A Markov chain model of a distribution grid with electric vehicles and solar power

We consider a dynamic model of electric vehicle (EV) charging in a power distribution grid. We introduce uncertainty in the demand side, arising through consumer behavior, as well as the supply side, to account for intermittent renewable energy sources (RES). By developing a fluid approximation, we show that the invariant point of the stochastic process can be obtained by solving an AC-OPF problem with an exact convex relaxation, thereby creating a deterministic and computationally efficient analysis of the charging capacity of the network. We illustrate the accuracy of our fluid approximation by detailed simulation studies. Next to that, we use the model to assess both the impact of RES generation and the physical location of RES in the network. This way, we create a measure for the positioning of additional RES or local energy storing systems.