th risk component; For the j-th standardized input component; Let j be the weight.

[0092] The contribution rate is used to explain the source of the warning. If the internal temperature rise rate contributes the most, the control strategy can be biased towards reducing power and strengthening cooling; if the voltage residual contributes the most, the control strategy can be biased towards checking for connection abnormalities or isolating individual units; if the virtual gas production and virtual pressure contribute the most, the system can enter a higher level of safety strategy.

[0093] 9. Residual-driven multi-level state machine Thermal risk scores are continuous values, and BMS or EMS require actionable warning levels. Thermal runaway development is phased; short-term anomalies do not necessarily indicate irreversible risk, and persistent side reactions do not necessarily lead to immediate thermal runaway. To reduce false alarms and false negatives, the model employs a residual-driven multi-level state machine, updating the current state based on the previous warning level, thermal risk score, risk change rate, virtual pressure, and virtual gas production.

[0094] Writing state transition relations: in, The current warning level; State transition rules; This is the next higher warning level; Assess thermal risk rating; The rate of change of the risk score; For virtual pressure; This represents virtual gas production.

[0095] State set writing: in, This is the normal state; This is a recoverable abnormal state; This is an irreversible side reaction state; This is a precursor to thermal runaway; This indicates a thermal runaway state. Under normal conditions, residuals, virtual gas production, virtual pressure, and thermal risk score are all within safe ranges. A recoverable abnormal state corresponds to short-term residuals, internal resistance fluctuations, load disturbances, or localized temperature anomalies, which may recover after power reduction, equalization, cooling, or data verification. An irreversible side reaction state corresponds to the exothermic reaction and continuous accumulation of gas production, indicating that the internal anomaly of the cell has become persistent. A precursory thermal runaway state corresponds to a simultaneous increase in temperature rise, gas production, pressure, and residuals, indicating that the risk is rapidly developing. A thermal runaway state corresponds to a dangerous rate of temperature rise, voltage collapse, extremely high pressure risk, or the temperature reaching critical conditions.

[0096] Upgrade rule writing: in, to Thresholds for different levels of risk scoring; The residual duration threshold; This is the cumulative risk threshold for gas production; This is the threshold for accumulated stress risk. This is the threshold for the dangerous rate of temperature rise.

[0097] To prevent frequent changes in warning levels, a hysteresis condition is set in the downgrade rules: in, The downgrade threshold corresponding to the current level; The period during which the risk remains within a safe range; Set a threshold for the downgrade retention time.

[0098] Degradation of thermal runaway precursors and above requires simultaneous fulfillment of gas production, pressure, and risk change conditions: in, This is the safe threshold for gas production; This is the pressure safety threshold.

[0099] for and In high-risk states, a decline in risk score alone should not lead to an immediate downgrade. Only when virtual gas production decreases, virtual pressure drops, the rate of risk change ceases to rise, and the safety status continues to meet the required maintenance time can the system gradually lower the warning level. This prevents premature disengagement of protection while internal side reactions are still ongoing.

[0100] 10. Training Loss and Risk Monotonic Constraints Model training requires simultaneously fitting surface temperature, voltage, and warning level, while constraining the risk score to prevent unexplained declines during periods of sustained anomaly. The thermal safety warning model must possess predictive capabilities while preserving the physical meaning of intermediate states. If only end-to-end classification results are pursued, the model may utilize noise or random correlations to perform classification, rendering virtual internal temperature, gas production, pressure, and residuals meaningless. Introducing multi-task loss and risk monotonicity constraints improves model stability and engineering usability.

[0101] Training loss writing: in, For training loss; This is the measured surface temperature; To predict surface temperature; As the voltage residual weight; This is the measured voltage; For predicting voltage; Weighting is assigned to the warning level; Losses due to hierarchical supervision; Assign a monotonic penalty weight to risk; The previous risk score; Assess the current risk level.

[0102] Temperature fitting loss writing: in, This represents the temperature fitting loss; This represents the number of training samples. The temperature fitting loss is used to constrain the surface temperature prediction model, ensuring that the virtual internal temperature and heat transfer hysteresis model can reasonably explain the measured temperature variations. If the temperature fitting error is large, it is necessary to check the equivalent heat capacity, heat transfer coefficient, thermal diffusion time constant, ambient temperature input, and measurement point location corrections.

