The widespread adoption of lithium-ion batteries in electric vehicles and energy storage systems is continuously challenged by critical safety concerns, primarily thermal runaway. As a pivotal stage preceding thermal runaway, the internal short circuit (ISC) fault within a lithium-ion battery initiates localized self-discharge and intense joule heating. This process can rapidly escalate, leading to catastrophic failure if not detected promptly. Conventional diagnostic methods relying solely on terminal voltage, current, and surface temperature measurements often fail to provide early or accurate warnings for ISC, especially in lithium iron phosphate (LFP) batteries with their characteristic flat open-circuit voltage plateau. Consequently, there is a pressing need for novel diagnostic techniques capable of probing the internal state of the battery. Electrochemical Impedance Spectroscopy (EIS), a non-destructive technique sensitive to internal electrochemical kinetics, presents a promising avenue. This article details our research into developing an online ISC diagnosis strategy for lithium-ion batteries, centered on real-time EIS measurement for internal temperature estimation.
Our work commenced with the implementation of a practical online EIS measurement scheme. We utilized a specialized battery management (DNB) chip with integrated EIS functionality, mounted on a flexible circuit board attached directly to the cell tabs. To ensure measurement accuracy comparable to laboratory-grade equipment, we identified and corrected systematic errors inherent in the embedded chip’s measurement approach. The deviation between the chip’s raw measurements and those from a precision potentiostat was analyzed across frequencies, states of charge (SOC: 20%, 50%, 80%), and temperatures (10°C, 25°C). The analysis revealed a constant offset in the real part of the impedance and a frequency-linear deviation in the imaginary part, attributed to contact resistance and inductive coupling in the measurement leads, respectively. We applied the following correction formulas:
$$ Z_{compRe} = Z_{measRe} + R_{Re} $$
$$ Z_{compIm} = Z_{measIm} + M_{Im} \cdot f + R_{Im} $$
where \(Z_{compRe}\) and \(Z_{compIm}\) are the corrected real and imaginary impedance, \(Z_{measRe}\) and \(Z_{measIm}\) are the measured values, \(f\) is the measurement frequency, and \(R_{Re}\), \(M_{Im}\), \(R_{Im}\) are correction parameters. The parameters, determined by fitting experimental data, were found to be independent of the lithium-ion battery’s SOC and temperature, confirming they were artifacts of the measurement setup. The average correction parameters are summarized below.
| Parameter | Average Value |
|---|---|
| \(R_{Re}\) | 0.585 mΩ |
| \(M_{Im}\) | -0.029 mΩ/Hz |
| \(R_{Im}\) | 3.387 mΩ |
The performance of the corrected online EIS measurement system was validated. The results showed excellent agreement with the potentiostat. In the frequency range from 1 kHz to 0.1 Hz, the relative error of the impedance magnitude was predominantly below 5%. For frequencies below 100 Hz, the absolute error in the impedance phase angle was less than 2°. This validated scheme enabled reliable online acquisition of the lithium-ion battery’s electrochemical impedance spectrum.
We then investigated the EIS response of a lithium-ion battery under an ISC condition. A nail penetration test was conducted on an LFP cell at 80% SOC to induce an internal short circuit. The EIS was measured immediately after penetration and at subsequent intervals. The results indicated a clear leftward shift of the EIS spectrum over time, with a significant reduction in the mid-to-low frequency impedance associated with charge transfer and diffusion processes. This evolution was attributed to the gradual temperature rise within the lithium-ion battery caused by persistent joule heating at the short-circuit site. This experiment underscored that EIS contains features responsive to the thermal effects of an ISC.
To decouple the effect of temperature from other factors like self-discharge, we conducted a controlled experiment to establish the direct relationship between the internal temperature of a lithium-ion battery and its EIS. Cells at various SOCs were placed in a thermal chamber, stabilized at different temperatures from 15°C to 70°C, and their EIS was measured. The results, exemplified for a 50% SOC cell, demonstrated that increasing temperature consistently reduced the overall impedance and caused the mid-frequency semicircle to shrink dramatically, eventually becoming indistinguishable at higher temperatures. The Bode plots revealed that temperature had a profound impact on the imaginary part and phase angle in the 10-200 Hz range.
The next critical step was to extract impedance features that are highly sensitive to temperature but relatively invariant to SOC and state of health (SOH), which is essential for a robust estimation model. We analyzed the impedance phase angle and imaginary part at six candidate frequencies within 10-200 Hz: 9.5, 24.8, 49.5, 99.2, 158.3, and 198.4 Hz. Box-plot analysis confirmed that variations due to temperature dominated over those caused by SOC changes or mild self-discharge currents. The Pearson correlation coefficients between these features and temperature were calculated. The results, presented in the table below, showed that the phase angle at frequencies above 99.2 Hz had an extremely strong correlation ( > 0.9) with the temperature of the lithium-ion battery.
