The rapid global expansion of renewable energy infrastructure and electrified transportation has created an unprecedented demand for high-performance, reliable, and safe energy storage solutions. At the heart of this transformation lies the li ion battery, prized for its high energy density, long cycle life, and decreasing cost. However, the practical application of a li ion battery rarely involves a single cell. To meet the voltage and capacity requirements of electric vehicles, grid storage, and other high-power applications, hundreds or even thousands of individual li ion battery cells must be connected in series and parallel to form a battery pack. This assembly process introduces a critical challenge: cell-to-cell inconsistency.
Inconsistency among individual li ion battery cells—variations in capacity, internal resistance, self-discharge rate, and aging characteristics—is an inevitable result of minute differences in the complex manufacturing process. These inconsistencies, if not managed, are magnified in a pack configuration. They lead to uneven state-of-charge (SOC) distribution during operation, causing some cells to be over-stressed while others are under-utilized. This accelerates the degradation of the weakest cell, reduces the usable energy and power of the entire pack, compromises safety margins, and ultimately shortens the pack’s service life. Battery Management Systems (BMS) employ cell balancing techniques to mitigate these effects, but these are corrective measures that add cost, complexity, and energy loss. A more fundamental and cost-effective strategy is to maximize the initial consistency of the li ion battery cells selected for assembly through precise sorting.
Traditional sorting methods in li ion battery production lines predominantly rely on static parameters measured at a specific point in time. The most common method is capacity sorting, where cells are grouped based on their measured discharge capacity. Other methods may incorporate internal resistance (DCIR or ACIR) or open-circuit voltage (OCV). While simple and fast, these static methods have a significant limitation: they ensure consistency only at the measured state (e.g., fully charged or discharged) but do not guarantee that the cells will behave identically throughout the entire dynamic charge and discharge process. The voltage trajectory of a li ion battery during operation is a rich source of information, reflecting underlying electrochemical properties such as electrode kinetics, lithium inventory, and phase transition behavior. Two cells with identical static capacity can exhibit different voltage profiles due to variations in internal impedance or electrode homogeneity, leading to divergence in performance under dynamic load conditions in a pack.
Therefore, the next generation of sorting technology must evolve from static snapshot-based methods to dynamic characteristic-based methods. The core idea is to group cells that exhibit similar behavioral patterns over time, specifically during standardized charge and discharge cycles. This promises to yield battery packs with superior dynamic consistency, leading to enhanced longevity, safety, and energy utilization. The challenge has been that implementing dynamic sorting typically requires additional, time-consuming testing protocols, increasing production cost and time. Our work addresses this by leveraging the big data already generated during the standard formation and grading processes on the li ion battery production line. We propose a novel, high-precision sorting method that extracts key dynamic features from existing production data without introducing new test procedures, thereby enabling efficient and accurate dynamic consistency sorting at scale.
1. Production Line Data and Feature Engineering for Li-ion Battery Sorting
Our methodology is built upon the foundational principle of utilizing existing data streams within the li ion battery manufacturing workflow. The specific data utilized comes from the “grading” or “capacity sorting” stage, which is a standard procedure for every commercial li ion battery cell. This stage serves the dual purpose of activating the cell (formation) and measuring its capacity. We collected a dataset comprising voltage and current profiles from this stage for 30,975 commercial lithium iron phosphate (LFP) li ion battery cells, each with a rated capacity of 106 Ah.
1.1 Data Acquisition from the Grading Process
The grading process for these LFP cells consists of a standardized charge-discharge sequence, as shown schematically in previous work. The process can be summarized in three key steps conducted at a controlled temperature (typically 25°C):
- Constant Current-Constant Voltage (CC-CV) Charge: The cell is charged with a constant current (0.5C rate) until the voltage reaches 3.8 V. The charging then continues at this constant voltage until the current decays to a cutoff value of 5 A.
