Abstract. The rapid deployment of grid-scale lithium-ion battery energy storage systems has brought thermal runaway safety into focus. This study proposes an ultra-early warning method for thermal runaway of the energy storage battery based on dynamic strain signals. The strain generation mechanism of a 100 Ah prismatic lithium iron phosphate (LFP) energy storage battery is first analyzed theoretically. Then, a series of thermal runaway experiments is conducted under different states of charge (SOC) and micro-overcharge conditions by using a self-developed multi-purpose experimental platform. The results show that the casing strain of the energy storage battery responds sensitively to internal gas accumulation and pressure build-up, and exhibits several characteristic nodes before the safety valve opens. The strain rise rate shows a turning point at 10 µε/s, followed by a peak strain rate and a peak strain value, both occurring prior to pressure venting. Normal charge–discharge cycles generate stable strain variations with peak values below 1000 µε and peak strain rates below 0.6 µε/s, enabling reliable threshold discrimination. Micro-overcharge experiments reveal that 108% SOC is a critical threshold beyond which the risk of thermal runaway increases abruptly. Based on these findings, a three-level early-warning model is constructed over the full charge–discharge cycle of the energy storage battery, providing an average earliest warning time of approximately 450 s before the safety valve opens. The proposed strain-based methodology offers a promising solution for the early safety monitoring of energy storage battery systems.
Key words: energy storage battery; thermal runaway; early warning; strain; micro-overcharge.
1. Introduction
Lithium-ion batteries have become the dominant technology for electrochemical energy storage owing to their high energy density, low self-discharge rate, long cycle life, and mature manufacturing chain. Among various cathode chemistries, lithium iron phosphate (LFP) batteries are widely used in large-scale energy storage stations because of their low cost, long calendar life, and better thermal stability compared with nickel-rich ternary counterparts. In China, more than 90% of the newly installed electrochemical energy storage capacity in 2024 adopted LFP-based energy storage battery products. The growing share of energy storage battery systems in power grids is accompanied by a corresponding increase in safety risks. In recent years, fire and explosion accidents in energy storage power plants have been reported repeatedly in different countries. These accidents have caused tremendous economic losses and public safety concerns, and they clearly reveal that the current safety monitoring methods are not yet sufficient to ensure the reliable operation of energy storage battery systems.
The core hazard of lithium-ion batteries originates from thermal runaway, a self-accelerating chain of exothermic reactions inside the cell. During thermal runaway, the energy storage battery releases a large amount of combustible gas, toxic vapor, and heat. The released gases can form flammable or even explosive mixtures when mixed with air, making firefighting extremely difficult. The battery itself contains active cathode material that may release oxygen at elevated temperatures, enabling self-sustained combustion even in an oxygen-deficient environment. Therefore, early detection of thermal runaway is of critical importance for the safe operation of energy storage battery systems.
Numerous early-warning technologies have been proposed in the literature. Surface temperature monitoring is the most commonly used method, but it suffers from signal delay due to the thermal inertia of the battery casing and the cooling effect of the ambient environment. Electrical signals such as voltage, current, and impedance can reflect some internal states, but they are not sufficiently sensitive in the early stage of side reactions. Gas sensors can detect characteristic gaseous products before fire occurs, but in a sealed battery the gas remains inside the casing until the safety valve opens, which means that gas detection inevitably lags behind the actual onset of thermal runaway. Acoustic emission methods based on the venting sound of the safety valve also belong to the post-venting category. Expansion force monitoring has shown promising capabilities because internal gas pressure generates measurable force on the battery surface before the safety valve opens. However, the expansion force signal often requires complex mechanical decoupling models, and its sensitivity in the extremely early stage is comparatively limited.
The casing deformation of the energy storage battery, i.e., the dynamic strain signal, is directly coupled to the internal pressure evolution and thus can serve as a high-sensitivity indicator of internal gas generation. Since gas generation begins at the very early stage of side reactions, the strain signal is expected to provide a much earlier warning than temperature, gas, or acoustic signals. In addition, strain measurement is non-intrusive, low-cost, and easy to integrate into battery module structures. In this study, the strain behavior of a 100 Ah prismatic LFP energy storage battery is systematically investigated. The objectives are: (1) to clarify the strain generation mechanism during thermal runaway; (2) to reveal the spatial distribution and typical evolution process of strain under overheating conditions; (3) to characterize the strain behavior under normal charging and discharging cycles; (4) to identify the influences of SOC and micro-overcharge on thermal runaway strain characteristics; and (5) to construct a full charge–discharge-cycle early-warning model based on dynamic strain signals for the energy storage battery.
