  We develop and analyze a measure-valued fluid model keeping track of parking
and charging requirements of electric vehicles in a local distribution grid. We
show how this model arises as an accumulation point of an appropriately scaled
sequence of stochastic network models. The invariant point of the fluid model
encodes the electrical characteristics of the network and the stochastic
behavior of its users, and it is characterized, when it exists, by the solution
of a so-called Alternating Current Optimal Power Flow (ACOPF) problem.
