A Fluid Model of an Electric Vehicle Charging Network

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. Our analysis incorporates load-flow models that describe the laws of electricity. Specifically, we consider the alternating current (AC) and the linearized Distflow power flow models and show a continuity property of the associated power allocation functions.