2. Experimental Platform and Methods
2.1 Battery Selection
All experiments in this study were performed on prismatic LFP cells. The battery specifications are listed in Table 1. The rated capacity is 100 Ah, the voltage window is 2.5–3.6 V, and the mass is approximately 1.9 kg. The cells were manufactured for energy storage applications and have an aluminum-alloy casing with a safety valve on the top. Before the experiments, the plastic shrink film wrapping the battery casing was removed to allow strain gauge attachment and to avoid the damping effect of the polymer film.
Table 1. Main specifications of the energy storage battery sample.
| Parameter | Value |
|---|---|
| Rated capacity | 100 Ah |
| Maximum charging voltage | 3.6 V |
| Minimum cut-off voltage | 2.5 V |
| Dimensions (H × L × W) | 21.6 cm × 13.5 cm × 3.5 cm |
| Mass | 1.9 ± 0.1 kg |
| Gravimetric energy density | 173.7 Wh/kg |
2.2 Thermal Runaway Experimental Platform
A multifunctional experimental platform was constructed to support thermal runaway tests under various conditions. The main body is a stainless-steel combustion chamber with internal dimensions of 2 m × 2 m × 2 m. The chamber is equipped with a smoke collecting hood, an exhaust duct, and a variable-speed fan to discharge gas products after the safety valve opens. A high-temperature-resistant explosion-proof observation window is installed on one side of the chamber to allow real-time visual observation of the battery during the experiments. The chamber also provides thermal and electrical protection for the surrounding environment.
2.3 Measurement Systems
The experimental setup includes the following major measurement systems:
(1) Heating device. A silicone-rubber heating plate with dimensions of 15 cm × 20 cm × 2 mm and a rated power of 500 W was used to apply external heating. The heating plate was powered by a control box with over-temperature protection.
(2) Temperature measurement. K-type armored thermocouples with a diameter of 1 mm and a length of 30 cm were used to measure battery surface temperatures. The thermocouples were connected to a multi-channel data acquisition instrument with a sampling interval of 1 s. The measurement accuracy is ±1.5 °C.
(3) Charging/discharging device. A Neware 10 V–100 A dual-channel battery tester was used to charge and discharge the battery under programmed protocols. The tester records current, voltage, capacity, and auxiliary parameters.
(4) Force measurement. A planar pressure sensor with a size of 150 mm × 150 mm and a measurement range up to 20 kN was mounted on the large face of the battery. The force data were acquired by a high-resolution display and recorded on a computer through an RS485 interface. The accuracy of the force sensor is 0.25%.
(5) Strain measurement. High-temperature-resistant foil strain gauges with a resistance of 120 Ω and a gauge factor of 2.0 were used. The acceptable operating temperature range is −20 to 200 °C. The strain gauges were adhered to the battery casing using a two-component CH-31 epoxy adhesive. A 5-channel single-bridge 120 Ω strain acquisition module was used for data recording. The measurement accuracy is 0.01%.
(6) Mass measurement. A high-precision electronic balance with a range of 0–40 kg and a resolution of 0.1 g was used to monitor the mass variation of the battery during thermal runaway.
(7) Video recording. A SONY high-definition camera with a frame rate of 50 fps and a resolution of 1080P was used to record the entire test process through the observation window.
(8) Scanning electron microscopy. A TESCAN VEGA Compact scanning electron microscope (SEM) was used to characterize the micro-morphology of the battery casing before and after thermal runaway.
Table 2. Main instruments and measurement uncertainties.
| Instrument | Model | Accuracy |
|---|---|---|
| Strain acquisition module | CMCU-08 | 0.01% |
| Force sensor | PLD204DP | 0.25% |
| Thermocouple | K-type | ±1.5 °C |
| Battery tester | Neware 10 V–100 A | 0.1% of reading |
| Electronic balance | — | 0.1 g resolution |
2.4 Experimental Design
Before each test, the battery was cycled twice at 0.5 C using a constant-current constant-voltage (CC-CV) charging protocol and a constant-current (CC) discharging protocol. The cell was then allowed to rest for 24 hours to ensure consistent initial conditions. The plastic wrapping on the battery surface was removed, and strain gauges were attached to the casing. All strain gauges were aligned with the centerline of the side face of the battery to minimize positional deviation.
For thermal runaway experiments, the battery was fixed in a clamping fixture inside the combustion chamber. The fixture layering, from the reaction frame to the battery, was: pressure sensor, mica plate, battery, heating plate, and another mica plate. A preload force of 1000 N was applied to simulate practical module constraints. Figure 1 in the original experimental setup shows the relative positions of the heating plate, force sensor, thermocouples, and strain gauges. The thermocouple for monitoring the backside temperature was fixed at the center of the opposite large face, and three additional thermocouples were arranged along the centerline of the backside. In the thermal runaway tests, the fully charged battery was heated by the 500 W heating plate with single-side heating. All data acquisition devices were started simultaneously with the heating. Once the safety valve opened, the exhaust fan was switched on. When thermal runaway was fully triggered, the heating plate was switched off. The experiment was terminated after the surface temperature decreased significantly.
