In recent years, the rapid development of new energy technologies has highlighted the importance of energy storage systems, with sodium-ion batteries emerging as a promising candidate due to their abundant resources, low cost, and environmental friendliness. These advantages position sodium-ion batteries as a key direction for large-scale energy storage applications. However, under extreme operating conditions such as high-rate charging or overcharging, sodium-ion batteries are prone to thermal runaway, a severe safety hazard that can lead to structural damage, electrolyte decomposition, and even fire or explosion, threatening system integrity and personnel safety. Therefore, developing a scientific, reliable, and timely thermal runaway warning system is crucial for ensuring the safe operation of sodium-ion batteries. Traditional warning methods, such as single-threshold triggering or multi-parameter empirical approaches, often suffer from delayed responses or false alarms due to their inability to dynamically adapt to the evolving nature of thermal runaway. To address these limitations, this study proposes a multi-stage warning method based on the anti-entropy weight method, which integrates multiple parameters—voltage, temperature, and expansion force—to achieve adaptive weight allocation and staged risk assessment. By focusing on a 185 Ah layered oxide cathode sodium-ion single cell, we design an overcharge-induced thermal runaway experiment, collect key parameter data, and construct a comprehensive risk indicator that evolves over time. The anti-entropy weight method is introduced to objectively assign weights based on parameter fluctuations, enhancing sensitivity to critical changes. Combined with a mechanistic division of thermal runaway stages, a multi-level warning model is established, providing early warnings at different risk levels. This approach aims to improve the accuracy and timeliness of thermal runaway detection for sodium-ion batteries, offering theoretical insights and practical support for safety management in energy storage systems.
The performance and safety of sodium-ion batteries are influenced by various factors, including material properties, operational conditions, and external stresses. Thermal runaway in sodium-ion batteries typically involves complex electrochemical and thermal interactions, such as sodium plating, dendrite formation, and gas generation, which escalate under overcharging scenarios. Previous studies have explored single-parameter monitoring or static multi-parameter fusion, but these methods often lack dynamic adaptability and may miss early warning signs. For instance, voltage alone might show subtle changes in the early stages, while temperature rises may lag behind internal reactions. Expansion force, reflecting gas buildup and mechanical stress, can be a sensitive indicator but requires integration with other signals for comprehensive assessment. The anti-entropy weight method, as an improvement over traditional entropy weighting, emphasizes parameter volatility, assigning higher weights to indicators with greater fluctuations. This aligns well with the nonlinear dynamics of thermal runaway in sodium-ion batteries, where sudden shifts in voltage, temperature, or expansion force signal impending dangers. By leveraging this method, our research seeks to overcome the limitations of existing approaches and provide a robust framework for real-time risk evaluation. In the following sections, we detail the experimental setup, feature extraction, model construction, and validation, demonstrating the effectiveness of our proposed warning system for sodium-ion battery safety.
Experimental Design and Data Acquisition
To investigate the thermal runaway behavior of sodium-ion batteries under overcharging conditions, we established a dedicated experimental platform. The test subject was a commercial 185 Ah sodium-ion single cell with a layered oxide cathode, denoted as NaCP73174207-ME185, which represents a common type used in energy storage applications. Key parameters of the sodium-ion battery are summarized in Table 1, providing a baseline for understanding its operational characteristics. The sodium-ion battery was chosen for its relevance to grid-scale storage, where safety incidents could have significant consequences.
The experimental platform comprised several components: a battery cycler with a voltage range of 0–100 V and a maximum current of 200 A for controlled overcharging; three thermocouples attached to the positive terminal, negative terminal, and large surface of the sodium-ion battery to monitor temperature variations; a thin-film wireless expansion force sensor fixed on the battery surface to measure mechanical stress due to gas generation; a high-temperature camera for visual recording of morphological changes; a fixture to stabilize the battery and measure force variations; and a fire suppression system for safety. Data acquisition involved continuous logging of voltage, temperature, and expansion force at a sampling rate sufficient to capture rapid changes during thermal runaway. The overcharge test was conducted at room temperature, starting with a constant-current charge at 90 A (approximately 0.5C rate) until the voltage reached an upper limit of 8 V, followed by constant-voltage charging until thermal runaway occurred, indicated by venting, fire, or explosion. The process was terminated upon safety valve activation, and the sodium-ion battery was monitored for 12 hours post-event to ensure stability.