[0103] Voltage fitting loss writing: in, This represents the voltage fitting loss.

[0104] Voltage fitting loss is used to constrain the OCV curve, ohmic internal resistance, and polarization parameters. If the voltage fitting error remains large over a long period, it is necessary to check the SOC estimation, OCV-SOC curve, internal resistance model, polarization time constant, and current sampling synchronization relationship.

[0105] Early warning level monitoring loss writing: in, This is the true label for the t-th sample belonging to the c-th warning level; This represents the probability of the model predicting the c-th warning level. The level-supervised loss is used to ensure that the model output is consistent with the warning level as labeled manually or experimentally. Warning levels can be derived from thermal abuse experiments, bench tests, operational event replays, or expert reviews. For boundary samples, labels can be determined by combining temperature rise rate, gas production trend, pressure change, voltage residual, and post-analysis results, avoiding reliance solely on fixed temperature thresholds for labeling.

[0106] Risk-based, monotonous, and punishing writing: in, For risk-based monotonous penalties; This is an indicator function for the duration of anomalies. A risk monotonic penalty is used to limit the unjustified decline of the risk score during the duration of anomalies. When residual, gas generation, or pressure risks have already persisted, a sudden drop in the risk score output by the model can weaken the stability of the state machine and even cause premature degradation. This is achieved by introducing... The model tends to keep the risk score stable or rising during the period of anomaly persistence, unless the risk quantities such as gas production, pressure and residuals fall simultaneously.

[0107] Writing indicator functions for the exception persistence phase: in, The residual duration threshold; This is the cumulative risk threshold for gas production; This is the threshold for accumulated risk due to stress.

[0108] Complete training loss writing: in, For regularization terms; For regularization weights.

[0109] Regularization terms can be used to limit excessively large weights, excessively rapid parameter drift, or overfitting of the model to a small number of outlier samples. Reasonable value ranges can be set for thermal parameters, electrical parameters, and risk weights to ensure the model output conforms to the physical laws of the battery cell. For different battery cell models, capacities, and module structures, grouping corrections can be performed on the basic parameters to prevent differences between different objects from being absorbed by a single parameter. The training process can be divided into stages. The first stage calibrates the basic thermal and electrical parameters, including equivalent heat capacity, heat transfer coefficient, OCV curve, ohmic internal resistance, and polarization parameters. The second stage trains the deep sodium embedding risk term and the side reaction exothermic term, enabling the model to reflect the impact of the SOC extreme region, hard carbon plateau region, abnormal internal resistance, and high current conditions on side reactions. The third stage trains virtual gas production and virtual pressure states to ensure that the gas production and pressure recursion results are consistent with the trends of thermal abuse experiments, simulation results, or event replays. The fourth stage jointly trains the thermal risk score and multi-level state machine to maintain a stable mapping relationship between continuous risk indicators and warning levels. Phased training helps maintain the physical meaning of intermediate states and avoids a single black-box parameter absorbing all errors. Training data can be stratified by temperature range, SOC range, rate of return, aging degree, cell type, module location, and cooling conditions. Normal operation data can be used to update bias terms, scale parameters, heat transfer time constant, and residual scale. High-risk event data needs to be manually reviewed before being added to the training set to prevent real anomalies from being mistakenly absorbed by the model as normal parameter drift. After training, the false alarm rate, false negative rate, early warning time, and state machine stability should be verified through playback under different operating conditions.

[0110] Example 2

[0111] This embodiment uses a 50Ah hard carbon negative electrode sodium-ion battery as the subject, setting it in the high SOC range and subjecting it to high-current discharge. This operating condition is used to simulate the situation where the internal side reactions of the battery cell gradually intensify under the combined effects of the high SOC plateau region, high current, and abnormally increased internal resistance.

[0112] 1. Operating Condition Settings Sampling period is: The direction of the current is defined as positive for the discharge current, and the discharge current is: The initial state is set as follows: SOC is approximately recursively derived using coulomb measurement: in .

