Robust Charging and Discharging Coordination of Electric Vehicles with State Dynamics Uncertainties

This article studies a class of electric vehicle (EV) charging and discharging coordination problems considering specific uncertainties involved in the dynamics of EV’s state of charge (SOC). A robust strategy is explored for EVs such that it is always feasible with respect to all the uncertainties. More specifically, based on the so-called robust positive invariant (RPI) set introduced by Bertsekas et al. to describe the effect of the disturbances, a deterministic optimization problem is formulated by removing the uncertainty part in the state dynamics. Then, based upon the implemented optimal solution to the formulated deterministic problem, design a decentralized coordination strategy which is shown to be feasible for all the uncertainties and guarantee the robust optimality. Furthermore, in order to reduce the conservatism and improve the robust optimality, a sequence of robust disturbance sets, instead of the RPI set, is applied for the underlying coordination problem with a fixed terminal time. Numerical simulations are presented to verify the developed results in this work.