For normal charge–discharge tests, the battery was subjected to repeated CC-CV charge and CC discharge cycles. During the tests, strain, voltage, and current data were recorded simultaneously. Three independent repeated experiments were conducted to verify repeatability.
In addition, continuous overcharging tests and micro-overcharge tests were performed. The battery was overcharged at a constant current of 50 A to various states of charge above 100% SOC. After reaching the target SOC, the charging was stopped, and the battery was immediately heated to trigger thermal runaway. The detailed experimental cases are summarized in Table 3.
Table 3. Summary of experimental cases and test conditions.
| Case No. | Battery capacity (Ah) | SOC | Test mode |
|---|---|---|---|
| 1 | 100 | 0% | Overheating thermal runaway |
| 2 | 100 | 20% | Overheating thermal runaway |
| 3 | 100 | 40% | Overheating thermal runaway |
| 4 | 100 | 60% | Overheating thermal runaway |
| 5 | 100 | 80% | Overheating thermal runaway |
| 6 | 100 | 100% | Overheating thermal runaway |
| 7 | 100 | 100% → continuous | Continuous overcharging |
| 8–13 | 100 | 102%, 104%, 106%, 108%, 110%, 112% | Micro-overcharge then overheating |
3. Strain Generation Mechanism and Behavioral Characteristics of the Energy Storage Battery
3.1 Theoretical Strain Generation Mechanism
Under single-side overheating conditions, the temperature near the heating plate rises first, triggering exothermic side reactions in the internal materials. The decomposition of the solid electrolyte interphase (SEI) film and the reactions between the negative electrode and electrolyte release gas species such as CO2, C2H4, and CO. In addition, the evaporation of volatile components in the electrolyte contributes to gas accumulation. The internal pressure of the energy storage battery is therefore composed of three parts:
$$
P_{\mathrm{int}} = P_r + P_{\mathrm{eva}} + P_{\mathrm{exp}} \tag{1}
$$
where \(P_{\mathrm{int}}\) is the total internal pressure, \(P_r\) is the pressure contributed by side-reaction gas generation, \(P_{\mathrm{eva}}\) is the pressure from electrolyte evaporation, and \(P_{\mathrm{exp}}\) is the pressure increase caused by thermal expansion of the existing gases.
Under the high-temperature environment inside the battery, the gas phase can be approximated as an ideal gas. The ideal gas equation gives:
$$
P_{\mathrm{int}} V = nRT \tag{2}
$$
where \(n\) is the amount of gas species, \(V\) is the internal gas volume, \(R\) is the universal gas constant, and \(T\) is the absolute temperature. As \(T\) and \(n\) increase synchronously during the side reactions, \(P_{\mathrm{int}}\) rises progressively.
To further connect the internal pressure with the external strain, a small square area on the side face of the battery casing is analyzed. The force balance in the tangential direction is expressed as:
$$
2 s l \sigma_{\varphi} \sin \varphi = P_{\mathrm{int}} l^2 \tag{3}
$$
where \(s\) is the casing thickness, \(l\) is the side length of the selected square region, \(\sigma_{\varphi}\) is the tangential stress, and \(\varphi\) is the bending angle of the shell. Combining Eq. (2) and Eq. (3), the tangential stress is derived as:
$$
\sigma_{\varphi} = \frac{P_{\mathrm{int}} l}{2s \sin \varphi} = \frac{nRT l}{2 s V \sin \varphi} \tag{4}
$$
During the thermal runaway process, the internal stress is continuously loaded. The strain response of the casing is therefore a monotonically increasing function of the tangential stress:
$$
\varepsilon = f(\sigma_{\varphi}) \tag{5}
$$
For a given energy storage battery, the magnitude of the strain is primarily determined by the amount of gas generated inside. Since the strain responds instantaneously to gas generation, it can reliably reflect the internal state in real-time and provide earlier warning than parameters such as surface temperature or voltage.
The key exothermic reactions that contribute to gas generation during the early stage of thermal runaway include SEI film decomposition and electrolyte decomposition. A typical SEI decomposition reaction can be written as:
$$
\mathrm{(CH_2OCO_2Li)_2 \rightarrow Li_2CO_3 + C_2H_4 + CO_2 + \frac{1}{2}O_2}
$$
The reaction between intercalated lithium in the negative electrode and ethylene carbonate solvent is:
$$
\mathrm{2Li + C_3H_4O_3\,(EC) \rightarrow Li_2CO_3 + C_2H_4}
$$
The decomposition of LiPF6, the commonly used conducting salt, is described by:
$$
\mathrm{LiPF_6 \rightarrow LiF + PF_5}
$$
In LFP-based cells, the cathode is relatively stable, but at very high temperatures it may also release oxygen:
$$
\mathrm{2LiFePO_4 \rightarrow Fe_2P_2O_7 + \frac{1}{2}O_2}
$$
These gas-generating reactions contribute directly to the internal pressure build-up and subsequent casing strain of the energy storage battery.
