  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 a charge or
discharge cycle. These dynamics are represented by a first-order equivalent
circuit model and validated against experimental data. To demonstrate how
current and SOC imbalance leads to cell degradation, we developed a successive
update 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. 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.

Systems and Control;Systems and Control