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