Noncooperative and Cooperative Optimization of Electric Vehicle Charging Under Demand Uncertainty: A Robust Stackelberg Game

This paper studies the problem of energy charging using a robust Stackelberg game approach in a power system composed of an aggregator and multiple electric vehicles (EVs) in the presence of demand uncertainty, where the aggregator and EVs are considered to be a leader and multiple followers, respectively. We propose two different robust approaches under demand uncertainty: a noncooperative optimization and a cooperative design. In the robust noncooperative approach, we formulate the energy charging problem as a competitive game among self-interested EVs, where each EV chooses its own demand strategy to maximize its own benefit selfishly. In the robust cooperative model, we present an optimal distributed energy scheduling algorithm that maximizes the sum benefit of the connected EVs. We theoretically prove the existence and uniqueness of robust Stackelberg equilibrium for the two approaches and develop distributed algorithms to converge to the global optimal solution that are robust against the demand uncertainty. Moreover, we extend the two robust models to a time-varying power system to handle the slowly varying environments. Simulation results show the effectiveness of the robust solutions in uncertain environments.