Optimal Control of Film Growth in Lithium-Ion Battery Packs via Relay Switches

Recent advances in lithium-ion battery modeling suggest unequal but controlled and carefully timed charging of individual cells by reduce degradation. This paper compares anode-side film formation for a standard equalization scheme versus unequal charging through switches that are controlled by deterministic dynamic programming (DDP) and DDP-inspired heuristic algorithms. A static map for film growth rate is derived from a first-principles battery model adopted from the electrochemical engineering literature. Using this map, we consider two cells that are connected in parallel via relay switches. The key results are the following: 1) optimal unequal and delayed charging indeed reduces film buildup, and 2) a near-optimal state feedback controller can be designed from the DDP solution and film growth rate convexity properties. The simulation results indicate that the heuristic state feedback controller achieves near optimal performance relative to the DDP solution, with significant reduction in film growth compared to charging both cells equally, for several film growth models. Moreover, the algorithms achieve similar film reduction values on the full electrochemical model. These results correlate with the convexity properties of the film growth map. Hence, this paper demonstrates that unequal charging may indeed reduce film growth, given certain convexity properties exist, lending promise to the concept for improving battery pack life.