3.2 Microscopic Evidence of Shell Deformation
SEM images of the battery casing were taken before and after thermal runaway to observe the microscopic deformation features. In the pristine state, the casing surface was smooth and uniform, with clear processing marks and no observable cracks. After thermal runaway, the casing surface exhibited significant wrinkling and visible stretching marks. At higher magnification, the microstructure showed a stepped arrangement from the center toward the edges, which is characteristic of plastic deformation. Some regions displayed tearing at the boundaries, indicating that the casing underwent tensile and shear failure under the combined action of high internal pressure and high temperature. These microscopic observations support the conclusion that the external strain reflects the internal stress state of the energy storage battery and is therefore a valid monitoring signal.
3.3 Spatial Characteristics of Strain: Theoretical Analysis
The side face of the battery casing can be treated as a thin plate because the ratio of the casing thickness to the minimum in-plane dimension is less than 1/20. Assuming that the four edges of the side face are fixed, the boundary conditions are:
$$
\omega\big|_{x=0}=\omega\big|_{x=a}=0,\quad
\left.\frac{\partial \omega}{\partial x}\right|_{x=0}=\left.\frac{\partial \omega}{\partial x}\right|_{x=a}=0,
$$
$$
\omega\big|_{y=0}=\omega\big|_{y=b}=0,\quad
\left.\frac{\partial \omega}{\partial y}\right|_{y=0}=\left.\frac{\partial \omega}{\partial y}\right|_{y=b}=0
$$
where \(a\) and \(b\) are the width and height of the side face, respectively. The deflection \(\omega\) can be expressed by the double Fourier series:
$$
\omega = \sum_{m=1}^{\infty}\sum_{n=1}^{\infty} A_{mn} \sin\frac{m\pi x}{a}\sin\frac{n\pi y}{b} \tag{6}
$$
When the internal pressure is uniformly distributed on the side wall, the load is a constant \(q_0\). Substituting the series into the governing equation of thin-plate bending \(D\nabla^4\omega=q_0\), the coefficients are:
$$
A_{mn} = \frac{c_{mn}}{D\pi^4\left(\dfrac{m^2}{a^2}+\dfrac{n^2}{b^2}\right)^2}
$$
The deflection distribution is then:
$$
\omega = \frac{16q_0}{D\pi^6}
\sum_{\substack{m=1,3,5,\dots \\ n=1,3,5,\dots}}
\frac{\sin\dfrac{m\pi x}{a}\sin\dfrac{n\pi y}{b}}
{mn\left(\dfrac{m^2}{a^2}+\dfrac{n^2}{b^2}\right)^2}
\tag{7}
$$
According to the deflection expression, the maximum deflection occurs at the center of the side face, i.e., at \(x=a/2\), \(y=b/2\). Therefore, the maximum strain is expected at the center of the battery side face. This location is the most sensitive region for strain monitoring of the energy storage battery.
3.4 Spatial Characteristics of Strain: Experimental Verification
To verify the theoretical prediction, three strain gauges were adhered along the centerline of the battery side face in the vertical direction at equal intervals. In the 100% SOC overheating test, the center strain gauge \(\varepsilon_2\) recorded the largest peak strain of 8137.6 µε, which was approximately 20% and 30% higher than the upper gauge \(\varepsilon_3\) and the lower gauge \(\varepsilon_1\), respectively. The center strain gauge also exhibited the fastest strain rise rate after 300 s and reached its peak earlier than the other two positions. Photographs of the battery after thermal runaway confirmed that the bulge deformation was most significant at the center of the side face. These results indicate that the side-face center should be selected as the preferred mounting position for strain-based monitoring of the energy storage battery.
3.5 Typical Strain Evolution During Thermal Runaway
Figure 3 in the original experiment describes the typical thermal runaway development process of a 100% SOC energy storage battery. The strain evolution can be divided into five characteristic stages, which are summarized in Table 4.