- High-Rate Constant Current Discharge (Part 1): Immediately following the charge, the cell is discharged at a 1C rate for a fixed duration of 40 minutes. This step operates while the cell is at a high SOC, where higher discharge currents are permissible.
- Low-Rate Constant Current Discharge (Part 2): After the 40-minute high-rate pulse, the discharge continues at a lower rate (1/3C) until the cell voltage drops to the lower cutoff voltage of 2.0 V.
Following this grading test, the cell undergoes a “recharge to shipping SOC” procedure for safe storage and transportation. This involves a CC-CV charge to 3.2 V (0.33C, 5A cutoff) followed by a brief 0.5C constant current charge for 15 minutes. Voltage and current were sampled at 1 Hz throughout both the grading and recharge processes. The grading data forms the basis for our dynamic feature extraction and sorting, while the subsequent recharge data is reserved for an independent evaluation of the sorting method’s effectiveness.
1.2 Dynamic Sorting Feature Extraction
The central innovation of our method lies in transforming the raw voltage-time curves from the grading stage into a set of concise yet highly informative dynamic features. We extract four key features, two from the charge phase and two from the discharge phase, which collectively capture the cell’s electrochemical fingerprint.
Charge Phase Features: The CC-CV charge voltage curve for an LFP li ion battery has a characteristic sigmoidal shape due to the two-phase equilibrium of the LFP electrode. A more revealing transformation is the incremental capacity (dQ/dV) analysis. The dQ/dV curve, obtained by differentiating the charge capacity with respect to voltage, typically exhibits a single prominent peak for LFP chemistry. This peak corresponds to the major phase transition plateau. Its properties are sensitive to cell state and internal characteristics.
We calculate the dQ/dV curve using a robust numerical method suitable for production data. The voltage axis is discretized with a fixed, small interval $$ \delta V $$ (e.g., 4 mV). For each discrete voltage point $$ V_i $$, we identify all sampling points where the voltage falls within $$ [V_i, V_i + \delta V] $$. Let the number of such points be $$ N_i $$, the constant charging current be $$ I $$, and the time sampling interval be $$ \delta \tau $$. The dQ/dV value at $$ V_i $$ is then approximated by:
$$
\frac{dQ}{dV}\bigg|_{V_i} = \frac{N_i I \delta \tau}{\delta V}
$$
From this derived curve, we extract two features:
- Peak Voltage ($$ V_m $$): The voltage value at which the dQ/dV curve reaches its maximum. This reflects the equilibrium potential of the main redox reaction and is influenced by internal resistance and electrode polarization.
- Peak Height ($$ \frac{dQ}{dV}_m $$): The magnitude of the dQ/dV peak. This relates to the quantity of active material participating in the phase transition and the sharpness of the voltage plateau.
Discharge Phase Features: From the two-stage discharge, we extract features that capture dynamic behavior under load.
- First-Stage Discharge End Voltage ($$ V_1 $$): The terminal voltage at the end of the 40-minute, 1C constant current discharge pulse. As all cells experience the same current for the same duration, variations in $$ V_1 $$ directly reflect differences in internal resistance and the depth of discharge achieved during this high-rate segment.
- Total Discharge Capacity ($$ \Delta Q $$): The total Ah discharged from the start of the 1C pulse until the voltage reaches 2.0 V. This is the conventional static capacity measurement. Including it ensures our dynamic method retains the valuable information from the industry-standard metric.
Thus, each li ion battery is represented by a four-dimensional feature vector $$ \mathbf{x} = [V_m, (dQ/dV)_m, V_1, \Delta Q]^T $$, which encodes its unique dynamic signature from the production line test.
