The safe and reliable operation of lithium-ion battery packs is paramount, especially as they form the cornerstone of modern electric vehicles and large-scale energy storage systems. Among various potential failure modes, the internal short-circuit (ISC) fault within a lithium-ion battery cell is particularly insidious and hazardous. This fault occurs when the separator between the cathode and anode fails, allowing direct contact and creating an internal current path. This leads to uncontrolled self-discharge, localized heat generation, and can rapidly escalate into thermal runaway—a catastrophic event involving fire and explosion. Therefore, developing effective, real-time diagnostic methods for ISC faults is a critical research challenge for enhancing the safety and longevity of lithium-ion battery systems.
Existing diagnostic approaches can be broadly categorized into those targeting single cells and those for series-connected packs. Single-cell methods often rely on model-based state estimation, such as using Extended Kalman Filters (EKF) to estimate the state-of-charge (SOC) discrepancy caused by the internal leakage current. While accurate, these methods require precise battery models and are computationally intensive. For battery packs, methods often exploit the voltage divergence between the faulty cell and healthy peers. However, many pack-level algorithms still involve complex modeling or significant computation, posing challenges for practical deployment in Battery Management Systems (BMS) with limited resources.
To address the gap for a simple yet effective pack-level diagnostic tool, this work proposes a data-driven fault diagnosis method based on a Mean Normalization (MN) value analysis, enhanced with a smoothing filter. The core principle is straightforward: an ISC fault causes the voltage of the affected lithium-ion battery cell to deviate from the pack’s average voltage over time. By normalizing each cell’s voltage relative to the pack’s statistics, this deviation is amplified into a clear fault signature.
Theoretical Foundation of the Mean Normalization (MN) Method
Consider a series-connected lithium-ion battery pack consisting of \( n \) cells. Let \( U_j(t_i) \) represent the terminal voltage of the \( j \)-th cell at time sample \( t_i \), where \( j = 1, 2, …, n \). For each time instance \( t_i \), we calculate the following pack statistics:
- Maximum cell voltage: \( U_{\text{max}}(t_i) = \max(U_1(t_i), U_2(t_i), …, U_n(t_i)) \)
- Minimum cell voltage: \( U_{\text{min}}(t_i) = \min(U_1(t_i), U_2(t_i), …, U_n(t_i)) \)
- Mean cell voltage: \( U_{\text{mean}}(t_i) = \frac{1}{n} \sum_{j=1}^{n} U_j(t_i) \)
The Mean Normalization (MN) value for cell \( j \) at time \( t_i \) is then defined as:
$$ Z_j(t_i) = \frac{U_j(t_i) – U_{\text{mean}}(t_i)}{U_{\text{max}}(t_i) – U_{\text{min}}(t_i)} $$
This formulation offers significant advantages for fault detection in a lithium-ion battery pack:
- Amplification of Fault Signature: For a healthy cell under normal operation, its voltage \( U_j(t_i) \) closely tracks the pack mean \( U_{\text{mean}}(t_i) \), resulting in an \( Z_j(t_i) \) value oscillating near zero. When an ISC occurs in cell \( k \), its voltage \( U_k(t_i) \) begins to drop relative to others due to self-discharge. Consequently, the numerator \( (U_k – U_{\text{mean}}) \) becomes increasingly negative. Simultaneously, the presence of this low-voltage cell increases the denominator \( (U_{\text{max}} – U_{\text{min}}) \). The combined effect causes \( Z_k(t_i) \) for the faulty lithium-ion battery cell to trend negatively and diverge markedly from the cluster of healthy cells.
- Inherent Adaptability: The MN value is self-referential to the pack’s own state, making it adaptable to different operating conditions (e.g., charging, discharging, rest) and pack aging states. It inherently accounts for the overall voltage spread of the lithium-ion battery pack.
The behavior of the MN value for a faulty lithium-ion battery cell can be summarized as follows:
$$ \text{If ISC occurs in cell } k: \quad U_k(t) \downarrow \quad \Rightarrow \quad (U_k – U_{\text{mean}}) \downarrow \quad \text{and} \quad (U_{\text{max}} – U_{\text{min}}) \uparrow \quad \Rightarrow \quad Z_k(t) \downarrow \text{ significantly}. $$
For healthy cells, the change in the denominator often offsets minor changes in the numerator, keeping their \( Z_j(t) \) relatively stable.
Signal Smoothing Using Adaptive Kalman Filtering
In a real-world BMS, voltage measurements are contaminated with noise from sensors and electromagnetic interference. This noise propagates into the calculated MN values, causing high-frequency fluctuations that can obscure the underlying fault trend and potentially trigger false alarms. Therefore, smoothing the \( Z_j(t_i) \) sequence is essential for reliable diagnosis.
