Maximizing charging efficiency of lithium-ion and lead-acid batteries using optimal control theory

Optimal charging of stand-alone lead-acid and lithium-ion batteries is studied in this paper. The objective is to maximize the charging efficiency. In the lithium-ion case two scenarios are studied. First only electronic resistance is considered and in the next step the effect of polarization resistance is also included. By considering constant model parameters for the lithium-ion battery analytical solutions exists for both scenarios using Pontryagins minimum principle. In lead-acid chemistry the variation of total internal resistance with state of charge (SOC) is considerable and the optimal charging problem results in a set of two nonlinear differential equations with one initial and a final condition to be satisfied. This so called two point boundary value problem is solved numerically.