Asymptotic assessment of distribution voltage profile using a nonlinear ODE model

The promising increase of Electric Vehicles (EVs) in our society poses a challenging problem on the impact assessment their charging/discharging to power distribution grids. This paper addresses framework nonlinear differential equations. Specifically, we address ODE (Ordinary Differential Equation) model for representing spatial profile voltage phasor along feeder, which has been recently introduced literature. is then formulated as two-point boundary value model. In this derive an asymptotic charcterisation solutions through standard regular perturbation method. provides mathematically-rigor and quantitative method assessing how EVs affects voltage. Effectiveness established with simulations both simple practical configurations grid.