We employ an Adaptive Extended Kalman Filter (AEKF) for this purpose. The AEKF is chosen for its ability to recursively estimate the state of a dynamic system while adapting to changing noise statistics, providing robust performance for the non-stationary signals from a lithium-ion battery pack. The state-space model for filtering the MN value of a single cell is defined as follows:
State Transition Equation:
$$ x_{k} = A_{k} x_{k-1} + w_{k} $$
where \( x_k = Z_j(t_k) \) is the state (the true MN value), \( A_k = 1 \) (assuming a random walk model), and \( w_k \) is the process noise with covariance \( Q_k \).
Measurement Equation:
$$ y_{k} = x_{k} + v_{k} $$
where \( y_k \) is the noisy measured MN value calculated directly from voltage readings, and \( v_k \) is the measurement noise with covariance \( R_k \).
The standard Kalman filter recursion involves prediction and update steps. The adaptive mechanism involves continuously estimating and updating the noise covariances \( Q_k \) and \( R_k \) based on the innovation sequence (the difference between the measurement and the prediction). A common approach uses a forgetting factor \( b \) (with \( 0 < b < 1 \)):
Innovation: \( \xi_{k} = y_{k} – x_{k|k-1} \)
Adaptive update for measurement noise covariance:
$$ R_{k} = (1 – d_k) R_{k-1} + d_k (\xi_k \xi_k^T – P_{k|k-1}) $$
where \( d_k = (1 – b)/(1 – b^{k}) \), and \( P_{k|k-1} \) is the predicted state covariance.
A similar logic can be applied to update \( Q_k \). This adaptive feature allows the filter to smooth the MN value trajectory effectively, even as the statistical properties of the noise change during different operational phases of the lithium-ion battery pack.
The Integrated Fault Diagnosis Algorithm
The complete diagnostic algorithm for the lithium-ion battery pack is executed in the following steps, which can be efficiently implemented in a BMS:
| Step | Action | Description |
|---|---|---|
| 1 | Data Acquisition | Sample terminal voltages \( U_j \) for all \( n \) cells in the lithium-ion battery pack at time \( t_k \). |
| 2 | MN Value Calculation | Compute \( U_{\text{mean}} \), \( U_{\text{max}} \), \( U_{\text{min}} \) for the pack. Calculate raw MN value \( Z_j^{\text{raw}}(t_k) \) for each cell using Eq. (1). |
| 3 | Signal Smoothing | Apply the AEKF to each cell’s sequence of \( Z_j^{\text{raw}} \) to obtain the smoothed, denoised MN value \( Z_j^{\text{filtered}}(t_k) \). |
| 4 | Fault Detection | Monitor \( Z_j^{\text{filtered}}(t_k) \) for each lithium-ion battery cell. If \( Z_j^{\text{filtered}}(t_k) \) crosses a predefined negative threshold \( \tau \) (e.g., \( \tau = -0.5 \)) and remains beyond it, flag cell \( j \) as faulty. |
| 5 | Alert & Management | Trigger a diagnostic alarm and initiate appropriate battery management actions (e.g., current limit, request for service). |
The threshold \( \tau \) is determined empirically through extensive testing on the specific lithium-ion battery pack chemistry and configuration. It must be set to avoid false positives from normal voltage imbalances while being sensitive enough to detect incipient ISC faults.
Experimental Validation and Results
To validate the proposed method, experiments were conducted on an 18-cell series-connected (18S1P) lithium-ion battery pack using LiFePO₄ (LFP) cells. The key specifications of the test subject are summarized below:
| Parameter | Cell Specification | Pack Specification |
|---|---|---|
| Chemistry | Lithium Iron Phosphate (LFP) | – |
| Nominal Capacity | 302 Ah | 17.5 kWh |
| Voltage Range | 2.5 V – 3.65 V | 45 V – 65.7 V |
| Configuration | – | 18S1P |
A hardware-in-the-loop test platform was used, comprising a battery cycler, a thermal chamber, and a data acquisition system. The Dynamic Stress Test (DST) profile was applied to simulate real-world driving loads on the lithium-ion battery pack.
Internal Short-Circuit Fault Simulation: Accurately triggering a real ISC inside a sealed lithium-ion battery cell is dangerous and non-repeatable. Therefore, a widely accepted method of connecting an external shunt resistor \( R_{sh} \) across the terminals of a selected cell was used to mimic the electrical behavior of an ISC. The equivalent leakage current is given by \( I_{leak} = U_{cell} / R_{sh} \). A smaller \( R_{sh} \) simulates a more severe (“harder”) short. For these tests, \( R_{sh} = 100 \Omega \) was used to simulate a soft internal short circuit in the lithium-ion battery cell.
