An Energy-Optimal Warm-Up Strategy for Li-Ion Batteries and Its Approximations

The resistance of lithium-ion cells increases at subzero temperatures reducing the cells' power availability. One way to improve a cell's performance in these adverse operation conditions is to proactively heat them. This paper considers the scenario in which a cell is heated from both inside and outside; a current is drawn from the cell to power a convective heater and Joule heating warms the cell from inside. A method to derive the time-limited energy-optimal current policy is presented, analyzed, and numerically solved. It is proven that the optimal current policy is a sequence of constant voltage, constant current, and rest phases. Using this observation, two rule-based approximations of the optimal solution are presented and their relative performance is compared to conclude that the inclusion of the rest phase has the potential to decrease energy consumption by ~9%. To build and compare these approximations, new tools related to the estimation of the time-limited backward reachable set of nonlinear systems are presented.