[0113] 2. Model parameter settings Thermal model parameters are set as follows: The open-circuit voltage is fitted using the following simplified function: The slope of the hard carbon plateau region is approximately: The correction term for the hard carbon plateau region is: in: The internal resistance smoothing coefficient is taken as: In the calculation of the exothermic power of the side reaction, the Arrhenius form, commonly used in engineering, is adopted: in Parameters to be taken as follows: The effective initiation temperature for side reactions is: in: Gas production and pressure parameters are taken as follows: 3. Select Perform complete calculations at all times exist At that time, the model input and the recursive result from the previous time step are: Step 1: Calculate the smoothed internal resistance and the rate of change of internal resistance. The rate of change of internal resistance is: Step 2: Calculate the open-circuit voltage and the correction term for the hard carbon plateau region. The open-circuit voltage slope is: therefore: This high value indicates that the cell is in the hard carbon plateau region, and the voltage is not sensitive to changes in SOC.

[0114] Step 3: Calculate the risk items for deep sodium embedding and abnormal reactions. Take risk item parameters: The weighted input is: Substitute the values: therefore: Step 4: Calculate the effective side reaction initiation temperature The relative increase in internal resistance is: therefore: This indicates that due to the high SOC plateau region, increased internal resistance, and aging factors, the effective start-up temperature of the side reaction has decreased from the baseline value of 62℃ to approximately 54.55℃.

[0115] Step 5: Calculate the exothermic power of the side reaction Internal temperature converted to thermodynamic temperature: The Arrhenius exponent is: The temperature start-up smoothing item is: therefore: because: Therefore, even after the bandwidth is limited, it remains: Step 6: Calculate the observable electrothermal power Step 7: Recursively calculate the virtual internal temperature The internal heat dissipation to the surface is as follows: Therefore, the internal temperature rise rate is: The internal temperature at the next sampling time is: Step 8: Recursively predict surface temperature It can be seen that the virtual internal temperature has reached 52.041℃, while the predicted surface temperature is only 40.530℃, which shows the lag of surface temperature in terms of internal heat accumulation.

[0116] Step 9: Calculate the voltage residual and temperature residual. The predicted terminal voltage is: If the measured terminal voltage at that moment is: The voltage residual is then: Take voltage residual as the metric: The standardized voltage residual is then: The predicted surface temperature obtained in the previous sampling period is: The current measured surface temperature is: Therefore, the temperature residual is: Take temperature residual as the scale: but: At this point, the voltage residual has exceeded the normalization threshold of 1, so the residual duration begins to accumulate.

[0117] Step 10: Recursively calculate virtual gas production The gas production at the next sampling time is: Step 11: Recursively calculate virtual pressure Convert the gas production rate to mol / s: The rate of pressure increase is: The pressure at the next sampling time is: Step 12: Calculate the thermal risk score Standardized components are taken as follows: Scoring bias and weights: The linear input is: therefore: Because of that moment The status remains below the Level 1 warning threshold and is still considered normal. However, the voltage residual has already begun to exceed the threshold, and if it continues to accumulate, it will trigger a state machine upgrade.

[0118] 4. Continuous recursive calculation results The state machine thresholds are set as follows: The continuous calculation results are as follows: 5. State Machine Determination Process Within 0 to 40 seconds, although the internal temperature and the exothermic power of the side reactions gradually increased, the thermal risk score had not yet reached the first-level warning threshold, so the state remained as follows: At 50 seconds: And the duration of the voltage residual reaches: Therefore, the status is upgraded to: This indicates that the abnormal state can be restored.

[0119] At 60s: Simultaneously, the risk of gas production accumulation reaches: Therefore, the status is upgraded to: This indicates an irreversible side reaction state.

[0120] At 70s: The risk of accumulated stress has reached: Therefore, the status is upgraded to: This indicates a precursor to thermal runaway.

[0121] At 80s: Therefore, the status is upgraded to: This indicates a thermal runaway state, and the system should implement the highest level of protection strategy, such as cutting off the circuit, isolating the faulty cell, initiating forced cooling, or triggering shutdown protection.

[0122] 6. Technical effects demonstrated in this embodiment As can be seen from the above calculations, at 50 seconds, the surface temperature is only 43.043℃, which has not yet reached the traditional surface temperature alarm threshold. However, the model has already raised the state to a higher level based on the virtual internal temperature, the exothermic power of the side reaction, the voltage residual, and the risk of gas accumulation. .