1.3 Performance Consistency Evaluation Metrics
To objectively evaluate the effectiveness of any li ion battery sorting method, we need metrics that quantify the consistency of a group of cells. We propose a multi-faceted evaluation based on the independent “recharge to shipping SOC” data, which was not used for sorting. This tests how well cells grouped by our method behave in a subsequent, standardized operation. We define six evaluation metrics covering both static and dynamic aspects of performance during this recharge phase.
| Consistency Aspect | Evaluation Metric | Symbol |
|---|---|---|
| Incremental Capacity Curve | dQ/dV Peak Height | $$ P_{dq} $$ |
| Incremental Capacity Curve | dQ/dV Peak Voltage | $$ V_{dq} $$ |
| Terminal Voltage | Recharge Starting Voltage | $$ V_{start} $$ |
| Terminal Voltage | Recharge Ending Voltage (CV phase start) | $$ V_{end} $$ |
| Charging Regime | Ratio of CC Charge Capacity to Total Charge Capacity | $$ R_{cc/cv} $$ |
| Dynamic Profile | Average Pairwise Distance between Voltage-Time Curves | $$ D_{volt} $$ |
For a sorted group (or “bin”) of cells $$ C_i $$ containing $$ n $$ cells, we calculate the standard deviation for the first five scalar metrics. For a group with excellent consistency, these standard deviations should be minimal. For the voltage curve consistency, we calculate the average Euclidean distance between all unique pairs of normalized voltage-time vectors within the bin. Let $$ \mathbf{r}_j $$ be the voltage vector for cell $$ j $$ in the bin. The average voltage distance $$ a_{C_i} $$ is computed as:
$$
a_{C_i} = \frac{\sum_{p=1}^{n-1} \sum_{q=p+1}^{n} \| \text{norm}(\mathbf{r}_p) – \text{norm}(\mathbf{r}_q) \|_2 }{ \binom{n}{2} }
$$
where $$ \text{norm}(\cdot) $$ denotes min-max normalization of the voltage vector. A lower $$ a_{C_i} $$ indicates more similar dynamic charging behavior.
Finally, to obtain a single score representing the overall performance consistency (OPC) of a bin, we aggregate all six normalized metrics:
$$
\text{OPC}_{C_i} = \frac{1}{6} \left( \sigma_{P_{dq}}^{norm} + \sigma_{V_{dq}}^{norm} + \sigma_{V_{start}}^{norm} + \sigma_{V_{end}}^{norm} + \sigma_{R_{cc/cv}}^{norm} + a_{C_i}^{norm} \right)
$$
where $$ \sigma^{norm} $$ denotes the min-max normalized standard deviation. A lower OPC score signifies superior consistency across all evaluated performance dimensions for that group of li ion battery cells.
2. The Dynamic Sorting Algorithm for Li-ion Battery Production
The proposed sorting framework comprises three sequential stages: dynamic feature extraction (described in Section 1.2), anomaly cell screening, and finally, clustering-based sorting of normal cells.
2.1 Anomaly Li-ion Battery Screening via Mahalanobis Distance
Prior to sorting, it is crucial to identify and remove anomalous li ion battery cells from the production batch. These outliers, which could result from manufacturing defects, can severely distort the results of clustering algorithms by pulling cluster centers and increasing within-cluster variance. We employ the Mahalanobis distance for multivariate outlier detection as it accounts for the scale and correlations between our four extracted features.
For a feature vector $$ \mathbf{x} $$ from the dataset with mean vector $$ \boldsymbol{\mu} $$ and covariance matrix $$ \boldsymbol{\Sigma} $$, the Mahalanobis distance $$ D_M(\mathbf{x}) $$ is defined as:
$$
D_M(\mathbf{x}) = \sqrt{(\mathbf{x} – \boldsymbol{\mu})^T \boldsymbol{\Sigma}^{-1} (\mathbf{x} – \boldsymbol{\mu})}
$$
A cell is flagged as anomalous if its $$ D_M(\mathbf{x}) $$ exceeds a predetermined threshold. By analyzing the distribution of distances from our dataset, a threshold of $$ D_M = 5 $$ was selected, effectively identifying cells that are multivariate outliers. This step filtered out 355 cells (approximately 1.15% of the total), ensuring a cleaner dataset for reliable clustering.
