This article formulates and solves a multiobjective fast charging-minimum degradation optimal control problem (OCP) for a lithium-ion battery module made of series-connected cells equipped with an active balancing circuitry. The cells in the module are subject to heterogeneity induced by manufacturing defects and nonuniform operating conditions. Each cell is expressed via a coupled nonlinear electrochemical, thermal, and aging model and the direct collocation approach is employed to transcribe the OCP into a nonlinear programming problem (NLP). The proposed OCP is formulated under two different schemes of charging operation: 1) same charging time (OCP-SCT) and 2) different charging time (OCP-DCT). The former assumes simultaneous charging of all cells irrespective of their initial conditions, whereas the latter allows for different charging times of the cells to account for heterogeneous initial conditions. The problem is solved for a module with two series-connected cells with intrinsic heterogeneity among them in terms of state of charge and state of health. Results show that the OCP-DCT scheme provides more flexibility to deal with heterogeneity, boasting of lower temperature increase, charging current amplitudes, and degradation. Finally, a comparison with the common practice of constant current (CC) charging over a long-term cycling operation shows that promising savings, in terms of retained capacity, are attainable under both control (OCP-SCT and OCP-DCT) schemes.
Azimi, V., Allam, A., & Onori, S. (2023). Extending Life of Lithium-Ion Battery Systems by Embracing Heterogeneities via an Optimal Control-Based Active Balancing Strategy. IEEE Transactions on Control Systems Technology, 31(3), 1235–1249. https://doi.org/10.1109/TCST.2022.3215610