Current Imbalance in Dissimilar Parallel-Connected Batteries and the Fate of Degradation Convergence

Abstract This paper proposes an analytical framework describing how initial capacity and resistance variability in parallel-connected battery cells may inflict additional variability or reduce variability while the cells age. We derive closed-form equations for current and SOC imbalance dynamics within any given charge or discharge cycle. These dynamics are represented by a first-order equivalent circuit model with a linear open circuit voltage behavior and validated against experimental data. To demonstrate how current and SOC imbalance leads to cell degradation, we developed a simplified, incremental degradation update scheme based on the solid electrolyte interphase growth mechanism. We propose a scheme in which the inter-cycle imbalance dynamics update the intra-cycle degradation dynamics, and vice versa. Using this framework, we demonstrate that current imbalance can cause convergent degradation trajectories, consistent with previous reports. However, we also demonstrate that different degradation assumptions, such as those associated with SOC imbalance, may cause divergent degradation in some cases. We finally highlight the role of different cell chemistries, including different OCV function nonlinearities, on system behavior, and derive analytical bounds on the SOC imbalance using Lyapunov analysis.