Dynamic Charging Policies for Residential Electric Vehicles: A Structural Analysis

Problem Definition: Dynamic electricity tariffs give households an incentive to shift electric-vehicle charging across hours and days. Charging tonight can take advantage of favorable prices and reduce the need for public charging after a long trip. Waiting may offer cheaper future charging and avoid the fixed cost of initiating a session. Charging-rate limits and overnight price differences generate a convex procurement cost, which we call the price stack. Energy can be carried across days while travel and future prices remain uncertain. We study a household that chooses its departure state of charge (SOC) each evening based on the arrival SOC, the current price stack, and forecasts of future prices. Methodology/Results: We formulate the problem as a finite-horizon Markov decision process with stochastic trip demand and characterize the optimal charging policy. We show that the decision separates into whether to charge and how much to charge. The household charges when a charging margin exceeds the fixed home-charging cost, while the conditional target depends on the price stack and the marginal value of stored energy. We identify conditions under which the charging region has a threshold structure and show that, under a flat tariff, the policy has a forecast-dependent (s,S) structure. We construct instances with disconnected charging regions and show that restricting the household to no charging or full charging can break the threshold structure even when the unrestricted policy has one. Finally, replacing the distribution of future price curves by its mean curve can overstate optimal expected cost. Managerial Implications: Smart-charging systems can benefit from allowing charging amounts to adapt to the vehicle's SOC and overnight price conditions rather than imposing full-or-nothing charging. Single-threshold charging rules should be used only when the conditions supporting such a structure are satisfied. Forecast systems should preserve the distribution of future price curves rather than replace it with a mean curve.