Closed-form Solution to Optimized CC-CV Charging of Li-ion Batteries Under Charging Time and Energy Loss Constraints

This paper considers the problem of optimal charging in rechargeable Li-ion batteries. Particularly, this paper considers the constant-current constant-voltage (CC-CV) charging strategy, which is widely used in practice for Li-ion battery charging. At present, the charging current during the CC stage is set to a predetermined value such as 0.8 C -rate to minimize energy loss and temperature rise. Some recent works derived the optimal charging current for the CC-CV protocol in a discrete-time state space model. The present paper considers the continuous time version of the problem with constraints on charging time and energy loss. The proposed work in this paper builds on previous work in which the total energy loss and the charging time of the CC-CV strategy were analytically derived. Based on this relation, a cost function was developed by assigning normalized weights for charging time and energy loss, respectively. In this paper, a Newton-Raphson-based optimization technique is implemented on the closed-form costfunction under charging time and energy loss constraints. For the closed-form derivations, a straight-line OCV-SOC model, popularly called the Unnewehr model, was assumed. The proposed approach in this paper is evaluated using data collected from a battery simulator that was based on the characteristic parameters obtained from a cylindrical Li-ion battery.