Minimum-Time Charging of Energy Storage in Microgrids via Approximate Conic Relaxation

We study the problem of maximizing energy transfer to a load in a DC microgrid while respecting constraints on bus voltages and currents, and accounting for the impact of neighboring constant power loads. Both the objective and dynamic constraints give rise to indefinite quadratic terms, resulting in a non-convex optimization problem. Through change of variables and relaxations we develop a second-order cone program that exactly captures the indefinite constraints and closely approximates the indefinite objective. We demonstrate how this can be used to design nearly optimal charging profiles for periodic pulsed loads in real time.