Table 4. Five stages of strain evolution during the typical thermal runaway of the energy storage battery.
| Stage | Time interval | Strain behavior | Dominant mechanism |
|---|---|---|---|
| I | \(t < t_{abn}\) | Slow increase | Local gas accumulation caused by initial side reactions |
| II | \(t_{abn} < t < t_{\varepsilon p}\) | Rapid increase; \(d\varepsilon/dt \ge 10\) µε/s | Accelerated gas generation, local internal short circuit, shell plastic deformation |
| III | \(t_{\varepsilon p} < t < t_V\) | Strain peak then gradual decline | Non-uniform shell deformation; strain gauge measures regional average |
| IV | \(t_V < t < t_{TR}\) | Strain drops | Pressure relief through the safety valve |
| V | \(t > t_{TR}\) | Strain rises again | Violent exothermic reactions and massive high-temperature gas release |
In Stage I, the strain rise rate is low because gas generation is limited to the region near the heating plate. In Stage II, a turning point appears when the strain rise rate reaches approximately 10 µε/s. At this moment, the expansion force on the large face also exhibits a turning point with a rise rate of about 7.5 N/s. This synchronized change indicates the onset of accelerated internal reactions. In Stage III, the strain reaches a peak value of 8137.6 µε before the safety valve opens. The subsequent decline of the strain is caused by the outward propagation of the bulging zone from the center to the edges, so that the regional average strain decreases. In Stage IV, the gas is released through the safety valve, the internal pressure drops, and the elastic part of the deformation recovers, causing an abrupt decrease in the strain signal. In Stage V, thermal runaway is fully triggered; the temperature rises sharply, and the casing is subjected to a secondary expansion due to the massive production of high-temperature gases.
3.6 Strain Behavior Under Normal Charging and Discharging Conditions
To distinguish abnormal strain from normal operating strain, the energy storage battery was subjected to repeated CC-CV charge and CC discharge cycles. Figure 4 in the original experiment presents the strain response during the first charge–discharge cycle. The following observations were made:
(1) During the constant-current (CC) charging stage, the strain gradually increases and reaches a maximum near the end of CC charging. In the first cycle, the strain increase is more pronounced because the cell is initially at a lower temperature and the input current produces additional Joule heat, enhancing the thermal expansion effect. The peak strain is approximately 600 µε.
(2) During the constant-voltage (CV) charging stage, the charging current decreases rapidly, the internal heating rate reduces, and the strain exhibits a nearly linear decline. The strain rate becomes negative, with a minimum value around −0.15 µε/s.
(3) During the subsequent constant-current discharging stage, the strain first remains almost stable and then increases sharply near the end of discharge. The peak strain at the end of discharge is around 670 µε. This late-stage increase is attributed to the mechanical stress caused by inhomogeneous lithium deintercalation in the electrode particles at low SOC.
In the second and third cycles, the strain behavior is similar except that the CC charging stage no longer shows a significant strain rise because the battery temperature is already elevated from the previous cycle. The peak strain and the strain rate characteristics are repeatable across cycles. The maximum strain variation during normal operation is below 1000 µε, and the peak strain rate lies between 0.3 and 0.5 µε/s. These values are much lower than the thresholds selected for thermal runaway warning.
Table 5. Peak strain and peak strain rate of three repeated normal charge–discharge experiments.
| Experiment | Strain peak of cycle 1 (µε) | Strain rate peak of cycle 1 (µε/s) | Strain peak of cycle 2 (µε) | Strain rate peak of cycle 2 (µε/s) |
|---|---|---|---|---|
| Repetition 1 | 670.4 | 0.5 | 667.5 | 0.4 |
| Repetition 2 | 818.2 | 0.3 | 812.9 | 0.3 |
| Repetition 3 | 443.9 | 0.3 | 438.6 | 0.3 |
4. Strain Characteristics Under Key Influencing Factors
4.1 Influence of State of Charge
The state of charge (SOC) is one of the most important factors affecting the thermal runaway behavior of the energy storage battery. In this study, tests were conducted at SOC levels of 0%, 20%, 40%, 60%, 80%, and 100%. The experimental results are summarized in Table 6.
Table 6. Key time nodes of thermal runaway under different SOCs.
| SOC | \(t_{abn}\) (s) | \(t_{\varepsilon rp}\) (s) | \(t_{\varepsilon p}\) (s) | \(t_V\) (s) | \(t_{TR}\) (s) | \(\Delta t_1\) (s) | \(\Delta t_2\) (s) | \(\Delta t_3\) (s) |
|---|---|---|---|---|---|---|---|---|
| 0% | 680 | 881 | 999 | 1201 | — | 521 | 320 | 202 |
| 20% | 576 | 787 | 869 | 1017 | — | 441 | 230 | 148 |
| 40% | 534 | 761 | 810 | 979 | — | 445 | 218 | 169 |
| 60% | 646 | 845 | 919 | 1015 | 1235 | 369 | 170 | 96 |
| 80% | 616 | 883 | 954 | 1056 | 1234 | 440 | 173 | 102 |
| 100% | 528 | 768 | 798 | 941 | 1068 | 413 | 173 | 143 |
From Table 6, it can be observed that the three characteristic strain nodes, \(t_{abn}\), \(t_{\varepsilon rp}\), and \(t_{\varepsilon p}\), all appear before the safety valve opening time \(t_V\). The corresponding average lead times are 438 s, 214 s, and 143 s, respectively. In general, lower SOC yields longer lead times, which provides more time for emergency response. For the 0% SOC cell, the earliest warning signal appears as much as 521 s before the safety valve opens.
