Heuristic Versus Optimal Charging of Supercapacitors, Lithium-Ion, and Lead-Acid Batteries: An Efficiency Point of View

Electrical energy storage systems are extensively utilized in applications, including electrified vehicles, renewable power generation, and electronic devices. While discharging events are a function of the power demand, the charging procedure is often controllable. This paper evaluates different charging strategies for stand-alone supercapacitors (SCs), lithium-ion (Li-ion), and lead-acid batteries. Constant power and optimal charging strategies are formulated and the corresponding charging currents are obtained. Efficiency analysis for different charging strategies and charging times (slow and fast) is performed. The identical objective function for all modules is to minimize the resistive losses during a given charging time by utilizing Pontryagin's minimum principle. An analytical solution exists for the SC case, which is constant current charging. The variation of the total internal resistance with state of charge in lead-acid chemistry is considerable, and the optimal charging problem results in a two-point boundary value problem. In case of the Li-ion battery, the model includes the electronic as well as polarization resistance. Furthermore, in order to investigate the influence of temperature on the optimal charging of the Li-ion battery, a constrained optimal control problem for a three state electrothermal model is formulated and solved using dynamic programming.