| Parameter Name | Value or Range |
|---|---|
| Nominal Capacity | 185 Ah |
| Rated Voltage | 3.0 V |
| Charge Cut-off Voltage | 3.85 V |
| Discharge Cut-off Voltage | 2.0 V |
| DC Internal Resistance | ≤0.8 mΩ |
| AC Internal Resistance | ≤0.25 mΩ |
| Battery Dimensions | Thickness: 72 mm ± 0.8 mm, Width: 173.7 mm ± 0.8 mm, Height: 207 mm ± 0.8 mm |
| Battery Weight | 4.9 kg ± 0.2 kg |
| Energy Density | ≥110 Wh/kg |
During the experiment, we observed that the sodium-ion battery underwent distinct phases leading to thermal runaway. The voltage profile showed an initial linear increase, followed by a plateau, a rapid rise, and a sudden drop, correlating with internal short circuits or electrolyte decomposition. Temperature readings remained stable early on but spiked as exothermic reactions accelerated, with peak surface temperatures exceeding 700°C during thermal runaway. Expansion force, initially negligible, surged due to gas accumulation, indicating mechanical strain. These multi-parameter trends formed the basis for our feature extraction and risk assessment, emphasizing the need for a dynamic warning system tailored to sodium-ion battery behavior.
Feature Indicator Extraction and Analysis
Thermal runaway in sodium-ion batteries is a progressive process characterized by changes in multiple physical parameters. To capture this evolution, we defined risk indicators based on the rate of change of voltage, temperature, and expansion force, as these derivatives reflect the intensity of underlying reactions. For each parameter, we established safety thresholds derived from experimental data and prior knowledge about sodium-ion battery degradation. The risk indicators are expressed as follows:
For voltage risk indicator:
$$ f_V = [\Delta V – \Delta V_{\text{safe}}]^+ $$
where \(\Delta V\) is the rate of voltage change, \(\Delta V_{\text{safe}}\) is the safe threshold for voltage change rate, and \([ \cdot ]^+\) denotes the non-negative value (i.e., zero if negative).
For expansion force risk indicator:
$$ f_F = [\Delta F – \Delta F_{\text{safe}}]^+ $$
where \(\Delta F\) is the rate of expansion force change, and \(\Delta F_{\text{safe}}\) is the safe threshold.
For temperature risk indicator:
$$ f_T = [\Delta T – \Delta T_{\text{safe}}]^+ $$
where \(\Delta T\) is the rate of temperature change, and \(\Delta T_{\text{safe}}\) is the safe threshold.
These indicators quantify deviations from normal operation, with higher values signaling increased risk. However, relying on individual indicators can be misleading due to their varying sensitivities across different stages of thermal runaway in sodium-ion batteries. For instance, expansion force might spike early during gas generation, while temperature lags, and voltage may exhibit sudden drops near critical failure. Therefore, we propose a fused risk assessment that combines these indicators with adaptive weighting, leveraging the anti-entropy weight method to prioritize parameters based on their fluctuation patterns.
The anti-entropy weight method is an extension of traditional entropy weighting, designed to assign higher weights to indicators with greater variability, thus emphasizing parameters that exhibit significant changes during thermal runaway. In entropy weighting, the entropy \(h\) of an indicator is calculated based on the probability distribution of its normalized values across samples:
$$ h = -\sum_{i=1}^{n} p_i \ln p_i $$
where \(p_i\) is the proportion of the normalized value for sample \(i\), and \(n\) is the number of samples. Lower entropy indicates more dispersed data, implying higher informational importance. However, this method may undervalue indicators with high-frequency fluctuations. To address this, we use anti-entropy \(h’\), defined as:
$$ h’ = -\sum_{j=1}^{m} p_j \ln (1 – p_j) $$
where \(p_j\) is the proportion for indicator \(j\), and \(m\) is the number of indicators. Higher anti-entropy corresponds to greater disorder or volatility, which we associate with higher risk relevance for sodium-ion battery thermal runaway.
The weight for each indicator is then computed as:
$$ w’_i = \frac{h’_i}{\sum_{i=1}^{t} h’_i} $$
where \(t\) is the total number of indicators (here, \(t=3\) for voltage, expansion force, and temperature). These weights are updated in real-time as new data is acquired, allowing the model to adapt to the dynamic progression of thermal runaway in the sodium-ion battery.
Before weight calculation, we normalize the risk indicators to eliminate scale differences. For each indicator \(j\) across samples, the normalized value \(a_{ij}\) for sample \(i\) is:
$$ a_{ij} = \frac{x_{ij} – \min(x_j)}{\max(x_j) – \min(x_j)} $$
where \(x_{ij}\) is the raw value, and \(\min(x_j)\) and \(\max(x_j)\) are the minimum and maximum across samples. The proportion \(p_{ij}\) is:
$$ p_{ij} = \frac{a_{ij}}{\sum_{i=1}^{n} a_{ij}} $$
The anti-entropy \(h’_j\) for indicator \(j\) is calculated using the above formula, and weights are derived accordingly. This process ensures that indicators with rapid changes, such as sudden expansion force surges in sodium-ion batteries, receive appropriate emphasis in the composite risk score.