The peak strain and the peak expansion force exhibit an increasing trend with SOC. This can be attributed to the higher content of active lithium and the greater amount of flammable electrolyte in a fully charged cell, which promotes more intense side reactions. Moreover, the peak strain of the energy storage battery appears before the safety valve opens in all SOC cases, which confirms the robustness of strain as a pre-venting early-warning parameter.
The relationship between strain and expansion force in the early stage of thermal runaway is non-linear. The mean curve indicates that the strain increases exponentially with expansion force, which reflects the accelerating gas generation rate as the internal temperature and reaction rate increase. An empirical exponential correlation can be written as:
$$
\varepsilon = \varepsilon_0 + A \exp\left(\frac{F – F_0}{B}\right) \tag{8}
$$
where \(F\) is the expansion force, \(\varepsilon_0\), \(A\), \(B\), and \(F_0\) are fitting parameters. This relationship further confirms that the strain signal is highly sensitive to internal gas generation.
4.2 Early Characteristic Nodes and Rate Analysis
The time-derivative analysis of the characteristic parameters provides a more distinct indication of the onset of acceleration. Figure 4 in the original experiment shows the rate curves of strain, expansion force, and temperature for different SOC conditions. The strain rate curve exhibits a clear turning point at \(d\varepsilon/dt = 10\) µε/s. This turning point is denoted as \(t_{abn}\). At the same moment, the expansion force rate also shows a turning point around 7.5 N/s, whereas the temperature rise rate remains below 0.2 °C/s. Therefore, compared with temperature and expansion force, the strain rate signal exhibits a more obvious abrupt-change feature.
The peak strain rate occurs at \(t_{\varepsilon rp}\), which is followed by the strain peak at \(t_{\varepsilon p}\). Both nodes appear before the safety valve opening. The three time nodes are defined as follows:
$$
\Delta t_1 = t_V – t_{abn}
$$
$$
\Delta t_2 = t_V – t_{\varepsilon rp}
$$
$$
\Delta t_3 = t_V – t_{\varepsilon p}
$$
For SOC values ranging from 0% to 100%, these three indicators provide sufficient warning time. The earliest warning node \(t_{abn}\) corresponds to the onset of SEI decomposition and the beginning of accelerated gas generation.
4.3 Continuous Overcharging Characteristics
In practical operations, the energy storage battery may be subjected to overcharging due to inconsistency among cells or BMS faults. Continuous overcharging tests were conducted to investigate the thermal runaway characteristics under this electrical abuse condition. The charging current was fixed at 50 A (0.5 C), and the charging process continued until the voltage reached the device safety limit of 10 V.
The overcharging process could be divided into three stages:
(1) In the early stage (0–500 s), the voltage increases linearly from 3.4 V to about 4.8 V. The strain and temperature increase slowly, while the expansion force remains almost unchanged. The strain rate is about 2 µε/s, which is much lower than the threshold of 10 µε/s. This stage is characterized by the latent stage of thermal runaway.
(2) In the second stage (500–1200 s), the voltage stabilizes at about 5.5 V. When the overcharged SOC reaches approximately 108%, the expansion force begins to increase linearly, and the strain rise rate also increases. The strain reaches a peak of 4258.2 µε, and the expansion force reaches a peak of 12416.6 N. The safety valve opens at approximately 116.6% SOC. The strain and expansion force exhibit a clear turning point at 108% SOC, indicating that the internal side reactions are significantly accelerated.
(3) After the safety valve opens, the expansion force drops sharply, while the strain first shows a slight decrease and then increases again. The temperature rises more rapidly, but the voltage reaches the cut-off limit of 10 V, suggesting that a large-scale internal short circuit has not yet been formed. Therefore, the overcharging process under this condition does not induce full thermal runaway.
The mechanical deformation caused by continuous overcharging is less severe than that caused by overheating. After overcharging, the casing bulge is relatively mild, and the peak strain is about half of the peak value obtained in the overheating test. This is because overcharging-induced gas generation is accompanied by less heat release, and the moderate temperature limits the plastic deformation of the aluminum casing.
4.4 Strain Response During Micro-overcharging
For a more detailed investigation, micro-overcharge experiments were conducted up to 102%, 104%, 106%, 108%, 110%, and 112% SOC. Table 7 summarizes the key parameter changes during the micro-overcharging process.