2.2 K-means Clustering for Dynamic Grouping
With anomalous cells removed, the core sorting of normal li ion battery cells is performed using the K-means clustering algorithm. K-means is an unsupervised learning method well-suited for this task due to its efficiency with large datasets and its intuitive goal of minimizing within-cluster variance.
Given the preprocessed dataset of $$ m $$ cells $$ \{\mathbf{x}^{(1)}, \mathbf{x}^{(2)}, …, \mathbf{x}^{(m)}\} $$ and a chosen number of clusters $$ K $$ (e.g., $$ K=4 $$ for creating four performance bins), the algorithm proceeds iteratively:
- Initialization: Randomly select $$ K $$ data points as initial cluster centroids $$ \boldsymbol{\mu}_1, \boldsymbol{\mu}_2, …, \boldsymbol{\mu}_K $$.
- Assignment Step: For each cell $$ i $$, assign it to the cluster whose centroid is closest in Euclidean distance.
$$
c^{(i)} := \arg \min_{j} \| \mathbf{x}^{(i)} – \boldsymbol{\mu}_j \|^2, \quad j \in \{1, 2, …, K\}
$$
where $$ c^{(i)} $$ denotes the cluster index assigned to cell $$ i $$. - Update Step: Recalculate the centroid of each cluster as the mean of all points assigned to it.
$$
\boldsymbol{\mu}_j := \frac{\sum_{i=1}^{m} \mathbb{1}\{c^{(i)} = j\} \mathbf{x}^{(i)}}{\sum_{i=1}^{m} \mathbb{1}\{c^{(i)} = j\}}
$$
where $$ \mathbb{1}\{\cdot\} $$ is the indicator function.
Steps 2 and 3 are repeated until the cluster assignments stabilize, minimizing the within-cluster sum of squares (distortion function $$ J $$):
$$
J(c, \boldsymbol{\mu}) = \sum_{i=1}^{m} \| \mathbf{x}^{(i)} – \boldsymbol{\mu}_{c^{(i)}} \|^2
$$
The result is a partition of the li ion battery cells into $$ K $$ distinct groups, where cells within the same group have similar dynamic feature vectors.
3. Sorting Results and Discussion for Li-ion Battery Consistency
We implemented our dynamic sorting method (using $$ K=4 $$ clusters) on the screened dataset and compared its performance against two benchmarks: the traditional Capacity Sorting method (sorting cells into 4 bins based solely on $$ \Delta Q $$) and a Random Sorting method. The bins from each method were ordered by their mean capacity for comparison.
3.1 Static Capacity Consistency
Table 1 summarizes the capacity statistics for each bin from the three methods. As expected, Random Sorting shows no meaningful separation in mean capacity and exhibits the largest standard deviations, confirming its ineffectiveness. Both Capacity Sorting and our Dynamic Sorting successfully create bins with distinct mean capacities. Notably, Capacity Sorting produces bins with slightly lower within-bin capacity standard deviations than Dynamic Sorting. This is expected and even logical, as Capacity Sorting explicitly optimizes for this single static parameter. However, this apparent superiority in static capacity consistency is misleading, as it does not translate to better overall performance consistency, which is the true objective for pack assembly.
| Sorting Method | Bin | Mean Capacity (Ah) | Capacity Std. Dev. (Ah) |
|---|---|---|---|
| Random | 1 | 107.571 | 0.416 |
| 2 | 107.527 | 0.457 | |
| 3 | 107.521 | 0.462 | |
| 4 | 107.538 | 0.449 | |
| Capacity-Based | 1 | 106.214 | 0.180 |
| 2 | 107.142 | 0.238 | |
| 3 | 107.833 | 0.258 | |
| 4 | 108.704 | 0.164 | |
| Dynamic (Proposed) | 1 | 107.108 | 0.324 |
| 2 | 107.488 | 0.327 | |
| 3 | 107.689 | 0.307 | |
| 4 | 108.040 | 0.344 |
3.2 Comprehensive Dynamic Performance Consistency
The true test of a li ion battery sorting method lies in the operational consistency of the resulting groups. We evaluated the bins from both Capacity Sorting and our Dynamic Sorting using the six independent metrics defined in Section 1.3, derived from the recharge data. Visual inspection of the dQ/dV curves from the recharge phase for randomly selected cells from each bin clearly shows that bins created by Dynamic Sorting have significantly higher curve overlap than those from Capacity Sorting, indicating superior electrochemical consistency.
