On the Optimality of Procrastination Policy for EV Charging Under Net Energy Metering

We address the problem of behind-the-meter EV charging by a prosumer, co-optimized with rooftop solar, electric battery, and flexible consumption devices such as water heaters and HVAC systems. We consider a scenario involving a time-of-use net energy metering tariff, alongside stochastic solar production and random EV charging demand, a finite-horizon surplus-maximization problem is formulated. We show that a procrastination threshold policy that delays EV charging to the last possible moment is optimal when EV charging is cooptimized with flexible demand, and the policy thresholds can be easily computed offline. When battery storage is part of the co-optimization, we show that the prosumer's net consumption is a two-threshold piecewise linear function of the behind-the-meter renewable generation under the optimal policy, and the procrastination threshold policy remains optimal, although the thresholds cannot be computed easily. We propose a straightfor-ward myopic solution which becomes optimal strategy when the storage state of charge doesn't reach boundary, and demonstrate in a numerical simulation that involves real-world data.