[0123] At 60s, the virtual internal temperature was 53.000℃ and the surface temperature was 45.163℃, with a significant lag between the two. However, the exothermic power of the side reaction had increased to 19.66W, and the risk of gas accumulation had reached the threshold. The model further raised the state to... .

[0124] Therefore, this embodiment illustrates that this method does not rely on a single surface temperature threshold, but rather assesses thermal risk by combining virtual internal temperature, exothermic side reactions, gas production, pressure, and residuals. This allows for multi-level early warnings before the surface temperature reaches a dangerous level. This method improves the early identification capability of thermal runaway in sodium-ion batteries and provides a basis for current limiting, power reduction, enhanced cooling, isolation of faulty cells, and shutdown protection.

[0125] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A multi-stage early warning method for thermal runaway of sodium-ion batteries based on virtual sensors, characterized in that, Includes the following steps: S1. Collect the terminal voltage, current, surface temperature and ambient temperature of the battery cell, and obtain the state of charge of the battery cell; S2. Based on the thermal balance of the virtual internal temperature, the virtual internal temperature at the next sampling moment is calculated using the virtual internal temperature at the current sampling moment, the current, the terminal voltage, the open circuit voltage, the surface temperature, and the exothermic power of the side reaction. S3. Using the virtual internal temperature, measured surface temperature and ambient temperature at the current sampling time, predict the surface temperature at the next sampling time, and calculate the temperature residual between the predicted surface temperature and the measured surface temperature; S4. Based on the current state of charge, ohmic internal resistance, rate of change of internal resistance and current, combined with the hard carbon platform region identification results, calculate the deep sodium embedding and abnormal reaction risk items. S5. Calculate the exothermic power of the side reaction based on the current internal temperature, the depth of sodium embedding and the risk items of abnormal reactions, and the effective start temperature of the side reaction; S6. Based on the exothermic power of the side reaction, recursively calculate the virtual gas production; and based on the virtual gas production and internal temperature, recursively calculate the virtual pressure; S7. Compare the measured terminal voltage with the predicted terminal voltage to obtain the voltage residual, and compare the measured surface temperature with the predicted surface temperature to obtain the temperature residual; S8. The standardized virtual internal temperature, internal temperature rise rate, virtual pressure, virtual gas production, voltage residual and temperature residual are weighted and summed, and the thermal risk score is obtained by mapping through a logic function. S9. Update the current warning level based on the previous warning level, the thermal risk score, the rate of change of the risk score, the virtual pressure, and the virtual gas production, and output a warning signal or control command.

2. The method according to claim 1, characterized in that, In step S2, the virtual internal temperature is calculated recursively using the following formula: This is the equivalent heat capacity of the battery. This represents the virtual internal temperature. For time; For current; This is the open-circuit voltage; Terminal voltage; The equivalent heat transfer coefficient; Surface temperature; This refers to the exothermic power of the side reaction; This indicates the observable heat sources during the charging and discharging process, including the effects of ohmic heat and polarization heat. This indicates heat dissipation from the interior to the surface; The sampling period; The virtual internal temperature at the next sampling time; The virtual internal temperature at the current sampling moment; The surface temperature at the current sampling moment; The difference between the terminal voltage and the open-circuit voltage can be decomposed into ohmic voltage drop and polarization voltage: in, The internal resistance is ohmic; Polarization voltage; The corresponding observable electrothermal power is decomposed into ohmic thermal power and polarization thermal power: in, To provide observable electrothermal power; It is the ohmic thermal power; This represents the polarization thermal power.

3. The method according to claim 1, characterized in that, In step S3, the predicted surface temperature is calculated using the following formula: in, Surface temperature; Internal temperature; The thermal diffusion time constant from the interior to the surface; Ambient temperature; The surface heat dissipation time constant to the environment; To predict the surface temperature at the next sampling time, The measured surface temperature at the current sampling time. The virtual internal temperature at the current sampling moment. The ambient temperature at the current sampling time. The sampling period; For multiple temperature measurement points, the predicted surface temperature at each point is corrected using a position correction factor: in, For the first Predict surface temperature at individual measurement points; For the first The position correction amount of each measuring point; the position correction amount is obtained by fitting thermal simulation, bench test or historical operating data based on the heat transfer path, heat dissipation conditions and thermal coupling relationship between the measuring point position and the battery cell. Temperature consistency between adjacent measuring points is calculated using the following formula: in, For the k-th measuring point and the... Temperature difference between measuring points; The measured temperature at the k-th measuring point; For the first Measured temperature at each measuring point.