Scenario 1: Single Cell ISC Fault
The diagnostic algorithm was first tested with an ISC fault induced in a single cell. Two representative cell positions were tested: Cell #1 (at the edge of the pack) and Cell #5 (near the middle). The voltage profiles, raw MN values, and AEKF-smoothed MN values were recorded.
When the ISC was applied to Cell #1, its voltage began to decay relative to the other cells. The corresponding raw MN value for Cell #1 immediately started a negative drift but was noisy. After processing with the AEKF, the smoothed MN value for Cell #1 showed a clear, monotonic decrease, eventually crossing the detection threshold of \( \tau = -0.5 \). The MN values for all other healthy lithium-ion battery cells remained clustered near zero. This provided a unambiguous fault indication. The algorithm successfully identified the fault regardless of the cell’s position within the pack. Furthermore, when the shunt resistor was removed (simulating a transient or cleared fault), the MN value for Cell #1 recovered back towards the healthy cluster, and the fault flag was automatically cleared, demonstrating the algorithm’s ability to handle non-persistent anomalies.
Scenario 2: Multiple Simultaneous Cell ISC Faults
A more challenging scenario involving concurrent ISC faults in three cells (Cells #2, #10, and #15) was tested to evaluate the algorithm’s robustness. The results confirmed that the method remained effective. The smoothed MN values for the three faulty lithium-ion battery cells diverged negatively and crossed the threshold, while the healthy cells’ MN values stayed within the normal bounds. This experiment validated that the proposed method is not limited to single-fault scenarios and can diagnose multiple independent internal short-circuit faults within the same lithium-ion battery pack.
The table below summarizes the key outcomes from the experimental validation:
| Test Scenario | Faulty Cell(s) | Algorithm Detection Result | Time to Clear Detection (Post-Fault Clearance) |
|---|---|---|---|
| Single Fault – Edge | Cell #1 | Correctly identified. MN value crossed threshold. | ~5 minutes |
| Single Fault – Middle | Cell #5 | Correctly identified. MN value crossed threshold. | ~5 minutes |
| Multiple Faults | Cells #2, #10, #15 | All three faulty cells correctly identified. | N/A (faults sustained) |
Discussion and Advantages
The proposed MN-based method offers several compelling advantages for diagnosing internal short-circuit faults in lithium-ion battery packs:
- Computational Simplicity: The core calculation involves basic arithmetic operations (min, max, mean, subtraction, division) on measured voltages. This is far less computationally demanding than model-based methods requiring real-time parameter identification and complex state estimation, making it highly suitable for resource-constrained embedded BMS.
- Model-Free Approach: It does not require an accurate electrochemical or equivalent circuit model of the lithium-ion battery. This eliminates errors associated with model inaccuracy and parameter drift over the battery’s lifespan.
- Effective Noise Immunity: The integration of the Adaptive Kalman Filter effectively suppresses measurement noise, revealing the underlying fault trend and significantly improving diagnostic reliability.
- Clear Fault Signature: The divergence of the MN value provides a visually and algorithmically clear indicator, simplifying threshold-based detection logic.
The method’s performance is inherently tied to the voltage measurement precision and sampling rate of the BMS. Higher precision and faster sampling will enable earlier detection of softer short circuits. Furthermore, the choice of the threshold \( \tau \) is a critical practical consideration. It requires calibration based on historical data from the specific lithium-ion battery pack type to account for its inherent cell-to-cell variability under normal operation.
Conclusion
This paper presented a practical and effective data-driven method for diagnosing internal short-circuit faults in series-connected lithium-ion battery packs. By leveraging the Mean Normalization value to amplify the voltage deviation of a faulty cell and employing an Adaptive Kalman Filter for robust signal smoothing, the method transforms subtle voltage discrepancies into clear fault indicators. Experimental validation on an LFP battery pack demonstrated successful diagnosis in both single-cell and multi-cell ISC fault scenarios. The algorithm’s simplicity, model-free nature, and computational efficiency make it a highly attractive candidate for implementation in real-world Battery Management Systems to enhance the safety monitoring of lithium-ion battery packs. Future work will focus on extending the method to quantify the severity of the short circuit (e.g., estimating the equivalent shunt resistance) and integrating it with other diagnostic algorithms for a comprehensive lithium-ion battery pack health management system.