Regularised dynamic optimal transportation of electric vehicles over networks considering strategic charging pricing

A dynamic optimal transport problem of electric vehicles (EVs) over a network is investigated. The EVs are considered to be transported from their initial locations to the destination nodes for charging purposes. In our framework, the operators of charging stations are strategic, and each of them designs their charging pricing optimally to maximise the revenue. Since EVs play an essential role as power loads at the charging stations, the designed transport strategy by the EV operator has an impact on the market energy price which in turn influences the charging prices. Therefore, to design an efficient transport plan, the EV operator needs to take into account its influence on the charging pricing and the market energy price due to their complex interplay. To achieve this goal, a unified framework is proposed for optimal EV transportation by considering factors including the delay, charging cost, and real-time social demand of EVs over a finite-time horizon. The balanced dynamic optimal transport strategy is enabled through a combined quadratic and entropic regularisation. To compute the equilibrium pricing for all charging stations, an iterative particle-swarm optimisation scheme is designed which addresses a high-dimensional nonlinear optimisation problem. Finally, case studies are used to illustrate and corroborate the obtained results.