A quantitative comparison of the normalized evaluation metrics is presented in Table 2. For every single performance metric—from dQ/dV characteristics and terminal voltages to charging regime ratio and voltage curve similarity—the average standard deviation (or distance) across the four bins is consistently and significantly lower for the Dynamic Sorting method.
| Evaluation Metric | Capacity-Based Sorting | Dynamic Sorting (Proposed) | Improvement |
|---|---|---|---|
| $$ \sigma_{P_{dq}} $$ (dQ/dV Peak Height) | 0.8855 | 0.8158 | -7.87% |
| $$ \sigma_{V_{dq}} $$ (dQ/dV Peak Voltage) | 0.7819 | 0.6797 | -13.07% |
| $$ \sigma_{V_{start}} $$ (Start Voltage) | 0.6815 | 0.5529 | -18.86% |
| $$ \sigma_{V_{end}} $$ (End Voltage) | 0.7268 | 0.5621 | -22.66% |
| $$ \sigma_{R_{cc/cv}} $$ (CC/CV Ratio) | 0.6818 | 0.5886 | -13.67% |
| $$ a_{volt} $$ (Voltage Curve Distance) | 0.7235 | 0.5804 | -19.77% |
| Overall Performance Consistency (OPC) Score | 0.7468 | 0.6299 | -15.65% |
The most critical result is the Overall Performance Consistency (OPC) score. Our Dynamic Sorting method achieves an OPC of 0.6299, which represents a 15.65% improvement over the Capacity Sorting method’s score of 0.7468. This substantial improvement demonstrates that by focusing on the dynamic voltage curve characteristics inherent in standard production line data, we can group li ion battery cells into bins with markedly higher homogeneity in their actual operational behavior. This enhanced dynamic consistency is paramount for building longer-lasting, safer, and more efficient battery packs, as it ensures cells within a module or pack will age more uniformly and experience less electrical stress during use.
4. Conclusion
In this work, we have developed and validated a novel, practical methodology for high-precision sorting of li ion battery cells based on their dynamic operational characteristics. The method is uniquely advantageous as it leverages the vast amount of big data already generated during the standard grading process on the production line, requiring no additional testing procedures, time, or energy consumption. By extracting four key dynamic features—dQ/dV peak voltage and height from the charge curve, and the first-stage discharge end voltage alongside total capacity—we create a multi-dimensional fingerprint for each cell. A robust pre-processing step using Mahalanobis distance removes anomalous cells, ensuring clustering fidelity. The subsequent application of the K-means algorithm efficiently groups cells with similar dynamic signatures.
When evaluated against the industry-standard capacity sorting method using a comprehensive set of independent performance metrics, our dynamic sorting method demonstrated a decisive improvement. The overall performance consistency of the resulting cell groups was enhanced by 15.65%. This proves that while static capacity is an important parameter, it is insufficient for ensuring cells will behave consistently under real dynamic operating conditions. Our method provides a superior, data-driven solution for forming well-matched li ion battery groups directly from the production line.
Future work will focus on validating the long-term benefits of this dynamic sorting approach. This includes conducting extensive cycle-life testing on battery packs assembled from dynamically sorted cells to quantitatively assess the improvement in aging synchronization and pack longevity compared to those built from capacity-sorted cells. Furthermore, integrating this sorting framework with digital twin and machine learning models for predictive performance and lifetime estimation of assembled packs represents a promising direction for smart li ion battery manufacturing and management.