Lithium-ion batteries have attractive features for many applications, and are widely used as high-energy density storage devices. The internal electrochemical and chemical reactions occurring during charge/discharge make Li-ion batteries sensitive to demand sequences and operating conditions. Battery management systems are necessary to keep cells within acceptable operating ranges to prolong life, reduce charging losses, and mitigate failure. One particular area of recent investigation is incorporating pulsed perturbations in charging protocols. Typical arguments for pulsed perturbations involve reduced chemical impedance and reduced electrode/electrolyte polarization which decrease losses, and electrode diffusion capabilities which can reduce losses and mitigate plating. However, published experimental and simulation evidence is contradictory, with some either arguing in favor pulsed charging and some indicating no effect or worse performance. While experimental results are useful, the measurable results are subtle enough that experimental conditions and uncertainty can be a plausible argument against both positive and negative results. In this work, we ask the following question: What are the features of a battery as a dynamic system that must appear in order for optimal charging sequences to include a periodic component? The answer to this question is then used to illuminate whether some of the physical, mechanistic explanations for the positive effects of perturbations are valid.

The analysis considers two cases: finding the current trajectory to minimize the energy required to supply a fixed amount of charge to a battery, and finding the current trajectory to maximize the charge supplied to the battery while meeting constraints on internal variables related to the deposition of lithium on the anode electrode. Under the assumption that the trajectories for the relevant battery parameters can be predicted using a linear time-invariant dynamic system, analytic solutions are obtained. Using these analytic solutions, we extract conditions on the battery model that must be satisfied in order for the solutions to contain a periodic component. In the case of energy minimization, it can be shown that the the electrochemical impedance must approach the imaginary axis, while in the case of meeting constraints, a necessary condition is developed involving the response of the internal variables to an impulse in charging current. By examining the impedance spectra and impulse responses of typical Li-ion batteries, these results indicate that that pulsed or sinusoidal perturbations do not appear in the optimal charging sequence. It should be emphasized that this analysis does not provide definitive arguments for or against pulse charging or any evidence against any particular experimental results. However, this study provides important guidance when considering a physical explanation for the benefits of pulsed or sinusoidal ripple charging.