Lithium-ion (li ion battery) technology has become ubiquitous, powering everything from portable electronics to electric vehicles due to its high energy density and long cycle life. However, safety remains a paramount concern, with thermal runaway incidents posing significant risks of fire and explosion. Among the various failure mechanisms, the internal short circuit (ISC) is a primary initiator of thermal runaway. While ISCs caused by mechanical abuse (crushing) or thermal abuse (overheating) often manifest rapidly with clear signs, those induced by electrical abuse, particularly over-discharge, present a more insidious challenge. In the initial and prolonged stages of evolution, an over-discharge-induced ISC generates minimal heat and exhibits negligible voltage deviation, making it extremely difficult to detect using conventional monitoring of electrical and thermal signatures. As this fault silently deepens with subsequent charge-discharge cycles, it can eventually precipitate a catastrophic failure. Therefore, developing a reliable early detection method for this specific failure mode is critical for enhancing the safety and reliability of li ion battery systems.
Electrochemical Impedance Spectroscopy (EIS) offers a powerful, non-destructive tool for probing the internal state of a li ion battery. It characterizes the cell’s response to a small-amplitude alternating current across a wide frequency range, producing a spectrum that reflects various internal electrochemical processes—from ion migration in the electrolyte to charge transfer at electrode interfaces and solid-state diffusion within active materials. When an internal short circuit occurs, it alters the battery’s internal structure and electrochemical parameters, which in turn modifies its EIS signature. This study focuses on leveraging the sensitivity of EIS to develop a detection methodology for over-discharge-induced ISCs that is robust against common operating condition variations like State of Charge (SOC) and temperature.
The core principle of an over-discharge-induced ISC in a li ion battery involves the dissolution of the copper current collector from the anode. During severe over-discharge, the anode potential rises abnormally high, reaching the oxidation potential of copper. This causes Cu ions to dissolve into the electrolyte, migrate through the separator, and get reduced/plated onto the cathode surface. Over repeated cycles, this process leads to the growth of copper dendrites, which can ultimately penetrate the separator, creating a metallic bridge between the cathode and anode—an internal short circuit. This micro-shunt path results in persistent self-discharge and gradual degradation of the li ion battery’s internal components.
Experimental Methodology and Baseline Characterization
The research utilized commercial 18650 cylindrical lithium iron phosphate (LFP) li ion battery cells with a nominal capacity of 1100 mAh. To ensure consistency, all cells underwent a pre-conditioning protocol involving several charge-discharge cycles. Their basic performance was verified, as summarized in Table 1.
| Cell ID | Charge Capacity (Ah) | Discharge Capacity (Ah) | Coulombic Efficiency (%) |
|---|---|---|---|
| 1 | 1.092 | 1.090 | 99.82 |
| 2 | 1.098 | 1.095 | 99.72 |
| 3 | 1.093 | 1.092 | 99.91 |
| 4 | 1.098 | 1.096 | 99.82 |
| 5 | 1.095 | 1.091 | 99.63 |
| 6 | 1.096 | 1.092 | 99.64 |
The EIS of fresh cells was measured at 25°C and 50% SOC, showing excellent consistency. The obtained Nyquist plot (imaginary vs. real impedance) for an LFP li ion battery typically features a high-frequency intercept on the real axis, a depressed semicircle in the mid-frequency range, and a low-frequency Warburg tail. This behavior is accurately represented by an equivalent circuit model (ECM). The chosen ECM consists of an ohmic resistance (Ro) in series with a parallel combination of a charge-transfer resistance (Rct) and a constant phase element (CPE, representing the double-layer capacitance), followed by a Warburg element (Zw) for diffusion. The model is expressed as:
$$Z(\omega) = R_o + \frac{1}{\frac{1}{R_{ct}} + (j\omega)^n Q} + Z_w$$
where $Q$ and $n$ are parameters of the CPE, $\omega$ is the angular frequency, and $j$ is the imaginary unit. This model provided an excellent fit to the experimental EIS data, validating its use for parameter extraction.
Influence of Operating Conditions on EIS of a Healthy Li Ion Battery
To identify a robust diagnostic parameter, it is crucial first to understand how the EIS of a healthy li ion battery varies with normal operating conditions, namely SOC and temperature.
Impact of State of Charge (SOC): EIS measurements were taken at different SOC levels (0%, 25%, 50%, 75%, 100%) and temperatures (5°C, 25°C, 45°C). A key finding was that the high-frequency real-axis intercept, corresponding to the ohmic resistance Ro, remained virtually constant across all SOC levels at a given temperature. In contrast, the mid-frequency semicircle (related to Rct) and the low-frequency Warburg diffusion tail changed significantly. For instance, at 25°C, Rct generally decreased with increasing SOC, while the diffusion resistance showed a “U-shaped” trend, increasing at very low and very high SOC due to concentration polarization effects. This indicates that Ro is largely independent of the lithium concentration in the electrodes for a healthy li ion battery.
Impact of Temperature: Temperature has a profound effect on all kinetic processes within a li ion battery. EIS measurements across a 5°C to 45°C range showed that all impedance parameters (Ro, Rct, Zw) increased as temperature decreased, with changes being most dramatic at lower temperatures. The increase in Ro is attributed to higher electrolyte viscosity and reduced ionic mobility. The strong temperature dependence of Rct and diffusion follows the Arrhenius relationship for chemical reaction rates and the temperature-dependent diffusion coefficient. Crucially, within the mild temperature range of 25°C to 45°C, the variation in Ro was minimal. The change rates for the fitted parameters between different temperature ranges are quantified in Table 2.
| Fitted Parameter | Change Rate (5°C to 25°C) | Change Rate (25°C to 45°C) |
|---|---|---|
| Ro | -7.52% | -1.51% |
| Rct | -727.58% | -530.79% |
| Zw | -135.67% | -105.94% |
This analysis reveals a critical insight: the ohmic resistance Ro of a healthy li ion battery is relatively insensitive to changes in SOC and is very stable across the typical operating temperature range of 25°C to 45°C. This makes it a promising candidate for a fault detection parameter, provided it shows sensitivity to the internal short circuit.
