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This paper formulates and solves a multi-objective fast charging-minimumdegradation optimal control problem (OCP) for a lithium-ion battery module madeof series-connected cells equipped with an active balancing circuitry. Thecells in the module are subject to heterogeneity induced by manufacturingdefects and non-uniform operating conditions. Each cell is expressed via acoupled nonlinear electrochemical, thermal, and aging model and the directcollocation approach is employed to transcribe the OCP into a nonlinearprogramming problem (NLP). The proposed OCP is formulated under two differentschemes of charging operation: (i) same-charging-time (OCP-SCT) and (ii)different-charging-time (OCP-DCT). The former assumes simultaneous charging ofall cells irrespective of their initial conditions, whereas the latter allowsfor different charging times of the cells to account for heterogeneous initialconditions. The problem is solved for a module with two series-connected cellswith intrinsic heterogeneity among them in terms of state of charge and stateof health. Results show that the OCP-DCT scheme provides more flexibility todeal with heterogeneity, boasting of lower temperature increase, chargingcurrent amplitudes, and degradation. Finally, comparison with the commonpractice of constant current (CC) charging over a long-term cycling operationshows that promising savings, in terms of retained capacity, are attainableunder both the control (OCP-SCT and OCP-DCT) schemes.

Extending life of Lithium-ion battery systems by embracing heterogeneities via an optimal control-based active balancing strategy