Optimal charging of batteries via a single particle model with electrolyte and thermal dynamics

This paper seeks to derive insight on battery charging control using electrochemistry models. Directly using full order complex multi-partial differential equation (PDE) electrochemical battery models is difficult and sometimes impossible to implement. This paper develops an approach for obtaining optimal charge control schemes, while ensuring safety through constraint satisfaction. An optimal charge control problem is mathematically formulated via a coupled reduced order electrochemical-thermal model which conserves key electrochemical and thermal state information. The Legendre-Gauss-Radau (LGR) pseudo-spectral method with adaptive multi-mesh-interval collocation is employed to solve the resulting nonlinear multi-state optimal control problem. Minimum time charge protocols are analyzed in detail subject to solid and electrolyte phase concentration constraints, as well as temperature constraints. The optimization scheme is examined using different input current bounds, and an insight on battery design for fast charging is provided.