| Frequency (Hz) | Corr. (Imaginary Part) | Corr. (Phase Angle) |
|---|---|---|
| 9.5 | 0.847 | 0.895 |
| 24.8 | 0.899 | 0.941 |
| 49.5 | 0.929 | 0.964 |
| 99.2 | 0.952 | 0.982 |
| 158.3 | 0.962 | 0.987 |
| 198.4 | 0.964 | 0.989 |
Based on the sensitivity and correlation analysis, the phase angles at 24.8, 49.5, 99.2, and 158.3 Hz were selected for model development. Since electrochemical kinetics follow the Arrhenius law, we adopted an Arrhenius-type equation to model the relationship between the selected phase angle \(\phi\) and the absolute internal temperature \(T_{in}\) of the lithium-ion battery:
$$ \phi = k \cdot \exp\left(\frac{E_A}{RT_{in}}\right) + \phi’ $$
where \(k\), \(E_A\), \(R\), and \(\phi’\) are fitting parameters. This equation can be rearranged to estimate temperature:
$$ T_{in}(^\circ C) = M \cdot \frac{1}{\ln\left(\frac{\phi – \phi’}{k}\right)} – 273.15 $$
where \(M = E_A/R\). The model was fitted using EIS data from cells at different SOCs and temperatures. All fits yielded a coefficient of determination \(R^2\) greater than 0.98, confirming an excellent fit. The temperature estimation performance was evaluated. The phase angle-based estimation was found to be superior to the imaginary-part-based method, especially at higher temperatures. Among the frequencies, the phase angle at 99.2 Hz (\(\phi^*\)) provided the most accurate and stable estimation, with a maximum error below 4°C and an average error less than 1°C within the 15-65°C range. Therefore, the final internal average temperature estimation model for the lithium-ion battery is:
$$ T_{est} (^\circ C) = \frac{3328.79}{\ln\left( \frac{\phi^* – 35.01}{-4.76 \times 10^{-4}} \right)} – 273.15 $$
Equipped with the capability to estimate the internal temperature of a lithium-ion battery in real-time via EIS, we developed an ISC diagnosis strategy. The core idea is that an ISC introduces significant joule heat, causing an abnormal rise in the battery’s internal temperature and heat generation rate. We employed a lumped-parameter thermal model:
$$ q = C_{th}\left( \frac{dT_b}{dt} + \frac{T_b – T_a}{R_{th}C_{th}} \right) $$
where \(q\) is the total heat generation rate, \(C_{th}\) is the thermal capacitance, \(R_{th}\) is the thermal resistance, \(T_b\) is the bulk (internal) temperature, and \(T_a\) is the ambient temperature. The heat generation for a lithium-ion battery with an ISC is:
$$ q = I(U_{OCV} – U_t) + U_t I_{sc} $$
where \(I\) is the applied current, \(U_{OCV}\) is the open-circuit voltage, \(U_t\) is the terminal voltage, and \(I_{sc}\) is the internal short-circuit current. Discretizing and combining these equations yields a linear form in the unknown parameters \(I_{sc}\) and \(1/R_{th}\):
$$ y_k = \phi_k \cdot \theta_k $$
with \(y_k = (T_{b,k+1} – T_{b,k})/\Delta t – I_k(U_{OCV,k} – U_{t,k})/C_{th}\), \(\phi_k = [U_{t,k}/C_{th},\ (T_{a,k} – T_{b,k})/C_{th}]\), and \(\theta_k = [I_{sc,k},\ 1/R_{th,k}]^T\). The internal temperature \(T_b\) is provided by our EIS-based estimator. We then applied a Recursive Least Squares (RLS) algorithm with a forgetting factor \(\lambda=0.998\) to online identify the parameter vector \(\theta_k\):
$$ G_k = \frac{L_{k-1}\phi_k}{\lambda + \phi_k^T L_{k-1}\phi_k} $$
$$ L_k = (L_{k-1} – G_k\phi_k^T L_{-1})\lambda^{-1} $$
$$ \theta_k = \theta_{k-1} – G_k(y_k – \phi_k^T\theta_{k-1}) $$
The identified \(I_{sc,k}\) allows for the calculation of the equivalent ISC resistance \(R_{sc,k} = U_{t,k}/I_{sc,k}\). A fault is diagnosed when the estimated \(I_{sc}\) exceeds a predefined threshold (e.g., 1 A).
The proposed strategy was validated experimentally on a pack of four series-connected LFP cells. An internal short circuit was induced in one cell via a 6mm deep nail penetration at 25°C. The pack underwent a complex profile including discharge, rest, and post-fault discharge. Throughout the test, the online EIS system continuously measured the phase angle at 99.2 Hz to estimate the internal temperature of each lithium-ion battery. For comparison, a diagnosis strategy based on surface temperature measurements was also run in parallel. The reference ISC resistance was determined to be 2.284 Ω from a post-test CCCV charge curve. The diagnosis results are summarized below.
| Metric | Surface-Temp-Based Strategy | EIS Internal-Temp-Based Strategy (Ours) |
|---|---|---|
| Time to Diagnose ISC | 2045 s | 578 s |
| Estimated \(R_{sc}\) (Ω) | 3.361 | 2.678 |
| Error vs. Reference (2.284 Ω) | 47% | 17% |
The results demonstrate the superior performance of our EIS-based internal temperature estimation strategy for lithium-ion battery ISC diagnosis. It detected the fault approximately 1,400 seconds earlier than the surface-temperature-based method. Furthermore, the estimation accuracy for the critical ISC resistance parameter improved by 30%, providing a more reliable quantification of the fault severity. This work establishes a framework for using online EIS, not just as a diagnostic snapshot, but as a continuous monitor of the internal thermal state of a lithium-ion battery, enabling early and accurate warning against one of the most critical failure modes leading to thermal runaway.