Impact of Over-discharge-Induced Internal Short Circuit on EIS
To simulate the realistic scenario of a weak cell in a series string being over-discharged, an experimental method was devised. A test li ion battery at 88% SOC was connected in series with three helper cells at 100% SOC. The pack was then subjected to repeated charge-discharge cycles. During discharge, the test cell was driven into over-discharge (beyond 0V), inducing copper dissolution and the initiation of an internal short circuit. The depth of over-discharge was controlled to be 112% of the cell’s nominal capacity to ensure ISC initiation without immediate thermal runaway.
EIS was measured after each over-discharge cycle. The results showed a clear and consistent trend: the Nyquist plots progressively shifted to the right with increasing cycle count. Fitting the data to the ECM confirmed that all parameters—Ro, Rct, and Zw—increased monotonically as the internal short circuit worsened.
The increase in Ro is particularly significant for detection. It is attributed to the degradation of the internal electrical contacts, especially between the anode active material and the dissolving copper current collector. The contact resistance (Ra) can be described by the Schottky contact current theory. The current $I$ is given by:
$$I = AA^*T^2 \exp\left(-\frac{q\phi_B}{kT}\right) \left[ \exp\left(\frac{qE}{nkT}\right) – 1 \right]$$
where $A$ is the contact area, $A^*$ is the Richardson constant, $q$ is the electron charge, $\phi_B$ is the barrier height, $k$ is Boltzmann’s constant, $E$ is the bias voltage, and $n$ is the ideality factor. The differential contact resistance is:
$$R_a = \left( \frac{dI}{dE} \right)^{-1}$$
Combining these equations shows that $R_a$ is inversely proportional to the contact area $A$. The dissolution of the copper current collector during over-discharge reduces the effective contact area $A$ between the anode material and the current collector, leading to a measurable increase in the overall ohmic resistance Ro of the li ion battery. Simultaneously, the deposition of copper on the cathode and damage to electrode structures increase the charge-transfer and diffusion impedances.
Parameter Selection and Practical Detection Method
The experimental findings guide the selection of an optimal feature for ISC detection:
- Robustness: The parameter should be minimally affected by normal SOC variation and temperature fluctuations in the 25-45°C range.
- Sensitivity: The parameter should exhibit a clear and consistent change in response to the development of an internal short circuit in the li ion battery.
Ro perfectly meets these criteria. However, extracting Ro requires full-spectrum EIS measurement and subsequent ECM fitting, which is computationally intensive for online monitoring.
A highly effective simplification is proposed: use the real part of the impedance at a single high frequency (e.g., 1000 Hz) as a direct proxy for Ro. At high frequencies, the capacitive and diffusion elements of the li ion battery have negligible impedance, so the measured value ($Z_{\text{real}}@1\text{kHz}$) is essentially equal to the ohmic resistance. This was verified experimentally, as shown in the comparison below, where $Z_{\text{real}}@1\text{kHz}$ closely tracks the fitted Ro value under all conditions (SOC, temperature, ISC).
$$Z_{\text{real}}(f=1000\ \text{Hz}) \approx R_o$$
This single-frequency measurement is fast, requires no complex fitting, and is easy to implement in a battery management system (BMS). The detection logic is based on trend analysis, not absolute thresholding, to account for initial cell-to-cell variations in a li ion battery pack:
- Normal Cell: The $Z_{\text{real}}@1\text{kHz}$ value remains stable over consecutive cycles, with fluctuations typically within 0.001 Ω.
- Faulty Cell (with evolving ISC): The $Z_{\text{real}}@1\text{kHz}$ value shows a distinct and steady increasing trend over consecutive cycles (e.g., an increase >0.01 Ω over 5 cycles).
Experimental Validation
The proposed method was rigorously validated. A li ion battery pack consisting of one cell preconditioned for ISC (at 88% SOC) and three healthy cells (100% SOC) underwent multiple charge-discharge cycles. The $Z_{\text{real}}@1\text{kHz}$ for each cell was monitored at the end of discharge in each cycle, under different ambient temperatures (25°C and 35°C).
The results were conclusive: In every test scenario, the healthy cells’ impedance at 1000 Hz remained on a stable, flat trend line. In stark contrast, the cell undergoing over-discharge-induced internal short circuit exhibited a clear and monotonically rising trend in its $Z_{\text{real}}@1\text{kHz}$ value, easily distinguishing it from the normal cells. This confirms the method’s effectiveness and its robustness against moderate temperature variations during operation of the li ion battery pack.
Conclusion
This work establishes a practical and reliable method for the early detection of over-discharge-induced internal short circuits in lithium-ion batteries. By systematically analyzing the influence of SOC, temperature, and fault severity on the electrochemical impedance spectrum, the ohmic resistance (and its practical single-frequency equivalent) was identified as an ideal diagnostic parameter. Its inherent stability during normal operation of a li ion battery, coupled with its sensitivity to the contact degradation caused by copper dissolution during ISC, forms the basis of the technique.
The proposed solution—monitoring the trend of the real part of impedance at 1000 Hz—is particularly advantageous. It is fast, non-invasive, requires minimal computational overhead, and functions accurately across typical states of charge and operating temperatures. Implementing this EIS-based monitoring strategy in battery management systems can provide an early warning for a particularly stealthy and dangerous failure mode, significantly enhancing the safety and longevity of li ion battery packs in electric vehicles and energy storage systems.