Co-estimation of branch current and state of charge for inconsistent two-cell parallel lithium-ion battery packs

Conventional state of charge (SOC) estimation methods for parallel-connected lithium-ion battery packs often approximate the current of each cell using an equally divided pack current. However, differences in capacity, internal resistance, SOC, and aging state lead to uneven branch current distribution and consequently reduce individual-cell SOC estimation accuracy. To address this issue, this study proposes a co-estimation framework for the two branch currents and individual-cell SOC. A cascaded dual deep neural network is developed for branch current estimation, in which the first network estimates the individual branch currents from the measured pack voltage and total current, while the second network compensates for the remaining residual errors. A first-order equivalent circuit model is established for each cell, and total least squares is employed for parameter identification to reduce the influence of current and voltage measurement errors. A Sage–Husa adaptive square-root cubature Kalman filter is subsequently developed for individual-cell SOC estimation through adaptive noise covariance updating and square-root covariance propagation. Experiments conducted on a two-cell parallel-connected battery system under different operating cycles, temperatures, and aging states show that the maximum absolute SOC estimation error does not exceed 3.25% under the tested conditions. These results indicate satisfactory estimation performance for the investigated laboratory configuration. Ablation studies further confirm the effectiveness of the key components in the proposed framework. The proposed method provides an effective approach for branch current and SOC estimation in parallel-connected lithium-ion battery packs.