Table 7. Key parameter variations of the energy storage battery during micro-overcharging.
| Overcharge range (SOC) | \(\Delta\varepsilon\) (µε) | \(\Delta F\) (N) | \(\Delta T\) (°C) | \(\Delta U\) (V) |
|---|---|---|---|---|
| 100%–102% | 97.8 | 9.8 | 2 | 1.33 |
| 100%–104% | 826.9 | 49 | 5 | 1.43 |
| 100%–106% | 1228.8 | 98 | 9 | 1.69 |
| 100%–108% | 1489.6 | 196 | 12 | 2.01 |
| 100%–110% | 3353.9 | 1960 | 19 | 2.09 |
| 100%–112% | 4762.3 | 3371.2 | 24 | 2.04 |
When the overcharge amount is lower than 108% SOC, both strain and expansion force increase slowly and steadily. The strain rate is approximately 2 µε/s, and the peak strain remains below 1500 µε. When the overcharge state exceeds 108% SOC, the strain rise rate shows a clear turning point and the expansion force begins to increase rapidly. This indicates that 108% SOC is a critical threshold for the safety of the energy storage battery. Therefore, the turning point at 108% SOC can be used as a monitoring indicator for overcharge protection.
4.5 Thermal Runaway After Micro-overcharging
After micro-overcharging to target SOC values, the batteries were immediately heated by the 500 W heating plate. The thermal runaway characteristics are shown in Table 8.
Table 8. Key parameter nodes of thermal runaway for batteries with different micro-overcharge states.
| SOC | \(t_{abn}\) (s) | \(t_{\varepsilon rp}\) (s) | \(t_{\varepsilon p}\) (s) | \(t_V\) (s) | \(t_{TR}\) (s) | \(\Delta t_1\) (s) | \(\Delta t_2\) (s) | \(\Delta t_3\) (s) |
|---|---|---|---|---|---|---|---|---|
| 102% | 648 | 880 | 886 | 1100 | 1180 | 452 | 220 | 214 |
| 104% | 556 | 784 | 814 | 1026 | 1115 | 470 | 242 | 212 |
| 106% | 425 | 630 | 678 | 893 | 1007 | 468 | 263 | 215 |
| 108% | 32 | 478 | 598 | 821 | 1116 | 789 | 343 | 223 |
| 110% | 189 | 496 | 564 | 658 | 764 | 469 | 162 | 94 |
| 112% | 10 | 369 | 519 | 519 | 1120 | 509 | 150 | 0 |
As the overcharge level increases, the safety-valve opening time advances significantly, indicating faster risk formation. The strain and expansion force rise rates are significantly higher for batteries overcharged beyond 108% SOC. In the extreme case of 112% SOC, the strain peak and the safety-valve opening occur almost simultaneously, leaving no margin for warning at the third level. This indicates that overcharging beyond 108% SOC creates a much more dangerous state for the energy storage battery.
The strain rate curves of different micro-overcharge batteries exhibit a two-peak feature. The first weak peak is caused by rapid thermal expansion at the very beginning of heating. Its magnitude increases with the overcharge level because more pre-generated gas is present inside the battery. The second strong peak is caused by the massive gas release from intensified side reactions and appears at the onset of thermal runaway. The interval between the weak peak and the strong peak decreases with increasing overcharge level, indicating a shortened induction period.
5. Early Warning Model Over the Full Charge–Discharge Cycle
5.1 Distinction Between Normal and Abnormal Strain Behavior
The normal charge–discharge tests of the energy storage battery show that strain variations are smooth, cyclical, and generally below 1000 µε. The peak strain rate under normal operation is lower than 0.6 µε/s. During thermal runaway, in contrast, the strain rate exceeds 10 µε/s at the very beginning of the accelerated stage and eventually reaches a peak value of tens of µε/s. The peak strain during thermal runaway is generally above 6000 µε, which is more than one order of magnitude higher than the normal strain level. These significant differences provide a wide margin for threshold determination and false-alarm suppression.
5.2 Three-Level Early Warning Strategy
A three-level early warning strategy based on dynamic strain signals is proposed for the whole charge–discharge cycle of the energy storage battery. The warning levels and thresholds are summarized in Table 9.
Table 9. Proposed three-level early warning strategy based on strain signals.
| Level | Discriminant parameter | Threshold |
|---|---|---|
| I | \(d\varepsilon/dt\) | 10 µε/s |
| II | \(d\varepsilon/dt = \varepsilon_{rps}\) | Peak strain rate with 10% safety margin |
| III | \(\varepsilon = \varepsilon_{ps}\) | Peak strain with 10% safety margin |
Level I. The strain rise rate is calculated in real time. When \(d\varepsilon/dt\) reaches 10 µε/s, the first-level warning is triggered. This node corresponds to the onset of accelerated gas generation and SEI decomposition, and it occurs earlier than any other conventional warning signal.
