Quantification of ESS Cell Voltage Inconsistency Using Subspace Projection Based RPCA and Mahalanobis Distance

Large-Scale energy storage systems (ESSs) require quantitative methods for evaluating cell voltage inconsistency using operational data. In a battery rack composed of numerous series-connected cells, differences in state of charge, capacity, internal resistance, and degradation can result in different voltage behaviors even under the same operating conditions. This study proposes a quantitative method for evaluating relative cell voltage inconsistency based on Robust Principal Component Analysis (RPCA), subspace projection, and Mahalanobis Distance (MD). RPCA was applied to decompose the cell voltage matrix into a low rank component representing the common voltage variation shared among cells and a sparse component representing localized deviations. Singular Value Decomposition was then applied to the low-rank component to extract the dominant temporal subspace, and the original voltage trajectory of each cell was projected onto this subspace to obtain representative charging and discharging features. The two features were combined into a two-dimensional feature vector, and MD was calculated to quantify the relative deviation of each cell from the overall cell population. The proposed method was applied to four battery racks, each consisting of 238 cells, over three operating cycles under identical state-of-charge ranges and constant-power conditions. The results showed that most cells exhibited similar MD levels, whereas several cells repeatedly showed relatively high MD values across different cycles. Comparison of their original voltage trajectories confirmed persistent differences in charging and discharging behavior relative to cells with low MD values. In addition, many high-MD cells were located at the same positions within different modules, indicating that structural, measurement, wiring, or balancing effects should also be considered when interpreting the results. Therefore, the proposed MD-based index is more appropriately interpreted as a screening indicator for identifying cells with relatively distinct voltage behavior rather than as a direct indicator of cell degradation or failure.