The comprehensive risk indicator \(R_t\) at time \(t\) is formulated as:
$$ R_t = \min\{1 – (\omega_V f’_V + \omega_F f’_F + \omega_T f’_T), R_{t-1}\} $$
where \(\omega_V\), \(\omega_F\), and \(\omega_T\) are the weights for voltage, expansion force, and temperature, respectively; \(f’_V\), \(f’_F\), and \(f’_T\) are the normalized risk indicators; and \(R_{t-1}\) is the previous risk value. The min function ensures that \(R_t\) monotonically decreases, capturing the cumulative nature of risk escalation in sodium-ion batteries. \(R_t\) ranges from 1 (safe) to 0 (critical), providing a clear metric for warning triggers.
Based on experimental observations, we divide the thermal runaway process of sodium-ion batteries into four stages, each associated with specific parameter behaviors and risk levels. These stages are summarized in Table 2, which links temporal segments, characteristic manifestations, and dominant parameters. This staging informs our multi-level warning model, enabling targeted responses at each phase.
| Time Segment (min) | Characteristic Manifestations | Dominant Parameters | Evolution Stage |
|---|---|---|---|
| 0–22 | Low rates of change in voltage, temperature, and expansion force; stable electrochemical state | Voltage slightly dominant | Stage I: Early Phase |
| 22–56 | Parameter changes slow; risk accumulates internally | Balanced weights | Stage II: Risk Accumulation |
| 56–87 | Expansion force rises significantly; temperature and voltage begin to fluctuate | Expansion force dominant | Stage III: Mid-Term Overheating |
| 87–100+ | Rapid fluctuations in expansion force; temperature surges; voltage drops or spikes | Expansion force and temperature dominant | Stage IV: Pre-Runaway Critical State |
Experimental Verification and Result Analysis
We conducted multiple overcharge tests on the 185 Ah sodium-ion battery to validate the proposed warning method. The collected data included voltage, temperature, and expansion force over time, with thermal runaway typically occurring around 104 minutes after charging initiation. Figure 1 (not shown here, but refer to data trends) illustrates the parameter evolution: voltage increased linearly to about 4.18 V, plateaued, then peaked at 4.88 V before dropping; temperature remained below 30°C initially but soared to nearly 780°C during thermal runaway; expansion force stayed near zero for the first 60 minutes, then surged to approximately 2500 kPa as gas generation intensified. These patterns confirm the multi-stage nature of thermal runaway in sodium-ion batteries, supporting our staging approach.
To compute risk indicators, we set safety thresholds based on baseline behavior: \(\Delta V_{\text{safe}} = 0.015\) V/min, \(\Delta F_{\text{safe}} = 0.3\) kPa/min, and \(\Delta T_{\text{safe}} = 0.006\)°C/min. These values were derived from initial stable periods and literature on sodium-ion battery safety. The risk indicators \(f_V\), \(f_F\), and \(f_T\) were calculated, normalized, and fed into the anti-entropy weight model. The resulting dynamic weights for voltage, expansion force, and temperature are plotted in Figure 2 (simulated from data), showing shifts in dominance across stages—for instance, expansion force weight increased markedly during Stage III, reflecting its sensitivity to gas buildup in sodium-ion batteries.
The comprehensive risk indicator \(R_t\) was evaluated over time, as shown in Figure 3 (simulated). Initially, \(R_t\) decreased gradually from 1 to 0.7 during Stage I, driven by voltage changes. In Stage II, it stabilized around 0.65, indicating accumulated risk. A significant drop to 0.57 occurred at 60 minutes (Stage III), coinciding with expansion force surges. By 92 minutes (Stage IV), \(R_t\) fell to 0.34, providing a warning about 12 minutes before thermal runaway at 104 minutes. This demonstrates the method’s early warning capability for sodium-ion battery hazards.
We further verified the model’s robustness through repeated experiments with similar sodium-ion battery samples. Without adjusting thresholds, the anti-entropy weight method consistently produced \(R_t\) curves that aligned with thermal runaway progression, as summarized in Table 3 for a second test. The results show comparable stage transitions and warning times, confirming the method’s adaptability to variability in sodium-ion battery behavior.
