A two-stage stochastic optimization model for scheduling electric vehicle charging loads to relieve distribution-system constraints

•A two-stage stochastic optimization model to manage electric vehicle charging is proposed.•Sample average approximation and L-shaped method are used to solve the model.•Sequential sampling technique is used to control the sample size and solution quality.•Case study demonstrates benefits in reducing charging and infrastructure costs.•Model is compared to simple heuristics, which do not perform well.

Electric vehicles (EVs) hold promise to improve the energy efficiency and environmental impacts of transportation. However, widespread EV use can impose significant stress on electricity-distribution systems due to their added charging loads.This paper proposes a centralized EV charging-control model, which schedules the charging of EVs that have flexibility. This flexibility stems from EVs that are parked at the charging station for a longer duration of time than is needed to fully recharge the battery. The model is formulated as a two-stage stochastic optimization problem. The model captures the use of distributed energy resources and uncertainties around EV arrival times and charging demands upon arrival, non-EV loads on the distribution system, energy prices, and availability of energy from the distributed energy resources. We use a Monte Carlo-based sample-average approximation technique and an L-shaped method to solve the resulting optimization problem efficiently. We also apply a sequential sampling technique to dynamically determine the optimal size of the randomly sampled scenario tree to give a solution with a desired quality at minimal computational cost.We demonstrate the use of our model on a Central-Ohio-based case study. We show the benefits of the model in reducing charging costs, negative impacts on the distribution system, and unserved EV-charging demand compared to simpler heuristics. We also conduct sensitivity analyses, to show how the model performs and the resulting costs and load profiles when the design of the station or EV-usage parameters are changed.