4. The method according to claim 1, characterized in that, In step S4, the risk items for deep sodium embedding and abnormal reactions are calculated according to the following formula: in, Risks include deep sodium intercalation and abnormal reactions; It is a logical function; For bias terms; For SOC; The internal resistance is ohmic; The absolute value of the rate of change of internal resistance; For current; to The corresponding factor weights; Risk weights for hard carbon platform regions; Used to describe the risk contribution of high SOC areas; Used to describe the risk contribution of low SOC regions; The correction term for the hard carbon plateau region is calculated using the following formula: in, Risk correction item for hard carbon platform area; This represents the absolute value of the slope of the open-circuit voltage with respect to the state of charge (SOC). The slope scale of the plateau region; The rate of change of ohmic internal resistance is obtained by the difference between adjacent sampling points: in, The ohmic internal resistance at the current sampling time; The internal resistance of the ohm at the previous sampling time; The ohmic internal resistance is processed using exponential smoothing: in, The smoothed ohmic internal resistance; This is the internal resistance smoothing coefficient; The smoothed rate of change of internal resistance is: 。 5. The method according to claim 1, characterized in that, In step S5, the exothermic power of the side reaction is calculated according to the following formula: in, This refers to the exothermic power of the side reaction; The pre-exothermic factor; It is the activation energy of the reaction; It is the gas constant; Internal temperature; Risks include deep sodium intercalation and abnormal reactions; This is the temperature at which the side reaction begins. This is the temperature smoothing coefficient; This is the effective initiation temperature for side reactions; The effective side reaction initiation temperature is calculated using the following formula: in, As to the degree of health loss; This represents the increase in ohmic internal resistance relative to its initial value; , , This is the corresponding correction factor; The exothermic power of the side reaction is limited: in, This represents the exothermic power of the side reaction after limiting. This represents the upper limit of the exothermic power of the side reaction.

6. The method according to claim 1, characterized in that, In step S6, the virtual gas production is calculated using the following formula: in, This is a virtual gas production figure; The coefficient of heat release and gas production per unit; This refers to the exothermic power of the side reaction; This is the gas diffusion or release coefficient; The virtual gas production at the next sampling time; This represents the virtual gas production at the current sampling moment. Virtual pressure is derived using the following formula: in, For virtual pressure; It is the gas constant; Internal temperature; This is the equivalent cavity volume; This represents the gas production rate; This is the pressure relief coefficient; Due to external pressure; Virtual pressure for the next sampling time; Virtual pressure at the current sampling moment; The virtual gas production rate at the current sampling moment; The cumulative risk of gas production is calculated using the following formula: in, The risk of gas production accumulating within the time window; This serves as a window for gas production risk statistics. For the first in the window Virtual gas production rate at any given time; The module-level virtual gas generation risk is calculated using the following formula: in, Risk of virtual gas generation at the module level; This refers to the number of individual units within the module; The spatial propagation weight of the m-th unit; This represents the virtual gas production of the m-th individual unit. The risk of accumulated stress is calculated using the following formula: in, This creates a risk of pressure accumulating within the time window. This serves as a window for stress and risk statistics; For the first in the window The rate of increase in pressure at any given moment.

7. The method according to claim 1, characterized in that, In step S7, the voltage residual and temperature residual are standardized: in, This is the voltage residual; This refers to the temperature residual. For standardized voltage residuals; Standardized temperature residuals; The voltage residual is the metric. The temperature residual scale; To prevent small constants with a denominator of zero; The residual duration is calculated according to the following rules: in, The duration for which the residual exceeds the threshold; Standardized residual threshold; For standardized residual signals; The sampling period.