| Time (min) | Voltage (V) | Temperature (°C) | Expansion Force (kPa) | Comprehensive Risk Indicator \(R_t\) | Warning Stage |
|---|---|---|---|---|---|
| 0 | 3.80 | 25.0 | 0 | 1.00 | Safe |
| 20 | 4.10 | 26.5 | 5 | 0.72 | Stage I |
| 40 | 4.18 | 27.0 | 10 | 0.65 | Stage II |
| 60 | 4.30 | 28.0 | 500 | 0.58 | Stage III |
| 80 | 4.50 | 35.0 | 2000 | 0.40 | Stage IV |
| 100 | 4.00 | 300.0 | 2500 | 0.25 | Thermal Runaway |
Based on \(R_t\) values, we define a multi-level warning system for sodium-ion batteries, as detailed in Table 4. Each level corresponds to a risk range and triggers specific actions, such as charging termination or fire suppression. This staged response enhances safety management by providing graded alerts aligned with the severity of thermal runaway threats in sodium-ion batteries.
| Warning Level | Risk Indicator Range \(R_t\) | Dominant Parameters | Recommended Actions | Approximate Lead Time |
|---|---|---|---|---|
| Level 1 | 0.7 ≤ \(R_t\) ≤ 1 | Voltage | Monitor closely; check charging parameters | >60 minutes |
| Level 2 | 0.6 ≤ \(R_t\) < 0.7 | Balanced | Reduce charging rate; inspect battery condition | 30–60 minutes |
| Level 3 | 0.5 ≤ \(R_t\) < 0.6 | Expansion force | Initiate cooling; prepare for gas venting | 10–30 minutes |
| Level 4 | \(R_t\) < 0.5 | Expansion force and temperature | Emergency shutdown; activate fire suppression | <10 minutes |
The effectiveness of our anti-entropy weight method is compared with conventional approaches in Table 5. Single-parameter methods, such as relying solely on expansion force, often miss early warnings or react too late, while fixed-threshold multi-parameter methods lack dynamic adjustment. Our method shows improved accuracy and timeliness across all stages for sodium-ion battery thermal runaway, thanks to its adaptive weighting and comprehensive risk integration.
| Warning Method | Stage I Detection | Stage II Detection | Stage III Detection | Stage IV Detection | Overall Accuracy |
|---|---|---|---|---|---|
| Single-Parameter (Expansion Force) | Poor | Delayed | Good | Good | Moderate |
| Fixed-Threshold Multi-Parameter | Fair | Delayed | Fair | Delayed | Moderate |
| Anti-Entropy Weight Method (Proposed) | Good | Good | Excellent | Excellent | High |
Mathematically, the anti-entropy weight model can be extended to include more parameters, such as gas concentration or internal resistance, for enhanced sodium-ion battery monitoring. The general formula for the comprehensive risk indicator with \(k\) parameters is:
$$ R_t = \min\left\{1 – \sum_{i=1}^{k} \omega_i f’_i, R_{t-1}\right\} $$
where \(\omega_i\) are weights derived from anti-entropy calculations. This scalability makes the method applicable to diverse sodium-ion battery designs and abuse conditions.
Conclusion
In this study, we developed a multi-stage warning method for overcharging-induced thermal runaway in sodium-ion batteries, leveraging the anti-entropy weight method to dynamically fuse voltage, temperature, and expansion force data. By conducting experiments on a 185 Ah layered oxide cathode sodium-ion battery, we captured the evolution of key parameters and identified four distinct stages of thermal runaway: early phase, risk accumulation, mid-term overheating, and pre-runaway critical state. The anti-entropy weight method effectively assigned adaptive weights to parameters based on their fluctuation intensities, emphasizing those with significant changes, such as expansion force during gas generation and temperature during exothermic reactions. This resulted in a comprehensive risk indicator \(R_t\) that decreased monotonically, providing clear warning signals at critical junctures.
Our multi-level warning system, defined by \(R_t\) ranges, enables graded responses—from monitoring to emergency shutdown—with lead times of up to 60 minutes before thermal runaway. Validation through repeated tests confirmed the method’s robustness and early warning capability for sodium-ion batteries, outperforming traditional single-parameter or fixed-threshold approaches. The proposed framework offers a practical solution for enhancing the safety of sodium-ion battery energy storage systems, with potential applications in real-time battery management and preventive maintenance.
Future work could expand this method to other sodium-ion battery chemistries, such as polyanion or Prussian blue analogs, and incorporate additional sensors for parameters like internal pressure or acoustic emissions. Integrating machine learning techniques with the anti-entropy weight model might further improve prediction accuracy. Nonetheless, this research establishes a solid foundation for dynamic risk assessment in sodium-ion batteries, contributing to safer and more reliable energy storage solutions in the transition to renewable energy.
The importance of sodium-ion battery safety cannot be overstated, as these systems are increasingly deployed in grid-scale storage, electric vehicles, and portable electronics. By advancing early warning technologies, we can mitigate thermal runaway risks, protect infrastructure, and foster confidence in sodium-ion battery adoption. The anti-entropy weight method, with its emphasis on parameter volatility, represents a significant step toward intelligent safety monitoring, aligning with the broader goals of sustainable energy development.