A time-of-use pricing strategy for managing electric vehicle clusters

A demand response program for electric vehicles (EV) is proposed to control the charging decision process in EV clusters. This approach corresponds to a time-of-use solution which is an indirect method, based on prices, for inducing demand modifications on consumers. An aggregator of EV fleet acts as a dealer between an electricity market and consumers. The EV aggregator is a price-taker agent from the wholesale electricity market viewpoint and price designer when selling energy to consumers. A game-theoretical model based on a Stackelberg formulation is proposed to capture the interactions between the fleet operator and electric vehicle owners, avoiding the requirement of a price elasticity model for the EV clusters. The interaction between the agents is formulated as a bi-level optimization problem: At the upper-level, the aggregator maximizes its benefits whereas the lower-level represents the dynamic behaviour of rational drivers as a fleet. The EV operator faces uncertainty in wholesale prices when buying energy and when forecasting consumption behaviour, then random parameters are modelled in a scenario framework. The model performance is evaluated through a case study using historical data from car-sharing services in Italy, comparing the result with a fixed-prices model. It is shown that the proposed price-based scheme allows to increment the aggregator profit with respect to a fixed-price contract, producing also a load shifting effect in the charging profile of the fleet.