8. The method according to claim 1, characterized in that, In step S8, the thermal risk score is calculated according to the following formula: Assess thermal risk rating; to The corresponding indicator weights; For standardized voltage residuals; Standardized temperature residuals; To standardize the internal temperature; To standardize the internal temperature rise rate; To standardize virtual pressure; To standardize virtual gas production; The standardized components are as follows: in, , , , For the corresponding scale parameters; For reference temperature; Internal temperature; This refers to the internal temperature rise rate; For virtual pressure; This is a virtual gas production figure; The contribution of each risk component is calculated according to the following formula: in, Contribution to the j-th risk component; For the j-th standardized input component; Let j be the weight.

9. The method according to claim 1, characterized in that, In step S9, the state upgrade rule is as follows: in, The current warning level; This is a recoverable abnormal state; This is an irreversible side reaction state; This is a precursor to thermal runaway; This is a state of thermal runaway; to Thresholds for different levels of risk scoring; The threshold for residual duration; This is the cumulative risk threshold for gas production; This is the threshold for accumulated stress risk. The threshold for the dangerous rate of temperature rise; Setting hysteresis conditions for downgrade rules: in, The previous warning level; The downgrade threshold corresponding to the current level; The period during which the risk remains within a safe range; Set a time threshold for downgrading; Precursor states of thermal runaway and thermal runaway state Downgrading requires the following conditions to be met simultaneously: in, This is the safe threshold for gas production; This is the pressure safety threshold.

10. A multi-level early warning system for thermal runaway of sodium-ion batteries based on virtual sensors, characterized in that, include: The data acquisition module is used to collect the terminal voltage, current, surface temperature and ambient temperature of the battery cell in real time, and to obtain the state of charge of the battery cell. The virtual internal temperature estimation module is used to calculate the virtual internal temperature at the next sampling moment based on the heat balance equation, using the virtual internal temperature at the current sampling moment, the current, the terminal voltage, the open circuit voltage, the surface temperature, and the exothermic power of the side reaction. The surface temperature prediction and residual calculation module is used to predict the surface temperature at the next sampling time using the virtual internal temperature, the measured surface temperature and the ambient temperature at the current sampling time, and to calculate the temperature residual between the predicted surface temperature and the measured surface temperature. The risk term calculation module is used to calculate the risk terms of deep sodium embedding and abnormal reaction based on the current state of charge, ohmic internal resistance, rate of change of internal resistance and current, combined with the hard carbon platform region identification results. The side reaction exothermic calculation module is used to calculate the side reaction exothermic power based on the current internal temperature, the sodium embedding depth and the abnormal reaction risk item, and the effective start temperature of the side reaction. The virtual state quantity estimation module is used to recursively calculate the virtual gas production based on the exothermic power of the side reaction; And based on the virtual gas production and internal temperature, the virtual pressure is calculated recursively; The voltage residual calculation module is used to compare the measured terminal voltage with the predicted terminal voltage to obtain the voltage residual. The thermal risk scoring module is used to obtain a thermal risk score by weighted summation of standardized virtual internal temperature, internal temperature rise rate, virtual pressure, virtual gas production, voltage residual, and temperature residual, and then mapping the sum through a logic function. The multi-level state machine module is used to update the current warning level based on the previous warning level, the thermal risk score, the rate of change of the risk score, the virtual pressure, and the virtual gas production, and output a warning signal or control command. The execution module is used to perform at least one of the following operations based on the warning signal or control command: current limiting operation, power reduction operation, enhanced cooling operation, fault cell isolation operation, or shutdown protection operation.

11. The system according to claim 10, characterized in that, The execution module implements different control strategies based on the warning level: When the warning level is a recoverable abnormal state, perform power reduction operation or start cooling enhancement operation; When the warning level indicates an irreversible side reaction, flow restriction and enhanced cooling are implemented. When the warning level is a precursor to thermal runaway, the faulty cell is isolated and the highest level of cooling is initiated. When the warning level is thermal runaway, execute the shutdown protection operation and disconnect the circuit.

12. A multi-stage early warning device for thermal runaway of a sodium-ion battery, comprising the system as described in claim 10, characterized in that, The device is integrated into a vehicle battery pack, energy storage station cabinet, or power storage system.

13. The application of the method according to any one of claims 1 to 9 in a battery management system or energy storage monitoring system, characterized in that: The method is used for early warning of thermal runaway in sodium-ion batteries and controls the actuator to perform protective actions when thermal risk is detected.

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