Level II. The strain rise rate reaches its peak \(\varepsilon_{rps}\). Because the peak strain rate varies with SOC, an empirical relationship is established. For SOC values from 0% to 100%, the peak strain rate can be expressed as:
$$
\varepsilon_{rps} = 19.13 + 0.64\,SOC – 0.01\,SOC^2 + 5.53 \times 10^{-3}\,SOC^3 \tag{9}
$$
For SOC values from 100% to 108%, the following expression is obtained:
$$
\varepsilon_{rps} = -174095.712 + 5062.927\,SOC – 49.060\,SOC^2 + 0.158\,SOC^3 \tag{10}
$$
where SOC is expressed in percent. To avoid false alarms caused by battery-to-battery variation, a 10% safety margin is applied to the peak strain rate.
Level III. The strain signal reaches its peak value before the safety valve opens. The third-level warning is triggered when the measured strain exceeds 90% of the expected peak strain threshold \(\varepsilon_{ps}\). Table 10 lists the calibrated thresholds for different SOC values.
Table 10. Calibrated strain thresholds for level III warning.
| SOC (%) | \(\varepsilon_p\) (µε) | \(\varepsilon_{ps}\) (µε) |
|---|---|---|
| 20 | 6278.2 | 5650.4 |
| 40 | 7633.7 | 6870.3 |
| 60 | 8001.8 | 7201.6 |
| 80 | 10818.4 | 9736.6 |
| 100 | 8137.6 | 7323.8 |
| 102 | 8602.7 | 7742.4 |
| 104 | 11461.3 | 10315.2 |
| 106 | 11136.0 | 10022.4 |
| 108 | 15730.6 | 14157.5 |
For SOC values not listed in the table, the threshold is determined by using the nearest lower SOC level. For example, a battery at 30% SOC uses the threshold calibrated at 20% SOC. This practice is conservative because the peak strain generally increases with SOC, and using a lower-SOC threshold may generate an earlier but still valid warning.
5.3 Warning Time Analysis
Based on the experimental data, the earliest warning node \(t_{abn}\) can provide an average lead time of about 450 s before the safety valve opens for the energy storage battery in the SOC range of 0% to 108%. The second-level warning node \(t_{\varepsilon rp}\) provides about 200 s of lead time, and the third-level warning node \(t_{\varepsilon p}\) provides about 140 s of lead time. For high-SOC or severely overcharged cells, the lead time is reduced, but the first-level warning is still triggered before any fire risk is present. This leaves sufficient time for emergency measures such as disconnecting the battery, activating cooling systems, or evacuating personnel.
6. Conclusions
This study systematically investigated the dynamic strain behavior of a 100 Ah prismatic LFP energy storage battery under normal cycling, overheating, and overcharging conditions. The main conclusions are as follows:
(1) The strain of the energy storage battery casing is generated by internal pressure build-up, which originates from side-reaction gas generation, electrolyte evaporation, and thermal expansion of the gas phase. SEM characterization shows that the shell deformation involves stretching, dislocation, and fracture of the casing material. Theoretical analysis and experiments both confirm that the side-face center is the most sensitive location, with a peak strain about 20%–30% higher than at other positions.
(2) The typical strain evolution during overheating-induced thermal runaway can be divided into five stages. The strain rise rate exhibits a clear turning point at 10 µε/s, which is synchronized with the onset of accelerated expansion force increase. The strain reaches its peak before the safety valve opens, followed by a decline during the venting stage and a secondary rise during the thermal runaway stage. The strain signal provides several characteristic nodes for ultra-early warning.
(3) Under normal charge–discharge cycles, the strain variation of the energy storage battery is small, periodic, and repeatable. The peak strain is below 1000 µε, and the peak strain rate is below 0.6 µε/s. These values are far lower than the corresponding thermal-runaway thresholds, which makes false alarms unlikely.
(4) The SOC has a significant influence on both the thermal runaway intensity and the strain response. The characteristic strain nodes appear earlier at higher SOC levels, and the peak strain increases with SOC. The strain and expansion force exhibit an exponential relationship in the early stage of thermal runaway.
(5) Micro-overcharge tests reveal that 108% SOC is a critical safety threshold for the energy storage battery. When the overcharge state exceeds 108%, the strain rate and expansion force rise abruptly, the safety-valve opening time advances, and the risk of thermal runaway increases substantially. Therefore, the turning point at 108% SOC should be incorporated into overcharge warning algorithms.
(6) A three-level early warning model based on dynamic strain signals was established for the full charge–discharge cycle of the energy storage battery. The thresholds are set at \(d\varepsilon/dt = 10\) µε/s for the first level, the peak strain rate for the second level, and the peak strain for the third level. The model can provide an average earliest warning time of approximately 450 s before the safety valve opens, which demonstrates strong potential for practical application in energy storage safety monitoring.