Fast Charging of Lithium-ion Batteries by Mathematical Reformulation as Mixed Continuous-Discrete Simulation

Optimal charging problems for lithium-ion batteries aim to minimize charge time while maximizing battery lifetime. Real-time optimal control problems are typically solved with model predictive control (MPC) and empirical or simplified physics-based models. This article presents a mixed continuous-discrete (hybrid) approach to fast charging which simultaneously solves the battery system of equations and the embedded solution to the constraint-based control problem. We introduce general operating modes which move beyond conventional current/voltage/power simulations and allow battery models of any scale to simulate new charging modes such as constant temperature, constant concentration, and constant lithium plating overpotential. Example simulations with the new operating modes are shown and solved on the order of 10 ms using a rigorous porous electrode theory-based model with 351 equations. This approach enables nonlinear model predictive control to be implementable in real-time while directly using sophisticated physics-based battery models.